  In this work, we proposed a smooth transition wave equation from a quantum to
classical regime in the framework of von Neumann formalism for ensembles and
then obtained an equivalent scaled equation. This led us to develop a scaled
statistical theory following the well-known Wigner-Moyal approach of quantum
mechanics. This scaled nonequilibrium statistical mechanics has in it all the
ingredients of the classical and quantum theory described in terms of a
continuous parameter displaying all the dynamical regimes in between the two
extreme cases. Finally, a simple application of our scaled formalism consisting
of reflection from a mirror by computing various quantities, including
probability density plots, scaled trajectories, and arrival times, was
analyzed.


  Independent of stellar modelling, global seismic parameters of red giants
provide unique information on the individual stellar properties as well as on
stellar evolution. They allow us to measure key stellar parameters, such as the
stellar mass and radius, or to derive the distance of field stars. Furthermore,
oscillations with a mixed character directly probe the physical conditions in
the stellar core. Here, we explain how very precise seismic indices are
obtained, and how they can be used for monitoring stellar evolution and
performing Galactic archeology.


  Leaf venation is a pervasive example of a complex biological network,
endowing leaves with a transport system and mechanical resilience. Transport
networks optimized for efficiency have been shown to be trees, i.e. loopless.
However, dicotyledon leaf venation has a large number of closed loops, which
are functional and able to transport fluid in the event of damage to any vein,
including the primary veins. Inspired by leaf venation, we study two possible
reasons for the existence of a high density of loops in transport networks:
resilience to damage and fluctuations in load. In the first case, we seek the
optimal transport network in the presence of random damage by averaging over
damage to each link. In the second case, we seek the network that optimizes
transport when the load is sparsely distributed: at any given time most sinks
are closed. We find that both criteria lead to the presence of loops in the
optimum state.


  We demonstrate a Raman laser system based on phase modulation technology and
phase feedback control. The two laser beams with frequency difference of 6.835
GHz are modulated using electro-optic and acousto-optic modulators,
respectively. Parasitic frequency components produced by the electro-optic
modulator are filtered using a Fabry-Perot Etalon. A straightforward phase
feedback system restrains the phase noise induced by environmental
perturbations. The phase noise of the laser system stays below -125 rad2/Hz at
frequency offset higher than 500 kHz. Overall phase noise of the laser system
is evaluated by calculating the contribution of the phase noise to the
sensitivity limit of a gravimeter. The results reveal that the sensitivity
limited by the phase noise of our laser system is lower than that of a
state-of-art optical phase-lock loop scheme when a gravimeter operates at short
pulse duration, which makes the laser system a promising option for our future
application of atom interferometer.


  We investigate the random matrix configurations for two or three interacting
electrons in one-dimensional disordered systems. In a suitable non-interacting
localized electron basis we obtain a sparse random matrix with very long tails
which is different from a superimposed random band matrix usually thought to be
valid. The number of non-zero off-diagonal matrix elements is shown to decay
very weakly from the matrix diagonal and the non-zero matrix elements are
distributed according to a Lorentzian around zero with also very weakly
decaying parameters. The corresponding random matrix for three interacting
electrons is similar but even more sparse.


  We have derived and implemented a stress tensor formulation for the van
derWaals density functional (vdW-DF) with spin-polarization-dependent gradient
correction (GC) recently proposed by the authors [J. Phys. Soc. Jpn. 82, 093701
(2013)] and applied it to nonmagnetic and magnetic molecular crystals under
ambient condition. We found that the cell parameters of the molecular crystals
obtained with vdW-DF show an overall improvement compared with those obtained
using local density and generalized gradient approximations. In particular, the
original vdW-DF with GC gives the equilibrium structural parameters of solid
oxygen in the {\alpha}-phase, which are in good agreement with the experiment.


  We define a notion of Property (T) for an arbitrary $C^*$-algebra $A$
admitting a tracial state. We extend this to a notion of Property (T) for the
pair $(A,B),$ where $B$ is a $C^*$-subalgebra of $A.$ Let $\Gamma$ be a
discrete group and $C^*_r(\Gamma)$ its reduced algebra. We show that
$C^*_r(\Gamma)$ has Property (T) if and only if the group $\Gamma$ has Property
(T) . More generally, given a subgroup $\Lambda$ of $\Gamma$, the pair
$(C^*_r(\Gamma),C^*_r(\Lambda))$ has Property (T) if and only if the pair of
groups $(\Gamma, \Lambda)$ has Property (T).


  The features of the azimuthal-angle overfocusing of atoms sputtered from the
surface of the Ni (001) face are studied by molecular dynamics computer
simulation. The signal of overfocused atoms is found to be multi-valued with
respect to the initial azimuthal angle due to different mechanisms of
scattering. The overfocused atoms form separate maximum and can be detected in
experiments with angle and energy resolution separately from the focused and
the own atoms.


  This paper analyzes the stability of a reactiondiffusion equation coupled
with a finite-dimensional controller through Dirichlet boundary input and
Neumann boundary output. Going against the flow, we intend to propose numerical
certificates of instability for such interconnections. From one side, using
spectral methods, an analytical condition based on root locus analysis can
determine the instability regions in the parameters space and can sometimes be
tested. On the other side, using Lyapunov direct and converse approaches, two
sufficient conditions of instability are established in terms of linear matrix
inequalities. The novelties lie both in the type of system studied and in the
methods used. The numerical results demonstrate the performance of the
different criteria set up in this paper and allow us to conjecture that these
conditions seem to be necessary and sufficient.


  We present scanning tunneling microscopy studies of the LaOFeAs parent
compound of iron pnictide superconductors. Topographic imaging reveals two
types of atomically flat surfaces, corresponding to the exposed LaO layer and
FeAs layer respectively. On one type of surface, we observe strong standing
wave patterns induced by quasiparticle interference of two-dimensional surface
states. The distribution of scattering wavevectors exhibits pronounced two-fold
symmetry, consistent with the nematic electronic structure found in the
Ca(Fe1-xCox)2As2 parent state.


  Let $N_{\mathcal{P}}(n,H)$ denote the maximum number of copies of $H$ in an
$n$ vertex planar graph. The problem of bounding this function for various
graphs $H$ has been extensively studied since the 70's. A special case that
received a lot of attention recently is when $H$ is the path on $2m+1$
vertices, denoted $P_{2m+1}$. Our main result in this paper is that $$
N_{\mathcal{P}}(n,P_{2m+1})=O(m^{-m}n^{m+1})\;.$$ This improves upon the
previously best known bound by a factor $e^{m}$, which is best possible up to
the hidden constant, and makes a significant step towards resolving conjectures
of Gosh et al. and of Cox and Martin. The proof uses graph theoretic arguments
together with (simple) arguments from the theory of convex optimization.


  In this work, we explore the relevant methodology for the investigation of
interacting systems with contact interactions, and we introduce a class of
zonal estimators for path-integral Monte Carlo methods, designed to provide
physical information about limited regions of inhomogeneous systems.We
demonstrate the usefulness of zonal estimators by their application to a system
of trapped bosons in a quasiperiodic potential in two dimensions, focusing on
finite temperature properties across a wide range of values of the potential.
Finally, we comment on the generalization of such estimators to local
fluctuations of the particle numbers and to magnetic ordering in
multi-component systems, spin systems, and systems with nonlocal interactions.


  We present a polarimetric map of a 20'x20' area toward the Galactic center.
The polarization of point sources has been measured in the J, H, and Ks bands
using the near-infrared polarimetric camera SIRPOL on the 1.4 m telescope IRSF.
One percent or better accuracy of polarization degree is achieved for sources
with J<14.5, H<13.5, and Ks<12.0. Comparing the Stokes parameters between high
extinction stars and relatively low extinction ones, we have obtained a
polarization originating from magnetically aligned dust grains at the central
region of our Galaxy of at most 1-2 kpc. The distribution of the position
angles shows a peak at about 20 deg, nearly parallel to the Galactic plane,
suggesting a toroidal magnetic configuration. The derived direction of the
magnetic field is in good agreement with that obtained from
far-infrared/submillimeter observations, which detect polarized thermal
emission from dust in the molecular clouds at the Galactic center. Our results
show that by subtracting foreground components, near-infrared polarimetry
allows investigation of the magnetic field structure "at" the Galactic center.


  As NLP models become more complex, understanding their decisions becomes more
crucial. Counterfactuals (CFs), where minimal changes to inputs flip a model's
prediction, offer a way to explain these models. While Large Language Models
(LLMs) have shown remarkable performance in NLP tasks, their efficacy in
generating high-quality CFs remains uncertain. This work fills this gap by
investigating how well LLMs generate CFs for two NLU tasks. We conduct a
comprehensive comparison of several common LLMs, and evaluate their CFs,
assessing both intrinsic metrics, and the impact of these CFs on data
augmentation. Moreover, we analyze differences between human and LLM-generated
CFs, providing insights for future research directions. Our results show that
LLMs generate fluent CFs, but struggle to keep the induced changes minimal.
Generating CFs for Sentiment Analysis (SA) is less challenging than NLI where
LLMs show weaknesses in generating CFs that flip the original label. This also
reflects on the data augmentation performance, where we observe a large gap
between augmenting with human and LLMs CFs. Furthermore, we evaluate LLMs'
ability to assess CFs in a mislabelled data setting, and show that they have a
strong bias towards agreeing with the provided labels. GPT4 is more robust
against this bias and its scores correlate well with automatic metrics. Our
findings reveal several limitations and point to potential future work
directions.


  In the development of a presumed asymptotic expansion for lambda_d in
previous work, a basic step involved extracting the asymptotic behavior of a
sum as being dominated by the largest term in the sum. But this argument only
is valid when the terms in the sum are positive. In the case terms in the sum
are not all positive (some of the J_n are negative) we replace the `largest
term' argument by the route of this paper. The sum is replaced by a contour
integral. We then find a stationary point of the integrand that we conjecture
dominates the asymptotic behavior of the integral.


  Following the successful application of the U-Net to medical images, there
have been different encoder-decoder models proposed as an improvement to the
original U-Net for segmenting echocardiographic images. This study aims to
examine the performance of the state-of-the-art proposed models as well as the
original U-Net model by applying them to segment the endocardium of the Left
Ventricle in 2D automatically. The prediction outputs of the models are used to
evaluate the performance of the models by comparing the automated results
against the expert annotations (gold standard). Our results reveal that the
U-Net model outperforms other models by achieving an average Dice coefficient
of 0.92$ \pm 0.05$, and Hausdorff distance of 3.97$ \pm 0.82$.


