  Following unprecedented success on the natural language tasks, Transformers
have been successfully applied to several computer vision problems, achieving
state-of-the-art results and prompting researchers to reconsider the supremacy
of convolutional neural networks (CNNs) as {de facto} operators. Capitalizing
on these advances in computer vision, the medical imaging field has also
witnessed growing interest for Transformers that can capture global context
compared to CNNs with local receptive fields. Inspired from this transition, in
this survey, we attempt to provide a comprehensive review of the applications
of Transformers in medical imaging covering various aspects, ranging from
recently proposed architectural designs to unsolved issues. Specifically, we
survey the use of Transformers in medical image segmentation, detection,
classification, reconstruction, synthesis, registration, clinical report
generation, and other tasks. In particular, for each of these applications, we
develop taxonomy, identify application-specific challenges as well as provide
insights to solve them, and highlight recent trends. Further, we provide a
critical discussion of the field's current state as a whole, including the
identification of key challenges, open problems, and outlining promising future
directions. We hope this survey will ignite further interest in the community
and provide researchers with an up-to-date reference regarding applications of
Transformer models in medical imaging. Finally, to cope with the rapid
development in this field, we intend to regularly update the relevant latest
papers and their open-source implementations at
\url{https://github.com/fahadshamshad/awesome-transformers-in-medical-imaging}.


  The family of fifth order nonlinear evolution equations is studied. Some
traveling wave elliptic solutions are found. The classification of these exact
solutions is given.


  W and Z production at the LHC occur at small Bjorken x, and are thus subject
to the theoretical uncertainties of low-x physics. The implications of this for
the PDF uncertainties on W and Z production are discussed, including the
limitations this puts on their usefulness as luminosity monitors. The
possibility of using LHC measurements to improve PDF uncertainties is
discussed. Measurement of the W lepton decay spectra can improve the gluon
PDFs, whereas measurement of the lepton asymmetry can give new information on
valence distributions at small x.


  In the present work we study the gravitational effects of condensed dark
matter on strange stars. We consider self-interacting dark matter particles
with properties consistent with current observational constraints, and dark
matter inside the star is modelled as a Bose-Einstein condensate. We integrate
numerically the Tolman-Oppenheimer-Volkoff equations in the two-fluid formalism
assuming that strange stars are made of up to 4 per cent of dark matter. It is
shown that for a mass of the dark matter particles in the range $50 MeV-160
MeV$ strange stars are characterized by a maximum mass and radius similar to
the ones found for neutron stars.


  We examine the frequency shifts in low-degree helioseismic modes from the
Birmingham Solar-Oscillations Network (BiSON) covering the period from 1985 -
2016, and compare them with a number of global activity proxies well as a
latitudinally-resolved magnetic index. As well as looking at frequency shifts
in different frequency bands, we look at a parametrization of the shift as a
cubic function of frequency. While the shifts in the medium- and highfrequency
bands are very well correlated with all of the activity indices (with the best
correlation being with the 10.7 cm radio flux), we confirm earlier findings
that there appears to have been a change in the frequency response to activity
during solar cycle 23, and the low frequency shifts are less correlated with
activity in the last two cycles than they were in Cycle 22. At the same time,
the more recent cycles show a slight increase in their sensitivity to activity
levels at medium and higher frequencies, perhaps because a greater proportion
of activity is composed of weaker or more ephemeral regions. This lends weight
to the speculation that a fundamental change in the nature of the solar dynamo
may be in progress.


  Using a recent formulation of quantum mechanics without potential function,
we present a four-parameter system associated with the Wilson and Racah
polynomials. The continuum scattering states are written in terms of the Wilson
polynomials whose asymptotics gives the scattering amplitude and phase shift.
On the other hand, the finite number of discrete bound states are associated
with the Racah polynomials.
  We are honored to dedicate this work to Prof. Hashim A. Yamani on the
occasion of his 70th birthday.


  The black hole physics techniques and results are applied to find the set of
the exact solutions of the SU(3)-Yang-Mills equations in Minkowski spacetime in
the Lorentz gauge. All the solutions contain only the Coulomb-like or linear in
$r$ components of SU(3)-connection. This allows one to obtain some possible
exact and approximate solutions of the corresponding Dirac equation that can
describe the relativistic bound states. Possible application to the
relativistic models of mesons is also outlined.


  An open problem for autonomous driving is how to validate the safety of an
autonomous vehicle in simulation. Automated testing procedures can find
failures of an autonomous system but these failures may be difficult to
interpret due to their high dimensionality and may be so unlikely as to not be
important. This work describes an approach for finding interpretable failures
of an autonomous system. The failures are described by signal temporal logic
expressions that can be understood by a human, and are optimized to produce
failures that have high likelihood. Our methodology is demonstrated for the
safety validation of an autonomous vehicle in the context of an unprotected
left turn and a crosswalk with a pedestrian. Compared to a baseline importance
sampling approach, our methodology finds more failures with higher likelihood
while retaining interpretability.


  New calculations of the thermal and electrical electron conductivities are
performed for a broad range of physical parameters typical for envelopes of
neutron stars and cores of white dwarfs. We consider stellar matter composed of
astrophysically important chemical elements from H to Fe in the density range
from 10^2-10^4 g/ccm up to 10^7-10^{10} g/ccm, where atoms are fully ionized
and electrons are strongly degenerate. We have used modified ion structure
factors suggested in physics/9811052. In the ion liquid, these modifications
take into account, in an approximate way, instantaneous electron-band
structures that reduce the electron-ion scattering rate. In crystallized
matter, the new structure factors include multi-phonon processes important at
temperatures not very much lower than the melting temperature T_m. The
transport coefficients obtained differ significantly from those derived earlier
in the important temperature range T_m/5 < T < 5 T_m. The results of our
numerical calculations are fitted by analytical expressions convenient for
astrophysical applications.


  In this note, the existence of noninner automorphisms of order 2 for finite
2-groups of coclass 2 is proved. Combining our result with a recent one due to
Y. Guerboussa and M. Reguiat (see arXiv:1301.0085), we prove that every finite
$p$-group of coclass 2 has a noninner automorphism of order $p$ leaving the
center elementwise fixed.


  Structural distortions in nano-materials can induce dramatic changes in their
electronic properties. This situation is well manifested in graphene, a
two-dimensional honeycomb structure of carbon atoms with only one atomic layer
thickness. In particular, strained graphene can result in both charging effects
and pseudo-magnetic fields, so that controlled strain on a perfect graphene
lattice can be tailored to yield desirable electronic properties. Here we
describe the theoretical foundation for strain-engineering of the electronic
properties of graphene, and then provide experimental evidences for
strain-induced pseudo-magnetic fields and charging effects in monolayer
graphene. We further demonstrate the feasibility of nanoscale strain
engineering for graphene-based devices by means of theoretical simulations and
nano-fabrication technology.


  Advances in deep learning recognition have led to accurate object detection
with 2D images. However, these 2D perception methods are insufficient for
complete 3D world information. Concurrently, advanced 3D shape estimation
approaches focus on the shape itself, without considering metric scale. These
methods cannot determine the accurate location and orientation of objects. To
tackle this problem, we propose a framework that jointly estimates a metric
scale shape and pose from a single RGB image. Our framework has two branches:
the Metric Scale Object Shape branch (MSOS) and the Normalized Object
Coordinate Space branch (NOCS). The MSOS branch estimates the metric scale
shape observed in the camera coordinates. The NOCS branch predicts the
normalized object coordinate space (NOCS) map and performs similarity
transformation with the rendered depth map from a predicted metric scale mesh
to obtain 6d pose and size. Additionally, we introduce the Normalized Object
Center Estimation (NOCE) to estimate the geometrically aligned distance from
the camera to the object center. We validated our method on both synthetic and
real-world datasets to evaluate category-level object pose and shape.


  We provide an analysis of the recent work by Malaney-Weinstein on "Economics
as Gauge Theory" presented on November 10, 2021 at the Money and Banking
Workshop hosted by University of Chicago. In particular, we distill the
technical mathematics used in their work into a form more suitable to a wider
audience. Furthermore, we resolve the conjectures posed by Malaney-Weinstein,
revealing that they provide no discernible value for the calculation of index
numbers or rates of inflation. Our conclusion is that the main contribution of
the Malaney-Weinstein work is that it provides a striking example of how to
obscure simple concepts through an uneconomical use of gauge theory.


  This paper introduces a polynomial transformation model based on Weibull
distribution, whereby the analytical representation of the quantile function
for many probability distributions can be obtained. Firstly, the target random
variable $x$ with specified distribution is expressed as a polynomial of a
Weibull random variable $z$, the coefficients are conveniently determined by
the percentile matching method. Then, substituting $z$ with its quantile
function $z=\lambda [-ln(1-u)]^{1/k}$ gives the analytical expression of the
quantile function of $x$. Furthermore, using the probability weighted moments
matching method, this polynomial transformation model can be used for data
fitting. Through numerical experiment, it makes evident that the proposed model
is capable of handling some distributions close to binomial which are difficult
for the extant approaches, and the quantile functions of various distributions
are accurately approximated within the probit range $[10^{-4},1-10^{-4}]$.


  Melanoma is caused by the abnormal growth of melanocytes in human skin. Like
other cancers, this life-threatening skin cancer can be treated with early
diagnosis. To support a diagnosis by automatic skin lesion segmentation,
several Fully Convolutional Network (FCN) approaches, specifically the U-Net
architecture, have been proposed. The U-Net model with a symmetrical
architecture has exhibited superior performance in the segmentation task.
However, the locality restriction of the convolutional operation incorporated
in the U-Net architecture limits its performance in capturing long-range
dependency, which is crucial for the segmentation task in medical images. To
address this limitation, recently a Transformer based U-Net architecture that
replaces the CNN blocks with the Swin Transformer module has been proposed to
capture both local and global representation. In this paper, we propose
Att-SwinU-Net, an attention-based Swin U-Net extension, for medical image
segmentation. In our design, we seek to enhance the feature re-usability of the
network by carefully designing the skip connection path. We argue that the
classical concatenation operation utilized in the skip connection path can be
further improved by incorporating an attention mechanism. By performing a
comprehensive ablation study on several skin lesion segmentation datasets, we
demonstrate the effectiveness of our proposed attention mechanism.


