  We discuss multivariate Monte Carlo methods appropriate for X-ray dispersive
spectrometers. Dispersive spectrometers have many advantages for high
resolution spectroscopy in the X-ray band. Analysis of data from these
instruments is complicated by the fact that the instrument response functions
are multi-dimensional and relatively few X-ray photons are detected from
astrophysical sources. Monte Carlo methods are the natural solution to these
challenges, but techniques for their use are not well developed. We describe a
number of methods to produce a highly efficient and flexible multivariate Monte
Carlo. These techniques include multi-dimensional response interpolation and
multi-dimensional event comparison. We discuss how these methods have been
extensively used in the XMM-Newton Reflection Grating Spectrometer in-flight
calibration program. We also show several examples of a Monte Carlo applied to
observations of clusters of galaxies and elliptical galaxies with the
XMM-Newton observatory.


  The main purpose of this paper is to calculate exact quasiclassical
asymptotic of the quantum averages without any reference to the corresponding
quasiclassical asimptotic of the Schr\"odinger wave function {\Psi}(x,t)given
via Maslov canonical operator. We suggest a new asymptotic representation for
the quantum averages with position variable with localized initial data.


  We investigated noncollinear second harmonic generation form Zinc oxide
films, grown on glass substrates by dual ion beam sputtering technique. At a
fixed incidence angle, the generated signal is investigated by scanning the
polarization state of both fundamental beams. We show that the map of the
generated signal as a function of polarization states of both pump beams,
together with the analytical curves, allows to retrieve the orientation of the
optical axis and, eventually, its angular tilt, with respect to the surface
normal


  Metal halide perovskites feature excellent absorption, emission and charge
carrier transport properties. These materials are therefore very well suited
for photovoltaics applications where there is a growing interest. Still,
questions arise when looking at the unusual long carrier lifetime that,
regarding the micrometric diffusion length, would imply a very low diffusion
coefficient as compared to commonly used photovoltaic absorbers. In this paper,
we provide an experimental insight into this long lifetime of charge carriers
in slow-motion. Our approach relies on an improved model to analyze
time-resolved photoluminescence decays at multiple fluence levels that includes
charge carrier transport, photon recycling, and traps dynamics. The model is
verified on different interface properties. Moreover, we investigate various
perovskite absorbers such as mixed alloys with cesium content. For most of the
perovskite based materials we analyzed, the band-to-band recombination rate
remains close to the radiative limit, leading to the expected sub-microsecond
lifetime. The slow diffusion of charge carriers is observed with values of the
diffusion coefficient D around 5x10-3 cm2/s. Nonetheless, the power conversion
efficiency remains high. The observations might be related to the debated
coexistence of a direct and indirect bandgap slowing down the recombination
process.


  The Seiberg-Witten solution of N=2 supersymmetric SU(2) gauge theories with
matter is analysed as an isomonodromy problem. We show that the holomorphic
section describing the effective action can be deformed by moving its
singularities on the moduli space while keeping their monodromies invariant.
Well-known examples of isomonodromic sections are given by the correlators of
two-dimensional rational conformal field theories -- the conformal blocks. The
Seiberg-Witten section similarly admits the operations of braiding and fusing
of its singularities, which obey the Yang-Baxter and Pentagonal identities,
respectively. Using them, we easily find the complete expressions of the
monodromies with affine term, and the full quantum numbers of the BPS spectrum.
While the braiding describes the quark-monopole transmutation, the fusing
implies the superconformal points in the moduli space. In the simplest case of
three singularities, the supersymmetric sections are directly related to the
conformal blocks of the logarithmic minimal models.


  We derive transformation rules for test ideals and $F$-singularities under an
arbitrary finite surjective morphism $\pi : Y \to X$ of normal varieties in
prime characteristic $p > 0$. The main technique is to relate homomorphisms
$F_{*} O_{X} \to O_{X}$, such as Frobenius splittings, to homomorphisms $F_{*}
O_{Y} \to O_{Y}$. In the simplest cases, these rules mirror transformation
rules for multiplier ideals in characteristic zero. As a corollary, we deduce
sufficient conditions which imply that trace is surjective, i.e.
$Tr_{Y/X}(\pi_{*}O_{Y}) = O_{X}$.


  Automatic image cropping techniques are commonly used to enhance the
aesthetic quality of an image; they do it by detecting the most beautiful or
the most salient parts of the image and removing the unwanted content to have a
smaller image that is more visually pleasing. In this thesis, I introduce an
additional dimension to the problem of cropping, semantics. I argue that image
cropping can also enhance the image's relevancy for a given entity by using the
semantic information contained in the image. I call this problem, Semantic
Image Cropping. To support my argument, I provide a new dataset containing 100
images with at least two different entities per image and four ground truth
croppings collected using Amazon Mechanical Turk. I use this dataset to show
that state-of-the-art cropping algorithms that only take into account
aesthetics do not perform well in the problem of semantic image cropping.
Additionally, I provide a new deep learning system that takes not just
aesthetics but also semantics into account to generate image croppings, and I
evaluate its performance using my new semantic cropping dataset, showing that
using the semantic information of an image can help to produce better
croppings.


  We derive general frequency dependencies of the surface impedance modulus for
conductors without the dc dissipation, i. e. for superconductors or perfect
conductors. The frequency-dependent surface impedance was applied for the
solutions corresponding to the spatially dispersive eigenvalues of the
permittivity operator for conductors. We demonstrate that appropriately taken
into account effects of the spatial dispersion can give the general frequency
dependence of the surface impedance for the obtained solutions including that
for superconductor. It is shown that an incorporation of the spatial dispersion
leads to an appearance of the Meissner effect in perfect conductors in the same
manner as in superconductors.


  Federated Learning (FL) is a distributed machine learning paradigm that
enables learning models from decentralized local data. While FL offers
appealing properties for clients' data privacy, it imposes high communication
burdens for exchanging model weights between a server and the clients. Existing
approaches rely on model compression techniques, such as pruning and weight
clustering to tackle this. However, transmitting the entire set of weight
updates at each federated round, even in a compressed format, limits the
potential for a substantial reduction in communication volume. We propose
FedCode where clients transmit only codebooks, i.e., the cluster centers of
updated model weight values. To ensure a smooth learning curve and proper
calibration of clusters between the server and the clients, FedCode
periodically transfers model weights after multiple rounds of solely
communicating codebooks. This results in a significant reduction in
communication volume between clients and the server in both directions, without
imposing significant computational overhead on the clients or leading to major
performance degradation of the models. We evaluate the effectiveness of FedCode
using various publicly available datasets with ResNet-20 and MobileNet backbone
model architectures. Our evaluations demonstrate a 12.2-fold data transmission
reduction on average while maintaining a comparable model performance with an
average accuracy loss of 1.3% compared to FedAvg. Further validation of FedCode
performance under non-IID data distributions showcased an average accuracy loss
of 2.0% compared to FedAvg while achieving approximately a 12.7-fold data
transmission reduction.


  We report three-dimensional topological spin configurations including a novel
form of skyrmion-antiskyrmion coupling in D2d chiral magnets. The
skyrmion-antiskyrmion coupled string, consisting of skyrmions located in the
near-surface layers and antiskyrmions in the interior of the nanostructured
sample that are sewn together by emergent Bloch points, is a hybrid
three-dimensional soliton solution resulting from the application of
micromagnetic equations. We further provide experimental evidence of these 3D
topological skyrmionic strings in a FeNiPdP chiral magnet with S4 symmetry. Our
results demonstrate reversible topological magnetic transformations between
skyrmion-antiskyrmion and skyrmion-bubble strings, which are mediated by the
creation and annihilation of Bloch points.


  Symbolic execution is a well established method for test input generation.
Despite of having achieved tremendous success over numerical domains, existing
symbolic execution techniques for heap-based programs are limited due to the
lack of a succinct and precise description for symbolic values over unbounded
heaps. In this work, we present a new symbolic execution method for heap-based
programs based on separation logic. The essence of our proposal is
context-sensitive lazy initialization, a novel approach for efficient test
input generation. Our approach differs from existing approaches in two ways.
Firstly, our approach is based on separation logic, which allows us to
precisely capture preconditions of heap-based programs so that we avoid
generating invalid test inputs. Secondly, we generate only fully initialized
test inputs, which are more useful in practice compared to those partially
initialized test inputs generated by the state-of-the-art tools. We have
implemented our approach as a tool, called Java StarFinder, and evaluated it on
a set of programs with complex heap inputs. The results show that our approach
significantly reduces the number of invalid test inputs and improves the test
coverage.


  An extensive survey of gravitational-wave modes for uniform density stars is
presented. The study covers stars ranging in compactness from $R/M=100$ to the
limit of stability in general relativity: $R/M = 9/4$. We establish that polar
and axial gravitational-wave modes exist for all these stellar models.
Moreover, there are two distinct families of both axial and polar modes. We
discuss the physics of these modes and argue that one family is primarily
associated with the interior of the star, while the second family is mainly
associated with the stellar surface. We also show that the problem of axial
perturbations has all the essential features of the polar problem as far as
gravitational waves are concerned. This means that the axial problem is much
more important than has previously been assumed. We also find some surprising
features, such as avoided crossings between the polar gravitational-wave modes
and the Kelvin f-mode as the star becomes very compact. This seems to suggest
that the f-mode should be considered on equal footing with the polar w-modes
for ultracompact stars. All modes may have the main character of trapped modes
inside the curvature potential barrier for $R/M < 3$.


  Every finite simple group can be generated by two elements and, in fact,
every nontrivial element is contained in a generating pair. Groups with this
property are said to be $\frac{3}{2}$-generated, and the finite
$\frac{3}{2}$-generated groups were recently classified. Turning to infinite
groups, in this paper, we prove that the finitely presented simple group $T$ of
Thompson is $\frac{3}{2}$-generated. Moreover, we exhibit an element $\zeta \in
T$ such that for any nontrivial $\alpha \in T$, there exists $\gamma \in T$
such that $\langle \alpha, \zeta^\gamma \rangle = T$.


  We show that the two problems of computing the permanent of an $n\times n$
matrix of $\operatorname{poly}(n)$-bit integers and counting the number of
Hamiltonian cycles in a directed $n$-vertex multigraph with
$\operatorname{exp}(\operatorname{poly}(n))$ edges can be reduced to relatively
few smaller instances of themselves. In effect we derive the first
deterministic algorithms for these two problems that run in $o(2^n)$ time in
the worst case. Classic $\operatorname{poly}(n)2^n$ time algorithms for the two
problems have been known since the early 1960's. Our algorithms run in
$2^{n-\Omega(\sqrt{n/\log n})}$ time.