  Here we present a Bayesian method of including discrete measurements of
dispersion measure due to the interstellar medium in the direction of a pulsar
as prior information in the analysis of that pulsar. We use a simple simulation
to show the efficacy of this method, where the inclusion of the additional
measurements results in both a significant increase in the precision with which
the timing model parameters can be obtained, and an improved upper limit on the
amplitude of any red noise in the dataset. We show that this method can be
applied where no multi-frequency data exists across much of the dataset, and
where there is no simultaneous multi-frequency data for any given observing
epoch. Including such information in the analysis of upcoming International
Pulsar Timing Array (IPTA) and European Pulsar Timing Array (EPTA) data
releases could therefore prove invaluable in obtaining the most constraining
limits on gravitational wave signals within those datasets.


  In this paper, we conduct a comparative study on speaker-attributed automatic
speech recognition (SA-ASR) in the multi-party meeting scenario, a topic with
increasing attention in meeting rich transcription. Specifically, three
approaches are evaluated in this study. The first approach, FD-SOT, consists of
a frame-level diarization model to identify speakers and a multi-talker ASR to
recognize utterances. The speaker-attributed transcriptions are obtained by
aligning the diarization results and recognized hypotheses. However, such an
alignment strategy may suffer from erroneous timestamps due to the modular
independence, severely hindering the model performance. Therefore, we propose
the second approach, WD-SOT, to address alignment errors by introducing a
word-level diarization model, which can get rid of such timestamp alignment
dependency. To further mitigate the alignment issues, we propose the third
approach, TS-ASR, which trains a target-speaker separation module and an ASR
module jointly. By comparing various strategies for each SA-ASR approach,
experimental results on a real meeting scenario corpus, AliMeeting, reveal that
the WD-SOT approach achieves 10.7% relative reduction on averaged
speaker-dependent character error rate (SD-CER), compared with the FD-SOT
approach. In addition, the TS-ASR approach also outperforms the FD-SOT approach
and brings 16.5% relative average SD-CER reduction.


  The issues that arise when using the Cornwall-Jackiw-Tomboulis formalism in
multi-field theories are investigated. Particular attention is devoted to the
interplay between temperature effects, ultraviolet structure, and the
interdependence of the gap equations. Results are presented explicitly in the
case of the evaluation of the finite temperature effective potential of a
theory with two scalar fields which has attracted interest as a toy model for
symmetry nonrestoration at high temperatures. The lowest nontrivial order of
approximation of the Cornwall-Jackiw-Tomboulis effective potential is shown to
lead to consistent results, which are relevant for recent studies of symmetry
nonrestoration by Bimonte and Lozano.


  In the framework of Dyson-Schwinger equations (DSE), we compute the
$\gamma^*\gamma\to\pi^0$ transition form factor, $G(Q^2)$. For the first time,
in a continuum approach to quantun chromodynamics (QCD), it was possible to
compute $G(Q^2)$ on the whole domain of space-like momenta. Our result agrees
with CELLO, CLEO and Belle collaborations and, with the well-known asymptotic
QCD limit, $2f_\pi$. Our analysis unifies this prediction with that of the
pion's valence-quark parton distribution amplitude (PDA) and elastic
electromagnetic form factor.


  Computational chemistry allows researchers to experiment in sillico: by
running a computer simulations of a biological or chemical processes of
interest. Molecular dynamics with molecular mechanics model of interactions
simulates N-body problem of atoms$-$it computes movements of atoms according to
Newtonian physics and empirical descriptions of atomic electrostatic
interactions. These simulations require high performance computing resources,
as evaluations within each step are computationally demanding and billions of
steps are needed to reach interesting timescales. Current methods decompose the
spatial domain of the problem and calculate on parallel/distributed
infrastructures. Even the methods with the highest strong scaling hit the limit
at half a million cores: they are not able to cut the time to result if
provided with more processors. At the dawn of exascale computing with massively
parallel computational resources, we want to increase the level of parallelism
by incorporating parallel-in-time computation to molecular dynamics
simulations. Calculation of results in several successive time points
simultaneously without a priori knowledge has been examined with no major
success. We will study and implement a novel combinations of methods that
according to our theoretical analyses should achieve promising speed-up
compared to sequential-in-time calculation.


  This paper investigates the execution of tree-shaped task graphs using
multiple processors. Each edge of such a tree represents a large IO file. A
task can only be executed if all input and output files fit into memory, and a
file can only be removed from memory after it has been consumed. Such trees
arise, for instance, in the multifrontal method of sparse matrix factorization.
The maximum amount of memory needed depends on the execution order of the
tasks. With one processor the objective of the tree traversal is to minimize
the required memory. This problem was well studied and optimal polynomial
algorithms were proposed.
  Here, we extend the problem by considering multiple processors, which is of
obvious interest in the application area of matrix factorization. With the
multiple processors comes the additional objective to minimize the time needed
to traverse the tree, i.e., to minimize the makespan. Not surprisingly, this
problem proves to be much harder than the sequential one. We study the
computational complexity of this problem and provide an inapproximability
result even for unit weight trees. Several heuristics are proposed, each with a
different optimization focus, and they are analyzed in an extensive
experimental evaluation using realistic trees.


  The incidence energy $\mathscr{IE}(G)$ of a graph $G$, defined as the sum of
the singular values of the incidence matrix of a graph $G$, is a much studied
quantity with well known applications in chemical physics. The
Laplacian-energy-like invariant of $G$ is defined as the sum of square roots of
the Laplacian eigenvalues. In this paper, we obtain the closed-form formulae
expressing the incidence energy and the Laplacian-energy-like invariant of the
Union Jack lattice. Moreover, the explicit asymptotic values of these
quantities are calculated by utilizing the applications of analysis approach
with the help of calculational software.


  We prove the invariance of the Gibbs measure under the dynamics of the
three-dimensional cubic wave equation, which is also known as the hyperbolic
$\Phi^4_3$-model. This result is the hyperbolic counterpart to seminal works on
the parabolic $\Phi^4_3$-model by Hairer '14 and Hairer-Matetski '18. The heart
of the matter lies in establishing local in time existence and uniqueness of
solutions on the statistical ensemble, which is achieved by using a
para-controlled Ansatz for the solution, the analytical framework of the random
tensor theory, and the combinatorial molecule estimates. The singularity of the
Gibbs measure with respect to the Gaussian free field brings out a new caloric
representation of the Gibbs measure and a synergy between the parabolic and
hyperbolic theories embodied in the analysis of heat-wave stochastic objects.
Furthermore from a purely hyperbolic standpoint our argument relies on key new
ingredients that include a hidden cancellation between sextic stochastic
objects and a new bilinear random tensor estimate.


  Deterministic computational modeling of laser powder bed fusion (LPBF)
process fails to capture irregularities and roughness of the scan track, unless
expensive powder-scale analysis is used. In this work we developed a stochastic
computational modeling framework based on Markov Chain Monte Carlo (MCMC)
capable of capturing the irregularities of LPBF scan. The model is calibrated
against AFRL single track scan data using a specially designed tensor
decomposition method, i.e., Higher-Order Proper Generalized Decomposition
(HOPGD) that relies on non-intrusive data learning and construction of reduced
order surrogate models. Once calibrated, the stochastic model can be used to
predict the roughness and porosity at part scale at a significantly reduced
computational cost compared to detailed powder-scale deterministic simulations.
The stochastic simulation predictions are validated against AFRL multi-layer
and multitrack experiments and reported as more accurate when compared with
regular deterministic simulation results.


  Recently salient object detection has witnessed remarkable improvement owing
to the deep convolutional neural networks which can harvest powerful features
for images. In particular, state-of-the-art salient object detection methods
enjoy high accuracy and efficiency from fully convolutional network (FCN) based
frameworks which are trained from end to end and predict pixel-wise labels.
However, such framework suffers from adversarial attacks which confuse neural
networks via adding quasi-imperceptible noises to input images without changing
the ground truth annotated by human subjects. To our knowledge, this paper is
the first one that mounts successful adversarial attacks on salient object
detection models and verifies that adversarial samples are effective on a wide
range of existing methods. Furthermore, this paper proposes a novel end-to-end
trainable framework to enhance the robustness for arbitrary FCN-based salient
object detection models against adversarial attacks. The proposed framework
adopts a novel idea that first introduces some new generic noise to destroy
adversarial perturbations, and then learns to predict saliency maps for input
images with the introduced noise. Specifically, our proposed method consists of
a segment-wise shielding component, which preserves boundaries and destroys
delicate adversarial noise patterns and a context-aware restoration component,
which refines saliency maps through global contrast modeling. Experimental
results suggest that our proposed framework improves the performance
significantly for state-of-the-art models on a series of datasets.


  The late Kazuo Kondo left a hitherto unknown a priori particle theory which
provides predictions of massive particles which may be detected by the Large
Hadron Collider (LHC). This article briefly introduces Kondo's work and
documents the derivation and masses of his expected hyper-mesons,
hyper-hadrons, heavy leptons and massive neutrinos. Several particles in these
classes may have already been detected.


  This paper presents a novel grid-based NeRF called F2-NeRF (Fast-Free-NeRF)
for novel view synthesis, which enables arbitrary input camera trajectories and
only costs a few minutes for training. Existing fast grid-based NeRF training
frameworks, like Instant-NGP, Plenoxels, DVGO, or TensoRF, are mainly designed
for bounded scenes and rely on space warping to handle unbounded scenes.
Existing two widely-used space-warping methods are only designed for the
forward-facing trajectory or the 360-degree object-centric trajectory but
cannot process arbitrary trajectories. In this paper, we delve deep into the
mechanism of space warping to handle unbounded scenes. Based on our analysis,
we further propose a novel space-warping method called perspective warping,
which allows us to handle arbitrary trajectories in the grid-based NeRF
framework. Extensive experiments demonstrate that F2-NeRF is able to use the
same perspective warping to render high-quality images on two standard datasets
and a new free trajectory dataset collected by us. Project page:
https://totoro97.github.io/projects/f2-nerf.


