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We prove global existence of strong solutions to the drift-diffusion-Maxwell
system in two space dimension. We also provide an exponential growth estimate
for the $H^1$ norm of the solution.
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Scenario reduction (SR) aims to identify a small yet representative scenario
set to depict the underlying uncertainty, which is critical to scenario-based
stochastic optimization (SBSO) of power systems. Existing SR techniques
commonly aim to achieve statistical approximation to the original scenario set.
However, SR and SBSO are commonly considered into two distinct and decoupled
processes, which cannot guarantee a superior approximation of the original
optimality. Instead, this paper incorporates the SBSO problem structure into
the SR process and introduces a novel problem-driven scenario reduction
framework. Specifically, we transform the original scenario set in distribution
space into the decision applicability between scenarios in problem space.
Subsequently, the SR process, embedded by a distinctive problem-driven distance
metric, is rendered as a mixed-integer linear programming formulation to obtain
the representative scenario set while minimizing the optimality gap.
Furthermore, ex-ante and ex-post problem-driven evaluation indices are proposed
to evaluate the performance of SR. A two-stage stochastic economic dispatch
problem with renewable generation and energy storage validates the
effectiveness of the proposed framework. Numerical experiments demonstrate that
the proposed framework significantly outperforms existing SR methods by
identifying salient (e.g., worst-case) scenarios, and achieving an optimality
gap of less than 0.1% within acceptable computation time.
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We describe a novel non-parametric statistical hypothesis test of relative
dependence between a source variable and two candidate target variables. Such a
test enables us to determine whether one source variable is significantly more
dependent on a first target variable or a second. Dependence is measured via
the Hilbert-Schmidt Independence Criterion (HSIC), resulting in a pair of
empirical dependence measures (source-target 1, source-target 2). We test
whether the first dependence measure is significantly larger than the second.
Modeling the covariance between these HSIC statistics leads to a provably more
powerful test than the construction of independent HSIC statistics by
sub-sampling. The resulting test is consistent and unbiased, and (being based
on U-statistics) has favorable convergence properties. The test can be computed
in quadratic time, matching the computational complexity of standard empirical
HSIC estimators. The effectiveness of the test is demonstrated on several
real-world problems: we identify language groups from a multilingual corpus,
and we prove that tumor location is more dependent on gene expression than
chromosomal imbalances. Source code is available for download at
https://github.com/wbounliphone/reldep.
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Scaling exponents are the central quantitative prediction of theories of
turbulence and in-situ satellite observations of the high Reynolds number solar
wind flow have provided an extensive testbed of these. We propose a general,
instrument independent method to estimate the uncertainty of velocity field
fluctuations. We obtain the systematic shift that this uncertainty introduces
into the observed spectral exponent. This shift is essential for the correct
interpretation of observed scaling exponents. It is sufficient to explain the
contradiction between spectral features of the Elsasser fields observed in the
solar wind with both theoretical models and numerical simulations of
Magnetohydrodynamic turbulence.
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We propose a scheme which implements a controllable change of the state of
the target spin qubit in such a way that both the control and the target spin
qubits remain in their ground states. The interaction between the two spins is
mediated by an auxiliary spin, which can transfer to its excited state. Our
scheme suggests a possible relationship between the gate and adiabatic quantum
computation.
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A characterization of the two-terminal open-ring Aharonov-Bohm interferometer
is made by analyzing the phase space plots in the complex transmission
amplitude plane. Two types of plots are considered: type I plot which uses the
magnetic flux as the variable parameter and type II plot which uses the
electron momentum as the variable parameter. In type I plot, the trajectory
closes upon itself only when the ratio $R$ of the arm lengths (of the
interferometer) is a rational fraction, the shape and the type of the generated
flower-like pattern is sensitive to the electron momentum. For momenta
corresponding to discrete eigenstates of the perfect ring (i.e. the ring
without the leads), the trajectory passes through the origin a certain fixed
number of times before closing upon itself, whereas for arbitrary momenta it
never passes through the origin. Although the transmission coefficient is
periodic in the flux with the elementary flux quantum as the basic period, the
phenomenon of electron transmission is shown not to be so when analyzed via the
present technique. The periodicity is seen to spread over several flux units
whenever $R$ is a rational fraction whereas there is absolutely no periodicity
present when $R$ is an irrational number. In type II plot, closed trajectories
passing through the origin a number of times are seen for $R$ being a rational
fraction. The case R=1 (i.e. a symmetric ring) with zero flux is rather
pathological--it presents a closed loop surrounding the origin. For irrational
$R$ values, the trajectories never close.
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In this paper we study the Schwarzschild AdS black hole with a cloud of
string background in an extended phase space and investigate a new phase
transition related to the topological charge. By treating the topological
charge as a new charge for black hole solution we study its thermodynamics in
this new extended phase space. We treat by two approaches to study the phase
transition behavior via both $T-S$ and $P-v$ criticality and we find the
results confirm each other in a nice way. It is shown a cloud of strings
affects the critical physical quantities and it could be observed an
interesting Van der Waals-like phase transition in the extended thermodynamics.
The swallow tail-like behavior is also observed in Free Energy-Temperature
diagram. We observe in $a\to 0$ limit the small/large black hole phase
transition reduces to the Hawking-Page phase transition as we expects. We can
deduce that the impact of cloud of strings in Schwarzschild black hole can
bring Van der Waals-like black hole phase transition.
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We observed the nearby, low-density globular cluster M71 (NGC 6838) with the
Chandra X-ray Observatory to study its faint X-ray populations. Five X-ray
sources were found inside the cluster core radius, including the known
eclipsing binary millisecond pulsar (MSP) PSR J1953+1846A. The X-ray light
curve of the source coincident with this MSP shows marginal evidence for
periodicity at the binary period of 4.2 h. Its hard X-ray spectrum and
luminosity resemble those of other eclipsing binary MSPs in 47 Tuc, suggesting
a similar shock origin of the X-ray emission. A further 24 X-ray sources were
found within the half-mass radius, reaching to a limiting luminosity of 1.5
10^30 erg/s (0.3-8 keV). From a radial distribution analysis, we find that
18+/-6 of these 29 sources are associated with M71, somewhat more than
predicted, and that 11+/-6 are background sources, both galactic and
extragalactic. M71 appears to have more X-ray sources between L_X=10^30--10^31
erg/s than expected by extrapolating from other studied clusters using either
mass or collision frequency. We explore the spectra and variability of these
sources, and describe the results of ground-based optical counterpart searches.
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As deep learning models become popular, there is a lot of need for deploying
them to diverse device environments. Because it is costly to develop and
optimize a neural network for every single environment, there is a line of
research to search neural networks for multiple target environments
efficiently. However, existing works for such a situation still suffer from
requiring many GPUs and expensive costs. Motivated by this, we propose a novel
neural network optimization framework named Bespoke for low-cost deployment.
Our framework searches for a lightweight model by replacing parts of an
original model with randomly selected alternatives, each of which comes from a
pretrained neural network or the original model. In the practical sense,
Bespoke has two significant merits. One is that it requires near zero cost for
designing the search space of neural networks. The other merit is that it
exploits the sub-networks of public pretrained neural networks, so the total
cost is minimal compared to the existing works. We conduct experiments
exploring Bespoke's the merits, and the results show that it finds efficient
models for multiple targets with meager cost.
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For a number ring $\mathcal{O}$, Borel and Serre proved that
$\text{SL}_n(\mathcal{O})$ is a virtual duality group whose dualizing module is
the Steinberg module. They also proved that $\text{GL}_n(\mathcal{O})$ is a
virtual duality group. In contrast to $\text{SL}_n(\mathcal{O})$, we prove that
the dualizing module of $\text{GL}_n(\mathcal{O})$ is sometimes the Steinberg
module, but sometimes instead is a variant that takes into account a sort of
orientation. Using this, we obtain vanishing and nonvanishing theorems for the
cohomology of $\text{GL}_n(\mathcal{O})$ in its virtual cohomological
dimension.
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In this paper, we propose an innovative end-to-end subtitle detection and
recognition system for videos in East Asian languages. Our end-to-end system
consists of multiple stages. Subtitles are firstly detected by a novel image
operator based on the sequence information of consecutive video frames. Then,
an ensemble of Convolutional Neural Networks (CNNs) trained on synthetic data
is adopted for detecting and recognizing East Asian characters. Finally, a
dynamic programming approach leveraging language models is applied to
constitute results of the entire body of text lines. The proposed system
achieves average end-to-end accuracies of 98.2% and 98.3% on 40 videos in
Simplified Chinese and 40 videos in Traditional Chinese respectively, which is
a significant outperformance of other existing methods. The near-perfect
accuracy of our system dramatically narrows the gap between human cognitive
ability and state-of-the-art algorithms used for such a task.
|
In this paper we prove that if $E$ and $F$ are reflexive Banach spaces and
$G$ is a closed linear subspace of the space $\mathcal{P}_{w}(^{n}E;F)$ of all
$n$-homogeneous polynomials from $E$ to $F$ which are weakly continuous on
bounded sets, then $G$ is either reflexive or non-isomorphic to a dual space.
This result generalizes \cite[Theorem 2]{FEDER} and gives the solution to a
problem posed by Feder \cite[Problem 1]{FED}.
