  The Iwahori-Hecke algebra of type A acts on tensor product space of the
natural representation of the quantum superalgebra U_q(gl(m,n)). We show this
action of the Hecke algebra and the action of U_q(gl(m,n)) on the same space
determine commuting actions of each other. Together with this result and
Gyoja's q-analogue of the Young symmetrizer, we construct a highest weight
vector of each irreducible summmand of the tensor product space.


  Cross-lingual word embeddings (CLWE) have been proven useful in many
cross-lingual tasks. However, most existing approaches to learn CLWE including
the ones with contextual embeddings are sense agnostic. In this work, we
propose a novel framework to align contextual embeddings at the sense level by
leveraging cross-lingual signal from bilingual dictionaries only. We
operationalize our framework by first proposing a novel sense-aware cross
entropy loss to model word senses explicitly. The monolingual ELMo and BERT
models pretrained with our sense-aware cross entropy loss demonstrate
significant performance improvement for word sense disambiguation tasks. We
then propose a sense alignment objective on top of the sense-aware cross
entropy loss for cross-lingual model pretraining, and pretrain cross-lingual
models for several language pairs (English to German/Spanish/Japanese/Chinese).
Compared with the best baseline results, our cross-lingual models achieve
0.52%, 2.09% and 1.29% average performance improvements on zero-shot
cross-lingual NER, sentiment classification and XNLI tasks, respectively.


  Explicit dependencies of the local density of states and the magnetization
local density of states have been obtained around magnetic point defects in a
two-dimensional electron gas with Rashba spin-orbit interaction . The
expressions are given in the Born approximation for arbitrary magnitude and
orientation of the defect magnetic moment, and for arbitrary size of the
constant of spin-orbit interaction alpha/. On the basis of our asymptotically
exact formulas a procedure for the determination of the constant alpha/ in STM
experiments is proposed. The novel analytical results are compared with the
numerical and approximate results of previous work. At variance with earlier
work we find that that magnetic scattering in the presence of spin-orbit
interaction does not modify the local density of states and that the spin
texture resulting from in-plain orientation of the defect magnetic moment, and
elastic scattering, is not a purely in-plane spin texture.


  One-parameter analogs of the Heisenberg enveloping algebra were studied
previously by Kirkman and Small. In particular, they demonstrated how one may
obtain Hayashi's analog of the Weyl algebra as a primitive factor of this
algebra. We consider various two-parameter versions of this problem. Of
particular interest is the case when the parameters are dependent. Our study
allows us to consider the representation theory of a two-parameter version of
the Virasoro enveloping algebra.


  The composition of silicate dust in the diffuse interstellar medium and in
protoplanetary disks around young stars informs our understanding of the
processing and evolution of the dust grains leading up to planet formation.
Analysis of the well-known 9.7{\mu}m feature indicates that small amorphous
silicate grains represent a significant fraction of interstellar dust and are
also major components of protoplanetary disks. However, this feature is
typically modelled assuming amorphous silicate dust of olivine and pyroxene
stoichiometries. Here, we analyze interstellar dust with models of silicate
dust that include non-stoichiometric amorphous silicate grains. Modelling the
optical depth along lines of sight toward the extinguished objects Cyg OB2 No.
12 and {\zeta} Ophiuchi, we find evidence for interstellar amorphous silicate
dust with stoichiometry intermediate between olivine and pyroxene, which we
simply refer to as "polivene." Finally, we compare these results to models of
silicate emission from the Trapezium and protoplanetary disks in Taurus.


  Multi-view datasets offer diverse forms of data that can enhance prediction
models by providing complementary information. However, the use of multi-view
data leads to an increase in high-dimensional data, which poses significant
challenges for the prediction models that can lead to poor generalization.
Therefore, relevant feature selection from multi-view datasets is important as
it not only addresses the poor generalization but also enhances the
interpretability of the models. Despite the success of traditional feature
selection methods, they have limitations in leveraging intrinsic information
across modalities, lacking generalizability, and being tailored to specific
classification tasks. We propose a novel genetic algorithm strategy to overcome
these limitations of traditional feature selection methods for multi-view data.
Our proposed approach, called the multi-view multi-objective feature selection
genetic algorithm (MMFS-GA), simultaneously selects the optimal subset of
features within a view and between views under a unified framework. The MMFS-GA
framework demonstrates superior performance and interpretability for feature
selection on multi-view datasets in both binary and multiclass classification
tasks. The results of our evaluations on three benchmark datasets, including
synthetic and real data, show improvement over the best baseline methods. This
work provides a promising solution for multi-view feature selection and opens
up new possibilities for further research in multi-view datasets.


  Cycle polytopes of matroids have been introduced in combinatorial
optimization as a generalization of important classes of polyhedral objects
like cut polytopes and Eulerian subgraph polytopes associated to graphs. Here
we start an algebraic and geometric investigation of these polytopes by
studying their toric algebras, called cycle algebras, and their defining
ideals. Several matroid operations are considered which determine faces of
cycle polytopes that belong again to this class of polyhedral objects. As a key
technique used in this paper, we study certain minors of given matroids which
yield algebra retracts on the level of cycle algebras. In particular, that
allows us to use a powerful algebraic machinery. As an application, we study
highest possible degrees in minimal homogeneous systems of generators of
defining ideals of cycle algebras as well as interesting cases of cut polytopes
and Eulerian subgraph polytopes.


  In his 1935 Gedankenexperiment, Erwin Schr\"{o}dinger imagined a poisonous
substance which has a 50% probability of being released, based on the decay of
a radioactive atom. As such, the life of the cat and the state of the poison
become entangled, and the fate of the cat is determined upon opening the box.
We present an experimental technique that keeps the cat alive on any account.
This method relies on the time-resolved Hong-Ou-Mandel effect: two long,
identical photons impinging on a beam splitter always bunch in either of the
outputs. Interpreting the first photon detection as the state of the poison,
the second photon is identified as the state of the cat. Even after the
collapse of the first photon's state, we show their fates are intertwined
through quantum interference. We demonstrate this by a sudden phase change
between the inputs, administered conditionally on the outcome of the first
detection, which steers the second photon to a pre-defined output and ensures
that the cat is always observed alive.


  Results on the analysis of the hadronic final state in neutral current deep
inelastic scattering at HERA are presented; recent results on inclusive single
particle distributions, particle correlations and event shapes are highlighted.


  Bitcoin is a top-ranked cryptocurrency that has experienced huge growth and
survived numerous attacks. The protocols making up Bitcoin must therefore
accommodate the growth of the network and ensure security. Security of the
Bitcoin network depends on connectivity between the nodes. Higher connectivity
yields better security. In this paper we make two observations: (1) current
connectivity in the Bitcoin network is too low for optimal security; (2) at the
same time, increasing connectivity will substantially increase the bandwidth
used by the transaction dissemination protocol, making it prohibitively
expensive to operate a Bitcoin node. Half of the total bandwidth needed to
operate a Bitcoin node is currently used to just announce transactions. Unlike
block relay, transaction dissemination has received little attention in prior
work. We propose a new transaction dissemination protocol, Erlay, that not only
reduces the bandwidth consumption by 40% assuming current connectivity, but
also keeps the bandwidth use almost constant as the connectivity increases. In
contrast, the existing protocol increases the bandwidth consumption linearly
with the number of connections. By allowing more connections at a small cost,
Erlay improves the security of the Bitcoin network. And, as we demonstrate,
Erlay also hardens the network against attacks that attempt to learn the origin
node of a transaction. Erlay is currently being investigated by the Bitcoin
community for future use with the Bitcoin protocol.


  We present a simple and natural infinite game building an increasing chain of
finite-dimensional Banach spaces. We show that one of the players has a
strategy with the property that, no matter how the other player plays, the
completion of the union of the chain is linearly isometric to the Gurarii
space.


  In this paper, some main eigenvalues and eigenvectors of the politics matrix
are investigated. The number of upper-class families in a society is the number
of eigenvalues which are very close to 1. An algorithm to identify all the
upper-class families from the right and left eigenvectors of those eigenvalues
is developed.


  The bibliography compilation on magnetic monopoles is updated to include
references from 2000 till mid 2011. It is intended to contain all experimental
papers on the subject and only the theoretical papers which have specific
experimental implications.


  In this paper we investigate the innermost stable circular orbit (ISCO) of a
spinning test particle moving in the rotating Maxwell-dilaton black hole
spacetime. By using the Mathisson-Papapetrou-Dixon equations along with the
Tulczyjew spin-supplementary condition, we find the equations of motion in the
equatorial plane and, from the radial equation, it is obtained the effective
potential for the description of the particle's motion. The obtained
trajectories show that the ISCO radii for spinning particles moving in rotating
charged backgrounds are always smaller than those obtained in the corresponding
Kerr-Newman spacetimes. The increasing in the particle's spin produces a
decrease in the ISCO radius in all the studied cases, with a maximum value for
the spin and a corresponding minimum ISCO radius, obtained by imposing a
condition that guarantees the timelike nature of the particle's worldline.


  We study a model of resonant point-contact tunneling of a single
Luttinger-liquid lead, using the boundary state formulation. The model is
described by a single chiral Fermion in one dimensional space with one point
contact interaction at the origin. It is the simplest model of this type. By
folding the infinite line we map the model onto a non-chiral model on the half
infinite line and transcribe the point-contact tunneling interaction into a
boundary interaction. The tunneling interaction yields a non-local effective
action at the boundary. We explicitly construct the boundary state and evaluate
the current correlation functions. The contact interaction is shown to act on
the lower frequency modes more strongly.


  The contribution from the axial-vector meson exchange to the potential of the
muon-proton interaction in muonic hydrogen induced by anomalous axial-vector
meson coupling to two photon state is calculated. It is shown that such
contribution to the hyperfine splitting in muonic hydrogen is large and
important for a comparison with precise experimental data. In the light of our
result, the proton radius "puzzle" is discussed.


