  Narrow-Line Seyfert 1 (NLS1) Galaxies are an important type of active
galactic nucleus (AGN), generally expected to be accreting at high Eddington
rate. The properties of their outflows and importance of AGN feedback remain
intriguing. We report on the discovery of fast outflowing warm absorbers (WAs)
in the NLS1 PG 1001+054, with velocities in the range of 7000 to 9000
kilometers per second. They are identified with blueshifted Lyman alpha, N v
and Si iv lines in the high resolution ultraviolet (UV) spectra taken with the
Cosmic Origins Spectrograph (COS) onboard the Hubble Space Telescope (HST). We
perform photoionization modeling using XSTAR with three WAs. The derived
physical properties are typical of WAs in terms of ionization and column
density, whereas the outflow velocities are significantly higher. The estimated
location of these WAs ranges from 1 to 73 parsecs away from the AGN. Together
with previous detection of high ionization absorber in the X-ray for PG
1001+054, we suggest that the fast outflowing UV absorber is probably a part of
a multiphase outflow. Such structure is likely produced by the outflow launched
from AGN at accretion disk scale, which shocks the ambient ISM producing
stratified absorbers. Assuming contribution from the three WAs at tens of
parsecs, the estimated ratio between the kinetic power of the outflow and AGN
Eddington luminosity could reach 1.7 percent, raising the possibility of
sufficient influence on the host galaxy when compared to some theoretical
models for efficient AGN feedback.


  We consider empirical multi-dimensional Rare Events Point Processes that keep
track both of the time occurrence of extremal observations and of their
severity, for stochastic processes arising from a dynamical system, by
evaluating a given potential along its orbits. This is done both in the absence
and presence of clustering. A new formula for the piling of points on the
vertical direction of bi-dimensional limiting point processes, in the presence
of clustering, is given, which is then generalised for higher dimensions. The
limiting multi-dimensional processes are computed for systems with sufficiently
fast decay of correlations. The complete convergence results are used to study
the effect of clustering on the convergence of extremal processes, record time
and record values point processes. An example where the clustering prevents the
convergence of the record times point process is given.


  In this paper, we introduce a neural network framework for semi-supervised
clustering (SSC) with pairwise (must-link or cannot-link) constraints. In
contrast to existing approaches, we decompose SSC into two simpler
classification tasks/stages: the first stage uses a pair of Siamese neural
networks to label the unlabeled pairs of points as must-link or cannot-link;
the second stage uses the fully pairwise-labeled dataset produced by the first
stage in a supervised neural-network-based clustering method. The proposed
approach, S3C2 (Semi-Supervised Siamese Classifiers for Clustering), is
motivated by the observation that binary classification (such as assigning
pairwise relations) is usually easier than multi-class clustering with partial
supervision. On the other hand, being classification-based, our method solves
only well-defined classification problems, rather than less well specified
clustering tasks. Extensive experiments on various datasets demonstrate the
high performance of the proposed method.


  Recent years have witnessed significant advances in image deraining due to
the kinds of effective image priors and deep learning models. As each deraining
approach has individual settings (e.g., training and test datasets, evaluation
criteria), how to fairly evaluate existing approaches comprehensively is not a
trivial task. Although existing surveys aim to review of image deraining
approaches comprehensively, few of them focus on providing unify evaluation
settings to examine the deraining capability and practicality evaluation. In
this paper, we provide a comprehensive review of existing image deraining
method and provide a unify evaluation setting to evaluate the performance of
image deraining methods. We construct a new high-quality benchmark named
HQ-RAIN to further conduct extensive evaluation, consisting of 5,000 paired
high-resolution synthetic images with higher harmony and realism. We also
discuss the existing challenges and highlight several future research
opportunities worth exploring. To facilitate the reproduction and tracking of
the latest deraining technologies for general users, we build an online
platform to provide the off-the-shelf toolkit, involving the large-scale
performance evaluation. This online platform and the proposed new benchmark are
publicly available and will be regularly updated at http://www.deraining.tech/.


  Our goal in this paper is to identify certain naturally occurring colimits of
schemes and algebraic spaces. To do so, we use (and prove) some new Tannaka
duality theorems for maps of algebraic spaces.


  A novel and detailed convergence analysis is presented for a greedy algorithm
that was previously introduced for operator reconstruction problems in the
field of quantum mechanics. This algorithm is based on an offline/online
decomposition of the reconstruction process and on an ansatz for the unknown
operator obtained by an a priori chosen set of linearly independent matrices.
The presented convergence analysis focuses on linear-quadratic (optimization)
problems governed by linear differential systems and reveals the strong
dependence of the performance of the greedy algorithm on the observability
properties of the system and on the ansatz of the basis elements. Moreover, the
analysis allows us to use a precise (and in some sense optimal) choice of basis
elements for the linear case and led to the introduction of a new and more
robust optimized greedy reconstruction algorithm. This optimized approach also
applies to nonlinear Hamiltonian reconstruction problems, and its efficiency is
demonstrated by numerical experiments.


  An extended elastic eigenvector approach for adatom interactions is applied
to model Nitrogen c(2x2) Atom islands on Cu(001). Oscillating interactions
between adatom monomers or dimers are considered. Attractive pair interactions
of adatoms are able to describe agglomeration but fail to explain the size of
islands. Multisite interactions created by dimers, however, can explain the
size of islands if an interaction parameter is adjusted properly. Finite size
islands are formed when repulsive monomer interactions are balanced by
attractive monomer-dimer interactions. A simple model of nearest neighbour
attraction and s-3 repulsion is used as an example for the interaction
parameter search. Previous experimental studies have shown that in the low
coverage region Nitrogen atoms agglomerate to isolated square islands of about
5 nm x 5 nm size with a c(2x2) structure. With increasing coverage those
islands form regular patterns but do not touch below about 0.4 monolayers.
Previous experiments and calculations have shown that the square island pattern
show significant elastic effects. Different adatom structures within the
Nitrogen islands have been analyzed, a dimer step model is able to reproduce
the experimentally found island size. This model requires a molecular bond
between dimers formed by Nitrogen adatoms. The model is also used to compute
elastic interactions between islands and to check it against the experimentally
found island pattern. Shortcomings and limitations of the model are discussed
and open questions are formulated.


  We propose an automatic approach that extracts editing styles in a source
video and applies the edits to matched footage for video creation. Our Computer
Vision based techniques considers framing, content type, playback speed, and
lighting of each input video segment. By applying a combination of these
features, we demonstrate an effective method that automatically transfers the
visual and temporal styles from professionally edited videos to unseen raw
footage. We evaluated our approach with real-world videos that contained a
total of 3872 video shots of a variety of editing styles, including different
subjects, camera motions, and lighting. We reported feedback from survey
participants who reviewed a set of our results.


  Statistical NLP systems are frequently evaluated and compared on the basis of
their performances on a single split of training and test data. Results
obtained using a single split are, however, subject to sampling noise. In this
paper we argue in favour of reporting a distribution of performance figures,
obtained by resampling the training data, rather than a single number. The
additional information from distributions can be used to make statistically
quantified statements about differences across parameter settings, systems, and
corpora.


  In the spherical coordinate system with the center in the center of the
fullerene cage, the spherical coordinates of 20 carbon atoms forming the C20
cage have been calculated.


  Structural inequalities persist in society, conferring systematic advantages
to some people at the expense of others, for example, by giving them
substantially more influence and opportunities. Using bibliometric data about
authors of scientific publications, we identify two types of structural
inequalities in scientific citations. First, female authors, who represent a
minority of researchers, receive less recognition for their work (through
citations) relative to male authors; second, authors affiliated with top-ranked
institutions, who are also a minority, receive substantially more recognition
compared to other authors. We present a model for the growth of directed
citation networks and show that citations disparities arise from individual
preferences to cite authors from the same group (homophily), highly cited or
active authors (preferential attachment), as well as the size of the group and
how frequently new authors join. We analyze the model and show that its
predictions align well with real-world observations. Our theoretical and
empirical analysis also suggests potential strategies to mitigate structural
inequalities in science. In particular, we find that merely increasing the
minority group size does little to narrow the disparities. Instead, reducing
the homophily of each group, frequently adding new authors to a research field
while providing them an accessible platform among existing, established
authors, together with balanced group sizes can have the largest impact on
reducing inequality. Our work highlights additional complexities of mitigating
structural disparities stemming from asymmetric relations (e.g., directed
citations) compared to symmetric relations (e.g., collaborations).


  It is shown that the gravity acceleration just above a chamber filled with
gas or plasma at ultra-low pressure can be strongly reduced by applying an
Extra Low-Frequency (ELF) electromagnetic field across the gas or the plasma.
This Gravitational Shielding Effect is related to recent discovery of quantum
correlation between gravitational mass and inertial mass. According to the
theory samples hung above the gas or the plasma should exhibit a weight
decrease when the frequency of the electromagnetic field is decreased or when
the intensity of the electromagnetic field is increased. This Gravitational
Shielding Effect is unprecedented in the literature and can not be understood
in the framework of the General Relativity. From the technical point of view,
there are several applications for this discovery; possibly it will change the
paradigms of energy generation, transportation and telecommunications.


  We establish some important inequalities under the condition that the
weighted Ricci curvature $\mathrm{Ric}_{\infty}\geq K$ for some constant $K >0$
by using improved Bochner inequality and its integrated form. Firstly, we
obtain a sharp Poincar\'{e}-Lichnerowicz inequality. Further, we give a new
proof for logarithmic Sobolev inequality. Finally, we obtain an estimate of the
volume of geodesic balls.


  In recent years the Tsallis statistics is gaining popularity in describing
charged particle produc- tion and their properties, in particular pT spectra
and the multiplicities in high energy particle collisions. Motivated by its
success, an analysis of the LHC data of proton-proton collisions at ener- gies
ranging from 0.9 TeV to 7 TeV in different rapidity windows for charged
particle multiplicities has been done. A comparative analysis is performed in
terms of the Tsallis distribution, the Gamma distribution and the shifted-Gamma
distribution. An interesting observation on the inapplicability of these
distributions at sqrt{s}=7 TeV in the lower rapidity windows is intriguing. The
non-extensive nature of the Tsallis statistics is studied by determining the
entropic index and its energy depen- dence. The analysis is extrapolated to
predict the multiplicity distribution at sqrt{s}=14 TeV for one rapidity
window, |y| < 1.5 with the Tsallis function.


