  In the last two decades the structure of Extended Affine Lie algebras (EALA)
is extensively studied. In explicitly constructing an EALA, the centerless Lie
Torus play an important role. In this paper we consider the Universal central
extension of a centerless Lie Torus and classify the irreducible integrable
modules for them when the center acts non-trivially. They turn out to be
"highest weight modules" for direct sum of finitely many affine Lie algebras.


  We present a single-scattering formalism for incoherent resonant light
scattering by dilute quantum gas systems such as the atomic-trap Bose-Einstein
condensates. We show that resonant scattering gives access to more information
than the dynamical structure factor, familiar from non-resonant scattering. In
particular, we show that the detuning dependence of the incoherent scattering
cross-section allows the direct determination of the BEC pairing density $<
\psi \psi >$, which is a broken symmetry and provides evidence that the
condensate is not in a good number state.


  In this work, we consider an extension to parabolic problems of the
variational multiscale method with spectral approximation of the sub-scales. We
first discretize in time using a finite difference scheme and second, apply the
generalization of the spectral variational multi-scale method. To obtain error
estimations in convection-dominated flows, we find a helpful link between the
stabilized term expressed in terms of Green's functions and in terms of
spectral functions. Finally, we present some numerical tests to show the
reliability of the method. We consider the stationary one-dimensional
advection-diffusion-reaction equation and the evolutive one-dimensional
advection-diffusion equation.


  An entanglement monotone, which is invariant under the determinant 1 SLOCC
operations and measures the true quadripartite entanglement, is explicitly
constructed.


  Soft-granular media, such as dense emulsions, foams or tissues, exhibit
either fluid- or solid-like properties depending on the applied external
stresses. Whereas bulk rheology of such materials has been thoroughly
investigated, the internal structural mechanics of finite soft-granular
structures with free interfaces is still poorly understood. Here, we report the
spontaneous `crystallization' and `melting' inside a model soft granular
cluster -- a densely packed aggregate of $N\sim 30-40$ droplets engulfed by a
fluid film -- subject to a varying external flow. We develop new machine
learning tools to track the internal rearrangements in the quasi-2D cluster as
it transits a sequence of constrictions. As the cluster relaxes from a state of
strong mechanical deformations, we find differences in the dynamics of the
grains within the interior of the cluster and those at its rim, with the latter
experiencing larger deformations and less frequent rearrangements, effectively
acting as an elastic membrane around a fluid-like core. We conclude that the
observed structural-dynamical heterogeneity results from an interplay of the
topological constrains, due to the presence of a closed interface, and the
internal solid-fluid transitions. We discuss universality of such behavior in
various types of finite soft granular structures, including biological tissues.


  Contrastive loss has been increasingly used in learning representations from
multiple modalities. In the limit, the nature of the contrastive loss
encourages modalities to exactly match each other in the latent space. Yet it
remains an open question how the modality alignment affects the downstream task
performance. In this paper, based on an information-theoretic argument, we
first prove that exact modality alignment is sub-optimal in general for
downstream prediction tasks. Hence we advocate that the key of better
performance lies in meaningful latent modality structures instead of perfect
modality alignment. To this end, we propose three general approaches to
construct latent modality structures. Specifically, we design 1) a deep feature
separation loss for intra-modality regularization; 2) a Brownian-bridge loss
for inter-modality regularization; and 3) a geometric consistency loss for both
intra- and inter-modality regularization. Extensive experiments are conducted
on two popular multi-modal representation learning frameworks: the CLIP-based
two-tower model and the ALBEF-based fusion model. We test our model on a
variety of tasks including zero/few-shot image classification, image-text
retrieval, visual question answering, visual reasoning, and visual entailment.
Our method achieves consistent improvements over existing methods,
demonstrating the effectiveness and generalizability of our proposed approach
on latent modality structure regularization.


  Let G be a group such that its finite subgroups have bounded order, let d
denote the lowest common multiple of the orders of the finite subgroups of G,
and let K be a subfield of C that is closed under complex conjugation. Let U(G)
denote the algebra of unbounded operators affiliated to the group von Neumann
algebra N(G), and let D(KG,U(G)) denote the division closure of KG in U(G);
thus D(KG,U(G)) is the smallest subring of U(G) containing KG that is closed
under taking inverses. Suppose n is a positive integer, and \alpha \in
\Mat_n(KG). Then \alpha induces a bounded linear map \alpha: l^2(G)^n \to
\l^2(G)^n, and \ker\alpha has a well-defined von Neumann dimension \dim_{N(G)}
(\ker\alpha). This is a nonnegative real number, and one version of the Atiyah
conjecture states that d \dim_{N(G)}(\ker\alpha) \in Z. Assuming this
conjecture, we shall prove that if G has no nontrivial finite normal subgroup,
then D(KG,U(G)) is a d \times d matrix ring over a skew field. We shall also
consider the case when G has a nontrivial finite normal subgroup, and other
subrings of U(G) that contain KG.


  This study explores the role that the microstructure plays in determining the
macroscopic static response of porous elastic continua and exposes the
occurrence of position-dependent nonlocal effects that are strictly correlated
to the configuration of the microstructure. Then, a nonlocal continuum theory
based on variable-order fractional calculus is developed in order to accurately
capture the complex spatially distributed nonlocal response. The remarkable
potential of the fractional approach is illustrated by simulating the nonlinear
thermoelastic response of porous beams. The performance, evaluated both in
terms of accuracy and computational efficiency, is directly contrasted with
high-fidelity finite element models that fully resolve the pores' geometry.
Results indicate that the reduced-order representation of the porous
microstructure, captured by the synthetic variable-order parameter, offers a
robust and accurate representation of the multiscale material architecture that
largely outperforms classical approaches based on the concept of average
porosity.


  Robustness is a vital aspect to consider when deploying deep learning models
into the wild. Numerous studies have been dedicated to the study of the
robustness of vision transformers (ViTs), which have dominated as the
mainstream backbone choice for vision tasks since the dawn of 2020s. Recently,
some large kernel convnets make a comeback with impressive performance and
efficiency. However, it still remains unclear whether large kernel networks are
robust and the attribution of their robustness. In this paper, we first conduct
a comprehensive evaluation of large kernel convnets' robustness and their
differences from typical small kernel counterparts and ViTs on six diverse
robustness benchmark datasets. Then to analyze the underlying factors behind
their strong robustness, we design experiments from both quantitative and
qualitative perspectives to reveal large kernel convnets' intriguing properties
that are completely different from typical convnets. Our experiments
demonstrate for the first time that pure CNNs can achieve exceptional
robustness comparable or even superior to that of ViTs. Our analysis on
occlusion invariance, kernel attention patterns and frequency characteristics
provide novel insights into the source of robustness.


  In this paper, we consider a proximal linearized alternating direction method
of multipliers (PL-ADMM) for solving linearly constrained nonconvex and
possibly nonsmooth optimization problems. The algorithm is generalized by using
variable metric proximal terms in the primal updates and an over-relaxation
stepsize in the multiplier update. We prove that the sequence generated by this
method is bounded and its limit points are critical points. Under the powerful
Kurdyka-{\L ojasiewicz} properties we prove that the sequence has a finite
length thus converges, and we drive its convergence rates.


  Type-IIB supergravity in ten dimensions admits two consistent $Z_2$
truncations. After the insertion of D9-branes, one of them leads to the
low-energy action of type-I string theory, and it can be performed in two
different ways, in correspondence with the fact that there are two different
consistent ten-dimensional type-I string theories, namely the SO(32)
superstring and the $USp(32)$ model, in which supersymmetry is broken on the
D9-branes. We derive here the same results for Type-IIA theory compactified on
a circle in the presence of D8-branes. We also analyze the $\kappa$-symmetric
action for a brane charged with respect to the S-dual of the RR 10-form of
type-IIB, and we find that the tension of such an object has to scale like
$g_S^{-2}$ in the string frame. We give an argument to explain why this result
is in disagreement with the one obtained using Weyl rescaling of the brane
action, and we argue that this brane can only be consistently introduced if the
other $Z_2$ truncation of type-IIB is performed. Moreover, we find that one can
include a 10-form in type-IIA supersymmetry algebra, and also in this case the
corresponding $\kappa$-symmetric brane has a tension scaling like $g_S^{-2}$ in
the string frame.


  Within the low-energy effective Minimal Supersymmetric extension of the
Standard Model (effMSSM) we calculate the neutralino relic density taking into
account slepton-neutralino, squark-neutralino and neutralino/chargino-
neutralino coannihilation channels. By including squark (stop and sbottom)
coannihilation channels we extend our comparative study to all allowed
coannihilations and obtain the general result that all of them give sizable
contributions to the reduction of the neutralino relic density. Due to these
coannihilation processes some models (mostly with large neutralino masses)
enter into the cosmologically interesting region for relic density, but other
models leave this region. Nevertheless, in general, the predictions for direct
and indirect dark matter detection rates are not strongly affected by these
coannihilation channels in the effMSSM.


  Continuous Integration (CI) is a widely adopted practice for faster code
change integration and testing. Developers often migrate between CI systems in
pursuit of features like matrix building or better logging. However, this
migration is effort intensive and error-prone owing to limited knowledge of the
new CI system and its syntax. Moreover, these migrations require multiple
iterations and significant time to achieve stability in the new CI system, and
there is insufficient support for the automatic migration of CI configurations.
  To mitigate this, we propose a novel approach for CI system's automatic
migration: CIMig. Our approach utilizes Example-Based mining, where it extracts
translation rules and configuration patterns from existing migration examples,
and employs them to reproduce this migration in new contexts. To empirically
validate and evaluate our approach, we apply it to the migration between Travis
CI and GitHub Actions. We gathered learnings from 1001 projects, and then
applied them to migrate an evaluation set of 251 projects. This helped us
perform a qualitative and quantitative evaluation of CIMig, and we
contextualize our results by comparing them with those of the manual-rule-based
GitHub Actions Importer. Furthermore, our tool generated files that were rated
favorably by developers and saved them an average of 42.4 minutes over the
manual migration of these same projects. Our learning-based approach is also
more flexible, as proven by our ability to apply it to migrate GitHub Actions
files to Travis, which GitHub Actions Importer can not do. We believe CIMig is
the first approach of its kin to migrate CI systems and can be applied to other
software configuration system migrations. Our replication package is available
at [5].