  The BICEP2 collaboration reported recently a B-mode polarization of the
cosmic microwave background (CMB) radiation inconsistent with the null
hypothesis at a significance of > 5 {\sigma}. This result has been often
interpreted as a signature of primordial gravitational waves from cosmic
inflation, even if actually polarized dust emission may be at the origin of
such a signal. Even assuming that part of this CMB B-mode polarization really
corresponds to the early Universe dynamics, its interpretation in terms of
inflation and primordial gravitational waves is not the only possible one.
Alternative cosmologies such as pre-Big Bang patterns and the spinorial
space-time (SST) we introduced in 1996-97 can naturally account for such CMB
B-modes. In particular, the SST automatically generates a privileged space
direction (PSD) whose existence may have been confirmed by Planck data. If such
a PSD exists, it seems normal to infer that vector perturbations have been
present in the early Universe leading to CMB B-modes in suitable cosmological
patterns. Inflation would not be required to explain the BICEP2 result assuming
it really contains a primordial signal. More generally, pre-Big Bang
cosmologies can also generate gravitational waves in the early Universe without
any need for cosmic inflation. We further discuss here possible alternatives to
the inflationary interpretation of a primordial B-mode polarization of cosmic
microwave background radiation.


  Recent advances in computational modelling of atomic systems, spanning
molecules, proteins, and materials, represent them as geometric graphs with
atoms embedded as nodes in 3D Euclidean space. In these graphs, the geometric
attributes transform according to the inherent physical symmetries of 3D atomic
systems, including rotations and translations in Euclidean space, as well as
node permutations. In recent years, Geometric Graph Neural Networks have
emerged as the preferred machine learning architecture powering applications
ranging from protein structure prediction to molecular simulations and material
generation. Their specificity lies in the inductive biases they leverage - such
as physical symmetries and chemical properties - to learn informative
representations of these geometric graphs.
  In this opinionated paper, we provide a comprehensive and self-contained
overview of the field of Geometric GNNs for 3D atomic systems. We cover
fundamental background material and introduce a pedagogical taxonomy of
Geometric GNN architectures: (1) invariant networks, (2) equivariant networks
in Cartesian basis, (3) equivariant networks in spherical basis, and (4)
unconstrained networks. Additionally, we outline key datasets and application
areas and suggest future research directions. The objective of this work is to
present a structured perspective on the field, making it accessible to
newcomers and aiding practitioners in gaining an intuition for its mathematical
abstractions.


  Property testing has been extensively studied and its target is to determine
whether a given object satisfies a certain property or it is far from the
property. In this paper, we construct an efficient quantum algorithm which
tests if a given quantum oracle performs the group multiplication of a solvable
group. Our work is strongly based on the efficient classical testing algorithm
for Abelian groups proposed by Friedl, Ivanyos and Santha. Since every Abelian
group is a solvable group, our result is in a sense a generalization of their
result.


  The abundance of user-generated data in social media has incentivized the
development of methods to infer the latent attributes of users, which are
crucially useful for personalization, advertising and recommendation. However,
the current user profiling approaches have limited success, due to the lack of
a principled way to integrate different types of social relationships of a
user, and the reliance on scarcely-available labeled data in building a
prediction model. In this paper, we present a novel solution termed Collective
Semi-Supervised Learning (CSL), which provides a principled means to integrate
different types of social relationship and unlabeled data under a unified
computational framework. The joint learning from multiple relationships and
unlabeled data yields a computationally sound and accurate approach to model
user attributes in social media. Extensive experiments using Twitter data have
demonstrated the efficacy of our CSL approach in inferring user attributes such
as account type and marital status. We also show how CSL can be used to
determine important user features, and to make inference on a larger user
population.


  In this work we propose a new paradigm for designing efficient deep unrolling
networks using operator sketching. The deep unrolling networks are currently
the state-of-the-art solutions for imaging inverse problems. However, for
high-dimensional imaging tasks, especially the 3D cone-beam X-ray CT and 4D MRI
imaging, the deep unrolling schemes typically become inefficient both in terms
of memory and computation, due to the need of computing multiple times the
high-dimensional forward and adjoint operators. Recently researchers have found
that such limitations can be partially addressed by stochastic unrolling with
subsets of operators, inspired by the success of stochastic first-order
optimization. In this work, we propose a further acceleration upon stochastic
unrolling, using sketching techniques to approximate products in the
high-dimensional image space. The operator sketching can be jointly applied
with stochastic unrolling for the best acceleration and compression
performance. Our numerical experiments on X-ray CT image reconstruction
demonstrate the remarkable effectiveness of our sketched unrolling schemes.


  Spectral triples on the q-deformed spheres of dimension two and three are
reviewed.


  This work has the main objective to provide a detailed investigation of
cosmic ray propagation in magnetohydrodynamic turbulent fields generated by
forcing the fluid velocity field at large scales. It provides a derivation of
the particle mean free path dependences in terms of the turbulence level
described by the Alfv\'enic Mach number and in terms of the particle rigidity.
We use an upgrade version of the magnetohydrodynamic code {\tt RAMSES} which
includes a forcing module and a kinetic module and solve the Lorentz equation
for each particle. The simulations are performed using a 3 dimension periodical
box in the test-particle and magnetostatic limits. The forcing module is
implemented using an Ornstein-Uhlenbeck process. An ensemble average over a
large number of particle trajectories is applied to reconstruct the particle
mean free paths. We derive the cosmic ray mean free paths in terms of the
Alfv\'enic Mach numbers and particle reduced rigidities in different turbulence
forcing geometries. The reduced particle rigidity is $\rho=r_L/L$ where $r_L$
is the particle Larmor radius and $L$ is the simulation box length related to
the turbulence coherence or injection scale $L_{inj}$ by $L \sim 5 L_{inj}$. We
have investigated with a special attention compressible and solenoidal forcing
geometries. We find that compressible forcing solutions are compatible with the
quasi-linear theory or more advanced non-linear theories which predict a
rigidity dependence as $\rho^{1/2}$ or $\rho^{1/3}$. Solenoidal forcing
solutions at least at low or moderate Alfv\'enic numbers are not compatible
with the above theoretical expectations and require more refined arguments to
be interpreted. It appears especially for Alfv\'enic Mach numbers close to one
that the wandering of field lines controls perpendicular mean free path
solutions whatever the forcing geometry.


  Embodied agents need to be able to interact in natural language understanding
task descriptions and asking appropriate follow up questions to obtain
necessary information to be effective at successfully accomplishing tasks for a
wide range of users. In this work, we propose a set of dialog acts for
modelling such dialogs and annotate the TEACh dataset that includes over 3,000
situated, task oriented conversations (consisting of 39.5k utterances in total)
with dialog acts. TEACh-DA is one of the first large scale dataset of dialog
act annotations for embodied task completion. Furthermore, we demonstrate the
use of this annotated dataset in training models for tagging the dialog acts of
a given utterance, predicting the dialog act of the next response given a
dialog history, and use the dialog acts to guide agent's non-dialog behaviour.
In particular, our experiments on the TEACh Execution from Dialog History task
where the model predicts the sequence of low level actions to be executed in
the environment for embodied task completion, demonstrate that dialog acts can
improve end task success rate by up to 2 points compared to the system without
dialog acts.


  We present paraconductivity (AL) measurements in three different high
temperature superconductors: a melt textured $YBa_2Cu_3O_7$ sample, a
$Bi_2Sr_2CaCu_2O_8$ epitaxial thin film and a highly textured
$Bi_2Sr_2Ca_2Cu_3O_{10}$ tape. The crossovers between different temperature
regimes in excess conductivity have been analysed. The Lawrence-Doniach (LD)
crossover, which separates the 2D and 3D regimes, shifts from lower to higher
temperatures as the compound anisotropy decreases. Once the LD crossover is
overcome, the fluctuation conductivity of the three compounds shows the same
universal behaviour: for $\epsilon =\ln T/T_c > 0.23$ all the curves bend down
according to the $1/\epsilon^3$ law. This asymptotic behaviour was
theoretically predicted previously for the high temperature region where the
short wavelength fluctuations (SWF) become important.


  We prove, for an arbitrary finite root system, the periodicity conjecture of
Al.B.Zamolodchikov concerning Y-systems, a particular class of functional
relations arising in the theory of thermodynamic Bethe ansatz. Algebraically,
Y-systems can be viewed as families of rational functions defined by certain
birational recurrences formulated in terms of the underlying root system. In
the course of proving periodicity, we obtain explicit formulas for all these
rational functions, which turn out to always be Laurent polynomials.
  In a closely related development, we introduce and study a family of
simplicial complexes that can be associated to arbitrary root systems. In type
A, our construction produces Stasheff's associahedron, whereas in type B, it
gives the Bott-Taubes polytope, or cyclohedron. We enumerate the faces of these
complexes, prove that their geometric realization is always a sphere, and
describe them in concrete combinatorial terms for the classical types ABCD.


  The following dichotomy is established: A finitely generated, complex
Dedekind domain that is not commutative is simple. Weaker versions of this
dichotomy are proved for Dedekind prime rings and hereditary noetherian prime
rings.


  We consider the problem of identifying a parallel Wiener-Hammerstein
structure from Volterra kernels. Methods based on Volterra kernels typically
resort to coupled tensor decompositions of the kernels. However, in the case of
parallel Wiener-Hammerstein systems, such methods require nontrivial
constraints on the factors of the decompositions. In this paper, we propose an
entirely different approach: by using special sampling (operating) points for
the Jacobian of the nonlinear map from past inputs to the output, we can show
that the Jacobian matrix becomes a linear projection of a tensor whose rank is
equal to the number of branches. This representation allows us to solve the
identification problem as a tensor recovery problem.


  Einstein equations for several matter sources in Robertson-Walker and Bianchi
I type metrics, are shown to reduce to a kind of second order nonlinear
ordinary differential equation $\ddot{y}+\alpha f(y)\dot{y}+\beta f(y)\int{f(y)
dy}+\gamma f(y)=0$. Also, it appears in the generalized statistical mechanics
for the most interesting value q=-1. The invariant form of this equation is
imposed and the corresponding nonlocal transformation is obtained. The
linearization of that equation for any $\alpha, \beta$ and $\gamma$ is
presented and for the important case $f=by^n+k$ with $\beta=\alpha ^2
(n+1)/((n+2)^2)$ its explicit general solution is found. Moreover, the form
invariance is applied to yield exact solutions of same other differential
equations.


  Convex optimization recently emerges as a compelling framework for performing
super resolution, garnering significant attention from multiple communities
spanning signal processing, applied mathematics, and optimization. This article
offers a friendly exposition to atomic norm minimization as a canonical convex
approach to solve super resolution problems. The mathematical foundations and
performances guarantees of this approach are presented, and its application in
super resolution image reconstruction for single-molecule fluorescence
microscopy are highlighted.


  Several algorithms for tracking and for primary and secondary vertex
reconstruction have been developed by the ATLAS collaboration following
different approaches. This has allowed a thorough cross-check of the
performances of the algorithms and of the reconstruction software. The results
of the most recent studies on this topic are discussed and compared.


