  Large-time correlation functions have a pivotal role in extracting particle
masses from Euclidean lattice field theory calculations, however little is
known about the statistical properties of these quantities. In this work, the
asymptotic form of the distributions of the correlation functions at vanishing
momentum is determined for bosonic interacting lattice field theories with a
unique gapped vacuum. It is demonstrated that the deviations from the
asymptotic form at large Euclidean times can be utilized to determine the
spectrum of the theory.


  Magnetic small-angle neutron scattering (SANS) is ideally suited to provide
direct, reciprocal-space information of long-wavelength magnetic modulations,
such as helicoids, solitons, merons, or skyrmions. SANS of such structures in
thin films or micro-structured bulk materials is strongly limited by the tiny
scattering volume vis a vis the prohibitively large background scattering by
the substrate and support structures. Considering near-surface scattering
closely above the critical angle of reflection, where unwanted signal
contributions due to substrate or support structures becomes very small, we
establish equivalent scattering patterns of the helical, conical, skyrmion
lattice, and fluctuation-disordered phases in a polished bulk sample of MnSi
between conventional transmission and near-surface SANS geometries. This
motivates the prediction of a complete repository of scattering patterns
expected for thin films in the near-surface SANS geometry for each orientation
of the magnetic order with respect to the scattering plane.


  Being able to adjust the demand of electricity can be an effective means for
power system operators to compensate fluctuating renewable generation, to avoid
grid congestion, and to cope with other contingencies. Electric heating and
cooling systems of buildings can provide different demand response services
because their electricity consumption is inherently flexible because of their
thermal inertia. This paper reports on the results of a large-scale demand
response demonstration involving a population of more than 300 residential
buildings with heat pump installations. We show how the energetic behavior and
flexibility of individual systems can be identified autonomously based only on
energy meter data and outdoor air temperature measurements, and how the
aggregate demand response potential of the population can be quantified.
Various load reduction and rebound damping experiments illustrate the
effectiveness of the approach: the load reductions can be predicted precisely
and amount to 40-65% of the aggregate load, and the rebound can be damped
efficiently.


  We have simulated QCD at a finite chemical potential $\mu_I$ for isospin
($I_3$) to probe part of the phase diagram for nuclear matter. Preliminary
results suggest that for $\mu_I > \mu_c$, this theory forms a charged pion
condensate which spontaneously breaks $I_3$, and the isospin density is non
zero.


  Most of the deep learning-based speech enhancement models are learned in a
supervised manner, which implies that pairs of noisy and clean speech are
required during training. Consequently, several noisy speeches recorded in
daily life cannot be used to train the model. Although certain unsupervised
learning frameworks have also been proposed to solve the pair constraint, they
still require clean speech or noise for training. Therefore, in this paper, we
propose MetricGAN-U, which stands for MetricGAN-unsupervised, to further
release the constraint from conventional unsupervised learning. In MetricGAN-U,
only noisy speech is required to train the model by optimizing non-intrusive
speech quality metrics. The experimental results verified that MetricGAN-U
outperforms baselines in both objective and subjective metrics.


  We construct a deformed $SO/Sp$ Penner generating function responsible for
the close connection between $SO/Sp$ Chern-Simons gauge theories at large $N$
and the $SO/Sp$ Penner models. This construction is then shown to follow from a
sector of a Chern-Simons gauge theory with coupling constant $\lambda$. The
free energy and its continuum limit of the perturbative Chern-Simons gauge
theory are obtained from the Penner model. Finally, asymptotic expansions for
the logarithm of the gauge group volumes are given for every genus $g\geq 0$
and shown to be equivalent to the continuum limits of the $SO/Sp$ Chern-Simons
gauge theories and the $SO/Sp$ Penner models


  Intra-frame motion blurring, as a major challenge in free-breathing dynamic
MRI, can be reduced if high temporal resolution can be achieved. To address
this challenge, this work proposes a highly-accelerated 4D (3D+time) real-time
MRI framework with sub-second temporal resolution combining standard
stack-of-stars golden-angle radial sampling and tailored GRASP-Pro
(Golden-angle RAdial Sparse Parallel) reconstruction. Specifically, 4D
real-time MRI acquisition is performed continuously without motion gating or
sorting. The k-space centers in stack-of-stars radial data are organized to
guide estimation of a temporal basis, with which GRASP-Pro reconstruction is
employed to enforce joint low-rank subspace and sparsity constraints. This new
basis estimation strategy is the new feature proposed for subspace-based
reconstruction in this work to achieve high temporal resolution (e.g.,
sub-second/3D volume). It does not require sequence modification to acquire
additional navigation data, is compatible with commercially available
stack-of-stars sequences, and does not need an intermediate reconstruction
step. The proposed 4D real-time MRI approach was tested in abdominal motion
phantom, free-breathing abdominal MRI, and dynamic contrast-enhanced MRI
(DCE-MRI). With the ability to acquire each 3D image in less than one second,
intra-frame respiratory blurring can be intrinsically reduced for body
applications with our approach, which also eliminates the need for motion
detection and motion compensation.


  We consider the problem of finding the density of 1's in a configuration
obtained by $n$ iterations of a given cellular automaton (CA) rule, starting
from disordered initial condition. While this problems is intractable in full
generality for a general CA rule, we argue that for some sufficiently simple
classes of rules it is possible to express the density in terms of elementary
functions. Rules asymptotically emulating identity are one example of such a
class, and density formulae have been previously obtained for several of them.
We show how to obtain formulae for density for two further rules in this class,
160 and 168, and postulate likely expression for density for eight other rules.
Our results are valid for arbitrary initial density. Finally, we conjecture
that the density of 1's for CA rules asymptotically emulating identity always
approaches the equilibrium point exponentially fast.


  The weak bosons are bound states of fermions. Here the excitations of the
weak bosons are discussed. Especially we study the decays of these excited
states into weak bosons and photons.


  We consider supersymmetric grand unified theories with soft
supersymmetry-breaking scalar masses $m_0$ specified above the GUT scale
(super-GUTs) and patterns of Yukawa couplings motivated by upper limits on
flavour-changing interactions beyond the Standard Model. If the scalar masses
are smaller than the gaugino masses $m_{1/2}$, as is expected in no-scale
models, the dominant effects of renormalization between the input scale and the
GUT scale are generally expected to be those due to the gauge couplings, which
are proportional to $m_{1/2}$ and generation-independent. In this case, the
input scalar masses $m_0$ may violate flavour maximally, a scenario we call
MaxSFV, and there is no supersymmetric flavour problem. We illustrate this
possibility within various specific super-GUT scenarios that are deformations
of no-scale gravity.


  There are various methods for adapting LLMs to different domains. The most
common methods are prompting, finetuning, and RAG. In this work, we explore the
possibility of adapting a model using one of the PEFT methods - QLoRA. The
experiment aims to simulate human responses based on their interviews. The
simulation quality is assessed by comparing the quality of the style and the
quality of the generated facts.


  The detection of hazardous conditions near public transit stations is
necessary for ensuring the safety and accessibility of public transit. Smart
city infrastructures aim to facilitate this task among many others through the
use of computer vision. However, most state-of-the-art computer vision models
require thousands of images in order to perform accurate detection, and there
exist few images of hazardous conditions as they are generally rare. In this
paper, we examine the detection of snow-covered sidewalks along bus routes.
Previous work has focused on detecting other vehicles in heavy snowfall or
simply detecting the presence of snow. However, our application has an added
complication of determining if the snow covers areas of importance and can
cause falls or other accidents (e.g. snow covering a sidewalk) or simply covers
some background area (e.g. snow on a neighboring field). This problem involves
localizing the positions of the areas of importance when they are not
necessarily visible.
  We introduce a method that utilizes Structure from Motion (SfM) rather than
additional annotated data to address this issue. Specifically, our method
learns the locations of sidewalks in a given scene by applying a segmentation
model and SfM to images from bus cameras during clear weather. Then, we use the
learned locations to detect if and where the sidewalks become obscured with
snow. After evaluating across various threshold parameters, we identify an
optimal range at which our method consistently classifies different categories
of sidewalk images correctly. Although we demonstrate an application for snow
coverage along bus routes, this method can extend to other hazardous conditions
as well. Code for this project is available at
https://github.com/ind1010/SfM_for_BusEdge.


  The bilateral filter is a useful nonlinear filter which without smoothing
edges, it does spatial averaging. In the literature, the effectiveness of this
method for image denoising is shown. In this paper, an extension of this method
is proposed which is based on complex wavelet transform. In fact, the bilateral
filtering is applied to the low-frequency (approximation) subbands of the
decomposed image using complex wavelet transform, while the thresholding
approach is applied to the high frequency subbands. Using the bilateral filter
in the complex wavelet domain forms a new image denoising framework.
Experimental results for real data are provided, by which one can see the
effectiveness of the proposed method in eliminating noise.


  In this study, a novel non-negative tensor factorization (NTF)-based method
for vibration-based local damage detection in rolling element bearings is
proposed. As the diagnostic signal registered from a faulty machine is
non-stationary, the time-frequency method is frequently used as a primary
decomposition technique. It is proposed here to extract multi-linear NTF-based
components from a 3D array of time-frequency representations of an observed
signal partitioned into blocks. As a result, frequency and temporal informative
components can be efficiently separated from non-informative ones. The
experiments performed on synthetic and real signals demonstrate the high
efficiency of the proposed method with respect to the already known
non-negative matrix factorization approach.


  Orthogonal polynomials for the weight $x^{\nu} \exp(-x - t/x),\ x, t > 0, \nu
\in \mathbb{R}$ are investigated. Differential-difference equations, recurrence
relations, explicit representations, generating functions and Rodrigues-type
formula are obtained.


  In this paper we study some new von Neumann spectral invariants associated to
the Laplacian acting on L^2 differential forms on the universal cover of a
closed manifold. These invariants coincide with the Novikov-Shubin invariants
whenever there is no spectral gap in the spectrum of the Laplacian, and are
homotopy invariants in this case. In the presence of a spectral gap, they
differ in character and value from the Novikov-Shubin invariants. Under a
positivity assumption on these invariants, we prove that certain L^2 theta and
L^2 zeta functions defined by metric dependent combinatorial Laplacians acting
on $L^2$ cochains associated with a triangulation of the manifold, converge
uniformly to their analytic counterparts, as the mesh of the triangulation goes
to zero.


