  We introduce the path space over a general metrisable space. Elements of this
space are paths, which are pairs consisting of a closed subset of the real line
and a cadlag function that is defined on that subset and takes values in the
metrisable space. We equip the space of all paths with topologies that
generalise Skorohod's J1 and M1 topologies, prove that these topologies are
Polish, and derive compactness criteria.
  The central idea is that the closed graph (in case of the J1 topology) and
the filled-in graph (in case of the M1 topology) of a path can naturally be
viewed as totally ordered compact sets. We define a variant of the Hausdorff
metric that measures the distance between two compact sets, each of which is
equipped with a total order. We show that the topology generated by this metric
is Polish and derive a compactness criterion. Specialising to closed or
filled-in graphs then yields Skorohod's J1 and M1 topologies, generalised to
functions that need not all be defined on the same domain.


  To analyse stellar populations in galaxies a widely used method is to apply
theoretically derived responses of stellar spectra and line indices to element
abundance variations, hereafter referred to as response functions. These are
applied in a differential way, to base models, in order to generate spectra or
indices with different abundance patterns. In this paper sets of such response
functions for three different stellar evolutionary stages are tested with new
empirical [Mg/Fe] abundance data for the MILES stellar spectral library. Recent
theoretical models and observations are used to investigate the effects of
[Fe/H], [Mg/H] and overall [Z/H] on spectra, via ratios of spectra for similar
stars. Global effects of changes in abundance patterns are investigated
empirically through direct comparisons of similar stars from the MILES library,
highlighting the impact of abundance effects in the blue part of the spectrum,
particularly for lower temperature stars. It is found that the relative
behaviour of iron sensitive line indices are generally well predicted by
response functions, whereas Balmer line indices are not. Other indices tend to
show large scatter about the predicted mean relations. Implications for element
abundance and age studies in stellar populations are discussed and ways forward
are suggested to improve the match with behaviours of spectra and line strength
indices observed in real stars.


  Tracking an object's 6D pose, while either the object itself or the observing
camera is moving, is important for many robotics and augmented reality
applications. While exploiting temporal priors eases this problem,
object-specific knowledge is required to recover when tracking is lost. Under
the tight time constraints of the tracking task, RGB(D)-based methods are often
conceptionally complex or rely on heuristic motion models. In comparison, we
propose to simplify object tracking to a reinforced point cloud (depth only)
alignment task. This allows us to train a streamlined approach from scratch
with limited amounts of sparse 3D point clouds, compared to the large datasets
of diverse RGBD sequences required in previous works. We incorporate temporal
frame-to-frame registration with object-based recovery by frame-to-model
refinement using a reinforcement learning (RL) agent that jointly solves for
both objectives. We also show that the RL agent's uncertainty and a
rendering-based mask propagation are effective reinitialization triggers.


  The thermal instanton determinant for the gauge group $SU(2)$ can be reduced
to a form involving two simple functions. Various boundary conditions can
easily incorporated. Only a two dimensional integral has to be done
numerically. As an example we compute the contribution to the free energy of
$\mathcal{N}=1$ theory.


  Suppose n>2, let M,M' be n-dimensional connected complete finite-volume
hyperbolic manifolds with non-empty geodesic boundary, and suppose that the
fundamental group of M is quasi-isometric to the fundamental group of M' (with
respect to the word metric). Also suppose that if n=3, then the boundaries of M
and of M' are compact. We show that M is commensurable with M'. Moreover, we
show that there exist homotopically equivalent hyperbolic 3-manifolds with
non-compact geodesic boundary which are not commensurable with each other.
  We also prove that if M is as above and G is a finitely generated group which
is quasi-isometric to the fundamental group of M, then there exists a
hyperbolic manifold with geodesic boundary M'' with the following properties:
M'' is commensurable with M, and G is a finite extension of a group which
contains the fundamental group of M'' as a finite-index subgroup.


  Polyphonic sound event detection (polyphonic SED) is an interesting but
challenging task due to the concurrence of multiple sound events. Recently, SED
methods based on convolutional neural networks (CNN) and recurrent neural
networks (RNN) have shown promising performance. Generally, CNN are designed
for local feature extraction while RNN are used to model the temporal
dependency among these local features. Despite their success, it is still
insufficient for existing deep learning techniques to separate individual sound
event from their mixture, largely due to the overlapping characteristic of
features. Motivated by the success of Capsule Networks (CapsNet), we propose a
more suitable capsule based approach for polyphonic SED. Specifically, several
capsule layers are designed to effectively select representative frequency
bands for each individual sound event. The temporal dependency of capsule's
outputs is then modeled by a RNN. And a dynamic threshold method is proposed
for making the final decision based on RNN outputs. Experiments on the TUT-SED
Synthetic 2016 dataset show that the proposed approach obtains an F1-score of
68.8% and an error rate of 0.45, outperforming the previous state-of-the-art
method of 66.4% and 0.48, respectively.


  The paper considers one-dimensional flows of polytropic (calorically ideal)
gas. These flows include three cases of gas dynamics: plain one-dimensional
flows (one-dimensional space), radially symmetric flows in two-dimensional
space and spherically symmetric flows in three-dimensional space. Starting with
the difference schemes which have conservation laws of mass and energy (as well
as conservation of momentum and the center of mass motion for the plain
one-dimensional flows), we find difference schemes which also have additional
conservation laws for the special values of the adiabatic exponent $\gamma = 1
+ 1 /d $, where $d$ is the space dimension.


  The complex manifold CP^n x CP^{n+1} with symplectic form
\sigma_\mu=\sigma_{CP^n}+\mu\sigma_{CP^{n+1}}, where \sigma_{CP^n} and
\sigma_{CP^{n+1}} are normalized Fubini-Study forms, n a natural number and
\mu>1 a real number, contains a natural Lagrangian sphere L^{\mu}. We prove
that the Dehn twist along L^{\mu} is symplectically isotopic to the identity
for all \mu>1. This isotopy can be chosen so that it pointwise fixes a complex
hypersurface in CP^n x CP^{n+1} and lifts to the blow-up of CP^n x CP^{n+1}
along a complex n-dimensional submanifold.


  Program reduction is a prevalent technique to facilitate compilers' debugging
by automatically minimizing bug-triggering programs. Existing program reduction
techniques are either generic across languages (e.g., Perses and Vulcan) or
specifically customized for one certain language by employing language-specific
features, like C-Reduce. However, striking the balance between generality
across multiple programming languages and specificity to individual languages
in program reduction is yet to be explored. This paper proposes LPR, the first
technique utilizing LLMs to perform language-specific program reduction for
multiple languages. The core insight is to utilize both the language-generic
syntax level program reduction (e.g., Perses) and the language-specific
semantic level program transformations learned by LLMs. Alternately,
language-generic program reducers efficiently reduce programs into
1-tree-minimality, which is small enough to be manageable for LLMs; LLMs
effectively transform programs via the learned semantics to expose new
reduction opportunities for the language-generic program reducers to further
reduce the programs. Our extensive evaluation on 50 benchmarks across three
languages (C, Rust, and JavaScript) has highlighted LPR's practicality and
superiority over Vulcan, the state-of-the-art language-generic program reducer.
For effectiveness, LPR surpasses Vulcan by producing 24.93%, 4.47%, and 11.71%
smaller programs on benchmarks in C, Rust and JavaScript. Moreover, LPR and
Vulcan have demonstrated their potential to complement each other. By using
Vulcan on LPR's output for C programs, we achieve program sizes comparable to
those reduced by C-Reduce. For efficiency, LPR takes 10.77%, 34.88%, 36.96%
less time than Vulcan to finish all benchmarks in C, Rust and JavaScript,
separately.


  Modern information technology services largely depend on cloud
infrastructures to provide their services. These cloud infrastructures are
built on top of datacenter networks (DCNs) constructed with high-speed links,
fast switching gear, and redundancy to offer better flexibility and resiliency.
In this environment, network traffic includes long-lived (elephant) and
short-lived (mice) flows with partitioned and aggregated traffic patterns.
Although SDN-based approaches can efficiently allocate networking resources for
such flows, the overhead due to network reconfiguration can be significant.
With limited capacity of Ternary Content-Addressable Memory (TCAM) deployed in
an OpenFlow enabled switch, it is crucial to determine which forwarding rules
should remain in the flow table, and which rules should be processed by the SDN
controller in case of a table-miss on the SDN switch. This is needed in order
to obtain the flow entries that satisfy the goal of reducing the long-term
control plane overhead introduced between the controller and the switches. To
achieve this goal, we propose a machine learning technique that utilizes two
variations of reinforcement learning (RL) algorithms-the first of which is
traditional reinforcement learning algorithm based while the other is deep
reinforcement learning based. Emulation results using the RL algorithm show
around 60% improvement in reducing the long-term control plane overhead, and
around 14% improvement in the table-hit ratio compared to the Multiple Bloom
Filters (MBF) method given a fixed size flow table of 4KB.


  We study a one-dimensional Ising model with a magnetic field and show that
tilting the field induces a transition to quantum chaos. We explore the
stationary states of this Hamiltonian to show the intimate connection between
entanglement and avoided crossings. In general entanglement gets exchanged
between the states undergoing an avoided crossing with an overall enhancement
of multipartite entanglement at the closest point of approach, simultaneously
accompanied by diminishing two-body entanglement as measured by concurrence. We
find that both for stationary as well as nonstationary states, nonintegrability
leads to a destruction of two-body correlations and distributes entanglement
more globally.


  Energy harvesting has emerged as a powerful technology for complementing
current battery-powered communication systems in order to extend their
lifetime. In this paper a general framework is introduced for the optimization
of communication systems in which the transmitter is able to harvest energy
from its environment. Assuming that the energy arrival process is known
non-causally at the transmitter, the structure of the optimal transmission
scheme, which maximizes the amount of transmitted data by a given deadline, is
identified. Our framework includes models with continuous energy arrival as
well as battery constraints. A battery that suffers from energy leakage is
studied further, and the optimal transmission scheme is characterized for a
constant leakage rate.


  We propose a scheme to implement a supersensitive estimation of the coupling
strength in a hybrid optomechanical system which consists of a
cavity-Bose-Einstein condensate system coupled to an impurity. This method can
dramatically improve the estimation precision even when the involved photon
number is small. The quantum Fisher information indicates that the Heisenberg
scale sensitivity of the coupling rate could be obtained when the photon loss
rate is smaller than the corresponding critical value in the input of either
coherent state or squeezed state. The critical photon decay rate for the
coherent state is larger than that of the squeezed state, and the coherent
state input case is more robust against the photon loss than the squeezed state
case. We also present the measurement scheme which can saturate the quantum
Cram\'er-Rao bound.