  We use the semi-analytic model (SAM) of galaxy formation and evolution SAG
coupled with the MULTIDARK simulation MDPL2 to study the evolution of the
stellar mass-gas metallicity relation of galaxies (MZR). We test several
implementations of the dependence of the mass loading due to supernovae (SNe).
We find that no evolution in the normalization of the MZR is obtained unless we
introduce an explicit scaling of the reheated and ejected mass with redshift as
$(1+z)^\beta$. The latter is in agreement with results from the FIRE
simulations, and it should encompass small scale properties of the interstellar
medium varying over time, which are not captured in SAMs, as well as other
energy sources in addition to SNe. Increasing $\beta$ leads to stronger
evolution of the MZR normalization; $\beta = 1.9$ reproduces the observed MZR
in the range $0 < z < 3.5$. A stronger redshift dependence of outflows reduces
the levels of star formation at earlier epochs with the consequent decrease of
metal production. This leads to a slower increase of the gas metallicity
compared to the stellar mass build-up. The cold gas can be contaminated either
by receiving a direct injection of the material recycled by stellar winds and
SNe or by gas cooling. The relative role of each process for a given stellar
mass depends on the criterion adopted to regulate the fate of the recycled
material. However, modifying the metal loading of the outflows has mild impact
on the zero-point evolution and does not affect our conclusions.


  We consider the construction of a family $\{K_N\}$ of $3$-dimensional
Koch-type surfaces, with a corresponding family of $3$-dimensional Koch-type
``snowflake analogues" $\{\mathcal{C}_N\}$, where $N>1$ are integers with $N
\not\equiv 0 \,(\bmod\,\, 3)$. We first establish that the Koch surfaces $K_N$
are $s_N$-sets with respect to the $s_N$-dimensional Hausdorff measure, for
$s_N=\log(N^2+2)/\log(N)$ the Hausdorff dimension of each Koch-type surface
$K_N$. Using self-similarity, one deduces that the same result holds for each
Koch-type crystal $\mathcal{C}_N$. We then develop lower and upper
approximation monotonic sequences converging to the $s_N$-dimensional Hausdorff
measure on each Koch-type surface $K_N$, and consequently, one obtains upper
and lower bounds for the Hausdorff measure for each set $\mathcal{C}_N$. As an
application, we consider the realization of Robin boundary value problems over
the Koch-type crystals $\mathcal{C}_N$, for $N>2$.


  This article unifies and generalizes fundamental results related to
$n$-process asynchronous crash-prone distributed computing. More precisely, it
proves that for every $0\leq k \leq n$, assuming that process failures occur
only before the number of participating processes bypasses a predefined
threshold that equals $n-k$ (a participating process is a process that has
executed at least one statement of its code), an asynchronous algorithm exists
that solves consensus for $n$ processes in the presence of $f$ crash failures
if and only if $f \leq k$. In a very simple and interesting way, the "extreme"
case $k=0$ boils down to the celebrated FLP impossibility result (1985, 1987).
Moreover, the second extreme case, namely $k=n$, captures the celebrated mutual
exclusion result by E.W. Dijkstra (1965) that states that mutual exclusion can
be solved for $n$ processes in an asynchronous read/write shared memory system
where any number of processes may crash (but only) before starting to
participate in the algorithm (that is, participation is not required, but once
a process starts participating it may not fail). More generally, the
possibility/impossibility stated above demonstrates that more failures can be
tolerated when they occur earlier in the computation (hence the title).


  In this paper, the complete moment convergence for the partial sums of moving
average processes $\{X_n=\sum_{i=-\infty}^{\infty}a_iY_{i+n},n\ge 1\}$ is
proved under some proper conditions, where $\{Y_i,-\infty<i<\infty\}$ is a
doubly sequence of identically distributed, negatively dependent random
variables under sub-linear expectations and $\{a_i,-\infty<i<\infty\}$ is an
absolutely summable sequence of real numbers. The results established in
sub-linear expectation spaces generalize the corresponding ones in probability
space.


  The problem of small area estimation (SAE) is how to produce reliable
estimates of characteristics of interest such as means, counts, quantiles,
etc., for areas or domains for which only small samples or no samples are
available, and how to assess their precision. The purpose of this paper is to
review and discuss some of the new important developments in small area
estimation methods. Rao [Small Area Estimation (2003)] wrote a very
comprehensive book, which covers all the main developments in this topic until
that time. A few review papers have been written after 2003, but they are
limited in scope. Hence, the focus of this review is on new developments in the
last 7-8 years, but to make the review more self-contained, I also mention
shortly some of the older developments. The review covers both design-based and
model-dependent methods, with the latter methods further classified into
frequentist and Bayesian methods. The style of the paper is similar to the
style of my previous review on SAE published in 2002, explaining the new
problems investigated and describing the proposed solutions, but without
dwelling on theoretical details, which can be found in the original articles. I
hope that this paper will be useful both to researchers who like to learn more
on the research carried out in SAE and to practitioners who might be interested
in the application of the new methods.


  Dance generation, as a branch of human motion generation, has attracted
increasing attention. Recently, a few works attempt to enhance dance
expressiveness, which includes genre matching, beat alignment, and dance
dynamics, from certain aspects. However, the enhancement is quite limited as
they lack comprehensive consideration of the aforementioned three factors. In
this paper, we propose ExpressiveBailando, a novel dance generation method
designed to generate expressive dances, concurrently taking all three factors
into account. Specifically, we mitigate the issue of speed homogenization by
incorporating frequency information into VQ-VAE, thus improving dance dynamics.
Additionally, we integrate music style information by extracting genre- and
beat-related features with a pre-trained music model, hence achieving
improvements in the other two factors. Extensive experimental results
demonstrate that our proposed method can generate dances with high
expressiveness and outperforms existing methods both qualitatively and
quantitatively.


  Supersymmetric elementary string states in the compactified heterotic string
theory are described by small black holes that have zero area event horizon. In
this paper we compute the supersymmetric index of such elementary string states
using gravitational path integral. The dominant contribution to the path
integral comes from an Euclidean rotating black hole solution of the
supergravity theory with a finite area event horizon, but the logarithm of the
index, computed from the saddle point, vanishes. Nevertheless we show that the
solution is singular on certain subspaces of the horizon where higher
derivative corrections can be important, and once the higher derivative
corrections are taken into account the solution could yield a finite result for
the logarithm of the index whose form agrees with the microscopic results up to
an overall numerical constant. While the numerical constant is not determined
in our analysis, we show that it is independent of the details of the
compactification and even the number of non-compact dimensions, in agreement
with the microscopic results.


  We introduce a topology-based nonlinear network model of protein dynamics
with the aim of investigating the interplay of spatial disorder and
nonlinearity. We show that spontaneous localization of energy occurs
generically and is a site-dependent process. Localized modes of nonlinear
origin form spontaneously in the stiffest parts of the structure and display
site-dependent activation energies. Our results provide a straightforward way
for understanding the recently discovered link between protein local stiffness
and enzymatic activity. They strongly suggest that nonlinear phenomena may play
an important role in enzyme function, allowing for energy storage during the
catalytic process.


  We develop a method based on tensor networks to create localized single
particle excitations on top of strongly-correlated quantum spin chains. In
analogy to the problem of creating localized Wannier modes, this is achieved by
optimizing the gauge freedom of momentum excitations on top of matrix product
states. The corresponding wavepackets propagate almost dispersionless. The
time-dependent variational principle is used to scatter two such wavepackets,
and we extract the phase shift from the collision data. We also study
reflection and transmission coefficients of a wavepacket impinging on an
impurity.


  In this fluid dynamics video, we present various aspects of copepod behavior
at low Re.


  We consider doubly-periodic travelling waves at the surface of an infinitely
deep perfect fluid, only subjected to gravity $g$ and resulting from the
nonlinear interaction of two simply periodic travelling waves making an angle
$2\theta $ between them. \newline Denoting by $\mu =gL/c^{2}$ the dimensionless
bifurcation parameter ($L$ is the wave length along the direction of the
travelling wave and $c$ is the velocity of the wave), bifurcation occurs for
$\mu =\cos \theta$. For non-resonant cases, we first give a large family of
formal three-dimensional gravity travelling waves, in the form of an expansion
in powers of the amplitudes of two basic travelling waves. "Diamond waves" are
a particular case of such waves, when they are symmetric with respect to the
direction of propagation.\newline \emph{The main object of the paper is the
proof of existence} of such symmetric waves having the above mentioned
asymptotic expansion. Due to the \emph{occurence of small divisors}, the main
difficulty is the inversion of the linearized operator at a non trivial point,
for applying the Nash Moser theorem. This operator is the sum of a second order
differentiation along a certain direction, and an integro-differential operator
of first order, both depending periodically of coordinates. It is shown that
for almost all angles $\theta $, the 3-dimensional travelling waves bifurcate
for a set of "good" values of the bifurcation parameter having asymptotically a
full measure near the bifurcation curve in the parameter plane $(\theta ,\mu
).$


  The $\mathcal{R}$-height of a semigroup $S$ is the height of the poset of
$\mathcal{R}$-classes of $S,$ i.e. the supremum of the lengths of chains of
$\mathcal{R}$-classes. Given a semigroup $S$ with finite $\mathcal{R}$-height,
we establish bounds on the $\mathcal{R}$-height of bi-ideals, one-sided ideals
and two-sided ideals; in particular, these substructures inherit the property
of having finite $\mathcal{R}$-height. We then investigate whether these bounds
can be attained.


  It was known that one-point functions in the ABJM matrix model (obtained by
applying the localization technique to one-point functions of the half-BPS
Wilson loop operator in the ABJM theory) satisfy the Jacobi-Trudi formula,
which strongly indicates the integrable structure of the system. In this paper,
we identify the integrable structure of two-point functions in the ABJM matrix
model as the two-dimensional Toda lattice hierarchy. The identification implies
infinitely many non-linear differential equations for the generating function
of the two-point functions.


  Scalar-tensor theories of gravity can be formulated in the Jordan or in the
Einstein frame, which are conformally related. The issue of which conformal
frame is physical is a contentious one; we provide a straightforward example
based on gravitational waves in order to clarify the issue.


  We design two mechanisms for the recommender system to collect user ratings.
One is modified Laplace mechanism, and the other is randomized response
mechanism. We prove that they are both differentially private and preserve the
data utility.