  The layered antiferromagnet FePS$_3$ has been shown to undergo a structural
transition under pressure linked to an insulator-metal transition, with two
incompatible models previously proposed for the highest-pressure structure. We
present a study of the high-pressure crystal structures of FePS$_3$ using both
single-crystal and powder x-ray diffraction. We show that the highest pressure
transition involves a collapse of the inter-planar spacing of this material,
along with an increase in symmetry from a monoclinic to a trigonal structure,
to the exclusion of other models. The extent of this volume collapse is shown
to be sensitive to the presence of a helium pressure medium in the sample
environment, indicating that consideration of such experimental factors is
important for understanding high-pressure behaviours in this material.


  We study Steinhaus' theorem regarding statistical limits of measurable real
valued functions and we examine the validity of the classical theorems of
Measure Theory for statistical convergences.


  While Twitter provides an unprecedented opportunity to learn about breaking
news and current events as they happen, it often produces skepticism among
users as not all the information is accurate but also hoaxes are sometimes
spread. While avoiding the diffusion of hoaxes is a major concern during
fast-paced events such as natural disasters, the study of how users trust and
verify information from tweets in these contexts has received little attention
so far. We survey users on credibility perceptions regarding witness pictures
posted on Twitter related to Hurricane Sandy. By examining credibility
perceptions on features suggested for information verification in the field of
Epistemology, we evaluate their accuracy in determining whether pictures were
real or fake compared to professional evaluations performed by experts. Our
study unveils insight about tweet presentation, as well as features that users
should look at when assessing the veracity of tweets in the context of
fast-paced events. Some of our main findings include that while author details
not readily available on Twitter feeds should be emphasized in order to
facilitate verification of tweets, showing multiple tweets corroborating a fact
misleads users to trusting what actually is a hoax. We contrast some of the
behavioral patterns found on tweets with literature in Psychology research.


  The hydrophobic effect (HE) is commonly associated with the demixing of oil
and water at ambient conditions and plays the leading role in determining the
structure and stability of biomolecular assembly in aqueous solutions. On the
molecular scale HE has an entropic origin. It is believed that hydrophobic
particles induce order in the surrounding water by reducing the volume of con-
figuration space available for hydrogen bonding. Here we show with computer
simulation results that this traditional picture is not correct. Analyzing
collective fluctuations in water clusters we are able to provide a
fundamentally new picture of HE based on pronounced many-body correlations
affecting the switching of hydrogen bonds between molecules. These correlations
emerge as a non-local compensation of reduced fluctuations of local
electrostatic fields in the presence of an apolar solute.


  High-luminosity modern accelerators, like the Relativistic Heavy Ion Collider
(RHIC) at BNL and Large Hadron Collider (LHC) at CERN, inherently have event
pile-up scenarios which significantly contribute to physics events as a
background. While state-of-the-art tracking algorithms and detector concepts
take care of these event pile-up scenarios, several offline analytical
techniques are used to remove such events from the physics analysis. It is
still difficult to identify the remaining pile-up events in an event sample for
physics analysis. Since the fraction of these events is significantly small, it
may not be as serious of an issue for other analysis as it would be for an
event-by-event analysis. Particularly, when the characteristics of the
multiplicity distribution are observable, one needs to be very careful. In the
present work, we demonstrate how a small fraction of residual pile-up events
can change the moments and their ratios of an event-by-event net-proton
multiplicity distribution, which are sensitive to the dynamical fluctuations
due to the QCD critical point. For this study we assume that the individual
event-by-event proton and antiproton multiplicity distributions follow Poisson,
negative binomial or binomial distributions. We observe a significant effect in
cumulants and their ratios of net-proton multiplicity distributions due to
pile-up events, particularly at lower energies. It might be crucial to estimate
the fraction of pile-up events in the data sample while interpreting the
experimental observable for the critical point.


  Satellite radar altimetry is one of the most powerful techniques for
measuring sea surface height variations, with applications ranging from
operational oceanography to climate research. Over open oceans, altimeter
return waveforms generally correspond to the Brown model, and by inversion,
estimated shape parameters provide mean surface height and wind speed. However,
in coastal areas or over inland waters, the waveform shape is often distorted
by land influence, resulting in peaks or fast decaying trailing edges. As a
result, derived sea surface heights are then less accurate and waveforms need
to be reprocessed by sophisticated algorithms. To this end, this work suggests
a novel Spatio-Temporal Altimetry Retracking (STAR) technique. We show that
STAR enables the derivation of sea surface heights over the open ocean as well
as over coastal regions of at least the same quality as compared to existing
retracking methods, but for a larger number of cycles and thus retaining more
useful data. Novel elements of our method are (a) integrating information from
spatially and temporally neighboring waveforms through a conditional random
field approach, (b) sub-waveform detection, where relevant sub-waveforms are
separated from corrupted or non-relevant parts through a sparse representation
approach, and (c) identifying the final best set of sea surfaces heights from
multiple likely heights using Dijkstra's algorithm. We apply STAR to data from
the Jason-1, Jason-2 and Envisat missions for study sites in the Gulf of
Trieste, Italy and in the coastal region of the Ganges-Brahmaputra-Meghna
estuary, Bangladesh. We compare to several established and recent retracking
methods, as well as to tide gauge data. Our experiments suggest that the
obtained sea surface heights are significantly less affected by outliers when
compared to results obtained by other approaches.


  The dynamics of cold atoms in conservative optical lattices obviously depends
on the geometry of the lattice. But very similar lattices may lead to deeply
different dynamics. For example, in a 2D optical lattice with a square mesh,
the sign of the detuning plays a crucial role: in the blue detuned case,
trajectories of an atom inside a well are chaotic for high enough energies. On
the contrary, in the red detuned case, chaos is completely inhibited inside the
wells. Here, we study in details the dynamical regimes of atoms inside a well
of a red detuned lattice, with the aim to understand the dynamical mechanisms
leading to the disappearance of chaos. We show that the motions in the two
directions of space are frequency locked in most of the phase space, for most
of the parameters of the lattice and atoms. This synchronization, not as strict
as that of a dissipative system, is nevertheless a mechanism powerful enough to
explain that chaos cannot appear in red detuned lattices.


  We study the singularities for minimum time control-affine problems in 4D
with 2D controls. After regularization, the problem boils down to the study of
a bifurcation around some nilpotent equilibrium in the singular locus. We show
that the extremal flow - thus, the exponential map - is smooth on a
stratification, and therefore piece-wise smooth.


  Unsupervised summarization is a powerful technique that enables training
summarizing models without requiring labeled datasets. This survey covers
different recent techniques and models used for unsupervised summarization. We
cover extractive, abstractive, and hybrid models and strategies used to achieve
unsupervised summarization. While the main focus of this survey is on recent
research, we also cover some of the important previous research. We
additionally introduce a taxonomy, classifying different research based on
their approach to unsupervised training. Finally, we discuss the current
approaches and mention some datasets and evaluation methods.


  Physical systems which can be described by classical fields in classical
theory, can also be described by quantum states in quantum field theory. We
study the correspondence between the classical field and the quantum state
which both describe the same physical systems. We derive the quantum states
corresponding to the classical field in the representation expanded by the
eigenstates of quantum field operators. This allows us to directly observe the
spatial entanglement structure of quantum states and explore the differences
and relationships between quantum superposition and classical superposition. We
find that if two classical fields are identical in a certain spatial region,
then their corresponding quantum states have the same reduced density matrix in
that region. This indicates that knowing the classical field in a local region
is sufficient to immediately derive the reduced density matrix for that region.
According to the correspondence between classical observables and quantum
states, we derive the equation of motion in classical theory from the evolution
of quantum states in Yukawa theory. This leads to the relativistic classical
Yukawa theory, and we further obtain relativistic corrections to the Yukawa
potential.


  Inverse initial and inverse source problems of a time-fractional differential
equation with Bessel operator are considered. Results on existence and
uniqueness of solutions to these problems are presented. The solution method is
based on series expansions using a set of Bessel functions of order zero.
Convergence of the obtained series solutions is also discussed


  In this work, we present numerical results which support SO(5) symmetry as a
concept unifying superconductivity and antiferromagnetism in the
high-temperature superconductors. Using exact cluster diagonalization, we
verify the recently proposed SO(5) multiplet structures for a widely used
microscopic model, the t-J model. Our results show that the d-wave
superconducting ground states away from half-filling are obtained from the
higher spin states at half-filling through SO(5) rotations, that the dominant
low energy resonance in the dynamical spin correlation function corresponds to
a `pi-resonance' in the entire low doping region, and that the SO(5) symmetry
is robust against inclusion of longer ranged Coulomb repulsion and next-nearest
neighbor hopping.


  A unique class of local Higher Spin Gravities with propagating massless
fields in $4d$ - Chiral Higher Spin Gravity - was first found in the light-cone
gauge. We construct a covariant form of the corresponding field equations in
all orders, thus completing the previous analysis of arXiv:2204.10285. This
result is equivalent to taking the minimal model (in the sense of
$L_\infty$-algebras) of the jet-space BV-BRST formulation of Chiral Higher Spin
Gravity, thereby, containing also information about counterterms, anomalies,
etc.


  We show that an isoparametric submanifold of a complex hyperbolic plane,
according to the definition of Heintze, Liu and Olmos', is an open part of a
principal orbit of a polar action. We also show that there exists a
non-isoparametric submanifold of the complex hyperbolic plane that is
isoparametric according to the definition of Terng's. Finally, we classify
Terng-isoparametric submanifolds of two-dimensional complex space forms.


  In this study, we reconsider the states $Z_b(10610)$ and $Z_b(10650)$ by
investigating the presence of diquark-anti-diquark components as well as the
hadronic molecule components in the framework of effective field theory. The
different masses of pseudoscalar mesons such as $\pi^{0}$, $\eta_{8}$, and
$\eta_{0}$, as well as vector mesons like $\rho^{0}$ and $\omega$ violate the
OZI rule that is well depicted under the $[U(3)_L\otimes
U(3)_R]_{global}\otimes [U(3)_V]_{local}$ symmetry. To account for the
contribution of intermediate bosons of heavy masses within the OBE model, we
introduce an exponential form factor instead of the commonly used monopole form
factor in the past. By solving the coupled-channel Schr\"{o}dinger equation
with the Gaussian expansion method, our numerical results indicate that the
$Z_b(10610)$ and $Z_b(10650)$ states can be explained as hadronic molecules
slightly mixing with diquark-anti-diquark states.