  We consider the point process of signal strengths emitted from transmitters
in a wireless network and observed at a fixed position. In our model,
transmitters are placed deterministically or randomly according to a hard core
or Poisson point process and signals are subjected to power law path loss and
random propagation effects that may be correlated between transmitters.
  We provide bounds on the distance between the point process of signal
strengths and a Poisson process with the same mean measure, assuming correlated
log-normal shadowing. For "strong shadowing" and moderate correlations, we find
that the signal strengths are close to a Poisson process, generalizing a
recently shown analogous result for independent shadowing.


  We propose a stochastic model for the diffusion of topics entering a social
network modeled by a Watts-Strogatz graph. Our model sets into play an implicit
competition between these topics as they vie for the attention of users in the
network. The dynamics of our model are based on notions taken from real-world
OSNs like Twitter where users either adopt an exogenous topic or copy topics
from their neighbors leading to endogenous propagation. When instantiated
correctly, the model achieves a viral regime where a few topics garner
unusually good response from the network, closely mimicking the behavior of
real-world OSNs. Our main contribution is our description of how clusters of
proximate users that have spoken on the topic merge to form a large giant
component making a topic go viral. This demonstrates that it is not weak ties
but actually strong ties that play a major part in virality. We further
validate our model and our hypotheses about its behavior by comparing our
simulation results with the results of a measurement study conducted on real
data taken from Twitter.


  For communications in the presence of eavesdroppers, random components are
often used in code design to camouflage information from eavesdroppers. In
broadcast channels without eavesdroppers, Marton error-correcting coding
comprises random components which allow correlation between auxiliary random
variables representing independent messages. In this paper, we study if Marton
coding alone can ensure individual secrecy in the two-receiver discrete
memoryless broadcast channel with a passive eavesdropper. Our results show that
in accordance to the principle of Wyner secrecy coding, this is possible and
Marton coding alone guarantees individual secrecy. However, this comes with a
penalty of requiring stricter channel conditions.


  Recently suggested causal principal value and causal prescriptions for the
"spurious singularity" in light-cone gauge theories are nothing but the
different guises of usual Mandelstam-Leibbrandt prescription.


  We investigate synthesis of heavy elements in a collapsar. We have calculated
detailed composition of magnetically driven jets ejected from a collapsar,
which is based on long-term, magneto-hydrodynamic simulations of a rapidly
rotating massive star of 40Msun during core collapse. We follow evolution of
abundances of about 4000 nuclides from the collapse phase to the ejection phase
through the jet generation phase with use of two large nuclear reaction
networks. We find that the r-process successfully operates in the jets, so that
U and Th are synthesized abundantly when the progenitor has large magnetic
field of 10^{12} G and rapidly rotating core. Abundance pattern inside the jets
is similar compared to that of r-elements in the solar system. Heavy
neutron-rich nuclei \sim 0.01Msun can be ejected from the collapsar. The
detailed abundances depend on nuclear properties of mass model, beta-decay
rate, and fission, for nuclei near the neutron drip line. Furthermore, we find
that p-nuclei are produced without seed nuclei: not only light p-nuclei, such
as Se74, Kr78, Sr84, and Mo92, but also heavy p-nuclei, In113, Sn115, and
La138, can be abundantly synthesized in the jets. The amounts of p-nuclei in
the ejecta are much greater than those in core-collapse supernovae (SNe). In
particular, Mo92, In113, Sn115, and La138 deficient in the SNe, are
significantly produced in the ejecta.


  The superconducting diode effect has been recently reported in a variety of
systems and different symmetry breaking mechanisms have been examined. However,
the frequency range of these potentially important devices still remains
obscure. We investigated superconducting micro-bridges of Nb$_{3}$Sn in
out-of-plane magnetic fields; optimum magnetic fields of $\sim$10 mT generate
$\sim $10% diode efficiency, while higher fields of $\sim$15-20 mT quench the
effect. The diode changes its polarity with magnetic field reversal. We
documented superconductive diode rectification at frequencies up to 100 kHz,
the highest reported as of today. Interestingly, the bridge resistance during
diode operation reaches a value that is a factor of two smaller than in its
normal state, which is compatible with the vortex-caused mechanism of
resistivity. This is confirmed by finite element modeling based on
time-dependent Ginzburg-Landau equations. To explain experimental findings, no
assumption of lattice thermal inequilibrium was required. Dissimilar edges of
the superconductor strip can be responsible for the inversion symmetry breaking
by vortex penetration barrier; visual evidence of this opportunity was revealed
by scanning electron microscopy. Estimates are in favor of much higher (GHz)
range of frequencies for this type of diode.


  For positive integers $d$ and $n$, let $[n]^d$ be the set of all vectors
$(a_1,a_2,\dots, a_d)$, where $a_i$ is an integer with $0\leq a_i\leq n-1$. A
subset $S$ of $[n]^d$ is called a \emph{Sidon set} if all sums of two (not
necessarily distinct) vectors in $S$ are distinct.
  In this paper, we estimate two numbers related to the maximum size of Sidon
sets in $[n]^d$. First, let $\mathcal{Z}_{n,d}$ be the number of all Sidon sets
in $[n]^d$. We show that $\log (\mathcal{Z}_{n,d})=\Theta(n^{d/2})$, where the
constants of $\Theta$ depend only on $d$. Next, we estimate the maximum size of
Sidon sets contained in a random set $[n]^d_p$, where $[n]^d_p$ denotes a
random set obtained from $[n]^d$ by choosing each element independently with
probability $p$.


  We investigate the dynamics of an active particle in two-dimensional
spherical crystals, which provide an ideal environment to illustrate the
interplay of active particle and crystallographic defects. A moving active
particle is observed to be surrounded by localized topological defects,
becoming a dressed active particle. Such a physical picture characterizes both
the lattice distortion around the moving particle and the healing of the
distorted lattice in its trajectory. We find that the dynamical behaviors of an
active particle in both random and ballistic motions uniformly conform to this
featured scenario, whether the particle is initially a defect or not. We
further observe that the defect pattern around a dressed ballistic active
particle randomly oscillates between two well-defined wing-like defect motifs
regardless of its speed. The established physical picture of dressed active
particles in this work partially deciphers the complexity of the intriguing
nonequilibrium behaviors in active crystals, and opens the promising
possibility of introducing the activity to engineer defects, which has strong
connections with the design of materials.


  Motivated by the readout scheme in interferometric gravitational-wave
detectors, we consider the device which measures the expectation value of the
photon annihilation and creation operators for output optical field from the
main interferometer. As the result, the eight-port homodyne detection is
rediscovered as such a device. We evaluate the noise spectral density in this
measurement. We also briefly discuss on the application of our results to the
readout scheme of gravitational-wave detectors. We call this measurement scheme
to measure these expectation values as "double balanced homodyne detection."


  This is the initial paper in a series presenting the first optical detections
and subsequent follow-up spectroscopy of known Southern Galactic supernova
remnants (SNRs) previously discovered in the radio. These new detections come
from the AAO/UKST HAlpha survey of the Southern Galactic plane which has opened
up fresh opportunities to study Galactic remnants. Here we present the first
optical imaging and follow-up spectra of Galactic SNR G279.0+1.1 where a series
of 14 small-scale fragmented groups of HAlpha filaments have been discovered in
a ~2.3 deg. area centred on G279.0+1.1. Individually they are somewhat
inconspicuous but collectively they are completely enclosed within the overall
radio contours of this known SNR. Three of these filamentary groupings are
particularly prominent and optical spectra have been obtained across two of
them. Their morphological structure and spectral characteristics are typical of
optically detected SNR filaments. Very strong [S II] emission relative to H has
been detected with [S II]/HAlpha 0.7 and 1.1, confirming strong, shock heated
emission. This is sufficient to classify these filaments in the likely SNR
domain and therefore indicating a direct connection with the radio remnant.
Other typical SNR emission lines such as [O II] at 3727A, HBeta, [O III] at
4959 and 5007A, HAlpha and [N II] at 6548 and 6584A were also detected, lending
strong support to an SNR origin of these optical filaments. The value and
insights that these optical data can provide for known remnants are discussed
along with their relevance to the Galactic nitrogen abundance. A serendipitous
discovery of an adjacent H II region is also briefly described.


  We present new diagonal solutions of the reflection equation for elliptic
solutions of the star-triangle relation. The models considered are related to
the affine Lie algebras $A_n^{(1)},B_n^{(1)},C_n^{(1)},D_n^{(1)}$ and
$A_n^{(2)}$. We recover all known diagonal solutions associated with these
algebras and find how these solutions are related in the elliptic regime.
Furthermore, new solutions of the reflection equation follow for the associated
vertex models in the trigonometric limit.


  The non-LTE state of the hydrogen gas in isothermal transonic decretion disks
around a B1V star has been calculated by an iterative method in order to
explore the basic physical process in the disk. This dynamical model is
characterized by a density law in the equatorial plane of $\rho(R) \propto
R^{-3.5}$. The continuous radiation is calculated with the $\Lambda$ iteration
in the integral form, while we adopt a single-flight escape probability for
lines. We describe the non-LTE state, the radiation flow and conversion in the
disk. We conclude that the stellar Balmer continuum plays a key role in the
non-LTE state of the disk. The examination of the local energy gain and loss
suggests that the disk temperature has double minima along the equatorial plane
in the optically thick case: the intermediate region caused by deficient
ultraviolet radiation and the outer Lyman $\alpha$ cooling region. We have also
calculated some observable quantities, such as the spectral energy
distribution, the $UBV$ colors, the infrared excess and the Balmer line
profiles. Our calculations with the mass loss rate less than $10^{-10}
M_{\odot} {\rm yr}^{-1}$ reproduce the observed continuum quantities. However,
we could not get large H$\alpha$ emission strength observed in Be stars. We
suggest that the density gradient of the Be star disk is slower than that of
the isothermal decretion disk.


