  Logistics optimization nowadays is becoming one of the hottest areas in the
AI community. In the past year, significant advancements in the domain were
achieved by representing the problem in a form of graph. Another promising area
of research was to apply reinforcement learning algorithms to the above task.
In our work, we made advantage of using both approaches and apply reinforcement
learning on a graph. To do that, we have analyzed the most recent results in
both fields and selected SOTA algorithms both from graph neural networks and
reinforcement learning. Then, we combined selected models on the problem of
AMOD systems optimization for the transportation network of New York city. Our
team compared three algorithms - GAT, Pro-CNN and PTDNet - to bring to the fore
the important nodes on a graph representation. Finally, we achieved SOTA
results on AMOD systems optimization problem employing PTDNet with GNN and
training them in reinforcement fashion.
  Keywords: Graph Neural Network (GNN), Logistics optimization, Reinforcement
Learning


  The present paper finds new necessary and sufficient conditions for
$6$-dimensional closed and simply-connected manifolds of certain classes to
admit special generic maps into certain Euclidean spaces.
  The class of special generic maps naturally contains Morse functions with
exactly two singular points on spheres in so-called Reeb's theorem,
characterizing spheres topologically, and canonical projections of unit
spheres. Our paper concerns variants of Reeb's theorem. Several results are
known e. g. the cases where the manifolds of the targets are the plane and some
cases where the manifolds of the domains are closed and simply-connected. Our
paper concerns $6$-dimensional versions of a result of Nishioka, determining
$5$-dimensional closed and simply-connected manifolds admitting special generic
maps into Euclidean spaces completely. Closed and simply-connected manifolds
are central geometric objects in (classical) algebraic topology and
differential topology. The $6$-dimensional case is more complicated than the
$5$-dimensional one: they are classified via explicit algebraic systems.


  We study the uncertainty relation in the product form of variances and obtain
some new uncertainty relations with weight, which are shown to be tighter than
those derived from the Cauchy Schwarz inequality.


  Characteristics of the initial condensate in the recent experiment on
Bose-Einstein condensation (BEC) of ${}^{87}$Rb atoms in an anisotropic
magnetic trap is discussed. Given the aspect ratio $R$, the quality of BEC is
estimated. A simple analytical Ansatz for the initial condensate wave function
is proposed as a function of the aspect ratio which, in contrast to the
Baym-Pethick trial wave function, reproduces both the weak and the strong
intaraction limits and which is in better agreement with numerical results than
the latter.


  In this paper, we deal with soft MTL-algebras based on fuzzy sets. By means
of $\in$-soft sets and q-soft sets, some characterizations of (Boolean, G- and
MV-) filteristic soft MTL-algebras are investigated. Finally, we prove that a
soft set is a Boolean filteristic soft MTL-algebra if and only if it is both a
G-filteristic soft MTL-algebra and an MV-filteristic soft MTL-algebra.


  A population of primordial black holes formed in the early Universe could
contribute to at least a fraction of the black-hole merger events detectable by
current and future gravitational-wave interferometers. With the ever-increasing
number of detections, an important open problem is how to discriminate whether
a given event is of primordial or astrophysical origin. We systematically
present a comprehensive and interconnected list of discriminators that would
allow us to rule out, or potentially claim, the primordial origin of a binary
by measuring different parameters, including redshift, masses, spins,
eccentricity, and tidal deformability. We estimate how accurately future
detectors (such as the Einstein Telescope and LISA) could measure these
quantities, and we quantify the constraining power of each discriminator for
current interferometers. We apply this strategy to the GWTC-3 catalog of
compact binary mergers. We show that current measurement uncertainties do not
allow us to draw solid conclusions on the primordial origin of individual
events, but this may become possible with next-generation ground-based
detectors.


  The Gaia hypothesis postulates that life regulates its environment to be
favorable for its own survival. Most planets experience numerous perturbations
throughout their lifetimes such as asteroid impacts, volcanism, and the
evolution of their host star's luminosity. For the Gaia hypothesis to be
viable, life must be able to keep the conditions of its host planet habitable,
even in the face of these challenges. ExoGaia, a model created to investigate
the Gaia hypothesis, has been previously used to demonstrate that a randomly
mutating biosphere is in some cases capable of maintaining planetary
habitability. However, those model scenarios assumed that all non-biological
planetary parameters were static, neglecting the inevitable perturbations that
real planets would experience. To see how life responds to climate
perturbations to its host planet, we created three climate perturbations in
ExoGaia: one rapid cooling of a planet and two heating events, one rapid and
one gradual. The planets on which Gaian feedbacks emerge without climate
perturbations are the same planets on which life is most likely to survive each
of our perturbation scenarios. Biospheres experiencing gradual changes to the
environment are able to survive changes of larger magnitude than those
experiencing rapid perturbations, and the magnitude of change matters more than
the sign. These findings suggest that if the Gaia hypothesis is correct, then
typical perturbations that a planet would experience may be unlikely to disrupt
Gaian systems.


  The deuteron fragmentation by fast protons has been studied both near the
kinematics of quasi-free proton - proton scattering and far away from it. We
have concentrated on the interplay between different reaction mechanisms
associated with the antisymmetrization of the initial and final states and
rescattering contributions. A multiple-scattering-expansion technique has been
applied to evaluate the reaction amplitude. An essential element of this
approach in the momentum representation is the use of the effective nucleon-
nucleon interaction constructed by Love and Franey as a two-body t-matrix for
the incident proton scattering on a bound nucleon in the deuteron. Along with
the five-fold cross sections, the proton analyzing power and the deuteron
analyzing powers have been calculated as function of the momentum of the
outgoing fast proton. The results are compared with the data obtained by the
Gatchina-Saclay collaboration.


  A generalized Cauchy-Schwarz inequality is derived and applied to uncertainty
relation in quantum mechanics. We see a modification in the uncertainty
relation and minimum uncertainty wave packet.


  We study separability of the Hamilton-Jacobi and massive Klein-Gordon
equations in the general Myers-Perry black hole background in all dimensions.
Complete separation of both equations is carried out in cases when there are
two sets of equal black hole rotation parameters, which significantly enlarges
the rotational symmetry group. We explicitly construct a nontrivial irreducible
Killing tensor associated with the enlarged symmetry group which permits
separation. We also derive first-order equations of motion for particles in
these backgrounds and examine some of their properties.


  Hermitian, pluriclosed metrics with vanishing Bismut-Ricci form give a
natural extension of Calabi-Yau metrics to the setting of complex, non-K\"ahler
manifolds, and arise independently in mathematical physics. We reinterpret this
condition in terms of the Hermitian-Einstein equation on an associated
holomorphic Courant algebroid, and thus refer to solutions as Bismut
Hermitian-Einstein. This implies Mumford-Takemoto slope stability obstructions,
and using these we exhibit infinitely many topologically distinct complex
manifolds in every dimension with vanishing first Chern class which do not
admit Bismut Hermitian-Einstein metrics. This reformulation also leads to a new
description of pluriclosed flow in terms of Hermitian metrics on holomorphic
Courant algebroids, implying new global existence results, in particular on all
complex non-K\"ahler surfaces of nonnegative Kodaira dimension. On complex
manifolds which admit Bismut-flat metrics we show global existence and
convergence of pluriclosed flow to a Bismut-flat metric, which in turn gives a
classification of generalized K\"ahler structures on these spaces.


  Radionuclides sequestration through adsorption technology has attracted much
attention due to its unique characters such as high removal efficiency, low
cost, and ease of operation. In this work, the interaction mechanism of
N-functionalized Ti2C MXene (Ti2CN2) as a potential adsorbent for the removal
of strontium ions is investigated by using first principles method. Our results
show that surface N atoms are connected to Sr ions by a robust chemical N-Sr
bond, which provides a stronger interaction and greater capacity (1.291g g-1)
of Sr ion adsorption on Ti2CN2 than Ti2C with other surficial groups O, F and
OH. Furthermore, the thermal stability of the adsorption structure of Sr on
Ti2CN2 with full layer coverage at room temperature is verified by using ab
initio molecular dynamics simulations. Our results are expected to provide a
new perspective for the design of MXene materials as adsorbent for
radionuclide.


  Over-the-air federated learning (OTA-FL) exploits the inherent superposition
property of wireless channels to integrate the communication and model
aggregation. Though a naturally promising framework for wireless federated
learning, it requires care to mitigate physical layer impairments. In this
work, we consider a heterogeneous edge-intelligent network with different edge
device resources and non-i.i.d. user dataset distributions, under a general
non-convex learning objective. We leverage the Reconfigurable Intelligent
Surface (RIS) technology to augment OTA-FL system over simultaneous time
varying uplink and downlink noisy communication channels under imperfect CSI
scenario. We propose a cross-layer algorithm that jointly optimizes RIS
configuration, communication and computation resources in this general
realistic setting. Specifically, we design dynamic local update steps in
conjunction with RIS phase shifts and transmission power to boost learning
performance. We present a convergence analysis of the proposed algorithm, and
show that it outperforms the existing unified approach under heterogeneous
system and imperfect CSI in numerical results.


  This brief note in response to Wojciech Zurek's article "Quantum Darwinism,
classical reality, and the randomness of quantum jumps" (Physics Today, October
2014, page 44) points out extant rebuttals in the literature to some of the
author's key claims.


  We study a friction controlled slide of a body excited by random motions of
the foundation it is placed on. Specifically, we are interested in quantities
such as displacement, traveled distance, and energy loss due to friction.
Assuming that the random excitation is switched off at some time, it is shown
that the problem can be treated in an analytic, explicit, manner. Particularly,
we derive formulas for the moments of the displacement and distance, and also
for the average energy loss. To accomplish that we use the Pugachev-Sveshnikov
equation for the characteristic function of a continuous random process given
by a system of SDEs. This equation is solved by reduction to a parametric
Riemann boundary value problem of complex analysis.


