  Understanding how tangential singularities evolve under smoothing processes
was one of the first problem concerning regularization of Filippov systems. In
this paper, we are interested in $C^n$-regularizations of Filippov systems
around visible regular-tangential singularities of even multiplicity. More
specifically, using Fenichel Theory and Blow-up Methods, we aim to understand
how the trajectories of the regularized system transits through the region of
regularization. We apply our results to investigate $C^n$-regularizations of
boundary limit cycles with even multiplicity contact with the switching
manifold.


  We establish functional limit theorems for local, additive, interaction
functions of temporally evolving point processes. The dynamics are those of a
spatial Poisson process on the flat torus with points subject to a birth-death
mechanism, and which move according to Brownian motion while alive. The results
reveal the existence of a phase diagram describing at least three distinct
structures for the limiting processes, depending on the extent of the local
interactions and the speed of the Brownian motions. The proofs, which identify
three different limits, rely heavily on Malliavin-Stein bounds on a
representation of the dynamic point process via a distributionally equivalent
marked point process.


  A higher level analog of Weyl modules over multi-variable currents is
proposed. It is shown that the sum of their dual spaces form a commutative
algebra. The structure of these modules and the geometry of the projective
spectrum of this algebra is studied for the currents of dimension one and two.
Along the way we prove some particular cases of the conjectures in [FL1] and
propose a generalization of the notion of parking function representations.


  Two-pulse correlation is employed to investigate the temporal dynamics of
both two-photon photoluminescence (2PPL) and four-photon photoluminescence
(4PPL) in resonant and nonresonant nanoantennas excited at a wavelength of 800
nm. Our data are consistent with the same two-step model being the cause of
both 4PPL and 2PPL, implying that the first excitation step in 4PPL is a
three-photon sp->sp direct interband transition. Considering energy and parity
conservation, we also explain why 4PPL behavior is favored over three-and
five-photon photoluminescence in the power range below the damage threshold of
our antennas. Since sizeable 4PPL requires larger peak intensities of the local
field, we are able to select either 2PPL or 4PPL in the same gold nanoantennas
by choosing a suitable laser pulse duration. We thus provide a first consistent
model for the understanding of multiphoton photoluminescence generation in gold
nanoantennas, opening new perspectives for applications ranging from the
characterization of plasmonic resonances to biomedical imaging.


  The ASPIRE program, which is based on the Landau singularities and the method
of power geometry to unveil the regions required for the evaluation of a given
Feynman diagram asymptotically in a given limit, also allows for the evaluation
of scaling coming from the top facets. In this work, we relate the scaling
having equal components of the top facets of the Newton polytope to the maximal
cut of given Feynman integrals. We have therefore connected two independent
approaches to the analysis of Feynman diagrams.


  We discuss the use of Sloan Digital Sky Survey (SDSS) ugriz point-spread
function (PSF) photometry for setting the zero points of UBVRI CCD images. From
a comparison with the Landolt (1992) standards and our own photometry we find
that there is a fairly abrupt change in B, V, R, & I zero points around g, r, i
~ 14.5, and in the U zero point at u ~ 16. These changes correspond to where
there is significant interpolation due to saturation in the SDSS PSF fluxes.
There also seems to be another, much smaller systematic effect for stars with
g, r > 19.5. The latter effect is consistent with a small Malmquist bias.
Because of the difficulties with PSF fluxes of brighter stars, we recommend
that comparisons of ugriz and UBVRI photometry should only be made for
unsaturated stars with g, r and i in the range 14.5 - 19.5, and u in the range
16 - 19.5. We give a prescription for setting the UBVRI zero points for CCD
images, and general equations for transforming from ugriz to UBVRI.


  This paper presents the theory of non-smooth Lie group actions on chains of
Banach manifolds. The rigorous functional analytic spaces are given to deal
with quotients of such actions. A hydrodynamical example is studied in detail.


  Let $B$ be a Borel subgroup of $\mathrm{GL}_n(\mathbb{C})$ and $\mathbb{T}$ a
maximal torus contained in $B$. Then $\mathbb{T}$ acts on
$\mathrm{GL}_{n}(\mathbb{C})/B$ and every Schubert variety is
$\mathbb{T}$-invariant. We say that a Schubert variety is of complexity $k$ if
a maximal $\mathbb{T}$-orbit in $X_w$ has codimension $k$. In this paper, we
discuss topology, geometry, and combinatorics related to Schubert varieties of
complexity one.


  The Erd\H{o}s multiplication table problem asks what is the number of
distinct integers appearing in the $N\times N$ multiplication table. The order
of magnitude of this quantity was determined by Ford in 2008. In this paper we
study the number of $y-$smooth entries of the $N\times N$ multiplication table
that is to say entries with no prime factors greater than $y$.


  Motivated by conditional independence testing, an essential step in
constraint-based causal discovery algorithms, we study the nonparametric Von
Mises estimator for the entropy of multivariate distributions built on a kernel
density estimator. We establish an exponential concentration inequality for
this estimator. We design a test for conditional independence (CI) based on our
estimator, called VM-CI, which achieves optimal parametric rates under
smoothness assumptions. Leveraging the exponential concentration, we prove a
tight upper bound for the overall error of VM-CI. This, in turn, allows us to
characterize the sample complexity of any constraint-based causal discovery
algorithm that uses VM-CI for CI tests. To the best of our knowledge, this is
the first sample complexity guarantee for causal discovery for continuous
variables. Furthermore, we empirically show that VM-CI outperforms other
popular CI tests in terms of either time or sample complexity (or both), which
translates to a better performance in structure learning as well.


  We continue our consideration of a class of models describing the reversible
dynamics of $N$ Boolean variables, each with $K$ inputs. We investigate in
detail the behavior of the Hamming distance as well as of the distribution of
orbit lengths as $N$ and $K$ are varied. We present numerical evidence for a
phase transition in the behavior of the Hamming distance at a critical value
$K_c\approx 1.65$ and also an analytic theory that yields the exact bounds on
$1.5 \le K_c \le 2.$
  We also discuss the large oscillations that we observe in the Hamming
distance for $K<K_c$ as a function of time as well as in the distribution of
cycle lengths as a function of cycle length for moderate $K$ both greater than
and less than $K_c$. We propose that local structures, or subsets of spins
whose dynamics are not fully coupled to the other spins in the system, play a
crucial role in generating these oscillations. The simplest of these structures
are linear chains, called linkages, and rings, called circuits. We discuss the
properties of the linkages in some detail, and sketch the properties of
circuits. We argue that the observed oscillation phenomena can be largely
understood in terms of these local structures.


  We present results from an analysis of all data taken by the BICEP2/Keck CMB
polarization experiments up to and including the 2015 observing season. This
includes the first Keck Array observations at 220 GHz and additional
observations at 95 & 150 GHz. The $Q/U$ maps reach depths of 5.2, 2.9 and 26
$\mu$K$_{cmb}$ arcmin at 95, 150 and 220 GHz respectively over an effective
area of $\approx 400$ square degrees. The 220 GHz maps achieve a
signal-to-noise on polarized dust emission approximately equal to that of
Planck at 353 GHz. We take auto- and cross-spectra between these maps and
publicly available WMAP and Planck maps at frequencies from 23 to 353 GHz. We
evaluate the joint likelihood of the spectra versus a multicomponent model of
lensed-$\Lambda$CDM+$r$+dust+synchrotron+noise. The foreground model has seven
parameters, and we impose priors on some of these using external information
from Planck and WMAP derived from larger regions of sky. The model is shown to
be an adequate description of the data at the current noise levels. The
likelihood analysis yields the constraint $r_{0.05}<0.07$ at 95% confidence,
which tightens to $r_{0.05}<0.06$ in conjunction with Planck temperature
measurements and other data. The lensing signal is detected at $8.8 \sigma$
significance. Running maximum likelihood search on simulations we obtain
unbiased results and find that $\sigma(r)=0.020$. These are the strongest
constraints to date on primordial gravitational waves.


  Binary code clone analysis is an important technique which has a wide range
of applications in software engineering (e.g., plagiarism detection, bug
detection). The main challenge of the topic lies in the semantics-equivalent
code transformation (e.g., optimization, obfuscation) which would alter
representations of binary code tremendously. Another chal- lenge is the
trade-off between detection accuracy and coverage. Unfortunately, existing
techniques still rely on semantics-less code features which are susceptible to
the code transformation. Besides, they adopt merely either a static or a
dynamic approach to detect binary code clones, which cannot achieve high
accuracy and coverage simultaneously. In this paper, we propose a
semantics-based hybrid approach to detect binary clone functions. We execute a
template binary function with its test cases, and emulate the execution of
every target function for clone comparison with the runtime information
migrated from that template function. The semantic signatures are extracted
during the execution of the template function and emulation of the target
function. Lastly, a similarity score is calculated from their signatures to
measure their likeness. We implement the approach in a prototype system
designated as BinMatch which analyzes IA-32 binary code on the Linux platform.
We evaluate BinMatch with eight real-world projects compiled with different
compilation configurations and commonly-used obfuscation methods, totally
performing over 100 million pairs of function comparison. The experimental
results show that BinMatch is robust to the semantics-equivalent code
transformation. Besides, it not only covers all target functions for clone
analysis, but also improves the detection accuracy comparing to the
state-of-the-art solutions.


  We shed some light on the field theory interpretation of C-metric by
investigating the minimal surfaces which are homologous to the given boundary
regions. The accelerating black holes change the asymptotic structure of the
space-time. We focus on the geometry features of the minimal surface and study
how deep it reaches into the bulk. The regularized area of the minimal surface
is not well defined and we introduce a new quantity $D(m,\theta_0)$, defined as
the minimal surface divided by the area of the given boundary region, to study
the system.


  In this paper, we introduce the notion of a (generalized) right core inverse
and give its characterizations and expressions. Then, we provide the relation
schema of (one-sided) core inverses, (one-sided) pseudo core inverses and EP
elements.


  Four fermion processes at e+ e- colliders in a range of energy from 100 GeV
to 1 TeV are discussed and examples of results obtained with an event generator
presented. We also investigate the effects of the inclusion of initial state
QED corrections and QCD contributions.