  According to the widely accepted opinion, classical (statistical) physics
does not support objective indeterminism, since the statistical laws of
classical physics allow a deterministic hidden background, while --- as Arthur
Fine writes polemizing with Gr\"unbaum --- "{\sl the antilibertarian position
finds little room to breathe in a statistical world if we take laws of the
quantum theory as exemplars of the statistical laws in such a world. So, it
appears that, contrary to what Gr\"unbaum claims, the libertarians' 'could have
done otherwise' does indeed find support from indeterminism if we take the
indeterministic laws to be of the sort found in the quantum theory.}" In this
paper I will show that, quite the contrary, quantum mechanics does not save
free will. For instance, the EPR experiments are compatible with a
deterministic world. They admit a deterministic local hidden parameter
description if the deterministic model is 'allowed' to describe not only the
measurement outcomes, but also the outcomes of the 'decisions' whether this or
that measurement will be performed. So, the derivation of the freedom of the
will from quantum mechanics is a tautology: from the assumption that the world
is indeterministic it is derived that the world cannot be deterministic.


  A finitely generated group is said to be an automata group if it admits a
faithful self-similar finite-state representation on some regular $m$-tree. We
prove that if $G$ is a subgroup of an automata group, then for each finitely
generated abelian group $A$, the wreath product $A \wr G$ is a subgroup of an
automata group. We obtain, for example, that $C_2 \wr (C_{2} \wr \mathbb{Z})$,
$\mathbb{Z} \wr (C_2 \wr \mathbb{Z})$, $C_2 \wr (\mathbb{Z} \wr \mathbb{Z})$,
and $\mathbb{Z} \wr (\mathbb{Z} \wr \mathbb{Z})$ are subgroups of automata
groups. In the particular case $\mathbb{Z} \wr (\mathbb{Z} \wr \mathbb{Z})$, we
prove that it is a subgroup of a two-letters automata group; this solves
Problem 15.19 - (b) of the Kourovka Notebook proposed by A. M. Brunner and S.
Sidki in 2000 [8, 17].


  Observations in the near- and mid-ultraviolet (NUV: 2000--3500$\AA$)
performed with the NASA Swift UVOT instrument have revealed that
optically-normal SNe Ia feature NUV-optical color evolution that can be divided
into NUV-blue and NUV-red groups, with roughly one-third of the observed events
exhibiting NUV-blue color curves. Combined with an apparent correlation between
NUV-blue events and the detection of unburned carbon in the optical spectra,
the grouping might point to a fundamental difference within the normal SN Ia
classfication. Recognizing the dramatic temporal evolution of the NUV-optical
colors for all SNe Ia, as well as the existence of this sub-division, is
important for studies that compare nearby SNe Ia with intermediate or high-$z$
events, for the purpose of the cosmological utilization of SNe Ia. SN 2011fe is
shown to be of the NUV-blue groups, which will be useful towards interpretation
of the gamma-ray line results from the INTEGRAL SPI campaign on SN 2011fe.


  The motion of neutral particles with magnetic moments in an inhomogeneous
magnetic field is described in a quantum mechanical framework. The validity of
the semi-classical approximations which are generally used to describe these
phenomena is discussed. Approximate expressions for the evolution operator are
derived and compared to the exact calculations. Focusing and spin-flip
phenomena are predicted. The reliability of Stern-Gerlach experiments to
measure spin projections is assessed in this framework.


  The g_{9/2} shell of identical particles is the first one for which one can
have seniority-mixing effects. We consider three interactions: a delta
interaction that conserves seniority, a quadrupole-quadrupole (QQ) interaction
that does not, and a third one consisting of two-body matrix elements taken
from experiment (98Cd) that also leads to some seniority mixing. We deal with
proton holes relative to a Z=50,N=50 core. One surprising result is that, for a
four-particle system with total angular momentum I=4, there is one state with
seniority v=4 that is an eigenstate of any two-body interaction--seniority
conserving or not. The other two states are mixtures of v=2 and v=4 for the
seniority-mixing interactions. The same thing holds true for I=6. Another point
of interest is that the splittings E(I_{max})-E(I_{min}) are the same for three
and five particles with a seniority conserving interaction (a well known
result), but are equal and opposite for a QQ interaction. We also fit the
spectra with a combination of the delta and QQ interactions. The Z=40,N=40 core
plus g_{9/2} neutrons (Zr isotopes) is also considered, although it is
recognized that the core is deformed.


  This document focuses on modeling a complex situations to achieve an
advantage within a competitive context. Our goal is to devise the
characteristics of games to teach and exercise non-easily quantifiable tasks
crucial to the math-modeling process. A computerized game to exercise the
math-modeling process and optimization problem formulation is introduced. The
game is named The Formula 1 Championship, and models of the game were developed
in the computerized simulation platform MoNet. It resembles some situations in
which team managers must make crucial decisions to enhance their racing cars up
to the feasible, most advantageous conditions. This paper describes the game's
rules, limitations, and five Formula 1 circuit simulators used for the
championship development. We present several formulations of this situation in
the form of optimization problems. Administering the budget to reach the best
car adjustment to a set of circuits to win the respective races can be an
approach. Focusing on the best distribution of each Grand Prix's budget and
then deciding how to use the assigned money to improve the car is also the
right approach. In general, there may be a degree of conflict among these
approaches because they are different aspects of the same multi-scale
optimization problem. Therefore, we evaluate the impact of assigning the
highest priority to an element, or another, when formulating the optimization
problem. Studying the effectiveness of solving such optimization problems turns
out to be an exciting way of evaluating the advantages of focusing on one scale
or another. Another thread of this research directs to the meaning of the game
in the teaching-learning process. We believe applying the Formula 1 Game is an
effective way to discover opportunities in a complex-system situation and
formulate them to finally extract and concrete the related benefit to the
context described.


  Emerging brain network studies suggest that interactions between various
distributed neuronal populations may be characterized by an organized complex
topological structure. Many brain diseases are associated with altered
topological patterns of brain connectivity. Therefore, a key inquiry of
connectivity analysis is to identify network-level differentially expressed
connections that have low false positive rates, sufficient statistical power,
and high reproducibility. In this paper, we propose a novel statistical
approach to fulfill this goal by leveraging the topological structure of
differentially expressed functional connections or edges in a graphical
representation. We propose a new algorithm to automatically detect the latent
topology of a k-partite graph structure, and we also provide statistical
inferential techniques to test the detected topology. We evaluate our new
methods via extensive numerical studies. We also apply our new approach to
resting state fMRI data (24 cases and 18 controls) for Parkinson's disease
research. The detected connectivity network biomaker with the k-partite graph
topological structure reveals underlying neural features distinguishing
Parkinson's disease patients from healthy control subjects.


  In this paper we study the affine geometric structure of the graph of a
polynomial $f \in \mathbb{R} [x,y]$. We provide certain criteria to determine
when the parabolic curve is compact and when the unbounded component of its
complement is hyperbolic or elliptic. We analyse the extension to the real
projective plane of both fields of asymptotic lines and the Poincar\'e index of
its singular points when the surface is generic. Thus, we exhibit an index
formula for the field of asymptotic lines involving the number of connected
components of the projective Hessian curve of $f$ and the number of the special
parabolic points. As an application of this investigation, we obtain upper
bounds, respectively, for the number of special parabolic points having an
interior tangency and when they have an exterior tangency.


  It is shown that the unusual thermodynamic properties of matter within the
region of two-phase coexistence in hybrid stars result in a change of the
standard condition for beginning of convection. In particular, the thermal flux
transported by convection may be directed towards the stellar center. We
discuss favorable circumstances leading to such an effect of "inverse
convection" and its possible influence on the thermal evolution of hybrid
stars.


  We report results from a broadband spectral analysis of the low mass X-ray
binary MXB 1658-298 with the Swift/XRT and NuSTAR observations made during its
2015-2017 outburst. The source showed different spectral states and accretion
rates during this outburst. The source was in low/hard state during 2015; and
it was in high/soft state during the 2016 NuSTAR observations. This is the
first time that a comparison of the soft and hard spectral states during an
outburst is being reported in MXB 1658-298. Compared with the observation of
2015, the X-ray luminosity was about four times higher during 2016. The hard
state spectrum can be well described with models consisting of a
single-temperature blackbody component along with Comptonized disc emission, or
three component model comprising of multi-colour disc, single-temperature
blackbody and thermal Comptonization components. The soft state spectrum can be
described with blackbody or disc blackbody and Comptonization component, where
the neutron star surface (or boundary layer) is the dominant source for the
Comptonization seed photons. We have also found a link between the spectral
state of the source and the Fe K absorber. The absorption features due to
highly ionized Fe were observed only in the soft state. This suggests a
probable connection between accretion disc wind (or atmosphere) and spectral
state (or accretion state) of MXB 1658-298.


  In the last fifteen years, the high performance computing (HPC) community has
claimed for parallel programming environments that reconciles generality,
higher level of abstraction, portability, and efficiency for distributed-memory
parallel computing platforms. The Hash component model appears as an
alternative for addressing HPC community claims for fitting these requirements.
This paper presents foundations that will enable a parallel programming
environment based on the Hash model to address the problems of "debugging",
performance evaluation and verification of formal properties of parallel
program by means of a powerful, simple, and widely adopted formalism: Petri
nets.


  IC 10 is the nearest starburst irregular galaxy remarkable for its
anomalously high number of WR stars. We report the results of an analysis of
the emission spectra of HII-regions ionized by star clusters and WR stars based
on observations made with the 6-m telescope of the Special Astrophysical
Observatory of the Russian Academy of Sciences using MPFS field spectrograph
and SCORPIO focal reducer operating in the slit spectrograph mode. We determine
the masses and ages of ionizing star clusters in the violent star-forming
region of the galaxy in terms of the new evolutionary models of emission-line
spectra of HII-regions developed by Martin-Manjon et al. (2010). We estimate
the amount of stars needed to ionize the gas in the brightest HII-region HL 111
and report new determinations of oxygen abundance in HII regions.


  The only messenger radiation in the Universe which one can use to
statistically probe the Equation of State (EOS) of cold dense matter is that
originating from the near-field vicinities of compact stars. Constraining
gravitational masses and equatorial radii of rotating compact stars is a major
goal for current and future telescope missions, with a primary purpose of
constraining the EOS. From a Bayesian perspective it is necessary to carefully
discuss prior definition; in this context a complicating issue is that in
practice there exist pathologies in the general relativistic mapping between
spaces of local (interior source matter) and global (exterior spacetime)
parameters. In a companion paper, these issues were raised on a theoretical
basis. In this study we reproduce a probability transformation procedure from
the literature in order to map a joint posterior distribution of Schwarzschild
gravitational masses and radii into a joint posterior distribution of EOS
parameters. We demonstrate computationally that EOS parameter inferences are
sensitive to the choice to define a prior on a joint space of these masses and
radii, instead of on a joint space interior source matter parameters. We focus
on the piecewise-polytropic EOS model, which is currently standard in the field
of astrophysical dense matter study. We discuss the implications of this issue
for the field.