  For uniformly expanding maps on the interval, analogous versions of the
Berry-Ess\'een theorem are known but only with an unexplicit upper bound in
$O(1/\sqrt{n})$ without any constants being specified. In this paper, we use
the recent complex cone technique to prove an explicit Berry-Ess\'een estimate
with a reasonable constant for these maps. Our method is not limited to maps on
the interval however and should apply to many situations.


  By now, we have a product theorem in every finite simple group $G$ of Lie
type, with the strength of the bound depending only in the rank of $G$. Such
theorems have numerous consequences: bounds on the diameters of Cayley graphs,
spectral gaps, and so forth. For the alternating group Alt_n, we have a
quasipolylogarithmic diameter bound (Helfgott-Seress 2014), but it does not
rest on a product theorem.
  We shall revisit the proof of the bound for Alt_n, bringing it closer to the
proof for linear algebraic groups, and making some common themes clearer. As a
result, we will show how to prove a product theorem for Alt_n -- not of full
strength, as that would be impossible, but strong enough to imply the diameter
bound.


  We are concerned here with unrestricted maximum likelihood estimation in a
sparse $p_0$ model with covariates for directed networks. The model has a
density parameter $\nu$, a $2n$-dimensional node parameter $\bs{\eta}$ and a
fixed dimensional regression coefficient $\bs{\gamma}$ of covariates. Previous
studies focus on the restricted likelihood inference. When the number of nodes
$n$ goes to infinity, we derive the $\ell_\infty$-error between the maximum
likelihood estimator (MLE) $(\widehat{\bs{\eta}}, \widehat{\bs{\gamma}})$ and
its true value $(\bs{\eta}, \bs{\gamma})$. They are $O_p( (\log n/n)^{1/2} )$
for $\widehat{\bs{\eta}}$ and $O_p( \log n/n)$ for $\widehat{\bs{\gamma}}$, up
to an additional factor. This explains the asymptotic bias phenomenon in the
asymptotic normality of $\widehat{\bs{\gamma}}$ in
\cite{Yan-Jiang-Fienberg-Leng2018}. Further, we derive the asymptotic normality
of the MLE. Numerical studies and a data analysis demonstrate our theoretical
findings.


  We investigate the contribution of Interatomic Coulombic Decay induced by ion
impact in neon and argon dimers (Ne$_2$ and Ar$_2$) to the production of low
energy electrons. Our experiments cover a broad range of perturbation strengths
and reaction channels. We use 11.37 MeV/u S$^{14+}$, 0.125 MeV/u He$^{1+}$,
0.1625 MeV/u He$^{1+}$ and 0.150 MeV/u He$^{2+}$ as projectiles and study
ionization, single and double electron transfer to the projectile as well as
projectile electron loss processes. The application of a COLTRIMS reaction
microscope enables us to retrieve the three-dimensional momentum vectors of the
ion pairs of the fragmenting dimer into Ne$^{q+}$/Ne$^{1+}$ and
Ar$^{q+}$/Ar$^{1+}$ (q = 1, 2, 3) in coincidence with at least one emitted
electron.


  BaBar's observation of significant deviations of the pion transition form
factor (TFF) from the asymptotic expectation with $Q^2>9$ GeV$^2$ has brought a
serious crisis to a fundamental picture established for such a simplest
$q\bar{q}$ system by perturbative QCD, i.e. the dominance of collinear
factorization at high momentum transfers for the pion TFF. We show that
non-factorizable contributions due to open flavors in $\gamma\gamma^*\to\pi^0$
could be an important source that contaminates the pQCD asymptotic limit and
causes such deviations with $Q^2>9$ GeV$^2$. Within an effective Lagrangian
approach, the non-factorizable amplitudes can be related to intermediate hadron
loops, i.e. $K^{(*)}$ and $D^{(*)}$ etc, and their corrections to the $\pi^0$
and $\eta$ TFFs can be estimated.


  Max-point-tolerance graphs (MPTG) were studied by Catanzaro et al. in 2017
and the same class of graphs were introduced in the name of p-BOX(1) graphs by
Soto and Caro in 2015. In our paper we consider central-max-point tolerance
graphs (central MPTG) by taking the points of MPTG as center points of their
corresponding intervals. In course of study on this class of graphs we show
that the class of central MPTG is same as the class of unit max-tolerance
graphs. We prove the class of unit central max-point tolerance graphs is same
as that of proper central max-point tolerance graphs and both of them are
equivalent to the class of proper interval graphs. Next we introduce 50%
max-tolerance graphs and separate this class from unit max-tolerance graph
whereas for min-tolerance graphs 50% and unit denote the same graph class.
  Interval catch digraphs (ICD) was introduced by Maehera in 1984. In his
introducing paper Maehera proposed a conjecture for the characterization of
central interval catch digraph (central ICD) in terms of forbidden subdigraphs.
In this paper, we disprove the conjecture by showing counter examples. We find
close relation between a central MPTG and a central ICD. Also we characterize
this digraph by defining a suitable mapping from the vertex set to the real
line. Next we study oriented interval catch digraphs (oriented ICD). We
characterize augmented adjacency matrix of an oriented ICD when it is a
tournament. Also we characterize an oriented ICD whose underlying graph is a
tree. Further we obtain characterization of the adjacency matrix of a proper
interval catch digraph. Another important result is to provide forbidden
subdigraph characterization of those proper oriented interval catch digraphs
whose underlying undirected graph is chordal. In last section we discuss
relationships between these classes of graphs and digraphs.


  We consider the interactions between Dp-branes intersecting at an arbitrary
number of angles in the context of type II string theory. For cosmology
purposes we concentrate in the theory on R^{3,1} x T^6. Interpreting the
distance between the branes as the inflaton field, the branes can intersect at
most at two angles on the compact space. If the configuration is
non-supersymmetric we will have an interbrane potential that provides an
effective cosmological inflationary epoch at the four dimensional intersection
between the branes. The end of inflation occurs when the interbrane distance
becomes small compared with the string scale, where a tachyon develops
triggering the recombination of the branes. We study this recombination due to
tachyon instabilities and we find the possibility for the final configuration
to be again branes intersecting at two angles. This preserves the interesting
features that are present in the intersecting brane models from the string
model building point of view also after the end of inflation. This fact was not
present in the models of branes intersecting at just one angle. This kind of
recombination can be also important in other string contexts.


  We characterise the (Jacobson) radical of the analytic crossed product of
C_0(X) by the non-negative integers (Z_+), answering a question first raised by
Arveson and Josephson in 1969. In fact, we characterise the radical of analytic
crossed products of C_0(X) by (Z_+)^d. The radical consists of all elements
whose `Fourier coefficients' vanish on the recurrent points of the dynamical
system (and the first one is zero). The multi-dimensional version requires a
variation of the notion of recurrence, taking into account the various degrees
of freedom.


  Pattern-matching programming is an example of a rule-based programming style
developed in functional languages. This programming style is intensively used
in dialects of ML but is restricted to algebraic data-types. This restriction
limits the field of application. However, as shown by Giavitto and Michel at
RULE'02, case-based function definitions can be extended to more general data
structures called topological collections. We show in this paper that this
extension retains the benefits of the typed discipline of the functional
languages. More precisely, we show that topological collections and the
rule-based definition of functions associated with them fit in a polytypic
extension of mini-ML where type inference is still possible.


  Representations in the hidden layers of Deep Neural Networks (DNN) are often
hard to interpret since it is difficult to project them into an interpretable
domain. Graph Convolutional Networks (GCN) allow this projection, but existing
explainability methods do not exploit this fact, i.e. do not focus their
explanations on intermediate states. In this work, we present a novel method
that traces and visualizes features that contribute to a classification
decision in the visible and hidden layers of a GCN. Our method exposes hidden
cross-layer dynamics in the input graph structure. We experimentally
demonstrate that it yields meaningful layerwise explanations for a GCN sentence
classifier.


  We report an upper limit on the flux of relativistic monopoles based on the
non-observation of in-ice showers by the Radio Ice Cherenkov Experiment (RICE)
at the South Pole. We obtain a 95% C.L. limit of order 10^{-18}/(cm^2-s-sr) for
intermediate mass monopoles of 10^7<gamma<10^{12} at the anticipated energy
E=10^{16} GeV. This bound is over an order of magnitude stronger than all
previously published experimental limits for this range of boost parameters
gamma, and exceeds two orders of magnitude improvement over most of the range.
We review the physics of radio detection, describe a Monte Carlo simulation
including continuous and stochastic energy losses, and compare to previous
experimental limits.


  Specific matrix elements of exchange and correlation kernels in
time-dependent density-functional theory are computed. The knowledge of these
matrix elements not only constraints approximate time-dependent functionals,
but also allows to link different practical approaches to excited states,
either based on density-functional theory, or on many-body perturbation theory,
despite the approximations that have been performed to derive them.


  Evapotranspiration has a major control on continental surfaces dynamics in
forested boreal environments. For example, it has strong impacts on active
layer thickness, mainly because of its effect on water content within the upper
layers of the soil column. These are complex processes, depending not only on
climate forcings (atmospheric water demand) but also on physical,
geo-pedological and biological properties of the considered areas. Here we
propose a numerical investigation of evapotranspiration processes in the active
layer of slopes of a forested watershed in Central Siberia. The effect on
actual evapotranspiration of the spatial contrasts in terms of exposure, root
layer thickness and tree stand density within the watershed are simulated using
a recently developed high performance computing cryohydrogeological model,
permaFoam.


  In the recent paper `Well-posedness and regularity for a generalized
fractional Cahn-Hilliard system' (Atti Accad. Naz. Lincei Rend. Lincei Mat.
Appl. 30 (2019), 437-478 -- see also arXiv:1804.11290), the same authors have
studied viscous and nonviscous Cahn-Hilliard systems of two operator equations
in which nonlinearities of double-well type, like regular or logarithmic
potentials, as well as nonsmooth potentials with indicator functions, were
admitted. The operators appearing in the system equations are fractional powers
$A^{2r}$ and $B^{2\sigma}$ (in the spectral sense) of general linear operators
$A$ and $B$, which are densely defined, unbounded, selfadjoint, and monotone in
the Hilbert space $L^2(\Omega)$, for some bounded and smooth domain
$\Omega\subset{\mathbb{R}}^3$, and have compact resolvents. Existence,
uniqueness, and regularity results have been proved in the quoted paper. Here,
in the case of the viscous system, we analyze the asymptotic behavior of the
solution as the parameter $\sigma$ appearing in the operator $B^{2\sigma}$
decreasingly tends to zero. We prove convergence to a phase relaxation problem
at the limit, and we also investigate this limiting problem, in which an
additional term containing the projection of the phase variable on the kernel
of $B$ appears.