  Information flow between components of a system takes many forms and is key
to understanding the organization and functioning of large-scale, complex
systems. We demonstrate three modalities of information flow from time series X
to time series Y. Intrinsic information flow exists when the past of X is
individually predictive of the present of Y, independent of Y's past; this is
most commonly considered information flow. Shared information flow exists when
X's past is predictive of Y's present in the same manner as Y's past; this
occurs due to synchronization or common driving, for example. Finally,
synergistic information flow occurs when neither X's nor Y's pasts are
predictive of Y's present on their own, but taken together they are. The two
most broadly-employed information-theoretic methods of quantifying information
flow---time-delayed mutual information and transfer entropy---are both
sensitive to a pair of these modalities: time-delayed mutual information to
both intrinsic and shared flow, and transfer entropy to both intrinsic and
synergistic flow. To quantify each mode individually we introduce our
cryptographic flow ansatz, positing that intrinsic flow is synonymous with
secret key agreement between X and Y. Based on this, we employ an
easily-computed secret-key-agreement bound---intrinsic mutual
information&mdashto quantify the three flow modalities in a variety of systems
including asymmetric flows and financial markets.


  We describe an approach to quantum control of the quasiparticle excitations
in a trapped Bose-Einstein condensate based on adiabatic and diabatic changes
in the trap anisotropy. We describe our approach in the context of Landau-Zener
transition at the avoided crossings in the quasiparticle excitation spectrum.
We show that there can be population oscillation between different modes at the
specific aspect ratios of the trapping potential at which the mode energies are
almost degenerate. These effects may have implications in the expansion of an
excited condensate as well as the dynamics of a moving condensate in an atomic
wave guide with a varying width.


  We use variable-temperature (150--300\,K) single-crystal X-ray diffraction to
re-examine the interplay between structure and dynamics in the ambient phase of
the isotropic negative thermal expansion (NTE) material Cd(CN)$_2$. We find
strong experimental evidence for the existence of low-energy vibrational modes
that involve off-centering of Cd$^{2+}$ ions. These modes have the effect of
increasing network packing density---suggesting a mechanism for NTE that is
different to the generally-accepted picture of correlated Cd(C/N)$_4$ rotation
modes. Strong local correlations in the displacement directions of neighbouring
cadmium centres are evident in the existence of highly-structured diffuse
scattering in the experimental X-ray diffraction patterns. Monte Carlo
simulations suggest these patterns might be interpreted in terms of a basic set
of `ice-rules' that establish a mapping between the dynamics of Cd(CN)$_2$ and
proton ordering in cubic ice VII.


  The aim of this paper is to look at the evolution of massive stars in order
to determine whether or not the progenitor of V838 Mon may be a massive star.
In the first part of this paper, the evolution of massive stars around solar
metallicity is described, especially the evolution in the Hertzsprung-Russell
(HR) diagram. Then, using the observational constraints, the probable
progenitors (and their evolution) are described. Using models of single stars,
no progenitor can be found amongst massive stars that can satisfy all the
observational constraints. Wolf-Rayet stars (stars with initial masses above
about 30 solar masses, which have lost their hydrogen rich envelopes) could
explain 10 to 100 solar masses of circumstellar material but they are very
luminous (L > 100,000 solar luminosities). Main sequence stars crossing the HR
diagram and becoming red supergiants (RSG) can have very low effective
temperatures but take thousands of years to cross over. Be stars (fast rotating
stars with a mass around 10 solar masses), which form disk or B stars accreting
matter from a binary companion of a similar mass would need to be compared in
detail with the observational constraints. In the future, there will hopefully
be further observational constraints on the models coming from the mass and
nature (interstellar or circumstellar) of the material producing the light echo
and from a frequency estimate of spectacular objects such as V838 Mon.


  Text-to-image generative models can produce photo-realistic images for an
extremely broad range of concepts, and their usage has proliferated widely
among the general public. On the flip side, these models have numerous
drawbacks, including their potential to generate images featuring sexually
explicit content, mirror artistic styles without permission, or even
hallucinate (or deepfake) the likenesses of celebrities. Consequently, various
methods have been proposed in order to "erase" sensitive concepts from
text-to-image models. In this work, we examine five recently proposed concept
erasure methods, and show that targeted concepts are not fully excised from any
of these methods. Specifically, we leverage the existence of special learned
word embeddings that can retrieve "erased" concepts from the sanitized models
with no alterations to their weights. Our results highlight the brittleness of
post hoc concept erasure methods, and call into question their use in the
algorithmic toolkit for AI safety.


  The purpose of the present paper is to study the influence of wall-echo on
pressure fluctuations $p'$, and on statistical correlations containing $p'$,
{\em viz} redistribution $\phi_{ij}$, pressure diffusion $d_{ij}^{(p)}$, and
velocity/pressure-gradient $\Pi_{ij}$. We extend the usual analysis of
turbulent correlations containing pressure fluctuations in wall-bounded
\tsc{dns} computations [Kim J.: {\em J. Fluid Mech.} {\bf 205} (1989)
421--451], separating $p'$ not only into rapid $p_{(\mathrm{r})}'$ and slow
$p_{(\mathrm{s})}'$ parts [Chou P.Y.: {\em Quart. Appl. Math.} {\bf 3} (1945)
38--54], but further into volume ($p'_{(\mathrm{r};\mathfrak{V})}$ and
$p'_{(\mathrm{s};\mathfrak{V})}$) and surface (wall-echo; $p'_{(\mathrm{r};w)}$
and $p'_{(\mathrm{s};w)}$) terms. An algorithm, based on a Green's function
approach, is developed to compute the above splittings for various correlations
containing pressure fluctuations (redistribution, pressure diffusion,
velocity/pressure-gradient), in fully developed turbulent plane channel flow.
This exact analysis confirms previous results based on a method-of-images
approximation [Manceau R., Wang M., Laurence D.: {\em J. Fluid Mech.} {\bf 438}
(2001) 307--338] showing that, at the wall, $p'_{(\mathfrak{V})}$ and
$p'_{(w)}$ are usually of the same sign and approximately equal. The above
results are then used to study the contribution of each mechanism on the
pressure correlations in low Reynolds-number plane channel flow, and to discuss
standard second-moment-closure modelling practices.


  As a statistical tool to assist formative assessments in educational
settings, diagnostic classification models (DCMs) have been increasingly used
to provide diagnostic information regarding examinees' attributes. DCMs often
adopt a dichotomous division such as the mastery and non-mastery of attributes
to express the mastery states of attributes. However, many practical settings
involve different levels of mastery states rather than a simple dichotomy in a
single attribute. Although this practical demand can be addressed by
polytomous-attribute DCMs, their computational cost in a Markov chain Monte
Carlo estimation impedes their large-scale application due to the larger number
of polytomous-attribute mastery patterns than that of binary-attribute ones.
This study considers a scalable Bayesian estimation method for
polytomous-attribute DCMs and developed a variational Bayesian (VB) algorithm
for a polytomous-attribute saturated DCM -- a generalization of
polytomous-attribute DCMs -- by building on the existing literature on
polytomous-attribute DCMs and VB for binary-attribute DCMs. Furthermore, we
proposed the configuration of parallel computing for the proposed VB algorithm
to achieve better computational efficiency. Monte Carlo simulations revealed
that our method exhibited the high performance in parameter recovery under a
wide range of conditions. An empirical example is used to demonstrate the
utility of our method.


  The Frenkel-Kontorova model describes how an infinite chain of atoms
minimizes the total energy of the system when the energy takes into account the
interaction of nearest neighbors as well as the interaction with an exterior
environment. An almost-periodic environment leads to consider a family of
interaction energies which is stationary with respect to a minimal topological
dynamical system. We introduce, in this context, the notion of calibrated
configuration (stronger than the standard minimizing condition) and, for
continuous superlinear interaction energies, we show the existence of these
configurations for some environment of the dynamical system. Furthermore, in
one dimension, we give sufficient conditions on the family of interaction
energies to ensure, for any environment, the existence of calibrated
configurations when the underlying dynamics is uniquely ergodic. The main
mathematical tools for this study are developed in the frameworks of discrete
weak KAM theory, Aubry-Mather theory and spaces of Delone sets


  In this paper we give a discrete version of Hardy's uncertainty principle, by
using complex variable arguments, as in the classical proof of Hardy's
principle. Moreover, we give an interpretation of this principle in terms of
decaying solutions to the discrete Schr\"odinger and heat equations.


  We prove doubling inequalities for solutions of elliptic systems with an
iterated Laplacian as diagonal principal part and for solutions of the Lame'
system of isotropic linearized elasticity. These inequalities depend on global
properties of the solutions.


  Collisional energy loss of a fast particle in a medium is mostly due to the
medium polarization by the electromagnetic fields of the particle. A small
fraction of energy is carried away by the Cherenkov radiation. In chiral medium
there is an additional contribution to the energy loss due to induction of the
anomalous current proportional to the magnetic field. It causes the particle to
lose energy mostly in the form of the \emph{chiral} Cherenkov radiation. We
employ classical electrodynamics, adequate in a wide range of particle
energies, to compute the collisional energy loss by a fast particle in a
homogenous chiral plasma and apply the results to Quark-Gluon Plasma and a Weyl
semimetal. In the later case photon spectrum is strongly enhanced in the
ultraviolet and X-ray regions which makes it amenable to experimental
investigation. Our main observation is that while the collisional energy loss
in a non-chiral medium is a slow, at most logarithmic, function of energy $E$,
the chiral Cherenkov radiation is proportional to $E^2$ when the recoil is
neglected and to $E$ when it is taken into account.


  In this paper, we consider the constraint set $K$ of inequalities with
nonsmooth nonconvex constraint functions. We show that under Abadie's
constraint qualification the "perturbation property" of the best approximation
to any $x$ in $\R^n$ from a convex set $\tK:=C \cap K$ is characterized by the
strong conical hull intersection property (strong CHIP) of $C$ and $K,$ where
$C$ is a non-empty closed convex subset of $\R^n$ and the set $K$ is
represented by $K:=\{x\in \R^n : g_j(x) \le 0, \ \forall \ j=1,2,\ldots,m \}$
with $g_j : \R^n \lrar \R$ $(j=1,2, \cdots,m)$ is a tangentially convex
function at a given point $\bar x \in K.$ By using the idea of tangential
subdifferential and a non-smooth version of Abadie's constraint qualification,
we do this by first proving a dual cone characterization of the constraint set
$K.$ Moreover, we present sufficient conditions for which the strong CHIP
property holds. In particular, when the set $\tK$ is closed and convex, we show
that the Lagrange multiplier characterization of best approximation holds under
a non-smooth version of Abadie's constraint qualification. The obtained results
extend many corresponding results in the context of constrained best
approximation. Several examples are provided to clarify the results.