  An experiment is described which proves, using single photons only, that the
standard hidden variables assumptions (commonly used to derive Bell
inequalities) are inconsistent with quantum mechanics. The analysis is very
simple and transparent. In particular, it demonstrates that a classical wave
model for quantum mechanics is not ruled out by experiments demonstrating the
violation of the traditional hidden variable assumptions.


  When quantizing Conformal Dilaton Gravity there is a conformal anomaly which
starts at two loop order. This anomaly stems from evanescent operators on the
divergent parts of the effective action. The general form of the finite
counterterm which is necessary in order to insure cancellation of the Weyl
anomaly to every order in perturbation theory has been determined using only
conformal invariance . Those finite counterterms do not have any inverse power
of any mass scale in front of them (precisely because of conformal invariance)
and then they are not negligible in the low energy deep infrared limit. The
general form of the ensuing modifications to the scalar field equation of
motion has been determined and some physical consequences extracted.


  Large audio-video language models can generate descriptions for both video
and audio. However, they sometimes ignore audio content, producing audio
descriptions solely reliant on visual information. This paper refers to this as
audio hallucinations and analyzes them in large audio-video language models. We
gather 1,000 sentences by inquiring about audio information and annotate them
whether they contain hallucinations. If a sentence is hallucinated, we also
categorize the type of hallucination. The results reveal that 332 sentences are
hallucinated with distinct trends observed in nouns and verbs for each
hallucination type. Based on this, we tackle a task of audio hallucination
classification using pre-trained audio-text models in the zero-shot and
fine-tuning settings. Our experimental results reveal that the zero-shot models
achieve higher performance (52.2% in F1) than the random (40.3%) and the
fine-tuning models achieve 87.9%, outperforming the zero-shot models.


  In this paper, a novel framework is proposed for optimizing the operation and
performance of a large-scale, multi-hop millimeter wave (mmW) backhaul within a
wireless small cell network (SCN) that encompasses multiple mobile network
operators (MNOs). The proposed framework enables the small base stations (SBSs)
to jointly decide on forming the multi-hop, mmW links over backhaul
infrastructure that belongs to multiple, independent MNOs, while properly
allocating resources across those links. In this regard, the problem is
addressed using a novel framework based on matching theory that is composed to
two, highly inter-related stages: a multi-hop network formation stage and a
resource management stage. One unique feature of this framework is that it
jointly accounts for both wireless channel characteristics and economic factors
during both network formation and resource management. The multi-hop network
formation stage is formulated as a one-to-many matching game which is solved
using a novel algorithm, that builds on the so-called deferred acceptance
algorithm and is shown to yield a stable and Pareto optimal multi-hop mmW
backhaul network. Then, a one-to-many matching game is formulated to enable
proper resource allocation across the formed multi-hop network. This game is
then shown to exhibit peer effects and, as such, a novel algorithm is developed
to find a stable and optimal resource management solution that can properly
cope with these peer effects. Simulation results show that the proposed
framework yields substantial gains, in terms of the average sum rate, reaching
up to 27% and 54%, respectively, compared to a non-cooperative scheme in which
inter-operator sharing is not allowed and a random allocation approach. The
results also show that our framework provides insights on how to manage pricing
and the cost of the cooperative mmW backhaul network for the MNOs.


  The two-dimensional supersymmetric $\s$-model on a K\"ahler manifold has a
non-vanishing $\b$-function at four loops, but the $\b$-function at five loops
can be made to vanish by a specific choice of renormalisation scheme. We
investigate whether this phenomenon persists at six loops, and conclude that it
does not; there is a non-vanishing six-loop $\b$-function irrespective of
renormalisation scheme ambiguities.


  Let $K$ be a compact Hausdorff space and let $(f_n)_{n\in \N}$ be a pairwise
disjoint sequence of continuous functions from $K$ into $[0,1]$. We say that a
compact space $L$ \emph{adds supremum} of $(f_n)_{n\in \N}$ in $K$ if there
exists a continuous surjection $\pi:L\longrightarrow K$ such that there exists
$sup\{f_n\circ\pi:n\in \N\}$ in $C(L)$. Moreover, we expect that $L$ preserves
suprema of disjoint continuous functions which already existed in $C(K)$.
Namely, if $sup\{g_n:n\in \N\}$ exists in $C(K)$, we must have
$sup\{g_n\circ\pi:n\in \N\}$ in $C(L)$.
  This paper studies the preservation of connectedness in extensions by
continuous functions -- a technique developed by Piotr Koszmider to add suprema
of continuous functions on Hausdorff connected compact spaces -- proving the
following results:
  (1) If $K$ is a metrizable and locally connected compactum, then any
extension of $K$ by continuous functions is connected (but it may be not
locally connected).
  (2) There exists a disconnected extension of a metrizable connected compactum
$K$.
  (3) For any metrizable compactum $K$ there exists a disconnected $L$ which is
obtained from $K$ by finitely many extensions by continuous functions.


  Computational Grids, emerging as an infrastructure for next generation
computing, enable the sharing, selection, and aggregation of geographically
distributed resources for solving large-scale problems in science, engineering,
and commerce. As the resources in the Grid are heterogeneous and geographically
distributed with varying availability and a variety of usage and cost policies
for diverse users at different times and, priorities as well as goals that vary
with time. The management of resources and application scheduling in such a
large and distributed environment is a complex task. This thesis proposes a
distributed computational economy as an effective metaphor for the management
of resources and application scheduling. It proposes an architectural framework
that supports resource trading and quality of services based scheduling. It
enables the regulation of supply and demand for resources and provides an
incentive for resource owners for participating in the Grid and motives the
users to trade-off between the deadline, budget, and the required level of
quality of service. The thesis demonstrates the capability of economic-based
systems for peer-to-peer distributed computing by developing users'
quality-of-service requirements driven scheduling strategies and algorithms. It
demonstrates their effectiveness by performing scheduling experiments on the
World-Wide Grid for solving parameter sweep applications.


  For any affine-variety code we show how to construct an ideal whose solutions
correspond to codewords with any assigned weight. We classify completely the
intersections of the Hermitian curve with lines and parabolas (in the
$\mathbb{F}_{q^2}$ affine plane). Starting from both results, we are able to
obtain geometric characterizations for small-weight codewords for some families
of Hermitian codes over any $\mathbb{F}_{q^2}$. From the geometric
characterization, we obtain explicit formulae. In particular, we determine the
number of minimum-weight codewords for all Hermitian codes with $d\leq q$ and
all second-weight codewords for distance-$3,4$ codes.


  The distribution in frequency of optical spectral weight remaining under the
real part of the optical conductivity in the superconducting state of a d-wave
superconductor depends on impurity concentration, on the strength of the
impurity potential as well as on temperature and there is some residual
absorption even at T = 0. In BCS theory the important weight is confined to the
microwave region if the scattering is sufficiently weak. In an Eliashberg
formulation substantial additional weight is to be found in the incoherent,
boson assisted background which falls in the infrared and is not significantly
depleted by the formation of the condensate, although it is shifted as a result
of the opening of a superconducting gap.


  We introduce a library which provides an abstract data type of environments,
as a functor parameterized by a module defining variables, and a function which
builds environments for such variables with any Type of type. Usual operations
over environments are defined, along with an extensive set of basic and more
advanced properties. Moreover, we give an implementation using lists satisfying
all the required properties.


  We introduce a novel CNN-based feature point detector - GLAMpoints - learned
in a semi-supervised manner. Our detector extracts repeatable, stable interest
points with a dense coverage, specifically designed to maximize the correct
matching in a specific domain, which is in contrast to conventional techniques
that optimize indirect metrics. In this paper, we apply our method on
challenging retinal slitlamp images, for which classical detectors yield
unsatisfactory results due to low image quality and insufficient amount of
low-level features. We show that GLAMpoints significantly outperforms classical
detectors as well as state-of-the-art CNN-based methods in matching and
registration quality for retinal images. Our method can also be extended to
other domains, such as natural images. Training code and model weights are
available at https://github.com/PruneTruong/GLAMpoints_pytorch.


  Proximity of two different materials leads to an intricate coupling of
quasiparticles so that an unprecedented electronic state is often realized at
the interface. Here, we demonstrate a resonance-type many-body ground state in
graphene, a non-magnetic two-dimensional Dirac semimetal, when grown on SmB6, a
Kondo insulator, via thermal decomposition of fullerene molecules. This ground
state is typically observed in three-dimensional magnetic materials with
correlated electrons. Above the characteristic Kondo temperature of the
substrate, the electron band structure of pristine graphene remains almost
intact. As temperature decreases, however, the Dirac fermions of graphene
become hybridized with the Sm 4f states. Remarkable enhancement of the
hybridization and Kondo resonance is observed with further cooling and
increasing charge carrier density of graphene, evidencing the Kondo screening
of the Sm 4f local magnetic moment by the conduction electrons of graphene at
the interface. These findings manifest the realization of the Kondo effect in
graphene by the proximity of SmB6 that is tuned by temperature and charge
carrier density of graphene.


  We study the focusing NLS \begin{align}\label{nls_abstract} i\partial_t
u+\Delta_{x,y} u=-|u|^\alpha u\tag{NLS} \end{align} on the waveguide manifold
$\mathbb{R}^d\times\mathbb{T}$ in the intercritical regime
$\alpha\in(\frac{4}{d},\frac{4}{d-1})$. By assuming that the
\eqref{nls_abstract} is independent of $y$, it reduces to the focusing
intercritical NLS on $\mathbb{R}^d$, which is known to have standing wave and
finite time blow-up solutions. Naturally, we ask whether these special
solutions with non-trivial $y$-dependence exist. In this paper we give an
affirmative answer to this question. To that end, we introduce the concept of
\textit{semivirial} functional and consider a minimization problem $m_c$ on the
semivirial-vanishing manifold with prescribed mass $c$. We prove that for any
$c\in(0,\infty)$ the variational problem $m_c$ has a ground state optimizer
$u_c$ which also solves the standing wave equation $$-\Delta_{x,y}u_c+\beta_c
u_c=|u|^\alpha u $$ with some $\beta_c>0$. Moreover, we prove the existence of
a critical number $c_*\in(0,\infty)$ such that \begin{itemize} \item For
$c\in(0,c_*)$, any optimizer $u_c$ of $m_c$ must satisfy $\pt_y u_c\neq 0$.
\item For $c\in(c_*,\infty)$, any optimizer $u_c$ of $m_c$ must satisfy $\pt_y
u_c=0$. \end{itemize} Finally, we prove that the previously constructed ground
states characterize a sharp threshold for the bifurcation of scattering and
finite time blow-up solutions in dependence of the sign of the semivirial.


