  We consider deterministic homogenization (convergence to a stochastic
differential equation) for multiscale systems of the form \[
  x_{k+1} = x_k + n^{-1} a_n(x_k,y_k) + n^{-1/2} b_n(x_k,y_k), \quad y_{k+1} =
T_n y_k, \] where the fast dynamics is given by a family $T_n$ of nonuniformly
expanding maps. Part 1 builds on our recent work on martingale approximations
for families of nonuniformly expanding maps. We prove an iterated weak
invariance principle and establish optimal iterated moment bounds for such
maps. (The iterated moment bounds are new even for a fixed nonuniformly
expanding map T.) The homogenization results are a consequence of this together
with parallel developments on rough path theory in Part 2 by Chevyrev, Friz,
Korepanov, Melbourne & Zhang.


  We present some new theoretical and computational results for the stationary
points of bulk systems. First we demonstrate how the potential energy surface
can be partitioned into catchment basins associated with every stationary point
using a combination of Newton-Raphson and eigenvector-following techniques.
Numerical results are presented for a 256-atom supercell representation of a
binary Lennard-Jones system. We then derive analytical formulae for the number
of stationary points as a function of both system size and the Hessian index,
using a framework based upon weakly interacting subsystems. This analysis
reveals a simple relation between the total number of stationary points, the
number of local minima, and the number of transition states connected on
average to each minimum. Finally we calculate two measures of localisation for
the displacements corresponding to Hessian eigenvectors in samples of
stationary points obtained from the Newton-Raphson-based geometry optimisation
scheme. Systematic differences are found between the properties of eigenvectors
corresponding to positive and negative Hessian eigenvalues, and localised
character is most pronounced for stationary points with low values of the
Hessian index.


  Variability models allow effective building of many custom model variants for
various configurations. Lifted model checking for a variability model is
capable of verifying all its variants simultaneously in a single run by
exploiting the similarities between the variants. The computational cost of
lifted model checking still greatly depends on the number of variants (the size
of configuration space), which is often huge.
  One of the most promising approaches to fighting the configuration space
explosion problem in lifted model checking are variability abstractions. In
this work, we define a novel game-based approach for variability-specific
abstraction and refinement for lifted model checking of the full CTL,
interpreted over 3-valued semantics. We propose a direct algorithm for solving
a 3-valued (abstract) lifted model checking game. In case the result of model
checking an abstract variability model is indefinite, we suggest a new notion
of refinement, which eliminates indefinite results. This provides an iterative
incremental variability-specific abstraction and refinement framework, where
refinement is applied only where indefinite results exist and definite results
from previous iterations are reused.


  Assume that the coefficients of a polynomial in a complex variable are
Laurent polynomials in some complex parameters. The parameter space (a complex
torus) splits into strata corresponding to different combinations of
coincidence of the roots of the polynomial. For generic Laurent polynomials
with fixed Newton polyhedra the Euler characteristics of these strata are also
fixed. We provide explicit formulae for the Euler characteristics of the strata
in terms of the polyhedra of the Laurent polynomials in the cases of degrees 2
and 3. We also obtain some corollaries in combinatorial geometry, which follows
from two different ways of computing the Euler characteristic of the
bifurcation set for a reduced polynomial of degree 2.


  We propose a strategy for searching for theoretically-unanticipated new
physics which avoids a large trials factor by focusing on experimental
strengths. Searches for resonances decaying into pairs of visible particles are
experimentally very powerful due to the localized mass peaks and have a rich
history of discovery. Yet, due to a focus on subsets of theoretically-motivated
models, the landscape of such resonances is far from thoroughly explored. We
survey the existing set of searches, identify untapped experimental
opportunities and discuss the theoretical constraints on models which would
generate such resonances.


  We interpret extremal non-BPS black holes in four dimensions as threshold
bound states of four 1/2-BPS constituents. We verify the no-force condition for
each of the primitive constituents in the probe approximation. Our computations
are for a seed solution with $\bar{D0}-D4$ charges and equal $B$-fields, but
symmetries extend the result to any U-dual frame. We make the constituent model
for the $D0-D6$ system explicit, and also discuss a duality frame where the
constituents are $D3$ branes at angles. We demonstrate stability of the
constituent model in the weak coupling description of the constituent D-branes.
We discuss the relation between the BPS and non-BPS branches of configuration
space.


  Supermassive black holes in the centres of giant elliptical galaxies are
thought to induce chaos and eliminate triaxiality in their hosts. We address
whether this process operates in real systems, by modeling the stellar
kinematics of the old elliptical NGC 4365. This galaxy has a mean stellar
population age > 12 Gyr and is known for its kinematically decoupled core and
skew rotation at larger radii. We fit the two-dimensional mean velocity field
obtained by the SAURON integral-field spectrograph, and the isophotal
ellipticity and position-angle profiles, using the velocity field fitting
approach. We find NGC 4365 to be strongly triaxial (triaxiality parameter T
approximately 0.45) and somewhat flatter than it appears. Axisymmetry or near
axisymmetry (T < 0.1) is ruled out at > 95% confidence. In the most probable
orientation the long axis points roughly toward the observer, extending to the
southwest in projection. Strong triaxiality has persisted for hundreds of
dynamical times, ruling out black holes above 3 x 10^9 solar masses. The
M-sigma relation predicts 4 x 10^8 solar masses, which would not preclude
long-lived triaxiality and is consistent with the observations. NGC 4365 lends
support to a picture in which supermassive black holes, while omnipresent in
luminous giant elliptical galaxies, are not massive enough to alter their
global structure through chaos.


  Definition of a smooth action of a CQG on a compact, smooth manifold is given
and studied. It is shown that a smooth action is always injective. Furthermore
A necessary and sufficient condition for a lift of the smooth action as a
bimodule morphism on the bimodule of one forms has been deduced and it is also
shown to be equivalent to the condition of preserving some Riemannian inner
product on the manifold.


  In this paper we develop a new form of agent-based model for limit order
books based on heterogeneous trading agents, whose motivations are liquidity
driven. These agents are abstractions of real market participants, expressed in
a stochastic model framework. We develop an efficient way to perform
statistical calibration of the model parameters on Level 2 limit order book
data from Chi-X, based on a combination of indirect inference and
multi-objective optimisation. We then demonstrate how such an agent-based
modelling framework can be of use in testing exchange regulations, as well as
informing brokerage decisions and other trading based scenarios.


  A crucial feature not widely accounted for in local helioseismology is that
surface magnetic regions actually open a window from the interior into the
solar atmosphere, and that the seismic waves leak through this window, reflect
high in the atmosphere, and then re-enter the interior to rejoin the seismic
wave field normally confined there. In a series of recent numerical studies
using translation invariant atmospheres, we utilised a "directional
time-distance helioseismology" measurement scheme to study the implications of
the returning fast and Alfv\'en waves higher up in the solar atmosphere on the
seismology at the photosphere (Cally & Moradi 2013; Moradi & Cally 2014). In
this study, we extend our directional time-distance analysis to more realistic
sunspot-like atmospheres to better understand the direct effects of the
magnetic field on helioseismic travel-time measurements in sunspots. In line
with our previous findings, we uncover a distinct frequency-dependant
directional behaviour in the travel-time measurements, consistent with the
signatures of MHD mode conversion. We found this to be the case regardless of
the sunspot field strength or depth of its Wilson depression. We also isolated
and analysed the direct contribution from purely thermal perturbations to the
measured travel times, finding that waves propagating in the umbra are much
more sensitive to the underlying thermal effects of the sunspot.


  In this work, we present STOPNet, a framework for 6-DoF object suction
detection on production lines, with a focus on but not limited to transparent
objects, which is an important and challenging problem in robotic systems and
modern industry. Current methods requiring depth input fail on transparent
objects due to depth cameras' deficiency in sensing their geometry, while we
proposed a novel framework to reconstruct the scene on the production line
depending only on RGB input, based on multiview stereo. Compared to existing
works, our method not only reconstructs the whole 3D scene in order to obtain
high-quality 6-DoF suction poses in real time but also generalizes to novel
environments, novel arrangements and novel objects, including challenging
transparent objects, both in simulation and the real world. Extensive
experiments in simulation and the real world show that our method significantly
surpasses the baselines and has better generalizability, which caters to
practical industrial needs.


  We consider a Brans-Dicke cosmology in five-dimensional space-time.
Neglecting the quadratic and the mixed Brans-Dicke terms in the Einstein
equation, we derive a modified wave equation of the Brans-Dicke field. We show
that, at high energy limit, the 3-brane Brans-Dicke cosmology could be
described as the standard one by changing the equation of state. Finally as an
illustration of the purpose, we show that the dark energy component of the
universe agrees with the observations data.


  To allow for a comparison of theoretical predictions for spin chains with
experimental data, it is often important to take impurity effects as well as
interchain couplings into account. Here we present the field theory for finite
spin chains at finite temperature and calculate experimentally measurable
quantities like susceptibilities and nuclear magnetic resonance spectra. For
the interchain couplings we concentrate on geometries relevant for cuprate spin
chains like Sr$_2$CuO$_3$ and SrCuO$_2$. The field theoretical results are
compared to experimental as well as numerical data obtained by the density
matrix renormalization group.


  Gravitational wave (GW) observatories are discovering binary neutron star
mergers (BNSMs), and in at least one event we were able to track it down in
multiple wavelengths of light, which allowed us to identify the host galaxy.
Using a catalogue of local galaxies with inferred star formation histories and
adopting a BNSM delay time distribution (DTD) model, we investigate the
dependence of BNSM rate on an array of galaxy properties. Compared to the
intrinsic property distribution of galaxies, that of BNSM host galaxies is
skewed toward galaxies with redder colour, lower specific star formation rate,
higher luminosity, and higher stellar mass, reflecting the tendency of higher
BNSM rates in more massive galaxies. We introduce a formalism to efficiently
make forecast on using host galaxy properties to constrain DTD models. We find
comparable constraints from the dependence of BNSM occurrence distribution on
galaxy colour, specific star formation rate, and stellar mass, all better than
those from dependence on $r$-band luminosity. The tightest constraints come
from using individual star formation histories of host galaxies, which reduces
the uncertainties on DTD parameters by a factor of three or more. Substantially
different DTD models can be differentiated with about 10 BNSM detections. To
constrain DTD parameters at 10\% precision level requires about one hundred
detections, achievable with GW observations on a decade time scale.