  An exact solution is presented for tunneling through a negative-U d-fold
degenerate molecular quantum dot weakly coupled to electrical leads. The tunnel
current exhibits hysteresis if the level degeneracy of the negative-U dot is
larger than two (d>2). Switching occurs in the voltage range V1 < V < V2 as a
result of attractive electron correlations in the molecule, which open up a new
conducting channel when the voltage is above the threshold bias voltage V2.
Once this current has been established, the extra channel remains open as the
voltage is reduced down to the lower threshold voltage V1. Possible
realizations of the bi-stable molecular quantum dots are fullerenes, especially
C60, and mixed-valence compounds.


  We give in this short report a very simple proof that arbitrary random
variable with Borelian distribution in separable Banach space belongs with
probability one to a pre-image of some linear compact non-random operator.


  Spin glasses are canonical examples of complex matter. Although much about
their structure remains uncertain, they inform the description of a wide array
of complex phenomena, ranging from magnetic ordering in metals with impurities
to aspects of evolution, protein folding, climate models, combinatorial
optimization, and artificial intelligence. Indeed, spin glass theory forms a
mathematical basis for neuromorphic computing and brain modeling. Advancing
experimental insight into their structure requires repeatable control over
microscopic degrees of freedom. Here, we achieve this at the atomic level using
a quantum-optical system comprised of ultracold gases of atoms coupled via
photons resonating within a confocal cavity. This active quantum gas microscope
realizes an unusual type of transverse-field vector spin glass with all-to-all
connectivity. Spin configurations are observed in cavity emission and reveal
the emergence of replica symmetry breaking and nascent ultrametric structure as
signatures of spin-glass order. The driven-dissipative nature of the system
manifests as a nonthermal Parisi distribution, in qualitative correspondence
with Monte Carlo simulations. The controllability provided by this new
spin-glass system, potentially down to the quantum-spin-level, enables the
study of spin-glass physics in novel regimes with application to quantum neural
network computing.


  Given a unitary representation of a Lie group $G$ on a Hilbert space
$\mathcal{H}$, we develop the theory of $G$-invariant self-adjoint extensions
of symmetric operators both using von Neumann's theorem and the theory of
quadratic forms. We also analyze the relation between the reduction theory of
the unitary representation and the reduction of the $G$-invariant unbounded
operator. We also prove a $G$-invariant version of the representation theorem
for quadratic forms.
  The previous results are applied to the study of $G$-invariant self-adjoint
extensions of the Laplace-Beltrami operator on a smooth Riemannian manifold
with boundary on which the group $G$ acts. These extensions are labeled by
admissible unitaries $U$ acting on the $L^2$-space at the boundary and having
spectral gap at $-1$. It is shown that if the unitary representation $V$ of the
symmetry group $G$ is traceable, then the self-adjoint extension of the
Laplace-Beltrami operator determined by $U$ is $G$-invariant if $U$ and $V$
commute at the boundary. Various significant examples are discussed at the end.


  Medical image segmentation, or computing voxelwise semantic masks, is a
fundamental yet challenging task to compute a voxel-level semantic mask. To
increase the ability of encoder-decoder neural networks to perform this task
across large clinical cohorts, contrastive learning provides an opportunity to
stabilize model initialization and enhance encoders without labels. However,
multiple target objects (with different semantic meanings) may exist in a
single image, which poses a problem for adapting traditional contrastive
learning methods from prevalent 'image-level classification' to 'pixel-level
segmentation'. In this paper, we propose a simple semantic-aware contrastive
learning approach leveraging attention masks to advance multi-object semantic
segmentation. Briefly, we embed different semantic objects to different
clusters rather than the traditional image-level embeddings. We evaluate our
proposed method on a multi-organ medical image segmentation task with both
in-house data and MICCAI Challenge 2015 BTCV datasets. Compared with current
state-of-the-art training strategies, our proposed pipeline yields a
substantial improvement of 5.53% and 6.09% on Dice score for both medical image
segmentation cohorts respectively (p-value<0.01). The performance of the
proposed method is further assessed on natural images via the PASCAL VOC 2012
dataset, and achieves a substantial improvement of 2.75% on mIoU
(p-value<0.01).


  There are many conceivable possibilities of embedding the MSSM in string
theory. These proceedings describe an approach which is based on grand
unification in higher dimensions. This allows one to obtain global
string-derived models with the exact MSSM spectrum and built-in gauge coupling
unification. It turns out that these models exhibit various appealing features
such as (i) see-saw suppressed neutrino masses, (ii) an order one top Yukawa
coupling and potentially realistic flavor structures, (iii) non-Abelian
discrete flavor symmetries relaxing the supersymmetric flavor problem, (iv) a
hidden sector whose scale of strong dynamics is consistent with TeV-scale soft
masses, and (v) a solution to the mu-problem. The crucial and unexpected
property of these features is that they are not put in by hand nor explicitly
searched for but happen to occur automatically, and might thus be viewed as
"stringy surprises".


  Entanglement is closely related to some fundamental features of the dynamics
of composite quantum systems: quantum entanglement enhances the "speed" of
evolution of certain quantum states, as measured by the time required to reach
an orthogonal state. The concept of "speed" of quantum evolution constitutes an
important ingredient in any attempt to determine the fundamental limits that
basic physical laws impose on how fast a physical system can process or
transmit information. Here we explore the relationship between entanglement and
the speed of quantum evolution in the context of the quantum brachistochrone
problem. Given an initial and a final state of a composite system we consider
the amount of entanglement associated with the brachistochrone evolution
between those states, showing that entanglement is an essential resource to
achieve the alluded time-optimal quantum evolution.


  We develop axiomatics of highest weight categories and quasi-hereditary
algebras in order to incorporate two semi-infinite situations which are in
Ringel duality with each other; the underlying posets are either upper finite
or lower finite. We also consider various more general sorts of stratified
categories. In the upper finite cases, we give an alternative characterization
of these categories in terms of based quasi-hereditary algebras and based
stratified algebras, which are certain locally unital algebras possessing
triangular bases.


  A subset $X$ in the $d$-dimensional Euclidean space is called a $k$-distance
set if there are exactly $k$ distances between two distinct points in $X$.
Einhorn and Schoenberg conjectured that the vertices of the regular icosahedron
is the only 12-point three-distance set in $\mathbb{R}^3$ up to isomorphism. In
this paper, we prove the uniqueness of 12-point three-distance sets in
$\mathbb{R}^3$.


  Photoelectrochemical solar water splitting is a promising approach to convert
solar energy into sustainable hydrogen fuel using semiconductor electrodes. Due
to their visible light absorption properties, oxynitrides have shown to be
attractive photocatalysts for this application. In this study, the influence of
the preparation method of CaNbO2N particles on their morphological and optical
properties, and thereby their photoelectrochemical performance, is
investigated. The best performing CaNbO2N photoanode is produced by ammonolysis
of Nb enriched calcium niobium oxide. The enhanced photoactivity arises from an
enlarged surface area and superior visible light absorption properties. The
photoactivity of this photoanode was further enhanced by photodeposition of
Co-Pi co-catalyst and by atomic layer deposition of an Al2O3 overlayer. A
photocurrent density of 70 microA.cm-2 at 1.23 V vs RHE was achieved. The
observed enhancement of the photoelectrochemical performance after Co-Pi/Al2O3
deposition is the combined effect of the improved kinetics of oxygen evolution
due to the Co-Pi co-catalyst and the reduced surface recombination of the
photogenerated carriers at the Al2O3 surface layer.


  We theoretically study divergent fluctuations of dynamical events at
non-ergodic transitions. We first focus on the finding that a non-ergodic
transition can be described as a saddle connection bifurcation of an order
parameter for a time correlation function. Then, following the basic idea of
Ginzburg-Landau theory for critical phenomena, we construct a phenomenological
framework with which we can determine the critical statistical properties at
saddle connection bifurcation points. Employing this framework, we analyze a
model by considering the fluctuations of an instanton in space-time
configurations of the order parameter. We then obtain the exponents
characterizing the divergences of the length scale, the time scale and the
amplitude of the fluctuations of the order parameter at the saddle connection
bifurcation. The results are to be compared with those of previous studies of
the four-point dynamic susceptibility at non-ergodic transitions in glassy
systems.


  We present a manifestly Lorentz- and SO(2)-Duality-invariant local Quantum
Field Theory of electric charges, Dirac magnetic monopoles and dyons. The
manifest invariances are achieved by means of the PST-mechanism. The dynamics
for classical point particles is described by an action functional living on a
circle, if the Dirac-Schwinger quantization condition for electric and magnetic
charges holds. The inconsistent classical field theory depends on an arbitrary,
but fixed, external vector field, a generalization of the Dirac-string.
Nevertheless, the Quantum Field Theory, obtained from this classical action via
a functional integral approach, turns out to be independent of the particular
vector field chosen, and thus consistent, if the Dirac-Schwinger quantization
condition holds. We provide explicit expressions for the generating functionals
of observables, proving that they are Dirac-string independent. Since
Lorentz-invariance is manifest at each step, the quantum theory admits also a
manifestly diffeomorphism invariant coupling to external gravity. Relations
with previous formulations, and with SO(2)--non invariant theories are
clarified.


  Large language models (LLMs) have emerged as a cornerstone in real-world
applications with lengthy streaming inputs (e.g., LLM-driven agents). However,
existing LLMs, pre-trained on sequences with a restricted maximum length,
cannot process longer sequences due to the out-of-domain and distraction
issues. Common solutions often involve continual pre-training on longer
sequences, which will introduce expensive computational overhead and
uncontrollable change in model capabilities. In this paper, we unveil the
intrinsic capacity of LLMs for understanding extremely long sequences without
any fine-tuning. To this end, we introduce a training-free memory-based method,
InfLLM. Specifically, InfLLM stores distant contexts into additional memory
units and employs an efficient mechanism to lookup token-relevant units for
attention computation. Thereby, InfLLM allows LLMs to efficiently process long
sequences with a limited context window and well capture long-distance
dependencies. Without any training, InfLLM enables LLMs that are pre-trained on
sequences consisting of a few thousand tokens to achieve comparable performance
with competitive baselines that continually train these LLMs on long sequences.
Even when the sequence length is scaled to $1,024$K, InfLLM still effectively
captures long-distance dependencies. Our code can be found in
\url{https://github.com/thunlp/InfLLM}.


