  We investigate the Gauss-Bonnet black hole in five dimensional anti-de Sitter
spacetimes (GBAdS). We analyze all thermodynamic quantities of the GBAdS, which
is characterized by the Gauss-Bonnet coupling $c$ and mass $M$, comparing with
those of the Born-Infeld-AdS (BIAdS), Reissner-Norstr\"om-AdS black holes
(RNAdS), Schwarzschild-AdS (SAdS), and BTZ black holes. For $c<0$ we cannot
obtain the black hole with positively definite thermodynamic quantities of
mass, temperature, and entropy because the entropy does not satisfy the
area-law. On the other hand, for $c>0$, we find the BIAdS-like black hole,
showing that the coupling $c$ plays the role of pseudo-charge. Importantly, we
could not obtain the SAdS in the limits of $c\to 0$, which means that the GBAdS
is basically different from the SAdS. In addition, we clarify the connections
between thermodynamic and dynamical stability. Finally, we also conjecture that
if a black hole is big and thus globally stable, its quasinormal modes may take
analytic expressions.


  We investigate the thermodynamic limit of the exact solution, which is given
by an inhomogeneous $T-Q$ relation, of the one-dimensional supersymmetric $t-J$
model with unparallel boundary magnetic fields. It is shown that the
contribution of the inhomogeneous term at the ground state satisfies the
$L^{-1}$ scaling law, where $L$ is the system-size. This fact enables us to
calculate the surface (or boundary) energy of the system. The method used in
this paper can be generalized to study the thermodynamic limit and surface
energy of other models related to rational R-matrices.


  During crisis situations, social media allows people to quickly share
information, including messages requesting help. This can be valuable to
emergency responders, who need to categorise and prioritise these messages
based on the type of assistance being requested. However, the high volume of
messages makes it difficult to filter and prioritise them without the use of
computational techniques. Fully supervised filtering techniques for crisis
message categorisation typically require a large amount of annotated training
data, but this can be difficult to obtain during an ongoing crisis and is
expensive in terms of time and labour to create.
  This thesis focuses on addressing the challenge of low data availability when
categorising crisis messages for emergency response. It first presents domain
adaptation as a solution for this problem, which involves learning a
categorisation model from annotated data from past crisis events (source
domain) and adapting it to categorise messages from an ongoing crisis event
(target domain). In many-to-many adaptation, where the model is trained on
multiple past events and adapted to multiple ongoing events, a multi-task
learning approach is proposed using pre-trained language models. This approach
outperforms baselines and an ensemble approach further improves performance...


  In this paper we describe various limited-stretch models of nonlinear rubber
elasticity, each dependent on only the first invariant of the left Cauchy-Green
strain tensor and having only two independent material constants. The models
are described as limited-stretch, or restricted elastic, because the strain
energy and stress response become infinite at a finite value of the first
invariant. These models describe well the limited stretch of the polymer chains
of which rubber is composed. We discuss Gent's model which is the simplest
limited-stretch model and agrees well with experiment. Various statistical
models are then described: the one-chain, three-chain, four-chain and
Arruda-Boyce eight-chain models, all of which involve the inverse Langevin
function. A numerical comparison between the three-chain and eight-chain models
is provided. Next, we compare various models which involve approximations to
the inverse Langevin function with the exact inverse Langevin function of the
eight-chain model. A new approximate model is proposed that is as simple as
Cohen's original model but significantly more accurate. We show that
effectively the eight-chain model may be regarded as a linear combination of
the neo-Hookean and Gent models. Treloar's model is shown to have about half
the percentage error of our new model but it is much more complicated. For
completeness a modified Treloar model is introduced but this is only slightly
more accurate than Treloar's original model. For the deformations of uniaxial
tension, biaxial tension, pure shear and simple shear we compare the accuracy
of these models, and that of Puso, with the eight-chain model by means of
graphs and a table. Our approximations compare extremely well with models
frequently used and described in the literature, having the smallest mean
percentage error over most of the range of the argument.


  This paper continues the analysis begun in {\it Polytopes with mass linear
functions, Part I} of the structure of smooth moment polytopes $\Delta\subset
\ft^*$ that support a mass linear function $H \in \ft$. As explained there,
besides its purely combinatorial interest, this question is relevant to the
study of the homomorphism $\pi_1(T^n)\to \pi_1(\Symp(M_\Delta, \omega_\Delta))$
from the fundamental group of the torus $T^n$ to that of the group of
symplectomorphisms of the $2n$-dimensional symplectic toric manifold
$(M_\Delta, \omega_\Delta)$ associated to $\Delta$. In Part I, we made a
general investigation of this question and classified all mass linear pairs
$(\Delta, H)$ in dimensions up to three. The main result of the current paper
is a classification of all 4-dimensional examples. Along the way, we
investigate the properties of general constructions such as fibrations, blowups
and expansions (or wedges), describing their effect both on moment polytopes
and on mass linear functions. We end by discussing the relation of mass
linearity to Shelukhin's notion of full mass linearity. The two concepts agree
in dimensions up to and including 4. However full mass linearity may be the
more natural concept when considering the question of which blow ups preserve
mass linearity.


  Predictability estimates of ensemble prediction systems are uncertain due to
limited numbers of past forecasts and observations. To account for such
uncertainty, this paper proposes a Bayesian inferential framework that provides
a simple 6-parameter representation of ensemble forecasting systems and the
corresponding observations. The framework is probabilistic, and thus allows for
quantifying uncertainty in predictability measures such as correlation skill
and signal-to-noise ratios. It also provides a natural way to produce
recalibrated probabilistic predictions from uncalibrated ensembles forecasts.
The framework is used to address important questions concerning the skill of
winter hindcasts of the North Atlantic Oscillation for 1992-2011 issued by the
Met Office GloSea5 climate prediction system. Although there is much
uncertainty in the correlation between ensemble mean and observations, there is
strong evidence of skill: the 95% credible interval of the correlation
coefficient of [0.19,0.68] does not overlap zero. There is also strong evidence
that the forecasts are not exchangeable with the observations: With over 99%
certainty, the signal-to-noise ratio of the forecasts is smaller than the
signal-to-noise ratio of the observations, which suggests that raw forecasts
should not be taken as representative scenarios of the observations. Forecast
recalibration is thus required, which can be coherently addressed within the
proposed framework.


  Recently, a contact-resistance-measurement method was developed to detect the
minigap, hence the Andreev bound states (ABSs), in Josephson junctions
constructed on the surface of three-dimensional topological insulators (3D
TIs). In this work, we further generalize that method to the circumstance with
radio frequency (rf) irradiation. We find that with the increase of rf power,
the measured minigap becomes broadened and extends to higher energies, in a way
similar to the rf power dependence of the outer border of the Shapiro step
region. We show that the corresponding data of contact resistance under rf
irradiation can be well interpreted by using the resistively shunted Josephson
junction model (RSJ model) and the Blonder-Tinkham-Klapwijk (BTK) theory. Our
findings could be useful when using the contact-resistance-measurement method
to study the Majorana-related physics in topological insulator-based Josephson
junctions under rf irradiation.


  Using the Bogomolnyi inequality and the vanishing of topological charge at
the onset of nucleation of a new universe permits a simpler, more direct of how
topological defects(kinks and anti kinks) contribute to the onset of initial
conditions at the beginning of inflationary cosmology. We find that it is
possible to present inflationary cosmology with initial conditions with
di-quark pairs formed using an axion wall as a way to start formation of di
quarks as soliton-anti soltion type pairs. This allows for a transition to
inflationary cosmology congruent with with an initial nucleation state of
matter which would have a significant dark matter componet in the beginning.
The separation between the di-quark pairs constituents would be due to CP
violations in the initial phases of matter creation and would be a convenient
trigger for inflationary expansion.


  For a quasi-projective scheme M which carries a perfect obstruction theory,
we construct the virtual cobordism class of M. If M is projective, we prove
that the corresponding Chern numbers of the virtual cobordism class are given
by integrals of the Chern classes of the virtual tangent bundle. Further, we
study cobordism invariants of the moduli space of stable pairs introduced by
Pandharipande-Thomas. Rationality of the partition function is conjectured
together with a functional equation, which can be regarded as a generalization
of the rationality and 1/q <-> q symmetry of the Calabi-Yau case. We prove
rationality for nonsingular projective toric 3-folds by the theory of
descendents.


  Following Cayley, MacMahon, and Sylvester, define a non-unitary partition to
be an integer partition with no part equal to one, and let $\nu(n)$ denote the
number of non-unitary partitions of size $n$. In a 2021 paper, the sixth author
proved a formula to compute $p(n)$ by enumerating only non-unitary partitions
of size $n$, and recorded a number of conjectures regarding the growth of
$\nu(n)$ as $n\to \infty$. Here we refine and prove some of these conjectures.
For example, we prove $p(n) \sim \nu(n)\sqrt{n/\zeta(2)}$ as $n\to \infty$, and
give Ramanujan-like congruences between $p(n)$ and $\nu(n)$ such as
$p(5n)\equiv \nu(5n)\ (\operatorname{mod} 5)$.


  This paper presents a general method for producing randomly perturbed density
operators subject to different sets of constraints. The perturbed density
operators are a specified "distance" away from the state described by the
original density operator. This approach is applied to a bipartite system of
qubits and used to examine the sensitivity of various entanglement measures on
the perturbation magnitude. The constraint sets used include constant energy,
constant entropy, and both constant energy and entropy. The method is then
applied to produce perturbed random quantum states that correspond with those
obtained experimentally for Bell states on the IBM quantum device ibmq_manila.
The results show that the methodology can be used to simulate the outcome of
real quantum devices where noise, which is important both in theory and
simulation, is present.