  The recent proliferation of large-scale text-to-image models has led to
growing concerns that such models may be misused to generate harmful,
misleading, and inappropriate content. Motivated by this issue, we derive a
technique inspired by continual learning to selectively forget concepts in
pretrained deep generative models. Our method, dubbed Selective Amnesia,
enables controllable forgetting where a user can specify how a concept should
be forgotten. Selective Amnesia can be applied to conditional variational
likelihood models, which encompass a variety of popular deep generative
frameworks, including variational autoencoders and large-scale text-to-image
diffusion models. Experiments across different models demonstrate that our
approach induces forgetting on a variety of concepts, from entire classes in
standard datasets to celebrity and nudity prompts in text-to-image models. Our
code is publicly available at https://github.com/clear-nus/selective-amnesia.


  In this paper, we consider the coded-caching broadcast network with user
cooperation, where a server connects with multiple users and the users can
cooperate with each other through a cooperation network. We propose a
centralized coded caching scheme based on a new deterministic placement
strategy and a parallel delivery strategy. It is shown that the new scheme
optimally allocate the communication loads on the server and users, obtaining
cooperation gain and parallel gain that greatly reduces the transmission delay.
Furthermore, we show that the number of users who parallelly send information
should decrease when the users' caching size increases. In other words, letting
more users parallelly send information could be harmful. Finally, we derive a
constant multiplicative gap between the lower bound and upper bound on the
transmission delay, which proves that our scheme is order optimal.


  We prove some "high probability" results on the expected value of the mean
width for random perturbations of random polytopes. The random perturbations
are considered for Gaussian and $p$-stable random vectors, as well as uniform
distributions on $\ell_p^N$-balls and the unit sphere.


  In this paper we consider the inference rules of System P in the framework of
coherent imprecise probabilistic assessments. Exploiting our algorithms, we
propagate the lower and upper probability bounds associated with the
conditional assertions of a given knowledge base, automatically obtaining the
precise probability bounds for the derived conclusions of the inference rules.
This allows a more flexible and realistic use of System P in default reasoning
and provides an exact illustration of the degradation of the inference rules
when interpreted in probabilistic terms. We also examine the disjunctive Weak
Rational Monotony of System P+ proposed by Adams in his extended probability
logic.


  We show that with suitable restrictions on allowable trading strategies, one
has no arbitrage in settings where the traditional theory would admit arbitrage
possibilities. In particular, price processes that are not semimartingales are
possible in our setting, for example, fractional Brownian motion.


  We study possibilities for automated invariant generation in parametric
systems. We use (a refinement of) an algorithm for symbol elimination in theory
extensions to devise a method for iteratively strengthening certain classes of
safety properties to obtain invariants of the system. We identify conditions
under which the method is correct and complete, and situations in which the
method is guaranteed to terminate. We illustrate the ideas on various examples.


  This article describes the life and work of French astrophysicist Evry
Schatzman (1920-2010). He was a pioneer in the study of white dwarfs during the
1940s and was one of the proponents of the wave heating theory of the solar
corona. He made important contributions to the fields of internal stellar
structure, novae, mechanisms of acceleration of cosmic rays, the role of
turbulent diffusion in stellar evolution and its consequences for the lithium
abundance, and the rate of solar neutrinos. Schatzman is mostly recognized as
the creator of the French school of theoretical astrophysics. Although he was
not the first theoretician of astrophysics in his country, he was the first to
have felt the need for a rapid development of this subject in France, and the
first to teach it and to guide the path of many young researchers. Many of them
became involved, and some leaders, in space science.


  We live in a rich and varied acoustic world, which is experienced by
individuals or communities as a soundscape. Computational auditory scene
analysis, disentangling acoustic scenes by detecting and classifying events,
focuses on objective attributes of sounds, such as their category and temporal
characteristics, ignoring the effect of sounds on people and failing to explore
the relationship between sounds and the emotions they evoke within a context.
To fill this gap and to automate soundscape analysis, which traditionally
relies on labour-intensive subjective ratings and surveys, we propose the
soundscape captioning (SoundSCap) task. SoundSCap generates context-aware
soundscape descriptions by capturing the acoustic scene, event information, and
the corresponding human affective qualities. To this end, we propose an
automatic soundscape captioner (SoundSCaper) composed of an acoustic model,
SoundAQnet, and a general large language model (LLM). SoundAQnet simultaneously
models multi-scale information about acoustic scenes, events, and perceived
affective qualities, while LLM generates soundscape captions by parsing the
information captured by SoundAQnet to a common language. The soundscape
caption's quality is assessed by a jury of 16 audio/soundscape experts. The
average score (out of 5) of SoundSCaper-generated captions is lower than the
score of captions generated by two soundscape experts by 0.21 and 0.25,
respectively, on the evaluation set and the model-unknown mixed external
dataset with varying lengths and acoustic properties, but the differences are
not statistically significant. Overall, SoundSCaper-generated captions show
promising performance compared to captions annotated by soundscape experts. The
models' code, LLM scripts, human assessment data and instructions, and expert
evaluation statistics are all publicly available.


  Deep optical spectroscopic surveys of galaxies provide us a unique
opportunity to investigate rest-frame ultra-violet (UV) emission line
properties of galaxies at ${z \sim 2-4.5}$. Here we combine VLT/MUSE Guaranteed
Time Observations of the Hubble Deep Field South, Ultra Deep Field, COSMOS, and
several quasar fields with other publicly available data from VLT/VIMOS and
VLT/FORS2 to construct a catalogue of HeII${\lambda}$1640 emitters at
${z\sim2}$. The deepest areas of our MUSE pointings reach a ${3\sigma}$ line
flux limit of 3.1${\times}$10-19 erg/ s/ cm$^2$. After discarding broad line
active galactic nuclei we find 13 HeII${\lambda}$1640 detections from MUSE with
a median MUV = $-20.1$ and 21 tentative HeII${\lambda}$1640 detections from
other public surveys. Excluding Ly${\alpha}$, all except two galaxies in our
sample show at least one other rest-UV emission line, with
CIII]${\lambda}$1907,${\lambda}$1909 being the most prominent. We use
multi-wavelength data available in the Hubble legacy fields to derive basic
galaxy properties of our sample via spectral energy distribution fitting
techniques. Taking advantage of the high quality spectra obtained by MUSE
(${\sim10 - 30}$h of exposure time per pointing), we use photo-ionisation
models to study the rest-UV emission line diagnostics of the
HeII${\lambda}$1640 emitters. Line ratios of our sample can be reproduced by
moderately sub-solar photo-ionisation models, however, we find that including
effects of binary stars lead to degeneracies in most free parameters. Even
after considering extra ionising photons produced by extreme sub-solar
metallicity binary stellar models, photo-ionisation models are unable to
reproduce rest-frame HeII${\lambda}$1640 equivalent widths (${\sim}$ 0.2 - 10
A), thus additional mechanisms are necessary in models to match the observed
HeII${\lambda}$1640 properties.


  In hydrogen bonded systems, nuclear quantum effects such as zero-point motion
and tunneling can significantly affect their material properties through
underlying physical and chemical processes. Presently, direct observation of
the influence of nuclear quantum effects on the strength of hydrogen bonds with
resulting structural and electronic implications remains elusive, leaving
opportunities for deeper understanding to harness their fascinating properties.
We studied hydrogen-bonded one-dimensional quinonediimine molecular networks
which may adopt two isomeric electronic configurations via proton transfer.
Herein, we demonstrate that concerted proton transfer promotes a delocalization
of {\pi}-electrons along the molecular chain, which enhances the cohesive
energy between molecular units, increasing the mechanical stability of the
chain and giving rise to new electronic in-gap states localized at the ends.
These findings demonstrate the identification of a new class of isomeric
hydrogen bonded molecular systems where nuclear quantum effects play a dominant
role in establishing their chemical and physical properties. We anticipate that
this work will open new research directions towards the control of mechanical
and electronic properties of low-dimensional molecular materials via concerted
proton tunneling.


  The proliferation of edge devices and the rapid growth of IoT data have
called forth the edge computing paradigm. Function-as-a-service (FaaS) is a
promising computing paradigm to realize edge computing. This paper explores the
feasibility and advantages of FaaS-based edge computing. It also studies the
research challenges that should be addressed in the design of such systems,
which are 1) the quick decomposing and recomposing of applications, 2) the
trade-off between performance and isolation of sandbox mechanisms, and 3)
distributed scheduling. The challenges are illustrated by evaluating existing
FaaS-based edge platforms, AWS IoT Greengrass, and OpenFaaS.


  In this article we construct the fundamental solutions for the Klein-Gordon
equation in de Sitter spacetime. We use these fundamental solutions to
represent solutions of the Cauchy problem and to prove $L^p-L^q$ estimates for
the solutions of the equation with and without a source term.


  We perform a systematic study of the Zitterbewegung effect of fermions, which
are described by a Gaussian wave with broken spatial-inversion symmetry in a
three-dimensional low-energy Weyl semimetal. Our results show that the motion
of fermions near the Weyl points is characterized by rectilinear motion and
Zitterbewegung oscillation. The ZB oscillation is affected by the width of the
Gaussian wave packet, the position of the Weyl node, and the chirality and
anisotropy of the fermions. By introducing a one-dimensional cosine potential,
the new generated massless fermions have lower Fermi Velocities, which results
in a robust relativistic oscillation. Modulating the height and periodicity of
periodic potential demonstrates that the ZB effect of fermions in the different
Brillouin zones exhibits quasi-periodic behavior. These results may provide an
appropriate system for probing the Zitterbewegung effect experimentally.