  Recent measurements at LHC has inspired searches for TeV scale left-right
gauge theory originating from grand unified theories. We show that inclusion of
Planck-scale induced effects due to ${\rm dim.}5$ operator not only does away
with all the additional intermediate symmetries, but also it predicts the
minimal set of light Higgs scalars tailored after neutrino masses and dilepton,
or trilepton signals. The heavy-light neutrino mixings are predicted from
charged fermion mass fits in $SO(10)$ and LFV constraints which lead to new
predictions for dilepton or trilepton production signals. Including
fine-structure constant matching and two-loop, and threshold effects predicts
$M_{W_R}= g_{2R}\times 10^{4.3\pm 1.5 \pm 0.2}$ GeV and proton lifetime
$\tau_p=10^{36.15\pm 5.8\pm 0.2}$ yrs with $W_R$ gauge boson coupling
$g_{2R}=0.56-0.57$. Predictions on lepton flavour and lepton number violations
are accessible to ongoing experiments. Current CMS data on di-electron excess
at $\sqrt s= 8$ TeV are found to be consistent with $W_R$ gauge boson mass
$M_{W_R}\ge 1.9-2.2$ TeV which also agrees with the values obtained from dijet
resonance production data. We also discuss plausible explanations for diboson
production excesses observed at LHC and make predictions expected at $\sqrt s
=14$ TeV


  Equipping a deep model the abaility of few-shot learning, i.e., learning
quickly from only few examples, is a core challenge for artificial
intelligence. Gradient-based meta-learning approaches effectively address the
challenge by learning how to learn novel tasks. Its key idea is learning a deep
model in a bi-level optimization manner, where the outer-loop process learns a
shared gradient descent algorithm (i.e., its hyperparameters), while the
inner-loop process leverage it to optimize a task-specific model by using only
few labeled data. Although these existing methods have shown superior
performance, the outer-loop process requires calculating second-order
derivatives along the inner optimization path, which imposes considerable
memory burdens and the risk of vanishing gradients. Drawing inspiration from
recent progress of diffusion models, we find that the inner-loop gradient
descent process can be actually viewed as a reverse process (i.e., denoising)
of diffusion where the target of denoising is model weights but the origin
data. Based on this fact, in this paper, we propose to model the gradient
descent optimizer as a diffusion model and then present a novel
task-conditional diffusion-based meta-learning, called MetaDiff, that
effectively models the optimization process of model weights from Gaussion
noises to target weights in a denoising manner. Thanks to the training
efficiency of diffusion models, our MetaDiff do not need to differentiate
through the inner-loop path such that the memory burdens and the risk of
vanishing gradients can be effectvely alleviated. Experiment results show that
our MetaDiff outperforms the state-of-the-art gradient-based meta-learning
family in few-shot learning tasks.


  Flavor oscillations of neutrinos are analyzed in the framework of Brans-Dicke
theory of gravity. We find a shift of quantum mechanical phase of neutrino
proportional to $G_N\Delta m^2$ and depending on the parameter $\omega$.
Consequences on atmospheric, solar and astrophysical neutrinos are discussed.


  Given a K3 surface $X$ over a number field $K$ with potentially good
reduction everywhere, we prove that the set of primes of $K$ where the
geometric Picard rank jumps is infinite. As a corollary, we prove that either
$X_{\overline{K}}$ has infinitely many rational curves or $X$ has infinitely
many unirational specializations. Our result on Picard ranks is a special case
of more general results on exceptional classes for K3 type motives associated
to GSpin Shimura varieties. These general results have several other
applications. For instance, we prove that an abelian surface over a number
field $K$ with potentially good reduction everywhere is isogenous to a product
of elliptic curves modulo infinitely many primes of $K$.


  For safe and reliable deployment in the real world, autonomous agents must
elicit appropriate levels of trust from human users. One method to build trust
is to have agents assess and communicate their own competencies for performing
given tasks. Competency depends on the uncertainties affecting the agent,
making accurate uncertainty quantification vital for competency assessment. In
this work, we show how ensembles of deep generative models can be used to
quantify the agent's aleatoric and epistemic uncertainties when forecasting
task outcomes as part of competency assessment.


  Bosons which couple to two leptons and carry lepton number L=2, generically
called bileptons, appear in many extensions of the standard model. We review
the present constraints on bilepton parameters coming from low and high energy
data. In particular, we point out that the amplitude of $\mu-e$ conversion in
nuclei is enhanced by large logarithms if compared with the $\mu\to e\gamma$
one. Bilepton couplings will be tested most stringently at future colliders.
For wide range of neutrino masses the cross section of one of the processes
$e^-e^- (\mu^-\mu^-)\to \ell_i^-\ell_i^-,$ $i=e,\mu, \tau,$ mediated by scalar
triplet bilepton, has such a lower bound that it should be observed at future
facilities.


  With the rise of XML as a standard for representing business data, XML data
warehousing appears as a suitable solution for decision-support applications.
In this context, it is necessary to allow OLAP analyses on XML data cubes.
Thus, XQuery extensions are needed. To define a formal framework and allow
much-needed performance optimizations on analytical queries expressed in
XQuery, defining an algebra is desirable. However, XML-OLAP (XOLAP) algebras
from the literature still largely rely on the relational model. Hence, we
propose in this paper a rollup operator based on a pattern tree in order to
handle multidimensional XML data expressed within complex hierarchies.


  The nematic twist-bend ($\mathrm{N_{TB}}$) phase, exhibited by certain
thermotropic liquid crystalline (LC) dimers, represents a new orientationally
ordered mesophase -- the first distinct nematic variant discovered in many
years. The $\mathrm{N_{TB}}$ phase is distinguished by a heliconical winding of
the average molecular long axis (director) with a remarkably short (nanoscale)
pitch and, in systems of achiral dimers, with an equal probability to form
right- and left-handed domains. The $\mathrm{N_{TB}}$ structure thus provides
another fascinating example of spontaneous chiral symmetry breaking in nature.
The order parameter driving the formation of the heliconical state has been
theoretically conjectured to be a polarization field, deriving from the bent
conformation of the dimers, that rotates helically with the same nanoscale
pitch as the director field. It therefore presents a significant challenge for
experimental detection. Here we report a second harmonic light scattering
(SHLS) study on two achiral, $\mathrm{N_{TB}}$-forming LCs, which is sensitive
to the polarization field due to micron-scale distortion of the helical
structure associated with naturally-occurring textural defects. These defects
are parabolic focal conics of smectic-like "pseudo-layers", defined by planes
of equivalent phase in a coarse-grained description of the $\mathrm{N_{TB}}$
state. Our SHLS data are explained by a coarse-grained free energy density that
combines a Landau-deGennes expansion of the polarization field, the elastic
energy of a nematic, and a linear coupling between the two.


  We initiate the study of stability and pseudospectra of complex momentum
modes of asymptotically anti-de Sitter black holes. Similar to quasinormal
modes, these can be defined as the poles of the holographic Green's function,
albeit for real frequency and complex momentum. Their pseudospectra are in
stark contrast to the pseudospectra of quasinormal modes of AdS black holes.
Contrary to the case of quasinormal mode pseudospectra, the resolvent is
well-defined, and the numerical approximation shows fast convergence. At zero
frequency, complex momentum modes are stable normal modes of a Hermitian
operator. Even for large frequencies, they show only comparatively mild
spectral instability. We also find that local potential perturbations cannot
destabilize the lowest complex momentum mode.


  We study the phase transition to the superconducting state taking into
account the fluctuations of the order parameter and of the vector magnetic
field and discuss the question of the order of transition occuring in this
model. We use the field-theoretical renormalization group approach and consider
in two-loop approximation the gauge model for a superconductor, generalized to
a n/2 component complex order parameter. Special attention is being payed to
the fact, that the corresponding series might be asymptotic ones and therefore
have zero radius of convergence. We review different ways of analytical
continuation of the series and applying Pade analysis and Pade-Borel
resummation technique conclude that in the model under consideration still
exists a possibility for the second-order phase transition with the critical
exponents differing from those of a superfluid liquid.


  We overview the recent results on the shift of the spectrum and norm bounds
for variation of spectral subspaces of a Hermitian operator under an additive
Hermitian perturbation. Along with the known results, we present a new subspace
variation bound for the generic off-diagonal subspace perturbation problem. We
also demonstrate how some of the abstract results may work for few-body
Hamiltonians.


  By introducing a normal self-energy to incorporate the effects of magnetic
impurities, Kondo effects in single-walled metallic carbon nanotubes are
investigated within the Anderson model and Landauer formula. Magnetic
impurities induce Kondo resonance and bring a valley of conductance unction
near the Fermi level. The conductance of the nanotube increases with the
temperature in the low temperature range. Thermoelectric power induced by
magnetic impurities is gotten from Mott relation, and the calculations indicate
its dependence on the temperature could interpret the experiment well.


  It is shown that in strongly magnetized neutron stars, there exist upper
limits of magnetic field strength, beyond which the self energies for both
neutron and proton components of neutron star matter become complex in nature.
As a consequence they decay within the strong interaction time scale. However,
in the ultra-strong magnetic field case, when the zeroth Landau level is only
occupied by protons, the system again becomes stable against strong decay.


  Unfinished buildings are a constant throughout the history of architecture
and have given rise to intense debates on the opportuneness of their
completion, in addition to offering alibis for theorizing about the
compositional possibilities in coherence with the finished parts. The
development of Artificial Intelligence (AI) opens new avenues for the proposal
of possibilities for the completion of unfinished architectures. Specifically,
with the recent appearance of tools such as DALL-E, capable of completing
images guided by a textual description, it is possible to count on the help of
AI for architectural design tasks. In this article we explore the use of these
new AI tools for the completion of unfinished facades of historical temples and
analyse the still germinal stadium in the field of architectural graphic
composition.


  The aim of this paper is twofold. One is to introduce the class of harmonic
$\nu$-Bloch-type mappings as a generalization of harmonic $\nu$-Bloch mappings
and thereby we generalize some recent results of harmonic $1$-Bloch-type
mappings investigated recently by Efraimidis et al. \cite{EGHV}. The other is
to investigate some subordination principles for harmonic Bloch mappings and
then establish Bohr's theorem for these mappings and in a general setting, in
some cases.


