  We consider localization of gravity in domain wall solutions of Einstein's
gravity coupled to a scalar field with a generic potential. We discuss
conditions on the scalar potential such that domain wall solutions are
non-singular. Such solutions even exist for appropriate potentials which have
no minima at all and are unbounded below. Domain walls of this type have
infinite tension, while usual kink type of solutions interpolating between two
AdS minima have finite tension. Non-singular domain walls with infinite tension
might a priori avoid recent ``no-go'' theorems indicating impossibility of
supersymmetric embedding of kink type of domain walls in gauged supergravity.
We argue that (non-singular) domain walls are stable even if they have infinite
tension. This is essentially due to the fact that localization of gravity in
smooth domain walls is a Higgs mechanism corresponding to a spontaneous
breakdown of translational invariance. We point out that if the scalar
potential has no minima and approaches finite negative values at infinity, then
higher derivative terms are under control, and do not affect the cosmological
constant on the brane which is vanishing for such backgrounds. Nonetheless, we
also point out that higher curvature terms generically delocalize gravity, so
that the desired lower dimensional Newton's law is no longer reproduced.


  Silicon nitride (Si$_3$N$_4$) is an ever-maturing integrated platform for
nonlinear optics. Yet, due to the absence of second-order ($\chi^{(2)}$)
nonlinearity, Si$_3$N$_4$ is mostly considered for third-order ($\chi^{(3)}$)
nonlinear interactions. Recently, this limitation was overcome by optical
poling in both Si$_3$N$_4$ waveguides and microresonators via the photogalvanic
effect, resulting in the inscription of quasi-phase-matched $\chi^{(2)}$
gratings. Here, we report cascaded nonlinear effects in a normal dispersion
Si$_3$N$_4$ microresonator with combined $\chi^{(2)}$ and $\chi^{(3)}$
nonlinearities. We demonstrate that the photo-induced $\chi^{(2)}$ grating also
provides phase-matching for the sum-frequency generation process, enabling the
initiation and successive switching of primary combs at pump wavelength.
Additionally, the doubly resonant pump and second-harmonic fields allow for
cascaded third-harmonic generation, where a secondary optically written
$\chi^{(2)}$ grating is identified. Finally, we reach a low-noise, broadband
microcomb state evolved from the sum-frequency coupled primary comb. These
results expand the scope of cascaded effects in $\chi^{(2)}$ and $\chi^{(3)}$
microresonators.


  The $\Xi_c^0$ baryon is unstable and usually decays into charmless final
states by the $c \to s u\overline{d}$ transition. It can, however, also
disintegrate into a $\pi^-$ meson and a $\Lambda_c^+$ baryon via $s$ quark
decay or via $cs\to d c$ weak scattering. The interplay between the latter two
processes governs the size of the branching fraction ${\cal{B}}$$(\Xi_c^0\to
\pi^-\Lambda_c^+)$, first measured here to be $(0.55\pm 0.02 \pm 0.18)$%, where
the first uncertainty is statistical and second systematic. This result is
compatible with the larger of the theoretical predictions that connect models
of hyperon decays using partially conserved axial currents and SU(3) symmetry
with those involving the heavy-quark expansion and heavy-quark symmetry. In
addition, the branching fraction of the normalization channel,
${\cal{B}}(\Xi_c^+\to p K^- \pi^+) = (1.135 \pm 0.002 \pm 0.387)$% is measured.


  Using a fully covariant formalism given by Carter for the deformation
dynamics of p-branes governed by the Dirac-Nambu-Goto action in a curved
background, it is proved that the corresponding Witten's phase space is endowed
with a covariant symplectic structure, which can serve as a starting point for
a phase space quantization of such objects. Some open questions for further
research are outlined.


  Implementing optical-frequency combs with integrated photonics will enable
wider use of precision timing signals.Here, we explore the generation of an
octave-span, Kerr-microresonator frequency comb, using hybrid integration ofan
InP distributed-feedback laser and a SiN photonic-integrated circuit. We
demonstrate electrically pumped and fiber-packaged prototype systems, enabled
by self-injection locking. This direct integration of a laser and a
microresonatorcircuit without previously used intervening elements, like
optical modulators and isolators, necessitates understand-ing
self-injection-locking dynamics with octave-span Kerr solitons. In particular,
system architectures must adjust tothe strong coupling of microresonator
back-scattering and laser-microresonator frequency detuning that we
uncoverhere. Our work illustrates critical considerations towards realizing a
self-referenced frequency comb with integratedphotonics.


  Wilf posed the following problem: determine asymptotically as $n\to\infty$
the probability that a randomly chosen part size in a randomly chosen
composition of n has multiplicity m. One solution of this problem was given by
Hitczenko and Savage. In this paper, we study this question using the
techniques of generating functions and singularity analysis.


  Inference is the process of using facts we know to learn about facts we do
not know. A theory of inference gives assumptions necessary to get from the
former to the latter, along with a definition for and summary of the resulting
uncertainty. Any one theory of inference is neither right nor wrong, but merely
an axiom that may or may not be useful. Each of the many diverse theories of
inference can be valuable for certain applications. However, no existing theory
of inference addresses the tendency to choose, from the range of plausible data
analysis specifications consistent with prior evidence, those that
inadvertently favor one's own hypotheses. Since the biases from these choices
are a growing concern across scientific fields, and in a sense the reason the
scientific community was invented in the first place, we introduce a new theory
of inference designed to address this critical problem. We introduce hacking
intervals, which are the range of a summary statistic one may obtain given a
class of possible endogenous manipulations of the data. Hacking intervals
require no appeal to hypothetical data sets drawn from imaginary
superpopulations. A scientific result with a small hacking interval is more
robust to researcher manipulation than one with a larger interval, and is often
easier to interpret than a classical confidence interval. Some versions of
hacking intervals turn out to be equivalent to classical confidence intervals,
which means they may also provide a more intuitive and potentially more useful
interpretation of classical confidence intervals.


  The proliferation of unmanned aerial vehicles (UAVs) opens up new
opportunities for on-demand service provisioning anywhere and anytime, but also
exposes UAVs to a variety of cyber threats. Low/medium interaction honeypots
offer a promising lightweight defense for actively protecting mobile Internet
of things, particularly UAV networks. While previous research has primarily
focused on honeypot system design and attack pattern recognition, the incentive
issue for motivating UAV's participation (e.g., sharing trapped attack data in
honeypots) to collaboratively resist distributed and sophisticated attacks
remains unexplored. This paper proposes a novel game-theoretical collaborative
defense approach to address optimal, fair, and feasible incentive design, in
the presence of network dynamics and UAVs' multi-dimensional private
information (e.g., valid defense data (VDD) volume, communication delay, and
UAV cost). Specifically, we first develop a honeypot game between UAVs and the
network operator under both partial and complete information asymmetry
scenarios. The optimal VDD-reward contract design problem with partial
information asymmetry is then solved using a contract-theoretic approach that
ensures budget feasibility, truthfulness, fairness, and computational
efficiency. In addition, under complete information asymmetry, we devise a
distributed reinforcement learning algorithm to dynamically design optimal
contracts for distinct types of UAVs in the time-varying UAV network. Extensive
simulations demonstrate that the proposed scheme can motivate UAV's cooperation
in VDD sharing and improve defensive effectiveness, compared with conventional
schemes.


  Social media based indicators or altmetrics have been under scrutiny for the
last seven years. Their promise as alternative metrics for measuring scholarly
impact is still far from becoming a reality. Up to now, most studies have
focused on the understanding of the nature and relation of altmetric indicators
with citation data. Few papers have analysed research profiles based on
altmetric data. Most of these have related to researcher profiles and the
expansion of these tools among researchers. This paper aims at exploring the
coverage of the Altmetric.com database and its potential use in order to show
universities' research profiles in relationship with other databases. We
analyse a sample of four different Spanish universities.First, we observe a low
coverage of altmetric indicators with only 36 percent of all documents
retrieved from the Web of Science having an 'altmetric' score. Second, we
observe that for the four universities analysed, the area of Science shows
higher 'altmetric' scores that the rest of the research areas. Finally,
considering the low coverage of altmetric data at the institutional level, it
could be interesting for research policy makers to consider the development of
guidelines and best practices guides to ensure that researchers disseminate
adequately their research findings through social media.


  Automatic techniques in the context of motor speech disorders (MSDs) are
typically two-class techniques aiming to discriminate between dysarthria and
neurotypical speech or between dysarthria and apraxia of speech (AoS). Further,
although such techniques are proposed to support the perceptual assessment of
clinicians, the automatic and perceptual classification accuracy has never been
compared. In this paper, we investigate a three-class automatic technique and a
set of handcrafted features for the discrimination of dysarthria, AoS and
neurotypical speech. Instead of following the commonly used One-versus-One or
One-versus-Rest approaches for multi-class classification, a hierarchical
approach is proposed. Further, a perceptual study is conducted where speech and
language pathologists are asked to listen to recordings of dysarthria, AoS, and
neurotypical speech and decide which class the recordings belong to. The
proposed automatic technique is evaluated on the same recordings and the
automatic and perceptual classification performance are compared. The presented
results show that the hierarchical classification approach yields a higher
classification accuracy than baseline One-versus-One and One-versus-Rest
approaches. Further, the presented results show that the automatic approach
yields a higher classification accuracy than the perceptual assessment of
speech and language pathologists, demonstrating the potential advantages of
integrating automatic tools in clinical practice.


  In this paper, evolving wormholes in the context of brane-world scenario are
investigated. We have studied the possible dynamic solutions with different
forms of Ricci scalar. The possibility of existence of dynamic traversable
wormholes, without resorting to an exotic matter, has been studied. By using
the fact that the Einstein field equations are modified in 3+1 dimensions due
to the brane corrections, we investigate the exact solutions which satisfy null
energy condition. Asymptotic flatness is an important property of these
solutions. We discuss some physical and mathematical properties of the
solutions.


  We review the Pusey-Barret-Rudolph (PBR) theorem\cite{PBR} and their setup,
and arrive to the conclusion that the reality of a quantum state $\psi$ is
intrinsically attached to the measurement the system described by $\psi$ has
undergone. We show that a state that has not been measured can be regarded as
pure information, while a state that has been measured has to be regarded as a
physical property of a certain system, having a counterpart in reality. This
demonstration implies that the statement of PBR's theorem changes in a
meaningful way.