  We show how the efficiency of a logical Bell measurement (BM) can be
calculated for arbitrary CSS codes with the experimentally important constraint
of using only transversal static linear-optical BMs on the physical
single-photon qubit level. For this purpose, we utilize the codes' description
in terms of stabilizers in order to calculate general efficiencies for the
loss-free case, but also for specific cases including photon loss. These
efficiencies can be, for instance, used for obtaining transmission rates of
all-optical quantum repeaters. In the loss-free case, we demonstrate that the
important class of CSS codes with identical physical-qubit support for the two
logical Pauli ($Z$ and $X$) operators can only achieve a logical BM efficiency
of $\frac{1}{2}$ if one always employs the same ancilla-free static linear
optical BMs on the physical level. We apply our methods to various CSS codes
including two-dimensional planar color and planar surface codes. We then find
that in many cases, the fixed use of the standard linear optical BM for all
physical BMs is suboptimal and performing linear optical transformations before
doing the standard linear optical BM (still without any ancillary photons and
without any feedforward) can increase the efficiency enormously. In fact, using
this generalization in the no-loss (or sometimes also in the low-loss) case
allows us, on the one hand, to improve the logical BM efficiency of quantum
parity codes compared to previously known results and, on the other hand, it
also enables us to enhance the efficiency of two-dimensional planar color
codes, whose efficiency is otherwise subject to the above $\frac{1}{2}$ bound,
to arbitrarily close to unity.


  The vector space spanned by rooted forests admits two graded bialgebra
structures. The first is defined by A. Connes and D. Kreimer using admissible
cuts, and the second is defined by D. Calaque, K. Ebrahimi-Fard and the second
author using contraction of trees. In this article we define the doubling of
these two spaces. We construct two bialgebra structures on these spaces which
are in interaction, as well as two related associative products obtained by
dualization. We also show that these two bialgebras verify a commutative
diagram similar to the diagram verified D. Calaque, K. Ebrahimi-Fard and the
second author in the case of rooted trees Hopf algebra, and by the second
author in the case of cycle free oriented graphs.


  This review discusses the current status of supermassive black hole research,
as seen from a purely observational standpoint. Since the early '90s, rapid
technological advances, most notably the launch of the Hubble Space Telescope,
the commissioning of the VLBA and improvements in near-infrared speckle imaging
techniques, have not only given us incontrovertible proof of the existence of
supermassive black holes, but have unveiled fundamental connections between the
mass of the central singularity and the global properties of the host galaxy.
It is thanks to these observations that we are now, for the first time, in a
position to understand the origin, evolution and cosmic relevance of these
fascinating objects.


  The pseudo scalar form factor, which represents the pseudo scalar quark
density distribution due to finite quark masses on the nucleon, is shown to
manifest itself with the induced pseudo scalar form factor in the $L_0^+$
amplitude for the charged pion electro-production. Both form factors show their
own peculiar momentum dependence. Under the approximation on which the
Goldberg-Treimann relation holds, a sum of both form factors' contributions
accounts for the t-channel contribution in the charged pion electro-production
near threshold.


  Using a three neutrino framework we investigate bounds for the effective
Majorana neutrino mass matrix. The mass measured in neutrinoless double beta
decay is its (11) element. Lepton-number and -flavor violating processes
sensitive to each element are considered and limits on branching ratios or
cross sections are given. Those processes include $\mu^- e^+$ conversion, $K^+
\to \pi^- \mu^+ \mu^+$ or recently proposed high-energy scattering processes at
HERA. Including all possible mass schemes, the three solar solutions and other
allowed possibilities, there is a total of 80 mass matrices. The obtained
indirect limits are up to 14 orders of magnitude more stringent than direct
ones. It is investigated how neutrinoless double beta decay may judge between
different mass and mixing schemes as well as solar solutions. Prospects for
detecting processes depending on elements of the mass matrix are also
discussed.


  We investigate the space of abelian relations of planar webs admitting
infinitesimal automorphisms. As an application, we construct 4k-14 new
algebraic families of global exceptionnal k-webs on the projective plane, for
each k >4.


  The aim of this paper, is to study electrical cardiography problem. Thus, we
construct the state space system of this model as mathematical model. Moreover,
we present some definitions and results which is described some concepts of
linear control system analysis related to this problem. More precisely, the
sufficient conditions which characterize the observability notion of linear
dynamical controlled system are presented and discussed. Finally, we prove
that, the electrical cardiography model is completely observable system over
finite time.


  This paper introduces ViscoNet, a novel method that enhances text-to-image
human generation models with visual prompting. Unlike existing methods that
rely on lengthy text descriptions to control the image structure, ViscoNet
allows users to specify the visual appearance of the target object with a
reference image. ViscoNet disentangles the object's appearance from the image
background and injects it into a pre-trained latent diffusion model (LDM) model
via a ControlNet branch. This way, ViscoNet mitigates the style mode collapse
problem and enables precise and flexible visual control. We demonstrate the
effectiveness of ViscoNet on human image generation, where it can manipulate
visual attributes and artistic styles with text and image prompts. We also show
that ViscoNet can learn visual conditioning from small and specific object
domains while preserving the generative power of the LDM backbone.


  The scheme-dependence of the renormalization group (RG) flow has been
investigated in the local potential approximation for two-dimensional periodic,
sine-Gordon type field-theoric models discussing the applicability of various
functional RG methods in detail. It was shown that scheme-independent
determination of such physical parameters is possible as the critical frequency
(temperature) at which Kosterlitz-Thouless-Berezinskii type phase transition
takes place in the sine-Gordon and the layered sine-Gordon models, and the
critical ratio characterizing the Ising type phase transition of the massive
sine-Gordon model. For the latter case the Maxwell construction represents a
strong constraint on the RG flow which results in a scheme-independent infrared
value for the critical ratio. For the massive sine-Gordon model also the
shrinking of the domain of the phase with spontaneously broken periodicity is
shown to take place due to the quantum fluctuations.


  We present results from a high-resolution and large-scale hybrid (fluid
electrons and particle-in-cell protons) two-dimensional numerical simulation of
decaying turbulence. Two distinct spectral regions (separated by a smooth break
at proton scales) develop with clear power-law scaling, each one occupying
about a decade in wave numbers. The simulation results exhibit simultaneously
several properties of the observed solar wind fluctuations: spectral indices of
the magnetic, kinetic, and residual energy spectra in the magneto-hydrodynamic
(MHD) inertial range along with a flattening of the electric field spectrum, an
increase in magnetic compressibility, and a strong coupling of the cascade with
the density and the parallel component of the magnetic fluctuations at
sub-proton scales. Our findings support the interpretation that in the solar
wind large-scale MHD fluctuations naturally evolve beyond proton scales into a
turbulent regime that is governed by the generalized Ohm's law.


  We outline the theory of sets with distributive operations: multishelves and
multispindles, with examples provided by semi-lattices, lattices and skew
lattices. For every such a structure we define multi-term distributive homology
and show some of its properties. The main result is a complete formula for the
homology of a finite distributive lattice. We also indicate the answer for
unital spindles and conjecture the general formula for semi-lattices and some
skew lattices. Then we propose a generalization of a lattice as a set with a
number of idempotent operations satisfying the absorption law.


  In this paper, we have investigated a bulk viscous anisotropic Universe and
constrained its model parameters with recent $H(z)$ and Pantheon compilation
data. Using cosmic chronometric technique, we estimate the present value of
Hubble's constant as $H_{0} = 69.39 \pm 1.54~km~s^{-1}Mpc^{-1}$, $70.016 \pm
1.65~km~s^{-1}Mpc^{-1}$ and $69.36 \pm 1.42~km~s^{-1}Mpc^{-1}$ by bounding our
derived model with recent $H(z)$ data, Pantheon and joint $H(z)$ and Pantheon
data respectively. The present age of the Universe is specified as $t_0=
0.9796H_0^{-1}\sim 13.79$ Gyrs. The model favours a transitioning Universe with
the transition red-shift as $z_{t} = 0.73$. We have reconstructed the jerk
parameter using the observational data sets. From the analysis of the jerk
parameter, it is observed that, our derived model shows a marginal departure
from the concordance $\Lambda$CDM model.


  A phenomenological description of time evolution of atomic matter waves
inside a spiral shaped atomic-wave guide is presented in this report. We study
three related topics: (i) the effective Hamiltonian and the time-development
equation governing the matter waves; (ii) wavefunctions describing the matter
waves in the noncoplanar atom guide; (iii) showing that such wavefunctions
obtained is just the eigenstates of the atomic momentum operator. It is
believed that both the idea and the results presented here may have relevance
to some fundamental problems of atom optics.


  We consider the bottom-up holographic models for QCD which contain the
ultraviolet (UV) cutoff. Such models are supposed to describe exclusively the
low-energy sector of QCD. The introduction of UV cutoff in the soft wall model
is shown to result in a model with qualitatively different predictions. The
ensuing model seems to be able to incorporate the constituent quark mass. It is
also demonstrated that in order to reproduce the results of the usual soft wall
model for the vector and higher spin mesons in the presence of the UV cutoff
one can consider the flat bulk space with a modified dilaton background.


  Human linguistic capacity is often characterized by compositionality and the
generalization it enables -- human learners can produce and comprehend novel
complex expressions by composing known parts. Several benchmarks exploit
distributional control across training and test to gauge compositional
generalization, where certain lexical items only occur in limited contexts
during training. While recent work using these benchmarks suggests that
pretrained models achieve impressive generalization performance, we argue that
exposure to pretraining data may break the aforementioned distributional
control. Using the COGS benchmark of Kim and Linzen (2020), we test two
modified evaluation setups that control for this issue: (1) substituting
context-controlled lexical items with novel character sequences, and (2)
substituting them with special tokens represented by novel embeddings. We find
that both of these setups lead to lower generalization performance in T5
(Raffel et al., 2020), suggesting that previously reported results have been
overestimated due to uncontrolled lexical exposure during pretraining. The
performance degradation is more extreme with novel embeddings, and the
degradation increases with the amount of pretraining data, highlighting an
interesting case of inverse scaling.


  A manifestly relativistically covariant form of the van der Pol oscillator in
1+1 dimensions is studied. We show that the driven relativistic equations, for
which $x$ and $t$ are coupled, relax very quickly to a pair of identical
decoupled equations, due to a rapid vanishing of the ``angular momentum'' (the
boost in 1+1 dimensions). A similar effect occurs in the damped driven
covariant Duffing oscillator previously treated. This effect is an example of
entrainment, or synchronization (phase locking), of coupled chaotic systems.
The Lyapunov exponents are calculated using the very efficient method of Habib
and Ryne. We show a Poincar\'e map that demonstrates this effect and maintains
remarkable stability in spite of the inevitable accumulation of computer error
in the chaotic region. For our choice of parameters, the positive Lyapunov
exponent is about 0.242 almost independently of the integration method.


