  Undisturbed galaxy clusters are characterized by a massive and large
elliptical galaxy at their center, i.e. the Brightest Cluster Galaxy (BCG). How
these central galaxies form is still debated. According to most models, a
typical epoch for their assembly is z~1-2. We have performed a detailed
multi-wavelength analysis of the core of XDCPJ0044.0-2033 (XDCP0044), one of
the most massive and densest galaxy clusters currently known at redshift z~1.6,
whose central galaxy population shows high star formation compared to lower-z
clusters and an X-ray AGN located close to its center. SINFONI J-, H- and KMOS
YJ-, H- bands spectroscopic data have been analyzed, together with deep
archival HST photometric data in F105W, F140W, and F160W bands, Chandra X-ray,
radio JVLA data at 1-2 GHz, and ALMA band-6 observations. In the central region
of the cluster (~70x70 kpc^2), 2 systems of interacting galaxies have been
identified and studied (Complex A and B), with a total of 7 confirmed cluster
members. These galaxies show perturbed morphologies and 3 of them show signs of
AGN activity. In particular, 2 type-1 AGN with typical broad lines have been
found at the center of each complex (both of them X-ray obscured and highly
accreting; Eddington ratio ~0.5), while a type-2 AGN has been discovered in
Complex A. The AGN at the center of Complex B is also detected in X-ray while
the other 2 are spatially related to radio emission. The 3 AGN provide one of
the closest AGN triple at z>1 revealed so far with a minimum(maximum) projected
distance of ~10(40) kpc. The observation of high star formation, merger
signatures and nuclear activity in the core of XDCP0044 suggests that all these
processes are key ingredients in shaping the nascent BCG. According to our
data, XDCP0044 could form a typical massive galaxy of 10^12 Msun, hosting a
Black Hole of 2x10^8-10^9 Msun, in a time scale of the order of ~2.5 Gyrs.


  We show that the generalized Giulietti-Korchm\'aros curve is not a Galois
subcover of the Hermitian curve over $\mathbb{F}_{q^{2n}}$. This answers a
question raised by Garcia, G\"uneri and Stichtenoth.


  We give three constructions of a vertex-minimal triangulation of
$4$-dimensional real projective space $\mathbb{R}P^4$. The first construction
describes a $4$-dimensional sphere on $32$ vertices, which is a double cover of
a triangulated $\mathbb{R}P^4$ and has a large amount of symmetry. The second
and third constructions illustrate approaches to improving the known number of
vertices needed to triangulate $n$-dimensional real projective space. All three
constructions deliver the same combinatorial manifold, which is also the same
as the only known $16$-vertex triangulation of $\mathbb{R}P^4$. We also give a
short, simple construction of the $22$-point Witt design, which is closely
related to the complex we construct.


  Partial differential equations are ubiquitous in almost all applications of
mathematics, where they provide a natural mathematical description of many
phenomena involving change in physical, chemical, biological, and social
processes. The concept of entropy originated in thermodynamics and statistical
physics during the 19th century to describe the heat exchanges that occur in
the thermal processes in a thermodynamic system, while the original notion of
convexity is for sets and functions in mathematics. Since then, entropy and
convexity have become two of the most important concepts in mathematics. In
particular, nonlinear methods via entropy and convexity have been playing an
increasingly important role in the analysis of nonlinear partial differential
equations in recent decades. This opening article of the theme issue is
intended to provide an introduction to entropy, convexity, and related
nonlinear methods for the analysis of nonlinear partial differential equations.
We also provide a brief discussion about the content and contributions of the
papers that make up this theme issue.


  At least one in five of all planetary nebulae are the product of a common
envelope (CE) interaction, where the companion in-spirals into the envelope of
an asymptotic giant branch (AGB) star ejecting the nebula and leaving behind a
compact binary. In this work we carry out 3D smoothed particle hydrodynamics
simulations of the CE interaction between a 1.7 $M_{\odot}$ AGB star and a 0.6
$M_{\odot}$ companion. We model the AGB structure using a 1D stellar model
taken at the seventh thermal pulse. The interaction takes place when the giant
is on the expanding phase of the seventh thermal pulse and has a radius of 250
$R_{\odot}$. The post-CE orbital separations varies between 20 and 31
$R_{\odot}$, with the inclusion of recombination energy resulting in wider
separations. Based on the observed short in-spiral time-scales, we suggest that
thermal pulses can trigger CEs, extending the ability of AGB stars to capture
companions into CEs, that would lead to the prediction of a larger population
of post-AGB, post-CE binaries. Simulations that include a tabulated equation of
state unbind a great deal more gas, likely unbinding the entire envelope on
short time-scales. The shape of the CE after the in-spiral is more spherical
for AGB than red giant branch stars, and even more so if recombination energy
is included. We expect that the planetary nebula formed from this CE will have
different features from those predicted by Zou et al. 2020.


  We propose a supersymmetric extension of the dynamical dark energy function
and the corresponding scalar (super)potential in F(R) supergravity. Our model
is viable in the Einstein approximation, and also has an analytic (regular)
Wess-Zumino-type scalar superpotential. The hidden sector responsible for
spontaneous supersymmetry breaking is given.


  I analyze the density perturbations in a cosmological model with a scalar
field coupled to ordinary matter, such as one obtains in string theory and in
conformally transformed scalar-tensor theories. The spectrum of multipoles on
the last scattering surface and the power spectrum at the present are compared
with observations to derive bounds on the coupling constant and on the
exponential potential slope. It is found that the acoustic peaks and the power
spectrum are strongly sensitive to the model parameters. The models that best
fit the galaxy spectrum and satisfy the cluster abundance test have energy
density $\Omega_{\phi}\simeq 0.1$ and a scale factor expansion law $a\sim
t^{p}, p\simeq 0.68$.


  In static monitoring cameras, useful contextual information can stretch far
beyond the few seconds typical video understanding models might see: subjects
may exhibit similar behavior over multiple days, and background objects remain
static. Due to power and storage constraints, sampling frequencies are low,
often no faster than one frame per second, and sometimes are irregular due to
the use of a motion trigger. In order to perform well in this setting, models
must be robust to irregular sampling rates. In this paper we propose a method
that leverages temporal context from the unlabeled frames of a novel camera to
improve performance at that camera. Specifically, we propose an attention-based
approach that allows our model, Context R-CNN, to index into a long term memory
bank constructed on a per-camera basis and aggregate contextual features from
other frames to boost object detection performance on the current frame.
  We apply Context R-CNN to two settings: (1) species detection using camera
traps, and (2) vehicle detection in traffic cameras, showing in both settings
that Context R-CNN leads to performance gains over strong baselines. Moreover,
we show that increasing the contextual time horizon leads to improved results.
When applied to camera trap data from the Snapshot Serengeti dataset, Context
R-CNN with context from up to a month of images outperforms a single-frame
baseline by 17.9% mAP, and outperforms S3D (a 3d convolution based baseline) by
11.2% mAP.


  The form-factor bootstrap approach is applied to the perturbed minimal models
$M_{2,2n+3}$ in the direction of the primary field $\phi_{1,3}$. These theories
are integrable and contain $n$ massive scalar particles, whose $S$--matrix is
purely elastic. The form-factor equations do not refer to a specific operator.
We use this fact to classify the operator content of these models. We show that
the perturbed models contain the same number of primary fields as the conformal
ones. Explicit solutions are constructed and conjectured to correspond to the
off-critical primary fields $\phi_{1,k}$.


  The Square Kilometre Array is conceived as a telescope which will both test
fundamental physical laws and transform our current picture of the Universe.
However, the scientific challenges outlined in this book are today's
problems--will they still be the outstanding problems that will confront
astronomers in the period 2020 to 2050 and beyond, when the SKA will be in its
most productive years? If history is any example, the excitement of the SKA
will not be in the old questions which are answered, but the new questions that
will be raised by the new types of observations it will permit. The SKA is a
tool for as-yet-unborn users and there is an onus on its designers to allow for
the exploration of the unknown. We outline a philosophy for the design and
operation of the SKA that can lead the radio astronomers in the 21st century to
add to the many discoveries of new phenomena made by radio astronomers in the
20th century.


  Bitcoin as a cryptocurrency has been one of the most important digital coins
and the first decentralized digital currency. Deep neural networks, on the
other hand, has shown promising results recently; however, we require huge
amount of high-quality data to leverage their power. There are some techniques
such as augmentation that can help us with increasing the dataset size, but we
cannot exploit them on historical bitcoin data. As a result, we propose a
shallow Bidirectional-LSTM (Bi-LSTM) model, fed with feature engineered data
using our proposed method to forecast bitcoin closing prices in a daily time
frame. We compare the performance with that of other forecasting methods, and
show that with the help of the proposed feature engineering method, a shallow
deep neural network outperforms other popular price forecasting models.


  We study the effect of quantum statistics on the arrival time distribution of
quantum particles computed through the probability current density. It is shown
that symmetrization or asymmetrization of the wave function affects the arrival
time distribution for even freely propagating particles. In order to
investigate the effect of statistics on the weak equivalence principle in
quantum mechanics (WEQ), we then compute the mean arrival time for wave packets
in free fall. The violation of WEQ through the effect of statistics on the
mass-dependence of the mean arrival time is clearly exhibited. We finally
evaluate the effect of spin on the violation of WEQ using a different approach
by including an explicit spin-dependence in the probability current
distribution, and compare it with the approach using particle statistics. Our
results show WEQ re-emerges smoothly in the limit of large mass.


  When dealing with continuous single-objective problems, multimodality poses
one of the biggest difficulties for global optimization. Local optima are often
preventing algorithms from making progress and thus pose a severe threat. In
this paper we analyze how single-objective optimization can benefit from
multiobjectivization by considering an additional objective. With the use of a
sophisticated visualization technique based on the multi-objective gradients,
the properties of the arising multi-objective landscapes are illustrated and
examined. We will empirically show that the multi-objective optimizer MOGSA is
able to exploit these properties to overcome local traps. The performance of
MOGSA is assessed on a testbed of several functions provided by the COCO
platform. The results are compared to the local optimizer Nelder-Mead.