  Cryogenic microcalorimeters are key tools for high-resolution X-ray
spectroscopy due to their excellent energy resolution and quantum efficiency
close to 100%. Multiple types of microcalorimeters exist, some of which have
already proven outstanding performance. Nevertheless, they can't yet compete
with cutting-edge grating or crystal spectrometers. For this reason, novel
microcalorimeter concepts are continuously developed. One such concept is based
on the strong temperature dependence of the magnetic penetration depth of a
superconductor operated close to its transition temperature. This so-called
${\lambda}$-SQUID provides an in-situ tunable gain and promises to reach sub-eV
energy resolution. Here, we present some design considerations with respect to
the optimization of such a detector that are derived by analytic means. We
particularly show that for this detector concept the heat capacity of the
sensor should match the heat capacity of the absorber.


  A modification of the optimal fluctuation approach is applied to study the
tails of the free energy distribution function P(F) for an elastic string in
quenched disorder both in the regions of the universal behavior of P(F) and in
the regions of large fluctuations, where the behavior of P(F) is non-universal.
The difference between the two regimes is shown to consist in whether it is
necessary or not to take into account the renormalization of parameters by the
fluctuations of disorder in the vicinity of the optimal fluctuation.


  Utilizing the idea of extra large dimensions, it has been suggested that the
gauge and gravity couplings unification can happen at a scale as low as 1 TeV.
In this paper, we explore this phenomenological possibility within string
theory. In particular, we discuss how the proton decay bound can be satisfied
in Type I string theory. The string picture also suggests different scenarios
of gauge and gravitational couplings unification. The various scenarios are
explicitly illustrated with a specific 4-dimensional N=1 supersymmetric chiral
Type I string model with Pati-Salam-like gauge symmetry. We point out certain
features that should be generic in other Type I strings.


  We study the performance of long short-term memory networks (LSTMs) and
neural ordinary differential equations (NODEs) in learning latent-space
representations of dynamical equations for an advection-dominated problem given
by the viscous Burgers equation. Our formulation is devised in a non-intrusive
manner with an equation-free evolution of dynamics in a reduced space with the
latter being obtained through a proper orthogonal decomposition. In addition,
we leverage the sequential nature of learning for both LSTMs and NODEs to
demonstrate their capability for closure in systems which are not completely
resolved in the reduced space. We assess our hypothesis for two
advection-dominated problems given by the viscous Burgers equation. It is
observed that both LSTMs and NODEs are able to reproduce the effects of the
absent scales for our test cases more effectively than intrusive dynamics
evolution through a Galerkin projection. This result empirically suggests that
time-series learning techniques implicitly leverage a memory kernel for
coarse-grained system closure as is suggested through the Mori-Zwanzig
formalism.


  I discuss the construction of Simplified Models for Dark Matter searches at
the LHC. After reviewing the phylosophy and some simple example, I turn the
attention to the aspect of the theoretical consistency of these models.


  Deep learning has played a significant role in the success of facial
expression recognition (FER), thanks to large models and vast amounts of
labelled data. However, obtaining labelled data requires a tremendous amount of
human effort, time, and financial resources. Even though some prior works have
focused on reducing the need for large amounts of labelled data using different
unsupervised methods, another promising approach called active learning is
barely explored in the context of FER. This approach involves selecting and
labelling the most representative samples from an unlabelled set to make the
best use of a limited 'labelling budget'. In this paper, we implement and study
8 recent active learning methods on three public FER datasets, FER13, RAF-DB,
and KDEF. Our findings show that existing active learning methods do not
perform well in the context of FER, likely suffering from a phenomenon called
'Cold Start', which occurs when the initial set of labelled samples is not well
representative of the entire dataset. To address this issue, we propose
contrastive self-supervised pre-training, which first learns the underlying
representations based on the entire unlabelled dataset. We then follow this
with the active learning methods and observe that our 2-step approach shows up
to 9.2% improvement over random sampling and up to 6.7% improvement over the
best existing active learning baseline without the pre-training. We will make
the code for this study public upon publication at:
github.com/ShuvenduRoy/ActiveFER.


  Supervised multi-modal learning involves mapping multiple modalities to a
target label. Previous studies in this field have concentrated on capturing in
isolation either the inter-modality dependencies (the relationships between
different modalities and the label) or the intra-modality dependencies (the
relationships within a single modality and the label). We argue that these
conventional approaches that rely solely on either inter- or intra-modality
dependencies may not be optimal in general. We view the multi-modal learning
problem from the lens of generative models where we consider the target as a
source of multiple modalities and the interaction between them. Towards that
end, we propose inter- & intra-modality modeling (I2M2) framework, which
captures and integrates both the inter- and intra-modality dependencies,
leading to more accurate predictions. We evaluate our approach using real-world
healthcare and vision-and-language datasets with state-of-the-art models,
demonstrating superior performance over traditional methods focusing only on
one type of modality dependency.


  Colorectal cancer is among the most common malignancies and can develop from
high-risk colon polyps. Colonoscopy is an effective screening tool to detect
and remove polyps, especially in the case of precancerous lesions. However, the
missing rate in clinical practice is relatively high due to many factors. The
procedure could benefit greatly from using AI models for automatic polyp
segmentation, which provide valuable insights for improving colon polyp
detection. However, precise segmentation is still challenging due to variations
of polyps in size, shape, texture, and color. This paper proposes a novel
neural network architecture called AG-CUResNeSt, which enhances Coupled UNets
using the robust ResNeSt backbone and attention gates. The network is capable
of effectively combining multi-level features to yield accurate polyp
segmentation. Experimental results on five popular benchmark datasets show that
our proposed method achieves state-of-the-art accuracy compared to existing
methods.


  Background: A subset of histo-blood group antigens including ABO and Lewis
are oligosaccharide structures which may be conjugated to lipids or proteins.
They are known to be important recognition motifs not only in the context of
blood transfusions, but also in infection and cancer development. Scope of
review: Current knowledge on the molecular background and the implication of
histo-blood group glycans in the prevention and therapy of infectious and
non-communicable diseases, such as cancer and cardiovascular disease, is
presented. Major conclusions: Glycan-based histo-blood groups are associated
with intestinal microbiota com-position, the risk of various diseases as well
as therapeutic success of, e.g., vaccination. Their potential as prebiotic or
anti-microbial agents, as disease biomarkers and vaccine targets should be
further investigated in future studies. For this, recent and future
technological advancements will be of particular importance, especially with
regard to the unambiguous structural characterization of the glycan portion in
combination with information on the protein and lipid carriers of histo-blood
group-active glycans in large cohorts. General significance: Histo-blood group
glycans have a unique linking position in the complex net-work of genes,
oncodevelopmental biological processes, and disease mechanisms. Thus, they are
highly promising targets for novel approaches in the field of personalized
medicine.


  We demonstrate snake-like motion of graphene nanoribbons atop graphene and
hexagonal boron nitride (h-BN) substrates using fully-atomistic non-equilibrium
molecular dynamics simulations. The sliding dynamics of the edge-pulled
nanoribbons is found to be determined by the interplay between in-plane ribbon
elasticity and interfacial lattice mismatch. This results in an unusual
dependence of the friction-force on the ribbon's length, exhibiting an initial
linear rise that levels-off above a junction dependent threshold value dictated
by the pre-slip stress distribution within the slider. As part of this letter,
we present the LAMMPS implementation of the registry-dependent interlayer
potentials for graphene, h-BN, and their heterojunctions that were used herein,
which provide enhanced performance and accuracy.


  A spread code is a set of vector spaces of a fixed dimension over a finite
field Fq with certain properties used for random network coding. It can be
constructed in different ways which lead to different decoding algorithms. In
this work we present a new representation of spread codes with a minimum
distance decoding algorithm which is efficient when the codewords, the received
space and the error space have small dimension.


  Online monitoring user cardinalities (or degrees) in graph streams is
fundamental for many applications. For example in a bipartite graph
representing user-website visiting activities, user cardinalities (the number
of distinct visited websites) are monitored to report network anomalies. These
real-world graph streams may contain user-item duplicates and have a huge
number of distinct user-item pairs, therefore, it is infeasible to exactly
compute user cardinalities when memory and computation resources are
limited.Existing methods are designed to approximately estimate user
cardinalities, whose accuracy highly depends on parameters that are not easy to
set. Moreover, these methods cannot provide anytime-available estimation, as
the user cardinalities are computed at the end of the data stream. Real-time
applications such as anomaly detection require that user cardinalities are
estimated on the fly. To address these problems, we develop novel bit and
register sharing algorithms, which use a bit array and a register array to
build a compact sketch of all users' connected items respectively. Compared
with previous bit and register sharing methods, our algorithms exploit the
dynamic properties of the bit and register arrays (e.g., the fraction of zero
bits in the bit array at each time) to significantly improve the estimation
accuracy, and have low time complexity (O(1)) to update the estimations each
time they observe a new user-item pair. In addition, our algorithms are simple
and easy to use, without requirements to tune any parameter. We evaluate the
performance of our methods on real-world datasets. The experimental results
demonstrate that our methods are several times more accurate and faster than
state-of-the-art methods using the same amount of memory.


  A semigroup $S$ is called a weakly exponential semigroup if, for every couple
$(a,b)\in S\times S$ and every positive integer $n$, there is a non-negative
integer $m$ such that $(ab)^{n+m}=a^nb^n(ab)^m=(ab)^ma^nb^n$. A semigroup $S$
is called a $\Delta$-semigroup if the lattice of all congruences of $S$ is a
chain with respect to inclusion. The weakly exponential $\Delta$-semigroups
were described in [5]: A. Nagy, Weakly exponential $\Delta$-semigroups,
Semigroup Forum, 40(1990), 297-313. Although the existence of two types of them
(T2R and T2L semigroups) is an open question, Theorem 3.11 of [5] gives
necessary and sufficient conditions for a semigroup to be a T2R [T2L]
semigroup. In our present paper we give a little correction of condition (v) of
Theorem 3.11 of [5], and prove some new results which are addendum to the
problem: Doest there exist a T2R [T2L] semigroup?