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The physics of X-ray cavities in galaxy clusters is constrained by their
observed morphological evolution, which depends on such poorly-understood
properties as the turbulent density field and magnetic fields. Here we combine
numerical simulations that include subgrid turbulence and software that
produces synthetic X-ray observations to examine the evolution of X-ray
cavities in the the absence of magnetic fields. Our results reveal an
anisotropic size evolution that is very different from simplified, analytical
predictions. These differences highlight some of the key issues that must be
accurately quantified when studying AGN-driven cavities, and help to explain
why the inferred pV energy in these regions appears to be correlated with their
distance from the cluster center. Interpreting X-ray observations will require
detailed modeling of effects including mass-entrainment, distortion by drag
forces, and projection. Current limitations do not allow a discrimination
between purely hydrodynamic and magnetically-dominated models for X-ray
cavities.
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Motivated by statistical inference problems in high-dimensional time series
data analysis, we first derive non-asymptotic error bounds for Gaussian
approximations of sums of high-dimensional dependent random vectors on
hyper-rectangles, simple convex sets and sparsely convex sets. We investigate
the quantitative effect of temporal dependence on the rates of convergence to a
Gaussian random vector over three different dependency frameworks
($\alpha$-mixing, $m$-dependent, and physical dependence measure). In
particular, we establish new error bounds under the $\alpha$-mixing framework
and derive faster rate over existing results under the physical dependence
measure. To implement the proposed results in practical statistical inference
problems, we also derive a data-driven parametric bootstrap procedure based on
a kernel estimator for the long-run covariance matrices. We apply the unified
Gaussian and bootstrap approximation results to test mean vectors with combined
$\ell^2$ and $\ell^\infty$ type statistics, change point detection, and
construction of confidence regions for covariance and precision matrices, all
for time series data.
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We study non-axisymmetric oscillations of rapidly and differentially rotating
relativistic stars in the Cowling approximation. Our equilibrium models are
sequences of relativistic polytropes, where the differential rotation is
described by the relativistic $j$-constant law. We show that a small degree of
differential rotation raises the critical rotation value for which the
quadrupolar f-mode becomes prone to the CFS instability, while the critical
value of $T/|W|$ at the mass-shedding limit is raised even more. For softer
equations of state these effects are even more pronounced. When increasing
differential rotation further to a high degree, the neutral point of the CFS
instability first reaches a local maximum and is lowered afterwards. For stars
with a rather high compactness we find that for a high degree of differential
rotation the absolute value of the critical $T/|W|$ is below the corresponding
value for rigid rotation. We conclude that the parameter space where the CFS
instability is able to drive the neutron star unstable is increased for a small
degree of differential rotation and for a large degree at least in stars with a
higher compactness.
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Furstenberg-Zimmer structure theory refers to the extension of the dichotomy
between the compact and weakly mixing parts of a measure preserving dynamical
system and the algebraic and geometric descriptions of such parts to a
conditional setting, where such dichotomy is established relative to a factor
and conditional analogues of those algebraic and geometric descriptions are
sought. Although the unconditional dichotomy and the characterizations are
known for arbitrary systems, the relative situation is understood under certain
countability and separability hypotheses on the underlying groups and spaces.
The aim of this article is to remove these restrictions in the relative
situation and establish a Furstenberg-Zimmer structure theory in full
generality. As an independent byproduct, we establish a connection between the
relative analysis of systems in ergodic theory and the internal logic in
certain Boolean topoi.
|
Australian water infrastructure is more than a hundred years old, thus has
begun to show its age through water main failures. Our work concerns
approximately half a million pipelines across major Australian cities that
deliver water to houses and businesses, serving over five million customers.
Failures on these buried assets cause damage to properties and water supply
disruptions. We applied Machine Learning techniques to find a cost-effective
solution to the pipe failure problem in these Australian cities, where on
average 1500 of water main failures occur each year. To achieve this objective,
we construct a detailed picture and understanding of the behaviour of the water
pipe network by developing a Machine Learning model to assess and predict the
failure likelihood of water main breaking using historical failure records,
descriptors of pipes and other environmental factors. Our results indicate that
our system incorporating a nonparametric survival analysis technique called
"Random Survival Forest" outperforms several popular algorithms and expert
heuristics in long-term prediction. In addition, we construct a statistical
inference technique to quantify the uncertainty associated with the long-term
predictions.
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With the increasing interest in proximity and docking operations, there is a
growing interest in spacecraft relative motion control. This paper extends a
previously proposed constrained relative motion approach based on chained
positively invariant sets to the case where the spacecraft dynamics are
controlled using output feedback on noisy measurements and are subject to
stochastic disturbances. It is shown that non-convex polyhedral exclusion zone
constraints can be handled. The methodology consists of a virtual net of static
equilibria nodes in the Clohessy-Wiltshire-Hill frame. Connectivity between
nodes is determined through the use of chance-constrained admissible sets,
guaranteeing that constraints are met with a specified probability.
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We apply our recent formalism establishing new connections between the
geometry of moving space curves and soliton equations, to the nonlinear
Schr\"{o}dinger equation (NLS).
We show that any given solution of the NLS gets associated with three
distinct space curve evolutions. The tangent vector of the first of these
curves, the binormal vector of the second and the normal vector of the third,
are shown to satisfy the integrable Landau-Lifshitz (LL) equation
${\bf S}_u = {\bf S} \times {\bf S}_{ss}$, (${\bf S}^2=1$). These connections
enable us to find the three surfaces swept out by the moving curves associated
with the NLS. As an example, surfaces corresponding to a stationary envelope
soliton solution of the NLS are obtained.
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Like classical block codes, a locally repairable code also obeys the
Singleton-type bound (we call a locally repairable code {\it optimal} if it
achieves the Singleton-type bound). In the breakthrough work of \cite{TB14},
several classes of optimal locally repairable codes were constructed via
subcodes of Reed-Solomon codes. Thus, the lengths of the codes given in
\cite{TB14} are upper bounded by the code alphabet size $q$. Recently, it was
proved through extension of construction in \cite{TB14} that length of $q$-ary
optimal locally repairable codes can be $q+1$ in \cite{JMX17}. Surprisingly,
\cite{BHHMV16} presented a few examples of $q$-ary optimal locally repairable
codes of small distance and locality with code length achieving roughly $q^2$.
Very recently, it was further shown in \cite{LMX17} that there exist $q$-ary
optimal locally repairable codes with length bigger than $q+1$ and distance
propositional to $n$.
Thus, it becomes an interesting and challenging problem to construct new
families of $q$-ary optimal locally repairable codes of length bigger than
$q+1$.
In this paper, we construct a class of optimal locally repairable codes of
distance $3$ and $4$ with unbounded length (i.e., length of the codes is
independent of the code alphabet size). Our technique is through cyclic codes
with particular generator and parity-check polynomials that are carefully
chosen.
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This paper demonstrates the feasibility of learning to retrieve short
snippets of sheet music (images) when given a short query excerpt of music
(audio) -- and vice versa --, without any symbolic representation of music or
scores. This would be highly useful in many content-based musical retrieval
scenarios. Our approach is based on Deep Canonical Correlation Analysis (DCCA)
and learns correlated latent spaces allowing for cross-modality retrieval in
both directions. Initial experiments with relatively simple monophonic music
show promising results.
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We modify a three-field formulation of the Poisson problem with Nitsche
approach for approximating Dirichlet boundary conditions. Nitsche approach
allows us to weakly impose Dirichlet boundary condition but still preserves the
optimal convergence. We use the biorthogonal system for efficient numerical
computation and introduce a stabilisation term so that the problem is coercive
on the whole space. Numerical examples are presented to verify the algebraic
formulation of the problem.
|
It is known that quantum correlations exhibited by a maximally entangled
qubit pair can be simulated with the help of shared randomness, supplemented
with additional resources, such as communication, post-selection or non-local
boxes. For instance, in the case of projective measurements, it is possible to
solve this problem with protocols using one bit of communication or making one
use of a non-local box. We show that this problem reduces to a distributed
sampling problem. We give a new method to obtain samples from a biased
distribution, starting with shared random variables following a uniform
distribution, and use it to build distributed sampling protocols. This approach
allows us to derive, in a simpler and unified way, many existing protocols for
projective measurements, and extend them to positive operator value
measurements. Moreover, this approach naturally leads to a local hidden
variable model for Werner states.
|
We prove that a Moran model converges in probability to Eigen's quasispecies
model in the infinite population limit.
|
Motivated by portfolio allocation and linear discriminant analysis, we
consider estimating a functional $\mathbf{\mu}^T \mathbf{\Sigma}^{-1}
\mathbf{\mu}$ involving both the mean vector $\mathbf{\mu}$ and covariance
matrix $\mathbf{\Sigma}$. We study the minimax estimation of the functional in
the high-dimensional setting where $\mathbf{\Sigma}^{-1} \mathbf{\mu}$ is
sparse. Akin to past works on functional estimation, we show that the optimal
rate for estimating the functional undergoes a phase transition between regular
parametric rate and some form of high-dimensional estimation rate. We further
show that the optimal rate is attained by a carefully designed plug-in
estimator based on de-biasing, while a family of naive plug-in estimators are
proved to fall short. We further generalize the estimation problem and
techniques that allow robust inputs of mean and covariance matrix estimators.
Extensive numerical experiments lend further supports to our theoretical
results.