  We examine how implicit functions on ILB-Fr\'echet spaces can be obtained
without metric or norm estimates which are classically assumed. We obtain
implicit functions defined on a domain $D$ which is not necessarily open, but
which contains the unit open ball of a Banach space. The corresponding inverse
functions theorem is obtained, and we finish with an open question on the
adequate (generalized) notion of differentiation, needed for the corresponding
version of the Fr\"obenius theorem.


  It is shown that energy, entropy and the first law of the Martinez-Troncoso
black hole with electric charge and scalar hair (2006) can be consistently
described in a general Hamiltonian approach to black hole thermodynamics.


  Two-dimensional topological edge states, immunizing against defects and
disorders, have greatly revolutionized our scientific cognition on propagation
and scattering of acoustic waves. Recently, the similar states have been
predicted in three-dimensional acoustic systems consisting of chiral coupling
resonance cavities. However, the direct observation of topological surface
propagation, especially in a 3D acoustic system with simple scatterers but not
complicatedly coupling resonances, has still not been exploited. Here, we
design and fabricate a 3D acoustic semimetal composed of rotationally stacked
rods. This semimetal not only produces a linear Weyl degeneracy with a charge
of 1, but also yields a double Weyl point with a charge of 2. In its nontrivial
gaps, we discover the surface states associated with these Weyl points and
experimentally demonstrate the topologically protected one-way propagation of
acoustic waves. Due to its good fabricability and topological non-reciprocity,
this acoustic semimetal provides an excellent platform for the integration of
various acoustic devices, from a macroscopic scale to a nanoscale.


  We investigate the feasibility of representing a structured multi-dimensional
stellar atmosphere with a single one-dimensional average stratification for the
purpose of spectral diagnosis of the atmosphere's average spectrum. In
particular we construct four different one-dimensional stratifications from a
single snapshot of a magneto-hydrodynamic simulation of solar convection: one
by averaging its properties over surfaces of constant height, and three
different ones by averaging over surfaces of constant optical depth at 500 nm.
Using these models we calculate continuum, and atomic and molecular line
intensities and their center-to-limb variations. From analysis of the emerging
spectra we identify three main reasons why these average representations are
inadequate for accurate determination of stellar atmospheric properties through
spectroscopic analysis. These reasons are: non-linearity in the Planck function
with temperature, which raises the average emergent intensity of an
inhomogeneous atmosphere above that of an average-property atmosphere, even if
their temperature-optical depth stratification is identical; non-linearities in
molecular formation with temperature and density, which raise the abundance of
molecules of an inhomogeneous atmosphere over that in a one-dimensional model
with the same average properties; the anisotropy of convective motions, which
strongly affects the center-to-limb variation of line-core intensities. We
argue therefore that a one-dimensional atmospheric model that reproduces the
mean spectrum of an inhomogeneous atmosphere necessarily does not reflect the
average physical properties of that atmosphere, and are therefore inherently
unreliable.


  Aperiodic dynamical decoupling (DD) sequences of $\pi$ pulses are of great
interest to decoherence control and have been recently extended from
single-qubit to two-qubit systems. If the environmental noise power spectrum is
made available, then one may further optimize aperiodic DD sequences to reach
higher efficiency of decoherence suppression than known universal schemes. This
possibility is investigated in this work for the protection of two-qubit
states, using an exactly solvable pure dephasing model including both local and
nonlocal noise. The performance of optimized DD sequences in protecting
two-qubit states is compared with that achieved by nested Uhrig's DD
(nested-UDD) sequences, for several different types of noise spectrum. Except
for cases with noise spectrum decaying slowly in the high-frequency regime,
optimized DD sequences with tens of control pulses can perform orders of
magnitude better than that of nested-UDD. A two-qubit system with highly
unbalanced local noise is also examined to shed more light on a recent
experiment. Possible experiments that may be motivated by this work are
discussed.


  In this work we present a systematic study of AdS$_{d+1}$ loop amplitudes for
gluons and gravitons using momentum space techniques. Inspired by the recent
progress in tree level computation, we construct a differential operator that
can act on a scalar factor in order to generate gluon and graviton loop
integrands: this systematizes the computation for any given loop level Witten
diagram. We then give a general prescription in this formalism, and discuss it
for bubble, triangle, and box diagrams.


  We consider an acyclic network of single-server queues with heterogeneous
processing rates. It is assumed that each queue is fed by the superposition of
a large number of i.i.d. Gaussian processes with stationary increments and
positive drifts, which can be correlated across different queues. The flow of
work departing from each server is split deterministically and routed to its
neighbors according to a fixed routing matrix, with a fraction of it leaving
the network altogether.
  We study the exponential decay rate of the probability that the steady-state
queue length at any given node in the network is above any fixed threshold,
also referred to as the "overflow probability". In particular, we first
leverage Schilder's sample-path large deviations theorem to obtain a general
lower bound for the limit of this exponential decay rate, as the number of
Gaussian processes goes to infinity. Then, we show that this lower bound is
tight under additional technical conditions. Finally, we show that if the input
processes to the different queues are non-negatively correlated, non
short-range dependent fractional Brownian motions, and if the processing rates
are large enough, then the asymptotic exponential decay rates of the queues
coincide with the ones of isolated queues with appropriate Gaussian inputs.


  Beginning programmers struggle with the complex grammar of modern programming
languages like Java, and make lot of syntax errors. The diagnostic syntax error
messages from compilers and IDEs are sometimes useful, but often the messages
are cryptic and puzzling. Students could be helped, and instructors' time
saved, by automated repair suggestions when dealing with syntax errors. Large
samples of student errors and fixes are now available, offering the possibility
of data-driven machine-learning approaches to help students fix syntax errors.
Current machine-learning approaches do a reasonable job fixing syntax errors in
shorter programs, but don't work as well even for moderately longer programs.
We introduce SYNFIX, a machine-learning based tool that substantially improves
on the state-of-the-art, by learning to use compiler diagnostics, employing a
very large neural model that leverages unsupervised pre-training, and relying
on multi-label classification rather than autoregressive synthesis to generate
the (repaired) output. We describe SYNFIX's architecture in detail, and provide
a detailed evaluation. We have built SYNFIX into a free, open-source version of
Visual Studio Code; we make all our source code and models freely available.


  Iron is a candidate to replace cobalt in WC hardmetals, due to its lower cost
and toxicity. A WC-FeCr hardmetal was compression tested at 900-1200 {\deg}C.
Particular attention is paid to the steady-state creep rates and
stress-exponents (n) during isostress treatments. Three regimes of stress
dependence are observed. Two of these were previously reported for WC-Co: power
law creep (n~3) at medium stresses; and grain boundary sliding (n~1) at higher
stresses, generally >100MPa. A previously unreported low stress (<10MPa) regime
with an exponent of n~2 is also observed. By combining electron microscopy with
X-ray diffraction texture measurements, the low stress regime is attributed to
viscous flow of the binder, which is accommodated by diffusional creep in the
WC skeleton. The mechanism may be applicable to other hardmetals. Compared to
analogous WC-Co materials, WC-FeCr shows improved creep resistance below 1000
{\deg}C, which can be explained by its lower self-diffusivity, and a lower
solubility for WC than Co. However, at temperatures corresponding to liquid
eutectic formation (~1140 {\deg}C), its creep resistance becomes inferior.
These results indicate FeCr may be a suitable replacement for Co provided the
eutectic temperature is not exceeded.


  Let $G$ be a Lie-group and $\Ga\subset G$ a cocompact lattice. For a
finite-dimensional, not necessarily unitary representation $\om$ of $\Ga$ we
show that the $G$-representation on $L^2(\Ga\bs G,\om)$ admits a complete
filtration with irreducible quotients. As a consequence, we show the trace
formula for non-unitary twists and arbitrary locally compact groups.


  A sequential importance sampling algorithm is developed for the distribution
that results when a matrix of independent, but not identically distributed,
Bernoulli random variables is conditioned on a given sequence of row and column
sums. This conditional distribution arises in a variety of applications and
includes as a special case the uniform distribution over zero-one tables with
specified margins. The algorithm uses dynamic programming to combine hard
margin constraints, combinatorial approximations, and additional non-uniform
weighting in a principled way to give state-of-the-art results.


  Traditional neural networks represent everything as a vector, and are able to
approximate a subset of logical reasoning to a certain degree. As basic logic
relations are better represented by topological relations between regions, we
propose a novel neural network that represents everything as a ball and is able
to learn topological configuration as an Euler diagram. So comes the name Euler
Neural-Network (ENN). The central vector of a ball is a vector that can inherit
representation power of traditional neural network. ENN distinguishes four
spatial statuses between balls, namely, being disconnected, being partially
overlapped, being part of, being inverse part of. Within each status, ideal
values are defined for efficient reasoning. A novel back-propagation algorithm
with six Rectified Spatial Units (ReSU) can optimize an Euler diagram
representing logical premises, from which logical conclusion can be deduced. In
contrast to traditional neural network, ENN can precisely represent all 24
different structures of Syllogism. Two large datasets are created: one
extracted from WordNet-3.0 covers all types of Syllogism reasoning, the other
extracted all family relations from DBpedia. Experiment results approve the
superior power of ENN in logical representation and reasoning. Datasets and
source code are available upon request.


  Given a dominating set, how much smaller a dominating set can we find through
elementary operations? Here, we proceed by iterative vertex addition and
removal while maintaining the property that the set forms a dominating set of
bounded size. This can be seen as the optimization variant of the dominating
set reconfiguration problem, where two dominating sets are given and the
question is merely whether they can be reached one from another through
elementary operations. We show that this problem is PSPACE-complete, even if
the input graph is a bipartite graph, a split graph, or has bounded pathwidth.
On the positive side, we give linear-time algorithms for cographs, trees and
interval graphs. We also study the parameterized complexity of this problem.
More precisely, we show that the problem is W[2]-hard when parameterized by the
upper bound on the size of an intermediary dominating set. On the other hand,
we give fixed-parameter algorithms with respect to the minimum size of a vertex
cover, or $d+s$ where $d$ is the degeneracy and $s$ is the upper bound of
output solution.


  Motivated by applications in distributed storage, the notion of a locally
recoverable code (LRC) was introduced a few years back. In an LRC, any
coordinate of a codeword is recoverable by accessing only a small number of
other coordinates. While different properties of LRCs have been well-studied,
their performance on channels with random erasures or errors has been mostly
unexplored. In this paper, we analyze the performance of LRCs over such
stochastic channels. In particular, for input-symmetric discrete memoryless
channels, we give a tight characterization of the gap to Shannon capacity when
LRCs are used over the channel. Our results hold for a general notion of LRCs
that correct multiple local erasures.