  We study H I Lyman-alpha absorption observed by the Hubble Space Telescope
toward the nearby binary system Alpha Cen (G2 V+K0 V) and its distant companion
star Proxima Cen (M5.5 Ve). Absorption from heliospheric H I heated by the
solar wind/ISM interaction is observed toward both Alpha Cen and Proxima Cen.
Absorption from analogous "astrospheric" material surrounding the stars is
detected toward Alpha Cen, but not Proxima Cen. The nondetection of
astrospheric absorption toward Proxima Cen suggests that the stellar wind of
Proxima Cen must be significantly weaker than that of the Alpha Cen system. We
use hydrodynamic models of the astrospheres computed assuming different
mass-loss rates to predict astrospheric Lyman-alpha absorption for comparison
with the observations. The model that best matches the Alpha Cen data has a
mass-loss rate of twice the solar rate, and the models suggest an upper limit
of 0.2 solar for Proxima Cen. Finally, we note that the heliospheric absorption
observed toward Proxima Cen in 2000 May is identical to the heliospheric
absorption observed toward Alpha Cen in 1995 May, implying that the structure
of the outer heliosphere does not change significantly during the solar
activity cycle.


  The aim of this paper is to study the stochastic SIR equation with general
incidence functional responses and in which both natural death rates and the
incidence rate are perturbed by white noises. We derive a sufficient and almost
necessary condition for the extinction and permanence for an epidemic system
with multi noises \begin{equation*} \begin{cases}
dS(t)=\big[a_1-b_1S(t)-I(t)f(S(t),I(t))\big]dt + \sigma_1 S(t) dB_1(t)
-I(t)g(S(t),I(t))dB_3(t),\\ dI(t)=\big[-b_2I(t) + I(t)f(S(t),I(t))\big]dt +
\sigma_2I(t) dB_2(t) + I(t)g(S(t),I(t))dB_3(t). \end{cases} \end{equation*}
Moreover, the rate of all convergences of the solution are also established. A
number of numerical examples are given to illustrate our results


  Quantum lithography proposes to adopt entangled quantum states in order to
increase resolution in interferometry. In the present paper we experimentally
demonstrate that the output of a high-gain optical parametric amplifier can be
intense yet exhibits quantum features, namely, sub-Rayleigh fringes, as
proposed by Agarwal et al. (Phys. Rev. Lett. 86, 1389 (2001)). We investigate
multiphoton states generated by a high-gain optical parametric amplifier
operating with a quantum vacuum input for a gain values up to 2.5. The
visibility has then been increased by means of three-photon absorption. The
present article opens interesting perspectives for the implementation of such
an advanced interferometrical setup.


  Deep neural networks are vulnerable to adversarial attacks. Recent studies
about adversarial robustness focus on the loss landscape in the parameter space
since it is related to optimization and generalization performance. These
studies conclude that the difficulty of adversarial training is caused by the
non-smoothness of the loss function: i.e., its gradient is not Lipschitz
continuous. However, this analysis ignores the dependence of adversarial
attacks on model parameters. Since adversarial attacks are optimized for
models, they should depend on the parameters. Considering this dependence, we
analyze the smoothness of the loss function of adversarial training using the
optimal attacks for the model parameter in more detail. We reveal that the
constraint of adversarial attacks is one cause of the non-smoothness and that
the smoothness depends on the types of the constraints. Specifically, the
$L_\infty$ constraint can cause non-smoothness more than the $L_2$ constraint.
Moreover, our analysis implies that if we flatten the loss function with
respect to input data, the Lipschitz constant of the gradient of adversarial
loss tends to increase. To address the non-smoothness, we show that EntropySGD
smoothens the non-smooth loss and improves the performance of adversarial
training.


  We argue that the domain structure of deconfined QCD matter, which can be
inferred from the properties of the Polyakov loop, can simultaneously explain
the two most prominent experimentally verified features of the quark-gluon
plasma, namely its large opacity as well as its near ideal fluid properties.


  In this short note, we show that a von Neumann algebra can be written as the
linking von Neumann algebra of a W*-TRO if and only if it contains no abelian
direct summand. We also provide some new characterizations for nuclear TROs and
W*-exact TROs.


  We prove that the Jacobian of a general curve C of genus g=2a+1, with g>4,
can be realized as a Prym-Tyurin variety for the Brill-Noether curve
W^1_{a+2}(C). As a consequence of this result we are able to compute the class
of the sum of the secant divisors for the curve C, embedded with a complete
linear series g^{a-1}_{3a-2}


  The pseudo-fermion representation for $S=1/2$ quantum spins introduces
unphysical states in the Hilbert space which can be projected out using the
Popov-Fedotov trick. However, state-of-the-art implementation of the functional
renormalization group method for pseudo-fermions have so far omitted the
Popov-Fedotov projection. Instead, restrictions to zero temperature were made
and absence of unphysical contributions to the ground-state was assumed. We
question this belief by exact diagonalization of several small-system
counterexamples where unphysical states do contribute to the ground state. We
then introduce Popov-Fedotov projection to pseudo-fermion functional
renormalization, enabling finite temperature computations with only minor
technical modifications to the method. At large and intermediate temperatures,
our results are perturbatively controlled and we confirm their accuracy in
benchmark calculations. At lower temperatures, the accuracy degrades due to
truncation errors in the hierarchy of flow equations. Interestingly, these
problems cannot be alleviated by switching to the parquet approximation. We
introduce the spin projection as a method-intrinsic quality check. We also show
that finite temperature magnetic ordering transitions can be studied via
finite-size scaling.


  We study how different frame annotations complement one another when learning
continuous lexical semantics. We learn the representations from a tensorized
skip-gram model that consistently encodes syntactic-semantic content better,
with multiple 10% gains over baselines.


  Image fusion aims to generate a high-resolution multi/hyper-spectral image by
combining a high-resolution image with limited spectral information and a
low-resolution image with abundant spectral data. Current deep learning
(DL)-based methods for image fusion primarily rely on CNNs or Transformers to
extract features and merge different types of data. While CNNs are efficient,
their receptive fields are limited, restricting their capacity to capture
global context. Conversely, Transformers excel at learning global information
but are hindered by their quadratic complexity. Fortunately, recent
advancements in the State Space Model (SSM), particularly Mamba, offer a
promising solution to this issue by enabling global awareness with linear
complexity. However, there have been few attempts to explore the potential of
the SSM in information fusion, which is a crucial ability in domains like image
fusion. Therefore, we propose FusionMamba, an innovative method for efficient
image fusion. Our contributions mainly focus on two aspects. Firstly,
recognizing that images from different sources possess distinct properties, we
incorporate Mamba blocks into two U-shaped networks, presenting a novel
architecture that extracts spatial and spectral features in an efficient,
independent, and hierarchical manner. Secondly, to effectively combine spatial
and spectral information, we extend the Mamba block to accommodate dual inputs.
This expansion leads to the creation of a new module called the FusionMamba
block, which outperforms existing fusion techniques such as concatenation and
cross-attention. We conduct a series of experiments on five datasets related to
three image fusion tasks. The quantitative and qualitative evaluation results
demonstrate that our method achieves SOTA performance, underscoring the
superiority of FusionMamba. The code is available at
https://github.com/PSRben/FusionMamba.


  In a recent paper (cond-mat/9901130), the spatial distribution of unvisited
sites in the one-dimensional single-species annihilation process was
investigated. It was claimed that this distribution is characterized by a new
length scale, and that the corresponding dynamical exponent depends upon the
initial concentration. We show numerically that this assertion is erroneous.
Regardless of the initial concentration, this spatial distribution is
characterized by the diffusive length scale.


  Quantum non-locality based on the well-known Bell inequality is of kinematic
nature. A different type of quantum non-locality, the non-locality of the
quantum equation of motion, is recently put forward with connection to the
Aharonov-Bohm effect [Nature Phys. 6, 151 (2010)]. Evolution of the
displacement operator provides an example to manifest such dynamic quantum
non-locality. We propose an experiment using single-atom interferometry to test
such dynamic quantum non-locality. We show how to measure evolution of the
displacement operator with clod atoms in a spin-dependent optical lattice
potential and discuss signature to identify dynamic quantum non-locality under
a realistic experimental setting.


  This article is interested in the origin of the genetic code, it puts forward
a scenario of a simultaneous selection of the bases and amino acids and setting
up of a correlation between them. Each amino acid is associated with a pair of
its own kind, called the binding pair and each binding pair is associated with
the codon(s) corresponding to the same amino acid. An explanation is also
proposed about the origin of the start and stop codons.


  We present an astrometry and photometry catalogue of globular cluster (GC)
candidates detected with HST WFPC2 in a sample of 19 early-type galaxies,
appropriate for comparison to the low-mass X-ray binary (LMXB) populations
observed with Chandra. In a companion paper, we present the Chandra data and
investigate the relation between these populations. We demonstrate that,
although there is little evidence of a colour-magnitude correlation for the
GCs, after estimating mass and metallicity from the photometry, under the
assumption of a single age simple stellar population, there is a significant
positive correlation between mass and metallicity. We constrained [Z/H] =
(-2.1+/-0.2)+(0.25+/-0.04)log M, with a 1-sigma intrinsic scatter of 0.62 dex
in metallicity. If GCs are bimodal in metallicity this relation is consistent
with recent suggestions of a mass-metallicity relation only for metal-poor
clusters. Adopting a new technique to fit the GC luminosity function (GCLF)
accounting for incompleteness and the Eddington bias, we compute the V-band
local GC specific frequency (Sn) and specific luminosity (Sl) of each galaxy.
We show that Sl is the more robust measure of the richness of a GC population
where a significant fraction is undetected due to source detection
incompleteness. We find that the absolute magnitude of the GCLF turnover
exhibits intrinsic scatter from galaxy to galaxy of ~0.3mag (1-sigma), limiting
its accuracy as a standard distance measure.


  Tuning the electric properties of crystalline solids is at the heart of
material science and electronics. Generating the electric field-effect via an
external voltage is a clean, continuous and systematic method. Here, utilizing
the unique electric dipole locking in van der Waals (vdW) ferroelectric
alpha-In2Se3, we report a new approach to establish the electric gating effect,
where the electrostatic doping in the out-of-plane direction is induced and
controlled by an in-plane voltage. With the vertical vdW heterostructure of
ultrathin alpha-In2Se3 and MoS2, we validate an in-plane voltage gated coplanar
field-effect transistor (CP-FET) with distinguished and retentive on/off ratio.
Our results demonstrate unprecedented electric control of ferroelectricity,
which paves the way for integrating two-dimensional (2D) ferroelectric into
novel nanoelectronic devices with broad applications.