  The Solar Wind ANisotropies (SWAN) all-sky hydrogen Lyman-alpha camera on the
SOlar and Heliospheric Observer (SOHO) satellite observed the hydrogen coma of
comet C/2017 S3 (PanSTARRS) for the last month of its activity from 2018 July 4
to August 4 and what appears to have been its final disintegration just 11 days
before its perihelion on August 15. The hydrogen coma indicated water
production had a small outburst on July 8 at a heliocentric distance of 1.1AU
and then a much larger one on July 20 at 0.8 AU. Over the following two weeks
the water production dropped by more than a factor of ten after which it was no
longer detectable. The behavior is reminiscent of comet C/1999 S4 (LINEAR) in
2000, which had a few small outbursts on its inbound orbit and a major outburst
at a heliocentric distance of about 0.8 AU, which was close to its perihelion,
followed by its complete disintegration that was documented by several sets of
observations including SWAN. C/2017 S3 (PanSTARRS) however had a much larger
water production rate than C/ 1999 S4 (LINEAR). Here we estimate the size of
the nucleus of C/2017 S3 just before its final outburst and apparent
disintegration was estimated using the total amount of water produced during
its last weeks for a range of values of the refractory/ice ratio in the
nucleus. We also determine the size distribution of the disintegrating
particles as the comet faded.


  Using a Nd:YVO4 microchip laser with a relaxation frequency in the megahertz
range, we have experimentally compared a heterodyne interferometer based on a
Michelson configuration with an autodyne interferometer based on the laser
optical feedback imaging (LOFI) method regarding their signal to noise ratios.
In the heterodyne configuration, the beating between the reference beam and the
signal beam is realized outside the laser cavity while in the autodyne
configuration, the wave beating takes place inside the laser cavity and the
relaxation oscillations of the laser intensity then play an important part. For
a given laser output power, object under investigation and detection noise
level, we have determined the amplification gain of the LOFI interferometer
compared to the heterodyne interferometer. LOFI interferometry is demonstrated
to show higher performances than heterodyne interferometry for a wide range of
laser power and detection level of noise. The experimental results are in good
agreement with the theoretical predictions.


  We present strong bounds on the sum of three active neutrino masses ($\sum
m_{\nu}$) in various cosmological models. We use the following baseline
datasets: CMB temperature data from Planck 2015, BAO measurements from SDSS-III
BOSS DR12, the newly released SNe Ia dataset from Pantheon Sample, and a prior
on the optical depth to reionization from 2016 Planck Intermediate results. We
constrain cosmological parameters in $\Lambda CDM$ model with 3 massive active
neutrinos. For this $\Lambda CDM+\sum m_{\nu}$ model we find a upper bound of
$\sum m_{\nu} <$ 0.152 eV at 95$\%$ C.L. Adding the high-$l$ polarization data
from Planck strengthens this bound to $\sum m_{\nu} <$ 0.118 eV, which is very
close to the minimum required mass of $\sum m_{\nu} \simeq$ 0.1 eV for inverted
hierarchy. This bound is reduced to $\sum m_{\nu} <$ 0.110 eV when we also vary
r, the tensor to scalar ratio ($\Lambda CDM+r+\sum m_{\nu}$ model), and add an
additional dataset, BK14, the latest data released from the Bicep-Keck
collaboration. This bound is further reduced to $\sum m_{\nu} <$ 0.101 eV in a
cosmology with non-phantom dynamical dark energy ($w_0 w_a CDM+\sum m_{\nu}$
model with $w(z)\geq -1$ for all $z$). Considering the $w_0 w_a CDM+r+\sum
m_{\nu}$ model and adding the BK14 data again, the bound can be even further
reduced to $\sum m_{\nu} <$ 0.093 eV. For the $w_0 w_a CDM+\sum m_{\nu}$ model
without any constraint on $w(z)$, the bounds however relax to $\sum m_{\nu} <$
0.276 eV. Adding a prior on the Hubble constant ($H_0 = 73.24\pm 1.74$
km/sec/Mpc) from Hubble Space Telescope (HST), the above mentioned bounds
further improve to $\sum m_{\nu} <$ 0.117 eV, 0.091 eV, 0.085 eV, 0.082 eV,
0.078 eV and 0.247 eV respectively. This substantial improvement is mostly
driven by a more than 3$\sigma$ tension between Planck 2015 and HST
measurements of $H_0$ and should be taken cautiously. (abstract abridged)


  In this paper, a filtering approach for the 3D magnetic resonance imaging
(MRI) assuming a Rician model for noise is addressed. Our denoising method is
based on the Conventional Approach (CA) proposed to deal with the noise issue
in the squared domain of the acquired magnitude MRI, where the noise
distribution follows a Chi-square model rather than the Rician one. In the CA
filtering method, the local samples around each voxel is used to estimate the
unknown signal value. Intrinsically, such a method fails to achieve the best
results where the underlying signal values have different statistical
properties. On the contrary, our proposal takes advantage of the data
redundancy and self-similarity properties of real MR images to improve the
noise removal performance. In other words, in our approach, the statistical
momentums of the given 3D MR volume are first calculated to explore the similar
patches inside a defined search volume. Then, these patches are put together to
obtain the noise-free value for each voxel under processing. The experimental
results on the synthetic as well as the clinical MR data show our proposed
method outperforms the other compared denoising filters.


  Deep speaker embedding extractors have already become new state-of-the-art
systems in the speaker verification field. However, the problem of verification
score calibration for such systems often remains out of focus. An irrelevant
score calibration leads to serious issues, especially in the case of unknown
acoustic conditions, even if we use a strong speaker verification system in
terms of threshold-free metrics. This paper presents an investigation over
several methods of score calibration: a classical approach based on the
logistic regression model; the recently presented magnitude estimation network
MagnetO that uses activations from the pooling layer of the trained deep
speaker extractor and generalization of such approach based on separate scale
and offset prediction neural networks. An additional focus of this research is
to estimate the impact of score normalization on the calibration performance of
the system. The obtained results demonstrate that there are no serious problems
if in-domain development data are used for calibration tuning. Otherwise, a
trade-off between good calibration performance and threshold-free system
quality arises. In most cases using adaptive s-norm helps to stabilize score
distributions and to improve system performance. Meanwhile, some experiments
demonstrate that novel approaches have their limits in score stabilization on
several datasets.


  A new method of measuring the pressure anisotropy in the early stage of
heavy-ion collisions is discussed. It is shown that the transverse momentum
spectra, elliptic flow and interferometry radii are not sensitive to the early
anisotropy. We propose the directed flow as a measure of the early transverse
and longitudinal pressures. Calculations indicate that the transverse and
longitudinal pressures equilibrate in less than 0.25 fm/c.


  We discuss joint temporal and contemporaneous aggregation of $N$ independent
copies of AR(1) process with random-coefficient $a \in [0,1)$ when $N$ and time
scale $n$ increase at different rate. Assuming that $a$ has a density,
regularly varying at $a = 1$ with exponent $-1 < \beta < 1$, different joint
limits of normalized aggregated partial sums are shown to exist when
$N^{1/(1+\beta)}/n$ tends to (i) $\infty$, (ii) 0, (iii) $0 < \mu < \infty$.
The limit process arising under (iii) admits a Poisson integral representation
on $(0,\infty) \times C(\mathbb{R})$ and enjoys "intermediate" properties
between fractional Brownian motion limit in (i) and sub-Gaussian limit in (ii).


  We investigate the vertical metallicity gradients of five mono-age stellar
populations between 0 and 11 Gyr for a sample of 18 435 dwarf stars selected
from the cross-matched Tycho-Gaia Astrometric Solution (TGAS) and RAdial
Velocity Experiment (RAVE) Data Release 5. We find a correlation between the
vertical metallicity gradients and age, with no vertical metallicity gradient
in the youngest population and an increasingly steeper negative vertical
metallicity gradient for the older stellar populations. The metallicity at disc
plane remains almost constant between 2 and 8 Gyr, and it becomes significantly
lower for the $8 < \tau \leqslant 11$ Gyr population. The current analysis also
reveals that the intrinsic dispersion in metallicity increases steadily with
age. We discuss that our results are consistent with a scenario that (thin)
disc stars formed from a flaring (thin) star-forming disc.


  We examine the isentropic QCD equation of state within a quasi-particle model
being adjusted to first principle QCD calculations of two quark flavours. In
particular, we compare with Taylor expansion coefficients of energy and entropy
densities and with the isentropic trajectories describing the hydrodynamical
expansion of a heavy-ion collision fireball.


  A link is established between the spin-fermion (SF) model of the cuprates and
the approach based on the analogy between the physics of doped Mott insulators
in two dimensions and the physics of fermionic ladders. This enables one to use
nonperturbative results derived for fermionic ladders to move beyond the
large-N approximation in the SF model. It is shown that the paramagnon exchange
postulated in the SF model has exactly the right form to facilitate the
emergence of the fully gapped d-Mott state in the region of the Brillouin zone
at the hot spots of the Fermi surface. Hence the SF model provides an adequate
description of the pseudogap.


  In this work, we study solitary waves in a (2+1)-dimensional variant of the
defocusing nonlinear Schr\"odinger (NLS) equation, the so-called Camassa-Holm
NLS (CH-NLS) equation. We use asymptotic multiscale expansion methods to reduce
this model to a Kadomtsev--Petviashvili (KP) equation. The KP model includes
both the KP-I and KP-II versions, which possess line and lump soliton
solutions. Using KP solitons, we construct approximate solitary wave solutions
on top of the stable continuous-wave solution of the original CH-NLS model,
which are found to be of both the dark and anti-dark type. We also use direct
numerical simulations to investigate the validity of the approximate solutions,
study their evolution, as well as their head-on collisions.


  We consider the minimization problem of the functional given by the sum of
the fractional perimeter and a general Riesz potential, which is one
generalization of Gamow's liquid drop model. We first show the existence of
minimizers for any volumes if the kernel of the Riesz potential decays faster
than that of the fractional perimeter. Secondly, we show the existence of
generalized minimizers for any volumes if the kernel of the Riesz potential
just vanishes at infinity. Finally, we study the asymptotic behavior of
minimizers when the volume goes to infinity and we prove that a sequence of
minimizers converges to the Euclidean ball up to translations if the kernel of
the Riesz potential decays sufficiently fast.