  A nonnegative tensor has nonnegative rank at most 2 if and only if it is
supermodular and has flattening rank at most 2. We prove this result, then
explore the semialgebraic geometry of the general Markov model on phylogenetic
trees with binary states, and comment on possible extensions to tensors of
higher rank.


  Artificial intelligence (AI) has achieved superhuman performance in a growing
number of tasks, but understanding and explaining AI remain challenging. This
paper clarifies the connections between machine-learning algorithms to develop
AIs and the econometrics of dynamic structural models through the case studies
of three famous game AIs. Chess-playing Deep Blue is a calibrated value
function, whereas shogi-playing Bonanza is an estimated value function via
Rust's (1987) nested fixed-point method. AlphaGo's "supervised-learning policy
network" is a deep neural network implementation of Hotz and Miller's (1993)
conditional choice probability estimation; its "reinforcement-learning value
network" is equivalent to Hotz, Miller, Sanders, and Smith's (1994) conditional
choice simulation method. Relaxing these AIs' implicit econometric assumptions
would improve their structural interpretability.


  We study approximation theorems for the Euler characteristic of the
Vietoris-Rips and Cech filtration. The filtration is obtained from a Poisson or
binomial sampling scheme in the critical regime. We apply our results to the
smooth bootstrap of the Euler characteristic and determine its rate of
convergence in the Kantorovich-Wasserstein distance and in the Kolmogorov
distance.


  Let $M$ be a module. A {\em $\delta$-cover} of $M$ is an epimorphism from a
module $F$ onto $M$ with a $\delta$-small kernel. A $\delta$-cover is said to
be a {\em flat $\delta$-cover} in case $F$ is a flat module. In the present
paper, we investigate some properties of (flat) $\delta$-covers and flat
modules having a projective $\delta$-cover. Moreover, we study rings over which
every module has a flat $\delta$-cover and call them {\em right generalized
$\delta$-perfect} rings. We also give some characterizations of
$\delta$-semiperfect and $\delta$-perfect rings in terms of locally (finitely,
quasi-, direct-) projective $\delta$-covers and flat $\delta$-covers.


  We present a treatment of the nonlinear matter wave propagation inspired from
optical methods, which includes interaction effects within the atom optics
equivalent of the aberrationless approximation. The atom-optical ABCD matrix
formalism, considered so far for non-interacting clouds, is extended
perturbatively beyond the linear regime of propagation. This approach, applied
to discuss the stability of a matter-wave resonator involving a free-falling
sample, agrees very well with the predictions of the full nonlinear paraxial
wave equation. An alternative optical treatment of interaction effects, based
on the aberrationless approximation and suitable for cylindrical paraxial beams
of uniform linear density, is also adapted for matter waves.


  We report a search for a narrow ttbar resonance that decays into a
lepton+jets final state based on an integrated luminosity of 5.3/fb of
proton-antiproton collisions at sqrt{s}=1.96 TeV collected by the D0
Collaboration at the Fermilab Tevatron Collider. We set upper limits on the
production cross section of such a resonance multiplied by its branching
fraction to ttbar which we compare to predictions for a leptophobic topcolor Z'
boson. We exclude such a resonance at the 95% confidence level for masses below
835 GeV.


  The specific model studied is in the context of the modified measure
formulation the string or branes where tension appear as an additional
dynamical degree of freedom . We then consider the signed reparametrization
invariant volume element formulation of dynamical strings and branes and find
that the dynamical tension can produce positive tensions or negative tensions,
corresponding exactly to strings and branes and anti strings and anti branes
respectively. The anti strings are realized when a scalar time that defines the
modified measure runs in the opposite direction to the world sheet time. For
strings with positive tension, both times run in the same direction. The
situation resembles the situation in Relativistic Quantum Mechanics with
positive and negative energies, proper time of particles running forward with
respect of coordinate time , while for anti particles proper tome runs opposite
of coordinate time. An example where string anti string pair creation takes
place in analogy to the pair creation in an external electric field in QED
background field, this time in the presence of a background scalar field that
couples to the strings and locally changes the tension, the tension field.


  We provide the initial insight into the angle-differential photodetachment
spectra of fullerene anions beyond the dipole approximation by utilizing a
broadly used modelling of C$_{n}$. In the model, the C$_{n}$ cage is
approximated by a spherical attractive potential of a certain inner radius,
thickness and depth which binds an external electron, thereby turning into a
C$_{n}^{-}$ anion. It is demonstrated in the framework of the utilized model,
which a single-electron model in its essence, that the dipole and
dipole-quadrupole approximations might get broken down in the
angle-differential photodetachment spectra of fullerene anions, C$_{n}^{-}$, at
a great number of photon energies of only a few tens of eV. Moreover, the
breakdown occurrences are shown to start developing at lower photon energies,
and the frequency of the occurrences grows with increasing size of C$_{n}^{-}$.
The findings are demonstrated by direct calculations of angle-differential
photodetachment cross sections of the C$_{60}^{-}$, C$_{240}^{-}$,
C$_{540}^{-}$ and C$_{1500}^{-}$ anions. It is not clear beforehand how
electron correlation might affect the predicted anomalies in the C$_{n}^{-}$
angle-differential photodetachment spectra, so that the verification(s) of the
predicted breakdowns by means of more sophisticated theories is urged.


  In this note we study inverse spectral problems for canonical Hamiltonian
systems, which encompass a broad class of second order differential equations
on a half-line. Our goal is to extend the classical resultss developed in the
work of Marchenko, Gelfand-Levitan, and Krein to broader classes of canonical
systems and to illustrate the solution algorithms and formulas with a variety
of examples. One of the main ingredients of our approach is the use of
truncated Toeplitz operators, which complement the standard toolbox of the
Krein-de Branges theory of canonical systems.


  In this work, the analysis of the stacked projected temperature profile of
twelve galaxy clusters of the X-COP sample is performed via the SuperModel, a
tool for investigating the intracluster medium thermodynamic properties already
tested on many clusters since 2009. Two separate fits have been carried out: to
the joint X-ray and SZ projected temperature profiles and to the X-ray data
only. The entropy, thermal pressure and hydrostatic mass profiles of the
cluster sample and the level of the nonthermal pressure component in the
cluster outskirts are determined combining the deprojected temperature profile
with the stacked electron gas density profile corrected for clumpiness. The
first analysis gives results in good agreement with those reported in
Ghirardini et al. (2018): a modest presence of the nonthermal support and an
entropy profile that follows at distances beyond r500 the predicted power law
increase with slope 1.1. On the contrary, the results of the second analysis
are consistent with the findings obtained by the Suzaku observations, steep
temperature and flat entropy profiles, with a higher level of the nonthermal
pressure component in agreement with the values derived by numerical
simulations. The conclusion is that a steep temperature profile could be
present in the outskirts of the X-COP cluster sample instead of the flatter
temperature profile reported by SZ observations.


  The problem of determining cyclotomic numbers in terms of the solutions of
certain Diophantine systems has been treated by many authors since the age of
Gauss. In this paper we obtain an explicit expression for cyclotomic numbers of
order 2l^2 in terms of the coefficients of the Jacobi sums of lower orders. At
the end, we illustrate the nature of two matrices corresponding to two types of
cyclotomic numbers.


  The gamma distribution arises frequently in Bayesian models, but there is not
an easy-to-use conjugate prior for the shape parameter of a gamma. This
inconvenience is usually dealt with by using either Metropolis-Hastings moves,
rejection sampling methods, or numerical integration. However, in models with a
large number of shape parameters, these existing methods are slower or more
complicated than one would like, making them burdensome in practice. It turns
out that the full conditional distribution of the gamma shape parameter is well
approximated by a gamma distribution, even for small sample sizes, when the
prior on the shape parameter is also a gamma distribution. This article
introduces a quick and easy algorithm for finding a gamma distribution that
approximates the full conditional distribution of the shape parameter. We
empirically demonstrate the speed and accuracy of the approximation across a
wide range of conditions. If exactness is required, the approximation can be
used as a proposal distribution for Metropolis-Hastings.


  The one-way quantum deficit, a measure of quantum correlation, can exhibit
for X quantum states the regions (subdomains) with the phases $\Delta_0$ and
$\Delta_{\pi/2}$ which are characterized by constant (i.e., universal) optimal
measurement angles, correspondingly, zero and $\pi/2$ with respect to the
$z$-axis and a third phase $\Delta_\vartheta$ with the variable
(state-dependent) optimal measurement angle $\vartheta$. We build the complete
phase diagram of one-way quantum deficit for the XXZ subclass of symmetric X
states. In contrast to the quantum discord where the region for the phase with
variable optimal measurement angle is very tiny (more exactly, it is a very
thin layer), the similar region $\Delta_\vartheta$ is large and achieves the
sizes comparable to those of regions $\Delta_0$ and $\Delta_{\pi/2}$. This
instils hope to detect the mysterious fraction of quantum correlation with the
variable optimal measurement angle experimentally.


  We discuss the physics of sound propagation and charge diffusion in a plasma
with non-vanishing charge density. Our analysis culminates the program
initiated in arXiv:2108.03244 to construct an open effective field theory of
low-lying modes of the stress tensor and charge current in such plasmas. We
model the plasma holographically as a Reissner-Nordstrom-AdS black hole, and
study linearized fluctuations of longitudinally polarized scalar gravitons and
photons in this background. We demonstrate that the perturbations can be
decoupled and repackaged into the dynamics of two designer scalars, whose
gravitational coupling is modulated by a non-trivial dilatonic factor. The
holographic analysis allows us to isolate the phonon mode from the charge
diffusion mode, and identify the combination of currents that corresponds to
each of them. We use these results to obtain the real-time Gaussian effective
action, which includes both the retarded response and the associated stochastic
(Hawking) fluctuations, accurate to quartic order in gradients.