  The origin of a new kinematically identified metal-poor stellar stream, the
KFR08 stream, has not been established. We present stellar parameters, stellar
ages, and detailed elemental abundances for Na, Mg, Al, Si, Ca, Sc, Ti, Cr, Ni,
Zn, Sr, Y, Zr, Ba, La, and Eu for 16 KFR08 stream members based on analysis of
high resolution spectra. Based on the abundance ratios of 14 elements, we use
the chemical tagging method to identify the stars which have the same chemical
composition, and thus, might have a common birthplace, such as a cluster.
Although three stars were tagged with similar elemental abundances ratios, we
find that, statistically, it is not certain that they originate from a
dissolved star cluster. This conclusion is consistent with the large dispersion
of [Fe/H] ($\sigma_{\rm{[Fe/H]}} = 0.29$) among the 16 stream members. We find
that our stars are $\alpha$ enhanced and that the abundance patterns of the
stream members are well matched to the thick disk. In addition, most of the
stream stars have estimated stellar ages larger than 11 Gyr. These results,
together with the hot kinematics of the stream stars, suggest that the KFR08
stream is originated from the thick disk population which was perturbed by a
massive merger in the early universe.


  The equitangent locus of a convex plane curve consists of the points from
which the two tangent segments to the curve have equal length. The equitangent
problem concerns the relation between the curve and its equitangent locus. An
equitangent n-gon of a convex curve is a circumscribed n-gon whose vertices
belong to the equitangent locus. We are interested in curves that admit
1-parameter families of equitangent n-gons. We use methods of sub-Riemannian
geometry: we define a distribution on the space of polygons and study its
bracket generating properties. 1-parameter families of equitangent polygons
correspond to the curves, tangent to this distribution. This distribution is
closely related with the Birkhoff distribution on the space of plane polygons
with a fixed perimeter length whose study, in the framework of the billiard
ball problem, was pioneered by Yu. Baryshnikov, V. Zharnitsky and J. Landsberg


  We consider the many-body spectra of interacting bosonic quantum fields on a
lattice in the semiclassical limit of large particle number $N$. We show that
the many-body density of states can be expressed as a coherent sum over
oscillating long-wavelength contributions given by periodic, non-perturbative
solutions of the, typically non-linear, wave equation of the classical
(mean-field) limit. To this end we construct the semiclassical approximation
for both the smooth and oscillatory part of the many-body density of states in
terms of a trace formula starting from the exact path integral form of the
propagator between many-body quadrature states. We therefore avoid the use of a
complexified classical limit characteristic of the coherent state
representation. While quantum effects like vacuum fluctuations and gauge
invariance are exactly accounted for, our semiclassical approach captures
quantum interference and therefore is valid well beyond the Ehrenfest time
where naive quantum-classical correspondence breaks down. Remarkably, due to a
special feature of harmonic systems with incommesurable frequencies, our
formulas are generically valid also in the free-field case of non-interacting
bosons.


  For $\alpha>-1$ and $0<p<\infty$, we study weighted Bergman spaces $\mathcal
B^p_\alpha$ of harmonic functions on the real hyperbolic ball and obtain an
atomic decomposition of these spaces in terms of reproducing kernels. We show
that an $r$-separated sequence $\{a_m\}$ with sufficiently large $r$ is an
interpolating sequence for $\mathcal B^p_\alpha$. Using these we determine
precisely when a Bergman space $\mathcal B^p_\alpha$ is included in another
Bergman space $\mathcal B^q_\beta$.


  Reliable estimates of neutrino-nucleus reactions in the resonance-excitation
region play an important role in many of the on-going and planned neutrino
oscillation experiments. We study here neutrino-nucleus reactions in the
delta-particle excitation region with the use of neutrino pion-production
amplitudes calculated in a formalism in which the resonance contributions and
the background amplitudes are treated on the same footing. Our approach leads
to the neutrino-nucleus reaction cross sections that are significantly
different from those obtained in the conventional approach wherein only the
pure resonance amplitudes are taken into account. To assess the reliability of
our formalism, we calculate the electron-nucleus scattering cross sections in
the same theoretical framework; the calculated cross sections agree reasonably
well with the existing data.


  In this paper we study the Omega risk model with surplus-dependent tax
payments in a time-homogeneous diffusion setting. The new model incorporates
practical features from both the Omega risk model(Albrecher and Gerber and Shiu
(2011)) and the risk model with tax(Albrecher and Hipp (2007)). We explicitly
characterize the Laplace transform of the occupation time of an Azema-Yor
process(e.g. a process refracted by functionals of its running maximum) below a
constant level until the first hitting time of another Azema-Yor process or
until an independent exponential time. This result unifies and extends recent
literature(Li and Zhou (2013) and Zhang (2014)) incorporating some of their
results as special cases. We explicitly characterize the Laplace transform of
the time of bankruptcy in the Omega risk model with tax and discuss an
extension to integral functionals. Finally we present examples using a Brownian
motion with drift.


  Calculations of the direct radiative capture reactions are made for the
$^{48}$Ca$(n,\gamma)^{49}$Ca, $^7$Li$(n,\gamma)^8$Li and
$^{12}$C$(p,\gamma)^{13}$N reactions with the Perey-Buck type nonlocal
potentials using a potential model. Our results reproduce the experimental data
reasonably well. From comparisons with results obtained by using local
potentials, it is found that the cross sections of direct capture reactions may
change by around 25\% due to the nonlcality of nuclear potentials.


  According to the Weinstein splitting theorem, any Poisson manifold is
locally, near any given point, a product of a symplectic manifold with another
Poisson manifold whose Poisson structure vanishes at the point. Similar
splitting results are known e.g. for Lie algebroids, Dirac structures and
generalized complex structures. In this paper, we develop a novel approach
towards these results that leads to various generalizations, including their
equivariant versions as well as their formulations in new contexts.


  We show that in algebraically locally finite countable homogeneous structures
with a free stationary independence relation the small index property implies
the strong small index property. We use this and the main result of [15] to
deduce that countable free homogeneous structures in a locally finite
relational language have the strong small index property. We also exhibit new
continuum sized classes of $\aleph_0$-categorical structures with the strong
small index property whose automorphism groups are pairwise non-isomorphic.


  Background: Pharmacokinetic evaluation is one of the key processes in drug
discovery and development. However, current absorption, distribution,
metabolism, excretion prediction models still have limited accuracy. Aim: This
study aims to construct an integrated transfer learning and multitask learning
approach for developing quantitative structure-activity relationship models to
predict four human pharmacokinetic parameters. Methods: A pharmacokinetic
dataset included 1104 U.S. FDA approved small molecule drugs. The dataset
included four human pharmacokinetic parameter subsets (oral bioavailability,
plasma protein binding rate, apparent volume of distribution at steady-state
and elimination half-life). The pre-trained model was trained on over 30
million bioactivity data. An integrated transfer learning and multitask
learning approach was established to enhance the model generalization. Results:
The pharmacokinetic dataset was split into three parts (60:20:20) for training,
validation and test by the improved Maximum Dissimilarity algorithm with the
representative initial set selection algorithm and the weighted distance
function. The multitask learning techniques enhanced the model predictive
ability. The integrated transfer learning and multitask learning model
demonstrated the best accuracies, because deep neural networks have the general
feature extraction ability, transfer learning and multitask learning improved
the model generalization. Conclusions: The integrated transfer learning and
multitask learning approach with the improved dataset splitting algorithm was
firstly introduced to predict the pharmacokinetic parameters. This method can
be further employed in drug discovery and development.


  S.B. Rao conjectured in 1971 that graphic degree sequences are well quasi
ordered by a relation defined in terms of the induced subgraph relation. In
2008, M. Chudnovsky and P. Seymour proved this long standing Rao's Conjecture
by giving structure theorems for graphic degree sequences. In this paper, we
prove and use a variant of Dickson's Lemma from commutative semigroup theory to
give a short proof of the bounded degree case of Rao's Conjecture that is
independent of the Chudnovsky-Seymour structure theory. In fact, we
affirmatively answer two questions of N. Robertson, the first of which implies
the bounded degree case of Rao's Conjecture.


  In this report, we demonstrate that Ge-NWQD (nanowire quantum dots) at low
temperatures exhibit apparent Coulomb oscillations than that in Si-NWQD. These
oscillations gradually disappear as the temperature increases, indicating the
influence of phonon scattering. The increase in Coulomb oscillations enables
the device to exhibit multi-level characteristics at low voltage in quantum
flash, and the lower barrier high and high mobility of Ge make it advantageous
for increasing the storage capacity of quantum flash devices. This research
provides design guidelines for optimization of high-performance quantum flash
devices.


  Unconventional symmetry breaking without spin order,such as the rotational
symmetry breaking (=nematic or smectic) orders as well as the spontaneous
loop-current orders, have been recently reported in cuprate superconductors and
their related materials.They are theoretically represented by non-$A_{1g}$
symmetry breaking in self-energy, which we call the form factor $f_{k,q}$.In
this paper, we analyze typical Hubbard models by applying the
renormalization-group (RG) method, and find that various unconventional
ordering emerges due to the quantum interference among spin fluctuations. Due
to this mechanism,nematic ($q=0$) and smectic ($q \ne 0$)bond orders with
$d$-wave form factor appear $f_{k,q}\propto \cos k_x - \cos k_y$ in both
cuprates and $\kappa$-(BEDT-TTF)$_2$X. The derived bond orders naturally
explain the pseudogap behaviors in these compounds. The quantum interference
also induces various current orders with odd-parity form factor. For example,
we find the emergence of the charge and spin loop-current orders with $p$-wave
form factor in geometrically frustrated Hubbard models. Thus, rich quantum
phase transitions with $d$- and $p$-wave form factors are driven by the
paramagnon interference in many low-dimensional Hubbard models.