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Selection of descent direction at a point plays an important role in
numerical optimization for minimizing a real valued function. In this article,
a descent sequence is generated for the functions with bounded parameters to
obtain a critical point. First, sufficient condition for the existence of
descent direction is studied for this function and then a set of descent
directions at a point is determined using linear expansion. Using these results
a descent sequence of intervals is generated and critical point is
characterized. This theoretical development is justified with numerical
example.
|
The second postulate of special relativity states that the speed of light in
vacuum is independent of the emitter's motion. The test of this postulate so
far remains unexplored for gravitational radiation. We analyze data from the
LIGO-Virgo detectors to test this postulate within the ambit of a model where
the speed of the emitted GWs ($c'$) from a binary depends on a characteristic
velocity $\tilde{v}$ proportional to that of the reduced one-body system as $c'
= c + k\, \tilde{v}$, where $k$ is a constant. We have estimated the upper
bound on the 90\% credible interval over $k$ to be ${k \leq 8.3 \times
{10}^{-18}}$, which is several orders of magnitude more stringent compared to
previous bounds obtained from electromagnetic observations. The Bayes' factor
supports the second postulate with a strong evidence that the data is
consistent with the null hypothesis $k = 0$, upholding the principle of
relativity for gravitational interactions.
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An accurate calculation of their abundance is crucial for numerous aspects of
cosmology related to primordial black holes (PBHs). For example, placing
constraints on the primordial power spectrum from constraints on the abundance
of PBHs (or vice-versa), calculating the mass function observable today, or
predicting the merger rate of (primordial) black holes observable by
gravitational wave observatories such as LIGO, Virgo and KAGRA.
In this chapter, we will discuss the different methods used for the
calculation of the abundance of PBHs forming from large-amplitude cosmological
perturbations, assuming only a minimal understanding of modern cosmology.
Different parameters to describe cosmological perturbations will be considered
(including different choices for the window function), and it will be argued
that the compaction is typically the most appropriate choice. Different
methodologies for calculating the abundance and mass function are explained,
including \emph{Press-Schechter}-type and peaks theory approaches.
|
We report on the observation of dendritic flux avalanches in a large Niobium
single crystal. In contrast to avalanches observed in thin films, they appear
only in a very narrow temperature interval of about a tenth of a Kelvin near
the critical temperature of Nb. At a fixed temperature, we find two sets of
dendritic structures, which differ by the magnetic field required for their
formation and by the maximum distance the dendrites penetrate into the sample.
The effect is caused by dendritic flux penetration into thin superconducting
surface layers formed in the single crystal close to the critical temperature.
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We present a set of studies that tested the hypothesis that creative style is
recognizable within and across domains. Art students were shown two sets of
paintings, the first by five famous artists and the second by their art student
peers. For both sets, they guessed the creators of the works at above-chance
levels. In a similar study, creative writing students guessed at above-chance
levels which passages were written by which of five famous writers, and which
passages were written by which of their writing student peers. When creative
writing students were asked to produce works of art, they guessed at
above-chance levels which of their peers produced which artwork. Finally, art
students who were familiar with each other's paintings guessed at above-chance
levels which of their peers produced which non-painting artwork. The findings
support the hypothesis that creative styles are recognizable not just within
but also across domains. We suggest this is because all of an individual's
creative outputs are expressions of a particular underlying uniquely structured
self-organizing internal model of the world.
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Let $K_0$ be a compact convex subset of the plane $\mathbb R^2$, and assume
that $K_1\subseteq \mathbb R^2$ is similar to $K_0$, that is, $K_1$ is the
image of $K_0$ with respect to a similarity transformation $\mathbb
R^2\to\mathbb R^2$. Kira Adaricheva and Madina Bolat have recently proved that
if $K_0$ is a disk and both $K_0$ and $K_1$ are included in a triangle with
vertices $A_0$, $A_1$, and $A_2$, then there exist a $j\in \{0,1,2\}$ and a
$k\in\{0,1\}$ such that $K_{1-k}$ is included in the convex hull of
$K_k\cup(\{A_0,A_1, A_2\}\setminus\{A_j\})$. Here we prove that this property
characterizes disks among compact convex subsets of the plane. Actually, we
prove even more since we replace "similar" by "isometric" (also called
"congruent"). Circles are the boundaries of disks, so our result also gives a
characterization of circles.
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Practitioners commonly download pretrained machine learning models from open
repositories and finetune them to fit specific applications. We show that this
practice introduces a new risk of privacy backdoors. By tampering with a
pretrained model's weights, an attacker can fully compromise the privacy of the
finetuning data. We show how to build privacy backdoors for a variety of
models, including transformers, which enable an attacker to reconstruct
individual finetuning samples, with a guaranteed success! We further show that
backdoored models allow for tight privacy attacks on models trained with
differential privacy (DP). The common optimistic practice of training DP models
with loose privacy guarantees is thus insecure if the model is not trusted.
Overall, our work highlights a crucial and overlooked supply chain attack on
machine learning privacy.
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It is widely acknowledged that transparency of automated decision making is
crucial for deployability of intelligent systems, and explaining the reasons
why some decisions are "good" and some are not is a way to achieving this
transparency. We consider two variants of decision making, where "good"
decisions amount to alternatives (i) meeting "most" goals, and (ii) meeting
"most preferred" goals. We then define, for each variant and notion of
"goodness" (corresponding to a number of existing notions in the literature),
explanations in two formats, for justifying the selection of an alternative to
audiences with differing needs and competences: lean explanations, in terms of
goals satisfied and, for some notions of "goodness", alternative decisions, and
argumentative explanations, reflecting the decision process leading to the
selection, while corresponding to the lean explanations. To define
argumentative explanations, we use assumption-based argumentation (ABA), a
well-known form of structured argumentation. Specifically, we define ABA
frameworks such that "good" decisions are admissible ABA arguments and draw
argumentative explanations from dispute trees sanctioning this admissibility.
Finally, we instantiate our overall framework for explainable decision-making
to accommodate connections between goals and decisions in terms of decision
graphs incorporating defeasible and non-defeasible information.
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The q-special functions appear naturally in q-deformed quantum mechanics and
both sides profit from this fact. Here we study the relation between the
q-deformed harmonic oscillator and the q-Hermite polynomials. We discuss:
recursion formula, generating function, Christoffel-Darboux identity,
orthogonality relations and the moment functional.
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The term describing the coupling between total angular momentum and
energy-momentum in the hydrogen atom is isolated from the radial Dirac equation
and used to replace the corresponding orbital angular momentum coupling term in
the radial K-G equation. The resulting spin-corrected K-G equation is a second
order differential equation that contains no matrices. It is solved here to
generate the same energy eigenvalues for the hydrogen atom as the Dirac
equation.
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The one-bit quanta image sensor (QIS) is a photon-counting device that
captures image intensities using binary bits. Assuming that the analog voltage
generated at the floating diffusion of the photodiode follows a
Poisson-Gaussian distribution, the sensor produces either a ``1'' if the
voltage is above a certain threshold or ``0'' if it is below the threshold. The
concept of this binary sensor has been proposed for more than a decade, and
physical devices have been built to realize the concept. However, what benefits
does a one-bit QIS offer compared to a conventional multi-bit CMOS image
sensor? Besides the known empirical results, are there theoretical proofs to
support these findings?
The goal of this paper is to provide new theoretical support from a signal
processing perspective. In particular, it is theoretically found that the
sensor can offer three benefits: (1) Low-light: One-bit QIS performs better at
low-light because it has a low read noise, and its one-bit quantization can
produce an error-free measurement. However, this requires the exposure time to
be appropriately configured. (2) Frame rate: One-bit sensors can operate at a
much higher speed because a response is generated as soon as a photon is
detected. However, in the presence of read noise, there exists an optimal frame
rate beyond which the performance will degrade. A Closed-form expression of the
optimal frame rate is derived. (3) Dynamic range: One-bit QIS offers a higher
dynamic range. The benefit is brought by two complementary characteristics of
the sensor: nonlinearity and exposure bracketing. The decoupling of the two
factors is theoretically proved, and closed-form expressions are derived.
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We present the polarization images in the $J$, $H$, & $Ks$ bands of the Orion
Molecular Cloud 1 South region. The polarization images clearly show at least
six infrared reflection nebulae (IRNe) which are barely seen or invisible in
the intensity images. Our polarization vector images also identify the
illuminating sources of the nebulae: IRN 1 & 2, IRN 3, 4, & 5, and IRN 6 are
illuminated by three IR sources, Source 144-351, Source 145-356, and Source
136-355, respectively. Moreover, our polarization images suggest the candidate
driving sources of the optical Herbig-Haro objects for the first time; HH529, a
pair of HH202 and HH528 or HH 203/204, HH 530 and HH269 are originated from
Source 144-351, Source 145-356, and Source 136-355, respectively.
|
Backdoor learning has become an emerging research area towards building a
trustworthy machine learning system. While a lot of works have studied the
hidden danger of backdoor attacks in image or text classification, there is a
limited understanding of the model's robustness on backdoor attacks when the
output space is infinite and discrete. In this paper, we study a much more
challenging problem of testing whether sequence-to-sequence (seq2seq) models
are vulnerable to backdoor attacks. Specifically, we find by only injecting
0.2\% samples of the dataset, we can cause the seq2seq model to generate the
designated keyword and even the whole sentence. Furthermore, we utilize Byte
Pair Encoding (BPE) to create multiple new triggers, which brings new
challenges to backdoor detection since these backdoors are not static.
Extensive experiments on machine translation and text summarization have been
conducted to show our proposed methods could achieve over 90\% attack success
rate on multiple datasets and models.
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Transporting quantum information is an important prerequisite for quantum
computers. We study how this can be done in Heisenberg-coupled spin networks
using adiabatic control over the coupling strengths. We find that qudits can be
transferred and entangled pairs can be created between distant sites of
bipartite graphs with a certain balance between the maximum spin of both parts,
extending previous results that were limited to linear chains. The transfer
fidelity in a small star-shaped network is numerically analysed, and possible
experimental implementations are discussed.
