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We give a systematic and thorough study of geometric notions and results
connected to Minkowski's measure of symmetry and the extension of the
well-known Minkowski functional to arbitrary, not necessarily symmetric convex
bodies K on any (real) normed space X. Although many of the notions and results
we treat in this paper can be found elsewhere in the literature, they are
scattered and possibly hard to find. Further, we are not aware of a systematic
study of this kind and we feel that several features, connections and
properties - e.g. the connections between many equivalent formulations - are
new, more general and they are put in a better perspective now. In particular,
we prove a number of fundamental properties of the extended Minkowski
functional, including convexity, global Lipschitz boundedness, linear growth
and approximation of the classical Minkowski functional of the central
symmetrization of the body K.
Our aim is to present how in the recent years these notions proved to be
surprisingly relevant and effective in problems of approximation theory.
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Let $\mathbb{F}\subset \mathbb{G}$ be two filtrations and $S$ be a
$\mathbb{F}$ semimartingale possessing a $\mathbb{F}$ local martingale
deflator. Consider $\tau$ a $\mathbb{G}$ stopping time. We study the problem
whether $S^{\tau-}$ or $S^{\tau}$ can have $\mathbb{G}$ local martingale
deflators. A suitable theoretical framework is set up in this paper, within
which necessary/sufficient conditions for the problem to be solved have been
proved. Under these conditions, we will construct $\mathbb{G}$ local martingale
deflators for $S^{\tau-}$ or for $S^{\tau}$. Among others, it is proved that
$\mathbb{G}$ local martingale deflators are multiples of $\mathbb{F}$ local
martingale deflators, with a multiplicator coming from the multiplicative
decomposition of the Az\'ema supermartingale of $\tau$. The proofs of the
necessary/sufficient conditions require various results to be established about
Az\'ema supermartingale, about local martingale deflator, about filtration
enlargement, which are interesting in themselves.
Our study is based on a filtration enlargement setting. For applications, it
is important to have a method to infer the existence of such setting from the
knowledge of the market information. This question is discussed at the end of
the paper.
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In this thesis, I investigate various aspects of one of the most fundamental
questions in thermodynamics: what state transformations can quantum systems
undergo while interacting with a thermal bath under specific constraints? These
constraints may involve total energy conservation, memory effects, or
finite-size considerations. Addressing this question leads to (i) a
characterisation of the structure of the thermodynamic arrow of time, (ii) a
framework bridging the gap between memoryless and arbitrarily non-Markovian
thermodynamic processes, and (iii) a derivation of the famous
fluctuation-dissipation relation within a quantum information framework.
Finally, the last part of this thesis focuses on studying a ubiquitous
phenomenon in science, so-called catalysis. It involves using an auxiliary
system (a catalyst) to enable processes that would otherwise be impossible.
Over the last two decades, this notion has spread to the field of quantum
physics. However, this effect is typically described within a highly abstract
framework. Despite its successes, this approach struggles to fully capture the
behaviour of physically realisable systems, thereby limiting the applicability
of quantum catalysis in practical scenarios. Strikingly, I will demonstrate
this effect in a paradigmatic quantum optics setup, namely the Jaynes-Cummings
model, where an atom interacts with an optical cavity. The atom plays the role
of the catalyst and allows for the deterministic generation of non-classical
light in the cavity, as evidenced by sub-Poissonian statistics or Wigner
negativity.
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This paper presents a framework for the study of convergence when the nodes'
dynamics may be both piecewise smooth and/or nonidentical across the network.
Specifically, we derive sufficient conditions for global convergence of all
node trajectories towards the same bounded region of their state space. The
analysis is based on the use of set-valued Lyapunov functions and bounds are
derived on the minimum coupling strength required to make all nodes in the
network converge towards each other. We also provide an estimate of the
asymptotic bound $\epsilon$ on the mismatch between the node states at steady
state. The analysis is performed both for linear and nonlinear coupling
protocols. The theoretical analysis is extensively illustrated and validated
via its application to a set of representative numerical examples.
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We show that parameterized versions of splitting theorems in Morse theory can
be effectively used to generalize some famous bifurcation theorems for
potential operators. In particular, such generalizations based on the author's
recent splitting theorems [38, 39, 42, 43] and that of [8] are given though
potential operators in [42, 43] have weaker differentiability, even
discontinuous. As applications, we obtain many bifurcation results for
quasi-linear elliptic Euler equations and systems of higher order.
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The semi-Dirac semi-Weyl semi-metal has been of interest in recent years due
to its naturally occurring point Fermi surface and the associated exotic
band-structure near the Fermi surface, which is linear (graphene-like) in one
direction of the Brillouin zone, but quadratic in a direction perpendicular to
it. In this paper the effect of a magnetic adatom impurity in a semi-Dirac
system is studied. As in a metal, the magnetic impurity in a semi-Dirac system
interacts with the sea of conduction electrons and gives rise to magnetism. The
transition of the semi-Dirac system from the non-magnetic to the magnetic phase
is studied as a function of the impurity energy, the strength of hybridization
between the impurity and the bath as well as that of the electron electron
interaction at the impurity atom. The results are compared and contrasted with
those of graphene and ordinary metal. Since the semi-Dirac and the Dirac
dispersion share similar features,e.g, both are particle hole symmetric and
linear in one direction, the two systems share resemblances in their
characteristics in the presence of a magnetic impurity. But some features are
unique to the semi-Dirac dispersion.
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We present an experimental and theoretical study of electron tunnelling
through quantum dots which focusses the attention on the amplitude of the
current peaks as a function of magnetic field. We demonstrate that the
amplitudes of the current peaks in the tunnelling spectra show a dramatically
different behaviour as a function of the magnetic field, depending on the
angular momentum of the dot state through which tunnelling occurs. This is seen
in the non-monotonic behaviour of the current amplitude in magnetic field.
Furthermore, the magnetic field severely hinders tunnelling through states with
angular momentum parallel to the field, and in some cases it makes it
altogether impossible. This type of investigation allows us to directly probe
the details of the confined wave functions of the quantum dot.
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For arbitrary integer n, we describe a large class of right-angled Coxeter
systems for which the visual baundary (of the corresponding Coxeter-Davis
complex) is homeomorphic to the n-dimensional Sierpi\'nski compactum. We also
provide a necessary and sufficient condition for a planar simplicial complex L
under which the right-angled Coxeter system whose nerve is L has the visual
boundary homeomorphic to the Sierpi\'nski curve.
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First-principles-based modelings have been extremely successful in providing
crucial insights and predictions for complex biological functions and
phenomena. However, they can be hard to build and expensive to simulate for
complex living systems. On the other hand, modern data-driven methods thrive at
modeling many types of high-dimensional and noisy data. Still, the training and
interpretation of these data-driven models remain challenging. Here, we combine
the two types of methods to model stochastic neuronal network oscillations.
Specifically, we develop a class of first-principles-based artificial neural
networks to provide faithful surrogates to the high-dimensional, nonlinear
oscillatory dynamics produced by neural circuits in the brain. Furthermore,
when the training data set is enlarged within a range of parameter choices, the
artificial neural networks become generalizable to these parameters, covering
cases in distinctly different dynamical regimes. In all, our work opens a new
avenue for modeling complex neuronal network dynamics with artificial neural
networks.
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Most amino acids and sugars molecules occur in mirror, or chiral, images of
each other, knowns as enantiomers. However, life on Earth is mostly homochiral:
proteins contain almost exclusively L-amino acids, while only D-sugars appear
in RNA and DNA. The mechanism behind this fundamental asymmetry of life remains
unknown, despite much progress in the theoretical and experimental
understanding of homochirality in the past decades. We review three potential
mechanisms for the emergence of biological homochirality on primal Earth and
explore their implications for astrobiology: the first, that biological
homochirality is a stochastic process driven by local environmental
fluctuations; the second, that it is driven by circularly-polarized ultraviolet
radiation in star-forming regions; and the third, that it is driven by parity
violation at the elementary particle level. We argue that each of these
mechanisms leads to different observational consequences for the existence of
enantiomeric excesses in our solar system and in exoplanets, pointing to the
possibility that the search for life elsewhere will help elucidate the origins
of homochirality on Earth.
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We study the leading term of the holonomy map of a perturbed plane polynomial
Hamiltonian foliation. The non-vanishing of this term implies the
non-persistence of the corresponding Hamiltonian identity cycle. We prove that
this does happen for generic perturbations and cycles, as well for cycles which
are commutators in Hamiltonian foliations of degree two. Our approach relies on
the Chen's theory of iterated path integrals which we briefly resume.
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The exact solution of the asymmetric exclusion problem with N distinct
classes of particles (c = 1,2,...,N), with hierarchical order is presented.
In this model the particles (size 1) are located at lattice points, and
diffuse with equal asymmetric rates, but particles in a class c do not
distinguish those in the classes c' >c from holes (empty sites). We generalize
and solve exactly this model by considering the molecules in each distinct
class c =1,2,...,N with sizes s_c (s_c = 0,1,2,...), in units of lattice
spacing. The solution is derived by a Bethe ansatz of nested type.
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We build a setup for path integral quantization through the Faddeev-Jackiw
approach, extending it to include Grassmannian degrees of freedom, to be later
implemented in a model of generalized electrodynamics that involves
fourth-order derivatives in the components of a massive vector field being
endowed with gauge freedom, due to an additional scalar field. Namely, the
generalized Stueckelberg electrodynamics. In the first instance, we work on the
free case to gain some familiarity with the program and, subsequently, we add
the interaction with fermionic matter fields to complete our aim. In addition
to deriving the correct classical brackets for such a model, we get the full
expression for the associated generating functional and its associated
integration measure.
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The set of coupled equations for the self-consistent propagator and the field
expectation value is solved numerically with high accuracy in Euclidean space
at zero temperature and in the broken symmetry phase of the phi^4 model.