  Clusters of galaxies contain a fair sample of the universal baryonic mass
fraction. A combined analysis of the intracluster medium (ICM) within their
hydrostatic regions, as derived from both Sunyaev-Zeldovich effect (SZE)
measurements and X-ray images, makes it possible to constrain the cosmological
parameters. We consider both gas fraction estimates and angular diameter
distance measurements. Adopting median statistics, we find, at the 2-$\sigma$
level, the pressureless matter density, $\Omega_{\rm M0}$, to be between 0.30
and 0.40 and the Hubble constant, $H_0$, between 44 and 66 Km s$^{-1}$
Mpc$^{-1}$.


  Detecting and identifying user intent from text, both written and spoken,
plays an important role in modelling and understand dialogs. Existing research
for intent discovery model it as a classification task with a predefined set of
known categories. To generailze beyond these preexisting classes, we define a
new task of \textit{open intent discovery}. We investigate how intent can be
generalized to those not seen during training. To this end, we propose a
two-stage approach to this task - predicting whether an utterance contains an
intent, and then tagging the intent in the input utterance. Our model consists
of a bidirectional LSTM with a CRF on top to capture contextual semantics,
subject to some constraints. Self-attention is used to learn long distance
dependencies. Further, we adapt an adversarial training approach to improve
robustness and perforamce across domains. We also present a dataset of 25k
real-life utterances that have been labelled via crowd sourcing. Our
experiments across different domains and real-world datasets show the
effectiveness of our approach, with less than 100 annotated examples needed per
unique domain to recognize diverse intents. The approach outperforms
state-of-the-art baselines by 5-15% F1 score points.


  We demonstrate a single-photon stored-light interferometer, where a photon is
stored in a laser-cooled atomic ensemble in the form of a Rydberg polariton
with a spatial extent of $10 \times1\times1\mu m^3$. The photon is subject to a
Ramsey sequence, i.e. `split' into a superposition of two paths. After a delay
of up to 450 ns, the two paths are recombined to give an output dependent on
their relative phase. The superposition time of 450 ns is equivalent to a
free-space propagation distance of 135 m. We show that the interferometer
fringes are sensitive to external fields, and suggest that stored-light
interferometry could be useful for localized sensing applications.


  We study the statistical properties of interstellar dust polarization at high
Galactic latitude, using the Stokes parameter Planck maps at 353 GHz. Our aim
is to advance the understanding of the magnetized interstellar medium (ISM),
and to provide a model of the polarized dust foreground for cosmic microwave
background component-separation procedures. Focusing on the southern Galactic
cap, we examine the statistical distributions of the polarization fraction
($p$) and angle ($\psi$) to characterize the ordered and turbulent components
of the Galactic magnetic field (GMF) in the solar neighbourhood. We relate
patterns at large angular scales in polarization to the orientation of the mean
(ordered) GMF towards Galactic coordinates $(l_0,b_0)=(70^\circ \pm
5^\circ,24^\circ \pm 5^\circ)$. The histogram of $p$ shows a wide dispersion up
to 25 %. The histogram of $\psi$ has a standard deviation of $12^\circ$ about
the regular pattern expected from the ordered GMF. We use these histograms to
build a phenomenological model of the turbulent component of the GMF, assuming
a uniform effective polarization fraction ($p_0$) of dust emission. To model
the Stokes parameters, we approximate the integration along the line of sight
(LOS) as a sum over a set of $N$ independent polarization layers, in each of
which the turbulent component of the GMF is obtained from Gaussian realizations
of a power-law power spectrum. We are able to reproduce the observed $p$ and
$\psi$ distributions using: a $p_0$ value of (26 $\pm$ 3)%; a ratio of 0.9
$\pm$ 0.1 between the strengths of the turbulent and mean components of the
GMF; and a small value of $N$. We relate the polarization layers to the density
structure and to the correlation length of the GMF along the LOS.


  We show the existence of physical superluminal modes and acausality in the
Brans-Dicke type of extension of teleparallel gravity that includes F(T)
gravity and teleparallel dark energy as special cases. We derive the
characteristic hypersurface for the extra degrees of freedom in the theory,
thereby showing that the time evolution is not unique and closed causal curves
can appear. Furthermore, we present a concrete disastrous solution in Bianchi
type I spacetime, in which the anisotropy in expansion can be any function of
time, and thus anisotropy can emerge suddenly, a simple demonstration that the
theory is physically problematic.


  The standard cosmological model predicts the existence of a cosmic neutrino
background with a present density of about 110 cm^{-3} per flavour, which
affects big-bang nucleosynthesis, cosmic microwave background anisotropies, and
the evolution of large scale structures. We report on a precision calculation
of the cosmic neutrino background properties including the modification
introduced by neutrino oscillations. The role of a possible
neutrino-antineutrino asymmetry and the impact of non-standard
neutrino-electron interactions on the relic neutrinos are also briefly
discussed.


  In this paper we investigate a local to global principle for Galois
cohomology of number fields with coefficients in the Tate module of an abelian
variety. In \cite{bk13} G. Banaszak and the author obtained the sufficient
condition for the validity of the local to global principle for {\'e}tale
$K$-theory of a curve . This condition in fact has been established by means of
an analysis of the corresponding problem in the Galois cohomology. We show that
in some cases this result is the best possible i.e if this condition does not
hold we obtain counterexamples.
  We also give some examples of curves and their Jacobians. Finally, we prove
the dynamical version of the local to global principle for {\'e}tale $K$-theory
of a curve. The dynamical local to global principle for the groups of
Mordell-Weil type has recently been considered by S. Bara{\'n}czuk in
\cite{b17}. We show that all our results remain valid for Quillen $K$-theory of
${\cal X}$ if the Bass and Quillen-Lichtenbaum conjectures hold true for ${\cal
X}.$


  In this letter, we present a hybrid iterative decoder for non-binary low
density parity check (LDPC) codes over binary erasure channel (BEC), based on
which the recursion of the erasure probability is derived to design non-binary
LDPC codes with convergence-optimized degree distributions. The resulting
one-step decoding tree is cycle-free and achieves lower decoding complexity.
Experimental studies show that the proposed convergence-optimization algorithm
accelerates the convergence process by 33%.


  Cereal grains are a vital part of human diets and are important commodities
for people's livelihood and international trade. Grain Appearance Inspection
(GAI) serves as one of the crucial steps for the determination of grain quality
and grain stratification for proper circulation, storage and food processing,
etc. GAI is routinely performed manually by qualified inspectors with the aid
of some hand tools. Automated GAI has the benefit of greatly assisting
inspectors with their jobs but has been limited due to the lack of datasets and
clear definitions of the tasks.
  In this paper we formulate GAI as three ubiquitous computer vision tasks:
fine-grained recognition, domain adaptation and out-of-distribution
recognition. We present a large-scale and publicly available cereal grains
dataset called GrainSpace. Specifically, we construct three types of device
prototypes for data acquisition, and a total of 5.25 million images determined
by professional inspectors. The grain samples including wheat, maize and rice
are collected from five countries and more than 30 regions. We also develop a
comprehensive benchmark based on semi-supervised learning and self-supervised
learning techniques. To the best of our knowledge, GrainSpace is the first
publicly released dataset for cereal grain inspection.


  Following Losik's approach to Gelfand's formal geometry, certain
characteristic classes for codimension-one foliations coming from the
Gelfand-Fuchs cohomology are considered. Sufficient conditions for
non-triviality in terms of dynamical properties of generators of the holonomy
groups are found. The non-triviality for the Reeb foliations is shown; this is
in contrast with some classical theorems on the Godbillon-Vey class, e.g, the
Mizutani-Morita-Tsuboi Theorem about triviality of the Godbillon-Vey class of
foliations almost without holonomy is not true for the classes under
consideration. It is shown that the considered classes are trivial for a large
class of foliations without holonomy. The question of triviality is related to
ergodic theory of dynamical systems on the circle and to the problem of smooth
conjugacy of local diffeomorphisms. Certain classes are obstructions for the
existence of transverse affine and projective connections.


  A perfect PAC field containing an algebraically closed field is known to be
$C_1$, i.e., every degeneration of a Fano complete intersection has a point. We
prove that also every degeneration of a separably rationally connected variety
has a point.


  We critically assess limits on the maximum energy of protons accelerated
within superbubbles around massive stellar clusters, considering a number of
different scenarios. In particular, we derive under which circumstances
acceleration of protons above peta-electronvolt (PeV) energies can be expected.
While the external forward shock of the superbubble may account for
acceleration of particles up to 100 TeV, internal primary shocks such as
supernova remnants expanding in the low density medium or the collective wind
termination shock which forms around a young compact cluster provide more
favourable channels to accelerate protons up to 1 PeV, and possibly beyond.
Under reasonable conditions, clustered supernovae launching powerful shocks
into the magnetised wind of a young and compact massive star cluster are found
to be the most promising systems to accelerate protons above 10 PeV. On the
other hand, stochastic re-acceleration in the strongly turbulent plasma is
found to be much less effective than claimed in previous works, with a maximum
proton energy of at most a few hundred TeV.


  Recently, low-rank tensor completion has become increasingly attractive in
recovering incomplete visual data. Considering a color image or video as a
three-dimensional (3D) tensor, existing studies have put forward several
definitions of tensor nuclear norm. However, they are limited and may not
accurately approximate the real rank of a tensor, and they do not explicitly
use the low-rank property in optimization. It is proved that the recently
proposed truncated nuclear norm (TNN) can replace the traditional nuclear norm,
as an improved approximation to the rank of a matrix. In this paper, we propose
a new method called the tensor truncated nuclear norm (T-TNN), which suggests a
new definition of tensor nuclear norm. The truncated nuclear norm is
generalized from the matrix case to the tensor case. With the help of the low
rankness of TNN, our approach improves the efficacy of tensor completion. We
adopt the definition of the previously proposed tensor singular value
decomposition, the alternating direction method of multipliers, and the
accelerated proximal gradient line search method in our algorithm. Substantial
experiments on real-world videos and images illustrate that the performance of
our approach is better than those of previous methods.


