  Microwave Pressing is a promising way to reduce microwave sintering
temperatures and stabilize microwave powder materials processing. A
multi-physics simulation was conducted of the regulated pressure-assisted
microwave cavity. This simulation took into consideration resonance phenomena
and the nonlinear temperature-dependent material parameters of zirconia. The
intrinsic behaviors of microwave systems and zirconia make the regulation of
the microwave pressing difficult. However, the same phenomena can be used to
activate flash sintering. Flash microwave sintering uses high electric fields
of the resonant microwave profile, the Negative Temperature Behavior (NTC) of
zirconia resistivity, and the mechanical pressure applied to the powder via a
die compaction configuration. The resulting flash microwave pressing still
needs improvement in terms of the processed material structure homogeneity, but
it has the capacity to become the fastest sintering treatment as it allows room
temperature activation where the total process time only takes a few seconds.
In addition, this 10-20s processing technique has shown good potential for
improving the transparency of alumina pre-sintered specimens.


  A general methodology is proposed to differentiate the likelihood of
energetic-particle-driven instabilities to produce frequency chirping or
fixed-frequency oscillations. The method employs numerically calculated
eigenstructures and multiple resonance surfaces of a given mode in the presence
of energetic ion drag and stochasticity (due to collisions and
micro-turbulence). Toroidicity-induced, reversed-shear and beta-induced
Alfven-acoustic eigenmodes are used as examples. Waves measured in experiments
are characterized and compatibility is found between the proposed criterion
predictions and the experimental observation or lack of observation of chirping
behavior of Alfvenic modes in different tokamaks. It is found that the
stochastic diffusion due to micro-turbulence can be the dominant energetic
particle detuning mechanism near the resonances in many plasma experiments, and
its strength is the key as to whether chirping solutions are likely to arise.
The proposed criterion constitutes a useful predictive tool in assessing
whether the nature of the transport for fast ion losses in fusion devices will
be dominated by convective or diffusive processes.


  We calculate the average polarisability of two dimensional mesoscopic rings
in the presence of an Aharonov-Bohm flux. The screening is taken into account
self-consistently within a mean-field approximation. We investigate the effects
of statistical ensemble, finite frequency and disorder. We emphasize
geometrical effects which make the observation of field dependent
polarisability much more favourable on rings than on disks or spheres of
comparable radius. The ratio of the flux dependent to the flux independent part
is estimated for typical GaAs rings.


  Cross domain object detection is a realistic and challenging task in the
wild. It suffers from performance degradation due to large shift of data
distributions and lack of instance-level annotations in the target domain.
Existing approaches mainly focus on either of these two difficulties, even
though they are closely coupled in cross domain object detection. To solve this
problem, we propose a novel Target-perceived Dual-branch Distillation (TDD)
framework. By integrating detection branches of both source and target domains
in a unified teacher-student learning scheme, it can reduce domain shift and
generate reliable supervision effectively. In particular, we first introduce a
distinct Target Proposal Perceiver between two domains. It can adaptively
enhance source detector to perceive objects in a target image, by leveraging
target proposal contexts from iterative cross-attention. Afterwards, we design
a concise Dual Branch Self Distillation strategy for model training, which can
progressively integrate complementary object knowledge from different domains
via self-distillation in two branches. Finally, we conduct extensive
experiments on a number of widely-used scenarios in cross domain object
detection. The results show that our TDD significantly outperforms the
state-of-the-art methods on all the benchmarks. Our code and model will be
available at https://github.com/Feobi1999/TDD.


  In this contribution, we discuss the modeling and model reduction framework
known as the Loewner framework. This is a data-driven approach, applicable to
large-scale systems, which was originally developed for applications to linear
time-invariant systems. In recent years, this method has been extended to a
number of additional more complex scenarios, including linear parametric or
nonlinear dynamical systems. We will provide here an overview of the latter
two, together with time-domain extensions. Additionally, the application of the
Loewner framework is illustrated by a collection of practical test cases.
Firstly, for data-driven complexity reduction of the underlying model, and
secondly, for dealing with control applications of complex systems (in
particular, with feedback controller design).


  The Doubly Robust (DR) estimation of ATE can be carried out in 2 steps, where
in the first step, the treatment and outcome are modeled, and in the second
step the predictions are inserted into the DR estimator. The model
misspecification in the first step has led researchers to utilize Machine
Learning algorithms instead of parametric algorithms. However, existence of
strong confounders and/or Instrumental Variables (IVs) can lead the complex ML
algorithms to provide perfect predictions for the treatment model which can
violate the positivity assumption and elevate the variance of DR estimators.
Thus the ML algorithms must be controlled to avoid perfect predictions for the
treatment model while still learn the relationship between the confounders and
the treatment and outcome.
  We use two Neural network architectures and investigate how their
hyperparameters should be tuned in the presence of confounders and IVs to
achieve a low bias-variance tradeoff for ATE estimators such as DR estimator.
Through simulation results, we will provide recommendations as to how NNs can
be employed for ATE estimation.


  Completing an unordered partial point cloud is a challenging task. Existing
approaches that rely on decoding a latent feature to recover the complete
shape, often lead to the completed point cloud being over-smoothing, losing
details, and noisy. Instead of decoding a whole shape, we propose to decode and
refine a low-resolution (low-res) point cloud first, and then performs a
patch-wise noise-aware upsampling rather than interpolating the whole sparse
point cloud at once, which tends to lose details. Regarding the possibility of
lacking details of the initially decoded low-res point cloud, we propose an
iterative refinement to recover the geometric details and a symmetrization
process to preserve the trustworthy information from the input partial point
cloud. After obtaining a sparse and complete point cloud, we propose a
patch-wise upsampling strategy. Patch-based upsampling allows to better recover
fine details unlike decoding a whole shape, however, the existing upsampling
methods are not applicable to completion task due to the data discrepancy
(i.e., input sparse data here is not from ground-truth). Therefore, we propose
a patch extraction approach to generate training patch pairs between the sparse
and ground-truth point clouds, and an outlier removal step to suppress the
noisy points from the sparse point cloud. Together with the low-res recovery,
our whole method is able to achieve high-fidelity point cloud completion.
Comprehensive evaluations are provided to demonstrate the effectiveness of the
proposed method and its individual components.


  The Hales program to prove the Kepler conjecture on sphere packings consists
of five steps, which if completed, will jointly comprise a proof of the
conjecture. We carry out step five of the program [outlined in
math.MG/9811073], a proof that the local density of a certain combinatorial
arrangement, the pentahedral prism, is less than that of the face-centered
cubic lattice packing. We prove various relations on the local density using
computer-based interval arithmetic methods. Together, these relations imply the
local density bound.


  Purpose - To test major Web search engines on their performance on
navigational queries, i.e. searches for homepages. Design/methodology/approach
- 100 real user queries are posed to six search engines (Google, Yahoo, MSN,
Ask, Seekport, and Exalead). Users described the desired pages, and the results
position of these is recorded. Measured success N and mean reciprocal rank are
calculated. Findings - Performance of the major search engines Google, Yahoo,
and MSN is best, with around 90 percent of queries answered correctly. Ask and
Exalead perform worse but receive good scores as well. Research
limitations/implications - All queries were in German, and the German-language
interfaces of the search engines were used. Therefore, the results are only
valid for German queries. Practical implications - When designing a search
engine to compete with the major search engines, care should be taken on the
performance on navigational queries. Users can be influenced easily in their
quality ratings of search engines based on this performance. Originality/value
- This study systematically compares the major search engines on navigational
queries and compares the findings with studies on the retrieval effectiveness
of the engines on informational queries. Paper type - research paper


  A recent study revealed the dynamics of the charge sector of a
one-dimensional quarter-filled electronic system with extended Hubbard
interactions to be that of an effective pseudospin transverse-field Ising model
(TFIM) in the strong coupling limit. With the twin motivations of studying the
co-existing charge and spin order found in strongly correlated chain systems
and the effects of inter-chain couplings, we investigate the phase diagram of
coupled effective (TFIM) systems. A bosonisation and RG analysis for a two-leg
TFIM ladder yields a rich phase diagram showing Wigner/Peierls charge order and
Neel/dimer spin order. In a broad parameter regime, the orbital
antiferromagnetic phase is found to be stable. An intermediate gapless phase of
finite width is found to lie in between two charge-ordered gapped phases.
Kosterlitz-Thouless transitions are found to lead from the gapless phase to
either of the charge-ordered phases. A detailed analysis is also carried out
for the dimensional crossover physics when many such pseudospin systems are
coupled to one another. Importantly, the analysis reveals the key role of
critical quantum fluctuations in driving the strong dispersion in the
transverse directions, as well as a T=0 deconfinement transition. Our work is
potentially relevant for a unified description of a class of strongly
correlated, quarter-filled chain and ladder systems.