  We demonstrate the advantages of feedforward loops using a Boolean network,
which is one of the discrete dynamical models for transcriptional regulatory
networks. After comparing the dynamical behaviors of network embedded feedback
and feedforward loops, we found that feedforward loops can provide higher
temporal order (coherence) with lower entropy (randomness) in a temporal
program of gene expression. In addition, complexity of the state space that
increases with longer length of attractors and greater number of attractors is
also reduced for networks with more feedforward loops. Feedback loops show
opposite effects on dynamics of the networks. These results suggest that
feedforward loops are one of the favorable local structures in biomolecular and
neuronal networks.


  The standard neural machine translation model can only decode with the same
depth configuration as training. Restricted by this feature, we have to deploy
models of various sizes to maintain the same translation latency, because the
hardware conditions on different terminal devices (e.g., mobile phones) may
vary greatly. Such individual training leads to increased model maintenance
costs and slower model iterations, especially for the industry. In this work,
we propose to use multi-task learning to train a flexible depth model that can
adapt to different depth configurations during inference. Experimental results
show that our approach can simultaneously support decoding in 24 depth
configurations and is superior to the individual training and another flexible
depth model training method -- LayerDrop.


  Policy gradient (PG) gives rise to a rich class of reinforcement learning
(RL) methods. Recently, there has been an emerging trend to accelerate the
existing PG methods such as REINFORCE by the \emph{variance reduction}
techniques. However, all existing variance-reduced PG methods heavily rely on
an uncheckable importance weight assumption made for every single iteration of
the algorithms. In this paper, a simple gradient truncation mechanism is
proposed to address this issue. Moreover, we design a Truncated Stochastic
Incremental Variance-Reduced Policy Gradient (TSIVR-PG) method, which is able
to maximize not only a cumulative sum of rewards but also a general utility
function over a policy's long-term visiting distribution. We show an
$\tilde{\mathcal{O}}(\epsilon^{-3})$ sample complexity for TSIVR-PG to find an
$\epsilon$-stationary policy. By assuming the overparameterizaiton of policy
and exploiting the hidden convexity of the problem, we further show that
TSIVR-PG converges to global $\epsilon$-optimal policy with
$\tilde{\mathcal{O}}(\epsilon^{-2})$ samples.


  We consider a Prandtl model derived from MHD in the Prandtl-Hartmann regime
that has a damping term due to the effect of the Hartmann boundary layer. A
global-in-time well-posedness is obtained in the Gevrey function space with the
optimal index $2$. The proof is based on a cancellation mechanism through some
auxiliary functions from the study of the Prandtl equation and an observation
about the structure of the loss of one order tangential derivatives through
twice operations of the Prandtl operator


  We describe a sounding technique that allows us to improve spatial resolution
of Irkutsk Incoherent Scatter Radar without loosing spectral resolution. The
technique is based on transmitting of rectangle pulses of different duration in
various sounding runs and subtracting correlation matrixes. Theoretically and
experimentally we have shown, that subtraction of the mean-square parameters of
the scattered signal for different kinds of the sounding signal one from
another allows us to solve the problem within the framework of quasi-static
ionospheric parameters approximation.


  In high-power applications, multiple power MOSFETs are connected in parallel
and treated as a single switch in order to handle much larger total currents.
In this paper, a parallel power MOSFETs model from the turnoff state until they
reach their steady state is introduced. The model represents the relationship
between each power MOSFET's gate voltage and the current distribution among
them. The study's key purpose is to use the model for dealing with the
asymmetry in sharing current and power loss between these semiconductor devices
during the steady state region.


  We consider a Frobenius structure associated with the dispersionless
Kadomtsev-Petviashvili equation. This is done, essentially, by applying a
continuous analogue of the finite dimensional theory in the space of Schwartz
functions on the line. The potential of the Frobenius manifold is found to be a
logarithmic potential with quadratic external field. Following the construction
of the principal hierarchy, we construct a set of infinitely many commuting
flows, which extends the classical dKP hierarchy.


  SARS-CoV-2 has presented direct and indirect challenges to the scientific
community. One of the most prominent indirect challenges advents from the
mandatory use of face masks in a large number of countries. Face recognition
methods struggle to perform identity verification with similar accuracy on
masked and unmasked individuals. It has been shown that the performance of
these methods drops considerably in the presence of face masks, especially if
the reference image is unmasked. We propose FocusFace, a multi-task
architecture that uses contrastive learning to be able to accurately perform
masked face recognition. The proposed architecture is designed to be trained
from scratch or to work on top of state-of-the-art face recognition methods
without sacrificing the capabilities of a existing models in conventional face
recognition tasks. We also explore different approaches to design the
contrastive learning module. Results are presented in terms of masked-masked
(M-M) and unmasked-masked (U-M) face verification performance. For both
settings, the results are on par with published methods, but for M-M
specifically, the proposed method was able to outperform all the solutions that
it was compared to. We further show that when using our method on top of
already existing methods the training computational costs decrease
significantly while retaining similar performances. The implementation and the
trained models are available at GitHub.


  We study the dynamics of a collection of families of transcendental entire
functions which generalises the well-known exponential and cosine families. We
show that for functions in many of these families the Julia set, the escaping
set and the fast escaping set are all spiders' webs of positive area. This
result is unusual in that most of these functions lie outside the
Eremenko-Lyubich class B. This is also the first result on the area of a
spider's web.


  We study thermodynamic formalism for the family of robustly transitive
diffeomorphisms introduced by Ma\~n\'e, establishing existence and uniqueness
of equilibrium states for natural classes of potential functions. In
particular, we characterize the SRB measures for these diffeomorphisms as
unique equilibrium states for a suitable geometric potential. We also obtain
large deviations and multifractal results for the unique equilibrium states
produced by the main theorem.


  Consider a finite morphism f:X -> Y of smooth projective varieties over a
finite field k. Suppose X is the vanishing locus in projective N-space of at
most r forms of degree at most d. We show there is a constant C, depending only
on N, r, d and deg(f) such that if #k > C, then f(k):X(k) -> Y(k) is injective
if and only if it's surjective.


  We show that the space of metrics of positive scalar curvature on any
3-manifold is either empty or contractible. Second, we show that the
diffeomorphism group of every 3-dimensional spherical space form deformation
retracts to its isometry group. This proves the Generalized Smale Conjecture.
Our argument is independent of Hatcher's theorem in the $S^3$ case and in
particular it gives a new proof of the $S^3$ case.


  We study the color structure of disk galaxies in the Groth strip at redshifts
0.1<z<1.2. Our aim is to test formation models in which bulges form
before/after the disk. We find smooth color distributions with gentle outward
blueing across the galaxy image: bulges are not distinctly redder than their
disks; and bulge colors strongly correlate with global colors. The results
suggest a roughly coeval evolution of bulges and disks. About 50% of the nuclei
of galaxies with central light excesses above the outer exponential profile
hold passively evolving red populations. The remainder 50% are galaxies with
central blue colors similar to their disks. They may be bulges in formation, or
the central parts of disks with non-exponential surface brightness profiles.


  We begin with a prior observation by one of us that Thomas precession in the
nonrelativistic limit of the Dirac equation may be attributed to a nonabelian
Berry vector potential. We ask what object produces the nonabelian potential in
parameter space, in the same sense that the abelian vector potential arising in
the adiabatic transport of a nondegenerate level is produced by a monopole,
(centered at the point where the level becomes degenerate with another), as
shown by Berry. We find that it is a {\em meron}, an object in four euclidean
dimensions with instanton number ${1 \over 2}$, centered at the point where the
doubly degenerate positive and negative energy levels of the Dirac equation
become fourfold degenerate.


  In this work, we study the distortion of the exterior conformal modulus of a
symmetric quadrilateral, when stretched in the direction of the abscissa axis
with the coefficient $H\to \infty$. By using some facts from the theory of
elliptic integrals, we confirm that the asymptotic behavior of this modulus
does not depend on the shape of the boundary of the quadrilateral; moreover, it
is equivalent to $(1/\pi)\log H$ as $H\to \infty$.


  The implementation of the dynamics in Loop Quantum Gravity (LQG) is still an
open problem. Here, we discuss a tentative dynamics for the simplest class of
graphs in LQG: Two vertices linked with an arbitrary number of edges. We use
the recently introduced U(N) framework in order to construct SU(2) invariant
operators and define a global U(N) symmetry that will select the
homogeneous/isotropic states. Finally, we propose a Hamiltonian operator
invariant under area-preserving deformations of the boundary surface and we
identify possible connections of this model with Loop Quantum Cosmology.


  We discuss dark energy, dark matter and the hierarchy problem in the context
of a general non-commutative formulation of string theory. In this framework
dark energy is generated by the dynamical geometry of the dual spacetime while
dark matter, on the other hand, comes from the degrees of freedom dual to the
visible matter. This formulation of string theory is sensitive both to the IR
and UV scales and the Higgs scale is radiatively stable by being a geometric
mean of radiatively stable UV and IR scales. We also comment on various
phenomenological signatures of this novel approach to dark energy, dark matter
and the hierarchy problem. We find that this new view on the hierarchy problem
is realized in a toy model based on a non-holomorphic deformation of the
stringy cosmic string. Finally, we discuss a proposal for a new
non-perturbative formulation of string theory, which sheds light on M theory
and F theory, as well as on supersymmetry and holography.


  The PICOSEC Micromegas (MM) detector is a precise timing gaseous detector
based on a MM detector operating in a two-stage amplification mode and a
Cherenkov radiator. Prototypes equipped with cesium iodide (CsI) photocathodes
have shown promising time resolutions as precise as 24 picoseconds (ps) for
Minimum Ionizing Particles. However, due to the high hygroscopicity and
susceptibility to ion bombardment of the CsI photocathodes, alternative
photocathode materials are needed to improve the robustness of PICOSEC MM.
Diamond-like Carbon (DLC) film have been introduced as a novel robust
photocathode material, which have shown promising results. A batch of DLC
photocathodes with different thicknesses were produced and evaluated using
ultraviolet light. The quantum efficiency measurements indicate that the
optimized thickness of the DLC photocathode is approximately 3 nm. Furthermore,
DLC photocathodes show good resistance to ion bombardment in aging test
compared to the CsI photocathode. Finally, a PICOSEC MM prototype equipped with
DLC photocathodes was tested in muon beams. A time resolution of around 42 ps
with a detection efficiency of 97% for 150 GeV/c muons were obtained. These
results indicate the great potential of DLC as a photocathode for the PICOSEC
MM detector.