  The benefit of quantum computing for solving combinatorial optimization
problems (COPs) constitutes an open research question. In this work, we study
the performance of a shrinking algorithm for COPs. The algorithm leverages
correlations extracted from quantum or classical subroutines to recursively
simplify the problem. We compare the performance of the algorithm equipped with
correlations from the quantum approximate optimization algorithm (QAOA) as well
as the classical linear programming (LP) and semi-definite programming (SDP)
relaxations. This allows us to benchmark the utility of QAOA correlations
against established classical relaxation algorithms. We apply the recursive
algorithm to MaxCut problem instances with up to a hundred vertices at
different graph densities. Our results indicate that LP outperforms all other
approaches for low-density instances, while SDP excels for high-density
problems. Moreover, the shrinking algorithm proves to be a viable alternative
to established methods of rounding LP and SDP relaxations. In addition, the
recursive shrinking algorithm outperforms its bare counterparts for all three
types of correlations, i.e., LP with spanning tree rounding, the
Goemans-Williamson algorithm, and conventional QAOA. While the lowest depth
QAOA consistently yields worse results than the SDP, our tensor network
experiments show that the performance increases significantly for deeper QAOA
circuits.


  Let $\pi S(t)$ denote the argument of the Riemann zeta-function at the point
$s=\tfrac12+it$. Assuming the Riemann hypothesis, we give a new and simple
proof of the sharpest known bound for $S(t)$. We discuss a generalization of
this bound for a large class of $L$-functions including those which arise from
cuspidal automorphic representations of GL($m$) over a number field. We also
prove a number of related results including bounding the order of vanishing of
an $L$-function at the central point and bounding the height of the lowest zero
of an $L$-function.


  This paper introduces the $f$-EI$(\phi)$ algorithm, a novel iterative
algorithm which operates on measures and performs $f$-divergence minimisation
in a Bayesian framework. We prove that for a rich family of values of
$(f,\phi)$ this algorithm leads at each step to a systematic decrease in the
$f$-divergence and show that we achieve an optimum. In the particular case
where we consider a weighted sum of Dirac measures and the $\alpha$-divergence,
we obtain that the calculations involved in the $f$-EI$(\phi)$ algorithm
simplify to gradient-based computations. Empirical results support the claim
that the $f$-EI$(\phi)$ algorithm serves as a powerful tool to assist
Variational methods.


  Consider a sequence of Riemannian manifolds $(M^n_i,g_i)$ with scalar
curvatures and entropies bounded below by small constants $R_i,\mu_i
\geq-\epsilon_i$. The goal of this paper is to understand notions of
convergence and the structure of limits for such spaces. Even in the seemingly
rigid case $\epsilon_i\to 0$, we construct examples showing that such a
sequence may converge wildly in the Gromov-Hausdorff or Intrinsic Flat sense.
On the other hand, we will see that these classical notions of convergence are
the incorrect ones to consider. Indeed, even a metric space is the wrong
underlying category to be working on.
  Instead, we introduce $d_p$ convergence, a weaker notion of convergence that
is valid for a class of rectifiable Riemannian spaces. These rectifiable spaces
have well-behaved topology, measure theory, and analysis, though potentially
there will be no reasonably associated distance function. Under the $d_p$
notion of closeness, a space with almost nonnegative scalar curvature and small
entropy bounds must in fact be close to Euclidean space; this will constitute
our $\epsilon$-regularity theorem.
  More generally, we have a compactness theorem saying that sequences of
Riemannian manifolds $(M^n_i,g_i)$ with small lower scalar curvature and
entropy bounds $R_i,\mu_i \geq -\epsilon$ must $d_p$ converge to such a
rectifiable Riemannian space $X$. Comparing to the first paragraph, the
distance functions of $M_i$ may be degenerating, even though in a well-defined
sense the analysis cannot be. Applications for manifolds with small scalar and
entropy lower bounds include an $L^\infty$-Sobolev embedding and apriori $L^p$
scalar curvature bounds for $p<1$.


  Motor imagery-based brain-computer interfaces (BCIs) use an individuals
ability to volitionally modulate localized brain activity as a therapy for
motor dysfunction or to probe causal relations between brain activity and
behavior. However, many individuals cannot learn to successfully modulate their
brain activity, greatly limiting the efficacy of BCI for therapy and for basic
scientific inquiry. Previous research suggests that coherent activity across
diverse cognitive systems is a hallmark of individuals who can successfully
learn to control the BCI. However, little is known about how these distributed
networks interact through time to support learning. Here, we address this gap
in knowledge by constructing and applying a multimodal network approach to
decipher brain-behavior relations in motor imagery-based brain-computer
interface learning using MEG. Specifically, we employ a minimally constrained
matrix decomposition method (non-negative matrix factorization) to
simultaneously identify regularized, covarying subgraphs of functional
connectivity, to assess their similarity to task performance, and to detect
their time-varying expression. Individuals also displayed marked variation in
the spatial properties of subgraphs such as the connectivity between the
frontal lobe and the rest of the brain, and in the temporal properties of
subgraphs such as the stage of learning at which they reached maximum
expression. From these observations, we posit a conceptual model in which
certain subgraphs support learning by modulating brain activity in regions
important for sustaining attention. To test this model, we use tools that
stipulate regional dynamics on a networked system (network control theory), and
find that good learners display a single subgraph whose temporal expression
tracked performance and whose architecture supports easy modulation of brain
regions important for attention.


  Recent studies demonstrate that query expansions generated by large language
models (LLMs) can considerably enhance information retrieval systems by
generating hypothetical documents that answer the queries as expansions.
However, challenges arise from misalignments between the expansions and the
retrieval corpus, resulting in issues like hallucinations and outdated
information due to the limited intrinsic knowledge of LLMs. Inspired by Pseudo
Relevance Feedback (PRF), we introduce Corpus-Steered Query Expansion (CSQE) to
promote the incorporation of knowledge embedded within the corpus. CSQE
utilizes the relevance assessing capability of LLMs to systematically identify
pivotal sentences in the initially-retrieved documents. These corpus-originated
texts are subsequently used to expand the query together with LLM-knowledge
empowered expansions, improving the relevance prediction between the query and
the target documents. Extensive experiments reveal that CSQE exhibits strong
performance without necessitating any training, especially with queries for
which LLMs lack knowledge.


  The geodesic-light-cone (GLC) coordinates are a useful tool to analyse light
propagation and observations in cosmological models. In this article, we
propose a detailed, pedagogical, and rigorous introduction to this coordinate
system, explore its gauge degrees of freedom, and emphasize its interest when
geometric optics is at stake. We then apply the GLC formalism to the
homogeneous and anisotropic Bianchi I cosmology. More than a simple
illustration, this application (i) allows us to show that the Weinberg
conjecture according to which gravitational lensing does not affect the proper
area of constant-redshift surfaces is significantly violated in a globally
anisotropic universe; and (ii) offers a glimpse into new ways to constrain
cosmic isotropy from the Hubble diagram.


  Thermoacoustic instabilities are one of the most challenging problems faced
by gas turbine and rocket motor manufacturers. The key instability mechanism is
described by the {\it Rayleigh criterion}. The Rayleigh criterion does not
directly show how to alter a system to make it more stable. This is the
objective of sensitivity analysis. Because thermoacoustic systems have many
design parameters, adjoint sensitivity analysis has been proposed to obtain all
the sensitivities with one extra calculation. Although adjoint sensitivity
analysis can be carried out in both the time and the frequency domain, the
frequency domain is more natural for a linear analysis. Perhaps surprisingly,
the Rayleigh criterion has not yet been rigorously derived and comprehensively
interpreted in the frequency domain. The contribution of this theoretical paper
is threefold. First, the Rayleigh criterion is interpreted in the frequency
domain with integral formulae for the complex eigenvalue. Second, the first
variation of the Rayleigh criterion is calculated both in the time and
frequency domain, both with and without Lagrange multipliers (adjoint
variables). The Lagrange multipliers are physically related to the system's
observables. Third, an adjoint Rayleigh criterion is proposed. The paper also
points out that the conclusions of {\it Juniper, M. P. (2018), Phys. Rev.
Fluids, vol. 3, 110509} apply to the first variation of the Rayleigh criterion,
not to the Rayleigh criterion itself. The mathematical relations of this paper
can be used to compute sensitivities directly from measurable quantities to
enable optimal design.


  We investigate if the CP violation necessary for successful electroweak
baryogenesis may be sourced by the neutrino Yukawa couplings. In particular, we
consider an electroweak scale Seesaw realization with sizable Yukawas where the
new neutrino singlets form (pseudo)-Dirac pairs, as in the linear or inverse
Seesaw variants. We find that the baryon asymmetry obtained strongly depends on
how the neutrino masses vary within the bubble walls. Moreover, we also find
that flavour effects critically impact the final asymmetry obtained and that,
taking them into account, the observed value may be obtained in some regions of
the parameter space. This source of CP violation naturally avoids the strong
constraints from electric dipole moments and links the origin of the baryon
asymmetry of the Universe with the mechanism underlying neutrino masses.
Interestingly, the mixing of the active and heavy neutrinos needs to be sizable
and could be probed at the LHC or future collider experiments.


  We use computer simulation to investigate the topology of the potential
energy $V(\{{\bf R}\})$ and to search for doublewell potential's (DWP) in a
model glass . By a sequence of Newtonian and dissipative dynamics we find
different minima of $V(\{{\bf R}\})$ and the energy profile along the least
action paths joining them. At variance with previous suggestions, we find that
the parameters describing the DWP's are correlated among each others. Moreover,
the trajectory of the system in the 3$N$-d configurational phase space follows
a quasi-1-d manifold. The motion parallel to the path is characterized by jumps
between minima, and is nearly uncorrelated from the orthogonal, harmonic,
dynamics.


  We first show that a K\"ahler cone appears as the tangent cone of a complete
expanding gradient K\"ahler-Ricci soliton with quadratic curvature decay with
derivatives if and only if it has a smooth canonical model (on which the
soliton lives). This allows us to classify two-dimensional complete expanding
gradient K\"ahler-Ricci solitons with quadratic curvature decay with
derivatives. We then show that any two-dimensional complete shrinking gradient
K\"ahler-Ricci soliton whose scalar curvature tends to zero at infinity is, up
to pullback by an element of $GL(2,\,\mathbb{C})$, either the flat Gaussian
shrinking soliton on $\mathbb{C}^{2}$ or the $U(2)$-invariant shrinking
gradient K\"ahler-Ricci soliton of Feldman-Ilmanen-Knopf on the blowup of
$\mathbb{C}^{2}$ at one point. Finally, we show that up to pullback by an
element of $GL(n,\,\mathbb{C})$, the only complete shrinking gradient
K\"ahler-Ricci soliton with bounded Ricci curvature on $\mathbb{C}^{n}$ is the
flat Gaussian shrinking soliton and on the total space of
$\mathcal{O}(-k)\to\mathbb{P}^{n-1}$ for $0<k<n$ is the $U(n)$-invariant
example of Feldman-Ilmanen-Knopf. In the course of the proof, we establish the
uniqueness of the soliton vector field of a complete shrinking gradient
K\"ahler-Ricci soliton with bounded Ricci curvature in the Lie algebra of a
torus. A key tool used to achieve this result is the Duistermaat-Heckman
theorem from symplectic geometry. This provides the first step towards
understanding the relationship between complete shrinking gradient
K\"ahler-Ricci solitons and algebraic geometry.