Explicitly finite equations are derived with the adaptation of the
renormalization method of van Hees and Knoll [H. van Hees, J. Knoll, Phys. Rev.
D65, 025010 (2001)] to the case of non-vanishing field expectation value. The
set of renormalization conditions used in this method leads to the same set of
counterterms obtained recently in A. Patkos, Zs. Szep, Nucl. Phys. A811,
329-352 (2008). This makes possible the direct comparison of the accurate
solution of explicitly finite equations with the solution of renormalized
equations containing counterterms. The numerically efficient way of solving
iteratively these latter equations is obtained by deriving at each order of the
iteration new counterterms which evolve during the iteration process towards
the counterterms determined based on the asymptotic behavior of the converged
propagator. As shown at different values of the coupling, the use of these
evolving counterterms accelerates the convergence of the solution of the
equations.
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We propose a stochastic process driven by memory effect with novel
distributions including both exponential and leptokurtic heavy-tailed
distributions. A class of distribution is analytically derived from the
continuum limit of the discrete binary process with the renormalized
auto-correlation and the closed form moment generating function is obtained,
thus the cumulants are calculated and shown to be convergent. The other class
of distributions are numerically investigated. The concoction of the two
stochastic processes of the different signs of memory under regime switching
mechanism does incarnate power-law decay behavior, which strongly implies that
memory is the alternative origin of heavy-tail.
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We present results for the azimuthal anisotropy of charged hadron
distributions in A+A, p+A, d+A, and He3+A collisions within the IP-Glasma+MUSIC
model. Obtained anisotropies are due to the fluid dynamic response of the
system to the fluctuating initial geometry of the interaction region. While the
elliptic and triangular anisotropies in peripheral Pb+Pb collisions at
root-s=2.76 TeV are well described by the model, the same quantities in
root-s=5.02 TeV p+Pb collisions underestimate the experimental data. This
disagreement can be due to neglected initial state correlations or the lack of
a detailed description of the fluctuating spatial structure of the proton, or
both. We further present predictions for azimuthal anisotropies in p+Au, d+Au,
and He3+Au collisions at root-s=200 GeV. For d+Au and 3He+Au collisions we
expect the detailed substructure of the nucleon to become less important.
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Let G be a nilpotent complete p-valued group of finite rank and let k be a
field of characteristic p. We prove that every faithful prime ideal of the
Iwasawa algebra kG is controlled by the centre of G, and use this to show that
the prime spectrum of kG is a disjoint union of commutative strata. We also
show that every prime ideal of kG is completely prime. The key ingredient in
the proof is the construction of a non-commutative valuation on certain
filtered simple Artinian rings.
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UV radiation has been used as a disinfection strategy to deactivate a wide
range of pathogens, but existing irradiation strategies do not ensure
sufficient exposure of all environmental surfaces and/or require long
disinfection times. We present a near-optimal coverage planner for mobile UV
disinfection robots. The formulation optimizes the irradiation time efficiency,
while ensuring that a sufficient dosage of radiation is received by each
surface. The trajectory and dosage plan are optimized taking collision and
light occlusion constraints into account. We propose a two-stage scheme to
approximate the solution of the induced NP-hard optimization, and, for
efficiency, perform key irradiance and occlusion calculations on a GPU.
Empirical results show that our technique achieves more coverage for the same
exposure time as strategies for existing UV robots, can be used to compare UV
robot designs, and produces near-optimal plans. This is an extended version of
the paper originally contributed to ICRA2021.
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We study genericity of dynamical properties in the space of homeomorphisms of
the Cantor set and in the space of subshifts of a suitably large shift space.
These rather different settings are related by a Glasner-King type
correspondence: genericity in one is equivalent to genericity in the other.
By applying symbolic techniques in the shift-space model we derive new
results about genericity of dynamical properties for transitive and totally
transitive homeomorphisms of the Cantor set. We show that the isomorphism class
of the universal odometer is generic in the space of transitive systems. On the
other hand, the space of totally transitive systems displays much more varied
dynamics. In particular, we show that in this space the isomorphism class of
every Cantor system without periodic points is dense, and the following
properties are generic: minimality, zero entropy, disjointness from a fixed
totally transitive system, weak mixing, strong mixing, and minimal self
joinings. The last two stand in striking contrast to the situation in the
measure-preserving category. We also prove a correspondence between genericity
of dynamical properties in the measure-preserving category and genericity of
systems supporting an invariant measure with the same property.
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Next-generation accelerator concepts which hinge on the precise shaping of
beam distributions, demand equally precise diagnostic methods capable of
reconstructing beam distributions within 6-dimensional position-momentum
spaces. However, the characterization of intricate features within
6-dimensional beam distributions using conventional diagnostic techniques
necessitates hundreds of measurements, using many hours of valuable beam time.
Novel phase space reconstruction techniques are needed to substantially reduce
the number of measurements required to reconstruct detailed, high-dimensional
beam features in order to resolve complex beam phenomena, and as feedback in
precision beam shaping applications. In this study, we present a novel approach
to reconstructing detailed 6-dimensional phase space distributions from
experimental measurements using generative machine learning and differentiable
beam dynamics simulations. We demonstrate that for a collection of synthetic
beam distribution test cases that this approach can be used to resolve
6-dimensional phase space distributions using basic beam manipulations and as
few as 20 2-dimensional measurements of the beam profile, without the need for
prior data collection or model training. We also demonstrate an application of
the reconstruction method in an experimental setting at the Argonne Wakefield
Accelerator, where it is able to reconstruct the beam distribution and
accurately predict previously unseen measurements 75x faster than previous
methods.
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The extension of the highly-optimized local natural orbital (LNO) CCSD(T)
method is presented for high-spin open-shell molecules. The techniques enabling
the outstanding efficiency of the closed-shell LNO-CCSD(T) variant are adopted,
including the iteration- and redundancy-free MP2 and (T) formulations, as well
as the integral-direct, memory- and disk use economic, and OpenMP-parallel
algorithms. For large molecules, the efficiency of our open-shell LNO-CCSD(T)
method approaches that of its closed-shell parent method due to a novel
approximation for higher-order long-range spin-polarization effects. The
accuracy of open-shell LNO-CCSD(T) is extensively tested for radicals and
reactions thereof, ionization processes, as well as spin-state splittings and
transition-metal compounds. At the size range, where the canonical CCSD(T)
reference is accessible (up to 20-30 atoms) the average open-shell LNO-CCSD(T)
correlation energies are found to be 99.9-99.95% accurate, which translates
into average absolute deviations of a few tenth of a kcal/mol in the
investigated energy differences already with the default settings. This enables
the accurate modeling of large systems with complex electronic structure, as
illustrated on open-shell organic radicals and transition metal complexes of up
to 179 atoms, as well as on challenging biochemical systems, including up to
601 atoms and 11,000 basis functions. While the protein models involve
difficulties for local approximations, such as the spin states of a bounded
iron ion or an extremely delocalized singly occupied orbital, the corresponding
single-node LNO-CCSD(T) computations were feasible in a matter of days with 10s
to a 100 GB of memory use. Therefore, the new LNO-CCSD(T) implementation
enables highly-accurate computations for open-shell systems of unprecedented
size and complexity with widely accessible hardware.
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The U(2)_R x U(2)_L symmetry of QCD with two massless flavours is subject to
anomalies which affect correlation functions involving the singlet currents
A^0_\mu or V^0_\mu. These are relevant for pion-photon interactions, because -
for two flavours - the electromagnetic current contains a singlet piece. We
give the effective Lagrangian required for the corresponding low energy
analysis to next-to-leading order, without invoking an expansion in the mass of
the strange quark. In particular, the Wess-Zumino-Witten term that accounts for
the two-flavour anomalies within the effective theory is written down in closed
form.
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In this paper, a general framework is proposed for the analysis and
characterization of observability and diagnosability of finite state systems.
Observability corresponds to the reconstruction of the system's discrete state,
while diagnosability corresponds to the possibility of determining the past
occurrence of some particular states, for example faulty states. A unifying
framework is proposed where observability and diagnosability properties are
defined with respect to a critical set, i.e. a set of discrete states
representing a set of faults, or more generally a set of interest. These
properties are characterized and the involved conditions provide an estimation
of the delay required for the detection of a critical state, of the precision
of the delay estimation and of the duration of a possible initial transient
where the diagnosis is not possible or not required. Our framework makes it
possible to precisely compare some of the observability and diagnosability
notions existing in the literature with the ones introduced in our paper, and
this comparison is presented.
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In this paper, we discuss the Cram\'er-Lundberg model with investments, where
the price of the invested risk asset follows a geometric Brownian motion with
drift $a$ and volatility $\sigma> 0.$ By assuming there is a cap on the claim
sizes, we prove that the probability of ruin has at least an algebraic decay
rate if $2a/\sigma^2 > 1$. More importantly, without this assumption, we show
that the probability of ruin is certain for all initial capital $u$, if
$2a/\sigma^2 \le 1$.
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This paper discusses the design and performance of the time measurement
technique and of the synchronization systems of the CMS hadron calorimeter.
Time measurement performance results are presented from test beam data taken in
the years 2004 and 2006. For hadronic showers of energy greater than 100 GeV,
the timing resolution is measured to be about 1.2 ns. Time synchronization and
out-of-time background rejection results are presented from the Cosmic Run At
Four Tesla and LHC beam runs taken in the Autumn of 2008. The inter-channel
synchronization is measured to be within 2 ns.
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We provide exact and approximation methods for solving a geometric relaxation
of the Traveling Salesman Problem (TSP) that occurs in curve reconstruction:
for a given set of vertices in the plane, the problem Minimum Perimeter Polygon
(MPP) asks for a (not necessarily simply connected) polygon with shortest
possible boundary length. Even though the closely related problem of finding a
minimum cycle cover is polynomially solvable by matching techniques, we prove
how the topological structure of a polygon leads to NP-hardness of the MPP. On
the positive side, we show how to achieve a constant-factor approximation.