  We report the automated deployment of 5G services across a latency-aware,
semidisaggregated, and virtualized metro network. We summarize the key findings
in a detailed analysis of end-to-end latency, service setup time, and
soft-failure detection time.


  For a homogeneous polynomial $p$ in $\xi\in {\bf R}^n$ with Gevrey
coefficients, it is known that the Cauchy problem for any realization of $p$ is
well-posed in the Gevrey class of order $s<2$ if the characteristic roots are
real. In this note, we give examples showing the situation of the converse
direction, in particular the optimality of the Gevrey order $s=2$.


  We intend to promote the concept of mass functions for interdisciplinary
science education and communication. A mass function characterizes the
frequency distribution of the masses of objects in the universe. We present an
experiment to demonstrate this concept to a diverse audience of science
students, using popular LEGO toys. We discovered that the LEGO mass function is
surprisingly similar compared to mass functions of astronomical objects such as
stars and galaxies.


  In a previous paper, the author constructed frames and oversampling formulas
for band-limited functions, in the framework of the theory of shift-invariant
spaces. In this article we study the problem of recovering missing samples.
  We find a sufficient condition for the recovery of a finite set of missing
samples. The condition is expressed as a linear independence of the components
of a vector W over the space of trigonometric polynomials determined by the
frequencies of the missing samples. We apply the theory to the derivative
sampling of any order and we illustrate our results with a numerical
experiment.


  We describe a new cognitive ability, i.e., functional conceptual substratum,
used implicitly in the generation of several mathematical proofs and
definitions. Furthermore, we present an initial (first-order) formalization of
this mechanism together with its relation to classic notions like primitive
positive definability and Diophantiveness. Additionally, we analyze the
semantic variability of functional conceptual substratum when small syntactic
modifications are done. Finally, we describe mathematically natural inference
rules for definitions inspired by functional conceptual substratum and show
that they are sound and complete w.r.t. standard calculi.


  A growing body of research on probabilistic programs and causal models has
highlighted the need to reason compositionally about model classes that extend
directed graphical models. Both probabilistic programs and causal models define
a joint probability density over a set of random variables, and exhibit sparse
structure that can be used to reason about causation and conditional
independence. This work builds on recent work on Markov categories of
probabilistic mappings to define a category whose morphisms combine a joint
density, factorized over each sample space, with a deterministic mapping from
samples to return values. This is a step towards closing the gap between recent
category-theoretic descriptions of probability measures, and the operational
definitions of factorized densities that are commonly employed in probabilistic
programming and causal inference.


  The emergence of macroscopic order and patterns is a central paradigm in
systems of (self-)propelled agents, and a key component in the structuring of
many biological systems.The relationships between the ordering process and the
underlying microscopic interactions have been extensively explored both
experimentally and theoretically. While emerging patterns often show one
specific symmetry (e.g. nematic lane patterns or polarized traveling flocks),
depending on the symmetry of the alignment interactions patterns with different
symmetries can apparently coexist. Indeed, recent experiments with an actomysin
motility assay suggest that polar and nematic patterns of actin filaments can
interact and dynamically transform into each other. However, theoretical
understanding of the mechanism responsible remains elusive. Here, we present a
kinetic approach complemented by a hydrodynamic theory for agents with mixed
alignment symmetries, which captures the experimentally observed phenomenology
and provides a theoretical explanation for the coexistence and interaction of
patterns with different symmetries. We show that local, pattern-induced
symmetry breaking can account for dynamically coexisting patterns with
different symmetries. Specifically, in a regime with moderate densities and a
weak polar bias in the alignment interaction, nematic bands show a local
symmetry-breaking instability within their high-density core region, which
induces the formation of polar waves along the bands. These instabilities
eventually result in a self-organized system of nematic bands and polar waves
that dynamically transform into each other. Our study reveals a mutual feedback
mechanism between pattern formation and local symmetry breaking in active
matter that has interesting consequences for structure formation in biological
systems.


  Locally repairable codes, or locally recoverable codes (LRC for short) are
designed for application in distributed and cloud storage systems. Similar to
classical block codes, there is an important bound called the Singleton-type
bound for locally repairable codes. In this paper, an optimal locally
repairable code refers to a block code achieving this Singleton-type bound.
Like classical MDS codes, optimal locally repairable codes carry some very nice
combinatorial structures. Since introduction of the Singleton-type bound for
locally repairable codes, people have put tremendous effort on constructions of
optimal locally repairable codes. Due to hardness of this problem, there are
few constructions of optimal locally repairable codes in literature. Most of
these constructions are realized via either combinatorial or algebraic
structures.
  In this paper, we employ automorphism groups of rational function fields to
construct optimal locally repairable codes by considering the group action on
the projective lines over finite fields. It turns out that we are able to
construct optimal locally repairable codes with reflexibility of locality as
well as smaller alphabet size comparable to the code length. In particular, we
produce new families of $q$-ary locally repairable codes, including codes of
length $q+1$ via cyclic groups and codes via dihedral groups.


  We consider a Ginzburg-Landau partial differential equation in a bounded
interval, perturbed by weak spatio-temporal noise. As the interval length
increases, a transition between activation regimes occurs, in which the
classical Kramers rate diverges [R.S. Maier and D.L. Stein, Phys. Rev. Lett.
87, 270601 (2001)]. We determine a corrected Kramers formula at the transition
point, yielding a finite, though noise-dependent prefactor, confirming a
conjecture by Maier and Stein [vol. 5114 of SPIE Proceeding (2003)]. For both
periodic and Neumann boundary conditions, we obtain explicit expressions of the
prefactor in terms of Bessel and error functions.


  Environmental stresses such as drought and heat can cause substantial yield
loss in agriculture. As such, hybrid crops that are tolerant to drought and
heat stress would produce more consistent yields compared to the hybrids that
are not tolerant to these stresses. In the 2019 Syngenta Crop Challenge,
Syngenta released several large datasets that recorded the yield performances
of 2,452 corn hybrids planted in 1,560 locations between 2008 and 2017 and
asked participants to classify the corn hybrids as either tolerant or
susceptible to drought stress, heat stress, and combined drought and heat
stress. However, no data was provided that classified any set of hybrids as
tolerant or susceptible to any type of stress. In this paper, we present an
unsupervised approach to solving this problem, which was recognized as one of
the winners in the 2019 Syngenta Crop Challenge. Our results labeled 121
hybrids as drought tolerant, 193 as heat tolerant, and 29 as tolerant to both
stresses.


  Brightening of Hen 3-860, previously classified as an H$\alpha$ emitter, was
detected by the ASAS-SN survey at the end of the year 2016. We have obtained
the first spectroscopic observations of the transient and supplemented them
with photometric data from the DASCH archive of astronomical plates, ASAS and
ASAS-SN surveys. Based on the results of our analysis, we can classify the
object as a classical symbiotic star of the infrared type S, consisting of an
M2-3 giant with $T_{\rm g}$ $\sim$ 3 550 K, a radius $R_{\rm g}\sim$ 60 - 75
R$_{\odot}$, and a luminosity $L_{\rm g}\sim$ 540 - 760 L$_{\odot}$, and a hot
and luminous component ($T_{\rm h}$ $\sim$ $1-2 \times 10^5$ K and $L_{\rm h}
\sim 10^3 \rm L_\odot$). The system experienced at least four outbursts in the
last 120 years. In addition to the outbursts, its light curves revealed the
presence of eclipses of the hot component and its surrounding (relatively cool)
shell, which developed during the outburst and redistributed a fraction of the
radiation of the hot component into the optical, by the giant, classifying the
object as a representative of a group of eclipsing symbiotic stars. The
eclipses allowed us to reveal the orbital period of the system to be 602 days.


  We consider an infinite collection of agents who make decisions,
sequentially, about an unknown underlying binary state of the world. Each
agent, prior to making a decision, receives an independent private signal whose
distribution depends on the state of the world. Moreover, each agent also
observes the decisions of its last K immediate predecessors. We study
conditions under which the agent decisions converge to the correct value of the
underlying state. We focus on the case where the private signals have bounded
information content and investigate whether learning is possible, that is,
whether there exist decision rules for the different agents that result in the
convergence of their sequence of individual decisions to the correct state of
the world. We first consider learning in the almost sure sense and show that it
is impossible, for any value of K. We then explore the possibility of
convergence in probability of the decisions to the correct state. Here, a
distinction arises: if K equals 1, learning in probability is impossible under
any decision rule, while for K greater or equal to 2, we design a decision rule
that achieves it. We finally consider a new model, involving forward looking
strategic agents, each of which maximizes the discounted sum (over all agents)
of the probabilities of a correct decision. (The case, studied in previous
literature, of myopic agents who maximize the probability of their own decision
being correct is an extreme special case.) We show that for any value of K, for
any equilibrium of the associated Bayesian game, and under the assumption that
each private signal has bounded information content, learning in probability
fails to obtain.


  We present a highly flexible computational scheme for studying correlated
electrons confined by an arbitrary external potential in two-dimensional
semiconductor quantum dots. The method starts by a Lagrange mesh calculation
for the single-particle states, followed by the calculation of the Coulomb
interaction matrix elements between these, and combining both in the exact
diagonalization of the many-body Hamiltonian. We apply the method in simulation
of double quantum dot singlet-triplet qubits. We simulate the full quantum
control and dynamics of one singlet-triplet qubit. We also use our method to
provide an exact diagonalization based first-principles model for studying two
singlet-triplet qubits and their capacitative coupling via the long-distance
Coulomb interaction.