  The Clifford algebraic formulation of the Duffin-Kemmer-Petiau (DKP) algebras
is applied to recast the De Donder-Weyl Hamiltonian (DWH) theory as an
algebraic description independent of the matrix representation of the DKP
algebra. We show that the DWH equations for antisymmetric fields arise out of
the action of the DKP algebra on certain invariant subspaces of the Clifford
algebra which carry the representations of the fields. The matrix
representation-free formula for the bracket associated with the DKP form of the
DWH equations is also derived. This bracket satisfies a generalization of the
standard properties of the Poisson bracket


  We study topological excitations in spin-1 Bose-Einstein condensates trapped
in an elongated double-well optical potential. This system hosts a new
topological defect, the spin Josephson vortex (SJV), which forms due to the
competition between the inter-well atomic tunneling and short-range
ferromagnetic two-body interaction. We identify the spin structure and
formation dynamics of the SJV and determine the phase diagram of the system. By
exploiting the intrinsic stability of the SJV, we propose a dynamical method to
create SJVs under realistic experimental conditions.


  In this short report, we investigate the ability of the DCCA coefficient to
measure correlation level between non-stationary series. Based on a wide Monte
Carlo simulation study, we show that the DCCA coefficient can estimate the
correlation coefficient accurately regardless the strength of non-stationarity
(measured by the fractional differencing parameter $d$). For a comparison, we
also report the results for the standard Pearson's correlation coefficient. The
DCCA coefficient dominates the Pearson's coefficient for non-stationary series.


  Electrolyte design is critical for enabling next-generation batteries with
higher energy densities. Hydrofluoroether (HFE) solvents have drawn a lot of
attention as the electrolytes based on HFEs showed great promise to deliver
highly desired properties, including high oxidative stability, ionic
conductivity, as well as enhanced lithium metal compatibility. However, the
structure-dynamics-properties relationships and design principles for
high-performance HFE solvents are still poorly understood. Herein, we proposed
four novel asymmetric HFE designs by systematically varying polyether and
fluorocarbon structural building blocks. By leveraging molecular dynamics (MD)
modeling to analyze the solvation structures and predict the properties of the
corresponding 1 M lithium bis(fluorosulfonyl)imide (LiTFSI) solutions, we
downselected the most promising candidate based on high conductivity, solvation
species distribution, and oxidative stability for extensive electrochemical
characterizations. The formulated electrolyte demonstrated properties
consistent with the predictions from the simulations and showed much-improved
capacity retention as well as Coulombic efficiency compared to the baseline
electrolytes when cycled in lithium metal cells. This work exemplifies the
construction of candidate electrolytes from building block functional moieties
to engineer fundamental solvation structures for desired electrolyte properties
and guide the discovery and rational design of new solvent materials.


  Social group activity recognition is a challenging task extended from group
activity recognition, where social groups must be recognized with their
activities and group members. Existing methods tackle this task by leveraging
region features of individuals following existing group activity recognition
methods. However, the effectiveness of region features is susceptible to person
localization and variable semantics of individual actions. To overcome these
issues, we propose leveraging attention modules in transformers to generate
social group features. In this method, multiple embeddings are used to
aggregate features for a social group, each of which is assigned to a group
member without duplication. Due to this non-duplicated assignment, the number
of embeddings must be significant to avoid missing group members and thus
renders attention in transformers ineffective. To find optimal attention
designs with a large number of embeddings, we explore several design choices of
queries for feature aggregation and self-attention modules in transformer
decoders. Extensive experimental results show that the proposed method achieves
state-of-the-art performance and verify that the proposed attention designs are
highly effective on social group activity recognition.


  A measurement of the top--antitop ($t\bar{t}$) charge asymmetry is presented
using 2011 LHC data collected by the ATLAS detector corresponding to an
integrated luminosity of 4.6 fb$^{-1}$ at a centre-of-mass energy of 7 TeV. The
analysis is performed in the dilepton channel, and two different observables
are studied: $A^{\ell\ell}_{\mathrm{C}}$, based on the identified charged
leptons, and $A^{t\bar{t}}_{\mathrm{C}}$, based on the reconstructed $t\bar{t}$
final state. The asymmetries, measured to be $A^{\ell\ell}_{\mathrm{C}} = 0.024
\pm 0.015 \mathrm{(stat.)} \pm 0.009 \mathrm{(syst.)}$ and
$A^{t\bar{t}}_{\mathrm{C}} = 0.021 \pm 0.025 \mathrm{(stat.)} \pm 0.017
\mathrm{(syst.)}$, are in agreement with the Standard Model predictions.


  Distributed algorithms can be efficiently used for solving economic dispatch
problem (EDP) in power systems. To implement a distributed algorithm, a
communication network is required, making the algorithm vulnerable to noise
which may cause detrimental decisions or even instability. In this paper, we
propose an agent-based method which enables a fully distributed solution of the
EDP in power systems with noisy information exchange. Through the novel design
of the gradient tracking update and introducing suppression parameters, the
proposed algorithm can effectively alleviate the impact of noise and it is
shown to be more robust than the existing distributed algorithms. The
convergence of the algorithm is also established under standard assumptions.
Moreover, a strategy are presented to accelerate our proposed algorithm.
Finally, the algorithm is tested on several IEEE bus systems to demonstrate its
effectiveness and scalability.


  Although the performance of 3D human pose and shape estimation methods has
improved significantly in recent years, existing approaches typically generate
3D poses defined in camera or human-centered coordinate system. This makes it
difficult to estimate a person's pure pose and motion in world coordinate
system for a video captured using a moving camera. To address this issue, this
paper presents a camera motion agnostic approach for predicting 3D human pose
and mesh defined in the world coordinate system. The core idea of the proposed
approach is to estimate the difference between two adjacent global poses (i.e.,
global motion) that is invariant to selecting the coordinate system, instead of
the global pose coupled to the camera motion. To this end, we propose a network
based on bidirectional gated recurrent units (GRUs) that predicts the global
motion sequence from the local pose sequence consisting of relative rotations
of joints called global motion regressor (GMR). We use 3DPW and synthetic
datasets, which are constructed in a moving-camera environment, for evaluation.
We conduct extensive experiments and prove the effectiveness of the proposed
method empirically. Code and datasets are available at
https://github.com/seonghyunkim1212/GMR


  In this article we prove that estimator stability is enough to show that
leave-one-out cross validation is a sound procedure, by providing concentration
bounds in a general framework. In particular, we provide concentration bounds
beyond Lipschitz continuity assumptions on the loss or on the estimator. We
obtain our results by relying on random variables with distribution satisfying
the logarithmic Sobolev inequality, providing us a relatively rich class of
distributions. We illustrate our method by considering several interesting
examples, including linear regression, kernel density estimation, and
stabilized/truncated estimators such as stabilized kernel regression.


  We revisit the classical theory of ten-dimensional two-derivative gravity
coupled to fluxes, scalar fields, D-branes, anti D-branes and
Orientifold-planes. We show that such set-ups do not give rise to a
four-dimensional positive curvature spacetime with the isometries of de Sitter
spacetime. We further argue that a de Sitter solution in type IIB theory may
still be achieved if the higher-order curvature corrections are carefully
controlled. Our analysis relies on the derivation of the de Sitter condition
from an explicit background solution by going beyond the supergravity limit of
type IIB theory. As such this also tells us how the background supersymmetry
should be broken and under what conditions D-term uplifting can be realized
with non self-dual fluxes.


  We study in this paper the phase transition in superlattices formed by
alternate magnetic and ferroelectric layers, by the use of Monte Carlo
simulation. We study effects of temperature, external magnetic and electric
fields, magnetoelectric coupling at the interfaceon the phase transition.
Magnetic layers in this work are modeled as thin films of simple cubic lattice
with Heisenbergspins. Electrical polarizations of $\pm{1}$ are assigned at
simple cubic lattice sites in the ferroelectric layers. The transition
temperature, the layer magnetizations, the layer polarizations, the
susceptibility, the internal energy, the interface magnetization and
polarization are calculated.The layer magnetizations and polarizations as
functions of temperature are shown for various coupling interactions and field
values.Mean-field theory is also presented and compared to MC results.


  We address the constraints on the SUSY seesaw parameters arising from Lepton
Flavour Violation observables. Working in the Constrained Minimal
Supersymmetric Standard Model extended by three right-handed (s)neutrinos, we
study the predictions for the branching ratios of $l_j \to l_i \gamma$ and $l_j
\to 3 l_i$ channels. We impose compatibility with neutrino data, electric
dipole moment bounds, and further require a successful baryon asymmetry of the
Universe (via thermal leptogenesis). We emphasise the interesting interplay
between $\theta_{13}$ and the LFV muon decays, pointing out the hints on the
SUSY seesaw parameters that can arise from measurements of $\theta_{13}$ and
LFV branching ratios. This is a brief summary of the work of Ref.
\cite{Antusch:2006vw}.


  We consider random Hermitian matrices with independent upper triangular
entries. Wigner's semicircle law says that under certain additional
assumptions, the empirical spectral distribution converges to the semicircle
distribution. We characterize convergence to semicircle in terms of the
variances of the entries, under natural assumptions such as the Lindeberg
condition. The result extends to certain matrices with entries having infinite
second moments. As a corollary, another characterization of semicircle
convergence is given in terms of convergence in distribution of the row sums to
the standard normal distribution.


  A new method has been developed recently to derive Hawking radiations from
black holes based on considerations of gravitational and gauge anomalies at the
horizon gr-qc/0502074 hep-th/0602146. In this paper, we apply the method to
Myers-Perry black holes with multiple angular momenta in various dimensions by
using the dimensional reduction technique adopted in the case of
four-dimensional rotating black holes hep-th/0606018.


  More than a dozen microlensing events have been detected so far towards the
LMC and 2 towards the SMC. If all the lenses are in the Galactic halo, both the
LMC and the SMC events are expected to have similar time scales. However, the
first event towards the SMC, MACHO 97-SMC-1, had a time scale of 123 days which
is much larger than the typical time scale for the LMC events. From optical
depth estimates, we first show that the stars within the SMC play a dominant
role as gravitational lenses and can fully account for the observed
microlensing events, mainly due to its large physical depth. We also show that
if the lenses are within the Magellanic Clouds, then the SMC events should be
longer in duration than the LMC events, a fact that is consistent with the
observations. The time scale of the event implies that the mass of the lens is
>2 solar masses if it is in the Milky Way disk or halo, in which case the lens
is expected to be bright and should reveal itself in the spectrum. Here, we
present an optical spectrum of MACHO 97-SMC-1 which shows that the lens is not
in the Milky Way disk or halo, but is a low-mass star within the SMC. It is
worth noting here that MACHO SMC-98-1 is the only OTHER observed event towards
the SMC. This was a binary lens event where the caustic crossing time-scale as
observed by PLANET, MACHO, EROS and OGLE collaborations, suggests that the lens
is within the SMC. Furthermore, the only LMC event where the location of the
lens is known is the binary lens event MACHO LMC-9, for which the lens is also
within the LMC. Thus, ALL the 3 microlensing events towards the Magellanic
Clouds for which we have independent knowledge of the location of the lenses
are due to self-lensing within the Magellanic Clouds.