  Many problems of industrial interest are NP-complete, and quickly exhaust
resources of computational devices with increasing input sizes. Quantum
annealers (QA) are physical devices that aim at this class of problems by
exploiting quantum mechanical properties of nature. However, they compete with
efficient heuristics and probabilistic or randomised algorithms on classical
machines that allow for finding approximate solutions to large NP-complete
problems. While first implementations of QA have become commercially available,
their practical benefits are far from fully explored. To the best of our
knowledge, approximation techniques have not yet received substantial
attention. In this paper, we explore how problems' approximate versions of
varying degree can be systematically constructed for quantum annealer programs,
and how this influences result quality or the handling of larger problem
instances on given set of qubits. We illustrate various approximation
techniques on both, simulations and real QA hardware, on different seminal
problems, and interpret the results to contribute towards a better
understanding of the real-world power and limitations of current-state and
future quantum computing.


  Our understanding of the core-collapse supernova explosion mechanism is
incomplete. While the favoured scenario is delayed revival of the stalled shock
by neutrino heating, it is difficult to reliably compute explosion outcomes and
energies, which depend sensitively on the complex radiation hydrodynamics of
the post-shock region. The dynamics of the (non-)explosion depend sensitively
on how energy is transported from inside and near the proto-neutron star (PNS)
to material just behind the supernova shock. Although most of the PNS energy is
lost in the form of neutrinos, hydrodynamic and hydromagnetic waves can also
carry energy from the PNS to the shock. We show that gravity waves excited by
core PNS convection can couple with outgoing acoustic waves that present an
appreciable source of energy and pressure in the post-shock region. Using
one-dimensional simulations, we estimate the gravity wave energy flux excited
by PNS convection and the fraction of this energy transmitted upward to the
post-shock region as acoustic waves. We find wave energy fluxes near
$10^{51}\,\mathrm{erg}\,\mathrm{s}^{-1}$ are likely to persist for
$\sim1\,\mathrm{s}$ post-bounce. The wave pressure on the shock may exceed
$10\%$ of the thermal pressure, potentially contributing to shock revival and,
subsequently, a successful and energetic explosion. We also discuss how future
simulations can better capture the effects of waves, and more accurately
quantify wave heating rates.


  Simultaneous Machine Translation (SiMT) generates translations while reading
the source sentence, necessitating a policy to determine the optimal timing for
reading and generating words. Despite the remarkable performance achieved by
Large Language Models (LLM) across various NLP tasks, existing SiMT methods
predominantly focus on conventional transformers, employing a single model to
concurrently determine the policy and generate the translations. However, given
the complexity of SiMT, it is challenging to effectively address both tasks
with a single model. Therefore, there is a need to decouple the SiMT task into
policy-decision and translation sub-tasks. We propose SiLLM, which delegates
the two sub-tasks to separate agents, thereby incorporating LLM into SiMT. The
policy-decision agent is managed by a conventional SiMT model, responsible for
determining the translation policy. The translation agent, leveraging the
capabilities of LLM, generates translation using the partial source sentence.
The two agents collaborate to accomplish SiMT. To facilitate the application of
token-level policies determined by conventional SiMT models to LLM, we propose
a word-level policy adapted for LLM. Experiments on two datasets demonstrate
that, with a small amount of data for fine-tuning LLM, SiLLM attains
state-of-the-art performance.


  Marketing is the way we ensure our sales are the best in the market, our
prices the most accessible, and our clients satisfied, thus ensuring our brand
has the widest distribution. This requires sophisticated and advanced
understanding of the whole related network. Indeed, marketing data may exist in
different forms such as qualitative and quantitative data. However, in the
literature, it is easily noted that large bibliographies may be collected about
qualitative studies, while only a few studies adopt a quantitative point of
view. This is a major drawback that results in marketing science still focusing
on design, although the market is strongly dependent on quantities such as
money and time. Indeed, marketing data may form time series such as brand sales
in specified periods, brand-related prices over specified periods, market
shares, etc. The purpose of the present work is to investigate some marketing
models based on time series for various brands. This paper aims to combine the
dynamic mode decomposition and wavelet decomposition to study marketing series
due to both prices, and volume sales in order to explore the effect of the time
scale on the persistence of brand sales in the market and on the forecasting of
such persistence, according to the characteristics of the brand and the related
market competition or competitors. Our study is based on a sample of Saudi
brands during the period 22 November 2017 to 30 December 2021.


  We propose a novel activity-based profiling framework to estimate IoT users'
harvested energy based on their daily activities. Energy is harvested from
natural sources such as the kinetic movement of IoT users. The profiling
framework captures the users' physical activity data to define activity-based
profiles. These profiles are utilized to estimate the harvested energy by IoT
users. We train and evaluate our framework based on a real Fitbit dataset.


  In this paper, we study gradient-based classical extremum seeking (ES) for
uncertain n-dimensional (nD) static quadratic maps in the presence of known
large constant distinct input delays and large output constant delay with a
small time-varying uncertainty. This uncertainty may appear due to
network-based measurements. We present a quantitative analysis via a time-delay
approach to averaging. We assume that the Hessian has a nominal known part and
norm-bounded uncertainty, the extremum point belongs to a known box, whereas
the extremum value to a known interval. By using the orthogonal transformation,
we first transform the original static quadratic map into a new one with the
Hessian containing a nominal diagonal part. We apply further a time-delay
transformation to the resulting ES system and arrive at a time-delay system,
which is a perturbation of a linear time-delay system with constant
coefficients. Given large delays, we choose appropriate gains to guarantee
stability of this linear system. To find a lower bound on the dither frequency
for practical stability, we employ variation of constants formula and exploit
the delay-dependent positivity of the fundamental solutions of the linear
system with their tight exponential bounds. Sampled-data ES in the presence of
large distinct input delays is also presented. Explicit conditions in terms of
simple scalar inequalities depending on tuning parameters and delay bounds are
established to guarantee the practical stability of the ES control systems. We
show that given any large delays and initial box, by choosing appropriate gains
we can achieve practical stability for fast enough dithers and small enough
uncertainties.


  The spread of intelligent transportation systems in urban cities has caused
heavy computational loads, requiring a novel architecture for managing
large-scale traffic. In this study, we develop a method for globally
controlling traffic signals arranged on a square lattice by means of a quantum
annealing machine, namely the D-Wave quantum annealer. We first formulate a
signal optimization problem that minimizes the imbalance of traffic flows in
two orthogonal directions. Then we reformulate this problem as an Ising
Hamiltonian, which is fully compatible with quantum annealers. The new control
method is compared with a conventional local control method for a large
50-by-50 city, and the results exhibit the superiority of our global control
method in suppressing traffic imbalance over wide parameter ranges.
Furthermore, the solutions to the global control method obtained with the
quantum annealing machine are better than those obtained with conventional
simulated annealing. In addition, we prove analytically that the local and the
global control methods converge at the limit where cars have equal
probabilities for turning and going straight. These results are verified with
numerical experiments.


  Studying Binomial and Gaussian return dynamics in discrete time, we show how
excess volatility can be traded to create growth. We test our results on real
world data to confirm the observed model phenomena while also highlighting
implicit risks.


  Image captioning is a research hotspot where encoder-decoder models combining
convolutional neural network (CNN) and long short-term memory (LSTM) achieve
promising results. Despite significant progress, these models generate
sentences differently from human cognitive styles. Existing models often
generate a complete sentence from the first word to the end, without
considering the influence of the following words on the whole sentence
generation. In this paper, we explore the utilization of a human-like cognitive
style, i.e., building overall cognition for the image to be described and the
sentence to be constructed, for enhancing computer image understanding. This
paper first proposes a Mutual-aid network structure with Bidirectional LSTMs
(MaBi-LSTMs) for acquiring overall contextual information. In the training
process, the forward and backward LSTMs encode the succeeding and preceding
words into their respective hidden states by simultaneously constructing the
whole sentence in a complementary manner. In the captioning process, the LSTM
implicitly utilizes the subsequent semantic information contained in its hidden
states. In fact, MaBi-LSTMs can generate two sentences in forward and backward
directions. To bridge the gap between cross-domain models and generate a
sentence with higher quality, we further develop a cross-modal attention
mechanism to retouch the two sentences by fusing their salient parts as well as
the salient areas of the image. Experimental results on the Microsoft COCO
dataset show that the proposed model improves the performance of
encoder-decoder models and achieves state-of-the-art results.


  Tolerancing of assembly mechanisms is a major interest in the product life
cycle. One can distinguish several models with growing complexity, from
1-dimensional (1D) to 3-dimensional (3D) (including form deviations), and two
main tolerancing assumptions, the worst case and the statistical hypothesis.
This paper presents an approach to 3D statistical tolerancing using a new
acceptance criterion. Our approach is based on the 1D inertial acceptance
criterion that is extended to 3D and form acceptance. The modal
characterisation is used to describe the form deviation of a geometry as the
combination of elementary deviations (location, orientation and form). The
proposed 3D statistical tolerancing is applied on a simple mechanism with lever
arm. It is also compared to the traditional worst-case tolerancing using a
tolerance zone.


  One of the main challenges in multi-agent reinforcement learning is
scalability as the number of agents increases. This issue is further
exacerbated if the problem considered is temporally dependent. State-of-the-art
solutions today mainly follow centralized training with decentralized execution
paradigm in order to handle the scalability concerns. In this paper, we propose
time-dependent multi-agent transformers which can solve the temporally
dependent multi-agent problem efficiently with a centralized approach via the
use of transformers that proficiently handle the large input. We highlight the
efficacy of this method on two problems and use tools from statistics to verify
the probability that the trajectories generated under the policy satisfy the
task. The experiments show that our approach has superior performance against
the literature baseline algorithms in both cases.


