  Weprovethattheasymptoticsofergodicintegralsalonganinvariant foliation of a
toral Anosov diffeomorphism, or of a pseudo-Anosov diffeomorphism on a compact
orientable surface of higher genus, are determined (up to a logarithmic error)
by the action of the diffeomorphism on the cohomology of the surface. As a
consequence of our argument and of the results of Giulietti and Liverani [GL]
on horospherical averages, toral Anosov diffeomorphisms have no Ruelle
resonances in the open interval $(1,e^{h_{top}} )$.


  Social media has penetrated into multilingual societies, however most of them
use English to be a preferred language for communication. So it looks natural
for them to mix their cultural language with English during conversations
resulting in abundance of multilingual data, call this code-mixed data,
available in todays' world.Downstream NLP tasks using such data is challenging
due to the semantic nature of it being spread across multiple languages.One
such Natural Language Processing task is sentiment analysis, for this we use an
auto-regressive XLNet model to perform sentiment analysis on code-mixed
Tamil-English and Malayalam-English datasets.


  We review the theoretical framework for the calculation of particle
polarization in relativistic heavy ion collisions within the hydrodynamical
model. The covariant decomposition of the mean spin vector is presented and
open theoretical issues addressed.


  Most of the deployed IEEE 802.11e Wireless Local Area Networks (WLANs) use
infrastructure Basic Service Set (BSS) in which an Access Point (AP) serves as
a gateway between wired and wireless domains. We present the unfairness problem
between the uplink and the downlink flows of any Access Category (AC) in the
802.11e Enhanced Distributed Channel Access (EDCA) when the default settings of
the EDCA parameters are used. We propose a simple analytical model to calculate
the EDCA parameter settings that achieve weighted fair resource allocation for
all uplink and downlink flows. We also propose a simple model-assisted
measurement-based dynamic EDCA parameter adaptation algorithm. Moreover, our
dynamic solution addresses the differences in the transport layer and the
Medium Access Control (MAC) layer interactions of User Datagram Protocol (UDP)
and Transmission Control Protocol (TCP). We show that proposed Contention
Window (CW) and Transmit Opportunity (TXOP) limit adaptation at the AP provides
fair UDP and TCP access between uplink and downlink flows of the same AC while
preserving prioritization among ACs.


  Spurious correlations threaten the validity of statistical classifiers. While
model accuracy may appear high when the test data is from the same distribution
as the training data, it can quickly degrade when the test distribution
changes. For example, it has been shown that classifiers perform poorly when
humans make minor modifications to change the label of an example. One solution
to increase model reliability and generalizability is to identify causal
associations between features and classes. In this paper, we propose to train a
robust text classifier by augmenting the training data with automatically
generated counterfactual data. We first identify likely causal features using a
statistical matching approach. Next, we generate counterfactual samples for the
original training data by substituting causal features with their antonyms and
then assigning opposite labels to the counterfactual samples. Finally, we
combine the original data and counterfactual data to train a robust classifier.
Experiments on two classification tasks show that a traditional classifier
trained on the original data does very poorly on human-generated counterfactual
samples (e.g., 10%-37% drop in accuracy). However, the classifier trained on
the combined data is more robust and performs well on both the original test
data and the counterfactual test data (e.g., 12%-25% increase in accuracy
compared with the traditional classifier). Detailed analysis shows that the
robust classifier makes meaningful and trustworthy predictions by emphasizing
causal features and de-emphasizing non-causal features.


  We review recent lattice QCD results for the surface tension at the finite
temperature quark-hadron phase transition and discuss their implications on the
possible scale of inhomogeneities. In the quenched approximation the average
distance between nucleating centers is smaller than the diffusion length of a
protron, so that inhomogeneities are washed out by the time nucleosynthesis
sets in. Consequently the baryon density fluctuations formed by a QCD phase
transition in the early universe cannot significantly affect standard big-bang
nucleosynthesis calculations and certainly cannot allow baryons to close the
universe. At present lattice results are inconclusive when dynamical fermions
are included.


  With advancements in domain generalized stereo matching networks, models
pre-trained on synthetic data demonstrate strong robustness to unseen domains.
However, few studies have investigated the robustness after fine-tuning them in
real-world scenarios, during which the domain generalization ability can be
seriously degraded. In this paper, we explore fine-tuning stereo matching
networks without compromising their robustness to unseen domains. Our
motivation stems from comparing Ground Truth (GT) versus Pseudo Label (PL) for
fine-tuning: GT degrades, but PL preserves the domain generalization ability.
Empirically, we find the difference between GT and PL implies valuable
information that can regularize networks during fine-tuning. We also propose a
framework to utilize this difference for fine-tuning, consisting of a frozen
Teacher, an exponential moving average (EMA) Teacher, and a Student network.
The core idea is to utilize the EMA Teacher to measure what the Student has
learned and dynamically improve GT and PL for fine-tuning. We integrate our
framework with state-of-the-art networks and evaluate its effectiveness on
several real-world datasets. Extensive experiments show that our method
effectively preserves the domain generalization ability during fine-tuning.


  We present results from a study of fifteen red giant members of the
intermediate-metallicity globular cluster (GC) FSR 1758 using high-resolution
near-infrared spectra collected with the Apache Point Observatory Galactic
Evolution Experiment II survey (APOGEE-2), obtained as part of CAPOS (the bulge
Cluster APOgee Survey). Since its very recent discovery as a massive GC in the
bulge region, evoking the name Sequoia, this has been an intriguing object with
a highly debated origin, and initially led to the suggestion of a purported
progenitor dwarf galaxy of the same name. In this work, we use new
spectroscopic and astrometric data to provide additional clues to the nature of
FSR 1758. Our study confirms the GC nature of FSR 1758, and as such we report
for the first time the existence of the characteristic N-C anti-correlation and
Al-N correlation, revealing the existence of the multiple-population
phenomenon, similar to that observed in virtually all GCs. Furthermore, the
presence of a population with strongly enriched aluminium makes it unlikely FSR
1758 is the remnant nucleus of a dwarf galaxy, as Al-enhanced stars are
uncommon in dwarf galaxies. We find that FSR 1758 is slightly more metal rich
than previously reported in the literature, with a mean metallicity [Fe/H]
between $-1.43$ to $-1.36$ (depending on the adopted atmospheric parameters),
and with a scatter within observational error, again pointing to its GC nature.
Overall, the $\alpha$-enrichment ($\gtrsim+0.3$ dex), Fe-peak (Fe, Ni), light-
(C, N), and odd-Z (Al) elements follow the trend of intermediate-metallicity
GCs. ... A new examination of its dynamical properties with the
\texttt{GravPot16} model favors an association with the Gaia-Enceladus-Sausage
accretion event. Thus, paradoxically, the cluster that gave rise to the name of
the Sequoia dwarf galaxy does not appear to belong to this specific merging
event.


  Disorder scattering and spin-orbit coupling are together responsible for the
diffusion and relaxation of spin-density in time-reversal invariant systems. We
study spin-relaxation and diffusion in a two-dimensional electron gas with
Rashba spin-orbit coupling and spin-independent disorder, focusing on the role
of Rashba spin-orbit coupling in transport. Spin-orbit coupling contributes to
spin relaxation, transforming the quantum interference contribution to
conductivity from a negative weak localization (WL) correction to a positive
weak anti-localization (WAL) correction. The importance of spin channel mixing
in transport is largest in the regime where the Bloch state energy uncertainty
$\hbar/\tau$ and the Rashba spin-orbit splitting $\Delta_\mathrm{SO}$ are
comparable. We find that as a consequence of this spin channel mixing, the
WL-WAL crossover is non-monotonic in this intermediate regime, and use our
results to address recent experimental studies of transport at two-dimensional
oxide interfaces.


  Transient stability boundary (TSB) is an important tool in power system
online security monitoring, but practically it suffers from high computational
burden using state-of-the-art methods, such as time-domain simulation (TDS),
with numerous scenarios taken into account (e.g., operating points (OPs) and
N-1 contingencies). The purpose of this work is to establish a data-driven
framework to generate sufficient critical samples close to the boundary within
a limited time, covering all critical scenarios in current OP. Therefore,
accurate TSB can be periodically refreshed by tracking current OP in time. The
idea is to develop a search strategy to obtain more data samples near the
stability boundary, while traverse the rest part with fewer samples. To achieve
this goal, a specially designed transient index sensitivity based search
strategy and critical scenarios selection mechanism are proposed, in order to
find out the most representative scenarios and periodically update TSB for
online monitoring. Two case studies validate effectiveness of the proposed
method.


  This paper introduces the notion of twisted toric manifolds which is a
generalization of one of symplectic toric manifolds, and proves the weak
Delzant type classification theorem for them. The computation methods for their
fundamental groups, cohomology groups in general cases, and signatures in
four-dimensional cases are also given.


  Approximate matching (AM) is a concept in digital forensics to determine the
similarity between digital artifacts. An important use case of AM is the
reliable and efficient detection of case-relevant data structures on a
blacklist, if only fragments of the original are available. For instance, if
only a cluster of indexed malware is still present during the digital forensic
investigation, the AM algorithm shall be able to assign the fragment to the
blacklisted malware. However, traditional AM functions like TLSH and ssdeep
fail to detect files based on their fragments if the presented piece is
relatively small compared to the overall file size. A second well-known issue
with traditional AM algorithms is the lack of scaling due to the
ever-increasing lookup databases. We propose an improved matching algorithm
based on transformer models from the field of natural language processing. We
call our approach Deep Learning Approximate Matching (DLAM). As a concept from
artificial intelligence (AI), DLAM gets knowledge of characteristic blacklisted
patterns during its training phase. Then DLAM is able to detect the patterns in
a typically much larger file, that is DLAM focuses on the use case of fragment
detection. We reveal that DLAM has three key advantages compared to the
prominent conventional approaches TLSH and ssdeep. First, it makes the tedious
extraction of known to be bad parts obsolete, which is necessary until now
before any search for them with AM algorithms. This allows efficient
classification of files on a much larger scale, which is important due to
exponentially increasing data to be investigated. Second, depending on the use
case, DLAM achieves a similar or even significantly higher accuracy in
recovering fragments of blacklisted files. Third, we show that DLAM enables the
detection of file correlations in the output of TLSH and ssdeep even for small
fragment sizes.


