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I show how Hamilton's philosophical commitments led him to a causal
interpretation of classical mechanics. I argue that Hamilton's metaphysics of
causation was injected into his dynamics by way of a causal interpretation of
force. I then detail how forces remain indispensable to both Hamilton's
formulation of classical mechanics and what we now call Hamiltonian mechanics
(i.e., the modern formulation). On this point, my efforts primarily consist of
showing that the orthodox interpretation of potential energy is the
interpretation found in Hamilton's work. Hamilton called the potential energy
function the force-function because he believed that it represents forces at
work in the world. Multifarious non-historical arguments for this orthodox
interpretation of potential energy are provided, and matters are concluded by
showing that in classical Hamiltonian mechanics, facts about potential energies
of systems are grounded in facts about forces. Thus, if one can tolerate the
view that forces are causes of motions, then Hamilton provides one with a road
map for transporting causation into one of the most mathematically
sophisticated formulations of classical mechanics, viz., Hamiltonian mechanics.
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Scalable memories that can match the speeds of superconducting logic circuits
have long been desired to enable a superconducting computer. A superconducting
loop that includes a Josephson junction can store a flux quantum state in
picoseconds. However, the requirement for the loop inductance to create a
bi-state hysteresis sets a limit on the minimal area occupied by a single
memory cell. Here, we present a miniaturized superconducting memory cell based
on a Three-Dimensional (3D) Nb nano-Superconducting QUantum Interference Device
(nano-SQUID). The major cell area here fits within an 8*9 {\mu}m^2 rectangle
with a cross-selected function for memory implementation. The cell shows
periodic tunable hysteresis between two neighbouring flux quantum states
produced by bias current sweeping because of the large modulation depth of the
3D nano-SQUID (~66%). Furthermore, the measured Current-Phase Relations (CPRs)
of nano-SQUIDs are shown to be skewed from a sine function, as predicted by
theoretical modelling. The skewness and the critical current of 3D nano-SQUIDs
are linearly correlated. It is also found that the hysteresis loop size is in a
linear scaling relationship with the CPR skewness using the statistics from
characterisation of 26 devices. We show that the CPR skewness range of
{\pi}/4~3{\pi}/4 is equivalent to a large loop inductance in creating a stable
bi-state hysteresis for memory implementation. Therefore, the skewed CPR of 3D
nano-SQUID enables further superconducting memory cell miniaturization by
overcoming the inductance limitation of the loop area.
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The Bayesian Optimisation Algorithm (BOA) is an Estimation of Distribution
Algorithm (EDA) that uses a Bayesian network as probabilistic graphical model
(PGM). Determining the optimal Bayesian network structure given a solution
sample is an NP-hard problem. This step should be completed at each iteration
of BOA, resulting in a very time-consuming process. For this reason most
implementations use greedy estimation algorithms such as K2. However, we show
in this paper that significant changes in PGM structure do not occur so
frequently, and can be particularly sparse at the end of evolution. A
statistical study of BOA is thus presented to characterise a pattern of PGM
adjustments that can be used as a guide to reduce the frequency of PGM updates
during the evolutionary process. This is accomplished by proposing a new
BOA-based optimisation approach (FBOA) whose PGM is not updated at each
iteration. This new approach avoids the computational burden usually found in
the standard BOA. The results compare the performances of both algorithms on an
NK-landscape optimisation problem using the correlation between the ruggedness
and the expected runtime over enumerated instances. The experiments show that
FBOA presents competitive results while significantly saving computational
time.
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The present article is devoted to certain examples of functions whose
argument represented in terms of Cantor series.
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We investigate theoretically magnon-mediated superconductivity in a
heterostructure consisting of a normal metal and a two-sublattice
antiferromagnetic insulator. The attractive electron-electron pairing
interaction is caused by an interfacial exchange coupling with magnons residing
in the antiferromagnet, resulting in p-wave, spin-triplet superconductivity in
the normal metal. Our main finding is that one may significantly enhance the
superconducting critical temperature by coupling the normal metal to only one
of the two antiferromagnetic sublattices employing, for example, an
uncompensated interface. Employing realistic material parameters, the critical
temperature increases from vanishingly small values to values significantly
larger than 1 K as the interfacial coupling becomes strongly
sublattice-asymmetric. We provide a general physical picture of this
enhancement mechanism based on the notion of squeezed bosonic eigenmodes.
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Catalan words are particular growth-restricted words counted by the eponymous
integer sequence. In this article we consider Catalan words avoiding a pair of
patterns of length 3, pursuing the recent initiating work of the first and last
authors and of S. Kirgizov where (among other things) the enumeration of
Catalan words avoiding a patterns of length 3 is completed. More precisely, we
explore systematically the structural properties of the sets of words under
consideration and give enumerating results by means of recursive decomposition,
constructive bijections or bivariate generating functions with respect to the
length and descent number. Some of the obtained enumerating sequences are
known, and thus the corresponding results establish new combinatorial
interpretations for them.
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The 1/N expansion for the O(N) vector model in four dimensions is
reconsidered. It is emphasized that the effective potential for this model
becomes everywhere complex just at the critical point, which signals an
unstable vacuum. Thus a critical O(N) vector model cannot be consistently
defined in the 1/N expansion for four-dimensions, which makes the existence of
a double-scaling limit for this theory doubtful.
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We give a complete investigation of Morley's trisector theorem. If the
intersections of the half lines starting from the adjacent vertices of a
triangle form an equilateral triangle for an arbitrary triangle, then the half
lines are the angle trisectors. To derive the result we use elementary
trigonometry, Taylor series expansions, and solve systems of polynomial
equations step by step. As a byproduct we get a probably new trigonometric
identity.
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We present results of optical spectroscopic observations of candidates of
Lyman Break Galaxies (LBGs) at $z \sim 5$ in the region including the GOODS-N
and the J0053+1234 region by using GMOS-N and GMOS-S, respectively. Among 25
candidates, five objects are identified to be at $z \sim 5$ (two of them were
already identified by an earlier study) and one object very close to the
color-selection window turned out to be a foreground galaxy. With this
spectroscopically identified sample and those from previous studies, we derived
the lower limits on the number density of bright ($M_{UV}<-22.0$ mag) LBGs at
$z \sim 5$. These lower limits are comparable to or slightly smaller than the
number densities of UV luminosity functions (UVLFs) that show the smaller
number density among $z \sim 5$ UVLFs in literature. However, by considering
that there remain many LBG candidates without spectroscopic observations, the
number density of bright LBGs is expected to increase by a factor of two or
more. The evidence for the deficiency of UV luminous LBGs with large Ly$\alpha$
equivalent widths was reinforced. We discuss possible causes for the deficiency
and prefer the interpretation of dust absorption.
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Recently, some S-stars (S4711, S62, S4714) orbiting the supermassive black
hole (SMBH) in Sgr A$^\ast$ with short orbital periods ($7.6\,\mathrm{yr}\leq
P_\mathrm{b}\leq 12\,\mathrm{yr}$) were discovered. It was suggested that they
may be used to measure the general relativistic Lense-Thirring (LT) precessions
of their longitudes of ascending node $\mathit{\Omega}$ induced by the SMBH's
angular momentum $\boldsymbol{J}_\bullet$. In fact, the proposed numerical
estimates hold only in the particular case of a perfect alignment of
$\boldsymbol{J}_\bullet$ with the line of sight, which does not seem to be the
case. Moreover, also the inclination $I$ and the argument of perinigricon
$\omega$ undergo LT precessions for an arbitrary orientation of
$\boldsymbol{J}_\bullet$ in space. We explicitly show the analytical
expressions of $\dot
I^\mathrm{LT},\,\dot{\mathit{\Omega}}^\mathrm{LT},\,\omega^\mathrm{LT}$ in
terms of the SMBH's spin polar angles $i^\bullet,\,\varepsilon^\bullet$ by
finding the range of values for each of them in arcseconds per year
($^{\prime\prime}\,\mathrm{yr}^{-1}$). For each star, the corresponding values
of $i^\bullet_\mathrm{max},\,\varepsilon^\bullet_\mathrm{max}$ and
$i^\bullet_\mathrm{min},\,\varepsilon^\bullet_\mathrm{min}$ are determined as
well, along with those $i_0^\bullet,\,\varepsilon_0^\bullet$ that cancel the LT
precessions. The LT perinigricon precessions $\dot\omega^\mathrm{LT}$ are
overwhelmed by the systematic uncertainties in the Schwarzschild ones due to
the current errors in the stars' orbital parameters and the mass of Sgr
A$^\ast$ itself. [Abridged]
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Results of forward modelling of acoustic wave propagation in a realistic
solar sub-photosphere with two cases of steady horizontal flows are presented
and analysed by the means of local helioseismology. The simulations are based
on fully compressible ideal hydrodynamical modelling in a Cartesian grid. The
initial model is characterised by solar density and pressure stratifications
taken from the standard Model S and is adjusted in order to suppress convective
instability. Acoustic waves are excited by a non-harmonic source located below
the depth corresponding to the visible surface of the Sun. Numerical
experiments with coherent horizontal flows of linear and Gaussian dependences
of flow speed on depth are carried out. These flow fields may mimic horizontal
motions of plasma surrounding a sunspot, differential rotation or meridional
circulation. An inversion of the velocity profiles from the simulated travel
time differences is carried out. The inversion is based on the ray
approximation. The results of inversion are then compared with the original
velocity profiles. The influence of steady flow on the propagation of sound
waves through the solar interior is analysed. Further, we propose a method of
obtaining the travel-time differences for the waves propagating in
sub-photospheric solar regions with horizontal flows. The method employs
directly the difference between travel-time diagrams of waves propagating with
and against the background flow. The analysis shows that the flow speed
profiles obtained from inversion based on the ray approximation differ from the
original ones. The difference between them is caused by the fact that the wave
packets propagate along the ray bundle, which has a finite extent, and thus
reach deeper regions of the sub-photosphere in comparison with ray theory.
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We propose an immersed boundary scheme for the numerical resolution of the
Complete Electrode Model in Electrical Impedance Tomography, that we use as a
main ingredient in the resolution of inverse problems in medical imaging. Such
method allows to use a Cartesian mesh without accurate discretization of the
boundary, which is useful in situations where the boundary is complicated
and/or changing. We prove the convergence of our method, and illustrate its
efficiency with two dimensional direct and inverse problems.
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We study the phase diagram of a dipolar fermi gas at half-filling in a cubic
optical lattice with dipole moments aligned along the z-axis. The anisotropic
dipole-dipole interaction leads to the competition between pz-wave superfluid
and nematic charge-density-wave (CDW) orders at low temperatures. We find that
the superfluid phase survives with weak interactions and the CDW phase
dominates with strong interactions. In between, the supersolid phase appears as
a balance between superfluid and CDW orders. The superfluid density is
anisotropic in the supersolid and superfluid phases. In the CDW phase, there is
a semimetal to insulator transition with increase of the interaction strength.
