  We discuss the simplest mechanisms for generating neutrino masses at tree
level and one loop level. We find a significant number of new possibilities
where one can generate neutrino masses at the one-loop level by adding only two
new types of representations. These models have renormalizable interactions
that automatically conserve baryon number. Adding to the minimal standard model
a scalar color octet with SU(3) X SU(2) X U(1) quantum numbers, (8,2,1/2), and
a fermionic color octet in the fundamental or adjoint representation of SU(2)
one can generate neutrino masses in agreement with the experiment. Signals at
the LHC, and constraints from flavour violation are briefly discussed.


  We have developed and tested an antireflection (AR) coating method for
silicon lenses at cryogenic temperatures and millimeter wavelengths. Our
particular application is a measurement of the cosmic microwave background. The
coating consists of machined pieces of Cirlex glued to the silicon. The
measured reflection from an AR coated flat piece is less than 1.5% at the
design wavelength. The coating has been applied to flats and lenses and has
survived multiple thermal cycles from 300 to 4 K. We present the manufacturing
method, the material properties, the tests performed, and estimates of the loss
that can be achieved in practical lenses.


  In the era of digital markets, the challenge for consumers is discerning
quality amidst information asymmetry. While traditional markets use brand
mechanisms to address this issue, transferring such systems to internet-based
P2P markets, where misleading practices like fake ratings are rampant, remains
challenging. Current internet platforms strive to counter this through
verification algorithms, but these efforts find themselves in a continuous
tug-of-war with counterfeit actions.
  Exploiting the transparency, immutability, and traceability of blockchain
technology, this paper introduces a robust reputation voting system grounded in
it. Unlike existing blockchain-based reputation systems, our model harnesses an
intrinsically economically incentivized approach to bolster agent integrity. We
optimize this model to mirror real-world user behavior, preserving the
reputation system's foundational sustainability. Through Monte-Carlo
simulations, using both uniform and power-law distributions enabled by an
innovative inverse transform method, we traverse a broad parameter landscape,
replicating real-world complexity. The findings underscore the promise of a
sustainable, transparent, and formidable reputation mechanism. Given its
structure, our framework can potentially function as a universal, sustainable
oracle for offchain-onchain bridging, aiding entities in perpetually
cultivating their reputation. Future integration with technologies like Ring
Signature and Zero Knowledge Proof could amplify the system's privacy facets,
rendering it particularly influential in the ever-evolving digital domain.


  We present the observation that the process of stochastic model predictive
control can be formulated in the framework of iterated function systems. The
latter has a rich ergodic theory that can be applied to study the system's
long-run behavior. We show how such a framework can be realized for specific
problems and illustrate the required conditions for the application of relevant
theoretical guarantees.


  In this short letter we review Schwinger's formulation of Quantum Mechanics
and we argue that the mathematical structure behind Schwinger's "Symbolism of
Atomic Measurements" is that of a groupoid. In this framework, both the Hilbert
space (Schr\"{o}dinger picture) and the $C^{*}$-algebra (Heisenberg picture) of
the system turn out to be derived concepts, that is, they arise from the
underlying groupoid structure.


  It is usually assumed that relic neutrinos possess a Fermi-Dirac
distribution, acquired during thermal equilibrium in the Early Universe.
However, various mechanisms could introduce strong distortions in this
distribution. We perform a Bayesian likelihood analysis including the first
moments of the three active neutrino distributions as free parameters, and show
that current cosmological observations of light element abundances, Cosmic
Microwave Background (CMB) anisotropies and Large Scale Structures (LSS) are
compatible with very large deviations from the standard picture. We also
calculate the bounds on non-thermal distortions which can be expected from
future observations, and stress that CMB and LSS data alone will not be
sensitive enough in order to distinguish between non-thermal distortions in the
neutrino sector and extra relativistic degrees of freedom. This degeneracy
could be removed by additional constraints from primordial nucleosynthesis or
independent neutrino mass scale measurements.


  This paper shares my journey (tools used, design principles derived and
modeling pedagogy implemented) when creating electronic books-chapters (epub3
format) for computers and tablets using Easy Java/JavaScript Simulations, (old
name EJS, new EjsS) Modeling Tool. The theory underpinning this work grounded
on learning by doing through dynamic and interactive simulation-models that can
be more easily made sense of instead of the static nature of printed materials.
I started combining related computer models with supporting texts and
illustrations into a coherent chapter, a logical next step towards tighter
support for teachers and students ,developing prototypes electronic chapters on
the topics of Simple Harmonic Motion and Gravity customized for the
Singapore-Cambridge General Certificate of Education Advanced Level (A-level).
I aim to inspire more educators to create interactive and open educational
resources for the benefit of all. Prototypes:
http://iwant2study.org/ospsg/index.php/interactive-resources/physics/02-newtonian-mechanics/08-gravity/154-e-book-shm
http://iwant2study.org/ospsg/index.php/interactive-resources/physics/02-newtonian-mechanics/09-oscillations/153-e-book-gravity
and Apple iBook Store, Google Play Book and Kindle Book


  In this paper, we present a cross-modal recipe retrieval framework,
Transformer-based Network for Large Batch Training (TNLBT), which is inspired
by ACME~(Adversarial Cross-Modal Embedding) and H-T~(Hierarchical Transformer).
TNLBT aims to accomplish retrieval tasks while generating images from recipe
embeddings. We apply the Hierarchical Transformer-based recipe text encoder,
the Vision Transformer~(ViT)-based recipe image encoder, and an adversarial
network architecture to enable better cross-modal embedding learning for recipe
texts and images. In addition, we use self-supervised learning to exploit the
rich information in the recipe texts having no corresponding images. Since
contrastive learning could benefit from a larger batch size according to the
recent literature on self-supervised learning, we adopt a large batch size
during training and have validated its effectiveness. In the experiments, the
proposed framework significantly outperformed the current state-of-the-art
frameworks in both cross-modal recipe retrieval and image generation tasks on
the benchmark Recipe1M. This is the first work which confirmed the
effectiveness of large batch training on cross-modal recipe embeddings.


  We experimentally demonstrate generation of coherent propagating magnons in
ultra-thin magnetic-insulator films by spin-orbit torque induced by dc electric
current. We show that this challenging task can be accomplished by utilizing
magnetic-insulator films with large perpendicular magnetic anisotropy. We
demonstrate simple and flexible spin-orbit torque devices, which can be used as
highly efficient nanoscale sources of coherent propagating magnons for
insulator-based spintronic applications.


  Providing external knowledge to Large Language Models (LLMs) is a key point
for using these models in real-world applications for several reasons, such as
incorporating up-to-date content in a real-time manner, providing access to
domain-specific knowledge, and contributing to hallucination prevention. The
vector database-based Retrieval Augmented Generation (RAG) approach has been
widely adopted to this end. Thus, any part of external knowledge can be
retrieved and provided to some LLM as the input context. Despite RAG approach's
success, it still might be unfeasible for some applications, because the
context retrieved can demand a longer context window than the size supported by
LLM. Even when the context retrieved fits into the context window size, the
number of tokens might be expressive and, consequently, impact costs and
processing time, becoming impractical for most applications. To address these,
we propose CRAG, a novel approach able to effectively reduce the number of
prompting tokens without degrading the quality of the response generated
compared to a solution using RAG. Through our experiments, we show that CRAG
can reduce the number of tokens by at least 46\%, achieving more than 90\% in
some cases, compared to RAG. Moreover, the number of tokens with CRAG does not
increase considerably when the number of reviews analyzed is higher, unlike
RAG, where the number of tokens is almost 9x higher when there are 75 reviews
compared to 4 reviews.


  Isothermal-isobaric molecular dynamics simulations are used to examine the
microscopic structure and other properties of a model solution consisting of
NaCl salt dissolved in water-methanol mixture. The SPC/E water model and the
united atom model for methanol are combined with the force field for ions by
Dang [J. Amer. Chem. Soc., 1995, 117, 6954] to describe the entire system. Our
principal focus is to study the effects of two variables, namely, the solvent
composition and ion concentrations on the solution's density, on the structural
properties, self-diffusion coefficients of the species and the dielectric
constant. Moreover, we performed a detailed analysis of the first coordination
numbers of the species. Trends of the behaviour of the average number of
hydrogen bonds between solvent molecules are evaluated.


  In the last decade, scheduling of Directed Acyclic Graph (DAG) application in
the context of Grid environment has attracted attention of many researchers.
However, deployment of Grid environment requires skills, efforts, budget, and
time. Although various simulation toolkits or frameworks are available for
simulating Grid environment, either they support different possible studies in
Grid computing area or takes lot of efforts in molding them to make them
suitable for scheduling of DAG application. In this paper, we describe design
and implementation of GridSim based ready to use application scheduler for
scheduling of DAG application in Grid environment. The proposed application
scheduler supports supplying DAG application and configuration of Grid
resources through GUI. We also describe implementation of Min-Min static
scheduling algorithm for scheduling of DAG application to validate the proposed
scheduler. Our proposed DAG application scheduling simulator is useful, easy,
and time-saver.


  Despite their catastrophic implications in flood events, the mobilization and
transport of large, loose objects - termed Urban Flood Drifters (UFDs) - are
often overlooked in flood management. This oversight stems from our limited
understanding of how flowing water interacts with these heterogeneous objects.
To bridge this knowledge gap, we introduce a mechanistic stability model that
predicts the onset of UFD mobilization across a diverse array of loose objects,
from plastics to heavy vehicles. Built on an inventory of key physical
properties of UFDs, this model is also validated against existing mobilization
studies. Our model generates stability curves that delineate flow conditions
leading to their mobilization. We further enhance the reliability of our model
by incorporating a Monte Carlo-based probabilistic framework that accounts for
uncertainties and interdependencies among the input parameters. These
probabilistic stability curves enable us to estimate the likelihood of
mobilization for specific categories of UFDs under certain flow conditions.
When integrated with flood maps or two-dimensional (2D) hydrodynamic models,
our stability curves can guide urban planning efforts to predict and mitigate
the impacts of UFDs during extreme flood events.