  A visualization for dynamics of a qudit spin vector in a time-dependent
magnetic field is realized by means of mapping a solution for a spin vector on
the three-dimensional spherical curve (vector hodograph). The obtained results
obviously display the quantum interference of precessional and nutational
effects on the spin vector in the magnetic resonance. For any spin the bottom
bounds of the quantum speed limit time (QSL) are found. It is shown that the
bottom bound goes down when using multilevel spin systems. Under certain
conditions the non-nil minimal time, which is necessary to achieve the
orthogonal state from the initial one, is attained at spin S=2. An estimation
of the product of two and three standard deviations of the spin components are
presented. We discuss the dynamics of the mutual uncertainty, conditional
uncertainty and conditional variance in terms of spin standard deviations. The
study can find practical applications in the magnetic resonance, 3D
visualization of computational data and in designing of optimized information
processing devices for quantum computation and communication.


  Let $M$ be a Hopf--von Neuman algebra with the predual $M_*$ and $WAP(M)$ the
subspace in $M$ composed of weakly almost periodic functionals on $M_*$. The
main example of such an algebra is $M=L^\infty(\mathbb G)$ for a locally
compact quantum group $\mathbb G$. We define a pair of left/right spaces
$WAP_{iso,l}(M)$ and $WAP_{iso,r}(M)$ inside $WAP(M)$ and prove that they carry
invariant means. These spaces are currently the widest known to admit invariant
means in the quantum setting. In the case when $M=L^\infty(G)$ and $G$ is a
locally compact group, these spaces are equal to $WAP(G)$.


  Topological superconductivity, implying gapless protected surface states, has
recently been proposed to exist in the compound CuxBi2Se3. Unfortunately, low
diamagnetic shielding fractions and considerable inhomogeneity have been
reported in this compound. In an attempt to understand and improve on the
finite superconducting volume fractions, we have investigated the effects of
various growth and post-annealing conditions. With a melt-growth (MG) method,
diamagnetic shielding fractions of up to 56% in Cu0.3Bi2Se3 have been obtained,
the highest value reported for this method. We investigate the efficacy of
various quenching and annealing conditions, finding that quenching from
temperatures above 560C is essential for superconductivity, whereas quenching
from lower temperatures or not quenching at all is detrimental. A modified
floating zone (FZ) method yielded large single crystals but little
superconductivity. Even after annealing and quenching, FZ-grown samples had
much less chance of being superconducting than MG-grown samples. From the low
shielding fractions in FZ-grown samples and the quenching dependence, we
suggest that a metastable secondary phase having a small volume fraction in
most of the samples may be responsible for the superconductivity.


  We study in detail the transverse collective modes of simple holographic
models in presence of electromagnetic Coulomb interactions. We render the
Maxwell gauge field dynamical via mixed boundary conditions, corresponding to a
double trace deformation in the boundary field theory. We consider three
different situations: (i) a holographic plasma with conserved momentum, (ii) a
holographic (dirty) plasma with finite momentum relaxation and (iii) a
holographic viscoelastic plasma with propagating transverse phonons. We observe
two interesting new features induced by the Coulomb interactions: a mode
repulsion between the shear mode and the photon mode at finite momentum
relaxation, and a propagation-to-diffusion crossover of the transverse
collective modes induced by the finite electromagnetic interactions. Finally,
at large charge density, our results are in agreement with the transverse
collective mode spectrum of a charged Fermi liquid for strong interaction
between quasi-particles, but with an important difference: the gapped photon
mode is damped even at zero momentum. This property, usually referred to as
anomalous attenuation, is produced by the interaction with a quantum critical
continuum of states and might be experimentally observable in strongly
correlated materials close to quantum criticality, e.g. in strange metals.


  Within the framework of a local expansion of the logarithm of the O(N)
sigma-model vacuum functional, valid for slowly varying fields, the modified
Virasoro algebra is studied. The operator-like central charge term is given, up
to second order, for a general functional.


  Periodicity is one of the most fundamental structural characteristics of
systems occurring in nature. The properties of these systems depend strongly on
the symmetry of the underlying periodic structure. In solid state materials -
for example - the static and transport properties as well as the magnetic and
electronic characteristics are crucially influenced by the crystal symmetry. In
this context, hexagonal structures play an extremely important role and lead to
novel physics like that of carbon nanotubes or graphene. Here we report on the
first realization of ultracold atoms in a spin-dependent optical lattice with
hexagonal symmetry. We show how combined effects of the lattice and
interactions between atoms lead to a forced antiferromagnetic N\'eel order when
two spin-components localize at different lattice sites. We also demonstrate
that the coexistence of two components - one Mott-insulating and the other one
superfluid - leads to the formation of a forced supersolid. Our observations
are consistent with theoretical predictions using Gutzwiller mean-field theory.


  We consider the problem of interconverting a finite amount of resources
within all theories whose single-shot transformation rules are based on a
majorisation relation, e.g. the resource theories of entanglement and coherence
(for pure state transformations), as well as thermodynamics (for
energy-incoherent transformations). When only finite resources are available we
expect to see a non-trivial trade-off between the rate $r_n$ at which $n$
copies of a resource state $\rho$ can be transformed into $nr_n$ copies of
another resource state $\sigma$, and the error level $\varepsilon_n$ of the
interconversion process, as a function of $n$. In this work we derive the
optimal trade-off in the so-called moderate deviation regime, where the rate of
interconversion $r_n$ approaches its optimum in the asymptotic limit of
unbounded resources ($n\to\infty$), while the error $\epsilon_n$ vanishes in
the same limit. We find that the moderate deviation analysis exhibits a
resonance behaviour which implies that certain pairs of resource states can be
interconverted at the asymptotically optimal rate with negligible error, even
in the finite $n$ regime.


  (Abridged) The red giant clump has been recently argued to be a reliable
distance indicator for the galaxies in the Local Group. We re-address the
problem of the systematic magnitude differences (DeltaM_I) between the local
clump revealed by Hipparcos, and the clump stars observed in distant galaxies.
First, we present tables and equations with the theoretically-predicted clump
M_I as a function of age and metallicity, that allow the computation of
DeltaM_I for any given galaxy model. We then explain in some detail what
determines the distribution of masses, ages, and metallicities of clump stars
in a galaxy. We point out that in galaxies with recent/ongoing star formation,
the age distribution of clump stars is strongly biased toward younger (1-3 Gyr)
ages, and hence toward higher metallicities. Obviously, this does not happen in
galaxies with predominantly old stellar populations. We construct a model for
the local clump that is shown to produce distributions of metallicities,
colours, and magnitudes, similar to those derived from spectroscopic and
Hipparcos data. Bulge, Magellanic Clouds, and Carina dSph models are used to
analyse the values of DeltaM_I for these systems. We show how the clump-RR
Lyrae data is well reproduced by the models. However, despite this, the models
indicate that the linear DeltaM_I vs. [Fe/H] relations that have been derived
from the data are not general. Finally, we provide revised clump distances to
the Bulge, Magellanic Clouds, and Carina dSph. The largest DeltaM_I values are
found for the Magellanic Clouds and Carina dSph, which turn out to be located
at distance moduli 0.2-0.3 mag longer than indicated by works which ignore
population effects. The Galactic Bulge, instead, may be slightly closer (0.1
mag) than indicated by previous works based on the red clump.


  We report on double-differential inclusive cross-sections of the production
of secondary protons, charged pions, and deuterons, in the interactions with a
5% nuclear interaction length thick stationary tin target, of proton and pion
beams with momentum from \pm3 GeV/c to \pm15 GeV/c. Results are given for
secondary particles with production angles between 20 and 125 degrees.
Cross-sections on tin nuclei are compared with cross-sections on beryllium,
carbon, copper, tantalum and lead nuclei.


  Noncentrosymmetric superconductors with broken inversion symmetry $P$ offer
rich physical phenomena such as the upper critical magnetic field $H_{c2}$
beyond the Pauli limit and magnetoelectric effect. The relativistic spin-orbit
interaction (SOI) plays an essential role in these novel phenomena, which lifts
the Kramers degeneracy at each $\mathbf{k}$-point, and leads to the mixing of
the spin singlet-even parity and spin triplet odd-parity parings. On the other
hand, the time-reversal symmetry $T$ relates the two states at $\mathbf{k}$ and
$-\mathbf{k}$ points with the opposite spins, and the external magnetic field
$B$ further breaking $T$ leads to the directional dependence of the nonlinear
resistivity called magnetochiral anisotropy (MCA). Here we demonstrate
theoretically that the two-component nature of the order parameter, i.e., even
and odd pairings, leads to the gigantic enhancement of the MCA in the
fluctuation region, in Rashba superconductor as a representative example of
noncentrosymmetric system. This reveals the superconducting analogue of
"ferroelectric" appearing in the transport phenomena.


  A summary of recent results from the T2K experiment and discussion of near
future plans.


  This paper investigates model robustness in reinforcement learning (RL) to
reduce the sim-to-real gap in practice. We adopt the framework of
distributionally robust Markov decision processes (RMDPs), aimed at learning a
policy that optimizes the worst-case performance when the deployed environment
falls within a prescribed uncertainty set around the nominal MDP. Despite
recent efforts, the sample complexity of RMDPs remained mostly unsettled
regardless of the uncertainty set in use. It was unclear if distributional
robustness bears any statistical consequences when benchmarked against standard
RL. Assuming access to a generative model that draws samples based on the
nominal MDP, we characterize the sample complexity of RMDPs when the
uncertainty set is specified via either the total variation (TV) distance or
$\chi^2$ divergence. The algorithm studied here is a model-based method called
{\em distributionally robust value iteration}, which is shown to be
near-optimal for the full range of uncertainty levels. Somewhat surprisingly,
our results uncover that RMDPs are not necessarily easier or harder to learn
than standard MDPs. The statistical consequence incurred by the robustness
requirement depends heavily on the size and shape of the uncertainty set: in
the case w.r.t.~the TV distance, the minimax sample complexity of RMDPs is
always smaller than that of standard MDPs; in the case w.r.t.~the $\chi^2$
divergence, the sample complexity of RMDPs can often far exceed the standard
MDP counterpart.