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When functional data manifest amplitude and phase variations, a
commonly-employed framework for analyzing them is to take away the phase
variation through a function alignment and then to apply standard tools to the
aligned functions. A downside of this approach is that the important variations
contained in the phases are completely ignored. To combine both of amplitude
and phase variations, we propose a variant of principal component analysis
(PCA) that captures non-linear components representing the amplitude, phase and
their associations simultaneously. The proposed method, which we call
functional combined PCA, is aimed to provide more efficient dimension reduction
with interpretable components, in particular when the amplitudes and phases are
clearly associated. We model principal components by non-linearly combining
time-warping functions and aligned functions. A data-adaptive weighting
procedure helps our dimension reduction to attain a maximal explaining power of
observed functions. We also discuss an application of functional canonical
correlation analysis in investigation of the correlation structure between the
two variations. We show that for two sets of real data the proposed method
provides interpretable major non-linear components, which are not typically
found in the usual functional PCA.
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We revisit unitary representation of centrally extended (2 | 2) excitation
superalgebra. We find most generally that `pseudo-momentum', not lattice
momentum, diagonalizes spin chain Hamiltonian and leads to generalized dynamic
spin chain. All known results point to lattice momentum diagonalization for N=4
super Yang-Mills theory. Having different interacting structure, we ask if N=6
superconformal Chern-Simons theory provides an example of pseudo-momentum
diagonalization. For SO(6) sector, we study maximal shuffling and
next-to-maximal shuffling terms in the dilatation operator and compare them
with results expected from psu(2|2) superalgebbra and integrability. At two
loops, we rederive maximal shuffling term (3-site) and find perfect agreement
with known results. At four loops, we first find absence of next-to-maximal
shuffling term (4-site), in agreement with prediction based on integrability.
We next extract maximal shuffling term (5-site), the most relevant term for
checking the possibility of pseudo-momentum diagonalization. Curiously, we find
that result agrees with integraility prediction based on lattice momentum, as
in N=4 super Yang-Mills theory. Consistency of our results is fully ensured by
checks of renormalizability up to six loops.
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The structure of personal networks reflects how we organise and maintain
social relationships. The distribution of tie strengths in personal networks is
heterogeneous, with a few close, emotionally intense relationships and a larger
number of weaker ties. Recent results indicate this feature is universal across
communication channels. Within this general pattern, there is a substantial and
persistent inter-individual variation that is also similarly distributed among
channels. The reason for the observed universality is yet unclear -- one
possibility is that people's traits determine their personal network features
on any channel. To address this hypothesis, we need to compare an individual's
personal networks across channels, which is a non-trivial task: while we are
interested in measuring the differences in tie strength heterogeneity, personal
network size is also expected to vary a lot across channels. Therefore, for any
measure that compares personal networks, one needs to understand the
sensitivity with respect to network size. Here, we study different measures of
personal network similarity and show that a recently introduced
alter-preferentiality parameter and the Gini coefficient are equally suitable
measures for tie strength heterogeneity, as they are fairly insensitive to
differences in network size. With these measures, we show that the earlier
observed individual-level persistence of personal network structure cannot be
attributed to network size stability alone, but that the tie strength
heterogeneity is persistent too. We also demonstrate the effectiveness of the
two measures on multichannel data, where tie strength heterogeneity in personal
networks is seen to moderately correlate for the same users across two
communication channels (calls and text messages).
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A $\varrho$-saturating set of $\text{PG}(N,q)$ is a point set $\mathcal{S}$
such that any point of $\text{PG}(N,q)$ lies in a subspace of dimension at most
$\varrho$ spanned by points of $\mathcal{S}$. It is generally known that a
$\varrho$-saturating set of $\text{PG}(N,q)$ has size at least
$c\cdot\varrho\,q^\frac{N-\varrho}{\varrho+1}$, with $c>\frac{1}{3}$ a
constant. Our main result is the discovery of a $\varrho$-saturating set of
size roughly $\frac{(\varrho+1)(\varrho+2)}{2}q^\frac{N-\varrho}{\varrho+1}$ if
$q=(q')^{\varrho+1}$, with $q'$ an arbitrary prime power. The existence of such
a set improves most known upper bounds on the smallest possible size of
$\varrho$-saturating sets if $\varrho<\frac{2N-1}{3}$. As saturating sets have
a one-to-one correspondence to linear covering codes, this result improves
existing upper bounds on the length and covering density of such codes. To
prove that this construction is a $\varrho$-saturating set, we observe that the
affine parts of $q'$-subgeometries of $\text{PG}(N,q)$ having a hyperplane in
common, behave as certain lines of $\text{AG}\big(\varrho+1,(q')^N\big)$. More
precisely, these affine lines are the lines of the linear representation of a
$q'$-subgeometry $\text{PG}(\varrho,q')$ embedded in
$\text{PG}\big(\varrho+1,(q')^N\big)$.
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The low temperature specific heat C(B,T) of an YBa2Cu3O7.00 single crystal is
measured from 1.2 to 10 K in magnetic fields up to 14 T. The anisotropic
component Caniso(T,B)=C(T,B//c)-C(T,B//ab) is a pure vortex quantity obtained
directly from experiment. It follows a scaling relation predicted recently for
line nodes characteristic of d-wave vortices. Our experimental field and
temperature range corresponds to a crossover region where the limit
Caniso(T,B)is proportional to T*sqrt(B) does not strictly apply. The variation
of the entropy caused by the magnetic field at low T is thermodynamically
compatible with measurements near Tc.
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Coherent Raman Effect on Incoherent Light (CREIL), shifts the frequencies of
normally incoherent light without any blurring of the images or altering the
order of the spectra. CREIL operates in gases having quadrupolar resonances in
the megaherz range, and it is easily confused with Doppler effects. When CREIL
is taken into account, the propagation of light in cosmic low pressure gases
involves a complex combination of absorptions and frequency shifts. Current
star theory predicts very bright accreting neutron stars. These should be
small, very hot objects surrounded by dirty atomic hydrogen. CREIL predicts
spectra for these stars that have exactly the characteristics found in the
spectra of the quasars. The intrinsic redshifting in the extended photosphere
of Quasars as defined by CREIL events drastically reduces both the size and
distance to quasars, and clearly identifies the missing neutron stars as
quasar-like objects. A full interpretation of quasar spectra does not require
jets, dark matter, a variation of the fine structure constant, or an early
synthesis of iron. CREIL is useful in explaining other astrophysical problems,
such as redshifting proportional to the path of light through the corona of the
Sun. CREIL radiation transfers may explain the blueshifting of radio signals
from Pioneer 10 and 11.
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We consider near maximum-likelihood (ML) decoding of short linear block codes
based on neural belief propagation (BP) decoding recently introduced by
Nachmani et al.. While this method significantly outperforms conventional BP
decoding, the underlying parity-check matrix may still limit the overall
performance. In this paper, we introduce a method to tailor an overcomplete
parity-check matrix to (neural) BP decoding using machine learning. We consider
the weights in the Tanner graph as an indication of the importance of the
connected check nodes (CNs) to decoding and use them to prune unimportant CNs.
As the pruning is not tied over iterations, the final decoder uses a different
parity-check matrix in each iteration. For Reed-Muller and short low-density
parity-check codes, we achieve performance within 0.27 dB and 1.5 dB of the ML
performance while reducing the complexity of the decoder.
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The Boltzmann-Wallis-Jaynes' multiplicity argument is taken up and
elaborated. MaxEnt is proved and demonstrated to be just an asymptotic case of
looking for such a vector of absolute frequencies in a feasible set, which has
maximal probability of being generated by a uniform prior generator/pmf.
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Spark plasma discharges induce vortex rings and a hot gas kernel. We develop
a model to describe the late stage of the spark induced flow and the role of
the vortex rings in the entrainment of cold ambient gas and the cooling of the
hot gas kernel. The model is tested in a plasma-induced flow, using density and
velocity measurements obtained from simultaneous stereoscopic particle image
velocimetry (S-PIV) and background oriented schlieren (BOS). We show that the
spatial distribution of the hot kernel follows the motion of the vortex rings,
whose radial expansion increases with the electrical energy deposited during
the spark discharge. The vortex ring cooling model establishes that entrainment
in the convective cooling regime is induced by the vortex rings and governs the
cooling of the hot gas kernel, and the rate of cooling increases with the
electrical energy deposited during the spark discharge.
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PHOTOS Monte Carlo is widely used for simulating QED effects in decay of
intermediate particles and resonances. It can be easily connected to other main
process generators. In this paper we consider decaying processes gamma^* ->
pi^+ pi^-(gamma) and K^\pm -> pi^+ pi^- e^\pm nu (gamma) in the framework of
Scalar QED. These two processes are interesting not only for the technical
aspect of PHOTOS Monte Carlo, but also for precision measurement of
alpha_{QED}(M_Z), g-2, as well as pi pi scattering lengths.
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We introduce the Multiple Quantile Graphical Model (MQGM), which extends the
neighborhood selection approach of Meinshausen and Buhlmann for learning sparse
graphical models. The latter is defined by the basic subproblem of modeling the
conditional mean of one variable as a sparse function of all others. Our
approach models a set of conditional quantiles of one variable as a sparse
function of all others, and hence offers a much richer, more expressive class
of conditional distribution estimates. We establish that, under suitable
regularity conditions, the MQGM identifies the exact conditional independencies
with probability tending to one as the problem size grows, even outside of the
usual homoskedastic Gaussian data model. We develop an efficient algorithm for
fitting the MQGM using the alternating direction method of multipliers. We also
describe a strategy for sampling from the joint distribution that underlies the
MQGM estimate. Lastly, we present detailed experiments that demonstrate the
flexibility and effectiveness of the MQGM in modeling hetereoskedastic
non-Gaussian data.