  Llight-element abundances probing big bang nucleosynthesis and precision data
from cosmology probing the cosmic microwave background decoupling epoch have
hinted at the presence of extra relativistic degrees of freedom. This is widely
referred to as "dark radiation", suggesting the need for new light states in
the UV completion of the standard model. We provide a brief and concise
overview of the current observational status of such dark radiation and
investigate the interplay between two possible interpretations of the extra
light states: the right-handed partners of three Dirac neutrinos (which
interact with all fermions through the exchange of a new heavy vector meson)
and dark matter particles that were produced through a non-thermal mechanism,
such us late time decays of massive relics. This model ties together
cosmological indications of extra light states and the production of the heavy
vector particle at the LHC.


  We establish an $L^\infty\times L^2 \to L^2$ norm estimate for a bilinear
oscillatory integral along parabolas incorporating oscillatory factors
$e^{i|t|^{-\beta}}$.


  Programming language detection is a common need in the analysis of large
source code bases. It is supported by a number of existing tools that rely on
several features, and most notably file extensions, to determine file types. We
consider the problem of accurately detecting the type of files commonly found
in software code bases, based solely on textual file content. Doing so is
helpful to classify source code that lack file extensions (e.g., code snippets
posted on the Web or executable scripts), to avoid misclassifying source code
that has been recorded with wrong or uncommon file extensions, and also shed
some light on the intrinsic recognizability of source code files. We propose a
simple model that (a) use a language-agnostic word tokenizer for textual files,
(b) group tokens in 1-/2-grams, (c) build feature vectors based on N-gram
frequencies, and (d) use a simple fully connected neural network as classifier.
As training set we use textual files extracted from GitHub repositories with at
least 1000 stars, using existing file extensions as ground truth. Despite its
simplicity the proposed model reaches 85% in our experiments for a relatively
high number of recognized classes (more than 130 file types).


  This article is built upon three main ideas. First, for a class of monomial
ideals, it is proven that the multiplicity of an ideal equals the number of
realizations of its codimension (an intuitive concept that we define later).
Next, for an arbitrary graph G, we construct a monomial ideal M_G, and show
that the chromatic number of G is equal to the codimension of M_G. Finally, for
a class of graphs, we give a formula that computes the chromatic polynomial of
G, evaluated at the chromatic number of G, in terms of the codimension and
multiplicity of M_G. In particular, the formula applies to all graphs
satisfying the Erdos-Faber-Lov\'asz conjecture.


  Is a scientific research paper based on (i) public, online observational data
files and (ii) providing free-licensed software for reproducing its results
easy to reproduce by the same author a decade later? This paper attempts to
reproduce a cosmic topology observational paper published in 2008 and
satisfying both criteria (i) and (ii). The reproduction steps are defined
formally in a free-licensed git repository package "0807.4260" and
qualitatively in the current paper. It was found that the effort in upgrading
the Fortran 77 code at the heart of the software, interfaced with a C front
end, and originally compiled with g77, in the content of the contemporary
gfortran compiler, risked being too great to be justified on any short time
scale. In this sense, the results of RBG08 are not as reproducible as they
appeared to be, despite both (i) data availability and (ii) free-licensing and
public availability of the software. The software and a script to reproduce the
steps of this incomplete reproduction are combined in a new git repository
named 0807.4260, following the ArXiv identity code (arXiv:0807.4260) of RBG08.


  We compactify the classical moduli variety of compact Riemann surfaces by
attaching moduli of (metrized) graphs as boundary. The compactifications do not
admit the structure of varieties and patch together to form a big connected
moduli space in which $\sqcup_{g} M_{g}$ is open dense.
  The metrized graphs, which are often studied as "tropical curves", are
obtained as Gromov-Hausdorff collapse by fixing diameters of the hyperbolic
metrics of the Riemann surfaces. This phenomenon can be also seen as an
archemidean analogue of the tropicalization of Berkovich analytification of
$M_{g}$ (cf., [ACP]).


  This paper reports on the development of a Web platform to host the Mizar
Mathematical Library (MML). In recent years, the size of formalized
mathematical libraries has been drastically increasing, and this has led to a
growing demand for tools that support efficient and comprehensive browsing,
searching, and annotation of these libraries. This platform implements a Wiki
function to add comments to the HTMLized MML, three types of search function
(article, symbol, and theorem), and a function to show the dependency graph of
the MML. This platform is designed with consistency, scalability, and
interoperability as top priorities for long-term use.


  We report on the discovery of a significant and compact over-density of old
and metal-poor stars in the KiDS survey (data release 4). The discovery is
confirmed by deeper HSC-SSC data revealing the old Main Sequence Turn-Off of a
stellar system located at a distance from the sun of
$D_{\sun}=145^{+14}_{-13}$~kpc in the direction of the Sextans constellation.
The system has absolute integrated magnitude ($M_V=-3.9^{+0.4}_{-0.3}$),
half-light radius ($r_h=193^{+61}_{-46}$~pc), and ellipticity
($e=0.46^{+0.11}_{-0.15}$) typical of Ultra Faint Dwarf galaxies (UFDs). The
central surface brightness is near the lower limits of known local dwarf
galaxies of similar integrated luminosity, as expected for stellar systems that
escaped detection until now. The distance of the newly found system suggests
that it is likely a satellite of our own Milky Way, consequently, we
tentatively baptise it Sextans~II (KiDS-UFD-1).


  We present the results from deep 21 cm H I mapping of two nearby blue compact
dwarf galaxies (BCDGs), W1016+3754 and W2326+0608, using the Giant Metrewave
Radio Telescope (GMRT). These BCDGs are bright in mid-infrared (MIR) data and
undergoing active star formation. With the GMRT observations, we investigate
the role of cold neutral gas as the fuel resource of the current intensive star
formation activity. Star formation in these galaxies is likely to be due to the
infall of H I gas triggered by gravitational perturbation from nearby galaxies.
The BCDG W2326+0608 and nearby galaxy SDSS J232603.86+060835.8 share a common H
I envelope. We find star formation takes place in the high H I column density
gas ($\gtrsim 10^{21}$\,cm$^{-2}$) regions for both BCDGs. The recent starburst
and infall of metal-free gas have kept the metallicity low for the BCDG
W1016+3754. The metallicity for W2326+0608 is higher, possibly due to tidal
interaction with the nearby galaxy SDSS J232603.86+060835.8.


  Recognizing Activities of Daily Living (ADL) is a vital process for
intelligent assistive robots, but collecting large annotated datasets requires
time-consuming temporal labeling and raises privacy concerns, e.g., if the data
is collected in a real household. In this work, we explore the concept of
constructing training examples for ADL recognition by playing life simulation
video games and introduce the SIMS4ACTION dataset created with the popular
commercial game THE SIMS 4. We build Sims4Action by specifically executing
actions-of-interest in a "top-down" manner, while the gaming circumstances
allow us to freely switch between environments, camera angles and subject
appearances. While ADL recognition on gaming data is interesting from the
theoretical perspective, the key challenge arises from transferring it to the
real-world applications, such as smart-homes or assistive robotics. To meet
this requirement, Sims4Action is accompanied with a GamingToReal benchmark,
where the models are evaluated on real videos derived from an existing ADL
dataset. We integrate two modern algorithms for video-based activity
recognition in our framework, revealing the value of life simulation video
games as an inexpensive and far less intrusive source of training data.
However, our results also indicate that tasks involving a mixture of gaming and
real data are challenging, opening a new research direction. We will make our
dataset publicly available at https://github.com/aroitberg/sims4action.