  We consider a population structured by a space variable and a phenotypical
trait, submitted to dispersion, mutations, growth and nonlocal competition.
This population is facing an environmental gradient: the optimal trait for
survival depends linearly on the spatial variable. The survival or extinction
depends on the sign of an underlying principal eigenvalue. We investigate the
survival case when the initial data satisfies a so-called heavy tail condition
in the space-trait plane. Under these assumptions, we show that the solution
propagates in the favorable direction of survival by accelerating. We derive
some precise estimates on the location of the level sets corresponding to the
total population in the space variable, regardless of their traits. Our
analysis also reveals that the orientation of the initial heavy tail is of
crucial importance.


  Assuming that the relativistic universe is homogeneous and isotropic, we can
unambiguously determine its model and physical properties, which correspond
with the Einstein general theory of relativity (and with its two special
partial solutions: Einstein special theory of relativity and Newton gravitation
theory), quantum mechanics, and observations, too.


  The definition of a concise and effective testbed for Genetic Programming
(GP) is a recurrent matter in the research community. This paper takes a new
step in this direction, proposing a different approach to measure the quality
of the symbolic regression benchmarks quantitatively. The proposed approach is
based on meta-learning and uses a set of dataset meta-features---such as the
number of examples or output skewness---to describe the datasets. Our idea is
to correlate these meta-features with the errors obtained by a GP method. These
meta-features define a space of benchmarks that should, ideally, have datasets
(points) covering different regions of the space. An initial analysis of 63
datasets showed that current benchmarks are concentrated in a small region of
this benchmark space. We also found out that number of instances and output
skewness are the most relevant meta-features to GP output error. Both
conclusions can help define which datasets should compose an effective testbed
for symbolic regression methods.


  This chapter presents the development of a density functional theory
(DFT)-based method for accurate, reliable treatment of various resonances in
atoms. Many of these are known to be notorious for their strong correlation,
proximity to more than one thresholds, degeneracy with more than one minima.
Therefore these pose unusual challenges to both theoreticians and
experimentalists. Our method uses a work-function-based exchange potential in
conjunction with the popular gradient-corrected Lee-Yang-Parr correlation
functional. The resulting Kohn-Sham equation, in the non-relativistic
framework, is numerically solved accurately and efficiently by means of a
generalized pseudospectral method through a non-uniform, optimal spatial
discretization. This has been applied to a variety of excited states, such as
low and high states; single, double, triple as well as multiple excitations;
valence and core excitations; autoionizing states; satellites; hollow and
doubly-hollow states; very high-lying Rydberg resonances; etc., of atoms and
ions, with remarkable success. A thorough and systematic comparison with
literature data reveals that, for all these systems, the exchange-only results
are practically of Hartree-Fock quality; while with inclusion of correlation,
this offers excellent agreement with available experimental data as well as
those obtained from other sophisticated theoretical methods. Properties such as
individual state energies, excitation energies, radial densities as well as
various expectation values are studied. This helps us in predicting many states
for the first time.


  Motivated by a recent experiment on the bilayer
Y$_{1-x}$Ca$_{x}$Ba$_2$Cu$_3$O$_y$ superconductor and based on a bilayer $t-J$
model, we calculate the spin susceptibility at different doping densities in
the even and odd channels in a bilayer system. It is found that the intensity
of the resonance peak in the even channel is much weaker than that in the odd
one, with the resonance position being at a higher frequency. While this
difference decreases as the doping increases, and both the position and
amplitude of the resonance peaks in the two channels are very similar in the
deeply overdoped sample. Moreover, the resonance frequency in the odd channel
is found to be linear with the critical temperature $T_c$, while the resonance
frequency increases as doping decreases in the even channel and tends to
saturate at the underdoped sample. We elaborate the results based on the Fermi
surface topology and the d-wave superconductivity.


  There is now abundant evidence that the luminosity of the Galactic
super-massive black hole (SMBH) has not always been as low as it is nowadays.
The observation of varying non-thermal diffuse X-ray emission in molecular
complexes in the central 300 pc has been interpreted as delayed reflection of a
past illumination by bright outbursts of the SMBH. The observation of different
variability timescales of the reflected emission in the Sgr A molecular complex
can be well explained if the X-ray emission of at least two distinct and
relatively short events (i.e. about 10 years or less) is currently propagating
through the region. The number of such events or the presence of a
long-duration illumination are open questions.
  Variability of the reflected emission all over of the central 300 pc, in
particular in the 6.4 keV Fe Ka line, can bring strong constraints. To do so we
performed a deep scan of the inner 300 pc with XMM-Newton in 2012. Together
with all the archive data taken over the course of the mission, and in
particular a similar albeit more shallow scan performed in 2000-2001, this
allows for a detailed study of variability of the 6.4 keV line emission in the
region, which we present here.
  We show that the overall 6.4 keV emission does not strongly vary on average,
but variations are very pronounced on smaller scales. In particular, most
regions showing bright reflection emission in 2000-2001 significantly decrease
by 2012. We discuss those regions and present newly illuminated features. The
absence of bright steady emission argues against the presence of an echo from
an event of multi-centennial duration and most, if not all, of the emission can
likely be explained by a limited number of relatively short (i.e. up to 10
years) events.


  This is an expository article, written for a special edition of the journal
of the UMA (Union Matematica Argentina) commemorating the mathematician Misha
Cotlar. The article gives an introduction to the n-homology groups and surveys
some developments, with a particular emphasis on results pertaining to the
problem of calculating n-homology groups.


  Deformable image registration (DIR), aiming to find spatial correspondence
between images, is one of the most critical problems in the domain of medical
image analysis. In this paper, we present a novel, generic, and accurate
diffeomorphic image registration framework that utilizes neural ordinary
differential equations (NODEs). We model each voxel as a moving particle and
consider the set of all voxels in a 3D image as a high-dimensional dynamical
system whose trajectory determines the targeted deformation field. Our method
leverages deep neural networks for their expressive power in modeling dynamical
systems, and simultaneously optimizes for a dynamical system between the image
pairs and the corresponding transformation. Our formulation allows various
constraints to be imposed along the transformation to maintain desired
regularities. Our experiment results show that our method outperforms the
benchmarks under various metrics. Additionally, we demonstrate the feasibility
to expand our framework to register multiple image sets using a unified form of
transformation,which could possibly serve a wider range of applications.


  This paper introduces a framework for the bottom-up simulation of
SLD-resolution based on partial evaluation. The main idea is to use database
facts to represent a set of SLD goals. For deductive databases it is natural to
assume that the rules defining derived predicates are known at "compile time",
whereas the database predicates are known only later at runtime. The framework
is inspired by the author's own SLDMagic method, and a variant of Earley
deduction recently introduced by Heike Stephan and the author. However, it
opens a much broader perspective. [To appear in Theory and Practice of Logic
Programming (TPLP)]


  The focus of this paper is on a poorly understood invariant of a commutative
noetherian local ring $R$ with residue field $k$: the stable cohomology modules
$\hat{Ext}^{n}_R(k,k)$, defined for each $n\in\mathbb{Z}$ by Benson and
Carlson, Mislin, and Vogel; it coincides with Tate cohomology when $R$ is
Gorenstein. It is proved that important properties of $R$, such as being
regular, complete intersection, or Gorenstein, are detected by the $k$-rank of
$\hat{Ext}^{n}_R(k,k)$ for an arbitrary $n\in\mathbb{Z}$. Such numerical
characterizations are made possible by results on the structure of
$\mathbb{Z}$-graded $k$-algebra carried by $\hat{Ext}^{n}_R(k,k)$. It is proved
that in many cases this algebra is determined by the absolute cohomology
algebra through a canonical homomorphism
${Ext}^{n}_R(k,k)\to\hat{Ext}^{n}_R(k,k)$.


  We consider a quantum many-body model describing a system of electrons
interacting with themselves and hopping from one ion to another of a one
dimensional lattice. We show that the ground state energy of such system, as a
functional of the ionic configurations, has local minima in correspondence of
configurations described by smooth ${\pi\over p_F}$ periodic functions, if the
interaction is repulsive and large enough and $p_F$ is the Fermi momentum of
the electrons. This means physically that a $d=1$ metal develop a periodic
distortion of its reticular structure (Peierls instability). The minima are
found solving the Eulero-Lagrange equations of the energy by a contraction
method.


  In our recent dietary assessment field studies on passive dietary monitoring
in Ghana, we have collected over 250k in-the-wild images. The dataset is an
ongoing effort to facilitate accurate measurement of individual food and
nutrient intake in low and middle income countries with passive monitoring
camera technologies. The current dataset involves 20 households (74 subjects)
from both the rural and urban regions of Ghana, and two different types of
wearable cameras were used in the studies. Once initiated, wearable cameras
continuously capture subjects' activities, which yield massive amounts of data
to be cleaned and annotated before analysis is conducted. To ease the data
post-processing and annotation tasks, we propose a novel self-supervised
learning framework to cluster the large volume of egocentric images into
separate events. Each event consists of a sequence of temporally continuous and
contextually similar images. By clustering images into separate events,
annotators and dietitians can examine and analyze the data more efficiently and
facilitate the subsequent dietary assessment processes. Validated on a held-out
test set with ground truth labels, the proposed framework outperforms baselines
in terms of clustering quality and classification accuracy.


  In this paper we consider greedy scheduling algorithms in wireless networks,
i.e., the schedules are computed by adding links greedily based on some
priority vector. Two special cases are considered: 1) Longest Queue First (LQF)
scheduling, where the priorities are computed using queue lengths, and 2)
Static Priority (SP) scheduling, where the priorities are pre-assigned. We
first propose a closed-form lower bound stability region for LQF scheduling,
and discuss the tightness result in some scenarios. We then propose an lower
bound stability region for SP scheduling with multiple priority vectors, as
well as a heuristic priority assignment algorithm, which is related to the
well-known Expectation-Maximization (EM) algorithm. The performance gain of the
proposed heuristic algorithm is finally confirmed by simulations.


  In this paper we investigate the spin-current and its shot-noise spectrum in
a single-molecule quantum dot coupled with a local phonon mode. We pay special
attention on the effect of phonon on the quantum transport property. The
spin-polarization dependent current is generated by a rotating magnetic filed
applied in the quantum dot. Our results show the remarkable influence of phonon
mode on the zero-frequency shot noise. The electron-phonon interaction leads to
sideband peaks which are located exactly on the integer number of the phonon
frequency and moreover the peak-height is sensitive to the electron-phonon
coupling.