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LIGO's detection of gravitational waves from binary black hole mergers was an
unexpected surprise that immediately raised the question - what is the origin
of these black hole binaries? The "simplest" scenario is evolution of field
massive stellar binaries. However, other possibilities involving capture have
been proposed. We explore here one of the more interesting clues on this
puzzle: the relatively modest spins of the resulting black holes that imply
that the progenitor black holes were not spinning rapidly. More specifically we
consider the implication of observed distribution of, $\chi_{\rm eff}$, the
mass weighted projected (along the orbital axis) spins on the field evolution
scenario. In all cases $\chi_{\rm eff}$ is small and in two of the cases the
best fit value is negative. Only in one event the spin is positive at 90\%
credible. These observations are puzzling within the field binary scenario in
which positive higher spins ($\chi_{\rm eff} \ge 0.5$) are expected. At first
sight one may expect that this rules out the field evolutionary scenario.
Indeed we show that with typical parameters a significant fraction ($\ge 25\%$)
of the mergers should have high effective spin values. However, uncertainties
in the outcome of the common envelope phase (the typical separation and whether
the stars are rotating or not) and in the late stages of massive star evolution
(the strength of the winds) make it impossible to rule out, at present, these
scenarios. While observations of mergers with high effective spin will support
this scenario, future observations of negative spin mergers would rule it out.
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In this paper, we present a machine learning approach for estimating the
number of incident wavefronts in a direction of arrival scenario. In contrast
to previous works, a multilayer neural network with a cross-entropy objective
is trained. Furthermore, we investigate an online training procedure that
allows an adaption of the neural network to imperfections of an antenna array
without explicitly calibrating the array manifold. We show via simulations that
the proposed method outperforms classical model order selection schemes based
on information criteria in terms of accuracy, especially for a small number of
snapshots and at low signal-to-noise-ratios. Also, the online training
procedure enables the neural network to adapt with only a few online training
samples, if initialized by offline training on artificial data.
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Inverted solubility--a crystal melting upon cooling--is observed in a handful
of proteins, such as carbomonoxy hemoglobin and $\gamma$D-crystallin. In human
$\gamma$D-crystallin, the phenomenon is associated with the mutation of the
23$^\mathrm{rd}$ residue, a proline, to a threonine, serine or valine. One
proposed microscopic mechanism for this effect entails an increase in
hydrophobicity upon mutagenesis. Recent crystal structures of a double mutant
that includes the P23T mutation allows for a more careful investigation of this
proposal. Here, we first measure the surface hydrophobicity of various mutant
structures of this protein and determine that it does not discernibly increase
upon the mutating the 23$^\mathrm{rd}$ residue. We then investigate the
solubility inversion regime with a schematic patchy particle model that
includes one of three models for temperature-dependent patch energies: two of
the hydrophobic effect, and a more generic description. We conclude that while
solubility inversion due to the hydrophobic effect may be possible, microscopic
evidence to support it in $\gamma$D-crystallin is weak. More generally, we find
that solubility inversion requires a fine balance between patch strengths and
the temperature-dependent contribution, which may explain why inverted
solubility is not commonly observed in proteins. In any event, we also find
that the temperature-dependent interaction has only a negligible impact on the
critical properties of the $\gamma$D-crystallin, in line with previous
experimental observations.
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We have obtained Keck LRIS imaging and spectra for 29 globular clusters
associated with the lenticular galaxy NGC 524. Using the empirical calibration
of Brodie & Huchra we find that our spectroscopic sample spans a metallicity
range of --2.0 < [Fe/H] < 0. We have compared the composite spectrum of the
metal-poor ([Fe/H] < --1) and metal-rich clusters with stellar population
models and conclude that the clusters are generally old and coeval at the 2
sigma confidence level. To determine the mean [alpha/Fe] ratios of the globular
clusters, we have employed the Milone et al. 'alpha-enhanced' stellar
population models. We verified the reliability of these models by comparing
them with high S/N Galactic globular cluster data. We observe a weak trend of
decreasing [alpha/Fe] with increasing metallicity in the NGC 524 clusters.
Analysis of the cluster system kinematics reveals that the full sample exhibits
a rotation of 114+/-60 km/s around a position angle of 22+/-27 deg, and a
velocity dispersion of 186+/-29 km/s at a mean radius of 89 arcsec from the
galaxy centre. Subdividing the clusters into metal-poor and metal-rich
subcomponents we find that the metal-poor (17) clusters and metal-rich (11)
clusters have similar velocity dispersions (197+/-40 km/s and 169+/-47 km/s
respectively). The metal-poor clusters dominate the rotation in our sample with
147+/-75 km/s, whilst the metal-rich clusters show no significant rotation
(68+/-84 km/s). We derive a virial and projected mass estimation for NGC 524 of
between 4 and 13 x 10^11 Msun (depending on the assumed orbital distribution)
interior to 2 effective radii of this galaxy.
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Low-order models obtained through Galerkin projection of several physically
important systems (e.g., Rayleigh-B\'enard convection, mid-latitude
quasi-geostrophic dynamics, and vorticity dynamics) appear in the form of
coupled gyrostats. Forced dissipative chaos is an important phenomenon in these
models, and this paper introduces and identifies 'minimal chaotic models'
(MCMs), in the sense of having the fewest external forcing and linear
dissipation terms, for the class of models arising from an underlying gyrostat
core. The identification of MCMs reveals common conditions for chaos across a
wide variety of physical systems. It is shown here that a critical distinction
is whether the gyrostat core (without forcing or dissipation) conserves energy,
depending on whether the sum of the quadratic coefficients is zero. The paper
demonstrates that, for the energy-conserving condition of the gyrostat core,
the requirement of a characteristic pair of fixed points that repel the chaotic
flow dictates placement of forcing and dissipation in the minimal chaotic
models. In contrast if the core does not conserve energy, the forcing can be
arranged in additional ways for chaos to appear in the subclasses where linear
feedbacks render fewer invariants in the gyrostat core. In all cases, the
linear mode must experience dissipation for chaos to arise. The Volterra
gyrostat presents a clear example where the arrangement of fixed points
circumscribes more complex dynamics.
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This memoir is a summary of recent work, including collaborations with Erik
van Erp, Christian Voigt and Marco Matassa, compiled for the "Habilitation \`a
diriger des recherches".
We present various different approaches to constructing algebras of
pseudodifferential operators adapted to filtered and multifiltered manifolds
and some quantum analogues. A general goal is the study of index problems in
situations where standard elliptic theory is insufficient. We also present some
applications of these constructions.
We begin by presenting a characterization of pseudodifferential operators on
filtered manifolds in terms of distributions on the tangent groupoid which are
essentially homogeneous with respect to the natural
$\mathbb{R}^\times_+$-action. Next, we describe a rudimentary multifiltered
pseudodifferential theory on the full flag manifold $\mathcal{X}$ of a complex
semisimple Lie group $G$ which allows us to simultaneously treat longitudinal
pseudodifferential operators along every one of the canonical fibrations of
$\mathcal{X}$ over smaller flag manifolds. The motivating application is the
construction of a $G$-equivariant $K$-homology class from the
Bernstein-Gelfand-Gelfand complex of a semisimple group.
Finally, we discuss pseudodifferential operators on two classes of quantum
flag manifolds: quantum projective spaces and the full flag manifolds of
$SU_q(n)$. In particular, on the full flag variety of $SU_q(3)$ we obtain an
equivariant fundamental class from the Bernstein-Gelfand-Gelfand complex.
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We give an account of the results about limit cycle's uniqueness for
Li\'enard equations, from Levinson-Smith's one to the most recent ones. We
present a new uniqueness theorem in the line of Sansone-Massera's geometrical
approach.
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Determining the $CP$ property of the Higgs boson is important for a precision
test of the Standard Model as well as for the search for new physics. We
propose a novel jet substructure observable based on the azimuthal anisotropy
in a linearly polarized gluon jet that is produced in association with a Higgs
boson at hadron colliders, and demonstrate that it provides a new $CP$-odd
observable for determining the $CP$ property of the Higgs-top interaction. We
introduce a factorization formalism to define a polarized gluon jet function
with the insertion of an infrared-safe azimuthal observable to capture the
linear polarization.
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In this paper, we deal with a class of mean-field backward stochastic
differential equations (BSDEs) related to finite state, continuous time Markov
chains. We obtain the existence and uniqueness theorem and a comparison theorem
for solutions of one-dimensional mean-field BSDEs under Lipschitz condition.
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We study the geometric and combinatorial effect of smoothing an intersection
point in a collection of arcs or curves on a surface. We prove that all taut
arcs with fixed endpoints and all taut 1-manifolds with at least two
non-disjoint components on an orientable surface with negative Euler
characteristic admit a taut smoothing, and also that all taut arcs with free
endpoints admit a smoothing that is either taut or becomes taut after removing
at most one intersection. We deduce that for every Riemannian metric on a
surface, the shortest properly immersed arcs with at least $k$
self-intersections have exactly $k$ self-intersections when the endpoints of
the arc are fixed, and at most $k+1$ self-intersections otherwise, and that the
arc length spectrum is "coarsely ordered" by self-intersection number. Along
the way, we obtain partial analogous results in the case of curves.
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We investigate the language classes recognized by group automata over matrix
groups. For the case of $2 \times 2 $ matrices, we prove that the corresponding
group automata for rational matrix groups are more powerful than the
corresponding group automata for integer matrix groups. Finite automata over
some special matrix groups, such as the discrete Heisenberg group and the
Baumslag-Solitar group are also examined. We also introduce the notion of time
complexity for group automata and demonstrate some separations among related
classes. The case of linear-time bounds is examined in detail throughout our
repertory of matrix group automata.