  Integrating time-frequency resource conversion (TFRC), a new network resource
allocation strategy, with call admission control can not only increase the cell
capacity but also reduce network congestion effectively. However, the optimal
setting of TFRC-oriented call admission control suffers from the curse of
dimensionality, due to Markov chain-based optimization in a high-dimensional
space. To address the scalability issue of TFRC, in [1] we extend the study of
TFRC into the area of scheduling. Specifically, we study downlink scheduling
based on TFRC for an LTE-type cellular network, to maximize service delivery.
The service scheduling of interest is formulated as a joint request, channel
and slot allocation problem which is NP-hard. An offline deflation and
sequential fixing based algorithm (named DSFRB) with only polynomial-time
complexity is proposed to solve the problem. For practical online
implementation, two TFRC-enabled low-complexity algorithms, modified Smith
ratio algorithm (named MSR) and modified exponential capacity algorithm (named
MEC), are proposed as well. In this report, we present detailed numerical
results of the proposed offline and online algorithms, which not only show the
effectiveness of the proposed algorithms but also corroborate the advantages of
the proposed TFRC-based schedule techniques in terms of quality-of-service
(QoS) provisioning for each user and revenue improvement for a service
operator.


  Let $\mathcal{F}$ be written as $ f^{*}(\mathcal{G})$, where $\mathcal{G}$ is
a $1$-dimensional foliation on $ {\mathbb P^{n-1}}$ and $f:{\mathbb
P^n}--->{\mathbb P^{n-1}}$ a non-linear generic rational map. We use local
stability results of singular holomorphic foliations, to prove that: if $n\geq
4$, a foliation $\mathcal{F}$ by complex surfaces on $\mathbb P^n$ is globally
stable under holomorphic deformations. As a consequence, we obtain irreducible
components for the space of two-dimensional foliations in $\mathbb P^n$. We
present also a result which characterizes holomorphic foliations on ${\mathbb
P^n}, n\geq 4$ which can be obtained as a pull back of 1- foliations in
${\mathbb P^{n-1}}$ of degree $d\geq2$.


  The influence of a partial substitution with S, Te, Co, Ni and Cu atoms on
the electronic structure of the FeSe superconductor has been investigated
within the density functional theory. The results of the supercell calculations
reveal distinct changes of electronic structures of the substituted FeSe
systems, which can be responsible for their superconducting properties. The
replacement of Se atoms by Te or S ones yields imperfect nesting between the
holelike and electronlike Fermi surface (FS) sheets, which enhances magnetic
fluctuations responsible for superconducting pairing, thus leading to higher
values of the superconducting critical temperatures. Meanwhile, the
substitutions with transition-metal atoms for iron sites make more substantial
changes of the FSs topology, since the holelike cylinders shrink at the cost of
an enlargement of the electronlike ones. Thus, the superconducting pairing,
driven by the nesting between these sheets, weakens and superconductivity
disappears for a small percentage of dopants. The results support the idea of
spin-fluctuation mediated superconductivity in iron chalcogenides.


  New models of the attention-based random forests called LARF (Leaf
Attention-based Random Forest) are proposed. The first idea behind the models
is to introduce a two-level attention, where one of the levels is the "leaf"
attention and the attention mechanism is applied to every leaf of trees. The
second level is the tree attention depending on the "leaf" attention. The
second idea is to replace the softmax operation in the attention with the
weighted sum of the softmax operations with different parameters. It is
implemented by applying a mixture of the Huber's contamination models and can
be regarded as an analog of the multi-head attention with "heads" defined by
selecting a value of the softmax parameter. Attention parameters are simply
trained by solving the quadratic optimization problem. To simplify the tuning
process of the models, it is proposed to make the tuning contamination
parameters to be training and to compute them by solving the quadratic
optimization problem. Many numerical experiments with real datasets are
performed for studying LARFs. The code of proposed algorithms can be found in
https://github.com/andruekonst/leaf-attention-forest.


  The Higgs boson was the last fundamental piece of the Standard Model to be
experimentally confirmed. LHC is embarked in a quest to probe the possibility
that this particle provides a portal to new physics. One front of this quest
consists in measuring the interactions of the Higgs with itself and with other
SM particles to a high precision. In a more exotic front, the LHC is searching
for the possibility that a pair of Higgses (HH) is the evidence of a new
resonance. Such resonances are predicted in models with extended Higgs sectors,
extra dimensions, and in models with exotic bound states. In this paper we show
how scalar quirks in Folded Supersymmetry can give rise to HH resonances. We
point out a viable sector of the parameter space in which HH is the dominant
decay channel for these {\it squirkonium} bound states. We found that future
runs of the LHC could discover HH resonances in the range of 0.5 - 1.6 TeV
under reasonable assumptions. Furthermore, for a given mass and width of the HH
signal, the model predicts the branching ratio of the subsequent decay modes of
the heavy resonance. Finding the extra decay modes in the predicted pattern can
serve as a smoking gun to confirm the model.


  Cross-spectrum analysis is a commonly-used technique for the detection of
phase and amplitude noise of a signal in the presence of interfering noise. It
extracts the desired correlated noise from two time series in the presence of
uncorrelated interfering noise. Recently, we demonstrated that the
phase-inversion (anti-correlation) effect due to AM noise leakage can cause
complete or partial collapse of the cross-spectral function. In this paper, we
discuss the newly discovered effect of anti-correlated thermal noise that
originates from the common-mode power divider (splitter), an essential
component in a cross-spectrum noise measurement system. We studied this effect
for different power splitters and discuss its influence on the measurement of
thermal-noise limited oscillators. An oscillator whose thermal noise is
primarily set by the 50 ohm source resistance is referred to as a
thermally-limited oscillator. We provide theory, simulation and experimental
results. In addition, we expand this study to reveal how the presence of
ferrite-isolators and amplifiers at the output ports of the power splitters can
affect the oscillator noise measurements. Finally, we discuss a possible
solution to overcome this problem.


  Biological cell suspensions are known to show dielectric dispersions due to
the Maxwell-Wagner mechanism. Many examples are summarized in a number of
papers by Schwan [7, 9, 10]. By the application of an appropriate analysis to
the dielectric dispersion, it is possible to estimate electrical phase
parameters related to protoplasm and cell membrane. A dielectric theory of
interfacial polarization for a suspension of conducting particles (protoplasm)
covered with poorly conducting shells (plasma membrane) was developed by Pauly
and Schwan [7], and was satisfactory applied for low volume fractions of
suspended particles (less than about 0.2). The purpose of this paper is to
examine the change in yeast plasma membrane permittivity after heating
treatment, by using the Pauly and Schwan's theory.


  A majority digraph is a finite simple digraph $G=(V,\to)$ such that there
exist finite sets $A_v$ for the vertices $v\in V$ with the following property:
$u\to v$ if and only if "more than half of the $A_u$ are $A_v$". That is, $u\to
v$ if and only if $ |A_u \cap A_v | > \frac{1}{2} \cdot |A_u|$. We characterize
the majority digraphs as the digraphs with the property that every directed
cycle has a reversal. If we change $\frac{1}{2}$ to any real number $\alpha\in
(0,1)$, we obtain the same class of digraphs. We apply the characterization
result to obtain a result on the logic of assertions "most $X$ are $Y$" and the
standard connectives of propositional logic.


  We show that the recent measurements of $B_s-\bar{B}_s$ mass difference,
$\Delta m_s$, by D{\O} and CDF collaborations give very strong constraints on
MSSM scenario with large flavor mixing in the LL and/or RR sector of down-type
squark mass squared matrix. In particular, the region with large mixing angle
and large mass difference between scalar strange and scalar bottom is ruled out
by giving too large $\Delta m_s$. The allowed region is sensitive to the CP
violating phases $\delta_{L(R)}$. The $\Delta m_s$ constraint is most stringent
on the scenario with both LL and RR mixing. We also predict the time-dependent
CP asymmetry in $B_s \to \psi \phi$ decay and semileptonic asymmetry in $B_s\to
\ell X$ decay.


  This paper is a direct extension of our paper: "The Standard Model on
Non-Commutative Space-Time: Electroweak currents and Higgs sector",
hep-ph/0502249, now with strong interactions included. Apart from the
non-commutative corrections to Standard Model strong interactions, several new
interactions appear. The most interesting ones are gluonic interactions with
the electroweak sector. They are elaborated here in detail and the Feynman
rules for interactions up to O(gs^2 theta) are provided.


  We study a simple Markov chain, the switch chain, on the set of all perfect
matchings in a bipartite graph. This Markov chain was proposed by Diaconis,
Graham and Holmes as a possible approach to a sampling problem arising in
Statistics. We ask: for which classes of graphs is the Markov chain ergodic and
for which is it rapidly mixing? We provide a precise answer to the ergodicity
question and close bounds on the mixing question. We show for the first time
that the mixing time of the switch chain is polynomial in the case of monotone
graphs, a class that includes examples of interest in the statistical setting.


  Spectroscopic studies of Galactic O and B stars show that many stars with
masses above 8 M$_{\odot}$ are observed in the HR diagram just beyond the
Main-Sequence (MS) band predicted by stellar models computed with a moderate
overshooting. This may be an indication that the convective core sizes in stars
in the upper part of the HR diagram are larger than predicted by these models.
Combining stellar evolution models and spectroscopic parameters derived for a
large sample of Galactic O and B stars, including brand new information about
their projected rotational velocities, we reexamine the question of the
convective core size in MS massive stars. We confirm that for stars more
massive than about 8 M$_{\odot}$, the convective core size at the end of the MS
phase increases more rapidly with the mass than in models computed with a
constant step overshoot chosen to reproduce the main sequence width in the low
mass range (around 2 M$_{\odot}$). This conclusion is valid for both the cases
of non-rotating models and rotating models either with a moderate or a strong
angular momentum transport. The increase of the convective core mass with the
mass obtained from the TAMS position is, however, larger than the one deduced
from the surface velocity drop for masses above about 15 M$_{\odot}$. Although
observations available at the moment cannot decide what is the best choice
between the core sizes given by the TAMS and the velocity drop, we discuss
different methods to get out of this dilemma. At the moment, comparisons with
eclipsing binaries seem to favor the solution given by the velocity drop. While
we confirm the need for larger convective cores at higher masses, we find
tensions in-between different methods for stars more massive than 15
M$_{\odot}$. The use of single-aged stellar populations (non-interacting
binaries or stellar clusters) would be a great asset to resolve this tension.