Experimental implications are discussed.
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We provide alternative proofs of two recent Grothendieck theorems for jointly
completely bounded bilinear forms, originally due to Pisier and Shlyakhtenko
(Invent. Math. 2002) and Haagerup and Musat (Invent. Math. 2008). Our proofs
are elementary and are inspired by the so-called embezzlement states in quantum
information theory. Moreover, our proofs lead to quantitative estimates.
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In this work we present a systematic study of the three-dimensional extension
of the ring dark soliton examining its existence, stability, and dynamics in
isotropic harmonically trapped Bose-Einstein condensates. Detuning the chemical
potential from the linear limit, the ring dark soliton becomes unstable
immediately, but can be fully stabilized by an external cylindrical potential.
The ring has a large number of unstable modes which are analyzed through
spectral stability analysis. Furthermore, a few typical destabilization
dynamical scenarios are revealed with a number of interesting vortical
structures emerging such as the two or four coaxial parallel vortex rings. In
the process of considering the stability of the structure, we also develop a
modified version of the degenerate perturbation theory method for
characterizing the spectra of the coherent structure. This semi-analytical
method can be reliably applied to any soliton with a linear limit to explore
its spectral properties near this limit. The good agreement of the resulting
spectrum is illustrated via a comparison with the full numerical Bogolyubov-de
Gennes spectrum. The application of the method to the two-component ring
dark-bright soliton is also discussed.
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We propose and analyze a scalable and fully autonomous scheme for preparing
spatially distributed multiqubit entangled states in a dual-rail waveguide QED
setup. In this approach, arrays of qubits located along two separated
waveguides are illuminated by correlated photons from the output of a
nondegenerate parametric amplifier. These photons drive the qubits into
different classes of pure entangled steady states, for which the degree of
multipartite entanglement can be conveniently adjusted by the chosen pattern of
local qubit-photon detunings. Numerical simulations for moderate-sized networks
show that the preparation time for these complex multiqubit states increases at
most linearly with the system size and that one may benefit from an additional
speedup in the limit of a large amplifier bandwidth. Therefore, this scheme
offers an intriguing new route for distributing ready-to-use multipartite
entangled states across large quantum networks, without requiring any precise
pulse control and relying on a single Gaussian entanglement source only.
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We describe a way to complete a correlation matrix that is not fully
specified. Such matrices often arise in financial applications when the number
of stochastic variables becomes large or when several smaller models are
combined in a larger model. We argue that the proper completion to consider is
the matrix that maximizes the entropy of the distribution described by the
matrix. We then give a way to construct this matrix starting from the graph
associated with the incomplete matrix. If this graph is chordal our
construction will result in a proper correlation matrix. We give a detailed
description of the construction for a cross-currency model with six stochastic
variables and describe extensions to larger models involving more currencies.
|
Convolutional recurrent neural networks (CRNNs) have achieved
state-of-the-art performance for sound event detection (SED). In this paper, we
propose to use a dilated CRNN, namely a CRNN with a dilated convolutional
kernel, as the classifier for the task of SED. We investigate the effectiveness
of dilation operations which provide a CRNN with expanded receptive fields to
capture long temporal context without increasing the amount of CRNN's
parameters. Compared to the classifier of the baseline CRNN, the classifier of
the dilated CRNN obtains a maximum increase of 1.9%, 6.3% and 2.5% at F1 score
and a maximum decrease of 1.7%, 4.1% and 3.9% at error rate (ER), on the
publicly available audio corpora of the TUT-SED Synthetic 2016, the TUT Sound
Event 2016 and the TUT Sound Event 2017, respectively.
|
We propose BokehMe, a hybrid bokeh rendering framework that marries a neural
renderer with a classical physically motivated renderer. Given a single image
and a potentially imperfect disparity map, BokehMe generates high-resolution
photo-realistic bokeh effects with adjustable blur size, focal plane, and
aperture shape. To this end, we analyze the errors from the classical
scattering-based method and derive a formulation to calculate an error map.
Based on this formulation, we implement the classical renderer by a
scattering-based method and propose a two-stage neural renderer to fix the
erroneous areas from the classical renderer. The neural renderer employs a
dynamic multi-scale scheme to efficiently handle arbitrary blur sizes, and it
is trained to handle imperfect disparity input. Experiments show that our
method compares favorably against previous methods on both synthetic image data
and real image data with predicted disparity. A user study is further conducted
to validate the advantage of our method.
|
Network Function Virtualization (NFV) aims to simplify deployment of network
services by running Virtual Network Functions (VNFs) on commercial
off-the-shelf servers. Service deployment involves placement of VNFs and
in-sequence routing of traffic flows through VNFs comprising a Service Chain
(SC). The joint VNF placement and traffic routing is usually referred as SC
mapping. In a Wide Area Network (WAN), a situation may arise where several
traffic flows, generated by many distributed node pairs, require the same SC,
one single instance (or occurrence) of that SC might not be enough. SC mapping
with multiple SC instances for the same SC turns out to be a very complex
problem, since the sequential traversal of VNFs has to be maintained while
accounting for traffic flows in various directions. Our study is the first to
deal with SC mapping with multiple SC instances to minimize network resource
consumption. Exact mathematical modeling of this problem results in a quadratic
formulation. We propose a two-phase column-generation-based model and solution
in order to get results over large network topologies within reasonable
computational times. Using such an approach, we observe that an appropriate
choice of only a small set of SC instances can lead to solution very close to
the minimum bandwidth consumption.
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Recently, Lai and Rohatgi discovered a shuffling theorem for lozenge tilings
of doubly-dented hexagons, which generalized the earlier work of Ciucu. Later,
Lai proved an analogous theorem for centrally symmetric tilings, which
generalized some other previous work of Ciucu. In this paper, we give a unified
proof of these two shuffling theorems, which also covers the weighted case.
Unlike the original proofs, our arguments do not use the graphical condensation
method but instead rely on a well-known tiling enumeration formula due to Cohn,
Larsen, and Propp. Fulmek independently found a similar proof of Lai and
Rohatgi's original shuffling theorem. Our proof also gives a combinatorial
explanation for Ciucu's recent conjecture relating the total number and the
number of centrally symmetric lozenge tilings.
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We have used archive HST WFPC2 data for three elliptical galaxies (NGC 3379
in the Leo I group, and NGC 4472 and NGC 4406 in the Virgo cluster) to
determine their distances using the Surface Brightness Fluctuation (SBF) method
as described by Tonry and Schneider (1988). A comparison of the HST results
with the SBF distance moduli of Ciardullo et al (1993) shows significant
disagreement and suggests that the r.m.s. error on these ground-based distance
moduli is actually as large as +-0.25 mag. The agreement is only slightly
improved when we compare our results with the HST and ground-based SBF
distances from Ajhar et al (1997) and Tonry et al (1997); the comparison
suggests that a lower limit on the error of the HST SBF distance moduli is
+-0.17 mag. Overall, these results suggest that previously quoted measurement
errors may underestimate the true error in SBF distance moduli by at least a
factor of 2-3.
|
The Multipurpose InfraRed Imaging System (MIRIS) performed the MIRIS
Pa{\alpha} Galactic Plane Survey (MIPAPS), which covers the entire Galactic
plane within the latitude range of -3{\deg} < b < +3{\deg} at Pa{\alpha} (1.87
um). We present the first result of the MIPAPS data extracted from the
longitude range of l = 96.5{\deg}-116.3{\deg}, and demonstrate the data quality
and scientific potential of the data by comparing them with H{\alpha} maps
obtained from the INT Photometric H{\alpha} Survey (IPHAS) data. We newly
identify 90 H II region candidates in the WISE H II region catalog as definite
H II regions by detecting the Pa{\alpha} and/or H{\alpha} recombination lines,
out of which 53 H II regions are detected at Pa{\alpha}. We also report the
detection of additional 29 extended and 18 point-like sources at Pa{\alpha}. We
estimate the E(B-V) color excesses and the total Lyman continuum luminosities
for H II regions by combining the MIPAPS Pa{\alpha} and IPHAS H{\alpha} fluxes.
The E(B-V) values are found to be systematically lower than those estimated
from point stars associated with H II regions. Utilizing the MIPAPS Pa{\alpha}
and IPHAS H{\alpha} images, we obtain an E(B-V) map for the entire region of
the H II region Sh2-131 with an angular size of ~2.5{\deg}. The E(B-V) map
shows not only numerous high-extinction filamentary features but also negative
E(B-V) regions, indicating H{\alpha} excess. The H{\alpha} excess and the
systematic underestimation of E(B-V) are attributed to light scattered by dust.
|
Low temperature dependence of specific heat of one- dimensional
multicomponent systems at the commensurate- incommensurate phase transition
point is studied. It is found that for canonical systems, with a fixed total
number of particles, low temperature specific heat linearly depends on
temperature with a diverging prefactor.
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In this note, we show how to obtain a "characteristic power series" of
graphons -- infinite limits of dense graphs -- as the limit of normalized
reciprocal characteristic polynomials. This leads to a new characterization of
graph quasi-randomness and another perspective on spectral theory for graphons,
a complete description of the function in terms of the spectrum of the graphon
as a self-adjoint kernel operator. Interestingly, while we apply a standard
regularization to classical determinants, it is unclear how necessary this is.
|
The analysis of data on hyperon transverse momentum distributions, dN/dPt,
that were gathered from various experiments (ISR, STAR, UA1, UA5 and CDF)
reveals an important difference in the dynamics of multiparticle production in
proton-proton vs. antiproton-proton collisions in the region of transverse
momenta 0.3 GeV/c < Pt < 3 GeV/c. Hyperons produced with proton beams display
the sharp exponential slope at low Pt, while spectra prodused with antiproton
beam don't. Since LHC experiments have proton projectiles, the spectra of
baryon production should seem "softer" in comparison to expectations, because
the Monte Carlo simulations were based on the Tevatron antiproton-proton data.
From the point of view of Quark-Gluon String Model, the most important
contribution into the particle production spectra goes from antidiquark-diquark
string fragmentation that exists only in the topological diagram for
antiproton-proton collisions and is a very interesting object for investigation
even at lower energies. This study may have an impact not only on
interpretation of LHC results, but also on the cosmic ray physics and
astrophysics, where the baryon contribution into matter-antimatter asymmetry is
being studied.