  The EOS(R) scanner is a radiographic system that captures PA and lateral
images in standing posture. The system is widely used in diagnosis and
assessment of scoliosis, as it provides a low-dose alternative to traditional
X-ray and can capture full-body images. Furthermore, spacial calibration
between the two imaging views is implemented in hardware, facilitating 3D
reconstruction of imaging targets. In this paper, a brief description of the
system is followed by an explanation of the geometric relationship between 3D
space and radiographic image space.


  Past few years have seen an extensive use of RAM chips with wide I/O data
(e.g. 16, 32, 64 bits) in computer memory systems. These chips are highly
vulnerable to a special type of byte error, called an $m$-spotty byte error,
which can be effectively detected or corrected using byte error-control codes.
The MacWilliams identity provides the relationship between the weight
distribution of a code and that of its dual. The main purpose of this paper is
to present a version of the MacWilliams identity for $m$-spotty weight
enumerators over
$\mathbbm{F}_{2}+u\mathbbm{F}_{2}+\cdots+u^{m-1}\mathbbm{F}_{2}$ (shortly
$R_{u, m, 2}$).


  Bitcoin is the most popular cryptocurrency used worldwide. It provides
pseudonymity to its users by establishing identity using public keys as
transaction end-points. These transactions are recorded on an immutable public
ledger called Blockchain which is an append-only data structure. The popularity
of Bitcoin has increased unreasonably. The general trend shows a positive
response from the common masses indicating an increase in trust and privacy
concerns which makes an interesting use case from the analysis point of view.
Moreover, since the blockchain is publicly available and up-to-date, any
analysis would provide a live insight into the usage patterns which ultimately
would be useful for making a number of inferences by law-enforcement agencies,
economists, tech-enthusiasts, etc. In this paper, we study various applications
and techniques of performing data analytics over Bitcoin blockchain from a
graph theoretic perspective. We also propose a framework for performing such
data analytics and explored a couple of use cases using the proposed framework.


  In quantum mechanics, the space-fractional Schr\"{o}dinger equation provides
a natural extension of the standard Schr\"{o}dinger equation when the Brownian
trajectories in Feynman path integrals are replaced by Levy flights. Here an
optical realization of the fractional Schr\"{o}dinger equation, based on
transverse light dynamics in aspherical optical cavities, is proposed. As an
example a laser implementation of the fractional quantum harmonic oscillator is
presented, in which dual Airy beams can be selectively generated under off-axis
longitudinal pumping.


  It is crucial for maintaining the security of supply that transmission
networks continue to operate even if a single line fails. Modeling $\mathcal{N}
- 1$ security in power system capacity expansion problems introduces many extra
constraints if all possible outages are accounted for, which leads to a high
computational burden. Typical approaches to avoid this burden consider only a
subset of possible outages relevant to a given dispatch situation. However,
this relies on knowing the dispatch situation beforehand, and it is not
suitable for investment optimization problems where the generation fleet is not
known in advance. In this paper, we introduce a heuristic approach to model the
fully secured $\mathcal{N}-1$ feasible space using a smaller number of
constraints in a way that only depends on the topology of transmission
networks. In our proposed approach, the network's security is modelled by
comparing the polytope of the feasible space of nodal net power obtained from
the security-constrained linearized AC optimal power flow problem. To
approximate this polytope, a buffer capacity factor is defined for transmission
lines in the $\mathcal{N}-0$ secure case, thereby avoiding the introduction of
many additional constraints. In this way, three approaches are introduced for
obtaining a buffer capacity factor consisting of approximate, robust and
line-specific approaches. Finally, the performance of our proposed approaches
is assessed in different scales of transmission networks for determining the
proposed buffer capacity factors, contingency analysis and economic evaluation.
Moreover, we find that our proposed heuristics provide excellent approximations
of the fully secured $\mathcal{N}-1$ solutions with a much lower computational
burden.


  We present pulse phase spectroscopy of A 0535+26 in the energy range 35-200
keV from OSSE observations of its giant outburst in 1994. We discuss the phase
dependence of the continuum parameters and the cyclotron resonance feature
(CRF) at 110 keV already found in the phase averaged spectrum. We find that a
CRF is required at every phase. The behaviour of the line parameters with phase
and the pulse shape indicate that the emission occurs in a pencil-beam
geometry.


  Very recently, the Belle and BESIII experiments observed a new
charmonium-like state $X(3823)$, which is a good candidate for the $D$-wave
charmonium $\psi(1^3D_2)$. Because the $X(3823)$ is just near the $D\bar{D}^*$
threshold, the decay $X(3823)\to J/\psi\pi^+\pi^-$ can be a golden channel to
test the significance of coupled-channel effects. In this work, this decay is
considered including both the hidden-charm dipion and the usual quantum
chromodynamics multipole expansion (QCDME) contributions. The partial decay
width, the dipion invariant mass spectrum distribution
$\mathrm{d}\Gamma[X(3823)\to J/\psi\pi^+\pi^-]/\mathrm{d}m_{\pi^+\pi^-}$, and
the corresponding $\mathrm{d}\Gamma[X(3823)\to
J/\psi\pi^+\pi^-]/\mathrm{d}\cos\theta$ distribution are computed. Many
parameters are determined from existing experimental data, so the results
depend mainly only on one unknown phase between the QCDME and hidden-charm
dipion amplitudes.


  Plasmonic photocatalysis has facilitated rapid progress in enhancing
photocatalytic efficiency under visible light irradiation. Poor
visible-light-responsive photocatalytic materials and low photocatalytic
efficiency remain major challenges. Plasmonic metal-semiconductor
heterostructures where both the metal and semiconductor are photosensitive are
promising for light harvesting catalysis, as both components can absorb solar
light. Efficiency of photon capture can be further improved by structuring the
catalyst as a photonic crystal. Here we report the synthesis of photonic
crystal plasmonic photocatalyst materials using Au nanoparticle-functionalized
inverse opal (IO) photonic crystals. A catalyst prepared using a visible light
responsive semiconductor (V2O5) displayed over an order of magnitude increase
in reaction rate under green light excitation ($\lambda$=532 nm) compared to no
illumination. The superior performance of Au-V2O5 IO was attributed to spectral
overlap of the electronic band gap, localized surface plasmon resonance and
incident light source. Comparing the photocatalytic performance of Au-V2O5 IO
with a conventional Au-TiO2 IO catalyst, where the semiconductor band gap is in
the UV, revealed that optimal photocatalytic activity is observed under
different illumination conditions depending on the nature of the semiconductor.
For the Au-TiO2 catalyst, despite coupling of the LSPR and excitation source at
$\lambda$=532 nm, this was not as effective in enhancing photocatalytic
activity compared to carrying out the reaction under broadband visible light,
which is attributed to improved photon adsorption in the visible by the
presence of a photonic band gap, and exploiting slow light in the photonic
crystal to enhance photon absorption to create this synergistic type of
photocatalyst.


  We study harmonic functions for general Dirichlet forms. First we review
consequences of Fukushima's ergodic theorem for the harmonic functions in the
domain of the $ L^{p} $ generator. Secondly we prove analogues of Yau's and
Karp's Liouville theorems for weakly harmonic functions. Both say that weakly
harmonic functions which satisfy certain $ L^{p} $ growth criteria must be
constant. As consequence we give an integral criterion for recurrence.


  Photonic Time crystals (PTC) arise in time-modulated media when the frequency
of modulation of permittivity is on the order of twice the frequency of light
and are manifested by the generation and amplification of so-called time
reversed waves propagating in the direction opposite to the incoming light.
Superficially, the observed phenomenon bears resemblance to the widely known
phenomena of optical parametric generation (OPG) and amplification (OPA) using
second or third order optical nonlinearities. I show that while indeed the same
physical mechanism underpins both PTC and OPA , the difference arises from the
boundary conditions. Thus , while dispersion for both PTC and OPA exhibit the
same bandgap in momentum space, only in the case of PTC can one have
propagation in that bandgap with exponential amplification. I also show that
PTC can be engineered with both second and third order nonlinearities, and that
rather unexpectedly, modulating permittivity on the ultrafast (few fs) rate is
not a necessity, and that one can emulate all the PTC features using materials
with a few picoseconds response time commensurate with the propagation time
through the medium.


  We investigate the attractor mechanism for spherically symmetric extremal
black holes in a theory of general $R^2$ gravity in 4-dimensions, coupled to
gauge fields and moduli fields. For the general $R^2$ theory, we look for
solutions which are analytic near the horizon, show that they exist and enjoy
the attractor behavior. The attractor point is determined by extremization of
an effective potential at the horizon. This analysis includes the backreaction
and supports the validity of non-supersymmetric attractors in the presence of
higher derivative interactions. To include a wider class of solutions, we
continue our analysis for the specific case of a Gauss-Bonnet theory which is
non-topological, due to the coupling of Gauss-Bonnet terms to the moduli
fields. We find that the regularity of moduli fields at the horizon is
sufficient for attractor behavior. For the non-analytic sector, this regularity
condition in turns implies the minimality of the effective potential at the
attractor point.


  The solar program of the Astronomical Observatory of Madrid started in 1876.
For ten solar cycles, observations were made in this institution to determine
sunspot numbers and areas. The program was completed in 1986. The resulting
data have been published in various Spanish scientific publications. The
metadata allowed four periods of this program (with different observers and
instruments) to be identified. In the present work, the published data were
retrieved and digitized. Their subsequent analysis showed that most of these
data can be considered reliable given their very high correlation with
international reference indices (International Sunspot Number, Group Sunspot
Number, and Sunspot Area). An abrupt change emerged in the spots/groups ratio
in 1946 which lasted until 1972.


  Understanding hadronic interactions is crucial for investigating the
properties of unstable hadrons, since measuring physical quantities for
unstable hadrons including the resonance mass and decay width requires
simultaneous calculations of final scattering states. Recent studies of
hadronic scatterings and decays are reviewed from this point of view.
  The nuceon-nucleon and multi-nucleon interactions are very important to
understand the formation of nucleus from the first principle of QCD. These
interactions have been studied mainly by two methods, due originally to
L\"uscher and to HALQCD. The results obtained from the two methods are compared
in three channels, $I=2$ two-pion, H-dibaryon, and two-nucleon channels. So far
the results from the two methods for the two-nucleon channels are different
even at the level of the presence or absence of bound states. We then discuss
possible uncertainties in each method.
  Recent results on the binding energy for helium nuclei are also reviewed.