  In this study, we apply a novel combination of close proximity and room-scale
risk assessment approaches for people sharing public transport environments to
predict their contagion risk due to SARS-CoV-2 respiratory infection. In
particular, the individual infection risk of susceptible subjects and the
transmissibility of SARS-CoV-2 (expressed through the reproduction number) are
evaluated for two types of buses, differing in terms of exposure time and
crowding index: urban and long-distance buses. Infection risk and reproduction
number are calculated for different scenarios as a function of the ventilation
rates (both measured and estimated according to standards), crowding indexes,
and travel times. The results show that for urban buses, the close proximity
contribution significantly affects the maximum occupancy to maintain a
reproductive number of < 1. In particular, full occupancy of the bus would be
permitted only for an infected subject breathing, whereas for an infected
subject speaking, masking would be required. For long-distance buses, full
occupancy of the bus can be maintained only if specific mitigation solutions
are simultaneously applied. For example, for an infected person speaking for 1
h, appropriate filtration of the recirculated air and simultaneous use of FFP2
masks would permit full occupancy of the bus for a period of almost 8 h.
Otherwise, a high percentage of immunized persons (> 80%) would be needed.


  Electron-positron pair production from vacuum is studied in combined
background fields, a binding electric potential well and a laser field. The
production process is triggered by the interactions between the bound states in
the potential well and the continuum states in the Dirac sea. By tuning the
binding potential well, the pair production can be strongly affected by the
locality of the bound states. The narrower bound states in position space are
more efficient for pair production. This is in contrast to what is commonly
expected that the wider extended bound states have larger region to interact
with external fields and would thus create more particles. This surprise can be
explained as the more localized bound states have a much wider extension in the
momentum space, which can enhance the bound-continuum interactions in the
creation process. This enhancement manifests itself in both perturbative and
non-perturbative production regimes.


  Increasing evidences suggest that the Galactic halo is lumpy on kpc scales
due to the accretion of at least a dozen small galaxies (LMC/SMC, Sgr, Fornax
etc.). Faint stars in such lumpy structures can significant microlense a
background star with an optical depth $10^{-7}-10^{-6}$, which is comparable to
the observed value to the LMC (Alcock et al. 1996c). The observed several
microlensing events towards the LMC can be explained by a tidal debris tail
lying in the Magellanic plane if the progenitor of the Magellanic Clouds and
Stream and other satellite galaxies in the Magellanic plane has a mass about
twice that of the disc of the LMC. The LMC stars can either lense stars in the
debris tail behind the LMC, or be lensed by stars in the part of debris tail in
front of the LMC. The models are consistent with an elementary particle
dominated Galactic halo without massive compact halo objects (MACHOs). They
also differ from Sahu's (1994) LMC-self-lensing model by predicting a higher
optical depth and event rate and less concentration of events to the LMC
center.


  Some numerical calculations are presented on the dependence of the average
mode count and average mode density of electromagnetic cavities on their
specific geometric design, based on the generalized Weyl law. The analysis
focuses on a chaotic quasi-cubic cavity furnished with curved wave diffractors
placed on its interior surface. The focus is on a design that increases the
mode density and Q at relatively low frequencies. The results are of interest
in reducing the `lowest usable frequency' and increasing the maximum field
strength inside mode-stirred reverberation chambers.


  With the rapid development of crowdsourcing platforms that aggregate the
intelligence of Internet workers, crowdsourcing has been widely utilized to
address problems that require human cognitive abilities. Considering great
dynamics of worker arrival and departure, it is of vital importance to design a
task assignment scheme to adaptively select the most beneficial tasks for the
available workers. In this paper, in order to make the most efficient
utilization of the worker labor and balance the accuracy of answers and the
overall latency, we a) develop a parameter estimation model that assists in
estimating worker expertise, question easiness and answer confidence; b)
propose a \textit{quality-assured synchronized task assignment scheme} that
executes in batches and maximizes the number of potentially completed questions
(MCQ) within each batch. We prove that MCQ problem is NP-hard and present two
greedy approximation solutions to address the problem. The effectiveness and
efficiency of the approximation solutions are further evaluated through
extensive experiments on synthetic and real datasets. The experimental results
show that the accuracy and the overall latency of the MCQ approaches outperform
the existing online task assignment algorithms in the synchronized task
assignment scenario.


  We show that $L_1$-norm of linear combinations (with scalar or vector
coefficients) of products of i.i.d. nonnegative mean one random variables is
comparable to $l_1$-norm of coefficients.


  In recent years, there has been an increased need for the use of active
systems - systems required to act automatically based on events, or changes in
the environment. Such systems span many areas, from active databases to
applications that drive the core business processes of today's enterprises.
However, in many cases, the events to which the system must respond are not
generated by monitoring tools, but must be inferred from other events based on
complex temporal predicates. In addition, in many applications, such inference
is inherently uncertain. In this paper, we introduce a formal framework for
knowledge representation and reasoning enabling such event inference. Based on
probability theory, we define the representation of the associated uncertainty.
In addition, we formally define the probability space, and show how the
relevant probabilities can be calculated by dynamically constructing a Bayesian
network. To the best of our knowledge, this is the first work that enables
taking such uncertainty into account in the context of active systems.
herefore, our contribution is twofold: We formally define the representation
and semantics of event composition for probabilistic settings, and show how to
apply these extensions to the quantification of the occurrence probability of
events. These results enable any active system to handle such uncertainty.


  Generalizing previous work we propose how to superpose spinning black holes
in a Kerr-Schild initial slice. This superposition satisfies several physically
meaningful limits, including the close and the far ones. Further we consider
the close limit of two black holes with opposite angular momenta and explicitly
solve the constraint equations in this case. Evolving the resulting initial
data with a linear code, we compute the radiated energy as a function of the
masses and the angular momenta of the black holes.


  We prove that ideal sub-Riemannian manifolds (i.e., admitting no non-trivial
abnormal minimizers) support interpolation inequalities for optimal transport.
A key role is played by sub-Riemannian Jacobi fields and distortion
coefficients, whose properties are remarkably different with respect to the
Riemannian case. As a byproduct, we characterize the cut locus as the set of
points where the squared sub-Riemannian distance fails to be semiconvex,
answering to a question raised by Figalli and Rifford in [Geom. Funct. Anal.
(2010) 20: 124].
  As an application, we deduce sharp and intrinsic Borell-Brascamp-Lieb and
geodesic Brunn-Minkowski inequalities in the aforementioned setting. For the
case of the Heisenberg group, we recover in an intrinsic way the results
recently obtained by Balogh, Krist\'aly and Sipos in [Calc. Var. PDE (2018) 57:
61], and we extend them to the class of generalized H-type Carnot groups. Our
results do not require the distribution to have constant rank, yielding for the
particular case of the Grushin plane a sharp measure contraction property and a
sharp Brunn-Minkowski inequality.


  We present a computational study of the parametric excitation of spin waves
in thin film disks with a mode-resolved approach. The method involves
projecting out the time-dependent magnetization, computed using micromagnetics
simulations, onto the spatial profile of the eigenmodes that are obtained from
the linearization of the equations of motion. Unlike spectral analysis in the
frequency domain, the projection allows for the analysis of transient mode
dynamics under parametric excitation. We apply this method to parallel pumping
of quantized spin wave modes in in-plane magnetized thin-film disks, where
phenomena like frequency pulling, mutual phase locking, and higher-order magnon
scattering processes are identified.


  Now that theta13 is known to be large, a medium baseline reactor experiment
can observe the fine structure of the electron antineutrino survival
probability curve, approximately periodic oscillations in L/E with wavelength
4pi/Delta M^2_31. The periodicity with respect to L/E is broken by 2-3
oscillations which, in the case of the normal (inverted) hierarchy, shift the
first 16 oscillations nearly 1% higher (lower) and move the next 16 lower
(higher). The energy of each peak determines a particular combination of the
mass differences, for example cos^2(theta12)Delta M^2_31 + sin^2(theta12)Delta
M^2_32 for nearly all peaks visible at baselines under 40 km. Comparing these
combinations with each other or with NOvA results one can in principle
determine the mass hierarchy. Alternately, as the Fourier transforms of the 1-3
and 2-3 oscillation probabilities are out of phase by the 1-2 oscillation
probability, near the maximum of the 1-2 oscillation the complex phase of the
total survival probability can be used to determine the hierarchy. Two
interference effects make this task difficult. First, kilometer distances
between the reactors reduce the amplitudes of peaks below about 4 MeV. Second,
even reactors 100 or more kilometers away significantly obscure the 1-2
oscillation maximum, which also complicates a measurement of the solar mixing
angle with a single detector.


  We present a novel statistical treatment, the "metastatistics of extreme
events", for calculating the frequency of extreme events. This approach, which
is of general validity, is the proper statistical framework to address the
problem of data with statistical inhomogeneities. By use of artificial
sequences, we show that the metastatistics produce the correct predictions
while the traditional approach based on the generalized extreme value
distribution does not. An application of the metastatistics methodology to the
case of extreme event to rainfall daily precipitation is also presented.


  Given a finite transitive permutation group $G$, we investigate number fields
$F/\mathbb{Q}$ of Galois group $G$ whose discriminant is only divisible by
small prime powers. This generalizes previous investigations of number fields
with squarefree discriminant. In particular, we obtain a comprehensive result
on number fields with cubefree discriminant. Our main tools are
arithmetic-geometric, involving in particular an effective criterion on
ramification in specializations of Galois covers.


  With the advent of computers, one needs algebraic structures that can
simultaneously work with bulk data. One such algebraic structure, namely,
n-linear algebras of type I are introduced in this book and its applications to
n-Markov chains and n-Leontief models are given. These structures can be
thought of as the generalization of bilinear algebras and bivector spaces.
Several interesting n-linear algebra properties are proved.
  This book has four chapters. The first chapter just introduces n-group which
is essential for the definition of n-vector spaces and n-linear algebras of
type I. Chapter two gives the notion of n-vector spaces and several related
results which are analogues of the classical linear algebra theorems. In case
of n-vector spaces, we can define several types of linear transformations.
  The notion of n-best approximations can be used for error correction in
coding theory. The notion of n-eigen values can be used in deterministic modal
superposition principle for undamped structures, which can find its
applications in finite element analysis of mechanical structures with uncertain
parameters. Further, it is suggested that the concept of n-matrices can be used
in real world problems which adopts fuzzy models like Fuzzy Cognitive Maps,
Fuzzy Relational Equations and Bidirectional Associative Memories. The
applications of these algebraic structures are given in the third chapter. The
fourth chapter suggests problems to further a reader's understanding of the
subject.