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Objective: Global Maxwell Tomography (GMT) is a recently introduced
volumetric technique for noninvasive estimation of electrical properties (EP)
from magnetic resonance measurements. Previous work evaluated GMT using ideal
radiofrequency (RF) excitations. The aim of this simulation study was to assess
GMT performance with a realistic RF coil. Methods: We designed a
transmit-receive RF coil with $8$ decoupled channels for $7$T head imaging. We
calculated the RF transmit field ($B_1^+$) inside heterogeneous head models for
different RF shimming approaches, and used them as input for GMT to reconstruct
EP for all voxels. Results: Coil tuning/decoupling remained relatively stable
when the coil was loaded with different head models. Mean error in EP
estimation changed from $7.5\%$ to $9.5\%$ and from $4.8\%$ to $7.2\%$ for
relative permittivity and conductivity, respectively, when changing head model
without re-tuning the coil. Results slightly improved when an SVD-based RF
shimming algorithm was applied, in place of excitation with one coil at a time.
Despite errors in EP, RF transmit field ($B_1^+$) and absorbed power could be
predicted with less than $0.5\%$ error over the entire head. GMT could
accurately detect a numerically inserted tumor. Conclusion: This work
demonstrates that GMT can reliably reconstruct EP in realistic simulated
scenarios using a tailored 8-channel RF coil design at $7$T. Future work will
focus on construction of the coil and optimization of GMT's robustness to
noise, to enable in-vivo GMT experiments. Significance: GMT could provide
accurate estimations of tissue EP, which could be used as biomarkers and could
enable patient-specific estimation of RF power deposition, which is an unsolved
problem for ultra-high-field magnetic resonance imaging.
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Low-Rank Adaptation~(LoRA), which updates the dense neural network layers
with pluggable low-rank matrices, is one of the best performed parameter
efficient fine-tuning paradigms. Furthermore, it has significant advantages in
cross-task generalization and privacy-preserving. Hence, LoRA has gained much
attention recently, and the number of related literature demonstrates
exponential growth. It is necessary to conduct a comprehensive overview of the
current progress on LoRA. This survey categorizes and reviews the progress from
the perspectives of (1) downstream adaptation improving variants that improve
LoRA's performance on downstream tasks; (2) cross-task generalization methods
that mix multiple LoRA plugins to achieve cross-task generalization; (3)
efficiency-improving methods that boost the computation-efficiency of LoRA; (4)
data privacy-preserving methods that use LoRA in federated learning; (5)
application. Besides, this survey also discusses the future directions in this
field. At last, we provide a Github page
(https://github.com/ZJU-LLMs/Awesome-LoRAs.git) for readers to check the
updates and initiate discussions on this survey paper.
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Anisotropic flow of K's, anti-K's, and lambdas is studied in heavy ion
collisions at SPS and RHIC energies within the microscopic quark-gluon string
model. At SPS energy the directed flow of kaons differs considerably at
midrapidity from that of antikaons, while at RHIC energy kaon and antikaon
flows coincide. The change is attributed to formation of dense meson-dominated
matter at RHIC, where the differences in interaction cross-sections of hadrons
become unimportant. The directed flows of strange particles, $v_1^{K,\bar{K},
\Lambda}(y)$, have universal negative slope at $|y| \leq 2$ at RHIC. The
elliptic flow of strange hadrons is developed at midrapidity at times 3<t<10
fm/c. It increases almost linearly with rising p_t and stops to rise at p_t <
1.5 GeV/c reaching the same saturation value $v_2 ^{K,\Lambda}(p_t) \approx
10%$ in accord with experimental results.
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Along a microtubule, certain active motors propel themselves in one direction
whereas others propel themselves in the opposite direction. For example, the
cargo transporting motor proteins dynein and kinesin propel themselves towards
the so-called plus- and minus-ends of the microtubule, respectively, and in so
doing are able to pass one another, but not without interacting. We address the
emergent collective behavior of systems composed of many motors, some
propelling towards the plus-end and others propelling towards the minus-end. To
do this, we used an analogy between this strongly interacting,
far-from-equilibrium, classical stochastic many-motor system and a certain
quantum-mechanical many-body system evolving in imaginary time. We apply
well-known methods from quantum many-body theory, including self-consistent
mean-field theory and bosonization, to shed light on phenomena exhibited by the
many-motor system such as structure formation and the dynamics of collective
modes at low-frequencies and long-wavelengths. In particular, via the bosonized
description we find analogs of chiral Luttinger liquids, as well as a
qualitative transition in the nature of the low-frequency modes---from
propagating to purely dissipative---controlled by density and interaction
strength.
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High resolution (0.4 arcsec) Atacama Large Millimeter/submillimeter Array
(ALMA) Cycle 0 observations of HCO+(4-3) and HCN(4-3) toward a mid-stage
infrared bright merger VV114 have revealed compact nuclear (<200 pc) and
extended (3 - 4 kpc) dense gas distribution across the eastern part of the
galaxy pair. We find a significant enhancement of HCN(4-3) emission in an
unresolved compact and broad (290km/s) component found in the eastern nucleus
of VV114, and we suggest dense gas associated with the surrounding material
around an Active Galactic Nucleus (AGN), with a mass upper limit of < 4 x 10^8
Msun. The extended dense gas is distributed along a filamentary structure with
resolved dense gas concentrations (230pc; 10^6 Msun) separated by a mean
projected distance of 600 pc, many of which are generally consistent with the
location of star formation traced in Pa alpha emission. Radiative transfer
calculations suggest moderately dense (10^5 - 10^6 cm^-3) gas averaged over the
entire emission region. These new ALMA observations demonstrate the strength of
the dense gas tracers in identifying both the AGN and star formation activity
in a galaxy merger, even in the most dust enshrouded environments in the local
universe.
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The cores of neutron stars (NSs) near the maximum mass realize the most
highly compressed matter in the universe where quark degrees of freedom may be
liberated. Such a state of dense matter is hypothesized as quark matter (QM)
and its presence has awaited to be confirmed for decades in nuclear physics.
Gravitational waves from binary NS mergers are expected to convey useful
information called the equation of state (EOS). However, the signature for QM
with realistic EOS is not yet established. Here, we show that the gravitational
wave in the post-merger stage can distinguish the theory scenarios with and
without a transition to QM. Instead of adopting specific EOSs as studied
previously, we compile reliable EOS constraints from the ab initio approaches.
We demonstrate that early collapse to a black hole after NS merger signifies
softening of the EOS associated with the onset of QM in accord with ab initio
constraints. Nature of hadron-quark phase transition can be further constrained
by the condition that electromagnetic counterparts need to be energized by the
material left outside the remnant black hole.
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In this work, we tackle the task of learning generalizable 3D human Gaussians
from a single image. The main challenge for this task is to recover detailed
geometry and appearance, especially for the unobserved regions. To this end, we
propose single-view generalizable Human Gaussian model (HGM), a
diffusion-guided framework for 3D human modeling from a single image. We design
a diffusion-based coarse-to-fine pipeline, where the diffusion model is adapted
to refine novel-view images rendered from a coarse human Gaussian model. The
refined images are then used together with the input image to learn a refined
human Gaussian model. Although effective in hallucinating the unobserved views,
the approach may generate unrealistic human pose and shapes due to the lack of
supervision. We circumvent this problem by further encoding the geometric
priors from SMPL model. Specifically, we propagate geometric features from SMPL
volume to the predicted Gaussians via sparse convolution and attention
mechanism. We validate our approach on publicly available datasets and
demonstrate that it significantly surpasses state-of-the-art methods in terms
of PSNR and SSIM. Additionally, our method exhibits strong generalization for
in-the-wild images.
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In this work we introduce a new class of optimal tensor codes related to the
Ravagnani-type anticodes, namely the $j$-tensor maximum rank distance codes. We
show that it extends the family of $j$-maximum rank distance codes and contains
the $j$-tensor binomial moment determined codes (with respect to the
Ravagnani-type anticodes) as a proper subclass. We define and study the
generalized zeta function for tensor codes. We establish connections between
this object and the weight enumerator of a code with respect to the
Ravagnani-type anticodes. We introduce a new refinement of the invariants of
tensor codes exploiting the structure of product lattices of some classes of
anticodes and we derive the corresponding MacWilliams identities. In this
framework, we also define a multivariate version of the tensor weight
enumerator and we establish relations with the corresponding zeta function. As
an application we derive connections on the generalized tensor weights related
to the Delsarte and Ravagnani-type anticodes.
|
We studied the phase diagram of Sr$_3$Ru$_2$O$_7$ by means of heat capacity
and magnetocaloric effect measurements at temperatures as low as 0.06 K and
fields up to 12 T. We confirm the presence of a new quantum critical point at
7.5 T which is characterized by a strong non-Fermi-liquid behavior of the
electronic specific heat coefficient $\Delta$C/T $\sim$ -logT over more than a
decade in temperature,placing strong constraints on theories of its
criticality. In particular logarithmic corrections are found when the dimension
d is equal to the dynamic critical exponent z, in contrast to the conclusion
proposed recently [Y. Tokiwa et al., Phys. Rev. Lett. 116, 226402 (2016)].
Moreover, we achieved a clear determination of the new second thermodynamic
phase adjoining the first one at lower temperatures. Its thermodynamic features
differ significantly from those of the dominant phase and characteristics
expected of classical equilibrium phase transitions are not observed,
indicating fundamental differences in the phase formation.
|
We present new algorithms to compute fundamental properties of a Boolean
function given in truth-table form. Specifically, we give an O(N^2.322 log N)
algorithm for block sensitivity, an O(N^1.585 log N) algorithm for `tree
decomposition,' and an O(N) algorithm for `quasisymmetry.' These algorithms are
based on new insights into the structure of Boolean functions that may be of
independent interest. We also give a subexponential-time algorithm for the
space-bounded quantum query complexity of a Boolean function. To prove this
algorithm correct, we develop a theory of limited-precision representation of
unitary operators, building on work of Bernstein and Vazirani.
|
The critical behavior of a quenched random hypercubic sample of linear size
$L$ is considered, within the ``random-$T_{c}$'' field-theoretical mode, by
using the renormalization group method. A finite-size scaling behavior is
established and analyzed near the upper critical dimension $d=4-\epsilon$ and
some universal results are obtained. The problem of self-averaging is clarified
for different critical regimes.
|
In the context of XACML-based access control systems, an intensive testing
activity is among the most adopted means to assure that sensible information or
resources are correctly accessed. Unfortunately, it requires a huge effort for
manual inspection of results: thus automated verdict derivation is a key aspect
for improving the cost-effectiveness of testing. To this purpose, we introduce
XACMET, a novel approach for automated model-based oracle definition. XACMET
defines a typed graph, called the XAC-Graph, that models the XACML policy
evaluation. The expected verdict of a specific request execution can thus be
automatically derived by executing the corresponding path in such graph. Our
validation of the XACMET prototype implementation confirms the effectiveness of
the proposed approach.