  An overview about recent progress in the calculation of the heat kernel and
the one-loop effective action in quantum gravity and gauge theories is given.
We analyse the general structure of the standard Schwinger-De Witt asymptotic
expansion and discuss the applicability of that to the case of strongly curved
manifolds and strong background fields. We argue that the low-energy limit in
gauge theories and quantum gravity, when formulated in a covariant way, should
be related to background fields with covariantly constant curvature, gauge
field strength and potential term. It is shown that the condition of the
covariant constancy of the background curvatures brings into existence some Lie
algebra. The heat kernel operator for the Laplace operator is presented then as
an average over the corresponding Lie group with some nontrivial Gaussian
measure. Using this representation the heat kernel diagonal is obtained. The
result is expressed purely in terms of curvature invariants and is explicitly
covariant. Related topics concerning the structure of symmetric spaces and the
calculation of the effective action are discussed.


  We present a comprehensive study of the light-cone generalized parton
distribution (GPD) and quasi-GPD of a flavor-neutral meson in the 't Hooft
model, {\it i.e.}, two-dimensional QCD (\QCDtw) in the $N_c\to\infty$ limit.
With the aid of the Hamiltonian approach, we construct the light-cone GPD in
terms of the meson's light-cone wave function in the framework of light-front
quantization, and express the quasi-GPD in terms of the meson's Bars-Green wave
functions and the chiral angle in the framework of equal-time quantization. We
show that, both analytically and numerically, the quasi-GPD does approach the
light-cone GPD when the meson is boosted to the infinite momentum frame, which
justifies the tenet underlying the large momentum effective theory for the
off-forward parton distribution. Upon taking the forward limit, the light-cone
and quasi-GPDs reduce to the light-cone and quasi-PDFs. As a bonus, we take
this chance to correct the incomplete expression of the quasi-PDFs in the 't
Hooft model reported in our preceding work [Y. Jia et al. Phys. Rev. D 98,
054011 (2018)].


  We present magnetic torque, specific heat and thermal expansion measurements
combined with a piezo rotary positioner of the bulk transition metal
dichalcogenide (TMD) superconductor NbS2 in high magnetic fields applied
strictly parallel to its layer structure. The upper critical field of
superconducting TMDs in the 2D form is known to be dramatically enhanced by a
special form of Ising spin orbit coupling. This Ising superconductivity is very
robust against the Pauli limit for superconductivity. We find that
superconductivity beyond the Pauli limit still exists in bulk single crystals
of NbS2. However, the comparison of our upper critical field transition line
with numerical simulations rather points to the development of a
Fulde-Ferrell-Larkin-Ovchinnikov state above the Pauli limit as a cause. This
is also consistent with the observation of a magnetic field driven phase
transition in the thermodynamic quantities within the superconducting state
near the Pauli limit.


  Let $f:X\to C$ be a family of semistable K3 surfaces with non-empty set $S$
of singular fibres having infinite local monodromy. Then, when the so called
Arakelov-Yau inequality reaches equality, we prove that $C\setminus S$ is a
modular curve and the family comes essentially from a family of elliptic curves
through a so called Nikulin-Kummer construction. In particular, when $C=\BBb
P^1$, the family of elliptic curves must be one of Beauville's 6 examples where
Arakelov inequality reaches equality.


  We exhibit a class of effective field theories that have hierarchically small
Wilson coefficients for operators that are not protected by symmetries but are
not finely tuned. These theories possess bounded target spaces and vacua that
break space-time symmetries. We give a physical interpretation of these
theories as generalized solids with open boundary conditions. We show that
these theories realize unusual RG flows where higher dimensional (seemingly
irrelevant) operators become relevant even at weak coupling. Finally, we
present an example of a field theory whose vacuum energy relaxes to a
hierarchically small value compared to the UV cut-off.


  This paper is concerned with the inverse time-harmonic elastic scattering
problem of recovering unbounded rough surfaces in two dimensions. We assume
that elastic plane waves with different directions are incident onto a rigid
rough surface in a half plane. The elastic scattered field is measured on a
horizontal straight line segment within a finite distance above the rough
surface. A direct imaging algorithm is proposed to recover the unbounded rough
surface from the scattered near-field data, which involves only inner products
between the data. Numerical experiments are presented to show that the
inversion scheme is not only efficient but also accurate and robust with
respect to noise.


  The class of Ruddlesden-Popper type (PEA)$_2$PbI$_4$ perovskites comprises
two-dimensional (2D) structures whose optical properties are determined by
excitons with a large binding energy of about 260 meV. It complements the
family of other 2D semiconductor materials by having the band structure typical
for lead halide perovskites, that can be considered as inverted compared to
conventional III-V and II-VI semiconductors. Accordingly, novel spin phenomena
can be expected for them. Spin-flip Raman scattering is used here to measure
the Zeeman splitting of electrons and holes in a magnetic field up to 10 T.
From the recorded data, the electron and hole Land\'e factors ($g$-factors) are
evaluated, their signs are determined, and their anisotropies are measured. The
electron $g$-factor value changes from $+2.11$ out-of-plane to $+2.50$
in-plane, while the hole $g$-factor ranges between $-0.13$ and $-0.51$. The
spin flips of the resident carriers are arranged via their interaction with
photogenerated excitons. Also the double spin-flip process, where a resident
electron and a resident hole interact with the same exciton, is observed
showing a cumulative Raman shift. Dynamic nuclear spin polarization induced by
spin-polarized holes is detected in corresponding changes of the hole Zeeman
splitting. An Overhauser field of the polarized nuclei acting on the holes as
large as $0.6$ T can be achieved.


  We discuss efforts to determine the mass, radius, and surface composition of
the nearby compact object RX J185635-3754 from its multi-wavelength spectral
energy distribution. We compute non-magnetized model atmospheres and emergent
spectra for selected compositions and gravities, and discuss efforts to fit
existing and new observational data from ROSAT, EUVE and the HST. The spectral
energy distribution matches that expected from a heavy-element dominated
atmosphere, but not from a uniform temperature blackbody. Non-magnetic light
element atmospheres cannot be simultaneously reconciled with the optical and
X-ray data. We extend previous studies, which were limited to one fixed neutron
star mass and radius. For uniform temperature models dominated by heavy
elements, the redshift z is constrained to be 0.3 < z < 0.4 and the best-fit
mass and radius are M approx 0.9 solar masses and R approx 6 km (for a 61 pc
distance). These values for M and R together are not permitted for any
plausible equation of state, including that of a self-bound strange quark star.
A simplified two-temperature model allows masses and radii up to about 50%
larger, or a factor of 2 in the case of a black body. The observed luminosity
is consistent with the thermal emission of an isolated neutron star no older
than about 1 million years, the age inferred from available proper motion and
parallax information


  Determining the lack of association between an outcome variable and a number
of different explanatory variables is frequently necessary in order to
disregard a proposed model. This paper proposes a non-inferiority test for the
coefficient of determination (or squared multiple correlation coefficient),
R-squared, in a linear regression analysis with random predictors. The test is
derived from inverting a one-sided confidence interval based on a scaled
central F distribution.


  We propose a new strategy to physically implement a universal set of quantum
gates based on geometric phases accumulated in the nondegenerate eigenstates of
a designated invariant operator in a periodic physical system. The system is
driven to evolve in such a way that the dynamical phase shifts of the invariant
operator eigenstates are the same (or {\it mod} $2\pi$) while the corresponding
geometric phases are nontrivial.
  We illustrate how this strategy to work in a simple but typical NMR-type
qubit system.


  To any pair of commuting n x n nilpotent matrices it is associated a pair of
partitions of n. We describe a maximal nilpotent subalgebra of the centralizer
of a given nilpotent n x n matrix and prove a conjecture of Polona Oblak which
consists in an algorithm for the determination of the maximum partition which
forms with a given partition a pair with the previous property.


  We present a measurement of the W boson mass using 200/pb of data collected
in pbar p collisions at sqrt(s) = 1.96 TeV by the CDF II detector at Run II of
the Fermilab Tevatron. With a sample of 63964 W -> e nu candidates and 51128 W
-> mu nu candidates, we measure M_W = (80413 +- 34 (stat) +- 34 (syst) = 80413
+- 48) MeV/c^2. This is the most precise single measurement of the W boson mass
to date.


  We analyse solutions of the MHD equations around the electroweak transition
taking into account the effects of the chiral anomaly. It is shown that a
transition that is not of the first order has direct consequences on the
evolution of the asymmetry between left- and right-handed leptons. Assuming an
initial chiral asymmetry in the symmetric phase at temperatures higher than the
transition temperature, as well as the existence of magnetic fields, it is
demonstrated that the asymmetry typically grows with time, until it undergoes a
fast decrease at the transition, and then eventually gets damped at lower
temperatures in the broken phase. We argue that it is unlikely to have any
significant magnetic field amplification as a consequence of the electroweak
transition in the Standard model, even when the chiral anomaly is introduced.
The presence of a chiral asymmetry between left- and right-handed charge
carriers naturally leads to the creation of helical magnetic fields from
non-helical fields and this can have consequences on their subsequent
evolution.


  In this paper Estimation of Signal Parameters via Rotational Invariance
Techniques (ESPRIT) is developed for spectral estimation with single-snapshot
measurement. Stability and resolution analysis with performance guarantee for
Single-Snapshot ESPRIT (SS-ESPRIT) is the main focus. In the noise-free case,
exact reconstruction is guaranteed for any arbitrary set of frequencies as long
as the number of measurement data is at least twice the number of distinct
frequencies to be recovered. In the presence of noise and under the assumption
that the true frequencies are separated by at least two times Rayleigh's
Resolution Length, an explicit error bound for frequency reconstruction is
given in terms of the dynamic range and the separation of the frequencies. The
separation and sparsity constraint compares favorably with those of the leading
approaches to compressed sensing in the continuum.


  The ability to envisage the visual of a talking face based just on hearing a
voice is a unique human capability. There have been a number of works that have
solved for this ability recently. We differ from these approaches by enabling a
variety of talking face generations based on single audio input. Indeed, just
having the ability to generate a single talking face would make a system almost
robotic in nature. In contrast, our unsupervised stochastic audio-to-video
generation model allows for diverse generations from a single audio input.
Particularly, we present an unsupervised stochastic audio-to-video generation
model that can capture multiple modes of the video distribution. We ensure that
all the diverse generations are plausible. We do so through a principled
multi-modal variational autoencoder framework. We demonstrate its efficacy on
the challenging LRW and GRID datasets and demonstrate performance better than
the baseline, while having the ability to generate multiple diverse lip
synchronized videos.