  Over the past few years, graph representation learning (GRL) has been a
powerful strategy for analyzing graph-structured data. Recently, GRL methods
have shown promising results by adopting self-supervised learning methods
developed for learning representations of images. Despite their success,
existing GRL methods tend to overlook an inherent distinction between images
and graphs, i.e., images are assumed to be independently and identically
distributed, whereas graphs exhibit relational information among data
instances, i.e., nodes. To fully benefit from the relational information
inherent in the graph-structured data, we propose a novel GRL method, called
RGRL, that learns from the relational information generated from the graph
itself. RGRL learns node representations such that the relationship among nodes
is invariant to augmentations, i.e., augmentation-invariant relationship, which
allows the node representations to vary as long as the relationship among the
nodes is preserved. By considering the relationship among nodes in both global
and local perspectives, RGRL overcomes limitations of previous contrastive and
non-contrastive methods, and achieves the best of both worlds. Extensive
experiments on fourteen benchmark datasets over various downstream tasks
demonstrate the superiority of RGRL over state-of-the-art baselines. The source
code for RGRL is available at https://github.com/Namkyeong/RGRL.


  Soft robotics is an emerging technology in which engineers create flexible
devices for use in a variety of applications. In order to advance the wide
adoption of soft robots, ensuring their trustworthiness is essential; if soft
robots are not trusted, they will not be used to their full potential. In order
to demonstrate trustworthiness, a specification needs to be formulated to
define what is trustworthy. However, even for soft robotic grippers, which is
one of the most mature areas in soft robotics, the soft robotics community has
so far given very little attention to formulating specifications. In this work,
we discuss the importance of developing specifications during development of
soft robotic systems, and present an extensive example specification for a soft
gripper for pick-and-place tasks for grocery items. The proposed specification
covers both functional and non-functional requirements, such as reliability,
safety, adaptability, predictability, ethics, and regulations. We also
highlight the need to promote verifiability as a first-class objective in the
design of a soft gripper.


  Many typical applications of object detection operate within a prescribed
false-positive range. In this situation the performance of a detector should be
assessed on the basis of the area under the ROC curve over that range, rather
than over the full curve, as the performance outside the range is irrelevant.
This measure is labelled as the partial area under the ROC curve (pAUC). We
propose a novel ensemble learning method which achieves a maximal detection
rate at a user-defined range of false positive rates by directly optimizing the
partial AUC using structured learning.
  In order to achieve a high object detection performance, we propose a new
approach to extract low-level visual features based on spatial pooling.
Incorporating spatial pooling improves the translational invariance and thus
the robustness of the detection process. Experimental results on both synthetic
and real-world data sets demonstrate the effectiveness of our approach, and we
show that it is possible to train state-of-the-art pedestrian detectors using
the proposed structured ensemble learning method with spatially pooled
features. The result is the current best reported performance on the
Caltech-USA pedestrian detection dataset.


  We present new stellar mass functions at $z\sim6$, $z\sim7$, $z\sim8$,
$z\sim9$ and, for the first time, $z\sim10$, constructed from $\sim800$
Lyman-Break galaxies previously identified over the XDF/UDF, parallels and the
five CANDELS fields. Our study is distinctive due to (1) the much deeper
($\sim200$ hour) wide-area Spitzer/IRAC imaging at $3.6\mu$m and $4.5\mu$m from
the GOODS Re-ionization Era wide Area Treasury from Spitzer (GREATS) program
and (2) consideration of $z\sim6-10$ sources over a $3\times$ larger area than
previous HST+Spitzer studies. The Spitzer/IRAC data enable $\ge2\sigma$
rest-frame optical detections for an unprecedented $50\%$ of galaxies down to a
stellar mass limit of $\sim10^{8}\mathcal{M}_\odot$ across all redshifts.
Schechter fits to our volume densities suggest a combined evolution in
characteristic mass $\mathcal{M}^*$ and normalization factor $\phi^*$ between
$z\sim6$ and $z\sim8$. The stellar mass density (SMD) increases by
$\sim1000\times$ in the $\sim500$ Myr between $z\sim10$ and $z\sim6$, with
indications of a steeper evolution between $z\sim10$ and $z\sim8$, similar to
the previously-reported trend of the star-formation rate density. Strikingly,
abundance matching to the Bolshoi-Planck simulation indicates halo mass
densities evolving at approximately the same rate as the SMD between $z\sim10$
and $z\sim4$. Our results show that the stellar-to-halo mass ratios, a proxy
for the star-formation efficiency, do not change significantly over the huge
stellar mass build-up occurred from $z\sim10$ to $z\sim6$, indicating that the
assembly of stellar mass closely mirrors the build-up in halo mass in the first
$\sim1$ Gyr of cosmic history. JWST is poised to extend these results into the
"first galaxy" epoch at $z\gtrsim10$.


  To apply the Euler system method to a $p$-adic Galois representation $T$, one
needs the existence of a $\sigma \in G_{\mathbb{Q}(\mu_{p^{\infty}})}$ such
that $V/(\sigma-1)V$ is free of rank one over the coefficient ring: we say that
such a $\sigma$ is an Euler-suitable element for $V$. Given a non-CM classical
newform $f$ of weight $k \geq 2$ and character $\chi$, a classical newform $g$
of weight $1$ and character $\psi$, and a prime ideal $\mathfrak{p}$ of residue
characteristic $p$ of a sufficiently large number field, we consider the
situation where $V=V_{f,g,\mathfrak{p}}$ is the tensor product of the
$\mathfrak{p}$-adic representations attached to $f$ and $g$. D. Loeffler asked
the following question: is is true that if $\chi\psi \neq 1$, then there is an
Euler-suitable element for $V_{f,g,\mathfrak{p}}$ for all but finitely many
$\mathfrak{p}$? He gave a positive answer when $f,g$ had coprime conductors. We
give several weaker sufficient conditions to answer this question in the
affirmative. As an application, we remove some of the technical assumptions in
the version of the Bloch-Kato Conjecture proved in arXiv:1503.02888. We also
show that the general answer to the question is negative, by constructing a
family of counter-examples, and giving additional counter-examples that do not
fit in this family.


  Using scanning tunneling microscopy (STM) and Fourier Transform STM (FT-STM),
we have studied a point defect in an epitaxial graphene sample grown on silicon
carbide substrate. This analysis allows us to extract the quasiparticle energy
dispersion, and to give a first experimental proof of the validity of Fermi
liquid theory in graphene for a wide range of energies from -800 meV to +800
meV. We also find evidence of a strong threefold anisotropy in the standing
waves generated by the defect. We discuss possible relations between this
anisotropy, the chirality of the electrons, and the asymmetry between
graphene's two sublattices. All experimental measurements are compared and
related to theoretical T-matrix calculations.


  With the ever increasing complexity of specifications, manual sizing for
analog circuits recently became very challenging. Especially for innovative,
large-scale circuits designs, with tens of design variables, operating
conditions and conflicting objectives to be optimized, design engineers spend
many weeks, running time-consuming simulations, in their attempt at finding the
right configuration. Recent years brought machine learning and optimization
techniques to the field of analog circuits design, with evolutionary algorithms
and Bayesian models showing good results for circuit sizing. In this context,
we introduce a design optimization method based on Generalized Differential
Evolution 3 (GDE3) and Gaussian Processes (GPs). The proposed method is able to
perform sizing for complex circuits with a large number of design variables and
many conflicting objectives to be optimized. While state-of-the-art methods
reduce multi-objective problems to single-objective optimization and
potentially induce a prior bias, we search directly over the multi-objective
space using Pareto dominance and ensure that diverse solutions are provided to
the designers to choose from. To the best of our knowledge, the proposed method
is the first to specifically address the diversity of the solutions, while also
focusing on minimizing the number of simulations required to reach feasible
configurations. We evaluate the introduced method on two voltage regulators
showing different levels of complexity and we highlight that the proposed
innovative candidate selection method and survival policy leads to obtaining
feasible solutions, with a high degree of diversity, much faster than with GDE3
or Bayesian Optimization-based algorithms.


  The criticism of the experiment showing disconnected traces of photons
passing through a nested Mach-Zehnder interferometer is shown to be unfounded.


  Belle II is a Super $B$ Factory experiment, expected to record 50 ab$^{-1}$
of $e^+e^-$ collisions at the SuperKEKB accelerator until 2035. The large
samples of $B$ mesons, charm hadrons, and tau leptons produced in the clean
experimental environment of $e^+e^-$ collisions will provide the basis of a
broad and unique flavor-physics program. Belle II will pursue physics beyond
the Standard Model in many ways, for example: improving the precision of weak
interaction parameters, particularly Cabibbo-Kobayashi-Maskawa (CKM) matrix
elements and phases, and thus more rigorously test the CKM paradigm, measuring
lepton-flavor-violating parameters, and performing unique searches for
missing-mass dark matter events. Many key measurements will be made with
world-leading precision.


  We apply two methods to estimate the 21~cm bispectrum from data taken within
the Epoch of Reionisation (EoR) project of the Murchison Widefield Array (MWA).
Using data acquired with the Phase II compact array allows a direct bispectrum
estimate to be undertaken on the multiple redundantly-spaced triangles of
antenna tiles, as well as an estimate based on data gridded to the $uv$-plane.
The direct and gridded bispectrum estimators are applied to 21 hours of
high-band (167--197~MHz; $z$=6.2--7.5) data from the 2016 and 2017 observing
seasons. Analytic predictions for the bispectrum bias and variance for point
source foregrounds are derived. We compare the output of these approaches, the
foreground contribution to the signal, and future prospects for measuring the
bispectra with redundant and non-redundant arrays. We find that some triangle
configurations yield bispectrum estimates that are consistent with the expected
noise level after 10 hours, while equilateral configurations are strongly
foreground-dominated. Careful choice of triangle configurations may be made to
reduce foreground bias that hinders power spectrum estimators, and the 21~cm
bispectrum may be accessible in less time than the 21~cm power spectrum for
some wave modes, with detections in hundreds of hours.


  Surface fractal dimension Ds is a quantity describing the roughness of
pore-solid interface where all interactions between solid matrix and fluid in
the pore space occur. Ds also quantifies surface area; the higher the surface
fractal dimension the greater the surface area. Therefore, at some high enough
tension head, where a thin layer of water covers the pore-solid interface, one
should expect adsorbed water content to be related to Ds in water-wet porous
media. In this technical note, we develop a theoretical relationship between
the surface fractal dimension, Ds, and the adsorbed water content,
{\theta}_ads, using concepts from van der Waals and electrostatic forces. The
proposed model sheds light on constant coefficients of logarithmic equations
found empirically between Ds and water contents retained at 1500 and 10000 kPa
tension heads. Results also show that our theoretical model estimates Ds from
first physical principles for 164 soil samples accurately.