  For studying small-$x$ gluon saturation in forward dijet production in
high-energy dilute-dense collisions, the improved TMD (ITMD) factorization
formula was recently proposed. In the Color Glass Condensate (CGC) framework,
it represents the leading term of an expansion in inverse powers of the hard
scale. It contains the leading-twist TMD factorization formula relevant for
small gluon's transverse momentum $k_t$, but also incorporates an all-order
resummation of kinematical twists, resulting in a proper matching to
high-energy factorization at large $k_t$. In this paper, we evaluate the
accuracy of the ITMD formula quantitatively, for the case of quark dijet
production in high-energy proton-proton($p+p$) and proton-nucleus ($p+A$)
collisions at LHC energies. We do so by comparing the quark-antiquark azimuthal
angle $\Delta\phi$ distribution to that obtained with the CGC formula. For a
dijet with each quark momentum $p_t$ much larger than the target saturation
scale, $Q_s$, the ITMD formula is a good approximation to the CGC formula in a
wide range of azimuthal angle. It becomes less accurate as the jet $p_t$'s are
lowered, as expected, due to the presence of genuine higher-twists
contributions in the CGC framework, which represent multi-body scattering
effects absent in the ITMD formula. We find that, as the hard jet momenta are
lowered, the accuracy of ITMD start by deteriorating at small angles, in the
high-energy-factorization regime, while in the TMD regime near
$\Delta\phi=\pi$, very low values of $p_t$ are needed to see differences
between the CGC and the ITMD formula. In addition, the genuine twists
corrections to ITMD become visible for higher values of $p_t$ in $p+A$
collisions, compared to $p+p$ collisions, signaling that they are enhanced by
the target saturation scale.


  We investigate the properties of some recently developed variable-order
differential operators involving order transition functions of exponential
type. Since the characterisation of such operators is performed in the Laplace
domain it is necessary to resort to accurate numerical methods to derive the
corresponding behaviours in the time domain. In this regard, we develop a
computational procedure to solve variable-order fractional differential
equations of this novel class. Furthermore, we provide some numerical
experiments to show the effectiveness of the proposed techniques.


  On a journey, a backpack is a perfect place to store and organize the
necessary provisions and tools. Similarly, carrying and managing items is a
central part of most digital games, providing significant prospects for the
player experience. Even though VR games are gradually becoming more mature,
most of them still avoid this essential feature. Some of the reasons for this
deficit are the additional requirements and challenges that VR imposes on
developers to achieve a compelling user experience. We structure the ample
design space of VR inventories by analyzing popular VR games and developing a
structural taxonomy. We combine our insights with feedback from game developers
to identify the essential building blocks and design choices. Finally, we
propose meaningful design implications and demonstrate the practical use of our
work in action.


  Galaxy mergers are central to our understanding of galaxy formation,
especially within the context of hierarchical models. Besides having a large
impact on the star formation history, mergers are also able to influence gas
motions at the centre of galaxies and trigger an Active Galactic Nucleus (AGN).
In this paper, we present a case study of the Seyfert galaxy NGC 2992, which
together with NGC 2993 forms the early-stage merger system Arp 245. Using
Gemini Multi-Object Spectrograph (GMOS) integral field unit (IFU) data from the
inner 1.1 kpc of the galaxy we were able to spatially resolve the stellar
populations, the ionisation mechanism and kinematics of ionised gas. From full
spectral synthesis, we found that the stellar population is primarily composed
by old metal-rich stars (t $\geq$ 1.4 Gyr, $Z \geq 2.0$\zsun), with a
contribution of at most 30 per cent of the light from a young and metal-poor
population (t $\leq$ 100 Myr, $Z \leq 1.0$\zsun). We detect \halpha and \hbeta
emission from the Broad Line Region (BLR) with a Full Width at Half Maximum
(FWHM) of $\sim$ 2000\kms. The Narrow Line Region (NLR) kinematics presents two
main components: one from gas orbiting the galaxy disk and a blueshifted
(velocity $\approx$ -200\kms) outflow, possibly correlated with the radio
emission, with mass outflow rate of $\sim$ 2 M$_{\odot}$ yr$^{-1}$ and a
kinematic power of $\sim$ 2 $\times 10^{40}$ erg s$^{-1}$ (\Eout/\Lbol
$\approx$ 0.2 per cent). We also show even though the main ionisation mechanism
is the AGN radiation, ionisation by young stars and shocks may also contribute
to the emission line ratios presented in the innermost region of the galaxy.


  We calculate the one-loop flavor changing neutral current top quark decay t
-> cgg in the Standard Model. We demonstrate that the rate for t -> cgg exceeds
the rate for a single gluon emission t -> cg by about two orders of magnitude,
while the rate for t -> cq barq (q=u) is slightly smaller than for t -> cg.


  Scene text detection is a challenging problem in computer vision. In this
paper, we propose a novel text detection network based on prevalent object
detection frameworks. In order to obtain stronger semantic feature, we adopt
ResNet as feature extraction layers and exploit multi-level feature by
combining hierarchical convolutional networks. A vertical proposal mechanism is
utilized to avoid proposal classification, while regression layer remains
working to improve localization accuracy. Our approach evaluated on ICDAR2013
dataset achieves F-measure of 0.91, which outperforms previous state-of-the-art
results in scene text detection.


  This paper considers the maximum likelihood estimation of factor models of
high dimension, where the number of variables (N) is comparable with or even
greater than the number of observations (T). An inferential theory is
developed. We establish not only consistency but also the rate of convergence
and the limiting distributions. Five different sets of identification
conditions are considered. We show that the distributions of the MLE estimators
depend on the identification restrictions. Unlike the principal components
approach, the maximum likelihood estimator explicitly allows
heteroskedasticities, which are jointly estimated with other parameters.
Efficiency of MLE relative to the principal components method is also
considered.


  Private states are those quantum states from which a perfectly secure
cryptographic key can be extracted. They represent the basic unit of quantum
privacy. In this work we show that all states belonging to this class violate a
Bell inequality. This result establishes a connection between perfect privacy
and nonlocality in the quantum domain.


  Air pollution is associated with human diseases and has been found to be
related to premature mortality. In response, environmental policies have been
adopted in many countries, to decrease anthropogenic air pollution for the
improvement of long-term air quality, since most air pollutant sources are
anthropogenic. However, air pollution fluctuations have been found to strongly
depend on the weather dynamics. This raises a fundamental question: What are
the significant atmospheric processes that affect the local daily variability
of air pollution? For this purpose, we develop here a multi-layered network
analysis to detect the interlinks between the geopotential height of the upper
air (~5 km) and surface air pollution in both China and the USA. We find that
Rossby waves significantly affect air pollution fluctuations through the
development of cyclone and anticyclone systems, and further affect the local
stability of the air and the winds. The significant impacts of Rossby waves on
air pollution are found to underlie most of the daily fluctuations in air
pollution. Thus, the impact of Rossby waves on human life is greater than
previously assumed. The rapid warming of the Arctic could slow down Rossby
waves, thus increasing human health risks. Our method can help to determine the
risk assessment of such extreme events and can improve potential
predictability.


  We classify $su(N_c)$ gauge theories on $\mathbb R^3\times \mathbb S^1$ with
massless fermions in higher representations obeying periodic boundary
conditions along $\mathbb S^1$. In particular, we single out the class of
theories that is asymptotically free and weakly coupled in the infrared, and
therefore, is amenable to semi-classical treatment. Our study is conducted by
carefully identifying the vacua inside the affine Weyl chamber using Verma
bases and Frobenius formula techniques. Theories with fermions in pure
representations are generally strongly coupled. The only exceptions are the
four-index symmetric representation of $su(2)$ and adjoint representation of
$su(N_c)$. However, we find a plethora of admissible theories with fermions in
mixed representations. A sub-class of these theories have degenerate
perturbative vacua separated by domain walls. In particular, $su(N_c)$ theories
with fermions in the mixed representations adjoint$\oplus$fundamental and
adjoint$\oplus$two-index symmetric admit degenerate vacua that spontaneously
break the parity ${\cal P}$, charge conjugation ${\cal C}$, and time reversal
${\cal T}$ symmetries. These are the first examples of strictly weakly coupled
gauge theories on $\mathbb R^3 \times \mathbb S^1$ with spontaneously broken
${\cal C}$, ${\cal P}$, and ${\cal T}$ symmetries. We also compute the fermion
zero modes in the background of monopole-instantons. The monopoles and their
composites (topological molecules) proliferate in the vacuum leading to the
confinement of electric charges. Interestingly enough, some theories have also
accidental degenerate vacua, which are not related by any symmetry. These vacua
admit different numbers of fermionic zero modes, and hence, different kinds of
topological molecules. The lack of symmetry, however, indicates that such
degeneracy might be lifted by higher order corrections.


  Liquid-metal jet X-ray sources promise to deliver high photon fluxes, which
are unprecedented for laboratory based X-ray sources, because the regenerating
liquid-metal anode is less sensitive to damage caused by an increased electron
beam power density. For some quantitative X-ray analysis techniques, knowledge
of the absolute photon flux is needed. However, a precise experimental
determination of the photon flux of high-performance X-ray sources is
challenging, because a direct measurement results in significant dead time
losses in the detector or could even harm the detector. Indirect determinations
rely on data base values of attenuation or scattering cross sections leading to
large uncertainties. In this study we present an experimental determination of
the photon flux of a liquid-metal jet X-ray source by means of elastic and
inelastic photon scattering. Our approach allows for referencing the
unpolarized output radiation of the liquid-metal jet X-ray source to polarized
synchrotron radiation in a simple setup. Absolute photon fluxes per solid angle
are presented with a detailed uncertainty budget for the characteristic
emission lines of Ga K$\alpha$ and In K$\alpha$ for two different acceleration
voltages of the X-ray source. For a nominal setting of 200 W (70 kV, 2.857 mA)
the determined values for Ga K$\alpha$ and In K$\alpha$ are 6.0(5)$\times
10^{12}$ s$^{-1}$sr$^{-1}$ and 3.8(4)$\times 10^{11}$ s$^{-1}$sr$^{-1}$,
respectively.


  The cycling of metals between interstellar gas and dust is a critical aspect
of the baryon cycle of galaxies, yet our understanding of this process is
limited. This study focuses on understanding dust depletion effects in the low
metallicity regime (< 20% Zo) typical of cosmic noon. Using medium-resolution
UV spectroscopy from the COS onboard the Hubble Space Telescope, gas-phase
abundances and depletions of iron and sulfur were derived toward 18 sightlines
in local dwarf galaxies IC 1613 and Sextans A. The results show that the
depletion of Fe and S is consistent with that found in the Milky Way, LMC and
SMC. The depletion level of Fe increases with gas column density, indicating
dust growth in the interstellar medium (ISM). The level of Fe depletion
decreases with decreasing metallicity, resulting in the fraction of iron in gas
ranging from 3% in the MW to 9% in IC 1613 and ~19% in Sextans A. The
dust-to-gas and dust-to-metal ratios (D/G, D/M) for these dwarf galaxies were
estimated based on the MW relations between the depletion of Fe and other
elements. The study finds that D/G decreases only slightly sub-linearly with
metallicity, with D/M decreasing from 0.41 +/- 0.05 in the MW to 0.11 +/- 0.11
at 0.10 Zo (at log N(H) = 21 cm-2). The trend of D/G vs. metallicity using
depletion in local systems is similar to that inferred in Damped Ly-alpha
systems from abundance ratios but lies higher than the trend inferred from FIR
measurements in nearby galaxies.