  We provide a dual gravity description of a supersymmetric heavy nucleus,
following the idea of our previous paper arXiv:0809.3141. The supersymmetric
nucleus consists of a merginal bound state of $A$ baryons distributed over a
ball in 3 dimensions. In the gauge/string duality, the baryon in N=4 super
Yang-Mills (SYM) theory corresponds to a D5-brane wrapping S^5 of the AdS_5 x
S^5 spacetime, so the nucleus corresponds to a collection of $A$ D5-branes. We
take a large $A$ and a near horizon limits of a back-reacted geometry generated
by the wrapped $A$ D5-branes, where we find a gap in the supergravity
fluctuation spectrum. This spectrum is a gravity dual of giant resonances of
heavy nuclei, in the supersymmetric toy example of QCD.


  Converse magnetoelectric coupling in artificial multiferroics is generally
modelled through three possible mechanisms: charge transfer, strain mediated or
ion migration. Here we demonstrate a novel and highly reliable approach, where
electrically controlled morphological modifications control the ferromagnetic
response of a magnetoelectric heterostructure, specifically FexMn1-x
ferromagnetic films on ferroelectric PMN-PT (001) substrates. The ferroelectric
PMN-PT substrates present, in correspondence to electrical switching, fully
reversible morphological changes at the surface, to which correspond
reproducible modifications of the ferromagnetic response of the FexMn1-x films.
Topographic analysis by atomic force microscopy shows the formation of surface
cracks after application of a positive electric field up to 6 kV/cm, which
disappear after application of negative voltage of the same amplitude.
In-operando x-ray magnetic circular dichroic spectroscopy at Fe edge in
FexMn1-x layers shows local variations of dichroic signal up to a factor 2.5 as
a function of the electrically-driven morphological state. These findings
highlight the role of morphology and surface topography as a key aspect in
magnetoelectric coupling, whose proof of electrically reversible modification
of the magnetic response adds a new possibility in the design of multiferroic
heterostructures with electrically controlled functionalities.


  We combine a recent construction of a BRST-invariant, nonlinear massive gauge
fixing with the background field formalism. The resulting generating functional
preserves background-field invariance as well as BRST invariance of the quantum
field manifestly. The construction features BRST-invariant mass parameters for
the quantum gauge and ghost fields. The formalism employs a background
Nakanishi-Lautrup field which is part of the nonlinear gauge-fixing sector and
thus should not affect observables. We verify this expectation by computing the
one-loop effective action and the corresponding beta function of the gauge
coupling as an example. The corresponding Schwinger functional generating
connected correlation functions acquires additional one-particle reducible
terms that vanish on shell. We also study off-shell one-loop contributions in
order to explore the consequences of a nonlinear gauge fixing scheme involving
a background Nakanishi-Lautrup field. As an application, we show that our
formalism straightforwardly accommodates nonperturbative information about
propagators in the Landau gauge in the form of the so-called decoupling
solution. Using this nonperturbative input, we find evidence for the formation
of a gluon condensate for sufficiently large coupling, whose scale is set by
the BRST-invariant gluon mass parameter.


  We focus on an epidemiological model (the archetypical SIR system) defined on
graphs and study the asymptotic behavior of the solutions as the number of
vertices in the graph diverges. By relying on the theory of so called graphons
we provide a characterization of the limit and establish convergence results.
We also provide approximation results for both deterministic and random
discretizations.


  Pivotuner is a VST3/AU MIDI effect plugin that automatically tunes note data
in an adaptive pure intonation, in real time. Where previously pure intonation
was out of reach for most musicians due to difficulty and impracticality,
Pivotuner enables it to be achieved easily and straightforwardly by using novel
yet simple algorithms. This may lead to more widespread exploration of pure
intonation for a larger and more diverse crowd of musicians! This paper
includes a review of prior systems for adaptive pure intonation systems,
including Hermode Tuning/Kontakt Dynamic Pure Tuning and Just Intonation. The
paper introduces the notion of an adaptive tuning center and how it serves as a
flexible underlying concept for multiple tuning algorithms, as well as
extensions to offer greater control for performers, including pitch and tuning
center locking and resetting, and gradual interpolation between equal
temperament and pure intonation. The paper then showcases some pieces which use
Pivotuner effectively, then discusses areas for future exploration within
Pivotuner's feature set, and plans for future development.


  It is a very well known fact that the energy conditions concerning
traversable wormhole (WH) solutions of Einstein equations are violated.
Consequently, attempts to avoid the violation of the energy conditions
constitutes one of the main areas of research in WH physics. On the other hand,
the current literature shows us that noncommutativity is one of the most
promising candidates to help us to understand the physics of the early
Universe. However, since noncommutativity does not change the commutative
results, we also can expect that energy conditions violation near the throat
must occur. We will show here that the violation of the energy conditions,
described in a noncommutative space-time, has fixed conditions on the angular
momentum of a rotating WH with constant angular velocity. Also, we have
established a new theoretical bound on the NC constant, $\theta$, as a function
of some WH parameters.


  B-B-bar mixing involves three physical parameters: the magnitudes of the
off-diagonal elements of the mass and decay matrices and their relative phase.
They are related to the mass and width differences between the mass eigenstates
and to the CP asymmetry in flavour-specific decays, a_fs. Introducing a new
operator basis I present new, more precise theory predictions for the width
differences in the B_s and B_d systems: in the Standard Model one finds Delta
Gamma_s = 0.088 +/- 0.017 ps^{-1} and Delta Gamma_d = (26.7 +5.8/-6.5) *
10^{-4} ps^{-1}. Updates of the mass differences Delta M_d and Delta M_s and of
a_{fs}^d and a_{fs}^s are also presented. Then I discuss how various present
and future measurements can be combined to constrain new physics. The
extraction of a new CP phase phi_s^Delta from data on a_{fs}^s also profits
from our new operator basis. Confronting our new formulae with D0 data we find
that sin phi_s^Delta deviates from zero by 2 sigma.


  The primary goal of any company is to increase its profits by improving both
the quality of its products and how they are advertised. In this context,
neuromarketing seeks to enhance the promotion of products and generate a
greater acceptance on potential buyers. Traditionally, neuromarketing studies
have relied on a single biosignal to obtain feedback from presented stimuli.
However, thanks to new devices and technological advances studying this area of
knowledge, recent trends indicate a shift towards the fusion of diverse
biosignals. An example is the usage of electroencephalography for understanding
the impact of an advertisement at the neural level and visual tracking to
identify the stimuli that induce such impacts. This emerging pattern determines
which biosignals to employ for achieving specific neuromarketing objectives.
Furthermore, the fusion of data from multiple sources demands advanced
processing methodologies. Despite these complexities, there is a lack of
literature that adequately collates and organizes the various data sources and
the applied processing techniques for the research objectives pursued. To
address these challenges, the current paper conducts a comprehensive analysis
of the objectives, biosignals, and data processing techniques employed in
neuromarketing research. This study provides both the technical definition and
a graphical distribution of the elements under revision. Additionally, it
presents a categorization based on research objectives and provides an overview
of the combinatory methodologies employed. After this, the paper examines
primary public datasets designed for neuromarketing research together with
others whose main purpose is not neuromarketing, but can be used for this
matter. Ultimately, this work provides a historical perspective on the
evolution of techniques across various phases over recent years and enumerates
key lessons learned.


  I introduce a continuous-variable quantum topological data algorithm. The
goal of the quantum algorithm is to calculate the Betti numbers in persistent
homology which are the dimensions of the kernel of the combinatorial Laplacian.
I accomplish this task with the use of qRAM to create an oracle which organizes
sets of data. I then perform a continuous-variable phase estimation on a Dirac
operator to get a probability distribution with eigenvalue peaks. The results
also leverage an implementation of continuous-variable conditional swap gate.


  This document describes Pythia v0.1, the winning entry from Facebook AI
Research (FAIR)'s A-STAR team to the VQA Challenge 2018.
  Our starting point is a modular re-implementation of the bottom-up top-down
(up-down) model. We demonstrate that by making subtle but important changes to
the model architecture and the learning rate schedule, fine-tuning image
features, and adding data augmentation, we can significantly improve the
performance of the up-down model on VQA v2.0 dataset -- from 65.67% to 70.22%.
  Furthermore, by using a diverse ensemble of models trained with different
features and on different datasets, we are able to significantly improve over
the 'standard' way of ensembling (i.e. same model with different random seeds)
by 1.31%. Overall, we achieve 72.27% on the test-std split of the VQA v2.0
dataset. Our code in its entirety (training, evaluation, data-augmentation,
ensembling) and pre-trained models are publicly available at:
https://github.com/facebookresearch/pythia


  We introduce the use of a Gated Recurrent Unit (GRU) for influenza prediction
at the state- and city-level in the US, and experiment with the inclusion of
real-time flu-related Internet search data. We find that a GRU has lower
prediction error than current state-of-the-art methods for data-driven
influenza prediction at time horizons of over two weeks. In contrast with other
machine learning approaches, the inclusion of real-time Internet search data
does not improve GRU predictions.


  This update to my article on Congruent numbers, elliptic curves, and the
passage from the local to the global, which appeared in Resonance, December
2009, pp. 1183--1205
(https://www.ias.ac.in/describe/article/reso/014/12/1183-1205) and was posted
here as arXiv:0704.3783, covers a few recent advances in the arithmetic of
elliptic curves with special reference to the congruent number problem.


  The last several years have seen significant progress in using depth cameras
for tracking articulated objects such as human bodies, hands, and robotic
manipulators. Most approaches focus on tracking skeletal parameters of a fixed
shape model, which makes them insufficient for applications that require
accurate estimates of deformable object surfaces. To overcome this limitation,
we present a 3D model-based tracking system for articulated deformable objects.
Our system is able to track human body pose and high resolution surface
contours in real time using a commodity depth sensor and GPU hardware. We
implement this as a joint optimization over a skeleton to account for changes
in pose, and over the vertices of a high resolution mesh to track the subject's
shape. Through experimental results we show that we are able to capture dynamic
sub-centimeter surface detail such as folds and wrinkles in clothing. We also
show that this shape estimation aids kinematic pose estimation by providing a
more accurate target to match against the point cloud. The end result is highly
accurate spatiotemporal and semantic information which is well suited for
physical human robot interaction as well as virtual and augmented reality
systems.