  Continuing the study of bounded geometry for Riemannian foliations, begun by
Sanguiao, we introduce a chart-free definition of this concept. Our main
theorem states that it is equivalent to a condition involving certain normal
foliation charts. For this type of charts, it is also shown that the
derivatives of the changes of coordinates are uniformly bounded, and there are
nice partitions of unity. Applications to a trace formula for foliated flows
will given in a forthcoming paper.


  We consider a damped wave equation in a bounded domain. The damping is
nonlinear and is homogeneous with degree p -- 1 with p > 2. First, we show that
the energy of the strong solution in the supercritical case decays as a
negative power of t; the rate of decay is the same as in the subcritical or
critical cases, provided that the space dimension does not exceed ten. Next,
relying on a new differential inequality, we show that if the initial
displacement is further required to lie in L p , then the energy of the
corresponding weak solution decays logarithmically in the supercritical case.
Those new results complement those in the literature and open an important
breach in the unknown land of super-critical damping mechanisms.


  We investigate the source algebra class of a p-block with cyclic defect
groups of the group algebra of a finite group. By the work of Linckelmann this
class is parametrized by the Brauer tree of the block together with a sign
function on its vertices and an endo-permutation module of a defect group. We
prove that this endo-permutation module can be read off from the character
table of the group. We also prove that this module is trivial for all cyclic
p-blocks of quasisimple groups with a simple quotient which is a sporadic
group, an alternating group, a group of Lie type in defining characteristic, or
a group of Lie type in cross-characteristic for which the prime p is large
enough in a certain sense.


  We study asymptotics of the recurrence coefficients of orthogonal polynomials
associated to the generalized Jacobi weight, which is a weight function with a
finite number of algebraic singularities on $[-1,1]$. The recurrence
coefficients can be written in terms of the solution of the corresponding
Riemann-Hilbert problem for orthogonal polynomials. Using the steepest descent
method of Deift and Zhou, we analyze the Riemann-Hilbert problem, and obtain
complete asymptotic expansions of the recurrence coefficients. We will
determine explicitly the order $1/n$ terms in the expansions. A critical step
in the analysis of the Riemann-Hilbert problem will be the local analysis
around the algebraic singularities, for which we use Bessel functions of
appropriate order.


  We study the topology of a line singularity, which is a complex hypersurface
with non-isolated singularity given by a complex line. We describe the
degeneration of its Milnor fibre to the singular hypersurface by means of a
pair of polyhedra, one in the Milnor fibre and other in the singular fibre,
which are deformation retracts of the corresponding fibres; and a continuous
map taking the Milnor fibre to the singular fibre and the first polyhedron to
the second one, which restrict to a homeomorphism outside the polyhedra. In the
same sense, we also study the topology of a complex isolated singularity
hypersurface under a non-local viewpoint.


  It is the saturation of the transition temperature Tc in the range of 24 K
for known materials in the late sixties which triggered the search for
additional materials offering new coupling mechanisms leading in turn to higher
Tc's. As a result of this stimulation, superconductivity in organic matter was
discovered in tetramethyl-tetraselenafulvalene-hexafluorophosphate,
(TMTSF)2PF6, in 1979, in the laboratory founded at Orsay by Professor Friedel
and his colleagues in 1962. Although this conductor is a prototype example for
low-dimensional physics, we mostly focus in this article on the superconducting
phase of the ambient-pressure superconductor (TMTSF)2ClO4, in which the
superconducting phase has been studied most intensively among the TMTSF salts.
We shall present a series of experimental results supporting nodal d-wave
symmetry for the superconducting gap in these prototypical
quasi-one-dimensional conductors.


  Engineering long-range interacting spin systems with ultra cold atoms offers
the possibility to explore exotic magnetically ordered phases in
strongly-correlated scenarios. Quantum gases in optical cavities provide a
versatile experimental platform to further engineer photon-mediated
interactions and access the underlying microscopic processes by probing the
cavity field. Here, we study a two-component spin Bose-Hubbard system with
cavity-mediated interactions. We provide a comprehensive overview of its phase
diagram and transitions in experimentally relevant regimes. The interplay of
different energy scales yields a rich phase diagram with superfluid and
insulating phases exhibiting density modulation or spin ordering. In
particular, the combined effect of contact and global-range interactions gives
rise to an antiferromagnetically ordered phase for arbitrarily small
spin-dependent light-matter coupling, while long-range and inter-spin contact
interactions introduce regions of instability and phase separation in the phase
diagram. We further study the low energy excitations above the
antiferrogmagnetic phase. Besides particle-hole branches, it hosts
spin-exchange excitations with a tunable energy gap. The studied lattice model
can be readily realized in cold-atom experiments with optical cavities.


  The ice microstructure (grain boundaries) is a key feature used to study ice
evolution and to investigate past climatic changes. We studied a deep ice core,
in Dome Concordia, Antarctica, which records past mechanical deformations. We
measured a "texture tensor" which characterizes the pattern geometry and
reveals local heterogeneities of deformation along the core. These results
question key assumptions of the current models used for dating.


  Let $D$ be an integral domain and $\star$ a semistar operation stable and of
finite type on it. In this paper, we are concerned with the study of the
semistar (Krull) dimension theory of polynomial rings over $D$. We introduce
and investigate the notions of $\star$-universally catenarian and
$\star$-stably strong S-domains and prove that, every $\star$-locally finite
dimensional Pr\"{u}fer $\star$-multiplication domain is $\star$-universally
catenarian, and this implies $\star$-stably strong S-domain. We also give new
characterizations of $\star$-quasi-Pr\"{u}fer domains introduced recently by
Chang and Fontana, in terms of these notions.


  We investigate the possibility and consequences of the existence of particles
having negative relativistic masses, and show that their existence implies the
existence of faster- than-light particles (tachyons). Our proof requires only
two postulates concerning such particles: that it is possible for particles of
any (positive, negative or zero) relativistic mass to collide inelastically
with 'normal' (i.e. positive relativistic mass) particles, and that
four-momentum is conserved in such collisions.


  Magnetic reconnection requires, at least locally, a non-ideal plasma
response. In collisionless space and astrophysical plasmas, turbulence could
permit this instead of the too rare binary collisions. We investigated the
influence of turbulence on the reconnection rate in the framework of a single
fluid compressible MHD approach. The goal is to find out, whether unresolved,
sub-grid for MHD simulations, turbulence can enhance the reconnection process
in high Reynolds number astrophysical plasma. We solve, simultaneously with the
grid-scale MHD equations, evolution equations for the sub-grid turbulent energy
and cross helicity according to Yokoi's model (Yokoi (2013)) where turbulence
is self-generated and -sustained through the inhomogeneities of the mean
fields. Simulations of Harris and force free sheets confirm the results of
Higashimori et al. (2013) and new results are obtained about the dependence on
resistivity for large Reynolds number as well as guide field effects. The
amount of energy transferred from large to the small scales is enhanced in case
of fast turbulent reconnection and energy spectra are used to interpret the
obtained regime of reconnection controlled by the turbulence timescale
$\tau_t$. The overall process is even faster for larger Reynolds numbers
controlled by the background molecular resistivity $\eta$, as long as the
initial level of turbulence is not too large. This implies that turbulence
plays an important role on fast reconnection at situation of large Reynolds
number while the amplitude of turbulence can still be small.


  With the global color symmetry model (GCM) being extended to finite chemical
potential, the density dependence of the bag constant, the total energy and the
radius of a nucleon, as well as the quark condensate in nuclear matter are
investigated. A maximal nuclear matter density for the existence of the bag
with three quarks confined within is obtained. The calculated results indicate
that, before the maximal density is reached, the bag constant, the total energy
of a nucleon and the quark condensate decrease gradually, and the radius of a
nucleon increases, with the increasing of the nuclear matter density.
Nevertheless no sudden change emerges. As the maximal nuclear matter density is
reached, a phase transition from nucleons to quarks takes place and the chiral
symmetry is restored.


  We describe all the trees with the property that the corresponding edge ideal
of the square of the tree has a linear resolution. As a consequence, we give a
complete characterization of those trees $T$ for which the square is
co-chordal, that is the complement of the square, $(T^2)^c$, is a chordal
graph. For particular classes of trees such as paths and double brooms we
determine the Krull dimension and the projective dimension.


  We show that the renormalized quantum invariants of links and graphs in the
3-sphere, derived from tensor categories in ["Modified quantum dimensions and
re-normalized link invariants", arXiv:0711.4229] lead to modified 6j-symbols
and to new state sum 3-manifold invariants. We give examples of categories such
that the associated standard Turaev-Viro 3-manifold invariants vanish but the
secondary invariants may be non-zero. The categories in these examples are
pivotal categories which are neither ribbon nor semi-simple and have an
infinite number of simple objects.


  We compute the three-loop relation between the pole and the minimally
subtracted quark mass allowing for virtual effects from a second massive quark.
We also consider the analogue effects for the on-shell wave function
renormalization constant.


  We present the results of modelling archival observations of type Ib SN
1999dn. In the spectra, two He I absorption features are seen: a slower
component with larger opacity, and a more rapid He I component with smaller
opacity. Complementary results are obtained from modelling the bolometric light
curve of SN 1999dn, where a two-zone model (dense inner region, and less dense
outer region) provides a much better fit than a one-zone model. A key result we
find is that roughly equal amounts of radioactive material are found in both
regions. The two-zone analytical model provides a more realistic representation
of the structure of the ejecta, including mixing and asymmetries, which offers
a physical explanation for how the radioactive material is propelled to, and
mixed within, the outer regions. Our result supports the theoretical
expectation that the radioactive content in the outflow of a type Ib supernova
(SN) is thoroughly mixed. We fit our model to six additional SNe Ibc, of which
the majority of the SNe Ib are best described by the two-zone model, and the
majority of the SNe Ic by the one-zone model. Of the SNe Ic, only SN 2007gr was
best fit by the two-zone model, indicating that the lack of helium spectral
features for this event cannot be attributed to poor mixing.


  Starting from space-discretisation of Maxwell's equations, various classical
formulations are proposed for the simulation of electromagnetic fields. They
differ in the phenomena considered as well as in the variables chosen for
discretisation. This contribution presents a literature survey of the most
common approximations and formulations with a focus on their structural
properties. The differential-algebraic character is discussed and quantified by
the differential index concept.