When trying to solve MPP instances to provable optimality by means of integer
programming, an additional difficulty compared to the TSP is the fact that only
a subset of subtour constraints is valid, depending not on combinatorics, but
on geometry. We overcome this difficulty by establishing and exploiting
additional geometric properties. This allows us to reliably solve a wide range
of benchmark instances with up to 600 vertices within reasonable time on a
standard machine. We also show that using a natural geometry-based
sparsification yields results that are on average within 0.5% of the optimum.
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We define the notion of inseparable coverings of schemes and we propose a
ramification formalism for them, along the lines of the classical one. Using
this formalism we prove a formula analogous to the classical Riemann-Hurwitz
formula for generic torsors under infinitesimal diagonalizable group schemes.
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Exact expressions for certain integrated correlators of four half-BPS
operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory with gauge group
$SU(N)$ have been recently obtained thanks to a beautiful interplay between
supersymmetric localisation and modular invariance. The large-$N$ expansion at
fixed Yang-Mills coupling of such integrated correlators produces an asymptotic
series of perturbative terms, holographically related to higher derivative
interactions in the low energy expansion of the type IIB effective action, as
well as exponentially suppressed corrections at large $N$, interpreted as
contributions from coincident $(p,q)$-string world-sheet instantons. In this
work we define a manifestly modular invariant Borel resummation of the
perturbative large-$N$ expansion of these integrated correlators, from which we
extract the exact non-perturbative large-$N$ sectors via resurgence analysis.
Furthermore, we show that in the 't Hooft limit such modular invariant
non-perturbative completions reduce to known resurgent genus expansions.
Finally, we clarify how the same non-perturbative data is encoded in the
decomposition of the integrated correlators based on $\rm{SL}(2,\mathbb{Z})$
spectral theory.
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We consider operators in N=4 SYM theory which are dual, at strong coupling,
to classical strings rotating in S^5. Three point correlation functions of such
operators factorize into a universal contribution coming from the AdS part of
the string sigma model and a state-dependent S^5 contribution. Consequently a
similar factorization arises for the OPE coefficients. In this paper we
evaluate the AdS universal factor of the OPE coefficients which is explicitly
expressed just in terms of the anomalous dimensions of the three operators.
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With the rapid growth of blockchain, an increasing number of users have been
attracted and many implementations have been refreshed in different fields.
Especially in the cryptocurrency investment field, blockchain technology has
shown vigorous vitality. However, along with the rise of online business,
numerous fraudulent activities, e.g., money laundering, bribery, phishing, and
others, emerge as the main threat to trading security. Due to the openness of
Ethereum, researchers can easily access Ethereum transaction records and smart
contracts, which brings unprecedented opportunities for Ethereum scams
detection and analysis. This paper mainly focuses on the Ponzi scheme, a
typical fraud, which has caused large property damage to the users in Ethereum.
By verifying Ponzi contracts to maintain Ethereum's sustainable development, we
model Ponzi scheme identification and detection as a node classification task.
In this paper, we first collect target contracts' transactions to establish
transaction networks and propose a detecting model based on graph convolutional
network (GCN) to precisely distinguishPonzi contracts. Experiments on different
real-world Ethereum datasets demonstrate that our proposed model has promising
results compared with general machine learning methods to detect Ponzi schemes.
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Multi-task language models show outstanding performance for various natural
language understanding tasks with only a single model. However, these language
models utilize an unnecessarily large number of model parameters, even when
used only for a specific task. This paper proposes a novel training-free
compression method for multi-task language models using a pruning method.
Specifically, we use an attribution method to determine which neurons are
essential for performing a specific task. We task-specifically prune
unimportant neurons and leave only task-specific parameters. Furthermore, we
extend our method to be applicable in low-resource and unsupervised settings.
Since our compression method is training-free, it uses few computing resources
and does not destroy the pre-trained knowledge of language models. Experimental
results on the six widely-used datasets show that our proposed pruning method
significantly outperforms baseline pruning methods. In addition, we demonstrate
that our method preserves performance even in an unseen domain setting.
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Reconfigurable intelligent surface (RIS) provides a promising way to
proactively augment propagation environments for better transmission
performance in wireless communications. Existing multi-RIS works mainly focus
on link-level optimization with predetermined transmission paths, which cannot
be directly extended to system-level management, since they neither consider
the interference caused by undesired scattering of RISs, nor the performance
balancing between different transmission paths. To address this, we study an
innovative multi-hop multi-RIS communication system, where a base station (BS)
transmits information to a set of distributed users over multi-RIS
configuration space in a multi-hop manner. The signals for each user are
subsequently reflected by the selected RISs via multi-reflection line-of-sight
(LoS) links. To ensure that all users have fair access to the system to avoid
excessive number of RISs serving one user, we aim to find the optimal beam
reflecting path for each user, while judiciously determining the path
scheduling strategies with the corresponding beamforming design to ensure the
fairness. Due to the presence of interference caused by undesired scattering of
RISs, it is highly challenging to solve the formulated multi-RIS multi-path
beamforming optimization problem. To solve it, we first derive the optimal
RISs' phase shifts and the corresponding reflecting path selection for each
user based on its practical deployment location. With the optimized
multi-reflection paths, we obtain a feasible user grouping pattern for
effective interference mitigation by constructing the maximum independent sets
(MISs). Finally, we propose a joint heuristic algorithm to iteratively update
the beamforming vectors and the group scheduling policies to maximize the
minimum equivalent data rate of all users.
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Landau level gaps are important parameters for understanding electronic
interactions and symmetry-broken processes in bilayer graphene (BLG). Here we
present transport spectroscopy measurements of LL gaps in double-gated
suspended BLG with high mobilities in the quantum Hall regime. By using bias as
a spectroscopic tool, we measure the gap {\Delta} for the quantum Hall (QH)
state at filling factor {\nu}={\pm}4 and -2. The single-particle gap for
{\nu}=4 scales linearly with magnetic field B and is independent of the
out-of-plane electric field E. For the symmetry-broken {\nu}=-2 state, the
measured values of gap are 1.1 meV/T and 0.17 meV/T for singly-gated geometry
and dual-gated geometry at E=0, respectively. The difference between the two
values arises from the E-dependence of the gap, suggesting that the {\nu}=-2
state is layer polarized. Our studies provide the first measurements of the
gaps of the broken symmetry QH states in BLG with well-controlled E, and
establish a robust method that can be implemented for studying similar states
in other layered materials.
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We define monotone links on a torus, obtained as projections of curves in the
plane whose coordinates are monotone increasing. Using the work of
Morton-Samuelson, to each monotone link we associate elements in the double
affine Hecke algebra and the elliptic Hall algebra. In the case of torus knots
(when the curve is a straight line), we recover symmetric function operators
appearing in the rational shuffle conjecture.
We show that the class of monotone links viewed as links in $\mathbb R^3$
coincides with the class of Coxeter links, studied by Oblomkov-Rozansky in the
setting of the flag Hilbert scheme. When the curve satisfies a convexity
condition, we recover positroid links that we previously studied. In the convex
case, we conjecture that the associated symmetric functions are Schur positive,
extending a recent conjecture of Blasiak-Haiman-Morse-Pun-Seelinger, and we
speculate on the relation to Khovanov-Rozansky homology.
Our constructions satisfy a skein recurrence where the base case consists of
piecewise almost linear curves. We show that convex piecewise almost linear
curves give rise to algebraic links.
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We give an asymptotic formula for the number of elliptic curves over
$\mathbb{Q}$ with bounded Faltings height. Silverman has shown that the
Faltings height for elliptic curves over number fields can be expressed in
terms of modular functions and the minimal discriminant of the elliptic curve.
We use this to recast the problem as one of counting lattice points in a
particular region in $\mathbb{R}^2$.
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We consider statistical and algorithmic aspects of solving large-scale
least-squares (LS) problems using randomized sketching algorithms. Prior
results show that, from an \emph{algorithmic perspective}, when using sketching
matrices constructed from random projections and leverage-score sampling, if
the number of samples $r$ much smaller than the original sample size $n$, then
the worst-case (WC) error is the same as solving the original problem, up to a
very small relative error. From a \emph{statistical perspective}, one typically
considers the mean-squared error performance of randomized sketching
algorithms, when data are generated according to a statistical linear model. In
this paper, we provide a rigorous comparison of both perspectives leading to
insights on how they differ. To do this, we first develop a framework for
assessing, in a unified manner, algorithmic and statistical aspects of
randomized sketching methods. We then consider the statistical prediction
efficiency (PE) and the statistical residual efficiency (RE) of the sketched LS
estimator; and we use our framework to provide upper bounds for several types
of random projection and random sampling algorithms. Among other results, we
show that the RE can be upper bounded when $r$ is much smaller than $n$, while
the PE typically requires the number of samples $r$ to be substantially larger.
Lower bounds developed in subsequent work show that our upper bounds on PE can
not be improved.
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In this paper, we use the stochastic approximation method to estimate Sliced
Average Variance Estimation (SAVE). This method is known for its efficiency in
recursive estimation. Stochastic approximation is particularly effective for
constructing recursive estimators and has been widely used in density
estimation, regression, and semi-parametric models. We demonstrate that the
resulting estimator is asymptotically normal and root n consistent. Through
simulations conducted in the laboratory and applied to real data, we show that
it is faster than the kernel method previously proposed.
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The burgeoning demand for collaborative robotic systems to execute complex
tasks collectively has intensified the research community's focus on advancing
simultaneous localization and mapping (SLAM) in a cooperative context. Despite
this interest, the scalability and diversity of existing datasets for
collaborative trajectories remain limited, especially in scenarios with
constrained perspectives where the generalization capabilities of Collaborative
SLAM (C-SLAM) are critical for the feasibility of multi-agent missions.
Addressing this gap, we introduce S3E, an expansive multimodal dataset.