  We have investigated tidal forces and geodesic deviation motion in the
4D-Einstein-Gauss-Bonnet spacetime. Our results show that tidal force and
geodesic deviation motion depend sharply on the sign of Gauss-Bonnet coupling
constant. Comparing with Schwarzschild spacetime, the strength of tidal force
becomes stronger for the negative Gauss-Bonnet coupling constant, but is weaker
for the positive one. Moreover, tidal force behaves like those in the
Schwarzschild spacetime as the coupling constant is negative, and like those in
Reissner-Nordstr\"{o}m black hole as the constant is positive. We also present
the change of geodesic deviation vector with Gauss-Bonnet coupling constant
under two kinds of initial conditions.


  With the rapid development of big data and cloud computing, data management
has become increasingly challenging. Over the years, a number of frameworks for
data management and storage with various characteristics and features have
become available. Most of these are highly efficient, but ultimately create
data silos. It becomes difficult to move and work coherently with data as new
requirements emerge as no single framework can efficiently fulfill the data
management needs of diverse applications. A possible solution is to design
smart and efficient hierarchical (multi-tier) storage solutions. A hierarchical
storage system (HSS) is a meta solution that consists of different storage
frameworks organized as a jointly constructed large storage pool. It brings a
number of benefits including better utilization of the storage,
cost-efficiency, and use of different features provided by the underlying
storage frameworks. In order to maximize the gains of hierarchical storage
solutions, it is important that they include intelligent and autonomous
mechanisms for data management grounded in the features of the different
underlying frameworks. These decisions should be made according to the
characteristics of the dataset, tier status, and access patterns. These are
highly dynamic parameters and defining a policy based on the mentioned
parameters is a non-trivial task. This paper presents an open-source
hierarchical storage framework with a dynamic migration policy based on
reinforcement learning (RL). We present a mathematical model, a software
architecture, and an implementation based on both simulations and a live
cloud-based environment. We compare the proposed RL-based strategy to a
baseline of three rule-based policies, showing that the RL-based policy
achieves significantly higher efficiency and optimal data distribution in
different scenarios compared to the dynamic rule-based policies.


  We study oscillations in the eigenfunctions for a fractional Schr\"odinger
operator on the real line. An argument in the spirit of Courant's nodal domain
theorem applies to an associated local problem in the upper half plane and
provides a bound on the number of nodal domains for the extensions of the
eigenfunctions. Using the combinatorial properties of noncrossing partitions,
we turn the nodal domain bound into an estimate for the number of sign changes
in the eigenfunctions. We discuss applications in the periodic setting and the
Steklov problem on planar domains.


  The purpose of this paper is to establish an atomic decomposition for
functions in the weighted mixed norm space $A^{p,q}_\omega$ induced by a radial
weight $\omega$ in the unit disc admitting a two-sided doubling condition. The
obtained decomposition is further applied to characterize Carleson measures for
$A^{p,q}_\omega$, and bounded differentiation operators $D^{(n)}(f)=f^{(n)}$
acting from $A^{p,q}_\omega$ to $L^p_\mu$, induced by a positive Borel measure
$\mu$, on the full range of parameters $0<p,q,s<\infty$.


  The star-forming ability of a molecular cloud depends on the fraction of gas
it can cycle into the dense-phase. Consequently, one of the crucial questions
in reconciling star-formation in clouds is to understand the factors that
control this process. While it is widely accepted that the variation in ambient
conditions can alter significantly the ability of a cloud to spawn stars, the
observed variation in the star-formation rate in nearby clouds that experience
similar ambient conditions, presents an interesting question. In this work we
attempted to reconcile this variation within the paradigm of colliding flows.
To this end we develop self-gravitating, hydrodynamic realisations of identical
flows, but allowed to collide off-centre. Typical observational diagnostics
such as the gas-velocity dispersion, the fraction of dense-gas, the column
density distribution ({\small N-PDF}), the distribution of gas mass as a
function of $K$-band extinction and the strength of compressional/solenoidal
modes in the post-collision cloud were deduced for different choices of the
impact parameter of collision. We find that a strongly sheared cloud is
terribly inefficient in cycling gas into the dense phase and that such a cloud
can possibly reconcile the sluggish nature of star-formation reported for some
clouds. Within the paradigm of cloud-formation via colliding flows this is
possible in case of flows colliding with a relatively large impact parameter.
We conclude that compressional modes - though probably essential - are
insufficient to ensure a relatively higher star-formation efficiency in a
cloud.


  Semi-Supervised Visual Grounding (SSVG) is a new challenge for its sparse
labeled data with the need for multimodel understanding. A previous study,
RefTeacher, makes the first attempt to tackle this task by adopting the
teacher-student framework to provide pseudo confidence supervision and
attention-based supervision. However, this approach is incompatible with
current state-of-the-art visual grounding models, which follow the
Transformer-based pipeline. These pipelines directly regress results without
region proposals or foreground binary classification, rendering them unsuitable
for fitting in RefTeacher due to the absence of confidence scores. Furthermore,
the geometric difference in teacher and student inputs, stemming from different
data augmentations, induces natural misalignment in attention-based
constraints. To establish a compatible SSVG framework, our paper proposes the
ACTive REtraining approach for Semi-Supervised Visual Grounding, abbreviated as
ACTRESS. Initially, the model is enhanced by incorporating an additional
quantized detection head to expose its detection confidence. Building upon
this, ACTRESS consists of an active sampling strategy and a selective
retraining strategy. The active sampling strategy iteratively selects
high-quality pseudo labels by evaluating three crucial aspects: Faithfulness,
Robustness, and Confidence, optimizing the utilization of unlabeled data. The
selective retraining strategy retrains the model with periodic
re-initialization of specific parameters, facilitating the model's escape from
local minima. Extensive experiments demonstrates our superior performance on
widely-used benchmark datasets.


  Sufficient conditions are given for existence and uniqueness in
Smoluchowski's coagulation equation, for a wide class of coagulation kernels
and initial mass distributions. An example of non-uniqueness is constructed.
The stochastic coalescent is shown to converge weakly to the solution of
Smoluchowski's equation.


  The adsorption of flexible and highly charged polyelectrolytes onto
oppositely charged planar surfaces is investigated by means of Monte Carlo
simulations. The effect of image forces stemming from the dielectric
discontinuity at the substrate interface is considered. The influence, at fixed
polyelectrolyte volume fraction, of chain length and surface-charge density is
also considered. A detailed structural study, including monomer and fluid
charge distributions, is provided. It is demonstrated that image forces can
considerably reduce the degree of polyelectrolyte adsorption and concomitantly
inhibit the charge inversion of the substrate by polyelectrolytes.


  Motivated by applications requiring sparse or nonnegative controls, we
investigate reachability properties of linear infinite-dimensional control
problems under conic constraints. Relaxing the problem to convex constraints if
the initial cone is not already convex, we provide a constructive approach
based on minimising a properly defined dual functional, which covers both the
approximate and exact reachability problems. Our main results heavily rely on
convex analysis, Fenchel duality and the Fenchel-Rockafellar theorem. As a
byproduct, we uncover new sufficient conditions for approximate and exact
reachability under convex conic constraints. We also prove that these
conditions are in fact necessary. When the constraints are nonconvex, our
method leads to sufficient conditions ensuring that the constructed controls
fulfill the original constraints, which is in the flavour of bang-bang type
properties. We show that our approach encompasses and generalises several
works, and we obtain new results for different types of conic constraints and
control systems.


  Tracing back the instruction execution sequence to debug a multicore system
can be very time-consuming because the relationships of the instructions can be
very complex. For instructions that cannot be checked by the environment
immediately after their executions, the errors they triggered can propagate
through the instruction execution sequence. Our task is to find the
error-triggered instructions automatically. This paper presents an automatic
debugging tool that can leverage the synchronization points in the instruction
execution sequences of the multicore system being verified to locate the
instruction which results in simulation error automatically. To evaluate the
performance of the debugging tool, we analyze the complexity of the algorithms
and count the number of instructions executed to locate the aimed instruction.


  We define the operations of conformal change and elementary deformation in
the setting of generalized complex geometry. Then we apply Swann's twist
construction to generalized (almost) complex and Hermitian structures obtained
by these operations and establish necessary and sufficient conditions for the
Courant integrability of the resulting twisted structures. In particular, we
associate to any appropriate generalized Kahler manifold (M, G, \mathcal J )
with a Hamiltonian Killing vector field a new generalized Kahler manifold,
depending on the choice of a pair of non-vanishing functions and compatible
twist data. We study this construction when (M, G, \mathcal J) is (diagonal)
toric, with emphasis on the four dimensional case. In particular, we apply it
to deformations of the standard flat Kahler metric on C^{n}, the Fubini-Study
Kahler metric on CP^{2} and the so called admissible Kahler metrics on
Hirzebruch surfaces. As a further application, we recover the KK
(Kahler-Kahler) correspondence, which is obtained by specializing to the case
of an ordinary Kahler manifold.


  Based on spectra obtained at the Anglo-Australian Observatory, we present a
discussion of the metallicity of the galactic disc derived using Cepheids at
galactocentric distances 4-6 kpc. Our new results together with previous
gradient determination (Paper I) show that the overall abundance distribution
within the galactocentric distances 4-11 kpc cannot by represented by a single
gradient value. The distribution is more likely bimodal: it is flatter in the
solar neighbourhood with a small gradient, and steepens towards the galactic
center. The steepening begins at a distance of about 6.6 kpc.


  A ring $R$ is called weakly periodic if every $x \in R$ can be written in the
form $x = a + b,$ where $a$ is nilpotent and $b^m = b$ for some integer $m >
1.$ The aim of this note is to consider when a nonzero nilpotent element $r$ is
the period of some power map $f(x) = x^n,$ in the sense that $f(x + r) = f(x)$
for all $x \in R,$ and how this relates to the structure of weakly periodic
rings.
  In particular, we provide a new proof of the fact that weakly periodic rings
with central and torsion nilpotent elements are periodic commutative torsion
rings. We also prove that $x^n$ is periodic over such rings whenever $n$ is not
coprime with each of the additive orders of the nilpotent elements. These are
in fact the only periodic power maps over finite commutative rings with unity.
Finally, we describe and enumerate the distinct power maps over Corbas $(p, k,
\phi)$-rings, Galois rings, $\mathbb{Z}/n\mathbb{Z},$ and matrix rings over
finite fields.