  We address the problem of registering synchronized color (RGB) and
multi-spectral (MS) images featuring very different resolution by solving
stereo matching correspondences. Purposely, we introduce a novel RGB-MS dataset
framing 13 different scenes in indoor environments and providing a total of 34
image pairs annotated with semi-dense, high-resolution ground-truth labels in
the form of disparity maps. To tackle the task, we propose a deep learning
architecture trained in a self-supervised manner by exploiting a further RGB
camera, required only during training data acquisition. In this setup, we can
conveniently learn cross-modal matching in the absence of ground-truth labels
by distilling knowledge from an easier RGB-RGB matching task based on a
collection of about 11K unlabeled image triplets. Experiments show that the
proposed pipeline sets a good performance bar (1.16 pixels average registration
error) for future research on this novel, challenging task.


  We consider strong external difference families (SEDFs); these are external
difference families satisfying additional conditions on the patterns of
external diferences that occur, and were first defined in the context of
classifying optimal strong algebraic manipulation detection codes. We establish
new necessary conditions for the existence of (n; m; k; lambda)-SEDFs; in
particular giving a near-complete treatment of the lambda = 2 case. For the
case m = 2, we obtain a structural characterization for partition type SEDFs
(of maximum possible k and lambda), showing that these correspond to Paley
partial difference sets. We also prove a version of our main result for
generalized SEDFs, establishing non-trivial necessary conditions for their
existence.


  The SELEX experiment (Fermilab E781) is a 3-stage magnetic spectrometer for
the study of charm hadroproduction at large x_F using 600GeV/c Sigma-, pi-, and
p beams. New precise measurements of the Lambda_c, D0, and Ds lifetimes are
presented. Results on Lambda_c and D_s production for x_F>0.2 are reported as
well. The spectrometer was also used for hyperon physics, where we will show
measurements of the Sigma- charge radius, the polarization of inclusive
produced Lambda's, and the polarization of beam Sigma+.


  This paper presents a design methodology for optimal transmission energy
allocation at a sensor equipped with energy harvesting technology for remote
state estimation of linear stochastic dynamical systems. In this framework, the
sensor measurements as noisy versions of the system states are sent to the
receiver over a packet dropping communication channel. The packet dropout
probabilities of the channel depend on both the sensor's transmission energies
and time varying wireless fading channel gains. The sensor has access to an
energy harvesting source which is an everlasting but unreliable energy source
compared to conventional batteries with fixed energy storages. The receiver
performs optimal state estimation with random packet dropouts to minimize the
estimation error covariances based on received measurements. The receiver also
sends packet receipt acknowledgments to the sensor via an erroneous feedback
communication channel which is itself packet dropping.
  The objective is to design optimal transmission energy allocation at the
energy harvesting sensor to minimize either a finite-time horizon sum or a long
term average (infinite-time horizon) of the trace of the expected estimation
error covariance of the receiver's Kalman filter. These problems are formulated
as Markov decision processes with imperfect state information. The optimal
transmission energy allocation policies are obtained by the use of dynamic
programming techniques. Using the concept of submodularity, the structure of
the optimal transmission energy policies are studied. Suboptimal solutions are
also discussed which are far less computationally intensive than optimal
solutions. Numerical simulation results are presented illustrating the
performance of the energy allocation algorithms.


  In this paper, we assess whether using non-linear dimension reduction
techniques pays off for forecasting inflation in real-time. Several recent
methods from the machine learning literature are adopted to map a large
dimensional dataset into a lower dimensional set of latent factors. We model
the relationship between inflation and the latent factors using constant and
time-varying parameter (TVP) regressions with shrinkage priors. Our models are
then used to forecast monthly US inflation in real-time. The results suggest
that sophisticated dimension reduction methods yield inflation forecasts that
are highly competitive to linear approaches based on principal components.
Among the techniques considered, the Autoencoder and squared principal
components yield factors that have high predictive power for one-month- and
one-quarter-ahead inflation. Zooming into model performance over time reveals
that controlling for non-linear relations in the data is of particular
importance during recessionary episodes of the business cycle or the current
COVID-19 pandemic.


  Diacritization plays a pivotal role in improving readability and
disambiguating the meaning of Arabic texts. Efforts have so far focused on
marking every eligible character (Full Diacritization). Comparatively
overlooked, Partial Diacritzation (PD) is the selection of a subset of
characters to be marked to aid comprehension where needed. Research has
indicated that excessive diacritic marks can hinder skilled readers--reducing
reading speed and accuracy. We conduct a behavioral experiment and show that
partially marked text is often easier to read than fully marked text, and
sometimes easier than plain text. In this light, we introduce
Context-Contrastive Partial Diacritization (CCPD)--a novel approach to PD which
integrates seamlessly with existing Arabic diacritization systems. CCPD
processes each word twice, once with context and once without, and diacritizes
only the characters with disparities between the two inferences. Further, we
introduce novel indicators for measuring partial diacritization quality (SR,
PDER, HDER, ERE), essential for establishing this as a machine learning task.
Lastly, we introduce TD2, a Transformer-variant of an established model which
offers a markedly different performance profile on our proposed indicators
compared to all other known systems.


  We present results on the stability of quantum systems consisting of a
negative charge $-q_1$ with mass $m_{1}$ and two positive charges $q_2$ and
$q_3$, with masses $m_{2}$ and $m_{3}$, respectively. We show that, for given
masses $m_{i}$, each instability domain is convex in the plane of the variables
$(q_{1}/q_{2}, q_{1}/q_{3})$. A new proof is given of the instability of muonic
ions $(\alpha, p, \mu^-)$. We then study stability in some critical regimes
where $q_3\ll q_2$: stability is sometimes restricted to large values of some
mass ratios; the behaviour of the stability frontier is established to leading
order in $q_3/q_2$. Finally we present some conjectures about the shape of the
stability domain, both for given masses and varying charges, and for given
charges and varying masses.


  The application of AC electric fields in aqueous suspensions of anisotropic
particles leads to unbalanced liquid flows and nonlinear, induced-charge
electrophoretic (ICEP) motion. We report experimental observations of the
motion of "Janus" microparticles with one dielectric and one metal-coated
hemisphere induced by uniform fields of frequency 100 Hz - 10 kHz in NaCl
solutions. The motion is perpendicular to the field axis and persists after
particles are attracted to a glass wall. This phenomenon may find applications
in microactuators, microsensors, and microfluidic devices.


  The present theoretical status of the parameter for direct CP violation
epsilon'/epsilon in the Standard Model is reviewed and compared with most
recent experimental measurements of the same quantity. After collecting the
basic expressions for epsilon'/epsilon, the situation of hadronic matrix
element calculations is summarised. The matrix elements constitute the dominant
source of uncertainty for theoretical determinations of epsilon'/epsilon. For
central values of the input parameters, the numerical analysis then yields
results which are generally below the experimental data. Possible reasons for
these findings are discussed.


  The Lagrangian of a hypergraph is a crucial tool for studying hypergraph
extremal problems. Though Lagrangians of some special structure hypergraphs
have closed-form solutions, it is a challenging problem to compute the
Lagrangian of a general large scale hypergraph. In this paper, we exploit a
fast computational scheme involving the adjacency tensor of a hypergraph.
Furthermore, we propose to utilize the gradient projection method on a simplex
from nonlinear optimization for solving the Lagrangian of a large scale
hypergraph iteratively. Using the Lojasiewicz gradient inequality, we analyze
the global and local convergence of the gradient projection method. Numerical
experiments illustrate that the proposed numerical method could compute
Lagrangians of large scale hypergraphs efficiently.