  The aim of the steganography methods is to communicate securely in a
completely undetectable manner. LSB Matching and LSB Matching Revisited
steganography methods are two general and esiest methods to achieve this aim.
Being secured against first order steganalysis methods is the most important
feature of these methods. On the other hand, these methods don't consider inter
pixel dependency. Therefore, recently, several steganalysis methods are
proposed that by using co-occurrence matrix detect stego images that are hidden
by these steganography methods. Therefore, if incremental and decremental
operations are done adaptively as causes to less distortion on co-occurrence
matrix, these steganography methods will secure against steganalysis methods
that use this matrix. In this paper we are going to improve these two
steganography methods base on mentioned manner. On the other word, we hide the
message in the cover image based on LSB Matching and LSB Matching Revisited
method by using adaptive feature. Experimental results show that proposed
improvement causes to reduce distortions in co-occurrence matrix and these
methods being secure against some steganalysis methods that use this matrix to
detect stego images


  The Cooper pair box qubit of SQUID configuration enables the readout of the
qubit states by probing the effective Josephson inductance of the SQUID. This
is realized by coupling the qubit to a tank circuit which induces a small
alternating supercurrent in the SQUID loop. The effect of a small (but finite)
geometrical inductance of the loop on the eigenstates of the system is figured
out. The effect of qubit dephasing due to quadratic coupling to the tank
circuit is evaluated. It is shown that the rate of dephasing in the vicinity of
the magic points is relatively low unless the Josephson junctions forming the
qubit are rather dissimilar. In the vicinity of the avoided level-crossing
point such dephasing is always significant.


  Vector-symbolic architectures (VSAs) provide methods for computing which are
highly flexible and carry unique advantages. Concepts in VSAs are represented
by 'symbols,' long vectors of values which utilize properties of
high-dimensional spaces to represent and manipulate information. In this new
work, we combine efficiency of the operations provided within the framework of
the Fourier Holographic Reduced Representation (FHRR) VSA with the power of
deep networks to construct novel VSA based residual and attention-based neural
network architectures. Using an attentional FHRR architecture, we demonstrate
that the same network architecture can address problems from different domains
(image classification and molecular toxicity prediction) by encoding different
information into the network's inputs, similar to the Perceiver model. This
demonstrates a novel application of VSAs and a potential path to implementing
state-of-the-art neural models on neuromorphic hardware.


  Inspired by the similarity of mass gaps of $J/\psi$ and $\Upsilon$ families,
the prediction of missing higher charmonium with mass $4263$ MeV and very
narrow width is made. In addition, the properties of two charmonium-like
states, $X(3940)$ and $X(4160)$, and charmonium $\psi(4415)$ are discussed.
Here, $X(3940)$ as $\eta_c(3S)$ is established while the explanation of
$X(4160)$ to be $\eta_c(4S)$ is fully excluded and $\eta_c(4S)$ is typically a
very narrow state. These predictions can be accessible at BESIII, Belle and
BelleII in near future.


  PDE solutions are numerically represented by basis functions. Classical
methods employ pre-defined bases that encode minimum desired PDE properties,
which naturally cause redundant computations. What are the best bases to
numerically represent PDE solutions? From the analytical perspective, the
Kolmogorov $n$-width is a popular criterion for selecting representative basis
functions. From the Bayesian computation perspective, the concept of optimality
selects the modes that, when known, minimize the variance of the conditional
distribution of the rest of the solution. We show that these two definitions of
optimality are equivalent. Numerically, both criteria reduce to solving a
Singular Value Decomposition (SVD), a procedure that can be made numerically
efficient through randomized sampling. We demonstrate computationally the
effectiveness of the basis functions so obtained on several linear and
nonlinear problems. In all cases, the optimal accuracy is achieved with a small
set of basis functions.


  We study a unified mechanism for spin-density-wave (SDW) and
superconductivity in a minimal model, in which itinerant electrons and local
moments coexist as previously proposed for the iron pnictides [EPL, 88, 17010
(2009)]. The phase diagram obtained at the mean field level is in qualitative
agreement with the experiment, which shows how the magnetic and superconducting
(SC) instabilities are driven by the critial coupling between the
itinerant/localized electrons. The spin and charge response functions at the
random phase approximation (RPA) level further characterize the dynamical
evolution of the system. In particular, the dynamic spin susceptibility
displays a Goldstone mode in the SDW phase, which evolves into a gapped
resonance-like mode in the superconducting phase. The latter persists all the
way into the normal state above Tc, where a strong scattering between the
itinerant electrons and local moments is restored, as an essential feature of
the model.


  We investigate the acceleration and simultaneous radiative losses of
electrons in the vicinity of relativistic shocks. Particles undergo pitch angle
diffusion, gaining energy as they cross the shock by the Fermi mechanism and
also emitting synchrotron radiation in the ambient magnetic field. A
semi-analytic approach is developed which allows us to consider the behaviour
of the shape of the spectral cut-off and the variation of that cut-off with the
particle pitch angle. The implications for the synchrotron emission of
relativistic jets, such as those in gamma ray burst sources and blazars, are
discussed.


  In recurrent neural networks, learning long-term dependency is the main
difficulty due to the vanishing and exploding gradient problem. Many
researchers are dedicated to solving this issue and they proposed many
algorithms. Although these algorithms have achieved great success,
understanding how the information decays remains an open problem. In this
paper, we study the dynamics of the hidden state in recurrent neural networks.
We propose a new perspective to analyze the hidden state space based on an
eigen decomposition of the weight matrix. We start the analysis by linear state
space model and explain the function of preserving information in activation
functions. We provide an explanation for long-term dependency based on the
eigen analysis. We also point out the different behavior of eigenvalues for
regression tasks and classification tasks. From the observations on
well-trained recurrent neural networks, we proposed a new initialization method
for recurrent neural networks, which improves consistently performance. It can
be applied to vanilla-RNN, LSTM, and GRU. We test on many datasets, such as
Tomita Grammars, pixel-by-pixel MNIST datasets, and machine translation
datasets (Multi30k). It outperforms the Xavier initializer and kaiming
initializer as well as other RNN-only initializers like IRNN and sp-RNN in
several tasks.


  We construct the irreducible unipotent modules of the finite general linear
groups using tableaux. Our construction is analogous to that of James (1976)
for the symmetric groups, answering an open question as to whether such a
construction exists. Our modules are defined over any field containing a
nontrivial $p^\text{th}$ root of unity (where $p$ is the defining
characteristic of the group). We show that our modules are isomorphic to those
constructed by James (1984), although the two constructions utilize quite
different approaches. Finally we look closer at the complex irreducible
unipotent modules, providing motivation for our construction.


  This paper investigates the Harnack inequality for nonnegative solutions to
second-order parabolic equations in double divergence form. We impose
conditions where the principal coefficients satisfy the Dini mean oscillation
condition in $x$, while the drift and zeroth-order coefficients belong to
specific Morrey classes. Our analysis contributes to advancing the theoretical
foundations of parabolic equations in double divergence form, including
Fokker-Planck-Kolmogorov equations for probability densities.


  Digital soil mapping (DSM) is an advanced approach that integrates
statistical modeling and cutting-edge technologies, including machine learning
(ML) methods, to accurately depict soil properties and their spatial
distribution. Soil organic carbon (SOC) is a crucial soil attribute providing
valuable insights into soil health, nutrient cycling, greenhouse gas emissions,
and overall ecosystem productivity. This study highlights the significance of
spatial-temporal deep learning (DL) techniques within the DSM framework. A
novel architecture is proposed, incorporating spatial information using a base
convolutional neural network (CNN) model and spatial attention mechanism, along
with climate temporal information using a long short-term memory (LSTM)
network, for SOC prediction across Europe. The model utilizes a comprehensive
set of environmental features, including Landsat-8 images, topography, remote
sensing indices, and climate time series, as input features. Results
demonstrate that the proposed framework outperforms conventional ML approaches
like random forest commonly used in DSM, yielding lower root mean square error
(RMSE). This model is a robust tool for predicting SOC and could be applied to
other soil properties, thereby contributing to the advancement of DSM
techniques and facilitating land management and decision-making processes based
on accurate information.


  A sunflower with $r$ petals is a collection of $r$ sets over a ground set $X$
such that every element in $X$ is in no set, every set, or exactly one set.
Erd\H{o}s and Rado \cite{er} showed that a family of sets of size $n$ contains
a sunflower if there are more than $n!(r-1)^n$ sets in the family. Alweiss et
al. \cite{alwz} and subsequently Rao~\cite{rao} and Bell et al.~\cite{bcw}
improved this bound to $(O(r \log(n))^n$.
  We study the case where the pairwise intersections of the set family are
restricted. In particular, we improve the best-known bound for set families
when the size of the pairwise intersections of any two sets is in a set $L$. We
also present a new bound for the special case when the set $L$ is the
nonnegative integers less than or equal to $d$ using the techniques of Alweiss
et al. \cite{alwz}.


  Understanding the health impacts of air pollution is vital in public health
research. Numerous studies have estimated negative health effects of a variety
of pollutants, but accurately gauging these impacts remains challenging due to
the potential for unmeasured confounding bias that is ubiquitous in
observational studies. In this study, we develop a framework for sensitivity
analysis in settings with both multiple treatments and multiple outcomes
simultaneously. This setting is of particular interest because one can identify
the strength of association between the unmeasured confounders and both the
treatment and outcome, under a factor confounding assumption. This provides
informative bounds on the causal effect leading to partial identification
regions for the effects of multivariate treatments that account for the maximum
possible bias from unmeasured confounding. We also show that when negative
controls are available, we are able to refine the partial identification
regions substantially, and in certain cases, even identify the causal effect in
the presence of unmeasured confounding. We derive partial identification
regions for general estimands in this setting, and develop a novel
computational approach to finding these regions.