  The creation and justification of the methods for minimax estimation of
parameters of the external boundary value problems for the Helmholtz equation
in unbounded domains are considered. When observations are distributed in
subdomains, the determination of minimax estimates is reduced to the solution
of integro-differential equations in bounded domains. When observations are
distributed on a system of surfaces the problem is reduced to solving integral
equations on an unclosed bounded surface which is a union of the boundary of
the domain and this system of surfaces. Minimax estimation of the solutions to
the boundary value problems from point observations is also studied.


  \textit{Multiple Instance Learning} (MIL) is concerned with learning from
bags of instances, where only bag labels are given and instance labels are
unknown. Existent approaches in this field were mainly designed for the
bag-level label prediction (predict labels for bags) but not the instance-level
(predict labels for instances), with the task loss being only defined at the
bag level. This restricts their application in many tasks, where the
instance-level labels are more interested. In this paper, we propose a novel
algorithm, whose loss is specifically defined at the instance level, to address
instance-level label prediction in MIL. We prove that the loss of this
algorithm can be unbiasedly and consistently estimated without using instance
labels, under the i.i.d assumption. Empirical study validates the above
statements and shows that the proposed algorithm can achieve superior
instance-level and comparative bag-level performance, compared to
state-of-the-art MIL methods. In addition, it shows that the proposed method
can achieve similar results as the fully supervised model (trained with
instance labels) for label prediction at the instance level.


  Perinatal Asphyxia is one of the top three causes of infant mortality in
developing countries, resulting to the death of about 1.2 million newborns
every year. At its early stages, the presence of asphyxia cannot be
conclusively determined visually or via physical examination, but by medical
diagnosis. In resource-poor settings, where skilled attendance at birth is a
luxury, most cases only get detected when the damaging consequences begin to
manifest or worse still, after death of the affected infant. In this project,
we explored the approach of machine learning in developing a low-cost
diagnostic solution. We designed a support vector machine-based pattern
recognition system that models patterns in the cries of known asphyxiating
infants (and normal infants) and then uses the developed model for
classification of `new' infants as having asphyxia or not. Our prototype has
been tested in a laboratory setting to give prediction accuracy of up to
88.85%. If higher accuracies can be obtained, this research may be a key
contributor to the 4th Millennium Development Goal (MDG) of reducing mortality
in under-five children.


  We discuss the existence of a common colour-magnitude relation (CMR) of
metal-poor globular clusters and early-type galaxies, i.e. giant ellipticals,
normal ellipticals and lenticulars, dwarf ellipticals and lenticulars, and
dwarf spheroidals. Such CMR would cover a range of ~ 14 mag, extending from the
brightest galaxies, down to the globular clusters on the fainter side.


  The neutrino-heated "gain layer" immediately behind the stalled shock in a
core-collapse supernova is unstable to high-Reynolds-number turbulent
convection. We carry out and analyze a new set of 19 high-resolution
three-dimensional (3D) simulations with a three-species neutrino
leakage/heating scheme and compare with spherically-symmetric (1D) and
axisymmetric (2D) simulations carried out with the same methods. We study the
postbounce supernova evolution in a $15$-$M_\odot$ progenitor star and vary the
local neutrino heating rate, the magnitude and spatial dependence of
asphericity from convective burning in the Si/O shell, and spatial resolution.
Our simulations suggest that there is a direct correlation between the strength
of turbulence in the gain layer and the susceptability to explosion. 2D and 3D
simulations explode at much lower neutrino heating rates than 1D simulations.
This is commonly explained by the fact that nonradial dynamics allows accreting
material to stay longer in the gain layer. We show that this explanation is
incomplete. Our results indicate that the effective turbulent ram pressure
exerted on the shock plays a crucial role by allowing multi-D models to explode
at a lower postshock thermal pressure and thus with less neutrino heating than
1D models. We connect the turbulent ram pressure with turbulent energy at large
scales and in this way explain why 2D simulations are erroneously exploding
more easily than 3D simulations.


  We define the counting of holomorphic cylinders in log Calabi-Yau surfaces.
Although we start with a complex log Calabi-Yau surface, the counting is
achieved by applying methods from non-archimedean geometry. This gives rise to
new geometric invariants. Moreover, we prove that the counting satisfies a
property of symmetry. Explicit calculations are given for a del Pezzo surface
in detail, which verify the conjectured wall-crossing formula for the
focus-focus singularity. Our holomorphic cylinders are expected to give a
geometric understanding of the combinatorial notion of broken line by Gross,
Hacking, Keel and Siebert. Our tools include Berkovich spaces, tropical
geometry, Gromov-Witten theory and the GAGA theorem for non-archimedean
analytic stacks.


  A method is given for creating material with a desired refraction
coefficient. The method consists of embedding into a material with known
refraction coefficient many small particles of size $a$. The number of
particles per unit volume around any point is prescribed, the distance between
neighboring particles is $O(a^{\frac{2-\kappa}{3}})$ as $a\to 0$, $0<\kappa<1$
is a fixed parameter. The total number of the embedded particle is
$O(a^{\kappa-2})$. The physical properties of the particles are described by
the boundary impedance $\zeta_m$ of the $m-th$ particle,
$\zeta_m=O(a^{-\kappa})$ as $a\to 0$. The refraction coefficient is the
coefficient $n^2(x)$ in the wave equation $[\nabla^2+k^2n^2(x)]u=0$.


  The purpose of this paper is twofold. The first aim is based on the
Riesz--Thorin interpolation theorem. We establish several of the
Hausdorff--Young type theorems for the Quadratic Fourier transforms in (Ann.
Funct. Anal. 2014;5(1):10--23) and linear canonical transforms in (Mediterr. J.
Math. 2018;15,13), which were introduced by Castro et al. The second aim is to
investigate the boundedness of the oscillatory integral operator with
polynomial phases, which is also presented in the last section of the article.


  Recent numerical simulations of a disordered system (Preprint
arXiv:condmat/0307554) have shown the existence of two different relaxational
processes (called stimulated and spontaneous) characterizing the relaxation
observed in structural glasses. The existence of these two processes has been
claimed to be at the roots of the intermittency phenomenon observed in recent
experiments. Here we consider a generic system put in contact with a bath at
temperature T and characterized by an adiabatic slow relaxation (i.e. by a
negligible net heat flow from the system to the bath) in the aging state. We
focus on a simplified scenario (termed as partial equilibration) characterized
by the fact that $=0 (where only the spontaneous process is observable) and
whose microscopic stochastic dynamics is ergodic when constrained to the
constant energy surface. Three different effective temperatures can be defined:
a) from the fluctuation-dissipation theorem (FDT), b) from a fluctuation
theorem describing the statistical distribution of heat exchange events between
system and bath and c) from a set of observable-dependent microcanonical
relations in the aging state. In a partial equilibration scenario we show how
all three temperatures coincide reinforcing the idea that a statistical (rather
than thermometric) definition of a non-equilibrium temperature is physically
meaningful in aging systems. These results are explicitly checked in a simple
model system


  This PhD thesis deals with the Markov picture of developed turbulence from
the theoretical point of view. The thesis consists of two parts. The first part
introduces stochastic thermodynamics, the second part aims at transferring the
concepts of stochastic thermodynamics to developed turbulence. / Central in
stochastic thermodynamics are Markov processes. An elementary example is
Brownian motion. In contrast to macroscopic thermodynamics, the work done and
the entropy produced for single trajectories of the Brownian particles are
random quantities. Statistical properties of such fluctuating quantities are
central in the field of stochastic thermodynamics. Prominent results are
so-called fluctuation theorems which express the balance between production and
consumption of entropy and generalise the second law. / Turbulent cascades of
eddies are assumed to be the predominant mechanism of turbulence generation and
fix the statistical properties of developed turbulent flows. An intriguing
phenomenon of developed turbulence, known as small-scale intermittency, are
violent small-scale fluctuations in flow velocity that exceed any Gaussian
prediction. / In analogy to Brownian motion, it is demonstrated in the thesis
how the assumption of the Markov property leads to a Markov process for the
turbulent cascade that is equivalent to the seminal K62 model. In addition to
the K62 model, it is demonstrated how many other models of turbulence can be
written as a Markov process, including scaling laws, multiplicative cascades,
multifractal models and field-theoretic approaches. Based on the various Markov
processes, the production of entropy along the cascade and the corresponding
fluctuation theorems is discussed. In particular, experimental data indicates
that entropy consumption is linked to small-scale intermittency, and a
connection between entropy consumption and an inverse cascade is suggestive.


  The $C_{2v}$ symmetry of the W(110) surface influences strongly the
spin-polarized Dirac-cone-like surface state within a spin-orbit-induced
symmetry gap. We present a detailed angle-resolved photoemission study with
$s$- and $p$-polarized light along three different symmetry lines. The
Dirac-cone-like feature appears along $\bar{\Gamma}\bar{H}$ and
$\bar{\Gamma}\bar{S}$, while it is strongly deformed along
$\bar{\Gamma}\bar{N}$. A two-fold $\Sigma_{3}$ symmetry of the $d$-type surface
state is identified from photoemission experiments using linear polarized
light. Our results are well described by model calculations based on an
effective Hamiltonian with $C_{2v}$ symmetry including Rashba parameters up to
third order. The flattened Dirac cone of the surface state is caused by
hybridization with bulk continuum states of $\Sigma_{1}$ and $\Sigma_{2}$
symmetry. The spin texture of this state obtained from the model calculations
shows a quasi-one dimensional behavior. This finding opens a new avenue in the
study of $d$-electron-based persistent spin helix systems and/or weak
topological insulators.


  Employee theft and dishonesty is a major contributor to loss in the retail
industry. Retailers have reported the need for more automated analytic tools to
assess the liability of their employees. In this work, we train and optimize
several machine learning models for regression prediction and analysis on this
data, which will help retailers identify and manage risky employees. Since the
data we use is very high dimensional, we use feature selection techniques to
identify the most contributing factors to an employee's assessed risk. We also
use dimension reduction and data embedding techniques to present this dataset
in a easy to interpret format.


  A brief review is given of different methods used to determine the pattern
speeds of the Galactic bar and spiral arms. The Galactic bar rotates rapidly,
with corotation about halfway between the Galactic center and the Sun, and
outer Lindblad resonance not far from the solar orbit, R0. The Galactic spiral
arms currently rotate with a distinctly slower pattern speed, such that
corotation is just outside R0. Both structures therefore seem dynamically
decoupled.