  We show that the notion of generalized Berry phase i.e., non-abelian
holonomy, can be used for enabling quantum computation. The computational space
is realized by a $n$-fold degenerate eigenspace of a family of Hamiltonians
parametrized by a manifold $\cal M$. The point of $\cal M$ represents classical
configuration of control fields and, for multi-partite systems, couplings
between subsystem. Adiabatic loops in the control $\cal M$ induce non trivial
unitary transformations on the computational space. For a generic system it is
shown that this mechanism allows for universal quantum computation by composing
a generic pair of loops in $\cal M.$


  A meshfree Lagrangian method for the fluctuating hydrodynamic equations
(FHEs) with fluid-structure interactions is presented. Brownian motion of the
particle is investigated by direct numerical simulation of the fluctuating
hydrodynamic equations. In this framework a bidirectional coupling has been
introduced between the fluctuating fluid and the solid object. The force
governing the motion of the solid object is solely due to the surrounding fluid
particles. Since a meshfree formulation is used, the method can be extended to
many real applications involving complex fluid flows. A three-dimensional
implementation is presented. In particular, we observe the short and long-time
behaviour of the velocity autocorrelation function (VACF) of Brownian particles
and compare it with the analytical expression. Moreover, the Stokes-Einstein
relation is reproduced to ensure the correct long-time behaviour of Brownian
dynamics.


  Big data sources provide a significant opportunity for governments and
development stakeholders to sense and identify in near real time, economic
impacts of shocks on populations at high spatial and temporal resolutions. In
this study, we assess the potential of transaction and location based measures
obtained from automatic teller machine (ATM) terminals, belonging to a major
private sector bank in Indonesia, to sense in near real time, the impacts of
shocks across income groups. For each customer and separately for years 2014
and 2015, we model the relationship between aggregate measures of cash
withdrawals for each year, total inter-terminal distance traversed by the
customer for the specific year and reported customer income group. Results
reveal that the model was able to predict the corresponding income groups with
80% accuracy, with high precision and recall values in comparison to the
baseline model, across both the years. Shapley values suggest that the total
inter-terminal distance traversed by a customer in each year differed
significantly between customer income groups. Kruskal-Wallis test further
showed that customers in the lower-middle class income group, have
significantly high median values of inter-terminal distances traversed (7.21
Kms for 2014 and 2015) in comparison to high (2.55 Kms and 0.66 Kms for years
2014 and 2015), and low (6.47 Kms for 2014 and 2015) income groups. Although no
major shocks were noted in 2014 and 2015, our results show that lower-middle
class income group customers, exhibit relatively high mobility in comparison to
customers in low and high income groups. Additional work is needed to leverage
the sensing capabilities of this data to provide insights on, who, where and by
how much is the population impacted by a shock to facilitate targeted
responses.


  Galaxy mergers occur frequently in the early universe and bring multiple
supermassive black holes (SMBHs) into the nucleus, where they may eventually
coalesce. Identifying post-merger-scale (i.e., <~a few kpc) dual SMBHs is a
critical pathway to understanding their dynamical evolution and successive
mergers. While serendipitously discovering kpc-scale dual SMBHs at z<1 is
possible, such systems are elusive at z>2, but critical to constraining the
progenitors of SMBH mergers. The redshift z~2 also marks the epoch of peak
activity of luminous quasars, hence probing this spatial regime at high
redshift is of particular significance in understanding the evolution of
quasars. However, given stringent resolution requirements, there is currently
no confirmed <10 kpc physical SMBH pair at z>2. Here we report two sub-arcsec
double quasars at z>2 discovered from a targeted search with a novel
astrometric technique, demonstrating a high success rate (~50%) in this
systematic approach. These high-redshift double quasars could be the
long-sought kpc-scale dual SMBHs, or sub-arcsec gravitationally-lensed quasar
images. One of these double quasars (at z=2.95) was spatially resolved with
optical spectroscopy, and slightly favors the scenario of a physical quasar
pair with a projected separation of 3.5 kpc (0.46"). Follow-up observations of
double quasars discovered by this targeted approach will be able to provide the
first observational constraints on kpc-scale dual SMBHs at z>2.


  In a neighborhood of a (positive definite) Riemannian space in which special,
semigeodesic, coordinates are given, the metric tensor can be calculated from
its values on a suitable hypersurface and some of components of the curvature
tensor of type $(1,3)$ in the coordinate domain. Semigeodesic coordinates are a
generalization of the well-known Fermi coordinates, that play an important role
in mechanics and physics, are widely used in Minkowskian space, and in
differential geometry of Riemannian spaces in general. In the present paper, we
consider a more general situation. We introduce special pre-semigeodesic charts
characterized both geometrically and in terms of the connection, formulate a
version of the Peano's-Picard's-Cauchy-like Theorem on existence and uniqueness
of solutions of the initial values problems for systems of first-order ordinary
differential equations. Then we use the apparatus in a fixed pre-semigeodesic
chart of a manifold equipped with the linear symmetric connection. Our aim is
to reconstruct, or construct, the symmetric linear connection in some
neighborhood from the knowledge of the "initial conditions": the restriction of
the connection to a fixed $(n-1)$-dimensional surface $S$ and some of the
components of the curvature tensor $R$ in the "volume" (coordinate domain).
  By analogous methods, we retrieve (or construct) the metric tensor of type
$(0,4)$ of a pseudo-Riemannian manifold in a domain of semigeodesic coordinates
from the known restriction of the metric to some non-isotropic hypersurface and
some of the components of the curvature tensor in the volume. In comparison to
other authors, we give shorter proofs of constructive character based on
classical results on first order ODEs (ordinary differential equations).


  We study cumulants of $q$-step closed and non-closed walks on the Erd\H
os-R\'enyi-type random graphs of long-range percolation radius model in the
limit when number of vertices $N$, concentration $c$, and interaction radius
$R$ tend to infinity. These cumulants represent terms of cumulant expansion of
the free energy of discrete analogs of matrix models widely known in
theoretical and mathematical physics. Using a diagram technique, we show that
the leading term $F_k^{(q)}$ of the normalized cumulant of $k$-th order can be
associated with one or another family of tree-type diagrams, in dependence of
the asymptotic behavior of parameters $cR/N$ for non-closed walks and
$c^2R/N^2$ for closed walks, respectively. Adapting the Pr\"ufer codification
procedure to such diagrams, we get explicit expressions for the number of
tree-type diagrams of $k$ elements and show that in certain cases, $F_k^{(q)}$
can be bounded from above by the $k$-th moment of the sum of $k(q-1)+1$
independent Bernoulli random variables. These results allow us to prove Limit
Theorems for the numbers of $q$-step walks in random graphs and to show that in
the additional limiting transition of infinite $q$, the term $F_k^{(q)}$,
considered for large values of $k$, admits an upper bound that asymptotically
coincides with that of the $k$-th moment of the Compound Poisson distribution.


  We use stellar population synthesis modeling to analyze the host galaxy
properties of a sample of 33 UV-selected, narrow-lined active galactic nuclei
(AGNs) at z ~ 2 - 3. In order to quantify the contribution of AGN emission to
host galaxy broadband spectral energy distributions (SEDs), we use the
subsample of 11 AGNs with photometric coverage spanning from rest-frame UV
through near-IR wavelengths. Modeling the SEDs of these objects with a linear
combination of stellar population and AGN templates, we infer the effect of the
AGN on derived stellar population parameters. We also estimate the typical bias
in derived stellar populations for AGNs lacking rest-frame near-IR wavelength
coverage, and develop a method for inferring the true host galaxy properties.
We compare AGN host galaxy properties to those of a sample of UV-selected,
star-forming non-AGNs in the same redshift range, including a subsample
carefully matched in stellar mass. Although the AGNs have higher masses and
SFRs than the full non-active sample, their stellar population properties are
consistent with those of the mass-selected sample, suggesting that the presence
of an AGN is not connected with the cessation of star-formation activity in
star-forming galaxies at z ~ 2 - 3. We suggest that a correlation between M_BH
and galaxy stellar mass is already in place at this epoch. Assuming a roughly
constant Eddington ratio for AGNs at all stellar masses, we are unable to
detect the AGNs in low-mass galaxies because they are simply too faint.


  The understanding of flux jumps in the high temperature superconductors is of
importance since the occurrence of these jumps may limit the perspectives of
the practical use of these materials. In this work we present the experimental
study of the role of heavy ion irradiation in stabilizing the HTSC against flux
jumps by comparing un-irradiated and 7.5 10^10 Kr-ion/cm2 irradiated
(YxTm1-x)Ba2Cu3O7 single crystals. Using pulsed field magnetization
measurements, we have applied a broad range of field sweep rates from 0.1T/s up
to 1800 T/s to investigate the behavior of the flux jumps. The observed flux
jumps, which may be attributed to thermal instabilities, are incomplete and
have different amplitudes. The flux jumps strongly depend on the magnetic
field, on the magneto-thermal history of the sample, on the magnetic field
sweep rate, on the critical current density jc, on the temperature and on the
thermal contact with the bath in which the sample is immersed.


  CSAW (conditioned self-avoiding walk) is a model of protein folding that
combines SAW (self-avoiding walk) with Monte-Carlo. It simulates the Brownian
motion of a chain molecule in the presence of interactions, both among chain
residues, and with the environment. In a first model that includes the
hydrophobic effect and hydrogen bonding, a chain of 30 residues folds into a
native state with stable secondary and tertiary structures. The process starts
with a rapid collapse into an intermediate "molten globule", which slowly
decays into the native state afer a relatively long quiescent period. The
behavior of the radius of gyration mimics experimental data.


  We study eta-invariants on odd dimensional manifolds with boundary. The
dependence on boundary conditions is best summarized by viewing the
(exponentiated) eta-invariant as an element of the (inverse) determinant line
of the boundary. We prove a gluing law and a variation formula for this
invariant. This yields a new, simpler proof of the holonomy formula for the
determinant line bundle of a family of Dirac operators, also known as the
``global anomaly'' formula.
  This paper is written using AMSTeX 2.1, which can be obtained via ftp from
the American Mathematical Society (instructions included). A postscript file
with figures was submitted separately in uuencoded tar-compressed format.


  Neural network based generative models with discriminative components are a
powerful approach for semi-supervised learning. However, these techniques a)
cannot account for model uncertainty in the estimation of the model's
discriminative component and b) lack flexibility to capture complex stochastic
patterns in the label generation process. To avoid these problems, we first
propose to use a discriminative component with stochastic inputs for increased
noise flexibility. We show how an efficient Gibbs sampling procedure can
marginalize the stochastic inputs when inferring missing labels in this model.
Following this, we extend the discriminative component to be fully Bayesian and
produce estimates of uncertainty in its parameter values. This opens the door
for semi-supervised Bayesian active learning.