  Collective cell migration plays an essential role in vertebrate development,
yet the extent to which dynamically changing microenvironments influence this
phenomenon remains unclear. Observations of the distribution of the
extracellular matrix (ECM) component fibronectin during the migration of
loosely connected neural crest cells (NCCs) lead us to hypothesize that NCC
remodeling of an initially punctate ECM creates a scaffold for trailing cells,
enabling them to form robust and coherent stream patterns. We evaluate this
idea in a theoretical setting by developing an individual-based computational
model that incorporates reciprocal interactions between NCCs and their ECM. ECM
remodeling, haptotaxis, contact guidance, and cell-cell repulsion are
sufficient for cells to establish streams in silico, however additional
mechanisms, such as chemotaxis, are required to consistently guide cells along
the correct target corridor. Further model investigations imply that contact
guidance and differential cell-cell repulsion between leader and follower cells
are key contributors to robust collective cell migration by preventing stream
breakage. Global sensitivity analysis and simulated gain- and loss-of-function
experiments suggest that long-distance migration without jamming is most likely
to occur when leading cells specialize in creating ECM fibers, and trailing
cells specialize in responding to environmental cues by upregulating mechanisms
such as contact guidance.


  We put together the results of XMM-Newton observations of a number of
representative group and cluster samples at low and high redshifts. These
results confirm the entropy ramp as an explanation of the observed scaling
relations. We observe a mild evolution in the entropy of clusters. The observed
degree of evolution is consistent with expectations of the shock heating at a
fixed overdensity (500) with respect to the critical density in LCDM. The study
of the evolution in the pressure scaling imposes strong requirements in the
definition of the average temperature of the cluster. The scaling temperature
should be consistent to better than the 10% level. Once such a consistency is
achieved, no additional evolution in the pressure has been detected in addition
to the prediction of the shock heating in the LCDM Universe.


  Motivated by a scarcity of simple and analytically tractable models of
superconductivity from strong repulsive interactions, we introduce a simple
tight-binding lattice model of fermions with repulsive interactions that
exhibits unconventional superconductivity (beyond BCS theory). The model
resembles an idealized conductor-dielectric-conductor trilayer. The Cooper pair
consists of electrons on opposite sides of the dielectric, which mediates the
attraction. In the strong coupling limit, we use degenerate perturbation theory
to show that the model reduces to a superconducting hard-core Bose-Hubbard
model. Above the superconducting critical temperature, an analog of pseudo-gap
physics results where the fermions remain Cooper paired with a large
single-particle energy gap.


  We show that if $A$ and $H$ are Hopf algebras that have equivalent tensor
categories of comodules, then one can transport what we call a free
Yetter-Drinfeld resolution of the counit of $A$ to the same kind of resolution
for the counit of $H$, exhibiting in this way strong links between the
Hochschild homologies of $A$ and $H$. This enables us to get a finite free
resolution of the counit of $\mathcal B(E)$, the Hopf algebra of the bilinear
form associated to an invertible matrix $E$, generalizing an ealier
construction of Collins, Hartel and Thom in the orthogonal case $E=I_n$. It
follows that $\B(E)$ is smooth of dimension 3 and satisfies Poincar\'e duality.
Combining this with results of Vergnioux, it also follows that when $E$ is an
antisymetric matrix, the $L^2$-Betti numbers of the associated discrete quantum
group all vanish. We also use our resolution to compute the bialgebra
cohomology of $\B(E)$ in the cosemisimple case.


  We study the kinetic roughening of the single-step (SS) growth model with a
tunable parameter $p$ in $1+1$ and $2+1$ dimensions by performing extensive
numerical simulations. We show that there exists a very slow crossover from an
intermediate regime dominated by the Edwards-Wilkinson class to an asymptotic
regime dominated by the Kardar-Parisi-Zhang (KPZ) class for any $p
<\frac{1}{2}$. We also identify the crossover time, the nonlinear coupling
constant, and some nonuniversal parameters in the KPZ equation as a function
$p$. The effective nonuniversal parameters are continuously decreasing with
$p$, but not in a linear fashion. Our results provide complete and conclusive
evidence that the SS model for $p \neq \frac{1}{2}$ belongs to the KPZ
universality class in $2+1$ dimensions.


  An evolving problem in the field of spatial and ecological statistics is that
of preferential sampling, where biases may be present due to a relationship
between sample data locations and a response of interest. This field of
research bears a striking resemblance to the longstanding problem of
informative sampling within survey methodology, although with some important
distinctions. With the goal of promoting collaborative effort within and
between these two problem domains, we make comparisons and contrasts between
the two problem statements. Specifically, we review many of the solutions
available to address each of these problems, noting the important differences
in modeling techniques. Additionally, we construct a series of simulation
studies to examine some of the methods available for preferential sampling, as
well as a comparison analyzing heavy metal biomonitoring data.


  In this era of Big Data, due to expeditious exchange of information on the
web, words are being used to denote newer meanings, causing linguistic shift.
With the recent availability of large amounts of digitized texts, an automated
analysis of the evolution of language has become possible. Our study mainly
focuses on improving the detection of new word senses. This paper presents a
unique proposal based on network features to improve the precision of new word
sense detection. For a candidate word where a new sense (birth) has been
detected by comparing the sense clusters induced at two different time points,
we further compare the network properties of the subgraphs induced from novel
sense cluster across these two time points. Using the mean fractional change in
edge density, structural similarity and average path length as features in an
SVM classifier, manual evaluation gives precision values of 0.86 and 0.74 for
the task of new sense detection, when tested on 2 distinct time-point pairs, in
comparison to the precision values in the range of 0.23-0.32, when the proposed
scheme is not used. The outlined method can therefore be used as a new post-hoc
step to improve the precision of novel word sense detection in a robust and
reliable way where the underlying framework uses a graph structure. Another
important observation is that even though our proposal is a post-hoc step, it
can be used in isolation and that itself results in a very decent performance
achieving a precision of 0.54-0.62. Finally, we show that our method is able to
detect the well-known historical shifts in 80% cases.


  We study the non-abelian extension for the splitting of a scalar field into
chiral components. Using this procedure we find a non ambiguous way of coupling
a non abelian chiral scalar field to gravity. We start with a (non-chiral) WZW
model covariantly coupled to a background metric and, after the splitting,
arrive at two chiral Wess-Zumino-Witten (WZW) models coupled to gravity.


  Hot scalar electrodynamics is adopted as a toy model for a hot gluon plasma
to display some aspects of the compulsory resummation of hard thermal loops
when next-to-leading order quantities at soft momentum scales are to be
calculated. [Talk given by A.K.R. at a one-day meeting dedicated to the memory
of Tanguy ALTHERR, held on November 4, 1994 at CERN, Geneva. To appear in a
Gedenkschrift published by World Scientific.]


  Monolayer transition metal dichalcogenides (TMDs) with strong spin-orbit
coupling combined with broken inversion symmetry, leading to a coupling of spin
and valley degrees of freedom, make these materials highly interesting for
potential spintronics and valleytronic applications. However, engineering the
spin-orbit coupling (SOC) at room temperature as demand after device
fabrication is still a great challenge for their practical applications. Here
we reversibly engineer the spin-orbit coupling of monolayer MoS2 by laser
irradiation under controlled gas environments, where the spin-orbit splitting
has been effectively regulated within 120 meV to 200 meV. Furthermore, the
photoluminescence (PL) intensity of B exciton can be invertible manipulation
over 2 orders of magnitude. We attribute the engineering of spin-orbit
splitting to the reduction of binding energy combined with band
renormalization, originating from the enhanced absorption coefficient of
monolayer MoS2 under inert gases and subsequent the significantly boosted
carrier concentrations. Reflectance contrast spectra during the engineering
stage provide unambiguous proof to support our interpretation. Our approach
offers a new avenue to actively control the SOC strength in TMDs materials at
room temperature and paves the way for designing innovative spintronics
devices.


  We present a detailed examination on the coronal nonthermal emissions during
the preflare phase of the X4.8 flare that occurred on 2002 July 23. The
microwave (17 GHz and 34 GHz) data obtained with Nobeyama Radioheliograph, at
Nobeyama Solar Radio Observatory and the hard X-ray (HXR) data taken with {\it
Reuven Ramaty High Energy Solar Spectroscopic Imager} obviously showed
nonthermal sources that are located above the flare loops during the preflare
phase. We performed imaging spectroscopic analyses on the nonthermal emission
sources both in microwaves and in HXRs, and confirmed that electrons are
accelerated from several tens of keV to more than 1 MeV even in this phase. If
we assume the thin-target model for the HXR emission source, the derived
electron spectral indices ($\sim 4.7$) is the same value as that from
microwaves ($\sim 4.7$) within the observational uncertainties, which implies
that the distribution of the accelerated electrons follows a single power-law.
The number density of the microwave-emitting electrons is, however, larger than
that of the HXR-emitting electrons, unless we assume low ambient plasma density
of about $1.0 \times 10^9$ cm$^{-3}$ for the HXR-emitting region. If we adopt
the thick-target model for the HXR emission source, on the other hand, the
electron spectral index ($\sim 6.7$) is much different, while the gap of the
number density of the accelerated electrons is somewhat reduced.


  Experiments often yield non-identically distributed data for statistical
analysis. Tests of hypothesis under such set-ups are generally performed using
the likelihood ratio test, which is non-robust with respect to outliers and
model misspecification. In this paper, we consider the set-up of
non-identically but independently distributed observations and develop a
general class of test statistics for testing parametric hypothesis based on the
density power divergence. The proposed tests have bounded influence functions,
are highly robust with respect to data contamination, have high power against
contiguous alternatives, and are consistent at any fixed alternative. The
methodology is illustrated by the simple and generalized linear regression
models with fixed covariates.


  The hypergraph states are pure multipartite quantum states corresponding to a
hypergraph. It is an equal superposition of the states belonging to the
computational basis. Given any hypergraph, we can construct a hypergraph state
determined by a Boolean function. In contrast, we can find a hypergraph,
corresponding to a Boolean function. This investigation develops a number of
combinatorial structures concerned with the hypergraph states. For instance,
the elements of the computational basis generate a lattice. The chains and
antichains in this lattice assist us to find the equation of the Boolean
function explicitly as well as to find a hypergraph. In addition, we
investigate the entanglement property of the hypergraph states in terms of
their combinatorial structures. We demonstrate several classes of hypergraphs,
such that every cut of equal length on the corresponding hypergraph states has
an equal amount of entanglement.


  This paper first reviews the reversible data hiding scheme, of Liu et al. in
2018, for JPEG images. After that, a novel reversible data hiding scheme, in
which modification directions of partial nonzero quantized alternating current
(AC) coefficients are utilized to decrease distortion and file size increase
caused by data hiding, is proposed. Experimental results have shown that the
proposed scheme has indeed advantages in visual quality and smaller increase in
file size of marked JPEG images while compared to the state-of-the-art scheme
with the same embedding payload so far.