  The spectrum of radially excited hadrons provides much information about the
confinement forces in QCD. The confinement is realized most naturally in terms
of the QCD string whose quantization gives rise to the radially excited modes.
We propose an alternative framework for the description of the excited
spectrum. Namely we put forward some effective field models in which the
hadrons acquire masses due to interaction with a scalar field modeling the
non-perturbative gluon vacuum. The effective potential for this field is
periodic with an infinite number of non-equivalent vacua. The radially excited
hadrons emerge as elementary excitations over different vacua. We construct
explicit examples for such effective theories in the meson sector. An
interesting byproduct of the considered models is the existence of a classical
field configuration in each vacuum. Depending on the model, it can represent a
domain wall, Nielsen-Olesen vortex or 't Hooft-Polyakov monopole. In the pure
scalar sector, it is shown that the first quantum correction leads to splitting
of the radially excited modes into two nearly degenerate states. Such a
phenomenon has some phenomenological support. The presented approach may be
also viewed as an alternative framework to the bottom-up AdS/QCD models where
the radial excitations appear on the classical level as well.


  The aim of this paper is to obtain new fine properties of entropy solutions
of nonlinear scalar conservation laws. For this purpose, we study some
"fractional $BV$ spaces" denoted $BV^s$, for $0 < s \leq 1$, introduced by Love
and Young in 1937. The $BV^s(\R)$ spaces are very closed to the critical
Sobolev space $W^{s,1/s}(\R)$. We investigate these spaces in relation with
one-dimensional scalar conservation laws. $BV^s$ spaces allow to work with less
regular functions than BV functions and appear to be more natural in this
context. We obtain a stability result for entropy solutions with $BV^s$ initial
data. Furthermore, for the first time we get the maximal $W^{s,p}$ smoothing
effect conjectured by P.-L. Lions, B. Perthame and E. Tadmor for all nonlinear
degenerate convex fluxes.


  A numerical set is a co-finite subset of the natural numbers that contains
zero. Its Frobenius number is the largest number in its complement. Each
numerical set has an associated semigroup $A(T)=\{t\mid t+T\subseteq T\}$,
which has the same Frobenius number as $T$. For a fixed Frobenius number $f$
there are $2^{f-1}$ numerical sets. It is known that there is a number $\gamma$
close to $0.484$ such that the ratio of these numerical sets that are mapped to
$N_f=\{0\}\cup(f,\infty)$ is asymptotically $\gamma$. We identify a collection
of families $N(D,f)$ of numerical semigroups such that for a fixed $D$ the
ratio of the $2^{f-1}$ numerical sets that are mapped to $N(D,f)$ converges to
a positive limit as $f$ goes to infinity. We denote the limit as $\gamma_D$,
these constants sum up to $1$ meaning that they asymptotically account for
almost all numerical sets.


  This article deals with universal deformations of dihedral representations
with a particular focus on the question when the universal deformation is
dihedral. Results are obtained in three settings: (1) representation theory,
(2) algebraic number theory, (3) modularity. As to (1), we prove that the
universal deformation is dihedral if all infinitesimal deformations are
dihedral. Concerning (2) in the setting of Galois representations of number
fields, we give sufficient conditions to ensure that the universal deformation
relatively unramified outside a finite set of primes is dihedral, and discuss
in how far these conditions are necessary. As side-results, we obtain cases of
the unramified Fontaine-Mazur conjecture, and in many cases positively answer a
question of Greenberg and Coleman on the splitting behaviour at p of p-adic
Galois representations attached to newforms. As to (3), we prove a modularity
theorem of the form `R=T' for parallel weight one Hilbert modular forms for
cases when the minimal universal deformation is dihedral.


  Layered franckeite is a natural superlattice composed of two alternating
layers of different compositions, SnS$_2$- and PbS-like. This creates
incommensurability between the two species along the planes of the layers,
resulting in spontaneous symmetry-break periodic ripples in the \textit{a}-axis
orientation. Nevertheless, natural franckeite heterostructure has shown
potential for optoelectronic applications mostly because it is a semiconductor
with 0.7 eV bandgap, air-stable, and can be easily exfoliated down to ultrathin
thicknesses. Here, we demonstrate that few-layer franckeite shows a highly
anisotropic nonlinear optical response due to its lattice structure, which
allow for the identification of the ripple axis. Moreover, we find that the
highly anisotropic third-harmonic emission strongly varies with material
thickness. These features are further corroborated by a theoretical nonlinear
susceptibility model and the nonlinear transfer matrix method. Overall, our
findings help to understand this material and propose a characterization method
that could be used in other layered materials and heterostructures to assign
their characteristic axes.


  Machine translation (MT) is an important task in natural language processing
(NLP) as it automates the translation process and reduces the reliance on human
translators. With the resurgence of neural networks, the translation quality
surpasses that of the translations obtained using statistical techniques for
most language-pairs. Up until a few years ago, almost all of the neural
translation models translated sentences independently, without incorporating
the wider document-context and inter-dependencies among the sentences. The aim
of this survey paper is to highlight the major works that have been undertaken
in the space of document-level machine translation after the neural revolution,
so that researchers can recognise the current state and future directions of
this field. We provide an organisation of the literature based on novelties in
modelling and architectures as well as training and decoding strategies. In
addition, we cover evaluation strategies that have been introduced to account
for the improvements in document MT, including automatic metrics and
discourse-targeted test sets. We conclude by presenting possible avenues for
future exploration in this research field.


  This is a presentation of explicit methods to construct higher local class
field theory by using topological K-groups, explicit symbols and a
generalization of Neukirch-Hazewinkel's axiomatic approaches. The existence
theorem is discussed as well.


  In this paper we study synchronization of random clustered networks
consisting of Kuramoto oscillators. More specifically, by developing a
mean-field analysis, we find that the presence of cycles of order three does
not play an important role on network synchronization, showing that the
synchronization of random clustered networks can be described by tree-based
theories, even for high values of clustering. In order to support our findings,
we provide numerical simulations considering clustered and non-clustered
networks, which are in good agreement with our theoretical results.


  We give a derivation for the value of inf-sup constant for the bilinear form
(p, div u). We prove that the value of inf-sup constant is equal to 1.0 in all
cases and is independent of the size and shape of the domain. Numerical tests
for validation of inf-sup constants is performed using finite dimensional
spaces defined in \cite{2020jain} on two test domains i) a square of size
$\Omega = [0,1]^2$, ii) a square of size $\Omega = [0,2]^2$, for varying mesh
sizes and polynomial degrees. The numeric values are in agreement with the
theoretical value of inf-sup term.


  The investigation about the volume of a black hole is closely related to the
quantum nature of the black hole. The entropy is a significant concept for
this. A recent work by Majhi and Samanta [Phys. Lett. B 770 (2017) 314] after
us presented a similar conclusion that the entropy associated with the volume
is proportional to the surface area of the black hole, but the proportionality
coefficient is different from our earlier result. In this paper, we clarify the
difference and show that their calculation is unrelated to the interior of the
black hole.


  Understanding the physical origin of deformation mechanisms in random alloys
requires an understanding of their average behavior and, equally important, the
role of local fluctuations around the average. Material properties of random
alloys can be computed using direct simulations on random configurations but
some properties are very difficult to compute, for others it is not even fully
understood how to compute them using random sampling, in particular,
interaction energies between multiple defects. To that end, we develop an
atomistic model that does the averaging on the level of interatomic potentials.
Then, the problem of averaging via random sampling is bypassed since computing
material properties on random configurations reduces to computing material
properties on a single crystal, the average alloy.
  We develop our average model on the class of linear machine-learning
interatomic potentials. To that end, using tools from higher-order statistics,
we derive an analytic expansion of the average many-body per-atom energy in
terms of average tensor products of the feature vectors that scales linearly
with the size of an atomic neighborhood. In order to avoid forming higher-order
tensors composed of products of feature vectors, we develop an implementation
using equivariant tensor network potentials in which the feature vectors are
contracted to small-sized tensors before taking the average. We show that our
average model predicts the compact screw dislocation core structure in the
NbMoTaW medium-entropy alloy, in agreement with density functional theory, as
opposed to state-of-the-art average embedded atom method potentials that
predict artificial polarized cores. Hence, we anticipate that our model will
become useful for understanding mechanistic origins of material properties and
for developing predictive models of mechanical properties of random alloys.


  We consider systems of word equations and their solution sets. We discuss
some fascinating properties of those, namely the size of a maximal independent
set of word equations, and proper chains of solution sets of those. We recall
the basic results, extend some known results and formulate several fundamental
problems of the topic.


  In order to address the selection mechanism that is responsible for the
unique lamellar orientation observed in block copolymers under oscillatory
shears, we use a constitutive law for the dissipative part of the stress tensor
that respects the uniaxial symmetry of a lamellar phase. An interface
separating two domains oriented parallel and perpendicular to the shear is
shown to be hydrodynamically unstable, a situation analogous to the thin layer
instability of stratified fluids under shear. The resulting secondary flows
break the degeneracy between parallel and perpendicular lamellar orientation,
leading to a preferred perpendicular orientation in certain ranges of
parameters of the polymer and of the shear.


  In order to understand how the soft X-ray spectra vary we present the
Hardness Ratio 1 versus Count Rates (HR1-CTs) correlation of 8 Narrow-line
Seyfert 1 Galaxies (NLS1s) and 14 Broad-line Seyfert1 Galaxies (BLS1s) obtained
during the ROSAT PSPC pointing observations. According to our criteria, six of
the NLS1s show a positive HR1-CTs correlation, and seven of the BLS1s display
an anti-correlation of HR1 versus CTs. The other 2 NLS1s and 7 BLS1s do not
show a clear HR1-CTs correlation. From these we can see that the NLS1s
statistically show a different spectral shape variability with flux change from
the BLS1s: the spectra of NLS1s become harder as total flux increases while
those of BLS1s soften. We attribute the different spectral variations to a
strong stable 'soft excess' in NLS1s, while it is weak in BLS1s. For two types
of objects, the power law component similarly becomes softer with increasing
intensity. These imply that the soft excess originates from the Big Blue Bump
and power law emission is from Compton upscattering of UV or Soft X-ray
photons. Our results are consistent with what is widely accepted that NLS1s
have smaller black hole masses and higher accretion rates than BLS1s.