  Let $\eta$ be the weight $1/2$ Dedekind function. A unification and
generalization of the integrals $\int_0^\infty f(x)\eta^n(ix)dx$, $n=1,3$, of
Glasser \cite{glasser2009} is presented. Simple integral inequalities as well
as some $n=2$, $4$, $6$, $8$, $9$, and $14$ examples are also given. A
prominent result is that $$\int_0^\infty \eta^6 (ix)dx= \int_0^\infty x\eta^6
(ix)dx ={1 \over {8\pi}}\left({{\Gamma(1/4)} \over {\Gamma(3/4)}}\right)^2,$$
where $\Gamma$ is the Gamma function. The integral $\int_0^1 x^{-1} \ln x
~\eta(ix)dx$ is evaluated in terms of a reducible difference of pairs of the
first Stieltjes constant $\gamma_1(a)$.


  We have recently proposed a pre-quantum, pre-space-time theory as a
matrix-valued Lagrangian dynamics on an octonionic space-time. This theory
offers the prospect of unifying internal symmetries of the standard model with
pre-gravitation. We explain why such a quantum gravitational dynamics is in
principle essential even at energies much smaller than Planck scale. The
dynamics can also predict the values of free parameters of the low energy
standard model: these parameters arising in the Lagrangian are related to the
algebra of the octonions which define the underlying non-commutative space-time
on which the dynamical degrees of freedom evolve. These free parameters are
related to the exceptional Jordan algebra $J_3(8)$ which describes the three
fermion generations. We use the octonionic representation of fermions to
compute the eigenvalues of the characteristic equation of this algebra, and
compare the resulting eigenvalues with known mass ratios for quarks and
leptons. We show that the ratios of the eigenvalues correctly reproduce the
[square root of the] known mass ratios. In conjunction with the trace dynamics
Lagrangian, these eigenvalues also yield a theoretical derivation of the low
energy fine structure constant.


  High Power Target systems are key elements in future neutrino and other rare
particle production in accelerators. These systems transform an intense source
of protons into secondary particles of interest to enable new scientific
discoveries. As beam intensity and energies increase, target systems face
significant challenges. Radiation damages and thermal shocks in target
materials were identified as the leading cross-cutting challenges of high-power
target facilities. Target material R&D to address these challenges are
essential to enable and ensure reliable operation of future-generation
accelerators. Irradiation facilities and alternative methods are critical to
provide a full support of material R&D and better address these critical
challenges.


  One-loop scattering amplitudes in string theories involve configuration-space
integrals over genus-one surfaces with coefficients of Kronecker-Eisenstein
series in the integrand. A conjectural genus-one basis of integrands under Fay
identities and integration by parts was recently constructed out of chains of
Kronecker-Eisenstein series. In this work, we decompose a variety of more
general genus-one integrands into the conjectural chain basis. The explicit
form of the expansion coefficients is worked out for infinite families of cases
where the Kronecker-Eisenstein series form cycles. Our results can be used to
simplify multiparticle amplitudes in supersymmetric, heterotic and bosonic
string theories and to investigate loop-level echoes of the field-theory
double-copy structures of string tree-level amplitudes. The multitude of basis
reductions in this work strongly validate the recently proposed chain basis and
stimulate mathematical follow-up studies of more general configuration-space
integrals with additional marked points or at higher genus.


  Strategies for the generation of periodic discrete structures with identical
two-point correlation are developed. Starting from a pair of root structures,
which are not related by translation, phase inversion or axis reflections,
child structures of arbitrary resolution (i.e., pixel or voxel numbers) and
number of phases (i.e., material phases/species) can be generated by means of
trivial embedding based phase extension, application of kernels and/or phase
coalescence, such that the generated structures inherit the
two-point-correlation equivalence. Proofs of the inheritance property are
provided by means of the Discrete Fourier Transform theory. A Python 3
implementation of the results is offered by the authors through the Github
repository https://github.com/DataAnalyticsEngineering/EQ2PC in order to make
the provided results reproducible and useful for all interested readers.
Examples for the generation of structures are demonstrated, together with
applications in the homogenization theory of periodic media.


  This article considers the spatially inhomogeneous, non-cutoff Boltzmann
equation. We construct a large-data classical solution given bounded,
measurable initial data with uniform polynomial decay of mild order in the
velocity variable. Our result requires no assumption of strict positivity for
the initial data, except locally in some small ball in phase space. We also
obtain existence results for weak solutions when our decay and positivity
assumptions for the initial data are relaxed. Because the regularity of our
solutions may degenerate as $t \rightarrow 0$, uniqueness is a challenging
issue. We establish weak-strong uniqueness under the additional assumption that
the initial data possesses no vacuum regions and is H\"older continuous. As an
application of our short-time existence theorem, we prove global existence near
equilibrium for bounded, measurable initial data that decays at a finite
polynomial rate in velocity.


  Motivated by a remark and a question of Nicholas Katz, we characterize the
tangent space of the space of Fuchsian equations with given generic exponents
inside the corresponding moduli space of logarithmic connections: we construct
a weight 1 Hodge structure on the tangent space of the moduli of logarithmic
connections such that deformations of Fuchsian equations correspond to the
$(1,0)$-part.


  Attosecond streaking is one of the most fundamental processes in attosecond
science allowing for a mapping of temporal (i.e. phase) information on the
energy domain. We show that on the single-particle level attosecond streaking
time shifts contain spectral phase information associated with the
Eisenbud-Wigner-Smith (EWS) time delay, provided the influence of the streaking
infrared field is properly accounted for. While the streaking phase shifts for
short-ranged potentials agree with the associated EWS delays, Coulomb
potentials require special care. We show that the interaction between the
outgoing electron and the combined Coulomb and IR laser fields lead to a
streaking phase shift that can be described classically.


  This paper addresses the problem of identifying a lower dimensional space
where observed data can be sparsely represented. This under-complete dictionary
learning task can be formulated as a blind separation problem of sparse sources
linearly mixed with an unknown orthogonal mixing matrix. This issue is
formulated in a Bayesian framework. First, the unknown sparse sources are
modeled as Bernoulli-Gaussian processes. To promote sparsity, a weighted
mixture of an atom at zero and a Gaussian distribution is proposed as prior
distribution for the unobserved sources. A non-informative prior distribution
defined on an appropriate Stiefel manifold is elected for the mixing matrix.
The Bayesian inference on the unknown parameters is conducted using a Markov
chain Monte Carlo (MCMC) method. A partially collapsed Gibbs sampler is
designed to generate samples asymptotically distributed according to the joint
posterior distribution of the unknown model parameters and hyperparameters.
These samples are then used to approximate the joint maximum a posteriori
estimator of the sources and mixing matrix. Simulations conducted on synthetic
data are reported to illustrate the performance of the method for recovering
sparse representations. An application to sparse coding on under-complete
dictionary is finally investigated.


  The spectral response and physical features of the 2D Hubbard-Holstein model
are calculated both in equilibrium at zero and low chemical dopings, and after
an ultra short powerful light pulse, in undoped systems. At equilibrium and at
strong charge-lattice couplings, the optical conductivity reveals a 3-peak
structure in agreement with experimental observations. After an ultra short
pulse and at nonzero electron-phonon interaction, phonon and spin subsystems
oscillate with the phonon period $T_{ph} \approx 80$ fs. The decay time of the
phonon oscillations is about 150-200 fs, similar to the relaxation time of the
charge system. We propose a criterion for observing these oscillations in high
$T_c$ compounds: the time span of the pump light pulse $\tau_{pump}$ has to be
shorter than the phonon oscillation period $T_{ph}$.


  We develop a renormalization group formalism for the compactified
Randall-Sundrum scenario wherein the extra-dimensional radius serves as the
scaling parameter. Couplings on the hidden brane scale as we move within local
effective field theories with varying size of the warped extra dimension. We
consider this RG approach applied to U(1) gauge theories and gravity. We use
this method to derive a low energy effective theory.


  This study investigates the causal relationship between patent grants and
firms' dynamics in the Information and Communication Technology (ICT) industry,
as the latter is a peculiar sector of modern economies, often under the lens of
antitrust authorities. For our purpose, we exploit matched information about
financial accounts and patenting activity in 2009-2017 by 179,660 companies
operating in 39 countries. Preliminarily, we show how bigger companies are less
than 2% of the sample, although they concentrate about 89% of the grants
obtained in the period of analyses. Thus, we test that patent grants in the ICT
industry have a significant and large impact on market shares and firm size of
smaller companies (31.5% and 30.7%, respectively) in the first year after the
grants, while we have no evidence of an impact for bigger companies. After a
novel instrumental variable strategy that exploits information at the level of
patent offices, we confirm that most of the effects on smaller companies are
due to the protection of property rights and not to the innovative content of
inventions. Finally, we never observe a significant impact on either
profitability or productivity for any firm size category. Eventually, we
discuss how our findings support the idea that the ICT industry is a case of
endogenous R&D sunk costs, which prevent profit margins from rising in the
presence of a relatively high market concentration.


  We investigate several spin-related phenomena in a confined two-dimensional
electron gas (2DEG) using the Hartree-Fock approximation for the mutual Coulomb
interaction of the electrons. The exchange term of the interaction causes a
large splitting of the spin levels whenever the chemical potential lies within
a Landau band (LB). This splitting can be reinterpreted as an enhancement of an
effective g-factor, g*. The increase of g* when a LB is half filled can be
accompanied by a spontaneous formation of a static spin-inversion state (SIS)
whose details depend on the system sision state (SIS) whose details depend on
the system size. The coupling of the states of higher LB's into the lowest band
by the Coulomb interaction of the 2DEG is essential for the SIS to occur. The
far-infrared absorption of the system, relatively insensitive to the spin
splitting, develops clear signs of the SIS.