  We discuss two combinatorical ways of generalizing the definition of expander
graphs and Ramanujan graphs, to quotients of buildings of higher dimension. The
two possible definitions are equivalent for affine buildings, giving the notion
of an Lp-expander complex. We calculate explicit spectral gaps on many
combinatorical operators, on any Lp-expander complex.
  We associate with any complex a natural "zeta function", generalizing the
Ihara-Hashimoto zeta function of a finite graph. We generalize a well known
theorem of Hashimoto, showing that a complex is Ramanujan if and only if the
zeta function satisfies the Riemann hypothesis.


  We discuss tableaux for the Implicational Propositional Calculus and show how
they may be used to establish its completeness.


  Using Kauffman's model of flat knotted ribbons, we demonstrate how all
regular polygons of at least seven sides can be realised by ribbon
constructions of torus knots. We calculate length to width ratios for these
constructions thereby bounding the Ribbonlength of the knots. In particular, we
give evidence that the closed (respectively, truncation) Ribbonlength of a
(q+1,q) torus knot is (2q+1)cot(\pi/(2q+1)) (resp., 2q cot(\pi/(2q+1))). Using
these calculations, we provide the bounds c_1 \leq 2/\pi and c_2 \geq 5/3
cot(\pi/5) for the constants c_1 and c_2 that relate Ribbonlength R(K) and
crossing number C(K) in a conjecture of Kusner: c_1 C(K) \leq R(K) \leq c_2
C(K).


  High resolution reconstruction of complicated objects from incomplete and
noisy data can be achieved by solving modulation equations iteratively under
physical constraints. This direct demodulation method is a powerful technique
for dealing with inverse problem in general case. Spectral and image
restorations and computerized tomography are only particular cases of general
demodulation. It is possible to reconstruct an object in higher dimensional
space from observations by a simple lower dimensional instrument through direct
demodulation. Our simulations show that wide field and high resolution images
of space hard X-rays and soft gamma rays can be obtained by a collimated
non-position-sensitive detector without coded aperture masks.


  Continuation model predictive control (MPC), introduced by T. Ohtsuka in
2004, uses Krylov-Newton approaches to solve MPC optimization and is suitable
for nonlinear and minimum time problems. We suggest particle continuation MPC
in the case, where the system dynamics or constraints can discretely change
on-line. We propose an algorithm for on-line controller implementation of
continuation MPC for ensembles of predictions corresponding to various
anticipated changes and demonstrate its numerical effectiveness for a test
minimum time problem arriving to a destination. Simultaneous on-line particle
computation of ensembles of controls, for several dynamically changing system
dynamics, allows choosing the optimal destination on-line and adapt it as
needed.


  We have used diffusion Monte Carlo (DMC) calculations to study the structural
properties of magnesium hydride (MgH$_2$), including the pressure-volume
equation of state, the cohesive energy and the enthalpy of formation from
magnesium bulk and hydrogen gas. The calculations employ pseudopotentials and
B-spline basis sets to expand the single particle orbitals used to construct
the trial wavefunctions. Extensive tests on system size, time step, and other
sources of errors, performed on periodically repeated systems of up to 1050
atoms, show that all these errors together can be reduced to below 10 meV per
formula unit. We find excellent agreement with the experiments for the
equilibrium volume of both the Mg and the MgH$_2$ crystals. The cohesive energy
of the Mg crystal is found to be 1.51(1) eV, and agrees perfectly with the
experimental value of 1.51 eV. The enthalpy of formation of MgH$_2$ from Mg
bulk and H$_2$ gas is found to be $0.85 \pm 0.01$ eV/formula unit, or $82 \pm
1$ kJ/mole, which is off the experimental one of $76.1 \pm 1$ kJ/mole only by 6
kJ/mole. This shows that DMC can almost achieve chemical accuracy (1 kcal/mole)
on this system. Density functional theory errors are shown to be much larger,
and depend strongly on the functional employed.


  This paper aims at providing a first step toward a qualitative theory for a
new class of chemotaxis models derived from the celebrated Keller-Segel system,
with the main novelty being that diffusion is nonlinear with flux delimiter
features. More precisely, as a prototypical representative of this class we
study radially symmetric solutions of the parabolic-elliptic system (see the
text).
  Under the initial condition $u|_{t=0}=u_0>0$ and no-flux boundary conditions
in balls $\Omega\subset\mathbb{R}^n$, where $\chi>0$ and
$\mu:=\frac{1}{|\Omega|} \int_\Omega u_0$.\abs
  The main results assert the existence of a unique classical solution,
extensible in time up to a maximal $T_{max} \in (0,\infty]$ which has the
property that $$\mbox{if} \quad T_{max}<\infty \quad \mbox{then}
\quad\limsup_{t\nearrow T_{max}} \|u(\cdot,t)\|_{L^\infty(\Omega)}=\infty.
\qquad \qquad (\star)$$
  The proof therefore is mainly based on comparison methods, which firstly
relate pointwise lower and upper bounds for the spatial gradient $u_r$ to
$L^\infty$ bounds for $u$ and to {\em upper bounds} for $z:=\frac{u_t}{u}$;
secondly, another comparison argument involving nonlocal nonlinearities
provides an appropriate control of $z_+$ in terms of bounds for $u$ and
$|u_r|$, with suitably mild dependence on the latter.
  As a consequence of ($\star$) by means of suitable a priori estimates it is
moreover shown that the above solutions are global and bounded when either
$$n\ge 2 \ \mbox{ and } \chi<1, \qquad \mbox{or} \qquad n=1, \ \chi>0 \ \mbox{
and } m<m_c, $$ with $m_c:=\frac{1}{\sqrt{\chi^2-1}}$ if $\chi>1$ and
$m_c:=\infty$ if $\chi\le 1$. That these conditions are essentially optimal
will be shown in a forthcoming paper in which ($\star$) will be used to derive
complementary results on the occurrence of solutions blowing up in finite time
with respect to the norm of $u$ in $L^\infty(\Omega)$.


  Let $\alpha\in(0,1)$, $K\geq 1$, and $d=2\frac{1+\alpha K}{1+K}$. Given a
compact set $E\subset\C$, it is known that if $\H^d(E)=0$ then $E$ is removable
for $\alpha$-H\"older continuous $K$-quasiregular mappings in the plane. The
sharpness of the index $d$ is shown with the construction, for any $t>d$, of a
set $E$ of Hausdorff dimension $\dim(E)=t$ which is not removable. In this
paper, we improve this result and construct compact nonremovable sets $E$ such
that $0<\H^d(E)<\infty$. For the proof, we give a precise planar
$K$-quasiconformal mapping whose H\"older exponent is strictly bigger than
$\frac{1}{K}$, and that exhibits extremal distortion properties.


  According to Letourmy and Vendramin, a representation of a skew brace is a
pair of representations on the same vector space, one for the additive group
and the other for the multiplicative group, that satisfies a certain
compatibility condition. Following their definition, we shall explain how some
of the results from representation theory of groups, such as Maschke's theorem
and Clifford's theorem, extend naturally to that of skew braces. We shall also
give some concrete examples to illustrate that skew brace representations are
more difficult to classify than group representations.


  We investigate the implications of a possible excess of the electron neutrino
events in the Super-Kamiokande atmospheric neutrino experiment. The excess, if
real, leads to constraints on the $\nu_\mu \leftrightarrow \nu_e$, $\nu_\mu
\leftrightarrow \nu_\tau$ and $\nu_e \leftrightarrow \nu_\tau$ oscillation
parameters. Specifically, the excess impies that $\nu_e - \nu_\mu$ and $\nu_\mu
- \nu_\tau$ mixings are large and $\nu_e - \nu_\tau$ mixing is small. We show
that the electron neutrino excess favors the large mixing angle MSW solution of
the solar neutrino problem.


  Models with 3-branes in extra dimensions typically imply the existence of a
radion, phi that can mix with the Higgs, h, thereby modifying the Higgs
properties and the prospects for its detectability at the LHC. The presence of
the phi will extend the scope of the LHC searches. Detection of both the phi
and the h might be possible. In this paper, we study the complementarity of the
observation of gg -> h, with h -> gamma gamma or h -> ZZ -> 4 leptons, and gg
-> phi -> ZZ -> 4 leptons at the LHC in the context of the Randall-Sundrum
model. The potential for determining the nature of the detected scalar(s) at
the LHC and at an e+e- linear collider is discussed, both separately and in
combination.


  Biofilms are a cluster of bacteria embedded in extracellular polymeric
substances (EPS) that contain a complex composition of polysaccharides,
proteins, and extracellular DNA (eDNA). Desirable mechanical properties of the
biofilms are critical for their survival, propagation, and dispersal, and the
response of mechanical properties to different treatment conditions also sheds
light on biofilm control and eradication in vivo and on engineering surfaces.
However, it is challenging yet important to interrogate mechanical behaviors of
biofilms with a high spatial resolution because biofilms are very
heterogeneous. Moreover, biofilms are viscoelastic, and their time-dependent
mechanical behavior is difficult to capture. Herein, we developed a powerful
technique that combines the high spatial resolution of the atomic force
microscope (AFM) with a rigorous history-dependent viscoelastic analysis to
deliver highly spatial-localized biofilm properties within a wide
time-frequency window. By exploiting the use of static force spectroscopy in
combination with an appropriate viscoelastic framework, we highlight the
intensive amount of time-dependent information experimentally available that
has been largely overlooked. It is shown that this technique provides a
detailed nanorheological signature of the biofilms even at the single-cell
level. We share the computational routines that would allow any user to perform
the analysis from experimental raw data. The detailed localization of
mechanical properties in space and in time-frequency domain provides insights
on the understanding of biofilm stability, cohesiveness, dispersal, and
control.