|
The tippedisk is a mathematical-mechanical archetype for a peculiar
friction-induced instability phenomenon leading to the inversion of an
unbalanced spinning disk, being reminiscent to (but different from) the
well-known inversion of the tippetop. A reduced model of the tippedisk, in the
form of a three-dimensional ordinary differential equation, has been derived
recently, followed by a preliminary local stability analysis of stationary
spinning solutions. In the current paper, a global analysis of the reduced
system is pursued using the framework of singular perturbation theory. It is
shown how the presence of friction leads to slow-fast dynamics and the creation
of a two-dimensional slow manifold. Furthermore, it is revealed that a
bifurcation scenario involving a homoclinic bifurcation and a Hopf bifurcation
leads to an explanation of the inversion phenomenon. In particular, a
closed-form condition for the critical spinning speed for the inversion
phenomenon is derived. Hence, the tippedisk forms an excellent
mathematical-mechanical problem for the analysis of global bifurcations in
singularly perturbed dynamics.
|
Context. The Class 0 protostellar binary IRAS 16293-2422 is an interesting
target for (sub)millimeter observations due to, both, the rich chemistry toward
the two main components of the binary and its complex morphology. Its proximity
to Earth allows the study of its physical and chemical structure on solar
system scales using high angular resolution observations. Such data reveal a
complex morphology that cannot be accounted for in traditional, spherical 1D
models of the envelope. Aims. The purpose of this paper is to study the
environment of the two components of the binary through 3D radiative transfer
modeling and to compare with data from the Atacama Large
Millimeter/submillimeter Array. Such comparisons can be used to constrain the
protoplanetary disk structures, the luminosities of the two components of the
binary and the chemistry of simple species. Methods. We present 13CO, C17O and
C18O J=3-2 observations from the ALMA Protostellar Interferometric Line Survey
(PILS), together with a qualitative study of the dust and gas density
distribution of IRAS 16293-2422. A 3D dust and gas model including disks and a
dust filament between the two protostars is constructed which qualitatively
reproduces the dust continuum and gas line emission. Results and conclusions.
Radiative transfer modeling of source A and B, with the density solution of an
infalling, rotating collapse or a protoplanetary disk model, can match the
constraints for the disk-like emission around source A and B from the observed
dust continuum and CO isotopologue gas emission. If a protoplanetary disk model
is used around source B, it has to have an unusually high scale-height in order
to reach the dust continuum peak emission value, while fulfilling the other
observational constraints. Our 3D model requires source A to be much more
luminous than source B; LA ~ 18 $L_\odot$ and LB ~ 3 $L_\odot$.
|
This paper introduces a novel metaheuristic algorithm, known as the efficient
multiplayer battle game optimizer (EMBGO), specifically designed for addressing
complex numerical optimization tasks. The motivation behind this research stems
from the need to rectify identified shortcomings in the original MBGO,
particularly in search operators during the movement phase, as revealed through
ablation experiments. EMBGO mitigates these limitations by integrating the
movement and battle phases to simplify the original optimization framework and
improve search efficiency. Besides, two efficient search operators:
differential mutation and L\'evy flight are introduced to increase the
diversity of the population. To evaluate the performance of EMBGO
comprehensively and fairly, numerical experiments are conducted on benchmark
functions such as CEC2017, CEC2020, and CEC2022, as well as engineering
problems. Twelve well-established MA approaches serve as competitor algorithms
for comparison. Furthermore, we apply the proposed EMBGO to the complex
adversarial robust neural architecture search (ARNAS) tasks and explore its
robustness and scalability. The experimental results and statistical analyses
confirm the efficiency and effectiveness of EMBGO across various optimization
tasks. As a potential optimization technique, EMBGO holds promise for diverse
applications in real-world problems and deep learning scenarios. The source
code of EMBGO is made available in
\url{https://github.com/RuiZhong961230/EMBGO}.
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We report the results of a CGRO 3-week observation of the binary system
containing the 47 ms pulsar PSR B1259-63 orbiting around a Be star companion in
a very eccentric orbit. The PSR B1259-63 binary is a unique system for the
study of the interaction of a rapidly rotating pulsar with time-variable
nebular surroundings. CGRO observed the PSR B1259-63 system in coincidence with
its most recent periastron passage (January 3-23, 1994). Unpulsed and
non-thermal hard X-ray emission was detected up to 200 keV, with a photon index
$1.8 \pm 0.2$ and a flux of ~4 mCrab, corresponding to a luminosity of a few
10^{34} erg/s at the distance of 2 kpc. The hard X-ray flux and spectrum
detected by CGRO agrees with the X-ray emission measured by simultaneous ASCA
observations. EGRET upper limits are significant, and exclude strong inverse
Compton cooling in the PSR B1259-63 system. We interpret the observed
non-thermal emission as synchrotron radiation of shocked electron/positron
pairs of the relativistic pulsar wind interacting with the mass outflow from
the Be star. Our results clearly indicate, for the first time in a binary
pulsar, that high energy emission can be shock-powered rather than caused by
accretion. The lack of X-ray/gamma-ray pulsations constrains models of
high-energy emission from rapidly rotating pulsars.
|
How the fluctuation-exchange (FLEX) approximation and the Fermi-liquid theory
fail to explain the anomalous behavior of the Hall coefficient in the normal
state of high-Tc superconductors is clarified.
|
With 5394 security certificates of IT products and systems, the Common
Criteria for Information Technology Security Evaluation have bred an ecosystem
entangled with various kind of relations between the certified products. Yet,
the prevalence and nature of dependencies among Common Criteria certified
products remains largely unexplored. This study devises a novel method for
building the graph of references among the Common Criteria certified products,
determining the different contexts of references with a supervised
machine-learning algorithm, and measuring how often the references constitute
actual dependencies between the certified products. With the help of the
resulting reference graph, this work identifies just a dozen of certified
components that are relied on by at least 10% of the whole ecosystem -- making
them a prime target for malicious actors. The impact of their compromise is
assessed and potentially problematic references to archived products are
discussed.
|
The deformations of multi-$\la$ hypernuclei corresponding to even-even core
nuclei ranging from $^8$Be to $^{40}$Ca with 2, 4, 6, and 8 hyperons are
studied in the framework of the deformed Skyrme-Hartree-Fock approach. It is
found that the deformations are reduced when adding 2 or 8 $\la$ hyperons, but
enhanced when adding 4 or 6 $\la$ hyperons. These differences are attributed to
the fact that $\la$ hyperons are filled gradually into the three deformed $p$
orbits, of which the [110]1/2$^-$ orbit is prolately deformed and the
degenerate [101]1/2$^-$ and [101]3/2$^-$ orbits are oblately deformed.
|
We have searched for intermediate-scale anisotropy in the arrival directions
of ultrahigh-energy cosmic rays with energies above 57~EeV in the northern sky
using data collected over a 5 year period by the surface detector of the
Telescope Array experiment. We report on a cluster of events that we call the
hotspot, found by oversampling using 20$^\circ$-radius circles. The hotspot has
a Li-Ma statistical significance of 5.1$\sigma$, and is centered at
R.A.=146.7$^{\circ}$, Dec.=43.2$^{\circ}$. The position of the hotspot is about
19$^{\circ}$ off of the supergalactic plane. The probability of a cluster of
events of 5.1$\sigma$ significance, appearing by chance in an isotropic
cosmic-ray sky, is estimated to be 3.7$\times$10$^{-4}$ (3.4$\sigma$).
|
We critically evaluate the treatment of the notion of measurement in the
Consistent Histories approach to quantum mechanics. We find such a treatment
unsatisfactory because it relies, often implicitly, on elements external to
those provided by the formalism. In particular, we note that, in order for the
formalism to be informative when dealing with measurement scenarios, one needs
to assume that the appropriate choice of framework is such that apparatuses are
always in states of well defined pointer positions after measurements. The
problem is that there is nothing in the formalism to justify this assumption.
We conclude that the Consistent Histories approach, contrary to what is claimed
by its proponents, fails to provide a truly satisfactory resolution for the
measurement problem in quantum theory.
|
A distribution matcher (DM) encodes a binary input data sequence into a
sequence of symbols (codeword) with desired target probability distribution.
The set of the output codewords constitutes a codebook (or code) of a DM.
Constant-composition DM (CCDM) uses arithmetic coding to efficiently encode
data into codewords from a constant-composition (CC) codebook. The CC
constraint limits the size of the codebook, and hence the coding rate of the
CCDM. The performance of CCDM degrades with decreasing output length. To
improve the performance for short transmission blocks we present a class of
multi-composition (MC) codes and an efficient arithmetic coding scheme for
encoding and decoding. The resulting multi-composition DM (MCDM) is able to
encode more data into distribution matched codewords than the CCDM and achieves
lower KL divergence, especially for short block messages.
|
We present a method for characterizing image-subtracted objects based on
shapelet analysis to identify transient events in ground-based time-domain
surveys. We decompose the image-subtracted objects onto a set of discrete
Zernike polynomials and use their resulting coefficients to compare them to
other point-like objects. We derive a norm in this Zernike space that we use to
score transients for their point-like nature and show that it is a powerful
comparator for distinguishing image artifacts, or residuals, from true
astrophysical transients. Our method allows for a fast and automated way of
scanning overcrowded, wide-field telescope images with minimal human
interaction and we reduce the large set of unresolved artifacts left
unidentified in subtracted observational images. We evaluate the performance of
our method using archival intermediate Palomar Transient Factory and Dark
Energy Camera survey images. However, our technique allows flexible
implementation for a variety of different instruments and data sets. This
technique shows a reduction in image subtraction artifacts by 99.95% for
surveys extending up to hundreds of square degrees and has strong potential for
automated transient identification in electromagnetic follow-up programs
triggered by the Laser Interferometer Gravitational Wave Observatory-Virgo
Scientific Collaboration.
|
Skin cancer is one of the major types of cancers with an increasing incidence
over the past decades. Accurately diagnosing skin lesions to discriminate
between benign and malignant skin lesions is crucial to ensure appropriate
patient treatment. While there are many computerised methods for skin lesion
classification, convolutional neural networks (CNNs) have been shown to be
superior over classical methods. In this work, we propose a fully automatic
computerised method for skin lesion classification which employs optimised deep
features from a number of well-established CNNs and from different abstraction
levels. We use three pre-trained deep models, namely AlexNet, VGG16 and
ResNet-18, as deep feature generators. The extracted features then are used to
train support vector machine classifiers. In the final stage, the classifier
outputs are fused to obtain a classification. Evaluated on the 150 validation
images from the ISIC 2017 classification challenge, the proposed method is
shown to achieve very good classification performance, yielding an area under
receiver operating characteristic curve of 83.83% for melanoma classification
and of 97.55% for seborrheic keratosis classification.
|
In this work we study the excitatory AMPA, and NMDA, and inhibitory GABAA
receptor mediated dynamical changes in neuronal networks of neonatal rat cortex
in vitro. Extracellular network-wide activity was recorded with 59 planar
electrodes simultaneously under different pharmacological conditions. We
analyzed the changes of overall network activity and network-wide burst
frequency between baseline and AMPA receptor (AMPA-R) or NMDA receptor (NMDA-R)
driven activity, as well as between the latter states and disinhibited
activity. Additionally, spatiotemporal structures of pharmacologically modified
bursts and recruitment of electrodes during the network bursts were studied.