  We give a full proof to Agol's announcement on the classification of non-free
Kleinian groups generated by two parabolic transformations.


  Motivated by recent experiments and a theoretical analysis of the gap
equation for the propagator of Dirac quasiparticles, we assume that the physics
underlying the recently observed removal of sublattice and spin degeneracies in
graphene in a strong magnetic field is connected with the generation of both
Dirac masses and spin gaps. The consequences of such a scenario for the
existence of the gapless edge states with zigzag and armchair boundary
conditions are discussed. In the case of graphene on a half-plane with a zigzag
edge, there are gapless edge states in the spectrum only when the spin gap
dominates over the mass gap. In the case of an armchair edge, however, the
existence of the gapless edge states depends on the specific type of mass gaps.


  Using the data schemes developed by Arrondo-Sols-Speiser, we give a rigorous
definition of algebraic differential equations on the complex projective space
$P^n$. For an algebraic subvariety $S \subseteq P^n$, we present an explicit
formula for the degree of the divisor of solutions of a differential equation
on $S$ and give some examples of applications. We extend the technique and
result to the real case.


  We made an interferometric Michelson type setup and a simple holographic
setup to demonstrate the feasibility of interferometric and holographic
techniques by means of a diode laser. The laser was made by using a common
diode available as a penlight element (less than R$ 15,00 value) and a simple
stabilized 110 VCA- 3 VCC power supply. Interference fringes and holograms of
small objects where obtained very similar to those of a helium-neon laser based
setup.


  This paper considers a generalization of the Path Finding (PF) with refueling
constraints referred to as the Refuelling Path Finding (RF-PF) problem. Just
like PF, the RF-PF problem is defined over a graph, where vertices are gas
stations with known fuel prices, and edge costs depend on the gas consumption
between the corresponding vertices. RF-PF seeks a minimum-cost path from the
start to the goal vertex for a robot with a limited gas tank and a limited
number of refuelling stops. While RF-PF is polynomial-time solvable, it remains
a challenge to quickly compute an optimal solution in practice since the robot
needs to simultaneously determine the path, where to make the stops, and the
amount to refuel at each stop. This paper develops a heuristic search algorithm
called Refuel A* (RF-A* ) that iteratively constructs partial solution paths
from the start to the goal guided by a heuristic function while leveraging
dominance rules for state pruning during planning. RF-A* is guaranteed to find
an optimal solution and runs more than an order of magnitude faster than the
existing state of the art (a polynomial time algorithm) when tested in large
city maps with hundreds of gas stations.


  We describe the homotopy types of Vietoris-Rips complexes of hypercube graphs
at scale $3$. We represent the vertices in the hypercube graph $Q_m$ as the
collection of all subsets of $[m]=\{1, 2, \ldots, m\}$ and equip $Q_m$ with the
metric using symmetric difference distance. It is proved in \cite{AA22} that
the Vietoris-Rips complexes of hypercube graphs $Q_m$ at scale $2$,
$\mathcal{VR}(Q_m; 2)$, is homotopy equivalent to $c_m$-many spheres with
dimension $3$ where $c_m=\sum_{0\leq j< i<m} (j+1)(2^{m-2}-2^{i-1})$. Questions
are raised in \cite{AA22} for determining the homotopy types of
$\mathcal{VR}(Q_m, r)$ with large scales $r=3, 4, \ldots, m-2$. We prove that
for $m\geq 5$, $$\mathcal{VR}(Q_m; 3)\simeq (\bigvee_{2^{m-4}\cdot{m\choose 4}}
S^7) \vee (\bigvee_{\sum_{i=4}^{m-1}2^{i-4}\cdot{i\choose 4}} S^4).$$


  We have explored the evening transition using data from eighty days of
observations across two fog seasons at the Kempegowda International Airport,
Bengaluru (KIAB). Through field experiments and simulations integrating aerosol
interaction in a radiation-conduction model, we elucidate the impact of
aerosols on longwave cooling of the Atmospheric Boundary Layer (ABL). Field
observations indicate that under calm and clear-sky conditions, the evening
transition typically results in a distinct vertical thermal structure called
the Lifted Temperature Minimum (LTM). We observe that the prevailing profile
near the surface post-sunset is the LTM-profile. Additionally, the occurrence
of LTM is observed to increase with decreases in downward and upward longwave
flux, soil sensible heat flux, wind speed, and turbulent kinetic energy
measured at two meters above ground level (AGL). In such scenarios, the
intensity of LTM-profiles is primarily governed by aerosol-induced longwave
heating rate (LHR) within the surface layer. Furthermore, the presence of
clouds leads to increased downward flux, causing the disappearance of LTM,
whereas shallow fog can enhance LTM intensity, as observed in both field
observations and simulations. Usually, prevailing radiation models
underestimate aerosol-induced longwave heating rate (LHR) by an order, compared
to actual field observations. We attribute this difference to aerosol-induced
radiation divergence. We show that impact of aerosol-induced LHR extends
hundreds of meters into the inversion layer, affecting temperature profiles and
potentially influencing processes such as fog formation. As the fog layer
develops, LHR strengthens at its upper boundary, however, we highlight the
difficulty in detecting this cooling using remote instruments such as microwave
radiometer.


  Complex, dynamic networks underlie many systems, and understanding these
networks is the concern of a great span of important scientific and engineering
problems. Quantitative description is crucial for this understanding yet, due
to a range of measurement problems, many real network datasets are incomplete.
Here we explore how accidentally missing or deliberately hidden nodes may be
detected in networks by the effect of their absence on predictions of the speed
with which information flows through the network. We use Symbolic Regression
(SR) to learn models relating information flow to network topology. These
models show localized, systematic, and non-random discrepancies when applied to
test networks with intentionally masked nodes, demonstrating the ability to
detect the presence of missing nodes and where in the network those nodes are
likely to reside.


  We consider forced active scalar equations with even and homogeneous degree 0
drift operator on $\mathbb T^d$. Inspired by the non-uniqueness construction
for dyadic fluid models, by implementing a sum-difference convex integration
scheme we obtain non-unique weak solutions for the active scalar equation in
space $C_t^0C_x^\alpha$ with $\alpha<\frac{1}{2d+1}$. We note that in 1D, the
regularity $\alpha<\frac13$ is sharp as the energy identity is satisfied for
solutions in $C^\alpha$ with $\alpha>\frac13$. Without external forcing, Isett
and Vicol constructed non-unique weak solutions for such active scalar
equations with spatial regularity $C_x^\alpha$ for $\alpha<\frac{1}{4d+1}$.


  Human-aware navigation is a complex task for mobile robots, requiring an
autonomous navigation system capable of achieving efficient path planning
together with socially compliant behaviors. Social planners usually add costs
or constraints to the objective function, leading to intricate tuning processes
or tailoring the solution to the specific social scenario. Machine Learning can
enhance planners' versatility and help them learn complex social behaviors from
data. This work proposes an adaptive social planner, using a Deep Reinforcement
Learning agent to dynamically adjust the weighting parameters of the cost
function used to evaluate trajectories. The resulting planner combines the
robustness of the classic Dynamic Window Approach, integrated with a social
cost based on the Social Force Model, and the flexibility of learning methods
to boost the overall performance on social navigation tasks. Our extensive
experimentation on different environments demonstrates the general advantage of
the proposed method over static cost planners.


  Wada and Suyari proposed a two-parameter generalization of Shannon-Khinchin
axioms (TGSK axioms) [T. Wada and H. Suyari, Physics Letters A, 368(3)]. We
derive a new class of entropies which differs from Wada-Suyari's class by
fixing the incorrectness which occurs in the mentioned paper. Also, we consider
a two-parameter class of entropies derived from the maxent principle proposed
in [Kaniadakis, G. and Lissia, M. and Scarfone, AM, Physica A: Statistical
Mechanics and its Applications, 340(1)]. We rederived this class by changing
initial condition, obtaining the same class as our class derived from TGSK
axioms.


  We enumerate the state diagrams of the twist knot shadow which consist of the
disjoint union of two trivial knots. The result coincides with the maximal
number of regions into which the plane is divided by a given number of circles.
We then establish a bijection between the state enumeration and this particular
partition of the plane by means of binary words.


  Recent gravity discussions of a traversable wormhole indicate that in
holographic systems signals generated by a source could reappear long after
they have dissipated, with the need of only performing some simple operations.
In this paper we argue the phenomenon, to which we refer as "regenesis", is
universal in general quantum chaotic many-body systems, and elucidate its
underlying physics. The essential elements behind the phenomenon are: (i)
scrambling which in a chaotic system makes out-of-time-ordered correlation
functions (OTOCs) vanish at large times; (ii) the entanglement structure of the
state of the system. The latter aspect also implies that the regenesis
phenomenon requires fine tuning of the initial state. Compared to other
manifestations of quantum chaos such as the initial growth of OTOCs which deals
with early times, and a random matrix-type energy spectrum which reflects very
large time behavior, regenesis concerns with intermediate times, of order the
scrambling time of a system. We also study the phenomenon in detail in general
two-dimensional conformal field theories in the large central charge limit, and
highlight some interesting features including a resonant enhancement of
regenesis signals near the scrambling time and their oscillations in coupling.
Finally, we discuss gravity implications of the phenomenon for systems with a
gravity dual, arguing that there exist regimes for which traversability of a
wormhole is quantum in nature, i.e. cannot be associated with a semi-classical
spacetime causal structure.


  Let $A$ be an MV-algebra. An $(\odot,\vee)$-derivation on $A$ is a map $d:
A\to A$ satisfying: $d(x \odot y) = (d(x) \odot y) \vee(x \odot d(y))$ for all
$x, y \in A$. This paper initiates the study of $(\odot,\vee)$-derivations on
MV-algebras. Several families of $(\odot,\vee)$-derivations on an MV-algebra
are explicitly constructed to give realizations of the underlying lattice of an
MV-algebra as lattices of $(\odot,\vee)$-derivations. Furthermore,
$(\odot,\vee)$-derivations on a finite MV-chain are enumerated and the
underlying lattice is described.


  A unified model is developed within the context of the braneworld paradigm,
where a single scalar field can act as both the inflaton field in the very
early universe and also as strong, self-interacting dark matter in the
post-inflationary universe. Reheating proceeds due to the overproduction and
subsequent evaporation of primordial black holes. Observational constraints,
most notably from gravitational waves, are satisfied if the probability of PBH
formation is sufficiently high.