  We discuss several results in electrostatics: Onsager's inequality, an
extension of Earnshaw's theorem, and a result stemming from the celebrated
conjecture of Maxwell on the number of points of electrostatic equilibrium.
Whenever possible, we try to provide a brief historical context and references.


  Parafermions are the simplest generalizations of Majorana fermions that
realize topological order. We propose a less restrictive notion of topological
order in 1D open chains, which generalizes the seminal work by Fendley [J.
Stat. Mech., P11020 (2012)]. The first essential property is that the
groundstates are mutually indistinguishable by local, symmetric probes, and the
second is a generalized notion of zero edge modes which cyclically permute the
groundstates. These two properties are shown to be topologically robust, and
applicable to a wider family of topologically-ordered Hamiltonians than has
been previously considered. An an application of these edge modes, we formulate
a new notion of twisted boundary conditions on a closed chain, which guarantees
that the closed-chain groundstate is topological, i.e., it originates from the
topological manifold of degenerate states on the open chain. Finally, we
generalize these ideas to describe symmetry-breaking phases with a
parafermionic order parameter. These exotic phases are condensates of
parafermion multiplets, which generalizes Cooper pairing in superconductors.
The stability of these condensates are investigated on both open and closed
chains.


  We present the full public release of all data from the TNG50, TNG100 and
TNG300 simulations of the IllustrisTNG project. IllustrisTNG is a suite of
large volume, cosmological, gravo-magnetohydrodynamical simulations run with
the moving-mesh code Arepo. TNG includes a comprehensive model for galaxy
formation physics, and each TNG simulation self-consistently solves for the
coupled evolution of dark matter, cosmic gas, luminous stars, and supermassive
blackholes from early time to the present day, z=0. Each of the flagship runs
-- TNG50, TNG100, and TNG300 -- are accompanied by lower-resolution and
dark-matter only counterparts, and we discuss scientific and numerical cautions
and caveats relevant when using TNG. Full volume snapshots are available at 100
redshifts; halo and subhalo catalogs at each snapshot and merger trees are also
released. The data volume now directly accessible online is ~1.1 PB, including
2,000 full volume snapshots and ~110,000 high time-resolution subbox snapshots.
Data access and analysis examples are available in IDL, Python, and Matlab. We
describe improvements and new functionality in the web-based API, including
on-demand visualization and analysis of galaxies and halos, exploratory
plotting of scaling relations and other relationships between galactic and halo
properties, and a new JupyterLab interface. This provides an online,
browser-based, near-native data analysis platform which supports user
computation with fully local access to TNG data, alleviating the need to
download large simulated datasets.


  A practical electronic structure method in which a two-body functional is the
fundamental variable is constructed. The basic formalism of our method is
equivalent to Hartree-Fock density matrix functional theory [M. Levy in {\it
Density Matrices and Density Functionals}, Ed. R. Erdahl and V. H. Smith Jr.,
D. Reidel, (1987)]. The implementation of the method consists of solving
Hartree-Fock equations and using the resulting orbitals to calculate two-body
corrections to account for correlation. The correction terms are constructed so
that the energy of the system in the absence of external potentials can be made
to correspond to approximate expressions for the energy of the homogeneous
electron gas. In this work the approximate expressions we use are based on the
high-density limit of the homogeneous electron gas. Self-interaction is
excluded from the two-body functional itself. It is shown that our pair density
based functional does not suffer from the divergence present in many density
functionals when homogeneous scaling is applied. Calculations based on our pair
density functional lead to quantitative results for the correlation energies of
atomic test cases.


  Recent paper "TVOR: Finding Discrete Total Variation Outliers Among
Histograms" [arXiv:2012.11574] introduces the Total Variation Outlier
Recognizer (TVOR) method for identification of outliers among a given set of
histograms. After providing a theoretical discussion of the method and
verifying its success on synthetic and population census data, it applies the
TVOR model to histograms of ages of Holocaust victims produced using United
States Holocaust Memorial Museum data. It purports to identify the list of
victims of the Jasenovac concentration camp as potentially suspicious. In this
comment paper, we show that the TVOR model and its assumptions are grossly
inapplicable to the considered dataset. When applied to the considered data,
the model is biased in assigning a higher outlier score to histograms of larger
sizes, the set of data points is extremely sparse around the point of interest,
the dataset has not been reviewed to remove obvious data processing errors,
and, contrary to the model requirements, the distributions of the victims' ages
naturally vary significantly across victim lists.


  The emergence of large language models (LLMs) has revolutionized the way we
interact with graphs, leading to a new paradigm called GraphLLM. Despite the
rapid development of GraphLLM methods in recent years, the progress and
understanding of this field remain unclear due to the lack of a benchmark with
consistent experimental protocols. To bridge this gap, we introduce GLBench,
the first comprehensive benchmark for evaluating GraphLLM methods in both
supervised and zero-shot scenarios. GLBench provides a fair and thorough
evaluation of different categories of GraphLLM methods, along with traditional
baselines such as graph neural networks. Through extensive experiments on a
collection of real-world datasets with consistent data processing and splitting
strategies, we have uncovered several key findings. Firstly, GraphLLM methods
outperform traditional baselines in supervised settings, with LLM-as-enhancers
showing the most robust performance. However, using LLMs as predictors is less
effective and often leads to uncontrollable output issues. We also notice that
no clear scaling laws exist for current GraphLLM methods. In addition, both
structures and semantics are crucial for effective zero-shot transfer, and our
proposed simple baseline can even outperform several models tailored for
zero-shot scenarios. The data and code of the benchmark can be found at
https://github.com/NineAbyss/GLBench.


  We investigate particular cosmological models, based either on tachyon fields
or on perfect fluids, for which soft future singularities arise in a natural
way. Our main result is the description of a smooth crossing of the soft
singularity in models with an anti-Chaplygin gas or with a particular tachyon
field in the presence of dust. Such a crossing is made possible by certain
transformations of matter properties. Some of these cosmological evolutions
involving tachyons are compatible with SNIa data. We compute numerically their
dynamics involving a first soft singularity crossing, a turning point and a
second soft singulatity crossing during recollapse, ending in a Big Crunch
singularity.


  We theoretically explore atomic Bose-Einstein condensates (BECs) subject to
position-dependent spin-orbit coupling (SOC). This SOC can be produced by
cyclically laser coupling four internal atomic ground (or metastable) states in
an environment where the detuning from resonance depends on position. The
resulting spin-orbit coupled BEC phase-separates into domains, each of which
contain density modulations - stripes - aligned either along the x or y
direction. In each domain, the stripe orientation is determined by the sign of
the local detuning. When these stripes have mismatched spatial periods along
domain boundaries, non-trivial topological spin textures form at the interface,
including skyrmions-like spin vortices and anti-vortices. In contrast to
vortices present in conventional rotating BECs, these spin-vortices are stable
topological defects that are not present in the corresponding homogenous
stripe-phase spin-orbit coupled BECs.


  We examine the Kaluza-Klein theory for warped flux compactifications of type
$II\ b $ string theory on a Minkowski spacetime $ M_4$ times a conic Calabi-Yau
orientifold $X_6$. The region glued along the internal space directions to the
bulk of $X_6$ is modeled by the warped undeformed conifold $\calc _6$. The
resulting classical vacum solution of Klebanov-Tseytlin solution, valid at
large radial distances from the conic singularity, describes a spacetime
asymptotic to $ AdS_5 $ times the conifold compact base $ T^{1,1}$. The metric
tensor, axio-dilaton and antisymmetric fields part of the 10-d supergravity
multiplet bosonic sector decompose into towers of scalar and tensor fields of
fixed mass associated to harmonic modes of $T^{1,1}$ and $M_4$. The warped
throat deformations by compactification effects are described by means of
AdS/CFT duality. The applications are developed within the hard wall
approximation for a truncated $ AdS_5 $ spacetime ending on flat boundaries.
Numerical results are presented for the mass spectra and interactions of a
selected set of singlet and charged modes and for the interactions of graviton
modes with embedded branes. We examine the possibility that an interacting gas
of warped massive modes produced after brane-antibrane inflation might reheat
the universe and leave cold dark matter relics.


  The article has two parts. The first part is devoted to proving a singular
version of the logarithmic Kodaira-Akizuki-Nakano vanishing theorem of Esnault
and Viehweg. This is then used to prove other vanishing theorems. In the second
part these vanishing theorems are used to prove an Arakelov-Parshin type
boundedness result for families of canonically polarized varieties with
rational Gorenstein singularities.


  The capacity of the Gaussian wiretap channel model is analyzed when there are
multiple antennas at the sender, intended receiver and eavesdropper. The
associated channel matrices are fixed and known to all the terminals. A
computable characterization of the secrecy capacity is established as the
saddle point solution to a minimax problem. The converse is based on a
Sato-type argument used in other broadcast settings, and the coding theorem is
based on Gaussian wiretap codebooks.
  At high signal-to-noise ratio (SNR), the secrecy capacity is shown to be
attained by simultaneously diagonalizing the channel matrices via the
generalized singular value decomposition, and independently coding across the
resulting parallel channels. The associated capacity is expressed in terms of
the corresponding generalized singular values. It is shown that a semi-blind
"masked" multi-input multi-output (MIMO) transmission strategy that sends
information along directions in which there is gain to the intended receiver,
and synthetic noise along directions in which there is not, can be arbitrarily
far from capacity in this regime.
  Necessary and sufficient conditions for the secrecy capacity to be zero are
provided, which simplify in the limit of many antennas when the entries of the
channel matrices are independent and identically distributed. The resulting
scaling laws establish that to prevent secure communication, the eavesdropper
needs 3 times as many antennas as the sender and intended receiver have
jointly, and that the optimimum division of antennas between sender and
intended receiver is in the ratio of 2:1.


  Magnetotransport measurements performed on several well-characterized highly
oriented pyrolitic graphite and single crystalline Kish graphite samples reveal
a reentrant metallic behavior in the basal-plane resistance at high magnetic
fields, when only the lowest Landau levels are occupied. The results suggest
that the quantum Hall effect and Landau-level-quantization-induced
superconducting correlations are relevant to understand the metallic-like
state(s) in graphite in the quantum limit.