  Generation of high fidelity photonic non-Gaussian states is a crucial
ingredient for universal quantum computation using continous-variable
platforms, yet it remains a challenge to do so efficiently. We present a
general framework for a probabilistic production of multimode non-Gaussian
states by measuring few modes of multimode Gaussian states via
photon-number-resolving detectors. We use Gaussian elements consisting of
squeezed displaced vacuum states and interferometers, the only non-Gaussian
elements consisting of photon-number-resolving detectors. We derive analytic
expressions for the output Wigner function, and the probability of generating
the states in terms of the mean and the covariance matrix of the Gaussian state
and the photon detection pattern. We find that the output states can be written
as a Fock basis superposition state followed by a Gaussian gate, and we derive
explicit expressions for these parameters. These analytic expressions show
exactly what non-Gaussian states can be generated by this probabilistic scheme.
Further, it provides a method to search for the Gaussian circuit and
measurement pattern that produces a target non-Gaussian state with optimal
fidelity and success probability. We present specific examples such as the
generation of cat states, ON states, Gottesman-Kitaev-Preskill states, NOON
states and bosonic code states. The proposed framework has potential
far-reaching implications for the generation of bosonic error-correction codes
that require non-Gaussian states, resource states for the implementation of
non-Gaussian gates needed for universal quantum computation, among other
applications requiring non-Gaussianity. The tools developed here could also
prove useful for the quantum resource theory of non-Gaussianity.


  We consider an out-of-equilibrium one-dimensional model for two electrical
double-layers. With a combination of exact calculations and Brownian Dynamics
simulations, we compute the relaxation time ($\tau$) for an electroneutral
salt-free suspension, made up of two fixed colloids, with $N$ neutralizing
mobile counterions. For $N$ odd, the two double-layers never decouple,
irrespective of their separation $L$; this is the regime of like-charge
attraction, where $\tau$ exhibits a diffusive scaling in $L^2$ for large $L$.
On the other hand, for even $N$, $L$ no longer is the relevant length scale for
setting the relaxation time; this role is played by the Bjerrum length. This
leads to distinctly different dynamics: for $N$ even, thermal effects are
detrimental to relaxation, increasing $\tau$, while they accelerate relaxation
for $N$ odd. Finally, we also show that the mean-field theory is recovered for
large $N$ and moreover, that it remains an operational treatment down to
relatively small values of $N$ ($N>3$).


  We investigate possibility of emission of the bremsstrahlung photons in
nuclear reactions with hypernuclei for the first time. A new model of the
bremsstrahlung emission which accompanies interactions between $\alpha$
particles and hypernuclei is constructed, where a new formalism for the
magnetic momenta of nucleons and hyperon inside hypernucleus is added. For
first calculations, we choose $\alpha$ decay of the normal nucleus $^{210}{\rm
Po}$ and the hypernucleus $^{211}_{\Lambda}{\rm Po}$. We find that (1) emission
for the hypernucleus $^{211}_{\Lambda}{\rm Po}$ is larger than for normal
nucleus $^{210}{\rm Po}$, (2) difference between these spectra is small. We
propose a way how to find hypernuclei, where role of hyperon is the most
essential in emission of bremsstrahlung photons during $\alpha$ decay. As
demonstration of such a property, we show that the spectra for the hypernuclei
$^{107}_{\Lambda}{\rm Te}$ and $^{109}_{\Lambda}{\rm Te}$ are essentially
larger than the spectra for the normal nuclei $^{106}{\rm Te}$ and $^{108}{\rm
Te}$. Such a difference is explained by additional contribution of emission to
the full bremsstrahlung, which is formed by magnetic moment of hyperon inside
hypernucleus. The bremsstrahlung emission formed by such a mechanism, is of the
magnetic type. A new formula for fast estimations of bremsstrahlung spectra for
even-even hypernuclei is proposed, where role of magnetic moment of hyperon of
hypernucleus in formation of the bremsstrahlung emission is shown explicitly.
Such an analysis opens possibility of new experimental study of properties of
hypernuclei via bremsstrahlung study.


  The Pliable Index CODing (PICOD) problem is a variant of the Index Coding
(IC) problem, where the desired messages by the users, who are equipped with
message side information, is part of the optimization. This paper studies the
PICOD problem where users are subject to a privacy constraint. In particular,
the following spacial class of private PICODs is investigated: 1) the side
information structure is circular, and 2) each user can decode one and only one
message. The first condition is a special case of the "circular-arc network
topology hypergraph" class of PICOD studied in [Liu and D. Tuninetti, "Tight
information theoretic converse results for some pliable index coding problems,"
ITW, 2018], for which an optimal solution was given without the privacy
constraint. The second condition was first studied in [S. Sasi and B. S. Rajan,
"On pliable index coding," arXiv:1901.05809] and was motivated by the need to
keep content privacy is some distribution networks. This paper proposes both
converse and achievable bounds. The proposed achievable scheme not only
strictly outperforms the one in [S. Sasi and B. S. Rajan, "On pliable index
coding," arXiv:1901.05809] for some values of the system parameters, but it is
also information theoretically optimal in some settings. For the remaining
cases, the proposed linear code is shown to require at most one more
transmission than the converse bound derived by restricting the sender to only
use linear codes.


  Magnonics is a prospective beyond CMOS technology which uses magnons, the
quanta of spin waves, for low-power information processing. Many magnonic
concepts and devices were recently demonstrated at macro- and microscale, and
now these concepts need to be realized at nanoscale. Brillouin light scattering
spectroscopy and microscopy (BLS) has become a standard technique for spin wave
visualization and characterization, and enabled many pioneering magnonic
experiments. However, due to its fundamental limit in maximum detectable magnon
momentum, the conventional BLS cannot be used to detect nanoscale spin waves.
Here we show that optically induced Mie resonances in dielectric nanoparticles
can be used to extend the range of accessible spin wave wavevectors beyond the
BLS fundamental limit. The method is universal and can be used in many magnonic
experiments dealing with thermally excited as well as coherently excited
high-momentum, short-wavelength spin waves. This discovery significantly
extends the usability and relevance of the BLS technique for nanoscale magnonic
research.


  We present multi-wavelength observations of the very high energy (VHE, E >250
GeV) gamma-ray sources Mrk 421 and Mrk 501. The VHE data presented here were
taken with the Whipple Observatory 10m gamma-ray telescope. In the Mrk 421
campaign, conducted in 1995 April-May, correlations were observed between VHE
gamma-ray, X-ray, extreme ultraviolet (EUV) and possibly R-band emission. The
X-rays and gamma rays vary together with similar flux amplitude while the EUV
photons lag the X-rays and gamma rays by ~1 day and have a lower variability
amplitude. In the Mrk 501 campaign, conducted in 1997 April, a correlation was
also observed between the VHE gamma rays and X-rays with no delays apparent.
Here, the VHE gamma-ray variability is larger than the X-rays. The observations
also indicate that the synchrotron spectrum extends to 100 keV before cutting
off. For Mrk 421, the X-ray/VHE gamma-ray correlation indicates that delta > 38
and B > 0.03G. For Mrk 501, the correlation indicates a more modest delta > 2
and B > 0.09G.


  A phenomenon of racial segregation in U.S. cities is a multifaceted area of
study. A recent advancement in this field is the development of a methodology
that transforms census population count-by-race data into a grid of monoracial
cells. This format enables assessment of heterogeneity of segregation within a
city. This paper leverages such a grid for the quantification of
race-constrained population patterns, allowing for the calculation and mapping
of binary segregation patterns within arbitrary region. A key innovation is the
application of Multifractal Analysis (MFA) to quantify the residency patterns
of race-constrained populations. The residency pattern is characterized by a
multifractal spectrum function, where the independent variable is a local
metric of pattern's "gappiness", and the dependent variable is proportional to
the size of the sub-pattern consisting of all locations having the same value
of this metric. In the context of binary populations, the gappiness of the
race-constrained population's pattern is intrinsically linked to its
segregation. This paper provides a comprehensive description of the
methodology, illustrated with examples focusing on the residency pattern of
Black population in the central region of Washington, DC. Further, the
methodology is demonstrated using a sample of residency patterns of Black
population in fourteen large U.S. cities. By numerically describing each
pattern through a multifractal spectrum, the fourteen patterns are clustered
into three distinct categories, each having unique characteristics. Maps of
local gappiness and segregation for each city are provided to show the
connection between the nature of the multifractal spectrum and the
corresponding residency and segregation patterns. This method offers an
excellent quantification of race-restricted residency and residential
segregation patterns within U.S. cities.


  We provide quantitative gradient bounds for solutions to certain parabolic
equations with unbalanced polynomial growth and non-smooth coefficients.


  The paper shortly presents the role of Stochastic Processes Theory in the
present day Quantum Theory, and the relation to Operational Quantum Physics.
The dynamics of an open quantum system is studied on a usual example from
Quantum Optics, suggesting the definition of a Neumark-type dilation for the
non-thermal states.


  The tropical overturning circulation is examined in a moist aquaplanet
general circulation model forced using a non-interactive sea surface
temperature (SST) distribution that varies between a present-day Earth-like
profile and one that is globally uniform. A traditional Hadley Cell (HC)-like
flow is observed in all experiments along with the poleward transport of heat
and angular momentum. In simulations with non-zero SST gradients, latent heat
released from organized convection near the equator sets up a deep tropical
cell; midlatitude baroclinic Rossby waves flux heat and angular momentum
poleward, reinforcing the thermally direct circulation. As the imposed SST
gradient is weakened, the HC transitions from a thermally and eddy-driven
regime to one that's completely eddy-driven. When the SST is globally uniform,
equatorial waves concentrate precipitation in the tropics and facilitate the
lower-level convergence necessary for the ascending branch of the HC.
Conventional midlatitude Rossby waves become very weak, but upper-level
baroclinicity generates waves that cause equatorward transport of heat and
poleward transport of momentum. Moreover, these upper-level waves induce a
circulation that opposes the time-mean HC, thus highlighting the role of
tropical waves in driving a traditional overturning flow for uniform SSTs. In
all cases, anomalies associated with the tropical waves closely resemble those
that sum to give the upper-level zonal mean divergent outflow. Through their
ability to modulate tropical rainfall and the related latent heating,
equatorial waves cause considerable hemispheric asymmetry in the HC and impart
synoptic and intraseasonal variability to the tropical overturning circulation.