  Training neural networks requires increasing amounts of memory. Parameter
sharing can reduce memory and communication costs, but existing methods assume
networks have many identical layers and utilize hand-crafted sharing strategies
that fail to generalize. We introduce Neural Parameter Allocation Search
(NPAS), a novel task where the goal is to train a neural network given an
arbitrary, fixed parameter budget. NPAS covers both low-budget regimes, which
produce compact networks, as well as a novel high-budget regime, where
additional capacity can be added to boost performance without increasing
inference FLOPs. To address NPAS, we introduce Shapeshifter Networks (SSNs),
which automatically learn where and how to share parameters in a network to
support any parameter budget without requiring any changes to the architecture
or loss function. NPAS and SSNs provide a complete framework for addressing
generalized parameter sharing, and can also be combined with prior work for
additional performance gains. We demonstrate the effectiveness of our approach
using nine network architectures across four diverse tasks, including ImageNet
classification and transformers.


  We answer a question of Benjamini and Schramm by proving that under
reasonable conditions, quotienting a graph strictly increases the value of its
percolation critical parameter $p_c$. More precisely, let $\mathcal{G}=(V,E)$
be a quasi-transitive graph with $p_c(\mathcal{G})<1$, and let $G$ be a
nontrivial group that acts freely on $V$ by graph automorphisms. Assume that
$\mathcal{H}:=\mathcal{G}/G$ is quasi-transitive. Then one has
$p_c(\mathcal{G})<p_c(\mathcal{H})$. We provide results beyond this setting: we
treat the case of general covering maps and provide a similar result for the
uniqueness parameter $p_u$, under an additional assumption of boundedness of
the fibres. The proof makes use of a coupling built by lifting the exploration
of the cluster, and an exploratory counterpart of Aizenman-Grimmett's essential
enhancements.


  The collisional drift wave instability in a straight magnetic field
configuration is studied within a full-F gyro-fluid model, which relaxes the
Oberbeck-Boussinesq (OB) approximation. Accordingly, we focus our study on
steep background density gradients. In this regime we report on corrections by
factors of order one to the eigenvalue analysis of former OB approximated
approaches as well as on spatially localised eigenfunctions, that contrast
strongly with their OB approximated equivalent. Remarkably, non-modal phenomena
arise for large density inhomogeneities and for all collisionalities. As a
result, we find initial decay and non-modal growth of the free energy and
radially localised and sheared growth patterns. The latter non-modal effect
sustains even in the nonlinear regime in the form of radially localised
turbulence or zonal flow amplitudes.


  I review work on the influence of inhomogeneities in the matter distribution
on the determination of the luminosity distance of faraway sources, and the
connection to the perceived cosmological acceleration.


  We analyze time evolution of a spherically symmetric collapsing matter from a
point of view that black holes evaporate by nature. We first consider a
spherical thin shell that falls in the metric of an evaporating Schwarzschild
black hole of which the radius $a(t)$ decreases in time. The important point is
that the shell can never reach $a(t)$ but it approaches $a(t)-a(t)\frac{d
a(t)}{d t}$. This situation holds at any radius because the motion of a shell
in a spherically symmetric system is not affected by the outside. In this way,
we find that the collapsing matter evaporates without forming a horizon.
Nevertheless, a Hawking-like radiation is created in the metric, and the object
looks the same as a conventional black hole from the outside. We then discuss
how the information of the matter is recovered. We also consider a black hole
that is adiabatically grown in the heat bath and obtain the interior metric. We
show that it is the self-consistent solution of $G_{\mu\nu}=8\pi G \langle
T_{\mu\nu} \rangle$ and that the four-dimensional Weyl anomaly induces the
radiation and a strong angular pressure. Finally, we analyze the internal
structures of the charged and the slowly rotating black holes.


  A numerical solver for the elastic wave eigenmodes in acoustic waveguides of
inhomogeneous cross-section is presented. Operating under the assumptions of
linear, isotropic materials, it utilizes a finite-difference method on a
staggered grid to solve for the acoustic eigenmodes of the vector-field elastic
wave equation. Free, fixed, symmetry, and anti-symmetry boundary conditions are
implemented, enabling efficient simulation of acoustic structures with
geometrical symmetries and terminations. Perfectly matched layers are also
implemented, allowing for the simulation of radiative (leaky) modes. The method
is analogous to eigenmode solvers ubiquitously employed in electromagnetics to
find waveguide modes, and enables design of acoustic waveguides as well as
seamless integration with electromagnetic solvers for optomechanical device
design. The accuracy of the solver is demonstrated by calculating
eigenfrequencies and mode shapes for common acoustic modes in several simple
geometries and comparing the results to analytical solutions where available or
to numerical solvers based on more computationally expensive methods.


  Shell models of turbulence are representation of turbulence equations in
Fourier domain. Various shell models along with numerical simulations have been
studied earlier. One of the most suitable shell model of turbulence is so
called sabra shell model. The existence, uniqueness and regularity property of
this model are extensively studied in \cite{PBT}. In this paper we have
addressed stabilization problems related to sabra shell model of turbulence. We
have studied internal stabilization via finite dimensional controller. Moreover
we have also studied optimal robust control problem by solving an infinite time
horizon max-min control problem. We first prove the $H^ \infty$ stabilization
of the linearized system and charatarize it in terms of a feedback operator by
solving an algebric ricatti equation. Finally we show that the control will
asymptotically stabilize the nonlinear system.


  Despite a mounting evidence that the same gradients which active colloids use
for swimming, induce important cross-interactions (phoretic interaction), they
are still ignored in most many-body descriptions, perhaps to avoid complexity
and a zoo of unknown parameters. Here we derive a simple model, which reduces
phoretic far-field interactions to a pair-interaction whose strength is mainly
controlled by one genuine parameter (swimming speed). The model suggests that
phoretic interactions are generically important for autophoretic colloids
(unless effective screening of the phoretic fields is strong) and should
dominate over hydrodynamic interactions for the typical case of half-coating
and moderately nonuniform surface mobilities. Unlike standard minimal models,
but in accordance with canonical experiments, our model generically predicts
dynamic clustering in active colloids at low density. This suggests that
dynamic clustering can emerge from the interplay of screened phoretic
attractions and active diffusion.


  A fundamental issue in the AdS/CFT correspondence is the wormhole growth
paradox. Susskind's conjectured resolution of the paradox was to equate the
volume of the wormhole with the circuit complexity of its dual quantum state in
the CFT. We study the ramifications of this conjecture from a
complexity-theoretic perspective. Specifically we give evidence for the
existence of computationally pseudorandom states in the CFT, and argue that
wormhole volume is measureable in a non-physical but computational sense, by
amalgamating the experiences of multiple observers in the wormhole. In other
words the conjecture equates a quantity which is difficult to compute with one
which is easy to compute. The pseudorandomness argument further implies that
this is a necessary feature of any resolution of the wormhole growth paradox,
not just of Susskind's Complexity=Volume conjecture. As a corollary we conclude
that either the AdS/CFT dictionary map must be exponentially complex, or the
quantum Extended Church-Turing thesis must be false in quantum gravity.


  Magnetic properties for the one-dimensional multicomponent quantum spin
system with the excitation gap are studied based on the integrable spin model
introduced by Bariev {\it et al}. By exactly computing the magnetization, we
show how the characteristic structure with plateaus and cusps appears in the
magnetization process. To study low-energy dynamics of the system, we apply the
finite-size scaling analysis to the excitation spectrum, and thereby evaluate
the power-law exponent as well as the enhancement factor for the
low-temperature NMR relaxation rate $1/T_1$. We discuss the critical properties
of $1/T_1$ around plateaus and cusps in the magnetization curve.


  I consider the non-equilibrium DC transport of electrons through a quantum
system with a thermoelectric response. This system may be any nanostructure or
molecule modeled by the nonlinear scattering theory which includes Hartree-like
electrostatic interactions exactly, and certain dynamic interaction effects
(decoherence and relaxation) phenomenologically. This theory is believed to be
a reasonable model when single-electron charging effects are negligible. I
derive three fundamental bounds for such quantum systems coupled to multiple
macroscopic reservoirs, one of which may be superconducting. These bounds
affect nonlinear heating (such as Joule heating), work and entropy production.
Two bounds correspond to the first law and second law of thermodynamics in
classical physics. The third bound is quantum (wavelength dependent), and is as
important as the thermodynamic ones in limiting the capabilities of mesoscopic
heat-engines and refrigerators. The quantum bound also leads to Nernst's
unattainability principle that the quantum system cannot cool a reservoir to
absolute zero in a finite time, although it can get exponentially close.


  We introduce topological skyrmion semimetal phases of matter, characterized
by bulk electronic structures with topological defects in ground state
observable textures over the Brillouin zone (BZ), rather than topological
degeneracies in band structures. We present and characterize toy models for
these novel topological phases, focusing on realizing such topological defects
in the ground state spin expectation value texture over the BZ. We find
generalized Fermi arc bulk-boundary correspondences and chiral anomaly response
signatures, including Fermi arc-like states which do not terminate with
topological band structure degeneracies in the bulk, but rather with
topological defects in the spin texture of bulk insulators. We also consider
novel boundary conditions for topological semimetals, in which the 3D bulk is
mapped to a 2D bulk plus 0D defect. Given the experimental significance of
topological semimetals, our work paves the way to broad experimental study of
topological skyrmion phases and the quantum skyrmion Hall effect.