  We introduce the use of deep learning ensembles for real-time, gravitational
wave detection of spinning binary black hole mergers. This analysis consists of
training independent neural networks that simultaneously process strain data
from multiple detectors. The output of these networks is then combined and
processed to identify significant noise triggers. We have applied this
methodology in O2 and O3 data finding that deep learning ensembles clearly
identify binary black hole mergers in open source data available at the
Gravitational-Wave Open Science Center. We have also benchmarked the
performance of this new methodology by processing 200 hours of open source,
advanced LIGO noise from August 2017. Our findings indicate that our approach
identifies real gravitational wave sources in advanced LIGO data with a false
positive rate of 1 misclassification for every 2.7 days of searched data. A
follow up of these misclassifications identified them as glitches. Our deep
learning ensemble represents the first class of neural network classifiers that
are trained with millions of modeled waveforms that describe quasi-circular,
spinning, non-precessing, binary black hole mergers. Once fully trained, our
deep learning ensemble processes advanced LIGO strain data faster than
real-time using 4 NVIDIA V100 GPUs.


  The Homeomorphic Embedding relation has been amply used for defining
termination criteria of symbolic methods for program analysis, transformation,
and verification. However, homeomorphic embedding has never been investigated
in the context of order-sorted rewrite theories that support symbolic execution
methods modulo equational axioms. This paper generalizes the symbolic
homeomorphic embedding relation to order-sorted rewrite theories that may
contain various combinations of associativity and/or commutativity axioms for
different binary operators. We systematically measure the performance of
increasingly efficient formulations of the homeomorphic embedding relation
modulo associativity and commutativity axioms. From our experimental results,
we conclude that our most efficient version indeed pays off in practice.


  We consider Bayesian linear regression with sparsity-inducing prior and
design efficient sampling algorithms leveraging posterior contraction
properties. A quasi-likelihood with Gaussian spike-and-slab (that is favorable
both statistically and computationally) is investigated and two algorithms
based on Gibbs sampling and Stochastic Localization are analyzed, both under
the same (quite natural) statistical assumptions that also enable valid
inference on the sparse planted signal. The benefit of the Stochastic
Localization sampler is particularly prominent for data matrix that is not
well-designed.


  The quantum spin liquid material herbertsmithite is described by an
antiferromagnetic Heisenberg model on the kagome lattice with non-negligible
Dzyaloshinskii-Moriya interaction~(DMI). A well established phase transition to
the $\mathbf q=0$ long-range order occurs in this model when the DMI strength
increases, but the precise nature of a small-DMI phase remains controversial.
Here, we describe a new phase obtained from Schwinger-boson mean-field theory
that is stable at small DMI, and which can explain the dispersionless spectrum
seen in inelastic neutron scattering experiment by Han et al (Nature (London)
492, 406 (2012)}). It is a time-reversal symmetry breaking $\mathbb Z_2$ spin
liquid, with the unique property of a small and constant spin gap in an
extended region of the Brillouin zone. The phase diagram as a function of DMI
and spin size is given, and dynamical spin structure factors are presented.


  In representation learning (RL), how to make the learned representations easy
to interpret and less overfitted to training data are two important but
challenging issues. To address these problems, we study a new type of
regulariza- tion approach that encourages the supports of weight vectors in RL
models to have small overlap, by simultaneously promoting near-orthogonality
among vectors and sparsity of each vector. We apply the proposed regularizer to
two models: neural networks (NNs) and sparse coding (SC), and develop an
efficient ADMM-based algorithm for regu- larized SC. Experiments on various
datasets demonstrate that weight vectors learned under our regularizer are more
interpretable and have better generalization performance.


  We present a data definition framework that enables the convenient
specification of data types in ACL2s, the ACL2 Sedan. Our primary motivation
for developing the data definition framework was pedagogical. We were teaching
undergraduate students how to reason about programs using ACL2s and wanted to
provide them with an effective method for defining, testing, and reasoning
about data types in the context of an untyped theorem prover. Our framework is
now routinely used not only for pedagogical purposes, but also by advanced
users.
  Our framework concisely supports common data definition patterns, e.g. list
types, map types, and record types. It also provides support for polymorphic
functions. A distinguishing feature of our approach is that we maintain both a
predicative and an enumerative characterization of data definitions.
  In this paper we present our data definition framework via a sequence of
examples. We give a complete characterization in terms of tau rules of the
inclusion/exclusion relations a data definition induces, under suitable
restrictions. The data definition framework is a key component of
counterexample generation support in ACL2s, but can be independently used in
ACL2, and is available as a community book.


  Quantum computation requires coherently controlling the evolutions of qubits.
Usually, these manipulations are implemented by precisely designing the
durations (such as the $\pi$-pulses) of the Rabi oscillations and tunable
interbit coupling. Relaxing this requirement, here we show that the desired
population transfers between the logic states can be deterministically realized
(and thus quantum computation could be implemented) both adiabatically and
non-adiabatically, by performing the duration-insensitive quantum
manipulations. Our proposal is specifically demonstrated with the surface-state
of electrons floating on the liquid helium, but could also be applied to the
other artificially controllable systems for quantum computing.


  We introduce an algebraic version of the Katsura $C^*$-algebra of a pair
$A,B$ of integer matrices and an algebraic version of the Exel-Pardo
$C^*$-algebra of a self-similar action on a graph. We prove a Graded Uniqueness
Theorem for such algebras and construct a homomorphism of the latter into a
Steinberg algebra that, under mild conditions, is an isomorphism. Working with
Steinberg algebras over non-Hausdorff groupoids we prove that in the unital
case, our algebraic version of Katsura $C^*$-algebras are all isomorphic to
Steinberg algebras.


  The master equation for the reduced density matrix of a charged particle
interacting with a translation invariant weakly coupled environment is
considered. The electric current is renormalized by the system-environment
interaction, leading to a direct signature of the environment in the
bremsstrahlung. The general solution is given in the absence of the external
electromagnetic field and the spread and the decoherence of a wave packet are
followed. The increased complexity and importance of the boundary conditions
for the density matrix are pointed out.


  Modern Terrestrial Cerenkov Telescopes and Array Scintillators facing the
Horizons may soon reveal far Cosmic Rays or nearer PeVs-EeVs Neutrino Showers
Astronomy. Indeed UHE neutrino interactions in air, leading to Horizontal
Showers, may take place through several channels: the main Glashow resonant
one, the charged nuclear interactions and the neutral current events. Analogous
events occur also for the neutrino-nucleon events.
  These interactions are producing hadronic or electromagnetic showers at the
far horizons and their correlated secondaries Cerenkov flashes. Comparable
interactions are producing, inside the Earth, the Horizontal, but Up-going
ultra-relativistic tau, whose decay in flight is source of tau Air Showers
(Uptaus and HorTaus); Horizontal Tau Air-Showers are rarely (one-two order of
magnitude) enhanced by highest mountain chains at horizons, as in AUGER
experimental site; their hadronic or electromagnetic traces are preferentially
at PeV-EeV energies; their tracks are amplified by their muon-gamma bundles
whose signals are above the random noises and better disentangled by Cerenkov
flashes in time coincidence. More exotic UHE SUSY interactions at tens PeVs-EeV
energy may blaze at Horizons. Anyway common High Energy Cosmic rays at
PeVs-EeVs energy must traces their presence in Magic-like Cerenkov Telescopes
at horizons. Present Magic Telescopes facing the Horizons are, at equal given
time, almost comparable with the Amanda underground neutrino detector.


  In this paper we formally analyse the use of sparse filtering algorithms to
perform covariate shift adaptation. We provide a theoretical analysis of sparse
filtering by evaluating the conditions required to perform covariate shift
adaptation. We prove that sparse filtering can perform adaptation only if the
conditional distribution of the labels has a structure explained by a cosine
metric. To overcome this limitation, we propose a new algorithm, named periodic
sparse filtering, and carry out the same theoretical analysis regarding
covariate shift adaptation. We show that periodic sparse filtering can perform
adaptation under the looser and more realistic requirement that the conditional
distribution of the labels has a periodic structure, which may be satisfied,
for instance, by user-dependent data sets. We experimentally validate our
theoretical results on synthetic data. Moreover, we apply periodic sparse
filtering to real-world data sets to demonstrate that this simple and
computationally efficient algorithm is able to achieve competitive
performances.


  Labelled tableaux have been a traditional approach to define satisfiability
checking procedures for Modal Logics. In many cases, they can also be used to
obtained tight complexity bounds and lead to efficient implementations of
reasoning tools. More recently, it has been shown that the expressive power
provided by the operators characterizing Hybrid Logics (nominals and
satisfiability modalities) can be used to internalize labels, leading to
well-behaved inference procedures for fairly expressive logics. The resulting
procedures are attractive because they do not use external mechanisms outside
the language of the logic at hand, and have good logical and computational
properties.
  Lately, many proof systems based on Hybrid Logic have been investigated, in
particular related to Modal Logics featuring some form of data comparison.
  In this paper, we introduce an internalized tableaux calculus for XPath,
arguably one of the most prominent approaches for querying semistructured data.
More precisely, we define data-aware tableaux for XPath featuring data
comparison operators and enriched with nominals and the satisfiability
modalities from Hybrid Logic. We prove that the calculus is sound, complete and
terminating. Moreover, we show that tableaux can be constructed in polynomial
space, without compromising completeness, establishing in this way that the
satisfiability problem for the considered logic is PSPACE-complete. Finally, we
explore different extensions of the calculus, in particular to handle data
trees and other frame classes.


  The identification of hadronically decaying heavy states, such as vector
bosons, the Higgs, or the top quark, produced with large transverse boosts has
been and will continue to be a central focus of the jet physics program at the
Large Hadron Collider (LHC). At a future hadron collider working at an
order-of-magnitude larger energy than the LHC, these heavy states would be
easily produced with transverse boosts of several TeV. At these energies, their
decay products will be separated by angular scales comparable to individual
calorimeter cells, making the current jet substructure identification
techniques for hadronic decay modes not directly employable. In addition, at
the high energy and luminosity projected at a future hadron collider, there
will be numerous sources for contamination including initial- and final-state
radiation, underlying event, or pile-up which must be mitigated. We propose a
simple strategy to tag such "hyper-boosted" objects that defines jets with
radii that scale inversely proportional to their transverse boost and combines
the standard calorimetric information with charged track-based observables. By
means of a fast detector simulation, we apply it to top quark identification
and demonstrate that our method efficiently discriminates hadronically decaying
top quarks from light QCD jets up to transverse boosts of 20 TeV. Our results
open the way to tagging heavy objects with energies in the multi-TeV range at
present and future hadron colliders.