  A list of 4,131 dwarfs, subgiants, and giants located, or suspected to be
located, within 33 parsecs of the Sun is presented. All the stars are drawn
from the new LSPM-north catalog of 61,976 stars with annual proper motions
larger than 0.15''/yr$. Trigonometric parallax measurements are found in the
literature for 1,676 of the stars in the sample; photometric and spectroscopic
distance moduli are found for another 783 objects. The remaining 1,672 objects
are reported here as nearby star candidates for the first time. Photometric
distance moduli are calculated for the new stars based on the (M_V,V-J)
relationship, calibrated with the subsample of stars which have trigonometric
parallaxes. The list of new candidates includes 539 stars which are suspected
to be within 25 parsecs of the Sun, including 63 stars estimated to be within
only 15 parsecs. The current completeness of the census of nearby stars in the
northern sky is discussed in light of the new candidates presented here. It is
estimated that 32% (18%) of nuclear burning stars within 33 parsecs (25
parsecs) of the Sun remain to be located. The missing systems are expected to
have proper motions below the 0.15''/yr limit of the LSPM catalog.


  Layer-wise relevance propagation (LRP) is a widely used and powerful
technique to reveal insights into various artificial neural network (ANN)
architectures. LRP is often used in the context of image classification. The
aim is to understand, which parts of the input sample have highest relevance
and hence most influence on the model prediction. Relevance can be traced back
through the network to attribute a certain score to each input pixel. Relevance
scores are then combined and displayed as heat maps and give humans an
intuitive visual understanding of classification models. Opening the black box
to understand the classification engine in great detail is essential for domain
experts to gain trust in ANN models. However, there are pitfalls in terms of
model-inherent artifacts included in the obtained relevance maps, that can
easily be missed. But for a valid interpretation, these artifacts must not be
ignored. Here, we apply and revise LRP on various ANN architectures trained as
classifiers on geospatial and synthetic data. Depending on the network
architecture, we show techniques to control model focus and give guidance to
improve the quality of obtained relevance maps to separate facts from
artifacts.


  The idea of posing a command following or tracking control problem as an
input reconstruction problem is explored in the paper. For a class of square
MIMO systems with known dynamics, by pretending that reference commands are
actual outputs of the system, input reconstruction methods can be used to
determine control action that will result in a system following desired
reference commands. A feedback controller which is a combination of an unbiased
state estimator and an input reconstructor that ensures unbiased tracking of
reference commands is proposed. Simulations and real-time implementation are
presented to demonstrate utility of the proposed idea. Conditions under which
proposed controller may be used for non-square systems are also discussed.


  We present an analytical approach to the problem of the multiphoton
absorption and Rabi oscillations in an armchair graphene nanoribbon (AGNR) in
the presence of a time-oscillating strong electric field induced by a light
wave directed parallel to the ribbon axis. The two-dimensional Dirac equation
for the massless electron subject to the ribbon confinement is employed. In the
resonant approximation the electron-hole pair production rate, associated with
the electron transitions between the valence and conduction size-quantized
subbands, the corresponding multiphoton absorption coefficient and the
frequency of the Rabi oscillations are obtained in an explicit form. We trace
the dependencies of the above quantities on the ribbon width and electric field
strength for both the multiphoton assisted and tunneling regimes relevant to
the time-oscillating and practically constant electric field, respectively. A
significant enhancement effect of the oscillating character of the electric
field on the intersubband transitions is encountered. Our analytical results
are in qualitative agreement with those obtained for the graphene layer by
numerical methods. Estimates of the expected experimental values for the
typically employed AGNR and laser parameters show that both the Rabi
oscillations and multiphoton absorption are accessible in the laboratory. The
data relevant to the intersubband tunneling makes the AGNR a 1D condensed
matter analog in which the quantum electrodynamic vacuum decay can be detected
by applying an external laboratory electric field.


  Given two sets of positive integers $A$ and $B$, let $AB := \{ab : a \in A,\,
b \in B\}$ be their product set and put $A^k := A \cdots A$ ($k$ times $A$) for
any positive integer $k$. Moreover, for every positive integer $n$ and every
$\alpha \in [0,1]$, let $\mathcal{B}(n, \alpha)$ denote the probabilistic model
in which a random set $A \subseteq \{1, \dots, n\}$ is constructed by choosing
independently every element of $\{1, \dots, n\}$ with probability $\alpha$. We
prove that if $A_1, \dots, A_s$ are random sets in $\mathcal{B}(n_1, \alpha_1),
\dots, \mathcal{B}(n_s, \alpha_s)$, respectively, $k_1, \dots, k_s$ are fixed
positive integers, $\alpha_i n_i \to +\infty$, and $1/\alpha_i$ does not grow
too fast in terms of a product of $\log n_j$; then $|A_1^{k_1} \cdots
A_s^{k_s}| \sim \frac{|A_1|^{k_1}}{k_1!}\cdots\frac{|A_s|^{k_s}}{k_s!}$ with
probability $1 - o(1)$. This is a generalization of a result of Cilleruelo,
Ramana, and Ramar\'e, who considered the case $s = 1$ and $k_1 = 2$.


  We study the dynamics and resulting score distribution of three-agent games
where after each competition a single agent wins and scores a point. A single
competition is described by a triplet of numbers $p$, $t$ and $q$ denoting the
probabilities that the team with the highest, middle or lowest accumulated
score wins. We study the full family of solutions in the regime, where the
number of agents and competitions is large, which can be regarded as a
hydrodynamic limit. Depending on the parameter values $(p,q,t)$, we find six
qualitatively different asymptotic score distributions and we also provide a
qualitative understanding of these results. We checked our analytical results
against numerical simulations of the microscopic model and find these to be in
excellent agreement. The three agent game can be regarded as a social model
where a player can be favored or disfavored for advancement, based on his/her
accumulated score. It is also possible to decide the outcome of a three agent
game through a mini tournament of two-a gent competitions among the
participating players and it turns out that the resulting possible score
distributions are a subset of those obtained for the general three agent-games.
We discuss how one can add a steady and democratic decline rate to the model
and present a simple geometric construction that allows one to write down the
corresponding score evolution equations for $n$-agent games.


  We present a review of AGB star evolution, with emphasis on the
nucleosynthesis occurring in these stars. In particular, we discuss hot and
cool bottom burning, observational constraints, and analysis of meteoritic
grains. This paper was presented at the 32nd Liege Colloquium "Stellar
Evolution: What Should Be Done ?"


  It is argued that, in a hot plasma interacting with thermal radiation, there
exist the radiation-induced solitary waves different from the types of
nonlinear waves in plasmas known so far. There are extensive observational
evidence for the propagation of these specific density waves in the hot plasmas
of various astrophysical objects. Radiation produces also non-adiabatic density
perturbations analogues to the second sound in the liquid helium.


  Neural style transfer is an emerging technique which is able to endow
daily-life images with attractive artistic styles. Previous work has succeeded
in applying convolutional neural networks (CNNs) to style transfer for
monocular images or videos. However, style transfer for stereoscopic images is
still a missing piece. Different from processing a monocular image, the two
views of a stylized stereoscopic pair are required to be consistent to provide
observers a comfortable visual experience. In this paper, we propose a novel
dual path network for view-consistent style transfer on stereoscopic images.
While each view of the stereoscopic pair is processed in an individual path, a
novel feature aggregation strategy is proposed to effectively share information
between the two paths. Besides a traditional perceptual loss being used for
controlling the style transfer quality in each view, a multi-layer view loss is
leveraged to enforce the network to coordinate the learning of both the paths
to generate view-consistent stylized results. Extensive experiments show that,
compared against previous methods, our proposed model can produce stylized
stereoscopic images which achieve decent view consistency.


  We present a new method for the derivation of convolution identities for
finite sums of products of Bernoulli numbers. Our approach is motivated by the
role of these identities in quantum field theory and string theory. We first
show that the Miki identity and the Faber-Pandharipande-Zagier (FPZ) identity
are closely related, and give simple unified proofs which naturally yield a new
Bernoulli number convolution identity. We then generalize each of these three
identities into new families of convolution identities depending on a
continuous parameter. We rederive a cubic generalization of Miki's identity due
to Gessel and obtain a new similar identity generalizing the FPZ identity. The
generalization of the method to the derivation of convolution identities of
arbitrary order is outlined. We also describe an extension to identities which
relate convolutions of Euler and Bernoulli numbers.


  We compare the theoretical frameworks and the phenomenological applications
of the factorization approaches to exclusive $B$ meson decays, which include
QCD-improved factorization, perturbative QCD, and soft-collinear effective
theory. Recent progress on two-body nonleptonic $B$ meson decays made in these
approaches are reviewed.


  We investigate the dynamics of the hepatitis B virus by integrating
variable-order calculus and discrete analysis. Specifically, we utilize the
Caputo variable-order difference operator in this study. To establish the
existence and uniqueness results of the model, we employ a fixed-point
technique. Furthermore, we prove that the model exhibits bounded and positive
solutions. Additionally, we explore the local stability of the proposed model
by determining the basic reproduction number. Finally, we present several
numerical simulations to illustrate the richness of our results.


  We study su(2) and su(1,1) displaced number states. Those states are
eigenstates of density-dependent interaction systems of quantized radiation
field with classical current. Those states are intermediate states
interpolating between number and displaced number states. Their photon number
distribution, statistical and squeezing properties are studied in detail. It is
show that these states exhibit strong nonclassical properties.


  We present Atacama Large Millimeter/submillimeter Array (ALMA) observations
of molecular line emission from d216-0939, one of the largest and most massive
protoplanetary disks in the Orion Nebula Cluster (ONC). We model the spectrally
resolved HCO$^+$ (4--3), CO (3--2), and HCN (4--3) lines observed at 0\farcs5
resolution to fit the temperature and density structure of the disk. We also
weakly detect and spectrally resolve the CS (7--6) line but do not model it.
The abundances we derive for CO and HCO$^+$ are generally consistent with
expected values from chemical modeling of protoplanetary disks, while the HCN
abundance is higher than expected. We dynamically measure the mass of the
central star to be $2.17\pm0.07\,M_\odot$ which is inconsistent with the
previously determined spectral type of K5. We also report the detection of a
spatially unresolved high-velocity blue-shifted excess emission feature with a
measurable positional offset from the central star, consistent with a Keplerian
orbit at $60\pm20\,\mathrm{au}$. Using the integrated flux of the feature in
HCO$^+$ (4--3), we estimate the total H$_2$ gas mass of this feature to be at
least $1.8-8\,M_\mathrm{Jupiter}$, depending on the assumed temperature. The
feature is due to a local temperature and/or density enhancement consistent
with either a hydrodynamic vortex or the expected signature of the envelope of
a forming protoplanet within the disk.