  In the Gaussian-modulated coherent states (GMCS) quantum key distribution
(QKD) protocol, Alice prepares quantum states \emph{actively}: for each
transmission, Alice generates a pair of Gaussian-distributed random numbers,
encodes them on a weak coherent pulse using optical amplitude and phase
modulators, and then transmits the Gaussian-modulated weak coherent pulse to
Bob. Here we propose a \emph{passive} state preparation scheme using a thermal
source. In our scheme, Alice splits the output of a thermal source into two
spatial modes using a beam splitter. She measures one mode locally using
conjugate optical homodyne detectors, and transmits the other mode to Bob after
applying appropriate optical attenuation. Under normal conditions, Alice's
measurement results are correlated to Bob's, and they can work out a secure
key, as in the active state preparation scheme. Given the initial thermal state
generated by the source is strong enough, this scheme can tolerate high
detector noise at Alice's side. Furthermore, the output of the source does not
need to be single mode, since an optical homodyne detector can selectively
measure a single mode determined by the local oscillator. Preliminary
experimental results suggest that the proposed scheme could be implemented
using an off-the-shelf amplified spontaneous emission source.


  Small fraction of isocurvature perturbations may exist and correlate with
adiabatic perturbations in the primordial perturbations. Naively switching off
isocurvature perturbations may lead to biased results. We study the effect of
dark matter isocurvature on the structure formation through N-body simulations.
From the best fit values, we run four sets of simulation with different initial
conditions and different box sizes. We find that, if the fraction of dark
matter isocurvature is small, we can not detect its signal through matter power
spectrum and two point correlation function with large scale survey. However,
the halo mass function can give an obvious signal. Compared to 5% difference on
matter power spectrum, it can get 37% at $z = 3$ on halo mass function. This
indicates that future high precise cluster count experiment can give stringent
constraints on dark matter isocurvature perturbations.


  A magnetised flux rope model, "Flux Rope in 3D" (FRi3D) is used in the
framework of European Heliospheric Forecasting Information Asset (EUHFORIA) for
studying the evolution and propagation of coronal mass ejections (CME). In this
paper, we rectify the mistake in the mentioned magnetic field profile of the
FRi3D model used in Maharana et al., 2022, and we clarify the actual profile
used in that work. In addition, we provide the recent updates introduced to the
FRi3D implementation in EUHFORIA like optimising the "ai.fri3d" python package
to reduce computational time and exploring different CME leg disconnection
methods to make the numerical implementation more stable.


  The outbreak of COVID-19 caused by SARS-CoV-2 has rapidly spread worldwide
and has caused over 1,400,000 infections and 80,000 deaths. There are currently
no drugs or vaccines with proven efficacy for its prevention and little
knowledge was known about the pathogenicity mechanism of SARS-CoV-2 infection.
Previous studies showed both virus and host-derived MicroRNAs (miRNAs) played
crucial roles in the pathology of virus infection. In this study, we use
computational approaches to scan the SARS-CoV-2 genome for putative miRNAs and
predict the virus miRNA targets on virus and human genome as well as the host
miRNAs targets on virus genome. Furthermore, we explore miRNAs involved
dysregulation caused by the virus infection. Our results implicated that the
immune response and cytoskeleton organization are two of the most notable
biological processes regulated by the infection-modulated miRNAs. Impressively,
we found hsa-miR-4661-3p was predicted to target the S gene of SARS-CoV-2, and
a virus-encoded miRNA MR147-3p could enhance the expression of TMPRSS2 with the
function of strengthening SARS-CoV-2 infection in the gut. The study may
provide important clues for the mechisms of pathogenesis of SARS-CoV-2.


  We suggest a method of reduction of mixed absolute and relative boundary
conditions to pure ones. The case of rank two tensor is studied in detail. For
four-dimensional disk the corresponding heat kernel is expressed in terms of
scalar heat kernels. The result for scaling behavior $\zeta (0)$ agrees with
previous calculations.


  The role of baroclinicity, which arises from the misalignment of pressure and
density gradients, is well-known in the vorticity equation, yet its role in the
kinetic energy budget has never been obvious. Here, we show that baroclinicity
appears naturally in the kinetic energy budget after carrying out the
appropriate scale decomposition. Strain generation by pressure and density
gradients, both barotropic and baroclinic, also results from our analysis.
These two processes underlie the recently identified mechanism of "baropycnal
work," which can transfer energy across scales in variable density flows. As
such, baropycnal work is markedly distinct from pressure-dilatation into which
the former is implicitly lumped in Large Eddy Simulations. We provide numerical
evidence from 1,024^3 direct numerical simulations of compressible turbulence.
The data shows excellent pointwise agreement between baropycnal work and the
nonlinear model we derive, supporting our interpretation of how it operates.


  We adapt a fitness function from evolutionary game theory as a mechanism for
aggregation and dispersal in a partial differential equation (PDE) model of two
interacting populations, described by density functions $u$ and $v$. We
consider a spatial model where individuals migrate up local fitness gradients,
seeking out locations where their given traits are more advantageous. The
resulting system of fitness gradient equations is a degenerate system having
spatially structured, smooth, steady state solutions characterized by constant
fitness throughout the domain. When populations are viewed as predator and
prey, our model captures prey aggregation behavior consistent with Hamilton's
selfish herd hypothesis. We also present weak steady state solutions in 1d that
are continuous but in general not smooth everywhere, with an associated fitness
that is discontinuous, piecewise constant. We give numerical examples of
solutions that evolve toward such weak steady states. We also give an example
of a spatial Lotka--Volterra model, where a fitness gradient flux creates
instabilities that lead to spatially structured steady states. Our results also
suggest that when fitness has some dependence on local interactions, a
fitness-based dispersal mechanism may act to create spatial variation across a
habitat.


  5G and beyond mobile networks will support heterogeneous use cases at an
unprecedented scale, thus demanding automated control and optimization of
network functionalities customized to the needs of individual users. Such
fine-grained control of the Radio Access Network (RAN) is not possible with the
current cellular architecture. To fill this gap, the Open RAN paradigm and its
specification introduce an open architecture with abstractions that enable
closed-loop control and provide data-driven, and intelligent optimization of
the RAN at the user level. This is obtained through custom RAN control
applications (i.e., xApps) deployed on near-real-time RAN Intelligent
Controller (near-RT RIC) at the edge of the network. Despite these premises, as
of today the research community lacks a sandbox to build data-driven xApps, and
create large-scale datasets for effective AI training. In this paper, we
address this by introducing ns-O-RAN, a software framework that integrates a
real-world, production-grade near-RT RIC with a 3GPP-based simulated
environment on ns-3, enabling the development of xApps and automated
large-scale data collection and testing of Deep Reinforcement Learning-driven
control policies for the optimization at the user-level. In addition, we
propose the first user-specific O-RAN Traffic Steering (TS) intelligent
handover framework. It uses Random Ensemble Mixture, combined with a
state-of-the-art Convolutional Neural Network architecture, to optimally assign
a serving base station to each user in the network. Our TS xApp, trained with
more than 40 million data points collected by ns-O-RAN, runs on the near-RT RIC
and controls its base stations. We evaluate the performance on a large-scale
deployment, showing that the xApp-based handover improves throughput and
spectral efficiency by an average of 50% over traditional handover heuristics,
with less mobility overhead.


  Privacy laws and regulations enforce data-driven systems, e.g., recommender
systems, to erase the data that concern individuals. As machine learning models
potentially memorize the training data, data erasure should also unlearn the
data lineage in models, which raises increasing interest in the problem of
Machine Unlearning (MU). However, existing MU methods cannot be directly
applied into recommendation. The basic idea of most recommender systems is
collaborative filtering, but existing MU methods ignore the collaborative
information across users and items. In this paper, we propose a general
erasable recommendation framework, namely LASER, which consists of Group module
and SeqTrain module. Firstly, Group module partitions users into balanced
groups based on their similarity of collaborative embedding learned via
hypergraph. Then SeqTrain module trains the model sequentially on all groups
with curriculum learning. Both theoretical analysis and experiments on two
real-world datasets demonstrate that LASER can not only achieve efficient
unlearning, but also outperform the state-of-the-art unlearning framework in
terms of model utility.