  J.-P. Thouvenot and the author showed via different approaches that the
centralizer of a mixing rank-one infinite measure preserving transformation was
trivial. In this note the author presents his joining proof. We also consider
constructions with algebraic spacers as well as a class of Sidon constructions
to produce new examples of mixing rank one transformations. In connection with
Gordin's question on the existence of homoclinic ergodic actions for a zero
entropy system we also discuss Poisson suspensions of some modifications of
Sidon rank one constructions.


  Accretion induced collapse (AIC) may be responsible for the formation of some
interesting neutron star binaries, e.g., millisecond pulsars, intermediate-mass
binary pulsars, etc. It has been suggested that oxygen-neon white dwarfs (ONe
WDs) can increase their mass to the Chandrasekhar limit by multiple He-shell
flashes, leading to AIC events. However, the properties of He-shell flashes on
the surface of ONe WDs are still not well understood. In this article, we aim
to study He-shell flashes on the surface of ONe WDs in a systematic approach.
We investigated the long-term evolution of ONe WDs accreting He-rich material
with various constant mass-accretion rates by time-dependent calculations with
the stellar evolution code Modules for Experiments in Stellar Astrophysics
(MESA), in which the initial ONe WD masses range from 1.1 to 1.35 M . We found
that the mass-retention efficiency increases with the ONe WD mass and the
mass-accretion rate, whereas both the nova cycle duration and the ignition mass
decrease with the ONe WD mass and the mass-accretion rate. We also present the
nuclear products in different accretion scenarios. The results presented in
this article can be used in the future binary population synthesis studies of
AIC events.


  In order to improve the quality of synthesized videos, currently, one
predominant method involves retraining an expert diffusion model and then
implementing a noising-denoising process for refinement. Despite the
significant training costs, maintaining consistency of content between the
original and enhanced videos remains a major challenge. To tackle this
challenge, we propose a novel formulation that considers both visual quality
and consistency of content. Consistency of content is ensured by a proposed
loss function that maintains the structure of the input, while visual quality
is improved by utilizing the denoising process of pretrained diffusion models.
To address the formulated optimization problem, we have developed a
plug-and-play noise optimization strategy, referred to as Noise Calibration. By
refining the initial random noise through a few iterations, the content of
original video can be largely preserved, and the enhancement effect
demonstrates a notable improvement. Extensive experiments have demonstrated the
effectiveness of the proposed method.


  A precise estimation of the computational complexity in Shor's factoring
algorithm under the condition that the large integer we want to factorize is
composed by the product of two prime numbers, is derived by the results related
to number theory. Compared with Shor's original estimation, our estimation
shows that one can obtain the solution under such a condition, by less
computational complexity.


  The Casimir force is a spectacular consequence of the existence of vacuum
fluctuations and thus deserves a place in courses on quantum theory. We argue
that the scattering approach within a one-dimensional field theory is well
suited to discuss the Casimir effect. It avoids in a transparent way
divergences appearing in the evaluation of the vacuum energy. Furthermore, the
scattering approach connects in a natural manner to the standard discussion of
one-dimensional scattering problems in a quantum theory course. Finally, it
allows to introduce students to the methods employed in the current research
literature to determine the Casimir force in real-world systems.


  We analyze the second Fourier coefficient $v_2$ of the pion azimuthal
distribution in non-central heavy-ion collisions in a relativistic hydrodynamic
model. The exact treatment of the decay kinematics of resonances leads to
almost vanishing azimuthal anisotropy of pions near the midrapidity, while the
matter elliptic flow is in-plane at freeze-out. In addition, we reproduce the
rapidity dependence of $v_2$ for pions measured in non-central Pb + Pb
collisions at 158$A$ GeV. This suggests that resonance particles as well as
stable particles constitute the in-plane flow and are important ingredients for
the understanding of the observed pion flow.


  This paper presents a procedure to retrieve subsets of relevant documents
from large text collections for Content Analysis, e.g. in social sciences.
Document retrieval for this purpose needs to take account of the fact that
analysts often cannot describe their research objective with a small set of key
terms, especially when dealing with theoretical or rather abstract research
interests. Instead, it is much easier to define a set of paradigmatic documents
which reflect topics of interest as well as targeted manner of speech. Thus, in
contrast to classic information retrieval tasks we employ manually compiled
collections of reference documents to compose large queries of several hundred
key terms, called dictionaries. We extract dictionaries via Topic Models and
also use co-occurrence data from reference collections. Evaluations show that
the procedure improves retrieval results for this purpose compared to
alternative methods of key term extraction as well as neglecting co-occurrence
data.


  A method for the calculation of translationally invariant wave functions for
systems of identical fermions with arbitrary potential of pair interaction is
developed. It is based on the well-known result that the essential dynamic part
of the Hamiltonian for the system of identical particles is the Reduced
Hamiltonian operator describing relative movement of two particles inside the
system. The eigenfunctions of this operator take into account all correlations
caused by interaction. These eigenfunctions are basic for the construction of
the components (i.e. the functions with a lower degree of antisymmetry) of the
system wave functions. The main problem of this approach appears to be
antisymmetrization of the components. The developed universal algorithm for
antisymmetrization gives a possibility to perform this operation in a simple
way and keep numerical approximations under control.


  The incorporation of prior knowledge into learning is essential in achieving
good performance based on small noisy samples. Such knowledge is often
incorporated through the availability of related data arising from domains and
tasks similar to the one of current interest. Ideally one would like to allow
both the data for the current task and for previous related tasks to
self-organize the learning system in such a way that commonalities and
differences between the tasks are learned in a data-driven fashion. We develop
a framework for learning multiple tasks simultaneously, based on sharing
features that are common to all tasks, achieved through the use of a modular
deep feedforward neural network consisting of shared branches, dealing with the
common features of all tasks, and private branches, learning the specific
unique aspects of each task. Once an appropriate weight sharing architecture
has been established, learning takes place through standard algorithms for
feedforward networks, e.g., stochastic gradient descent and its variations. The
method deals with domain adaptation and multi-task learning in a unified
fashion, and can easily deal with data arising from different types of sources.
Numerical experiments demonstrate the effectiveness of learning in domain
adaptation and transfer learning setups, and provide evidence for the flexible
and task-oriented representations arising in the network.


  The aim of this paper is to extend basic understanding of Engel structures
through developing geometric constructions which are canonical to a certain
degree and the dynamics of Cauchy characteristics in the transverse spaces
which may exhibit elliptic, parabolic, or hyperbolic natures in typical cases.


  We report on the detection of two Ne VIII absorbers, at z = 0.61907 and z =
0.57052 in the HST/COS spectrum of background quasars SDSS J 080908.13+461925.6
and SBS 1122+594 respectively. The Ne VIII 770 line is at $\sim 3\sigma$
significance. In both instances, the NeVIII is found to be tracing gas with $T
\gtrsim 10^5$ K, predominantly collisionally ionized, with moderate densities
of $n_{H} \lesssim 10^{-4}$ $cm^{-3}$, sub-solar metallicities and total
hydrogen column densities of $N(H) \gtrsim 10^{19}$ $cm^{2}$. In the z =
0.61907 absorber, the low, intermediate ions and O VI are consistent with
origin in photoionized gas, with the O VI potentially having some contribution
from the warm collisional phase traced by Ne VIII. The z = 0.57052 system has H
I absorption in at least three kinematically distinct components, with one of
them having $b (H I) = 49 {\pm} 11$ $km s^{-1}$. The intermediate ionization
lines, O VI and Ne VIII are coincident in velocity with this component. Their
different line widths suggest warm temperatures of $T = (0.5 - 1.5) \times
10^5$ K. Both absorbers are residing in regions where there are several
luminous ($ \gtrsim L^*$) galaxies. The absorber at z = 0.57052 is within the
virial radius of a $2.6L^*$ galaxy, possibly associated with shock heated
circumgalactic material.


  Progress on many Natural Language Processing (NLP) tasks, such as text
classification, is driven by objective, reproducible and scalable evaluation
via publicly available benchmarks. However, these are not always representative
of real-world scenarios where text classifiers are employed, such as sentiment
analysis or misinformation detection. In this position paper, we put forward
two points that aim to alleviate this problem. First, we propose to extend text
classification benchmarks to evaluate the explainability of text classifiers.
We review challenges associated with objectively evaluating the capabilities to
produce valid explanations which leads us to the second main point: We propose
to ground these benchmarks in human-centred applications, for example by using
social media, gamification or to learn explainability metrics from human
judgements.


  We use the principal component analysis (PCA) to study geomagnetic activity
at annual resolution using a network of 26 magnetic stations in 1966-2015, and
an extended network of 40 stations in 1980-2015. The first principal component
(PC1) describes the long-term evolution of global geomagnetic activity, and has
an excellent correlation with indices like the Kp/Ap index. The two networks
give identical results for PC1. The second principal component (PC2) is highly
correlated with the annual percentage of high-speed streams (HSS). The extended
network has a slightly higher sensitivity to HSSs. We verify the non-trivial
latitudinal distribution of the second empirical orthogonal function (EOF2). We
find that the amplitude of the 22-year variation of geomagnetic activity has a
closely similar latitudinal distribution as EOF2. This verifies that the
22-year variation of geomagnetic activity is related to HSSs. The most likely
cause is the Russell-McPherron mechanism.


  The cross section of neutrino-induced neutral-current coherent $\pi^0$
production on a carbon-dominated target is measured in the NOvA near detector.
This measurement uses a narrow-band neutrino beam with an average neutrino
energy of 2.7\,GeV, which is of interest to ongoing and future long-baseline
neutrino oscillation experiments. The measured, flux-averaged cross section is
$\sigma = 13.8\pm0.9 (\text{stat})\pm2.3 (\text{syst}) \times
10^{-40}\,\text{cm}^2/\text{nucleus}$, consistent with model prediction. This
result is the most precise measurement of neutral-current coherent $\pi^0$
production in the few-GeV neutrino energy region.


  We define and derive basic properties of the notion of Rota-Baxter operator
on anti-flexible algebra. Pre-anti-flexible algebra structure and associated
left(right)-symmetric algebra are constructed from a given Rota-Baxter operator
on an anti-flexible algebra. The notion of $\mathcal{O}$-operator on
anti-flexible algebra are recalled and use to build left(right)-symmetric
algebra as well as related properties. Furthermore, we introduce Nijenhuis
anti-flexible algebra and derive associated properties. Nijenhuis operator on
anti-flexible algebra is used to build pre-anti-flexible algebra structure and
related left(right)-symmetric algebra.