  In this paper, we prove a stability result on k mod p multisets of points in
PG(2,q), q = p^h. The particular case k=0 is used to describe small weight
codewords of the code generated by the lines of PG(2, q), as linear combination
of few lines. Earlier results proved this for codewords with weight less than
2.5q, while our result is valid until cq sqrt(q). It is sharp when 27<q square
and h>=4. When q is a prime, De Boeck and Vandendriessche constructed a
codeword of weight 3p-3 that is not the linear combination of three lines. We
characterise their example.


  Recurrent neural networks and Transformers have recently dominated most
applications in hyperspectral (HS) imaging, owing to their capability to
capture long-range dependencies from spectrum sequences. However, despite the
success of these sequential architectures, the non-ignorable inefficiency
caused by either difficulty in parallelization or computationally prohibitive
attention still hinders their practicality, especially for large-scale
observation in remote sensing scenarios. To address this issue, we herein
propose SpectralMamba -- a novel state space model incorporated efficient deep
learning framework for HS image classification. SpectralMamba features the
simplified but adequate modeling of HS data dynamics at two levels. First, in
spatial-spectral space, a dynamical mask is learned by efficient convolutions
to simultaneously encode spatial regularity and spectral peculiarity, thus
attenuating the spectral variability and confusion in discriminative
representation learning. Second, the merged spectrum can then be efficiently
operated in the hidden state space with all parameters learned input-dependent,
yielding selectively focused responses without reliance on redundant attention
or imparallelizable recurrence. To explore the room for further computational
downsizing, a piece-wise scanning mechanism is employed in-between,
transferring approximately continuous spectrum into sequences with squeezed
length while maintaining short- and long-term contextual profiles among
hundreds of bands. Through extensive experiments on four benchmark HS datasets
acquired by satellite-, aircraft-, and UAV-borne imagers, SpectralMamba
surprisingly creates promising win-wins from both performance and efficiency
perspectives.


  An interesting distributed adaptive CSMA MAC protocol, called adaptive CSMA,
was proposed recently to schedule any strictly feasible achievable rates inside
the capacity region. Of particular interest is the fact that the adaptive CSMA
can achieve a system utility arbitrarily close to that is achievable under a
central scheduler. However, a specially designed transport-layer rate
controller is needed for this result. An outstanding question is whether the
widely-installed TCP Reno is compatible with adaptive CSMA and can achieve the
same result. The answer to this question will determine how close to practical
deployment adaptive CSMA is. Our answer is yes and no. First, we observe that
running TCP Reno directly over adaptive CSMA results in severe starvation
problems. Effectively, its performance is no better than that of TCP Reno over
legacy CSMA (IEEE 802.11), and the potentials of adaptive CSMA cannot be
realized. Fortunately, we find that multi-connection TCP Reno over adaptive
CSMA with active queue management can materialize the advantages of adaptive
CSMA. NS-2 simulations demonstrate that our solution can alleviate starvation
and achieve fair and efficient rate allocation. Multi-connection TCP can be
implemented at either application or transport layer. Application-layer
implementation requires no kernel modification, making the solution readily
deployable in networks running adaptive CSMA.


  Classical, self-consistent theory of statistical mechanics was developed for
the thermodynamic and conservative Hamiltonian systems. Later there were many
attempts (Sinai-Bowen-Ruelle's temperature, Tsallis' non-extensive theory) to
apply similar formalism to non-Hamiltonian dynamical systems. Although these
theories reveal aspects of complex behavior, they have limited applicability.
This paper applies the classical Gibbs-Boltzmann statistical mechanics to
complex systems such as i.i.d. processes, multifractals, and non-Hamiltonian
dynamical systems with strange attractors. The effective thermolization of
stochastic noise in the system is introduced and the formalism of a ruling
(governing, free energy) potential is developed.


  We investigate the ground state behavior of the Dicke-Hubbard model including
counter-rotating-terms. By generalizing an extended coherent state approach
within mean-field theory, we self-consistently obtain the ground state energy
and delocalized order parameter. Localization-delocalization quantum phase
transition of photons is clearly observed by breaking the parity symmetry.
Particularly, Mott lobes are fully suppressed, and the delocalized order
parameter shows monotonic enhancement by increasing qubit-cavity coupling
strength, in sharp contrast to the Dicke-Hubbard model under rotating-wave
approximation. Moreover, the corresponding phase boundaries are stabilized by
decreasing photon hopping strength, compared to the Rabi-Hubbard model.


  We studied the decay psi(2S) to gamma eta_c(2S) with 25.9 million psi(2S)
events collected with the CLEO-c detector. No psi(2S) to gamma eta_c(2S) decays
were observed in any of the eleven exclusive eta_c(2S) decay modes studied. The
product branching fraction upper limits were determined for all modes. The 90%
confidence level upper limit of branching fraction of psi(2S) to gamma eta_c
(2S) was obtained.


  A universal characterization of non-Markovianity for any open hybrid quantum
systems is presented. This formulation is based on the negativity volume of the
generalized Wigner function, which serves as an indicator of the quantum
correlations in any composite quantum systems. It is shown, that the proposed
measure can be utilized for any single or multi-partite quantum system,
containing any discrete or continuous variables. To demonstrate its power in
revealing non-Markovianity in such quantum systems, we additionally consider a
few illustrative examples.


  Interference effects in finite sections of one-dimensional moir\'e crystals
are investigated using a Landauer-B\"uttiker formalism within the tight-binding
approximation. We explain interlayer transport in double-wall carbon nanotubes
and design a predictive model. Wave function interference is visible at the
mesoscale: in the strong coupling regime, as a periodic modulation of quantum
conductance and emergent localized states; in the localized-insulating regime,
as a suppression of interlayer transport, and oscillations of the density of
states. These results could be exploited to design quantum electronic devices.


  In this paper, we investigate the usage of large language models (LLMs) to
improve the performance of competitive speech recognition systems. Different
from previous LLM-based ASR error correction methods, we propose a novel
multi-stage approach that utilizes uncertainty estimation of ASR outputs and
reasoning capability of LLMs. Specifically, the proposed approach has two
stages: the first stage is about ASR uncertainty estimation and exploits N-best
list hypotheses to identify less reliable transcriptions; The second stage
works on these identified transcriptions and performs LLM-based corrections.
This correction task is formulated as a multi-step rule-based LLM reasoning
process, which uses explicitly written rules in prompts to decompose the task
into concrete reasoning steps. Our experimental results demonstrate the
effectiveness of the proposed method by showing 10% ~ 20% relative improvement
in WER over competitive ASR systems -- across multiple test domains and in
zero-shot settings.


  The inner crust of a neutron star is a superfluid and inhomogeneous system,
consisting of a lattice of nuclei immersed in a sea of neutrons. We perform a
quantum calculation of the associated pairing gap and compare it to the results
one obtains in the Local Density Approximation (LDA). It is found that the LDA
overestimates the spatial dependence of the gap, and leads to a specific heat
of the system which is too large at low temperatures, as compared with the
quantal result. This is caused by the neglect of proximity effects and the
delocalized character of the single-particle wavefunctions close to the Fermi
energy. It is possible to introduce an alternative, simple semiclassical
approximation of the pairing gap which leads to a specific heat that is in good
agreement with the quantum calculation.


  We obtain a topological and equivariant classification of closed, connected
three-dimensional Alexandrov spaces admitting a local isometric circle action.
We show, in particular, that such spaces are homeomorphic to connected sums of
some closed 3-manifold with a local circle action and finitely many copies of
the suspension of the real projective plane.


  In geometry processing, numerical optimization methods often involve solving
sparse linear systems of equations. These linear systems have a structure that
strongly resembles to adjacency graphs of the underlying mesh. We observe how
classic linear solvers behave on this specific type of problems. For the sake
of simplicity, we minimise either the squared gradient or the squared
Laplacian, evaluated by finite differences on a regular 1D or 2D grid. We
observed the evolution of the solution for both energies, in 1D and 2D, and
with different solvers: Jacobi, Gauss-Seidel, SSOR (Symmetric successive
over-relaxation) and CG (conjugate gradient [She94]). Plotting results at
different iterations allows to have an intuition of the behavior of these
classic solvers.


  Linear discriminant analysis (LDA) is a popular technique to learn the most
discriminative features for multi-class classification. A vast majority of
existing LDA algorithms are prone to be dominated by the class with very large
deviation from the others, i.e., edge class, which occurs frequently in
multi-class classification. First, the existence of edge classes often makes
the total mean biased in the calculation of between-class scatter matrix.
Second, the exploitation of l2-norm based between-class distance criterion
magnifies the extremely large distance corresponding to edge class. In this
regard, a novel self-weighted robust LDA with l21-norm based pairwise
between-class distance criterion, called SWRLDA, is proposed for multi-class
classification especially with edge classes. SWRLDA can automatically avoid the
optimal mean calculation and simultaneously learn adaptive weights for each
class pair without setting any additional parameter. An efficient re-weighted
algorithm is exploited to derive the global optimum of the challenging l21-norm
maximization problem. The proposed SWRLDA is easy to implement, and converges
fast in practice. Extensive experiments demonstrate that SWRLDA performs
favorably against other compared methods on both synthetic and real-world
datasets, while presenting superior computational efficiency in comparison with
other techniques.


  We study the entanglement entropy in confining theories with gravity duals
using the holographic prescription of Ryu and Takayanagi. The entanglement
entropy between a region and its complement is proportional to the minimal area
of a bulk hypersurface ending on their border. We consider a disk in 2+1
dimensions and a ball in 3+1 dimensions and find in both cases two types of
bulk hypersurfaces with different topology, similar to the case of the slab
geometry considered by Klebanov, Kutasov and Murugan. Depending on the value of
the radius, one or the other type of hypersurfaces dominates the calculation of
entanglement entropy. In 2+1 dimensions a useful measure of topological order
of the ground state is the topological entanglement entropy, which is defined
to be the constant term in the entanglement entropy of a disk in the limit of
large radius. We compute this quantity and find that it vanishes for confining
gauge theory, in accord with our expectations. In 3+1 dimensions the analogous
quantity is shown to be generically nonzero and cutoff-dependent.