  Aims. In order to better model massive B-type stars, we need to understand
the physical processes taking place in slowly pulsating B (SPB) stars,
chemically peculiar Bp stars, and non-pulsating normal B stars co-existing in
the same part of the H-R diagram.
  Methods. We carry out a comparative study between samples of confirmed and
well-studied SPB stars and a sample of well-studied Bp stars with known periods
and magnetic field strengths. We determine their evolutionary state using
accurate HIPPARCOS parallaxes and Geneva photometry. We discuss the occurrence
and strengths of magnetic fields as well as the occurrence of stellar pulsation
among both groups. Further, we make a comparison of Geneva photometric
variability for both kinds of stars.
  Results. The group of Bp stars is significantly younger than the group of SPB
stars. Longitudinal magnetic fields in SPB stars are weaker than those of Bp
stars, suggesting that the magnetic field strength is an important factor for B
type stars to become chemically peculiar. The strongest magnetic fields appear
in young Bp stars, indicating a magnetic field decay in stars at advanced ages.
Rotation periods of Bp and pulsation periods of SPB stars are of the same order
and the behaviour of Geneva photometric variability of some Bp stars cannot be
distinguished from the variability of SPB stars, illustrating the difficulty to
interpret the observed variability of the order of days for B-type stars. We
consider the possibility that pulsation could be responsible for the
variability among chemically peculiar stars. In particular, we show that a
non-linear pulsation model is not excluded by photometry for the Bp star
HD175362.


  We study private broadcasting of two messages to two groups of receivers over
independent parallel channels. One group consists of an arbitrary number of
receivers interested in a common message, whereas the other group has only one
receiver. Each message must be kept confidential from the receiver(s) in the
other group. Each of the sub-channels is degraded, but the order of receivers
on each channel can be different. While corner points of the capacity region
were characterized in earlier works, we establish the capacity region and show
the optimality of a superposition strategy. For the case of parallel Gaussian
channels, we show that a Gaussian input distribution is optimal. We also
discuss an extension of our setup to broadcasting over a block-fading channel
and demonstrate significant performance gains using the proposed scheme over a
baseline time-sharing scheme.


  In this work, we simulate the COVID-19 pandemic dynamics in a population
modeled as a network of groups wherein infection can propagate both via
intra-group and via inter-group interactions. Our results emphasize the
importance of diminishing the inter-group infections in the effort of
substantial flattening and delaying of the epi(demiologic) curve with
concomitant mitigation of disastrous economy and social consequences. To
exemplify with a limiting case, splitting a population into m (say, 5 or 10)
noninteracting groups while keeping intra-group interaction unchanged yields a
stretched epidemiologic curve having the maximum number of daily infections
reduced and postponed in time by the same factor $m$ (5 or 10). More generally,
our study suggests a practical approach to fight against SARS-CoV-2 virus
spread based on population splitting into groups and minimizing intermingling
between them. This strategy can be pursued by large-scale infrastructure
reorganization of activity at different levels in big logistic units (e.g.,
large productive networks, factories, enterprises, warehouses, schools,
(seasonal) harvest work). Importantly, unlike total lockdwon strategy, the
proposed approach prevents economic ruin and keeps social life at a more
bearable level than distancing everyone from anyone. Last but not least, the
declaration, for the first time in Europe, that COVID-19 epidemic ended in the
two million people Slovenia may be taken as confirming the advantage of the
strategy proposed in this paper.


  The spectra and images obtained through broadband BVR filters for Jupiter
famaly comet P/2011 P1 were analyzed. We observed the comet on November 24,
2011, when its heliocentric distance was 5.43 AU. Two dimensional long slit
spectra and photometric images were obtained using the focal reducer SCORPIO
attached to the prime focus of the 6-m telescope BTA (SAO RAS, Russia). The
spectra cover the wavelength range of 4200-7000 {\AA}. No emissions of C2 and
CO+, which are expected in this wavelength region, were detected above 3 sigma
level. An upper limit in gas production rate of C2 is expected to be 1.1*10^24
mol*s^-1. The continuum shows a reddening effect with the normalized gradient
of reflectivity along dispersion of 5.1% per 1000 {\AA}. The color indices
(B-V)=0.89 and (V-R) = 0.42 for the nucleus region or (B-V)=0.68 and (V-R)=0.39
for the coma region, which are derived from the photometric data, also evidence
that the color of the cometary nucleus and dust are redder with respect to the
Sun. The dust coma like a spiral galaxy adge on was fitted using a Monte Carlo
model.


  Machine learning models have achieved significant milestones in various
domains, for example, computer vision models have an exceptional result in
object recognition, and in natural language processing, where Large Language
Models (LLM) like GPT can start a conversation with human-like proficiency.
However, abstract reasoning remains a challenge for these models, Can AI really
thinking like a human? still be a question yet to be answered. Raven
Progressive Matrices (RPM) is a metric designed to assess human reasoning
capabilities. It presents a series of eight images as a problem set, where the
participant should try to discover the underlying rules among these images and
select the most appropriate image from eight possible options that best
completes the sequence. This task always be used to test human reasoning
abilities and IQ. Zhang et al proposed a dataset called RAVEN which can be used
to test Machine Learning model abstract reasoning ability. In this paper, we
purposed Vision Transformer Contrastive Network which build on previous work
with the Contrastive Perceptual Inference network (CoPiNet), which set a new
benchmark for permutationinvariant models Raven Progressive Matrices by
incorporating contrast effects from psychology, cognition, and education, and
extends this foundation by leveraging the cutting-edge Vision Transformer
architecture. This integration aims to further refine the machine ability to
process and reason about spatial-temporal information from pixel-level inputs
and global wise features on RAVEN dataset.


  Redshift drift refers to the phenomena that redshift of cosmic objects is a
function of time. Measurement of redshift drift is of fundamental importance in
physical cosmology and can be utilized to distinguish different cosmological
models. Redshift drift can be expressed in two distinct methods. The first
method is related to cosmography, where the Redshift drift is given as a series
expansion of cosmological parameters, while the second method is written as a
function of Hubble parameter and its time derivatives which ultimately involve
field equations of a chosen theory of gravity. By equating corresponding terms
from both the series, the model parameter(s) of any modified theory of gravity
can be constrained. The present note aims at constraining the model parameter
$\zeta$ of $f(R,T)$ gravity theory where $f(R,T)= R + \zeta T$. By equating
linear terms in redshift $z$ from both the series, we constrain $\zeta$ in the
range $-0.51 \kappa^{2} \lesssim \zeta \lesssim -0.47 \kappa^{2}$, where
$\kappa^{2}=\frac{8 \pi G}{c^{4}}$.


  We consider the problem of recovering off-the-grid spikes from linear
measurements. The state of the art Over-Parametrized Continuous Orthogonal
Matching Pursuit (OP-COMP) with Projected Gradient Descent (PGD) successfully
recovers those signals. In most cases, the main computational cost lies in a
unique global descent on all parameters (positions and amplitudes). In this
paper, we propose to improve this algorithm by accelerating this descent step.
We introduce a new algorithm, based on Block Coordinate Descent, that takes
advantages of the sparse structure of the problem. Based on qualitative
theoretical results, this algorithm shows improvement in calculation times in
realistic synthetic microscopy experiments.


  Variability in the time series brightness of a star on a timescale of 8
hours, known as 'flicker', has been previously demonstrated to serve as a proxy
for the surface gravity of a star by Bastien et al. (2013). Although surface
gravity is crucial for stellar classification, it is the mean stellar density
which is most useful when studying transiting exoplanets, due to its direct
impact on the transit light curve shape. Indeed, an accurate and independent
measure of the stellar density can be leveraged to infer subtle properties of a
transiting system, such as the companion's orbital eccentricity via
asterodensity profiling. We here calibrate flicker to the mean stellar density
of 439 Kepler targets with asteroseismology, allowing us to derive a new
empirical relation given by
$\log_{10}(\rho_{\star}\,[\mathrm{kg}\,\mathrm{m}^{-3}]) = 5.413 - 1.850
\log_{10}(F_8\,[\mathrm{ppm}])$. The calibration is valid for stars with
$4500$K$<T_{\mathrm{eff}}<6500$K, $K_P<14$ and flicker estimates corresponding
to stars with $3.25<\log g_{\star}<4.43$. Our relation has a model error in the
stellar density of 31.7% and so has $\sim8$ times lower precision than that
from asteroseismology but is applicable to a sample $\sim40$ times greater.
Flicker therefore provides an empirical method to enable asterodensity
profiling on hundreds of planetary candidates from present and future missions.


  We consider a spin-$1/2$ Bose-Einstein condensate with equal Rashba and
Dresselhaus spin-orbit coupling. After reviewing some relevant features of the
quantum phases of the system, we present a short study on how their properties
are changed by the presence of non-zero magnetic detunings and spin-asymmetric
interactions. At small values of the Raman coupling and of the magnetic field
the so-called stripe phase occurs, which displays both superfluidity and
periodic density modulations, in analogy with supersolids. We finally review a
recent proposal (Phys. Rev. A 90, 041604) to improve the visibility of the
fringes, based on the space separation of the two spin components into a 2D
bi-layer configuration and on the application of a $\pi/2$ Bragg pulse, and we
show that this new configuration also yields a sizable increase of the
stability of the stripe phase against magnetic fluctuations.


  Antiferromagnetic semiconductors are new alternative materials for spintronic
applications and spin valves. In this work, we report a detailed investigation
of two antiferromagnetic semiconductors AMnAs (A = Li, LaO), which are
isostructural to the well-known LiFeAs and LaOFeAs superconductors. Here we
present a comparison between the structural, magnetic, and electronic
properties of LiMnAs, LaOMnAs and related materials. Interestingly, both LiMnAs
and LaOMnAs show a variation in resistivity with more than five orders of
magnitude, making them particularly suitable for use in future electronic
devices. From neutron and X-ray diffraction measurements on LiMnAs we have
observed a magnetic phase transition corresponding to the Neel temperature of
373.8 K, and a structural transition from the tetragonal to the cubic phase at
768 K. These experimental results are supported by density functional theory
(DFT) calculations.