  In this article, using an exemplar-based approach, we investigate the
inpainting problem, introducing a new mathematical functional, whose
minimization determines the quality of the reconstructions. The new functional
expression takes into account of fnite differences terms, in a similar fashion
to what happens in the theoretical Sobolev spaces. Moreover, we introduce a new
priority index to determine the scanning order of the points to inpaint,
prioritizing the uncertainty reduction in the choice. The achieved results
highlight important theoretical-connected aspects of the inpainting by patch
procedure.


  When we can not assume a large amount of annotated data , active learning is
a good strategy. It consists in learning a model on a small amount of annotated
data (annotation budget) and in choosing the best set of points to annotate in
order to improve the previous model and gain in generalization. In deep
learning, active learning is usually implemented as an iterative process in
which successive deep models are updated via fine tuning, but it still poses
some issues. First, the initial batch of annotated images has to be
sufficiently large to train a deep model. Such an assumption is strong,
especially when the total annotation budget is reduced. We tackle this issue by
using an approach inspired by transfer learning. A pre-trained model is used as
a feature extractor and only shallow classifiers are learned during the active
iterations. The second issue is the effectiveness of probability or feature
estimates of early models for AL task. Samples are generally selected for
annotation using acquisition functions based only on the last learned model. We
introduce a novel acquisition function which exploits the iterative nature of
AL process to select samples in a more robust fashion. Samples for which there
is a maximum shift towards uncertainty between the last two learned models
predictions are favored. A diversification step is added to select samples from
different regions of the classification space and thus introduces a
representativeness component in our approach. Evaluation is done against
competitive methods with three balanced and imbalanced datasets and outperforms
them.


  A simple scheme for conditional generation of nonclassical light with
sub-Poissonian photon-number statistics is proposed. The method utilizes
entanglement of signal and idler modes in two-mode squeezed vacuum state
generated in optical parametric amplifier. A quadrature component of the idler
mode is measured in balanced homodyne detector and only those experimental runs
where the absolute value of the measured quadrature is higher than certain
threshold are accepted. If the threshold is large enough then the conditional
output state of signal mode exhibits reduction of photon-number fluctuations
below the coherent-state level.


  We have fabricated a lateral double barrier magnetic tunnel junction (MTJ)
which consists of a single self-assembled InAs quantum dot (QD) with
ferromagnetic Co leads. The MTJ shows clear hysteretic tunnel magnetoresistance
(TMR) effect, which is evidence for spin transport through a single
semiconductor QD. The TMR ratio and the curve shapes are varied by changing the
gate voltage.


  Federated learning (FL) is a decentralized and privacy-preserving machine
learning technique in which a group of clients collaborate with a server to
learn a global model without sharing clients' data. One challenge associated
with FL is statistical diversity among clients, which restricts the global
model from delivering good performance on each client's task. To address this,
we propose an algorithm for personalized FL (pFedMe) using Moreau envelopes as
clients' regularized loss functions, which help decouple personalized model
optimization from the global model learning in a bi-level problem stylized for
personalized FL. Theoretically, we show that pFedMe's convergence rate is
state-of-the-art: achieving quadratic speedup for strongly convex and sublinear
speedup of order 2/3 for smooth nonconvex objectives. Experimentally, we verify
that pFedMe excels at empirical performance compared with the vanilla FedAvg
and Per-FedAvg, a meta-learning based personalized FL algorithm.


  This paper introduces a novel hybrid mathematical modeling approach that
effectively couples Partial Differential Equations (PDEs) with Ordinary
Differential Equations (ODEs), exemplified through the simulation of
epidemiological processes. The hybrid model aims to integrate the spatially
detailed representation of disease dynamics provided by PDEs with the
computational efficiency of ODEs. In the presented epidemiological use-case,
this integration allows for the rapid assessment of public health interventions
and the potential impact of infectious diseases across large populations. We
discuss the theoretical formulation of the hybrid PDE-ODE model, including the
governing equations and boundary conditions. The model's capabilities are
demonstrated through detailed simulations of disease spread in synthetic
environments and real-world scenarios, specifically focusing on the regions of
Lombardy, Italy, and Berlin, Germany. Results indicate that the hybrid model
achieves a balance between computational speed and accuracy, making it a
valuable tool for policymakers in real-time decision-making and scenario
analysis in epidemiology and potentially in other fields requiring similar
modeling approaches.


  We investigate the interaction between scalar fields and radiation in the
framework of warm inflationary models by using the irreversible thermodynamics
of open systems with matter creation/annihilation. We consider the scalar
fields and radiation as an interacting two component cosmological fluid in a
homogeneous, spatially flat and isotropic Friedmann-Robertson-Walker (FRW)
Universe. The thermodynamics of open systems as applied together with the
gravitational field equations to the two component cosmological fluid leads to
a generalization of the elementary scalar field-radiation interaction model,
which is the theoretical basis of warm inflationary models, with the decay
(creation) pressures explicitly considered as parts of the cosmological fluid
energy-momentum tensor. Specific models describing coherently oscillating
scalar waves, scalar fields with a constant potential, and scalar fields with a
Higgs type potential are considered in detail. For each case exact and
numerical solutions of the gravitational field equations with scalar
field-radiation interaction are obtained, and they show the transition from an
accelerating inflationary phase to a decelerating one. The theoretical
predictions of the warm inflationary scenario with irreversible matter creation
are also compared in detail with the Planck 2018 observational data, and
constraints on the free parameters of the model are obtained.


  In the paper, we investigate the lifting of recollements with respect to
Gorenstein-projective modules. Specifically, a homological ring epimorphism can
induce a lifting of the recollement of the stable category of finitely
generated Gorenstein-projective modules; the recollement of the bounded
Gorenstein derived categories of some upper triangular matrix algebras can be
lifted to the homotopy category of Gorenstein-projective modules. As a
byproduct, we give a sufficient and necessary condition on the upper triangular
matrix algebra T_{n}(A) to be of finite CM-type for an algebra A of finite
CM-type.


  Let ${\mathcal X}$ be a space of homogeneous type in the sense of Coifman and
Weiss and ${\mathcal D}$ a collection of balls in $\cx$. The authors introduce
the localized atomic Hardy space $H^{p, q}_{\mathcal D}({\mathcal X})$ with
$p\in (0,1]$ and $q\in[1,\infty]\cap(p,\infty]$, the localized Morrey-Campanato
space ${\mathcal E}^{\alpha, p}_{\mathcal D}({\mathcal X})$ and the localized
Morrey-Campanato-BLO space $\widetilde{\mathcal E}^{\alpha, p}_{\mathcal
D}({\mathcal X})$ with $\az\in{\mathbb R}$ and $p\in(0, \infty)$ and establish
their basic properties including $H^{p, q}_{\mathcal D}({\mathcal X})=H^{p,
\infty}_{\mathcal D}({\mathcal X})$ and several equivalent characterizations
for ${\mathcal E}^{\alpha, p}_{\mathcal D}({\mathcal X})$ and $\wz{\mathcal
E}^{\alpha, p}_{\mathcal D}({\mathcal X})$. Especially, the authors prove that
when $p\in(0,1]$, the dual space of $H^{p, \infty}_{\mathcal D}({\mathcal X})$
is ${\mathcal E}^{1/p-1, 1}_{\mathcal D}({\mathcal X})$. Let $\rho$ be an
admissible function modeled on the known auxiliary function determined by the
Schr\"odinger operator. Denote the spaces ${\mathcal E}^{\alpha, p}_{\mathcal
D}({\mathcal X})$ and $\widetilde{\mathcal E}^{\alpha, p}_{\mathcal
D}({\mathcal X})$, respectively, by ${\mathcal E}^{\alpha, p}_{\rho}({\mathcal
X})$ and $\widetilde{\mathcal E}^{\alpha, p}_{\rho}({\mathcal X})$, when
${\mathcal D}$ is determined by $\rho$. The authors then obtain the boundedness
from ${\mathcal E}^{\alpha, p}_{\rho}({\mathcal X})$ to $\widetilde{\mathcal
E}^{\alpha, p}_{\rho}({\mathcal X})$ of the radial and the Poisson semigroup
maximal functions and the Littlewood-Paley $g$-function which are defined via
kernels modeled on the semigroup generated by the Schr\"odinger operator.


  We present the first optical observations of a Gamma Ray Burst (GRB)
afterglow using the 2-m robotic Liverpool Telescope (LT), which is owned and
operated by Liverpool John Moores University and situated on La Palma. We
briefly discuss the capabilities of LT and its suitability for rapid follow-up
observations of early optical and infrared GRB light curves. In particular, the
combination of aperture, site, instrumentation and rapid response (robotic
over-ride mode aided by telescope's rapid slew and fully-opening enclosure)
makes the LT ideal for investigating the nature of short bursts, optically-dark
bursts, and GRB blast-wave physics in general. We briefly describe the LT's key
position in the RoboNet-1.0 network of robotic telescopes. We present the LT
observations of GRB041006 and use its gamma-ray properties to predict the time
of the break in optical light curve, a prediction consistent with the
observations.


  In this paper, the design of a wireless communication device relying
exclusively on energy harvesting is considered. Due to the inability of
rechargeable energy sources to charge and discharge at the same time, a
constraint we term the energy half-duplex constraint, two rechargeable energy
storage devices (ESDs) are assumed so that at any given time, there is always
one ESD being recharged. The energy harvesting rate is assumed to be a random
variable that is constant over the time interval of interest. A
save-then-transmit (ST) protocol is introduced, in which a fraction of time
{\rho} (dubbed the save-ratio) is devoted exclusively to energy harvesting,
with the remaining fraction 1 - {\rho} used for data transmission. The ratio of
the energy obtainable from an ESD to the energy harvested is termed the energy
storage efficiency, {\eta}. We address the practical case of the secondary ESD
being a battery with {\eta} < 1, and the main ESD being a super-capacitor with
{\eta} = 1. The optimal save-ratio that minimizes outage probability is
derived, from which some useful design guidelines are drawn. In addition, we
compare the outage performance of random power supply to that of constant power
supply over the Rayleigh fading channel. The diversity order with random power
is shown to be the same as that of constant power, but the performance gap can
be large. Furthermore, we extend the proposed ST protocol to wireless networks
with multiple transmitters. It is shown that the system-level outage
performance is critically dependent on the relationship between the number of
transmitters and the optimal save-ratio for single-channel outage minimization.
Numerical results are provided to validate our proposed study.