  Analog-to-digital converters (ADCs) allow physical signals to be processed
using digital hardware. Their conversion consists of two stages: Sampling,
which maps a continuous-time signal into discrete-time, and quantization, i.e.,
representing the continuous-amplitude quantities using a finite number of bits.
ADCs typically implement generic uniform conversion mappings that are ignorant
of the task for which the signal is acquired, and can be costly when operating
in high rates and fine resolutions. In this work we design task-oriented ADCs
which learn from data how to map an analog signal into a digital representation
such that the system task can be efficiently carried out. We propose a model
for sampling and quantization that facilitates the learning of non-uniform
mappings from data. Based on this learnable ADC mapping, we present a mechanism
for optimizing a hybrid acquisition system comprised of analog combining,
tunable ADCs with fixed rates, and digital processing, by jointly learning its
components end-to-end. Then, we show how one can exploit the representation of
hybrid acquisition systems as deep network to optimize the sampling rate and
quantization rate given the task by utilizing Bayesian meta-learning
techniques. We evaluate the proposed deep task-based ADC in two case studies:
the first considers symbol detection in multi-antenna digital receivers, where
multiple analog signals are simultaneously acquired in order to recover a set
of discrete information symbols. The second application is the beamforming of
analog channel data acquired in ultrasound imaging. Our numerical results
demonstrate that the proposed approach achieves performance which is comparable
to operating with high sampling rates and fine resolution quantization, while
operating with reduced overall bit rate.


  We present measurements of the dimensionless spin parameters and inner-disk
inclination of two stellar mass black holes. The spin parameter of SWIFT
J1753.5-0127 and GRO J1655-40 are estimated by modelling the strong reflection
signatures present in their XMM-Newton observations. Using a newly developed,
self-consistent reflection model which includes the blackbody radiation of the
disk as well as the effect of Comptonisation, blurred with a relativistic line
function, we infer the spin parameter of SWIFT J1753.5-0127 to be 0.76
+0.11-0.15. The inclination of this system is estimated at 55+2-7 degrees. For
GRO J1655-40 we find that the disk is significantly misaligned to the orbital
plane, with an innermost inclination of 30+5-10 degrees. Allowing the
inclination to be a free parameter we find a lower limit for the spin of 0.90,
this value increases to that of a maximal rotating black hole when the
inclination is set to that of the orbital plane of J1655-40. Our technique is
independent of the black hole mass and distance, uncertainties in which are
among the main contributors to the spin uncertainty in previous works.


  We consider the system identification problem of estimating a dynamical
parameter of a Markovian quantum open system (the atom maser), by performing
continuous time measurements in the system's output (outgoing atoms). Two
estimation methods are investigated and compared. On the one hand, the maximum
likelihood estimator (MLE) takes into account the full measurement data and is
asymptotically optimal in terms of its mean square error. On the other hand,
the `likelihood-free' method of approximate Bayesian computation (ABC) produces
an approximation of the posterior distribution for a given set of summary
statistics, by sampling trajectories at different parameter values and
comparing them with the measurement data via chosen statistics.
  Our analysis is performed on the atom maser model, which exhibits interesting
features such as bistability and dynamical phase transitions, and has
connections with the classical theory of hidden Markov processes. Building on
previous results which showed that atom counts are poor statistics for certain
values of the Rabi angle, we apply MLE to the full measurement data and
estimate its Fisher information. We then select several correlation statistics
such as waiting times, distribution of successive identical detections, and use
them as input of the ABC algorithm. The resulting posterior distribution
follows closely the data likelihood, showing that the selected statistics
contain `most' statistical information about the Rabi angle.


  The observed orbital period distribution of cataclysmic variables (CVs), the
space density derived from observations, and the observed orbital period
minimum are known to disagree with theoretical predictions since decades. More
recently, the white dwarf (WD) masses in CVs have been found to significantly
exceed those of single WDs, which is in contrast to theoretical expectations as
well. We here claim that all these problems are related and can be solved if
CVs with low-mass white dwarfs are driven into dynamically unstable mass
transfer due to consequential angular momentum loss (CAML). Indeed, assuming
CAML increases as a function of decreasing white dwarf mass can bring into
agreement the predictions of binary population models and the observed
properties of the CV population. We speculate that a common envelope like
evolution of CVs with low-mass WDs following a nova eruption might be the
physical process behind our empirical prescription of CAML.


  The entropy-area spectrum of a black hole has been a long-standing and
unsolved problem. Based on a recent methodology introduced by two of the
authors, for the black hole radiation (Hawking effect) as tunneling effect, we
obtain the entropy spectrum of a black hole. In Einstein's gravity, we show
that both entropy and area spectrum are evenly spaced. But in more general
theories (like Einstein-Gauss-Bonnet gravity), although the entropy spectrum is
equispaced, the corresponding area spectrum is not.


  In this paper we develop a quantum optical method to detect the axion-nucleon
interaction. We ultilize a levitated optomechanical system consisting of a
silica nanosphere and an optical cavity here. We translate the trapping
positions of the nanosphere, resulting the shift of its resonance frequency,
which can be determined from measuring the resulting resonance shift in the
transmission spectrum. Furthermore, The frequency shift can be related to the
additional forces due to two-axion exchange via substraction. Based on noise
ananlysis, estimation and calculation, we set the stringent prospective
constraints for the coupling constants of axion-neucleon interaction $g_{an}$
and $g_{ap}$. In the case of $g_{an}^2 = g_{ap}^2$ , our constraints are most
stringent at an ultrawide axion mass range approximately from $10^{-4}\mu eV$
to $10$ $eV$ .


  We investigate topological Hall effects in a metallic antiferromagnetic (AFM)
thin film and/or at the interface of an AFM insulator-normal metal bilayer with
a single skyrmion in the diffusive regime. To determine the spin and charge
Hall currents, we employed a Boltzmann kinetic equation with both
spin-dependent and spin-flip scatterings. The interaction between conduction
electrons and static skyrmions is included in the Boltzmann equation via the
corresponding emergent magnetic field arising from the skyrmion texture. We
compute intrinsic and extrinsic contributions to the topological spin Hall
effect and spin accumulation, induced by an AFM skyrmion. We show that although
the spin Hall current vanishes rapidly outside the skyrmion, the spin
accumulation can be finite at the edges far from the skyrmion, provided the
spin diffusion length is longer than the skyrmion radius. In addition, We show
that in the presence of a spin-dependent relaxation time, the topological
charge Hall effect is finite and we determine the corresponding Hall voltage.
Our results may help to explore antiferromagnetic skyrmions by electrical means
in real materials.


  The recent discovery of gravitational waves from GW170817, associated with a
short Gamma-Ray Burst (GRB) at a distance of $40$Mpc, has demonstrated that
short GRBs can occur locally and at a reasonable rate. Furthermore,
gravitational waves enable us to detect close by GRBs, even when we are
observing at latitudes far from the jet's axis. We consider here Compton
echoes, the scattered light from the prompt and afterglow emission. Compton
echoes, an as yet undetected counterpart of GRBs, peak in X-rays and maintain a
roughly constant flux for hundreds to thousands of years after the burst.
Though too faint to be detected in typical cosmological GRBs, a fraction of
close by bursts with a sufficiently large energy output in X-rays, and for
which the surrounding medium is sufficiently dense, may indeed be observed in
this way. The detection of a Compton echo could provide unique insight into the
burst properties and the environment's density structure. In particular, it
could potentially determine whether or not there was a successful jet that
broke through the compact binary merger ejecta. We discuss here the properties
and expectations from Compton echoes and suggest methods for detectability.