  About 2100 star-forming galaxy protocluster candidates at z=1-4 were
identified at sub-mm wavelengths in the Planck all sky survey. Follow-up
spectroscopic observations of a few candidates have confirmed the presence of
actual galaxy overdensities with large star-formation rates. In this work, we
use state-of-the-art hydrodynamical simulations to investigate whether the
Planck high-z sub-mm sources are progenitors of massive clusters at z=0. To
match the PHz sources with simulated halos, we select the most star-forming
halos from z = 3 to z =1.3 in the TNG300 simulation. The total star formation
rate (SFR) of the simulated protocluster candidates is computed from the SFR of
all the galaxies within an aperture corresponding to the Planck beam size,
including those along the line-of-sight. The simulations reproduce the Planck
derived SFRs as the sum of both, the SFR of at least one of the most SF high-z
halo, and the average contribution from SF sources along the line-of-sight.
Focusing on the spectroscopically confirmed PHz protoclusters, we compare the
observed properties of their galaxy members with those in the most SF simulated
halos. We find a good agreement in the stellar mass and SFR distributions, and
in the galaxy number counts, but the SFR-stellar mass relation of the simulated
galaxies tends to be shifted to lower SFRs with respect to the observed one.
Based on the estimated final masses of the simulated halos, we infer that
between 63% and 72% of the Planck selected protoclusters will evolve into
massive galaxy clusters at z=0. Despite contamination from star-forming
galaxies along the line of sight, we confirm the efficiency of Planck to select
star-forming protoclusters at Cosmic Noon with the simulations, and provide a
new criterion for selecting the most massive cluster progenitors at high-z,
using observables like the number of galaxy members and their SFR distribution.


  The generic fiber of a Lagrangian fibration on an irreducible holomorphic
symplectic manifold is an abelian variety. Associate a polarization type to
such Lagrangian fibrations coming from polarizations on a generic fiber. We
prove that this polarization type is constant in families of Lagrangian
fibrations. Further, we determine the polarization type of K3^[n]-type
fibrations and conjecture that the polarization type should only depend on the
deformation type of the total space.


  As shown recently [Phys. Rev. E 95, 033307 (2017)], spheroidal harmonics
expansions are well suited for the external solution of Laplace's equation for
a point source outside a spherical object. Their intrinsic singularity matches
the line singularity of the analytic continuation of the solution and the
series solution converges much faster than the standard spherical harmonic
solution. Here we extend this approach to internal potentials using the Kelvin
transformation, i.e. radial inversion, of the spheroidal coordinate system.
This transform converts the standard series solution involving regular solid
spherical harmonics into a series of irregular spherical harmonics. We then
substitute the expansion of irregular spherical harmonics in terms of
transformed irregular spheroidal harmonics into the potential. The spheroidal
harmonic solution fits the image line singularity of the solution exactly and
converges much faster. We also discuss why a solution in terms of regular solid
spheroidal harmonics cannot work, even though these functions are finite
everywhere in the sphere. We also present the analogous solution for an
internal point source, and two new relationships between the solid spherical
and spheroidal harmonics.


  Designing a molecule with desired properties is one of the biggest challenges
in drug development, as it requires optimization of chemical compound
structures with respect to many complex properties. To augment the compound
design process we introduce Mol-CycleGAN - a CycleGAN-based model that
generates optimized compounds with high structural similarity to the original
ones. Namely, given a molecule our model generates a structurally similar one
with an optimized value of the considered property. We evaluate the performance
of the model on selected optimization objectives related to structural
properties (presence of halogen groups, number of aromatic rings) and to a
physicochemical property (penalized logP). In the task of optimization of
penalized logP of drug-like molecules our model significantly outperforms
previous results.


  The quantum master equation is an important tool in the study of quantum open
systems. It is often derived under a set of approximations, chief among them
the Born (factorization) and Markov (neglect of memory effects) approximations.
In this article we study the paradigmatic model of quantum Brownian motion of
an harmonic oscillator coupled to a bath of oscillators with a Drude-Ohmic
spectral density. We obtain analytically the \emph{exact} solution of the
Heisenberg-Langevin equations, with which we study correlation functions in the
asymptotic stationary state. We compare the \emph{exact} correlation functions
to those obtained in the asymptotic long time limit with the quantum master
equation in the Born approximation \emph{with and without} the Markov
approximation. In the latter case we implement a systematic derivative
expansion that yields the \emph{exact} asymptotic limit under the factorization
approximation \emph{only}. We find discrepancies that could be significant when
the bandwidth of the bath $\Lambda$ is much larger than the typical scales of
the system. We study the \emph{exact} interaction energy as a \emph{proxy} for
the correlations missed by the Born approximation and find that its dependence
on $\Lambda$ is similar to the \emph{discrepancy} between the exact solution
and that of the quantum master equation in the Born approximation. We quantify
the regime of validity of the quantum master equation in the Born approximation
with or without the Markov approximation in terms of the system's relaxation
rate $\gamma$, its \emph{unrenormalized} natural frequency $\Omega$ and
$\Lambda$: $\gamma/\Omega \ll 1$ and \emph{also} $\gamma \Lambda/\Omega^2 \ll
1$. The reliability of the Born approximation is discussed within the context
of recent experimental settings and more general environments.


  Corvids, apes, and children solve The Crow and The Pitcher task (from Aesop's
Fables) indicating a causal understanding of the task. By cumulatively
interacting with different objects, how can cognitive agents abstract the
underlying cause-effect relations to predict affordances of novel objects? We
address this question by re-enacting the Aesop's Fable task on a robot and
present a) a brain-guided neural model of semantic-episodic memory; with b)
four task-agnostic learning rules that compare expectations from recalled past
episodes with the current scenario to progressively extract the hidden causal
relations. The ensuing robot behaviours illustrate causal learning; and
predictions for novel objects converge to Archimedes' principle, independent of
both the objects explored during learning and the order of their cumulative
exploration.


  I discuss how to obtain angular decay distributions for sequential cascade
decays using helicity methods. The angular decay distributions follow from a
reasonably simple master formula involving bilinear forms of helicity
amplitudes and Wigner's $d$ functions. I discuss in some detail the issue of
gauge invariance for off-shell gauge bosons. As a technical exercise I
calculate the linear relation between the helicity amplitudes and the invariant
amplitudes of semileptonic and rare baryon decays. I discuss two explicit
examples of angular decay distributions for (i) the decay $t\to b+W^+(\to
\ell^+\nu_\ell)$ (which leads to the notion of the helicity fractions of the
$W^+$), and (ii) the sequential decay $\Lambda_b\to\Lambda(\to
p\pi^-)+J/\psi(\to \ell^+\ell^-)$.


  In this paper, we find all the Conformal Killing Vectors (CKVs) and their Lie
Algebra for the recently reported [cqg1] spherically symmetric, shear-free
separable metric spacetimes with non-vanishing energy or heat flux. We also
solve the geodesic equatios of motion for the spacetime under consideration.


  We address and quantify the role of non-adiabaticity ("memory effects") in
the exchange-correlation (xc) functional of time-dependent density functional
theory (TDDFT) for describing non-linear dynamics of many-body systems.
Time-dependent resonant processes are particularly challenging for available
TDDFT approximations, due to their strong non-linear and non-adiabatic
character. None of the known approximate density functionals are able to cope
with this class of problems in a satisfactory manner. In this work we look at
the prototypical example of the resonant processes by considering Rabi
oscillations within the exactly soluble 2-site Hubbard model. We construct the
exact adiabatic xc functional and show that (i) it does not reproduce correctly
resonant Rabi dynamics, (ii) there is a sizable non-adiabatic contribution to
the exact xc potential, which turns out to be small only at the beginning and
at the end of the Rabi cycle when the ground state population is dominant. We
then propose a "two-level" approximation for the time-dependent xc potential
which can capture Rabi dynamics in the 2-site problem. It works well both for
resonant and for detuned Rabi oscillations and becomes essentially exact in the
linear response regime. This new, fully non-adiabatic and explicit density
functional constitutes one of the main results of the present work.


  Test-time domain adaptation aims to adapt a source pre-trained model to a
target domain without using any source data. Existing works mainly consider the
case where the target domain is static. However, real-world machine perception
systems are running in non-stationary and continually changing environments
where the target domain distribution can change over time. Existing methods,
which are mostly based on self-training and entropy regularization, can suffer
from these non-stationary environments. Due to the distribution shift over time
in the target domain, pseudo-labels become unreliable. The noisy pseudo-labels
can further lead to error accumulation and catastrophic forgetting. To tackle
these issues, we propose a continual test-time adaptation approach~(CoTTA)
which comprises two parts. Firstly, we propose to reduce the error accumulation
by using weight-averaged and augmentation-averaged predictions which are often
more accurate. On the other hand, to avoid catastrophic forgetting, we propose
to stochastically restore a small part of the neurons to the source pre-trained
weights during each iteration to help preserve source knowledge in the
long-term. The proposed method enables the long-term adaptation for all
parameters in the network. CoTTA is easy to implement and can be readily
incorporated in off-the-shelf pre-trained models. We demonstrate the
effectiveness of our approach on four classification tasks and a segmentation
task for continual test-time adaptation, on which we outperform existing
methods. Our code is available at \url{https://qin.ee/cotta}.


  If $k\geq 0$, then a $k$-edge-coloring of a graph $G$ is an assignment of
colors to edges of $G$ from the set of $k$ colors, so that adjacent edges
receive different colors. A $k$-edge-colorable subgraph of $G$ is maximum if it
is the largest among all $k$-edge-colorable subgraphs of $G$. For a graph $G$
and $k\geq 0$, let $\nu_{k}(G)$ be the number of edges of a maximum
$k$-edge-colorable subgraph of $G$. In 2010 Mkrtchyan et al. proved that if $G$
is a cubic graph, then $\nu_2(G)\leq \frac{|V|+2\nu_3(G)}{4}$. This result
implies that if the cubic graph $G$ contains a perfect matching, in particular
when it is bridgeless, then $\nu_2(G)\leq \frac{\nu_1(G)+\nu_3(G)}{2}$. One may
wonder whether there are other interesting graph-classes, where a relation
between $\nu_2(G)$ and $\frac{\nu_1(G)+\nu_3(G)}{2}$ can be proved. Related
with this question, in this paper we show that $\nu_{k}(G) \geq
\frac{\nu_{k-i}(G) + \nu_{k+i}(G)}{2}$ for any bipartite graph $G$, $k\geq 0$
and $i=0,1,...,k$.