Our results show that AMPA-R and NMDA-R receptors have clearly distinct roles
in network dynamics. AMPA-Rs are in greater charge to initiate network wide
bursts. Therefore NMDA-Rs maintain the already initiated activity. GABAA
receptors (GABAA-Rs) inhibit AMPA-R driven network activity more strongly than
NMDA-R driven activity during the bursts.
|
There are two major routes to address the ubiquitous family of inverse
problems appearing in signal and image processing, such as denoising or
deblurring. A first route relies on Bayesian modeling, where prior
probabilities are used to embody models of both the distribution of the unknown
variables and their statistical dependence with the observed data. The
estimation process typically relies on the minimization of an expected loss
(e.g. minimum mean squared error, or MMSE). The second route has received much
attention in the context of sparse regularization and compressive sensing: it
consists in designing (often convex) optimization problems involving the sum of
a data fidelity term and a penalty term promoting certain types of unknowns
(e.g., sparsity, promoted through an 1 norm). Well known relations between
these two approaches have lead to some widely spread misconceptions. In
particular, while the so-called Maximum A Posterori (MAP) estimate with a
Gaussian noise model does lead to an optimization problem with a quadratic
data-fidelity term, we disprove through explicit examples the common belief
that the converse would be true. It has already been shown [7, 9] that for
denoising in the presence of additive Gaussian noise, for any prior probability
on the unknowns, MMSE estimation can be expressed as a penalized least squares
problem, with the apparent characteristics of a MAP estimation problem with
Gaussian noise and a (generally) different prior on the unknowns. In other
words, the variational approach is rich enough to build all possible MMSE
estimators associated to additive Gaussian noise via a well chosen penalty. We
generalize these results beyond Gaussian denoising and characterize noise
models for which the same phenomenon occurs. In particular, we prove that with
(a variant of) Poisson noise and any prior probability on the unknowns, MMSE
estimation can again be expressed as the solution of a penalized least squares
optimization problem. For additive scalar denois-ing the phenomenon holds if
and only if the noise distribution is log-concave. In particular, Laplacian
denoising can (perhaps surprisingly) be expressed as the solution of a
penalized least squares problem. In the multivariate case, the same phenomenon
occurs when the noise model belongs to a particular subset of the exponential
family. For multivariate additive denoising, the phenomenon holds if and only
if the noise is white and Gaussian.
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We give a complete characterization of those $f: [0,1] \to X$ (where $X$ is a
Banach space which admits an equivalent Fr\'echet smooth norm) which allow an
equivalent $C^2$ parametrization. For $X=\R$, a characterization is well-known.
However, even in the case $X=\R^2$, several quite new ideas are needed.
Moreover, the very close case of parametrizations with a bounded second
derivative is solved.
|
The Marchenko phase-equivalent transformation of the Schr\"{o}dinger equation
for two coupled channels is discussed. The combination of the Marchenko
transformations valid in the Bargmann potential case is suggested.
|
This second paper of the series (see the first one in [1]) models the
dynamics and structure of upper hurricane layer in adiabatic approximation.
Formulation of simplified aerodynamic model allows analytically express the
radial istributions of pressure and wind speed components. The vertical
evolution of these distributions and hurricane structure in the layer are
described by a coupled set of equations for the vertical mass flux and vertical
momentum balance, averaged over the eye wall cross section. Several realistic
predictions of the model are demonstrated, including the change of directions
for the component of radial wind speed and angular velocity of hurricane with
altitude.
|
Being an assembly of identical upright helixes, a chiral sculptured thin film
(CSTF) exhibits the circular Bragg phenomenon and can therefore be used as a
circular- polarization filter in a spectral regime called the circular Bragg
regime. This has been already demonstrated in the near-infrared and
short-wavelength infrared regimes. If two CSTFs are fabricated in identical
conditions to differ only in the helical pitch, and if both are made of a
material whose bulk refractive index is constant in a wide enough spectral
regime, then the center wavelengths of the circular Bragg regimes of the two
CSTFs must be in the same ratio as their helical pitches by virtue of the scale
invariance of the frequency-domain Maxwell postulates. This theoretical result
was confirmed by measuring the linear-transmittance spectrums of two
zinc-selenide CSTFs with helical pitches in the ratio 1:7:97. The center
wavelengths were found to be in the ratio 1:7:1, the deviation from the ratio
of helical pitches being explainable at least in part be- cause the bulk
refractive index of zinc selenide decreased a little with wavelength. We
concluded that CSTFs can be fabricated to function as circular-polarization
filters in the mid-wavelength infrared regime.
|
Given a graph $F$, let $I(F)$ be the class of graphs containing $F$ as an
induced subgraph. Let $W[F]$ denote the minimum $k$ such that $I(F)$ is
definable in $k$-variable first-order logic. The recognition problem of $I(F)$,
known as Induced Subgraph Isomorphism (for the pattern graph $F$), is solvable
in time $O(n^{W[F]})$. Motivated by this fact, we are interested in determining
or estimating the value of $W[F]$. Using Olariu's characterization of paw-free
graphs, we show that $I(K_3+e)$ is definable by a first-order sentence of
quantifier depth 3, where $K_3+e$ denotes the paw graph. This provides an
example of a graph $F$ with $W[F]$ strictly less than the number of vertices in
$F$. On the other hand, we prove that $W[F]=4$ for all $F$ on 4 vertices except
the paw graph and its complement. If $F$ is a graph on $t$ vertices, we prove a
general lower bound $W[F]>(1/2-o(1))t$, where the function in the little-o
notation approaches 0 as $t$ inreases. This bound holds true even for a related
parameter $W^*[F]\le W[F]$, which is defined as the minimum $k$ such that
$I(F)$ is definable in the infinitary logic $L^k_{\infty\omega}$. We show that
$W^*[F]$ can be strictly less than $W[F]$. Specifically, $W^*[P_4]=3$ for $P_4$
being the path graph on 4 vertices.
Using the lower bound for $W[F]$, we also obtain a succintness result for
existential monadic second-order logic: A usage of just one monadic quantifier
sometimes reduces the first-order quantifier depth at a super-recursive rate.
|
End-to-end spoken language understanding (SLU) models are a class of model
architectures that predict semantics directly from speech. Because of their
input and output types, we refer to them as speech-to-interpretation (STI)
models. Previous works have successfully applied STI models to targeted use
cases, such as recognizing home automation commands, however no study has yet
addressed how these models generalize to broader use cases. In this work, we
analyze the relationship between the performance of STI models and the
difficulty of the use case to which they are applied. We introduce empirical
measures of dataset semantic complexity to quantify the difficulty of the SLU
tasks. We show that near-perfect performance metrics for STI models reported in
the literature were obtained with datasets that have low semantic complexity
values. We perform experiments where we vary the semantic complexity of a
large, proprietary dataset and show that STI model performance correlates with
our semantic complexity measures, such that performance increases as complexity
values decrease. Our results show that it is important to contextualize an STI
model's performance with the complexity values of its training dataset to
reveal the scope of its applicability.
|
Mechanical characterization of brain tissue has been investigated extensively
by various research groups over the past fifty years. These properties are
particularly important for modelling Traumatic Brain Injury (TBI). In this
research, we present the design and calibration of a High Rate Tension Device
(HRTD) capable of performing tests up to a maximum strain rate of 90/s. We use
experimental and numerical methods to investigate the effects of inhomogeneous
deformation of porcine brain tissue during tension at different specimen
thicknesses (4.0-14.0 mm), by performing tension tests at a strain rate of
30/s. One-term Ogden material parameters (mu = 4395.0 Pa, alpha = -2.8) were
derived by performing an inverse finite element analysis to model all
experimental data. A similar procedure was adopted to determine Young's modulus
(E= 11200 Pa) of the linear elastic regime. Based on this analysis, brain
specimens of aspect ratio (diameter/thickness) S < 1.0 are required to minimise
the effects of inhomogeneous deformation during tension tests.
|
Deterministically growing (wild-type) populations which seed stochastically
developing mutant clones have found an expanding number of applications from
microbial populations to cancer. The special case of exponential wild-type
population growth, usually termed the Luria-Delbr\"uck or Lea-Coulson model, is
often assumed but seldom realistic. In this article we generalise this model to
different types of wild-type population growth, with mutants evolving as a
birth-death branching process. Our focus is on the size distribution of clones
- that is the number of progeny of a founder mutant - which can be mapped to
the total number of mutants. Exact expressions are derived for exponential,
power-law and logistic population growth. Additionally for a large class of
population growth we prove that the long time limit of the clone size
distribution has a general two-parameter form, whose tail decays as a
power-law. Considering metastases in cancer as the mutant clones, upon
analysing a data-set of their size distribution, we indeed find that a
power-law tail is more likely than an exponential one.
|
We report on the discovery of HAT-P-11b, the smallest radius transiting
extrasolar planet (TEP) discovered from the ground, and the first hot Neptune
discovered to date by transit searches. HAT-P-11b orbits the bright (V=9.587)
and metal rich ([Fe=H] = +0.31 +/- 0.05) K4 dwarf star GSC 03561-02092 with P =
4.8878162 +/- 0.0000071 days and produces a transit signal with depth of 4.2
mmag. We present a global analysis of the available photometric and
radial-velocity data that result in stellar and planetary parameters, with
simultaneous treatment of systematic variations. The planet, like its near-twin
GJ 436b, is somewhat larger than Neptune (17Mearth, 3.8Rearth) both in mass Mp
= 0.081 +/- 0.009 MJ (25.8 +/- 2.9 Mearth) and radius Rp = 0.422 +/- 0.014 RJ
(4.73 +/- 0.16 Rearth). HAT-P-11b orbits in an eccentric orbit with e = 0.198
+/- 0.046 and omega = 355.2 +/- 17.3, causing a reflex motion of its parent
star with amplitude 11.6 +/- 1.2 m/s, a challenging detection due to the high
level of chromospheric activity of the parent star. Our ephemeris for the
transit events is Tc = 2454605.89132 +/- 0.00032 (BJD), with duration 0.0957
+/- 0.0012 d, and secondary eclipse epoch of 2454608.96 +/- 0.15 d (BJD). The
basic stellar parameters of the host star are M* = 0.809+0.020-0.027 Msun, R* =
0.752 +/- 0.021 Rsun and Teff = 4780 +/- 50 K. Importantly, HAT-P-11 will lie
on one of the detectors of the forthcoming Kepler mission. We discuss an
interesting constraint on the eccentricity of the system by the transit light
curve and stellar parameters. We also present a blend analysis, that for the
first time treats the case of a blended transiting hot Jupiter mimicing a
transiting hot Neptune, and proves that HAT-P-11b is not such a blend.