  We propose to study a generalization of the Klebanov-Polyakov-Witten (KPW)
construction for the algebra of observables in the $c = 1$ string model to
theories with $c > 1$. We emphasize the algebraic meaning of the KPW
construction for $c = 1$ related to occurrence of a {\it model} of {\it SU}(2)
as original structure on the algebra of observables. The attempts to preserve
this structure in generalizations naturally leads to consideration of
$W$-gravities. As a first step in the study of these generalized KPW
constructions we design explicitly the subsector of the space of observables in
appropriate $W_G$-string theory, which forms the {\it model} of $G$ for any
simply laced {\it G}. The {\it model} structure is confirmed by the fact that
corresponding one-loop Kac-Rocha-Caridi $W_G$-characters for $c = r_G$ sum into
a chiral (open string) $k=1$ $G$-WZW partition function.


  From the perspective of bond relaxation and vibration, we have reconciled the
Raman shifts of graphene under the stimuli of the number-of-layer,
uni-axial-strain, pressure, and temperature in terms of the response of the
length and strength of the representative bond of the entire specimen to the
applied stimuli. Theoretical unification of the measurements clarifies that:
(i) the opposite trends of Raman shifts due to number-of-layer reduction
indicate that the G-peak shift is dominated by the vibration of a pair of atoms
while the D- and the 2D-peak shifts involves z-neighbor of a specific atom;
(ii) the tensile strain-induced phonon softening and phonon-band splitting
arise from the asymmetric response of the C3v bond geometry to the C2v
uni-axial bond elongation; (iii) the thermal-softening of the phonons
originates from bond expansion and weakening; and (iv) the pressure- stiffening
of the phonons results from bond compression and work hardening. Reproduction
of the measurements has led to quantitative information about the referential
frequencies from which the Raman frequencies shift, the length, energy, force
constant, Debye temperature, compressibility, elastic modulus of the C-C bond
in graphene, which is of instrumental importance to the understanding of the
unusual behavior of graphene.


  We study manifolds arising as spaces of sections of complex manifolds
fibering over the projective line with normal bundle of each section isomorphic
to several copies of O(k). Such manifolds provide a natural setting for certain
integrable systems, "monopoles", which comprise the Bogomolny hierarchy and the
self-dual hierarchy.


  Quark-hadron matter at finite temperature and density is studied using a
two-flavor, color SU(2) (P)NJL model. The hadronic effective Lagrangian,
derived by bosonization of the quark fields and renormalized using the Eguchi
method, emerges in the form of an extended linear sigma model with meson and
diquark-baryon fields. Chiral and diquark condensates are studied as functions
of temperature and baryon density. Masses of mesons and diquark-baryons are
calculated with and without the Polyakov loop effect. We investigate the
equation of state of quark-hadron matter by taking into account the
contributions of mesons and diquark-baryons in addition to the quark
quasiparticles.


  We discuss the temporal picture of electron collisions with fullerene. Within
the framework of a Dirac bubble potential model for the fullerene shell, we
calculate the time delay in slow-electron elastic scattering by it. It appeared
that the time of transmission of an electron wave packet through the Dirac
bubble potential sphere that simulates a real potential of the C60 reaches up
to 104 attoseconds. Resonances in the time delays are due to the temporary
trapping of electron into quasi-bound states before it leaves the interaction
region. As concrete targets we choose almost ideally spherical endohedrals C20,
C60, C72, and C80. We present dependences of time-delay upon collision energy.


  A population of globular clusters (GCs) has been recently established by the
Fermi-LAT telescope as a new class of GeV $\gamma$-ray sources. Leptons
accelerated to TeV energies, in the inner magnetospheres of MSPs or in their
wind regions, should produce $\gamma$-rays through the inverse Compton
scattering in the dense radiation field from the huge population of stars. We
have conducted deep observations of the globular cluster M15 with the MAGIC
telescopes and used 165 hrs in order to search for $\gamma$-ray emission. A
strong upper limit on the TeV $\gamma$-ray flux $<3.2\times
10^{-13}\mathrm{cm^{-2}s^{-1}}$ above 300 GeV ($<0.26\%$ of the Crab nebula
flux) has been obtained. We interpret this limit as a constraint on the
efficiency of the acceleration of leptons in the magnetospheres of the MSPs. We
constrain the injection rate of relativistic leptons, $\eta_{\rm e}$, from the
MSPs magnetospheres and their surrounding. We conclude that $\eta_{\rm e}$ must
be lower than expected from the modelling of high energy processes in MSP inner
magnetospheres. For leptons accelerated with the power law spectrum in the MSP
wind regions, $\eta_{\rm e}$ is constrained to be much lower than derived for
the wind regions around classical pulsars. These constraints are valid for the
expected range of magnetic field strengths within the GC and for the range of
likely energies of leptons injected from the inner magnetospheres, provided
that the leptons are not removed from the globular cluster very efficiently due
to advection process. We discuss consequences of these constraints for the
models of radiation processes around millisecond pulsars.


  A simple extension of the minimal left-right symmetric supersymmetric grand
unified theory model is constructed by adding two pairs of superfields. This
naturally violates the partial Yukawa unification predicted by the minimal
model. After including supergravity corrections, we find that this extended
model naturally supports hilltop F-term hybrid inflation along its trivial
inflationary path with only a very mild tuning of the initial conditions. With
a convenient choice of signs of the terms in the Kahler potential, we can
reconcile the inflationary scale with the supersymmetric grand unified theory
scale. All the current data on the inflationary observables are readily
reproduced. Inflation is followed by non-thermal leptogenesis via the decay of
the right-handed neutrinos emerging from the decay of the inflaton and any
possible washout of the lepton asymmetry is avoided thanks to the violation of
partial Yukawa unification. The extra superfields also assist us in reducing
the reheat temperature so as to satisfy the gravitino constraint. The observed
baryon asymmetry of the universe is naturally reproduced consistently with the
neutrino oscillation parameters.


  We study the behavior of an open quantum system, with an $N$--dimensional
space of states, whose density matrix evolves according to a non--unitary map
defined in two steps: A unitary step, where the system evolves with an
evolution operator obtained by quantizing a classically chaotic map (baker's
and Harper's map are the two examples we consider). A non--unitary step where
the evolution operator for the density matrix mimics the effect of diffusion in
the semiclassical (large $N$) limit. The process of decoherence and the
transition from quantum to classical behavior are analyzed in detail by means
of numerical and analitic tools. The existence of a regime where the entropy
grows with a rate which is independent of the strength of the diffusion
coefficient is demonstrated. The nature of the processes that determine the
production of entropy is analyzed.


  After a brief introduction on nodal superconductors, we review the
topological defects in triplet superconductors such as UPt$_{3}$,
Sr$_{2}$RuO$_{4}$, etc. This is in part motivated by the surprising discovery
of Ana Celia Mota and her colleagues that in some triplet superconductors the
flux motion is completely impeded (the ideal pinning). Among topological
defects the most prominent is Abrikosov's vortex with quantum flux $\phi_{0}=
\frac{hc}{2e}$. Abrikosov's vortex is universal and ubiquitous and seen in both
conventional and unconventional superconductors by the Bitter decoration
technique, small angle neutron scattering (SANS), scanning tunneling microscopy
(STM), micromagnetometer and more recently by Lorentz electron micrograph. In
order to interpret the experiment by Mota et al a variety of textures are
proposed. In particular, in analogy to superfluid $^{3}$He-A the
$\hat{\ell}$-soliton and $\hat{d}$-soliton play the prominent role. We review
these notions and point out possible detection of these domain walls and
half-quantum vortices in some triplet superconductors.


  Current-induced dynamics of twisted domain walls and skyrmions in
ferromagnetic perpendicularly magnetized multilayers is studied through
three-dimensional micromagnetic simulations and analytical modeling. It is
shown that such systems generally exhibit a Walker breakdown-like phenomenon in
the presence of current-induced damping-like spin-orbit torque. Above a
critical current threshold, corresponding to typical velocities of the order
tens of m/s, domain walls in some layers start to precess with frequencies in
the gigahertz regime, which leads to oscillatory motion and a significant drop
in mobility. This phenomenon originates from complex stray field interactions
and occurs for a wide range of multilayer materials and structures that include
at least three ferromagnetic layers and finite Dzyaloshinskii-Moriya
interaction. An analytical model is developed to describe the precessional
dynamics in multilayers with surface-volume stray field interactions, yielding
qualitative agreement with micromagnetic simulations.


  The quantification of diversification benefits due to risk aggregation plays
a prominent role in the (regulatory) capital management of large firms within
the financial industry. However, the complexity of today's risk landscape makes
a quantifiable reduction of risk concentration a challenging task. In the
present paper we discuss some of the issues that may arise. The theory of
second-order regular variation and second-order subexponentiality provides the
ideal methodological framework to derive second-order approximations for the
risk concentration and the diversification benefit.


  The pure electroweak three-loop mechanism for the induced electric and
chromoelectric dipole moments of quarks is studied in the Kobayashi-Maskawa
model with three and four generations. In the standard three generation case,
this mechanism is found to produce a negligible contribution to the electric
dipole moment of neutron. In the presence of the fourth heavy generation,
however, pure electroweak corrections are important and might be several times
larger than the corresponding QCD contribution for the masses of heaviest
quarks $\sim$ 500-600 GeV. The resulting electric dipole moment of neutron
naturally arises at the level of $10^{-29} \,e\cdot cm$. The effects of the
fourth generation physics are parametrized at standard electroweak scale by the
presence of the effective charged right-handed currents.


  We study to what extent the Bitcoin blockchain security permanently depends
on the underlying distribution of cryptocurrency market outcomes. We use daily
blockchain and Bitcoin data for 2014-2019 and employ the ARDL approach. We test
three equilibrium hypotheses: (i) sensitivity of the Bitcoin blockchain to
mining reward; (ii) security outcomes of the Bitcoin blockchain and the
proof-of-work cost; and (iii) the speed of adjustment of the Bitcoin blockchain
security to deviations from the equilibrium path. Our results suggest that the
Bitcoin price and mining rewards are intrinsically linked to Bitcoin security
outcomes. The Bitcoin blockchain security's dependency on mining costs is
geographically differenced - it is more significant for the global mining
leader China than for other world regions. After input or output price shocks,
the Bitcoin blockchain security reverts to its equilibrium security level.