  In most astrophysical processes involving synchrotron radiation, the
pitch-angle distribution of the electrons is assumed to be isotropic. However,
if electrons are accelerated anisotropically, e.g, in a relativistic shock wave
with an ordered magnetic field or in magnetic reconnection regions, the
electron pitch angles might be anisotropic. In this work, we study synchrotron
radiation from electrons with a pitch-angle distribution with respect to a
large-scale uniform magnetic field. Assuming that the pitch-angle distribution
is normal with a scatter of $\sigma_p$ and that the viewing direction is where
the pitch-angle direction peaks, we find that for electrons with a Lorentz
factor $\gamma$, the observed flux satisfies $F_\nu\propto\nu^{2/3}$ for
$\nu\ll\nu_{\rm cr}$ ($\nu_{\rm cr}$ is the critical frequency of synchrotron),
if $\sigma_p\lesssim1/\gamma$ is satisfied. On the other hand, if
$\sigma_p\gg1/\gamma$, the spectrum below $\nu_{\rm cr}$ is a broken power law
with a break frequency $\nu_{\rm br}\sim2\nu_{\rm cr}/\sigma_p^3\gamma^3$,
e.g., $F_\nu\propto\nu^{2/3}$ for $\nu\ll\nu_{\rm br}$ and
$F_\nu\propto\nu^{1/3}$ for $\nu_{\rm br}\ll\nu\ll\nu_{\rm cr}$. Thus the
ultimate synchrotron line of death is $F_\nu\propto\nu^{2/3}$. We discuss the
application of this theory to blazars and gamma-ray bursts (GRBs).


  Let $V\in\mathbb{Q}(i)(\a_1,\dots,\a_n)(\q_1,\q_2)$ be a rationally
parametrized planar homogeneous potential of homogeneity degree $k\neq -2, 0,
2$. We design an algorithm that computes polynomial \emph{necessary} conditions
on the parameters $(\a_1,\dots,\a_n)$ such that the dynamical system associated
to the potential $V$ is integrable. These conditions originate from those of
the Morales-Ramis-Sim\'o integrability criterion near all Darboux points. The
implementation of the algorithm allows to treat applications that were out of
reach before, for instance concerning the non-integrability of polynomial
potentials up to degree $9$. Another striking application is the first complete
proof of the non-integrability of the \emph{collinear three body problem}.


  Single molecule fluorescence detection of barium is investigated for
enhancing the sensitivity and robustness of a neutrinoless double beta decay
($0\nu\beta\beta$) search in $^{136}$Xe, the discovery of which would alter our
understanding of the nature of neutrinos and the early history of the Universe.
A key developmental step is the synthesis of barium-selective chemosensors
capable of incorporation into ongoing experiments in high-pressure $^{136}$Xe
gas. Here we report turn-on fluorescent naphthalimide chemosensors containing
monoaza- and diaza-crown ethers as agents for single Ba$^{2+}$ detection.
Monoaza-18-crown-6 ether naphthalimide sensors showed sensitivity primarily to
Ba$^{2+}$ and Hg$^{2+}$, whereas two diaza-18-crown-6 ether naphthalimides
revealed a desirable selectivity toward Ba$^{2+}$. Solution-phase fluorescence
and NMR experiments support a photoinduced electron transfer mechanism enabling
turn-on fluorescence sensing in the presence of barium ions. Changes in
ion-receptor interactions enable effective selectivity between competitive
barium, mercury, and potassium ions, with detailed calculations correctly
predicting fluorescence responses. With these molecules, dry-phase single
Ba$^{2+}$ ion imaging with turn-on fluorescence is realized using oil-free
microscopy techniques. This represents a significant advance toward a practical
method of single Ba$^{2+}$ detection within large volumes of $^{136}$Xe,
plausibly enabling a background-free technique to search for the hypothetical
process of $0\nu\beta\beta$.


  The formula for dark energy density derived by Gurzadyan and Xue provides a
value of density parameter of dark energy in remarkable agreement with current
cosmological datasets, unlike numerous phenomenological dark energy scenarios
where the corresponding value is postulated. This formula suggests the
possibility of variation of physical constants such as the speed of light and
the gravitational constant. Considering several cosmological models based on
that formula and deriving the cosmological equations for each case, we show
that, in all models source terms appear in the continuity equation. So, one one
hand, GX models make up a rich set covering a lot of currently proposed models
of dark energy, on the other hand, they reveal hidden symmetries, with a
particular role of the separatrix $\Omega_m=2/3$, and link with the issue of
the content of physical constants.


  Using Single Electron Capacitance Spectroscopy, we study electron additions
in quantum dots containing two potential minima separated by a shallow barrier.
Analysis of addition spectra in magnetic field allows us to distinguish whether
electrons are localized in either potential minimum or delocalized over the
entire dot. We demonstrate that high magnetic field abruptly splits up a
low-density droplet into two smaller fragments, each residing in a potential
minimum. An unexplained cancellation of electron repulsion between electrons in
these fragments gives rise to paired electron additions.


  It has been a widely belief that for a planar convex domain with two
coordinate axes of symmetry, the location of maximal norm of gradient of
torsion function is either linked to contact points of largest inscribed circle
or connected to points on boundary of minimal curvature. However, we show that
this is not quite true in general. Actually, we derive the precise formula for
the location of maximal norm of gradient of torsion function on nearly ball
domains in $\mathbb{R}^n$, which displays nonlocal nature and thus does not
inherently establish a connection to the aforementioned two types of points.
Consequently, explicit counterexamples can be straightforwardly constructed to
illustrate this deviation from conventional understanding. We also prove that
for a rectangular domain, the maximum of the norm of gradient of torsion
function exactly occurs at the centers of the faces of largest $(n-1)$-volume.


  Using a new implicit discretization scheme, we study in this paper the
existence and uniqueness of strong solutions for a class of Lur'e dynamical
systems where the set-valued feedback depends on both time and state. This work
is a generalization of \cite{abc} where the time-dependent set-valued feedback
is considered to acquire only weak solutions. Obviously, strong solutions and
implicit discretization scheme are nice properties, especially for numerical
simulation. We also provide some conditions such that the solutions are
exponentially attractive. The obtained results can be used to study the
time-varying Lur'e systems with errors in data. Our result is new even the
set-valued feedback depends only on the time.


  Given a matrix order $n$, a restart parameter $m$ ($m < n$), a decreasing
positive sequence $f(0) > f(1) > ... > f(q) \geq 0$, where $q < n/m$, it is
shown that there exits an $n$-by-$n$ matrix $A$ and a vector $r_0$ with
$\|r_0\|=f(0)$ such that $\|r_k\|=f(k)$, $k=1,...,q$, where $r_k$ is the
residual at cycle $k$ of restarted GMRES with restart parameter $m$ applied to
the linear system $Ax=b$, with initial residual $r_0=b-Ax_0$. Moreover, the
matrix $A$ can be chosen to have any desired eigenvalues. We can also construct
arbitrary cases of stagnation; namely, when $f(0) > f(1) > ... > f(i) = f(i+1)
\geq 0 $ for any $i <q $. The restart parameter can be fixed or variable.


  We demonstrate how the orientation of the Rb cell can significantly affect
the intensity and spectral characteristics of both the frequency up- and
down-converted fields generated by nonlinear processes in Rb vapour. The
efficiency of parametric wave mixing in Rb vapour excited to the 5D5/2 level by
two-colour resonant laser light can be significantly increased by seeding the
excitation region with coherent and directional radiation at 5.23 um that is
resonant with the population inverted 5D5/2-6P3/2 transition. It has been shown
that the process of velocity insensitive two-photon excitation is central to
understanding the observed coherent blue and mid-IR light enhancements and that
the velocity insensitive and velocity selective two-photon excitations could
produce two co-existing but spectrally and spatially distinguishable mid-IR
fields at 5.23 um.


  Muon-spin rotation (muSR) experiments are often used to study the magnetic
field distribution in type-II superconductors in the vortex state. Based on the
determination of the magnetic penetration depth it is frequently
speculated---also controversially---about the order-parameter symmetry of the
studied superconductors. This article reports on a combined muSR and
magnetization study of the mixed state in the cuprate high-temperature
superconductor La_{1.83}Sr_{0.17}CuO_{4} in a low magnetic field of 20 mT
applied along the c axis of a single crystal. The macroscopic magnetization
measurements reveal substantial differences for various cooling procedures.
Yet, indicated changes in the vortex dynamics between different temperature
regions as well as the results of the microscopic muSR experiments are
virtually independent of the employed cooling cycles. Additionally, it is found
that the mean magnetic flux density, locally probed by the muons, strongly
increases at low temperatures. This can possibly be explained by a non-random
sampling of the spatial field distribution of the vortex lattice in this
cuprate superconductor caused by intensified vortex pinning.


  We study the regularity of weak solutions for two elliptic systems involving
the $n$-Laplacian and a critical nonlinearity in the right hand side:
$H$-systems and $n$-harmonic maps into compact Riemannian manifolds. Under the
assumptions that the solutions belong to $W^{n/2,2}$ in an even dimension $n$,
we prove their continuty.
  The tools used in the proof involve Hardy spaces and BMO, and the
Rivi\`{e}re--Uhlenbeck decomposition (with estimates in Morrey spaces). A
prominent role is played by the Coifman--Rochberg--Weiss commutator theorem.


  One of the most subtle points in the modern relativistic models for
microarcsecond astrometrical observations is the treatment of the influence of
translational motion of gravitating bodies on the light propagation. This paper
describes numerical simulations of the light propagation in the gravitational
field of moving gravitating bodies as well as summarizes the underlying theory.
The simulations include high-precision numerical integrations of both
post-Newtonian and post-Minkowskian differential equations of light propagation
and a detailed comparison of the results of the numerical integrations with
various available approximate analytical formulas. The simulations has been
performed both for hypothetical bodies with various parameters of trajectories
as well as for all the major bodies of the solar system using the JPL ephemeris
DE405/LE405 to calculate their motion.
  It is shown that for the accuracy of $\sim 0.2$ $\mu$as it is sufficient to
use the well-known solution for the light propagation in the field of a
motionless mass monopole and substitute in that solution the position of the
body at the moment of closest approach between the actual trajectory of the
body and the unperturbed light path (as it was first suggested by Hellings
(1986)). For a higher accuracy one should use either the post-Newtonian
solution for uniformly moving bodies (Klioner & Kopeikin, 1992) or the
post-Minkowskian solution for arbitrarily moving bodies (Kopeikin & Schaefer,
1999). For astrometric observations performed from within the solar system
these two solutions guarantee the accuracy of $\sim 0.002$ $\mu$as and are
virtually indistinguishable from each other.