|
The magnetic dipole and electric quadrupole hyperfine constants of Aluminium
($^{27}Al$) atom are computed using the relativistic coupled cluster (CC) and
unitary coupled cluster (UCC) methods. Effects of electron correlations are
investigated using different levels of CC approximations and truncation
schemes. The ionization potentials, excitation energies, transition
probabilities, oscillator strengths and nuclear quadrupole moment are computed
to assess the accuracy of these schemes. The nuclear quadrupole moment obtained
from the present CC and UCC calculations in the singles and doubles
approximations are 142.5 mbarn and 141.5 mbarn respectively. The discrepancies
between our calculated IPs and EEs and their measured values are better than
0.3%. The other one-electron properties reported here are also in excellent
agreement with the measurements.
|
This article proves that if M is a smooth manifold of dimension at least
four, then for generic choice of metric on M, all prime parametrized minimal
surfaces in M are free of branch points and lie on nondegenerate critical
submanifolds for the two-variable energy function which have the same dimension
as the group of complex automorphisms of the domain Riemann surface.
|
For $1\leq p\leq \infty$ and $\alpha>0$, Besov spaces $B^p_\alpha$ play a key
role in the theory of $\alpha$-M\"obius invariant function spaces. In some
sense, $B^1_\alpha$ is the minimal $\alpha$-M\"obius invariant function space,
$B^2_\alpha$ is the unique $\alpha$-M\"obius invariant Hilbert space, and
$B^\infty_\alpha$ is the maximal $\alpha$-M\"obius invariant function space. In
this paper, under the $\alpha$-M\"obius invariant pairing and by the space
$B^\infty_\alpha$, we identify the predual and dual spaces of $B^1_\alpha$. In
particular, the corresponding identifications are isometric isomorphisms. The
duality theorem via the $\alpha$-M\"obius invariant pairing for $B^p_\alpha$
with $p>1$ is also given.
|
In case of salient subject recognition, computer algorithms have been heavily
relied on scanning of images from top-left to bottom-right systematically and
apply brute-force when attempting to locate objects of interest. Thus, the
process turns out to be quite time consuming. Here a novel approach and a
simple solution to the above problem is discussed. In this paper, we implement
an approach to object manipulation and detection through segmentation map,
which would help to desaturate or, in other words, wash out the background of
the image. Evaluation for the performance is carried out using the Jaccard
index against the well-known Ground-truth target box technique.
|
Generalized estimating equations (GEE) are of great importance in analyzing
clustered data without full specification of multivariate distributions. A
recent approach jointly models the mean, variance, and correlation coefficients
of clustered data through three sets of regressions (Luo and Pan, 2022). We
observe that these estimating equations, however, are a special case of those
of Yan and Fine (2004) which further allows the variance to depend on the mean
through a variance function. The proposed variance estimators may be incorrect
for the variance and correlation parameters because of a subtle dependence
induced by the nested structure of the estimating equations. We characterize
model settings where their variance estimation is invalid and show the variance
estimators in Yan and Fine (2004) correctly account for such dependence. In
addition, we introduce a novel model selection criterion that enables the
simultaneous selection of the mean-scale-correlation model. The sandwich
variance estimator and the proposed model selection criterion are tested by
several simulation studies and real data analysis, which validate its
effectiveness in variance estimation and model selection. Our work also extends
the R package geepack with the flexibility to apply different working
covariance matrices for the variance and correlation structures.
|
Fluid flows in nature and applications are frequently subject to periodic
velocity modulations. Surprisingly, even for the generic case of flow through a
straight pipe, there is little consensus regarding the influence of pulsation
on the transition threshold to turbulence: while most studies predict a
monotonically increasing threshold with pulsation frequency (i.e. Womersley
number, $\alpha$), others observe a decreasing threshold for identical
parameters and only observe an increasing threshold at low $\alpha$. In the
present study we apply recent advances in the understanding of transition in
steady shear flows to pulsating pipe flow. For moderate pulsation amplitudes we
find that the first instability encountered is subcritical (i.e. requiring
finite amplitude disturbances) and gives rise to localized patches of
turbulence ("puffs") analogous to steady pipe flow. By monitoring the impact of
pulsation on the lifetime of turbulence we map the onset of turbulence in
parameter space. Transition in pulsatile flow can be separated into three
regimes. At small Womersley numbers the dynamics are dominated by the decay
turbulence suffers during the slower part of the cycle and hence transition is
delayed significantly. As shown in this regime thresholds closely agree with
estimates based on a quasi steady flow assumption only taking puff decay rates
into account. The transition point predicted in the zero $\alpha$ limit equals
to the critical point for steady pipe flow offset by the oscillation Reynolds
number. In the high frequency limit puff lifetimes are identical to those in
steady pipe flow and hence the transition threshold appears to be unaffected by
flow pulsation. In the intermediate frequency regime the transition threshold
sharply drops (with increasing $\alpha$) from the decay dominated (quasi
steady) threshold to the steady pipe flow level.
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Poisoning attacks have emerged as a significant security threat to machine
learning algorithms. It has been demonstrated that adversaries who make small
changes to the training set, such as adding specially crafted data points, can
hurt the performance of the output model. Some of the stronger poisoning
attacks require the full knowledge of the training data. This leaves open the
possibility of achieving the same attack results using poisoning attacks that
do not have the full knowledge of the clean training set.
In this work, we initiate a theoretical study of the problem above.
Specifically, for the case of feature selection with LASSO, we show that
full-information adversaries (that craft poisoning examples based on the rest
of the training data) are provably stronger than the optimal attacker that is
oblivious to the training set yet has access to the distribution of the data.
Our separation result shows that the two setting of data-aware and
data-oblivious are fundamentally different and we cannot hope to always achieve
the same attack or defense results in these scenarios.
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Given the stellar density near the galactic center, close encounters between
compact object binaries and the supermassive black hole are a plausible
occurrence. We present results from a numerical study of close to 13 million
such encounters. Consistent with previous studies, we corroborate that, for
binary systems tidally disrupted by the black hole, the component of the binary
remaining bound to the hole has eccentricity ~ 0.97 and circularizes
dramatically by the time it enters the classical LISA band. Our results also
show that the population of surviving binaries merits attention. These binary
systems experience perturbations to their internal orbital parameters with
potentially interesting observational consequences. We investigated the regions
of parameter space for survival and estimated the distribution of orbital
parameters post-encounter. We found that surviving binaries harden and their
eccentricity increases, thus accelerating their merger due gravitational
radiation emission and increasing the predicted merger rates by up to 1%.
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The use of floating bipolar electrodes in electrowinning cells of copper
constitutes a nonconventional technology that promises economic and operational
impacts. This thesis presents a computational tool for the simulation and
analysis of such electrochemical cells. A new model is developed for floating
electrodes and a method of finite difference is used to obtain the
threedimensional distribution of the potential and the field of current density
inside the cell. The analysis of the results is based on a technique for the
interactive visualization of three-dimensional vectorial fields as lines of
flow.
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We describe the PDFI_SS software library, which is designed to find the
electric field at the Sun's photosphere from a sequence of vector magnetogram
and Doppler velocity measurements, and estimates of horizontal velocities
obtained from local correlation tracking using the recently upgraded FLCT code.
The library, a collection of Fortran subroutines, uses the "PDFI" technique
described by Kazachenko et al. (2014), but modified for use in spherical,
Plate-Carr\'ee geometry on a staggered grid. The domain over which solutions
are found is a subset of the global spherical surface, defined by
user-specified limits of colatitude and longitude. Our staggered-grid approach,
based on that of Yee (1966), is more conservative and self-consistent compared
to the centered, Cartesian grid used by Kazachenko et al. (2014). The library
can be used to compute an end-to-end solution for electric fields from data
taken by the HMI instrument aboard NASA's SDO Mission. This capability has been
incorporated into the HMI pipeline processing system operating at SDO's JSOC.
The library is written in a general and modular way so that the calculations
can be customized to modify or delete electric field contributions, or used
with other data sets. Other applications include "nudging" numerical models of
the solar atmosphere to facilitate assimilative simulations. The library
includes an ability to compute "global" (whole-Sun) electric field solutions.
The library also includes an ability to compute Potential Magnetic Field
solutions in spherical coordinates. This distribution includes a number of test
programs which allow the user to test the software.
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The structure of the Cu(110) surface is studied at high temperatures using a
combination of lattice-gas Monte Carlo and molecular dynamics methods with
identical many-atom interactions derived from the effective medium theory. The
anisotropic six-vertex model is used in the interpretation of the lattice-gas
results. We find a clear roughening transition around T_R=1000K and
T_R/T_M=0.81. Molecular dynamics reveals the clustering of surface defects as
the atomistic mechanism of the transition and allows us to estimate
characteristic time scales. For the system of size 50x50, the time scale of the
local roughening at 1150 K of an initially smooth surface is of the order of
100 ps.
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The theory of factor-equivalence of integral lattices gives a far reaching
relationship between the Galois module structure of units of the ring of
integers of a number field and its arithmetic. For a number field $K$ that is
Galois over $\mathbb{Q}$ or an imaginary quadratic field, we prove a necessary
and sufficient condition on the quotients of class numbers of subfields of $K$,
for the quotient $E_{K}$ of the group of units of the ring of integers of $K$
by the subgroup of roots of unity to be factor equivalent to the standard
cyclic Galois module. By using strong arithmetic properties of totally real
$p$-rational number fields, we prove that the non-abelian $p$-rational
$p$-extensions of $\mathbb{Q}$ do not have Minkowski units, which extends a
result of Burns to non-abelian number fields. We also study the relative Galois
module structure of $E_{L}$ for varying Galois extensions $L/F$ of totally real
$p$-rational number fields whose Galois groups are isomorphic to a fixed finite
group $G$. In that case, we prove that there is a finite set $\Omega$ of
$\mathbb{Z}_p[G]$-lattices such that for every $L$, $\mathbb{Z}_{p}
\otimes_{\mathbb{Z}} E_{L}$ is factor equivalent to $\mathbb{Z}_{p}[G]^{n}
\oplus X$ as $\mathbb{Z}_p[G]$-lattices for some $X \in \Omega$ and an integer
$n \geq 0$.