  We review recent developments in the theoretical investigation of the nucleon
polarizabilities. We first report on the static polarizabilities as measured in
real Compton scattering, comparing and interpreting the results from various
theoretical approaches. In a second step, we extend the discussion to the
generalized polarizabilities which can be accessed in virtual Compton
scattering, showing how the information encoded in these quantities can provide
a spatial interpretation of the induced polarization densities in the nucleon.


  A method for measuring the transmittivity of optical samples by using
squeezed--vacuum radiation is illustrated. A squeezed vacuum field generated by
a below--threshold optical parametric oscillator is propagated through a
nondispersive medium and detected by a homodyne apparatus. The variance of the
detected quadrature is used for measuring the transmittivity. With this method
it is drastically reduced the number of photons passing through the sample
during the measurement interval. The results of some tests are reported.


  Creating a large-scale dataset of abnormality annotation on medical images is
a labor-intensive and costly task. Leveraging weak supervision from readily
available data such as radiology reports can compensate lack of large-scale
data for anomaly detection methods. However, most of the current methods only
use image-level pathological observations, failing to utilize the relevant
anatomy mentions in reports. Furthermore, Natural Language Processing
(NLP)-mined weak labels are noisy due to label sparsity and linguistic
ambiguity. We propose an Anatomy-Guided chest X-ray Network (AGXNet) to address
these issues of weak annotation. Our framework consists of a cascade of two
networks, one responsible for identifying anatomical abnormalities and the
second responsible for pathological observations. The critical component in our
framework is an anatomy-guided attention module that aids the downstream
observation network in focusing on the relevant anatomical regions generated by
the anatomy network. We use Positive Unlabeled (PU) learning to account for the
fact that lack of mention does not necessarily mean a negative label. Our
quantitative and qualitative results on the MIMIC-CXR dataset demonstrate the
effectiveness of AGXNet in disease and anatomical abnormality localization.
Experiments on the NIH Chest X-ray dataset show that the learned feature
representations are transferable and can achieve the state-of-the-art
performances in disease classification and competitive disease localization
results. Our code is available at https://github.com/batmanlab/AGXNet


  We study the process of electron-positron annihilation into back-to-back
jets, where in each jet a pair of hadrons is detected. The orientation of these
two pairs with respect to each other can be used to extract the interference
fragmentation functions in a clean way, for instance from BELLE or BABAR
experiment data. This is of relevance for studies of the transversity
distribution function.
  In particular, we focus on two azimuthal asymmetries. The first one has
already been studied by Artru and Collins, but is now expressed in terms of
interference fragmentation functions. The second asymmetry is new and involves
a function that is related to longitudinal jet handedness. This asymmetry
offers a different way of studying handedness correlations.


  We show that using coherent, spatially resolved spectroscopy, complex hybrid
wave functions can be disentangled into the individual wave functions of the
individual emitters. This way, detailed information on the coupling of the
individual emitters, not available in far-field spectroscopy can be obtained.
The proposed quantum state tomography relies on the ability to selectively
excite each emitter individually by spatially localized pulses. Simulations of
coupled semiconductor Ga/InAs quantum dots, using light fields available in
current nanoplasmonics, show that even undesired resonances can be removed from
measured spectra. The method can also be applied to study the internal coupling
of pigments in photosythesis and artificial light harvesting.


  From the modeling and simulation results of presupernova evolution of massive
stars, it was found that isotopes of iron, $^{54,55,56}$Fe, play a significant
role inside the stellar cores, primarily decreasing the electron-to-baryon
ratio ($Y_{e}$) mainly via electron capture processes thereby reducing the
pressure support. The neutrinos produced, as a result of these capture
processes, are transparent to the stellar matter and assist in cooling the core
thereby reducing the entropy. The structure of the presupernova star is altered
both by the changes in $Y_{e}$ and the entropy of the core material. Here we
present the microscopic calculation of Gamow-Teller strength distributions for
isotopes of iron. The calculation is also compared with other theoretical
models and experimental data. Presented also are stellar electron capture rates
and associated neutrino cooling rates, due to isotopes of iron, in a form
suitable for simulation and modeling codes. It is hoped that the nuclear inputs
presented here should assist core-collapse simulators in the process of
fine-tuning of the $Y_{e}$ parameter during various phases of presupernova
evolution of massive stars. A reliable and accurate time evolution of this
parameter is a possible key to generate a successful explosion in modeling of
core-collapse supernovae.


  Electrons/positrons produced in a pulsar magnetosphere emit synchrotron
radiation, which is widely believed as the origin of the non-thermal X-ray
emission detected from pulsars. Particles are produced by curvature photons
emitted from accelerated particles in the magnetosphere. These curvature
photons are detected as pulsed $\gamma$-ray emissions from pulsars with age
$\lesssim10^6$ yr. Using $\gamma$-ray observations and analytical model, we
impose severe constraints on the synchrotron radiation as a mechanism of the
non-thermal X-ray emission. In most middle-aged pulsars ($\sim10^5-10^6$ yr)
which photon-photon pair production is less efficient in their magnetosphere,
we find that the synchrotron radiation model is difficult to explain the
observed non-thermal X-ray emission.


  We review a recent experiment with ultracold atoms in 3D optical lattices
where we have observed a novel kind of bound state of two atoms which is based
on repulsive interactions between the particles. These repulsively bound pairs
exhibit long lifetimes, even under conditions when they collide with one
another. Stable repulsively bound objects should be viewed as a general
phenomenon and their existence will be ubiquitous in cold atoms lattice
physics. Although the experiment described here is based on bosonic Rb atoms,
other composites with fermions or Bose-Fermi mixtures should exist in an
analogous manner. Furthermore, repulsively bound objects could also be formed
with more than two particles. In the following we will first explain the
theoretical background of repulsively atom pairs. Afterwards we will present
the experiments which demonstrate several key properties of the pairs. Finally
we give a short discussion of how these repulsively bound pairs relate to bound
states in some other physical systems.


  Results are reported of an experimental search for the unique, rapidly
varying temporal pattern of solar axions coherently converting into photons via
the Primakoff effect in a single crystal germanium detector. This conversion is
predicted when axions are incident at a Bragg angle with a crystalline plane.
The analysis of approximately 1.94 kg.yr of data from the 1 kg DEMOS detector
in Sierra Grande, Argentina, yields a new laboratory bound on axion-photon
coupling of $g_{a\gamma \gamma} < 2.7\cdot 10^{-9}$ GeV$^{-1}$, independent of
axion mass up to ~ 1 keV.


  We consider the null controllability problem for the wave equation, and
analyse a stabilized finite element method formulated on a global, unstructured
spacetime mesh. We prove error estimates for the approximate control given by
the computational method. The proofs are based on the regularity properties of
the control given by the Hilbert Uniqueness Method, together with the stability
properties of the numerical scheme. Numerical experiments illustrate the
results.


  We use angle-resolved photoemission spectroscopy and full-potential
linearized augmented-plane-wave (FP-LAPW) calculations to study the electronic
structure of BaCo2As2. The Fermi surface (FS) maps and the corresponding band
dispersion data (at 90 K and 200 K) reveal a small electron pocket at the
center and a large electron pocket at the corner of the Brillouin zone.
Therefore the nesting between electron and hole FS pockets is absent in this
compound, in contrast to the parent compounds of FeAs-based high-T_c
superconductors. The electronic structure at about 500 meV binding energy is
very similar to features at the chemical potential in BaFe2As2. This indicates
that complete substitution of Co for Fe causes a nearly rigid shift in the
Fermi energy by adding two electrons per formula unit without significant
changes in the band dispersions. The experimental FS topology as well as band
dispersion data are in reasonable agreement with the FP-LAPW calculations.


  Collinear and canted magnetic motifs in haematite were investigated by
Kokubun et al. (2008) using x-ray Bragg diffraction magnified at the iron
K-edge, and analyses of observations led to various potentially interesting
conclusions. We demonstrate that the reported analyses for both non-resonant
and resonant magnetic diffraction at low energies near the absorption K-edge
are not appropriate. In its place, we apply a radically different formulation,
thoroughly tried and tested, that incorporates all magnetic contributions to
resonant x-ray diffraction allowed by the established chemical and magnetic
structures. Essential to a correct formulation of diffraction by a magnetic
crystal with resonant ions at sites that are not centres of inversion symmetry
are parity-odd atomic multipoles, time-even (polar) and time-odd
(magneto-electric), that arise from enhancement by the electric-dipole (E1) -
electric-quadrupole (E2) event. Analyses of azimuthal-angle scans on two
space-group forbidden reflections, hexagonal (0, 0, 3)h and (0, 0, 9)h,
collected by Kokubun et al. above and below the Morin temperature (TM = 250K),
allow us to obtain good estimates of contributing polar and magneto-electric
multipoles, including the iron anapole. We show, beyond reasonable doubt, that
available data are inconsistent with parity-even events only (E1-E1 and E2-
E2). For future experiments, we show that chiral states of haematite couple to
circular polarization and differentiate E1-E2 and E2-E2 events, while the
collinear motif supports magnetic charges.


  We present a new approach to quantum general relativity based on the idea of
Feynman to treat the graviton in Einstein's theory as a point particle field
subject to quantum fluctuations just as any such field is in the well-known
Standard Model of the electroweak and strong interactions. We show that by
using resummation techniques based on the extension of the methods of Yennie,
Frautschi and Suura to Feynman's formulation of Einstein's theory, we get
calculable loop corrections that are even free of UV divergences. One further
by-product of our analysis is that we can apply it to a large class of
interacting field theories, both renormalizable and non-renormalizable, to
render their UV divergences finite as well. We illustrate our results with
applications of some phenomenological interest.


  Variability is a common characteristic of magnetically active stars. Flaring
variability is usually interpreted as the observable consequence of transient
magnetic reconnection processes happening in the stellar outer atmosphere.
Stellar flares have been observed now across 11 decades in
wavelength/frequency/energy; such a large span implies that a range of physical
processes takes place during such events. Despite the fact that stellar radio
flares have long been recognized and studied, key unanswered questions remain.
I will highlight what, in my opinion, are some of these questions. I will also
describe recent results on stellar flare emissions at radio wavelengths,
discussing the nature of coherent and incoherent emissions and the prospects of
wide-field radio imaging telescopes for studying such events.