  The theory of non-gravitational interaction between a pressure-less dark
matter (DM) and dark energy (DE) is a phenomenologically rich cosmological
domain which has received magnificent attention in the community. In the
present article we have considered some interacting scenarios with some novel
features: the interaction functions do not depend on the external parameters of
the universe, rather, they depend on the intrinsic nature of the dark
components; the assumption of unidirectional flow of energy between DM and DE
has been extended by allowing the possibility of bidirectional energy flow
characterized by some sign shifting interaction functions; and the DE equation
of state has been considered to be either constant or dynamical in nature.
These altogether add new ingredients in this context, and, we performed the
phase space analysis of each interacting scenario in order to understand their
global behaviour. According to the existing records in the literature, this
combined picture has not been reported elsewhere. From the analyses, we
observed that the DE equation of state as well as the coupling parameter(s) of
the interaction models can significantly affect the nature of the critical
points. It has been found that within these proposed sign shifting interacting
scenarios, it is possible to obtain stable late time attractors which may act
as global attractors corresponding to an accelerating expansion of the
universe. The overall outcomes of this study clearly highlight that the sign
shifting interaction functions are quite appealing in the context of
cosmological dynamics and they deserve further attention.


  We present theoretical prospects for creating p-wave paired BCS states of
magnetic trapped fermionic atoms. Based on our earlier proposal of using dc
electric fields to control both the strength and anisotropic characteristic of
atom-atom interaction and our recently completed multi-channel atomic collision
calculations we discover that p-wave pairing with $^{40}$K and $^{82,84,86}$Rb
in the low field seeking maximum spin polarized state represent excellent
choices for achieving superfluid BCS states; and may be realizable with current
technology in laser cooling, magnetic trapping, and evaporative/sympathetic
cooling, provided the required strong electric field can be applied. We also
comment on the prospects of similar p-wave paired BCS states in $^{6}$Li, and
more generally on creating other types exotic BCS states. Our study will open a
new area in the vigorous pursuit to create a quantum degenerate fermionic atom
vapor.


  We define the notion of the partial order of ends of the Cayley graph of a
semigroup. We prove that the structure of the ends of a semigroup is invariant
under change of finite generating set and at the same time is inherited by
subsemigroups and extensions of finite Rees index. We prove an analogue of
Hopf's Theorem, stating that a group has 1, 2 or infinitely many ends, for left
cancellative semigroups and that the cardinality of the set of ends is
invariant in subsemigroups and extension of finite Green index in left
cancellative semigroups.


  This paper develops the high-order accurate entropy stable finite difference
schemes for one- and two-dimensional special relativistic hydrodynamic
equations. The schemes are built on the entropy conservative flux and the
weighted essentially non-oscillatory (WENO) technique as well as explicit
Runge-Kutta time discretization. The key is to technically construct the
affordable entropy conservative flux of the semi-discrete second-order accurate
entropy conservative schemes satisfying the semi-discrete entropy equality for
the found convex entropy pair. As soon as the entropy conservative flux is
derived, the dissipation term can be added to give the semi-discrete entropy
stable schemes satisfying the semi-discrete entropy inequality with the given
convex entropy function. The WENO reconstruction for the scaled entropy
variables and the high-order explicit Runge-Kutta time discretization are
implemented to obtain the fully-discrete high-order schemes. Several numerical
tests are conducted to validate the accuracy and the ability to capture
discontinuities of our entropy stable schemes.


  In this paper we mainly focus on the curvature perturbation generated at the
end of multi-field inflation, such as the multi-brid inflation. Since the
curvature perturbation is produced on the super-horizon scale, the bispectrum
and trispectrum have a local shape. The size of bispectrum is measured by
$f_{NL}$ and the trispectrum is characterized by two parameters $\tau_{NL}$ and
$g_{NL}$. For simplicity, the trajectory of inflaton is assumed to be a
straight line in the field space and then the entropic perturbations do not
contribute to the curvature perturbation during inflation. As long as the
background inflaton path is not orthogonal to the hyper-surface for inflation
to end, the entropic perturbation can make a contribution to the curvature
perturbation at the end of inflation and a large local-type non-Gaussiantiy is
expected. An interesting thing is that the non-Gaussianity parameters are
completely determined by the geometric properties of the hyper-surface of the
end of inflation. For example, $f_{NL}$ is proportional to the curvature of the
curve on this hyper-surface along the adiabatic direction and $g_{NL}$ is
related to the change of the curvature radius per unit arc-length of this
curve. Both $f_{NL}$ and $g_{NL}$ can be positive or negative respectively, but
$\tau_{NL}$ must be positive and not less than $({6\over 5}f_{NL})^2$.


  Comprehensive inelastic neutron-scattering measurements were performed to
study the soft optical phonons in La2-xSrxCuO4 at x=0.10, 0.12 and 0.18. We
found at x=0.18 that the softening of Z-point phonon, suggesting incipient
structural transition from the low-temperature orthorhombic (LTO) to
low-temperature tetragonal (LTT) phase, breaks at Tc, which is consistent with
the previous report by Lee et al. for the optimally doped x=0.15 sample. As for
x=0.10 and 0.12, on the other hand, the softening continues even below Tc. It
is thus clarified that the breaking of soft phonon is characteristic of
La2-xSrxCuO4 in the optimally and overdoped regions. In the course of studying
the soft phonons, we discovered that a central peak remains above the LTO to
high-temperature tetragonal (HTT) phase transition at Ts1 and splits into
incommensurate components along the (1 1 0)HTT direction at higher
temperatures. This is a common feature for both x=0.12 and 0.18 and their
temperature dependences of the splitting 2d can be scaled by using a
renormalized temperature T/Ts1. In the high temperature limit, d saturates
around d ~ 0.12 r.l.u., which value is close to the splitting of incommensurate
magnetic signals. This implies that the incipient lattice modulation starts
appearing at very high temperature. Details of this modulation and its
relations with other properties are, however, not yet clarified.


  new defect-assisted mechanism of multiphonon intraband carrier relaxation in
semiconductor quantum dots, where the carrier is found in a coherent
superposition of the initial, final, and defect states, is proposed. It is
shown that this mechanism is capable of explaining the observed trends in
temperature dependences of the intraband relaxation rates for PbSe and CdSe
colloidal nanocrystal quantum dots.


  A dynamical system perturbed by white noise in a neighborhood of an unstable
fixed point is considered. We obtain the exit asymptotics in the limit of
vanishing noise intensity. This is a refinement of a result by Kifer (1981).


  The local atomic disorder and the electronic structure in the environment of
manganese atoms in LaMnO_3 has been studied by x-ray absorption spectroscopy,
over a temperature range (300K to 870K) covering the orbital ordering
transition (710K). The Mn-O distances splitting into short and long bonds (1.95
and 2.15A) is kept across the transition temperature, so that the MnO_6
octahedra remain locally Jahn-Teller distorted. Discontinuities in the Mn local
structure are identified in the extended x-ray fine structure spectra at this
temperature, associated to a reduction of the disorder in the super-exchange
angle and to the removal of the anisotropy in the radial disorder within the
coordination shell. Subtle changes in the electronic local structure also take
place at the Mn site at the transition temperature. The near edge spectra show
a small drop of the Mn 4p hole count and a small enhancement in the pre-edge
structures at the transition temperature. These features are associated to an
increase of the covalence of the Mn-O bonds. Our results shed light on the
local electronic and structural phenomena in a model of order-disorder
transition, where the cooperative distortion is overcome by the thermal
disorder.


  The Seebeck and Nernst coefficients $S$ and $\nu$ of the cuprate
superconductor YBa$_2$Cu$_3$O$_y$ (YBCO) were measured in a single crystal with
doping $p = 0.12$ in magnetic fields up to H = 28 T. Down to T=9 K, $\nu$
becomes independent of field by $H \simeq 30$ T, showing that superconducting
fluctuations have become negligible. In this field-induced normal state, $S/T$
and $\nu/T$ are both large and negative in the $T \to 0$ limit, with the
magnitude and sign of $S/T$ consistent with the small electron-like Fermi
surface pocket detected previously by quantum oscillations and the Hall effect.
The change of sign in $S(T)$ at $T \simeq 50$ K is remarkably similar to that
observed in La$_{2-x}$Ba$_x$CuO$_4$, La$_{2-x-y}$Nd$_y$Sr$_x$CuO$_4$ and
La$_{2-x-y}$Eu$_y$Sr$_x$CuO$_4$, where it is clearly associated with the onset
of stripe order. We propose that a similar density-wave mechanism causes the
Fermi surface reconstruction in YBCO.


  We derive an invariant form of the current-induced switching condition in
spin-transfer devices and show that for energy minima and maxima the "switching
ability" of the current is determined by the spin torque divergence. In
contrast, energy saddle points are normally stabilized by current-induced
merging with other equilibria. Our approach provides new predictions for
several experimental setups and shows the limitations of some frequently used
approximations.


  We prove that arithmetic is interpretable in any indecomposable polynomial
ring (in any set of variables), and in addition we provide an alternative
uniform proof of undecidability for all members in this class of rings.


  Cyclists and pedestrians account for a significant share of fatalities and
serious injuries in the road transport system. In order to protect them,
advanced driver assistance systems are being developed and introduced to the
market, including autonomous emergency braking and steering systems (AEBSS)
that autonomously perform braking or an evasive manoeuvre by steering in case
of a pending collision, in order to avoid the collision or mitigate its
severity. This study proposes a new prospective framework for quantifying
safety benefit of AEBSS for the protection of cyclists and pedestrians in terms
of saved lives and reduction in the number of people suffering serious
injuries. The core of the framework is a novel application of Bayesian
inference in such a way that prior information from counterfactual simulation
is updated with new observations from real-world testing of a prototype AEBSS.
As an illustration of the method, the framework is applied for safety benefit
assessment of the AEBSS developed in the European Union (EU) project PROSPECT.
In this application of the framework, counterfactual simulation results based
on the German In-Depth Accident Study Pre-Crash Matrix (GIDAS-PCM) data were
combined with results from real-world tests on proving grounds. The proposed
framework gives a systematic way for the combination of results from different
sources and can be considered for understanding the real-world benefit of new
AEBSS. Additionally, the Bayesian modelling approach used in this paper has a
great potential to be used in a wide range of other research studies.


  Using the strong electromagnetic fields in peripheral heavy ion collisions
gives rise to a number of interesting possibilities of applications in both
photon-photon and photon-hadron physics. We look at the theoretical foundations
of the equivalent photon approximation and the specific problems in the heavy
ion case. The interesting physics processes that can be studied in this way are
outlined. Electron positron pair production plays a special role. We look at
multiple pair production and Coulomb corrections as typical strong field
effects. But electron positron pair production is also an important loss
process and has some practical applications.