  Affine hamiltonians are defined in the paper and their study is based
especially on the fact that in the hyperregular case they are dual objects of
lagrangians defined on affine bundles, by mean of natural Legendre maps. The
variational problems for affine hamiltonians and lagrangians of order $k\geq 2$
are studied, relating them to a Hamilton equation. An Ostrogradski type theorem
is proved: the Hamilton equation of an affine familtonian $h$ is equivalent
with Euler-Lagrange equation of its dual lagrangian $L$. Zermelo condition is
also studied and some non-trivial examples are given.


  The so-called lithium depletion boundary (LDB) provides a secure and
independent tool for deriving the ages of young open clusters.In this context,
our goal is to determine membership for a sample of 147 photometrically
selected candidates of the young open cluster IC 4665 and to use confirmed
members to establish an age based on the LDB. Employing the FLAMES multi-object
spectrograph on VLT/UT2, we have obtained intermediate-resolution spectra of
the cluster candidates. The spectra were used to measure radial velocities and
to infer the presence of the Li I 670.8 nm doublet and Halpha emission. We have
identified 39 bona fide cluster members based on radial velocity, Halpha
emission, and Li absorption. The mean radial velocity of IC 4665 is found to be
vrad=-15.95 +/- 1.13 km/s. Confirmed cluster members display a sharp transition
in magnitude between stars with and without lithium, both in the Im vs. Im-z
and in the Ks vs. Im-Ks diagrams.From this boundary, we deduce a cluster age of
27.7^(+4.2)_(-3.5) +/- 1.1 +/- 2 Myr. IC 4665 is the fifth cluster for which an
LDB age has been determined, and it is the youngest cluster among these five.
Thus, the LDB is established from relatively bright stars still in the
contracting pre-main sequence phase. The mass of the boundary is M*=0.24 +/-
0.04 Msun. The LDB age agrees well with the ages derived from isochrone fitting
of both low and high mass, turn-off stars, a result similar to what is found in
the slightly older NGC 2547.


  In the present paper, we prove that a topological space admits a functorial
Lindel\"ofification if and only if its realcompactification is Lindel\"of. To
investigate the functorial Lindel\"ofifiability of a topological space, for
each topological property $\mathsf{P}$, we introduce the notion of "functorial
$\mathsf{P}$-ification" and give an explicit construction of the functorial
$\mathsf{P}$-ification. Moreover, for a discrete space $X$, we discuss the
functorial $|X|$-Lindel\"ofifiability of $X$ and study relationships with
properties of the cardinal $|X|$. Finally, we apply our results concerning
functorial $\kappa$-Lindel\"ofifiability (for some cardinal $\kappa$) to the
space of ordinals and construct several functorial $\kappa$-Lindel\"ofifiable
spaces.


  We study gauge and gravitational anomalies of fermions and 2-form fields on
eight-dimensional spin manifolds. Possible global gauge anomalies are
classified by spin bordism groups $\Omega^{\text{spin}}_9(BG)$ which we
determine by spectral sequence techniques, and we also identify their explicit
generator manifolds. It turns out that a fermion in the adjoint representation
of any simple Lie group, and a gravitino in $8d$ $\mathcal{N}=1$ supergravity
theory, have anomalies. We discuss how a 2-form field, which also appears in
supergravity, produces anomalies which cancel against these fermion anomalies
in a certain class of supergravity theories. In another class of theories, the
anomaly of the gravitino is not cancelled by the 2-form field, but by
topological degrees of freedom. It gives a restriction on the topology of
spacetime manifolds which is not visible at the level of differential-form
analysis.


  We consider the Isobe-Kakinuma model for water waves, which is obtained as
the system of Euler-Lagrange equations for a Lagrangian approximating Luke's
Lagrangian for water waves. We show that the Isobe-Kakinuma model also enjoys a
Hamiltonian structure analogous to the one exhibited by V. E. Zakharov on the
full water wave problem and, moreover, that the Hamiltonian of the
Isobe-Kakinuma model is a higher order shallow water approximation to the one
of the full water wave problem.


  We study the vacuum structure of the U(N) gauge model with partially broken
N=2 supersymmetry. From the analysis of the classical vacua of this model, we
point out that in addition to the ordinary N=1 supersymmetric vacua, there are
vacua with negative gauge coupling constants, which preserve another N=1
supersymmetry. These latter vacua can be analyzed by using SUSY/non-SUSY
duality which is recently proposed by Aganagic, Beem, Seo and Vafa. A dual
description of these in UV is U(N) gauge theory where the supersymmetry is
broken by spurion superfields. Following them, we see that there are
supersymmetry preserving vacua as well as supersymmetry breaking vacua of low
energy effective theory.


  The Hamilton-Jacobi formalism for fermionic systems is studied. We derive the
HJ equations from the canonical transformation procedure, taking into account
the second class constraints typical of these systems. It is shown that these
constraints ensure the consistency of the solution, according to the
characteristics of fermionic systems. The explicit solutions for simple
examples are computed. Some aspects related to canonical transformations and to
quantization are discussed.


  The directed network model describing chiral edge states on the surface of a
cylindrical 3D quantum Hall system is known to map to a one-dimensional quantum
ferromagnetic spin chain. Using the spin wave expansion for this chain, we
determine the universal functions for the crossovers between the 2D chiral
metallic and 1D metallic regimes in the mean and variance of the conductance
along the cylinder, to first nontrivial order.


  We describe a Martin-L\"of-style dependent type theory, called Cocon, that
allows us to mix the intensional function space that is used to represent
higher-order abstract syntax (HOAS) trees with the extensional function space
that describes (recursive) computations. We mediate between HOAS
representations and computations using contextual modal types. Our type theory
also supports an infinite hierarchy of universes and hence supports type-level
computation thereby providing metaprogramming and (small-scale) reflection. Our
main contribution is the development of a Kripke-style model for Cocon that
allows us to prove normalization. From the normalization proof, we derive
subject reduction and consistency. Our work lays the foundation to incorporate
the methodology of logical frameworks into systems such as Agda and bridges the
longstanding gap between these two worlds.


  The applications concerning vehicular networks benefit from the vision of
beyond 5G and 6G technologies such as ultra-dense network topologies, low
latency, and high data rates. Vehicular networks have always faced data privacy
preservation concerns, which lead to the advent of distributed learning
techniques such as federated learning. Although federated learning has solved
data privacy preservation issues to some extent, the technique is quite
vulnerable to model inversion and model poisoning attacks. We assume that the
design of defense mechanism and attacks are two sides of the same coin.
Designing a method to reduce vulnerability requires the attack to be effective
and challenging with real-world implications. In this work, we propose
simulated poisoning and inversion network (SPIN) that leverages the
optimization approach for reconstructing data from a differential model trained
by a vehicular node and intercepted when transmitted to roadside unit (RSU). We
then train a generative adversarial network (GAN) to improve the generation of
data with each passing round and global update from the RSU, accordingly.
Evaluation results show the qualitative and quantitative effectiveness of the
proposed approach. The attack initiated by SPIN can reduce up to 22% accuracy
on publicly available datasets while just using a single attacker. We assume
that revealing the simulation of such attacks would help us find its defense
mechanism in an effective manner.


  Recent developments in the theory of weak decays of heavy flavours are
reviewed. Applications to exclusive semileptonic B decays, the semileptonic
branching ratio and charm counting, beauty lifetimes, and hadronic B decays are
discussed.


  We construct a family of maximal commutative subalgebras in the tensor
product of n copies of the universal enveloping algebra U(g) of a semisimple
Lie algebra g. This family is parameterized by collections \mu; z_1,...,z_n,
where \mu \in g^*, and z_1,...,z_n are pairwise distinct complex numbers. The
construction presented here generalizes the famous construction of the higher
Gaudin hamiltonians due to Feigin, Frenkel, and Reshetikhin. For n=1, our
construction gives a quantization of the family of maximal Poisson-commutative
subalgebras in S(g) obtained by the argument shift method. Next, we describe
natural representations of commutative algebras of our family in tensor
products of finite-dimensional g-modules as certain degenerations of the Gaudin
model. In the case of g=sl_r we prove that our commutative subalgebras have
simple spectrum in tensor products of finite-dimensional g-modules for generic
\mu and z_i. This implies simplicity of spectrum in the "generic" sl_r Gaudin
model.


  Following our previous papers (hep-th/0212158 and hep-th/0303126) we complete
the construction of the parafermionic theory with the symmetry Z_N based on the
second solution of Fateev-Zamolodchikov for the corresponding parafermionic
chiral algebra. In the present paper we construct the Z_N parafermionic theory
for N even. Primary operators are classified according to their transformation
properties under the dihedral group (Z_N x Z_2, where Z_2 stands for the Z_N
charge conjugation), as two singlets, doublet 1,2,...,N/2-1, and a disorder
operator. In an assumed Coulomb gas scenario, the corresponding vertex
operators are accommodated by the Kac table based on the weight lattice of the
Lie algebra D_{N/2}. The unitary theories are representations of the coset
SO_n(N) x SO_2(N) / SO_{n+2}(N), with n=1,2,.... We suggest that physically
they realise the series of multicritical points in statistical systems having a
Z_N symmetry.


  Top-down attention allows people to focus on task-relevant visual
information. Is the resulting perceptual boost task-dependent in naturalistic
settings? We aim to answer this with a large-scale computational experiment.
First, we design a collection of visual tasks, each consisting of classifying
images from a chosen task set (subset of ImageNet categories). The nature of a
task is determined by which categories are included in the task set. Second, on
each task we train an attention-augmented neural network and then compare its
accuracy to that of a baseline network. We show that the perceptual boost of
attention is stronger with increasing task-set difficulty, weaker with
increasing task-set size and weaker with increasing perceptual similarity
within a task set.


  This article discusses dependence on initial conditions in natural and social
sciences with focus on physical science. The main focus is on the newly
discovered rough dependence on initial data.


  The performance of automatic speech recognition (ASR) systems severely
degrades when multi-talker speech overlap occurs. In meeting environments,
speech separation is typically performed to improve the robustness of ASR
systems. Recently, location-based training (LBT) was proposed as a new training
criterion for multi-channel talker-independent speaker separation. Assuming
fixed array geometry, LBT outperforms widely-used permutation-invariant
training in fully overlapped utterances and matched reverberant conditions.
This paper extends LBT to conversational multi-channel speaker separation. We
introduce multi-resolution LBT to estimate the complex spectrograms from low to
high time and frequency resolutions. With multi-resolution LBT, convolutional
kernels are assigned consistently based on speaker locations in physical space.
Evaluation results show that multi-resolution LBT consistently outperforms
other competitive methods on the recorded LibriCSS corpus.