  It has been shown that differences in fecundity variance can influence the
probability of invasion of a genotype in a population, i.e. a genotype with
lower variance in offspring number can be favored in finite populations even if
it has a somewhat lower mean fitness than a competitor. In this paper,
Gillespie's results are extended to population genetic systems with explicit
age structure, where the demographic variance (variance in growth rate)
calculated in the work of Engen and colleagues is used as a generalization of
"variance in offspring number" to predict the interaction between deterministic
and random forces driving change in allele frequency. By calculating the
variance from the life history parameters, it is shown that selection against
variance in the growth rate will favor a genotypes with lower stochasticity in
age specific survival and fertility rates. A diffusion approximation for
selection and drift in a population with two genotypes with different life
history matrices (and therefore, different growth rates and demographic
variances) is derived and shown to be consistent with individual based
simulations. It is also argued that for finite populations, perturbation
analyses of both the growth rate and demographic variances may be necessary to
determine the sensitivity of "fitness" (broadly defined) to changes in the life
history parameters.


  We derive a closed equation of motion for the current density of an
inhomogeneous quantum many-body system under the assumption that the
time-dependent wave function can be described as a geometric deformation of the
ground-state wave function. By describing the many-body system in terms of a
single collective field we provide an alternative to traditional approaches,
which emphasize one-particle orbitals. We refer to our approach as continuum
mechanics for quantum many-body systems. In the linear response regime, the
equation of motion for the displacement field becomes a linear fourth-order
integro-differential equation, whose only inputs are the one-particle density
matrix and the pair correlation function of the ground-state. The complexity of
this equation remains essentially unchanged as the number of particles
increases. We show that our equation of motion is a hermitian eigenvalue
problem, which admits a complete set of orthonormal eigenfunctions under a
scalar product that involves the ground-state density. Further, we show that
the excitation energies derived from this approach satisfy a sum rule which
guarantees the exactness of the integrated spectral strength. Our formulation
becomes exact for systems consisting of a single particle, and for any
many-body system in the high-frequency limit. The theory is illustrated by
explicit calculations for simple one- and two-particle systems.


  Just like decent classical difference-difference systems define symplectic
maps on suitable phase spaces, their counterparts with properly ordered
noncommutative entries come as Heisenberg equations of motion for corresponding
quantum discrete-discrete models. We observe how this idea applies to a
difference-difference counterpart of the Liouville equation. We produce
explicit forms of of its evolution operator for the two natural space-time
coordinate systems. We discover that discrete-discrete models inherit crucial
features of their continuous-time parents like locality and integrability while
the new-found algebraic transparency promises a useful progress in some
branches of Quantum Inverse Scattering Method.


  Using a countable support product of creature forcing posets, we show that
consistently, for uncountably many different functions the associated Yorioka
ideals' uniformity numbers can be pairwise different. In addition we show that,
in the same forcing extension, for two other types of simple cardinal
characteristics parametrised by reals (localisation and anti-localisation
cardinals), for uncountably many parameters the corresponding cardinals are
pairwise different.


  BES data on the sigma pole are refitted taking into account new information
on coupling of sigma to KK and eta-eta. The fit also includes Cern-Munich data
on pi-pi elastic phases shifts and Ke4 data, and gives a pole position of 500
+- 30 - i(264 +- 30) MeV. However, there is a clear discrepancy with the sigma
pole position recently predicted by Caprini et al. using the Roy equation. This
discrepancy may be explained naturally by uncertainties arising from
inelasticity in KK and eta-eta channels and mixing between sigma and f0(980).
Adding freedom to accomodate these uncertainties gives an optimum compromise
with a pole position of 472 +- 30 - i(271 +- 30) MeV.


  The robustness of an ecological network quantifies the resilience of the
ecosystem it represents to species loss. It corresponds to the proportion of
species that are disconnected from the rest of the network when extinctions
occur sequentially. Classically, the robustness is calculated for a given
network, from the simulation of a large number of extinction sequences. The
link between network structure and robustness remains an open question. Setting
a joint probabilistic model on the network and the extinction sequences allows
analysis of this relation.
  Bipartite stochastic block models have proven their ability to model
bipartite networks e.g. plant-pollinator networks: species are divided into
blocks and interaction probabilities are determined by the blocks of
membership. Analytical expressions of the expectation and variance of
robustness are obtained under this model, for different distributions of
primary extinction sequences. The impact of the network structure on the
robustness is analyzed through a set of properties and numerical illustrations.
The analysis of a collection of bipartite ecological networks allows us to
compare the empirical approach to our probabilistic approach, and illustrates
the relevance of the latter when it comes to computing the robustness of a
partially observed or incompletely sampled network.


  The degree of linear polarization in solar flares has not yet been precisely
determined despite multiple attempts to measure it with different missions. The
high energy range in particular has very rarely been explored, due to its
greater instrumental difficulties. We approached the subject using the Reuven
Ramaty High Energy Spectroscopic Imager (RHESSI) satellite to study 6 X-class
and 1 M-class flares in the energy range between 100 keV and 350 keV. Using
RHESSI as a polarimeter requires the application of strict cuts to the event
list in order to extract those photons that are Compton scattered between two
detectors. Our measurements show polarization values between 2% and 54%, with
errors ranging from 10% to 26% in 1 sigma level. In view of the large
uncertainties in both the magnitude and direction of the polarization vector,
the results can only reject source models with extreme properties.


  CConsider a bipartite quantum system consisting of two subsystems A and B.
The reduced density matrix ofA a is obtained by taking the partial trace with
respect to B. In this work, we will show that the Wigner distribution of this
reduced density matrix is obtained by integrating the total Wigner distribution
with respect to the phase space variables corresponding to subsystem B. The
proof we give is rigorous (as opposed to those found in the literature) and
makes use of the Weyl--Wigner--Moyal phase space formalism. Our main result is
applied to general Gaussian mixed states, of which it gives a particularly
simple and precise description. We also briefly discuss the purification of a
mixed state from the Wigner formalism point of view.


  In this note we evaluate the expectation and variance of the waiting time to
complete $m$ parallel collections of coupons, in the case of coupons which
arrives independently, one by one and with equal probabilities.


  A wavelet is a special case of a vector in a separable Hilbert space that
generates a basis under the action of a collection, or system, of unitary
operators. We will describe the operator-interpolation approach to wavelet
theory using the local commutant of a system. This is really an abstract
application of the theory of operator algebras to wavelet theory. The concrete
applications of this method include results obtained using specially
constructed families of wavelet sets. A frame is a sequence of vectors in a
Hilbert space which is a compression of a basis for a larger space. This is not
the usual definition in the frame literature, but it is easily equivalent to
the usual definition. Because of this compression relationship between frames
and bases, the unitary system approach to wavelets (and more generally:
wandering vectors) is perfectly adaptable to frame theory. The use of the local
commutant is along the same lines as in the wavelet theory. Finally, we discuss
constructions of frames with special properties using targeted decompositions
of positive operators, and related problems.


  We present a look at Ookami, a project providing community access to a
testbed supercomputer with the ARM-based A64FX processors developed by a
collaboration between RIKEN and Fujitsu and deployed in the Japanese
supercomputer Fugaku. We describe the project, provide details about the user
base and education/training program, and present highlights from performance
studies of two astrophysical simulation codes.


  The density matrix renormalization group (DMRG) is a powerful method to treat
static correlation. Here we present an inexpensive way to add additional
dynamic correlation energy to a DMRG self-consistent field (DMRG) wave function
using pair-density functional theory (PDFT). We applied this new approach,
called DMRG-PDFT, to study singlet-triplet gaps in polyacenes and
polyacetylenes that require active spaces larger than the feasibility limit of
the conventional complete active-space self-consistent field (CASSCF) method.
The results match reasonably well the most reliable literature values and have
only a moderate dependence on the compression of the initial DMRG wave
function. Furthermore, DMRG-PDFT is significantly less expensive than other
commonly applied ways of adding additional correlation to DMRG, such as DMRG
followed by multireference perturbation theory or multireference configuration
interaction.


  We review recent B physics results from the CDF and Dzero experiments in
p-pbar collisions at sqrt(s) = 1.96 TeV. Using a data sample of 1.4-6.0 fb-1
collected by the CDF II detector we present searches for New Physics in Bs
sector and some competitive results with B-factories in the B/charm sector. In
the first category we report the BR in Bs -> J/psi f0(980) decays and the
time-integrated mixing probability chi-bar of B mesons. In the second category
BR and Acp in doubly Cabibbo-suppressed B+- -> D0 h+- decays and
time-integrated CP violation in D0 -> h+ h- are presented.


  This study addresses the challenges in parameter estimation of stochastic
differential equations driven by non-Gaussian noises, which are critical in
understanding dynamic phenomena such as price fluctuations and the spread of
infectious diseases. Previous research highlighted the potential of LSTM
networks in estimating parameters of alpha stable Levy driven SDEs but faced
limitations including high time complexity and constraints of the LSTM chaining
property. To mitigate these issues, we introduce the PEnet, a novel
CNN-LSTM-based three-stage model that offers an end to end approach with
superior accuracy and adaptability to varying data structures, enhanced
inference speed for long sequence observations through initial data feature
condensation by CNN, and high generalization capability, allowing its
application to various complex SDE scenarios. Experiments on synthetic datasets
confirm PEnet significant advantage in estimating SDE parameters associated
with noise characteristics, establishing it as a competitive method for SDE
parameter estimation in the presence of Levy noise.


  Let M be a smooth manifold, and let O(M) be the poset of open subsets of M.
Let C be a category that has a zero object and all small limits. A homogeneous
functor (in the sense of manifold calculus) of degree k from O(M) to C is
called very good if it sends isotopy equivalences to isomorphisms. In this
paper we show that the category VGHF of such functors is equivalent to the
category of contravariant functors from the fundamental groupoid of Conf(k, M)
to C, where Conf(k, M) stands for the unordered configuration space of k points
in M. As a consequence of this result, we show that the category VGHF is
equivalent to the category of representations of the fundamental group of
Conf(k, M) in C, provided that Conf(k, M) is connected. We also introduce a
subcategory of vector bundles that we call very good vector bundles, and we
show that it is abelian, and equivalent to a certain category of very good
functors.