  We present the logic BL_Chang, an axiomatic extension of BL (see P. H\'ajek -
Metamathematics of fuzzy logic - 1998, Kluwer) whose corresponding algebras
form the smallest variety containing all the ordinal sums of perfect MV-chains.
We will analyze this logic and the corresponding algebraic semantics in the
propositional and in the first-order case. As we will see, moreover, the
variety of BL_Chang-algebras will be strictly connected to the one generated by
Chang's MV-algebra (that is, the variety generated by all the perfect
MV-algebras): we will also give some new results concerning these last
structures and their logic.


A short and mean paper.


  Propagation of short laser pulses in a medium of Lambda-atoms in the
intuitive sequence and under conditions of adiabatic following is studied. The
regime of superluminal propagation is obtained and the conditions of efficient
population transfer in the medium are analyzed.


  The features of alternative approach of non-equilibrium evolution
thermodynamics are shown on the example of theory of vacancies by opposed to
the classic prototype of Landau theory. On this foundation a strict theory of
the melting of metals, based on development of Frenkel ideas about the vacancy
mechanism of such phenomena, is considered. The phenomenon of melting is able
to be described as a discontinuous phase transition, while the traditional
Frenkel's solution in the region of low-concentration of vacancies can describe
such transition only as continuous one. The problem of limiting transition of
shear modulus to zero values in the liquid state, as well as the problem of the
influence of extended state of vacancies on their mobility, is discussed.


  A rigorous formalism for determining the electric dipole polarizability of a
three-hadron bound complex in the case that the system has only one bound
(ground) state has been elaborated. On its basis, by applying a model wave
function that takes into account specific features of the structure of the
lightest hypernucleus and using the known low-energy experimental data for the
p-n and lambda-d systems as input data, we have calculated the value of the
electric dipole polarizability of the lambda hypertriton. It follows from our
study that the polarizability of the lambda hypertriton is close to 3 fm^3
exceeding the polarizabilities of the ordinary three-nucleon nuclei by an order
of magnitude.


  We have classified the point-like X-ray sources detected by the SRG/eROSITA
telescope in the deep Lockman Hole survey. The goal was to separate the sources
into Galactic and extragalactic objects. In this work have used the results of
our previous cross-match of X-ray sources with optical catalogs. To classify
SRG/eROSITA sources we have used the flux ratio $F_{x}/F_{o}$ and information
about the source optical extent. As a result, of the 6885 X-ray sources in the
eROSITA catalog 357 sources have been classified as Galactic and 5929 and as
extragalactic. 539 out of 6885 have been treated as hostless, i.e., having no
optical counterparts in the optical catalogs under consideration. 60 have
remained unclassified due to the insufficient reliability of optical
photometry. Recall and precision for the extragalactic sources are 99.9 and
98.9% (respectively) and 91.6 and 99.7% for the Galactic sources. Using this
classification, we have constructed the curves of cumulative number counts for
the Galactic and extragalactic sources in the Lockman Hole field. The code that
accompanies this paper is available at
https://github.com/mbelveder/ero-lh-class.git.


  Semi-infinite quantum spin chains display spin autocorrelations near the
boundary with power-law exponents that are given by boundary conformal field
theories. We show that NMR measurements on spinless impurities that break a
quantum spin chain lead to a spin-lattice relaxation rate 1/T_1^edge that has a
temperature dependence which is a direct probe of the anomalous boundary
exponents. For the antiferromagnetic S=1/2 spin chain, we show that 1/T_1^edge
behaves as T (log T)^2 instead of (log T)^1/2 for a bulk measurement. We show
that, in the case of a one-dimensional conductor described by a Luttinger
liquid, a similar measurement leads to a relaxation rate 1/T_1^{edge} behaving
as T, independent of the anomalous exponent K_rho.


  A graph is nearly embedded in a surface if it consists of graph $G_0$ that is
embedded in the surface, together with a bounded number of vortices having no
large transactions. It is shown that every large wall (or grid minor) in a
nearly embedded graph, many rows of which intersect the embedded subgraph $G_0$
of the near-embedding, contains a large subwall that is planarly embedded
within $G_0$. This result provides some hidden details needed for a strong
version of the Robertson and Seymour's excluded minor theorem as presented in
[K. Kawarabayashi, B. Mohar, Some recent progress and applications in graph
minor theory, Graphs Combin. 23 (2007) 1-46].


  I propose that much recent history can be explained by hypothesizing that
sometime during the last quarter of 2016, the history of the world underwent a
macroscopic quantum tunneling event, creating, according to the Many Worlds
Interpretation, a new branch of the multiverse in which my consciousness and
that of my readers is now trapped. The failure of much political polling is
then understood by assuming that the particular branch we are on had very low
amplitude in the quantum wave function of the multiverse. In this view, one
must take a different attitude towards alternative facts than that proposed by
the mainstream media. We know that quantum tunneling can change the low energy
laws of physics in the different branches of the wave function. Alternative
facts may simply be the reflection of the media's ignorance of the state of the
world after a quantum transition of this magnitude.


  The nonlinear propagation of the dust-acoustic bright and dark envelope
solitons in an opposite polarity dusty plasma system (composed of non-extensive
$q$-distributed electrons, isothermal ions, and positively as well as
negatively charged warm dust) have been theoretically investigated. The
reductive perturbation method (which is valid for a small, but finite amplitude
limit) is employed to derive the nonlinear Schr\"{o}dinger equation. Two types
of modes (namely, fast and slow dust-acoustic (DA) modes) have been observed.
The conditions for the modulational instability (MI) and its growth rate in the
unstable regime of the DA waves are significantly modified by the effects of
non-extensive electrons, dust mass, temperatures of different plasma species,
etc. The implications of the obtained results from our current investigation in
space (viz. Jupiters magnetosphere, upper mesosphere, and comets tails) and
laboratory (e.g. direct current and radio-frequency discharges, plasma
processing reactors, fusion plasma devices, and solid-fuel combustion products,
etc.) dusty plasmas are briefly discussed.


  A deeper understanding of pedestrian dynamics is essential to improve crowd
flows in public spaces such as train stations. It is essential to understand
both the physical and the psychological processes present in this context.
However, current research on train boarding behavior is limited in scope and
mainly focuses on how group level variables such as number of
boarders/deboarders influence train boarding efficiency. Viewing pedestrian
dynamics through a psychological lens is important for a detailed understanding
of the train boarding context and to recognize target areas for improving crowd
flows. At Dutch train stations, boarders follow a social norm of waiting at the
train door until deboarding is complete. Although people generally adhere to
this norm, the way it is executed may not be optimal for deboarding efficiency.
We investigate how waiting boarders form a deboarding channel (a corridor where
deboarders exit the train) which is a macroscopic structure formed by
pedestrians, and how this channel in turn influences the efficiency of
deboarding. Analyzing a dataset with 3278 boarding events at Utrecht Centraal
Station in the Netherlands from 2017 - 2020 (a subset of a trajectory dataset
that captures 100,000 trajectories per day), we found that higher numbers of
boarders and a higher ratio of boarders to deboarders, reduced the width of the
deboarding channel, and a lower width was associated with lower deboarding
efficiency. These results shift the focus from group level variables to
identifying macroscopic structures that are formed when pedestrians interact
within a social system and provide specific target areas where
nudges/behavioral interventions could be implemented.


  We study the tradeoff between the statistical error and communication cost of
distributed statistical estimation problems in high dimensions. In the
distributed sparse Gaussian mean estimation problem, each of the $m$ machines
receives $n$ data points from a $d$-dimensional Gaussian distribution with
unknown mean $\theta$ which is promised to be $k$-sparse. The machines
communicate by message passing and aim to estimate the mean $\theta$. We
provide a tight (up to logarithmic factors) tradeoff between the estimation
error and the number of bits communicated between the machines. This directly
leads to a lower bound for the distributed \textit{sparse linear regression}
problem: to achieve the statistical minimax error, the total communication is
at least $\Omega(\min\{n,d\}m)$, where $n$ is the number of observations that
each machine receives and $d$ is the ambient dimension. These lower results
improve upon [Sha14,SD'14] by allowing multi-round iterative communication
model. We also give the first optimal simultaneous protocol in the dense case
for mean estimation.
  As our main technique, we prove a \textit{distributed data processing
inequality}, as a generalization of usual data processing inequalities, which
might be of independent interest and useful for other problems.


  The conditions leading to flat dispersionless frequency bands in truly
one-dimensional parity-time ($\cal PT$) symmetric metamaterials comprising
split-ring resonators (SRRs) arranged in a binary pattern are obtained
analytically. In this paradigmatic system, in which the SRRs are coupled
through both electric and magnetic dipole-dipole forces, flat-bands may arise
from tailoring its natural parameters (such as, e.g., the coupling coefficients
between SRRs) and not from geometrical effects. For sets of parameters which
values are tailored to flatten the upper band of the spectrum, the solution of
the corresponding quadratic eigenvalue problem reveals the existence of
compact, two-site localized eigenmodes. Numerical simulations confirm the
existence and the dynamic stability of such modes, which can be formed through
the evolution of single-site initial excitations without disorder or
nonlinearity.


  We compare the cross section for exclusive $J/\psi$ photoproduction
calculated at NLO in the collinear factorization approach with HERA and LHCb
data. Using the optimum scale formalism together with the subtraction of the
low $k_t<Q_0$ contribution from the NLO coefficient function to avoid double
counting we show that the existing global parton distribution functions (PDFs)
are consistent with the data within their uncertainties. However, at low $x$
the uncertainties of the present global PDFs are large. On the other hand, the
accuracy of the LHCb data are rather good. Therefore, these data provide the
possibility to directly measure the gluon PDF over the very large interval of
$x$, $10^{-6}<x<10^{-2}$, at a fixed low scale.