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The aim is to present the ability of a network of transitions as a nonlinear
tool providing a graphical representation of a time series. This representation
is used for cardiac RR-intervals in follow-up observation of changes in heart
rhythm of patients recovering after heart transplant.
|
We study here the steady state attained in a granular gas of inelastic rough
spheres that is subject to a spatially uniform random volume force. The
stochastic force has the form of the so-called white noise and acts by adding
impulse to the particle translational velocities. We work out an analytical
solution of the corresponding velocity distribution function from a Sonine
polynomial expansion that displays energy non-equipartition between the
translational and rotational modes, translational and rotational kurtoses, and
translational-rotational velocity correlations. By comparison with a numerical
solution of the Boltzmann kinetic equation (by means of the Direct Simulation
Monte Carlo method) we show that our analytical solution provides a good
description that is quantitatively very accurate in certain ranges of
inelasticity and roughness. We also find three important features that make the
forced granular gas steady state very different from the homogeneous cooling
state (attained by an unforced granular gas). First, the marginal velocity
distributions are always close to a Maxwellian. Second, there is a continuous
transition to the purely smooth limit (where the effects of particle rotations
are ignored). And third, the angular translational-rotational velocity
correlations show a preference for a quasiperpendicular mutual orientation
(which is called "lifted-tennis-ball" behavior).
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Using all-atomic molecular dynamics(MD) simulations, we show that various
substrates could induce interfacial water (IW) to form the same ice-like oxygen
lattice but different hydrogen polarity order, and regulate the heterogeneous
ice nucleation on the IW. We develop an efficient MD method to probe the shape,
structure of ice nuclei and the corresponding supercooling temperatures. We
find that the polarization of hydrogens in IW increases the surface tension
between the ice nucleus and the IW, thus lifts the free energy barrier of
heterogeneous ice nucleation. The results show that not only the oxygen lattice
order but the hydrogen disorder of IW on substrates are required to effectively
facilitate the freezing of atop water.
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A study of 3D pixel sensors of cell size 50 {\mu}m x 50 {\mu}m fabricated at
IMB-CNM using double-sided n-on-p 3D technology is presented. Sensors were
bump-bonded to the ROC4SENS readout chip. For the first time in such a
small-pitch hybrid assembly, the sensor response to ionizing radiation in a
test beam of 5.6 GeV electrons was studied. Results for non-irradiated sensors
are presented, including efficiency, charge sharing, signal-to-noise, and
resolution for different incidence angles.
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We show that the apparent horizon and the region near $r=0$ of an evaporating
charged, rotating black hole are timelike. It then follows that for black holes
in nature, which invariably have some rotation, have a channel, via which
classical or quantum information can escape to the outside, while the black
hole shrinks in size. We discuss implications for the information loss problem.
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Quantum Liouville theory is analyzed in terms of the infinite dimensional
representations of $U_Qsl(2,C)$ with q a root of unity. Making full use of
characteristic features of the representations, we show that vertex operators
in this Liouville theory are factorized into `classical' vertex operators and
those which are constructed from the finite dimensional representations of
$U_qsl(2,C)$. We further show explicitly that fusion rules in this model also
enjoys such a factorization. Upon the conjecture that the Liouville action
effectively decouples into the classical Liouville action and that of a quantum
theory, correlation functions and transition amplitudes are discussed,
especially an intimate relation between our model and geometric quantization of
the moduli space of Riemann surfaces is suggested. The most important result is
that our Liouville theory is in the strong coupling region, i.e., the central
charge c_L satisfies $1<c_L<25$. An interpretation of quantum space-time is
also given within this formulation.
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Large language models (LLMs) and Vision-Language Models (VLMs) have been
proven to excel at multiple tasks, such as commonsense reasoning. Powerful as
these models can be, they are not grounded in the 3D physical world, which
involves richer concepts such as spatial relationships, affordances, physics,
layout, and so on. In this work, we propose to inject the 3D world into large
language models and introduce a whole new family of 3D-LLMs. Specifically,
3D-LLMs can take 3D point clouds and their features as input and perform a
diverse set of 3D-related tasks, including captioning, dense captioning, 3D
question answering, task decomposition, 3D grounding, 3D-assisted dialog,
navigation, and so on. Using three types of prompting mechanisms that we
design, we are able to collect over 300k 3D-language data covering these tasks.
To efficiently train 3D-LLMs, we first utilize a 3D feature extractor that
obtains 3D features from rendered multi- view images. Then, we use 2D VLMs as
our backbones to train our 3D-LLMs. By introducing a 3D localization mechanism,
3D-LLMs can better capture 3D spatial information. Experiments on ScanQA show
that our model outperforms state-of-the-art baselines by a large margin (e.g.,
the BLEU-1 score surpasses state-of-the-art score by 9%). Furthermore,
experiments on our held-in datasets for 3D captioning, task composition, and
3D-assisted dialogue show that our model outperforms 2D VLMs. Qualitative
examples also show that our model could perform more tasks beyond the scope of
existing LLMs and VLMs. Project Page: : https://vis-www.cs.umass.edu/3dllm/.
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In terms of the concepts of state and state transition, a new algorithm-State
Transition Algorithm (STA) is proposed in order to probe into classical and
intelligent optimization algorithms. On the basis of state and state
transition, it becomes much simpler and easier to understand. As for continuous
function optimization problems, three special operators named rotation,
translation and expansion are presented. While for discrete function
optimization problems, an operator called general elementary transformation is
introduced. Finally, with 4 common benchmark continuous functions and a
discrete problem used to test the performance of STA, the experiment shows that
STA is a promising algorithm due to its good search capability.
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Birefringence, an inherent characteristic of optically anisotropic materials,
is widely utilized in various imaging applications ranging from material
characterizations to clinical diagnosis. Polarized light microscopy enables
high-resolution, high-contrast imaging of optically anisotropic specimens, but
it is associated with mechanical rotations of polarizer/analyzer and relatively
complex optical designs. Here, we present a novel form of
polarization-sensitive microscopy capable of birefringence imaging of
transparent objects without an optical lens and any moving parts. Our method
exploits an optical mask-modulated polarization image sensor and
single-input-state LED illumination design to obtain complex and birefringence
images of the object via ptychographic phase retrieval. Using a camera with a
pixel resolution of 3.45 um, the method achieves birefringence imaging with a
half-pitch resolution of 2.46 um over a 59.74 mm^2 field-of-view, which
corresponds to a space-bandwidth product of 9.9 megapixels. We demonstrate the
high-resolution, large-area birefringence imaging capability of our method by
presenting the birefringence images of various anisotropic objects, including a
birefringent resolution target, liquid crystal polymer depolarizer, monosodium
urate crystal, and excised mouse eye and heart tissues.
|
Let $X_1,X_2,...$ be independent random variables with zero means and finite
variances, and let $S_n=\sum_{i=1}^nX_i$ and $V^2_n=\sum_{i=1}^nX^2_i$. A
Cram\'{e}r type moderate deviation for the maximum of the self-normalized sums
$\max_{1\leq k\leq n}S_k/V_n$ is obtained. In particular, for identically
distributed $X_1,X_2,...,$ it is proved that $P(\max_{1\leq k\leq n}S_k\geq
xV_n)/(1-\Phi (x))\rightarrow2$ uniformly for $0<x\leq\mathrm{o}(n^{1/6})$
under the optimal finite third moment of $X_1$.
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For each real number $\Lambda$ a Lie algebra of nonlinear vector fields on
three dimensional Euclidean space is reported. Although each algebra is
mathematically isomorphic to $gl(3,{\bf R})$, only the $\Lambda=0$ vector
fields correspond to the usual generators of the general linear group. The
$\Lambda < 0$ vector fields integrate to a nonstandard action of the general
linear group; the $\Lambda >0$ case integrates to a local Lie semigroup. For
each $\Lambda$, a family of surfaces is identified that is invariant with
respect to the group or semigroup action. For positive $\Lambda$ the surfaces
describe fissioning nuclei with a neck, while negative $\Lambda$ surfaces
correspond to exotic bubble nuclei. Collective models for neck and bubble
nuclei are given by irreducible unitary representations of a fifteen
dimensional semidirect sum spectrum generating algebra $gcm(3)$ spanned by its
nonlinear $gl(3,{\bf R})$ subalgebra plus an abelian nonlinear inertia tensor
subalgebra.
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Feature selection reduces the dimensionality of data by identifying a subset
of the most informative features. In this paper, we propose an innovative
framework for unsupervised feature selection, called fractal autoencoders
(FAE). It trains a neural network to pinpoint informative features for global
exploring of representability and for local excavating of diversity.
Architecturally, FAE extends autoencoders by adding a one-to-one scoring layer
and a small sub-neural network for feature selection in an unsupervised
fashion. With such a concise architecture, FAE achieves state-of-the-art
performances; extensive experimental results on fourteen datasets, including
very high-dimensional data, have demonstrated the superiority of FAE over
existing contemporary methods for unsupervised feature selection. In
particular, FAE exhibits substantial advantages on gene expression data
exploration, reducing measurement cost by about $15$\% over the widely used
L1000 landmark genes. Further, we show that the FAE framework is easily
extensible with an application.
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The paper is devoted to the realization of wireless enabled clothing,
employing recent new technologies in electronics, textile, and renewable power.
This new wireless enabled clothing architecture is modular and
distributed,allowing for customization in functionality and clothing designs.