  This paper defines a novel Bayesian inverse problem to infer an
infinite-dimensional uncertain operator appearing in a differential equation,
whose action on an observable state variable affects its dynamics. Inference is
made tractable by parametrizing the operator using its eigendecomposition. The
plausibility of operator inference in the sparse data regime is explored in
terms of an uncertain, generalized diffusion operator appearing in an evolution
equation for a contaminant's transport through a heterogeneous porous medium.
Sparse data are augmented with prior information through the imposition of
deterministic constraints on the eigendecomposition and the use of qualitative
information about the system in the definition of the prior distribution.
Limited observations of the state variable's evolution are used as data for
inference, and the dependence on the solution of the inverse problem is studied
as a function of the frequency of observations, as well as on whether or not
the data is collected as a spatial or time series.


  We describe recent theoretical work on the final stage of accretion when
material passes from an accretion disk onto a white dwarf surface. Our
calculations focus on understanding the latitudinal spreading and
differentially rotating profile of this material, so we call it the ``spreading
layer'' (SL) model. The SL typically extends to an angle of 0.01-0.1 radians,
with respect to the equator. At low accretion rates ($\dot{M}\la10^{18} {\rm g
s}^{-1}$) the amount of spreading is small, so that the dissipated energy is
radiated back into the accretion disk. When the accretion rate is high, such as
in dwarf novae, symbiotic binaries, and supersoft sources, the material spreads
to higher latitudes to be more easily observed. The SL may contain shallow
surface modes, and we propose that such waves could produce dwarf nova
oscillations (DNOs). This hypothesis naturally explains many key properties of
DNOs, including their frequency range, sinusoidal nature, sensitivity to
accretion rate, and why they are only seen during outburst.


  We consider irreversible and coupled reversible-irreversible nonlinear
port-Hamiltonian systems and the respective sets of thermodynamic equilibria.
In particular, we are concerned with optimal state transitions and output
stabilization on finite-time horizons. We analyze a class of optimal control
problems, where the performance functional can be interpreted as a linear
combination of energy supply, entropy generation, or exergy supply. Our results
establish the integral turnpike property towards the set of thermodynamic
equilibria providing a rigorous connection of optimal system trajectories to
optimal steady states. Throughout the paper, we illustrate our findings by
means of two examples: a network of heat exchangers and a gas-piston system.


  To develop a high-density and long-life lithium-ion battery, a technology is
needed that allows non-destructive visualization of the spatial distribution of
deteriorated parts after cycle test. In the present study, we measured the
distribution of the magnetic field leaking from the lithium-ion battery during
its operation. Based on the measurement results, we evaluated the current
density distribution inside a battery using the electric current reconstruction
process. With respect to the changes in an internal state of the lithium-ion
battery associated with cycle deterioration, we successfully visualized the
spatial changes in the conductivity distribution inside the lithium-ion
battery.


  Coronavirus disease 2019 (COVID-19) has rapidly become a global health
concern after its first known detection in December 2019. As a result, accurate
and reliable advance warning system for the early diagnosis of COVID-19 has now
become a priority. The detection of COVID-19 in early stages is not a
straightforward task from chest X-ray images according to expert medical
doctors because the traces of the infection are visible only when the disease
has progressed to a moderate or severe stage. In this study, our first aim is
to evaluate the ability of recent \textit{state-of-the-art} Machine Learning
techniques for the early detection of COVID-19 from chest X-ray images. Both
compact classifiers and deep learning approaches are considered in this study.
Furthermore, we propose a recent compact classifier, Convolutional Support
Estimator Network (CSEN) approach for this purpose since it is well-suited for
a scarce-data classification task. Finally, this study introduces a new
benchmark dataset called Early-QaTa-COV19, which consists of 1065 early-stage
COVID-19 pneumonia samples (very limited or no infection signs) labelled by the
medical doctors and 12 544 samples for control (normal) class. A detailed set
of experiments shows that the CSEN achieves the top (over 97%) sensitivity with
over 95.5% specificity. Moreover, DenseNet-121 network produces the leading
performance among other deep networks with 95% sensitivity and 99.74%
specificity.


  The differences between the experimental and Relativistic Mean Field binding
energies have been calculated for a large number of even-even nuclei from A=50
to 220. Excluding certain mass regions, the differences, after suitable
corrections for particular isotope chains, are found to be proportional to the
Casten factor $P$, chosen as a measure of n-p interaction strength in a
nucleus. Results for even-$Z$ odd-$N$ nuclei are also seen to follow the same
relation, if the odd-even mass difference is taken into account following the
semiempirical formula. This indicates that the n-p interaction is the major
contributor to the difference between the calculated and the experimental
binding energies.


  We report the development of a new tool to determine the origin of
quasi-periodic oscillations (QPOs) in accretion disk systems. The technique
uses the source energy spectrum and the energy dependence of the QPO fractional
amplitude to restrict the location of the emission region of the modulated
photons, which are assumed to originate in the inner accretion disk. Both Monte
Carlo and semi-analytical methods are presented. We assume the accretion disk
is enshrouded by a slab atmosphere of hot electrons in which unsaturated
Compton scattering produces the high-energy spectrum. Properties of the
atmosphere, in particular the electron temperature, are assumed functions of
radius from the central compact object. We show that our model reproduces the
observed energy dependence of the fractional amplitude of the 67 Hz QPO in GRS
1915+105 if the QPO is assumed to originate within five gravitational radii
from the innermost stable circular orbit.


  Pursuing artificial intelligence for biomedical science, a.k.a. AI Scientist,
draws increasing attention, where one common approach is to build a copilot
agent driven by Large Language Models (LLMs). However, to evaluate such
systems, people either rely on direct Question-Answering (QA) to the LLM
itself, or in a biomedical experimental manner. How to precisely benchmark
biomedical agents from an AI Scientist perspective remains largely unexplored.
To this end, we draw inspiration from one most important abilities of
scientists, understanding the literature, and introduce BioKGBench. In contrast
to traditional evaluation benchmark that only focuses on factual QA, where the
LLMs are known to have hallucination issues, we first disentangle
"Understanding Literature" into two atomic abilities, i) "Understanding" the
unstructured text from research papers by performing scientific claim
verification, and ii) Ability to interact with structured Knowledge-Graph
Question-Answering (KGQA) as a form of "Literature" grounding. We then
formulate a novel agent task, dubbed KGCheck, using KGQA and domain-based
Retrieval-Augmented Generation (RAG) to identify the factual errors of existing
large-scale knowledge graph databases. We collect over two thousand data for
two atomic tasks and 225 high-quality annotated data for the agent task.
Surprisingly, we discover that state-of-the-art agents, both daily scenarios
and biomedical ones, have either failed or inferior performance on our
benchmark. We then introduce a simple yet effective baseline, dubbed BKGAgent.
On the widely used popular knowledge graph, we discover over 90 factual errors
which provide scenarios for agents to make discoveries and demonstrate the
effectiveness of our approach. The code and data are available at
https://github.com/westlake-autolab/BioKGBench.


  Quantum steering inequalities allow to demonstrate the presence of
entanglement between two parties when one of the two measurement device is not
trusted. In this paper we show that quantum steering can be demonstrated for
arbitrary low detection efficiency by using two-qubit non-maximally entangled
states. Our result can have important applications in one-sided
device-independent quantum key distribution.


  Several distinct concepts of temperature appear in the holographic
description of de Sitter space. Conflating these has led to confusion and
inconsistent claims. The double-scaled limit of SYK is a concrete model in
which we can examine and explain these different concepts of temperature. This
note began as an addendum to our paper ``Comments on a Paper by Narovlansky and
Verlinde" but in the process of writing it we learned new things -- interesting
in their own right -- that we wish to report here.


  Social media has become extremely influential when it comes to policy making
in modern societies, especially in the western world, where platforms such as
Twitter allow users to follow politicians, thus making citizens more involved
in political discussion. In the same vein, politicians use Twitter to express
their opinions, debate among others on current topics and promote their
political agendas aiming to influence voter behaviour. In this paper, we
attempt to analyse tweets of politicians from three European countries and
explore the virality of their tweets. Previous studies have shown that tweets
conveying negative sentiment are likely to be retweeted more frequently. By
utilising state-of-the-art pre-trained language models, we performed sentiment
analysis on hundreds of thousands of tweets collected from members of
parliament in Greece, Spain and the United Kingdom, including devolved
administrations. We achieved this by systematically exploring and analysing the
differences between influential and less popular tweets. Our analysis indicates
that politicians' negatively charged tweets spread more widely, especially in
more recent times, and highlights interesting differences between political
parties as well as between politicians and the general population.


  In 2015, Germany introduced a national minimum wage. While the literature
agrees on at most limited negative effects on the overall employment level, we
go into detail and analyze the impact on the working hours dimension and on the
subset of minijobs. Using data from the German Structure of Earnings Survey in
2010, 2014, and 2018, we find empirical evidence that the minimum wage
significantly reduces inequality in hourly and monthly wages. While various
theoretical mechanisms suggest a reduction in working hours, these remain
unchanged on average. However, minijobbers experience a notable reduction in
working hours which can be linked to the specific institutional framework.
Regarding employment, the results show no effects for regular jobs, but there
is a noteworthy decline in minijobs, driven by transitions to regular
employment and non-employment. The transitions in non-employment imply a wage
elasticity of employment of -0.1 for minijobs. Our findings highlight that the
institutional setting leads to heterogeneous effects of the minimum wage.