  We study spontaneous emission of a photon during the transitions between
relativistic Landau states of an electron in a constant magnetic field that can
reach the Schwinger value of $H_c = 4.4 \times 10^9$ T. In contrast to the
conventional method in which detection of both the final electron and the
photon is implied in a certain basis, here we derive the photon state as it
evolves from the process itself. It is shown that the emitted photon state
represents a twisted Bessel beam propagating along the field axis with a total
angular momentum (TAM) projection onto this axis $\ell-\ell'$ where $\ell$ and
$\ell'$ are the TAM of the initial electron and of the final one, respectively.
Thus, the majority of the emitted photons turn out to be twisted with
$\ell-\ell' \gtrsim 1$, even when the magnetic field reaches the critical value
of $H\sim H_c$. The transitions without a change of the electron angular
momentum, $\ell'=\ell$, are possible, yet much less probable. We also compare
our findings with those for a spinless charged particle and demonstrate their
good agreement for the transitions without change of the electron spin
projection even in the critical fields, while the spin-flip transitions are
generally suppressed. In addition, we argue that whereas the ambiguous choice
of an electron spin operator affects the differential probability of emission,
this problem can partially be circumvented for the photon evolved state because
it is the electron TAM rather than the spin alone that defines the TAM of the
emitted twisted photon.


  In the imaginay-time formalism of thermal field theory, and also in the
real-time formalism but by means of some redefined physical propagators for
scalar bound states by diagonalization of four-point function matrices, we
reexamine the Nambu-Goldstone mechanism of electroweak symmetry breaking in a
one-generation fermion condensate scheme, based on the Schwinger-Dyson equation
in the fermion bubble diagram approximation, and compare the obtained results.
We have reached the conclusion that in both the formalisms, the Goldstone
theorem of spontaneous electroweak symmetry breaking is rigorously true for the
case of mass-degenerate two flavors of fermions and only approximately valid at
low energy scales for the mass-nondegenerate case, in spite of existence of
some difference between the two formalisms in the imaginary parts of the
denominators of the propagators for scalar bound states. When the two flavors
of fermions have unequal nonzero masses, the induced possible fluctuation
effect for the Higgs particle is negligible if the momentum cut-off in the zero
temperature loops is large enough. All the results show physical equivalence of
the two formalisms in the present discussed problems.


  We establish two-sided Gaussian bounds for fundamental solutions of general
non-divergence form parabolic operators with H\"older continuous coefficients.
The result we obtain is essentially based on parametrix method.


  We develop a fast algorithm to construct the robustness degradation function,
which describes quantitatively the relationship between the proportion of
systems guaranteeing the robustness requirement and the radius of the
uncertainty set. This function can be applied to predict whether a controller
design based on an inexact mathematical model will perform satisfactorily when
implemented on the true system.


  Halide perovskites are perceived to be the promising class of materials for
optoelectronics, spinorbitronics and topological electronics due to presence of
strong spin-orbit coupling and polarized field. Here, we develop a Hamiltonian
using quasi-degenerate perturbation theory to describe polarized field driven
band structures and unique topological phases such as Dirac semimetallic rings
for the universal class of Halide perovskites including both inorganic and
hybrid members. The spin textures obtained through this theoretical model
captures minute effects of polarization and hence can be used as a modern tool
to determine the polarized field directions which have significant influence on
spinorbitronics. The analysis brings out the concepts of hybrid spin textures
intermixing the effects of valence and conduction bands under topological
quantum phase transitions, and spin texture binaries where alignment of the
spins are reversed between domains in the momentum space with sharp boundaries.
The results are validated through density functional calculations.


  The dynamics in the photosphere is governed by the multi-scale turbulent
convection termed as granulation and supergranulation. It is important to
derive 3-dimensional velocity vectors to understand the nature of the turbulent
convection. However, it is difficult to obtain the velocity component
perpendicular to the line-of-sight, which corresponds to the horizontal
velocity in disk center observations. We developed a convolutional neural
network model with a multi-scale deep learning architecture. The method
consists of multiple convolutional kernels with various sizes of the receptive
fields, and it performs convolution for spatial and temporal axes. The network
is trained with data from three different numerical simulations of turbulent
convection, and we introduced a coherence spectrum to assess the horizontal
velocity fields that were derived at each spatial scale. The multi-scale deep
learning method successfully predicts the horizontal velocities for each
convection simulation in terms of the global-correlation-coefficient, which is
often used for evaluating the prediction accuracy of the methods. The coherence
spectrum reveals the strong dependence of the correlation coefficients on the
spatial scales. Although coherence spectra are higher than 0.9 for large-scale
structures, they drastically decrease to less than 0.3 for small-scale
structures wherein the global-correlation-coefficient indicates a high value of
approximately 0.95. We determined that this decrease in the coherence spectrum
occurs around the energy injection scales. The accuracy for the small-scale
structures is not guaranteed solely by the global-correlation-coefficient. To
improve the accuracy in small-scales, it is important to improve the loss
function for enhancing the small-scale structures and to utilize other physical
quantities related to the non-linear cascade of convective eddies as input
data.


  In this paper we study certain families of motives, which arise as direct
summands of the cohomology of the Dwork family. We computationally find
examples of interesting families with the following three properties. Firstly,
their geometric monodromy group is Zariski dense in $\operatorname{SL}_n$.
Secondly, they realise many different unipotent operators as the monodromy
operator at $t = \infty$. Thirdly, all their Hodge numbers are $\leq 1$.
  This has consequences for Galois representations. Namely, if a nilpotent
operator $N$ appears as the monodromy at $t = \infty$ in one of our families,
we can construct potentially automorphic representations with $\ell$-adic
monodromy given by $N$ at a fixed prime $p$. As another application, we obtain
a new proof of some cases of the recent local-global compatibility theorem of
Matsumoto.


  We obtain a trace formula for algebraic differential operators which the
corresponding analytic results have been proved by M. Engeli and G. Felder


  We derived an asymptotic bound the accuracy of the estimation when we use the
quantum correlation in the measuring apparatus. It is also proved that this
bound can be achieved in any model in the quantum two-level system. Moreover,
we show that this bound of such a model cannot be attained by any quantum
measurement with no quantum correlation in the measuring apparatus. That is, in
such a model, the quantum correlation can improve the accuracy of the
estimation in an asymptotic setting.


  We have developed an efficient algorithm for the maximum likelihood joint
tracking and association problem in a strong clutter for GMTI data. By using an
iterative procedure of the dynamic logic process "from vague-to-crisp," the new
tracker overcomes combinatorial complexity of tracking in highly-cluttered
scenarios and results in a significant improvement in signal-to-clutter ratio.


  Researchers have used machine learning approaches to identify motion sickness
in VR experience. These approaches demand an accurately-labeled, real-world,
and diverse dataset for high accuracy and generalizability. As a starting point
to address this need, we introduce `VR.net', a dataset offering approximately
12-hour gameplay videos from ten real-world games in 10 diverse genres. For
each video frame, a rich set of motion sickness-related labels, such as
camera/object movement, depth field, and motion flow, are accurately assigned.
Building such a dataset is challenging since manual labeling would require an
infeasible amount of time. Instead, we utilize a tool to automatically and
precisely extract ground truth data from 3D engines' rendering pipelines
without accessing VR games' source code. We illustrate the utility of VR.net
through several applications, such as risk factor detection and sickness level
prediction. We continuously expand VR.net and envision its next version
offering 10X more data than the current form. We believe that the scale,
accuracy, and diversity of VR.net can offer unparalleled opportunities for VR
motion sickness research and beyond.


  We introduce Hopf polyads in order to unify Hopf monads and group actions on
monoidal categories. A polyad is a lax functor from a small category (its
source) to the bicategory of categories, and a Hopf polyad is a comonoidal
polyad whose fusion operators are invertible. The main result states that the
lift of a Hopf polyad is a strong (co)monoidal action-type polyad (or strong
monoidal pseudofunctor). The lift of a polyad is a new polyad having simpler
structure but the same category of modules. We show that, under certain
assumptions, a Hopf polyad can be `wrapped up' into a Hopf monad. This
generalizes the fact that finite group actions on tensor categories can be seen
as Hopf monads. Hopf categories in the sense of Batista, Caenepeel and
Vercruysse can be viewed as Hopf polyads in a braided setting via the notion of
Hopf polyalgebras. As a special case of the main theorem, we generalize a
description of the center of graded fusion category due to Turaev and
Virelizier to tensor categories: if $C$ is a $G$-graded (locally bounded)
tensor category, then $G$ acts on the relative center of $C$ with respect to
the degree one part $C_1$, and the equivariantization of this action is the
center of $C$.


  Let K be any compact set in the complex plane that has a connected
complement, let A(K) be the uniforn algebra of all continuous complex functions
on K that are holomorphic on the interior of K, let bK be the topological
boundary of K, let z be in K, and let M be the maximal ideal of functions in
A(K) that are 0 at z. Using only facts from classical complex analytic function
theory, and without using any results from the theory of analytic capacity, we
prove the following: z is an element of bK iff z is a peak point for A(K) iff z
belongs to the Shilov boundary for A(K) iff z belongs to the Bishop minimal
boundary for A(K) iff M has a bounded approximate identity iff the Bishop
one-quarter - three-quarter property holds at z iff z is a strong boundary
point for A(K). More specifically, the only results used in all proofs are from
classical complex analytic function theory, properties of open connected sets
in the complex plane, the Caratheodory extension theorem, the Riemann mapping
theorem, Euler's formula, Rudin's estimates for finite complex products,
properties of linear fractional transformations, the alpha root function in the
complex plane, some new and striking Jordan curve constructions (Jordan kissing
paths), and the Cohen factorization theorem. No results are used from the
theory of analytic capacity, the theory of representing or annihilating
measures, Dirichlet algebra theory, Choquet boundary theory, or the
Walsh-Lebesgue theorem.