  Proceedings supplement for conference poster at Neutrino 2010, Athens,
Greece.


  A laser is not necessarily a sophisticated device: Pumping energy into an
amplifying medium randomly filled with scatterers, a powder for instance, makes
a perfect "random laser." In such a laser, the absence of mirrors greatly
simplifies laser design, but control over emission directionality or frequency
tunability is lost, seriously hindering prospects for this otherwise simple
laser. Lately, we proposed a novel approach to harness random lasers, inspired
by spatial shaping methods recently employed for coherent light control in
complex media. Here, we experimentally implement this method in an optofluidic
random laser where scattering is weak and modes extend spatially and strongly
overlap, making individual selection a priori impossible. We show that control
over laser emission can indeed be regained even in this extreme case by
actively shaping the spatial profile of the optical pump. This unique degree of
freedom, which has never been exploited, allows selection of any desired
wavelength and shaping of lasing modes, without prior knowledge of their
spatial distribution. Mode selection is achieved with spectral selectivity down
to 0.06nm and more than 10dB side-lobe rejection. This experimental method
paves the way towards fully tunable and controlled random lasers and can be
transferred to other class of lasers.


  In many applications, synchronizing audio with visuals is crucial, such as in
creating graphic animations for films or games, translating movie audio into
different languages, and developing metaverse applications. This review
explores various methodologies for achieving realistic facial animations from
audio inputs, highlighting generative and adaptive models. Addressing
challenges like model training costs, dataset availability, and silent moment
distributions in audio data, it presents innovative solutions to enhance
performance and realism. The research also introduces a new taxonomy to
categorize audio-visual synchronization methods based on logistical aspects,
advancing the capabilities of virtual assistants, gaming, and interactive
digital media.


  Virtual fermionic N_f = 1 and N_f = 2 contributions to Bhabha scattering are
combined with realistic real corrections at next-to-next-to-leading order in
QED. The virtual corrections are determined by the package bha_nnlo_hf, and
real corrections with the Monte Carlo generators Bhagen-1Ph, Helac-Phegas and
Ekhara. Numerical results are discussed at the energies of and with realistic
cuts used at the Phi factory DAFNE, at the B factories PEP-II and KEK, and at
the charm/tau factory BEPC II. We compare these complete calculations with the
approximate ones realized in the generator BabaYaga@NLO used at meson factories
to evaluate their luminosities. For realistic reference event selections we
find agreement for the NNLO leptonic and hadronic corrections within 0.07% or
better and conclude that they are well accounted for in the generator by
comparison with the present experimental accuracy.


  In mobile Internet ecosystem, Mobile Users (MUs) purchase wireless data
services from Internet Service Provider (ISP) to access to Internet and acquire
the interested content services (e.g., online game) from Content Provider (CP).
The popularity of intelligent functions (e.g., AI and 3D modeling) increases
the computation-intensity of the content services, leading to a growing
computation pressure for the MUs' resource-limited devices. To this end, edge
computing service is emerging as a promising approach to alleviate the MUs'
computation pressure while keeping their quality-of-service, via offloading
some computation tasks of MUs to edge (computing) servers deployed at the local
network edge. Thus, Edge Service Provider (ESP), who deploys the edge servers
and offers the edge computing service, becomes an upcoming new stakeholder in
the ecosystem. In this work, we study the economic interactions of MUs, ISP,
CP, and ESP in the new ecosystem with edge computing service, where MUs can
acquire the computation-intensive content services (offered by CP) and offload
some computation tasks, together with the necessary raw input data, to edge
servers (deployed by ESP) through ISP. We first study the MU's Joint Content
Acquisition and Task Offloading (J-CATO) problem, which aims to maximize his
long-term payoff. We derive the off-line solution with crucial insights, based
on which we design an online strategy with provable performance. Then, we study
the ESP's edge service monetization problem. We propose a pricing policy that
can achieve a constant fraction of the ex-post optimal revenue with an extra
constant loss for the ESP. Numerical results show that the edge computing
service can stimulate the MUs' content acquisition and improve the payoffs of
MUs, ISP, and CP.


  This work proposes a method of wind farm scenario generation to support
real-time optimization tools and presents key findings therein. This work draws
upon work from the literature and presents an efficient and scalable method for
producing an adequate number of scenarios for a large fleet of wind farms while
capturing both spatial and temporal dependencies. The method makes
probabilistic forecasts using conditional heteroscedastic regression for each
wind farm and time horizon. Past training data is transformed (using the
probabilistic forecasting models) into standard normal samples. A Gaussian
copula is estimated from the normalized samples and used in real-time to
enforce proper spatial and temporal dependencies. The method is evaluated using
historical data from MISO and performance within the MISO real-time look-ahead
framework is discussed.


  Mid-infrared photometry of the Wolf-Rayet star HD 38030 in the Large
Magellanic Cloud from the NEOWISE-R mission show it to have undergone a
dust-formation episode in 2018 and the dust to have cooled in 2019-20. New
spectroscopy with the MagE spectrograph on the Magellan I Baade Telescope in
2019 and 2020 show absorption lines attributable to a companion of type near
O9.7III-IV. We found a significant shift in the radial velocity of the C IV
5801-12 blend compared with the RVs measured in 1984 and 1993. The results
combine to suggest that HD 38030 is a colliding-wind binary having short-lived
dust formation episodes, like the Galactic systems WR 140 and WR 19, but at
intervals in excess of 20 yr.


  Lasso is a celebrated method for variable selection in linear models, but it
faces challenges when the variables are moderately or strongly correlated. This
motivates alternative approaches such as using a non-convex penalty, adding a
ridge regularization, or conducting a post-Lasso thresholding. In this paper,
we compare Lasso with 5 other methods: Elastic net, SCAD, forward selection,
thresholded Lasso, and forward backward selection. We measure their
performances theoretically by the expected Hamming error, assuming that the
regression coefficients are iid drawn from a two-point mixture and that the
Gram matrix is block-wise diagonal. By deriving the rates of convergence of
Hamming errors and the phase diagrams, we obtain useful conclusions about the
pros and cons of different methods.


  For building question answering systems and natural language interfaces,
semantic parsing has emerged as an important and powerful paradigm. Semantic
parsers map natural language into logical forms, the classic representation for
many important linguistic phenomena. The modern twist is that we are interested
in learning semantic parsers from data, which introduces a new layer of
statistical and computational issues. This article lays out the components of a
statistical semantic parser, highlighting the key challenges. We will see that
semantic parsing is a rich fusion of the logical and the statistical world, and
that this fusion will play an integral role in the future of natural language
understanding systems.


  A factor copula model is proposed in which factors are either simulable or
estimable from exogenous information. Point estimation and inference are based
on a simulated methods of moments (SMM) approach with non-overlapping
simulation draws. Consistency and limiting normality of the estimator is
established and the validity of bootstrap standard errors is shown. Doing so,
previous results from the literature are verified under low-level conditions
imposed on the individual components of the factor structure. Monte Carlo
evidence confirms the accuracy of the asymptotic theory in finite samples and
an empirical application illustrates the usefulness of the model to explain the
cross-sectional dependence between stock returns.


  The formation mechanism of neutron stars with extremely large magnetic field
strengths (magnetars) remains unclear. Some formation scenarios predict that
magnetars should be born with extremely high space velocities, >1000 km/s.
Using the Long Baseline Array in Australia, we have measured the proper motion
of the intermittently radio-bright magnetar J1550-5418 (1E 1547.0-5408) to be
9.2 +/- 0.6 mas/yr. For a likely distance of 6 +/- 2 kpc, the implied
transverse velocity is 280 + 130 - 120 km/s after correcting for Galactic
rotation. Along with the ~200 km/s transverse velocity measured for the
magnetar XTE J1810-197, this result suggests that formation pathways producing
large magnetic fields do not require very large birth kicks.


  This letter proposes the inverse LDM' and LU factorizations of a matrix
partitioned into 2x2 blocks, which include the square-root and division free
version. The proposed squareroot and division free inverse LDM' factorization
is applied to compute the initial estimation error covariance matrix Q for the
recursive V-BLAST algorithm, which can save K-1 divisions (where K is the
number of transmit antennas), and requires about the same computational
complexity as the corresponding algorithm to compute Q in the existing
recursive V-BLAST algorithm [8], [9]. The proposed square-root and division
free inverse LDM' factorization can also be applied to propose the square-root
and division free implementation for the squareroot V-BLAST algorithm in [5],
where the wide-sense Givens rotation in [14] is utilized. With respect to the
existing squareroot V-BLAST algorithms [5], [6], the proposed square-root and
division free V-BLAST algorithm requires about the same computational
complexity, and can avoid the square-root and division operations.


  This paper presents TextComplexityDE, a dataset consisting of 1000 sentences
in German language taken from 23 Wikipedia articles in 3 different
article-genres to be used for developing text-complexity predictor models and
automatic text simplification in German language. The dataset includes
subjective assessment of different text-complexity aspects provided by German
learners in level A and B. In addition, it contains manual simplification of
250 of those sentences provided by native speakers and subjective assessment of
the simplified sentences by participants from the target group. The subjective
ratings were collected using both laboratory studies and crowdsourcing
approach.


  In complex vector spaces maximal sets of equiangular lines, known as SICs,
are related to real quadratic number fields in a dimension dependent way. If
the dimension is of the form $n^2+3$ the base field has a fundamental unit of
negative norm, and there exists a SIC with anti-unitary symmetry. We give eight
examples of exact solutions of this kind, for which we have endeavoured to make
them as simple as we can---as a belated reply to the referee of an earlier
publication, who claimed that our exact solution in dimension 28 was too
complicated to be fit to print. An interesting feature of the simplified
solutions is that the components of the fiducial vectors largely consist of
algebraic units.


  In this note we present a simple Lax description of the hierarchy of the
intermediate long wave equation (ILW hierarchy). Although the linear inverse
scattering problem for the ILW equation itself was well known, here we give an
explicit expression for all higher flows and their Hamiltonian structure in
terms of a single Lax difference-differential operator.