  Using analog beamforming in mmWave frequency bands we can focus the energy
towards a receiver to achieve high throughput. However, this requires the
network to quickly find the best downlink beam configuration in the face of
non-IID data. We propose a personalized Federated Learning (FL) method to
address this challenge, where we learn a mapping between uplink Sub-6GHz
channel estimates and the best downlink beam in heterogeneous scenarios with
non-IID characteristics. We also devise FedLion, a FL implementation of the
Lion optimization algorithm. Our approach reduces the signaling overhead and
provides superior performance, up to 33.6% higher accuracy than a single FL
model and 6% higher than a local model.


  We study the turbulent dynamics of a relativistic (2 + 1)-dimensional fluid
placed in a stochastic gravitational potential. We demonstrate that the
dynamics of the fluid can be obtained using a dual holographic description
realized by an asymptotically Anti-de Sitter black brane driven by a random
boundary metric. Using the holographic duality we study the inverse cascade
energy power spectrum of the fluid and show that it is compatible with that of
a compressible fluid flow. We calculate the local energy dissipation and the
local fluid velocity distribution which provide other measures of the
holographic fluid turbulence.


  We show that the counting class LWPP [FFK94] remains unchanged even if one
allows a polynomial number of gap values rather than one. On the other hand, we
show that it is impossible to improve this from polynomially many gap values to
a superpolynomial number of gap values by relativizable proof techniques.
  The first of these results implies that the Legitimate Deck Problem (from the
study of graph reconstruction) is in LWPP (and thus low for PP, i.e., $\rm
PP^{\mbox{Legitimate Deck}} = PP$) if the weakened version of the
Reconstruction Conjecture holds in which the number of nonisomorphic preimages
is assumed merely to be polynomially bounded. This strengthens the 1992 result
of K\"{o}bler, Sch\"{o}ning, and Tor\'{a}n [KST92] that the Legitimate Deck
Problem is in LWPP if the Reconstruction Conjecture holds, and provides
strengthened evidence that the Legitimate Deck Problem is not NP-hard.
  We additionally show on the one hand that our main LWPP robustness result
also holds for WPP, and also holds even when one allows both the rejection- and
acceptance- gap-value targets to simultaneously be polynomial-sized lists; yet
on the other hand, we show that for the #P-based analog of LWPP the behavior
much differs in that, in some relativized worlds, even two target values
already yield a richer class than one value does. Despite that nonrobustness
result for a #P-based class, we show that the #P-based "exact counting" class
$\rm C_{=}P$ remains unchanged even if one allows a polynomial number of target
values for the number of accepting paths of the machine.


  Coded aperture snapshot spectral imaging (CASSI) is a technique used to
reconstruct three-dimensional hyperspectral images (HSIs) from one or several
two-dimensional projection measurements. However, fewer projection measurements
or more spectral channels leads to a severly ill-posed problem, in which case
regularization methods have to be applied. In order to significantly improve
the accuracy of reconstruction, this paper proposes a fast alternating
minimization algorithm based on the sparsity and deep image priors (Fama-SDIP)
of natural images. By integrating deep image prior (DIP) into the principle of
compressive sensing (CS) reconstruction, the proposed algorithm can achieve
state-of-the-art results without any training dataset. Extensive experiments
show that Fama-SDIP method significantly outperforms prevailing leading methods
on simulation and real HSI datasets.


  This paper proposes a novel method for vision-based metric cross-view
geolocalization (CVGL) that matches the camera images captured from a
ground-based vehicle with an aerial image to determine the vehicle's geo-pose.
Since aerial images are globally available at low cost, they represent a
potential compromise between two established paradigms of autonomous driving,
i.e. using expensive high-definition prior maps or relying entirely on the
sensor data captured at runtime.
  We present an end-to-end differentiable model that uses the ground and aerial
images to predict a probability distribution over possible vehicle poses. We
combine multiple vehicle datasets with aerial images from orthophoto providers
on which we demonstrate the feasibility of our method. Since the ground truth
poses are often inaccurate w.r.t. the aerial images, we implement a
pseudo-label approach to produce more accurate ground truth poses and make them
publicly available.
  While previous works require training data from the target region to achieve
reasonable localization accuracy (i.e. same-area evaluation), our approach
overcomes this limitation and outperforms previous results even in the strictly
more challenging cross-area case. We improve the previous state-of-the-art by a
large margin even without ground or aerial data from the test region, which
highlights the model's potential for global-scale application. We further
integrate the uncertainty-aware predictions in a tracking framework to
determine the vehicle's trajectory over time resulting in a mean position error
on KITTI-360 of 0.78m.


  The surrogate model-based uncertainty quantification method has drawn much
attention in many engineering fields. Polynomial chaos expansion (PCE) and deep
learning (DL) are powerful methods for building a surrogate model. However, PCE
needs to increase the expansion order to improve the accuracy of the surrogate
model, which causes more labeled data to solve the expansion coefficients, and
DL also requires a lot of labeled data to train the deep neural network (DNN).
First of all, this paper proposes the adaptive arbitrary polynomial chaos (aPC)
and proves two properties about the adaptive expansion coefficients. Based on
the adaptive aPC, a semi-supervised deep adaptive arbitrary polynomial chaos
expansion (Deep aPCE) method is proposed to reduce the training data cost and
improve the surrogate model accuracy. For one hand, the Deep aPCE method uses
two properties of the adaptive aPC to assist in training the DNN based on only
a small amount of labeled data and many unlabeled data, significantly reducing
the training data cost. On the other hand, the Deep aPCE method adopts the DNN
to fine-tune the adaptive expansion coefficients dynamically, improving the
Deep aPCE model accuracy with lower expansion order. Besides, the Deep aPCE
method can directly construct accurate surrogate models of the high dimensional
stochastic systems without complex dimension-reduction and model decomposition
operations. Five numerical examples and an actual engineering problem are used
to verify the effectiveness of the Deep aPCE method.


  We present Text2Gestures, a transformer-based learning method to
interactively generate emotive full-body gestures for virtual agents aligned
with natural language text inputs. Our method generates emotionally expressive
gestures by utilizing the relevant biomechanical features for body expressions,
also known as affective features. We also consider the intended task
corresponding to the text and the target virtual agents' intended gender and
handedness in our generation pipeline. We train and evaluate our network on the
MPI Emotional Body Expressions Database and observe that our network produces
state-of-the-art performance in generating gestures for virtual agents aligned
with the text for narration or conversation. Our network can generate these
gestures at interactive rates on a commodity GPU. We conduct a web-based user
study and observe that around 91% of participants indicated our generated
gestures to be at least plausible on a five-point Likert Scale. The emotions
perceived by the participants from the gestures are also strongly positively
correlated with the corresponding intended emotions, with a minimum Pearson
coefficient of 0.77 in the valence dimension.


  The coronavirus disease (COVID-19) is an unparalleled crisis leading to a
huge number of casualties and security problems. In order to reduce the spread
of coronavirus, people often wear masks to protect themselves. This makes face
recognition a very difficult task since certain parts of the face are hidden. A
primary focus of researchers during the ongoing coronavirus pandemic is to come
up with suggestions to handle this problem through rapid and efficient
solutions. In this paper, we propose a reliable method based on occlusion
removal and deep learning-based features in order to address the problem of the
masked face recognition process. The first step is to remove the masked face
region. Next, we apply three pre-trained deep Convolutional Neural Networks
(CNN) namely, VGG-16, AlexNet, and ResNet-50, and use them to extract deep
features from the obtained regions (mostly eyes and forehead regions). The
Bag-of-features paradigm is then applied to the feature maps of the last
convolutional layer in order to quantize them and to get a slight
representation comparing to the fully connected layer of classical CNN.
Finally, Multilayer Perceptron (MLP) is applied for the classification process.
Experimental results on Real-World-Masked-Face-Dataset show high recognition
performance compared to other state-of-the-art methods.


  We explore the hypothesis that the population of Martian Trojans is the
result of a balance between the production of new asteroids ("YORPlets")
through the YORP effect and their eventual escape from the Trojan clouds
through Yarkovsky-driven orbital evolution. Our principal observables are:
(5261) Eureka, its family of 8 asteroids and the family-less Trojans (101429)
1998 VF31 & (121514) 1999 UJ7. We model the population evolution as a
birth-death random process and assume it is in a steady state. We then simulate
the discovery of Trojans to-date and find that family members of 101429 and
121514, if they exist, are intrinsically more difficult to detect than
Eureka's. Their non-discovery can be used as evidence of their non-existence
only under the assumption that their brightness relative to the parent asteroid
is similar to that in the Eureka family. To find out how efficiently Mars
Trojans are lost from the Trojan clouds due to the Yarkovsky effect, we carry
out dynamical simulations of test particles originating from these parent
bodies. We find that objects originating from Eureka and 121514 begin escaping
after ~1 Gyr, but that those from 101429 are already lost by that time,
probably due to that asteroid's proximity to an eccentricity-type secular
resonance within Mars's co-orbital region. This is the likely cause behind the
absence of Trojans in the orbital vicinity of 101429. In contrast, the solitary
status of 121514 points to an intrinsic inability of the asteroid to produce
YORPlets during the most recent ~20% of the solar system's history, a finding
potentially related to 121514's present, low angular momentum rotational state,
unless the Eureka family formed rapidly during a single fission event.


  We provide characterization of the strong termination property of the CCV
(complete call-by-value) lambda-mu calculus introduced in the first part of
this series of the paper. The calculus is complete with respect to the standard
continuation-passing style (CPS) semantics. The union-intersection type systems
for the calculus is developed in the previous paper. We characterize the strong
normalizability of terms of the calculus in terms of the CPS semantics and
typeability.