  The thermodynamic uncertainty relation (TUR) provides a universal entropic
bound for the precision of the fluctuation of the charge transfer for example
for a class of continuous time stochastic processes. However, its extension to
general nonequilibrium dynamics is still an unsolved problem. In this Letter,
we show TUR for an arbitrary finite time in terms of exchange fluctuation
theorem applied to ensemble of copies of the original system by assuming a
physical regularity condition for the probability distribution. As a nontrivial
practical consequence, we obtain universal scaling relations among the mean and
variance of the charge transfer in short time regime. In this manner, we can
deepen our understanding on a link between two important rigorous relations,
i.e., the fluctuation theorem and the thermodynamic uncertainty relation.


  The two-user Gaussian interference channel (G-IC) is revisited, with a
particular focus on practically amenable discrete input signalling and treating
interference as noise (TIN) receivers. The corresponding deterministic
interference channel (D-IC) is first investigated and coding schemes that can
achieve the entire capacity region of D-IC under TIN are proposed. These
schemes are then systematically translate into multi-layer superposition coding
schemes based on purely discrete inputs for the real-valued G-IC. Our analysis
shows that the proposed scheme is able to achieve the entire capacity region to
within a constant gap for all channel parameters. To the best of our knowledge,
this is the first constant-gap result under purely discrete signalling and TIN
for the entire capacity region and all the interference regimes. Furthermore,
the approach is extended to obtain coding scheme based on discrete inputs for
the complex-valued G-IC. For such a scenario, the minimum distance and the
achievable rate of the proposed scheme under TIN are analyzed, which takes into
account the effects of random phase rotations introduced by the channels.
Simulation results show that our scheme is capable of approaching the capacity
region of the complex-valued G-IC and significantly outperforms Gaussian
signalling with TIN in various interference regimes.


  We analyze the Schr\"odingerisation method for quantum simulation of a
general class of non-unitary dynamics with inhomogeneous source terms. The
Schr\"odingerisation technique, introduced in \cite{JLY22a,JLY23}, transforms
any linear ordinary and partial differential equations with non-unitary
dynamics into a system under unitary dynamics via a warped phase transition
that maps the equations into a higher dimension, making them suitable for
quantum simulation. This technique can also be applied to these equations with
inhomogeneous terms modeling source or forcing terms or boundary and interface
conditions, and discrete dynamical systems such as iterative methods in
numerical linear algebra, through extra equations in the system. Difficulty
airses with the presense of inhomogeneous terms since it can change the
stability of the original system.
  In this paper, we systematically study--both theoretically and
numerically--the important issue of recovering the original variables from the
Schr\"odingerized equations, even when the evolution operator contains unstable
modes. We show that even with unstable modes, one can still construct a stable
scheme, yet to recover the original variable one needs to use suitable data in
the extended space. We analyze and compare both the discrete and continuous
Fourier transforms used in the extended dimension, and derive corresponding
error estimates, which allows one to use the more appropriate transform for
specific equations. We also provide a smoother initialization for the
Schrod\"odingerized system to gain higher order accuracy in the extended space.
We homogenize the inhomogeneous terms with a stretch transformation, making it
easier to recover the original variable. Our recovering technique also provides
a simple and generic framework to solve general ill-posed problems in a
computationally stable way.


  Graph Neural Network (GNN) is a powerful model to learn representations and
make predictions on graph data. Existing efforts on GNN have largely defined
the graph convolution as a weighted sum of the features of the connected nodes
to form the representation of the target node. Nevertheless, the operation of
weighted sum assumes the neighbor nodes are independent of each other, and
ignores the possible interactions between them. When such interactions exist,
such as the co-occurrence of two neighbor nodes is a strong signal of the
target node's characteristics, existing GNN models may fail to capture the
signal. In this work, we argue the importance of modeling the interactions
between neighbor nodes in GNN. We propose a new graph convolution operator,
which augments the weighted sum with pairwise interactions of the
representations of neighbor nodes. We term this framework as Bilinear Graph
Neural Network (BGNN), which improves GNN representation ability with bilinear
interactions between neighbor nodes. In particular, we specify two BGNN models
named BGCN and BGAT, based on the well-known GCN and GAT, respectively.
Empirical results on three public benchmarks of semi-supervised node
classification verify the effectiveness of BGNN -- BGCN (BGAT) outperforms GCN
(GAT) by 1.6% (1.5%) in classification accuracy.Codes are available at:
https://github.com/zhuhm1996/bgnn.


  Methods: Observing the large pc-scale Stokes I mm dust continuum emission
with the IRAM 30m telescope and the intermediate-scale (<0.1pc) polarized submm
dust emission with the Submillimeter Array toward a sample of 20 high-mass
star-forming regions allows us to quantify the dependence of the fragmentation
behaviour of these regions depending on the density and magnetic field
structures.
  Results: We infer density distributions n~r^{-p} of the regions with typical
power-law slopes p around ~1.5. There is no obvious correlation between the
power-law slopes of the density structures on larger clump scales (~1pc) and
the number of fragments on smaller core scales (<0.1pc). Comparing the
large-scale single-dish density profiles to those derived earlier from
interferometric observations at smaller spatial scales, we find that the
smaller-scale power-law slopes are steeper, typically around ~2.0. The
flattening toward larger scales is consistent with the star-forming regions
being embedded in larger cloud structures that do not decrease in density away
from a particular core. Regarding the magnetic field, for several regions it
appears aligned with filamentary structures leading toward the densest central
cores. Furthermore, we find different polarization structures with some regions
exhibiting central polarization holes whereas other regions show polarized
emission also toward the central peak positions. Nevertheless, the polarized
intensities are inversely related to the Stokes I intensities. We estimate
magnetic field strengths between ~0.2 and ~4.5mG, and we find no clear
correlation between magnetic field strength and the fragmentation level of the
regions. Comparison of the turbulent to magnetic energies shows that they are
of roughly equal importance in this sample. The mass-to-flux ratios range
between ~2 and ~7, consistent with collapsing star-forming regions.


  All Hamiltonian complexity results to date have been proven by constructing a
local Hamiltonian whose ground state -- or at least some low-energy state -- is
a "computational history state", encoding a quantum computation as a
superposition over the history of the computation. We prove that all
history-state Hamiltonians must be critical. More precisely, for any
circuit-to-Hamiltonian mapping that maps quantum circuits to local Hamiltonians
with low-energy history states, there is an increasing sequence of circuits
that maps to a growing sequence of Hamiltonians with spectral gap closing at
least as fast as O(1/n) with the number of qudits n in the circuit. This result
holds for very general notions of history state, and also extends to
quasi-local Hamiltonians with exponentially-decaying interactions.
  This suggests that QMA-hardness for gapped Hamiltonians (and also
BQP-completeness of adiabatic quantum computation with constant gap) either
require techniques beyond history state constructions. Or gapped Hamiltonians
cannot be QMA-hard (respectively, BQP-complete).


  We present spectra of an M-type, binary star system (LDS 5606) that belongs
to the nearby ~20 Myr old beta Pictoris moving group. Both stars are very
dusty; the dustier member displays optical emission lines from eight elements
indicative of ongoing mass accretion. The spectra of both stars contain oxygen
forbidden line emission at 6302 and 5579 A, consistent with a recent model of
far ultraviolet photodissociation of OH molecules in a circumstellar disk.
These are the oldest dwarf stars presently known to display such a phenomenon.
The spectral energy distribution of the dustier star indicates substantial
quantities of dust as hot as 900 K, and its fractional infrared luminosity
(L_IR)/L_bol) is almost as large as that of the main sequence record holder,
V488 Per. The LDS 5606 binary joins a remarkable group of very dusty, old, T
Tauri stars that belong to widely separated multiple systems.


  Object-oriented programming (OOP) is one of the most popular paradigms used
for building software systems. However, despite its industrial and academic
popularity, OOP is still missing a formal apparatus similar to
$\lambda$-calculus, which functional programming is based on. There were a
number of attempts to formalize OOP, but none of them managed to cover all the
features available in modern OO programming languages, such as C++ or Java. We
have made yet another attempt and created $\varphi$-calculus. We also created
EOLANG (also called EO), an experimental programming language based on
$\varphi$-calculus.


  This paper introduces a general multi-class approach to weakly supervised
classification. Inferring the labels and learning the parameters of the model
is usually done jointly through a block-coordinate descent algorithm such as
expectation-maximization (EM), which may lead to local minima. To avoid this
problem, we propose a cost function based on a convex relaxation of the
soft-max loss. We then propose an algorithm specifically designed to
efficiently solve the corresponding semidefinite program (SDP). Empirically,
our method compares favorably to standard ones on different datasets for
multiple instance learning and semi-supervised learning as well as on
clustering tasks.


  Observations of the core of the giant radio galaxy NGC315 made with VLBI
interferometers are discussed in the context of a relativistic jet. The
sidedness asymmetry suggests Doppler favoritism from a relativistic jet. The
presence of moving features in the jet as well as jet counter--jet brightness
ratios hint at an accelerating, relativistic jet. An increasing jet velocity is
also supported by a comparison of the jet's observed properties with the
predictions of an adiabatic expansion model. On the parsec scale, the jet is
unpolarized at a wavelength of 6 cm to a very high degree in clear distinction
to the high polarization seen on the kiloparsec scale.


  Analytic calculations in the infrared regime of nonabelian gauge theories are
hampered by the presence of Gribov copies which results in some ambiguity in
the gauge-fixing procedure. This problem shares strong similarities with the
issue of finding the true ground state among a large number of metastable
states, a typical situation in the field of statistical physics of disordered
systems. Building on this analogy, we propose a new gauge-fixing procedure
which, we argue, makes more explicit the influence of the Gribov copies. A
1-loop calculation shows that the dynamics of these copies can lead to the
spontaneous generation of a gauge-dependent gluon mass.


  In this paper, we develop a hierarchical aerial computing framework composed
of high altitude platform (HAP) and unmanned aerial vehicles (UAVs) to compute
the fully offloaded tasks of terrestrial mobile users which are connected
through an uplink non-orthogonal multiple access (UL-NOMA). To better assess
the freshness of information in computation-intensive applications the
criterion of age of information (AoI) is considered. In particular, the problem
is formulated to minimize the average AoI of users with elastic tasks, by
adjusting UAVs trajectory and resource allocation on both UAVs and HAP, which
is restricted by the channel state information (CSI) uncertainty and multiple
resource constraints of UAVs and HAP. In order to solve this non-convex
optimization problem, two methods of multi-agent deep deterministic policy
gradient (MADDPG) and federated reinforcement learning (FRL) are proposed to
design the UAVs trajectory, and obtain channel, power, and CPU allocations. It
is shown that task scheduling significantly reduces the average AoI. This
improvement is more pronounced for larger task sizes. On one hand, it is shown
that power allocation has a marginal effect on the average AoI compared to
using full transmission power for all users. Compared with traditional
transmission schemes, the simulation results show our scheduling scheme results
in a substantial improvement in average AoI.