  We investigate the flow of an electrolyte through a rigid nanochannel
decorated with a surface charge pattern. Employing lattice Boltzmann and
dissipative particle dynamics methods, as well as analytical theory, we show
that the electro-hydrodynamic coupling leads to two distinct flow regimes. The
accompanying discontinuous transition between slow, ionic, and fast, Poiseuille
flows is observed at intermediate ion concentrations, channel widths, and
electrostatic coupling strengths. These findings indicate routes to design
nanochannels containing a typical aqueous electrolyte that exhibit a digital
on/off flux response, which could be useful for nanofluidics and ionotronic
applications.


  We model SYK (Sachdev-Ye-Kitaev) interactions in disordered graphene flakes
up to 300 000 atoms ($\sim$100 nm in diameter) subjected to an out-of-plane
magnetic field $B$ of 5-20 Tesla within the tight-binding formalism. We
investigate two sources of disorder: (i) irregularities at the system
boundaries, and (ii) bulk vacancies, -- for a combination of which we find
conditions which could be favorable for the formation of the phase with SYK
features under realistic experimental conditions above the liquid helium
temperature.


  We show how to embed spacelike slices of the Schwarzschild wormhole (or
Einstein-Rosen bridge) in R3. Graphical images of embeddings are given,
including depictions of the dynamics of this nontraversable wormhole at
constant Kruskal times up to, and beyond, the "pinching off" at Kruskal times
\pm1.


  Unlike traditional third-person cameras mounted on robots, a first-person
camera, captures a person's visual sensorimotor object interactions from up
close. In this paper, we study the tight interplay between our momentary visual
attention and motor action with objects from a first-person camera. We propose
a concept of action-objects---the objects that capture person's conscious
visual (watching a TV) or tactile (taking a cup) interactions. Action-objects
may be task-dependent but since many tasks share common person-object spatial
configurations, action-objects exhibit a characteristic 3D spatial distance and
orientation with respect to the person.
  We design a predictive model that detects action-objects using EgoNet, a
joint two-stream network that holistically integrates visual appearance (RGB)
and 3D spatial layout (depth and height) cues to predict per-pixel likelihood
of action-objects. Our network also incorporates a first-person coordinate
embedding, which is designed to learn a spatial distribution of the
action-objects in the first-person data. We demonstrate EgoNet's predictive
power, by showing that it consistently outperforms previous baseline
approaches. Furthermore, EgoNet also exhibits a strong generalization ability,
i.e., it predicts semantically meaningful objects in novel first-person
datasets. Our method's ability to effectively detect action-objects could be
used to improve robots' understanding of human-object interactions.


  We find an exact solution for the stability limit of relativistic charged
spheres for the case of constant gravitational mass density and constant charge
density. We argue that this provides an absolute stability limit for any
relativistic charged sphere in which the gravitational mass density decreases
with radius and the charge density increases with radius. We then provide a
cruder absolute stability limit that applies to any charged sphere with a
spherically symmetric mass and charge distribution. We give numerical results
for all cases. In addition, we discuss the example of a neutral sphere
surrounded by a thin, charged shell.


  The Stackelberg prediction game (SPG) has been extensively used to model the
interactions between the learner and data provider in the training process of
various machine learning algorithms. Particularly, SPGs played prominent roles
in cybersecurity applications, such as intrusion detection, banking fraud
detection, spam filtering, and malware detection. Often formulated as NP-hard
bi-level optimization problems, it is generally computationally intractable to
find global solutions to SPGs. As an interesting progress in this area, a
special class of SPGs with the least squares loss (SPG-LS) have recently been
shown polynomially solvable by a bisection method. However, in each iteration
of this method, a semidefinite program (SDP) needs to be solved. The resulted
high computational costs prevent its applications for large-scale problems. In
contrast, we propose a novel approach that reformulates a SPG-LS as a single
SDP of a similar form and the same dimension as those solved in the bisection
method. Our SDP reformulation is, evidenced by our numerical experiments,
orders of magnitude faster than the existing bisection method. We further show
that the obtained SDP can be reduced to a second order cone program (SOCP).
This allows us to provide real-time response to large-scale SPG-LS problems.
Numerical results on both synthetic and real world datasets indicate that the
proposed SOCP method is up to 20,000+ times faster than the state of the art.


  Background: The next-to-next-to-next-to-leading order (N3LO) nuclear energy
density functional extends the standard Skyrme functional with new terms
depending on higher-order derivatives of densities, introduced to gain better
precision in the nuclear many-body calculations. A thorough study of the
transformation properties of the functional with respect to different
symmetries is required, as a step preliminary to the adjustment of the coupling
constants. Purpose: Determine to which extent the presence of higher-order
derivatives in the functional can be compatible with the continuity equation.
In particular, to study the relations between the validity of the continuity
equation and invariance of the functional under gauge transformations. Methods:
Derive conditions for the validity of the continuity equation in the framework
of time-dependent density functional theory. The conditions apply separately to
the four spin-isospin channels of the one-body density matrix. Results: We
obtained four sets of constraints on the coupling constants of the N3LO energy
density functional that guarantee the validity of the continuity equation in
all spin-isospin channels. In particular, for the scalar-isoscalar channel, the
constraints are the same as those resulting from imposing the standard U(1)
local-gauge-invariance conditions. Conclusions: Validity of the continuity
equation in the four spin-isospin channels is equivalent to the local-gauge
invariance of the energy density functional. For vector and isovector channels,
such validity requires the invariance of the functional under local rotations
in the spin and isospin spaces.


  Owning up to the authors' occasional mixed performances when playing darts we
follow up on the ingenious work to determine the optimal aim to score high by
Tibshirani et. al [JRS A 174, 213 (2011)] and expand on maximal expected reward
lines assuming spread profiles beyond the standard case of an isotropic
distribution by investigating situations in which a players' aiming quality
differs in horizontal and vertical direction, arguably representing more
realistic profiles. To render the theoretical findings applicable, we determine
regions $\Gamma$ on the dart board that may serve as an aid to players in order
to maximise their score depending on whether said areas are hit sufficiently
often. Lastly we compare all three strategies with the simple approaches to
always aim for triple 20 or bulls eye respectively, probing their usefulness.


  Due to its crucial role in identity and access management in modern
enterprise networks, Active Directory (AD) is a top target of Advanced
Persistence Threat (APT) actors. Conventional intrusion detection systems (IDS)
excel at identifying malicious behaviors caused by malware, but often fail to
detect stealthy attacks launched by APT actors. Recent advance in
provenance-based IDS (PIDS) shows promises by exposing malicious system
activities in causal attack graphs. However, existing approaches are restricted
to intra-machine tracing, and unable to reveal the scope of attackers'
traversal inside a network. We propose HADES, the first PIDS capable of
performing accurate causality-based cross-machine tracing by leveraging a novel
concept called logon session based execution partitioning to overcome several
challenges in cross-machine tracing. We design HADES as an efficient on-demand
tracing system, which performs whole-network tracing only when it first
identifies an authentication anomaly signifying an ongoing AD attack, for which
we introduce a novel lightweight authentication anomaly detection model rooted
in our extensive analysis of AD attacks. To triage attack alerts, we present a
new algorithm integrating two key insights we identified in AD attacks. Our
evaluations show that HADES outperforms both popular open source detection
systems and a prominent commercial AD attack detector.


  This paper proposes a fully decentralized federated learning (FL) scheme for
Internet of Everything (IoE) devices that are connected via multi-hop networks.
Because FL algorithms hardly converge the parameters of machine learning (ML)
models, this paper focuses on the convergence of ML models in function spaces.
Considering that the representative loss functions of ML tasks e.g, mean
squared error (MSE) and Kullback-Leibler (KL) divergence, are convex
functionals, algorithms that directly update functions in function spaces could
converge to the optimal solution. The key concept of this paper is to tailor a
consensus-based optimization algorithm to work in the function space and
achieve the global optimum in a distributed manner. This paper first analyzes
the convergence of the proposed algorithm in a function space, which is
referred to as a meta-algorithm, and shows that the spectral graph theory can
be applied to the function space in a manner similar to that of numerical
vectors. Then, consensus-based multi-hop federated distillation (CMFD) is
developed for a neural network (NN) to implement the meta-algorithm. CMFD
leverages knowledge distillation to realize function aggregation among adjacent
devices without parameter averaging. An advantage of CMFD is that it works even
with different NN models among the distributed learners. Although CMFD does not
perfectly reflect the behavior of the meta-algorithm, the discussion of the
meta-algorithm's convergence property promotes an intuitive understanding of
CMFD, and simulation evaluations show that NN models converge using CMFD for
several tasks. The simulation results also show that CMFD achieves higher
accuracy than parameter aggregation for weakly connected networks, and CMFD is
more stable than parameter aggregation methods.


  We use holography to study sensitive dependence on initial conditions in
strongly coupled field theories. Specifically, we mildly perturb a thermofield
double state by adding a small number of quanta on one side. If these quanta
are released a scrambling time in the past, they destroy the local two-sided
correlations present in the unperturbed state. The corresponding bulk geometry
is a two-sided AdS black hole, and the key effect is the blueshift of the early
infalling quanta relative to the $t = 0$ slice, creating a shock wave. We
comment on string- and Planck-scale corrections to this setup, and discuss
points that may be relevant to the firewall controversy.


  We consider the Cauchy problem of the nonlinear heat equation $u_t -\Delta u=
u^{b},\ u(0,x)=u_0$, with $b\geq 2$ and $b\in \mathbb{N}$. We prove that
initial data $u_0\in \mathcal{S}(\mathbb{R}^{n})$ (the Schwartz
class)arbitrarily small in the scale invariant Besov-norm$\dot B^{-2/b}_{n(b-1)
b/2,q}(\mathbb{R}^{n})$, can produce solutions that blow up in finite time. The
case $b=3$ answers a question raised by Yves Meyer.Our result also proves that
the smallness assumption put in an earlier work by C. Miao, B.~Yuan and B.
Zhang, for the global-in-time solvability, is essentially optimal.


  We investigate the position of the Buchen-Kelly density in a family of
entropy maximising densities which all match European call option prices for a
given maturity observed in the market. Using the Legendre transform which links
the entropy function and the cumulant generating function, we show that it is
both the unique continuous density in this family and the one with the greatest
entropy. We present a fast root-finding algorithm that can be used to calculate
the Buchen-Kelly density, and give upper boundaries for three different
discrepancies that can be used as convergence criteria. Given the call prices,
arbitrage-free digital prices at the same strikes can only move within upper
and lower boundaries given by left and right call spreads. As the number of
call prices increases, these bounds become tighter, and we give two examples
where the densities converge to the Buchen-Kelly density in the sense of
relative entropy when we use centered call spreads as proxies for digital
prices. As pointed out by Breeden and Litzenberger, in the limit a continuous
set of call prices completely determines the density.