  In a computational study we reveal a novel dynamical instability of
excitation waves in the heartmuscle. The instability manifests itself as
gradual local increase in the duration of the actionpotential which causes
formation and hypermeandering of spiral waves. The mechanism is causedby
stretch-activated currents that cause wave front-tail collisions and beat to
beat elongation of theaction potential duration due to biexcitability. We
discuss the importance of the instability for theonset and dynamics of cardiac
arrhythmias.


  The increasing usage of machine learning models raises the question of the
reliability of these models. The current practice of testing with limited data
is often insufficient. In this paper, we provide a framework for automated test
data synthesis to test black-box ML/DL models. We address an important
challenge of generating realistic user-controllable data with model agnostic
coverage criteria to test a varied set of properties, essentially to increase
trust in machine learning models. We experimentally demonstrate the
effectiveness of our technique.


  For any n-dimensional compact Riemannian Manifold $M$ with smooth metric $g$,
by employing the heat kernel embedding introduced by B\'erard-Besson-Gallot'94,
we intrinsically construct a canonical family of conformal embeddings
$C_{t,k}$: $M\rightarrow\mathbb{R}^{q(t)}$, with $t>0$ sufficiently small,
$q(t)\gg t^{-\frac{n}{2}}$, and $k$ as a function of $O(t^l)$ in proper sense.
Our approach involves finding all these canonical conformal embeddings, which
shows the distinctions from the isometric embeddings introduced by Wang-Zhu'15.


  Inspired by a recent paper of I. Grama, E. Le Page and M. Peign\'e, we
consider a sequence $(g_n)_{n \geq 1}$ of i.i.d. random $d\times d$-matrices
with non-negative entries and study the fluctuations of the process $(\log
\vert g_n\cdots g_1\cdot x\vert )_{n \geq 1}$ for any non-zero vector $x$ in
$\mathbb R^d$ with non-negative coordinates. Our method involves approximating
this process by a martingale and studying harmonic functions for its
restriction to the upper half line. Under certain conditions, the probability
for this process to stay in the upper half real line up to time $n$ decreases
as $c \over \sqrt n$ for some positive constant $c$.


  We derive the field correction to the Berry curvature of Bloch electrons,
which can be traced back to a positional shift due to the interband mixing
induced by external electromagnetic fields. The resulting semiclassical
dynamics is accurate to second order in the fields, in the same form as before,
provided that the wave packet energy is derived up to the same order. As
applications, we discuss the orbital magnetoelectric polarizability and predict
nonlinear anomalous Hall effects.


  In this paper, we enriched Ant Colony Optimization (ACO) with interval
outranking to develop a novel multiobjective ACO optimizer to approach problems
with many objective functions. This proposal is suitable if the preferences of
the Decision Maker (DM) can be modeled through outranking relations. The
introduced algorithm (named Interval Outranking-based ACO, IO-ACO) is the first
ant-colony optimizer that embeds an outranking model to bear vagueness and
ill-definition of DM preferences. This capacity is the most differentiating
feature of IO-ACO because this issue is highly relevant in practice. IO-ACO
biases the search towards the Region of Interest (RoI), the privileged zone of
the Pareto frontier containing the solutions that better match the DM
preferences. Two widely studied benchmarks were utilized to measure the
efficiency of IO-ACO, i.e., the DTLZ and WFG test suites. Accordingly, IO-ACO
was compared with two competitive many-objective optimizers: The
Indicator-based Many-Objective ACO and the Multiobjective Evolutionary
Algorithm Based on Decomposition. The numerical results show that IO-ACO
approximates the Region of Interest (RoI) better than the leading
metaheuristics based on approximating the Pareto frontier alone.


  Elasticity is a cloud property that enables applications and its execution
systems to dynamically acquire and release shared computational resources on
demand. Moreover, it unfolds the advantage of economies of scale in the cloud
through a drop in the average costs of these shared resources. However, it is
still an open challenge to achieve a perfect match between resource demand and
provision in autonomous elasticity management. Resource adaptation decisions
essentially involve a trade-off between economics and performance, which
produces a gap between the ideal and actual resource provisioning. This gap, if
not properly managed, can negatively impact the aggregate utility of a cloud
customer in the long run. To address this limitation, we propose a technical
debt-aware learning approach for autonomous elasticity management based on a
reinforcement learning of elasticity debts in resource provisioning; the
adaptation pursues strategic decisions that trades off economics against
performance. We extend CloudSim and Burlap to evaluate our approach. The
evaluation shows that a reinforcement learning of technical debts in elasticity
obtains a higher utility for a cloud customer, while conforming expected levels
of performance.


  We give a short direct proof for the degeneration formula of Gromov-Witten
invariants including its cycle version for degenerations with smooth singular
locus in the setting of minimal/basic stable log maps of Abramovich-Chen, Chen,
Gross-Siebert.


  Hyperledger Fabric (HLF) is a modular and extensible permissioned blockchain
platform released to open-source and hosted by the Linux Foundation. The
platform's design exhibits principles required by enterprise grade business
applications like supply-chains, financial transactions, asset management, food
safety, and many more. For that end HLF introduces several innovations, two of
which are smart contracts in general purpose languages (\emph{chaincode} in
HLF), and flexible endorsement policies, which govern whether a transaction is
considered valid.
  Typical blockchain applications are comprised of two tiers: the first tier
focuses on the modelling of the data schema and embedding of business rules
into the blockchain by means of smart contracts (\emph{chaincode}) and
endorsment policies; and the second tier uses the SDK (Software Development
Kit) provided by HLF to implement client side application logic.
  However there is a gap between the two tiers that hinders the rapid adoption
of changes in the chaincode and endorsement policies within the client SDK.
Currently, the chaincode location and endorsement policies are statically
configured into the client SDK. This limits the reliability and availability of
the client in the event of changes in the platform, and makes the platform more
difficult to use. In this work we address and bridge the gap by describing the
design and implementation of \emph{Service Discovery}.
  \emph{Service Discovery} provides APIs which allow dynamic discovery of the
configuration required for the client SDK to interact with the platform,
alleviating the client from the burden of maintaining it. This enables the
client to rapidly adapt to changes in the platform, thus significantly
improving the reliability of the application layer. It also makes the HLF
platform more consumable, simplifying the job of creating blockchain
applications.


  We study $\alpha$-adic expansions of numbers in an extension field, that is
to say, left infinite representations of numbers in the positional numeration
system with the base $\alpha$, where $\alpha$ is an algebraic conjugate of a
Pisot number $\beta$. Based on a result of Bertrand and Schmidt, we prove that
a number belongs to $\mathbb{Q}(\alpha)$ if and only if it has an eventually
periodic $\alpha$-expansion. Then we consider $\alpha$-adic expansions of
elements of the extension ring $\mathbb{Z}[\alpha^{-1}]$ when $\beta$ satisfies
the so-called Finiteness property (F). In the particular case that $\beta$ is a
quadratic Pisot unit, we inspect the unicity and/or multiplicity of
$\alpha$-adic expansions of elements of $\mathbb{Z}[\alpha^{-1}]$. We also
provide algorithms to generate $\alpha$-adic expansions of rational numbers.


  The accuracy of the Arthurs-Kelly model of a simultaneous measurement of
position and momentum is analysed using concepts developed by Braginsky and
Khalili in the context of measurements of a single quantum observable. A
distinction is made between the errors of retrodiction and prediction. It is
shown that the distribution of measured values coincides with the initial state
Husimi function when the retrodictive accuracy is maximised, and that it is
related to the final state anti-Husimi function (the P representation of
quantum optics) when the predictive accuracy is maximised. The disturbance of
the system by the measurement is also discussed. A class of minimally
disturbing measurements is characterised. It is shown that the distribution of
measured values then coincides with one of the smoothed Wigner functions
described by Cartwright.


  Let $(X,Y)$ be a random couple in $S\times T$ with unknown distribution $P$
and $(X_1,Y_1),...,(X_n,Y_n)$ be i.i.d. copies of $(X,Y).$ Denote $P_n$ the
empirical distribution of $(X_1,Y_1),...,(X_n,Y_n).$ Let $h_1,...,h_N:S\mapsto
[-1,1]$ be a dictionary that consists of $N$ functions. For $\lambda \in
{\mathbb{R}}^N,$ denote $f_{\lambda}:=\sum_{j=1}^N\lambda_jh_j.$ Let
$\ell:T\times {\mathbb{R}}\mapsto {\mathbb{R}}$ be a given loss function and
suppose it is convex with respect to the second variable. Let $(\ell \bullet
f)(x,y):=\ell(y;f(x)).$ Finally, let $\Lambda \subset {\mathbb{R}}^N$ be the
simplex of all probability distributions on $\{1,...,N\}.$ Consider the
following penalized empirical risk minimization problem
\begin{eqnarray*}\hat{\lambda}^{\varepsilon}:={\mathop {argmin}_{\lambda\in
\Lambda}}\Biggl[P_n(\ell \bullet f_{\lambda})+\varepsilon
\sum_{j=1}^N\lambda_j\log \lambda_j\Biggr]\end{eqnarray*} along with its
distribution dependent version \begin{eqnarray*}\lambda^{\varepsilon}:={\mathop
{argmin}_{\lambda\in \Lambda}}\Biggl[P(\ell \bullet f_{\lambda})+\varepsilon
\sum_{j=1}^N\lambda_j\log \lambda_j\Biggr],\end{eqnarray*} where
$\varepsilon\geq 0$ is a regularization parameter. It is proved that the
``approximate sparsity'' of $\lambda^{\varepsilon}$ implies the ``approximate
sparsity'' of $\hat{\lambda}^{\varepsilon}$ and the impact of ``sparsity'' on
bounding the excess risk of the empirical solution is explored. Similar results
are also discussed in the case of entropy penalized density estimation.


  We investigate $(2+1)$-dimensional discretized directed polymers in Gaussian
random media. By numerically calculating the probability distribution function
of overlap between two independent and identical systems on a common random
potential, we show that there is no replica symmetry breaking. We also show
that while the mean-squared displacement of one polymer end exhibits
superdiffusive behavior, the mean-squared relative distance of two polymer ends
exhibits subdiffusive behavior.


  We discuss the compactification of type I strings on a torus with additional
background gauge flux on the D9-branes. The solutions to the cancellation of
the RR tadpoles display various phenomenologically attractive features:
supersymmetry breaking, chiral fermions and the opportunity to reduce the rank
of the gauge group as desired. We also point out the equivalence of the concept
of various different background fields and noncommutative deformations of the
geometry on the individual D9-branes by constructing the relevant boundary
states to describe such objects.