  We study the problem of learning with selectively labeled data, which arises
when outcomes are only partially labeled due to historical decision-making. The
labeled data distribution may substantially differ from the full population,
especially when the historical decisions and the target outcome can be
simultaneously affected by some unobserved factors. Consequently, learning with
only the labeled data may lead to severely biased results when deployed to the
full population. Our paper tackles this challenge by exploiting the fact that
in many applications the historical decisions were made by a set of
heterogeneous decision-makers. In particular, we analyze this setup in a
principled instrumental variable (IV) framework. We establish conditions for
the full-population risk of any given prediction rule to be point-identified
from the observed data and provide sharp risk bounds when the point
identification fails. We further propose a weighted learning approach that
learns prediction rules robust to the label selection bias in both
identification settings. Finally, we apply our proposed approach to a
semi-synthetic financial dataset and demonstrate its superior performance in
the presence of selection bias.


  In this paper we present new general convergence results about the behaviour
of the Distributed Bellman-Ford (DBF) family of routing protocols, which
includes distance-vector protocols (e.g. RIP) and path-vector protocols (e.g.
BGP). Our results apply to ``policy-rich" protocols, by which we mean protocols
that can have complex policies (e.g. conditional route transformations) that
violate traditional assumptions made in the standard presentation of
Bellman-Ford protocols.
  First, we propose a new algebraic model for abstract routing problems which
has fewer primitives than previous models and can represent more expressive
policy languages. The new model is also the first to allow concurrent reasoning
about distance-vector and path-vector protocols.
  Second, we demonstrate how DBF routing protocols are instances of a larger
class of asynchronous iterative algorithms, for which there already exist
powerful results about convergence. These results allow us to build upon
conditions previously shown by Sobrinho to be sufficient and necessary for the
convergence of path-vector protocols and strengthen them: we show that, with a
minor modification, they also apply to distance-vector protocols; we prove they
guarantee that the final routing solution reached is unique, thereby
eliminating the possibility of anomalies such as BGP wedgies; we relax the
model of asynchronous communication, showing that the results still hold if
routing messages can be lost, reordered, and duplicated.
  Thirdly, our model and our accompanying theoretical results have been fully
formalised in the Agda theorem prover. The resulting library is a powerful tool
for quickly prototyping and formally verifying new policy languages. As an
example, we formally verify the correctness of a policy language with many of
the features of BGP including communities, conditional policy, path-inflation
and route filtering.


  Vision-based Continuous Sign Language Recognition (CSLR) aims to recognize
unsegmented signs from image streams. Overfitting is one of the most critical
problems in CSLR training, and previous works show that the iterative training
scheme can partially solve this problem while also costing more training time.
In this study, we revisit the iterative training scheme in recent CSLR works
and realize that sufficient training of the feature extractor is critical to
solving the overfitting problem. Therefore, we propose a Visual Alignment
Constraint (VAC) to enhance the feature extractor with alignment supervision.
Specifically, the proposed VAC comprises two auxiliary losses: one focuses on
visual features only, and the other enforces prediction alignment between the
feature extractor and the alignment module. Moreover, we propose two metrics to
reflect overfitting by measuring the prediction inconsistency between the
feature extractor and the alignment module. Experimental results on two
challenging CSLR datasets show that the proposed VAC makes CSLR networks
end-to-end trainable and achieves competitive performance.


  We describe a new method for determining total gas-phase abundances for the
Galactic ISM with minimal ionization uncertainties. For sight lines toward
globular clusters containing both UV-bright stars and radio pulsars, one can
measure column densities of HI and several metal ions using UV absorption
measurements and of H II using radio dispersion measurements, thereby
minimizing ionization uncertainties. We apply this method to the globular
cluster Messier 3 sight line using FUSE and HST ultraviolet spectroscopy of the
post-asymptotic giant branch star von Zeipel 1128 and radio observations by
Ransom et al. of millisecond pulsars. Ionized hydrogen is 45+/-5% of the total
along this sight line, the highest measured fraction along a high-latitude
pulsar sight line. We derive total gas-phase abundances log N(S)/N(H) =
-4.87+/-0.03 and log N(Fe)/N(H) = -5.27+/-0.05. Our derived sulfur abundance is
in excellent agreement with recent solar system determinations of Asplund,
Grevesse, & Sauval, but -0.14 dex below the solar system abundance typically
adopted in studies of the ISM. The iron abundance is ~-0.7 dex below the solar
system abundance, consistent with significant depletion. Abundance estimates
derived by simply comparing S II and Fe II to H I are +0.17 and +0.11 dex
higher, respectively, than our measurements. Ionization corrections to the
gas-phase abundances measured in the standard way are, therefore, significant
compared with the measurement uncertainties along this sight line. The
systematic uncertainties associated with the uncertain contribution to the
electron column density from ionized helium could raise these abundances by
<+0.03 dex (+7%). [Abridged]


  The interaction energy between a water molecule and graphitic structured
clusters terminated by hydrogen atoms is analyzed by ab initio methods and
decomposed into electrostatic, induction, Pauli repulsion, and correlation
energy contributions. Contributions to the energy which are due solely to the
perimeter of the clusters are identified. These can be isolated and discarded
which greatly simplifies the problem of extrapolation to the large cluster
limit. The remaining terms are intrinsic to the interaction of a water molecule
with real graphitic layers and an explicit analytical form is given for the
potential energy surface. The minimum energy configuration is found to have
both hydrogen atoms of the water molecule pointing symmetrically away from the
graphitic plane. The electronic interaction in this mode is -16.8 +/- 1.7
kJ/mol for water-graphite and the zero point energy is estimated as 1.3 kJ/mol.


  In SU(3) simplest little Higgs model, a characteristic particle is the light
pseudoscalar boson eta, it leads interesting signals in the LHC/ILC and is
studied in literature with different parameterizations. In this work, we show
that these different descriptions for eta particle are equivalent up to some
SU(3) rotations as long as we suitably redefine the pseudo Goldstone boson
fields. We evaluate the necessary SU(3) rotations and built up explicit
expressions for redefined fields.


  In many cases beam coupling impedances or wake fields are calculated with
computer simulator such as CST Studio Suite, GdfidL Electromagnetic Field
Simulator and so on. But evaluation with the stretched-wire method is still
very useful by its flexibility to the change of the device-under-test
configuration, speed to get results and, more than anything, its accessibility
on the real devices. One of the drawbacks in the practical procedure,
difficulty of Thru-Reflect-Line calibration, is overcome using the calibration
method recently introduced in high frequency vector network analyzers, "2-X
THRU de-embedding". Here the procedure is explained in detail. The method has
been successfully applied to RF cavity and FX kicker measurement in the J-PARC
MR.


  On the grounds of a Feynman-Kac--type formula for Hamiltonian lattice systems
we derive analytical expressions for the matrix elements of the evolution
operator. These expressions are valid at long times when a central limit
theorem applies. As a remarkable result we find that the ground-state energy as
well as all the correlation functions in the ground state are determined
semi-analytically by solving a simple scalar equation. Furthermore, explicit
solutions of this equation are obtained in the noninteracting case.


  The interplay of almost degenerate levels in quantum dots and molecular
junctions with possibly different couplings to the reservoirs has lead to many
observable phenomena, such as the Fano effect, transmission phase slips and the
SU(4) Kondo effect. Here we predict a dramatic repeated disappearance and
reemergence of the SU(4) and anomalous SU(2) Kondo effects with increasing gate
voltage. This phenomenon is attributed to the level occupation switching which
has been previously invoked to explain the universal transmission phase slips
in the conductance through a quantum dot. We use analytical arguments and
numerical renormalization group calculations to explain the observations and
discuss their experimental relevance and dependence on the physical parameters.


  Fragmentation and fission of giant molecular clouds occasionally results in a
pair of gravitationally bound star clusters that orbit their mutual centre of
mass for some time, under the influence of internal and external perturbations.
We investigate the evolution of binary star clusters with different orbital
configurations, with a particular focus on the Galactic tidal field. We carry
out $N$-body simulations of evolving binary star clusters and compare our
results with estimates from our semi-analytic model. The latter accounts for
mass loss due to stellar evolution and two-body relaxation, and for evolution
due to external tides. Using the semi-analytic model we predict the long-term
evolution for a wide range of initial conditions. It accurately describes the
global evolution of such systems, until the moment when a cluster merger is
imminent. $N$-body simulations are used to test our semi-analytic model and
also to study additional features of evolving binary clusters, such as the
kinematics of stars, global cluster rotation, evaporation rates, and the
cluster merger process. We find that the initial orientation of a binary star
cluster with respect to the Galactic field, and also the initial orbital phase,
are crucial for its fate. Depending on these properties, the binaries may
experience orbital reversal, spiral-in, or vertical oscillation about the
Galactic plane before they actually merge at $t\approx100$~Myr, and produce
rotating star clusters with slightly higher evaporation rates. The merger
process of a binary cluster induces an outburst that ejects $\sim10\%$ of the
stellar members into the Galactic field.


  We present first results of a long-term project which aims at multi-scale,
multi-physics simulations of wind accretion in microquasars and high-mass X-ray
binaries. The 3D hydrodynamical simulations cover all scales, from the
circum-binary environment down to the immediate vicinity of the black hole. We
first introduce the numerical method and parallelization strategy of the AMR
A-MAZE code. We then discuss some preliminary results of how, and on what
scales, an accretion disk is formed around the black hole. We finally present
some characteristics of this disk, which is far from Keplerian. We emphasize
that on all scales shocks play a decisive role for the accretion process and
the process of structure formation -- for the formation of the large scale,
nearly coherent structure of the disk, but also for the formation of turbulent
fluctuations.


  We present the itinerant coherent-potential approximation(ICPA), an analytic,
translationally invariant and tractable form of augmented-space-based,
multiple-scattering theory in a single-site approximation for harmonic phonons
in realistic random binary alloys with mass and force-constant disorder.
  We provide expressions for quantities needed for comparison with experimental
structure factors such as partial and average spectral functions and derive the
sum rules associated with them. Numerical results are presented for Ni_{55}
Pd_{45} and Ni_{50} Pt_{50} alloys which serve as test cases, the former for
weak force-constant disorder and the latter for strong. We present results on
dispersion curves and disorder-induced widths. Direct comparisons with the
single-site coherent potential approximation(CPA) and experiment are made which
provide insight into the physics of force-constant changes in random alloys.
The CPA accounts well for the weak force-constant disorder case but fails for
strong force-constant disorder where the ICPA succeeds.