  Consider weakly nonlinear complex Ginzburg--Landau (CGL) equation of the
form: $$ u_t+i(-\Delta u+V(x)u)=\epsilon\mu\Delta u+\epsilon \mathcal{P}(
u),\quad x\in {R^d}\,, \quad(*)
  $$ under the periodic boundary conditions, where $\mu\geqslant0$ and
$\mathcal{P}$ is a smooth function. Let $\{\zeta_1(x),\zeta_2(x),\dots\}$ be
the $L_2$-basis formed by eigenfunctions of the operator $-\Delta +V(x)$. For a
complex function $u(x)$, write it as $u(x)=\sum_{k\geqslant1}v_k\zeta_k(x)$ and
set $I_k(u)=\frac{1}{2}|v_k|^2$. Then for any solution $u(t,x)$ of the linear
equation $(*)_{\epsilon=0}$ we have $I(u(t,\cdot))=const$. In this work it is
proved that if equation $(*)$ with a sufficiently smooth real potential $V(x)$
is well posed on time-intervals $t\lesssim \epsilon^{-1}$, then for any its
solution $u^{\epsilon}(t,x)$, the limiting behavior of the curve
$I(u^{\epsilon}(t,\cdot))$ on time intervals of order $\epsilon^{-1}$, as
$\epsilon\to0$, can be uniquely characterized by a solution of a certain
well-posed effective equation: $$ u_t=\epsilon\mu\triangle u+\epsilon F(u), $$
where $F(u)$ is a resonant averaging of the nonlinearity $\mathcal{P}(u)$. We
also prove a similar results for the stochastically perturbed equation, when a
white in time and smooth in $x$ random force of order $\sqrt\epsilon$ is added
to the right-hand side of the equation.
  The approach of this work is rather general. In particular, it applies to
equations in bounded domains in $R^d$ under Dirichlet boundary conditions.


  A theoretical description for the radial density profile of a finite number
of identical charged particles confined in a harmonic trap is developed for
application over a wide range of Coulomb coupling (or, equivalently,
temperatures) and particle numbers. A simple mean field approximation
neglecting correlations yields a density profile which is monotonically
decreasing with radius for all temperatures, in contrast to molecular dynamics
simulations and experiments showing shell structure at lower temperatures. A
more complete theoretical description including charge correlations is
developed here by an extension of the hypernetted chain approximation,
developed for bulk fluids, to the confined charges. The results reproduce all
of the qualitative features observed in molecular dynamics simulations and
experiments. These predictions are then tested quantitatively by comparison
with new benchmark Monte Carlo simulations. Quantitative accuracy of the theory
is obtained for the selected conditions by correcting the hypernetted chain
approximation with a representation for the associated bridge functions.


  The behavior of maximum likelihood estimates (MLEs) and the likelihood ratio
statistic in a family of problems involving pointwise nonparametric estimation
of a monotone function is studied. This class of problems differs radically
from the usual parametric or semiparametric situations in that the MLE of the
monotone function at a point converges to the truth at rate $n^{1/3}$ (slower
than the usual $\sqrt{n}$ rate) with a non-Gaussian limit distribution. A
framework for likelihood based estimation of monotone functions is developed
and limit theorems describing the behavior of the MLEs and the likelihood ratio
statistic are established. In particular, the likelihood ratio statistic is
found to be asymptotically pivotal with a limit distribution that is no longer
$\chi^2$ but can be explicitly characterized in terms of a functional of
Brownian motion. Applications of the main results are presented and potential
extensions discussed.


  Single-cell RNA sequencing (scRNA-seq) enables dissecting cellular
heterogeneity in tissues, resulting in numerous biological discoveries. Various
computational methods have been devised to delineate cell types by clustering
scRNA-seq data where the clusters are often annotated using prior knowledge of
marker genes. In addition to identifying pure cell types, several methods have
been developed to identify cells undergoing state transitions which often rely
on prior clustering results. Present computational approaches predominantly
investigate the local and first-order structures of scRNA-seq data using graph
representations, while scRNA-seq data frequently displays complex
high-dimensional structures. Here, we present a tool, scGeom for exploiting the
multiscale and multidimensional structures in scRNA-seq data by inspecting the
geometry via graph curvature and topology via persistent homology of both cell
networks and gene networks. We demonstrate the utility of these structural
features for reflecting biological properties and functions in several
applications where we show that curvatures and topological signatures of cell
and gene networks can help indicate transition cells and developmental potency
of cells. We additionally illustrate that the structural characteristics can
improve the classification of cell types.


  Nonlinear generation of high frequency mode (HFM) by toroidal Alfven
eigenmode (TAE) observed in HL-2A tokamak is analyzed using nonlinear
gyrokinetic theory. It is found that, the HFM can be dominated by $|nq-m|=1$
perturbations with predominantly ideal magnetohydrodynamic if the two primary
TAEs are co-propagating; while the HFM can be characterized by $nq-m=0$
electrostatic perturbations if the two primary TAEs are counter-propagating.
Here, $n$ and $m$ are respectively the toroidal and poloidal mode numbers, and
$q$ is the safety factor. The nonlinear process is sensitive to the equilibrium
magnetic geometry of the device.


  We consider a generalization of the 2-dimensional (2D) quantum-Hall insulator
to a non-compact, non-Abelian gauge group, the Heisenberg-Weyl group. We show
that this kind of insulator is actually a layered 3D insulator with nontrivial
topology. We further show that nontrivial combinations of quantized transverse
conductivities can be engineered with the help of a staggered potential. We
investigate the robustness and topological nature of this conductivity and
connect it to the surface modes of the system. We also propose a simple
experimental realization with ultracold atoms in 3D confined to a 2D square
lattice with the third dimension being mapped to a gauge coordinate.


  To prove presence of chaos for fractals, a new mathematical concept of
abstract similarity is introduced. As an example, the space of symbolic strings
on a finite number of symbols is proved to possess the property. Moreover,
Sierpinski fractals, Koch curve as well as Cantor set satisfy the definition. A
similarity map is introduced and the problem of chaos presence for the sets is
solved by considering the dynamics of the map. This is true for Poincare,
Li-Yorke and Devaney chaos, even in multi-dimensional cases. Original numerical
simulations which illustrate the results are delivered.


  Although a variety of methods have been proposed for sequential
recommendation, it is still far from being well solved partly due to two
challenges. First, the existing methods often lack the simultaneous
consideration of the global stability and local fluctuation of user preference,
which might degrade the learning of a user's current preference. Second, the
existing methods often use a scalar based weighting schema to fuse the
long-term and short-term preferences, which is too coarse to learn an
expressive embedding of current preference. To address the two challenges, we
propose a novel model called Time Lag aware Sequential Recommendation (TLSRec),
which integrates a hierarchical modeling of user preference and a time lag
sensitive fine-grained fusion of the long-term and short-term preferences.
TLSRec employs a hierarchical self-attention network to learn users' preference
at both global and local time scales, and a neural time gate to adaptively
regulate the contributions of the long-term and short-term preferences for the
learning of a user's current preference at the aspect level and based on the
lag between the current time and the time of the last behavior of a user. The
extensive experiments conducted on real datasets verify the effectiveness of
TLSRec.


  We introduce an effective edge network theory to characterize the boundary
topology of coupled edge states generated from various types of topological
insulators. Two examples studied are a two-dimensional second-order topological
insulator and three-dimensional topological fullerenes, which involve multi-leg
junctions. As a consequence of bulk-edge correspondence, these edge networks
can faithfully predict properties such as the energy and fractional charge
related to the bound states (edge solitons) in the aforementioned systems,
including several aspects that were previously complicated or obscure.


  The unphysical spin-2 massive degrees of freedom in higher derivative gravity
may be either massive unphysical ghosts or tachyonic ghosts. In the last case
there is no Planck-scale threshold protecting vacuum cosmological solutions
from instabilities. Within the anomaly-induced action formalism the
photon-driven IR running of the coefficient of the Weyl-squared term makes the
ghost eventually becoming tachyon, that should produce a gravitational
explosion of vacuum. This effect is stable under higher loop corrections and
takes place also in known versions of perturbative quantum gravity. However,
the contribution of massless fields in the far IR are not the same in flat and
de~Sitter spaces. In the asymptotically deSitter case one can observe a kind of
IR decoupling, which protects the cosmological solution from the future
tachyonic instabilities.


  W-algebra (of finite type) W is a certain associative algebra associated with
a semisimple Lie algebra, say g, and its nilpotent element, say e. The goal of
this paper is to study the category O for W introduced by Brundan, Goodwin and
Kleshchev. We establish an equivalence of this category with certain category
of g-modules. In the case when e is of principal Levi type (this is always so
when g is of type A) the category of g-modules in interest is the category of
generalized Whittaker modules introduced McDowel and studied by Milicic-Soergel
and Backelin.


  We show that a recent proposal for the quantization of gravity based on
discrete space-time implies a modification of standard quantum mechanics that
naturally leads to a loss of coherence in quantum states of the type discussed
by Milburn. The proposal overcomes the energy conservation problem of
previously proposed decoherence mechanisms stemming from quantum gravity.
Mesoscopic quantum systems (as Bose--Einstein condensates) appear as the most
promising testing grounds for an experimental verification of the mechanism.


  We present a new conjecture for the $SU_q(N)$ Perk-Schultz models. This
conjecture extends a conjecture presented in our article (Alcaraz FC and
Stroganov YuG (2002) J. Phys. A vol. 35 pg. 6767-6787, and also in
cond-mat/0204074).


  We propose a new method for solving an important problem of astronomy that
arises in observations with ultrahigh-angular-resolution interferometers. This
method is based on the application of the theory of artificial neural networks.
We propose and compute a multiparameter model for a celestial object like Sgr
A*. For this model we have numerically constructed a number of probable images
for neural network training. After neural network training on these images, the
quality of its operation has been tested on another series of images from the
same model. We have proven that a neural network can recognize and classify
celestial objects (also obtained from interferometers) virtually no worse than
can be done by a human.


  The theoretical description of the physics of multi-jets in hadronic
collisions at high energies is based on "merging" methods, which combine
short-timescale production of jets with long-timescale evolution of partonic
showers. We point out potential implications of the evolution of transverse
momentum dependent (TMD) distributions on the structure of multi-jet states at
high energies, and in particular on the theoretical systematics associated with
multi-jet merging. To analyze this, we propose a new merging methodology, and
illustrate its impact by comparing our theoretical results with experimental
measurements for Z-boson + jets production at the Large Hadron Collider (LHC).


  Basaltic rocks occur widely on the terrestrial planets and differentiated
asteroids, including the asteroid 4 Vesta. We conducted a shock recovery
experiment with decaying compressive pulses on a terrestrial basalt at Chiba
Institute of Technology, Japan. The sample recorded a range of pressures, and
shock physics modeling was conducted to add a pressure scale to the observed
shock features. The shocked sample was examined by optical and electron
microscopy, electron back-scattered diffractometry, and Raman spectroscopy. We
found that localized melting occurs at a lower pressure (~10 GPa) than
previously thought (>20 GPa). The shocked basalt near the epicenter represents
shock degree C of a recently proposed classification scheme for basaltic
eucrites and, as such, our results provide a pressure scale for the
classification scheme. Finally, we estimated the total fraction of the basaltic
eucrites classified as shock degree C to be ~15% by assuming the impact
velocity distribution onto Vesta.