  Time harmonic inverse scattering using accurate forward models is often
computationally expensive. On the other hand, the use of computationally
efficient solvers, such as the Born approximation, may fail if the targets do
not satisfy the assumptions of the simplified model. In the Bayesian framework
for inverse problems, one can construct a statistical model for the errors that
are induced when approximate solvers are used, and hence increase the domain of
applicability of the approximate model. In this paper, we investigate the error
structure that is induced by the Born approximation and show that the Bayesian
approximation error approach can be used to partially recover from these
errors. In particular, we study the model problem of reconstruction of the
index of refraction of a penetrable medium from measurements of the far field
pattern of the scattered wave.


  The electronic structure of Co/Cu(001) and Fe/Cr(001) magnetic multilayers
has been investigated within the local density approximation combined with
dynamical mean field theory. Our calculation shows enhanced density of states
at the Fermi level, suggesting that electronic correlations might play an
important role in the transport properties of multilayers.


  We review constraints on additional Z' bosons predicted in supersymmetric
(SUSY) E_6 models from electroweak experiments - Z-pole experiments, mW
measurements and the low-energy neutral current (LENC) experiments. Four
representative models - \chi,\psi, \eta, \nu models - are studied in some
detail. We find that the improved data of parity violation in cesium atom,
which is 2.2-\sigma away from the Standard Model (SM) prediction, could be
explained by the exchange of the heavy mass eigenstate Z_2 in the intermediate
state. The improvement over the SM can be found in \chi, \eta, \nu models,
where the total \chi^2 of the fit to the 26 data points decreases by about five
units, owing to the better fit to the atomic parity violation. Impacts of the
kinetic mixing between the U(1)_Y and U(1)' gauge bosons on the \chi^2-analysis
are studied. We find that the Z' model with (\beta_E, \delta)=(-\pi/4,0.2),
where \beta_E is the mixing angle between Z_\chi and Z_\psi bosons and \delta
denotes the kinetic mixing, shows the most excellent fit to the data: the total
\chi^2 decreases by about seven units as compared to the SM. We introduce the
effective mixing parameter \zeta, a combination of the mass and the kinetic
mixing parameters. The 95% CL lower mass bound of Z_2 can be shown as a
function of \zeta. A theoretical prediction on \zeta and the U(1)'gauge
coupling g_E is studied for the \chi,\psi,\eta and \nu models by assuming the
minimal particle content of the SUSY E_6 models.


  Both CDF and D{\O}experiments have been searching for evidence of physics
beyond the standard model (SM) using the Tevatron $p\bar{p}$ collider at
Fermilab. We report on recent searches in the $B$ flavor sector, especially
decays via flavor changing neutral current processes (FCNC), $B^0_{(s)} \to
e^+\mu^-$ and $B^0_{s} to \mu^+ \mu^-$, at the Tevatron.


  In this comment, we show that the model introduced in Hess et al. Phys. Rev.
Lett. {\bf 130}, 207001 (2023) fails the topological gap protocol (TGP)
(Pikulin et al., arXiv:2103.12217 and M. Aghaee et al., Phys. Rev. B 107,
245424 (2023)). In addition, we discuss this model in the broader context of
how the TGP has been benchmarked.


  The hypercontractivity is proved for the Markov semigroup associated to a
class of finite/infinite dimensional stochastic Hamiltonian systems.
  Consequently, the Markov semigroup is exponentially convergent to the
invariant probability measure in entropy (thus, also in $L^2$), and is compact
for large time. Since the log-Sobolev inequality is invalid for the associated
Dirichlet form, we introduce a general result on the hypercontractivity using
the Harnack inequality with power. The main results are illustrated by concrete
examples.


  We present a method to identify distant solar system objects in long-term
wide-field asteroid survey data, and conduct a search for them in the
Pan-STARRS1 (PS1) image data acquired from 2010 to mid-2015. We demonstrate
that our method is able to find multi-opposition orbital links, and we present
the resulting orbital distributions which consist of 154 Centaurs, 255
classical Trans-Neptunian Objects (TNOs), 121 resonant TNOs, 89 Scattered Disc
Objects (SDOs) and 10 comets. Our results show more than half of these are new
discoveries, including a newly discovered 19th magnitude TNO. Our identified
objects do not show clustering in their argument of perihelia, which if
present, might support the existence of a large unknown planetary-sized object
in the outer solar system.


  Audio is an important medium in people's daily life, hidden information can
be embedded into audio for covert communication. Current audio information
hiding techniques can be roughly classed into time domain-based and transform
domain-based techniques. Time domain-based techniques have large hiding
capacity but low imperceptibility. Transform domain-based techniques have
better imperceptibility, but the hiding capacity is poor. This paper proposes a
new audio information hiding technique which shows high hiding capacity and
good imperceptibility. The proposed audio information hiding method takes the
original audio signal as input and obtains the audio signal embedded with
hidden information (called stego audio) through the training of our private
automatic speech recognition (ASR) model. Without knowing the internal
parameters and structure of the private model, the hidden information can be
extracted by the private model but cannot be extracted by public models. We use
four other ASR models to extract the hidden information on the stego audios to
evaluate the security of the private model. The experimental results show that
the proposed audio information hiding technique has a high hiding capacity of
48 cps with good imperceptibility and high security. In addition, our proposed
adversarial audio can be used to activate an intrinsic backdoor of DNN-based
ASR models, which brings a serious threat to intelligent speakers.


  Every attack begins with gathering information about the target. The entry
point for network breaches are often vulnerabilities in internet facing
websites, which often rely on an off-the-shelf Content Management System (CMS).
Bot networks and human attackers alike rely on automated scanners to gather
information about the CMS software installed and potential vulnerabilities. To
increase the security of websites using a CMS, it is desirable to make the use
of CMS scanners less reliable. The aim of this work is to extend the current
knowledge about cyber deception in regard to CMS. To demonstrate this, a
WordPress Plugin called 'SCANTRAP' was created, which uses simulation and
dissimulation in regards to plugins, themes, versions, and users. We found that
the resulting plugin is capable of obfuscating real information and to a
certain extent inject false information to the output of one of the most
popular WordPress scanners, WPScan, without limiting the legitimate
functionality of the WordPress installation.


  The authors introduce a general mechanism, based on electrostatic and
magnetostatic considerations, for designing three-dimensional isotopic
metamaterials that possess an enhanced refractive index over an extremely large
frequency range. The mechanism allows nearly independent control of effective
electric permittivity and magnetic permeability without the use of resonant
elements.


  Since 1984, many authors have studied the dynamics of maps of the form
$\mathcal{E}_a(z) = e^z - a$, with $a > 1$. It is now well-known that the Julia
set of such a map has an intricate topological structure known as a Cantor
bouquet, and much is known about the dynamical properties of these functions.
  In recent papers some of these ideas have been generalised to a class of
quasiregular maps in $\mathbb{R}^3$, which, in a precise sense, is analogous to
the class of maps of the form $\mathcal{E}_a$. Our goal in this paper is to
make similar generalisations in $\mathbb{R}^2$. In particular, we show that
there is a large class of continuous maps, which, in general, are not even
quasiregular, but are closely analogous to the map $\mathcal{E}_a$, and have
very similar dynamical properties. In some sense this shows that many of the
interesting dynamical properties of the map $\mathcal{E}_a$ arise from its
elementary function theoretic structure, rather than as a result of
analyticity.


  We have used the Nancay Radio Telescope to obtain new global HI data for 16
giant low surface brightness (LSB) galaxies. Our targets have optical
luminosities and disk scale lengths at the high end for spiral galaxies
(L_B~10^10 Lsun and h_r>~6 kpc for H_0=75 km/s/Mpc), but they have diffuse
stellar disks, with mean disk surface brightnesses ~1 magnitude or more fainter
than normal giant spirals. Thirteen of the galaxies previously had been
detected in HI by other workers, but the published HI observations were either
confused, resolved by the telescope beam, of low signal-to-noise, or showed
significant discrepancies between different authors. For the other 3 galaxies,
no HI data were previously available. Several of the galaxies were resolved by
the Nancay 3.6' E-W beam, so global parameters were derived from multiple-point
mapping observations. Typical HI masses for our sample are ~10^10 Msun, with
M_HI/L_B=0.3-1.7 (in solar units). All of the observed galaxies have published
optical surface photometry, and we have compiled key optical measurements for
these objects from the literature. We frequently find significant variations
among physical parameters of giant LSB galaxies reported by various workers.


  We investigate the transition of the polarized photon structure function
$g_1^\gamma(x,Q^2,P^2)$ when the target photon shifts from on-shell ($P^2=0$)
to far off-shell ($P^2\gg \Lambda^2$) region. The analysis is performed to the
next-to-leading order in QCD. The first moment of $g_1^\gamma$ which vanishes
for the real photon, turns to be a negative value when target photon becomes
off-shell. The explicit $P^2$-dependence of the first moment sum rule as well
as of the structure function $g_1^\gamma(x,Q^2,P^2)$ as a function of $x$ is
studied in the framework of the vector meson dominance model.


  In [5], Elnitsky constructed three elegant bijections between classes of
reduced words for Type $\mathrm{A}$, $\mathrm{B}$ and $\mathrm{D}$ families of
Coxeter groups and certain tilings of polygons. This paper offers a particular
generalization of this concept to all finite Coxeter Groups in terms of
embeddings into the Symmetric Group.
  [5] Elnitsky, Serge. Rhombic tilings of polygons and classes of reduced words
in Coxeter groups. PhD dissertation, University of Michigan, 1993.


  We discuss the unique opportunities for maser astrometry with the inclusion
of the Square Kilometre Array (SKA) in Very Long Baseline Interferometry (VLBI)
networks. The first phase of the SKA will enable observations of hydroxyl and
methanol masers, positioning the latter to an accuracy of 5 microarcseconds,
and the second phase may allow water maser observations. These observations
will provide trigonometric distances with errors as small as 1%. The unrivalled
sensitivity of the SKA will enable large-scale surveys and, through joint
operations, will turn any VLBI network into a fast astrometry device. Both
evolved stars and high mass star formation regions will be accessible
throughout the (Southern) Milky Way, completing our understanding of the
content, dynamics and history of our Galaxy. Maser velocities and proper
motions will be measurable in the Local Group of galaxies and beyond, providing
new insights into their kinematics and evolution.