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In a previous paper [3] we computed cohomology groups H^5 (Gamma_0 (N), \C),
where Gamma_0 (N) is a certain congruence subgroup of SL (4, \Z), for a range
of levels N. In this note we update this earlier work by extending the range of
levels and describe cuspidal cohomology classes and additional boundary
phenomena found since the publication of [3]. The cuspidal cohomology classes
in this paper are the first cuspforms for GL(4) concretely constructed in terms
of Betti cohomology.
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Throughout the course of mathematical history, generalizations of previously
understood concepts and structures have led to the fruitful development of the
hierarchy of number systems, non-euclidean geometry, and many other epochal
phases in mathematical progress. In the study of formalized theories of
arithmetic, it is only natural to consider the extension from the standard
model of Peano arithmetic, $\langle \mathbb{N},+,\times,\leq,0,1 \rangle$, to
non-standard models of arithmetic. The existence of non-standard models of
Peano arithmetic provided motivation in the early $20^{th}$ century for a
variety of questions in model theory regarding the classification of models up
to isomorphism and the properties that non-standard models of Peano arithmetic
have. This paper presents these questions and the necessary results to prove
Tennenbaum's Theorem, which draws an explicit line between the properties of
standard and non-standard models; namely, that no countable non-standard model
of Peano arithmetic is recursive. These model-theoretic results have
contributed to the foundational framework within which research programs
developed by Skolem, Rosser, Tarski, Mostowski and others have flourished.
While such foundational topics were crucial to active fields of research during
the middle of the $20^{th}$ century, numerous open questions about models of
arithmetic, and model theory in general, still remain pertinent to the realm of
$21^{st}$ century mathematical discourse.
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The recent discovery of a spectacular dust plume in the system 2XMM
J160050.7-514245 (referred to as "Apep") suggested a physical origin in a
colliding-wind binary by way of the "Pinwheel" mechanism. Observational data
pointed to a hierarchical triple-star system, however several extreme and
unexpected physical properties seem to defy the established physics of such
objects. Most notably, a stark discrepancy was found in the observed outflow
speed of the gas as measured spectroscopically in the line-of-sight direction
compared to the proper motion expansion of the dust in the sky plane. This
enigmatic behaviour arises at the wind base within the central Wolf-Rayet
binary: a system that has so far remained spatially unresolved. Here we present
an updated proper motion study deriving the expansion speed of Apep's dust
plume over a two-year baseline that is four times slower than the spectroscopic
wind speed, confirming and strengthening the previous finding. We also present
the results from high-angular-resolution near-infrared imaging studies of the
heart of the system, revealing a close binary with properties matching a
Wolf-Rayet colliding-wind system. Based on these new observational constraints,
an improved geometric model is presented yielding a close match to the data,
constraining the orbital parameters of the Wolf-Rayet binary and lending
further support to the anisotropic wind model.
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The charge $F_1(0)$ and the magnetic $F_2(0)$ form factors of heavy charged
leptons have been shown in the framework of the perturbation theory to have
imaginary part. The imaginary parts of the form factors for muon and tau lepton
have been calculated at the two-loop level in the Standard Model. The effects
where these imaginary parts could manifest themselves are discussed.
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A generalist robot equipped with learned skills must be able to perform many
tasks in many different environments. However, zero-shot generalization to new
settings is not always possible. When the robot encounters a new environment or
object, it may need to finetune some of its previously learned skills to
accommodate this change. But crucially, previously learned behaviors and models
should still be suitable to accelerate this relearning. In this paper, we aim
to study how generative models of possible outcomes can allow a robot to learn
visual representations of affordances, so that the robot can sample potentially
possible outcomes in new situations, and then further train its policy to
achieve those outcomes. In effect, prior data is used to learn what kinds of
outcomes may be possible, such that when the robot encounters an unfamiliar
setting, it can sample potential outcomes from its model, attempt to reach
them, and thereby update both its skills and its outcome model. This approach,
visuomotor affordance learning (VAL), can be used to train goal-conditioned
policies that operate on raw image inputs, and can rapidly learn to manipulate
new objects via our proposed affordance-directed exploration scheme. We show
that VAL can utilize prior data to solve real-world tasks such drawer opening,
grasping, and placing objects in new scenes with only five minutes of online
experience in the new scene.
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With the emergence of collaborative robots (cobots), human-robot
collaboration in industrial manufacturing is coming into focus. For a cobot to
act autonomously and as an assistant, it must understand human actions during
assembly. To effectively train models for this task, a dataset containing
suitable assembly actions in a realistic setting is crucial. For this purpose,
we present the ATTACH dataset, which contains 51.6 hours of assembly with 95.2k
annotated fine-grained actions monitored by three cameras, which represent
potential viewpoints of a cobot. Since in an assembly context workers tend to
perform different actions simultaneously with their two hands, we annotated the
performed actions for each hand separately. Therefore, in the ATTACH dataset,
more than 68% of annotations overlap with other annotations, which is many
times more than in related datasets, typically featuring more simplistic
assembly tasks. For better generalization with respect to the background of the
working area, we did not only record color and depth images, but also used the
Azure Kinect body tracking SDK for estimating 3D skeletons of the worker. To
create a first baseline, we report the performance of state-of-the-art methods
for action recognition as well as action detection on video and
skeleton-sequence inputs. The dataset is available at
https://www.tu-ilmenau.de/neurob/data-sets-code/attach-dataset .
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In the paper, the thermoEMF of powder-based thermoelectric materials (TEM) is
calculated. The calculation is made on the assumption of power dependence of
mean free path on energy. The thermoEMF decreases with increasing the average
radius of powder particles, however, it drastically increases with an increase
in power exponent in the law of dependence of the mean free path of relaxation
time on energy (scattering index). Therefore, it turns out that the thermoEMF
of powder-based TEM with a higher scattering index can be even greater than the
thermoEMF of a single-crystal material with a low scattering index. As a
consequence, a significant increase in the thermoEMF and, hence, in the
thermoelectric figure of merit of TEM in going to powder materials, especially
in the case of degenerate electron gas, can be expected only if dielectric or
vacuum barriers between powder particles do not lead to a significant decrease
in electrical conductivity. At the same time, tunnelling through the
abovementioned barriers should provide such an energy filtration of charge
carriers, which leads both to an increase in the proportion of "useful" charge
carriers with energy greater than the chemical potential, and to an increase in
the scattering index. However, experimentally, there is no significant increase
in thermoEMF in going from single-crystal materials to powders, most likely
because such energy filtering does not take place.
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We investigated the paramagnetic resonance in single crystals of LiCuVO$_4$
with special attention to the angular variation of the absorption spectrum. To
explain the large resonance linewidth of the order of 1 kOe, we analyzed the
anisotropic exchange interaction in the chains of edge-sharing CuO$_6$
octahedra, taking into account the ring-exchange geometry of the
nearest-neighbor coupling via two symmetric rectangular Cu-O bonds. The
exchange parameters, which can be estimated from theoretical considerations,
nicely agree with the parameters obtained from the angular dependence of the
linewidth. The anisotropy of this magnetic ring exchange is found to be much
larger than it is usually expected from conventional estimations which neglect
the bonding geometry. Hence, the data yield the evidence that in copper oxides
with edge-sharing structures the role of the orbital degrees of freedom is
strongly enhanced. These findings establish LiCuVO$_4$ as one-dimensional
compound at high temperatures.
PACS: 76.30.-v, 76.30.Fc, 75.30.Et
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Topologically ordered systems exhibit large-scale correlation in their ground
states, which may be characterized by quantities such as topological
entanglement entropy. We propose that the concept of irreducible many-body
correlation, the correlation that cannot be implied by all local correlations,
may also be used as a signature of topological order. In a topologically
ordered system, we demonstrate that for a part of the system with holes, the
reduced density matrix exhibits irreducible many-body correlation which becomes
reducible when the holes are removed. The appearance of these irreducible
correlations then represents a key feature of topological phase. We analyze the
many-body correlation structures in the ground state of the toric code model in
an external magnetic field, and show that the topological phase transition is
signaled by the irreducible many-body correlations.
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An integration of distributionally robust risk allocation into sampling-based
motion planning algorithms for robots operating in uncertain environments is
proposed. We perform non-uniform risk allocation by decomposing the
distributionally robust joint risk constraints defined over the entire planning
horizon into individual risk constraints given the total risk budget.
Specifically, the deterministic tightening defined using the individual risk
constraints is leveraged to define our proposed exact risk allocation
procedure. Our idea of embedding the risk allocation technique into sampling
based motion planning algorithms realises guaranteed conservative, yet
increasingly more risk feasible trajectories for efficient state space
exploration.
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When the bulk geometry in AdS/CFT contains a black hole, the boundary
reconstruction of a given bulk operator will often necessarily depend on the
choice of black hole microstate, an example of state dependence. As a result,
whether a given bulk operator can be reconstructed on the boundary at all can
depend on whether the black hole is described by a pure state or thermal
ensemble. We refine this dichotomy, demonstrating that the same boundary
operator can often be used for large subspaces of black hole microstates,
corresponding to a constant fraction $\alpha$ of the black hole entropy. In the
Schrodinger picture, the boundary subregion encodes the $\alpha$-bits (a
concept from quantum information) of a bulk region containing the black hole
and bounded by extremal surfaces. These results have important consequences for
the structure of AdS/CFT and for quantum information. Firstly, they imply that
the bulk reconstruction is necessarily only approximate and allow us to place
non-perturbative lower bounds on the error when doing so. Second, they provide
a simple and tractable limit in which the entanglement wedge is
state-dependent, but in a highly controlled way. Although the state dependence
of operators comes from ordinary quantum error correction, there are clear
connections to the Papadodimas-Raju proposal for understanding operators behind
black hole horizons. In tensor network toy models of AdS/CFT, we see how state
dependence arises from the bulk operator being `pushed' through the black hole
itself. Finally, we show that black holes provide the first `explicit' examples
of capacity-achieving $\alpha$-bit codes. Unintuitively, Hawking radiation
always reveals the $\alpha$-bits of a black hole as soon as possible. In an
appendix, we apply a result from the quantum information literature to prove
that entanglement wedge reconstruction can be made exact to all orders in
$1/N$.