  Mining causality from text is a complex and crucial natural language
understanding task corresponding to the human cognition. Existing studies at
its solution can be grouped into two primary categories: feature engineering
based and neural model based methods. In this paper, we find that the former
has incomplete coverage and inherent errors but provide prior knowledge; while
the latter leverages context information but causal inference of which is
insufficiency. To handle the limitations, we propose a novel causality
detection model named MCDN to explicitly model causal reasoning process, and
furthermore, to exploit the advantages of both methods. Specifically, we adopt
multi-head self-attention to acquire semantic feature at word level and develop
the SCRN to infer causality at segment level. To the best of our knowledge,
with regards to the causality tasks, this is the first time that the Relation
Network is applied. The experimental results show that: 1) the proposed
approach performs prominent performance on causality detection; 2) further
analysis manifests the effectiveness and robustness of MCDN.


  Marine buoy is an important part of underwater acoustic communication system.
It is of great significance to track and locate it. It is widely used in ocean
environment three - dimensional monitoring, underwater multimedia
communication, underwater mobile carrier navigation and positioning, marine
resources detection, remote control of submarine topography mapping and
offshore oil industry, data acquisition, etc. This paper describes the
application of the monitoring service of GPRS / GPS module at Marine buoy. It
can achieve real - time location of underwater acoustic communication devices
and route tracking to avoid the loss of the device, as well as assist to
retrieve the lost device.


  We clarify the relation between the Dixmier-Douady class on the space of self
adjoint Fredholm operators (`universal B-field') and the curvature of
determinant bundles over infinite-dimensional Grassmannians. In particular, in
the case of Dirac type operators on a three dimensional compact manifold we
obtain a simple and explicit expression for both forms.


  We continue our study of the optical properties of the solar gravitational
lens (SGL). Taking the next step beyond representing it as an idealized
monopole, we now characterize the gravitational field of the Sun using an
infinite series of multipole moments. We consider the propagation of
electromagnetic (EM) waves in this gravitational field within the first
post-Newtonian approximation of the general theory of relativity. The problem
is formulated within the Mie diffraction theory. We solve Maxwell's equations
for the EM wave propagating in the background of a static gravitational field
of an extended gravitating body, while accounting for multipole contributions.
Using a wave-theoretical approach and the eikonal approximation, we find an
exact closed form solution for the Debye potentials and determine the EM field
at an image plane in the strong interference region of the lens. The resulting
EM field is characterized by a new diffraction integral. We study this solution
and show how the presence of multipoles affects the optical properties of the
lens, resulting in distinct diffraction patterns. We identify the gravitational
deflection angle with the individual contributions due to each of the
multipoles. Treating the Sun as an extended, axisymmetric, rotating body, we
show that each zonal harmonics causes light to diffract into an area whose
boundary is a caustic of a particular shape. The appearance of the caustics
modifies the point-spread function (PSF) of the lens, thus affecting its
optical properties. The new wave-theoretical solution allows the study
gravitational lensing by a realistic lens that possesses an arbitrary number of
gravitational multipoles. This {\em angular eikonal method} represents an
improved treatment of realistic gravitational lensing. It may be used for a
wave-optical description of many astrophysical lenses.


  We show that Oeljeklaus-Toma manifolds $X(K, U)$ where $K$ is a number field
of signature $(s, t)$ such that $s\geq 1,$ $t\geq 2$ and $s\geq 2t$ admit no
lck metric. Combined with the earlier results by K. Oeljeklaus - M. Toma and A.
Dubickas this completely solves the problem of existence of LCK metrics on
Oeljeklaus-Toma manifolds.


  We revisit the Fermi two-atoms problem in the framework of disordered
systems. In our model we consider a two-qubits system linearly coupled with a
quantum massless scalar field. We analyze the energy transfer between the
qubits under different experimental perspectives. In addition, we assume that
the coefficients of the Klein-Gordon equation are random functions of the
spatial coordinates. The disordered medium is modeled by a centered, stationary
and Gaussian process. We demonstrate that the classical notion of causality
emerges only in the wave zone in the presence of random fluctuations of the
light cone. Possible repercussions are discussed.


  We generalize and prove a result which was first shown by Zippin, and was
explicitly formulated by Benyamini.


  We review recent results on the semiclassical behaviour of Schr\"{o}dinger
operators with Neumann boundary conditions. In this setting, the validity of
Weyl's law requires additional conditions on the potential. We will explain the
techniques needed to control the number of bound states near the boundary, thus
leading to universal estimates on the number of bound states.


  Machine learning (ML)-based content moderation tools are essential to keep
online spaces free from hateful communication. Yet, ML tools can only be as
capable as the quality of the data they are trained on allows them. While there
is increasing evidence that they underperform in detecting hateful
communications directed towards specific identities and may discriminate
against them, we know surprisingly little about the provenance of such bias. To
fill this gap, we present a systematic review of the datasets for the automated
detection of hateful communication introduced over the past decade, and unpack
the quality of the datasets in terms of the identities that they embody: those
of the targets of hateful communication that the data curators focused on, as
well as those unintentionally included in the datasets. We find, overall, a
skewed representation of selected target identities and mismatches between the
targets that research conceptualizes and ultimately includes in datasets. Yet,
by contextualizing these findings in the language and location of origin of the
datasets, we highlight a positive trend towards the broadening and
diversification of this research space.


  Progress in experimental techniques at nanoscale made measurements of noise
in molecular junctions possible. These data are important source of information
not accessible through average flux measurements. Emergence of optoelectronics,
recently shown possibility of strong light-matter couplings, and developments
in the field of quantum thermodynamics are making counting statistics
measurements of even higher importance. Theoretical methods for noise
evaluation in first principles simulations can be roughly divided into
approaches applicable in the case of weak intra-system interactions, and those
treating strong interactions for systems weakly coupled to baths. We argue that
due to structure of its diagrammatic expansion and the fact of utilizing
many-body states as a basis of its formulation recently introduced
nonequilibrium Hubbard Green functions formulation is a relatively inexpensive
method suitable for evaluation of noise characteristics in first principles
simulations over wide range of parameters. We illustrate viability of the
approach by simulations of noise and noise spectrum within generic models for
non-, weakly and strongly interacting systems. Results of the simulations are
compared to exact data (where available) and to simulations performed within
approaches best suited for each of the three parameter regimes.


  In the first part of this work, we study the absolutely continuous operators
which are defined on fuction spaces with wide sense. In the second part, we
show some results concerning the absoltely continuous operators when the
function spaces (with wide sense) are interpolation spaces.


  We construct coherent states of the massless and massive representations of
the Poincar\'e group. They are parameterised by points on the classical state
space of spinning particles. Their properties are explored, with special
emphasis on the geometrical structures on the state space.


  I discuss the (2,2)-formalism of general relativity based on the
(2,2)-fibration of a generic 4-dimensional spacetime of the Lorentzian
signature. In this formalism general relativity is describable as a Yang-Mills
gauge theory defined on the (1+1)-dimensional base manifold, whose local gauge
symmetry is the group of the diffeomorphisms of the 2-dimensional fibre
manifold. After presenting the Einstein's field equations in this formalism, I
solve them for spherically symmetric case to obtain the Schwarzschild solution.
Then I discuss possible applications of this formalism.


  We present measurements of bulk properties of the matter produced in Au+Au
collisions at $\sqrt{s_{NN}}=$ 7.7, 11.5, 19.6, 27, and 39 GeV using identified
hadrons ($\pi^\pm$, $K^\pm$, $p$ and $\bar{p}$) from the STAR experiment in the
Beam Energy Scan (BES) Program at the Relativistic Heavy Ion Collider (RHIC).
Midrapidity ($|y|<$0.1) results for multiplicity densities $dN/dy$, average
transverse momenta $\langle p_T \rangle$ and particle ratios are presented. The
chemical and kinetic freeze-out dynamics at these energies are discussed and
presented as a function of collision centrality and energy. These results
constitute the systematic measurements of bulk properties of matter formed in
heavy-ion collisions over a broad range of energy (or baryon chemical
potential) at RHIC.


  The sandpile group of a connected graph $G$, defined to be the torsion part
of the cokernel of the graph Laplacian, is a subtle graph invariant with
combinatorial, algebraic, and geometric descriptions. Extending and improving
previous works on the sandpile group of hypercubes, we study the sandpile
groups of the Cayley graphs of $\mathbb{F}_2^r$, focusing on their poorly
understood Sylow-$2$ component. We find the number of Sylow-$2$ cyclic factors
for "generic" Cayley graphs and deduce a bound for the non-generic ones.
Moreover, we provide a sharp upper bound for their largest Sylow-$2$ cyclic
factors. In the case of hypercubes, we give exact formulae for the largest
$n-1$ Sylow-$2$ cyclic factors. Some key ingredients of our work include the
natural ring structure on these sandpile groups from representation theory, and
calculation of the $2$-adic valuations of binomial sums via the combinatorics
of carries.


  We present META-MT, a meta-learning approach to adapt Neural Machine
Translation (NMT) systems in a few-shot setting. META-MT provides a new
approach to make NMT models easily adaptable to many target domains with the
minimal amount of in-domain data. We frame the adaptation of NMT systems as a
meta-learning problem, where we learn to adapt to new unseen domains based on
simulated offline meta-training domain adaptation tasks. We evaluate the
proposed meta-learning strategy on ten domains with general large scale NMT
systems. We show that META-MT significantly outperforms classical domain
adaptation when very few in-domain examples are available. Our experiments
shows that META-MT can outperform classical fine-tuning by up to 2.5 BLEU
points after seeing only 4, 000 translated words (300 parallel sentences).