  We are reporting on terahertz generation from organic crystal BNA using a
1.15 to 1.55 um near infrared pump. We observed a very large emission spectrum
extending up to 7 THz, compared to 2.5 THz from Ti:Sa pump in previous reports.
The maximum optical-to-THz conversion efficiency in our experiment was 0.8% at
1 kHz repetition rate and without saturation leading to a peak electric field
of 1 GV/m. Our results show pronounced phase matching privilege for intense
terahertz generation using a pump in the 1.15 to 1.25 um range where high
energy near infrared pump sources operate.


  In this paper the notion of Markov move from Algebraic Statistics is used to
analyze the weighted kappa indices in rater agreement problems. In particular,
the problem of the maximum kappa and its dependence on the choice of the
weighting schemes are discussed. The Markov moves are also used in a simulated
annealing algorithm to actually find the configuration of maximum agreement.


  In this paper, we study a kernel smoothing approach for denoising a tensor
field. Particularly, both simulation studies and theoretical analysis are
conducted to understand the effects of the noise structure and the structure of
the tensor field on the performance of different smoothers arising from using
different metrics, viz., Euclidean, log-Euclidean and affine invariant metrics.
We also study the Rician noise model and compare two regression estimators of
diffusion tensors based on raw diffusion weighted imaging data at each voxel.


  We introduce a theoretical approach to determine the spin structure of
harmonically trapped atoms with two-body zero-range interactions subject to an
equal mixture of Rashba and Dresselhaus spin-orbit coupling created through
Raman coupling of atomic hyperfine states. The spin structure of bosonic and
fermionic two-particle systems with finite and infinite two-body interaction
strength $g$ is calculated. Taking advantage of the fact that the $N$-boson and
$N$-fermion systems with infinitely large coupling strength $g$ are
analytically solvable for vanishing spin-orbit coupling strength $k_{so}$ and
vanishing Raman coupling strength $\Omega$, we develop an effective spin model
that is accurate to second-order in $\Omega$ for any $k_{so}$ and infinite $g$.
The three- and four-particle systems are considered explicitly. It is shown
that the effective spin Hamiltonian, which contains a Heisenberg exchange term
and an anisotropic Dzyaloshinskii-Moriya exchange term, describes the
transitions that these systems undergo with the change of $k_{so}$ as a
competition between independent spin dynamics and nearest-neighbor spin
interactions.


  In order to improve the classification accuracy of transient stability
assessment of power systems, a novel method based on local learning machine and
an improved bacterial colony chemotaxis (BCC) algorithm is proposed, where
local learning machine(LLM) is used to build a TSA model. Considering the
possible real-time information provided by PMU, a group of system-level
classification features extracted from the power system operation parameters
are employed as inputs, and the stability result is used as output of the LLM
model. The relation ship between input and output is trained and the ideal
model is obtained by applying the improved BCC combined with chaotic search
strategy to determine the optimal parameters of LLM automatically. The
effectiveness of the proposed method is shown by the simulation results on the
New England 10-unit-39-bus power system.


  We consider an approach to credit risk in which the information about the
time of bankruptcy is modelled using a Brownian bridge that starts at zero and
is conditioned to equal zero when the default occurs. This raises the question
whether the default can be foreseen by observing the evolution of the bridge
process. Unlike in most standard models for credit risk, we allow the
distribution of the default time to be singular. Using a well known fact from
parabolic potential theory, we provide a sufficient condition for its
predictability.


  This paper studies the numerical deformation that time-domain integration
(TDI) methods introduce to the shape of the coupling between the dynamic modes
and variables of power system models. To this aim, we employ a small-signal
stability analysis (SSSA)-based framework where such mode-shape deformation is
efficiently identified by comparing the modal participation factors (PFs) of
the power system model with the PFs of the discrete-time system that is derived
from the application of the TDI method. The proposed approach is illustrated
for TDI methods commonly used in dynamic power system calculations.


  Understanding the fundamental dynamics of topological vortex and antivortex
naturally formed in micro/nanoscale ferromagnetic building blocks under
external perturbations is crucial to magnetic vortex based information
processing and spintronic devices. All previous studies have focused on
magnetic vortex-core switching via external magnetic fields, spin-polarized
currents, or spin waves, which have largely prohibited the investigation of
novel spin configurations that could emerge from the ground states in
ferromagnetic disks and their underlying dynamics. Here, we report in situ
visualization of femtosecond laser quenching induced magnetic vortex change in
various symmetric ferromagnetic Permalloy disks by Lorentz phase imaging using
4D electron microscopy. Besides the switching of magnetic vortex chirality and
polarity, we observed with distinct occurrence frequencies a plenitude of
complex magnetic structures that have never been observed by magnetic field or
current assisted switching. These complex magnetic structures consist of a
number of newly created topological magnetic defects (vortex and antivortex)
strictly conserving the topological winding number, demonstrating the direct
impact of topological invariant on the magnetization dynamics in ferromagnetic
disks. Their spin configurations show mirror or rotation symmetry due to the
geometrical confinement of the disks. Combined micromagnetic simulations with
the experimental observations reveal the underlying magnetization dynamics and
formation mechanism of the optical quenching induced complex magnetic
structures. Their distinct occurrence rates are pertinent to their
formation-growth energetics and pinning effects at the disk edge. Based on
these findings, we propose a paradigm of optical-quenching-assisted fast
switching of vortex cores for the control of magnetic vortex based information
recording and spintronic devices.


  In this paper we show that the critical Eisenstein series of weight 2,
E_{2}^{crit_{p}}, is smooth in the eigencurve C(l), where l is a prime. We also
show that E_{2}^{crit_{p},ord_{l}} is smooth in the full eigencurve C^{full}(l)
and E_{2}^{crit_{p},ord_{l_{1}},ord_{l_{2}}} is non-smooth in the full
eigencurve C^{full}(l_{1}l_{2}). Further, we show that, E_{2}^{crit_{p}}, is
\'etale over the weight space in the eigencurve C(l). As a consequence, we show
that level lowering conjecture of Paulin fails to hold at
E_{2}^{crit_{p},ord_{l}}.


  The Lamb Shift (LS) of Hydrogenlike atom is evaluated by a simple method of
quantum electrodynamics in noncovariant form, based on the relativistic
stationary Schr\"odinger equation. An induced term proportional to
$\overrightarrow{p}^4$ in the effective Hamiltonian is emphasized. Perturbative
calculation of second order leads to the LS of $ 1S_{1/2}$ state and that of
$2S_{1/2}-2P_{1/2}$ states in H atom with the high accuracy within 0.1%


  The joint detection of GW~170817/GRB 170817 confirmed the long-standing
theory that binary neutron star mergers produce short gamma-ray burst (sGRB)
jets that can successfully break out of the surrounding ejecta. At the same
time, the association with a kilonova provided unprecedented information
regarding the physical properties (such as masses and velocities) of the
different ejecta constituents. Combining this knowledge with the observed
luminosities and durations of cosmological sGRBs detected by the Burst Alert
Telescope (BAT) onboard the Neil Gehrels Swift Observatory, we revisit the
breakout conditions of sGRB jets. Assuming self-collimation of sGRB jets does
not play a critical role, we find that the time interval between the binary
merger and the launching of a typical sGRB jet is $\lesssim0.1$~s. We also show
that for a fraction of at least $\sim 30\%$ of sGRBs, the usually adopted
assumption of static ejecta is inconsistent with observations, even if the
polar ejecta mass is an order of magnitude smaller than the one in GRB 170817.
Our results disfavour magnetar central engines for powering cosmological sGRBs,
limit the amount of energy deposited in the cocoon prior to breakout, and
suggest that the observed delay of $\sim 1.$7~s in GW 170817 /GRB 170817
between the gravitational wave and $\gamma$-ray signals is likely dominated by
the propagation time of the jet to the $\gamma$-ray production site.


  We report on the growth of domains of standing waves in electroconvection in
a nematic liquid crystal. An ac voltage is applied to the system, forming an
initial state that consists of travelling striped patterns with two different
wavenumbers, zig and zag rolls. The standing waves are generated by suddenly
applying a periodic modulation of the amplitude of the applied voltage that is
approximately resonant with the travelling frequency of the pattern. By varying
the modulation frequency, we are able to vary the steady-state, average
wavenumber. We characterize the growth by measuring the structure factor for
the pattern, the amplitude of the pattern, and the domain-wall length. An
interesting feature of the growth is that the evolution of the domain-wall
length is strongly affected by changing the selected wavenumber; whereas, the
evolution of the structure factor is less sensitive to such changes.


  Under the perturbative picture of planetary microlensing, the planet is
considered to act as a uniform-shear Chang-Refsdal lens on one of the two
images produced by the host star that comes close to the angular Einstein
radius of the planet, leaving the other image unaffected. However, this
uniform-shear approximation is only valid for isolated planetary caustics and
breaks down in the resonant regime. Recently, the planetary-caustic degeneracy
arising from the above formalism is found to generalize to the regime of
central and resonant caustics, indicating that the perturbative picture and
Chang-Refsdal lens approximation may have been under-explored in the past.
Here, I introduce a new variable-shear Chang-Refsdal lens approximation, which
not only supports central and resonant caustics, but also enables full
magnification maps to be calculated analytically. Moreover, I introduce the
generalized perturbative picture, which relaxes the required proximity between
the planet and the image being perturbed in the previous work. Specifically,
the planet always perturbs the image in the same half of the lens plane as the
planet itself, leaving the other image largely unaffected. It is demonstrated
how this new framework results in the offset degeneracy as a consequence of
physical symmetry. The generalized perturbative picture also points to an
approach to solve the two-body lens equation semi-analytically. The analytic
and semi-analytic microlensing solutions associated with this work may allow
for substantially faster light-curve calculations and modeling of observed
events. A python implementation is provided.


  The advancing maturity of photonic integrated circuit (PIC) fabrication
technology enables the high integration of an increasing number of optical
components onto a single chip. With the incremental circuit complexity, the
calibration of active phase shifters in a large-scale PIC becomes a crucially
important issue. The traditional one-by-one calibration techniques encounter
significant hurdles with the propagation of calibration errors, and achieving
the decoupling of all phase shifters for independent calibration is not
straightforward. To address this issue, we propose a machine-learning approach
for globally calibrating the large-scale PIC. Our method utilizes a custom
network to simultaneously learn the nonlinear phase-current relations for all
thermo-optic phase shifters on the PIC by minimizing the negative likelihood of
the measurement datasets. Moreover, the reflectivities of all static
beamsplitter components can also be synchronizedly extracted using this
calibration method. As an example, a quantum walk PIC with a circuit depth of
12 is calibrated, and a programmable discrete-time quantum walk is
experimentally demonstrated. These results will greatly benefit the
applications of large-scale PICs in photonic quantum information processing.