  Shallow water wave phenomena find their analogue in optics through a nonlocal
nonlinear Schr\"odinger (NLS) model in $(2+1)$-dimensions. We identify an
analogue of surface tension in optics, namely a single parameter depending on
the degree of nonlocality, which changes the sign of dispersion, much like
surface tension does in the shallow water wave problem. Using multiscale
expansions, we reduce the NLS model to a Kadomtsev-Petviashvilli (KP) equation,
which is of the KPII (KPI) type, for strong (weak) nonlocality.


  The unique properties of organic semiconductors make them versatile base
materials for many applications ranging from light emitting diodes to
transistors. The low spin-orbit coupling typical for carbon-based materials and
the resulting long spin lifetimes give rise to a large influence of the
electron spin on charge transport which can be exploited in spintronic devices
or to improve solar cell efficiencies. Magnetic resonance techniques are
particularly helpful to elucidate the microscopic structure of paramagnetic
states in semiconductors as well as the transport processes they are involved
in. However, in organic devices the nature of the dominant spin-dependent
processes is still subject to considerable debate. Using multi-frequency pulsed
electrically detected magnetic resonance (pEDMR), we show that the
spin-dependent response of P3HT/PCBM solar cells at low temperatures is
governed by bipolar polaron pair recombination involving the positive and
negative polarons in P3HT and PCBM, respectively, thus excluding a unipolar
bipolaron formation as the main contribution to the spin-dependent charge
transfer in this temperature regime. Moreover the polaron-polaron coupling
strength and the recombination times of polaron pairs with parallel and
antiparallel spins are determined. Our results demonstrate that the pEDMR pulse
sequences recently developed for inorganic semiconductor devices can very
successfully be transferred to the study of spin and charge transport in
organic semiconductors, in particular when the different polarons can be
distinguished spectrally.


  We present the equivalence between the fuzzy core and the core under minimal
assumptions. Due to the exact version of the Lyapunov convexity theorem in
Banach spaces, we clarify that the additional structure of commodity spaces and
preferences is unnecessary whenever the measure space of agents is "saturated".
As a spin-off of the above equivalence, we obtain the coincidence of the core,
the fuzzy core, and the Schmeidler's restricted core under minimal assumptions.
The coincidence of the fuzzy core and the restricted core has not been
articulated anywhere.


  This study introduces an innovative approach aimed at the efficient pruning
of neural networks, with a particular focus on their deployment on edge
devices. Our method involves the integration of the Lottery Ticket Hypothesis
(LTH) with the Knowledge Distillation (KD) framework, resulting in the
formulation of three distinct pruning models. These models have been developed
to address scalability issue in recommender systems, whereby the complexities
of deep learning models have hindered their practical deployment. With
judicious application of the pruning techniques, we effectively curtail the
power consumption and model dimensions without compromising on accuracy.
Empirical evaluation has been performed using two real world datasets from
diverse domains against two baselines. Gratifyingly, our approaches yielded a
GPU computation-power reduction of up to 66.67%. Notably, our study contributes
to the field of recommendation system by pioneering the application of LTH and
KD.


  We measure electronic transport through point contacts in the high-mobility
electron gas in a Ga[Al]As heterostructure at different temperatures and bulk
electron densities. The conductance through all point contacts increases with
increasing temperature in a temperature window around $T \sim 10 K$ for all
investigated electron densities and point contact widths. For high electron
densities this conductance exceeds the fundamental ballistic limit (Sharvin
limit). These observations are in agreement with a viscous electron transport
model and previous experiments in graphene.


  Offline reinforcement learning (RL), also known as batch RL, aims to optimize
policy from a large pre-recorded dataset without interaction with the
environment. This setting offers the promise of utilizing diverse,
pre-collected datasets to obtain policies without costly, risky, active
exploration. However, commonly used off-policy algorithms based on Q-learning
or actor-critic perform poorly when learning from a static dataset. In this
work, we study why off-policy RL methods fail to learn in offline setting from
the value function view, and we propose a novel offline RL algorithm that we
call Pessimistic Offline Policy Optimization (POPO), which learns a pessimistic
value function to get a strong policy. We find that POPO performs surprisingly
well and scales to tasks with high-dimensional state and action space,
comparing or outperforming several state-of-the-art offline RL algorithms on
benchmark tasks.


  We change the definition of the vertex representations. As a result the
vertex representations has one parameter.


  We construct the first globally consistent semi-realistic Type I string vacua
on an elliptically fibered manifold where the zero modes of the Euclidean
D1-instanton sector allow for the generation of non-perturbative Majorana
masses of an intermediate scale. In another class of global models, a D1-brane
instanton can generate a Polonyi-type superpotential breaking supersymmetry at
an exponentially suppressed scale.


  Dynamics of entanglement is investigated on the basis of exactly solvable
models of multiple-quantum (MQ) NMR spin dynamics. It is shown that the time
evolution of MQ coherences of systems of coupled nuclear spins in solids is
directly connected with dynamics of the quantum entanglement. We studied
analytically dynamics of entangled states for two- and three-spin systems
coupled by the dipole-dipole interaction. In this case dynamics of the quantum
entanglement is uniquely determined by the time evolution of MQ coherences of
the second order. The real part of the density matrix describing MQ dynamics in
solids is responsible for MQ coherences of the zeroth order while its imaginary
part is responsible for the second order. Thus, one can conclude that dynamics
of the entanglement is connected with transitions from the real part of the
density matrix to the imaginary one and vice versa. A pure state which
generalizes the GHZ and W states is found. Different measures of the
entanglement of this state are analyzed for three-partite systems.


  We present a silicon-nitride-based optical phased array with built-in
focusing and steering capability, that operates at 522 nm and is aimed at
complementing a micro-electrode array for joint electrical and optical probing
of retinal tissue. It achieves subcellular resolution with a beam diameter of
1.4 um at a focal point located above the chip. Targeted cellular excitation
can be achieved by steering the beam through a combination of wavelength tuning
and simplified thermo-optical phase shifters with a single electrical input for
each of transverse beam steering and selection of the focal plane.


  We simulate phase separated fluids using the Cahn-Hillard fluctuating
hydrodynamic (CH-FHD) model and measure the statistical properties of capillary
waves generated by thermal fluctuations. Our measurements are in good agreement
with stochastic lubrication theory and molecular dynamics simulations but
differ significantly from recent CH-FHD results by Zhang et al. (Phys. Rev. E
109 024208 (2024)). Specifically, we find that capillary wave statistics at
thermodynamic equilibrium are independent of transport properties, namely
viscosity and species diffusion.


  Prior AI breakthroughs in complex games have focused on either the purely
adversarial or purely cooperative settings. In contrast, Diplomacy is a game of
shifting alliances that involves both cooperation and competition. For this
reason, Diplomacy has proven to be a formidable research challenge. In this
paper we describe an agent for the no-press variant of Diplomacy that combines
supervised learning on human data with one-step lookahead search via regret
minimization. Regret minimization techniques have been behind previous AI
successes in adversarial games, most notably poker, but have not previously
been shown to be successful in large-scale games involving cooperation. We show
that our agent greatly exceeds the performance of past no-press Diplomacy bots,
is unexploitable by expert humans, and ranks in the top 2% of human players
when playing anonymous games on a popular Diplomacy website.


  We study horizon shells and soldering freedom for extreme black holes and how
supertranslation-like Bondi-Metzner-Sachs (BMS) symmetries appear as soldering
transformations. Further, for a null shell placed infinitesimally close to the
horizon of an extreme Reissner-Nordstr$\ddot{o}$m (RN) black hole, we show
superrotation-like symmetries also arise as soldering freedom. Next,
considering the interaction of impulsive gravitational waves supported at the
horizon shell with test particles, we study how the "memory" (or the imprints)
of BMS-like symmetries gets encoded in the geodesics (test particles) crossing
the shell. Our study shows, timelike test particles get displaced from their
initial plane when they cross the horizon shell. For a null geodesic congruence
crossing the horizon shell, the optical tensors corresponding to the congruence
suffer jumps. In both the cases, the changes are induced by BMS parameters that
constitute the gravity wave and matter degrees of freedom of the shell.


  The property and casualty (P&C) insurance industry faces challenges in
developing claim predictive models due to the highly right-skewed distribution
of positive claims with excess zeros. To address this, actuarial science
researchers have employed "zero-inflated" models that combine a traditional
count model and a binary model. This paper investigates the use of boosting
algorithms to process insurance claim data, including zero-inflated telematics
data, to construct claim frequency models. Three popular gradient boosting
libraries - XGBoost, LightGBM, and CatBoost - are evaluated and compared to
determine the most suitable library for training insurance claim data and
fitting actuarial frequency models. Through a comprehensive analysis of two
distinct datasets, it is determined that CatBoost is the best for developing
auto claim frequency models based on predictive performance. Furthermore, we
propose a new zero-inflated Poisson boosted tree model, with variation in the
assumption about the relationship between inflation probability $p$ and
distribution mean $\mu$, and find that it outperforms others depending on data
characteristics. This model enables us to take advantage of particular CatBoost
tools, which makes it easier and more convenient to investigate the effects and
interactions of various risk features on the frequency model when using
telematics data.


  We employ effective mass theory for degenerate hole-bands to calculate the
acceptor binding energies for Be, Mg, Zn, Ca, C and Si substitutional acceptors
in GaN and AlN. The calculations are performed through the 6$\times $6
Rashba-Sheka-Pikus and the Luttinger-Kohn matrix Hamiltonians for wurtzite (WZ)
and zincblende (ZB) crystal phases, respectively. An analytic representation
for the acceptor pseudopotential is used to introduce the specific nature of
the impurity atoms. The energy shift due to polaron effects is also considered
in this approach. The ionization energy estimates are in very good agreement
with those reported experimentally in WZ-GaN. The binding energies for ZB-GaN
acceptors are all predicted to be shallower than the corresponding impurities
in the WZ phase. The binding energy dependence upon the crystal field splitting
in WZ-GaN is analyzed. Ionization levels in AlN are found to have similar
`shallow' values to those in GaN, but with some important differences, which
depend on the band structure parameterizations, especially the value of crystal
field splitting used.


  A line L is a transversal to a family F of convex objects in R^d if it
intersects every member of F. In this paper we show that for every integer d>2
there exists a family of 2d-1 pairwise disjoint unit balls in R^d with the
property that every subfamily of size 2d-2 admits a transversal, yet any line
misses at least one member of the family. This answers a question of Danzer
from 1957.