Captured by a fleet of unmanned ground vehicles traversing four distinct
collaborative trajectory paradigms, S3E encompasses 13 outdoor and 5 indoor
sequences. These sequences feature meticulously synchronized and spatially
calibrated data streams, including 360-degree LiDAR point cloud,
high-resolution stereo imagery, high-frequency inertial measurement units
(IMU), and Ultra-wideband (UWB) relative observations. Our dataset not only
surpasses previous efforts in scale, scene diversity, and data intricacy but
also provides a thorough analysis and benchmarks for both collaborative and
individual SLAM methodologies. For access to the dataset and the latest
information, please visit our repository at https://pengyu-team.github.io/S3E.
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Spectrum pooling allows multiple operators, or tenants, to share the same
frequency bands. This work studies the optimization of spectrum pooling for the
downlink of a multi-tenant Cloud Radio Access Network (C-RAN) system in the
presence of inter-tenant privacy constraints. The spectrum available for
downlink transmission is partitioned into private and shared subbands, and the
participating operators cooperate to serve the user equipments (UEs) on the
shared subband. The network of each operator consists of a cloud processor (CP)
that is connected to proprietary radio units (RUs) by means of finite-capacity
fronthaul links. In order to enable interoperator cooperation, the CPs of the
participating operators are also connected by finite-capacity backhaul links.
Inter-operator cooperation may hence result in loss of privacy. Fronthaul and
backhaul links are used to transfer quantized baseband signals. Standard
quantization is considered first. Then, a novel approach based on the idea of
correlating quantization noise signals across RUs of different operators is
proposed to control the trade-off between distortion at UEs and inter-operator
privacy. The problem of optimizing the bandwidth allocation, precoding, and
fronthaul/backhaul compression strategies is tackled under constraints on
backhaul and fronthaul capacity, as well as on per-RU transmit power and
inter-operator privacy. For both cases, the optimization problems are tackled
using the concave convex procedure (CCCP), and extensive numerical results are
provided.
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Small cell networks are seen as a promising technology for boosting the
performance of future wireless networks. In this paper, we propose a novel
context-aware user-cell association approach for small cell networks that
exploits the information about the velocity and trajectory of the users while
also taking into account their quality of service (QoS) requirements. We
formulate the problem in the framework of matching theory with externalities in
which the agents, namely users and small cell base stations (SCBSs), have
strict interdependent preferences over the members of the opposite set. To
solve the problem, we propose a novel algorithm that leads to a stable matching
among the users and SCBSs. We show that the proposed approach can better
balance the traffic among the cells while also satisfying the QoS of the users.
Simulation results show that the proposed matching algorithm yields significant
performance advantages relative to traditional context-unaware approaches.
|
We present a theory of superconducting pairing originating from soft critical
fluctuations near isospin-polarized states in rhombohedral trilayer graphene.
Using a symmetry-based approach, we determine possible isospin order types and
derive the effective electron-electron interactions mediated by isospin
fluctuations. Superconductitivty arising due to these interactions has symmetry
and order parameter structure that depend in a unique way on the "mother"
isospin order. This model naturally leads to a superconducting phase adjacent
to isospin-ordering phase transition, which mimics the behavior observed in
experiment. The symmetry of the paired state predicted for the isospin order
type inferred in experiments matches the observations. These findings support a
scenario of superconductivity originating from electron-electron interactions.
|
Based on the continuous time random walk, we derive the Fokker-Planck
equations with Caputo-Fabrizio fractional derivative, which can effectively
model a variety of physical phenomena, especially, the material heterogeneities
and structures with different scales. Extending the discretizations for
fractional substantial calculus [Chen and Deng, \emph{ ESAIM: M2AN.}
\textbf{49}, (2015), 373--394], we first provide the numerical discretizations
of the Caputo-Fabrizio fractional derivative with the global truncation error
$\mathcal{O}(\tau^\nu)$ $ (\nu=1,2,3,4)$. Then we use the derived schemes to
solve the Caputo-Fabrizio fractional diffusion equation. By analysing the
positive definiteness of the stiffness matrices of the discretized
Caputo-Fabrizio operator, the unconditional stability and the convergence with
the global truncation error $\mathcal{O}(\tau^2+h^2)$ are theoretically proved
and numerical verified.
|
We propose a superconducting instability where microscopic supercurrent loops
form spontaneously within a unit cell at the superconducting transition
temperature with only uniform, onsite and intra-orbital singlet pairing. As a
result of the circulating currents time-reversal symmetry is spontaneously
broken in the superconducting state. Using Ginzburg-Landau theory, we describe
in detail how these currents emerge in a toy model. We discuss the
crystallographic symmetry requirements to realize such a state and show that
they are met by the Re6X (X=Zr, Hf, Ti) family of time-reversal symmetry
breaking, but otherwise seemingly conventional, superconductors. We estimate an
upper bound for the resulting internal fields and find it to be consistent with
recent muon-spin relaxation experiments.
|
Microlensing of stars places significant constraints on sub-planetary-mass
compact objects, including primordial black holes, as dark matter candidates.
As the lens' Einstein radius in the source plane becomes comparable to the size
of the light source, however, source amplification is strongly suppressed,
making it challenging to constrain lenses with a mass at or below $10^{-10}$
solar masses, i.e. asteroid-mass objects. Current constraints, using Subaru HSC
observations of M31, assume a fixed source size of one solar radius. Here we
point out that the actual stars in M31 bright enough to be used for
microlensing are typically much larger. We correct the HSC constraints by
constructing a source size distribution based on the M31 PHAT survey and on a
synthetic stellar catalogue, and by correspondingly weighing the finite-size
source effects. We find that the actual HSC constraints are weaker by up to
almost three orders of magnitude in some cases, broadening the range of masses
for which primordial black holes can be the totality of the cosmological dark
matter by almost one order of magnitude.
|
Internet services contribute a large fraction of worldwide carbon emission
nowadays, in a context of increasing number of companies tending to provide and
more and more developers use Internet services. Noticeably, a trend is those
service providers are trying to reduce their carbon emissions by utilizing
on-site or off-site renewable energy in their datacenters in order to attract
more customers. With such efforts have been paid, there are still some users
who are aggressively calling for even cleaner Internet services. For example,
over 500,000 Facebook users petitioned the social networking site to use
renewable energy to power its datacenter. However, it seems impossible for such
demand to be satisfied merely from the inside of those production datacenters,
considering the transition cost and stability. Outside the existing Internet
services, on the other hand, may easily set up a proxy service to attract those
renewable-energy-sensitive users, by 1) using carbon neutral or even
over-offsetting cloud instances to bridge the end user and traditional Internet
services; and 2) estimating and offsetting the carbon emissions from the
traditional Internet services. In our paper, we proposed GreenMail, which is a
general IMAP proxy caching system that connects email users and traditional
email services. GreenMail runs on green web hosts to cache users' emails on
green cloud instances. Besides, it offsets the carbon emitted by traditional
backend email services. With GreenMail, users could set a carbon emission
constraint and use traditional email service without breaking any code
modification of user side and email server side.
|
We discuss an ongoing study of the connection between galaxy
merging/interaction and AGN activity, based on integral field spectroscopy. We
focus on the search for AGN ionization in the central regions of mergers,
previously not classified as AGNs. We present here the science case, the
current status of the project, and plans for future observations.
|
In this paper we revisit the idea of measuring the magnetic dipole moments of
the charm baryons and, in particular, of charmed Lambda by studying the spin
precession induced by the strong effective magnetic field inside the channels
of a bent crystal. We present a detailed sensitivity study showing the
feasibility of such an experiment at the LHC in the coming years.
|
With the widespread use of biometric recognition, several issues related to
the privacy and security provided by this technology have been recently raised
and analysed. As a result, the early common belief among the biometrics
community of templates irreversibility has been proven wrong. It is now an
accepted fact that it is possible to reconstruct from an unprotected template a
synthetic sample that matches the bona fide one. This reverse engineering
process, commonly referred to as \textit{inverse biometrics}, constitutes a
severe threat for biometric systems from two different angles: on the one hand,
sensitive personal data (i.e., biometric data) can be derived from compromised
unprotected templates; on the other hand, other powerful attacks can be
launched building upon these reconstructed samples. Given its important
implications, biometric stakeholders have produced over the last fifteen years
numerous works analysing the different aspects related to inverse biometrics:
development of reconstruction algorithms for different characteristics;
proposal of methodologies to assess the vulnerabilities of biometric systems to
the aforementioned algorithms; development of countermeasures to reduce the
possible effects of attacks. The present article is an effort to condense all
this information in one comprehensive review of: the problem itself, the
evaluation of the problem, and the mitigation of the problem. The present
article is an effort to condense all this information in one comprehensive
review of: the problem itself, the evaluation of the problem, and the
mitigation of the problem.
|
Simulating thin and extended galactic disks has long been a challenge in
computational astrophysics. We introduce the NIHAO-UHD suite of cosmological
hydrodynamical simulations of Milky Way mass galaxies and study stellar disk
properties such as stellar mass, size and rotation velocity which agree well
with observations of the Milky Way and local galaxies. In particular, the
simulations reproduce the age-velocity dispersion relation and a
multi-component stellar disk as observed for the Milky Way. Half of our
galaxies show a double exponential vertical profile, while the others are well
described by a single exponential model which we link to the disk merger
history. In all cases, mono-age populations follow a single exponential whose
scale height varies monotonically with stellar age and radius. The scale length
decreases with stellar age while the scale height increases. The general
structure of the stellar disks is already set at time of birth as a result of
the inside-out and upside-down formation. Subsequent evolution modifies this
structure by increasing both the scale length and height of all mono-age
populations. Thus, our results put tight constraints on how much dynamical
memory stellar disks can retain over cosmological timescales. Our simulations
demonstrate that it is possible to form thin galactic disks in cosmological
simulations provided there are no significant stellar mergers at low redshifts.