  The scanning Fabry-Perot interferometer (FPI) - is the oldest method of
optical 3D spectroscopy. It is still in use because of the high spectral
resolution it provides over a large field of view. The history of the
application of this method for the study of extended ob jects (nebulae and
galaxies) and the technique of data reduction and analysis are discussed. The
paper focuses on the performing observations with the scanning FPI on the 6-m
telescope of the Special Astrophysical Observatory of the Russian Academy of
Sciences (SAO RAS). The instrument is currently used as a part of the SCORPIO-2
multimode focal reducer. The results of studies of various galactic and
extragalactic objects with the scanning FPI on the 6-m telescope - star-forming
regions and young stellar objects, spiral, ring, dwarf and interacting
galaxies, ionization cones of active galactic nuclei, galactic winds, etc. are
briefly discussed. Further prospects for research with the scanning FPI of the
SAO RAS are discussed.


  The available sites for ions in a typical disordered ionic conductor are
determined. For this purpose we devised a straightforward algorithm which via
cluster analysis identifies these sites from long time ionic trajectories below
the glass transition. This is exemplified for a lithium silicate glass
(Li_2O)_x (SiO_2)_(1-x) for x = 0.5 and x = 0.1. We find for both
concentrations that the number of sites is only slightly bigger than the number
of ions. This result suggests a theoretical description of the dynamics in
terms of mobile vacancies as most appropriate. Furthermore identification of
the ionic sites allows one to obtain detailed characteristics of the ionic
motion, e.g. quantification of correlated forward-backward jumps.


  We prove a result on the representation of squares by second degree
polynomials in the field of $p$-adic meromorphic functions in order to solve
positively B\"uchi's $n$ squares problem in this field (that is, the problem of
the existence of a constant $M$ such that any sequence $(x_n^2)$ of $M$ - not
all constant - squares whose second difference is the constant sequence $(2)$
satisfies $x_n^2=(x+n)^2$ for some $x$). We prove (based on works by Vojta) an
analogous result for function fields of characteristic zero, and under a
Conjecture by Bombieri, an analogous result for number fields. Using an
argument by B\"uchi, we show how the obtained results improve some theorems
about undecidability for the field of $p$-adic meromorphic functions and the
ring of $p$-adic entire functions.


  We perform accurate investigation of stability of localized vortices in an
effectively two-dimensional ("pancake-shaped") trapped BEC with negative
scattering length. The analysis combines computation of the stability
eigenvalues and direct simulations. The states with vorticity S=1 are stable in
a third of their existence region, $0<N<(1/3)N_{\max}^{(S=1)}$, where $N$ is
the number of atoms, and $N_{\max}^{(S=1)}$ is the corresponding collapse
threshold. Stable vortices easily self-trap from arbitrary initial
configurations with embedded vorticity. In an adjacent interval, $(1/3)N_{\max
}^{(S=1)}<N<$ $\allowbreak 0.43N_{\max}^{(S=1)}$, the unstable vortex
periodically splits in two fragments and recombines. At $N>$ $\allowbreak
0.43N_{\max}^{(S=1)}$, the fragments do not recombine, as each one collapses by
itself. The results are compared with those in the full 3D Gross-Pitaevskii
equation. In a moderately anisotropic 3D configuration, with the aspect ratio
$\sqrt{10}$, the stability interval of the S=1 vortices occupies $\approx 40%$
of their existence region, hence the 2D limit provides for a reasonable
approximation in this case. For the isotropic 3D configuration, the stability
interval expands to 65% of the existence domain. Overall, the vorticity
heightens the actual collapse threshold by a factor of up to 2. All vortices
with $S\geq 2$ are unstable.


  We present an efficient scheme for the generation of NOON states of photons
in circuit QED assisted by a superconducting charge qutrit. It is completed
with two kinds of manipulations, that is, the resonant operation on the qutrit
and the resonator, and the single-qubit operation on the qutrit, and they both
are high-fidelity operations. Compared with the one by a superconducting
transmon qutrit proposed by Su et al. (Sci. Rep. 4, 3898 (2014)), our scheme
does not require to maintain the qutrit in the third excited state with a long
time, which relaxes the difficulty of its implementation in experiment.
Moreover, the level anharmonicity of a charge qutrit is larger and it is better
for us to tune the different transitions of the charge qutrit resonant to the
resonator, which makes our scheme faster than others.


  A two-dimensional atomic mass spring system is investigated for critical
fracture loads and its crack path geometry. We rigorously prove that, in the
discrete-to-continuum limit, the minimal energy of a crystal under uniaxial
tension leads to a universal cleavage law and energy minimizers are either
homogeneous elastic deformations or configurations that are completely cracked
and do not store elastic energy. Beyond critical loading, the specimen
generically cleaves along a unique optimal crystallographic hyperplane. For
specific symmetric crystal orientations, however, cleavage might fail. In this
case a complete characterization of possible limiting crack geometries is
obtained.


  The existence of a full asymptotic expansion for the heat content asymptotics
of an operator of Laplace type with classical Zaremba boundary conditions on a
smooth manifold is established. The first three coefficients in this asymptotic
expansion are determined in terms of geometric invariants; partial information
is obtained about the fourth coefficient.


  This article is concerned with the kinetic modeling, by means of the Vlasov
equation, of charged particles under the influence of a strong external
electromagnetic field, i.e. when epsilon^2, the dimensionless cyclotron period,
tends to zero. This leads us to split the velocity variable in the Vlasov
equation into fluid and random components. The latter is supposed to have a
large magnitude of order 1/epsilon (which corresponds to the low Mach number
regime). In the limit epsilon -> 0, the resulting model is a hybrid model which
couples a kinetic description of the microscopic random motion of the particles
to a fluid description of the macroscopic behavior of the plasma. The
microscopic model is a first-order partial differential system for the
distribution function, which is averaged over the ultra-fast Larmor gyration
and the fast parallel motion along the magnetic field lines. The perpendicular
component (with respect to the magnetic field lines) of the bulk velocity is
governed by the classical relations describing the E X B and diamagnetic
drifts, while its parallel component satisfies an elliptic equation along the
magnetic field lines.


  In this note we outline how a modest violation in the conservation of mass
during the merger of two PBHs affects the PBH mass spectrum that we previously
obtained using a Boltzmann equation model for the evolution of the mass
spectrum with no mass loss. We find that if the initial cosmological redshift
is on the order 10$^{12}$, then the fraction of primordial holes with masses
greater than $10^{3}$ solar masses appears be close to what is required to
provide the seeds for galaxies. In addition we note that as a result of rapid
collisions and strong coupling to electromagnetic radiation for temperatures
$>$ GeV (Chapline 2018), there will be an effective low mass cutoff in the mass
spectrum for PBH masses less than a certain PBH mass less than than
$0.1M_{\odot}$. We also point out that this cutoff in the mass spectrum below
$\sim 0.1 M_\odot$ can be confirmed by combining future microlensing
observations from the Roman Space Telescope and the Vera C. Rubin Observatory
with astrometric observations.


  One-shot skeleton action recognition, which aims to learn a skeleton action
recognition model with a single training sample, has attracted increasing
interest due to the challenge of collecting and annotating large-scale skeleton
action data. However, most existing studies match skeleton sequences by
comparing their feature vectors directly which neglects spatial structures and
temporal orders of skeleton data. This paper presents a novel one-shot skeleton
action recognition technique that handles skeleton action recognition via
multi-scale spatial-temporal feature matching. We represent skeleton data at
multiple spatial and temporal scales and achieve optimal feature matching from
two perspectives. The first is multi-scale matching which captures the
scale-wise semantic relevance of skeleton data at multiple spatial and temporal
scales simultaneously. The second is cross-scale matching which handles
different motion magnitudes and speeds by capturing sample-wise relevance
across multiple scales. Extensive experiments over three large-scale datasets
(NTU RGB+D, NTU RGB+D 120, and PKU-MMD) show that our method achieves superior
one-shot skeleton action recognition, and it outperforms the state-of-the-art
consistently by large margins.


  In this paper, we study the sampling problem for first-order logic proposed
recently by Wang et al. -- how to efficiently sample a model of a given
first-order sentence on a finite domain? We extend their result for the
universally-quantified subfragment of two-variable logic $\mathbf{FO}^2$
($\mathbf{UFO}^2$) to the entire fragment of $\mathbf{FO}^2$. Specifically, we
prove the domain-liftability under sampling of $\mathbf{FO}^2$, meaning that
there exists a sampling algorithm for $\mathbf{FO}^2$ that runs in time
polynomial in the domain size. We then further show that this result continues
to hold even in the presence of counting constraints, such as $\forall
x\exists_{=k} y: \varphi(x,y)$ and $\exists_{=k} x\forall y: \varphi(x,y)$, for
some quantifier-free formula $\varphi(x,y)$. Our proposed method is
constructive, and the resulting sampling algorithms have potential applications
in various areas, including the uniform generation of combinatorial structures
and sampling in statistical-relational models such as Markov logic networks and
probabilistic logic programs.


  Scattering of electromagnetic (EM) waves by many small particles (bodies),
embedded in a thin layer, is studied. Physical properties of the particles are
described by their boundary impedances. The thin layer of depth of the order
$O(a)$ with many embedded in it small particles of characteristic size $a$, is
described by a boundary condition on the surface of the layer. The limiting
interface boundary condition is obtained for the effective EM field in the
limiting medium, in the limit $a\to 0$, where the number $M(a)$ of the
particles tends to infinity at a suitable rate.


  Let $G$ be a linear algebraic group, over a field $F$. We show that $G$ is
isomorphic to the automorphism group scheme of a smooth projective $F$-variety,
defined as the blow-up of a projective space, along a suitable smooth
subvariety.


  The notion of chiral prime concatenations is studied as a recursive
construction of prime numbers starting from a seed set and with appropriate
blocks to define the primality growth, generation by generation, either from
the right or from the left. Several basic questions are addressed like whether
chiral concatenation is a symmetric process, an endless process, as well as the
calculation of largest chiral prime numbers. In particular, the largest
left-concatenated prime number is constructed. It is a unique prime number of
24 digits. By introducing anomalous left-concatenations of primes we can
surpass the limit of 24 digits for left-concatenated primes. It is conjectured
that prime numbers are left chiral under anomalous concatenations.