  Recent study of overdoped La$_{2-x}$Sr$_x$CuO$_4$ cuprate superconductor thin
films by Bo\v{z}ovi\'{c} {\it et al.} has revealed several unexpected findings,
most notably the violation of the BCS description which was believed to
adequately describe overdoped cuprates. In particular, it was found that the
superfluid density in La$_{2-x}$Sr$_x$CuO$_4$ films decreases on the overdoped
side as a linear function of critical temperature T$_c$, which was taken as
evidence for the violation of the Homes' law. We show explicitly that the law
is indeed violated, and as the main reason for violation we find that the
superfluid density in Bo\v{z}ovi\'{c}'s films is suppressed more strongly than
in bulk samples. Based on the existing literature data, we show that the
superfluid density in bulk cuprate samples does not decrease with doping, but
instead tends to saturate on the overdoped side. The result is also supported
by our recent measurement of a heavily overdoped bulk La$_{2-x}$Sr$_x$CuO$_4$
sample. Moreover, this saturation of superfluid density might not be limited to
cuprates, as we find evidence for similar behavior in two pnictide
superconductor families. We argue that quantum phase fluctuations play an
important role in suppressing the superfluid density in thin films.


  We introduce a theory of probabilistic renormalization for series, the
renormalized values being encoded in the expectation of a certain random
variable on the set of natural numbers. We identify a large class of weakly
renormalizable series of Dirichlet type, whose analysis depends on the
properties of a (infinite order) difference operator that we call Bernoulli
operator. For the series in this class, we show that the probabilistic
renormalization is compatible with analytic continuation. The general zeta
series for $s\neq 1$ is found to be strongly renormalizable and its
renormalized value is given by the Riemann zeta function.


  The structural and magnetic properties of ball-milled Fe75Cu4Ni4Mo2B15 alloy
have been investigated through powder X-ray diffraction studies, magnetization
and magnetoimpedance measurements. The particle size decreased rapidly with
ball-milling up to 165 hours and then remained as a constant with further hours
of milling while, the lattice expanded with milling time up to 165 hours and
contracted back with further milling. Saturation magnetization is found to
decrease rapidly up to 165 hours of milling and then started decreasing slowly
with further milling time. Magnetoimpedance studies were carried out in pellets
and thin films of Fe75Cu4Ni4Mo2B15. Magnetoimpedance in pellet is observed to
be ~2.5% at 5Hz whereas, in thin films, it is observed to be ~1.5% at 3 MHz.


  In this essay we aim to explore the Geometric aspects of the Calabi
Conjecture and highlight the techniques of nonlinear Elliptic PDE theory used
by S.T. Yau [SY] in obtaining a solution to the problem. Yau proves the
existence of a Geometric structure using differential equations, giving
importance to the idea that deep insights into geometry can be obtained by
studying solutions of such equations. Yau's proof of the existence of a
specific class of metrics have found a natural interpretation in recent
developments in Theoretical Physics most notably in the formulation of String
Theory. We will also attempt to explore the importance of a special case of
Yau's solution known as Calabi-Yau Manifolds in the context of holonomy.


  We adapt a technique of Kisin to construct and study crystalline deformation
rings of $G_K$ for a finite extension $K/\mathbb{Q}_p$. This is done by
considering a moduli space of Breuil--Kisin modules, satisfying an additional
Galois condition, over the universal deformation ring. For $K$ unramified over
$\mathbb{Q}_p$ and Hodge--Tate weights in $[0,p]$, we study the geometry of
this space. As a consequence we prove that, under a mild cyclotomic-freeness
assumption, all crystalline representations of an unramified extension of
$\mathbb{Q}_p$, with Hodge--Tate weights in $[0,p]$, are potentially
diagonalisable.


  Recent studies have put into question the belief that emergent abilities in
language models are exclusive to large models. This skepticism arises from two
observations: 1) smaller models can also exhibit high performance on emergent
abilities and 2) there is doubt on the discontinuous metrics used to measure
these abilities. In this paper, we propose to study emergent abilities in the
lens of pre-training loss, instead of model size or training compute. We
demonstrate that the models with the same pre-training loss, but different
model and data sizes, generate the same performance on various downstream
tasks. We also discover that a model exhibits emergent abilities on certain
tasks -- regardless of the continuity of metrics -- when its pre-training loss
falls below a specific threshold. Before reaching this threshold, its
performance remains at the level of random guessing. This inspires us to
redefine emergent abilities as those that manifest in models with lower
pre-training losses, highlighting that these abilities cannot be predicted by
merely extrapolating the performance trends of models with higher pre-training
losses.


  Curvilinear structures frequently appear in microscopy imaging as the object
of interest. Crystallographic defects, i.e., dislocations, are one of the
curvilinear structures that have been repeatedly investigated under
transmission electron microscopy (TEM) and their 3D structural information is
of great importance for understanding the properties of materials. 3D
information of dislocations is often obtained by tomography which is a
cumbersome process since it is required to acquire many images with different
tilt angles and similar imaging conditions. Although, alternative stereoscopy
methods lower the number of required images to two, they still require human
intervention and shape priors for accurate 3D estimation. We propose a fully
automated pipeline for both detection and matching of curvilinear structures in
stereo pairs by utilizing deep convolutional neural networks (CNNs) without
making any prior assumption on 3D shapes. In this work, we mainly focus on 3D
reconstruction of dislocations from stereo pairs of TEM images.


  High annotation cost for training machine learning classifiers has driven
extensive research in active learning and self-supervised learning. Recent
research has shown that in the context of supervised learning different active
learning strategies need to be applied at various stages of the training
process to ensure improved performance over the random baseline. We refer to
the point where the number of available annotations changes the suitable active
learning strategy as the phase transition point. In this paper, we establish
that when combining active learning with self-supervised models to achieve
improved performance, the phase transition point occurs earlier. It becomes
challenging to determine which strategy should be used for previously unseen
datasets. We argue that existing active learning algorithms are heavily
influenced by the phase transition because the empirical risk over the entire
active learning pool estimated by these algorithms is inaccurate and influenced
by the number of labeled samples. To address this issue, we propose a novel
active learning strategy, neural tangent kernel clustering-pseudo-labels
(NTKCPL). It estimates empirical risk based on pseudo-labels and the model
prediction with NTK approximation. We analyze the factors affecting this
approximation error and design a pseudo-label clustering generation method to
reduce the approximation error. We validate our method on five datasets,
empirically demonstrating that it outperforms the baseline methods in most
cases and is valid over a wider range of training budgets.


  This paper gives necessary conditions and slightly stronger sufficient
conditions for a holomorphic function to be the Segal-Bargmann transform of a
function in L^p(R^d) with respect to a Gaussian measure. The proof relies on a
family of inversion formulas for the Segal-Bargmann transform, which can be
"tuned" to give the best estimates for a given value of p.


  Using extensive Monte Carlo simulations we study numerically and analytically
a photogalvanic effect, or ratchet, of directed electron transport induced by a
microwave radiation on a semidisk Galton board of antidots in graphene. A
comparison between usual two-dimensional electron gas (2DEG) and electrons in
graphene shows that ratchet currents are comparable at very low temperatures.
However, a large mean free path in graphene should allow to have a strong
ratchet transport at room temperatures. Also in graphene the ratchet transport
emerges even for unpolarized radiation. These properties open promising
possibilities for room temperature graphene based sensitive photogalvanic
detectors of microwave and terahertz radiation.


  Principled accountability for autonomous decision-making in uncertain
environments requires distinguishing intentional outcomes from negligent
designs from actual accidents. We propose analyzing the behavior of autonomous
agents through a quantitative measure of the evidence of intentional behavior.
We model an uncertain environment as a Markov Decision Process (MDP). For a
given scenario, we rely on probabilistic model checking to compute the ability
of the agent to influence reaching a certain event. We call this the scope of
agency. We say that there is evidence of intentional behavior if the scope of
agency is high and the decisions of the agent are close to being optimal for
reaching the event. Our method applies counterfactual reasoning to
automatically generate relevant scenarios that can be analyzed to increase the
confidence of our assessment. In a case study, we show how our method can
distinguish between 'intentional' and 'accidental' traffic collisions.


  Motivated by the construction of Bach flat neutral signature Riemannian
extensions, we study the space of parallel trace free tensors of type $(1,1)$
on an affine surface. It is shown that the existence of such a parallel tensor
field is characterized by the recurrence of the symmetric part of the Ricci
tensor.


  Social Media is a cyber-security risk for every business. What do people
share on the Internet? Almost everything about oneself is shared: friendship,
demographics, family, activities, and work-related information. This could
become a potential risk in every business if the organization's policies,
training and technology fail to properly address these issues. In many cases,
it is the employees' behaviour that can put key company information at danger.
Social media has turned into a reconnaissance tool for malicious actors and
users accounts are now seen as a goldmine for cyber criminals. Investigation of
Social Media is in the embryonic stage and thus, is not yet well understood.
This research project aims to collect and analyse open-source data from
LinkedIn, discover data leakage and analyse personality types through software
as a service (SAAS). The final aim of the study is to understand if there are
behavioral factors that can predicting one's attitude toward disclosing
sensitive data.


  An improved criterion for distinguishing conditions in which classical or
quantum behavior occurs is developed by comparing classical and quantum
mechanical measures of size while incorporating spatial and temporal
restrictions on wave packet formation associated with limitations on spatial
extent and duration.


  We apply the large-deviation method to study trajectories in dissipative
quantum systems. We show that in the long time limit the statistics of quantum
jumps can be understood from thermodynamic arguments by exploiting the analogy
between large-deviation and free-energy functions. This approach is
particularly useful for uncovering properties of rare dissipative trajectories.
We also prove, via an explicit quantum mapping, that rare trajectories of one
system can be realized as typical trajectories of an alternative system.


  Representing 3D objects and scenes with neural radiance fields has become
very popular over the last years. Recently, surface-based representations have
been proposed, that allow to reconstruct 3D objects from simple photographs.
However, most current techniques require an accurate camera calibration, i.e.
camera parameters corresponding to each image, which is often a difficult task
to do in real-life situations. To this end, we propose a method for learning 3D
surfaces from noisy camera parameters. We show that we can learn camera
parameters together with learning the surface representation, and demonstrate
good quality 3D surface reconstruction even with noisy camera observations.