Most of the stellar mass is formed in-situ with only a few percent
($\lesssim5\%$) brought in by merging satellites at early times. Redshift zero
snapshots and halo catalogues are publicly available.
|
We present an exact solution of superstring theory that interpolates in time
between an initial type 0 phase and a final phase whose physics is exactly that
of the bosonic string. The initial theory is deformed by closed-string tachyon
condensation along a lightlike direction. In the limit of large tachyon vev,
the worldsheet conformal field theory precisely realizes the Berkovits-Vafa
embedding of bosonic string theory into superstring theory. Our solution
therefore connects the bosonic string dynamically with the superstring,
settling a longstanding question about the relationship between the two
theories.
|
How can we justify the validity of our computer security methods? This
meta-methodological question is related to recent explorations on the science
of computer security, which have been hindered by computer security's unique
properties. We confront this by developing a taxonomy of properties and
methods. Interdisciplinary foundations provide a solid grounding for a set of
essential concepts, including a decision tree for characterizing adversarial
interaction. Several types of invalidation and general ways of addressing them
are described for technical methods. An interdisciplinary argument from theory
explains the role that meta-methodological validation plays in the adversarial
science of computer security.
|
We study the effect of non-homogeneous out-of-plane magnetic field on the
behaviour of 2D spatially indirect excitons. Due to the difference of magnetic
field acting on electrons and holes the total Lorentz force affecting the
center of mass motion of an indirect exciton appears. Consequently, an indirect
exciton acquires an effective charge proportional to the gradient of the
magnetic field. The appearance of the Lorentz force causes the Hall effect for
neutral bosons which can be detected by measurement of the spatially
inhomogeneous blueshift of the photoluminescence using counter-flow experiment.
|
Shortest paths in treespace, which represent minimal deformations between
trees, are unique and can be computed in polynomial time. The ability to
quickly compute shortest paths has enabled new approaches for statistical
analysis of populations of trees and phylogenetic inference. This paper gives a
new algorithm for updating geodesic paths when the end points are dynamic. Such
algorithms will be especially useful when optimizing for objectives that are
functions of distances from a search point to other points e.g. for finding a
tree which has the minimum average distance to a collection of trees. Our
method for updating treespace shortest paths is based on parametric sensitivity
analysis of the maximum flow subproblems that are optimized when solving for a
treespace geodesic.
|
Van der Waals heterostructures have recently garnered interest for
application in high-performance photovoltaic materials. Consequently,
understanding the basic electronic characteristics of these heterostructures is
important for their utilisation in optoelectronic devices. The electronic
structures and bond relaxation of two-dimensional (2D) Sb/transition metal
disulfides (TMDs, MoSe2, and MoTe2) van der Waals heterostructures were
systematically studied using the bond-charge (BC) correlation and hybrid
density functional theory. We found that the Sb/MoSe2 and Sb/MoTe2
heterostructures had indirect band gaps of 0.701 and 0.808 eV, respectively;
further, these heterostructures effectively modulated the band gaps of MoSe2
(1.463 eV) and MoTe2 (1.173 eV). The BC correlation revealed four bonding and
electronic contributions (electron-holes, antibonding, nonbonding, and bonding
states) of the heterostructures. Our results provide an in-depth understanding
of the Sb/TMD van der Waals heterojunction, which should be utilised to design
2D metal/semiconductor-based devices.
|
We develop an embedded boundary method (EBM) to solve the two-phase
incompressible flow with piecewise constant density. The front tracking method
is used to track the interface. The fractional step methods are used to solve
the incompressible Navier-Stokes equations while the EBM is used in the
projection step to solve an elliptic interface problem for the pressure with a
jump equal to the surface tension force across the interface. Several examples
are used to verify the accuracy of the method.
|
Emission at far-infrared wavelengths makes up a significant fraction of the
total light detected from galaxies over the age of Universe. Herschel provides
an opportunity for studying galaxies at the peak wavelength of their emission.
Our aim is to provide a benchmark for models of galaxy population evolution and
to test pre-existing models of galaxies. With the Herschel Multi-tiered
Extra-galactic survey, HerMES, we have observed a number of fields of different
areas and sensitivity using the SPIRE instrument on Herschel. We have
determined the number counts of galaxies down to ~20 mJy. Our constraints from
directly counting galaxies are consistent with, though more precise than,
estimates from the BLAST fluctuation analysis. We have found a steep rise in
the Euclidean normalised counts at <100 mJy. We have directly resolved 15% of
the infrared extra-galactic background at the wavelength near where it peaks.
|
We consider the sequential decision optimization on the periodic environment,
that occurs in a wide variety of real-world applications when the data involves
seasonality, such as the daily demand of drivers in ride-sharing and dynamic
traffic patterns in transportation. In this work, we focus on learning the
stochastic periodic world by leveraging this seasonal law. To deal with the
general action space, we use the bandit based on Gaussian process (GP) as the
base model due to its flexibility and generality, and propose the Periodic-GP
method with a temporal periodic kernel based on the upper confidence bound.
Theoretically, we provide a new regret bound of the proposed method, by
explicitly characterizing the periodic kernel in the periodic stationary model.
Empirically, the proposed algorithm significantly outperforms the existing
methods in both synthetic data experiments and a real data application on
Madrid traffic pollution.
|
With the development of ultra intense laser technology, MeV ions from the
laser foil interaction have been obtained by different mechanisms, such as
target normal sheath acceleration, radiation pressure acceleration,
collisionless shock acceleration, breakout afterburner, and a combination of
different mechanisms. These energetic ion beams can be applied in fast ignition
for inertial confinement fusion, medical therapy, and proton imaging. However,
these ions are mainly accelerated in the laser propagation direction, and the
ion acceleration in an azimuthal orientation is scarcely mentioned. Here, a
doughnut Laguerre Gaussian LG laser is used for the first time to study the
laser plasma interaction in the relativistic intensity regime in three
dimensional particle in cell simulations. Studies have shown that a novel
rotation of the plasma is produced from the hollow screw like drill of a LG
mode laser. The angular momentum of the protons in the longitudinal direction
produced by the LG laser is remarkably enhanced compared with that produced by
the usual laser pulses, such as linearly and circularly polarized gaussian
pulses. Moreover, the particles, including electrons and ions, can be trapped
and uniformly compressed in the dark central minimum of the doughnut LG pulse.
Such hollow structured LG laser may be used to investigate some difficult
problems, such as screw like drilling in the inertial confinement fusion, laser
driven particle accelerations, and pulsars in the astrophysical environment.
|
We construct $C^\infty$ solutions to the one-dimensional nonlinear wave
equation $$ u_{tt} - u_{xx} - \tfrac{2(p+2)}{p^2} |u|^p u=0 \quad \text{with}
\quad p>0 $$ that blow up on any prescribed uniformly space-like $C^\infty$
hypersurface. As a corollary, we show that smooth solutions can blow up (at the
first instant) on an arbitrary compact set.
We also construct solutions that blow up on general space-like $C^k$
hypersurfaces, but only when $4/p$ is not an integer and $k > (3p+4)/p$.
|
The contribution contains the preface to the Proceedings to the 23rd
International Workshop "What Comes Beyond the Standard Models", July 04 -- July
12, 2020, Bled, Slovenia, [Virtual Workshop -- July 6.--10. 2020], Volume 1:
Invited Talks and Volume 2: Further Talks And Scientific Debuts, published in
Bled workshops in physics, Vol.21, No. 1 and 2, DMFA-Zalo\v{z}nistvo,
Ljubljana, Dec. 2020, links to (most of) the published contributions, section
(by M.Yu. Khlopov) on VIA and virtual conference at Bled 2020, and two poems by
Astri Kleppe.
|
The ubiquity of distributed machine learning (ML) in sensitive public domain
applications calls for algorithms that protect data privacy, while being robust
to faults and adversarial behaviors. Although privacy and robustness have been
extensively studied independently in distributed ML, their synthesis remains
poorly understood. We present the first tight analysis of the error incurred by
any algorithm ensuring robustness against a fraction of adversarial machines,
as well as differential privacy (DP) for honest machines' data against any
other curious entity. Our analysis exhibits a fundamental trade-off between
privacy, robustness, and utility. To prove our lower bound, we consider the
case of mean estimation, subject to distributed DP and robustness constraints,
and devise reductions to centralized estimation of one-way marginals. We prove
our matching upper bound by presenting a new distributed ML algorithm using a
high-dimensional robust aggregation rule. The latter amortizes the dependence
on the dimension in the error (caused by adversarial workers and DP), while
being agnostic to the statistical properties of the data.
|
Post-common envelope binary systems evolve when matter is transferred from
the primary star at a rate that cannot be accommodated by its secondary
companion. A common envelope forms which is subsequently ejected resulting in a
system with a binary period frequently between 2 and 3 hours. Where
circumbinary companions are predicted, it remains unclear whether they form
before or after the common envelope ejection. From observations of eclipse time
variations (ETVs), exoplanet databases e.g. NASA Exoplanet Archive, list
typically a dozen systems with confirmed circumbinary planets. Here we examine
seven of these systems, discuss other possible causes and consider whether, for
these dynamic systems, the ETV methodology is a reliable indicator of planetary
companions. The systems selected were those where we could determine precise
eclipse timings, free from significant extraneous effects such as pulsations,
and present 163 new times of minima permitting us to test existing models. Over
thirty circumbinary models have been proposed for these seven systems and note
all, other than the latest model for NY Vir which remains to be fully tested,
fail within a year to accurately predict eclipse times. In examining
alternative mechanisms we find that magnetic effects could contribute
significantly in two of the seven systems studied. We conclude that the
structure of these dynamic systems, with the extreme temperature differences
and small binary separations, are not fully understood and that many factors
may contribute to the observed ETVs.