  The Besicovitch projection theorem states that if a subset $E$ of the plane
has finite length in the sense of Hausdorff measure and is purely unrectifiable
(so its intersection with any Lipschitz graph has zero length), then almost
every orthogonal projection of $E$ to a line will have zero measure. In other
words, the Favard length of a purely unrectifiable $1$-set vanishes. In this
article, we show that when linear projections are replaced by certain nonlinear
projections called curve projections, this result remains true. In fact, we go
further and use multiscale analysis to prove a quantitative version of this
Besicovitch nonlinear projection theorem. Roughly speaking, we show that if a
subset of the plane has finite length in the sense of Hausdorff and is nearly
purely unrectifiable, then its Favard curve length is very small. Our
techniques build on those of Tao, who in [Tao09] proves a quantification of the
original Besicovitch projection theorem.


  Recent studies have illuminated that Large Language Models (LLMs) exhibit
substantial potential in the realm of RTL (Register Transfer Level) code
generation, with notable advancements evidenced by commercial models such as
GPT-4 and Claude3-Opus. Despite their proficiency, these commercial LLMs often
raise concerns regarding privacy and security. Conversely, open-source LLMs,
which offer solutions to these concerns, have inferior performance in RTL code
generation tasks to commercial models due to the lack of highquality
open-source RTL datasets. To address this issue, we introduce OriGen, a fully
open-source framework featuring self-reflection capabilities and a dataset
augmentation methodology for generating high-quality, large-scale RTL code. We
propose a novel code-to-code augmentation methodology that leverages knowledge
distillation to enhance the quality of the open-source RTL code datasets.
Additionally, OriGen is capable of correcting syntactic errors by leveraging a
self-reflection process based on feedback from the compiler. The
self-reflection ability of the model is facilitated by a carefully constructed
dataset, which comprises a comprehensive collection of samples. Experimental
results demonstrate that OriGen remarkably outperforms other open-source
alternatives in RTL code generation, surpassing the previous best-performing
LLM by 9.8% on the VerilogEval-Human benchmark. Furthermore, OriGen exhibits
superior capabilities in self-reflection and error rectification, surpassing
GPT-4 by 18.1% on the benchmark designed to evaluate the capability of
self-reflection.


  Braginsky, Gorodetsky, and Vyatchanin have shown that thermo-refractive
fluctuations are an important source of noise in interferometric
gravitational-wave detectors. In particular, the thermo-refractive noise in the
GEO600 beamsplitter is expected to make a substantial contribution to the
interferometer's total noise budget. Here we present a new computation of the
GEO600 thermo-refractive noise which takes into account the beam's elliptical
profile and, more importantly, the fact that the laser beam induces a standing
electromagnetic wave in the beamsplitter. The use of updated parameters results
in the overall reduction of the calculated noise amplitude by a factor of about
5 in the low-frequency part of the GEO600 band, compared to the previous
estimates. We also find, by contrast with previous calculations, that
thermo-refractive fluctuations result in white noise between 600 Hz and 39 MHz,
at a level of $8.5\cdot 10^{-24}$Hz$^{-1/2}$. Finally, we describe a new type
of thermal noise, which we call the thermo-chemical noise. This is caused by a
random motion of optically-active chemical impurities or structural defects in
the direction along a steep intensity gradient of the standing wave. We discuss
the potential relevance of the thermo-chemical noise for GEO600.


  Relativistic hydrodynamics of classic plasmas is derived from the microscopic
model in the limit of ideal plasmas. The chain of equations is constructed step
by step starting from the concentration evolution. It happens that the energy
density and the momentum density do not appear at such approach, but new
relativistic-hydrodynamic variables appear in the model. These variables has no
nonrelativistic analogs, but they are reduced to the concentration, the
particle current, the pressure (the flux of the particle current) if
relativistic effects are dropped. These variables are reduced to functions of
the concentration, the particle current, the pressure if the thermal velocities
are dropped in compare with the relativistic velocity field. Final equations
are presented in the monopole limit of the meanfield (the selfconsistent field)
approximation. Hence, the contributions of the electric dipole moment, magnetic
dipole moment, electric quadrupole moment, etc of the macroscopically
infinitesimal element of volume appearing in derived equations are dropped.


  We investigate the scattering off three nonoverlapping disks equidistantly
spaced along a line in the two-dimensional plane with the radii of the outer
disks equal and the radius of the inner disk varied. This system is a
two-dimensional scattering analog to the double-well-potential (bound state)
problem in one dimension. In both systems the symmetry splittings between
symmetric and antisymmetric states or resonances, respectively, have to be
traced back to tunneling effects, as semiclassically the geometrical periodic
orbits have no contact with the vertical symmetry axis. We construct the
leading semiclassical ``creeping'' orbits that are responsible for the symmetry
splitting of the resonances in this system. The collinear three-disk-system is
not only one of the simplest but also one of the most effective systems for
detecting creeping phenomena. While in symmetrically placed n-disk systems
creeping corrections affect the subleading resonances, they here alone
determine the symmetry splitting of the 3-disk resonances in the semiclassical
calculation. It should therefore be considered as a paradigm for the study of
creeping effects. PACS numbers: 03.65.Sq, 03.20.+i, 05.45.+b


  In the rapidly evolving landscape of medical documentation, transcribing
clinical dialogues accurately is increasingly paramount. This study explores
the potential of Large Language Models (LLMs) to enhance the accuracy of
Automatic Speech Recognition (ASR) systems in medical transcription. Utilizing
the PriMock57 dataset, which encompasses a diverse range of primary care
consultations, we apply advanced LLMs to refine ASR-generated transcripts. Our
research is multifaceted, focusing on improvements in general Word Error Rate
(WER), Medical Concept WER (MC-WER) for the accurate transcription of essential
medical terms, and speaker diarization accuracy. Additionally, we assess the
role of LLM post-processing in improving semantic textual similarity, thereby
preserving the contextual integrity of clinical dialogues. Through a series of
experiments, we compare the efficacy of zero-shot and Chain-of-Thought (CoT)
prompting techniques in enhancing diarization and correction accuracy. Our
findings demonstrate that LLMs, particularly through CoT prompting, not only
improve the diarization accuracy of existing ASR systems but also achieve
state-of-the-art performance in this domain. This improvement extends to more
accurately capturing medical concepts and enhancing the overall semantic
coherence of the transcribed dialogues. These findings illustrate the dual role
of LLMs in augmenting ASR outputs and independently excelling in transcription
tasks, holding significant promise for transforming medical ASR systems and
leading to more accurate and reliable patient records in healthcare settings.


  We show that the low-energy electronic structure of arbitrarily stacked
graphene multilayers with nearest-neighbor interlayer tunneling consists of
chiral pseudospin doublets. Although the number of doublets in an $N$-layer
system depends on the stacking sequence, the pseudospin chirality sum is always
$N$. $N$-layer stacks have $N$ distinct Landau levels at E=0 for each spin and
valley, and quantized Hall conductivity $\sigma_{xy} = \pm(4 e^2/h)(N/2+n)$
where $n$ is a non-negative integer.


  We report the observation of a current-phase relation dominated by the second
Josephson harmonic in superconductor-ferromagnet-superconductor junctions. The
exotic current-phase relation is realized in the vicinity of a
temperature-controlled 0-to-$\pi$ junction transition, at which the first
Josephson harmonic vanishes. Direct current-phase relation measurements, as
well as Josephson interferometry, non-vanishing supercurrent and half-integer
Shapiro steps at the 0-$\pi$ transition self-consistently point to an intrinsic
second harmonic term, making it possible to rule out common alternative origins
of half-periodic behavior. While surprising for diffusive multimode junctions,
the large second harmonic is in agreement with theory predictions for thin
ferromagnetic interlayers.


  We consider the focusing modified Zakharov-Kuznetsov (mZK) equation in two
space dimensions. We prove that solutions which blow up in finite time in the
$H^1(\R^{2})$ norm have the property that they concentrate a non-trivial
portion of their mass (more precisely, at least the amount equal to the mass of
the ground state) at blow-up time. For finite-time blow-up solutions in the
$H^s(\R^2)$ norm for $\frac{17}{18} < s < 1$, we prove a slightly weaker
result. Moreover, we prove that the stronger concentration result can be
extended to the range $ \frac{17}{18} < s \le 1$ under an additional assumption
on the upper bound of the blow-up rate of the solution. The main tools used
here are the $I$-method and a profile decomposition theorem for a bounded
family of $H^1(\R^{2})$ functions.


  Content-based image retrieval (CBIR) is an essential part of computer vision
research, especially in medical expert systems. Having a discriminative image
descriptor with the least number of parameters for tuning is desirable in CBIR
systems. In this paper, we introduce a new simple descriptor based on the
histogram of local Radon projections. We also propose a very fast
convolution-based local Radon estimator to overcome the slow process of Radon
projections. We performed our experiments using pathology images (KimiaPath24)
and lung CT patches and test our proposed solution for medical image
processing. We achieved superior results compared with other histogram-based
descriptors such as LBP and HoG as well as some pre-trained CNNs.


  The grand challenges of contemporary fundamental physics---dark matter, dark
energy, vacuum energy, inflation and early universe cosmology, singularities
and the hierarchy problem---all involve gravity as a key component. And of all
gravitational phenomena, black holes stand out in their elegant simplicity,
while harbouring some of the most remarkable predictions of General Relativity:
event horizons, singularities and ergoregions. The hitherto invisible landscape
of the gravitational Universe is being unveiled before our eyes: the historical
direct detection of gravitational waves by the LIGO-Virgo collaboration marks
the dawn of a new era of scientific exploration. Gravitational-wave astronomy
will allow us to test models of black hole formation, growth and evolution, as
well as models of gravitational-wave generation and propagation. It will
provide evidence for event horizons and ergoregions, test the theory of General
Relativity itself, and may reveal the existence of new fundamental fields. The
synthesis of these results has the potential to radically reshape our
understanding of the cosmos and of the laws of Nature. The purpose of this work
is to present a concise, yet comprehensive overview of the state of the art in
the relevant fields of research, summarize important open problems, and lay out
a roadmap for future progress.


  We give new proofs for certain bilateral basic hypergeometric summation
formulas using the symmetries of the corresponding series. In particular, we
present a proof for Bailey's $_3\psi_3$ summation formula as an application. We
also prove a multiple series analogue of this identity by considering
hyperoctahedral group symmetries of higher ranks.