  Results are presented of a search for supersymmetric particles in events with
large missing transverse momentum and at least one heavy flavour jet candidate
in sqrt{s} = 7 TeV proton-proton collisions. In a data sample corresponding to
an integrated luminosity of 35 pb-1 recorded by the ATLAS experiment at the
Large Hadron Collider, no significant excess is observed with respect to the
prediction for Standard Model processes. For R-parity conserving models in
which sbottoms (stops) are the only squarks to appear in the gluino decay
cascade, gluino masses below 590 GeV (520 GeV) are excluded at the 95% C.L. The
results are also interpreted in an MSUGRA/CMSSM supersymmetry breaking scenario
with tan(beta)=40 and in an SO(10) model framework.


  Transformation elasticity, by analogy with transformation acoustics and
optics, converts material domains without altering wave properties, thereby
enabling cloaking and related effects. By noting the similarity between
transformation elasticity and the theory of incremental motion superimposed on
finite pre-strain it is shown that the constitutive parameters of
transformation elasticity correspond to the density and moduli of
small-on-large theory. The formal equivalence indicates that transformation
elasticity can be achieved by selecting a particular finite (hyperelastic)
strain energy function, which for isotropic elasticity is semilinear strain
energy. The associated elastic transformation is restricted by the requirement
of statically equilibrated pre-stress. This constraint can be cast as $\tr
{\mathbf F} =$ constant, where $\mathbf{F}$ is the deformation gradient,
subject to symmetry constraints, and its consequences are explored both
analytically and through numerical examples of cloaking of anti-plane and
in-plane wave motion.


  We study and analyze the recent observations of the top pair production
$\sigma (p\bar p\to t \bar t)$ at TeVatron through flavor conserving and flavor
violating channels ${\it via}$ vector and tensor unparticles. The unparticle
sector is considered with the possibility of being a color singlet or octet.
The modified unparticle propagator is used to investigate the contribution of
these unparticles to the observed $A_{FB}^{t\bar t}$ (forward backward
asymmetry in top pair production) and the spin correlation at TeVatron. We have
also studied the impact of the flavor violating couplings of unparticles to the
third generation quarks on (a) pair production of same sign tops/antitops
$\sigma (p\bar p\to tt+\bar t \bar t)$ at TeVatron and (b) the partial top
decay width for $\Gamma_{\cal U}(t\to u\,{\cal U}^V)$.
  We find that a large region of parameter space is consistent with the
measurements of \tt production cross-section, \afbt and spin correlation
coefficient at TeVatron and observe that the top decay width measurement
constrains the flavor violating coupling of vector unparticles more severely
than the same sign top/antitop production at TeVatron. We also predict the best
point-set in the model parameter space for specific choices of \du
corresponding to $\chi^2_{\rm min}$ evaluated using the \mttb spectrum of \afbt
from the data set of Run II of TeVatron at the integrated luminosity 8.7
fb$^{-1}$. Our results and analysis are consistent even with unparticle
theories having broken scale invariance as long as the infrared cut-off scale
is much less than the top pair production threshold.


  Correlated Basis Function perturbation theory is used to evaluate the zero
temperature response $S(q,\omega)$ of $^3$He-$^4$He mixtures for inelastic
neutron scattering, at momentum transfers $q$ ranging from $1.1$ to $1.7
\AA^{-1}$. We adopt a Jastrow correlated ground state and a basis of correlated
particle-hole and phonon states. We insert correlated one particle-one hole and
one-phonon states to compute the second order response. The decay of the
one-phonon states into two-phonon states is accounted for in boson-boson
approximation. The full response is splitted into three partial components
$S_{\alpha \beta}(q,\omega)$, each of them showing a particle-hole bump and a
one phonon, delta shaped peak, which stays separated from the multiphonon
background. The cross term $S_{34}(q,\omega)$ results to be of comparable
importance to $S_{33}(q,\omega)$ in the particle-hole sector and to
$S_{44}(q,\omega)$ in the phonon one. Once the one-phonon peak has been
convoluted with the experimental broadening, the computed scattering function
is in semiquantitative agreement with recent experimental measurements.


  We look at colourings of $r$-uniform hypergraphs, focusing our attention on
unique colourability and gaps in the chromatic spectrum. The pattern of an edge
$E$ in an $r$-uniform hypergraph $H$ whose vertices are coloured is the
partition of $r$ induced by the colour classes of the vertices in $E$. Let $Q$
be a set of partitions of $r$. A $Q$-colouring of $H$ is a colouring of its
vertices such that only patterns appearing in $Q$ are allowed. We first show
that many known hypergraph colouring problems, including Ramsey theory, can be
stated in the language of $Q$-colourings. Then, using as our main tools the
notions of $Q$-colourings and $\Sigma$-hypergraphs, we define and prove a
result on tight colourings, which is a strengthening of the notion of unique
colourability. $\Sigma$-hypergraphs are a natural generalisation of
$\sigma$-hypergraphs introduced by the first two authors in an earlier paper.
We also show that there exist $\Sigma$-hypergraphs with arbitrarily large
$Q$-chromatic number and chromatic number but with bounded clique number.
Dvorak et al. have characterised those $Q$ which can lead to a hypergraph with
a gap in its $Q$-spectrum. We give a short direct proof of the necessity of
their condition on $Q$. We also prove a partial converse for the special case
of $\Sigma$-hypergraphs. Finally, we show that, for at least one family $Q$
which is known to yield hypergraphs with gaps, there exist no
$\Sigma$-hypergraphs with gaps in their $Q$-spectrum.


  We investigate finite temperature properties in the half-filled
three-component (colors) fermion systems. It is clarified that a color
density-wave (CDW) state is more stable than a color-selective
"antiferromagnetic" (CSAF) state against thermal fluctuations. The reentrant
behavior in the phase boundary for the CSAF state is found. We also address the
maximum critical temperature of the translational symmetry breaking states in
the multicomponent fermionic systems.


  Using functional techniques, we prove, to all orders of perturbation theory,
that lattice vector gauge theories with Ginsparg Wilson fermions are
renormalizable. For two or more massless fermions, they satisfy a flavour
mixing axial vector Ward identity. It involves a lattice specific part that is
quadratic in the vertex functional and classically irrelevant. We show that it
stays irrelevant under renormalization. This means that in the continuum limit
the (standard) chiral symmetry becomes restored. In particular, the flavour
mixing current does not require renormalization.


  It is a classical theorem of Loewner that the systole of a Riemannian torus
can be bounded in terms of its area. We answer a question of a similar flavor
of Robert Young showing that if $T$ is a Riemannian 2-torus with boundary in
$\mathbb R ^n$, such that the boundary curve is a standard unit circle, then
the length of the shortest non-contractible loop in $T$ is bounded in terms of
the area of $T$.


  An elementary proof of the attainability of random coding exponent with
linear codes for additive channels is presented. The result and proof are from
Hamada (Proc. ITW, Chendu, China, 2006), and the present material explains the
proof in detail for those unfamiliar with elementary calculations on
probabilities related to linear codes.


  Transneptunian objects (TNOs) are bodies populating the Kuiper Belt and they
are believed to retain the most pristine and least altered material of the
solar system. The Herschel Open Time Key Program entitled "TNOs are Cool: A
survey of the trans-Neptunian region" has been awarded 373 h to investigate the
albedo, size distribution and thermal properties of TNOs and Centaurs. Here we
focus on the brightest targets observed by both the PACS and SPIRE multiband
photometers: the dwarf planet Haumea, six TNOs (Huya, Orcus, Quaoar, Salacia,
2002 UX25, and 2002 TC302), and two Centaurs (Chiron and Chariklo). Flux
densities are derived from PACS and SPIRE instruments using optimised data
reduction methods. The spectral energy distribution obtained with the Herschel
PACS and SPIRE instruments over 6 bands (centred at 70, 100, 160, 250, 350, and
500 $\mu$m), and with Spitzer-MIPS at 23.7 and 71.4 $\mu$m has been modelled
with the NEATM thermal model in order to derive the albedo, diameter, and
beaming factor. For the Centaurs Chiron and Chariklo and for the 1000 km sized
Orcus and Quaoar, a thermophysical model was also run to better constrain their
thermal properties. We derive the size, albedo, and thermal properties,
including thermal inertia and surface emissivity, for the 9 TNOs and Centaurs.
Several targets show a significant decrease in their spectral emissivity
longwards of $\sim$300 $\mu$m and especially at 500 $\mu$m. Using our size
estimations and the mass values available in the literature, we also derive the
bulk densities for the binaries Quaoar/Weywot (2.18$^{+0.43}_{-0.36}$
g/cm$^3$), Orcus/Vanth (1.53$^{+0.15}_{-0.13}$ g/cm$^3$), and Salacia/Actea
(1.29$^{+0.29}_{-0.23}$ g/cm$^3$). Quaoar's density is similar to that of the
other dwarf planets Pluto and Haumea, and its value implies high contents of
refractory materials mixed with ices.


  In previous work, a novel supervised framework implementing a binary
classifier was presented that obtained excellent results for side effect
discovery. Interestingly, unique side effects were identified when different
binary classifiers were used within the framework, prompting the investigation
of applying a multiple classifier system. In this paper we investigate tuning a
side effect multiple classifying system using genetic algorithms. The results
of this research show that the novel framework implementing a multiple
classifying system trained using genetic algorithms can obtain a higher partial
area under the receiver operating characteristic curve than implementing a
single classifier. Furthermore, the framework is able to detect side effects
efficiently and obtains a low false positive rate.


  We consider theoretically light scattering by a resonant layer that
periodically moves in real space. At small frequencies of motion the scattered
light spectrum reveals the frequency shift that is governed by the Doppler
effect. At higher motion frequencies, the scattered light spectra acquire
sidebands stemming from the Raman effect. We investigate the crossover between
these two regimes and propose a realistic quantum well structure for its
observation.


  The present work theoretically investigates the probability of generation of
entangled electron-photon pair in high-energy Compton scattering of unpolarized
electrons and photons due to scattering-channel-exchange mechanism. The study
suggests that the scattering of unpolarized electrons and photons with nearly
equal energy of the order of MeV at cross-channel can create entangled pair of
up-spin electron and RCP photon or down-spin electron and LCP photon. The
entanglement is quite strong exhibiting jump-concurrence for particular
directions of scattering however not limited by the Kapitza-Dirac restriction.
Such strong electron-photon entanglement is observed to be highly selective
along the directions of scattering on the surface of two opposite cones at 45
degree around the electron-detector axis and on the plane perpendicular to it,
the latter one exhibiting maximal entanglement. The work predicts that
spin-polarization entangled electron-photon pairs are highly possible to be
found in practical experiments of high-energy Compton scattering with specific
directional selectivity.