  We investigate finite deterministic automata in sets with non-homogeneous
atoms: integers with successor. As there are uncount- ably many deterministic
finite automata in this setting, we restrict our attention to automata with
semilinear transition function. The main re- sults is a minimization procedure
for semilinear automata. The proof is subtle and refers to decidability of
existential Presburger arithmetic with divisibility predicates. Interestingly,
the minimization is not obtained by the standard partition refinement
procedure, and we demonstrate that this procedure does not necessarily
terminate for semilinear automata.


  A new doping mechanism is described, whereby a doping impurity does not
simply transfer charge to the bands of a host semiconductor or semimetal, but
rearranges the core energy levels deep in the valence band of the host. This,
in turn, leads to a redistribution of all electrons in the host, and, if
designed properly, changes the location of the Fermi level EF and the density
of conducting charge carriers near EF. The principle is proven experimentally
in elemental Bi, whereby group III elements In and Ga dope Bi p-type, in spite
of the fact that all three atoms are trivalent in the solid state. Electronic
structure calculations show the formation of a hyperdeep defect state (HDS) and
its effect on the EF in Bi doped with In (Bi:In) and Ga (Bi:Ga). The HDS at -5
to -6 eV below the EF of elemental Bi hybridizes with the Bi 6p electrons, and
deprives the Bi valence band of two electrons per impurity atom. This then
perturbs the electron count in the solid and lowers the EF. The charge on the
impurity atoms is unchanged. In principle, this doping action does not result
in the appearance of ionized impurities that scatter conduction electrons and
holes in conventional doping. Experimentally, Shubnikov - de Haas and Hall
Effect measurements show that adding In to Bi results in an increase in the
density of holes. Thermoelectric, galvanomagnetic and thermomagnetic data are
given for single-crystal and polycrystalline samples. In-doping leads to an
enhancement of the thermoelectric figure of merit, which suggests that the new
doping mechanism also gives a route to develop better thermoelectric materials.
The same mechanism is at work for Sn-doped Bi (Bi:Sn), although here ionized
impurity scattering is not avoided.


  We explore properties of Cauchy-Stieltjes families that have no counterpart
in exponential families. We relate the variance function of the iterated
Cauchy-Stieltjes family to the pseudo-variance function of the initial
Cauchy-Stieltjes family. We also investigate when the domain of means can be
extended beyond the "natural domain".


  We study an Eisenstein series of weight $20/9$, level $11$ whose multiplier
system is the same as $\eta^{44/9}(\tau)\eta^{-4/9}(11\tau)$. We prove that it
is a modular form and obtain its Fourier expansion.


  We study estimation in the linear model $y=A\beta^\star+\epsilon$, in a
Bayesian setting where $\beta^\star$ has an entrywise i.i.d. prior and the
design $A$ is rotationally-invariant in law. In the large system limit as
dimension and sample size increase proportionally, a set of related conjectures
have been postulated for the asymptotic mutual information, Bayes-optimal mean
squared error, and TAP mean-field equations that characterize the Bayes
posterior mean of $\beta^\star$. In this work, we prove these conjectures for a
general class of signal priors and for arbitrary rotationally-invariant designs
$A$, under a "high-temperature" condition that restricts the range of
eigenvalues of $A^\top A$. Our proof uses a conditional second-moment method
argument, where we condition on the iterates of a version of the Vector AMP
algorithm for solving the TAP mean-field equations.


  This paper investigates situations where a property of a ring can be tested
on a set of "prime right ideals." Generalizing theorems of Cohen and Kaplansky,
we show that every right ideal of a ring is finitely generated (resp.
principal) iff every "prime right ideal" is finitely generated (resp.
principal), where the phrase "prime right ideal" can be interpreted in one of
many different ways. We also use our methods to show that other properties can
be tested on special sets of right ideals, such as the right artinian property
and various homological properties. Applying these methods, we prove the
following noncommutative generalization of a result of Kaplansky: a (left and
right) noetherian ring is a principal right ideal ring iff all of its maximal
right ideals are principal. A counterexample shows that the left noetherian
hypothesis cannot be dropped. Finally, we compare our results to earlier
generalizations of Cohen's and Kaplansky's theorems in the literature.


  The concept of p-ordering for a prime p was introduced by Manjul Bhargava (in
his PhD thesis) to develop a generalized factorial function over an arbitrary
subset of integers. This notion of p-ordering provides a representation of
polynomials modulo prime powers, and has been used to prove properties of roots
sets modulo prime powers. We focus on the complexity of finding a p-ordering
given a prime p, an exponent k and a subset of integers modulo p^k.
  Our first algorithm gives a p-ordering for set of size n in time O(nk\log p),
where set is considered modulo p^k. The subsets modulo p^k can be represented
succinctly using the notion of representative roots (Panayi, PhD Thesis, 1995;
Dwivedi et.al, ISSAC, 2019); a natural question would be, can we find a
p-ordering more efficiently given this succinct representation. Our second
algorithm achieves precisely that, we give a p-ordering in time O(d^2k\log p +
nk \log p + nd), where d is the size of the succinct representation and n is
the required length of the p-ordering. Another contribution that we make is to
compute the structure of roots sets for prime powers p^k, when k is small. The
number of root sets have been given in the previous work (Dearden and Metzger,
Eur. J. Comb., 1997; Maulick, J. Comb. Theory, Ser. A, 2001), we explicitly
describe all the root sets for p^2, p^3 and p^4.


  A Mn4 single-molecule magnet displays asymmetric Berry-phase interference
patterns in the transverse-field (HT) dependence of the magnetization tunneling
probability when a longitudinal field (HL) is present, contrary to symmetric
patterns observed for HL=0. Reversal of HL results in a reflection of the
transverse-field asymmetry about HT=0, as expected on the basis of the
time-reversal invariance of the spin-orbit Hamiltonian which is responsible for
the tunneling oscillations. A fascinating motion of Berry-phase minima within
the transverse-field magnitude-direction phase space results from a competition
between noncollinear magnetoanisotropy tensors at the two distinct Mn sites.


  Rayleigh-B\'{e}nard convection in horizontal layers of binary fluid mixtures
heated from below with realistic horizontal boundary conditions is studied
theoretically using multi-mode Galerkin expansions. For positive separation
ratios the main difference between the mixtures and pure fluids lies in the
existence of stable three dimensional patterns near onset in a wide range of
the parameter space. We evaluated the stationary solutions of roll, crossroll,
and square convection and we determined the location of the stability
boundaries for many parameter combinations thereby obtaining the Busse balloon
for roll and square patterns.


  In this paper, we propose a deep neural network architecture for object
recognition based on recurrent neural networks. The proposed network, called
ReNet, replaces the ubiquitous convolution+pooling layer of the deep
convolutional neural network with four recurrent neural networks that sweep
horizontally and vertically in both directions across the image. We evaluate
the proposed ReNet on three widely-used benchmark datasets; MNIST, CIFAR-10 and
SVHN. The result suggests that ReNet is a viable alternative to the deep
convolutional neural network, and that further investigation is needed.


  Simulating showers of particles in highly-granular detectors is a key
frontier in the application of machine learning to particle physics. Achieving
high accuracy and speed with generative machine learning models would enable
them to augment traditional simulations and alleviate a major computing
constraint. This work achieves a major breakthrough in this task by, for the
first time, directly generating a point cloud of a few thousand space points
with energy depositions in the detector in 3D space without relying on a
fixed-grid structure. This is made possible by two key innovations: i) Using
recent improvements in generative modeling we apply a diffusion model to
generate photon showers as high-cardinality point clouds. ii) These point
clouds of up to $6,000$ space points are largely geometry-independent as they
are down-sampled from initial even higher-resolution point clouds of up to
$40,000$ so-called Geant4 steps. We showcase the performance of this approach
using the specific example of simulating photon showers in the planned
electromagnetic calorimeter of the International Large Detector (ILD) and
achieve overall good modeling of physically relevant distributions.


  CoGeNT employs p-type point-contact (PPC) germanium detectors to search for
Weakly Interacting Massive Particles (WIMPs). By virtue of its low energy
threshold and ability to reject surface backgrounds, this type of device allows
an emphasis on low-mass dark matter candidates (wimp mass of about 10 GeV/c2).
We report on the characteristics of the PPC detector presently taking data at
the Soudan Underground Laboratory, elaborating on aspects of shielding, data
acquisition, instrumental stability, data analysis, and background estimation.
A detailed background model is used to investigate the low energy excess of
events previously reported, and to assess the possibility of temporal
modulations in the low-energy event rate. Extensive simulations of all
presently known backgrounds do not provide a viable background explanation for
the excess of low-energy events in the CoGeNT data, or the previously observed
temporal variation in the event rate. Also reported on for the first time is a
determination of the surface (slow pulse rise time) event contamination in the
data as a function of energy. We conclude that the CoGeNT detector technology
is well suited to search for the annual modulation signature expected from dark
matter particle interactions in the region of WIMP mass and coupling favored by
the DAMA/LIBRA results


  Creating catchy slogans is a demanding and clearly creative job for ad
agencies. The process of slogan creation by humans involves finding key
concepts of the company and its products, and developing a memorable short
phrase to describe the key concept. We attempt to follow the same sequence, but
with an evolutionary algorithm. A user inputs a paragraph describing describing
the company or product to be promoted. The system randomly samples initial
slogans from a corpus of existing slogans. The initial slogans are then
iteratively mutated and improved using an evolutionary algorithm. Mutation
randomly replaces words in an individual with words from the input paragraphs.
Internal evaluation measures a combination of grammatical correctness, and
semantic similarity to the input paragraphs. Subjective analysis of output
slogans leads to the conclusion that the algorithm certainly outputs valuable
slogans. External evaluation found that the slogans were somewhat successful in
conveying a message, because humans were generally able to select the correct
promoted item given a slogan.


  This paper develops an adaptive PID autotuner for multicopters, and presents
simulation and experimental results. The autotuner consists of adaptive digital
control laws based on retrospective cost adaptive control implemented in the
PX4 flight stack. A learning trajectory is used to optimize the autopilot
during a single flight. The autotuned autopilot is then compared with the
default PX4 autopilot by flying a test trajectory constructed using the
second-order Hilbert curve. In order to investigate the sensitivity of the
autotuner to the quadcopter dynamics, the mass of the quadcopter is varied, and
the performance of the autotuned and default autopilot is compared. It is
observed that the autotuned autopilot outperforms the default autopilot.