  Radio polarisation images of the jets of Active Galactic Nuclei (AGN) can
provide a deep insight into the launching and collimation mechanisms of
relativistic jets. However, even at VLBI scales, resolution is often a limiting
factor in the conclusions that can be drawn from observations. The Maximum
Entropy Method (MEM) is a deconvolution algorithm that can outperform the more
common CLEAN algorithm in many cases, particularly when investigating
structures present on scales comparable to or smaller than the nominal beam
size with "super-resolution". A new implementation of the MEM suitable for
single- or multiple-wavelength VLBI polarisation observations has been
developed and is described here. Monte Carlo simulations comparing the
performances of CLEAN and MEM at reconstructing the properties of model images
are presented; these demonstrate the enhanced reliability of MEM over CLEAN
when images of the fractional polarisation and polarisation angle are
constructed using convolving beams that are appreciably smaller than the full
CLEAN beam. The results of using this new MEM software to image VLBA
observations of the AGN 0716+714 at six different wavelengths are presented,
and compared to corresponding maps obtained with CLEAN. MEM and CLEAN maps of
Stokes $I$, the polarised flux, the fractional polarisation and the
polarisation angle are compared for convolving beams ranging from the full
CLEAN beam down to a beam one-third of this size. MEM's ability to provide more
trustworthy polarisation imaging than a standard CLEAN-based deconvolution when
convolving beams appreciably smaller than the full CLEAN beam are used is
discussed.


  We consider the nonlinear Helmholtz (NLH) equation describing the beam
propagation in a planar waveguide with Kerr-like nonlinearity under
non-paraxial approximation. By applying the Lie symmetry analysis, we determine
the Lie point symmetries and the corresponding symmetry reductions in the form
of ordinary differential equations (ODEs) with the help of the optimal systems
of one-dimensional subalgebras. Our investigation reveals an important fact
that in spite of the original NLH equation being non-integrable, its symmetry
reductions are of Painlev\'e integrable. We study the resulting sets of
nonlinear ODEs analytically either by constructing the integrals of motion
using the modified Prelle-Singer method or by obtaining explicit travelling
wave-like solutions including solitary and symbiotic solitary wave solutions.
Also, we carry out a detailed numerical analysis of the reduced equations and
obtain multi-peak nonlinear wave trains. As a special case of the NLH equation,
we also make a comparison between the symmetries of the present NLH system and
that of the standard nonlinear Schr\"odinger equation for which symmetries are
long available in the literature.


  We study a recurrence defined on a three dimensional lattice and prove that
its values are Laurent polynomials in the initial conditions with all
coefficients equal to one. This recurrence was studied by Propp and by Fomin
and Zelivinsky. Fomin and Zelivinsky were able to prove Laurentness and
conjectured that the coefficients were 1. Our proof establishes a bijection
between the terms of the Laurent polynomial and the perfect matchings of
certain graphs, generalizing the theory of Aztec diamonds. In particular, this
shows that the coefficients of this polynomial, and polynomials obtained by
specializing its variables, are positive, a conjecture of Fomin and Zelevinsky.


  The binary fraction of unevolved massive stars is thought to be 70-100% but
there are few observational constraints on the binary fraction of the evolved
version of a subset of these stars, the red supergiants (RSGs). Here we
identify a complete sample of RSGs in the Large Magellanic Cloud (LMC) using
new spectroscopic observations and archival UV, IR and broadband optical
photometry. We find 4090 RSGs with log L/Lo > 3.5 with 1820 of them having log
L/Lo > 4, which we believe is our completeness limit. We additionally
spectroscopically confirmed 38 new RSG+B star binaries in the LMC, bringing the
total known up to 55. We then estimated the binary fraction using a k-nearest
neighbors algorithm that classifies stars as single or binary based on
photometry with a spectroscopic sample as a training set. We take into account
observational biases such as line-of-sight stars and binaries in eclipse while
also calculating model-dependent corrections for RSGs with companions that our
observations were not designed to detect. Based on our data, we find an initial
result of 13.5 +7.56/-6.67% for RSGs with O or B-type companions. Using the
Binary Population and Spectral Synthesis (BPASS) models to correct for
unobserved systems, this corresponds to a total RSG binary fraction of 19.5
+7.6/-6.7%. This number is in broad agreement with what we would expect given
an initial OB binary distribution of 70%, a predicted merger fraction of 20-30%
and a binary interaction fraction of 40-50%.


  Database theory and database practice are typically the domain of computer
scientists who adopt what may be termed an algorithmic perspective on their
data. This perspective is very different than the more statistical perspective
adopted by statisticians, scientific computers, machine learners, and other who
work on what may be broadly termed statistical data analysis. In this article,
I will address fundamental aspects of this algorithmic-statistical disconnect,
with an eye to bridging the gap between these two very different approaches. A
concept that lies at the heart of this disconnect is that of statistical
regularization, a notion that has to do with how robust is the output of an
algorithm to the noise properties of the input data. Although it is nearly
completely absent from computer science, which historically has taken the input
data as given and modeled algorithms discretely, regularization in one form or
another is central to nearly every application domain that applies algorithms
to noisy data. By using several case studies, I will illustrate, both
theoretically and empirically, the nonobvious fact that approximate
computation, in and of itself, can implicitly lead to statistical
regularization. This and other recent work suggests that, by exploiting in a
more principled way the statistical properties implicit in worst-case
algorithms, one can in many cases satisfy the bicriteria of having algorithms
that are scalable to very large-scale databases and that also have good
inferential or predictive properties.


  Face recognition (FR) has reached a high technical maturity. However, its use
needs to be carefully assessed from an ethical perspective, especially in
sensitive scenarios. This is precisely the focus of this paper: the use of FR
for the identification of specific subjects in moderately to densely crowded
spaces (e.g. public spaces, sports stadiums, train stations) and law
enforcement scenarios. In particular, there is a need to consider the trade-off
between the need to protect privacy and fundamental rights of citizens as well
as their safety. Recent Artificial Intelligence (AI) policies, notably the
European AI Act, propose that such FR interventions should be proportionate and
deployed only when strictly necessary. Nevertheless, concrete guidelines on how
to address the concept of proportional FR intervention are lacking to date.
This paper proposes a framework to contribute to assessing whether an FR
intervention is proportionate or not for a given context of use in the above
mentioned scenarios. It also identifies the main quantitative and qualitative
variables relevant to the FR intervention decision (e.g. number of people in
the scene, level of harm that the person(s) in search could perpetrate,
consequences to individual rights and freedoms) and propose a 2D graphical
model making it possible to balance these variables in terms of ethical cost vs
security gain. Finally, different FR scenarios inspired by real-world
deployments validate the proposed model. The framework is conceived as a simple
support tool for decision makers when confronted with the deployment of an FR
system.


  Bouvel and Pergola introduced the notion of minimal permutations in the study
of the whole genome duplication-random loss model for genome rearrangements.
Let $\mathcal{F}_d(n)$ denote the set of minimal permutations of length $n$
with $d$ descents, and let $f_d(n)= |\mathcal{F}_d(n)|$. They derived that
$f_{n-2}(n)=2^{n}-(n-1)n-2$ and $f_n(2n)=C_n$, where $C_n$ is the $n$-th
Catalan number. Mansour and Yan proved that $f_{n+1}(2n+1)=2^{n-2}nC_{n+1}$. In
this paper, we consider the problem of counting minimal permutations in
$\mathcal{F}_d(n)$ with a prescribed set of ascents. We show that such
structures are in one-to-one correspondence with a class of skew Young
tableaux, which we call $2$-regular skew tableaux. Using the determinantal
formula for the number of skew Young tableaux of a given shape, we find an
explicit formula for $f_{n-3}(n)$. Furthermore, by using the Knuth equivalence,
we give a combinatorial interpretation of a formula for a refinement of the
number $f_{n+1}(2n+1)$.


  In this paper we study the asymptotic nonlinear dynamics of scalar semilinear
parabolic problems reaction-diffusion type when the diffusion coefficient
becomes large in a subregion which is interior to the domain. We obtain, under
suitable assumptions, that the family of attractors behaves continuously and we
exhibit the rate of convergence. An accurate description of localized large
diffusion is necessary.


  In this paper we introduce a new method which employs the concept of
"Orientation Vectors" to train a feed forward neural network and suitable for
problems where large dimensions are involved and the clusters are
characteristically sparse. The new method is not NP hard as the problem size
increases. We `derive' the method by starting from Kolmogrov's method and then
relax some of the stringent conditions. We show for most classification
problems three layers are sufficient and the network size depends on the number
of clusters. We prove as the number of clusters increase from N to N+dN the
number of processing elements in the first layer only increases by d(logN), and
are proportional to the number of classes, and the method is not NP hard.
  Many examples are solved to demonstrate that the method of Orientation
Vectors requires much less computational effort than Radial Basis Function
methods and other techniques wherein distance computations are required, in
fact the present method increases logarithmically with problem size compared to
the Radial Basis Function method and the other methods which depend on distance
computations e.g statistical methods where probabilistic distances are
calculated. A practical method of applying the concept of Occum's razor to
choose between two architectures which solve the same classification problem
has been described. The ramifications of the above findings on the field of
Deep Learning have also been briefly investigated and we have found that it
directly leads to the existence of certain types of NN architectures which can
be used as a "mapping engine", which has the property of "invertibility", thus
improving the prospect of their deployment for solving problems involving Deep
Learning and hierarchical classification. The latter possibility has a lot of
future scope in the areas of machine learning and cloud computing.


  Quantum dynamics of strongly correlated systems is a challenging problem.
Although the low energy fractional excitations of one dimensional integrable
models are often well-understood, exploring quantum dynamics in these systems
remains challenging in the gapless regime, especially at intermediate and high
energies. Based on the algebraic Bethe ansatz formalism, we study spin dynamics
in a representative one dimensional strongly correlated model, {\it i.e. }, the
antiferromagnetic spin-$\frac{1}{2}$ XXZ chain with the Ising anisotropy, via
the form-factor formulae. Various excitations at different energy scales are
identified crucial to the dynamic spin structure factors under the guidance of
sum rules. At small magnetic polarizations, gapless excitations dominate the
low energy spin dynamics arising from the magnetic-field-induced
incommensurability. In contrast, spin dynamics at intermediate and high
energies is characterized by the two- and three-string states, which are
multi-particle excitations based on the commensurate N\'eel ordered background.
Our work is helpful for experimental studies on spin dynamics in both condensed
matter and cold atom systems beyond the low energy effective Luttinger liquid
theory. Based on an intuitive physical picture, we speculate that the dynamic
feature at high energies due to the multi-particle anti-bound state excitations
can be generalized to non-integrable spin systems.