  In this paper, we proposed an evolving model via the hypergraph to illustrate
the evolution of the citation network. In the evolving model, we consider the
mechanism combined with preferential attachment and the aging influence.
Simulation results show that the proposed model can characterize the citation
distribution of the real system very well. In addition, we give the analytical
result of the citation distribution using the master equation. Detailed
analysis showed that the time decay factor should be the origin of the same
citation distribution between the proposed model and the empirical result. The
proposed model might shed some lights in understanding the underlying laws
governing the structure of real citation networks.


  The shapes of jets with transverse energies, E_T(jet), up to 45 GeV produced
in neutral- and charged-current deep inelastic e+p scattering (DIS) at Q**2 >
100 GeV**2 have been measured with the ZEUS detector at HERA. Jets are
identified using a cone algorithm in the eta-phi plane with a cone radius of
one unit. The jets become narrower as E_T(jet) increases. The jet shapes in
neutral- and charged-current DIS are found to be very similar. The jets in
neutral-current DIS are narrower than those in resolved processes in
photoproduction and closer to those in direct-photon processes for the same
ranges in E_T(jet) and jet pseudorapidity. The jet shapes in DIS are observed
to be similar to those in e+e- interactions and narrower than those in pbarp
collisions for comparable E_T(jet). Since the jets in e+e- interactions and e+p
DIS are predominantly quark initiated in both cases, the similarity in the jet
shapes indicates that the pattern of QCD radiation within a quark jet is to a
large extent independent of the hard scattering process in these reactions.


  The paper is devoted to the thermodynamics of normal surface electromagnetic
fields within a nonuniform dispersive and absorptive system. This system is
formed by vacuum and lossy medium separated by a plane interface. As a medium,
we used dielectric and metal samples characterized by local and nonlocal
optical properties. Thermodynamic properties of surface eigenmodes of plane
interfaces are discussed. Various definitions of density of states and spectral
characteristics of surface polaritons in equilibrium at the interface formed by
vacuum and lossy medium are described and discussed. All formulas for
thermodynamic functions are represented in terms of density of states. The
generalized density of states is calculated based on the Barash-Ginzburg theory
and dispersion relations for the surface states in different approaches. It is
exemplified that different definitions of the density of states are identical
in the case of dissipationless materials. The spectral functions and integrated
over all frequencies thermodynamic characteristics and their temperature
dependences are demonstrated.


  In this paper, we consider a general form of the analogue of Ramanujan's sum
in the ring of polynomials over a finite field. We first prove some
multiplicative properties of such functions before considering their finite
Fourier series and some specific examples. In the end, we also prove a result
about the Dirichlet series of such functions.


  The MapReduce framework has been generating a lot of interest in a wide range
of areas. It has been widely adopted in industry and has been used to solve a
number of non-trivial problems in academia. Putting MapReduce on strong
theoretical foundations is crucial in understanding its capabilities. This work
links MapReduce to the BSP model of computation, underlining the relevance of
BSP to modern parallel algorithm design and defining a subclass of BSP
algorithms that can be efficiently implemented in MapReduce.


  Cosmological simulations have been used to study interacting galaxies as a
function of galaxy pair separation, enabling comparisons with observational
studies of galaxy pairs. The study of interacting galaxies as a function of
time (i.e. merger stage) has mostly been limited to high resolution merger
simulations, due to the poor time sampling available in cosmological
simulations. Building on an earlier study of galaxy pairs in the IllustrisTNG
cosmological simulations, we reconstruct the orbits of galaxy pairs involving
massive galaxies ($M_* > 10^{10}M_{\odot}$) at redshifts of $0 \leq z < 1$,
using a novel kinematic interpolation scheme to model the orbits in between the
IllustrisTNG snapshots (which are separated by 162 Myr on average). We assess
the accuracy of these interpolations using a pre-existing suite of merger
simulations, and find that kinematic interpolations provide a remarkable
improvement in accuracy compared with interpolations that use only radial
separations or 3D positions. We find that nearly 90 per cent of the closest
pairs ($r < 25$ kpc) have had a pericentre encounter within the past Gyr. Many
of these close pairs are found on rapidly shrinking orbits, and roughly 85 per
cent of these pairs will merge within 1 Gyr. However, approximately 3 per cent
of these close pairs appear to be flyby systems that will never merge. These
reconstructed orbits will be used in future studies to investigate how and when
galaxy properties change during close encounters and mergers between galaxies
in IllustrisTNG.


  The critical behavior of semi-infinite $d$-dimensional systems with
$n$-component order parameter $\bm{\phi}$ and short-range interactions is
investigated at an $m$-axial bulk Lifshitz point whose wave-vector instability
is isotropic in an $m$-dimensional subspace of $\mathbb{R}^d$. The associated
$m$ modulation axes are presumed to be parallel to the surface, where $0\le
m\le d-1$. An appropriate semi-infinite $|\bm{\phi}|^4$ model representing the
corresponding universality classes of surface critical behavior is introduced.
It is shown that the usual O(n) symmetric boundary term $\propto \bm{\phi}^2$
of the Hamiltonian must be supplemented by one of the form $\mathring{\lambda}
\sum_{\alpha=1}^m(\partial\bm{\phi}/\partial x_\alpha)^2$ involving a
dimensionless (renormalized) coupling constant $\lambda$. The implied boundary
conditions are given, and the general form of the field-theoretic
renormalization of the model below the upper critical dimension
$d^*(m)=4+{m}/{2}$ is clarified. Fixed points describing the ordinary, special,
and extraordinary transitions are identified and shown to be located at a
nontrivial value $\lambda^*$ if $\epsilon\equiv d^*(m)-d>0$. The surface
critical exponents of the ordinary transition are determined to second order in
$\epsilon$. Extrapolations of these $\epsilon$ expansions yield values of these
exponents for $d=3$ in good agreement with recent Monte Carlo results for the
case of a uniaxial ($m=1$) Lifshitz point. The scaling dimension of the surface
energy density is shown to be given exactly by $d+m (\theta-1)$, where
$\theta=\nu_{l4}/\nu_{l2}$ is the anisotropy exponent.


  Context: Very-high-energy (VHE; E>100 GeV) {\gamma}-ray emission from blazars
inevitably gives rise to electron-positron pair production through the
interaction of these {\gamma}-rays with the Extragalactic Background Light
(EBL). Depending on the magnetic fields in the proximity of the source, the
cascade initiated from pair production can result in either an isotropic halo
around an initially beamed source or a magnetically broadened cascade flux.
Aims: Both extended pair halo (PH) and magnetically broadened cascade (MBC)
emission from regions surrounding the blazars 1ES 1101-232, 1ES 0229+200 and
PKS 2155-304 were searched for, using VHE {\gamma}-ray data taken with the High
Energy Stereoscopic System (H.E.S.S.), and high energy (HE; 100 MeV<E<100 GeV)
{\gamma}-ray data with the Fermi Large Area Telescope (LAT). Methods: By
comparing the angular distributions of the reconstructed gamma-ray events to
the angular profiles calculated from detailed theoretical models, the presence
of PH and MBC was investigated. Results: Upper limits on the extended emission
around 1ES 1101-232, 1ES 0229+200 and PKS 2155-304 are found to be at a level
of few percent of the Crab nebula flux above 1 TeV, depending on the assumed
photon index of the cascade emission. Assuming strong Extra-Galactic Magnetic
Field (EGMF) values, > 10$^{-12}$G, this limits the production of pair halos
developing from electromagnetic cascades. For weaker magnetic fields, in which
electromagnetic cascades would result in magnetically broadened cascades, EGMF
strengths in the range (0.3 - 3)$\times 10^{-15}$G were excluded for PKS
2155-304 at the 99% confidence level, under the assumption of a 1 Mpc coherence
length.


  A general stability analysis is presented for the determination of the
transition from incoherent to coherent behavior in an ensemble of globally
coupled, heterogeneous, continuous-time dynamical systems. The formalism allows
for the simultaneous presence of ensemble members exhibiting chaotic and
periodic behavior, and, in a special case, yields the Kuramoto model for
globally coupled periodic oscillators described by a phase. Numerical
experiments using different types of ensembles of Lorenz equations with a
distribution of parameters are presented.


  Given the great success of large language models (LLMs) across various tasks,
in this paper, we introduce LLM-ST, a novel and effective speech translation
model constructed upon a pre-trained LLM. By integrating the large language
model (LLM) with a speech encoder and employing multi-task instruction tuning,
LLM-ST can produce accurate timestamped transcriptions and translations, even
from long audio inputs. Furthermore, our findings indicate that the
implementation of Chain-of-Thought (CoT) prompting can yield advantages in the
context of LLM-ST. Through rigorous experimentation on English and Chinese
datasets, we showcase the exceptional performance of LLM-ST, establishing a new
benchmark in the field of speech translation. Demo:
https://speechtranslation.github.io/llm-st/.


  We present the XMM-Newton first light image, taken in January 2000 with the
EPIC pn camera during the instrument's commissioning phase, when XMM-Newton was
pointing towards the Large Magellanic Cloud (LMC). The field is rich in
different kinds of X-ray sources: point sources, supernova remnants (SNRs) and
diffuse X-ray emission from LMC interstellar gas. The observations are of
unprecedented sensitivity, reaching a few 10^32 erg/s for point sources in the
LMC. We describe how these data sets were analysed and discuss some of the
spectroscopic results. For the SNR N157B the power law spectrum is clearly
steeper than previously determined from ROSAT and ASCA data. The existence of a
significant thermal component is evident and suggests that N157B is not a
Crab-like but a composite SNR. Most puzzling is the spectrum of the LMC hot
interstellar medium, which indicates a significant overabundance of Ne and Mg
of a few times solar.