  Radio detections of ultracool dwarfs provide insight into their magnetic
fields and the dynamos that maintain them, especially at the very bottom of the
main sequence, where other activity indicators dramatically weaken. Until
recently, radio emission was only detected in the M and L dwarf regimes, but
this has changed with the Arecibo detection of rapid polarized flares from the
T6.5 dwarf 2MASS J10475385+2124234. Here, we report the detection of
quasi-quiescent radio emission from this source at 5.8 GHz using the Karl G.
Jansky Very Large Array. The luminosity is {\nu}L_{\nu} = (1.3 +- 0.4) x 10^22
erg/s, a factor of ~100 times fainter than the Arecibo flares. Our detection is
the lowest-luminosity yet achieved for an ultracool dwarf. Although the
emission is fully consistent with being steady, unpolarized, and broadband, we
find tantalizing hints for variability. We exclude the presence of
short-duration flares as seen by Arecibo, although this is not unexpected given
estimates of the duty cycle. Follow-up observations of this object will offer
the potential to constrain its rotation period, electron density, and the
strength and configuration of the magnetic field. Equally important, follow-up
will address the question of whether the electron cyclotron maser instability,
which is thought to produce the flares seen by Arecibo, also operates in the
very different parameter regime of the emission we detect, or whether instead
this ultracool dwarf exhibits both maser and gyrosynchrotron radiation,
potentially originating from substantially different locations.


  Let $\mathfrak{g}$ be a vector space and $[,],[,]'$ be a pair of Lie brackets
on $\mathfrak{g}$. By definition they are compatible if $[,]+[,]'$ is again a
Lie bracket. Such pairs play important role in bihamiltonian and $r$-matrix
formalisms in the theory of integrable systems.
  We propose an approach to a long standing problem of classification of such
pairs in the case when one of them, say $[,]$, is semisimple. It is known that
any such pair is determined by a linear operator on $(\mathfrak{g},[,])$, which
is defined up to adding a derivation. We propose a special fixing of this
operator to get rid of this ambiguity and consider the operators preserving the
root decomposition with respect to a Cartan subalgebra. The classification
leads to two disjoint classes of pairs depending on the symmetry properties of
the corresponding operator with respect to the Killing form. Within each class
we recover known examples and obtain new ones. We present a list of examples in
each case and conjecture the completeness of these lists.


  Temperature inversion due to velocity filtration, a mechanism originally
proposed to explain the heating of the solar corona, is demonstrated to occur
also in a simple paradigmatic model with long-range interactions, the
Hamiltonian mean-field model. Using molecular dynamics simulations, we show
that when the system settles into an inhomogeneous quasi-stationary state in
which the velocity distribution has suprathermal tails, the temperature and
density profiles are anticorrelated: denser parts of the system are colder than
dilute ones. We argue that this may be a generic property of long-range
interacting systems.


  Classical compartmental models in epidemiology often struggle to accurately
capture real-world dynamics due to their inability to address the inherent
heterogeneity of populations. In this paper, we introduce a novel approach that
incorporates heterogeneity through a mobility variable, transforming the
traditional ODE system into a system of integro-differential equations that
describe the dynamics of population densities across different compartments.
Our results show that, for the same basic reproduction number, our
mobility-based model predicts a smaller final pandemic size compared to classic
compartmental models, whose population densities are represented as Dirac delta
functions in our density-based framework. This addresses the overestimation
issue common in many classical models. Additionally, we demonstrate that the
time series of the infected population is sufficient to uniquely identify the
mobility distribution. We reconstruct this distribution using a
machine-learning-based framework, providing both theoretical and algorithmic
support to effectively constrain the mobility-based model with real-world data.


  Bayesian inference paradigms are regarded as powerful tools for solution of
inverse problems. However, when applied to inverse problems in physical
sciences, Bayesian formulations suffer from a number of inconsistencies that
are often overlooked. A well known, but mostly neglected, difficulty is
connected to the notion of conditional probability densities. Borel, and later
Kolmogorov's (1933/1956), found that the traditional definition of conditional
densities is incomplete: In different parameterizations it leads to different
results. We will show an example where two apparently correct procedures
applied to the same problem lead to two widely different results. Another type
of inconsistency involves violation of causality. This problem is found in
model selection strategies in Bayesian inversion, such as Hierarchical Bayes
and Trans-Dimensional Inversion where so-called hyperparameters are included as
variables to control either the number (or type) of unknowns, or the prior
uncertainties on data or model parameters. For Hierarchical Bayes we
demonstrate that the calculated 'prior' distributions of data or model
parameters are not prior-, but posterior information. In fact, the calculated
'standard deviations' of the data are a measure of the inability of the forward
function to model the data, rather than uncertainties of the data. For
trans-dimensional inverse problems we show that the so-called evidence is, in
fact, not a measure of the success of fitting the data for the given choice (or
number) of parameters, as often claimed. We also find that the notion of
Natural Parsimony is ill-defined, because of its dependence on the parameter
prior. Based on this study, we find that careful rethinking of Bayesian
inversion practices is required, with special emphasis on ways of avoiding the
Borel-Kolmogorov inconsistency, and on the way we interpret model selection
results.


  The dynamics of gradient and Hamiltonian flows with particular application to
flows on adjoint orbits of a Lie group and the extension of this setting to
flows on a loop group are discussed. Different types of gradient flows that
arise from different metrics including the so-called normal metric on adjoint
orbits of a Lie group and the K\"ahler metric are compared. It is discussed how
a K\"ahler metric can arise from a complex structure induced by the Hilbert
transform. Hybrid and metriplectic flows that arise when one has both
Hamiltonian and gradient components are examined. A class of metriplectic
systems that is generated by completely antisymmetric triple brackets is
described and for finite-dimensional systems given a Lie algebraic
interpretation. A variety of explicit examples of the several types of flows
are given.


  The entropy of a quantum-statistical system which is classically approximated
by a general stationary eternal black hole is studied by means of a
microcanonical functional integral. This approach opens the possibility of
including explicitly the internal degrees of freedom of a physical black hole
in path integral descriptions of its thermodynamical properties. If the
functional integral is interpreted as the density of states of the system, the
corresponding entropy equals ${cal S} = A_H/4 - A_H/4 =0$ in the semiclassical
approximation, where $A_H$ is the area of the black hole horizon. The
functional integral reflects the properties of a pure state.


  We introduce and study a family of quantum fields, associated to
delta-interactions in one dimension. These fields are analogous to holonomic
quantum fields of M. Sato, T. Miwa and M. Jimbo. Corresponding field operators
belong to an infinite-dimensional representation of the group $SL(2,\Rb)$ in
the Fock space of ordinary harmonic oscillator. We compute form factors of such
fields and their correlation functions, which are related to the determinants
of Schroedinger operators with a finite number of point interactions. It is
also shown that these determinants coincide with tau functions, obtained
through the trivialization of the $\mathrm{det}^*$-bundle over a Grassmannian
associated to a family of Schroedinger operators.


  Deep Reinforcement Learning (DRL) techniques have received significant
attention in control and decision-making algorithms. Most applications involve
complex decision-making systems, justified by the algorithms' computational
power and cost. While model-based versions are emerging, model-free DRL
approaches are intriguing for their independence from models, yet they remain
relatively less explored in terms of performance, particularly in applied
control. This study conducts a thorough performance analysis comparing the
data-driven DRL paradigm with a classical state feedback controller, both
designed based on the same cost (reward) function of the linear quadratic
regulator (LQR) problem. Twelve additional performance criteria are introduced
to assess the controllers' performance, independent of the LQR problem for
which they are designed. Two Deep Deterministic Policy Gradient (DDPG)-based
controllers are developed, leveraging DDPG's widespread reputation. These
controllers are aimed at addressing a challenging setpoint tracking problem in
a Non-Minimum Phase (NMP) system. The performance and robustness of the
controllers are assessed in the presence of operational challenges, including
disturbance, noise, initial conditions, and model uncertainties. The findings
suggest that the DDPG controller demonstrates promising behavior under rigorous
test conditions. Nevertheless, further improvements are necessary for the DDPG
controller to outperform classical methods in all criteria. While DRL
algorithms may excel in complex environments owing to the flexibility in the
reward function definition, this paper offers practical insights and a
comparison framework specifically designed to evaluate these algorithms within
the context of control engineering.


  This EPTCS volume contains the joint proceedings for the fourth international
workshop on Formal Methods for Autonomous Systems (FMAS 2022) and the fourth
international workshop on Automated and verifiable Software sYstem DEvelopment
(ASYDE 2022), which were held on the 26th and 27th of September 2022. FMAS 2022
and ASYDE 2022 were held in conjunction with 20th International Conference on
Software Engineering and Formal Methods (SEFM'22), at Humboldt University in
Berlin.
  For FMAS, this year's workshop was our return to having in-person attendance
after two editions of FMAS that were entirely online because of the
restrictions necessitated by COVID-19. We were also keen to ensure that FMAS
2022 remained easily accessible to people who were unable to travel, so the
workshop facilitated remote presentation and attendance.
  The goal of FMAS is to bring together leading researchers who are using
formal methods to tackle the unique challenges presented by autonomous systems,
to share their recent and ongoing work. Autonomous systems are highly complex
and present unique challenges for the application of formal methods. Autonomous
systems act without human intervention, and are often embedded in a robotic
system, so that they can interact with the real world. As such, they exhibit
the properties of safety-critical, cyber-physical, hybrid, and real-time
systems. We are interested in work that uses formal methods to specify, model,
or verify autonomous and/or robotic systems; in whole or in part. We are also
interested in successful industrial applications and potential directions for
this emerging application of formal methods.


  This study focuses on the design of multiple Arabic diacritical marks and to
developing a model that generates the stacking of multiples Arabic diacritics
in order to integrate it into a system of Arabic composition. The problem
concerns the presence of multiple diacritics on a single basic letter. This
model is based on the layering composition. The combination of diacritics with
letters requires a basic layering to combine any diacritics in the word with
their base letter, without having to deal individually and separately each pair
of base letter and diacritics.


  Improved calculations of X-ray spectra for supernova remnants (SNRs) in the
Sedov-Taylor phase are reported, which for the first time include reliable
atomic data for Fe L-shell lines. This new set of Sedov models also allows for
a partial collisionless heating of electrons at the blast wave and for energy
transfer from ions to electrons through Coulomb collisions. X-ray emission
calculations are based on the updated Hamilton-Sarazin spectral model. The
calculated X-ray spectra are succesfully interpreted in terms of three
distribution functions: the electron temperature and ionization timescale
distributions, and the ionization timescale averaged electron temperature
distribution. The comparison of Sedov models with a frequently used single
nonequilibrium ionization (NEI) timescale model reveals that this simple model
is generally not an appropriate approximation to X-ray spectra of SNRs. We find
instead that plane-parallel shocks provide a useful approximation to X-ray
spectra of SNRs, particularly for young SNRs. Sedov X-ray models described
here, together with simpler plane shock and single ionization timescale models,
have been implemented as standard models in the widely used XSPEC v11 spectral
software package.