  We analyze the variability in the X-ray lightcurves of the black hole
candidate Cygnus X-1 by linear and nonlinear time series analysis methods.
While a linear model describes the over-all second order properties of the
observed data well, surrogate data analysis reveals a significant deviation
from linearity. We discuss the relation between shot noise models usually
applied to analyze these data and linear stochastic autoregressive models. We
debate statistical and interpretational issues of surrogate data testing for
the present context. Finally, we suggest a combination of tools from linear
andnonlinear time series analysis methods as a procedure to test the
predictions of astrophysical models on observed data.


  In this paper, we for the first time prove local solvability and stability of
the inverse Sturm-Liouville problem with complex-valued singular potential and
with polynomials of the spectral parameter in the boundary conditions. The
proof method is constructive. It is based on the reduction of the inverse
problem to a linear equation in the Banach space of bounded infinite sequences.
We prove that, under a small perturbation of the spectral data, the main
equation of the inverse problem remains uniquely solvable. Furthermore, we
derive new reconstruction formulas for obtaining the problem coefficients from
the solution of the main equation and get stability estimates for the recovered
coefficients.


  Nowadays the question `what is complexity?' is a challenge to be answered.
This question is triggering a great quantity of works in the frontier of
physics, biology, mathematics and computer science. Even more when this century
has been told to be the century of Complexity. Although there seems to be no
urgency to answer the above question, many different proposals that have been
developed to this respect can be found in the literature. In this context,
several articles concerning statistical complexity and stochastic processes are
collected in this chapter.


  We propose and analyze a multiscale time integrator Fourier pseudospectral
(MTI-FP) method for solving the Klein-Gordon (KG) equation with a dimensionless
parameter $0<\varepsilon\leq1$ which is inversely proportional to the speed of
light. In the nonrelativistic limit regime, i.e. $0<\varepsilon\ll1$, the
solution to the KG equation propagates waves with amplitude at $O(1)$ and
wavelength at $O(\varepsilon^2)$ in time and $O(1)$ in space, which causes
significantly numerical burdens due to the high oscillation in time. The MTI-FP
method is designed by adapting a multiscale decomposition by frequency (MDF) to
the solution at each time step and applying an exponential wave integrator to
the nonlinear Schr\"{o}dinger equation with wave operator under well-prepared
initial data for $\varepsilon^2$-frequency and $O(1)$-amplitude waves and a
KG-type equation with small initial data for the reminder waves in the MDF. We
rigorously establish two independent error bounds in $H^2$-norm to the MTI-FP
method at $O(h^{m_0}+\tau^2+\varepsilon^2)$ and
$O(h^{m_0}+\tau^2/\varepsilon^2)$ with $h$ mesh size, $\tau$ time step and
$m_0\ge2$ an integer depending on the regularity of the solution, which
immediately imply that the MTI-FP converges uniformly and optimally in space
with exponential convergence rate if the solution is smooth, and uniformly in
time with linear convergence rate at $O(\tau)$ for all $\varepsilon\in(0,1]$
and optimally with quadratic convergence rate at $O(\tau^2)$ in the regimes
when either $\varepsilon=O(1)$ or $0<\varepsilon\le \tau$. Numerical results
are reported to confirm the error bounds and demonstrate the efficiency and
accuracy of the MTI-FP method for the KG equation, especially in the
nonrelativistic limit regime.


  Let $E/F$ be a non Archimedean local field and $\psi:\frac{E}{F}\to
\mathbb{C}$ a non trivial character. Using harmonic analysis on Harish-Chandra
Schwartz spaces, we prove that if $n$ is an integer at least equal to two and
$\pi$ is a square integrable representation of $GL_n(E)$ such that
$\gamma(\pi,\pi',\psi)=1$ for any $GL_{n-1}(F)$-distinguished tempered
representation $\pi'$ of $GL_{n-1}(E)$, then $\pi$ is $GL_n(F)$-distinguished.


  Purely hydrodynamic numerical experiments into the evolution of astrophysical
discs typically include some sort of viscosity in order to cause accretion. In
this paper, we demonstrate an alternative method of implementing viscous
forces, with extremely good angular momentum conservation properties. The
method is based on altering the cell fluxes, rather than incorporating a
viscous force. We test this method on the classical `ring spreading' problem,
and demonstrate angular momentum conservation at the $10^{-8}$ level.


  The aim of this work is to study global $3$-webs with vanishing curvature. We
wish to investigate degree $3$ foliations for which their dual web is flat. The
main ingredient is the Legendre transform, which is an avatar of classical
projective duality in the realm of differential equations. We find a
characterization of degree $3$ foliations whose Legendre transform are webs
with zero curvature.


  In the present article we showcase how the reheating era can be described
properly in the context of Einstein-Gauss-Bonnet gravity assuming that the
primordial gravitational waves propagate with the velocity of light. The
equations of the duration of reheating along with the reheating temperature are
derived and as demonstrated, their expressions are quite similar to the case of
a canonical scalar field where now the second derivative of the Gauss-Bonnet
scalar coupling function appears and effectively alters the numerical value of
the scalar potential. The appearance of such term is reminiscing of a $\lambda
R$ model of gravity where $\lambda$ is now dynamical. We consider two viable
inflationary models of interest, the former involves an error function as
scalar Gauss-Bonnet coupling function and the latter a Woods-Saxon scalar
potential. It is shown that for both models the aforementioned quantities can
be in agreement with theoretical expectations. The only constraint that is
needed is the assumption that the second time derivative of the Gauss-Bonnet
scalar coupling function is actually lesser than the Planck mass squared, that
is $\ddot\xi<\frac{M_{Pl}^2}{8}$ in order to obtain a viable description. We
find that a free parameter of the theory and specifically the potential
amplitude for the Woods-Saxon model during the inflationary era, dictates the
effective equations of state and therefore the reheating epoch can be described
either by a type of stiff matter with EoS parameter equal to unity or by an EoS
parameter close to that of the radiation.


  There is an ongoing debate about the origin and even the very existence of a
high degree of linear polarization of some chromospheric spectral lines
observed in solar flares. The standard explanation of these measurements is in
terms of the impact polarization caused by non-thermal proton and/or electron
beams. In this work, we study the possible role of resonance line polarization
due to radiation anisotropy in the inhomogeneous medium of the flare ribbons.
We consider a simple two-dimensional model of the flaring chromosphere and we
solve self-consistently the non-LTE problem taking into account the role of
resonant scattering polarization and of the Hanle effect. Our calculations show
that the horizontal plasma inhomogeneities at the boundary of the flare ribbons
can lead to a significant radiation anisotropy in the line formation region
and, consequently, to a fractional linear polarization of the emergent
radiation of the order of several percent. Neglecting the effects of impact
polarization, our model can provide a clue for resolving some of the common
observational findings, namely: (1) why a high degree of polarization appears
mainly at the edges of the flare ribbons; (2) why polarization can also be
observed during the gradual phase of a flare; (3) why polarization is mostly
radial or tangential. We conclude that the radiation transfer in the realistic
multi-dimensional models of solar flares needs to be considered as an essential
ingredient for understanding the observed spectral line polarization.


  We studied the single dimer dynamics in a lattice diffusive model as a
function of particle density in the high densification regime. The mean square
displacement is found to be subdiffusive both in one and two dimensions. The
spatial dependence of the self part of the van Hove correlation function
displays as function of $r$ a single peak and signals a dramatic slow down of
the system for high density. The self intermediate scattering function is
fitted to the Kohlrausch-Williams-Watts law. The exponent $\beta$ extracted
from the fits is density independent while the relaxation time $\tau$ follows a
scaling law with an exponent 2.5.


  The most general basis of operators parametrizing a low-scale departure from
the SM particle content is constructed. The SM gauge invariance is enforced,
and operators of lowest dimensions are retained separately for a new light
neutral particle of spin 0, 1/2, 1, and 3/2. The basis is further decomposed
into couplings to the SM Higgs/gauge fields, to pairs of quark/lepton fields,
and to baryon/lepton number violating combinations of fermion fields. This
basis is then used to systematically investigate the discovery potential of the
rare FCNC decays of the K and B mesons with missing energy in the final state.
The most sensitive decay modes in the s to d, b to d, and b to s sectors are
identified and compared for each type of couplings to the new invisible state.


  Tail risk protection is in the focus of the financial industry and requires
solid mathematical and statistical tools, especially when a trading strategy is
derived. Recent hype driven by machine learning (ML) mechanisms has raised the
necessity to display and understand the functionality of ML tools. In this
paper, we present a dynamic tail risk protection strategy that targets a
maximum predefined level of risk measured by Value-At-Risk while controlling
for participation in bull market regimes. We propose different weak
classifiers, parametric and non-parametric, that estimate the exceedance
probability of the risk level from which we derive trading signals in order to
hedge tail events. We then compare the different approaches both with
statistical and trading strategy performance, finally we propose an ensemble
classifier that produces a meta tail risk protection strategy improving both
generalization and trading performance.


  We give an alternate formulation of pseudo-coherence over an arbitrary
derived stack X. The full subcategory of pseudo-coherent objects forms a stable
sub-infinity-category of the derived category associated to X. Using relative
Tor-amplitude we define a derived stack classifying pseudo-coherent objects.
For reasonable base schemes, this classifies the bounded derived category. In
the case that X is a projective derived scheme flat over the base, we show the
moduli is locally geometric and locally of almost finite type. Using this
result, we prove the existence of a derived motivic Hall algebra associated to
X.


  The first-order, in terms of electron-interaction in the perturbation theory,
of the proper linear response function $\Pi ({\bf k}, \omega )$ gives rise to
the exchange-contribution to the dielectric function $\epsilon ({\bf k} ,
\omega)$ in the electron liquid. Its imaginary part, $Im \Pi_1 ({\bf k},
\omega)$, is calculated exactly. An analytical expression for $Im \Pi_1 ({\bf
k}, \omega)$ is derived which after refinement has a quite simple form.


  In machine learning ensemble methods have demonstrated high accuracy for the
variety of problems in different areas. Two notable ensemble methods widely
used in practice are gradient boosting and random forests. In this paper we
present InfiniteBoost - a novel algorithm, which combines important properties
of these two approaches. The algorithm constructs the ensemble of trees for
which two properties hold: trees of the ensemble incorporate the mistakes done
by others; at the same time the ensemble could contain the infinite number of
trees without the over-fitting effect. The proposed algorithm is evaluated on
the regression, classification, and ranking tasks using large scale, publicly
available datasets.