  A convex body K has associated with it a unique circumscribed ellipsoid CE(K)
with minimum volume, and a unique inscribed ellipsoid IE(K) with maximum
volume. We first give a unified, modern exposition of the basic theory of these
extremal ellipsoids using the semi-infinite programming approach pioneered by
Fritz John in his seminal 1948 paper. We then investigate the automorphism
groups of convex bodies and their extremal ellipsoids. We show that if the
automorphism group of a convex body K is large enough, then it is possible to
determine the extremal ellipsoids CE(K) and IE(K) exactly, using either
semi-infinite programming or nonlinear programming. As examples, we compute the
extremal ellipsoids when the convex body K is the part of a given ellipsoid
between two parallel hyperplanes, and when K is a truncated second order cone
or an ellipsoidal cylinder.


  We use the dS/CFT correspondence and bulk gravity to predict the form of the
renormalized holographic three-point correlation function of the operator which
is dual to the inflaton field perturbation during single-field, slow-roll
inflation. Using Maldcaena's formulation of the correspondence, this correlator
can be related to the three-point function of the curvature perturbation
generated during single-field inflation, and we find exact agreement with
previous bulk QFT calculations. This provides a consistency check on existing
derivations of the non-Gaussianity from single-field inflation and also yields
insight into the nature of the dS/CFT correspondence. As a result of our
calculation, we obtain the properly renormalized dS/CFT one-point function,
including boundary contributions where derivative interactions are present in
the bulk. In principle, our method may be employed to derive the n-point
correlators of the inflationary curvature perturbation within the context of
(n-1)th-order perturbation theory, rather than nth-order theory as in
conventional approaches.


  The classical-field formalism has been widely applied in the calculation of
normal correlation functions, and the characterization of condensation, in
finite-temperature Bose gases. Here we discuss the extension of this method to
the calculation of more general correlations, including the so-called anomalous
correlations of the field, without recourse to symmetry-breaking assumptions.
Our method is based on the introduction of U(1)-symmetric classical-field
variables analogous to the modified quantum ladder operators of
number-conserving approaches to the degenerate Bose gas, and allows us to
rigorously quantify the anomalous and non-Gaussian character of the field
fluctuations. We compare our results for anomalous correlation functions with
the predictions of mean-field theories, and demonstrate that the nonlinear
classical-field dynamics incorporate a full description of many-body processes
which modify the effective mean-field potentials experienced by condensate and
noncondensate atoms. We discuss the role of these processes in shaping the
condensate mode, and thereby demonstrate the consistency of the Penrose-Onsager
definition of the condensate orbital in the classical-field equilibrium. We
consider the contribution of various noncondensate-field correlations to the
overall suppression of density fluctuations and interactions in the field, and
demonstrate the distinct roles of phase and density fluctuations in the
transition of the field to the normal phase.


  With the success of large language models (LLMs), integrating the vision
model into LLMs to build vision-language foundation models has gained much more
interest recently. However, existing LLM-based large multimodal models (e.g.,
Video-LLaMA, VideoChat) can only take in a limited number of frames for short
video understanding. In this study, we mainly focus on designing an efficient
and effective model for long-term video understanding. Instead of trying to
process more frames simultaneously like most existing work, we propose to
process videos in an online manner and store past video information in a memory
bank. This allows our model to reference historical video content for long-term
analysis without exceeding LLMs' context length constraints or GPU memory
limits. Our memory bank can be seamlessly integrated into current multimodal
LLMs in an off-the-shelf manner. We conduct extensive experiments on various
video understanding tasks, such as long-video understanding, video question
answering, and video captioning, and our model can achieve state-of-the-art
performances across multiple datasets. Code available at
https://boheumd.github.io/MA-LMM/.


  Algorithmic music composition is a way of composing musical pieces with
minimal to no human intervention. While recurrent neural networks are
traditionally applied to many sequence-to-sequence prediction tasks, including
successful implementations of music composition, their standard supervised
learning approach based on input-to-output mapping leads to a lack of note
variety. These models can therefore be seen as potentially unsuitable for tasks
such as music generation. Generative adversarial networks learn the generative
distribution of data and lead to varied samples. This work implements and
compares adversarial and non-adversarial training of recurrent neural network
music composers on MIDI data. The resulting music samples are evaluated by
human listeners, their preferences recorded. The evaluation indicates that
adversarial training produces more aesthetically pleasing music.


  We are concerned with the general problem of proving the existence of joint
distributions of two discrete random variables $M$ and $N$ subject to
infinitely many constraints of the form $\mathbb{P}\left(M=i,N=j\right)=0$. In
particular, the variable $M$ has a countably infinite range and the other
variable $N$ is uniformly distributed with finite range. The constraints placed
on the joint distribution will require, for some $j$'s in the range of $N$,
$p\left(i,j\right)=0$ for infinitely many values of $i$ in the range of $M$. To
prove the existence of such a joint distribution, we provide a technique that
furnishes the existence of an $\infty\times n$ matrix consisting of
non-negative real numbers whose row and column sums are known, with zeros in
infinitely many pre-specified locations.


  Using hydrodynamical $N$-body simulations, we show that the observed
structure and kinematics of the extremely metal-poor, dwarf irregular galaxy
DDO 68 is compatible with a merger event with at least two smaller satellite
galaxies. We were able to obtain a self-consistent model that simultaneously
reproduces several of its observed features, including: the very asymmetric and
disturbed shape of the stellar component, the overall HI distribution and its
velocity field, the arc-like stellar structure to the west, the low-surface
brightness stellar stream to the north. The model implies the interaction of
the main progenitor of DDO 68 with two systems with dynamical masses
$7\times10^8\,M_{\odot}$ and almost $10^8\,M_{\odot}$ -- 1/20 and 1/150 times
the dynamical mass of DDO 68, respectively. We show that the merger between DDO
68 and the most massive of its satellites offers a route to explain the large
offset of DDO 68 from the mass-metallicity relation. Assuming that the
interacting galaxies have metallicities prior to the merger compatible with
those of galaxies with similar stellar masses, we provide quantitative evidence
that gas mixing alone does not suffice at diluting the gas of the two
components; according to our simulations, the HII regions observed along the
Cometary Tail trace the low metallicity of the accreted satellite rather than
that of DDO 68's main body. In this case, the mass corresponding to the low
metallicity is that of the secondary body and DDO 68 becomes consistent with
the mass-metallicity relation.


  It has been shown that an inhomogeneously broadened optical transition shaped
into an atomic frequency comb can store a large number of temporal modes of the
electromagnetic field at the single photon level without the need to increase
the optical depth of the storage material. The readout of light modes is made
efficient thanks to the rephasing of the optical-wavelength coherence similarly
to photon echo-type techniques and the re-emission time is given by the comb
structure. For on-demand readout and long storage times, two control fields are
used to transfer back and forth the optical coherence into a spin wave. Here,
we present a detailed analysis of the spin wave storage based on chirped
adiabatic control fields. In particular, we verify that chirped fields require
significantly weaker intensities than $\pi$-pulses. The price to pay is a
reduction of the multimode storage capacity that we quantify for realistic
material parameters associated with solids doped with rare-earth-metal ions.


  Entanglement is not only important for understanding the fundamental
properties of many-body systems, but also the crucial resource enabling quantum
advantages in practical information processing tasks. While previous works on
entanglement formation and networking focus on discrete-variable systems,
light---as the only travelling carrier of quantum information in a network---is
bosonic and thus requires a continuous-variable description in general. In this
work, we extend the study to continuous-variable quantum networks. By mapping
the ensemble-averaged entanglement dynamics on an arbitrary network to a
random-walk process on a graph, we are able to exactly solve the entanglement
dynamics and reveal unique phenomena. We identify squeezing as the source of
entanglement generation, which triggers a diffusive spread of entanglement with
a parabolic light cone. The entanglement distribution is directly connected to
the probability distribution of the random walk, while the scrambling time is
determined by the mixing time of the random walk. The dynamics of bipartite
entanglement is determined by the boundary of the bipartition; An operational
witness of multipartite entanglement, based on advantages in sensing tasks, is
introduced to characterize the multipartite entanglement growth. A surprising
linear superposition law in the entanglement growth is predicted by the theory
and numerically verified, when the squeezers are sparse in space-time, despite
the nonlinear nature of the entanglement dynamics. We also give exact solution
to the equilibrium entanglement distribution (Page curves), including its
fluctuations, and found various shapes dependent on the average squeezing
density and strength.


  To incorporate prior knowledge as well as measurement uncertainties in the
traditional long short term memory (LSTM) neural networks, an efficient sparse
Bayesian training algorithm is introduced to the network architecture. The
proposed scheme automatically determines relevant neural connections and adapts
accordingly, in contrast to the classical LSTM solution. Due to its
flexibility, the new LSTM scheme is less prone to overfitting, and hence can
approximate time dependent solutions by use of a smaller data set. On a
structural nonlinear finite element application we show that the
self-regulating framework does not require prior knowledge of a suitable
network architecture and size, while ensuring satisfying accuracy at reasonable
computational cost.


  This paper proposes a method to vibration analysis in order to on-line
monitoring of milling process quality. Adapting envelope analysis to
characterize the milling tool materials is an important contribution to the
qualitative and quantitative characterization of milling capacity and a step by
modeling the three-dimensional cutting process. An experimental protocol was
designed and developed for the acquisition, processing and analyzing
three-dimensional signal. The vibration envelope analysis is proposed to detect
the cutting capacity of the tool with the optimization application of cutting
parameters. The research is focused on FFT Fourier transform optimization of
vibration analysis and vibration envelope to evaluate the dynamic behavior of
the machine/ tool/workpiece


  In a baryon-symmetric universe, the baryon asymmetry observed for visible
matter is matched by an equal and opposite asymmetry for dark matter, thereby
closely connecting the number densities of both types of matter. This is a
necessary step towards the goal of explaining the mystery of why the visible
and dark matter densities are observed to be similar. In this talk, a way of
producing such a universe from bubble nucleation during a first-order phase
transition is reviewed. The process is an analog of electroweak baryogenesis.