  Learnable keypoint detectors and descriptors are beginning to outperform
classical hand-crafted feature extraction methods. Recent studies on
self-supervised learning of visual representations have driven the increasing
performance of learnable models based on deep networks. By leveraging
traditional data augmentations and homography transformations, these networks
learn to detect corners under adverse conditions such as extreme illumination
changes. However, their generalization capabilities are limited to corner-like
features detected a priori by classical methods or synthetically generated
data.
  In this paper, we propose the Correspondence Network (CorrNet) that learns to
detect repeatable keypoints and to extract discriminative descriptions via
unsupervised contrastive learning under spatial constraints. Our experiments
show that CorrNet is not only able to detect low-level features such as
corners, but also high-level features that represent similar objects present in
a pair of input images through our proposed joint guided backpropagation of
their latent space. Our approach obtains competitive results under viewpoint
changes and achieves state-of-the-art performance under illumination changes.


  FU Tau A is a young very low mass object in the Taurus star forming region
which was previously found to have strong X-ray emission and to be anomalously
bright for its spectral type. In this study we discuss these characteristics
using new information from quasi-simultaneous photometric and spectroscopic
monitoring. From photometric time series obtained with the 2.2m telescope on
Calar Alto we measure a period of ~4d for FU Tau A, most likely the rotation
period. The short-term variations over a few days are consistent with the
rotational modulation of the flux by cool, magnetically induced spots. In
contrast, the photometric variability on timescales of weeks and years can only
be explained by the presence of hot spots, presumably caused by accretion. The
hot spot properties are thus variable on timescales exceeding the rotation
period, maybe due to long-term changes in the accretion rate or geometry. The
new constraints from the analysis of the variability confirm that FU Tau A is
affected by magnetically induced spots and excess luminosity from accretion.
However, accretion is not sufficient to explain its anomalous position in the
HR diagram. In addition, suppressed convection due to magnetic activity and/or
an early evolutionary stage need to be invoked to fully account for the
observed properties. These factors cause considerable problems in estimating
the mass of FU Tau A and other objects in this mass/age regime, to the extent
that it appears questionable if it is feasible to derive the Initial Mass
Function for young low-mass stars and brown dwarfs.


  The kinetic energy in tidal flows, when converted into heat, can affect the
internal structure of a star and shift its location on a color-magnitude
diagram from that of standard models. In this paper we explore the impact of
injecting heat into stars with masses near the main sequence turnoff mass (1.26
$M_\odot$) of the open cluster M67. The heating rate is obtained from the tidal
shear energy dissipation rate which is calculated from first principles by
simultaneously solving the equations that describe orbital motion and the
response of a star's layers to the gravitational, Coriolis, centrifugal, gas
pressure and viscous forces. The stellar structure models are computed with
MESA. We focus on the effects of injecting heat in pulses lasting 0.01 Gyr, a
timeframe consistent with the synchonization timescale in binary systems. We
find that the location of the tidally perturbed stars in the M67
color-magnitude diagram is shifted to significantly higher luminosities and
effective temperatures than predicted by the standard model isochrone and
include locations corresponding to some of the Blue Straggler Stars. Because
tidal heating takes energy from the orbit causing it to shrink, Blue Straggler
Stars could be merger or mass-transfer progenitors as well as products of these
processes.


  The main purpose of the paper is to investigate the possibility of applying
Chen-Stein approach to estimate the $\chi^2$ distance between Poisson
distribution and a sum of independent indicators. Earlier results concerning
$\chi^2$ distance between above mentioned distributions either used analytical
approach heavily based on the analysis of the generating functions or on rather
lengthy and complicated elementary calculations. Applying Chen-Stein approach
we succeed in providing a very quick proof of upper bounds for $\chi^2$
distance that are of comparable strength to the earlier estimates obtained by
other approaches.


  A method to predict the aeroelastic pitch response of an airfoil to gusts is
presented. The prediction is based on energy maps generated by high-fidelity
fluid dynamic simulations of the airfoil with prescribed pitch oscillations.
The energy maps quantify the exchange of energy between the pitching airfoil
and the flow, and serve as manifolds over which the dynamical states of
aeroelastic airfoil system grow, decay and attain stationary states. This
method allows us to study the full nonlinear response of the system to large
gusts, and predict the growth and saturation of aeroelastic pitch
instabilities. We also show that the manifold topology in these maps can be
used to make informed modifications to the system parameters in order to
control the response to gusts.


  Polycyclic Aromatic Hydrocarbon (PAH) emission features dominate the
mid-infrared spectra of star-forming galaxies and can be useful to calibrate
star formation rates and diagnose ionized states of grains. However, the PAH
3.3 micron feature has not been studied as much as other PAH features since it
is weaker than others and resides outside of Spitzer capability. In order to
detect and calibrate the 3.3 micron PAH emission and investigate its potential
as a star formation rate indicator, we carried out an AKARI mission program,
AKARI mJy Unbiased Survey of Extragalactic Survey (AMUSES) and compare its
sample with various literature samples. We obtained 2 ~5 micron low resolution
spectra of 20 flux-limited galaxies with mixed SED classes, which yields the
detection of the 3.3 micron PAH emission from three out of 20 galaxies. For the
combined sample of AMUSES and literature samples, the 3.3 micron PAH
luminosities correlate with the infrared luminosities of star-forming galaxies,
albeit with a large scatter (1.5 dex). The correlation appears to break down at
the domain of ultra-luminous infrared galaxies (ULIRGs), and the power of the
3.3 micron PAH luminosity as a proxy for the infrared luminosity is hampered at
log[L(PAH3.3)/(erg/sec)] > -42.0. Possible origins for this deviation in the
correlation are discussed, including contribution from AGN and strongly
obscured YSOs, and the destruction of PAH molecules in ULIRGs.


  Heckman et al. (2005) used the Galaxy Evolution Explorer (GALEX) UV imaging
survey to show that there exists a rare population of nearby compact
UV-luminous galaxies (UVLGs) that closely resembles high redshift Lyman break
galaxies (LBGs). We present HST images in the UV, optical, and Ha, and
resimulate them at the depth and resolution of the GOODS/UDF fields to show
that the morphologies of UVLGs are also similar to those of LBGs. Our sample of
8 LBG analogs thus provides detailed insight into the connection between star
formation and LBG morphology. Faint tidal features or companions can be seen in
all of the rest-frame optical images, suggesting that the starbursts are the
result of a merger or interaction. The UV/optical light is dominated by
unresolved (~100-300 pc) super starburst regions (SSBs). A detailed comparison
with the galaxies Haro 11 and VV 114 at z=0.02 indicates that the SSBs
themselves consist of diffuse stars and (super) star clusters. The structural
features revealed by the new HST images occur on very small physical scales and
are thus not detectable in images of high redshift LBGs, except in a few cases
where they are magnified by gravitational lensing. We propose, therefore, that
LBGs are mergers of gas-rich, relatively low-mass (~10^10 Msun) systems, and
that the mergers trigger the formation of SSBs. If galaxies at high redshifts
are dominated by SSBs, then the faint end slope of the luminosity function is
predicted to have slope alpha~2. Our results are the most direct confirmation
to date of models that predict that the main mode of star formation in the
early universe was highly collisional.


  We propose a new way to compute the radius of convergence for Quaternionic
hyperholomorphic functions and for Octonion analytic functions. We extend the
theorem of Cauchy Hadamard and the theorem of Abel on convergence of series to
Quaternionic analysis with the Fueter Operator, to Quaternionic analysis with
the Moisil Theodoresco operator and to the Octonion analysis with the Fueter
operator.


  We analyze the masses and spatial distributions of fourteen young stellar
groups in Taurus, Lupus3, ChaI, and IC348. These nearby groups, which typically
contain 20 to 40 members, have membership catalogs complete to ~0.02 M_sun, and
are sufficiently young that their locations should be similar to where they
formed. These groups show five properties seen in clusters having many more
stars and much greater surface density of stars: (1) a broad range of masses,
(2) a concentration of the most massive star towards the centre of the group,
(3) an association of the most massive star with a high surface density of
lower-mass stars, (4) a correlation of the mass of the most massive star with
the total mass of the group, and (5) the distribution of a large fraction of
the mass in a small fraction of the stars.


  Generative AI image models may inadvertently generate problematic
representations of people. Past research has noted that millions of users
engage daily across the world with these models and that the models, including
through problematic representations of people, have the potential to compound
and accelerate real-world discrimination and other harms (Bianchi et al, 2023).
In this paper, we focus on addressing the generation of problematic
associations between demographic groups and semantic concepts that may reflect
and reinforce negative narratives embedded in social data. Building on
sociological literature (Blumer, 1958) and mapping representations to model
behaviors, we have developed a taxonomy to study problematic associations in
image generation models. We explore the effectiveness of fine tuning at the
model level as a method to address these associations, identifying a potential
reduction in visual quality as a limitation of traditional fine tuning. We also
propose a new methodology with twice-human-in-the-loop (T-HITL) that promises
improvements in both reducing problematic associations and also maintaining
visual quality. We demonstrate the effectiveness of T-HITL by providing
evidence of three problematic associations addressed by T-HITL at the model
level. Our contributions to scholarship are two-fold. By defining problematic
associations in the context of machine learning models and generative AI, we
introduce a conceptual and technical taxonomy for addressing some of these
associations. Finally, we provide a method, T-HITL, that addresses these
associations and simultaneously maintains visual quality of image model
generations. This mitigation need not be a tradeoff, but rather an enhancement.


  To explore the structure of the QCD phase diagram in high baryon density
domain, several high-energy nuclear collision experiments in a wide range of
beam energies are currently performed or planned using many accelerator
facilities. In these experiments search for a first-order phase transition and
the QCD critical point is one of the most important topics. To find the
signature of the phase transition, experimental data should be compared to
appropriate dynamical models which quantitatively describe the process of the
collisions. In this study we develop a new dynamical model on the basis of the
non-equilibrium hadronic transport model JAM and 3+1D hydrodynamics. We show
that the new model reproduce well the experimental beam-energy dependence of
hadron yields and particle ratio by the partial thermalization of the system in
our core-corona approach.