  In this paper we analyze the relaxed form of a shape optimization problem
with state equation $\{{array}{ll} -div \big(a(x)Du\big)=f\qquad\hbox{in}D
\hbox{boundary conditions on}\partial D. {array}.$ The new fact is that the
term $f$ is only known up to a random perturbation $\xi(x,\omega)$. The goal is
to find an optimal coefficient $a(x)$, fulfilling the usual constraints
$\alpha\le a\le\beta$ and $\displaystyle\int_D a(x) dx\le m$, which minimizes a
cost function of the form $$\int_\Omega\int_Dj\big(x,\omega,u_a(x,\omega)\big)
dx dP(\omega).$$ Some numerical examples are shown in the last section, to
stress the difference with respect to the case with no perturbation.


  We correct an error in the second part of Theorem 3 of our original paper
(arXiv:1512.07161).


  The existence of a minimal and fundamental length scale, say, the Planck
length, is a characteristic feature of almost all the models of quantum
gravity. The presence of the fundamental length is expected to lead to an
improved ultra-violet behavior of the semi-classical propagators. The
hypothesis of path integral duality provides a prescription to evaluate the
modified propagator of a free, quantum scalar field in a given spacetime,
taking into account the existence of the fundamental length in a locally
Lorentz invariant manner. We use this prescription to compute the quantum
gravitational modifications to the propagators in spacetimes with constant
curvature, and show that: (i) the modified propagators are ultra-violet finite,
and (ii) the modifications are non-perturbative in the Planck length. We
discuss the implications of our results.


  For any hyperelliptic curve X, we give an explicit basis of the first de-Rham
cohomology of X in terms of \v{C}ech cohomology. We use this to produce a
family of curves in characteristic p>2 for which the Hodge-de-Rham short exact
sequence does not split equivariantly; this generalises a result of Hortsch.
Further, we use our basis to show that the hyperelliptic involution acts on the
first de-Rham cohomology by multiplication by -1, i.e., acts as the identity
when p=2.


  We report results of three searches for scalar top quark. Two of the searches
look for direct production of scalar top quark followed by the decay of the
scalar quark to charm quark and neutralino or bottom and chargino. The third
search looks for top quark decaying to scalar top and neutralino followed by
the decay of scalar top to bottom quark and neutralino. We find no evidence for
the presence of scalar top quark in any of the searches. Therefore, depending
on the search we set limits on the production cross-section, $BR(t \to
\tilde{t}_1 + \tilde{\chi}_{1}^{0})$, or $m_{\tilde{t}}$ vs.
$m_{\tilde{\chi}_{1}^{0}}$.


  The angular distributions of the rare decays $B^+ \to K^+\mu^+\mu^-$ and $B^0
\to K^0_{\rm\scriptscriptstyle S}\mu^+\mu^-$ are studied with data
corresponding to 3$~$fb$^{-1}$ of integrated luminosity, collected in
proton-proton collisions at 7 and 8$~$TeV centre-of-mass energies with the LHCb
detector. The angular distribution is described by two parameters, $F_{\rm H}$
and the forward-backward asymmetry of the dimuon system $A_{\rm FB}$, which are
determined in bins of the dimuon mass squared. The parameter $F_{\rm H}$ is a
measure of the contribution from (pseudo)scalar and tensor amplitudes to the
decay width. The measurements of $A_{\rm FB}$ and $F_{\rm H}$ reported here are
the most precise to date and are compatible with predictions from the Standard
Model.


  We consider a matrix space based on the spin degree of freedom, describing
both a Hilbert state space, and its corresponding symmetry operators. Under the
requirement that the Lorentz symmetry be kept, at given dimension, scalar
symmetries, and their representations are determined. Symmetries are flavor or
gauge-like, with fixed chirality. After spin 0, 1/2, and 1 fields are obtained
in this space, we construct associated interactive gauge-invariant
renormalizable terms, showing their equivalence to a Lagrangian formulation,
using as example the previously studied (5+1)-dimensional case, with many
standard-model connections. At 7+1 dimensions, a pair of Higgs-like scalar
Lagrangian is obtained naturally producing mass hierarchy within a fermion
flavor doublet.


  Machine learning (ML) systems in natural language processing (NLP) face
significant challenges in generalizing to out-of-distribution (OOD) data, where
the test distribution differs from the training data distribution. This poses
important questions about the robustness of NLP models and their high accuracy,
which may be artificially inflated due to their underlying sensitivity to
systematic biases. Despite these challenges, there is a lack of comprehensive
surveys on the generalization challenge from an OOD perspective in text
classification. Therefore, this paper aims to fill this gap by presenting the
first comprehensive review of recent progress, methods, and evaluations on this
topic. We furth discuss the challenges involved and potential future research
directions. By providing quick access to existing work, we hope this survey
will encourage future research in this area.


  For $n > 2$, let $\Gamma$ denote either $SL(n, Z)$ or $Sp(n, Z)$. We give a
practical algorithm to compute the level of the maximal principal congruence
subgroup in an arithmetic group $H\leq \Gamma$. This forms the main component
of our methods for computing with such arithmetic groups $H$. More generally,
we provide algorithms for computing with Zariski dense groups in $\Gamma$. We
use our GAP implementation of the algorithms to solve problems that have
emerged recently for important classes of linear groups.


  We describe the fringe packet tracking system used to equalise the optical
path lengths at the Infrared Optical Telescope Array (IOTA) interferometer. The
measurement of closure phases requires obtaining fringes on three baselines
simultaneously. This is accomplished using an algorithm based on double Fourier
interferometry for obtaining the wavelength-dependent phase of the fringes and
a group delay tracking algorithm for determining the position of the fringe
packet. The comparison between data acquired with and without the fringe packet
tracker shows about a factor 3 reduction of the error on the closure-phase
measurement. The fringe packet tracker has been able so far to track fringes of
signal-to-noise as low as 1.8 for stars as faint as mH=7.0.


  The structural changes of TlCoCl$_3$ around phase IV (68 K $<T<$ 75 K) were
studied by single-crystal neutron diffraction measurement. The present
investigation revealed that a small but definite Bragg peak at (${1/6} {1/6}
2$) appeared only in phase IV. A precursor phenomenon of the phase V ($T<$ 68
K) structure in the phase IV temperatures was also identified as the
coexistence of a slightly broadened (${1/4} {1/4} 2$) Bragg peak. We confirmed
that intermediate phase IV is a stable, nontransient, single phase with
$2\sqrt{3}a\times 2\sqrt{3}a\times c$ unit cells. A possible sequence of
structural phase transitions was proposed.


  We show how Geophysics may illustrate and thus improve classical Mechanics
lectures concerning the study of Coriolis force effects. We are then interested
in atmospheric as well as oceanic phenomena we are familiar with, and are for
that reason of pedagogical and practical interest. Our aim is to model them in
a very simple way to bring out the physical phenomena that are involved.


  Gold nanospheres (Au NSs) and gold nanorods (Au NRs) are traditional noble
metal plasmonic nanomaterials. Particularly, Au NRs with tunable longitudinal
plasmon resonance from visible to the near infrared (NIR) range were suitable
for high efficient photothermal applications due to extended light receiving
range. In this work, we synthesized Au NRs and Au NSs of similar volume, and
subsequently developed them into Au NR/PVDF and Au NS/PVDF nanofilm, both of
which exhibited excellent solar photothermal performance evaluated by solar
photothermal experiments. We found that Au NR/PVDF nanofilm showed higher solar
photothermal performance than Au NS/PVDF nanofilm. Through detailed analysis,
such as morphological characterization, optical measurement, and finite element
method (FEM) modeling, we found that the plasmonic coupling effects inside the
aggregated Au NRs nanoclusters contributed to the spectral blue-shifts and
intensified photothermal performance. As compared to Au NS/PVDF nanofilms, Au
NR/PVDF nanofilm exhibited higher efficient light-to-heat conversion rate,
because of the extended light receiving range and high absorbance, as the
result of strong plasmonic interactions inside nanoclusters, which was further
validated by monochromatic laser photothermal experiments and FEM simulations.
Our work proved that the Au NRs have huge potential for plasmonic solar
photothermal applications, and are envisioned for novel plasmonic applications.


  Charge carriers in bilayer graphene occupy two parabolic continua of
electron-like and hole-like states which differ by the alignment between
carrier pseudospin and its momentum, the property known as chirality. Due to
chirality conservation, a strong confining potential can host unusual bound
states: electron levels cloaked into the hole continuum. The energy levels and
the wave functions of the cloaked states can be obtained by solving the
Schr\"odinger equation for a massive non-chiral particle in the p-wave channel
in two dimensions. Eventually, cloaked states slowly decay into the continuum,
via trigonal warping effects. We discuss the key properties of cloaked states
in circularly symmetric potentials, and show that cloaking should be observable
in quantum corral geometries via scanning tunneling probe measurements.


  Scene synthesis is a challenging problem with several industrial
applications. Recently, substantial efforts have been directed to synthesize
the scene using human motions, room layouts, or spatial graphs as the input.
However, few studies have addressed this problem from multiple modalities,
especially combining text prompts. In this paper, we propose a language-driven
scene synthesis task, which is a new task that integrates text prompts, human
motion, and existing objects for scene synthesis. Unlike other single-condition
synthesis tasks, our problem involves multiple conditions and requires a
strategy for processing and encoding them into a unified space. To address the
challenge, we present a multi-conditional diffusion model, which differs from
the implicit unification approach of other diffusion literature by explicitly
predicting the guiding points for the original data distribution. We
demonstrate that our approach is theoretically supportive. The intensive
experiment results illustrate that our method outperforms state-of-the-art
benchmarks and enables natural scene editing applications. The source code and
dataset can be accessed at https://lang-scene-synth.github.io/.


  In this paper, we introduce a variation of the notion of topological phase
reflecting metric structure of the position space. This framework contains not
only periodic and non-periodic systems with symmetries in Kitaev's periodic
table but also topological crystalline insulators. We also define the bulk and
edge indices as invariants taking values in the twisted equivariant
$\mathrm{K}$-groups of Roe algebras as generalizations of existing invariants
such as the Hall conductance or the Kane--Mele $\mathbb{Z}_2$-invariant. As a
consequence, we obtain a new mathematical proof of the bulk-edge correspondence
by using the coarse Mayer-Vietoris exact sequence.