  If the electroweak Higgs vacuum expectation value $v$ in early universe is
$\sim 1 \%$ higher than its present value $v_0=246$ GeV, the $^7$Li puzzle in
BBN and the CMB/$\Lambda$CDM tension with late-universe measurements on Hubble
parameter are mitigated. We propose a model of an axion coupled to the Higgs
field, named ``axi-Higgs'', with its mass $m_a \sim 10^{-30} - 10^{-29}\,{\rm
eV}$ and decay constant $f_a \sim 10^{17} - 10^{18}\,{\rm GeV}$, to achieve
this goal. The axion initial value $a_{\rm ini}$ yields an initial $\Delta
v_{\rm ini}/v_0 \sim 0.01$ throughout the BBN-recombination epoch and a percent
level contribution to the total matter density today. Because of its very large
de Broglie wavelength, this axion matter density $\omega_a$ suppresses the
matter power spectrum, alleviating the CMB/$\Lambda$CDM $S_8/\sigma_8$ tension
with the weak-lensing data. It also explains the recently reported isotropic
cosmic birefringence by its coupling with photons. Adding the axion ($m \sim
10^{-22}\,$eV) in the fuzzy dark matter model to the axi-Higgs model allows
bigger $\Delta v_{\rm rec}$ and $\omega_a$ to address the Hubble and
$S_8/\sigma_8$ tensions simultaneously. The model predicts that $\Delta v$ may
be detected by the spectral measurements of quasars, while its oscillation may
be observed in the atomic clock measurements.


  We show there exist UV-complete field-theoretic models in general dimension,
including $2+1$, with the spontaneous breaking of a global symmetry, which
persists to the arbitrarily high temperatures. Our example is a conformal
vector model with the $O(N)\times \mathbb{Z}_2$ symmetry at zero temperature.
Using conformal perturbation theory we establish $\mathbb{Z}_2$ symmetry is
broken at finite temperature for $N>10$. Similar to recent constructions, in
the infinite $N$ limit our model has a non-trivial conformal manifold, a moduli
space of vacua, which gets deformed at finite temperature. Furthermore, in this
regime the model admits a persistent breaking of $O(N)$ in $2+1$ dimensions,
therefore providing another example where the Coleman-Hohenberg-Mermin-Wagner
theorem can be bypassed.


  We prove that the number of edges of a multigraph $G$ with $n$ vertices is at
most $O(n^2\log n)$, provided that any two edges cross at most once, parallel
edges are noncrossing, and the lens enclosed by every pair of parallel edges in
$G$ contains at least one vertex. As a consequence, we prove the following
extension of the Crossing Lemma of Ajtai, Chv\'atal, Newborn, Szemer\'edi and
Leighton, if $G$ has $e \geq 4n$ edges, in any drawing of $G$ with the above
property, the number of crossings is
$\Omega\left(\frac{e^3}{n^2\log(e/n)}\right)$. This answers a question of
Kaufmann et al. and is tight up to the logarithmic factor.


  Recently, mirror symmetry is derived as T-duality applied to gauge systems
that flow to non-linear sigma models. We present some of its applications to
study quantum geometry involving D-branes. In particular, we show that one can
employ D-branes wrapped on torus fibers to reproduce the mirror duality itself,
realizing the program of Strominger-Yau-Zaslow in a slightly different context.
Floer theory of intersecting Lagrangians plays an essential role.


  Gradient-based Monte Carlo sampling algorithms, like Langevin dynamics and
Hamiltonian Monte Carlo, are important methods for Bayesian inference. In
large-scale settings, full-gradients are not affordable and thus stochastic
gradients evaluated on mini-batches are used as a replacement. In order to
reduce the high variance of noisy stochastic gradients, Dubey et al. [2016]
applied the standard variance reduction technique on stochastic gradient
Langevin dynamics and obtained both theoretical and experimental improvements.
In this paper, we apply the variance reduction tricks on Hamiltonian Monte
Carlo and achieve better theoretical convergence results compared with the
variance-reduced Langevin dynamics. Moreover, we apply the symmetric splitting
scheme in our variance-reduced Hamiltonian Monte Carlo algorithms to further
improve the theoretical results. The experimental results are also consistent
with the theoretical results. As our experiment shows, variance-reduced
Hamiltonian Monte Carlo demonstrates better performance than variance-reduced
Langevin dynamics in Bayesian regression and classification tasks on real-world
datasets.


We smooth the singularities of a strictly hyperbolized smooth cube manifold.


  Total and partial density of states, frequency dependent complex refractive
index including extinction coefficient, optical conductivity and transmission
of MgxZn1-xO (0 \leq x \leq 1) in rocksalt and wurtzite phases are calculated
using full potential linearized augmented plane wave (FP-LAPW) method. The real
part of refractive index decreases while the extinction coefficient, optical
conductivity and transmission for rocksalt phase increases with the increase in
Mg concentration. In wurtzite phase, ordinary and extraordinary indices
decreases while extinction coefficient, optical conductivity and transmission
increases in parallel as well as perpendicular to c-axis with the increase in
the Mg concentration.


  An entangled state prepared in a decoherence free sub-space together with a
Ramsey type measurement can probe parity violation in heavy alkali ions like
Ba+ or Ra+. Here we propose an experiment with Ba+ as an example to measure the
small parity violating effect in this system. It has been shown that a
measurement on a maximally correlated system will reduce the uncertainty as
compared to that on a single ion measurement. In addition it also provides a
feasible solution to measure the nuclear spin dependent part of the total
parity violating light shift in an ionic system which has so far not been
addressed.


  We present a comprehensive study of the optical properties of InAs/InP
self-assembled quantum dots (QDs) using an empirical pseudopotential method and
configuration interaction treatment of the many-particle effects. The results
are compared to those of InAs/GaAs QDs. The main results are: (i) The alignment
of emission lines of neutral exciton, charged exciton and biexciton in InAs/InP
QDs is quite different from that in InAs/GaAs QDs. (ii) The hidden correlation
in InAs/InP QDs is 0.7 - 0.9 meV, smaller than that in InAs/GaAs QDs. (iii) The
radiative lifetimes of neutral exciton, charged exciton and biexciton in
InAs/InP QDs are about twice longer than those in InAs/GaAs QDs. (v) The phase
diagrams of few electrons and holes in InAs/InP QDs differ greatly from those
in InAs/GaAs QDs. The filling orders of electrons and holes are shown to obey
the Hund's rule and Aufbau principle, and therefore the photoluminescence
spectra of highly charged excitons are very different from those of InAs/GaAs
QDs.


  We propose various composite $\pi$-pulse sequences for implementing robust
z-axis rotation gates widely used in quantum information processing (QIP)
scenarios, and discuss their error tolerance of the pulse strength error (PSE)
and off-resonance error (ORE), i.e., two typical systematic errors in NMR
systems. Compared to existing composite gates, our designed composite pulses
exhibit higher gate fidelity and shorter sequence time cost. Furthermore, such
short pulse sequences are generalized by simple analytic formulas which can
suppress these errors to any desired order simultaneously with linear length
scaling, indicating an efficient construction of them with arbitrary accuracy.


  In this paper, we propose the {\alpha}-Lomax distribution as a new compound
fading channel model. This new distribution generalizes the recently introduced
Lomax fading channel model. It is worth noting that the Lomax distribution is a
decreasing function, while the {\alpha}-Lomax is a unimodal function, offering
greater flexibility in modeling wireless fading channels. In particular, we
derive closed-form expressions for the probability density function and
cumulative distribution function for the instantaneous signal-to-noise ratio
(SNR). Additionally, we provide closed-form expressions for several fundamental
performance metrics, including outage probability, average bit error rate, and
channel capacity. Furthermore, we derive closed-form expression for the average
block-length error rate in short-packet communications. Moreover, we fit the
PDF of the proposed channel model to empirical data obtained from a
device-to-device communication system. We also offer simple and accurate
approximations for these expressions in the high SNR regime.


  In this work, we investigate the relation between the concept of
``information rate'', an information geometric method for measuring the speed
of the time evolution of the statistical states of a stochastic process, and
stochastic thermodynamics quantities like entropy rate and entropy production.
Then, we propose the application of entropy rate and entropy production to
different practical applications such as abrupt event detection, correlation
analysis, and control engineering. Specifically, by utilising the Fokker-Planck
equation of multi-variable linear stochastic processes described by Langevin
equations, we calculate the exact value for information rate, entropy rate, and
entropy production and derive various inequalities among them. Inspired by
classical correlation coefficients and control techniques, we create
entropic-informed correlation coefficients as abrupt event detection methods
and information geometric cost functions as optimal thermodynamic control
policies, respectively. The methods are analysed via the numerical simulations
of common prototypical systems.


  Let $G$ be a finite group. Let $k(G)$ denote the number of conjugacy classes
of $G$ and let $m(G)$ denote the least positive integer $n$ such that the union
of any $n$ distinct non-trivial conjugacy classes of $G$ together with the
identity of $G$ is a subgroup of $G$. We prove that $m(G)=k(G)-1$ for all
$m(G)\ge 2$.


  Creating and labelling datasets of videos for use in training Human Activity
Recognition models is an arduous task. In this paper, we approach this by using
3D rendering tools to generate a synthetic dataset of videos, and show that a
classifier trained on these videos can generalise to real videos. We use five
different augmentation techniques to generate the videos, leading to a wide
variety of accurately labelled unique videos. We fine tune a pre-trained I3D
model on our videos, and find that the model is able to achieve a high accuracy
of 73% on the HMDB51 dataset over three classes. We also find that augmenting
the HMDB training set with our dataset provides a 2% improvement in the
performance of the classifier. Finally, we discuss possible extensions to the
dataset, including virtual try on and modeling motion of the people.