  This work is a comment on Ryder's derivation of the Dirac equation, with
emphasis on the physical contents of this equation: the notion of particles and
antiparticles according to the Stueckelberg-Feynman interpretation, the
opposite intrinsic parity between particles and antiparticles, and the spin.


  Superconductors with noncentrosymmetric crystal structures such as
Li2T3B(T:Pd,Pt) have been the focus of in-depth research with their parity
mixing nature. In this study, we focused our research on non-magnetic impurity
effect in Li2T3B (T: Pd, Pt). The nature of the pair breaking by non-magnetic
impurity in the parity mixing superconducting state is still unclear. We
prepared different quality samples of Li2Pd3B and Li2Pt3B by changing
conditions in synthesizing, and sample qualities were estimated by residual
resistivity. Spin singlet dominant superconductor Li2Pd3B exhibits the weak Tc
suppression attributed by nonmagnetic impurity and defects, while Hc2 (0) value
increased. This behavior is similar in ordinary s-wave superconductor. On the
other hand, for the spin triplet dominant superconductor Li2Pt3B, it was
suggested that the Cooper pair was broken and superconducting gap was decreased
by non-magnetic impurities and defects. Li2Pt3B is similar to unconventional
superconducting state.


  Let $(a,b,c)$ be pairwise relatively prime integers such that $a^2 + b^2 =
c^2$. In 1956, Je{\'s}manowicz conjectured that the only solution of $a^x + b^y
= c^z$ in positive integers is $(x,y,z)=(2,2,2)$. In this note we prove a
polynomial analogue of this conjecture.


  By means of an effective potential associated to a constrained equilibrium
measure and apt to study frozen systems, we investigate glassy freezing in
simple liquids in the hypernetted chain (HNC) approximation. Differently from
other classical approximations of liquid theory, freezing is naturally embedded
in the HNC approximation. We get a detailed description of the freezing
transition that is analogous to the one got in a large class of mean-field long
range spin glass. We compare our findings with Monte Carlo simulations of the
same system and conclude that many of the qualitative features of the
transition are captured by the approximated theory.


  We use a Gaussian Process Regression (GPR) strategy that was recently
developed [3,16,17] to analyze different types of curves that are commonly
encountered in parametric eigenvalue problems. We employ an offline-online
decomposition method. In the offline phase, we generate the basis of the
reduced space by applying the proper orthogonal decomposition (POD) method on a
collection of pre-computed, full-order snapshots at a chosen set of parameters.
Then, we generate our GPR model using four different Mat\'{e}rn covariance
functions. In the online phase, we use this model to predict both eigenvalues
and eigenvectors at new parameters. We then illustrate how the choice of each
covariance function influences the performance of GPR. Furthermore, we discuss
the connection between Gaussian Process Regression and spline methods and
compare the performance of the GPR method against linear and cubic spline
methods. We show that GPR outperforms other methods for functions with a
certain regularity.


  For a positive linear map F and a normal matrix N, we show that |F(N)| is
bounded by some simple linear combinations in the unitary orbit of F(|N|).
Several elegant sharp inequalities are derived, especially for the Schur
product.


  We study effective descent $ \mathcal V $-functors for cartesian monoidal
categories $ \mathcal V $ with finite limits. This study is carried out via the
properties enjoyed by the $2$-functor $ \mathcal V \mapsto
\mathsf{Fam}(\mathcal V) $, results about effective descent of bilimits of
categories, and the fact that the enrichment $2$-functor preserves certain
bilimits. Since these results rely on an understanding of (effective) descent
morphisms in $ \mathsf{Fam}(\mathcal V) $, we briefly study those epimorphisms
when $ \mathcal V $ is a regular category.


  We explore the effect of the magnetic Prandtl number Pm on energy and
dissipation in fully resolved direct numerical simulations of steady-state,
mechanically forced homogeneous magnetohydrodynamic turbulence in the range Pm
= 1/32 to 32. We compare the spectra and show that if the simulations are not
fully resolved, the steepness of the scaling of the kinetic-to-magnetic
dissipation ratio with Pm is overestimated. We also present results of decaying
turbulence with helical and nonhelical magnetic fields, where we find
nonhelical reverse spectral transfer for Pm < 1. The results of this systematic
analysis have applications including stars, planetary dynamos, and accretion
disks.


  Describing the dynamics of a city is a crucial step to both understanding the
human activity in urban environments and to planning and designing cities
accordingly. Here we describe the collective dynamics of New York City and
surrounding areas as seen through the lens of Twitter usage. In particular, we
observe and quantify the patterns that emerge naturally from the hourly
activities in different areas of New York City, and discuss how they can be
used to understand the urban areas. Using a dataset that includes more than 6
million geolocated Twitter messages we construct a movie of the geographic
density of tweets. We observe the diurnal "heartbeat" of the NYC area. The
largest scale dynamics are the waking and sleeping cycle and commuting from
residential communities to office areas in Manhattan. Hourly dynamics reflect
the interplay of commuting, work and leisure, including whether people are
preoccupied with other activities or actively using Twitter. Differences
between weekday and weekend dynamics point to changes in when people wake and
sleep, and engage in social activities. We show that by measuring the average
distances to the heart of the city one can quantify the weekly differences and
the shift in behavior during weekends. We also identify locations and times of
high Twitter activity that occur because of specific activities. These include
early morning high levels of traffic as people arrive and wait at air
transportation hubs, and on Sunday at the Meadowlands Sports Complex and Statue
of Liberty. We analyze the role of particular individuals where they have large
impacts on overall Twitter activity. Our analysis points to the opportunity to
develop insight into both geographic social dynamics and attention through
social media analysis.


  We study the perturbative stability of Euclidean axion-dilaton wormholes that
asymptotically approach flat space, both with a massless and a massive dilaton,
and focussing on homogeneous perturbations. We find massless wormholes to
always be perturbatively stable. The phenomenologically more relevant case of a
massive dilaton presents us with a wide variety of wormhole solutions,
depending on the dilaton coupling and mass, and on the axion charge. We find
that the solutions with the smallest dilaton potential are perturbatively
stable and dominant, even in cases where the wormhole solutions are not
continuously connected to the massless case by decreasing the mass. For
branches of solutions emanating from a bifurcation point, one side of the
branch always contains a negative mode in its spectrum, rendering such
solutions unstable. The existence of classes of perturbatively stable wormhole
solutions with massive dilaton sharpens the puzzles associated with Euclidean
wormholes.


  Geometrical invariance, in particular affine invariance, has been recently
proposed as an important principle underlying the production of hand movements.
However, tests of affine invariance have traditionally been applied to the
consequences of this principle rather to the principle itself. Here, we
designed and performed an original, direct, test of affine invariance in a
scribbling experiment. In each of the 10800 pairs of randomly-selected
scribbling segments, we compared the time parameterizations obtained by
transforming the first segment using four different transportation rules -
affine, equi-affine, Euclidian and constant - with the experimentally-observed
parameterization of the second segment. We observed that, when the two paths
are affinely-similar, the affine transportation of the first segment yields the
time parameterization that best matches the experimental parameterization of
the second segment, which directly demonstrates the existence of affine
invariance in the production of hand movements.


  Using a recently developed perturbation theory for uasinormal modes (QNM's),
we evaluate the shifts in the real and imaginary parts of the QNM frequencies
due to a quasi-static perturbation of the black hole spacetime. We show the
perturbed QNM spectrum of a black hole can have interesting features using a
simple model based on the scalar wave equation.


  Domain adaptation aims to enable Large Language Models (LLMs) to generalize
domain datasets unseen effectively during the training phase. However, factors
such as the size of the model parameters and the scale of training data are
general influencers and do not reflect the nuances of domain adaptation
performance. This paper investigates the fine-grained factors affecting domain
adaptation performance, analyzing the specific impact of `words' in training
data on summarization tasks. We propose quantifying dataset learning difficulty
as the learning difficulty of generative summarization, which is determined by
two indicators: word-based compression rate and abstraction level. Our
experiments conclude that, when considering dataset learning difficulty, the
cross-domain overlap and the performance gain in summarization tasks exhibit an
approximate linear relationship, which is not directly related to the number of
words. Based on this finding, predicting a model's performance on unknown
domain datasets is possible without undergoing training.


  Large-scale accretion shocks around massive clusters of galaxies, generically
expected in the cold dark matter scenario of cosmological structure formation,
are shown to be plausible sources of the observed ultrahigh energy cosmic rays
(UHECRs) by accelerating a mixture of heavy nuclei including the iron group
elements. Current observations can be explained if the source composition at
injection for the heavier nuclei is somewhat enhanced from simple expectations
for the accreting gas. The proposed picture should be clearly testable by
current and upcoming facilities in the near future through characteristic
features in the UHECR spectrum, composition and anisotropy, in particular the
rapid increase of the average mass composition with energy from $10^{19}$ to
$10^{20}$ eV.


  The information-theoretic definition of quantum correlation, e.g., quantum
discord, is measurement dependent. By considering the more general quantum
measurements, weak measurements, which include the projective measurement as a
limiting case, we show that while weak measurements can enable one to capture
more quantumness of correlation in a state, it can also induce other
counterintuitive quantum effects. Specifically, we show that the general
measurements with different strengths can impose different orderings for
quantum correlations of some states. It can also modify the monogamous
character for certain classes of states as well which may diminish the
usefulness of quantum correlation as a resource in some protocols. In this
sense, we say that the weak measurements play a dual role in defining quantum
correlation.


  We use a new, exact approach in calculating the energy density measured by an
observer living on a brane embedded in a charged black hole spacetime. We find
that the bulk Weyl tensor gives rise to non-linear terms in the energy density
and pressure in the FRW equations for the brane. Remarkably, these take exactly
the same form as the ``unconventional'' terms found in the cosmology of branes
embedded in pure AdS, with extra matter living on the brane. Black hole driven
cosmologies have the benefit that there is no ambiguity in splitting the
braneword energy momentum into tension and additional matter. We propose a new,
enlarged relationship between the two descriptions of braneworld cosmology. We
also study the exact thermodynamics of the field theory and present a
generalised Cardy-Verlinde formula in this set up.