Are studied the implications for supply chains,distribution channels, and cost
benefits. Modular wireless enabled clothing offers significant personalization
opportunities at costs comparable with mobile terminals.
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A word $s$ of letters on edges of underlying graph $\Gamma$ of deterministic
finite automaton (DFA) is called synchronizing if $s$ sends all states of the
automaton to a unique state. J. \v{C}erny discovered in 1964 a sequence of
$n$-state complete DFA possessing a minimal synchronizing word of length
$(n-1)^2$. The hypothesis, mostly known today as \v{C}erny conjecture, claims
that $(n-1)^2$ is a precise upper bound on the length of such a word over
alphabet $\Sigma$ of letters on edges of $\Gamma$ for every complete $n$-state
DFA. The hypothesis was formulated in 1966 by Starke. Algebra with nonstandard
operation over special class of matrices induced by words in the alphabet of
labels on edges is used to prove the conjecture. The proof is based on the
connection between length of words $u$ and dimension of the space generated by
solution $L_x$ of matrix equation $M_uL_x=M_s$ for synchronizing word $s$, as
well as on relation between ranks of $M_u$ and $L_x$. Important role below
placed the notion of pseudo inverseL matrix, sometimes reversible.
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Generating stable and robust grasps on arbitrary objects is critical for
dexterous robotic hands, marking a significant step towards advanced dexterous
manipulation. Previous studies have mostly focused on improving differentiable
grasping metrics with the assumption of precisely known object geometry.
However, shape uncertainty is ubiquitous due to noisy and partial shape
observations, which introduce challenges in grasp planning. We propose,
SpringGrasp planner, a planner that considers uncertain observations of the
object surface for synthesizing compliant dexterous grasps. A compliant
dexterous grasp could minimize the effect of unexpected contact with the
object, leading to more stable grasp with shape-uncertain objects. We introduce
an analytical and differentiable metric, SpringGrasp metric, that evaluates the
dynamic behavior of the entire compliant grasping process. Planning with
SpringGrasp planner, our method achieves a grasp success rate of 89% from two
viewpoints and 84% from a single viewpoints in experiment with a real robot on
14 common objects. Compared with a force-closure based planner, our method
achieves at least 18% higher grasp success rate.
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We investigate the possible origin of the transiting giant planet
WD1856+534b, the first strong exoplanet candidate orbiting a white dwarf,
through high-eccentricity migration (HEM) driven by the Lidov-Kozai (LK)
effect. The host system's overall architecture is an hierarchical quadruple in
the '2+2' configuration, owing to the presence of a tertiary companion system
of two M-dwarfs. We show that a secular inclination resonance in 2+2 systems
can significantly broaden the LK window for extreme eccentricity excitation ($e
\gtrsim 0.999$), allowing the giant planet to migrate for a wide range of
initial orbital inclinations. Octupole effects can also contribute to the
broadening of this 'extreme' LK window. By requiring that perturbations from
the companion stars be able to overcome short-range forces and excite the
planet's eccentricity to $e \simeq 1$, we obtain an absolute limit of $a_{1}
\gtrsim 8 \, {\rm AU} \, (a_{3} / 1500 \, {\rm AU})^{6/7}$ for the planet's
semi-major axis just before migration (where $a_{3}$ is the semi-major axis of
the 'outer' orbit). We suggest that, to achieve a wide LK window through the
2+2 resonance, WD1856b likely migrated from $30 \, {\rm AU} \lesssim a_{1}
\lesssim 60 \, {\rm AU}$, corresponding to $\sim 10$--$20 \, {\rm AU}$ during
the host's main-sequence phase. We discuss possible difficulties of all
flavours of HEM affecting the occurrence rate of short-period giant planets
around white dwarfs.
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The topology of one-dimensional chiral systems is captured by the winding
number of the Hamiltonian eigenstates. Here we show that this invariant can be
read-out by measuring the mean chiral displacement of a single-particle
wavefunction that is connected to a fully localized one via a unitary and
translational-invariant map. Remarkably, this implies that the mean chiral
displacement can detect the winding number even when the underlying Hamiltonian
is quenched between different topological phases. We confirm experimentally
these results in a quantum walk of structured light.
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We prove new endpoint bounds for the lacunary spherical maximal operator and
as a consequence obtain almost everywhere pointwise convergence of lacunary
spherical means for functions locally in $L\log\log\log L(\log\log\log\log
L)^{1+\epsilon}$ for any $\epsilon>0$.
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We report on the reinforcement of superconductivity in a system consisting of
a narrow superconducting wire weakly coupled to a diffusive metallic film. We
analyze the effective phase-only action of the system by a perturbative
renormalization-group and a self-consistent variational approach to obtain the
critical points and phases at T=0. We predict a quantum phase transition
towards a superconducting phase with long-range order as a function of the wire
stiffness and coupling to the metal. We discuss implications for the DC
resistivity of the wire.
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Parametrizations of Equation of state parameter as a function of the scale
factor or redshift are frequently used in dark energy modeling. The question
investigated in this paper is if parametrizations proposed in the literature
are compatible with the dark energy being a barotropic fluid. The test of this
compatibility is based on the functional form of the speed of sound squared,
which for barotropic fluid dark energy follows directly from the function for
the Equation of state parameter. The requirement that the speed of sound
squared should be between 0 and speed of light squared provides constraints on
model parameters using analytical and numerical methods. It is found that this
fundamental requirement eliminates a large number of parametrizations as
barotropic fluid dark energy models and puts strong constraints on parameters
of other dark energy parametrizations.
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This paper examines how to minimize the energy consumption of a user
equipment (UE) when transmitting short data payloads. The receiving base
station (BS) controls a reconfigurable intelligent surface (RIS), which
requires additional pilot signals to be configured, to improve the channel
conditions. The challenge is that the pilot signals increase the energy
consumption and must be balanced against energy savings during data
transmission. We derive a formula for the energy consumption, including both
pilot and data transmission powers and the effects of imperfect channel state
information and discrete phase-shifts.
To shorten the pilot length, we propose dividing the RIS into subarrays of
multiple elements using the same reflection coefficient. The pilot power and
subarray size are tuned to the payload length to minimize the energy
consumption. Analytical results show that there exists a unique
energy-minimizing solution. For small payloads and when the direct path loss
between the BS and UE is weak compared to the path loss via the RIS, the
solution is using subarrays with many elements and low pilot power and vice
versa. The optimal percentage of energy spent on pilot signaling is in the
order of 10-40%.
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Depth cues are known to be useful for visual perception. However, direct
measurement of depth is often impracticable. Fortunately, though, modern
learning-based methods offer promising depth maps by inference in the wild. In
this work, we adapt such depth inference models for object segmentation using
the objects' "pop-out" prior in 3D. The "pop-out" is a simple composition prior
that assumes objects reside on the background surface. Such compositional prior
allows us to reason about objects in the 3D space. More specifically, we adapt
the inferred depth maps such that objects can be localized using only 3D
information. Such separation, however, requires knowledge about contact surface
which we learn using the weak supervision of the segmentation mask. Our
intermediate representation of contact surface, and thereby reasoning about
objects purely in 3D, allows us to better transfer the depth knowledge into
semantics. The proposed adaptation method uses only the depth model without
needing the source data used for training, making the learning process
efficient and practical. Our experiments on eight datasets of two challenging
tasks, namely camouflaged object detection and salient object detection,
consistently demonstrate the benefit of our method in terms of both performance
and generalizability.
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It has been recently shown that a chiral molecule accelerates linearly along
a spatially uniform magnetic field, as a result of the parity-time symmetry
breaking induced in its QED self-interaction. In this work we extend this
result to fundamental particles which present EW self-interaction, in which
case parity is violated by the EW interaction itself. In particular, we
demonstrate that, in a spatially uniform and adiabatically time-varying
magnetic field, an unpolarized proton coupled to the leptonic vacuum acquires a
kinetic momentum antiparallel to the magnetic field, whereas virtual leptons
gain an equivalent $Casimir$ $momentum$ in the opposite direction. That
momentum is proportional to the magnetic field and to the square of Fermi's
constant. We prove that the kinetic energy of the proton is a magnetic energy
which forms part of its EW self-energy.
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One of the most significant developments in the history of human being is the
invention of a way of keeping records of human knowledge, thoughts and ideas.
In 1926, the work of several thinkers such as Edouard Le Roy, Vladimir
Vernadsky and Teilhard de Chardin led to the concept of noosphere, thus the
idea that human cognition and knowledge transforms the biosphere coming to be
something like the planet's thinking layer. At present, is commonly accepted by
some thinkers that the Internet is the medium that brings life to noosphere.
According to Vinge and Kurzweil's technological singularity hypothesis,
noosphere would be in the future the natural environment in which
'human-machine superintelligence' emerges after to reach the point of
technological singularity. In this paper we show by means of a numerical model
the impossibility that our civilization reaches the point of technological
singularity in the near future. We propose that this point may be reached when
Internet data centers are based on "computer machines" to be more effective in
terms of power consumption than current ones. We speculate about what we have
called 'Nooscomputer' or N-computer a hypothetical machine which would consume
far less power allowing our civilization to reach the point of technological
singularity.
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We review the effects of winds from massive O and B stars on the surrounding
medium over the various stages of stellar evolution. Furthermore we discuss
some of the implications for SNe and GRB evolution within this wind-blown
medium.
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Inspired by Schoutens' results, we introduce a variant of sharp $F$-purity
and sharp $F$-injectivity in equal characteristic zero via ultraproducts. As an
application, we show that if $R\to S$ is pure and $S$ is of dense $F$-pure
type, then $R$ is of dense $F$-pure type.