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We compute the radiative corrections to the mass of a test boson field in an
inflating space-time. The calculations are carried out in case of a boson part
of a supersymmetric chiral multiplet. We show that its mass is preserved up to
logarithmic divergences both in ultraviolet and infrared domains. Consequences
of these results for inflationary models are discussed.
|
Next-generation high-power lasers that can be focused to intensities
exceeding 10^23 W/cm^2 are enabling new physics and applications. The physics
of how these lasers interact with matter is highly nonlinear, relativistic, and
can involve lowest-order quantum effects. The current tool of choice for
modeling these interactions is the particle-in-cell (PIC) method. In strong
fields, the motion of charged particles and their spin is affected by radiation
reaction. Standard PIC codes usually use Boris or its variants to advance the
particles, which requires very small time steps in the strong-field regime to
obtain accurate results. In addition, some problems require tracking the spin
of particles, which creates a 9D particle phase space (x, u, s). Therefore,
numerical algorithms that enable high-fidelity modeling of the 9D phase space
in the strong-field regime are desired. We present a new 9D phase space
particle pusher based on analytical solutions to the position, momentum and
spin advance from the Lorentz force, together with the semi-classical form of
RR in the Landau-Lifshitz equation and spin evolution given by the
Bargmann-Michel-Telegdi equation. These analytical solutions are obtained by
assuming a locally uniform and constant electromagnetic field during a time
step. The solutions provide the 9D phase space advance in terms of a particle's
proper time, and a mapping is used to determine the proper time step for each
particle from the simulation time step. Due to the analytical integration, the
constraint on the time step needed to resolve trajectories in ultra-high fields
can be greatly reduced. We present single-particle simulations and full PIC
simulations to show that the proposed particle pusher can greatly improve the
accuracy of particle trajectories in 9D phase space for given laser fields. A
discussion on the numerical efficiency of the proposed pusher is also provided.
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Within the paradigm of non-perturbative Einstein gravity we study continuous
manifolds which possess de Sitter interiors and Kerr exteriors. These manifolds
could represent the spacetime of rotating gravastars or other similar black
hole mimickers. The scheme presented here allows for a $C^{n}$ transition from
the exactly de Sitter interior to the exactly Kerr exterior, with $n$
arbitrarily large. Generic properties that such models must possess are
discussed, such as the changing of the topology of the ergosphere from $S^{2}$
to $S^{1}\times S^{1}$. It is shown how in the outer layers of the transition
region (the "atmosphere" as it is often called in astrophysics) the
dominant/weak and strong energy conditions can be respected. However, much like
in the case of its static spherically symmetric gravastar counterpart, there
must be some assumptions imposed in the atmosphere for the energy conditions to
hold. These assumptions turn out to not be severe. The class of manifolds
presented here are expected to possess all the salient features of the fully
generic case. Strictly speaking, a number of the results are also applicable to
the locally anti-de Sitter core scenario, although we focus on the case of a
positive cosmological constant.
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We investigate quantum aspects of Gopakumar-Minwalla-Strominger (GMS)
solutions of noncommutative field theory (NCFT) at large noncommutativity
limit, $\theta \to \infty$. Building upon a quantitative map between operator
formulation of 2-(respectively, (2+1))-dimensional NCFTs and large $N$ matrix
models of $c=0$ (respectively, $c=1$) noncritical strings, we show that GMS
solutions are quantum mechanically sensible only if we make appropriate joint
scaling of $\theta$ and $N$. For 't Hooft's planar scaling, GMS solutions are
replaced by large $N$ saddle-point solutions. GMS solutions are recovered from
saddle-point solutions at small 't Hooft coupling regime, but are destabilized
at large 'tHooft coupling regime by quantum effects. We make comparisons
between these large $N$ effects and recently studied infrared effects in NCFTs.
We estimate U(N) symmetry breaking gradient effects and argue that they are
suppressed only at small 't Hooft coupling regime.
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We consider the pion-photon transition form factor at low to intermediate
spacelike momenta within the theoretical framework of light-cone sum rules. We
derive predictions which take into account all currently known contributions
stemming from QCD perturbation theory up to the next-to-next-to-leading order
(NNLO) and by including all twist terms up to order six. In order to enable a
more detailed comparison with forthcoming high-precision data, we also estimate
the main systematic theoretical uncertainties, stemming from various sources,
and discuss their influence on the calculations --- in particular the dominant
one related to the still uncalculated part of the NNLO contribution. The
analysis addresses, in broad terms, also the role of the twist-two pion
distribution amplitude derived with different approaches.
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This paper presents the first results of the two-phase flow simulation
obtained using recently introduced physical, mathematical and numerical model
of the intermittency region between two-phases (Wac{\l}awczyk 2017, 2021). The
statistical interpretation of the intermittency region evolution equations
allows to account for the non-equilibrium effects in the domain separating two
phases. The source of non-equilibrium are spatial variations in the ratio of
work done by volume and interfacial forces governing its width. As the
statistical description of the two-phase flow differs from the deterministic
two-phase flow models known in the literature, in the present work we focus
discussion of the results on these differences. To this goal, the rising two
dimensional gas bubble is studied; differences between equilibrium and
non-equilibrium solutions are investigated. It is argued the statistical
description of the intermittency region has potential to account for physical
phenomena not considered previously in the computer simulations of two-phase
flow.
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We consider dense wireless random-access networks, modeled as systems of
particles with hard-core interaction. The particles represent the network users
that try to become active after an exponential back-off time, and stay active
for an exponential transmission time. Due to wireless interference, active
users prevent other nearby users from simultaneous activity, which we describe
as hard-core interaction on a conflict graph. We show that dense networks with
aggressive back-off schemes lead to extremely slow transitions between dominant
states, and inevitably cause long mixing times and starvation effects.
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We look for spectral type differential equations for the generalized Jacobi
polynomials found by T.H. Koornwinder in 1984 and for the Sobolev-Laguerre
polynomials. We introduce a method which makes use of computeralgebra packages
like Maple and Mathematica and we will give some preliminary results.
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We consider gravity in 2+1 dimensions in presence of extended stationary
sources with rotational symmetry. We prove by direct use of Einstein's
equations that if i) the energy momentum tensor satisfies the weak energy
condition, ii) the universe is open (conical at space infinity), iii) there are
no CTC at space infinity, then there are no CTC at all.
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A trie $\mathcal{T}$ is a rooted tree such that each edge is labeled by a
single character from the alphabet, and the labels of out-going edges from the
same node are mutually distinct. Given a trie $\mathcal{T}$ with $n$ edges, we
show how to compute all distinct palindromes and all maximal palindromes on
$\mathcal{T}$ in $O(n)$ time, in the case of integer alphabets of size
polynomial in $n$. This improves the state-of-the-art $O(n \log h)$-time
algorithms by Funakoshi et al. [PCS 2019], where $h$ is the height of
$\mathcal{T}$. Using our new algorithms, the eertree with suffix links for a
given trie $\mathcal{T}$ can readily be obtained in $O(n)$ time. Further, our
trie-based $O(n)$-space data structure allows us to report all distinct
palindromes and maximal palindromes in a query string represented in the trie
$\mathcal{T}$, in output optimal time. This is an improvement over an existing
(na\"ive) solution that precomputes and stores all distinct palindromes and
maximal palindromes for each and every string in the trie $\mathcal{T}$
separately, using a total $O(n^2)$ preprocessing time and space, and reports
them in output optimal time upon query.
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Observations of Her X-1 by the Extreme Ultraviolet Explorer (EUVE) at the end
of the x-ray Short High state are reported here. Her X-1 is found to exhibit a
strong orbital modulation of the EUV flux, with a large dip superposed on a
broad peak around orbital phase 0.5 when the neutron star is closest the
observer. Alternate mechanisms for producing the observed EUV lightcurve are
modeled. We conclude that: i) the x-ray heated surface of the companion is too
cool to produce enough emission; ii) the accretion disk can produce enough
emission but does not explain the orbital modulation; iii) reflection of x-rays
off of the companion can produce the shape and intensity of the observed
lightcurve. The only viable cause for the large dip at orbital phase 0.5 is
shadowing of the companion by the accretion disk.
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The internal control problem for the Kadomstev-Petviashvili II equation,
known as KP-II, is the object of study in this paper. The controllability in
$L^2(T)$ from vertical strip is proved using the Hilbert Unique Method through
the techniques of semiclassical and microlocal analysis. Additionally, a
negative result for the controllability in $L^2(T)$ from horizontal strip is
also showed.
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We study interacting bosons in a two dimensional bipartite optical lattice.
By focusing on the regime where the first three excited bands are nearly
degenerate we derive a three orbital tight-binding model which captures the
most relevant features of the bandstructure. In addition, we also derive a
corresponding generalized Bose-Hubbard model and solve it numerically under
different situations, both with and without a confining trap. It is especially
found that the hybridization between sublattices can strongly influence the
phase diagrams and in a trap enable even appearances of condensed phases
intersecting the same Mott insulating plateaus.
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We propose a novel value approximation method, namely Eigensubspace
Regularized Critic (ERC) for deep reinforcement learning (RL). ERC is motivated
by an analysis of the dynamics of Q-value approximation error in the
Temporal-Difference (TD) method, which follows a path defined by the
1-eigensubspace of the transition kernel associated with the Markov Decision
Process (MDP). It reveals a fundamental property of TD learning that has
remained unused in previous deep RL approaches. In ERC, we propose a
regularizer that guides the approximation error tending towards the
1-eigensubspace, resulting in a more efficient and stable path of value
approximation. Moreover, we theoretically prove the convergence of the ERC
method. Besides, theoretical analysis and experiments demonstrate that ERC
effectively reduces the variance of value functions. Among 26 tasks in the
DMControl benchmark, ERC outperforms state-of-the-art methods for 20. Besides,
it shows significant advantages in Q-value approximation and variance
reduction. Our code is available at https://sites.google.com/view/erc-ecml23/.
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We report on the elastic contact between a spherical lens and a patterned
substrate, composed of an hexagonal lattice of cylindrical pillars. The stress
field and the size of the contact area are obtained by means of numerical
methods (discrete Green's function superposition and iterative bisection-like
methods). For small indentations, a transition from a Hertzian to a
Boussinesq-Cerruti-like behavior is observed when the surface fraction of the
substrate that is covered by pillars is increased. In particular, we present a
master curve defined by two dimensionless parameters, which allows to predict
the stress at the center of contact region in terms of the surface fraction
occupied by pillars. The transition between the limiting contact regimes,
Hertzian and Boussinesq-Cerruti-like, is well described by a rational function.
Additionally, a simple model to describe the Boussines-Cerruti-like contact
between the lens and a single elastic pillar, which takes into account the
pillar geometry and the elastic properties of the two bodies, is presented.
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Calculations of the bootstrap current for the TJ-II stellarator are
presented. DKES and NEO-MC codes are employed; the latter has allowed, for the
first time, the precise computation of the bootstrap transport coefficient in
the long mean free path regime of this device. The low error bars allow a
precise convolution of the monoenergetic coefficients, which is confirmed by
error analysis. The radial profile of the bootstrap current is presented for
the first time for the 100_44_64 configuration of TJ-II for three different
collisionality regimes. The bootstrap coefficient is then compared to that of
other configurations of TJ-II regularly operated. The results show qualitative
agreement with toroidal current measurements; precise comparison with real
discharges is ongoing.
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Subsets and Splits