  We introduce a random differential operator, that we call the
$\mathtt{CS}_\tau$ operator, whose spectrum is given by the $\mbox{Sch}_\tau$
point process introduced by Kritchevski, Valk\'o and Vir\'ag (2012) and whose
eigenvectors match with the description provided by Rifkind and Vir\'ag (2018).
This operator acts on $\mathbf{R}^2$-valued functions from the interval $[0,1]$
and takes the form: $$ 2 \begin{pmatrix} 0 & -\partial_t \\ \partial_t & 0
\end{pmatrix} + \sqrt{\tau} \begin{pmatrix} d\mathcal{B} + \frac1{\sqrt 2}
d\mathcal{W}_1 & \frac1{\sqrt 2} d\mathcal{W}_2\\ \frac1{\sqrt 2}
d\mathcal{W}_2 & d\mathcal{B} - \frac1{\sqrt 2} d\mathcal{W}_1\end{pmatrix}\,,
$$ where $d\mathcal{B}$, $d\mathcal{W}_1$ and $d\mathcal{W}_2$ are independent
white noises. Then, we investigate the high part of the spectrum of the
Anderson Hamiltonian $\mathcal{H}_L := -\partial_t^2 + dB$ on the segment
$[0,L]$ with white noise potential $dB$, when $L\to\infty$. We show that the
operator $\mathcal{H}_L$, recentred around energy levels $E \sim L/\tau$ and
unitarily transformed, converges in law as $L\to\infty$ to $\mathtt{CS}_\tau$
in an appropriate sense. This allows to answer a conjecture of Rifkind and
Vir\'ag (2018) on the behavior of the eigenvectors of $\mathcal{H}_L$. Our
approach also explains how such an operator arises in the limit of
$\mathcal{H}_L$. Finally we show that at higher energy levels, the Anderson
Hamiltonian matches (asymptotically in $L$) with the unperturbed Laplacian
$-\partial_t^2$. In a companion paper, it is shown that at energy levels much
smaller than $L$, the spectrum is localized with Poisson statistics: the
present paper therefore identifies the delocalized phase of the Anderson
Hamiltonian.


  We exploit the renormalization-group approach to establish the {\em exact}
infrared behavior of an interacting Bose system at zero temperature. The
local-gauge symmetry in the broken-symmetry phase is implemented through the
associated Ward identities, which reduce the number of independent running
couplings to a single one. For this coupling the $\epsilon$-expansion can be
controlled to all orders in $\epsilon$ ($=3-d$). For spatial dimensions $1 < d
\leq 3$ the Bogoliubov fixed point is unstable towards a different fixed point
characterized by the divergence of the longitudinal correlation function. The
Bogoliubov linear spectrum, however, is found to be independent from the
critical behavior of this correlation function, being exactly constrained by
Ward identities. The new fixed point properly gives a finite value of the
coupling among transverse fluctuations, but due to virtual intermediate
longitudinal fluctuations the effective coupling affecting the transverse
correlation function flows to zero. As a result, no transverse anomalous
dimension is present. This treatment allows us to recover known results for the
quantum Bose gas in the context of a unifying framework and also to reveal the
non-trivial skeleton structure of its perturbation theory.


  We prove global existence for the one-dimensional cubic non-linear
Schr\"odinger equation in modulation spaces $M_{p,p'}$ for $p$ sufficiently
close to $2$. In contrast to known results, our result requires no smallness
condition on initial data. The proof adapts a splitting method inspired by work
of Vargas-Vega and Hyakuna-Tsutsumi to the modulation space setting and
exploits polynomial growth of the free Schr\"odinger group on modulation
spaces.


  In this article we have extended the original work of Chandrasekhar on the
structure of white dwarfs to the two-dimensional case. Although such
two-dimensional stellar objects are hypothetical in nature, we strongly believe
that the work presented in this article may be prescribed as Master of Science
level class problem for the students in physics.


  This Letter reports the first scientific results from the observation of
antineutrinos emitted by fission products of $^{235}$U at the High Flux Isotope
Reactor. PROSPECT, the Precision Reactor Oscillation and Spectrum Experiment,
consists of a segmented 4 ton $^6$Li-doped liquid scintillator detector
covering a baseline range of 7-9 m from the reactor and operating under less
than 1 meter water equivalent overburden. Data collected during 33 live-days of
reactor operation at a nominal power of 85 MW yields a detection of 25461 $\pm$
283 (stat.) inverse beta decays. Observation of reactor antineutrinos can be
achieved in PROSPECT at 5$\sigma$ statistical significance within two hours of
on-surface reactor-on data-taking. A reactor-model independent analysis of the
inverse beta decay prompt energy spectrum as a function of baseline constrains
significant portions of the previously allowed sterile neutrino oscillation
parameter space at 95% confidence level and disfavors the best fit of the
Reactor Antineutrino Anomaly at 2.2$\sigma$ confidence level.


  We study the syzygies of canonical curves of genus $g$ over an algebraically
closed field $\mathbb{F}$ with Char $\mathbb{F}=p>0$. We give a new proof of
generic Green's Conjecture for $p\geq\frac{g+4}{2}$. With the ingredients in
the proof of even genus case, we prove Geometric Syzygy Conjecture for a
general smooth curve of even genus $g=2k$ assuming $p>2k$.


  The iterative development process is a framework used to design products and
applications across a wide range of domains. It centers around building
prototypes, testing them, and updating based on the test results. We discuss
how we applied this technique to create Fractal Emergence, an interactive piece
of mathematical art.


  Let $f_1,\dots,f_k\in\mathbb{R}[X]$ be polynomials of degree at most $d$ with
$f_1(0)=\dots=f_k(0)=0$. We show that there is an integer $n<x$ such that the
fractional parts $\|f_i(n)\|\ll x^{c/k}$ for all $1\le i\le k$ and for some
constant $c=c(d)$ depending only on $d$. This is essentially optimal in the
$k$-aspect, and improves on earlier results of Schmidt who showed the same
result with $c/k^2$ in place of $c/k$.


  Our knowledge of the Sun, its atmosphere, long term activity and space
weather potential is severely limited by the lack of good observations of the
polar and far-side regions. Observations from a polar vantage point would
revolutionize our understanding of the mechanism of solar activity cycles,
polar magnetic field reversals, the internal structure and dynamics of the Sun
and its atmosphere. Only with extended (many day) observations of the polar
regions can the polar flows be determined down to the tachocline where the
dynamo is thought to originate. Rapid short period polar orbits, using in situ
and remote sensing instrumentation, distributed over a small number of
spacecraft, will provide continuous 360o coverage of the solar surface and
atmosphere in both longitude and latitude for years on end. This unprecedented
full coverage will enable breakthrough studies of the physical connection
between the solar interior, the solar atmosphere, the solar wind, solar
energetic particles and the inner heliosphere at large. A potential
implementation, the Solar Polar Diamond Explorer (SPDEx) built upon the Solar
Polar Imager mission design, involves up to four small spacecraft in a 0.48-AU
orbit with an inclination of 75o. The orbit is achieved using solar sails or
ion engines, both technologies already demonstrated in space.


  Multimodal language analysis often considers relationships between features
based on text and those based on acoustical and visual properties. Text
features typically outperform non-text features in sentiment analysis or
emotion recognition tasks in part because the text features are derived from
advanced language models or word embeddings trained on massive data sources
while audio and video features are human-engineered and comparatively
underdeveloped. Given that the text, audio, and video are describing the same
utterance in different ways, we hypothesize that the multimodal sentiment
analysis and emotion recognition can be improved by learning (hidden)
correlations between features extracted from the outer product of text and
audio (we call this text-based audio) and analogous text-based video. This
paper proposes a novel model, the Interaction Canonical Correlation Network
(ICCN), to learn such multimodal embeddings. ICCN learns correlations between
all three modes via deep canonical correlation analysis (DCCA) and the proposed
embeddings are then tested on several benchmark datasets and against other
state-of-the-art multimodal embedding algorithms. Empirical results and
ablation studies confirm the effectiveness of ICCN in capturing useful
information from all three views.


  We solve the time-dependent Dirac equation for a muon which is initially
bound to a fissioning actinide nucleus. The computations are carried out on a
3-D cartesian lattice utilizing the Basis-Spline collocation method. The muon
dynamics is sensitive to the nuclear energy dissipation between the outer
fission barrier and the scission point. From a comparison with experimental
data we find a dissipated energy of about 10 MeV and a fission time delay due
to friction of order $2 \times 10^{-21}$ s.


  Factorization Machines (FM), a general predictor that can efficiently model
feature interactions in linear time, was primarily proposed for collaborative
recommendation and have been broadly used for regression, classification and
ranking tasks. Subspace Encoding Factorization Machine (SEFM) has been proposed
recently to overcome the expressiveness limitation of Factorization Machines
(FM) by applying explicit nonlinear feature mapping for both individual
features and feature interactions through one-hot encoding to each input
feature. Despite the effectiveness of SEFM, it increases the memory cost of FM
by $b$ times, where $b$ is the number of bins when applying one-hot encoding on
each input feature. To reduce the memory cost of SEFM, we propose a new method
called Binarized FM which constraints the model parameters to be binary values
(i.e., 1 or $-1$). Then each parameter value can be efficiently stored in one
bit. Our proposed method can significantly reduce the memory cost of SEFM
model. In addition, we propose a new algorithm to effectively and efficiently
learn proposed FM with binary constraints using Straight Through Estimator
(STE) with Adaptive Gradient Descent (Adagrad). Finally, we evaluate the
performance of our proposed method on eight different classification datasets.
Our experimental results have demonstrated that our proposed method achieves
comparable accuracy with SEFM but with much less memory cost.


  The performance of a dynamic dictionary is measured mainly by its update
time, lookup time, and space consumption. In terms of update time and lookup
time there are known constructions that guarantee constant-time operations in
the worst case with high probability, and in terms of space consumption there
are known constructions that use essentially optimal space. However, although
the first analysis of a dynamic dictionary dates back more than 45 years ago
(when Knuth analyzed linear probing in 1963), the trade-off between these
aspects of performance is still not completely understood. In this paper we
settle two fundamental open problems: - We construct the first dynamic
dictionary that enjoys the best of both worlds: it stores n elements using
(1+epsilon)n memory words, and guarantees constant-time operations in the worst
case with high probability. Specifically, for any epsilon = \Omega((\log\log n
/ \log n)^{1/2} ) and for any sequence of polynomially many operations, with
high probability over the randomness of the initialization phase, all
operations are performed in constant time which is independent of epsilon. The
construction is a two-level variant of cuckoo hashing, augmented with a
"backyard" that handles a large fraction of the elements, together with a
de-amortized perfect hashing scheme for eliminating the dependency on epsilon.
- We present a variant of the above construction that uses only (1+o(1))B bits,
where B is the information-theoretic lower bound for representing a set of size
n taken from a universe of size u, and guarantees constant-time operations in
the worst case with high probability, as before. This problem was open even in
the amortized setting. One of the main ingredients of our construction is a
permutation-based variant of cuckoo hashing, which significantly improves the
space consumption of cuckoo hashing when dealing with a rather small universe.