  We study the nonlocal equation $$-\varepsilon^2 \Delta u_\varepsilon + V
u_\varepsilon = \varepsilon^{-\alpha} \bigl(I_\alpha \ast \lvert
u_\varepsilon\rvert^p\bigr) \lvert u_\varepsilon \rvert^{p - 2}
u_\varepsilon\quad\text{in \(\mathbf{R}^N\)}, $$ where $N \ge 1$, $\alpha \in
(0, N)$, $I_\alpha (x) = A_\alpha/\lvert x \rvert^{N - \alpha}$ is the Riesz
potential and $\varepsilon > 0$ is a small parameter. We show that if the
external potential $V \in C (\mathbb{R}^N; [0, \infty))$ has a local minimum
and $p \in [2, (N + \alpha)/(N - 2)_+)$ then for all small $\varepsilon > 0$
the problem has a family of solutions concentrating to the local minimum of $V$
provided that: either $p > 1 + \max (\alpha, \frac{\alpha + 2}{2})/(N - 2)_+$,
or $p > 2$ and $\liminf_{\lvert x\rvert \to \infty} V (x) \lvert x \rvert^2 >
0$, or $p = 2$ and $\inf_{x \in \mathbb{R}^N} V (x) (1 + \lvert x \rvert^{N -
\alpha}) > 0$. Our assumptions on the decay of $V$ and admissible range of
$p\ge 2$ are optimal. The proof uses variational methods and a novel nonlocal
penalization technique that we develop in this work.


  This report explains the basic theory and common terminology of quantum
physics without assuming any knowledge of physics. It was written by a group of
applied mathematicians while they were reading up on the subject. The intended
audience consists of applied mathematicians, computer scientists, or anyone
else who wants to improve their understanding of quantum physics. We assume
that the reader is familiar with fundamental concepts of linear algebra,
differential equations, and to some extent the theory of Hilbert spaces. Most
of the material can be found in the book by Nielsen and Chuang and in the
lecture notes on open quantum systems by Lidar. Another excellent online source
of information is Wikipedia, even though most of its articles on quantum
physics assume a solid understanding of physics.


  It is essential that healthcare professionals and members of the healthcare
community can access and easily understand patient experiences in the real
world, so that care standards can be improved and driven towards personalised
drug treatment. Social media platforms and message boards are deemed suitable
sources of patient experience information, as patients have been observed to
discuss and exchange knowledge, look for and provide support online. This paper
tests the hypothesis that not all online patient experience information can be
treated and collected in the same way, as a result of the inherent differences
in the way individuals talk about their journeys, in different therapeutic
domains and or data sources.
  We used linguistic analysis to understand and identify similarities between
datasets, across patient language, between data sources (Reddit, SocialGist)
and therapeutic domains (cardiovascular, oncology, immunology, neurology). We
detected common vocabulary used by patients in the same therapeutic domain
across data sources, except for immunology patients, who use unique vocabulary
between the two data sources, and compared to all other datasets. We combined
linguistically similar datasets to train classifiers (CNN, transformer) to
accurately identify patient experience posts from social media, a task we refer
to as patient voice classification. The cardiovascular and neurology
transformer classifiers perform the best in their respective comparisons for
the Reddit data source, achieving F1-scores of 0.865 and 1.0 respectively. The
overall best performing classifier is the transformer classifier trained on all
data collected for this experiment, achieving F1-scores ranging between 0.863
and 0.995 across all therapeutic domain and data source specific test datasets.


  Consider the middle perversity intersection cohomology groups of various
compactifications of a Hermitian locally symmetric space. Rapoport and
independently Goresky and MacPherson have conjectured that these groups
coincide for the reductive Borel-Serre compactification and the
Baily-Borel-Satake compactification. This paper describes the theory of
L-modules and how it is used to solve the conjecture. More generally we
consider a Satake compactification for which all real boundary components are
equal-rank. Details will be given elsewhere (math.RT/0112251). As another
application of L-modules, we prove a vanishing theorem for the ordinary
cohomology of a locally symmetric space. This answers a question raised by
Tilouine.


  We consider a Kantorovich potential associated to an optimal transportation
problem between measures that are not necessarily absolutely continuous with
respect to the Lebesgue measure, but are comparable to the Lebesgue measure
when restricted to balls with radius greater than some $\delta>0$. Our main
results extend the classical regularity theory of optimal transportation to
this framework. In particular, we establish both H\"older and Sobolev
regularity results for Kantorovich potentials up to some critical length scale
depending on $\delta$. Our assumptions are very natural in the context of the
numerical computation of optimal maps, which often involves approximating by
sums of Dirac masses some measures that are absolutely continuous with
densities bounded away from zero and infinity on their supports.


  As the integration and the miniaturization of electronics devices, design
space become narrower and interactions between design factors affect their
reliability. This paper presents a methodology of quantifying the interaction
of each design factor in electronics devices. Thermal fatigue reliability of
BGA assembly was assessed with the consideration of the interaction between
design factors. Sensitivity analysis shows the influence of each design factor
to inelastic strain range of a solder joint characterizing the thermal fatigue
life if no interaction occurs. However, there is the interaction in BGA
assembly since inelastic strain range depends on not only a mismatch in CTE but
also a warpage of components. Clustering can help engineers to clarify the
relation between design factors. The variation in the influence was taken to
quantify the interaction of each design factor. Based on the interaction,
simple evaluating approach of inelastic strain range for the BGA assembly was
also developed. BGA package was simplified into a homogeneous component and
equivalent CTE wascalculated from the warpage of BGA and PCB. The estimated
equation was derived by using the response surface method as a function of
design factors. Based upon these analytical results, design engineers can rate
each factor's effect on reliability and assess the reliability of their basic
design plan at the concept design stage.


  We study the motion of smooth, closed, strictly convex hypersurfaces in
$\mathbb{R}^{n+1}$ expanding in the direction of their normal vector field with
speed depending on the $k$th elementary symmetric polynomial of the principal
radii of curvature $\sigma_k$ and support function $h$. A homothetic
self-similar solution to the flow that we will consider in this paper, if
exists, is a solution of the well-known $L_p$-Christoffel-Minkowski problem
$\varphi h^{1-p}\sigma_k=c$. Here $\varphi$ is a preassigned positive smooth
function defined on the unit sphere, and $c$ is a positive constant. For $1\leq
k\leq n-1, p\geq k+1$, assuming the spherical hessian of
$\varphi^{\frac{1}{p+k-1}}$ is positive definite, we prove the $C^{\infty}$
convergence of the normalized flow to a homothetic self-similar solution. One
of the highlights of our arguments is that we do not need the constant rank
theorem/deformation lemma of Guan-Ma and thus we give a partial answer to a
question raised in Guan-Xia. Moreover, for $k=n, p\geq n+1$, we prove the
$C^{\infty}$ convergence of the normalized flow to a homothetic self-similar
solution without imposing any further condition on $\varphi.$ In the final
section of the paper, for $1\leq k<n$, we will give an example that spherical
hessian of $\varphi^{\frac{1}{p+k-1}}$ is negative definite at some point and
the solution to the flow loses its smoothness.


  Starting with Hoare Logic over 50 years ago, numerous sound and relatively
complete program logics have been devised to reason about the diverse programs
encountered in the real world. This includes reasoning about computational
effects, particularly those effects that cause the program execution to branch
into multiple paths due to, e.g., nondeterministic or probabilistic choice.
  The recently introduced Outcome Logic reimagines Hoare Logic with effects at
its core, using an algebraic representation of choice to capture a variety of
effects. In this paper, we give the first relatively complete proof system for
Outcome Logic, handling general purpose looping for the first time. We also
show that this proof system applies to programs with various effects and that
it facilitates the reuse of proof fragments across different kinds of
specifications.


  We solve the coupled gap equations for the $\sigma$- and $\pi$-bands of
MgB$_2$ in the vortex state and calculate the resulting field dependencies of
the specific heat coefficient $\gamma$ and the thermal conductivity $\kappa $.
The crucial parameters of the theory are the interband pairing interaction
$\lambda_{\pi\sigma}$ and the ratio $s=\xi_{\sigma}/\xi_{\pi}$ of the coherence
lengths. For reasonably small $\lambda_{\pi\sigma}$ and s, the small gap
$\Delta_{\pi}$ decreases with increasing magnetic field $H$ much faster than
the large gap $\Delta_{\sigma} $. This gives rise to the observed rapid
increase of $\gamma_{\pi}$ and $\kappa_{\pi}$ for small fields while
$\gamma_{\sigma}$ and $\kappa_{\sigma}$ exhibit conventional field
dependencies. Inclusion of intraband impurity scattering yields fairly good
agreement with experiments for applied fields along the c axis.