  We present the first results of an observational project, which addresses the
period changing behaviour of a sample of high-amplitude delta Scuti stars. In
this paper we discuss the double-mode nature of V567 Ophiuchi. It was observed
on 15 nights in two consecutive years in order to resolve the long-standing
ambiguity related to its secondary period. A frequency analysis of almost 5000
individual single-filtered CCD V measurements resulted in two independent
frequencies (f_1=6.6879 c/d and f_2=11.8266 c/d) with a ratio of f_1/f_2=0.565.
Earlier data taken from the literature were used to refine the dominant period,
and the re-analysis supports the existence of the secondary period. Possible
asteroseismological implications are briefly discussed.


  We study spin dynamics of excitons confined in self-assembled CdSe quantum
dots by means of optical orientation in magnetic field. At zero field the
exciton emission from QDs populated via LO phonon-assisted absorption shows a
circular polarization of 14%. The polarization degree of the excitonic emission
increases dramatically when a magnetic field is applied. Using a simple model,
we extract the exciton spin relaxation times of 100 ps and 2.2 ns in the
absence and presence of magnetic field, respectively. With increasing
temperature the polarization of the QD emission gradually decreases.
Remarkably, the activation energy which describes this decay is independent of
the external magnetic field, and, therefore, of the degeneracy of the exciton
levels in QDs. This observation implies that the temperature-induced
enhancement of the exciton spin relaxation is insensitive to the energy level
degeneracy and can be attributed to the same excited state distribution.


  'The trend is your friend' is a common saying, the difficulty lies in
determining if and when you are in a trend. Is the trend strong enough to
trade? When does the trend reverse and how are you going to determine this? We
will try and answer at least some of these questions here. We are deriving a
novel indicator to measure the power of a trend using digital signal processing
techniques, separating the Signal from the Noise. We apply these to examples as
well as real data and evaluate the accuracy of these and the relation to PNL
performance of the 'Volatility Index' trend following algorithm devised by J.
Welles Wilder Jr. in 1978.


  Chern insulators are states of matter characterized by a quantized Hall
conductance, gapless edge modes but also a singular response to monopole
configurations of an external electromagnetic field. In this paper, we describe
the nature of such a singular response and show how it can be used to define a
class of operators acting as non-local order parameters. These operators
characterize the Chern-insulator states in the following way: for a given
state, there exists a corresponding operator which has an algebraically
decaying two-point function in that particular state, while it decays
exponentially in all other states. The behaviour of the order parameter is
defined only in terms of the electromagnetic response, and not from any
microscopic properties, and we therefore claim to have found a generic order
parameter for the Chern insulating states. We support this claim by numerically
evaluating the order parameters for different insulating states. We also show
how our construction can be generalized to other states with topological
electromagnetic response, and use the states with a quantized magnetoelectric
effect in three dimensions as an example. Besides providing novel insights into
topological states of matter, our construction can be exploited to efficiently
diagnose such states numerically.


  Observation has not yet determined whether the distribution of spin vectors
of galaxies is truly random. It is unclear whether is there any large-scale
symmetry-breaking in the distribution of the vorticity field in the universe.
Here, we present a formulation to evaluate the dipole component D_{max} of the
observed spin distribution, whose statistical significance sigma_{D} can be
calibrated by the expected amplitude for 3D random walk (random flight)
simulations.
  We apply this formulation to evaluate the dipole component in the
distribution of Sloan Digital Sky Survey (SDSS) spirals. Shamir(2017a)
published a catalog of spiral galaxies from the SDSS DR8, classifying them with
his pattern recognition tool into clockwise and counterclockwise (Z-spiral and
S-spirals, respectively). He found significant photometric asymmetry in their
distribution. We have confirmed that this sample provides dipole asymmetry up
to a level of sigma_{D}=4.00.
  However, we also found that the catalog contains a significant number of
multiple entries of the same galaxies. After removing the duplicated entries,
the number of samples shrunk considerably to 45%. The actual dipole asymmetry
observed for the 'cleaned' catalog is quite modest, sigma_{D}=0.29. We conclude
that SDSS data alone does not support the presence of a large-scale
symmetry-breaking in the spin vector distribution of galaxies in the local
universe. The data are compatible with a random distribution.


  We study the large-time behavior of global energy class solutions of the one
dimensional nonlinear Schr\"odinger equation with a general localized potential
term and a defocusing nonlinear term. By using a new type of interaction
Morawetz estimate localized to an exterior region, we prove that these
solutions decompose into a free wave and a weakly localized part which is
asymptotically orthogonal to any fixed free wave. We further show that the
$L^2$ norm of this weakly localized part is concentrated in the region $|x|
\leq t^{1/2+}$, and that the energy ($\dot{H}^1$) norm is concentrated in $|x|
\leq t^{1/3+}$.


  A gravitational theory of a scalar field non-minimally coupled with torsion
and boundary term is considered with the aim to construct Lorentzian wormholes.
Geometrical parameters including shape and redshift functions are obtained for
these solutions. We adopt the formalism of Noether Gauge Symmetry Approach in
order to find symmetries, Lie brackets and invariants (conserved quantities).
Furthermore by imposing specific forms of potential function, we are able to
calculate metric coefficients and discuss their geometrical behavior.


  We study the $L\to l l' l' \nu_l \nu_L$ decays ($L=\tau,\mu$; $l,l'=\mu,e$)
in the Standard Model (SM) and in the effective field theory (EFT) description
of the weak charged current at low energy, both for polarized and unpolarized
$L$, keeping the $l,l'$ mass dependence. We clarify the discrepancy between two
previous SM calculations of the decay rate improving their precision. The
recent $3.5\,\sigma$ anomaly found in $\tau\to e \gamma\bar{\nu}_e\nu_\tau$
could be checked using our precise prediction for the $\tau\to e e e
\bar{\nu}_e\nu_\tau$ decays, which shall be measured analyzing already existing
data from the first generation B-factories. It is shown how measurements of the
di-$l'$ mass distribution (with appropriate cuts) and $T$-asymmetries are able
to reveal the corresponding lepton flavor violating (LFV) processes without
neutrinos in the final state.


  One percent of redshift z~0.1 Active Galactic Nuclei (AGNs) show velocity
splitting of a few hundred km/s in the narrow emission lines in spatially
integrated spectra. Such line profiles have been found to arise from the bulk
motion of ionized gas clouds associated with galactic-scale outflows, merging
pairs of galaxies each harboring a supermassive black hole (SMBH), and/or
galactic-scale disk rotation. It remains unclear, however, how the frequency of
narrow-line velocity splitting may depend on AGN luminosity. Here we study the
correlation between the fraction of Type 2 AGNs with double-peaked narrow
emission lines and AGN luminosity as indicated by [O III]5007 emission-line
luminosity L_[O III]. We combine the sample of Liu et al. (2010) at z~0.1 with
a new sample of 178 Type 2 AGNs with double-peaked [O III] emission lines at
z~0.5. We select the new sample from a parent sample of 2089 Type 2 AGNs from
the SDSS-III/Baryon Oscillation Spectroscopic Survey. We find a statistically
significant (~4.2\sigma) correlation between L_[O III] and the fraction of
objects that exhibit double-peaked narrow emission lines among all Type 2 AGNs,
corrected for selection bias and incompleteness due to [O III] line width,
equivalent width, splitting velocity, and/or equivalent width ratio between the
two velocity components. Our result suggests that galactic-scale outflows
and/or merging pairs of SMBHs are more prevalent in more powerful AGNs,
although spatially resolved follow up observations are needed to resolve the
origin(s) for the narrow-line velocity splitting for individual AGNs.


  With the urgent need to implement the EU countries pledges and to monitor the
effectiveness of Green Deal plan, Monitoring Reporting and Verification tools
are needed to track how emissions are changing for all the sectors. Current
official inventories only provide annual estimates of national CO$_2$ emissions
with a lag of 1+ year which do not capture the variations of emissions due to
recent shocks including COVID lockdowns and economic rebounds, war in Ukraine.
Here we present a near-real-time country-level dataset of daily fossil fuel and
cement emissions from January 2019 through December 2021 for 27 EU countries
and UK, which called Carbon Monitor Europe. The data are calculated separately
for six sectors: power, industry, ground transportation, domestic aviation,
international aviation and residential. Daily CO$_2$ emissions are estimated
from a large set of activity data compiled from different sources. The goal of
this dataset is to improve the timeliness and temporal resolution of emissions
for European countries, to inform the public and decision makers about current
emissions changes in Europe.


  We consider large uniform labeled random graphs in different classes with few
induced $P_4$ ($P_4$ is the graph consisting of a single line of $4$ vertices)
which generalize the case of cographs. Our main result is the convergence to a
Brownian limit object in the space of graphons. As a by-product we obtain new
asymptotic enumerative results for all these graph classes. We also obtain
typical density results for a wide variety of induced subgraphs. These
asymptotics hold at a smaller scale than what is observable through the graphon
convergence. Our proofs rely on tree encoding of graphs. We then use mainly
combinatorial arguments, including the symbolic method and singularity
analysis.


  A new variation of blockchain proof of work algorithm is proposed to
incentivize the timely execution of image processing algorithms. A sample image
processing algorithm is proposed to determine interesting images using analysis
of the entropy of pixel subsets within images. The efficacy of the image
processing algorithm is examined using two small sets of training and test
data. The interesting image algorithm is then integrated into a simplified
blockchain mining proof of work algorithm based on Bitcoin. The incentive of
cryptocurrency mining is theorized to incentivize the execution of the
algorithm and thus the retrieval of images that satisfy a minimum requirement
set forth by the interesting image algorithm. The digital storage implications
of running an image- based blockchain are then examined mathematically.


  Distributionally-robust optimization is often studied for a fixed set of
distributions rather than time-varying distributions that can drift
significantly over time (which is, for instance, the case in finance and
sociology due to underlying expansion of economy and evolution of
demographics). This motivates understanding conditions on probability
distributions, using the Wasserstein distance, that can be used to model
time-varying environments. We can then use these conditions in conjunction with
online stochastic optimization to adapt the decisions. We considers an online
proximal-gradient method to track the minimizers of expectations of smooth
convex functions parameterised by a random variable whose probability
distributions continuously evolve over time at a rate similar to that of the
rate at which the decision maker acts. We revisit the concepts of estimation
and tracking error inspired by systems and control literature and provide
bounds for them under strong convexity, Lipschitzness of the gradient, and
bounds on the probability distribution drift. Further, noting that computing
projections for a general feasible sets might not be amenable to online
implementation (due to computational constraints), we propose an exact penalty
method. Doing so allows us to relax the uniform boundedness of the gradient and
establish dynamic regret bounds for tracking and estimation error. We further
introduce a constraint-tightening approach and relate the amount of tightening
to the probability of satisfying the constraints.