  In this paper, we propose a novel supervised single-channel speech
enhancement method combing the the Kullback-Leibler divergence-based
non-negative matrix factorization (NMF) and hidden Markov model (NMF-HMM). With
the application of HMM, the temporal dynamics information of speech signals can
be taken into account. In the training stage, the sum of Poisson, leading to
the KL divergence measure, is used as the observation model for each state of
HMM. This ensures that a computationally efficient multiplicative update can be
used for the parameter update of the proposed model. In the online enhancement
stage, we propose a novel minimum mean-square error (MMSE) estimator for the
proposed NMF-HMM. This estimator can be implemented using parallel computing,
saving the time complexity. The performance of the proposed algorithm is
verified by objective measures. The experimental results show that the proposed
strategy achieves better speech enhancement performance than state-of-the-art
speech enhancement methods. More specifically, compared with the traditional
NMF-based speech enhancement methods, our proposed algorithm achieves a 5\%
improvement for short-time objective intelligibility (STOI) and 0.18
improvement for perceptual evaluation of speech quality (PESQ).


  We explore the top-$K$ rank aggregation problem. Suppose a collection of
items is compared in pairs repeatedly, and we aim to recover a consistent
ordering that focuses on the top-$K$ ranked items based on partially revealed
preference information. We investigate the Bradley-Terry-Luce model in which
one ranks items according to their perceived utilities modeled as noisy
observations of their underlying true utilities. Our main contributions are
two-fold. First, in a general comparison model where item pairs to compare are
given a priori, we attain an upper and lower bound on the sample size for
reliable recovery of the top-$K$ ranked items. Second, more importantly,
extending the result to a random comparison model where item pairs to compare
are chosen independently with some probability, we show that in slightly
restricted regimes, the gap between the derived bounds reduces to a constant
factor, hence reveals that a spectral method can achieve the minimax optimality
on the (order-wise) sample size required for top-$K$ ranking. That is to say,
we demonstrate a spectral method alone to be sufficient to achieve the
optimality and advantageous in terms of computational complexity, as it does
not require an additional stage of maximum likelihood estimation that a
state-of-the-art scheme employs to achieve the optimality. We corroborate our
main results by numerical experiments.


  In recent years lot of interest has been observed in the nucleus-nucleus
collisions at RHIC energies in phenomena related to high $p_{t}$ physics
\cite{ref1}. The suppression of high $p_{t}$ particles and disappearance of
back-to-back jets compared to the scaling with number of binary nucleon-nucleon
collisions indicates that a nearly perfect liquid is produced in these
collisions. Results on self shadowing of high $p_{t}$ events are presented
using hadron multiplicity associated to high $p_{t}$ and unbiased events in
nucleus-nucleus collisions \cite{ref2} obtained from the hijing event
generator.


  Estimation of large covariance matrices has drawn considerable recent
attention, and the theoretical focus so far has mainly been on developing a
minimax theory over a fixed parameter space. In this paper, we consider
adaptive covariance matrix estimation where the goal is to construct a single
procedure which is minimax rate optimal simultaneously over each parameter
space in a large collection. A fully data-driven block thresholding estimator
is proposed. The estimator is constructed by carefully dividing the sample
covariance matrix into blocks and then simultaneously estimating the entries in
a block by thresholding. The estimator is shown to be optimally rate adaptive
over a wide range of bandable covariance matrices. A simulation study is
carried out and shows that the block thresholding estimator performs well
numerically. Some of the technical tools developed in this paper can also be of
independent interest.


  A non-dissipative model for vortex motion in thin superconductors is
considered. The Lagrangian is a Galilean invariant version of the
Ginzburg--Landau model for time-dependent fields, with kinetic terms linear in
the first time derivatives of the fields. It is shown how, for certain values
of the coupling constants, the field dynamics can be reduced to first order
differential equations for the vortex positions. Two vortices circle around one
another at constant speed and separation in this model.


  Considered herein are the family of nonlinear equations with both dispersive
and dissipative homogeneous terms appended. Solutions of these equations that
start with finite energia decay to zero as time goes to infinity. We present an
asymptotic form which renders explicit the influence of the dissipative,
dispersive and nonlinear effect in this decay. We obtain the second term in the
asymptotic expansion, as time goes to infinity of the solutions of this
equations and the complete asymptotic expansion, as time goes to infinity, of
the linearized equations.


  The recent work on stanene as quantum spin Hall insulators made us
investigate bilayer stanene using first principle calculations. With an aim of
improving and developing new properties, via modulating the stacking order (and
angle) of the bilayers. This stacking of layers has been proven technique for
modulating the properties of monolayer materials. Here we design multiple
bilayer systems, with different stacking angles and AA and AB configurations.
Rather observing an improvement in bandgap due to spin-orbit coupling (SOC), we
witness a splitting of the band due to SOC, a characteristic behavior of
stacked MoS2 sheets. This splitting of the bands gives rise to different,
independent and distinct spin-up and spin-down channels, manifesting a valley
dependent spin polarization. Also, as a contrast to stacked MoS2 system we
notice in our system the stacking angle and order, does effect electronic
states.


  In this note we derive a solution to the Schr\"odinger-type backward equation
which satisfies a necessary boundary condition used in hitting-time problems
[as described in Hern\'andez-del-Valle (2010a)]. We do so by using an idea
introduced by Bluman and Shtelen (1996) which is worked out in
Hern\'andez-del-Valle (2010b). This example is interesting since it is
independent of the parameter $\lambda$, namely: \kappa(s,x)=\frac{x}{\sqrt{2\pi
s}}\exp{-\frac{(x+\int_0^sf'(u))^2}{2s}}. and suggest a procedure to generating
more vanishing solutions and $x=0$.


  An example is constructed of a local ring and a module of finite type and
finite projective dimension over that ring such that the module is not rigid.
This shows that the rigidity conjecture is false.


  We investigate the $O(a)$ improved quark action on anisotropic lattice as a
potential framework for the heavy quark, which may enable precision computation
of hadronic matrix elements of heavy-light mesons. The relativity relations of
heavy-light mesons as well as of heavy quarkonium are examined on a quenched
lattice with spatial lattice cutoff $a_\sigma^{-1} \simeq$ 1.6 GeV and the
anisotropy $\xi=4$. We find that the bare anisotropy parameter tuned for the
massless quark describes both the heavy-heavy and heavy-light mesons within 2%
accuracy for the quark mass $a_\sigma m_Q < 0.8$, which covers the charm quark
mass. This bare anisotropy parameter also successfully describes the
heavy-light mesons in the quark mass region $a_\sigma m_Q \leq 1.2$ within the
same accuracy. Beyond this region, the discretization effects seem to grow
gradually. The anisotropic lattice is expected to extend by a factor $\xi$ the
quark mass region in which the parameters in the action tuned for the massless
limit are applicable for heavy-light systems with well controlled systematic
errors.


  We study a system of equations governing liquid and gas flow in porous media.
The gas phase is homogeneous while the liquid phase is composed of a liquid
component and dissolved gas component. It is assumed that the gas component is
weakly soluble in the liquid. We formulate a weak solution of the
initial-boundary value problem and prove the existence theorem by passing to
the limit in regularizations of the problem. Hypothesis of low solubility is
given precise mathematical meaning.


  Correlations of two protons emitted near midrapidity in p+Pb collisions at
450 GeV/c and S+Pb collisions at 200A GeV/c are presented, as measured by the
NA44 Experiment. The correlation effect, which arises as a result of final
state interactions and Fermi-Dirac statistics, is related to the space-time
characteristics of proton emission. The measured source sizes are smaller than
the size of the target lead nucleus but larger than the sizes of the
projectiles. A dependence on the collision centrality is observed; the source
size increases with decreasing impact parameter. Proton source sizes near
midrapidity appear to be smaller than those of pions in the same interactions.
Quantitative agreement with the results of RQMD (v1.08) simulations is found
for p+Pb collisions. For S+Pb collisions the measured correlation effect is
somewhat weaker than that predicted by the model simulations, implying either a
larger source size or larger contribution of protons from long-lived particle
decays.


  In this paper, we present a generalizable model-free 6-DoF object pose
estimator called Gen6D. Existing generalizable pose estimators either need
high-quality object models or require additional depth maps or object masks in
test time, which significantly limits their application scope. In contrast, our
pose estimator only requires some posed images of the unseen object and is able
to accurately predict the poses of the object in arbitrary environments. Gen6D
consists of an object detector, a viewpoint selector and a pose refiner, all of
which do not require the 3D object model and can generalize to unseen objects.
Experiments show that Gen6D achieves state-of-the-art results on two model-free
datasets: the MOPED dataset and a new GenMOP dataset collected by us. In
addition, on the LINEMOD dataset, Gen6D achieves competitive results compared
with instance-specific pose estimators. Project page:
https://liuyuan-pal.github.io/Gen6D/.


  Comment on T.S. van Erp, S. Cuesta-Lopez, J.-G. Hagmann, and M. Peyrard,
Phys. Rev. Lett. 95, 218104 (2005) [arXiv: physics/0508094].


  This paper reports on our diagrammatic approach to characterize the gauge
dependence of Quantum Electrodynamics in the linear covariant gauge. Our
dimensionally independent technique is purely based on a perturbative analysis
and allows us to construct the full expansion in the gauge~parameter of a
Green's function from its value in a particular gauge (such as the Feynman or
Landau gauge). Further, we clarify the compatiblity of perturbation theory and
the Landau-Khalatnikov-Fradkin transform.


  Proving that a cryptographic protocol is correct for secrecy is a hard task.
One of the strongest strategies to reach this goal is to show that it is
increasing, which means that the security level of every single atomic message
exchanged in the protocol, safely evaluated, never deceases. Recently, two
families of functions have been proposed to measure the security level of
atomic messages. The first one is the family of interpretation-functions. The
second is the family of witness-functions. In this paper, we show that the
witness-functions are more efficient than interpretation-functions. We give a
detailed analysis of an ad-hoc protocol on which the witness-functions succeed
in proving its correctness for secrecy while the interpretation-functions fail
to do so.