  Much research has been carried out to understand the emergence of cooperation
in simulated social networks of competing individuals. Such research typically
implements a population as a single connected network. Here we adopt a more
realistic premise; namely that populations consist of multiple networks, whose
members migrate from one to another. Specifically, we isolate the key elements
of the scenario where a minority of members from a cooperative network migrate
to a network populated by defectors. Using the public goods game to model
group-wise cooperation, we find that under certain circumstances, the concerted
actions of a trivial number of such migrants will catalyse widespread
behavioural change throughout an entire population. Such results support a
wider argument: that the general presence of some form of disruption
contributes to the emergence of cooperation in social networks, and
consequently that simpler models may encode a determinism that precludes the
emergence of cooperation.


  In this paper, we present a novel system for predicting vessel turnaround
time, based on machine learning and standardized port call data. We also
investigate the use of specific external maritime big data, to enhance the
accuracy of the available data and improve the performance of the developed
system. An extensive evaluation is performed in Port of Bordeaux, where we
report the results on 11 years of historical port call data and provide
verification on live, operational data from the port. The proposed automated
data-driven turnaround time prediction system is able to perform with increased
accuracy, in comparison with the current manual expert-based system in Port of
Bordeaux.


  The requirement that the laws of physics must be invariant under
point-dependent transformations of the units of length, time, and mass is used
as a selection principle while studying different generic effective theories of
gravity. Thereof theories with non-minimal coupling of the dilaton both to the
curvature and to the Lagrangian of the matter fields seem to represent the most
viable low-energy [and low-curvature] description of gravity. Consequently, the
cosmological singularity problem is treated within the context of string
cosmology with non-minimal coupling of the dilaton to a barotropic gas of
solitonic p-brane. The results obtained are to be interpreted on the grounds of
Weyl-integrable geometry. The implications of these results for the Mach's
principle are briefly discussed.


  Physical constraints on the sources of fast radio bursts are few, and
therefore viable theoretical models are many. However, no one model can match
all the available observational characteristics, meaning that these radio
bursts remain one of the most mysterious phenomena in astrophysics.


  Let $(W,H,\mu)$ be the classical Wiener space, assume that $U=I_W+u$ is an
adapted perturbation of identity satisfying the Girsanov identity. Then, $U$ is
invertible if and only if the kinetic energy of $u$ is equal to the relative
entropy of the measure induced with the action of $U$ on the Wiener measure
$\mu$, in other words $U$ is invertible if and only if $$ \half
\int_W|u|_H^2d\mu=\int_W \frac{dU\mu}{d\mu}\log\frac{dU\mu}{d\mu}d\mu . $$


  The best finite Fourier Series for a smooth surface $h(x,y)$ closest to the
positions of heads of amphiphiles in the least-square sense, agrees fully with
the Fourier coefficients obtained by a direct summation over raw data points.
Both metods produce structure factors $S(q)$ containing all necessary features:
small-q divergence, a minimum, the raise to the ubiquitous nearest neighbor
peak near $q=2\pi/$(coll.diameter) and further peaks. The Laurent series is
also discussed.


  In our experiment, an interface between a viscous liquid and air is deformed
by a sink flow of constant flow rate to form a sharp tip. Using a microscope,
the interface shape is recorded down to a tip size of 1 $\rm{\mu m}$. The
curvature at the tip is controlled by the distance $h$ between the tip and the
sink. As a critical distance $h^{\star}$ is approached, the curvature diverges
like $1/(h-h^{\star})^3$ and the tip becomes cone-shaped. As the distance to
the sink is decreased further, the opening angle of the cone vanishes like
$h^2$. No evidence for air entrainment was found, except when the tip was
inside the orifice.


  This work deals with the possible solution of the solar neutrino problem in
the framework of the resonant neutrino spin-flavor precession scenario. The
event rate results from the solar neutrino experiments as well as the recoil
electron energy spectrum from SuperKamiokande are used to constrain the free
parameters of the neutrino in this model. We consider two kinds of magnetic
profiles inside the sun. For both cases, a static and a twisting field are
discussed.


  Sparse regularization such as $\ell_1$ regularization is a quite powerful and
widely used strategy for high dimensional learning problems. The effectiveness
of sparse regularization has been supported practically and theoretically by
several studies. However, one of the biggest issues in sparse regularization is
that its performance is quite sensitive to correlations between features.
Ordinary $\ell_1$ regularization can select variables correlated with each
other, which results in deterioration of not only its generalization error but
also interpretability. In this paper, we propose a new regularization method,
"Independently Interpretable Lasso" (IILasso). Our proposed regularizer
suppresses selecting correlated variables, and thus each active variable
independently affects the objective variable in the model. Hence, we can
interpret regression coefficients intuitively and also improve the performance
by avoiding overfitting. We analyze theoretical property of IILasso and show
that the proposed method is much advantageous for its sign recovery and
achieves almost minimax optimal convergence rate. Synthetic and real data
analyses also indicate the effectiveness of IILasso.


  We use the Hyper Suprime-Cam Subaru Strategic Program S19A shape catalog to
construct weak lensing shear-selected cluster samples. From aperture mass maps
covering $\sim 510$~deg$^2$ created using a truncated Gaussian filter, we
construct a catalog of 187 shear-selected clusters that correspond to mass map
peaks with the signal-to-noise ratio larger than 4.7. Most of the
shear-selected clusters have counterparts in optically-selected clusters, from
which we estimate the purity of the catalog to be higher than 95\%. The sample
can be expanded to 418 shear-selected clusters with the same signal-to-noise
ratio cut by optimizing the shape of the filter function and by combining weak
lensing mass maps created with several different background galaxy selections.
We argue that dilution and obscuration effects of cluster member galaxies can
be mitigated by using background source galaxy samples and adopting the filter
function with its inner boundary larger than about $2'$. The large samples of
shear-selected clusters that are selected without relying on any baryonic
tracer are useful for detailed studies of cluster astrophysics and cosmology.


  The efficiency to identify jets containing $b$-hadrons ($b$-jets) is measured
using a high purity sample of dileptonic top quark-antiquark pairs ($t\bar{t}$)
selected from the 36.1 fb$^{-1}$ of data collected by the ATLAS detector in
2015 and 2016 from proton-proton collisions produced by the Large Hadron
Collider at a centre-of-mass energy $\sqrt{s}=13$ TeV. Two methods are used to
extract the efficiency from $t\bar{t}$ events, a combinatorial likelihood
approach and a tag-and-probe method. A boosted decision tree, not using
$b$-tagging information, is used to select events in which two $b$-jets are
present, which reduces the dominant uncertainty in the modelling of the flavour
of the jets. The efficiency is extracted for jets in a transverse momentum
range from 20 to 300 GeV, with data-to-simulation scale factors calculated by
comparing the efficiency measured using collision data to that predicted by the
simulation. The two methods give compatible results, and achieve a similar
level of precision, measuring data-to-simulation scale factors close to unity
with uncertainties ranging from 2% to 12% depending on the jet transverse
momentum.


  Security for machine learning has begun to become a serious issue for present
day applications. An important question remaining is whether emerging quantum
technologies will help or hinder the security of machine learning. Here we
discuss a number of ways that quantum information can be used to help make
quantum classifiers more secure or private. In particular, we demonstrate a
form of robust principal component analysis that, under some circumstances, can
provide an exponential speedup relative to robust methods used at present. To
demonstrate this approach we introduce a linear combinations of unitaries
Hamiltonian simulation method that we show functions when given an imprecise
Hamiltonian oracle, which may be of independent interest. We also introduce a
new quantum approach for bagging and boosting that can use quantum
superposition over the classifiers or splits of the training set to aggregate
over many more models than would be possible classically. Finally, we provide a
private form of $k$--means clustering that can be used to prevent an all
powerful adversary from learning more than a small fraction of a bit from any
user. These examples show the role that quantum technologies can play in the
security of ML and vice versa. This illustrates that quantum computing can
provide useful advantages to machine learning apart from speedups.


  The visible band (band A) of Photoluminescence spectra of high-purity
synthesized diamond is analyzed by deconvolution technique. A set of eight
lines with distinct peak energy are found. The peak energy and the width of
these lines were either constant or varies very slightly with temperature. The
amplitude of the lines are significantly temperature. The closeness of the
temperature that the amplitudes of these lines reach their minimum and the
temperature which the Free-exiton emission is maximum at, is an indication of
the competition between these too effects.


  We investigate the nature of the unidentified very-high-energy (VHE)
gamma-ray object, HESS J1832-093, in a multi-wavelength context. Based on X-ray
variability and spectral index ($\Gamma_X\sim\,1.5$), and its broad-band
spectrum (which was remarkably similar to HESS J0632+057, a confirmed gamma-ray
binary), HESS J1832-093 has been considered to be a strong gamma-ray binary
candidate in previous works. In this work, we provide further evidence for this
scenario. We obtained a spectrum of its IR counterpart using Gemini/Flamingo,
finding absorption lines that are usually seen in massive stars, in particular
O stars. We also obtained a rather steep ATCA spectrum
($\alpha=-1.18^{+1.04}_{-0.88}$) which prefers a gamma-ray binary over an AGN
scenario. Based on spatial-spectral analysis and variability search, we found
that 4FGL J1832.9-0913 is possible to be associated with SNR G22.7-0.2 rather
than with HESS J1832-093 only.


  The recent observation of a common red-noise process in pulsar timing arrays
(PTAs) suggests that the detection of nanohertz gravitational waves might be
around the corner. However, in order to confidently attribute this red process
to gravitational waves, one must observe the Hellings-Downs curve -- the
telltale angular correlation function associated with a gravitational-wave
background. This effort is complicated by the complex modelling of pulsar
noise. Without proper care, mis-specified noise models can lead to
false-positive detections. Background estimation using bootstrap methods such
as sky scrambles and phase shifts, which use the data to characterize the
noise, are therefore important tools for assessing significance. We investigate
the ability of current PTA experiments to estimate their background with
"quasi-independent" scrambles -- characterized by a statistical "match" below
the fiducial value: $|M|<0.1$. We show that sky scrambling is affected by
"saturation" after $O(10)$ quasi-independent realizations; subsequent scrambles
are no longer quasi-independent. We show phase scrambling saturates after
$O(100)$ quasi-independent realizations. With so few independent scrambles, it
is difficult to make reliable statements about the $\gtrsim 5 \sigma$ tail of
the null distribution of the detection statistic. We discuss various methods by
which one may increase the number of independent scrambles. We also consider an
alternative approach wherein one re-frames the background estimation problem so
that the significance is calculated using statistically dependent scrambles.
The resulting $p$-value is in principle well-defined but may be susceptible to
failure if assumptions about the data are incorrect.