  We address the problem of non-parametric density estimation under the
additional constraint that only privatised data are allowed to be published and
available for inference. For this purpose, we adopt a recent generalisation of
classical minimax theory to the framework of local $\alpha$-differential
privacy and provide a lower bound on the rate of convergence over Besov spaces
$B^s_{pq}$ under mean integrated $\mathbb L^r$-risk. This lower bound is
deteriorated compared to the standard setup without privacy, and reveals a
twofold elbow effect. In order to fulfil the privacy requirement, we suggest
adding suitably scaled Laplace noise to empirical wavelet coefficients. Upper
bounds within (at most) a logarithmic factor are derived under the assumption
that $\alpha$ stays bounded as $n$ increases: A linear but non-adaptive wavelet
estimator is shown to attain the lower bound whenever $p \geq r$ but provides a
slower rate of convergence otherwise. An adaptive non-linear wavelet estimator
with appropriately chosen smoothing parameters and thresholding is shown to
attain the lower bound within a logarithmic factor for all cases.


  Model-assisted, two-stage forest survey sampling designs provide a means to
combine airborne remote sensing data, collected in a sampling mode, with field
plot data to increase the precision of national forest inventory estimates,
while maintaining important properties of design-based inventories, such as
unbiased estimation and quantification of uncertainty. In this study, we
present a comprehensive set of model-assisted estimators for domain-level
attributes in a two-stage sampling design, including new estimators for
densities, and compare the performance of these estimators with standard
poststratified estimators. Simulation was used to assess the statistical
properties (bias, variability) of these estimators, with both simple random and
systematic sampling configurations, and indicated that 1) all estimators were
generally unbiased. and 2) the use of lidar in a sampling mode increased the
precision of the estimators at all assessed field sampling intensities, with
particularly marked increases in precision at lower field sampling intensities.
Variance estimators are generally unbiased for model-assisted estimators
without poststratification, while model-assisted estimators with
poststratification were increasingly biased as field sampling intensity
decreased. In general, these results indicate that airborne remote sensing,
collected in a sampling mode, can be used to increase the efficiency of
national forest inventories.


  Trajectories are fundamental to winning in alpine skiing. Tools enabling the
analysis of such curves can enhance the training activity and enrich
broadcasting content. In this paper, we propose SkiTraVis, an algorithm to
visualize the sequence of points traversed by a skier during its performance.
SkiTraVis works on monocular videos and constitutes a pipeline of a visual
tracker to model the skier's motion and of a frame correspondence module to
estimate the camera's motion. The separation of the two motions enables the
visualization of the trajectory according to the moving camera's perspective.
We performed experiments on videos of real-world professional competitions to
quantify the visualization error, the computational efficiency, as well as the
applicability. Overall, the results achieved demonstrate the potential of our
solution for broadcasting media enhancement and coach assistance.


  Detailed 3D reconstruction and photo-realistic relighting of digital humans
are essential for various applications. To this end, we propose a novel
sparse-view 3d human reconstruction framework that closely incorporates the
occupancy field and albedo field with an additional visibility field--it not
only resolves occlusion ambiguity in multiview feature aggregation, but can
also be used to evaluate light attenuation for self-shadowed relighting. To
enhance its training viability and efficiency, we discretize visibility onto a
fixed set of sample directions and supply it with coupled geometric 3D depth
feature and local 2D image feature. We further propose a novel
rendering-inspired loss, namely TransferLoss, to implicitly enforce the
alignment between visibility and occupancy field, enabling end-to-end joint
training. Results and extensive experiments demonstrate the effectiveness of
the proposed method, as it surpasses state-of-the-art in terms of
reconstruction accuracy while achieving comparably accurate relighting to
ray-traced ground truth.


  Wigner distributions play a significant role in formulating the phase space
analogue of quantum mechanics. The Schrodinger wave-functional for solitons is
needed to derive it for solitons. The Wigner distribution derived can further
be used for calculating the charge distributions, current densities and wave
function amplitude in position or momentum space. It can be also used to
calculate the upper bound of the quantum speed limit time. We derive and
analyze the Wigner distributions for Kink and Sine-Gordon solitons by
evaluating the Schrodinger wave-functional for both solitons. The charge,
current density, and quantum speed limit for solitons are also discussed which
we obtain from the derived analytical expression of Wigner distributions.


  Recently, Bhat, Liebscher and Skeide exhibited an unusual example of product
system of Hilbert $C^*$ modules. Namely, a subsystem of a Fock system, that is
not Fock. Later, the authors defined the index of any product system of Hilbert
$C^*$-modules, generalizing earlier partial definitions. In this note we
compute the index of the mentioned interesting subsystem, and also we determine
all its units.


  In this work we present the results of the survey carried out on one of the
deepest X-ray fields observed by the XMM-Newton satellite. The 1.75 Ms Ultra
Narrow Deep Field (XMM175UNDF) survey is made by 13 observations taken over 2
years with a total exposure time of 1.75 Ms (1.372 Ms after flare-filtered) in
a field of $30' \times 30' $ centered around the blazar 1ES 1553+113. We
stacked the 13 observations reaching flux limits of $4.03 \times 10^{-16} $,
$1.3 \times 10^{-15}$, and $9.8 \times 10^{-16}\, erg\, s^{-1}\, cm^{-2}$ in
the soft $(0.2 - 2\, \mathrm{keV})$, hard $(2 - 12\, \mathrm{keV})$, and full
$(0.2 - 12\, \mathrm{keV})$ bands, respectively. Using a conservative threshold
of Maximum Likelihood significance of $ML \geq 6$, corresponding to $3\sigma$,
we detected 301 point-sources for which we derived positions, fluxes in
different bands, and hardness ratios. Thanks to an optical follow-up carried
out using the 10.4m the Gran Telescopio Canarias (GTC) on the same field in the
$u'g'r'i'z'$ bands, combined with WISE/2MASS IR data; we identified 244
optical/IR counterpart candidates for our X-ray sources and estimated their
X-ray luminosities, redshift distribution, X-ray/optical $-$ X-ray/IR flux
ratios, and absolute magnitudes. Finally, we divided this subsample in 40
non-active sources and 204 AGNs, of which 139 are classified as Seyfert
galaxies and 41 as Quasars.


  Pedestrian attribute recognition has been an emerging research topic in the
area of video surveillance. To predict the existence of a particular attribute,
it is demanded to localize the regions related to the attribute. However, in
this task, the region annotations are not available. How to carve out these
attribute-related regions remains challenging. Existing methods applied
attribute-agnostic visual attention or heuristic body-part localization
mechanisms to enhance the local feature representations, while neglecting to
employ attributes to define local feature areas. We propose a flexible
Attribute Localization Module (ALM) to adaptively discover the most
discriminative regions and learns the regional features for each attribute at
multiple levels. Moreover, a feature pyramid architecture is also introduced to
enhance the attribute-specific localization at low-levels with high-level
semantic guidance. The proposed framework does not require additional region
annotations and can be trained end-to-end with multi-level deep supervision.
Extensive experiments show that the proposed method achieves state-of-the-art
results on three pedestrian attribute datasets, including PETA, RAP, and
PA-100K.


  We study the discrete nonlinear Schr\"oinger equation with weak disorder,
focusing on the regime when the nonlinearity is, on the one hand, weak enough
for the normal modes of the linear problem to remain well resolved, but on the
other, strong enough for the dynamics of the normal mode amplitudes to be
chaotic for almost all modes. We show that in this regime and in the limit of
high temperature, the macroscopic density $\rho$ satisfies the nonlinear
diffusion equation with a density-dependent diffusion coefficient,
$D(\rho)=D_0\rho^2$. An explicit expression for $D_0$ is obtained in terms of
the eigenfunctions and eigenvalues of the linear problem, which is then
evaluated numerically. The role of the second conserved quantity (energy) in
the transport is also quantitatively discussed.


  Vision-and-Language Navigation (VLN) tasks require an agent to navigate
through the environment based on language instructions. In this paper, we aim
to solve two key challenges in this task: utilizing multilingual instructions
for improved instruction-path grounding and navigating through new environments
that are unseen during training. To address these challenges, we propose CLEAR:
Cross-Lingual and Environment-Agnostic Representations. First, our agent learns
a shared and visually-aligned cross-lingual language representation for the
three languages (English, Hindi and Telugu) in the Room-Across-Room dataset.
Our language representation learning is guided by text pairs that are aligned
by visual information. Second, our agent learns an environment-agnostic visual
representation by maximizing the similarity between semantically-aligned image
pairs (with constraints on object-matching) from different environments. Our
environment agnostic visual representation can mitigate the environment bias
induced by low-level visual information. Empirically, on the Room-Across-Room
dataset, we show that our multilingual agent gets large improvements in all
metrics over the strong baseline model when generalizing to unseen environments
with the cross-lingual language representation and the environment-agnostic
visual representation. Furthermore, we show that our learned language and
visual representations can be successfully transferred to the Room-to-Room and
Cooperative Vision-and-Dialogue Navigation task, and present detailed
qualitative and quantitative generalization and grounding analysis. Our code is
available at https://github.com/jialuli-luka/CLEAR


  We consider two types of matroids defined on the edge set of a graph $G$:
count matroids ${\cal M}_{k,\ell}(G)$, in which independence is defined by a
sparsity count involving the parameters $k$ and $\ell$, and the
(three-dimensional generic) cofactor matroid $\mathcal{C}(G)$, in which
independence is defined by linear independence in the cofactor matrix of $G$.
We give tight lower bounds, for each pair $(k,\ell)$, that show that if $G$ is
sufficiently highly connected, then $G-e$ has maximum rank for all $e\in E(G)$,
and ${\cal M}_{k,\ell}(G)$ is connected. These bounds unify and extend several
previous results, including theorems of Nash-Williams and Tutte ($k=\ell$), and
Lov\'asz and Yemini ($k=2, \ell=3$). We also prove that if $G$ is highly
connected, then the vertical connectivity of $\mathcal{C}(G)$ is also high.
  We use these results to generalize Whitney's celebrated result on the graphic
matroid of $G$ (which corresponds to ${\cal M}_{1,1}(G)$) to all count matroids
and to the three-dimensional cofactor matroid: if $G$ is highly connected,
depending on $k$ and $\ell$, then the count matroid ${\cal M}_{k,\ell}(G)$
uniquely determines $G$; and similarly, if $G$ is $14$-connected, then its
cofactor matroid $\mathcal{C}(G)$ uniquely determines $G$. We also derive
similar results for the $t$-fold union of the three-dimensional cofactor
matroid, and use them to prove that every $24$-connected graph has a spanning
tree $T$ for which $G-E(T)$ is $3$-connected, which verifies a case of a
conjecture of Kriesell.