  Active subspace is a model reduction method widely used in the uncertainty
quantification community. In this paper, we propose analyzing the internal
structure and vulnerability and deep neural networks using active subspace.
Firstly, we employ the active subspace to measure the number of "active
neurons" at each intermediate layer and reduce the number of neurons from
several thousands to several dozens. This motivates us to change the network
structure and to develop a new and more compact network, referred to as
{ASNet}, that has significantly fewer model parameters. Secondly, we propose
analyzing the vulnerability of a neural network using active subspace and
finding an additive universal adversarial attack vector that can misclassify a
dataset with a high probability. Our experiments on CIFAR-10 show that ASNet
can achieve 23.98$\times$ parameter and 7.30$\times$ flops reduction. The
universal active subspace attack vector can achieve around 20% higher attack
ratio compared with the existing approach in all of our numerical experiments.
The PyTorch codes for this paper are available online.


  The energy dependence of such characteristics as a ratio of the total number
of charged particles to the total flux of EAS Cherenkov radiation, a ratio of
E(thr)>=1GeV muon flux density at the distance of 600m from a shower core to
charged particle flux density, a ratio of the energy transferred to the
electromagnetic component of EAS to the primary particle energy is presented.
Their comparison with two-component mass composition of cosmic rays (p-Fe) in
the framework of calculations by a QGSJET model is given.


  We show that the homology torsion growth of a free-by-cyclic group with
polynomially growing monodromy vanishes in every dimension independently of the
choice of Farber chain. It follows that the integral torsion $\rho^\mathbb{Z}$
equals the $\ell^2$-torsion $\rho^{(2)}$ verifying a conjecture of L\"uck for
these groups.


  Federated Learning (FL) is a novel distributed machine learning which allows
thousands of edge devices to train model locally without uploading data
concentrically to the server. But since real federated settings are
resource-constrained, FL is encountered with systems heterogeneity which causes
a lot of stragglers directly and then leads to significantly accuracy reduction
indirectly. To solve the problems caused by systems heterogeneity, we introduce
a novel self-adaptive federated framework FedSAE which adjusts the training
task of devices automatically and selects participants actively to alleviate
the performance degradation. In this work, we 1) propose FedSAE which leverages
the complete information of devices' historical training tasks to predict the
affordable training workloads for each device. In this way, FedSAE can estimate
the reliability of each device and self-adaptively adjust the amount of
training load per client in each round. 2) combine our framework with Active
Learning to self-adaptively select participants. Then the framework accelerates
the convergence of the global model. In our framework, the server evaluates
devices' value of training based on their training loss. Then the server
selects those clients with bigger value for the global model to reduce
communication overhead. The experimental result indicates that in a highly
heterogeneous system, FedSAE converges faster than FedAvg, the vanilla FL
framework. Furthermore, FedSAE outperforms than FedAvg on several federated
datasets - FedSAE improves test accuracy by 26.7% and reduces stragglers by
90.3% on average.


  An adaptive algorithm, based on residual type a posteriori indicators of
errors measured in $L^{\infty}(L^2)$ and $L^2(L^2)$ norms, for a numerical
scheme consisting of implicit Euler method in time and discontinuous Galerkin
method in space for linear parabolic fourth order problems is presented. The a
posteriori analysis is performed for convex domains in two and three space
dimensions for local spatial polynomial degrees $r\ge 2$. The a posteriori
estimates are then used within an adaptive algorithm, highlighting their
relevance in practical computations, which results into substantial reduction
of computational effort.


  Neural field equations model population dynamics of large-scale networks of
neurons. Wave propagation in neural fields is often studied by constructing
traveling wave solutions in the wave coordinate frame. Nonequilibrium dynamics
are more challenging to study, due to the nonlinearity and nonlocality of
neural fields, whose interactions are described by the kernel of an integral
term. Here, we leverage interface methods to describe the threshold of wave
initiation away from equilibrium. In particular, we focus on traveling front
initiation in an excitatory neural field. In a neural field with a Heaviside
firing rate, neural activity can be described by the dynamics of the
interfaces, where the neural activity is at the firing threshold. This allows
us to derive conditions for the portion of the neural field that must be
activated for traveling fronts to be initiated in a purely excitatory neural
field. Explicit equations are possible for a single active (superthreshold)
region, and special cases of multiple disconnected active regions. The dynamic
spreading speed of the excited region can also be approximated asymptotically.
We also discuss extensions to the problem of finding the critical
spatiotemporal input needed to initiate waves.


  With the development of additive manufacturing, 3D printing technology has
become more common nowadays. We designed and 3D printed a cost-effective liquid
fluid pressure measurement device that can convert liquid pressure to air
pressure. Air pressure was measured by a low-cost manometer in this study. The
device can measure the pressure drop across artificial aortic heart valves at
different flow rate conditions. The main objective of this study is to utilize
3D printing technology to measure pressure loss through artificial aortic heart
valves. From the measured pressure drop, the energy loss of flow that occurs
through the artificial aortic heart valves can be estimated. In the experiment,
both mechanical and biological (bovine skin) aortic heart valves have been
tested at several different flow rate conditions. By doing so, we were able to
measure energy loss at different flow rates through the valves to test which
type and size of the heart valve have the lowest energy loss during operation.
Lower energy loss of the blood through the valve should have a lower burden to
a patients heart. This study provides an example of a new application of
additive manufacturing in liquid fluid pressure measurement devices and showed
an acceptable performance in the experiment.


  This paper provides a duality gap convergence analysis for the standard ADMM
as well as a linearized version of ADMM. It is shown that under appropriate
conditions, both methods achieve linear convergence. However, the standard ADMM
achieves a faster accelerated convergence rate than that of the linearized
ADMM. A simple numerical example is used to illustrate the difference in
convergence behavior.


  Current research on micro-mechanical resonators strives for quantum-limited
detection of the motion of macroscopic objects. Prerequisite to this goal is
the observation of measurement backaction consistent with quantum metrology
limits. However, thermal noise presently dominates measurements and precludes
ground-state preparation of the resonator. Here we establish the collective
motion of an ultracold atomic gas confined tightly within a Fabry-Perot optical
cavity as a system for investigating the quantum mechanics of macroscopic
bodies. The cavity-mode structure selects a single collective vibrational mode
that is measured by the cavity's optical properties, actuated by the cavity
optical field, and subject to backaction by the quantum force fluctuations of
this field. Experimentally, we quantify such fluctuations by measuring the
cavity-light-induced heating of the intracavity atomic ensemble. These
measurements represent the first observation of backaction on a macroscopic
mechanical resonator at the standard quantum limit.


  This study extracted and analyzed the linguistic speech patterns that
characterize Japanese anime or game characters. Conventional morphological
analyzers, such as MeCab, segment words with high performance, but they are
unable to segment broken expressions or utterance endings that are not listed
in the dictionary, which often appears in lines of anime or game characters. To
overcome this challenge, we propose segmenting lines of Japanese anime or game
characters using subword units that were proposed mainly for deep learning, and
extracting frequently occurring strings to obtain expressions that characterize
their utterances. We analyzed the subword units weighted by TF/IDF according to
gender, age, and each anime character and show that they are linguistic speech
patterns that are specific for each feature. Additionally, a classification
experiment shows that the model with subword units outperformed that with the
conventional method.


  The family Asteraceae include large number of Centaurea species which have
been applied in folk medicine. One of the family Asteraceae members is the
Centaurea damascena which authentically been tested for its antibacterial and
antioxidant activity as well as its toxicity. The aims of the study were to
determine the antimicrobial and antioxidant activities and toxicity of
methanolic plant extracts of Centaurea damascena. The methanolic extracts were
screened for their antibacterial activity against nine bacteria (Staphylococcus
aureus ATCC 43300, Bacillus subtilis ATCC 6633, Micrococcus luteus ATCC 10240,
and Staphylococcus epidermidis ATCC 12228, Escherichia coli ATCC 11293,
Pseudomonas aerugino and Klebsiella pneumoniae, Enterobacter aerogenes ATCC
13048 and Salmonella typhi ATCC19430). The antibacterial activity was assessed
by using the disc diffusion methods and the minimum inhibition concentrations
(MIC) using microdilution method. The extracts from Centaurea damascena
possessed antibacterial activity against several of the tested microorganisms.
The MIC of methanol extract of C. damascena ranged from 60 to 1100 microgram
per mL. Free radical scavenging capacity of the C. damascena methanol extract
was calculated by DPPH and FRAP test. DPPH radicals were scavenged with an IC50
value of 17.08 microgram per mL. Antioxidant capacities obtained by the FRAP
was 51.9 and expressed in mg Trolox per gram dry weight. The total phenolic
compounds of the methanol extracts of aerial parts, as estimated by
Folin_Ciocalteu reagent method, was about 460 mg GAE per gram. The phenolic
contents in the extracts highly correlate with their antioxidant activity,
confirming that the antioxidant activity of this plant extracts is considerably
phenolic contents-dependent.


  We investigate the low-energy physics of non-Hermitian quantum spin models
with $PT$-symmetry. To this end we consider the one-dimensional Ising chain and
the two-dimensional toric code in a non-Hermitian staggered field. For both
systems dual descriptions in terms of non-Hermitian staggered Ising
interactions in a conventional transverse field exist. We perform high-order
series expansions about the high- and low-field limit for both systems to
determine the ground-state energy per site and the one-particle gap. The
one-dimensional non-Hermitian Ising chain is known to be exactly solvable. Its
ground-state phase diagram consists of second-order quantum phase transitions,
which can be characterized by logarithmic singularities of the second
derivative of the ground-state energy and, in the symmetry-broken phase, the
gap closing of the low-field gap. In contrast, the gap closing from the
high-field phase is not accessible perturbatively due to the complex energy and
the occurrence of exceptional lines in the high-field gap expression. For the
two-dimensional toric code in a non-Hermitian staggered field we study the
quantum robustness of the topologically ordered phase by the gap closing of the
low-field gap. We find that the well-known second-order quantum phase
transition of the toric code in a uniform field extends into a large portion of
the non-Hermitian parameter space. However, the series expansions become
unreliable for a dominant anti-Hermitian field. Interestingly, the analysis of
the high-field gap reveals the potential presence of an intermediate region.


  The nu=5/2 fractional quantum Hall effect state has attracted great interest
recently, both as an arena to explore the physics of non-Abelian quasiparticle
excitations, and as a possible architecture for topological quantum information
processing. Here we use the conformal field theoretic description of the
Moore-Read state to provide clear tunneling signatures of this state in an
Aharonov-Bohm geometry. While not probing statistics directly, the measurements
proposed here would provide a first, experimentally tractable step towards a
full characterization of the 5/2 state.