  Quantum computing in terms of geometric phases, i.e. Berry or
Aharonov-Anandan phases, is fault-tolerant to a certain degree. We examine its
implementation based on Zeeman coupling with a rotating field and isotropic
Heisenberg interaction, which describe NMR and can also be realized in quantum
dots and cold atoms. Using a novel physical representation of the qubit basis
states, we construct $\pi/8$ and Hadamard gates based on Berry and
Aharonov-Anandan phases. For two interacting qubits in a rotating field, we
find that it is always impossible to construct a two-qubit gate based on Berry
phases, or based on Aharonov-Anandan phases when the gyromagnetic ratios of the
two qubits are equal. In implementing a universal set of quantum gates, one may
combine geometric $\pi/8$ and Hadamard gates and dynamical $\sqrt{\rm SWAP}$
gate.


  We have studied the optical and electrical spectra from an n i p LED as a
function of magnetic field. This sample incorporated three GaAs quantum wells
in the intrinsic region. This device had excess n type doping and as a result.
The quantum wells were populated by a two dimension Landau electron gas. The
broad B0 field emission band evolved into a series of discrete features in the
presence of a magnetic field. These were identified as interband transitions
between the different values of l. Landau levels associated with the sub-bands,
with the selection rule. An energy splitting between the two polarised
components was observed for each Landau level transition. This was found to be
equal to the sum of the conduction and valence band spin splittings. We used
the know value of electron g factor to determine the valence band spin
splittings. Our experimental values were compared to the numerically calculated
values and were found to be in reasonable agreement.


  The spatial extension and complexity of the eigenfunctions of an open
finite-size two-dimensional (2D) random system are systematically studied for a
random collection of systems ranging from weakly scattering to localized. The
eigenfunctions are obtained by introducing gain in the medium and pumping just
above threshold. All lasing modes are found to correspond to quasimodes of the
passive system, for all regimes of propagation. We demonstrate the existence of
multipeaked quasimodes or necklace states in 2D at the transition from
localized to diffusive, resulting from the coupling of localized states.


  The fractions of constant conductivity, i, where the conductivity is ie^2/h
are interpretted to arise from the summation of two frequencies, \omega_1+
\omega_2, type of processes so that the quantum Hall effect becomes a problem
of spectroscopic energy levels. We describe the conversion of resistivity to
the frequency spectrum. An effort is made to look at the recent articles from
the Phys. Rev. Lett. 1998-2001, to see if there are any data which does not
agree with our theory.
  It is found that all of the data agrees with our theory, The papers which
claim to provide the theoretical base are found to be irrelevant to the
experimental data.


  We study the problem of approximating the quality of a disperser. A bipartite
graph $G$ on $([N],[M])$ is a $(\rho N,(1-\delta)M)$-disperser if for any
subset $S\subseteq [N]$ of size $\rho N$, the neighbor set $\Gamma(S)$ contains
at least $(1-\delta)M$ distinct vertices. Our main results are strong
integrality gaps in the Lasserre hierarchy and an approximation algorithm for
dispersers.
  \begin{enumerate}
  \item For any $\alpha>0$, $\delta>0$, and a random bipartite graph $G$ with
left degree $D=O(\log N)$, we prove that the Lasserre hierarchy cannot
distinguish whether $G$ is an $(N^{\alpha},(1-\delta)M)$-disperser or not an
$(N^{1-\alpha},\delta M)$-disperser.
  \item For any $\rho>0$, we prove that there exist infinitely many constants
$d$ such that the Lasserre hierarchy cannot distinguish whether a random
bipartite graph $G$ with right degree $d$ is a $(\rho N,
(1-(1-\rho)^d)M)$-disperser or not a $(\rho N, (1-\Omega(\frac{1-\rho}{\rho d +
1-\rho}))M)$-disperser. We also provide an efficient algorithm to find a subset
of size exact $\rho N$ that has an approximation ratio matching the integrality
gap within an extra loss of
$\frac{\min\{\frac{\rho}{1-\rho},\frac{1-\rho}{\rho}\}}{\log d}$.
\end{enumerate}
  Our method gives an integrality gap in the Lasserre hierarchy for bipartite
expanders with left degree~$D$. $G$ on $([N],[M])$ is a $(\rho N,a)$-expander
if for any subset $S\subseteq [N]$ of size $\rho N$, the neighbor set
$\Gamma(S)$ contains at least $a \cdot \rho N$ distinct vertices. We prove that
for any constant $\epsilon>0$, there exist constants $\epsilon'<\epsilon,\rho,$
and $D$ such that the Lasserre hierarchy cannot distinguish whether a bipartite
graph on $([N],[M])$ with left degree $D$ is a $(\rho N,
(1-\epsilon')D)$-expander or not a $(\rho N, (1-\epsilon)D)$-expander.


  Speaker diarization consists of assigning speech signals to people engaged in
a dialogue. An audio-visual spatiotemporal diarization model is proposed. The
model is well suited for challenging scenarios that consist of several
participants engaged in multi-party interaction while they move around and turn
their heads towards the other participants rather than facing the cameras and
the microphones. Multiple-person visual tracking is combined with multiple
speech-source localization in order to tackle the speech-to-person association
problem. The latter is solved within a novel audio-visual fusion method on the
following grounds: binaural spectral features are first extracted from a
microphone pair, then a supervised audio-visual alignment technique maps these
features onto an image, and finally a semi-supervised clustering method assigns
binaural spectral features to visible persons. The main advantage of this
method over previous work is that it processes in a principled way speech
signals uttered simultaneously by multiple persons. The diarization itself is
cast into a latent-variable temporal graphical model that infers speaker
identities and speech turns, based on the output of an audio-visual association
process, executed at each time slice, and on the dynamics of the diarization
variable itself. The proposed formulation yields an efficient exact inference
procedure. A novel dataset, that contains audio-visual training data as well as
a number of scenarios involving several participants engaged in formal and
informal dialogue, is introduced. The proposed method is thoroughly tested and
benchmarked with respect to several state-of-the art diarization algorithms.


  Recent years have seen the development of many open-source ML fairness
toolkits aimed at helping ML practitioners assess and address unfairness in
their systems. However, there has been little research investigating how ML
practitioners actually use these toolkits in practice. In this paper, we
conducted the first in-depth empirical exploration of how industry
practitioners (try to) work with existing fairness toolkits. In particular, we
conducted think-aloud interviews to understand how participants learn about and
use fairness toolkits, and explored the generality of our findings through an
anonymous online survey. We identified several opportunities for fairness
toolkits to better address practitioner needs and scaffold them in using
toolkits effectively and responsibly. Based on these findings, we highlight
implications for the design of future open-source fairness toolkits that can
support practitioners in better contextualizing, communicating, and
collaborating around ML fairness efforts.


  We study certain top intersection products on the Hilbert scheme of points on
a nonsingular surface relative to an effective smooth divisor. We find a
formula relating these numbers to the corresponding intersection numbers on the
non-relative Hilbert schemes. In particular, we obtain a relative version of
the explicit formula found by Carlsson-Okounkov for the Euler class of the
twisted tangent bundle of the Hilbert schemes.


  The Abelian current algebra on the lattice is given from a series of the
independent Weyl pairs and the shift operator is constructed by this algebra.
So the realization of the operators of the braid group is obtained. For
$|q|\neq 1$ the shift operator is the product of the theta functions of the
generators $w_n$ of the current algebra. For $|q|=1$ it can be expressed by the
quantum dilogarithm of $w_n$.


  The goal of this work is to detect and recognize sequences of letters signed
using fingerspelling in British Sign Language (BSL). Previous fingerspelling
recognition methods have not focused on BSL, which has a very different signing
alphabet (e.g., two-handed instead of one-handed) to American Sign Language
(ASL). They also use manual annotations for training. In contrast to previous
methods, our method only uses weak annotations from subtitles for training. We
localize potential instances of fingerspelling using a simple feature
similarity method, then automatically annotate these instances by querying
subtitle words and searching for corresponding mouthing cues from the signer.
We propose a Transformer architecture adapted to this task, with a
multiple-hypothesis CTC loss function to learn from alternative annotation
possibilities. We employ a multi-stage training approach, where we make use of
an initial version of our trained model to extend and enhance our training data
before re-training again to achieve better performance. Through extensive
evaluations, we verify our method for automatic annotation and our model
architecture. Moreover, we provide a human expert annotated test set of 5K
video clips for evaluating BSL fingerspelling recognition methods to support
sign language research.


  We study gauge symmetry in F-theory in light of global aspects. For this, we
consider not only a simple (local) group, but also a semi-simple group with
Abelian factors. Once we specify the complete gauge group by decomposing the
discriminant, analogous to arranging 7-branes, we can derive the matter
contents, their localization and the relation to enhanced groups. Global
constraints coming from Calabi--Yau conditions and anomaly cancellations imply
a unified group. The semisiple group shows explicit formation of matter curves
and nontriviality of its embedding into exceptional group. Also the dual
heterotic string vacua with line bundles provide a guide on the unification.


  In this work, we present CEDR, a Compiler-integrated, Extensible Domain
Specific System on Chip Runtime ecosystem to facilitate research towards
addressing the challenges of architecture, system software and application
development with distinct plug-and-play integration points in a unified compile
time and run time workflow. We demonstrate the utility of CEDR on the Xilinx
Zynq MPSoC-ZCU102 for evaluating performance of pre-silicon hardware in the
trade space of SoC configuration, scheduling policy and workload complexity
based on dynamically arriving workload scenarios composed of real-life signal
processing applications scaling to thousands of application instances with FFT
and matrix multiply accelerators. We provide insights into the trade-offs
present in this design space through a number of distinct case studies. CEDR is
portable and has been deployed and validated on Odroid-XU3, X86 and Nvidia
Jetson Xavier based SoC platforms. Taken together, CEDR is a capable
environment for enabling research in exploring the boundaries of productive
application development, resource management heuristic development, and
hardware configuration analysis for heterogeneous architectures.