  We consider the point evaluation of the solution to interface problems with
geometric uncertainties, where the uncertainty in the obstacle is described by
a high-dimensional parameter $\boldsymbol{y}\in[-1,1]^d$, $d\in\mathbb{N}$. We
focus in particular on an elliptic interface problem and a Helmholtz
transmission problem. Point values of the solution in the physical domain
depend in general non-smoothly on the high-dimensional parameter, posing a
challenge when one is interested in building surrogates. Indeed, high-order
methods show poor convergence rates, while methods which are able to track
discontinuities usually suffer from the so-called curse of dimensionality. For
this reason, in this work we propose to build surrogates for point evaluation
using deep neural networks. We provide a theoretical justification for why we
expect neural networks to provide good surrogates. Furthermore, we present
extensive numerical experiments showing their good performance in practice. We
observe in particular that neural networks do not suffer from the curse of
dimensionality, and we study the dependence of the error on the number of point
evaluations (that is, the number of discontinuities in the parameter space), as
well as on several modeling parameters, such as the contrast between the two
materials and, for the Helmholtz transmission problem, the wavenumber.


  We have used different methods to obtain the bound states of a Hamiltonian of
a relativistic two scalar particle system in a local potential. The potentials
we are interested in are binding and confining potentials, that are associated
with particle exchange. The issues we concentrate on when comparing the
different methods are ease of numerical implementation, accuracy and stability.
To check our codes we have made use of several potentials for which the bound
states are known in the nonrelativistic situation. Finally we calculate the
bound states for the Yukawa potential in the relativistic situation and look at
the collapse of the wave functions in this situation.


  We suggest an application of dynamical Zeno effect to isolate a qubit in the
quantum memory unit against decoherence caused by coupling with the reservoir
having zero temperature. The method is based on using an auxiliary casing
system that mediate the qubit-reservoir interaction and is simultaneously
frequently erased to ground state. This screening procedure can be implemented
in the cavity QED experiments to store the atomic and photonic qubit states.


  We prove one direction of homological mirror symmetry for complete
intersections in algebraic tori, in all dimensions. The mirror geometry is not
a space but a LG model, i.e. a pair given by a space and a regular function. We
show that the Fukaya category of the complete intersection is equivalent to the
category of matrix factorizations of the LG pair. Our approach yields new
results also in the hypersurface setting, which was treated earlier by Gammage
and Shende. Our argument depends on breaking down the complete intersection
into smaller more manageable pieces, i.e. finite covers of products of higher
dimensional pairs-of-pants, thus implementing a program first suggested by
Seidel.


  Despite the impressive performance achieved by pre-trained
language-and-vision models in downstream tasks, it remains an open question
whether this reflects a proper understanding of image-text interaction. In this
work, we explore to what extent they handle basic linguistic constructions --
active-passive voice, coordination, and relative clauses -- that even preschool
children can typically master. We present BLA, a novel, automatically
constructed benchmark to evaluate multimodal models on these Basic Language
Abilities. We show that different types of Transformer-based systems, such as
CLIP, ViLBERT, and BLIP2, generally struggle with BLA in a zero-shot setting,
in line with previous findings. Our experiments, in particular, show that most
of the tested models only marginally benefit when fine-tuned or prompted with
construction-specific samples. Yet, the generative BLIP2 shows promising
trends, especially in an in-context learning setting. This opens the door to
using BLA not only as an evaluation benchmark but also to improve models' basic
language abilities.


  I explore the possibility that a quantum system S may be described completely
by the combination of its standard quantum state $|\psi\rangle$ and a (hidden)
quantum state $|\phi\rangle$ (that lives in the same Hilbert space), such that
the outcome of any standard projective measurement on the system S is
determined once the two quantum states are specified. I construct an algorithm
that retrieves the standard quantum-mechanical probabilities, which depend only
on $|\psi\rangle$, by assuming that the (hidden) quantum state $|\phi\rangle$
is drawn at random from some fixed probability distribution Pr(.) and by
averaging over Pr(.). Contextuality and Bell nonlocality turn out to emerge
automatically from this algorithm as soon as the dimension of the Hilbert space
of S is larger than 2. If $|\phi\rangle$ is not completely random, subtle
testable deviations from standard quantum mechanics may arise in sequential
measurements on single systems.


  We present a fit to the experimental charged lepton masses as coming from
radiative corrections in QED.


  Recent advances in predictive data analytics and ever growing digitalization
and connectivity with explosive expansions in industrial and consumer
Internet-of-Things (IoT) has raised significant concerns about security of
people's identities and data. It has created close to ideal environment for
adversaries in terms of the amount of data that could be used for modeling and
also greater accessibility for side-channel analysis of security primitives and
random number generators. Random number generators (RNGs) are at the core of
most security applications. Therefore, a secure and trustworthy source of
randomness is required to be found. Here, we present a differential circuit for
harvesting one of the most stochastic phenomenon in solid-state physics, random
telegraphic noise (RTN), that is designed to demonstrate significantly lower
sensitivities to other sources of noises, radiation and temperature
fluctuations. We use RTN in amorphous SrTiO3-based resistive memories to
evaluate the proposed true random number generator (TRNG). Successful
evaluation on conventional true randomness tests (NIST tests) has been shown.
Robustness against using predictive machine learning and side-channel attacks
have also been demonstrated in comparison with non-differential readouts
methods.


  Probabilistic solvers provide a flexible and efficient framework for
simulation, uncertainty quantification, and inference in dynamical systems.
However, like standard solvers, they suffer performance penalties for certain
stiff systems, where small steps are required not for reasons of numerical
accuracy but for the sake of stability. This issue is greatly alleviated in
semi-linear problems by the probabilistic exponential integrators developed in
this paper. By including the fast, linear dynamics in the prior, we arrive at a
class of probabilistic integrators with favorable properties. Namely, they are
proven to be L-stable, and in a certain case reduce to a classic exponential
integrator -- with the added benefit of providing a probabilistic account of
the numerical error. The method is also generalized to arbitrary non-linear
systems by imposing piece-wise semi-linearity on the prior via Jacobians of the
vector field at the previous estimates, resulting in probabilistic exponential
Rosenbrock methods. We evaluate the proposed methods on multiple stiff
differential equations and demonstrate their improved stability and efficiency
over established probabilistic solvers. The present contribution thus expands
the range of problems that can be effectively tackled within probabilistic
numerics.


  We explore and develop the mathematics of the theory of entanglement
measures. After a careful review and analysis of definitions, of preliminary
results, and of connections between conditions on entanglement measures, we
prove a sharpened version of a uniqueness theorem which gives necessary and
sufficient conditions for an entanglement measure to coincide with the reduced
von Neumann entropy on pure states. We also prove several versions of a theorem
on extreme entanglement measures in the case of mixed states. We analyse
properties of the asymptotic regularization of entanglement measures proving,
for example, convexity for the entanglement cost and for the regularized
relative entropy of entanglement.


  The purpose of this paper is to study the vanishing viscosity limit for the
d-dimensional Navier--Stokes equations in the whole space:
  \begin{equation*} \begin{cases} \partial_tu^\varepsilon+u^\varepsilon\cdot
\nabla u^\varepsilon-\varepsilon\Delta u^\varepsilon+\nabla p^\varepsilon=0,\\
\mathrm{div}\ u^\varepsilon=0. \end{cases} \end{equation*} We aim to presenting
a simple rigorous examples of initial data which generates the corresponding
solutions of the Navier--Stokes equations do exhibit anomalous dissipation.
Precisely speaking, we show that there are (classical) solutions for which the
dissipation rate of the kinetic energy is bounded away from zero.


  To satisfy rising energy needs and to handle the forthcoming worldwide
climate transformation, major research attention has been drawn to
environmentally friendly, renewable, and abundant energy resources. Hydrogen
plays an ideal and significant role is such resources, due to its
non-carbon-based energy and production through clean energy. In this work, we
have explored the catalytic activity of a newly predicted haeckelite boron
nitride quantum dot (haeck-BNQD), constructed from the infinite BN sheet, for
its utilization in hydrogen production. Density functional theory calculations
are employed to investigate geometry optimization, electronic and adsorption
mechanism of haeck-BNQD using Gaussian16 package, employing the hybrid B3LYP
and wB97XD functionals, along with 6- 31G(d,p) basis set. A number of physical
quantities such as HOMO/LUMO energies, the density of states, hydrogen atom
adsorption energies, Mulliken populations, Gibbs free energy, work functions,
overpotentials, etc., have been computed and analyzed in the context of the
catalytic performance of haeck-BNQD for the hydrogen-evolution reaction (HER).
Based on our calculations, we predict that the best catalytic performance will
be obtained for H adsorption on top of the squares or the octagons of
haeck-BNQD. We hope that our prediction of the most active catalytic sites on
haeck-BNQD for HER will be put to test in future experiments.


  Despite its crucial role in students' daily lives, commuting time remains an
underexplored dimension in higher education research. To address this gap, this
study focuses on challenges that students face in urban environments and
investigates the impact of commuting time on the academic performance of
first-year bachelor students of Politecnico di Milano, Italy. This research
employs an innovative two-step methodology. In the initial phase, machine
learning algorithms trained on privacy-preserving GPS data from anonymous users
are used to construct accessibility maps to the university and to obtain an
estimate of students' commuting times. In the subsequent phase, authors utilize
polynomial linear mixed-effects models and investigate the factors influencing
students' academic performance, with a particular emphasis on commuting time.
Notably, this investigation incorporates a causal framework, which enables the
establishment of causal relationships between commuting time and academic
outcomes. The findings underscore the significant impact of travel time on
students' performance and may support policies and implications aiming at
improving students' educational experience in metropolitan areas. The study's
innovation lies both in its exploration of a relatively uncharted factor and
the novel methodologies applied in both phases.


  We derive the Kullback-Leibler divergence for the normal-gamma distribution
and show that it is identical to the Bayesian complexity penalty for the
univariate general linear model with conjugate priors. Based on this finding,
we provide two applications of the KL divergence, one in simulated and one in
empirical data.