  The pooling layer is an essential component in the neural network based
speaker verification. Most of the current networks in speaker verification use
average pooling to derive the utterance-level speaker representations. Average
pooling takes every frame as equally important, which is suboptimal since the
speaker-discriminant power is different between speech segments. In this paper,
we present a unified attention-based pooling framework and combine it with the
multi-head attention. Experiments on the Fisher and NIST SRE 2010 dataset show
that involving outputs from lower layers to compute the attention weights can
outperform average pooling and achieve better results than vanilla attention
method. The multi-head attention further improves the performance.


  This paper investigates how to extract objects-of-interest without relying on
hand-craft features and sliding windows approaches, that aims to jointly solve
two sub-tasks: (i) rapidly localizing salient objects from images, and (ii)
accurately segmenting the objects based on the localizations. We present a
general joint task learning framework, in which each task (either object
localization or object segmentation) is tackled via a multi-layer convolutional
neural network, and the two networks work collaboratively to boost performance.
In particular, we propose to incorporate latent variables bridging the two
networks in a joint optimization manner. The first network directly predicts
the positions and scales of salient objects from raw images, and the latent
variables adjust the object localizations to feed the second network that
produces pixelwise object masks. An EM-type method is presented for the
optimization, iterating with two steps: (i) by using the two networks, it
estimates the latent variables by employing an MCMC-based sampling method; (ii)
it optimizes the parameters of the two networks unitedly via back propagation,
with the fixed latent variables. Extensive experiments suggest that our
framework significantly outperforms other state-of-the-art approaches in both
accuracy and efficiency (e.g. 1000 times faster than competing approaches).


  The spectral index images of the jet in the nearby radio galaxy M87 have
previously been shown with Very Long Baseline Interferometric arrays at 2-43
GHz. They exhibit flattening of the spectra at a location of inner (central)
spine and toward outer ridges. This could imply optical depth effects, lower
energy cutoff or stratification of the emitting particles energy distribution.
In this paper we employ simulations of multifrequency VLBI observations of M87
radio jet with various model brightness distributions. CLEAN deconvolution
errors produce significant features in the observed images. For intensity
images they result in the appearance of the inner ridge line in the
intrinsically edge brightened jet models. For spectral index images they
flatten the spectra in a series of stripes along the jet. Another bias
encountered in our simulations is steepening of the spectra in a low surface
brightness jet regions. These types of the imaging artefacts do not depend on
the model considered. We propose a methods for the compensation of the
systematics using only the observed data.


  We use the ROSAT North Ecliptic Pole (NEP) survey to construct a small, but
purely X-ray flux-limited sample of cataclysmic variable stars (CVs). The
sample includes only 4 systems, 2 of which (RX J1715.6+6856 and RX
J1831.7+6511) are new discoveries. We present time-resolved spectroscopy of the
new CVs and measure orbital periods of 1.64 \pm 0.02 h and 4.01\pm 0.03 h for
RX 1715.6+6856 and RX J1831.7+6511, respectively. We also estimate distances
for all the CVs in our sample, based mainly on their apparent brightness in the
infrared. The space density of the CV population represented by our small
sample is (1.1 +2.3/-0.7) 10^-5 pc^-3. We can also place upper limits on the
space density of any sub-population of CVs too faint to be included in the NEP
survey. In particular, we show that if the overall space density of CVs is as
high as 2 10^-4 pc^-3 (as has been predicted theoretically), the vast majority
of CVs must be fainter than L_X \simeq 2 10^29 erg/s.


  Vision based solutions for the localization of vehicles have become popular
recently. We employ an image retrieval based visual localization approach. The
database images are kept with GPS coordinates and the location of the retrieved
database image serves as an approximate position of the query image. We show
that localization can be performed via descriptors solely extracted from
semantically segmented images. It is reliable especially when the environment
is subjected to severe illumination and seasonal changes. Our experiments
reveal that the localization performance of a semantic descriptor can increase
up to the level of state-of-the-art RGB image based methods.


  The way we eat and what we eat, the way we move and the way we sleep
significantly impact the risk of becoming obese. These aspects of behavior
decompose into several personal behavioral elements including our food choices,
eating place preferences, transportation choices, sleeping periods and duration
etc. Most of these elements are highly correlated in a causal way with the
conditions of our local urban, social, regulatory and economic environment. To
this end, the H2020 project "BigO: Big Data Against Childhood Obesity"
(http://bigoprogram.eu) aims to create new sources of evidence together with
exploration tools, assisting the Public Health Authorities in their effort to
tackle childhood obesity. In this paper, we present the technology-based
methodology that has been developed in the context of BigO in order to: (a)
objectively monitor a matrix of a population's obesogenic behavioral elements
using commonly available wearable sensors (accelerometers, gyroscopes, GPS),
embedded in smart phones and smart watches; (b) acquire information for the
environment from open and online data sources; (c) provide aggregation
mechanisms to correlate the population behaviors with the environmental
characteristics; (d) ensure the privacy protection of the participating
individuals; and (e) quantify the quality of the collected big data.


  We prove a substantial extension of a well-known result due to Bennett and
Carl: The inclusion of a 2-concave symmetric Banach sequence space E into l_2
is (E,1)-summing, i.e. for every unconditionally summable sequence (x_n) in E
the scalar sequence (||x_n||_2) is contained in E. Various applications are
given, e.g. to the theory of eigenvalue distribution of compact operators and
approximation theory.


  It is widely accepted that a phenomenologically viable theory of jet
quenching for heavy ion collisions requires the understanding of medium-induced
parton energy loss beyond the limit of eikonal kinematics formulated by
Baier-Dokshitzer-Mueller-Peigne-Schiff and Zakharov (BDMPS-Z). Here, we
supplement a recently developed exact Monte Carlo implementation of the BDMPS-Z
formalism with elementary physical requirements including exact energy-momentum
conservation, a refined formulation of jet-medium interactions and a treatment
of all parton branchings on the same footing. We document the changes induced
by these physical requirements and we describe their kinematic origin.


  Semidefinite programming is a powerful tool in the design and analysis of
approximation algorithms for combinatorial optimization problems. In
particular, the random hyperplane rounding method of Goemans and Williamson has
been extensively studied for more than two decades, resulting in various
extensions to the original technique and beautiful algorithms for a wide range
of applications. Despite the fact that this approach yields tight approximation
guarantees for some problems, e.g., Max-Cut, for many others, e.g., Max-SAT and
Max-DiCut, the tight approximation ratio is still unknown. One of the main
reasons for this is the fact that very few techniques for rounding semidefinite
relaxations are known.
  In this work, we present a new general and simple method for rounding
semi-definite programs, based on Brownian motion. Our approach is inspired by
recent results in algorithmic discrepancy theory. We develop and present tools
for analyzing our new rounding algorithms, utilizing mathematical machinery
from the theory of Brownian motion, complex analysis, and partial differential
equations. Focusing on constraint satisfaction problems, we apply our method to
several classical problems, including Max-Cut, Max-2SAT, and MaxDiCut, and
derive new algorithms that are competitive with the best known results. To
illustrate the versatility and general applicability of our approach, we give
new approximation algorithms for the Max-Cut problem with side constraints that
crucially utilizes measure concentration results for the Sticky Brownian
Motion, a feature missing from hyperplane rounding and its generalizations


  Self-propelled Brownian particles show rich out-of-equilibrium physics, for
instance, the motility-induced phase separation (MIPS). While decades of
studying the structure of liquids have established a deep understanding of
passive systems, not much is known about correlations in active suspensions. In
this work we derive an approximate analytic theory for three-body correlations
and forces in systems of active Brownian disks starting from the many-body
Smoluchowski equation. We use our theory to predict the conditional forces that
act on a tagged particle and their dependence on the propulsion speed of
self-propelled disks. We identify preferred directions of these forces in
relation to the direction of propulsion and the positions of the surrounding
particles. We further relate our theory to the effective swimming speed of the
active disks, which is relevant for the physics of MIPS. To test and validate
our theory, we additionally run particle-resolved computer simulations, for
which we explicitly calculate the three-body forces. In this context, we
discuss the modeling of active Brownian swimmers with nearly hard interaction
potentials. We find very good agreement between our simulations and numerical
solutions of our theory, especially for the nonequilibrium pair-distribution
function. For our analytical results, we carefully discuss their range of
validity in the context of the different levels of approximation we applied.
This discussion allows us to study the individual contribution of particles to
three-body forces and to the emerging structure. Thus, our work sheds light on
the collective behavior, provides the basis for further studies of correlations
in active suspensions, sheds new light onto the collective behavior, and makes
a step towards an emerging liquid state theory.


  We prove the Hecke orbit conjecture of Chai--Oort for Shimura varieties of
Hodge type at primes of good reduction, under a mild assumption on the size of
the prime. Our proof uses a new generalisation of Serre--Tate coordinates for
deformation spaces of central leaves in such Shimura varieties, constructed
using work of Caraiani--Scholze and Kim. We use these coordinates to give a new
interpretation of Chai--Oort's notion of strongly Tate-linear subspaces of
these deformation spaces. This lets us prove upper bounds on the local
monodromy of these subspaces using the Cartier--Witt stacks of Bhatt--Lurie. We
also prove a rigidity result in the style of Chai--Oort for strongly
Tate-linear subspaces. Another main ingredient of our proof is a new result on
the local monodromy groups of $F$-isocrystals "coming from geometry", which
should be of independent interest.


  We show that any new physics (NP) which affects B decays with penguin
contributions can be absorbed by redefinitions of the standard-model (SM)
diagrammatic amplitudes. Hence, there are no clean signals of NP in such decays
unless there is an accurate theoretical estimate of parameters or a justifiable
approximation can be made. In all decays with penguin contributions, NP
simultaneously affects pairs of diagrams. The evidence for a large C' from fits
to B-> pi K data is naturally explained if NP contributes to P_EW, since NP
affects the P_EW and C' diagrams as a pair. The weak phase gamma measured in
B-> pi K decays will always agree with its SM value even in the presence of NP,
if the NP contributes in such a way that the amplitudes retain the SM form
after suitable redefinitions.