|
Strongly lensed systems with peculiar configurations allow us to probe the
local properties of the deflecting lens mass while simultaneously testing
general profile assumptions. The quasar HE0230$-$2130 is lensed by two galaxies
at similar redshifts ($\Delta z \sim 0.003$) into four observed images. Using
modeled quasar positions from fitting the brightness of the quasar images in
ground-based imaging data from the Magellan telescope, we find that lens-mass
models where each of these two galaxies is parametrized with a singular
power-law (PL) profile predict five quasar images. To interpret the quad
configuration of the system, we tested 12 different profile assumptions with
the aim of obtaining lens-mass models that correctly predict only four observed
images. We tested the effects of adopting: cored profiles for the lensing
galaxies; external shear; and additional profiles to represent a dark matter
clump. We find that half of our model classes can produce the correct image
multiplicity. By comparing the Bayesian evidence of different model
parametrizations, we favor two model classes: (i) one that incorporates two
singular PL profiles for the lensing galaxies and a cored isothermal sphere in
the region of the previously predicted fifth image (rNIS profile), and (ii) one
with a bigger lensing galaxy parametrized by a singular PL profile and the
smaller galaxy by a cored PL profile with external shear. We estimated the mass
of the rNIS clump for each candidate model of our final Markov chain Monte
Carlo sample, and find that only 2\% are in the range of $10^6 M_{\odot} \leq
M_{\rm rNIS}\leq 10^9 M_{\odot}$, which is the predicted mass range of dark
matter subhalos in cold dark matter simulations, or the mass of
dark-matter-dominated and low-surface-brightness galaxies. We therefore favor
the models with a cored mass distribution for the lens galaxy close to the
predicted fifth image.
|
This paper deals with Bayesian inference of a mixture of Gaussian
distributions. A novel formulation of the mixture model is introduced, which
includes the prior constraint that each Gaussian component is always assigned a
minimal number of data points. This enables noninformative improper priors such
as the Jeffreys prior to be placed on the component parameters. We demonstrate
difficulties involved in specifying a prior for the standard Gaussian mixture
model, and show how the new model can be used to overcome these. MCMC methods
are given for efficient sampling from the posterior of this model.
|
It is difficult to extract reliable criteria for causal locality from the
limited ingredients found in textbook quantum theory. In the end, Bell humbly
warned that his eponymous theorem was based on criteria that "should be viewed
with the utmost suspicion." Remarkably, by stepping outside the wave-function
paradigm, one can reformulate quantum theory in terms of old-fashioned
configuration spaces together with 'unistochastic' laws. These unistochastic
laws take the form of directed conditional probabilities, which turn out to
provide a hospitable foundation for encoding microphysical causal
relationships. This unistochastic reformulation provides quantum theory with a
simpler and more transparent axiomatic foundation, plausibly resolves the
measurement problem, and deflates various exotic claims about superposition,
interference, and entanglement. Making use of this reformulation, this paper
introduces a new principle of causal locality that is intended to improve on
Bell's criteria, and shows directly that systems that remain at spacelike
separation cannot exert causal influences on each other, according to that new
principle. These results therefore lead to a general hidden-variables
interpretation of quantum theory that is arguably compatible with causal
locality.
|
We investigate Dirac fermions in the antifferomagnetic metallic state of
iron-based superconduc- tors. Deriving an effective Hamiltonian for Dirac
fermions, we reveal that there exist two Dirac cones carrying the same
chirality, contrary to graphene, compensated by a Fermi surface with a
quadratic energy dispersion as a consequence of a non-trivial topological
property inherent in the band structure. We also find that the presence of the
Dirac fermions gives the difference of sign- change temperatures between the
Hall coefficient and the thermopower. This is consistent with available
experimental data.
|
We investigate the edge conductance of particles submitted to an Iwatsuka
magnetic field, playing the role of a purely magnetic barrier. We also consider
magnetic guides generated by generalized Iwatsuka potentials. In both cases we
prove quantization of the edge conductance. Next, we consider magnetic
perturbations of such magnetic barriers or guides, and prove stability of the
quantized value of the edge conductance. Further, we establish a sum rule for
edge conductances. Regularization within the context of disordered systems is
discussed as well.
|
According to standard quantum theory, the time evolution operator of a
quantum system is independent of the state of the system. One can, however,
consider systems in which this is not the case: the evolution operator may
depend on the density operator itself. The presence of such modifications of
quantum theory can be tested in long baseline oscillation experiments.
|
Recent advances have shown that implicit bias of gradient descent on
over-parameterized models enables the recovery of low-rank matrices from linear
measurements, even with no prior knowledge on the intrinsic rank. In contrast,
for robust low-rank matrix recovery from grossly corrupted measurements,
over-parameterization leads to overfitting without prior knowledge on both the
intrinsic rank and sparsity of corruption. This paper shows that with a double
over-parameterization for both the low-rank matrix and sparse corruption,
gradient descent with discrepant learning rates provably recovers the
underlying matrix even without prior knowledge on neither rank of the matrix
nor sparsity of the corruption. We further extend our approach for the robust
recovery of natural images by over-parameterizing images with deep
convolutional networks. Experiments show that our method handles different test
images and varying corruption levels with a single learning pipeline where the
network width and termination conditions do not need to be adjusted on a
case-by-case basis. Underlying the success is again the implicit bias with
discrepant learning rates on different over-parameterized parameters, which may
bear on broader applications.
|
In this paper we offer a review and bibliography of work on Hankel low-rank
approximation and completion, with particular emphasis on how this methodology
can be used for time series analysis and forecasting. We begin by describing
possible formulations of the problem and offer commentary on related topics and
challenges in obtaining globally optimal solutions. Key theorems are provided,
and the paper closes with some expository examples.
|
Edge states are studied for the two-dimensional Dirac equation in a circular
geometry. The properties of the two-component electromagnetic field are
discussed in terms of the three-component polarization field, which can form a
vortex structure near the Dirac node with a vorticity changing with the sign of
the Dirac mass. The Berry curvature of the polarization field is related to the
Berry curvature of the Dirac spinor state. This quantity is sensitive to a
change of boundary conditions. In particular, it vanishes for a geometry with a
single boundary but not for a geometry with two boundaries. This effect is
robust against the creation of a step-like edge inside the sample.
|
Measurements and data analysis have proved very effective in the study of the
Internet's physical fabric and have shown heterogeneities and statistical
fluctuations extending over several orders of magnitude. Here we analyze
performance measurements obtained by the PingER monitoring infrastructure. We
focus on the relationship between the Round-Trip-Time (RTT) and the
geographical distance. We define dimensionless variables that contain
information on the quality of Internet connections finding that their
probability distributions are characterized by a slow power-law decay
signalling the presence of scale-free features. These results point out the
extreme heterogeneity of the Internet since the transmission speed between
different points of the network exhibits very large fluctuations. The
associated scaling exponents appear to have fairly stable values in different
data sets and thus define an invariant characteristic of the Internet that
might be used in the future as a benchmark of the overall state of ``health''
of the Internet. The observed scale-free character should be incorporated in
models and analysis of Internet performance.
|
In this paper, the theoretical terms of contemporary cosmology are examined
as intellectual artefacts. An ontology and methodology are introduced for this
purpose, which includes defining the concept of a hypothetical object.
Introducing a hypothetical object is contrasted with the modification of
physical laws as alternative ways of explaining the discrepancy between
observations and theoretical predictions. Historical examples of theory choice,
which involved these alternatives, are discussed. This is followed by a study
of theory choice in contemporary cosmology. In particular, the focus is on the
case of dark matter and modified gravity as alternative explanations for
observed mass discrepancies in galaxies and galaxy clusters. These alternatives
are analyzed, and their similarities and differences to the historical examples
are pointed out.
|
The use of geometric invariants has recently played an important role in the
solution of classification problems in non-commutative ring theory. We
construct geometric invariants of non-commutative projectivizations, a
significant class of examples in non-commutative algebraic geometry.
|
We report on simulations of capillary filling of high-wetting fluids in
nano-channels with and without obstacles. We use atomistic (molecular dynamics)
and hydrokinetic (lattice-Boltzmann) approaches which point out clear evidence
of the formation of thin precursor films, moving ahead of the main capillary
front. The dynamics of the precursor films is found to obey a square-root law
as the main capillary front, z^2(t) ~ t, although with a larger prefactor,
which we find to take the same value for the different geometries (2D-3D) under
inspection. The two methods show a quantitative agreement which indicates that
the formation and propagation of thin precursors can be handled at a
mesoscopic/hydrokinetic level. This can be considered as a validation of the
Lattice-Boltzmann (LB) method and opens the possibility of using hydrokinetic
methods to explore space-time scales and complex geometries of direct
experimental relevance. Then, LB approach is used to study the fluid behaviour
in a nano-channel when the precursor film encounters a square obstacle. A
complete parametric analysis is performed which suggests that thin-film
precursors may have an important influence on the efficiency of
nanochannel-coating strategies.
|
Unsupervised domain adaptive person re-identification (Re-ID) methods
alleviate the burden of data annotation through generating pseudo supervision
messages. However, real-world Re-ID systems, with continuously accumulating
data streams, simultaneously demand more robust adaptation and anti-forgetting
capabilities. Methods based on image rehearsal addresses the forgetting issue
with limited extra storage but carry the risk of privacy leakage. In this work,
we propose a Color Prompting (CoP) method for data-free continual unsupervised
domain adaptive person Re-ID. Specifically, we employ a light-weighted prompter
network to fit the color distribution of the current task together with Re-ID
training. Then for the incoming new tasks, the learned color distribution
serves as color style transfer guidance to transfer the images into past
styles. CoP achieves accurate color style recovery for past tasks with adequate
data diversity, leading to superior anti-forgetting effects compared with image
rehearsal methods. Moreover, CoP demonstrates strong generalization performance
for fast adaptation into new domains, given only a small amount of unlabeled
images. Extensive experiments demonstrate that after the continual training
pipeline the proposed CoP achieves 6.7% and 8.1% average rank-1 improvements
over the replay method on seen and unseen domains, respectively. The source
code for this work is publicly available in
https://github.com/vimar-gu/ColorPromptReID.