  Deep neural networks (DNNs) are known to produce incorrect predictions with
very high confidence on out-of-distribution (OOD) inputs. This limitation is
one of the key challenges in the adoption of deep learning models in
high-assurance systems such as autonomous driving, air traffic management, and
medical diagnosis. This challenge has received significant attention recently,
and several techniques have been developed to detect inputs where the model's
prediction cannot be trusted. These techniques use different statistical,
geometric, or topological signatures. This paper presents a taxonomy of OOD
outlier inputs based on their source and nature of uncertainty. We demonstrate
how different existing detection approaches fail to detect certain types of
outliers. We utilize these insights to develop a novel integrated detection
approach that uses multiple attributes corresponding to different types of
outliers. Our results include experiments on CIFAR10, SVHN and MNIST as
in-distribution data and Imagenet, LSUN, SVHN (for CIFAR10), CIFAR10 (for
SVHN), KMNIST, and F-MNIST as OOD data across different DNN architectures such
as ResNet34, WideResNet, DenseNet, and LeNet5.


  Many contemporary applications, including smart homes and autonomous
vehicles, rely on the Internet of Things technology. While cloud computing
provides a multitude of valuable services for these applications, it generally
imposes constraints on latency-sensitive applications due to the significant
propagation delays. As a complementary technique to cloud computing, edge
computing situates computing resources closer to the data sources, which
reduces the latency and simultaneously alleviates the bandwidth pressure for
the cloud and enhances data security. While edge computing offers significant
advantages, it also presents significant challenges in access control -- a
critical component for safeguarding data. For instance, it is crucial to
implement access control mechanisms that are both effective and efficient on
resource-constrained devices, ensuring high security without compromising the
inherent low latency benefits of edge computing. These challenges drive the
development of innovative access control solutions tailored to meet the unique
requirements of edge computing environments. We classify related references
from the perspectives of multiple data lifecycles (including data collection,
storage, and usage), which thoroughly investigates the access control
techniques and helps readers understand them systematically. Finally, we
reflect on the classification and envisage future research directions.


  We present a general framework for portfolio risk management in discrete
time, based on a replicating martingale. This martingale is learned from a
finite sample in a supervised setting. The model learns the features necessary
for an effective low-dimensional representation, overcoming the curse of
dimensionality common to function approximation in high-dimensional spaces. We
show results based on polynomial and neural network bases. Both offer superior
results to naive Monte Carlo methods and other existing methods like
least-squares Monte Carlo and replicating portfolios.


  This work presents a theoretical and empirical evaluation of Anderson-Darling
test when the sample size is limited. The test can be applied in order to
backtest the risk factors dynamics in the context of Counterparty Credit Risk
modelling. We show the limits of such test when backtesting the distributions
of an interest rate model over long time horizons and we propose a modified
version of the test that is able to detect more efficiently an underestimation
of the model's volatility. Finally we provide an empirical application.


  In the near future, more and more machines will perform tasks in the vicinity
of human spaces or support them directly in their spatially bound activities.
In order to simplify the verbal communication and the interaction between
robotic units and/or humans, reliable and robust systems w.r.t. noise and
processing results are needed. This work builds a foundation to address this
task. By using a continuous representation of spatial perception in interiors
learned from trajectory data, our approach clusters movement in dependency to
its spatial context. We propose an unsupervised learning approach based on a
neural autoencoding that learns semantically meaningful continuous encodings of
spatio-temporal trajectory data. This learned encoding can be used to form
prototypical representations. We present promising results that clear the path
for future applications.


  The IceCube neutrino observatory uses $1\,\mathrm{km}^{3}$ of the natural
Antarctic ice near the geographic South Pole as optical detection medium. When
charged particles, such as particles produced in neutrino interactions, pass
through the ice with relativistic speed, Cherenkov light is emitted. This is
detected by IceCube's optical modules and from all these signals a particle
signature is reconstructed. A new kind of signature can be detected using light
emission from luminescence. This detection channel enables searches for exotic
particles (states) which do not emit Cherenkov light and currently cannot be
probed by neutrino detectors. Luminescence light is induced by highly ionizing
particles passing through matter due to excitation of surrounding atoms. This
process is highly dependent on the ice structure, impurities, pressure and
temperature which demands an in-situ measurement of the detector medium. For
the measurements at IceCube, a $1.7\,\mathrm{km}$ deep hole was used which
{vertically} overlaps with the glacial ice layers found in the IceCube volume
over a range of $350\,\mathrm{m}$. The experiment as well as the measurement
results are presented. The impact {of the results, which enable new kind of}
searches for new physics with neutrino telescopes, are discussed.


  One of the most efficient methods to obtain the vacuum expectation values for
the physical observables in the Casimir effect is based on the using the
Abel-Plana summation formula. This allows to derive the regularized quantities
by manifestly cutoff independent way and to present them in the form of
strongly converging integrals. However the applications of Abel- Plana formula
in usual form is restricted by simple geometries when the eigenmodes have a
simple dependence on quantum numbers. The author generalized the Abel-Plana
formula which essentially enlarges its application range. Based on this
generalization, formulae have been obtained for various types of series over
the zeros of some combinations of Bessel functions and for integrals involving
these functions. It have been shown that these results generalize the special
cases existing in literature. Further the derived summation formulae have been
used to summarize series arising in the mode summation approach to the Casimir
effect for spherically and cylindrically symmetric boundaries. This allows to
extract the divergent parts from the vacuum expectation values for the local
physical observables in the manifestly cutoff independent way. The present
paper reviews these results. Some new considerations are added as well.


  This paper proposes an innovative approach to improving quality control of
olive oil manufacturing and preventing damage to the machinery caused by
foreign objects. We developed a computer-vision-based system that monitors the
input of an olive grinder and promptly alerts operators if a foreign object is
detected, indicating it by using guided lasers, audio, and visual cues.


  Safely controlling unknown dynamical systems is one of the biggest challenges
in the field of control. Oftentimes, an approximate model of a system's
dynamics exists which provides beneficial information for the selection of
controls. However, differences between the approximate and true systems present
challenges as well as safety concerns. We propose an algorithm called
SAFE-SLOPE to safely evaluate points from a Gaussian process model of a
function when its Lipschitz constant is unknown. We establish theoretical
guarantees for the performance of SAFE-SLOPE and quantify how multi-fidelity
modeling improves the algorithm's performance. Finally, we demonstrate how
SAFE-SLOPE achieves lower cumulative regret than a naive sampling method by
applying it to find the control gains of a linear time-invariant system.


  Delivering Gbps high user rate over long distances (around 1 km) is
challenging, and the abundant spectrum available in millimeter wave band cannot
solve the challenge by its own due to the severe path loss and other
limitations. Since it is economically challenging to deploy wired backhaul
every few hundred meters, relays (e.g., wireless access points) have been
proposed to extend the coverage of a base station which has wired connection to
the core network. These relays, deployed every few hundred meters, serve the
users in their vicinity and are backhauled to the base station through wireless
connections. In this work, the wireless relayed backhaul design has been
formulated as a topology-bandwidth-power joint optimization problem, and the
influence of path loss, angular spread, array size, and RF power limitation on
the user rate has been evaluated. It has been shown that for a linear network
deployed along the street at 28 GHz, when high joint directional gain (50 dBi)
is available, 1 Gbps user rate within cell range of 1 km can be delivered using
1.5 GHz of bandwidth (using single polarization antennas). The user rates drop
precipitously when joint directional gain is reduced, or when the path loss is
much more severe. When the number of RF chains is limited, the benefit of
larger arrays will eventually be surpassed by the increased channel estimation
penalty as the effective beamforming gain saturates owing to the channel
angular spread.


  This paper proposes an energy-efficient scheme for multicell multiple-input,
multiple-output (MIMO) simultaneous transmit and reflect (STAR) reconfigurable
intelligent surfaces (RIS)-assisted broadcast channels by employing rate
splitting (RS) and improper Gaussian signaling (IGS). Regular RISs can only
reflect signals. Thus, a regular RIS can assist only when the transmitter and
receiver are in the reflection space of the RIS. However, a STAR-RIS can
simultaneously transmit and reflect, thus providing a 360-degrees coverage. In
this paper, we assume that transceivers may suffer from I/Q imbalance (IQI). To
compensate for IQI, we employ IGS. Moreover, we employ RS to manage intracell
interference. We show that RIS can significantly improve the energy efficiency
(EE) of the system when RIS components are carefully optimized. Additionally,
we show that STAR-RIS can significantly outperform a regular RIS when the
regular RIS cannot cover all the users. We also show that RS can highly
increase the EE comparing to treating interference as noise.


  We describe a method for associating some non-self-adjoint algebras to
Mauldin-Williams graphs and we study the Morita equivalence and isomorphism of
these algebras.
  We also investigate the relationship between the Morita equivalence and
isomorphism class of the C^{\ast} -correspondences associated with
Mauldin-Williams graphs and the dynamical properties of the Mauldin-Williams
graphs.


  Complex computer simulators are increasingly used across fields of science as
generative models tying parameters of an underlying theory to experimental
observations. Inference in this setup is often difficult, as simulators rarely
admit a tractable density or likelihood function. We introduce Adversarial
Variational Optimization (AVO), a likelihood-free inference algorithm for
fitting a non-differentiable generative model incorporating ideas from
generative adversarial networks, variational optimization and empirical Bayes.
We adapt the training procedure of generative adversarial networks by replacing
the differentiable generative network with a domain-specific simulator. We
solve the resulting non-differentiable minimax problem by minimizing
variational upper bounds of the two adversarial objectives. Effectively, the
procedure results in learning a proposal distribution over simulator
parameters, such that the JS divergence between the marginal distribution of
the synthetic data and the empirical distribution of observed data is
minimized. We evaluate and compare the method with simulators producing both
discrete and continuous data.


  When a system consisting of many interacting particles is set rotating, it
may form vortices. This is familiar to us from every-day life: you can observe
vortices while stirring your coffee or watching a hurricane. In the world of
quantum mechanics, famous examples of vortices are superconducting films and
rotating bosonic $^4$He or fermionic $^3$He liquids. Vortices are also observed
in rotating Bose-Einstein condensates in atomic traps and are predicted to
exist for paired fermionic atoms. Here we show that the rotation of trapped
particles with a repulsive interaction leads to a similar vortex formation,
regardless of whether the particles are bosons or (unpaired) fermions. The
exact, quantum mechanical many-particle wave function provides evidence that in
fact, the mechanism of this vortex formation is the same for boson and fermion
systems.