  We present a theory of magnetotransport phenomena related to the chiral
anomaly in Weyl semimetals. We show that conductivity, thermal conductivity,
thermoelectric and the sound absorption coefficients exhibit strong and
anisotropic magnetic field dependences. We also discuss properties of
magneto-plasmons and magneto-polaritons, whose existence is entirely determined
by the chiral anomaly. Finally, we discuss the conditions of applicability of
the quasi-classical description of electron transport phenomena related to the
chiral anomaly.


  The influence of a chemically or electrically heterogeneous distribution of
interaction sites at a planar substrate on the number density of an adjacent
fluid is studied by means of classical density functional theory (DFT). In the
case of electrolyte solutions the effect of this heterogeneity is particularly
long ranged, because the corresponding relevant length scale is set by the
Debye length which is large compared to molecular sizes. The DFT used here
takes the solvent particles explicitly into account and thus captures
phenomena, inter alia, due to ion-solvent coupling. The present approach
provides closed analytic expressions describing the influence of chemically and
electrically nonuniform walls. The analysis of isolated \delta-like
interactions, isolated interaction patches, and hexagonal periodic
distributions of interaction sites reveals a sensitive dependence of the fluid
density profiles on the type of the interaction, as well as on the size and the
lateral distribution of the interaction sites.


  We used optical confocal microscopy to study optical properties of diamond 50
nm nanocrystals first irradiated with an electron beam, then dispersed as a
colloidal solution and finally deposited on a silica slide. At room
temperature, under CW laser excitation at a wavelength of 514.5 nm we observed
perfectly photostable single Nitrogen-Vacancy (NV) colour defects embedded in
the nanocrystals. From the zero-phonon line around 575 nm in the spectrum of
emitted light, we infer a neutral NV0 type of defect. Such nanoparticle with
intrinsic fluorescence are highly promising for applications in biology where
long-term emitting fluorescent bio-compatible nanoprobes are still missing.


  We demonstrate, for the first time, an all-dielectric metamaterial resonator
in the mid-wave infrared based on high-index tellurium cubic inclusions.
Dielectric resonators are desirable compared to conventional metallo-dielectric
metamaterials at optical frequencies as they are largely angular invariant,
free of ohmic loss, and easily integrated into three-dimensional volumes. With
these low-loss, isotropic elements, disruptive optical metamaterial designs,
such as wide-angle lenses and cloaks, can be more easily realized.


  Denoting the Hausdorff dimension of the Fibonacci Hamiltonian with coupling
$\lambda$ by $\mathrm{HD}_\lambda$, we prove that for all but countably many
$\lambda$, the Hausdorff dimension of the spectrum of the square Fibonacci
Hamiltonian with coupling $\lambda$ is $\min\{2\mathrm{HD}_\lambda, 1\}$. Our
proof relies on the dynamics of the Fibonacci trace map in combination with the
recent result of M. Hochman and P. Shmerkin on the Hausdorff dimension of sums
of Cantor sets which are attractors of regular iterated function systems (Local
entropy averages and projections of fractal measures, Ann. Math. 175 (2012),
1001--1059).


  Recovering sharp images from dual-pixel (DP) pairs with disparity-dependent
blur is a challenging task.~Existing blur map-based deblurring methods have
demonstrated promising results. In this paper, we propose, to the best of our
knowledge, the first framework that introduces the contrastive language-image
pre-training framework (CLIP) to accurately estimate the blur map from a DP
pair unsupervisedly. To achieve this, we first carefully design text prompts to
enable CLIP to understand blur-related geometric prior knowledge from the DP
pair. Then, we propose a format to input a stereo DP pair to CLIP without any
fine-tuning, despite the fact that CLIP is pre-trained on monocular images.
Given the estimated blur map, we introduce a blur-prior attention block, a
blur-weighting loss, and a blur-aware loss to recover the all-in-focus image.
Our method achieves state-of-the-art performance in extensive experiments (see
Fig.~\ref{fig:teaser}).


  A unified approach to studying convergence and stochastic stability of
continuous time consensus protocols (CPs) is presented in this work. Our method
applies to networks with directed information flow; both cooperative and
noncooperative interactions; networks under weak stochastic forcing; and those
whose topology and strength of connections may vary in time. The graph
theoretic interpretation of the analytical results is emphasized. We show how
the spectral properties, such as algebraic connectivity and total effective
resistance, as well as the geometric properties, such the dimension and the
structure of the cycle subspace of the underlying graph, shape stability of the
corresponding CPs. In addition, we explore certain implications of the spectral
graph theory to CP design. In particular, we point out that expanders, sparse
highly connected graphs, generate CPs whose performance remains uniformly high
when the size of the network grows unboundedly. Similarly, we highlight the
benefits of using random versus regular network topologies for CP design. We
illustrate these observations with numerical examples and refer to the relevant
graph-theoretic results.
  Keywords: consensus protocol, dynamical network, synchronization, robustness
to noise, algebraic connectivity, effective resistance, expander, random graph


  We extend categorical semantics of monadic programming to reversible
computing, by considering monoidal closed dagger categories: the dagger gives
reversibility, whereas closure gives higher-order expressivity. We demonstrate
that Frobenius monads model the appropriate notion of coherence between the
dagger and closure by reinforcing Cayley's theorem; by proving that effectful
computations (Kleisli morphisms) are reversible precisely when the monad is
Frobenius; by characterizing the largest reversible subcategory of
Eilenberg-Moore algebras; and by identifying the latter algebras as
measurements in our leading example of quantum computing. Strong Frobenius
monads are characterized internally by Frobenius monoids.


  The phenomenon of PT (parity- and time-reversal) symmetry breaking is
conventionally associated with a change in the complex mode spectrum of a
non-Hermitian system that marks a transition from a purely oscillatory to an
exponentially amplified dynamical regime. In this work we describe a new type
of PT-symmetry breaking, which occurs in the steady-state energy distribution
of open systems with balanced gain and loss. In particular, we show that the
combination of nonlinear saturation effects and the presence of thermal or
quantum noise in actual experiments results in unexpected behavior that differs
significantly from the usual dynamical picture. We observe additional phases
with preserved or `weakly' broken PT symmetry, and an unconventional transition
from a high-noise thermal state to a low-amplitude lasing state with broken
symmetry and strongly reduced fluctuations. We illustrate these effects here
for the specific example of coupled mechanical resonators with
optically-induced loss and gain, but the described mechanisms will be essential
for a general understanding of the steady-state properties of actual
PT-symmetric systems operated at low amplitudes or close to the quantum regime.


  We study the basic integral equation in Lindhard's theory describing the
energy given to atomic motion by nuclear recoils in a pure material when the
atomic binding energy is taken into account. The numerical solution, which
depends only on the slope of the velocity-proportional electronic stopping
power and the binding energy, leads to an estimation of the ionization
efficiency which is in good agreement with the available experimental
measurements for Si and Ge. In this model, the quenching factor for nuclear
recoils features a cut-off at an energy equal to twice the assumed binding
energy. We argue that the model is a reasonable approximation for Ge even for
energies close to the cutoff, while for Si is valid up to recoil energies
greater than ~500 eV.


  Detailed elemental abundance patterns of metal-poor ([Fe/H] ~ -1~dex) stars
in the Galactic bulge indicate that a number of them are consistent with
globular cluster (GC) stars and may be former members of dissolved GCs. This
would indicate that a few per cent of the Galactic bulge was built up from
destruction and/or evaporation of globular clusters. Here an attempt is made to
identify such presumptive stripped stars originating from the massive, inner
Galaxy globular cluster NGC~6441 using its rich RR Lyrae variable star (RRL)
population. We present radial velocities of forty RRLs centered on the globular
cluster NGC~6441. All of the 13 RRLs observed within the cluster tidal radius
have velocities consistent with cluster membership, with an average radial
velocity of 24 +- 5~km/s and a star-to-star scatter of 11~km/s. This includes
two new RRLs that were previously not associated with the cluster. Eight RRLs
with radial velocities consistent with cluster membership but up to three time
the distance from the tidal radius are also reported. These potential
extra-tidal RRLs also have exceptionally long periods, which is a curious
characteristic of the NGC~6441 RRL population that hosts RRLs with periods
longer than seen anywhere else in the Milky Way. As expected of stripped
cluster stars, most are inline with the cluster's orbit. Therefore, either the
tidal radius of NGC~6441 is underestimated and/or we are seeing dissolving
cluster stars stemming from NGC~6441 that are building up the old spheroidal
bulge.


  We consider the problem of quantum temporal imaging in the case where the
time lens is implemented by a Sum Frequency Generation nonlinear process, in
particular when the device is operated close to 100% conversion efficiency. In
the general case where the time lens also presents a finite aperture and a
non-perfect phase-matching the relevant figures of merit, as for example the
temporal resolution, do not have an explicit expression. As a consequence, the
performances of imaging scheme are difficult to assess. Having a reliable
estimation of these figures of merits is particularly important because they
can be significantly different from the regime of low conversion efficiency
usually considered in classical temporal imaging. We show that this problem can
be approached in terms of the eigenmodes of the imaging scheme and we show how
its relevant figures of merit can be extracted from the modal description of
the imaging scheme. As a consequence we obtain criteria allowing to design
imaging schemes with close to unity efficiencies.


  The new quantum number is introduced. It is shown that the conservation of
-number results in the conservation of difference between baryon and lepton
numbers. The problem of quark-lepton symmetry is discussed. It is shown that
the nature of quark-lepton symmetry stems from the fact that the particles of
one generation are subject to the symmetry transformation represented by
4-group of diedr.


  We study boundedness, optimality and attainability of Trudinger-Moser type
maximization problems in the radial and the subcritical homogeneous Sobolev
spaces. In special cases, our inequalities are equivalent to the original
Trudinger-Moser inequalities via a harmonic transplantation. Also, our
inequality converges to the original Trudinger-Moser inequality as taking a
limit including optimal exponent and concentration limit. Finally, we consider
applications of our inequality to elliptic and parabolic problems with
exponential nonlinearity.