  The X$^-$ trion is essentially an electron bound to an exciton. However, due
to the composite nature of the exciton, there is no way to write an
exciton-electron interaction potential. We can overcome this difficulty by
using a commutation technique similar to the one we introduced for excitons
interacting with excitons, which allows to take exactly into account the
close-to-boson character of the excitons. From it, we can obtain the X$^-$
trion creation operator in terms of exciton and electron. We can also derive
the X$^-$ trion ladder diagram between an exciton and an electron. These are
the basic tools for future works on many-body effects involving trions.


  We study compact configurations with a nontrivial wormholelike spacetime
topology supported by a complex ghost scalar field with a quartic
self-interaction. For this case, we obtain regular asymptotically flat
equilibrium solutions possessing reflection symmetry. We then show their
instability with respect to linear radial perturbations.


  By the works of Yu, Kim and Hakim-Murnaghan, we have a parameterization and
construction of all supercuspidal representations of a reductive $p$-adic group
in terms of supercuspidal data, when $p$ is sufficiently large. In this paper,
we will define a correspondence of supercuspidal data via moment maps and theta
correspondences over finite fields. Then we will show that local theta
correspondences between supercuspidal representations are completely described
by this notion. In Appendix B, we give a short proof of a result of Pan on
"depth preservation".


  Several locally deterministic interpretations of quantum mechanics are
presented and reviewed. The fundamental differences between these
interpretations are made transparent by explicitly showing what information is
carried locally by each physical system in an idealized experimental test of
Bell's theorem. This also shows how each of these models can be locally causal
and deterministic. First, a model is presented which avoids Bell's arguments
through the assumption that space-time inflated from an initial singularity,
which encapsulates the entire past light cone of every event in the universe.
From this assumption, it is shown how quantum mechanics can produce locally
consistent reality by choosing one of many possible futures at the time of the
singularity. Secondly, we review and expand the Parallel Lives interpretation
of Brassard and Raymond-Robichaud, which maintains local causality and
determinism by abandoning the strictest notion of realism. Finally, the two
ideas are combined, resulting in a parallel lives model in which lives branch
apart earlier, under the assumption of a single unified interaction history.
The physical content of weak values within each model is discussed, along with
related philosophical issues concerning free will.


  Recently, J. Teunissen reported a fully explicit method, namely the
current-limit approach, which claimed to overcome the dielectric relaxation
time restriction for the drift-diffusion plasma fluid model. In this comment,
we point out that the current-limit approach is not mathematically consistent,
and discuss about the possible reason why the inconsistency was not visibly
noticed.


  In this paper we introduce the usage of guidance vector fields for the
coordination and formation flight of fixed-wing aircraft. In particular, we
describe in detail the technological implementation of the formation flight
control for a fully distributed execution of the algorithm by employing the
open-source project Paparazzi. In this context, distributed means that each
aircraft executes the algorithm on board, each aircraft only needs information
about its neighbors, and the implementation is straightforwardly scalable to an
arbitrary number of vehicles, i.e., the needed resources such as memory or
computational power not necessarily scale with the number of total aircraft.
The coordination is based on commanding the aircraft to track circumferences
with different radii but sharing the same center. Consequently, the vehicles
will travel different distances but with the same speeds in order to control
their relative angles in the circumference, i.e., their orbital velocities. We
show the effectiveness of the proposed design with actual formation flights
during the drone parade in IMAV2017.


  We study processes with unstable particles in intermediate time-like states.
It is shown that the amplitudes squared of such processes factor exactly in the
framework of the model of unstable particles with continuous masses. Decay
widths and cross sections can then be represented in a universal factorized
form for an arbitrary set of interacting particles. This exact factorization is
caused by specific structure of propagators in the model. We formulate the
factorization method and perform a phenomenological analysis of the
factorization effects. The factorization method considerably simplifies
calculations while leading to compact and reasonable results.


  In the recent paper [3] it was shown that the consistency of the quantum
theory of a sterile scalar coupled to massive fermions requires the inclusion
of odd-power terms in the potential of scalar self-interaction. One of the most
important examples of a sterile scalar is the inflaton, that is typically a
real scalar field which does not belong to representations of particle physics
gauge groups, such as $SU(2)$. Here we explore the effects of the odd-power
terms in the inflaton potential on main observables, such as the scalar
spectral index $n_s$ and the tensor-to-scalar ratio $r$, in the case of a
strong, non-minimal coupling of the inflaton to gravity.


  We propose a novel scenario of primordial inflation in which the inflaton
goes through a spiral motion starting from around the top of a symmetry
breaking potential. We show that, even though inflation takes place for a field
value much smaller than Planck scale, it is possible to obtain relatively large
tensor to scalar ratio ($r \sim 0.1$) without fine tuning. The inflationary
observables perfectly match Planck data.


  A nonvanishing spectral density of the low-lying eigenmodes of the Dirac
operator naturally is a signal for dynamical chiral symmetry breaking
(D$\chi$SB) via the Banks-Casher relation. The low-lying eigenmodes alone
saturate the pseudoscalar channel and the corresponding propagator successfully
reproduces the pion mass. In this paper we investigate the effects on the mass
generation of hadrons other than pions. The evolution of these masses upon
inclusion of an increasing number of the low-lying eigenmodes is confronted
with the hadron mass spectrum upon removal of such eigenmodes.


  Classical simulations of high-temperature nuclear spin dynamics in solids are
known to accurately predict relaxation for spin 1/2 lattices with a large
number of interacting neighbors. Once the number of interacting neighbors
becomes four or smaller, classical simulations lead to noticeable
discrepancies. Here we attempt to improve the performance of the classical
simulations by adding a term representing two-spin quantum correlations. The
method is tested for a spin-1/2 chain. It exhibits good performance at shorter
times, but, at longer times, it is hampered by a singular behavior of the
resulting equations of motion.


  The paper is devoted to regularity theory of generalized solutions to
semilinear wave equations with a small nonlinearity. The setting is the one of
Colombeau algebras of generalized functions. It is shown that in one space
dimension, an initial singularity at the origin propagates along the
characteristic lines emanating from the origin, as in the linear case. The
proof relies on a fixed point theorem in the ultra-metric topology on the
algebras involved. The paper takes up the initiating research of the 1970s on
anomalous singularities in classical solutions to semilinear hyperbolic
equations and transplants the methods into the Colombeau setting.


  Bars in disky galaxies can be formed by interactions with other systems,
including those of comparable mass. It has long been established that the
effect of such interactions on galaxy morphology depends strongly on the
orbital configuration, in particular the orientation of the intrinsic spin of
the galactic disk with respect to its orbital angular momentum. Prograde
encounters modify the morphology strongly, including the formation of tidally
induced bars, while retrograde flybys should have little effect on morphology.
Recent works on the subject reached conflicting conclusions, one using the
impulse approximation and claiming no dependence on this angle in the
properties of tidal bars. To resolve the controversy, we performed
self-consistent N-body simulations of hyperbolic encounters between two
identical Milky Way-like galaxies assuming different velocities and impact
parameters, with one of the galaxies on a prograde and the other on a
retrograde orbit. The galaxies were initially composed of an exponential
stellar disk and an NFW dark halo, and were stable against bar formation in
isolation for 3 Gyr. We find that strong tidally induced bars form only in
galaxies on prograde orbits. For smaller impact parameters and lower relative
velocities the bars are stronger and have lower pattern speeds. Stronger bars
undergo extended periods of buckling instability that thicken their vertical
structure. The encounters also lead to the formation of two-armed spirals with
strength inversely proportional to the strength of the bars. We conclude that
proper modeling of prograde and retrograde encounters cannot rely on the
simplest impulse approximation.


  This paper investigates the problem of inertial navigation system (INS)
filter design through the lens of symmetry. The extended Kalman filter (EKF)
and its variants, have been the staple of INS filtering for 50 years; however,
recent advances in inertial navigation systems have exploited matrix Lie group
structure to design stochastic filters and state observers that have been shown
to display superior performance compared to classical solutions. In this work
we consider the case where a vehicle has an inertial measurement unit (IMU) and
a global navigation satellite system (GNSS) receiver. We show that all the
modern variants of the EKF for these sensors can be interpreted as the recently
proposed Equivariant Filter (EqF) design methodology applied to different
choices of symmetry group for the INS problem. This leads us to propose two new
symmetries for the INS problem that have not been considered in the prior
literature, and provide a discussion of the relative strengths and weaknesses
of all the different algorithms. We believe the collection of symmetries that
we present here capture all the sensible choices of symmetry for this problem
and sensor suite, and that the analysis provided is indicative of the relative
real-world performance potential of the different algorithms.


  We prove the Tate conjecture for divisor classes and the Mumford-Tate
conjecture for the cohomology in degree 2 for varieties with $h^{2,0}=1$ over a
finitely generated field of characteristic 0, under a mild assumption on their
moduli. As an application of this general result, we prove the Tate and
Mumford-Tate conjectures for some classes of algebraic surfaces with $p_g=1$.


  This work is devoted to the discussion and characterization of the tensor
$2^{-(-)}$ meson spectrum, by making use of the Coulomb gauge Hamiltonian
approach to QCD, with the interactions being given by an improved confining
potential and a transverse hyperfine interaction, whose kernel is a Yukawa-type
potential. Our aim is to study the basic features of $2^{-(-)}$ mesons within
an unified framework through the whole range of quark masses. We concentrate
our investigation on predictions of expected but yet-unobserved ground states
of unflavored light mesons and on charmonium and bottomonium states. The
numerical results are compared with existing literature.


  It is strange but fruitful to think about the functions as random processes.
Any function can be viewed as a martingale (in many different ways) with
discrete time. But it can be useful to have continuous time too. Processes can
emulate functions, expectation of profit functional on the solution of
stochastic differential equation can emulate the functional on usual familiar
functions. The advantage is that now we have "all" admissible functions
"enumerated" as solutions of one stochastic differential equation, and choosing
the best function optimizing a given functional becomes a problem of choosing
the right control process. But such problem has been long since solved in the
part of mathematics called Stochastic Optimal Control. So-called Bellman
equation reduces an infinite dimensional problem of choosing the best control
to a finite dimensional (but non-linear as a rule) PDE called Bellman equation.
Its solution, called Bellman function of a given optimization problem, gives us
a lot of information about optimum and optimizers. This method gave some
interesting results in the classical Harmonic Analysis, having on the surface
nothing to do with probability. Sometimes the results obtained by this method
did not find "classical" proofs so far. It is especially well-suited to
estimates of singular integrals, probably because of the underlying
probabilistic structure of classical singular integrals.