  Following work on theories with SU(N) gauge groups, we perform a large-N
saddle-point approximation of the measure for ADHM multi-instantons in N=4
supersymmetric gauge theories with symplectic or orthogonal gauge groups. For
Sp(N) we find that a saddle-point only exists in the even instanton charge
sector. For either Sp(N) or SO(N) the saddle-point solution parametrizes AdS_5
x RP^5, the dual supergravity geometry in the AdS/CFT correspondence for these
theories. The instanton measure at large-N has the form of the partition
function of ten-dimensional N=1 supersymmetric gauge theory with a unitary
gauge group dimensionally reduced to zero dimensions.


  The analysis of the Rayleigh-B\'enard instability due to the mass diffusion
in a fluid-saturated horizontal porous layer is reconsidered. The standard
diffusion theory based on the variance of the molecular position growing
linearly in time is generalised to anomalous diffusion, where the variance is
modelled as a power-law function of time. A model of anomalous diffusion based
on a time-dependent mass diffusion coefficient is adopted, together with
Darcy's law, for momentum transfer, and the Boussinesq approximation, for the
description of the buoyant flow. A linear stability analysis is carried out for
a basic state where the solute has a potentially unstable concentration
distribution varying linearly in the vertical direction and the fluid is at
rest. It is shown that any, even slight, departure from the standard diffusion
process has a dramatic effect on the onset conditions of the instability. This
circumstance reveals a strong sensitivity to the anomalous diffusion index. It
is shown that subdiffusion yields instability for every positive mass diffusion
Rayleigh number, while superdiffusion brings stabilisation no matter how large
is the Rayleigh number. A discussion of the linear stability analysis based on
the Galilei-variant fractional-derivative model of subdiffusion is eventually
carried out.


  Motivated by examples of symmetrically constrained compositions, super convex
partitions, and super convex compositions, we initiate the study of partitions
and compositions constrained by graph Laplacian minors. We provide a complete
description of the multivariate generating functions for such compositions in
the case of trees. We answer a question due to Corteel, Savage, and Wilf
regarding super convex compositions, which we describe as compositions
constrained by Laplacian minors for cycles; we extend this solution to the
study of compositions constrained by Laplacian minors of leafed cycles.
Connections are established and conjectured between compositions constrained by
Laplacian minors of leafed cycles of prime length and algebraic/combinatorial
properties of reflexive simplices.


  We prove the Cauchy-Rassias stability of linear n-inner product preserving
mappings in $n$-inner product Banach spaces. We apply the Cauchy-Rassias
inequality that plays an influencial role in the subject of functional
equations. The inequality was introduced for the first time by Th.M.Rassias in
his paper entitled: On the stability of the linear mapping in Banach spaces,
Proc. Amer. Math.Soc. 72(1978), 297-300.


  The paper is devoted to the study of limiting behaviour of Besov capacities
$\capa (E;B_{p,q}^\a) (0<\a<1)$ of sets in $\R^n$ as $\a\to 1$ or $\a\to 0.$
Namely, let $E\subset \R^n$ and $$J_{p,q}(\a,
E)=[\a(1-\a)q]^{p/q}\capa(E;B_{p,q}^\a).$$ It is proved that if $1\le p<n, 1\le
q<\infty,$ and the set $E$ is open, then $J_{p,q}(\a, E)$ tends to the Sobolev
capacity $\capa(E;W_p^1)$ as $\a\to 1$. This statement fails to hold for
compact sets. Further, it is proved that if the set $E$ is compact and $1\le
p,q<\infty$, then $J_{p,q}(\a, E)$ tends to $2n^p|E|$ as $\a\to 0$ ($|E|$ is
the measure of $E$). For open sets it is not true.


  The Zener-Klein (ZK) interband tunneling in graphene layers (GLs) with the
lateral n-i-n and p-i-n junctions results in the nonlinear I-V characteristics
that can be used for the rectification and detection of the terahertz (THz)
signals. The transit time delay of the tunneling electrons and holes in the
depletion regions leads to the phase shift between the THz current and THz
voltage causing the negative dynamic conductance in a certain frequency range
and resulting in the so-called transit-time (TT) instability. The combination
of the ZK tunneling and the TT negative dynamic conductance enables resonant
THz detection and the amplification and generation of THz radiation. We propose
and evaluate the THz devices based on periodic cascade GL p-i-n structures
exhibiting the TT resonances (GPIN-TTDs). Such structures can serve as THz
amplifiers and, being placed in a Fabri-Perot cavity, or coupled to a THz
antenna or using a ring oscillator connection, as THz radiation sources.


  A quantum version of transition state theory based on a quantum normal form
(QNF) expansion about a saddle-centre-...-centre equilibrium point is
presented. A general algorithm is provided which allows one to explictly
compute QNF to any desired order. This leads to an efficient procedure to
compute quantum reaction rates and the associated Gamov-Siegert resonances. In
the classical limit the QNF reduces to the classical normal form which leads to
the recently developed phase space realisation of Wigner's transition state
theory. It is shown that the phase space structures that govern the classical
reaction d ynamicsform a skeleton for the quantum scattering and resonance
wavefunctions which can also be computed from the QNF. Several examples are
worked out explicitly to illustrate the efficiency of the procedure presented.


  We consider a family of cellular automata $\Phi(n,k)$ associated with
infinite reduced elements on the affine symmetric group $\hat S_n$, which is a
tropicalization of the rational maps introduced by two of the authors. We study
the soliton solutions for $\Phi(n,k)$ and explore a `duality' with the
$\mathfrak{sl}_n$-box-ball system.


  Submodular functions are set functions mapping every subset of some ground
set of size $n$ into the real numbers and satisfying the diminishing returns
property. Submodular minimization is an important field in discrete
optimization theory due to its relevance for various branches of mathematics,
computer science and economics. The currently fastest strongly polynomial
algorithm for exact minimization [LSW15] runs in time $\widetilde{O}(n^3 \cdot
\mathrm{EO} + n^4)$ where $\mathrm{EO}$ denotes the cost to evaluate the
function on any set. For functions with range $[-1,1]$, the best
$\epsilon$-additive approximation algorithm [CLSW17] runs in time
$\widetilde{O}(n^{5/3}/\epsilon^{2} \cdot \mathrm{EO})$. In this paper we
present a classical and a quantum algorithm for approximate submodular
minimization. Our classical result improves on the algorithm of [CLSW17] and
runs in time $\widetilde{O}(n^{3/2}/\epsilon^2 \cdot \mathrm{EO})$. Our quantum
algorithm is, up to our knowledge, the first attempt to use quantum computing
for submodular optimization. The algorithm runs in time
$\widetilde{O}(n^{5/4}/\epsilon^{5/2} \cdot \log(1/\epsilon) \cdot
\mathrm{EO})$. The main ingredient of the quantum result is a new method for
sampling with high probability $T$ independent elements from any discrete
probability distribution of support size $n$ in time $O(\sqrt{Tn})$. Previous
quantum algorithms for this problem were of complexity $O(T\sqrt{n})$.


  We study the Josephson effect in planar $SF_1F_2S$ junctions that consist of
conventional $s$-wave superconductors ($S$) connected by two metallic
monodomain ferromagnets ($F_1$ and $F_2$) with arbitrary transparency of
interfaces. We solve the scattering problem in the clean limit based on the
Bogoliubov-de Gennes equation for both spin-singlet and odd in frequency
spin-triplet pairing correlations. We calculate numerically the Josephson
current-phase relation $I(\phi)$. While the first harmonic of $I(\phi)$ is
completely generated by spin-singlet and short-range spin-triplet
superconducting correlations, for noncollinear magnetizations of ferromagnetic
layers the second harmonic has an additional long-range spin-triplet component.
Therefore, for strong ferromagnetic influence, the long-range spin-triplet
contribution to the second harmonic dominates. We find an exception due to the
geometric resonance for equal ferromagnetic layers when the first harmonic is
strongly enhanced. Both first and second harmonic amplitudes oscillate with
ferromagnetic layer thicknesses due to $0-\pi$ transitions. We study the
influence of interface transparencies and find additional resonances for finite
transparency of interface between ferromagnetic layers.


  Ensuring high-quality data is paramount for maximizing the performance of
machine learning models and business intelligence systems. However, challenges
in data quality, including noise in data capture, missing records, limited data
production, and confounding variables, significantly constrain the potential
performance of these systems. In this study, we propose an
architecture-agnostic algorithm, Gradient Guided Hypotheses (GGH), designed to
address these challenges. GGH analyses gradients from hypotheses as a proxy of
distinct and possibly contradictory patterns in the data. This framework
entails an additional step in machine learning training, where gradients can be
included or excluded from backpropagation. In this manner, missing and noisy
data are addressed through a unified solution that perceives both challenges as
facets of the same overarching issue: the propagation of erroneous information.
Experimental validation of GGH is conducted using real-world open-source
datasets, where records with missing rates of up to 98.5% are simulated.
Comparative analysis with state-of-the-art imputation methods demonstrates a
substantial improvement in model performance achieved by GGH. Specifically in
very high scarcity regimes, GGH was found to be the only viable solution.
Additionally, GGH's noise detection capabilities are showcased by introducing
simulated noise into the datasets and observing enhanced model performance
after filtering out the noisy data. This study presents GGH as a promising
solution for improving data quality and model performance in various
applications.


  As soon as the geometry expands quasi-exponentially the plasma sources are
customarily tuned to zero as if the duration of the inflationary phase was
immaterial for the gauge field fluctuations at large-scale. The serendipitous
disappearance of the plasma (or even the partial neglect of its effects)
depends on the symmetries of the system which are, in four space-time
dimensions and in the simplest Abelian case, the invariance under Weyl
rescaling and the electromagnetic duality symmetry. The quantum, thermal and
conducting initial conditions of inflationary magnetogenesis are classified and
discussed with the aim of determining when plasma effects can be effectively
disregarded. The speculative implications of a non-degenerate monopole plasma
for the conservation of the large-scale electric flux are briefly examined.