  A strong edge coloring of a graph $G$ is a proper edge coloring in which each
color class is an induced matching of $G$. In 1993, Brualdi and Quinn Massey
proposed a conjecture that every bipartite graph without $4$-cycles and with
the maximum degrees of the two partite sets $2$ and $\Delta$ admits a strong
edge coloring with at most $\Delta+2$ colors. We prove that this conjecture
holds for such graphs with $\Delta=3$. We also confirm the conjecture proposed
by Faudree et al. for subcubic bipartite graphs.


  Inspired by compressive sensing principles, we propose novel error control
coding techniques for communication systems. The information bits are encoded
in the support and the non-zero entries of a sparse signal. By selecting a
dictionary matrix with suitable dimensions, the codeword for transmission is
obtained by multiplying the dictionary matrix with the sparse signal.
Specifically, the codewords are obtained from the sparse linear combinations of
the columns of the dictionary matrix. At the decoder, we employ variations of
greedy sparse signal recovery algorithms. Using Gold code sequences and
mutually unbiased bases from quantum information theory as dictionary matrices,
we study the block error rate (BLER) performance of the proposed scheme in the
AWGN channel. Our results show that the proposed scheme has a comparable and
competitive performance with respect to the several widely used linear codes,
for very small to moderate block lengths. In addition, our coding scheme
extends straightforwardly to multi-user scenarios such as multiple access
channel, broadcast channel, and interference channel. In these multi-user
channels, if the users are grouped such that they have similar channel gains
and noise levels, the overall BLER performance of our proposed scheme will
coincide with an equivalent single-user scenario.


  We show the existence of weak solutions in the extended sense of the Cauchy
problem for the cubic nonlinear Schr\"odinger equation in the modulation space
$M_{2,q}^{s}(\mathbb R)$, $1\leq q\leq2$ and $s\geq0.$ In addition, for either
$s\geq 0$ and $1\leq q\leq\frac32$ or $\frac32<q\leq 2$ and
$s>\frac23-\frac1{q}$ we show that the Cauchy problem is unconditionally
wellposed in $M_{2,q}^{s}(\mathbb R).$ It is done with the use of the
differentiation by parts technique which had been previously used in the
periodic setting.


  We describe strongly attractive carriers in cuprates in the framework of a
simple quasi-one dimensional Hamiltonian with a local attraction. In contrast
with the conventional BCS theory there are two energy scales, a temperature
independent incoherent gap $\Delta_p$ and a temperature dependent coherent gap
$\Delta_c (T)$ combining into one temperature dependent global gap
$\Delta=(\Delta_p^2 +\Delta_c^2)^{1/2}$. The temperature dependence of the gap
and single particle (Giaver) tunnelling spectra in cuprates are quantitatively
described. A framework for understanding of two distinct energy scales observed
in Giaver tunnelling and electron-hole reflection experiments is provided.


  In this paper we relate the parity-odd part of two and three point
correlation functions in theories with exactly conserved or weakly broken
higher spin symmetries to the parity-even part which can be computed from free
theories. We also comment on higher point functions.
  The well known connection of CFT correlation functions with de-Sitter
amplitudes in one higher dimension implies a relation between parity-even and
parity-odd amplitudes calculated using non-minimal interactions such as
${\mathcal W}^3$ and ${\mathcal W}^2 {\widetilde {\mathcal W}}$. In the
flat-space limit this implies a relation between parity-even and parity-odd
parts of flat-space scattering amplitudes.


  The first overtone ($\Delta v$ = 2) bands of the monosubstituted
isotopologues of CO at 2.3 $\mu$m in the spectrum of Arcturus (K2 III), and of
the monosubstituted isotopologues of SiO at 4 $\mu$m in the spectrum of the red
giant HD196610 (M6 III) are modelled.
  To investigate problems involving the computation of the first overtone bands
of isotopologues of CO and SiO in spectra of late-type stars and to determine
isotopic abundances.
  We use fits of theoretical synthetic spectra to the observed stellar
molecular bands of CO and SiO to determine abundances of isotopes of C, O and
Si.
  Fits of synthetic spectra of the \CO first overtone bands at 2.3 $\mu$m
computed with three available line lists (Goorvitch, HITEMP2010 and Li et al.)
to the observed spectrum of Arcturus provide the same carbon abundance
[C]=$-0.6$ and isotopic ratio of carbon $^{12}$C/$^{13}$C=10 $\pm$ 2. However,
the quality of fits to the observed spectrum differ for three line lists used.
Furthermore, the derived oxygen isotopic ratio $^{16}$O/$^{18}$O = 2000 $\pm$
500 is larger than that known in the solar system where $^{16}$O/$^{18}$O =
500. The silicon isotopic ratio in the atmosphere of the red giant HD196610 is
revised. Using the ExoMol SiO line list with appropriate statistical weights
for the SiO isotopologues the `non-solar' ratio $^{28}$Si:$^{29}$Si:$^{30}$Si =
0.86$\pm$0.03:0.12$\pm$0.02:0.02$\pm$0.01 is obtained.
  We found that a) the computed isotopic carbon and silicon ratios determined
by the fits to the observed spectrum depend on the adopted abundance of C and
Si, respectively; b) Correct treatment of the nuclear spin degeneracies
parameter is of crucial importance for the use of nowadays HITRAN/ExoMol line
lists in the astrophysical computations.


  Research in oncology has changed the focus from histological properties of
tumors in a specific organ to a specific genomic aberration potentially shared
by multiple cancer types. This motivates the basket trial, which assesses the
efficacy of treatment simultaneously on multiple cancer types that have a
common aberration. Although the assumption of homogeneous treatment effects
seems reasonable given the shared aberration, in reality, the treatment effect
may vary by cancer type, and potentially only a subgroup of the cancer types
respond to the treatment. Various approaches have been proposed to increase the
trial power by borrowing information across cancer types, which, however, tend
to inflate the type I error rate. In this paper, we review some representative
Bayesian information borrowing methods for the analysis of early-phase basket
trials. We then propose a novel method called the Bayesian hierarchical model
with a correlated prior (CBHM), which conducts more flexible borrowing across
cancer types according to sample similarity. We did simulation studies to
compare CBHM with independent analysis and three information borrowing
approaches: the conventional Bayesian hierarchical model, the EXNEX approach
and Liu's two-stage approach. Simulation results show that all information
borrowing approaches substantially improve the power of independent analysis if
a large proportion of the cancer types truly respond to the treatment. Our
proposed CBHM approach shows an advantage over the existing information
borrowing approaches, with a power similar to that of EXNEX or Liu's approach,
but the potential to provide substantially better control of type I error rate.


  Generalized second law of thermodynamics in the Bianchi type I universe with
the generalized holographic Ricci dark energy model is studied in this paper.
The behavior of dark energy's equation of state parameter indicates that it is
matter-like in the early time of the universe but phantom-like in the future.
By analysing the evolution of the deviations of state parameter and the total
pressure of the universe, we find that for an anisotropic Bianchi type I
universe, it transits from a high anisotropy stage to a more homogeneous stage
in the near past. Using the normal entropy given by Gibbs' law of
thermodynamics, it is proved that the generalized second law of thermodynamics
does not always satisfied throughout the history of the universe when we assume
the universe is enclosed by the generalized Ricci scalar radius $R_{gr}$. It
becomes invalid in the near past to the future, and the formation of the
galaxies will be helpful in explaining such phenomenon, for that the galaxies's
formation is an entropy increase process. The negative change rates of the
horizon entropy and internal entropy occur in different period indicates that
the influences of galaxies formation is wiped from internal to the universe's
horizon.


  The clustering of dark halos depends not only on their mass but also on their
assembly history, a dependence we term `assembly bias'. Using a galaxy
formation model grafted onto the Millennium Simulation of the LCDM cosmogony,
we study how assembly bias affects galaxy clustering. We compare the original
simulation to `shuffled' versions where the galaxy populations are randomly
swapped among halos of similar mass, thus isolating the effects of correlations
between assembly history and environment at fixed mass. Such correlations are
ignored in the halo occupation distribution models often used populate dark
matter simulations with galaxies, but they are significant in our more
realistic simulation. Assembly bias enhances 2-point correlations by 10% for
galaxies with M_bJ-5logh brighter than -17, but suppresses them by a similar
amount for galaxies brighter than -20. When such samples are split by colour,
assembly bias is 5% stronger for red galaxies and 5% weaker for blue ones. Halo
central galaxies are differently affected by assembly bias than are galaxies of
all types. It almost doubles the correlation amplitude for faint red central
galaxies. Shuffling galaxies among halos of fixed formation redshift or
concentration in addition to fixed mass produces biases which are not much
smaller than when mass alone is fixed. Assembly bias must reflect a correlation
of environment with aspects of halo assembly which are not encoded in either of
these parameters. It induces effects which could compromise precision
measurements of cosmological parameters from large galaxy surveys.


  Waves can be used to probe and image an unknown medium. Passive imaging uses
ambient noise sources to illuminate the medium. This paper considers passive
imaging with moving sensors. The motivation is to generate large synthetic
apertures, which should result in enhanced resolution. However Doppler effects
and lack of reciprocity significantly affect the imaging process. This paper
discusses the consequences in terms of resolution and it shows how to design
appropriate imaging functions depending on the sensor trajectory and velocity.


  The electroweak phase transition (EWPT) in the secluded-$U(1)'$-extended MSSM
(sMSSM) is studied. Using the effective potential at zero and finite
temperatures, we search for the non-MSSM-like EWPT in which the light stop mass
is larger than the top quark mass. Scanning the parameters relevant to the
EWPT, the upper limits of the Higgs boson masses, which are consistent with the
strong first order EWPT, are derived. For the lightest CP-even and -odd Higgs
bosons, we find $m_{H_1}<160$ GeV and $m_{A_1}<250$ GeV, respectively. In the
sMSSM, the tree-level CP violation is possible by the complex soft
supersymmetry breaking masses. It is observed that such a CP-violating effect
does not spoil the strong first order EWPT for the typical parameter sets.


  Adversarial attack is aimed at fooling the target classifier with
imperceptible perturbation. Adversarial examples, which are carefully crafted
with a malicious purpose, can lead to erroneous predictions, resulting in
catastrophic accidents. To mitigate the effects of adversarial attacks, we
propose a novel purification model called CAP-GAN. CAP-GAN takes account of the
idea of pixel-level and feature-level consistency to achieve reasonable
purification under cycle-consistent learning. Specifically, we utilize the
guided attention module and knowledge distillation to convey meaningful
information to the purification model. Once a model is fully trained, inputs
would be projected into the purification model and transformed into clean-like
images. We vary the capacity of the adversary to argue the robustness against
various types of attack strategies. On the CIFAR-10 dataset, CAP-GAN
outperforms other pre-processing based defenses under both black-box and
white-box settings.