  We consider SDEs of the form $dX_t = |f(X_t)|/t^{\gamma} dt+1/t^{\gamma}
dB_t$, where $f(x)$ behaves comparably to $|x|^k$ in a neighborhood of the
origin, for $k\in [1,\infty)$. We show that there exists a threshold value
$:=\tilde{\gamma}$ for $\gamma$, depending on $k$, such that when $\gamma \in
(1/2, \tilde{\gamma})$ then $\mathbb{P}(X_n\rightarrow 0) = 0$, and for the
rest of the permissible values $\mathbb{P}(X_n\rightarrow 0)>0$. The previous
results extend for discrete processes that satisfy $X_{n+1}-X_n =
f(X_n)/n^\gamma +Y_n/n^\gamma$. Here, $Y_{n+1}$ are martingale differences that
are a.s. bounded.
  This result shows that for a function $F$, whose second derivative at
degenerate saddle points is of polynomial order, it is always possible to
escape saddle points via the iteration $X_{n+1}-X_n =F'(X_n)/n^\gamma
+Y_n/n^\gamma$ for a suitable choice of $\gamma$.


  Lack of trust between organisations and privacy concerns about their data are
impediments to an otherwise potentially symbiotic joint data analysis. We
propose DataRing, a data sharing system that allows mutually mistrusting
participants to query each others' datasets in a privacy-preserving manner
while ensuring the correctness of input datasets and query answers even in the
presence of (cheating) participants deviating from their true datasets. By
relying on the assumption that if only a small subset of rows of the true
dataset are known, participants cannot submit answers to queries deviating
significantly from their true datasets. We employ differential privacy and a
suite of cryptographic tools to ensure individual privacy for each
participant's dataset and data confidentiality from the system. Our results
show that the evaluation of 10 queries on a dataset with 10 attributes and
500,000 records is achieved in 90.63 seconds. DataRing could detect cheating
participant that deviates from its true dataset in few queries with high
accuracy.


  Heat-Bath Algorithmic Cooling is a set of techniques for producing highly
pure quantum systems by utilizing a surrounding heat-bath and unitary
interactions. These techniques originally used the thermal environment only to
fully thermalize ancillas at the environment temperature. Here we extend HBAC
protocols by optimizing over the thermalization strategy. We find, for any
$d$-dimensional system in an arbitrary initial state, provably optimal cooling
protocols with surprisingly simple structure and exponential convergence to the
ground state. Compared to the standard ones, these schemes can use fewer or no
ancillas and exploit memory effects to enhance cooling. We verify that the
optimal protocols are robusts to various deviations from the ideal scenario.
For a single target qubit, the optimal protocol can be well approximated with a
Jaynes-Cummings interaction between the system and a single thermal bosonic
mode for a wide range of environmental temperatures. This admits an
experimental implementation close to the setup of a micromaser, with a
performance competitive with leading proposals in the literature. The proposed
protocol provides an experimental setup that illustrates how non-Markovianity
can be harnessed to improve cooling. On the technical side we 1. introduce a
new class of states called maximally active states and discuss their
thermodynamic significance in terms of optimal unitary control, 2. introduce a
new set of thermodynamic processes, called $\beta$-permutations, whose access
is sufficient to simulate a generic thermalization process, 3. show how to use
abstract toolbox developed within the resource theory approach to
thermodynamics to perform challenging optimizations, while combining it with
open quantum system dynamics tools to approximate optimal solutions within
physically realistic setups.


  Fermi-LAT observations have strongly constrained dark matter annihilation
through the joint-likelihood analysis of dwarf spheroidal galaxies (dSphs).
These constraints are expected to be robust because dSphs have measurable dark
matter content and produce negligible astrophysical emission. However, each
dSph is dim, with a predicted flux that typically falls below the accuracy of
the background model. We show that this significantly diminishes the
reliability of previous joint-likelihood algorithms, and develop an improved
analysis that directly accounts for the effect of background mismodeling. This
method produces more robust limits and detections of dark matter in both real
and mock data. We calculate improved limits on the dark matter annihilation
cross-section, which differ by nearly a factor of two from previous analyses -
despite examining identical data.


  Arc flash is one of the main hazards when operating an electrical facility.
Without correct Personal Protective Equipment, the operator can be subjected to
severe including fatal injuries. By code, facilities are required to properly
label their electrical equipment that may be accessed by any operator. While
energized, the operator proximity to the equipment can provide the necessary
potential for an arc flash accident. The labels are mainly responsible for
displaying the equipment short circuit and arc flash levels and the minimum PPE
level required to operate it. These electrical hazard aspects become more
critical in testbed facilities, usually located inside research centers and
universities, where the electrical equipment is more frequently accessed by
students and researchers. This paper develops complete modeling of a real
microgrid testbed facility to perform short circuit and arc flash studies with
the main goal to label the devices accessed by the facility researchers.


  Spiking Neural Networks (SNNs) are biologically-inspired models that are
capable of processing information in streams of action potentials. However,
simulating and training SNNs is computationally expensive due to the need to
solve large systems of coupled differential equations. In this paper, we
introduce SparseProp, a novel event-based algorithm for simulating and training
sparse SNNs. Our algorithm reduces the computational cost of both the forward
and backward pass operations from O(N) to O(log(N)) per network spike, thereby
enabling numerically exact simulations of large spiking networks and their
efficient training using backpropagation through time. By leveraging the
sparsity of the network, SparseProp eliminates the need to iterate through all
neurons at each spike, employing efficient state updates instead. We
demonstrate the efficacy of SparseProp across several classical
integrate-and-fire neuron models, including a simulation of a sparse SNN with
one million LIF neurons. This results in a speed-up exceeding four orders of
magnitude relative to previous event-based implementations. Our work provides
an efficient and exact solution for training large-scale spiking neural
networks and opens up new possibilities for building more sophisticated
brain-inspired models.


  We provide a simple derivation of the extremal values of the superpotential
in massive vacua of N=1* SYM, making use of the required modular weight for the
central charge of BPS walls interpolating between these vacua. This modular
weight descends from the action of S-duality on the N=4 superalgebra which in
turn is inherited from its classical action on the dyon spectrum. We show that
this kinematic information, combined with minimal knowledge of the weak
coupling asymptotics, is sufficient to determine the exact vacuum
superpotentials in terms of Eisenstein series.


  Ensuring equitable privacy experiences remains a challenge, especially for
marginalised and vulnerable populations (MVPs) who often hesitate to
participate or use digital services due to concerns about the privacy of their
sensitive information. In response, security research has emphasised the
importance of inclusive security and privacy practices to facilitate meaningful
engagement of MVPs online. However, research in this area is still in its early
stages, with other MVPs yet to be considered (such as low-income groups, and
refugees), novel engagement methods yet to be explored, and limited support for
software developers in building applications and services for MVPs. In 2022, we
initiated a UK Research Council funded Equitable Privacy project to address
these gaps. Our goal is to prioritise the privacy needs and requirements of
MVPs in the design and development of software applications and services.
  We design and implement a new participatory research approach -- community
studybeds -- in collaboration with third-sector organisations that support MVPs
to identify and tackle the challenges these groups encounter. In this paper, we
share the initial reflections and experiences of the Equitable Privacy project,
particularly emphasising the utilisation of our community studybeds.


  An analytic model is presented that considers the evolution of a market of
durable goods. The model suggests that after introduction goods spread always
according to a Bass diffusion. However, this phase will be followed by a
diffusion process for durable consumer goods governed by a
variation-selection-reproduction mechanism and the growth dynamics can be
described by a replicator equation. Describing the aggregate sales as the sum
of first, multiple and replacement purchase the product life cycle can be
derived. Replacement purchase causes periodic variations of the sales
determined by the finite lifetime of the good (Juglar cycles). The model
suggests that both, Bass- and Gompertz diffusion may contribute to the product
life cycle of a consumer durable. The theory contains the standard equilibrium
view of a market as a special case. It depends on the time scale, whether an
equilibrium or evolutionary description is more appropriate. The evolutionary
framework is used to derive also the size, growth rate and price distribution
of manufacturing business units. It predicts that the size distribution of the
business units (products) is lognormal, while the growth rates exhibit a
Laplace distribution. Large price deviations from the mean price are also
governed by a Laplace distribution (fat tails). These results are in agreement
with empirical findings. The explicit comparison of the time evolution of
consumer durables with empirical investigations confirms the close relationship
between price decline and Gompertz diffusion, while the product life cycle can
be described qualitatively for a long time period.


  The error on a real quantity Y due to the graduation of the measuring
instrument may be asymptotically represented, when the graduation is regular
and fines down, by a Dirichlet form on R whose square field operator does not
depend on the probability law of Y as soon as this law possesses a continuous
density. This feature is related to the "arbitrary functions principle"
(Poincar'e, Hopf). We give extensions of this property to Rd and to the Wiener
space for some approximations of the Brownian motion. This gives new
approximations of the Ornstein-Uhlenbeck gradient. These results apply to the
discretization of some stochastic differential equations encountered in
mechanics.


  General relativistic quantum interference effects in the slowly rotating NUT
space-time as the Sagnac effect and the phase shift effect of interfering
particle in neutron interferometer are considered. It was found that in the
case of the Sagnac effect the influence of NUT parameter is becoming important
due to the fact that the angular velocity of the locally non rotating observer
must be larger than one in the Kerr space-time. In the case of neutron
interferometry it is found that due to the presence of NUT-parameter an
additional term in the phase shift of interfering particle emerges. This term
can be, in principle, detected by sensitive interferometer and derived results
can be further used in experiments to detect the gravitomagnetic charge.
Finally, as an example, we apply the obtained results to the calculation of the
UCN (ultra-cold neutrons) energy level modification in the slowly rotating NUT
space-time.