  The robust principles of treating interference as noise (TIN) when it is
sufficiently weak, and avoiding it when it is not, form the background for this
work. Combining TIN with the topological interference management (TIM)
framework that identifies optimal interference avoidance schemes, a baseline
TIM-TIN approach is proposed which decomposes a network into TIN and TIM
components, allocates the signal power levels to each user in the TIN
component, allocates signal vector space dimensions to each user in the TIM
component, and guarantees that the product of the two is an achievable number
of signal dimensions available to each user in the original network.


  This paper considers steady surface waves `riding' a Beltrami flow (a
three-dimensional flow with parallel velocity and vorticity fields). It is
demonstrated that the hydrodynamic problem can be formulated as two equations
for two scalar functions of the horizontal spatial coordinates, namely the
elevation $\eta$ of the free surface and the potential $\Phi$ defining the
gradient part (in the sense of the Hodge-Weyl decomposition) of the horizontal
component of the tangential fluid velocity there. These equations are written
in terms of a nonlocal operator $H(\eta)$ mapping $\Phi$ to the normal fluid
velocity at the free surface, and are shown to arise from a variational
principle. In the irrotational limit the equations reduce to the
Zakharov-Craig-Sulem formulation of the classical three-dimensional steady
water-wave problem, while $H(\eta)$ reduces to the familiar Dirichlet-Neumann
operator.


  The Tolman-Oppenheimer-Snyder description gives exact analytical solutions
for an Einstein-matter system describing total gravitational collapse of a
zero-pressure perfect-fluid sphere, representing a massive star which has
exhausted its nuclear fuel. The star collapses to a point of infinite density
within a finite comoving proper time interval $[0,t_{*}]$, and the exterior
metric matches the Schwarzchild black hole metric. The description is
re-expressed in terms of a 'density function'
$u(t)=(\rho(t)/\rho_{o}))^{1/3}=R^{-1}(t)$ for initial density
$u_{0}=R^{-1}(0)=1$ and radius $R(0)$, whereby the general-relativistic
formulation reduces to an autonomous nonlinear ODE for $u(t)$. The solution
blows up or is singular at $t=t_{*}=\pi/2(8\pi G/3\rho_{o})^{1/2}$. The blowup
interval $[0,t_{*}]$ is partitioned into domains
$[0,t_{\epsilon}]\bigcup[t_{\epsilon},t_{*}]$,with
$t_{*}=t_{\epsilon}+|\epsilon|$ and $|\epsilon|\ll 1$, so that $t_{\epsilon}$
can be infinitesimally close to $t_{*}$. Randomness or 'stochastic control' is
introduced via the 'switching on' of specific (white-noise) perturbations at
$t=t_{\epsilon}$. Hybrid nonlinear ODES-SDES are then 'engineered' over the
partition. Within the Ito interpretation, the resulting density function
diffusion $\overline{u(t)}$ is proved to be a martingale whose supremum,
volatility and higher-order moments are finite, bounded and singularity free
for all finite $t>t_{\epsilon}$. The collapse is (comovingly) eternal but never
becomes singular. Extensive and rigorous boundedness and no-blowup criteria are
established via various methods, and blowup probability is always zero. The
density singularity is therefore smoothed or 'noise-suppressed'. Within the
Stratanovitch interpretation, the singularity formation probability is unity;
however, null recurrence ensures the expected comoving time for this to occur
is now infinite.


  Based on a comparison of the SRG/eROSITA catalog of X-ray active stars and
the Gaia catalog, a sample of 502 peculiar objects was obtained for which Gaia,
on one hand, detects statistically significant values of parallax or proper
motion and, on the other hand, registers signs of the non zero source extent in
the optical band. In the log ($F_X/F_{\rm opt}$) - (G-RP) color diagram these
objects are separated from the balk of X-ray active stars and are located in
the region typical for the galaxies with active nuclei. According to the SIMBAD
database, about $\sim 50$% of them are confirmed AGNs and galaxies with
spectroscopically measured redshifts, and only $\sim$1.4% are confirmed
Galactic objects. Spectroscopic observations of 19 unidentified objects on the
RTT-150 telescope demonstrated, that 18 of them are AGNs at redshifts
$\sim$0.01-0.3, and one object is a M star in our Galaxy. We discuss various
scenarios explaining the nature of such peculiar objects.


  There is a family of constructions to produce orthomodular structures from
modular lattices, lattices that are M and M*-symmetric, relation algebras, the
idempotents of a ring, the direct product decompositions of a set or group or
topological space, and from the binary direct product decompositions of an
object in a suitable type of category. We show that an interval [0, a] of such
an orthomodular structure constructed from A is again an orthomodular structure
constructed from some B built from A. When A is a modular lattice, this B is an
interval of A, and when A is an object in a category, this B is a factor of A.


  The transition from the microscopic Heisenberg model to the macroscopic
elastic theory is carried out for the chiral magnetics of MnSi-type with the
B20 crystal structure. Both exchange and Dzyaloshinskii-Moriya (DM)
interactions are taken into account for the first, second, and third magnetic
neighbors. The particular components of the DM vectors of bonds are found,
which are responsible for (i) the global magnetic twist and (ii) the canting
between four different spin sublattices. A possible mechanism for effective
reinforcement of the global magnetic twist is suggested: it is demonstrated
that the components of the DM vectors normal to corresponding interatomic bonds
become very important for the twisting power. The Ruderman-Kittel-Kasuya-Yosida
(RKKY) theory is used for model calculation of exchange parameters. It is found
that just the interplay between the exchange parameters of several magnetic
shells rather than the signs of DM vectors can be responsible for the
concentration-induced reverse of the magnetic chirality recently observed in
the Mn_(1-x)Fe_xGe crystals.


  In recent years, searches of archival X-ray data have revealed galaxies
exhibiting nuclear quasi-periodic eruptions with periods of several hours.
These are reminiscent of the tidal disruption of a star by a supermassive black
hole, and the repeated, partial stripping of a white dwarf in an eccentric
orbit around a ~10^5 solar mass black hole provides an attractive model. A
separate class of periodic nuclear transients, with significantly longer
timescales, have recently been discovered optically, and may arise from the
partial stripping of a main-sequence star by a ~10^7 solar mass black hole. No
clear connection between these classes has been made. We present the discovery
of an X-ray nuclear transient which shows quasi-periodic outbursts with a
period of weeks. We discuss possible origins for the emission, and propose that
this system bridges the two existing classes outlined above. This discovery was
made possible by the rapid identification, dissemination and follow up of an
X-ray transient found by the new live \swift-XRT transient detector,
demonstrating the importance of low-latency, sensitive searches for X-ray
transients.


  We undertake a detailed study of the gaugings of two-dimensional Yang-Mills
theory by its intrinsic charge conjugation 0-form and centre 1-form global
symmetries, elucidating their higher algebraic and geometric structures, as
well as the meaning of dual lower form symmetries. Our derivations of orbifold
gauge theories make use of a combination of standard continuum path integral
methods, networks of topological defects, and techniques from higher gauge
theory. We provide a unified description of higher and lower form gauge fields
for a $p$-form symmetry in the geometric setting of $p$-gerbes, and derive
reverse orbifolds by the dual $(-1)$-form symmetries. We identify those
orbifolds in which charge conjugation symmetry is spontaneously broken, and
relate the breaking to mixed anomalies involving $(-1)$-form symmetries. We
extend these considerations to gaugings by the non-invertible 1-form symmetries
of two-dimensional Yang-Mills theory by introducing a notion of generalized
$\theta$-angle.