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Let $\Gamma$ be a surface group of higher genus. Let $\rho\_0: \Gamma \to
{PGL}(V)$ be a discrete faithful representation with image contained in the
natural embedding of ${SL}(2, {\mathbb R})$ in ${PGL}(3, {\mathbb R})$ as a
group preserving a point and a disjoint projective line in the projective
plane. We prove that such a representation is $(G,Y)$-Anosov (following the
terminology of \cite{labourieanosov}), where $Y$ is the frame bundle. More
generally, we prove that all the deformations $\rho: \Gamma \to {PGL}(3,
{\mathbb R})$ studied in \cite{barflag} are $(G,Y)$-Anosov. As a corollary, we
obtain all the main results of \cite{barflag}, and extend them to any small
deformation of $\rho\_0$, not necessarily preserving a point or a projective
line in the projective space: in particular, there is a
$\rho(\Gamma)$-invariant solid torus $\Omega$ in the flag variety. The quotient
space $\rho(\Gamma)\backslash\Omega$ is a flag manifold, naturally equipped
with two 1-dimensional transversely projective foliations arising from the
projections of the flag variety on the projective plane and its dual; if $\rho$
is strongly irreducible, these foliations are not minimal. More precisely, if
one of these foliations is minimal, then it is topologically conjugate to the
strong stable foliation of a double covering of a geodesic flow, and $\rho$
preserves a point or a projective line in the projective plane. All these
results hold for any $(G,Y)$-Anosov representation which is not quasi-Fuchsian,
i.e., does not preserve a strictly convex domain in the projective plane.
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We introduce a new technique for gradient normalization during neural network
training. The gradients are rescaled during the backward pass using
normalization layers introduced at certain points within the network
architecture. These normalization nodes do not affect forward activity
propagation, but modify backpropagation equations to permit a well-scaled
gradient flow that reaches the deepest network layers without experimenting
vanishing or explosion. Results on tests with very deep neural networks show
that the new technique can do an effective control of the gradient norm,
allowing the update of weights in the deepest layers and improving network
accuracy on several experimental conditions.
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We determine the pre-asymptotic critical behavior at the quantum
ferromagnetic transition in strongly disordered metals. We find that it is
given by effective power laws, in contrast to the previously analyzed
asymptotic critical behavior, which is valid only in an unobservably small
region. The consequences for analyzing experiments are discussed, in particular
ways to distinguish between critical behavior and Griffiths-phase effects.
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We give a self-contained algebraic description of a formal symplectic
groupoid over a Poisson manifold M. To each natural star product on M we then
associate a canonical formal symplectic groupoid over M. Finally, we construct
a unique formal symplectic groupoid `with separation of variables' over an
arbitrary Kaehler-Poisson manifold.
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We study dynamics of two-dimensional N=(0,1) supersymmetric gauge theories.
In particular, we propose that there is an infrared triality between certain
triples of theories with orthogonal and symplectic gauge groups. The proposal
is supported by matching of anomalies and elliptic genera. This triality can be
viewed as a (0,1) counterpart of the (0,2) triality proposed earlier by two of
the authors and A. Gadde. We also describe the relation between global
anomalies in gauge theoretic and sigma-model descriptions, filling in a gap in
the present literature.
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Accurate traffic forecasting is challenging due to the complex dependency on
road networks, various types of roads, and the abrupt speed change due to the
events. Recent works mainly focus on dynamic spatial modeling with adaptive
graph embedding or graph attention having less consideration for temporal
characteristics and in-situ modeling. In this paper, we propose a novel deep
learning model named TESTAM, which individually models recurring and
non-recurring traffic patterns by a mixture-of-experts model with three experts
on temporal modeling, spatio-temporal modeling with static graph, and dynamic
spatio-temporal dependency modeling with dynamic graph. By introducing
different experts and properly routing them, TESTAM could better model various
circumstances, including spatially isolated nodes, highly related nodes, and
recurring and non-recurring events. For the proper routing, we reformulate a
gating problem into a classification problem with pseudo labels. Experimental
results on three public traffic network datasets, METR-LA, PEMS-BAY, and
EXPY-TKY, demonstrate that TESTAM achieves a better indication and modeling of
recurring and non-recurring traffic. We published the official code at
https://github.com/HyunWookL/TESTAM
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Connectivity and reachability on temporal networks, which can describe the
spreading of a disease, decimation of information or the accessibility of a
public transport system over time, have been among the main contemporary areas
of study in complex systems for the last decade. However, while isotropic
percolation theory successfully describes connectivity in static networks, a
similar description has not been yet developed for temporal networks. Here
address this problem and formalize a mapping of the concept of temporal network
reachability to percolation theory. We show that the limited-waiting-time
reachability, a generic notion of constrained connectivity in temporal
networks, displays directed percolation phase transition in connectivity.
Consequently, the critical percolation properties of spreading processes on
temporal networks can be estimated by a set of known exponents characterising
the directed percolation universality class. This result is robust across a
diverse set of temporal network models with different temporal and topological
heterogeneities, while by using our methodology we uncover similar reachability
phase transitions in real temporal networks too. These findings open up an
avenue to apply theory, concepts and methodology from the well-developed
directed percolation literature to temporal networks.
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In this work, we leverage atomistic spin-lattice simulations to examine how
magnetic interactions impact the propagation of sound waves through a
ferromagnetic material. To achieve this, we characterize the sound wave
velocity in BCC iron, a prototypical ferromagnetic material, using three
different approaches that are based on the oscillations of kinetic energy,
finite-displacement derived forces, and corrections to the elastic constants,
respectively. Successfully applying these methods within the spin-lattice
framework, we find good agreement with the Simon effect including high order
terms. In analogy to experiments, morphic coefficients associated with the
transverse and longitudinal waves propagating along the [001] direction are
extracted from fits to the fractional change in velocity data. The present
efforts represent an advancement in magnetoelastic modelling capabilities which
can expedite the design of future magneto-acoustic devices.
|
This paper presents inference rules for Resource Description Framework (RDF),
RDF Schema (RDFS) and Web Ontology Language (OWL). Our formalization is based
on Notation 3 Logic, which extended RDF by logical symbols and created Semantic
Web logic for deductive RDF graph stores. We also propose OWL-P that is a
lightweight formalism of OWL and supports soft inferences by omitting complex
language constructs.
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There are different approaches for diffractive photoproduction of charmonia.
Recently, a new approach is proposed, in which charm quarks are taken as heavy
quarks and the nonperturbative effect related to charmonia can be handled with
nonrelativistic QCD. The interaction between the $c\bar c$ pair and the initial
hadron is through exchange of soft gluons. The exchange of soft gluons can be
studied with heavy quark effective theory and an expansion in the inverse of
charm quark mass $m_c$ can be employed. In this approach a simple formula for
the S-matrix can be derived by neglecting higher orders in $m_c^{-1}$ and
relativistic correction related to charmonia. The S-matrix is related to the
usual gluon distribution $g(x)$ at small $x$. This result is different than
those from other approaches. Confronting experiment the result is not in
agreement with experimental measurement because large errors from higher order
in $m_c^{-1}$ and from relativistic corrections. Nevertheless the ratio of
cross sections of $\jpsi$ and $\psi(2S)$ can be predicted more precisely than
cross-sections. In this letter we show that the ratio predicted in this
approach with an estimation of relativistic corrections is in good agreement
with the recent measurement at HERA.
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The $\Omega$-phase of the liquid sodium $\alpha$-$\Omega$ dynamo experiment
at NMIMT in cooperation with LANL has successfully demonstrated the production
of a high toroidal field, $B_{\phi} \simeq 8\times B_r$ from the radial
component of an applied poloidal magnetic field, $B_r$. This enhanced toroidal
field is produced by rotational shear in stable Couette flow within liquid
sodium at $Rm \simeq 120$. The small turbulence in stable Taylor-Couette flow
is caused by Ekman flow where $ (\delta v/v)^2 \sim 10^{-3} $. This high
$\Omega$-gain in low turbulence flow contrasts with a smaller $\Omega$-gain in
higher turbulence, Helmholtz-unstable shear flows. This result supports the
ansatz that large scale astrophysical magnetic fields are created within
semi-coherent large scale motions in which turbulence plays only a smaller
diffusive role that enables magnetic flux linkage.
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We present a method to calculate directly the K-matrices for the pion
electro-production processes in the framework of chiral quark models which
allows for a clean separation of the resonant amplitudes from the background.
The method is applied to the calculation of the multipole amplitudes M_{1+},
E_{1+}, and S_{1+} in the Delta channel within the Cloudy Bag Model. A good
overall description is found in a broad energy range.
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The evaluation of large language models is an essential task in the field of
language understanding and generation. As language models continue to advance,
the need for effective benchmarks to assess their performance has become
imperative. In the context of Traditional Chinese, there is a scarcity of
comprehensive and diverse benchmarks to evaluate the capabilities of language
models, despite the existence of certain benchmarks such as DRCD, TTQA, CMDQA,
and FGC dataset. To address this gap, we propose a novel set of benchmarks that
leverage existing English datasets and are tailored to evaluate language models
in Traditional Chinese. These benchmarks encompass a wide range of tasks,
including contextual question-answering, summarization, classification, and
table understanding. The proposed benchmarks offer a comprehensive evaluation
framework, enabling the assessment of language models' capabilities across
different tasks. In this paper, we evaluate the performance of GPT-3.5,
Taiwan-LLaMa-v1.0, and Model 7-C, our proprietary model, on these benchmarks.