  In this paper, main parameters for linac-ring type collider desinged for
producing $\phi $ particles copiously are estimated and potential of this
machine in particle physics researches is investigated. Moreover, parameters
for free electron laser and synchrotron radiation obtained from electron linac
and positron ring, respectively, are determined and applications of these
radiations are summarized.


  New high resolution spectroscopic and medium resolution spectropolarimetric
data, complemented with optical broad and narrow band imaging, of the B[e] star
HD 87643 are presented. The spectrum of HD 87643 exhibits the hybrid
characteristics well known to be representative of the group of B[e] stars; a
fast wind with an expansion velocity in excess of 1000 km/s is measured in the
hydrogen and helium lines, while a slower component is traced by lower
excitation lines and forbidden lines. Clues to the geometry of the rapidly
expanding circumstellar shell are provided by the startling polarization
changes across Halpha. Comparison with published schematic calculations
indicates that the polarizing material is located in a slowly rotating,
expanding disk structure. A hydrodynamical model is then presented whose
results are consistent with the original two-wind concept for B[e] stars and
exhibits kinematic properties that may well explain the observed spectral
features in HD 87643. The model calculations use as input a B star undergoing
mass loss, surrounded by an optically thick disk. The resulting configuration
consists of a fast polar wind from the star and a slowly expanding disk wind.
The model also predicts that the stellar wind at intermediate latitudes is
slower and denser than in the polar region.


  Significant progress in the development of highly adaptable and reusable
Artificial Intelligence (AI) models is expected to have a significant impact on
Earth science and remote sensing. Foundation models are pre-trained on large
unlabeled datasets through self-supervision, and then fine-tuned for various
downstream tasks with small labeled datasets. This paper introduces a
first-of-a-kind framework for the efficient pre-training and fine-tuning of
foundational models on extensive geospatial data. We have utilized this
framework to create Prithvi, a transformer-based geospatial foundational model
pre-trained on more than 1TB of multispectral satellite imagery from the
Harmonized Landsat-Sentinel 2 (HLS) dataset. Our study demonstrates the
efficacy of our framework in successfully fine-tuning Prithvi to a range of
Earth observation tasks that have not been tackled by previous work on
foundation models involving multi-temporal cloud gap imputation, flood mapping,
wildfire scar segmentation, and multi-temporal crop segmentation. Our
experiments show that the pre-trained model accelerates the fine-tuning process
compared to leveraging randomly initialized weights. In addition, pre-trained
Prithvi compares well against the state-of-the-art, e.g., outperforming a
conditional GAN model in multi-temporal cloud imputation by up to 5pp (or 5.7%)
in the structural similarity index. Finally, due to the limited availability of
labeled data in the field of Earth observation, we gradually reduce the
quantity of available labeled data for refining the model to evaluate data
efficiency and demonstrate that data can be decreased significantly without
affecting the model's accuracy. The pre-trained 100 million parameter model and
corresponding fine-tuning workflows have been released publicly as open source
contributions to the global Earth sciences community through Hugging Face.


  The elastic wave propagation is investigated in the beam lattice material
characterized by a square periodic cell with anti-tetrachiral microstructure.
With reference to the Floquet-Bloch spectrum, focus is made on the band
structure enrichments and modifications which can be achieved by equipping the
cellular microstructure with tunable local resonators. By virtue of its
composite mechanical nature, the so-built inertial meta-material gains enhanced
capacities of passive frequency-band filtering. Indeed the number, placement
and properties of the inertial resonators can be designed to open, shift and
enlarge the band gaps between one or more pairs of consecutive branches in the
frequency spectrum. In order to improve the meta-material performance, a
nonlinear optimization problem is formulated. The maximum of the largest band
gap amplitudes in the low-frequency range is selected as suited objective
function. Proper inequality constraints are introduced to restrict the optimal
solutions within a compact set of mechanical and geometric parameters,
including only physically realistic properties of both the lattice and
resonators. The optimization problems related to full and partial band gaps are
solved independently, by means of a globally convergent version of the
numerical method of moving asymptotes, combined with a quasi-Monte Carlo
multi-start technique. The optimal solutions are discussed and compared from
the qualitative and quantitative viewpoints, bringing to light the limits and
potential of the meta-material performance. The clearest trends emerging from
the numerical analyses are pointed out and interpreted from the physical
viewpoint. Finally, some specific recommendations about the microstructural
design of the meta-material are synthesized.


  Magnetocrystalline anisotropy (MCA) in doped Ce$_{2}$Co$_{17}$ and other
competing structures was investigated using density functional theory. We
confirmed that the MCA contribution from dumbbell Co sites is very negative.
Replacing Co dumbbell atoms with a pair of Fe or Mn atoms greatly enhance the
uniaxial anisotropy, which agrees quantitatively with experiment, and this
enhancement arises from electronic-structure features near the Fermi level,
mostly associated with dumbbell sites. With Co dumbbell atoms replaced by other
elements, the variation of anisotropy is generally a collective effect and
contributions from other sublattices may change significantly. Moreover, we
found that Zr doping promotes the formation of 1-5 structure that exhibits a
large uniaxial anisotropy, such that Zr is the most effective element to
enhance MCA in this system.


  The origin of grand design spiral structure in galaxies is still under debate
but one of promising scenarios involves tidal interactions. We use N-body
simulations to study the evolution of a Milky Way-size galaxy in a Virgo-like
cluster. The galaxy is placed on a typical eccentric orbit and evolved for 10
Gyr. We find that grand design spiral arms are triggered by pericenter passages
and later on they wind up and dissipate. The arms formed in the simulations are
approximately logarithmic, but are also dynamic, transient and recurrent.


  In this paper, we initiate the study of sub-pluriharmonic curves in
Cuntz-Toeplitz algebras and free pluriharmonic majorants on noncommutative
balls. We are lead to a characterization of the noncommutative Hardy space
$H^2_{\bf ball}$ in terms of free pluriharmonic majorants, and to a Schur type
description of the unit ball of $H^2_{\bf ball}$. These results are used to
solve a multivariable commutant lifting problem and provide a description of
all solutions.


  Let $m\geq 3$ be a positive integer. We prove that there are uncountably many
non-commensurable metabelian uniform pro-$p$ groups of dimension $m$.
Consequently, there are uncountably many non-commensurable finitely presented
pro-$p$ groups with minimal number of generators $m$ (and minimal number of
relations $ {m \choose 2}$).


  The observation of a new particle in the search for the Standard Model (SM)
Higgs boson at the LHC, reported by the ATLAS and CMS collaborations, is a
milestone in the quest to understand electroweak symmetry breaking. The
evidence at the level of 5 $\sigma$ for a Higgs boson-like particle has been
published by both experiments after a preliminary analysis of the data from the
LHC Run-I. Precision measurements of the new particle are of critical
importance. This document reviews the mass and spin measurement, the couplings
scale factor measurements and the limits on new physics derived from these
results.


  Monolayers of growing bacteria, confined within channel geometries, exhibit
self-organization into a highly aligned laminar state along the axis of the
channel. Although this phenomenon has been observed in experiments and
simulations under various boundary conditions, the underlying physical
mechanism driving this alignment remains unclear. In this study, we conduct
simulations of growing bacteria in 2D channel geometries perturbed by fixed
obstacles, either circular or arc-shaped, placed at the channel's center. Our
findings reveal that even sizable obstacles cause only short-ranged disruptions
to the baseline laminar state. These disruptions arise from a competition
between local planar anchoring and bulk laminar alignment. At smaller obstacle
sizes, bulk alignment fully dominates, while at larger sizes, planar anchoring
induces increasing local disruptions. Furthermore, our analysis indicates that
the resulting configurations of the bacterial system display a striking
resemblance to the arrangement of hard-rod smectic liquid crystals around
circular obstacles. This suggests that modeling hard-rod bacterial monolayers
as smectic, rather than nematic, liquid crystals may yield successful outcomes.
The insights gained from our study contribute to the expanding body of research
on bacterial growth in channels. Our work provides new perspectives on the
stability of the laminar state and extends our understanding to encompass more
intricate confinement schemes.


  Wakes behind spacecraft caused by supersonic drifting positive ions are
common in plasmas and disturb in situ measurements. We review the impact of
wakes on observations by the Electric Field and Wave double-probe instruments
on the Cluster satellites. In the solar wind, the equivalent spacecraft
charging is small compared to the ion drift energy and the wake effects are
caused by the spacecraft body and can be compensated for. We present statistics
of the direction, width, and electrostatic potential of wakes, and we compare
with an analytical model. In the low-density magnetospheric lobes, the
equivalent positive spacecraft charging is large compared to the ion drift
energy and an enhanced wake forms. In this case observations of the geophysical
electric field with the double-probe technique becomes extremely challenging.
Rather, the wake can be used to estimate the flux of cold (eV) positive ions.
For an intermediate range of parameters, when the equivalent charging of the
spacecraft is similar to the drift energy of the ions, also the charged wire
booms of a double-probe instrument must be taken into account. We discuss an
example of these effects from the MMS spacecraft near the magnetopause. We find
that many observed wake characteristics provide information that can be used
for scientific studies. An important example is the enhanced wakes used to
estimate the outflow of ionospheric origin in the magnetospheric lobes to about
${10}^{26}$ cold (eV) ions/s, constituting a large fraction of the mass outflow
from planet Earth.


  We study the equilibrium temperature distribution in a model for strongly
magnetized plasmas in dimension two and higher. Provided the magnetic field is
sufficiently structured (integrable in the sense that it is fibered by
co-dimension one invariant tori, on most of which the field lines ergodically
wander) and the effective thermal diffusivity transverse to the tori is small,
it is proved that the temperature distribution is well approximated by a
function that only varies across the invariant surfaces. The same result holds
for "nearly integrable" magnetic fields up to a "critical" size. In this case,
a volume of non-integrability is defined in terms of the temperature defect
distribution and related the non-integrable structure of the magnetic field,
confirming a physical conjecture of Paul-Hudson-Helander. Our proof crucially
uses a certain quantitative ergodicity condition for the magnetic field lines
on full measure set of invariant tori, which is automatic in two dimensions for
magnetic fields without null points and, in higher dimensions, is guaranteed by
a Diophantine condition on the rotational transform of the magnetic field.