  I discuss recent developments in the theoretical study of Higgs search at
LHC.


  We illustrate how to calculate the finite-temperature linear-response
conductance of quantum impurity models from the Matsubara Green function. A
continued fraction expansion of the Fermi distribution is employed which was
recently introduced by Ozaki [Phys. Rev. B 75, 035123 (2007)] and converges
much faster than the usual Matsubara representation. We give a simplified
derivation of Ozaki's idea using concepts from many-body condensed matter
theory and present results for the rate of convergence. In case that the Green
function of some model of interest is only known numerically, interpolating
between Matsubara frequencies is much more stable than carrying out an analytic
continuation to the real axis. We demonstrate this explicitly by considering an
infinite tight-binding chain with a single site impurity as an exactly-solvable
test system, showing that it is advantageous to calculate transport properties
directly on the imaginary axis. The formalism is applied to the single impurity
Anderson model, and the linear conductance at finite temperatures is calculated
reliably at small to intermediate Coulomb interactions by virtue of the
Matsubara functional renormalization group. Thus, this quantum many-body method
combined with the continued fraction expansion of the Fermi function
constitutes a promising tool to address more complex quantum dot geometries at
finite temperatures.


  Interstellar synchrotron emission depends on Galactic magnetic fields and on
cosmic-ray leptons. Observations of radio emission are an important tool for
studying cosmic-ray propagation models and interstellar electron spectrum and
distribution in the Galaxy. We present the latest developments in our modeling
of Galactic synchrotron emission with the GALPROP code, including polarization,
absorption, and free-free emission. Using surveys over a wide range of radio
frequencies and polarization measurements, we derive constraints on the
low-energy interstellar cosmic-ray electron spectrum, magnetic fields and
cosmic-ray propagation models. This work is of interest for studies of
interstellar gamma-ray emission with Fermi-LAT, and synchrotron for the Planck
mission.


  We present a new algorithm for anomaly detection called Anomaly Awareness.
The algorithm learns about normal events while being made aware of the
anomalies through a modification of the cost function. We show how this method
works in different Particle Physics situations and in standard Computer Vision
tasks. For example, we apply the method to images from a Fat Jet topology
generated by Standard Model Top and QCD events, and test it against an array of
new physics scenarios, including Higgs production with EFT effects and
resonances decaying into two, three or four subjets. We find that the algorithm
is effective identifying anomalies not seen before, and becomes robust as we
make it aware of a varied-enough set of anomalies.


  We introduce Neural Flow Maps, a novel simulation method bridging the
emerging paradigm of implicit neural representations with fluid simulation
based on the theory of flow maps, to achieve state-of-the-art simulation of
inviscid fluid phenomena. We devise a novel hybrid neural field representation,
Spatially Sparse Neural Fields (SSNF), which fuses small neural networks with a
pyramid of overlapping, multi-resolution, and spatially sparse grids, to
compactly represent long-term spatiotemporal velocity fields at high accuracy.
With this neural velocity buffer in hand, we compute long-term, bidirectional
flow maps and their Jacobians in a mechanistically symmetric manner, to
facilitate drastic accuracy improvement over existing solutions. These
long-range, bidirectional flow maps enable high advection accuracy with low
dissipation, which in turn facilitates high-fidelity incompressible flow
simulations that manifest intricate vortical structures. We demonstrate the
efficacy of our neural fluid simulation in a variety of challenging simulation
scenarios, including leapfrogging vortices, colliding vortices, vortex
reconnections, as well as vortex generation from moving obstacles and density
differences. Our examples show increased performance over existing methods in
terms of energy conservation, visual complexity, adherence to experimental
observations, and preservation of detailed vortical structures.


  We discuss the relation between the superradiance phenomenon and the
instability of rotating black holes in higher dimensions. In particular, we
point out that the superradiant instability of a massless scalar field around a
simply rotating Kerr-adS black hole implies the gravitational instability of
that black hole for tensor-type perturbations.


  Using a sample of 407 RR Lyrae stars extracted from SDSS Stripe 82, we study
the degree of substructure in the Galactic halo. We identify overdensities
associated with the known substructures of the Hercules-Aquila Cloud and the
Sagittarius Stream, and find a further previously-unknown substructure, the
Pisces Overdensity, at ~100 kpc from the Sun. Together, the three substructures
account for ~80% of our RR Lyrae sample. We also study the density distribution
of RR Lyraes in the halo and find that the profile is best fit by a broken
power law with an inner slope of -2.4 and a break radius of ~25 kpc, consistent
with previous studies. We conclude that the halo is predominantly made up of
the debris from in-falling satellites, with little or no underlying smooth
component.


  We show that non-linear electrodynamics may induce a photon to follow a
closed path in spacetime. We exhibit a specific case in which such closed
lightlike curve (CLC) appears


  In this paper, we prove an important cryptographic property of
$PE$-transformation proposed elsewhere. If $PE$-transformation is used as
encrypting function then after $n$ applications of it on arbitrary message the
distribution of $l$-tuples ($l=1,2,\dots, n$) is uniform. This property implies
the resistance of statistical kind of attack of this transformation. For
illustration of theoretical results, some experimental results are presented as
well.


  We consider the impact that temporal correlations in the measurement
statistics can have on the achievable precision in a sequential metrological
protocol. In this setting, and for a single quantum probe, we establish that it
is the transitions between the measurement basis states that plays the most
significant role in determining the precision, with the resulting conditional
Fisher information being interpretable as a rate of information acquisition.
Projective measurements are shown to elegantly demonstrate this in two
disparate estimation settings. Firstly, in determining the temperature of an
environment and, secondly, to ascertain a parameter of the system Hamiltonian.
In both settings we show that the sequential estimation approach can provide a
useful method to enhance the achievable precision.


  An explicit bound is given for the Kolmogorov distance between a mixture of
normal distributions and a normal distribution with properly chosen parameter
values. A random variable X has a mixture of normal distributions if its
conditional distribution given some sigma-algebra is normal. The bound depends
only on the first two moments of the first two conditional moments of X given
this sigma-algebra. As an application, the Yule-Ornstein-Uhlenbeck model, used
in the field of phylogenetic comparative methods, is considered. A bound is
derived for the Kolmogorov distance between the distribution of the average
value of a phenotypic trait over n related species and a normal distribution.
The bound goes to 0 as n goes to infinity, extending earlier limit theorems by
Bartoszek and Sagitov.


  Over-the-air computation (AirComp) enables fast wireless data aggregation at
the receiver through concurrent transmission by sensors in the application of
Internet-of-Things (IoT). To further improve the performance of AirComp under
unfavorable propagation channel conditions, we consider the problem of
computation distortion minimization in a reconfigurable intelligent surface
(RIS)-aided AirComp system. In particular, we take into account an additive
bounded uncertainty of the channel state information (CSI) and the total power
constraint, and jointly optimize the transceiver (Tx-Rx) and the RIS phase
design from the perspective of worst-case robustness by minimizing the mean
squared error (MSE) of the computation. To solve this intractable nonconvex
problem, we develop an efficient alternating algorithm where both solutions to
the robust sub-problem and to the joint design of Tx-Rx and RIS are obtained in
closed forms. Simulation results demonstrate the effectiveness of the proposed
method.


  We measure the spectral properties of a representative sub-sample of 187
quasars, drawn from the Parkes Half-Jansky, Flat-radio-spectrum Sample (PHFS).
Quasars with a wide range of rest-frame optical/UV continuum slopes are
included in the analysis: their colours range from 2 < B-K < 7.
  The median H-beta and [O III] emission-line equivalent widths of the red
quasar sub-sample are a factor of ten weaker than those of the blue quasar
sub-sample. Both the colours and the emission-line equivalent widths of the red
quasars can be explained by the addition of a featureless red synchrotron
continuum component to an otherwise normal blue quasar spectrum. The relative
strengths of the blue and red components span two orders of magnitude at
rest-frame 500nm. The blue component is weaker relative to the red component in
low optical luminosity sources. This suggests that the fraction of accretion
energy going into optical emission from the jet is greater in low luminosity
quasars.
  This synchrotron model does not, however, fit around 10% of the quasars,
which have both red colours and high equivalent width emission-lines. We
hypothesise that these red, strong-lined quasars have intrinsically weak Big
Blue Bumps.
  There is no discontinuity in spectral properties between the BL Lac objects
in our sample and the other quasars. The synchrotron emission component only
dominates the spectrum at longer wavelengths, so existing BL Lac surveys will
be biassed against high redshift objects.


  For classes O of structures on finite linear orders (permutations, ordered
graphs etc.) endowed with containment order cont (containment of permutations,
subgraph relation etc.), we investigate restrictions on the function f(n)
counting objects with size n in a lower ideal in (O, cont). We present a
framework of edge P-colored complete graphs (C(P), cont) which includes many of
these situations, and we prove for it two such restrictions (jumps in growth):
f(n) is eventually constant or f(n) >= n for all n>0; f(n)<n^c for all n>0 for
a constant c>0 or f(n) >= F_n for all n>0, F_n being the Fibonacci numbers.
This generalizes a fragment of a more detailed theorem of Balogh, Bollobas and
Morris on hereditary properties of ordered graphs.


  The newly discovered 16.35 days period for repeating FRB 180916.J0158+65
provides an essential clue for understanding the sources and emission mechanism
of repeating FRBs. Many models propose that the periodically repeating FRBs
might be related to binary star systems that contain at least one neutron star
(NSC-FRB system). It has been suggested that the NS "combed" by the strong wind
from a companion star might provide a solution. Following the "Binary Comb"
model, we use the population synthesis method to study in detail the properties
of the companion stars and the nature of NSC-FRB systems. Our main findings
are: 1) the companion star is most likely to be a B-type star; 2) the period of
16 days of FRB 180916 happens to fall in the most probable period range, which
may explain why FRB 180916 was the first detected periodically repeating FRB,
and we expect to observe more periodically repeating FRBs with periods around
10-30 days; 3) the birth rate for NSC-FRB system is large enough to fulfill the
event rate requirement set by the observation of FRB 180916, which supports the
proposal that NSC-FRB can provide one significant channel for producing
periodically repeating FRBs.