  We prove that the principal component of the exchange graph of hearts of a
graded skew-gentle algebra can be identified with the corresponding exchange
graph of S-graphs, using the geometric models and
$\operatorname{Int}=\operatorname{dim}\operatorname{Hom}$ formula in
Qiu-Zhang-Zhou. Using the same argument in Bridgeland-Smith,
Barbieri-M\"oller-Qiu-So and Christ-Haiden-Qiu, we extend this identification
to an isomorphism between the spaces of stability conditions and of quadratic
differentials.


  Stochastic Neighbor Embedding (SNE) methods minimize the divergence between
the similarity matrix of a high-dimensional data set and its counterpart from a
low-dimensional embedding, leading to widely applied tools for data
visualization. Despite their popularity, the current SNE methods experience a
crowding problem when the data include highly imbalanced similarities. This
implies that the data points with higher total similarity tend to get crowded
around the display center. To solve this problem, we introduce a fast
normalization method and normalize the similarity matrix to be doubly
stochastic such that all the data points have equal total similarities.
Furthermore, we show empirically and theoretically that the doubly
stochasticity constraint often leads to embeddings which are approximately
spherical. This suggests replacing a flat space with spheres as the embedding
space. The spherical embedding eliminates the discrepancy between the center
and the periphery in visualization, which efficiently resolves the crowding
problem. We compared the proposed method (DOSNES) with the state-of-the-art SNE
method on three real-world datasets and the results clearly indicate that our
method is more favorable in terms of visualization quality.


  The metric of a Schwarzschild solution in brane induced gravity in five
dimensions is studied. We find a nonperturbative solution for which an exact
expression on the brane is obtained. We also find a linearized solution in the
bulk and argue that a nonsingular exact solution in the entire space should
exist. The exact solution on the brane is highly nontrivial as it interpolates
between different distance scales. This part of the metric is enough to deduce
an important property -- the ADM mass of the solution is suppressed compared to
the bare mass of a static source. This screening of the mass is due to
nonlinear interactions which give rise to a nonzero curvature outside the
source. The curvature extends away from the source to a certain macroscopic
distance that coincides with the would-be strong interaction scale. The very
same curvature shields the source from strong coupling effects. The four
dimensional law of gravity, including the correct tensorial structure, is
recovered at observable distances. We find that the solution has no vDVZ
discontinuity and show that the gravitational field on the brane is always
weak, in spite of the fact that the solution is nonperturbative.


  In this paper we introduce the concept of a Cayley graph automatic group (CGA
group or graph automatic group, for short) which generalizes the standard
notion of an automatic group. Like the usual automatic groups graph automatic
ones enjoy many nice properties: these group are invariant under the change of
generators, they are closed under direct and free products, certain types of
amalgamated products, and finite extensions. Furthermore, the Word Problem in
graph automatic groups is decidable in quadratic time. However, the class of
graph automatic groups is much wider then the class of automatic groups. For
example, we prove that all finitely generated 2-nilpotent groups and
Baumslag-Solitar groups B(1,n) are graph automatic, as well as many other
metabelian groups.


  A 760 $\times$ 760 $\times$ 30 mm$^3$ plastic scintillation detector viewed
by photomultiplier tubes (PMTs) from four corners has been developed, and the
detector has been tested with cosmic rays and $\gamma$ rays. A
position-independent effective time T$_{eff}$ has been found, indicating this
detector can be used as a TOF detector. The hit position can also be
reconstructed by the time from four corners. A TOF resolution of 236 ps and a
position resolution of 48 mm have been achieved, and the detection efficiency
has also been investigated.


  We provide a short argument to establish a Beurling-Lax-Halmos theorem for
reproducing kernel Hilbert spaces whose kernel has a complete Nevanlinna-Pick
factor. We also record factorization results for pairs of nested invariant
subspaces.


  Developing Information Retrieval (IR) tools and techniques in African
languages suffers from the dual problems of a lack of algorithms and very small
test data collections. This affects the creation of practical IR systems and
limits the ability to apply IR to address human and socio-economic problems,
which is an urgent need in poor countries. This position paper presents an
overview of recent and current work conducted at the University of Cape Town in
this area. While many problems have been investigated at an early stage,
limited dataset sizes for local African languages still persists as a
significant limitation and stumbling block.


  The modulation transfer function (MTF) represents the frequency domain
response of imaging modalities. Here, we report a method for estimating the MTF
from sample images. Test images were generated from a number of images,
including those taken with an electron microscope and with an observation
satellite. These original images were convolved with point spread functions
(PSFs) including those of circular apertures. The resultant test images were
subjected to a Fourier transformation. The logarithm of the squared norm of the
Fourier transform was plotted against the squared distance from the origin.
Linear correlations were observed in the logarithmic plots, indicating that the
PSF of the test images can be approximated with a Gaussian. The MTF was then
calculated from the Gaussian-approximated PSF. The obtained MTF closely
coincided with the MTF predicted from the original PSF. The MTF of an x-ray
microtomographic section of a fly brain was also estimated with this method.
The obtained MTF showed good agreement with the MTF determined from an edge
profile of an aluminum test object. We suggest that this approach is an
alternative way of estimating the MTF, independently of the image type.


  Multi-label chest X-ray (CXR) recognition involves simultaneously diagnosing
and identifying multiple labels for different pathologies. Since pathological
labels have rich information about their relationship to each other, modeling
the co-occurrence dependencies between pathological labels is essential to
improve recognition performance. However, previous methods rely on state
variable coding and attention mechanisms-oriented to model local label
information, and lack learning of global co-occurrence relationships between
labels. Furthermore, these methods roughly integrate image features and label
embedding, ignoring the alignment and compactness problems in cross-modal
vector fusion.To solve these problems, a Bi-modal Bridged Graph Convolutional
Network (BB-GCN) model is proposed. This model mainly consists of a backbone
module, a pathology Label Co-occurrence relationship Embedding (LCE) module,
and a Transformer Bridge Graph (TBG) module. Specifically, the backbone module
obtains image visual feature representation. The LCE module utilizes a graph to
model the global co-occurrence relationship between multiple labels and employs
graph convolutional networks for learning inference. The TBG module bridges the
cross-modal vectors more compactly and efficiently through the GroupSum
method.We have evaluated the effectiveness of the proposed BB-GCN in two
large-scale CXR datasets (ChestX-Ray14 and CheXpert). Our model achieved
state-of-the-art performance: the mean AUC scores for the 14 pathologies were
0.835 and 0.813, respectively.The proposed LCE and TBG modules can jointly
effectively improve the recognition performance of BB-GCN. Our model also
achieves satisfactory results in multi-label chest X-ray recognition and
exhibits highly competitive generalization performance.


  We present a general-order spin-free formulation of the single-reference
closed-shell coupled-cluster method. We show that the working equations of a
fully biorthogonal contravariant projection formulation of the residual
equations, as near-universally used in closed-shell CCSD, can also be defined
at the CCSDT and CCSDTQ levels, despite singularities in the spin projection
manifolds. We describe permutation-group based techniques for obtaining and
simplifying the equations encountered in general second-quantization-based
methods; this includes a permutation group based approach of evaluating
second-quantized matrix elements into tensor contraction networks, and the use
of Portugal's double coset canonical representation technique [Int. J. Mod.
Phys. C 13, 859 (2002)] for eliminating redundant terms. A computer
implementation of our techniques is simple, because no operator-valued symbolic
algebra is required. Explicit working equation lists for closed-shell CCSD,
CCSDT, and CCSDTQ in the semi-biorthogonal formulation are provided. We also
release open-source computer programs for both deriving and numerically
evaluating these equations.


  Stochastic phenomena are often described by Langevin equations, which serve
as a mesoscopic model for microscopic dynamics. It is known since the work of
Parisi and Sourlas that reversible (or equilibrium) dynamics present
supersymmetries (SUSYs). These are revealed when the path-integral action is
written as a function not only of the physical fields, but also of Grassmann
fields representing a Jacobian arising from the noise distribution. SUSYs leave
the action invariant upon a transformation of the fields that mixes the
physical and the Grassmann ones. We show that, contrarily to the common belief,
it is possible to extend the known reversible construction to the case of
arbitrary irreversible dynamics, for overdamped Langevin equations with
additive white noise - provided their steady state is known. The construction
is based on the fact that the Grassmann representation of the functional
determinant is not unique, and can be chosen so as to present a generalization
of the Parisi-Sourlas SUSY. Our approach is valid both for
Martin-Siggia-Rose-Janssen-de Dominicis and for Onsager-Machlup actions. We
show how such SUSYs are related to time-reversal symmetries and allow one to
derive modified fluctuation-dissipation relations valid in non-equilibrium. We
give as a concrete example the results for the Kardar-Parisi-Zhang equation.


  We compare two opposite ways of performing a 3D reduction of the two-fermion
Bethe-Salpeter equation beyond the instantaneous approximation and Salpeter's
equation. The more usual method consists in performing an expansion around an
instantaneous approximation of the product of the free propagators
(propagator-approximated reduction). The second method starts with an
instantaneous approximation of the Bethe-Salpeter kernel (kernel-approximated
reduction). In both reductions the final 3D potential can be obtained by
following simple modified Feynman rules. The kernel-approximated reduction,
however, does not give the correct scattering amplitudes, and must thus be
limited to the computation of bound states. Our 3D reduction of the
three-fermion Bethe-Salpeter equation is inspired by these results. We expand
this equation around positive-energy instantaneous approximations of the three
two-body kernels, but these starting approximations are given by
propagator-approximated reductions at the two-body level. The three-fermion
Bethe-Salpeter equation is first transformed into a set of three coupled
equations for three wave functions depending each on one two-fermion total
energy, then into a set of three 3D equations and finally into a single 3D
equation. This last equation is rather complicated, as it combines three series
expansions, but we use it to write a manageable expression of the first-order
corrections to the energy spectrum.


  All spaces below are Tychonov. We define the projective pi-character p(X) of
a space X as the supremum of the values $\pi\chi(Y)$ where Y ranges over all
continuous images of X. Our main result says that every space X has a pi-base
whose order is at most p(X), that is every point in X is contained in at most
p(X)-many members of the pi-base. Since p(X) is at most t(X) for compact X,
this provides a significant generalization of a celebrated result of
Shapirovskii.