The evaluation results highlight that our model, Model 7-C, achieves
performance comparable to GPT-3.5 with respect to a part of the evaluated
capabilities. In an effort to advance the evaluation of language models in
Traditional Chinese and stimulate further research in this field, we have
open-sourced our benchmark and opened the model for trial.
|
Most prostate cancer survivors are confronted with disease-related and
treatment-related side effects that impact their quality of life. A tool that
combines specific physical activity coaching with the promotion of a healthy
lifestyle and self-management guidance might be a successful method to enhance
a lifestyle change in these patients. As a prerequisite for useful health
technology, it is important to consider a design process centred in the
patients. The aim of this study was to investigate the context of the problem
and the user needs to support the ideation of a low-fidelity prototype of a
tool to promote a healthy lifestyle among early-stage prostate cancer
survivors. A user-centred design approach was followed involving a
multidisciplinary team. The prototype was developed in 3 phases. In phase 1,
the context was studied with 2 systematic reviews of the state of practice and
consulting with 3 specialists in Oncology, resulting in a global use case and
main requirements. In phase 2, the needs and barriers of the users were studied
based on literature research and validated with 3 specialists, resulting in the
creation of 3 personas. In phase 3, 2 sessions were held to ideate and
prioritize possible app features, based on brainstorming and selection
techniques. Using the Ninja Mock and Proto.io software a low-fidelity prototype
was developed, resulting in 25 interactive screens. Understanding the user
needs and context seems to be essential to highlight key goals, hence
facilitating the bridge between ideation of the tool and the intended users
tasks and experiences. The conclusion of this first stage of the design process
brings valuable details (such as barriers of the users to technology and to
physical activity) for future iterations of design of the mobile app.
|
We study the non-equilibrium transport properties of a one-dimensional array
of dissipative quantum dots. Using the Keldysh formalism, we show that the
dots' dissipative nature leads to a spatial variation of the chemical
potential, which in disordered arrays, breaks the invariance of the current, I,
under bias reversal. Moreover, the array's nanoscopic size results in an
algebraic low-temperature dependence of I. Finally, we show that a local
Coulomb interaction splits the dots' electronic levels, resulting in a Coulomb
blockade, which is softened with increasing dissipation and array size.
|
We present measurements of bias triangles in several biasing configurations.
Thorough analysis of the data allows us to present data from all four possible
bias configurations on a single plot in chemical potential space. This
presentation allows comparison between different biasing directions to be made
in a clean and straightforward manner. Our analysis and presentation will prove
useful in demonstrations of Pauli-spin blockade where comparisons between
different biasing directions are paramount. The long term stability of the CMOS
compatible Si/SiO2 only architecture leads to the success of this analysis. We
also propose a simple variation to this analysis that will extend its use to
systems lacking the long term stability of these devices.
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This paper presents a novel method for unsupervised segmentation of pathology
images. Staging of lung cancer is a major factor of prognosis. Measuring the
maximum dimensions of the invasive component in a pathology images is an
essential task. Therefore, image segmentation methods for visualizing the
extent of invasive and noninvasive components on pathology images could support
pathological examination. However, it is challenging for most of the recent
segmentation methods that rely on supervised learning to cope with unlabeled
pathology images. In this paper, we propose a unified approach to unsupervised
representation learning and clustering for pathology image segmentation. Our
method consists of two phases. In the first phase, we learn feature
representations of training patches from a target image using the spherical
k-means. The purpose of this phase is to obtain cluster centroids which could
be used as filters for feature extraction. In the second phase, we apply
conventional k-means to the representations extracted by the centroids and then
project cluster labels to the target images. We evaluated our methods on
pathology images of lung cancer specimen. Our experiments showed that the
proposed method outperforms traditional k-means segmentation and the
multithreshold Otsu method both quantitatively and qualitatively with an
improved normalized mutual information (NMI) score of 0.626 compared to 0.168
and 0.167, respectively. Furthermore, we found that the centroids can be
applied to the segmentation of other slices from the same sample.
|
Cellular hit probabilities of alpha particles emitted by inhaled radon
progenies in sensitive bronchial epithelial cell nuclei were simulated at low
exposure levels to obtain useful data for the rejection or in support of the
linear-non-threshold (LNT) hypothesis. In this study, local distributions of
deposited inhaled radon progenies in airway bifurcation models were computed at
exposure conditions, which are characteristic of homes and uranium mines. Then,
maximum local deposition enhancement factors at bronchial airway bifurcations,
expressed as the ratio of local to average deposition densities, were
determined to characterize the inhomogeneity of deposition and to elucidate
their effect on resulting hit probabilities. The results obtained suggest that
in the vicinity of the carinal regions of the central airways the probability
of multiple hits can be quite high even at low average doses. Assuming a
uniform distribution of activity there are practically no multiple hits and the
hit probability as a function of dose exhibits a linear shape in the low dose
range. The results are quite the opposite in the case of hot spots revealed by
realistic deposition calculations, where practically all cells receive multiple
hits and the hit probability as a function of dose is non-linear in the average
dose range of 10-100 mGy.
|
This paper continues our study of radio pulsar emission-beam configurations
with the primary intent of extending study to the lowest possible frequencies.
Here we focus on a group of 133 more recently discovered pulsars, most of which
were included in the (100-200 MHz) LOFAR High Band Survey, observed with
Arecibo at 1.4 GHz and 327 MHz, and some observed at decameter wavelengths. Our
analysis framework is the core/double-cone beam model, and we took opportunity
to apply it as widely as possible, both conceptually and quantitatively, while
highlighting situations where modeling is difficult, or where its premises may
be violated. In the great majority of pulsars, beam forms consistent with the
core/double-cone model were identified. Moreover, we found that each pulsar's
beam structure remained largely constant over the frequency range available;
where profile variations were observed, they were attributable to different
component spectra and in some instances to varying conal beam sizes. As an
Arecibo population, many or most of the objects tend to fall in the Galactic
anticenter region and/or at high Galactic latitudes, so overall it includes a
number of nearer, older pulsars. We found a number of interesting or unusual
characteristics in some of the pulsars that would benefit from additional
study. The scattering levels encountered for this group are low to moderate,
apart from a few pulsars lying in directions more toward the inner Galaxy.
|
A heuristic hypothesis about domination of Bose-Einstein statistics in the
early Universe is suggested. The possibility of Bose-Einstein condensation
(BEC) of primordial baryon-antibaryon pairs is considered. In accordance with
this postulation enormous masses in the order of galactic mass may be
accumulated within the cosmic scales. At the certain threshold value of the
matter density the structural bosons decay into fermions and the sharp
breakdown of quantum-mechanical symmetry of the particles wave functions
occurs. Then, due to the Pauli principle of exclusion a large-scale phase
transition occurs because of enormous pressure jump of the matter. This
phenomenon might cause Cosmological Bang at the beginning stage of the Matter
Era. As a mechanism of accumulation of galactic mass much larger than the
configuration with structural bosons, a hypothetical BEC of elementary bosons
(gauge bosons $W^{\pm}$ and $Z^{0})$ is discussed as well.
|
The charged-particle's final state spectrum is derived from an analytic
perturbative solution for the relativistic viscous hydrodynamics. By taking
into account the longitudinal acceleration effect in relativistic viscous
hydrodynamics, the pseudorapidity spectrum describes well the nucleus-nucleus
colliding systems at RHIC and LHC. Based on both the extracted longitudinal
acceleration parameters $\lambda^{*}$ and a phenomenological description of the
$\lambda^{*}$, the charged-particle's pseudorapidity distributions for
$\sqrt{s_{NN}}$ = 5.44 TeV Xe+Xe collisions are computed from the final state
expression in a limited space-time rapidity $\eta_{s}$ region.
|
In this study, we conducted a numerical investigation on the Hall conductance
($\sigma_{Hall}$) of graphene based on the magnetic energy band structure
calculated using a nonperturbative magnetic-field-containing relativistic
tight-binding approximation (MFRTB) method. The nonperturbative MFRTB can
revisit two types of plateaus for the dependence of $\sigma_{Hall}$ on Fermi
energy. One set is characterized as wide plateaus (WPs). These WPs have filling
factors (FFs) of 2, 6, 10, 14, etc. and are known as the half-integer quantum
Hall effect. The width of WPs decreases with increasing FF, which exceeds the
decrease expected from the linear dispersion relation of graphene. The other
set is characterized by narrow plateaus (NPs), which have FFs of 0, 4, 8, 12,
etc. The NPs correspond to the energy gaps caused by the spin-Zeeman effect and
spin-orbit interaction. Furthermore, it was discovered that the degeneracy of
the magnetic energy bands calculated using the nonperturbative MFRTB method
leads to a quantized $\sigma_{Hall}$.
|
This work studies the behaviors of two large-population teams competing in a
discrete environment. The team-level interactions are modeled as a zero-sum
game while the agent dynamics within each team is formulated as a collaborative
mean-field team problem. Drawing inspiration from the mean-field literature, we
first approximate the large-population team game with its infinite-population
limit. Subsequently, we construct a fictitious centralized system and transform
the infinite-population game to an equivalent zero-sum game between two
coordinators. We study the optimal coordination strategies for each team via a
novel reachability analysis and later translate them back to decentralized
strategies that the original agents deploy. We prove that the strategies are
$\epsilon$-optimal for the original finite-population team game, and we further
show that the suboptimality diminishes when team size approaches infinity. The
theoretical guarantees are verified by numerical examples.
|
In 2+1 dimensional nonrelativistic Chern-Simons gauge theories on $S^2$ which
has a global $SU(M)$ symmetry, the semilocal Popov vortex equations are
obtained as Bogomolny equations by minimizing the energy in the presence of a
uniform external magnetic field. We study the equations with many flavors and
find several families of exact solutions. The equations are transformed to the
semilocal Liouville equations for which some exact solutions are known. In this
paper, we find new exact solutions of the semilocal Liouville equations. Using
these solutions, we construct solutions to the semilocal Popov equations. The
solutions are expressed in terms of one or more arbitrary rational functions on
$S^2$. Some simple solutions reduce to $CP^{M-1}$ lump configurations.
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