  We consider the recently introduced mimetic gravity, which is a
Weyl-symmetric extension of the General Relativity and which can play a role of
an imperfect fluid-like Dark Matter with a small sound speed. In this paper we
discuss in details how this higher- derivative scalar-tensor theory goes beyond
the construction by Horndeski, keeping only one scalar degree of freedom on top
of two standard graviton polarizations. In particular, we consider
representations of the theory in different sets of Weyl-invariant variables and
connect this framework to the singular Brans-Dicke theory. Further, we find
solution of equations of motion for the mimetic gravity in the synchronous
reference frame in a general curved spacetime. This solution is exact in the
test-field approximation or in the case of a shear-free spacetime without any
other matter.


  In recent years, natural language processing has gained significant
popularity in various sectors, including the legal domain. This paper presents
NeCo Team's solutions to the Vietnamese text processing tasks provided in the
Automated Legal Question Answering Competition 2023 (ALQAC 2023), focusing on
legal domain knowledge acquisition for low-resource languages through data
enrichment. Our methods for the legal document retrieval task employ a
combination of similarity ranking and deep learning models, while for the
second task, which requires extracting an answer from a relevant legal article
in response to a question, we propose a range of adaptive techniques to handle
different question types. Our approaches achieve outstanding results on both
tasks of the competition, demonstrating the potential benefits and
effectiveness of question answering systems in the legal field, particularly
for low-resource languages.


  We have studied semileptonic B decay to the exclusive charmless states pi,
rho/omega, eta and eta' using the full 15.5 fb^-1 CLEO Upsilon(4S) sample, with
measurements performed in subregions of phase space to minimize dependence on a
priori knowledge of the form factors involved. We find total branching
fractions B(B^0 -> pi^-l^+nu) = (1.37 +- 0.15_stat +- 0.11_sys) x 10^-4 and
B(B^0 -> rho^- l^+ nu) = (2.93 +- 0.37_stat +- 0.37_sys) x 10^-4. We find
evidence for B^+ -> eta' l^+ nu, with B(B^+ -> eta' l^+ nu) = (2.66 +-
0.80_stat +- 0.56_sys) x 10^-4 and 1.20 x 10^-4 < B(B^+ -> eta' l^+ nu) < 4.46
x 10^-4 (90% CL). We also limit B(B^+ -> eta l^+ nu) < 1.01 x 10^-4 (90% CL).
By combining our B -> pi l nu information with unquenched lattice calculations,
we find |V_ub| = (3.6 +- 0.4 +- 0.2 +0.6 -0.4) x 10^-3, where the errors are
statistical, experimental systematic, and theoretical systematic, respectively.


  In this article we consider algebraic structures on the homology of the space
of paths in a manifold with endpoints in a submanifold. The
Pontryagin-Chas-Sullivan product on the homology of this space had already been
investigated by Hingston and Oancea for a particular example. We consider this
product as a special case of a more general construction where we consider
pullbacks of the path space of a manifold under arbitrary maps. The product on
the homology of this space as well as the module structure over the
Chas-Sullivan ring are shown to be invariant under homotopies of the respective
maps. This in particular implies that the Pontryagin-Chas-Sullivan product as
well as the module structure on the space of paths with endpoints in a
submanifold are isomorphic for two homotopic embeddings of the submanifold.
Moreover, for null-homotopic embeddings of the submanifold this yields nice
formulas which we can be used to compute the product and the module structure
explicitly. We show that in the case of a null-homotopic embedding the homology
of the space of paths with endpoints in a submanifold is even an algebra over
the Chas-Sullivan ring. This property does not hold in general as we show with
a counterexample.


  In dynamical systems with divided phase space, the vicinity of the boundary
between regular and chaotic regions is often "sticky," that is, trapping orbits
from the chaotic region for long times. Here, we investigate the stickiness in
the simplest mushroom billiard, which has a smooth such boundary, but
surprisingly subtle behaviour. As a measure of stickiness, we investigate P(t),
the probability of remaining in the mushroom cap for at least time t given
uniform initial conditions in the chaotic part of the cap. The stickiness is
sensitively dependent on the radius of the stem r via the Diophantine
properties of rho = (2/\pi) arccos r. Almost all rho give rise to families of
marginally unstable periodic orbits (MUPOs) where P(t) ~ C/t, dominating the
stickiness of the boundary. Here we consider the case where rho is MUPO-free
and has continued fraction expansion with bounded partial quotients. We show
that t^2 P(t) is bounded, varying infinitely often between values whose ratio
is at least 32/27. When rho has an eventually periodic continued fraction
expansion, that is, a quadratic irrational, t^2 P(t) converges to a
log-periodic function. In general, we expect less regular behaviour, with upper
and lower exponents lying between 1 and 2. The results may shed light on the
parameter dependence of boundary stickiness in annular billiards and generic
area preserving maps.


  Robots often have to operate in discrete partially observable worlds, where
the states of world are only observable at runtime. To react to different world
states, robots need contingencies. However, computing contingencies is costly
and often non-optimal. To address this problem, we develop the improved path
tree optimization (PTO) method. PTO computes motion contingencies by
constructing a tree of motion paths in belief space. This is achieved by
constructing a graph of configurations, then adding observation edges to extend
the graph to belief space. Afterwards, we use a dynamic programming step to
extract the path tree. PTO extends prior work by adding a camera-based state
sampler to improve the search for observation points. We also add support to
non-euclidean state spaces, provide an implementation in the open motion
planning library (OMPL), and evaluate PTO on four realistic scenarios with a
virtual camera in up to 10-dimensional state spaces. We compare PTO with a
default and with the new camera-based state sampler. The results indicate that
the camera-based state sampler improves success rates in 3 out of 4 scenarios
while having a significant lower memory footprint. This makes PTO an important
contribution to advance the state-of-the-art for discrete belief space
planning.


  A Cremona transformation is a birational self-map of the projective space $
\mathbb{P}^{n} $. Cremona transformations of $ \mathbb{P}^{n} $ form a group
and this group has a rational action on subvarieties of $ \mathbb{P}^{n} $ and
hence on its Hilbert scheme. We study this action on the family of rational
curves of $ \mathbb{P}^{3} $ and we prove the rectifiability of any one
dimensional family. This shows that any uniruled surface is Cremona equivalent
to a scroll and it answers a question of Bogomolov-B\"ohning related to the
study of uniformly rational varieties. We provide examples of infinitely many
scrolls in the same Cremona orbit and we show that a "general" scroll is not in
the Cremona orbit of a "general" rational surface.


  Zero-sum Markov Games (MGs) has been an efficient framework for multi-agent
systems and robust control, wherein a minimax problem is constructed to solve
the equilibrium policies. At present, this formulation is well studied under
tabular settings wherein the maximum operator is primarily and exactly solved
to calculate the worst-case value function. However, it is non-trivial to
extend such methods to handle complex tasks, as finding the maximum over
large-scale action spaces is usually cumbersome. In this paper, we propose the
smoothing policy iteration (SPI) algorithm to solve the zero-sum MGs
approximately, where the maximum operator is replaced by the weighted LogSumExp
(WLSE) function to obtain the nearly optimal equilibrium policies. Specially,
the adversarial policy is served as the weight function to enable an efficient
sampling over action spaces.We also prove the convergence of SPI and analyze
its approximation error in $\infty -$norm based on the contraction mapping
theorem. Besides, we propose a model-based algorithm called Smooth adversarial
Actor-critic (SaAC) by extending SPI with the function approximations. The
target value related to WLSE function is evaluated by the sampled trajectories
and then mean square error is constructed to optimize the value function, and
the gradient-ascent-descent methods are adopted to optimize the protagonist and
adversarial policies jointly. In addition, we incorporate the
reparameterization technique in model-based gradient back-propagation to
prevent the gradient vanishing due to sampling from the stochastic policies. We
verify our algorithm in both tabular and function approximation settings.
Results show that SPI can approximate the worst-case value function with a high
accuracy and SaAC can stabilize the training process and improve the
adversarial robustness in a large margin.


  It is established that cyclotron resonance (CR) in a high-quality GaAs/AlGaAs
two-dimensional electron system (2DES) originates as a \textit{pure} resonance,
that does not hybridize with dimensional magnetoplasma excitations. The
magnetoplasma resonances form a fine structure of the CR. The observed fine
structure of the CR results from the interplay between coherent radiative and
incoherent collisional mechanisms of 2D plasma relaxation. We show that the
range of 2DES filling factors from which the phenomenon arises is intimately
connected to the fundamental fine-structure constant.


  We review the evolution of some statistical and thermodynamical quantities
measured in difference sizes of high-energy collisions at different energies.
We differentiate between intensive and extensive quantities and discuss the
importance of their distinguishability in characterizing possible critical
phenomena of nuclear collisions at various energies with different initial
conditions.


  In this paper, we investigate a two-dimensional photonic array featuring a
circular shape and an alternating gain and loss pattern. Our analysis revolves
around determining the presence and resilience of optical ring modes with
varying vorticity values. This investigation is conducted with respect to both
the array's length and the strength of the non-Hermitian parameter. For larger
values of array's length, we observe a reduction in the stability domain as the
non-Hermitian parameter increases. Interestingly, upon an increasing of
vorticity of the optical modes full stability windows emerge for shorter
lattice sizes regime.


  A novel method is proposed to measure the refractive indices (RIs) of the
materials of different transparent solid state media. To exploit the advantage
of non-contact measurement laser beam interferometry is used as an effective
technique for this purpose. The RIs of materials are also experimentally
determined with the aid of another laser based simple method. The derivations
of the working formulae for both the methods are presented. The experimental
values of RI of any glass sample found by the different methods are consistent
with each other and fall within the range of known values of RI for glass. Both
types of experiments can be set up rather easily in an undergraduate
laboratory. They can supplement other methods of finding refractive index like,
for example, methods based on the use of a spectrometer.


  For a finite Thurston type ordering < of the braid group B_{n}, we introduce
a new normal form of a dual positive braid which we call the C-normal form.
This normal form extends Fromentin's rotating normal form and the author's
C-normal form of positive braids. Using the C-normal form, we give a
combinatorial description of the restriction of the ordering < to the dual
braid monoids B_{n}^{+*}. We prove that the restriction to the dual positive
monoid (B_{n}^{+*},<) is a well-ordered set of order type
\omega^{\omega^{n-2}}.