  Alloying/doping in two-dimensional material has been important due to wide
range band gap tunability. Increasing the number of components would increase
the degree of freedom which can provide more flexibility in tuning the band gap
and also reduced the growth temperature. Here, we report synthesis of
quaternary alloys MoxW1-xS2ySe2(1-y) using chemical vapour deposition. The
composition of alloys has been tuned by changing the growth temperatures. As a
result, we can tune the bandgap which varies from 1.73 eV to 1.84 eV. The
detailed theoretical calculation supports the experimental observation and
shows a possibility of wide tunability of bandgap.


  The zero modes' Fock space for the extended chiral $su(2)$ WZNW model gives
room to a realization of the Grothendieck fusion ring of representations of the
restricted $U_q sl(2)$ quantum universal enveloping algebra (QUEA) at an even
($2h$-th) root of unity, and of its extension by the Lusztig operators. It is
shown that expressing the Drinfeld images of canonical characters in terms of
Chebyshev polynomials of the Casimir invariant $C$ allows a streamlined
derivation of the characteristic equation of $C$ from the defining relations of
the restricted QUEA. The properties of the fusion ring of the Lusztig's
extension of the QUEA in the zero modes' Fock space are related to the braiding
properties of correlation functions of primary fields of the extended
$su(2)_{h-2}$ current algebra model.


  Target detection algorithm based on deep learning needs high computer GPU
configuration, even need to use high performance deep learning workstation,
this not only makes the cost increase, also greatly limits the realizability of
the ground, this paper introduces a kind of lightweight algorithm for target
detection under the condition of the balance accuracy and computational
efficiency, MobileNet as Backbone performs parameter The processing speed is
30fps on the RTX2060 card for images with the CNN separator layer. The
processing speed is 30fps on the RTX2060 card for images with a resolution of
320*320.


  We have performed theoretical calculation of the nonlinear optical properties
in a quantum well (QW) with the hyperbolic confinement potential. Calculation
results reveal that the transition energy, oscillator strength, second-order
nonlinear optical rectification (OR), geometric factor and nonlinear optical
absorption (OA) are strongly affected by the parameters ($\alpha, \sigma$) of
the hyperbolic confinement potential. And an increment of the parameter
$\alpha$ reduces all these physical quantities, while an increment of the
parameter $\sigma$ enhances them, but not for geometric factor. In addition, it
is found that one can control the optical properties of QW by tuning these
parameters.


  Panoptic segmentation has recently unified semantic and instance
segmentation, previously addressed separately, thus taking a step further
towards creating more comprehensive and efficient perception systems. In this
paper, we present Panoster, a novel proposal-free panoptic segmentation method
for LiDAR point clouds. Unlike previous approaches relying on several steps to
group pixels or points into objects, Panoster proposes a simplified framework
incorporating a learning-based clustering solution to identify instances. At
inference time, this acts as a class-agnostic segmentation, allowing Panoster
to be fast, while outperforming prior methods in terms of accuracy. Without any
post-processing, Panoster reached state-of-the-art results among published
approaches on the challenging SemanticKITTI benchmark, and further increased
its lead by exploiting heuristic techniques. Additionally, we showcase how our
method can be flexibly and effectively applied on diverse existing semantic
architectures to deliver panoptic predictions.


  Real-world data from diverse domains require real-time scalable analysis.
Large-scale data processing frameworks or engines such as Hadoop fall short
when results are needed on-the-fly. Apache Spark's streaming library is
increasingly becoming a popular choice as it can stream and analyze a
significant amount of data. In this paper, we analyze large-scale geo-temporal
data collected from the USGODAE (United States Global Ocean Data Assimilation
Experiment) data catalog, and showcase and assess the ability of Spark stream
processing. We measure the latency of streaming and monitor scalability by
adding and removing nodes in the middle of a streaming job. We also verify the
fault tolerance by stopping nodes in the middle of a job and making sure that
the job is rescheduled and completed on other nodes. We design a full-stack
application that automates data collection, data processing and visualizing the
results. We also use Google Maps API to visualize results by color coding the
world map with values from various analytics.


  Thermal emission from a hot body is ubiquitous, yet its properties remain
inherently challenging to control due to its incoherent nature. Recent advances
in thermal emission manipulation have been unveiling exciting phenomena and new
opportunities for applications. In particular, judiciously patterned nanoscale
features over their surface have been shown to channel emission sources into
partially coherent beams with tailored directionality and frequency
selectivity. Yet, more sophisticated forms of control, such as spin-selective
and unidirectional thermal emission have remained elusive. Here, we
experimentally demonstrate single-layer metasurfaces emitting unidirectional,
narrowband thermal light in the infrared with arbitrary polarization states -
an operation enabled by photonic bound states in the continuum locally tailored
by a geometric phase controlling the temporal and spatial coherence of emitted
light. The demonstrated platform paves the way to a compactification paradigm
for metasurface optics, in which thermal emission or photoluminescence can feed
arbitrarily patterned beams without the need of external coherent sources.


  We study the dilute and ultracold unitary Bose gas, which is characterized by
a universal equation of state due to the diverging s-wave scattering length,
under a transverse harmonic confinement. From the hydrodynamic equations of
superfluids we derive an effective one-dimensional nonpolynomial Schr\"odinger
equation (1D NPSE) for the axial dynamics which, however, takes also into
account the transverse dynamics. Finally, by solving the 1D NPSE we obtain
meaningful analytical formulas for the dark (gray and black) solitons of the
bosonic system.


  This paper presents, using dynamical system theory, a framework for
investigating the turnpike property in nonlinear optimal control. First, it is
shown that a turnpike-like property appears in general dynamical systems with
hyperbolic equilibrium and then, apply it to optimal control problems to obtain
sufficient conditions for the turnpike occurs. The approach taken is geometric
and gives insights for the behaviors of controlled trajectories, allowing us to
find simpler proofs for existing results on the turnpike properties. Attempts
to remove smallness restrictions for initial and target states are also
discussed based on the geometry of (un)stable manifold and exponential
stabilizability of control systems.


  We present the 15 micron extragalactic source counts from the Final Analysis
Catalogue of the European Large Area ISO Survey southern hemisphere field S1,
extracted using the Lari method. The large number of extragalactic sources
(about 350) detected over this area between 0.5 and 100 mJy guarantee a high
statistical significance of the source counts in the previously poorly covered
flux density range between IRAS and the Deep ISOCAM Surveys. The bright counts
in S1 (> 2mJy) are consistent with a flat, Euclidean slope, suggesting the
dominance of a non-evolving population. In contrast, at fainter fluxes (< 2
mJy) our counts show a strong departure from no evolution models, with a very
steep super-Euclidean slope down to our flux limit. Strong luminosity and
density evolution is needed at least for the population of star-forming
galaxies, together with a luminosity break around 10^10.8 Lsun in their local
luminosity function in order to reproduce our sharp increase of the counts
below 2 mJy and the redshift distributions observed for 15 micron sources at
different flux levels. The contribution of the strongly evolving starburst
population (down to 50 microJy) to the 15 micron cosmic background is estimated
to be 2.2 nW m^-2 sr^-1 (67% of the total mid-infrared background estimate).


  The standard theoretical framework for fractional quantum anomalous Hall
effect (FQAH) assumes an isolated flat Chern band in the single particle level.
In this paper we challenges this paradigm for the FQAH recently observed in the
pentalayer rhombohedral stacked graphene aligned with hexagon boron nitride
(hBN). We show that the external moir\'e superlattice potential is simply a
perturbation in a model with continuous translation symmetry. Through Hartree
Fock calculation, we find that interaction opens a sizable remote band gap,
resulting an isolated narrow $C=1$ Chern band at filling $\nu=1$. From exact
diagonalization (ED) we identify FQAH phases at various fillings. But they
exist also in the calculations without any external moir\'e potential. We
suggest that the QAH insulator at $\nu=1$ should be viewed as an interaction
driven topological Wigner crystal with QAH effect, which is then pinned by a
small moir\'e potential. The $C=1$ QAH crystal is robust with a crystal period
around $10\mathrm{nm}$ in 4-layer, 5-layer, 6-layer and 7-layer graphene
systems. Our work suggests a new direction to exploring the interplay of
topology and FQAH with spontaneous crystal formation in the vanishing moir\'e
potential limit. We also propose a new system to generate and control both
honeycomb and triangular moir\'e superlattice potential through Coulomb
interaction from another control layer, which can stabilize or suppress the QAH
crystal depending on the density of the control layer.


  We analyze one-dimensional photonic superlattices which alternate layers of
air and a left-handed material. We assume Drude-type dispersive responses for
the dielectric permittivity and magnetic permeability of the left-handed
material. Maxwell's equations and the transfer-matrix technique are used to
derive the dispersion relation for the propagation of obliquely incident
optical fields. The photonic dispersion indicates that the growth-direction
component of the electric (or magnetic) field leads to the propagation of
electric (or magnetic) plasmon polaritons, for either TE or TM configurations.
Furthermore, we show that if the plasma frequency is chosen within the photonic
$<n(\omega)>=0$ zeroth-order bandgap, the coupling of light with plasmons
weakens considerably. As light propagation is forbidden in that particular
frequency region, the plasmon-polariton mode reduces to a pure plasmon mode.


  We present results of a search for WH -> lepton neutrino b bbar production in
ppbar collisions based on the analysis of 1.05 fb-1 of data collected by the D0
experiment at the Fermilab Tevatron, using a neural network for separating the
signal from backgrounds. No signal-like excess is observed, and we set 95 %
C.L. upper limits on the WH production cross section multiplied by the
branching ratio for H->bb for Higgs boson masses between 100 and 150 GeV. For a
Higgs boson mass of 115 GeV, we obtain an observed (expected) limit of 1.5
(1.4) pb, a factor of 11.4 (10.7) times larger than standard model prediction.


  It is known that one can formulate an action in teleparallel gravity which is
equivalent to general relativity, up to a boundary term. In this geometry we
have vanishing curvature, and non-vanishing torsion. The action is constructed
by three different contractions of torsion with specific coefficients. By
allowing these coefficients to be arbitrary we get the theory which is called
`new general relativity'. In this note, the Lagrangian for new general
relativity is written down in ADM-variables. In order to write down the
Hamiltonian we need to invert the velocities to canonical variables. However,
the inversion depends on the specific combination of constraints satisfied by
the theory (which depends on the coefficients in the Lagrangian). It is found
that one can combine these constraints in 9 different ways to obtain
non-trivial theories, each with a different inversion formula.