  Image restoration aims to recover the high-quality images from their degraded
observations. Since most existing methods have been dedicated into single
degradation removal, they may not yield optimal results on other types of
degradations, which do not satisfy the applications in real world scenarios. In
this paper, we propose a novel data ingredient-oriented approach that leverages
prompt-based learning to enable a single model to efficiently tackle multiple
image degradation tasks. Specifically, we utilize a encoder to capture features
and introduce prompts with degradation-specific information to guide the
decoder in adaptively recovering images affected by various degradations. In
order to model the local invariant properties and non-local information for
high-quality image restoration, we combined CNNs operations and Transformers.
Simultaneously, we made several key designs in the Transformer blocks
(multi-head rearranged attention with prompts and simple-gate feed-forward
network) to reduce computational requirements and selectively determines what
information should be persevered to facilitate efficient recovery of
potentially sharp images. Furthermore, we incorporate a feature fusion
mechanism further explores the multi-scale information to improve the
aggregated features. The resulting tightly interlinked hierarchy architecture,
named as CAPTNet, extensive experiments demonstrate that our method performs
competitively to the state-of-the-art.


  It is generally believed that the human visual system is biased towards the
recognition of shapes rather than textures. This assumption has led to a
growing body of work aiming to align deep models' decision-making processes
with the fundamental properties of human vision. The reliance on shape features
is primarily expected to improve the robustness of these models under covariate
shift. In this paper, we revisit the significance of shape-biases for the
classification of skin lesion images. Our analysis shows that different skin
lesion datasets exhibit varying biases towards individual image features.
Interestingly, despite deep feature extractors being inclined towards learning
entangled features for skin lesion classification, individual features can
still be decoded from this entangled representation. This indicates that these
features are still represented in the learnt embedding spaces of the models,
but not used for classification. In addition, the spectral analysis of
different datasets shows that in contrast to common visual recognition,
dermoscopic skin lesion classification, by nature, is reliant on complex
feature combinations beyond shape-bias. As a natural consequence, shifting away
from the prevalent desire of shape-biasing models can even improve skin lesion
classifiers in some cases.


  Zipf (1935) posited that wordforms are optimized to minimize utterances'
communicative costs. Under the assumption that cost is given by an utterance's
length, he supported this claim by showing that words' lengths are inversely
correlated with their frequencies. Communicative cost, however, can be
operationalized in different ways. Piantadosi et al. (2011) claim that cost
should be measured as the distance between an utterance's information rate and
channel capacity, which we dub the channel capacity hypothesis (CCH) here.
Following this logic, they then proposed that a word's length should be
proportional to the expected value of its surprisal (negative log-probability
in context). In this work, we show that Piantadosi et al.'s derivation does not
minimize CCH's cost, but rather a lower bound, which we term CCH-lower. We
propose a novel derivation, suggesting an improved way to minimize CCH's cost.
Under this method, we find that a language's word lengths should instead be
proportional to the surprisal's expectation plus its variance-to-mean ratio.
Experimentally, we compare these three communicative cost functions: Zipf's,
CCH-lower , and CCH. Across 13 languages and several experimental settings, we
find that length is better predicted by frequency than either of the other
hypotheses. In fact, when surprisal's expectation, or expectation plus
variance-to-mean ratio, is estimated using better language models, it leads to
worse word length predictions. We take these results as evidence that Zipf's
longstanding hypothesis holds.


  Hole spin qubits in quasi one-dimensional structures are a promising platform
for quantum information processing because of the strong spin-orbit interaction
(SOI). We present analytical results and discuss device designs that optimize
the SOI in Ge semiconductors. We show that at the magnetic field values at
which qubits are operated, orbital effects of magnetic fields can strongly
affect the response of the spin qubit. We study one-dimensional hole systems in
Ge under the influence of electric and magnetic fields applied perpendicularly
to the device. In our theoretical description, we include these effects
exactly. The orbital effects lead to a strong renormalization of the g-factor.
We find a sweet-spot of the nanowire (NW) g-factor where charge noise is
strongly suppressed and present an effective low-energy model that captures the
dependence of the SOI on the electromagnetic fields. Moreover, we compare
properties of NWs with square and circular cross-sections with ones of
gate-defined one-dimensional channels in two-dimensional Ge heterostructures.
Interestingly, the effective model predicts a flat band ground state for
fine-tuned electric and magnetic fields. By considering a quantum dot (QD)
harmonically confined by gates, we demonstrate that the NW g-factor sweet spot
is retained in the QD. Our calculations reveal that this sweet spot can be
designed to coincide with the maximum of the SOI, yielding highly coherent
qubits with large Rabi frequencies. We also study the effective g-factor of NWs
grown along different high symmetry axes and find that our model derived for
isotropic semiconductors is valid for the most relevant growth directions of
non-isotropic Ge NWs. Moreover, a NW grown along one of the three main
crystallographic axes shows the largest SOI. Our results show that the
isotropic approximation is not justified in Ge in all cases.


  We present a novel mechanism for thermalizing a system of particles in
equilibrium and nonequilibrium situations, based on specifically modeling
energy transfer at the boundaries via a microscopic collision process. We apply
our method to the periodic Lorentz gas, where a point particle moves
diffusively through an ensemble of hard disks arranged on a triangular lattice.
First, collision rules are defined for this system in thermal equilibrium. They
determine the velocity of the moving particle such that the system is
deterministic, time reversible, and microcanonical. These collision rules can
systematically be adapted to the case where one associates arbitrarily many
degrees of freedom to the disk, which here acts as a boundary. Subsequently,
the system is investigated in nonequilibrium situations by applying an external
field. We show that in the limit where the disk is endowed by infinitely many
degrees of freedom it acts as a thermal reservoir yielding a well-defined
nonequilibrium steady state. The characteristic properties of this state, as
obtained from computer simulations, are finally compared to the ones of the
so-called Gaussian thermostated driven Lorentz gas.


  Basic features of nonstrange vector and axial vector mesons are analyzed in
the framework of a chiral quark model that includes nonlocal four fermion
couplings. Unknown model parameters are determined from some input values of
masses and decay constants, while nonlocal form factors are taken from a fit to
lattice QCD results for effective quark propagators. Numerical results show a
good agreement with the observed meson phenomenology.


  We study almost minimizers for the thin obstacle problem with variable
H\"older continuous coefficients and zero thin obstacle and establish their
$C^{1,\beta}$ regularity on the either side of the thin space. Under an
additional assumption of quasisymmetry, we establish the optimal growth of
almost minimizers as well as the regularity of the regular set and a structural
theorem on the singular set. The proofs are based on the generalization of
Weiss- and Almgren-type monotonicity formulas for almost minimizers established
earlier in the case of constant coefficients.


  The 'Discussion & Debate' issue of this Euro. Phys. J. Special Topic volume
is: 'Can economics be a Physical Science?' I would rather address a more
general question: 'Can economics or sociology avoid joining Natural Science?'
and argue that mainstream or core economics or sociology can not escape joining
natural science.


  We have considered theoretically the feasibility of the broadband quantum
memory based on the resonant tripod-type atomic configuration. In this case,
the writing of a signal field is carried out simultaneously into two channels,
and characterized by an excitation of two spin waves of the atomic ensemble.
With simultaneous read out from both channels quantum properties of the
original signal are mapped on the retrieval pulse no worse than in the case of
memory based on Lambda-type atomic configuration. At the same time new
possibilities are opened up for manipulation of quantum states associated with
sequential reading out (and/or sequential writing) of signal pulses. For
example, the pulse in squeezed state is converted into two partially entangled
pulses with partially squeezed quadratures. Alternatively, two independent
signal pulses with orthogonal squeezed quadratures can be converted into two
entangled pulses.


  Let $G$ be a group and $H \le K \le G$. We say that $H$ is $c$-embedded in
$G$ with respect to $K$ if there is a subgroup $B$ of $G$ such that $G = HB$
and $H \cap B \le Z(K)$. Given a finite group $G$, a prime number $p$ and a
Sylow $p$-subgroup $P$ of $G$, we investigate the structure of $G$ under the
assumption that $N_G(P)$ is $p$-supersolvable or $p$-nilpotent and that certain
cyclic subgroups of $P$ with order $p$ or $4$ are $c$-embedded in $G$ with
respect to $P$. New characterizations of $p$-supersolvability and
$p$-nilpotence of finite groups will be obtained.


  The ``warp drive'' metric recently presented by Alcubierre has the problem
that an observer at the center of the warp bubble is causally separated from
the outer edge of the bubble wall. Hence such an observer can neither create a
warp bubble on demand nor control one once it has been created. In addition,
such a bubble requires negative energy densities. One might hope that
elimination of the first problem might ameliorate the second as well. We
analyze and generalize a metric, originally proposed by Krasnikov for two
spacetime dimensions, which does not suffer from the first difficulty. As a
consequence, the Krasnikov metric has the interesting property that although
the time for a one-way trip to a distant star cannot be shortened, the time for
a round trip, as measured by clocks on Earth, can be made arbitrarily short. In
our four dimensional extension of this metric, a ``tube'' is constructed along
the path of an outbound spaceship, which connects the Earth and the star.
Inside the tube spacetime is flat, but the light cones are opened out so as to
allow superluminal travel in one direction. We show that, although a single
Krasnikov tube does not involve closed timelike curves, a time machine can be
constructed with a system of two non-overlapping tubes. Furthermore, it is
demonstrated that Krasnikov tubes, like warp bubbles and traversable wormholes,
also involve unphysically thin layers of negative energy density, as well as
large total negative energies, and therefore probably cannot be realized in
practice.


  The forensic attribution of the handwriting in a digitized document to
multiple scribes is a challenging problem of high dimensionality. Unique
handwriting styles may be dissimilar in a blend of several factors including
character size, stroke width, loops, ductus, slant angles, and cursive
ligatures. Previous work on labeled data with Hidden Markov models, support
vector machines, and semi-supervised recurrent neural networks have provided
moderate to high success. In this study, we successfully detect hand shifts in
a historical manuscript through fuzzy soft clustering in combination with
linear principal component analysis. This advance demonstrates the successful
deployment of unsupervised methods for writer attribution of historical
documents and forensic document analysis.