  Optical fibers have been recognized as one of the most promising host
material for high phase coherence optical frequency transfer over thousands of
kilometers. In the pioneering work, the active phase noise cancellation (ANC)
technique has been widely used for suppressing the fiber phase noise introduced
by the environmental perturbations, in which an ideal phase detector with high
resolution and unlimited detection range is needed to extract the fiber phase
noise, in particular for noisy fiber links. We demonstrate the passive phase
noise cancellation (PNC) technique without the need of phase detector could be
preferable for noisy fiber links. To avoid the effect of the radio frequency
(RF) from the time base at the local site in the conventional active or passive
phase noise cancellation techniques, here we introduce a fiber-pigtailed
acousto-optic modulator (AOM) with two diffraction order outputs (0 and +1
order) with properly allocating the AOM-driving frequencies allowing to cancel
the time base effect. Using this technique, we demonstrate transfer of coherent
light through a 260 km noisy urban fiber link. The results show the effect of
the RF reference can be successfully removed. After being passively
compensated, {we demonstrate a fractional frequency instability of
$4.9\times10^{-14}$ at the integration time of 1 s and scales down to
$10^{-20}$ level at 10,000 s in terms of modified Allan deviation over the 260
km noisy urban fiber link}. The frequency uncertainty of the retrieved light
after transferring through this noise-compensated fiber link relative to that
of the input light achieves $(0.41\pm4.7)\times10^{-18}$. The proposed
technique opens a way to a broad distribution of an ultrastable frequency
reference with high coherence without any effects coming from the RF reference
and enables a wide range of applications beyond metrology over fiber networks.


  We present the results of studies of acoustic-gravity waves (AGWs) in the
upper atmosphere of the Earth. The work has been mainly aimed at studying the
peculiarities of atmospheric AGWs in the atmosphere based on the theoretical
models taking into account the properties of the real atmosphere and the model
verification based on spacecraft measurement data. This overview includes the
main results obtained by the authors over the last years. The details of the
calculations are contained in the authors' works cited here. The possibility of
the existence of new types of evanescent acoustic-gravity waves in the
isothermal atmosphere is theoretically predicted. A previously unknown
inelastic mode and a family of evanescent pseudo-modes are discussed. The
peculiarities of the propagation of the acoustic-gravity waves at the boundary
of two isothermal half-spaces with different temperatures are studied in
dependence of their spectral parameters and the magnitude of the temperature
jump at the boundary. The peculiarities of the interaction of acoustic-gravity
waves with spatially inhomogeneous atmospheric flows are also studied. It is
analyzed the observed effects that are a consequence of such interaction. The
influence of vertical non-isothermality on propagation of acoustic-gravity
waves including the modification of acoustic and gravitational regions
depending on the temperature is studied. On the basis of modified Navier-Stokes
and heat transfer equations, the influence of attenuation on the propagation of
acoustic-gravity waves in the atmosphere is analyzed. It is also considered the
attenuation of various types of evanescent acoustic-gravity waves in the
atmosphere. It is shown that the rotation of the atmosphere leads to the
modification of the continuous spectrum of evanescent acoustic-gravity waves
with frequencies greater than the Coriolis parameter.


  Using a fully analytical theory, we compute the leading order corrections to
the translational, rotational and translation-rotation coupling mobilities of
an arbitrary axisymmetric particle immersed in a Newtonian fluid moving near an
elastic cell membrane that exhibits resistance towards stretching and bending.
The frequency-dependent mobility corrections are expressed as general relations
involving separately the particle's shape-dependent bulk mobility and the
shape-independent parameters such as the membrane-particle distance, the
particle orientation and the characteristic frequencies associated with
shearing and bending of the membrane. This makes the equations applicable to an
arbitrary-shaped axisymmetric particle provided that its bulk mobilities are
known, either analytically or numerically. For a spheroidal particle, these
general relations reduce to simple expressions in terms of the particle's
eccentricity. We find that the corrections to the translation-rotation coupling
mobility are primarily determined by bending, whereas shearing manifests itself
in a more pronounced way in the rotational mobility. We demonstrate the
validity of the analytical approximations by a detailed comparison with
boundary integral simulations of a truly extended spheroidal particle. They are
found to be in a good agreement over the whole range of applied frequencies.


  K-theoretic Donaldson invariants are holomorphic Euler characteristics of
determinant line bundles on moduli spaces of sheaves on surfaces. We compute
generating functions of K-theoretic Donaldson invariants on the projective
plane and rational ruled surfaces. We apply this result to prove some cases of
Le Potier's strange duality.


  In this paper, we consider a class of Hessian type equations which include
the $(n-1)$ Monge-Amp\`{e}re equation on Riemannian manifolds. The \emph{a
priori} $C^2$ estimates and the existence of solutions are established.


  The dynamics of binary pulsars can be used to test different aspects of
gravitation. This is particularly important to constrain alternatives to
general relativity in regimes which are not probed by other methods. In this
short contribution, I will describe the case of theories of gravity without
Lorentz invariance. The latter are important in the context of quantum gravity
and modify the laws of gravity at basically all scales.


  We construct all possible Hamiltonian torus actions for which all the
non-empty reduced spaces are two dimensional (and not single points) and the
manifold is connected and compact, or, more generally, the moment map is proper
as a map to a convex set. This construction completes the classification of
tall complexity one spaces.


  Dyson demonstrated an equivalence between infinite-range Coulomb gas models
and classical random matrix ensembles for study of eigenvalue statistics. We
introduce finite-range Coulomb gas (FRCG) models via a Brownian matrix process,
and study them analytically and by Monte-Carlo simulations. These models yield
new universality classes, and provide a theoretical framework for study of
banded random matrices (BRM) and quantum kicked rotors (QKR). We demonstrate
that, for a BRM of bandwidth b and a QKR of chaos parameter {\alpha}, the
appropriate FRCG model has the effective range d = (b^2)/N = ({\alpha}^2)/N,
for large N matrix dimensionality. As d increases, there is a transition from
Poisson to classical random matrix statistics.


  This work is part of a series of studies focusing on the environment and the
properties of the X-ray selected active galactic nuclei (AGN) population from
the XXL survey. The present survey, given its large area, continuity, extensive
multiwavelength coverage, and large-scale structure information, is ideal for
this kind of study. Here, we focus on the XXL-South (XXL-S) field. Our main aim
is to study the environment of the various types of X-ray selected AGN and
investigate its possible role in AGN triggering and evolution. We studied the
large-scale (>1 Mpc) environment up to redshift z=1 using the nearest neighbour
distance method to compare various pairs of AGN types. We also investigated the
small-scale environment (<0.4 Mpc) by calculating the local overdensities of
optical galaxies. In addition, we built a catalogue of AGN concentrations with
two or more members using the hierarchical clustering method and we correlated
them with the X-ray galaxy clusters detected in the XXL survey. It is found
that radio detected X-ray sources are more obscured than non-radio ones, though
not all radio sources are obscured AGN. We did not find any significant
differences in the large-scale clustering between luminous and faint X-ray AGN,
or between obscured and unobscured ones, or between radio and non-radio
sources. At local scales (<0.4 Mpc), AGN typically reside in overdense regions,
compared to non-AGN; however, no differences were found between the various
types of AGN. A majority of AGN concentrations with two or more members are
found in the neighbourhood of X-ray galaxy clusters within <25-45 Mpc. Our
results suggest that X-ray AGN are typically located in supercluster filaments,
but they are also found in over- and underdense regions.


  The communication networks in real world often couple with each other to save
costs, which results in any network does not have a stand-alone function and
efficiency. To investigate this, in this paper we propose a transportation
model on two coupled networks with bandwidth sharing. We find that the
free-flow state and the congestion state can coexist in the two coupled
networks, and the free-flow path and congestion path can coexist in each
network. Considering three bandwidth-sharing mechanisms, random, assortative
and disassortative couplings, we also find that the transportation capacity of
the network only depends on the coupling mechanism, and the fraction of coupled
links only affects the performance of the system in the congestion state, such
as the traveling time. In addition, with assortative coupling, the
transportation capacity of the system will decrease significantly. However, the
disassortative coupling has little influence on the transportation capacity of
the system, which provides a good strategy to save bandwidth. Furthermore, a
theoretical method is developed to obtain the bandwidth usage of each link,
based on which we can obtain the congestion transition point exactly.


  The burgeoning of misleading or false information spread by untrustworthy
websites has, without doubt, created a dangerous concoction. Thus, it is not a
surprise that the threat posed by untrustworthy websites has emerged as a
central concern on the public agenda in many countries, including Czechia and
Slovakia. However, combating this harmful phenomenon has proven to be
difficult, with approaches primarily focusing on tackling consequences instead
of prevention, as websites are routinely seen as quasi-sovereign organisms.
Websites, however, rely upon a host of service providers, which, in a way, hold
substantial power over them. Notwithstanding the apparent power hold by such
tech stack layers, scholarship on this topic remains largely limited. This
article contributes to this small body of knowledge by providing a
first-of-its-kind systematic mapping of the back-end infrastructural support
that makes up the tech stacks of Czech and Slovak untrustworthy websites. Our
approach is based on collecting and analyzing data on top-level domain
operators, domain name Registrars, email providers, web hosting providers, and
utilized website tracking technologies of 150 Czech and Slovak untrustworthy
websites. Our findings show that the Czech and Slovak untrustworthy website
landscape relies on a vast number of back-end services spread across multiple
countries, but in key tech stack layers is nevertheless still heavily dominated
by locally based companies. Finally, given our findings, we discuss various
possible avenues of utilizing the numeral tech stack layers in combating online
disinformation.


  There is now a certain consensus that Transcription Factors (TFs) reach their
target sites, where they regulate gene transcription, via a mechanism dubbed
facilitated diffusion (FD). In FD, the TF cycles between events of 3D-diffusion
in solution (jumps), 1D-diffusion along DNA (sliding), and small jumps
(hopping) achieving association rates higher than for 3D-diffusion only. We
investigate the FD phenomenology through Molecular Dynamics simulations in the
framework of coarse-grained modeling. Despite the crude approximations, we show
that the model generates, upon varying equilibrium distance of the DNA-TF
interaction, a phenomenology matching a number of experimental and numerical
results obtained with more refined models. In particular, by focusing on the
kinematics of the process, we characterize the geometrical properties of TF
trajectories during sliding. We find that sliding occurs via helical paths
around the DNA helix leading to a coupling of translation along the DNA-axis
with rotation around it. The 1D-diffusion constant measured in simulations is
found to be interwoven with the geometrical properties of sliding and we
develop a simple argument able to quantitatively reproduce the measured values.