  Thermal Markovian dynamics is typically obtained by coupling a system to a
sufficiently hot bath with a large heat capacity. Here we present a scheme for
inducing Markovian dynamics using an arbitrarily small and cold heat bath. The
scheme is based on injecting phase noise to the small bath. Several unique
signatures of small bath are studied. We discuss realizations in ion traps and
superconducting qubits and show that it is possible to create an ideal setting
where the system dynamics is indifferent to the internal bath dynamics.


  The Casimir effect for rectangular boxes has been studied for several
decades. But there are still some points unclear. Recently, there are new
developments related to this topic, including the demonstration of the
equivalence of the regularization methods and the clarification of the
ambiguity in the regularization of the temperature-dependent free energy. Also,
the interesting quantum spring was raised stemming from the topological Casimir
effect of the helix boundary conditions. We review these developments together
with the general derivation of the Casimir energy of the $p$-dimensional cavity
in ($D+1$)-dimensional spacetime, paying special attention to the sign of the
Casimir force in a cavity with unequal edges. In addition, we also review the
Casimir piston, which is a configuration related to rectangular cavity.


  We consider autonomous stochastic ordinary differential equations (SDEs) and
weak approximations of their solutions for a general class of sufficiently
smooth path-dependent functionals f. Based on tools from functional It\^o
calculus, such as the functional It\^o formula and functional Kolmogorov
equation, we derive a general representation formula for the weak error
$E(f(X_T)-f(\tilde X_T))$, where $X_T$ and $\tilde X_T$ are the paths of the
solution process and its approximation up to time T. The functional
$f:C([0,T],R^d)\to R$ is assumed to be twice continuously Fr\'echet
differentiable with derivatives of polynomial growth. The usefulness of the
formula is demonstrated in the one dimensional setting by showing that if the
solution to the SDE is approximated via the linearly time-interpolated explicit
Euler method, then the rate of weak convergence for sufficiently regular f is
1.


  The optimal amount of dysprosium in the highly magnetostrictive rare-earth
compounds Tb$_{1-x}$Dy$_x$Fe$_2$ for room temperature applications has long
been known to be $x$=0.73 (Terfenol-D). Here, we derive this value from first
principles by calculating the easy magnetization direction and magnetostriction
as a function of composition and temperature. We use crystal field coefficients
obtained within density-functional theory to construct phenomenological
anisotropy and magnetoelastic constants. The temperature dependence of these
constants is obtained from disordered local moment calculations of the rare
earth magnetic order parameter. Our calculations find the critical Dy
concentration required to switch the magnetization direction at room
temperature to be $x_c$=0.78, with magnetostrictions $\lambda_{111}$=2700 and
$\lambda_{100}$=-430~ppm, close to the Terfenol-D values.


  Leveraging the symmetries inherent to specific data domains for the
construction of equivariant neural networks has lead to remarkable improvements
in terms of data efficiency and generalization. However, most existing research
focuses on symmetries arising from planar and volumetric data, leaving a
crucial data source largely underexplored: time-series. In this work, we fill
this gap by leveraging the symmetries inherent to time-series for the
construction of equivariant neural network. We identify two core symmetries:
*scale and translation*, and construct scale-translation equivariant neural
networks for time-series learning. Intriguingly, we find that scale-translation
equivariant mappings share strong resemblance with the wavelet transform.
Inspired by this resemblance, we term our networks Wavelet Networks, and show
that they perform nested non-linear wavelet-like time-frequency transforms.
Empirical results show that Wavelet Networks outperform conventional CNNs on
raw waveforms, and match strongly engineered spectrogram techniques across
several tasks and time-series types, including audio, environmental sounds, and
electrical signals. Our code is publicly available at
https://github.com/dwromero/wavelet_networks.


  In this paper we give a new basis, $\Lambda$, for the Homflypt skein module
of the solid torus, $\mathcal{S}({\rm ST})$, which was predicted by Jozef
Przytycki, using topological interpretation. The basis $\Lambda$ is different
from the basis $\Lambda^{\prime}$, discovered independently by Hoste--Kidwell
\cite{HK} and Turaev \cite{Tu} with the use of diagrammatic methods. For
finding the basis $\Lambda$ we use the generalized Hecke algebra of type B,
$\textrm{H}_{1,n}$, defined by the second author in \cite{La2}, which is
generated by looping elements and braiding elements and which is isomorphic to
the affine Hecke algebra of type A. Namely, we start with the well-known basis
of $\mathcal{S}({\rm ST})$, $\Lambda^{\prime}$, and an appropriate linear basis
$\Sigma_n$ of the algebra $\textrm{H}_{1,n}$. We then convert elements in
$\Lambda^{\prime}$ to linear combinations of elements in the new basic set
$\Lambda$. This is done in two steps: First we convert elements in
$\Lambda^{\prime}$ to elements in $\Sigma_n$. Then, using conjugation and the
stabilization moves, we convert these elements to linear combinations of
elements in $\Lambda$ by managing gaps in the indices of the looping elements
and by eliminating braiding tails in the words. Further, we define an ordering
relation in $\Lambda^{\prime}$ and $\Lambda$ and prove that the sets are
totally ordered. Finally, using this ordering, we relate the sets
$\Lambda^{\prime}$ and $\Lambda$ via a block diagonal matrix, where each block
is an infinite lower triangular matrix with invertible elements in the diagonal
and we prove linear independence of the set $\Lambda$. The infinite matrix is
then "invertible" and thus, the set $\Lambda$ is a basis for $\mathcal{S}({\rm
ST})$. The aim of this paper is to provide the basic algebraic tools for
computing skein modules of c.c.o. $3$-manifolds via algebraic means.


  We study the quantum controlled and probabilistic teleportation protocol via
a four-cluster state (Front. Phys. (2017) 12: 120306). The protocol cannot
achieve the goal that if the teleportation fails, it can be repeated without
copies of the teleported state. And the reason is that all the information of
the teleported state shifts to the receiver's particle after Bell measurement
and the information cannot shift back to the sender without other entangled
states. To realize the claimed goal, a new quantum controlled and probabilistic
teleportation protocol using the same four-cluster state is presented. Because
no information of the teleported stated is lost during the whole teleportation
process, the teleportation process can be repeated until the teleportation
success.


  We formulate the statistics of the discrete multicomponent fragmentation
event using a methodology borrowed from statistical mechanics. We generate the
ensemble of all feasible distributions that can be formed when a single integer
multicomponent mass is broken into fixed number of fragments and calculate the
combinatorial multiplicity of all distributions in the set. We define random
fragmentation by the condition that the probability of distribution be
proportional to its multiplicity and obtain the partition function and the mean
distribution in closed form. We then introduce a functional that biases the
probability of distribution to produce in a systematic manner fragment
distributions that deviate to any arbitrary degree from the random case. We
corroborate the results of the theory by Monte Carlo simulation and demonstrate
examples in which components in sieve cuts of the fragment distribution undergo
preferential mixing or segregation relative to the parent particle.


  We study vortex pattern formation in thin ferromagnetic films under the
action of strong spin-polarized currents. Considering the currents which are
polarized along the normal of the film plane, we determine the critical current
above which the film goes to a saturated state with all magnetic moments being
perpendicular to the film plane. We show that stable square vortex-antivortex
superlattices (\emph{vortex crystals}) appears slightly below the critical
current. The melting of the vortex crystal occurs with current further
decreasing. A mechanism of current-induced periodic vortex-antivortex lattice
formation is proposed. Micromagnetic simulations confirm our analytical results
with a high accuracy.


  The paper completely characterizes the primality of acyclic DFAs, where a DFA
$\mathcal{A}$ is prime if there do not exist DFAs
$\mathcal{A}_1,\dots,\mathcal{A}_t$ with $\mathcal{L}(\mathcal{A}) =
\bigcap_{i=1}^{t} \mathcal{L}({\mathcal{A}_i})$ such that each $\mathcal{A}_i$
has strictly less states than the minimal DFA recognizing the same language as
$\mathcal{A}$. A regular language is prime if its minimal DFA is prime. Thus,
this result also characterizes the primality of finite languages.
  Further, the $\mathsf{NL}$-completeness of the corresponding decision problem
$\mathsf{PrimeDFA}_{\text{fin}}$ is proven. The paper also characterizes the
primality of acyclic DFAs under two different notions of compositionality,
union and union-intersection compositionality.
  Additionally, the paper introduces the notion of S-primality, where a DFA
$\mathcal{A}$ is S-prime if there do not exist DFAs
$\mathcal{A}_1,\dots,\mathcal{A}_t$ with $\mathcal{L}(\mathcal{A}) =
\bigcap_{i=1}^{t} \mathcal{L}(\mathcal{A}_i)$ such that each $\mathcal{A}_i$
has strictly less states than $\mathcal{A}$ itself. It is proven that the
problem of deciding S-primality for a given DFA is $\mathsf{NL}$-hard. To do
so, the $\mathsf{NL}$-completeness of $\mathsf{2MinimalDFA}$, the basic problem
of deciding minimality for a DFA with at most two letters, is proven.


  We present a novel integration of an instruction-tuned large language model
(LLM) and end-to-end automatic speech recognition (ASR). Modern LLMs can
perform a wide range of linguistic tasks within zero-shot learning when
provided with a precise instruction or a prompt to guide the text generation
process towards the desired task. We explore using this zero-shot capability of
LLMs to extract linguistic information that can contribute to improving ASR
performance. Specifically, we direct an LLM to correct grammatical errors in an
ASR hypothesis and harness the embedded linguistic knowledge to conduct
end-to-end ASR. The proposed model is built on the hybrid connectionist
temporal classification (CTC) and attention architecture, where an
instruction-tuned LLM (i.e., Llama2) is employed as a front-end of the decoder.
An ASR hypothesis, subject to correction, is obtained from the encoder via CTC
decoding, which is then fed into the LLM along with an instruction. The decoder
subsequently takes as input the LLM embeddings to perform sequence generation,
incorporating acoustic information from the encoder output. Experimental
results and analyses demonstrate that the proposed integration yields promising
performance improvements, and our approach largely benefits from LLM-based
rescoring.


  We extend the results of M. Edjvet on balanced presentations and largeness by
giving conditions under which presentations with negative deficiency define
large groups.


  We use the largest open repository of public speaking---TED Talks---to
predict the ratings of the online viewers. Our dataset contains over 2200 TED
Talk transcripts (includes over 200 thousand sentences), audio features and the
associated meta information including about 5.5 Million ratings from
spontaneous visitors of the website. We propose three neural network
architectures and compare with statistical machine learning. Our experiments
reveal that it is possible to predict all the 14 different ratings with an
average AUC of 0.83 using the transcripts and prosody features only. The
dataset and the complete source code is available for further analysis.