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Polarization maintenance is a key technology for free-space quantum
communication. In this paper, we describe a polarization maintenance design of
a transmitting antenna with an average polarization extinction ratio of 887 : 1
by a local test. We implemented a feasible polarization-compensation scheme for
satellite motions that has a polarization fidelity more than 0.995. Finally, we
distribute entanglement to a satellite from ground for the first time with a
violation of Bell inequality by 2.312+-0.096.
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Fluid-solid reactions exist in many chemical and metallurgical process
industries. Several models describe these reactions such as volume reaction
model, grain model, random pore model and nucleation model. These models give
two nonlinear coupled partial differential equations (CPDE) that must be solved
numerically. A new approximate solution technique (quantized method) has been
introduced for some of these models in recent years. In this work, the various
fluid-solid reaction models with their quantized and numerical solutions have
been discussed.
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We extend the well-known trace formula for Hill's equation to general
one-dimensional Schr\"odinger operators. The new function $\xi$, which we
introduce, is used to study absolutely continuous spectrum and inverse
problems.
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We study training a single end-to-end (E2E) automatic speech recognition
(ASR) model for three languages used in Kazakhstan: Kazakh, Russian, and
English. We first describe the development of multilingual E2E ASR based on
Transformer networks and then perform an extensive assessment on the
aforementioned languages. We also compare two variants of output grapheme set
construction: combined and independent. Furthermore, we evaluate the impact of
LMs and data augmentation techniques on the recognition performance of the
multilingual E2E ASR. In addition, we present several datasets for training and
evaluation purposes. Experiment results show that the multilingual models
achieve comparable performances to the monolingual baselines with a similar
number of parameters. Our best monolingual and multilingual models achieved
20.9% and 20.5% average word error rates on the combined test set,
respectively. To ensure the reproducibility of our experiments and results, we
share our training recipes, datasets, and pre-trained models.
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We address the critical and universal aspects of counterion-condensation
transition at a single charged cylinder in both two and three spatial
dimensions using numerical and analytical methods. By introducing a novel
Monte-Carlo sampling method in logarithmic radial scale, we are able to
numerically simulate the critical limit of infinite system size (corresponding
to infinite-dilution limit) within tractable equilibration times. The critical
exponents are determined for the inverse moments of the counterionic density
profile (which play the role of the order parameters and represent the inverse
localization length of counterions) both within mean-field theory and within
Monte-Carlo simulations. In three dimensions (3D), correlation effects
(neglected within mean-field theory) lead to an excessive accumulation of
counterions near the charged cylinder below the critical temperature
(condensation phase), while surprisingly, the critical region exhibits
universal critical exponents in accord with the mean-field theory. In two
dimensions (2D), we demonstrate, using both numerical and analytical
approaches, that the mean-field theory becomes exact at all temperatures
(Manning parameters), when number of counterions tends to infinity. For finite
particle number, however, the 2D problem displays a series of peculiar singular
points (with diverging heat capacity), which reflect successive de-localization
events of individual counterions from the central cylinder. In both 2D and 3D,
the heat capacity shows a universal jump at the critical point, and the energy
develops a pronounced peak. The asymptotic behavior of the energy peak location
is used to locate the critical temperature, which is also found to be universal
and in accordance with the mean-field prediction.
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Optical phase conjugation (OPC) is a nonlinear technique used for
counteracting wavefront distortions, with various applications ranging from
imaging to beam focusing. Here, we present the design of a diffractive
wavefront processor to approximate all-optical phase conjugation operation for
input fields with phase aberrations. Leveraging deep learning, a set of passive
diffractive layers was optimized to all-optically process an arbitrary
phase-aberrated coherent field from an input aperture, producing an output
field with a phase distribution that is the conjugate of the input wave. We
experimentally validated the efficacy of this wavefront processor by 3D
fabricating diffractive layers trained using deep learning and performing OPC
on phase distortions never seen by the diffractive processor during its
training. Employing terahertz radiation, our physical diffractive processor
successfully performed the OPC task through a shallow spatially-engineered
volume that axially spans tens of wavelengths. In addition to this transmissive
OPC configuration, we also created a diffractive phase-conjugate mirror by
combining deep learning-optimized diffractive layers with a standard mirror.
Given its compact, passive and scalable nature, our diffractive wavefront
processor can be used for diverse OPC-related applications, e.g., turbidity
suppression and aberration correction, and is also adaptable to different parts
of the electromagnetic spectrum, especially those where cost-effective
wavefront engineering solutions do not exist.
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The canonical Schmidt decomposition of quantum states is discussed and its
implementation to the Quantum Computation Simulator is outlined. In particular,
the semiorder relation in the space of quantum states induced by the
lexicographic semiorder of the space of the Schmidt coefficients is discussed.
The appropriate sorting algorithms on the corresponding POSETs consisting from
quantum states are formulated and theirs computer implementations are being
tested.
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Incremental particle growth in turbulent protoplanetary nebulae is limited by
a combination of barriers that can slow or stall growth. Moreover, particles
that grow massive enough to decouple from the gas are subject to inward radial
drift which could lead to the depletion of most disk solids before
planetesimals can form. Compact particle growth is probably not realistic.
Rather, it is more likely that grains grow as fractal aggregates which may
overcome this so-called radial drift barrier because they remain more coupled
to the gas than compact particles of equal mass. We model fractal aggregate
growth and compaction in a viscously evolving solar-like nebula for a range of
turbulent intensities $\alpha_{\rm{t}} = 10^{-5}-10^{-2}$. We do find that
radial drift is less influential for porous aggregates over much of their
growth phase; however, outside the water snowline fractal aggregates can grow
to much larger masses with larger Stokes numbers more quickly than compact
particles, leading to rapid inward radial drift. As a result, disk solids
outside the snowline out to $\sim 10-20$ AU are depleted earlier than in
compact growth models, but outside $\sim 20$ AU material is retained much
longer because aggregate Stokes numbers there remain lower initially.
Nevertheless, we conclude even fractal models will lose most disk solids
without the intervention of some leap-frog planetesimal forming mechanism such
as the Streaming Instability (SI), though conditions for the SI are generally
never satisfied, except for a brief period %for a brief stage around $\sim 0.2$
Myr at the snowline for $\alpha_{\rm{t}}=10^{-5}$.
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Motivated by the recent discovery of superconductivity in the Sr-doped
layered nickelate NdNiO$_2$, we perform a systematic computational materials
design of layered nickelates that are dynamically stable and whose electronic
structure better mimics the electronic structure of high-$T_c$ cuprates than
NdNiO$_2$. While the Ni $3d$ orbitals are self-doped from the $d^9$
configuration in NdNiO$_2$ and the Nd-layer states form Fermi pockets, we find
more than 10 promising compounds for which the self-doping is almost or even
completely suppressed. We derive effective single-band models for those
materials and find that they are in the strongly-correlated regime. We also
investigate the possibility of palladate analogues of high-$T_c$ cuprates. Once
synthesized, these nickelates and palladates will provide a firm ground for
studying superconductivity in the Mott-Hubbard regime of the
Zaanen-Sawatzky-Allen classification.
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Graph convolutional networks (GCNs) have achieved great success in dealing
with data of non-Euclidean structures. Their success directly attributes to
fitting graph structures effectively to data such as in social media and
knowledge databases. For image processing applications, the use of graph
structures and GCNs have not been fully explored. In this paper, we propose a
novel encoder-decoder network with added graph convolutions by converting
feature maps to vertexes of a pre-generated graph to synthetically construct
graph-structured data. By doing this, we inexplicitly apply graph Laplacian
regularization to the feature maps, making them more structured. The
experiments show that it significantly boosts performance for image restoration
tasks, including deblurring and super-resolution. We believe it opens up
opportunities for GCN-based approaches in more applications.
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In this paper, we develop a unified framework for analyzing the tracking
error and dynamic regret of inexact online optimization methods under a variety
of settings. Specifically, we leverage the quadratic constraint approach from
control theory to formulate sequential semidefinite programs (SDPs) whose
feasible points naturally correspond to tracking error bounds of various
inexact online optimization methods including the inexact online gradient
descent (OGD) method, the online gradient descent-ascent method, the online
stochastic gradient method, and the inexact proximal online gradient method. We
provide exact analytical solutions for our proposed sequential SDPs, and obtain
fine-grained tracking error bounds for the online algorithms studied in this
paper. We also provide a simple routine to convert the obtained tracking error
bounds into dynamic regret bounds. The main novelty of our analysis is that we
derive exact analytical solutions for our proposed sequential SDPs under
various inexact oracle assumptions in a unified manner.
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Some preliminaries and basic facts regarding unbounded Wiener-Hopf operators
(WH) are provided. WH with rational symbols are studied in detail showing that
they are densely defined closed and have finite dimensional kernels and
deficiency spaces. The latter spaces as well as the domains and ranges are
explicitly determined. A further topic concerns semibounded WH. Expressing a
semibounded WH by a product of a closable operator and its adjoint this
representation allows for a natural self-adjoint extension. It is shown that it
coincides with the Friedrichs extension. Polar decomposition gives rise to a
Hilbert space isomorphism relating semibounded WH to singular integral
operators of a well-studied type based on the Hilbert transformation.
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The work contains a first attempt to treat the problem of routing in networks
with energy harvesting units. We propose HDR - a Hysteresis Based Routing
Algorithm and analyse it in a simple diamond network. We also consider a
network with three forwarding nodes. The results are used to give insight into
its application in general topology networks and to general harvesting
patterns.
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