  We are conducting a large survey of distant clusters of galaxies using radio
sources with bent jets and lobes as tracers. These radio sources are driven by
AGN and achieve their bent morphologies through interaction with the
surrounding gas found in clusters of galaxies. Based on low-redshift studies,
these types of sources can be used to identify clusters very efficiently. We
present initial results from our survey of 653 bent-double radio sources with
optical hosts too faint to appear in the SDSS. The sample was observed in the
infrared with Spitzer, and it has revealed $\sim$200 distant clusters or
proto-clusters in the redshift range $z\sim0.7 - 3.0$. The sample of
bent-doubles contains both quasars and radio galaxies enabling us to study both
radiative and kinetic mode feedback in cluster and group environments at a wide
range of redshifts.


  We consider Reeb dynamics on the 3-sphere associated to a tight contact form.
Our main result gives necessary and sufficient conditions for a periodic Reeb
orbit to bound a disk-like global section for the Reeb flow, when the contact
form is assumed to be non-degenerate.


  Consider a Kleinian singularity $ \mathbb{C}^2/\Gamma $, where $ \Gamma $ is
a finite subgroup of $ SL_2(\mathbb{C}) $. In this paper, we introduce a
natural stack compactifying the singularity by adding a smooth stacky divisor,
and we show that sets of framed sheaves on this stack satisfying certain
additional criteria are closely related to a class of Nakajima quiver
varieties. This partially extends our previous work on punctual Hilbert schemes
of Kleinian singularities.


  The classical methods of multivariate analysis are based on the eigenvalues
of one or two sample covariance matrices. In many applications of these
methods, for example to high dimensional data, it is natural to consider
alternative hypotheses which are a low rank departure from the null hypothesis.
For rank one alternatives, this note provides a representation for the joint
eigenvalue density in terms of a single contour integral. This will be of use
for deriving approximate distributions for likelihood ratios and linear
statistics used in testing.


  To perform contingent teaching and be responsive to students' needs during
class, lecturers must be able to quickly assess the state of their audience.
While effective teachers are able to gauge easily the affective state of the
students, as class sizes grow this becomes increasingly difficult and less
precise. The Wits Intelligent Teaching System (WITS) aims to assist lecturers
with real-time feedback regarding student affect. The focus is primarily on
recognising engagement or lack thereof. Student engagement is labelled based on
behaviour and postures that are common to classroom settings. These proxies are
then used in an observational checklist to construct a dataset of engagement
upon which a CNN based on AlexNet is successfully trained and which
significantly outperforms a Support Vector Machine approach. The deep learning
approach provides satisfactory results on a challenging, real-world dataset
with significant occlusion, lighting and resolution constraints.


  In view of the fundamental distinction between the force-controlled model and
the displacement-controlled model in buckling problems of structures and the
complexity of the asymptotic post-buckling analysis traditionally based on the
force-controlled model, alternatively, we provide a straightforward theoretical
procedure of the energy method for the buckling and post-buckling analysis
completely based on the displacement-controlled model. The Euler buckling
behavior is analytically tackled as a static displacement-controlled process as
an example of the theoretical procedure, where no force potential energy
component but compression and bending strain energy components are considered
precisely at the deformed configuration for the total potential energy of the
beams. Analytical solutions to the potential energy, structural deformation,
internal forces and their critical results are obtained in closed-form for the
beams with six typical boundary conditions. We find that these beams have only
one unique but universal normalized potential energy surface depending on two
dimensionless quantities. The valley bottom pathways on the potential energy
surface show that the critical buckling state is not only a bifurcation point
but also a valley-ridge inflection point, and the energy increases
quadratically before the point and increases linearly with a slope of 2 beyond
the point. The axial forces are gradually increasing during post-buckling, but
are almost constant, indicating a symmetric neutral bifurcation buckling. Our
theoretical expressions generally agree with the counterparts of the
force-controlled model but exactly indicate somewhat differences. The present
analytical procedure is basically useful to investigate any
displacement-controlled buckling problems of beams, plates and shells.


  Let $R$ be a finitely $\mathbb{N}$-graded algebra over a Noetherian ring. In
this paper we study the asymptotic behaviour of the so called $v$-number
$\mathrm{w}_P(J^{\underline{n}}M/I^{\underline{n}}N)$ as function of
$\underline{n}$ where $N\subset M$ are finitely generated $R$-modules, and
$I_1\subset J_1,\dots,I_r\subset J_r$ are homogeneous ideals. We prove that
$\mathrm{w}_P(M/I^{\underline{n}}N)$ and
$\mathrm{w}_P(I^{\underline{n}}M/I^{\underline{n}+\underline{1}}N)$ are
eventually the minimum of $r$ liner functions.


  This paper makes a formal study of asymptotically hyperbolic Einstein metrics
given, as conformal infinity, a conformal manifold with boundary. The space on
which such an Einstein metric exists thus has a finite boundary in addition to
the usual infinite boundary and a corner where the two meet. On the finite
boundary a constant mean curvature umbilic condition is imposed. First, recent
work of Nozaki, Takayanagi, and Ugajin is generalized and extended showing that
such metrics cannot have smooth compactifications for generic corners embedded
in the infinite boundary. A model linear problem is then studied: a formal
expansion at the corner is derived for eigenfunctions of the scalar Laplacian
subject to certain boundary conditions. In doing so, scalar ODEs are studied
that are of relevance for a broader class of boundary value problems and also
for the Einstein problem. Next, unique formal existence at the corner, up to
order at least equal to the boundary dimension, of Einstein metrics in a
cornered asymptotically hyperbolic normal form which are polyhomogeneous in
polar coordinates is demonstrated for arbitrary smooth conformal infinity.
Finally it is shown that, in the special case that the finite boundary is taken
to be totally geodesic, there is an obstruction to existence beyond this order,
which defines a conformal hypersurface invariant.


  A set of 41 nearby stars (closer than 25 pc) is investigated which have very
wide binary and common proper motion (CPM) companions at projected separations
between 1000 and $200 000$ AU. These companions are identified by astrometric
positions and proper motions from the NOMAD catalog. Based mainly on measures
of chromospheric and X-ray activity, age estimation is obtained for most of 85
identified companions. Color -- absolute magnitude diagrams are constructed to
test if CPM companions are physically related to the primary nearby stars and
have the same age. Our carefully selected sample includes three remote white
dwarf companions to main sequence stars and two systems (55 Cnc and GJ 777A) of
multiple planets and distant stellar companions. Ten new CPM companions,
including three of extreme separations, are found. Multiple hierarchical
systems are abundant; more than 25% of CPM components are spectroscopic or
astrometric binaries or multiples themselves. Two new astrometric binaries are
discovered among nearby CPM companions, GJ 264 and HIP 59000 and preliminary
orbital solutions are presented. The Hyades kinematic group (or stream) is
presented broadly in the sample, but we find few possible thick disk objects
and none halo stars. It follows from our investigation that moderately young
(age $\lesssim 1$ Gyr) thin disk dwarfs are the dominating species in the near
CPM systems, in general agreement with the premises of the dynamical survival
paradigm. Some of the multiple stellar systems with remote CPM companions
probably undergo the dynamical evolution on non-coplanar orbits, known as the
Kozai cycle.


  Usually microscopic electrostatic field around charged impurity ions is
neglected when the ionization energy is concerned. The ionization energy is
considered to be equal to that of a lonely impurity atom. Here the energy of
the electrostatic field around charged impurity ions in semiconductor is taken
into account. It is shown that the energy of this field contributes to decrease
in the effective ionization energy. At high enough current carriers
concentration the effective ionization energy becomes zero.


  We construct an algorithm that generates large, band-diagonal transition
matrices for a totally asymmetric exclusion process (TASEP) with local hopping
rate inhomogeneities. The matrices are diagonalized numerically to find
steady-state currents of TASEPs with local variations in hopping rate. The
results are then used to investigate clustering of slow codons along mRNA.
Ribosome density profiles near neighboring clusters of slow codons interact,
enhancing suppression of ribosome throughput when such bottlenecks are closely
spaced. Increasing the slow codon cluster size, beyond $\approx 3-4$, does not
significantly reduce ribosome current. Our results are verified by extensive
Monte-Carlo simulations and provide a biologically-motivated explanation for
the experimentally-observed clustering of low-usage codons.


  The goal of this paper is to study the behaviour of view-count in YouTube. We
first propose several bio-inspired models for the evolution of the view-count
of YouTube videos. We show, using a large set of empirical data, that the
view-count for 90% of videos in YouTube can indeed be associated to at least
one of these models, with a Mean Error which does not exceed 5%. We derive
automatic ways of classifying the view-count curve into one of these models and
of extracting the most suitable parameters of the model. We study empirically
the impact of videos' popularity and category on the evolution of its
view-count. We finally use the above classification along with the automatic
parameters extraction in order to predict the evolution of videos' view-count.


  We report on attosecond-scale control of high-harmonic and electron emission
from plasma mirrors driven by relativistic-intensity near-single-cycle
lightwaves at kHz repetition rate. By controlling the waveform of the intense
light transient, we reproducibly form a sub-cycle temporal intensity gate at
the plasma mirror surface, leading to the observation of extreme ultraviolet
spectral continua, characteristic of isolated attosecond pulse generation. We
also observe the correlated emission of a waveform-dependent relativistic
electron beam, paving the way towards fully lightwave-controlled dynamics of
relativistic plasma mirrors.


  Uniform and accurate photometric calibration plays an important role in the
current and next-generation wide-field imaging surveys. Herein, we review the
modern photometric calibration methods, including the classic standard star
method, "hardware/observation-driven" methods (such as the Ubercalibration,
Hypercalibration, and Forward Global Calibration Methods), and
"software/physics-driven" methods (e.g., the Stellar Locus Regression, Stellar
Locus, and Stellar Color Regression Methods). Further, we discuss their
advantages, limitations, and future developments toward millimagnitude
precision calibration.