  We focus on named entity recognition (NER) for Chinese social media. With
massive unlabeled text and quite limited labelled corpus, we propose a
semi-supervised learning model based on B-LSTM neural network. To take
advantage of traditional methods in NER such as CRF, we combine transition
probability with deep learning in our model. To bridge the gap between label
accuracy and F-score of NER, we construct a model which can be directly trained
on F-score. When considering the instability of F-score driven method and
meaningful information provided by label accuracy, we propose an integrated
method to train on both F-score and label accuracy. Our integrated model yields
7.44\% improvement over previous state-of-the-art result.


  We consider markets consisting of a set of indivisible items, and buyers that
have {\em sharp} multi-unit demand. This means that each buyer $i$ wants a
specific number $d_i$ of items; a bundle of size less than $d_i$ has no value,
while a bundle of size greater than $d_i$ is worth no more than the most valued
$d_i$ items (valuations being additive). We consider the objective of setting
prices and allocations in order to maximize the total revenue of the market
maker. The pricing problem with sharp multi-unit demand buyers has a number of
properties that the unit-demand model does not possess, and is an important
question in algorithmic pricing. We consider the problem of computing a revenue
maximizing solution for two solution concepts: competitive equilibrium and
envy-free pricing.
  For unrestricted valuations, these problems are NP-complete; we focus on a
realistic special case of "correlated values" where each buyer $i$ has a
valuation $v_i\qual_j$ for item $j$, where $v_i$ and $\qual_j$ are positive
quantities associated with buyer $i$ and item $j$ respectively. We present a
polynomial time algorithm to solve the revenue-maximizing competitive
equilibrium problem. For envy-free pricing, if the demand of each buyer is
bounded by a constant, a revenue maximizing solution can be found efficiently;
the general demand case is shown to be NP-hard.


  Precise measurement of the neutrino mixing angle $\theta_{13}$ is the primary
goal of the Double Chooz Experiment (DC), which is located in Chooz, France.
The inverse beta decay process provides a unique signature of reactor
anti-neutrino interactions, giving prompt signals from positron annihilation
and delayed signals from neutron capture by either Gadolinium (Gd) or Hydrogen
(H). This paper is dedicated to the latest nH analysis in Double Chooz.
Typically, The Gd analysis is primary since fewer background events are
involved. However, with accurate estimates of backgrounds and a precise
reconstruction of energy, the nH analysis gives a powerful independent
measurement of $\theta_{13}$.


  We explore the theoretical possibility of $^3P_0$ neutron superfluid in
dilute spin-polarized neutron matter, which may be relevant to the crust region
of a magnetized neutron star. In such a dilute regime where the neutron Fermi
energy is less than 1 MeV, the $^1S_0$ neutron superfluid can be suppressed by
a strong magnetic field of the compact star. In the low-energy limit relevant
for dilute neutron matter, the $^3P_0$ interaction is stronger than the $^3P_2$
one which is believed to induce the triplet superfluid in the core. We present
the ground-state phase diagram of dilute neutron matter with respect to the
magnetic field and numerically estimate the critical temperature of the $^3P_0$
neutron superfluid, which is found to exceed $10^7$ K.


  The operational meaning of spacetime fluctuations is discussed. Classical
spacetime geometry can be viewed as encoding the relations between the motions
of test particles in the geometry. By analogy, quantum fluctuations of
spacetime geometry can be interpreted in terms of the fluctuations of these
motions. Thus one can give meaning to spacetime fluctuations in terms of
observables which describe the Brownian motion of test particles. We will first
discuss some electromagnetic analogies, where quantum fluctuations of the
electromagnetic field induce Brownian motion of test particles. We next discuss
several explicit examples of Brownian motion caused by a fluctuating
gravitational field. These examples include lightcone fluctuations, variations
in the flight times of photons through the fluctuating geometry, and
fluctuations in the expansion parameter given by a Langevin version of the
Raychaudhuri equation. The fluctuations in this parameter lead to variations in
the luminosity of sources. Other phenomena which can be linked to spacetime
fluctuations are spectral line broadening and angular blurring of distant
sources.


  We show that under suitable non-degeneracy conditions, complete gradient flow
lines of the scalar curvature functional of a riemannian manifold perturb into
eternal forced mean curvature flows with large forcing term.


  Persistence, defined as the probability that a fluctuating signal has not
reached a threshold up to a given observation time, plays a crucial role in the
theory of random processes. It quantifies the kinetics of processes as varied
as phase ordering, reaction diffusion or interface relaxation dynamics. The
fact that persistence can decay algebraically with time with non trivial
exponents has triggered a number of experimental and theoretical studies.
However, general analytical methods to calculate persistence exponents cannot
be applied to the ubiquitous case of non-Markovian systems relaxing transiently
after an imposed initial perturbation. Here, we introduce a theoretical
framework that enables the non perturbative determination of persistence
exponents of $d$-dimensional Gaussian non-Markovian processes with general non
stationary dynamics relaxing to a steady state after an initial perturbation.
Two prototypical classes of situations are analyzed: either the system is
subjected to a temperature quench at initial time, or its past trajectory is
assumed to have been observed and thus known. Altogether, our results reveal
and quantify, on the basis of Gaussian processes, the deep impact of initial
perturbations on first-passage statistics of non-Markovian processes. Our
theory covers the case of spatial dimension higher than one, opening the way to
characterize non-trivial reaction kinetics for complex systems with
non-equilibrium initial conditions.


  We develop in this work a general version of paracontrolled calculus that
allows to treat analytically within this paradigm some singular partial
differential equations with the same efficiency as regularity structures. This
work deals with the analytic side of the story and offers a toolkit for the
study of such equations, under the form of a number of continuity results for
some operators. We illustrate the efficiency of this elementary approach on the
examples of the 3-dimensional generalised parabolic Anderson model equation and
the generalised KPZ equation driven by a (1+1)-dimensional space/time white
noise.


  The origin of the apparent thermalization in high-energy collisions is
investigated using the data of the ATLAS and CMS Collaborations at the LHC. For
this purpose, we analyze the transverse momentum distributions in the following
proton-proton collision processes, all at $\sqrt{s} = 13$ TeV: i) inclusive
inelastic $pp$ collisions; ii) single- and double-diffractive Drell-Yan
production $pp \to \mu^+ \mu^- X$; and iii) Higgs boson production. We confirm
the relation between the effective temperature and the hard scattering scale
observed at lower energies, and find that it extends even to the Higgs boson
production process. In addition we find that the thermal component disappears
in diffractive events (even though many charged hadrons are still produced). We
discuss the implications of our study for the mechanism of multi-particle
production -- in particular, we test the hypothesis about the link between
quantum entanglement and thermalization in high-energy collisions.


  Because of the advantages of easy deployment, low cost and non-contact,
computer vision-based structural displacement acquisition technique has
received wide attention and research in recent years. However, the displacement
field acquisition of large-scale structures is a challenging topic due to the
contradiction of camera field of view and resolution. This paper presents a
large-scale structural displacement field calculation framework with integrated
computer vision and physical constraints using only one camera. Firstly, the
full-field image of the large-scale structure is obtained by processing the
multi-view image using image stitching technique; secondly, the full-field
image is meshed and the node displacements are calculated using an improved
template matching method; and finally, the non-node displacements are described
using shape functions considering physical constraints. The developed framework
was validated using a scaled bridge model and evaluated by the proposed
evaluation index for displacement field calculation accuracy. This paper can
provide an effective way to obtain displacement fields of large-scale
structures efficiently and cost-effectively.


  The Leibniz rule for fractional Riemann-Liouville derivative is studied in
algebra of functions defined by Laplace convolution. This algebra and the
derived Leibniz rule are used in construction of explicit form of
stationary-conserved currents for linear fractional differential equations. The
examples of the fractional diffusion in 1+1 and the fractional diffusion in d+1
dimensions are discussed in detail. The results are generalized to the mixed
fractional-differential and mixed sequential fractional-differential systems
for which the stationarity-conservation laws are obtained. The derived currents
are used in construction of stationary nonlocal charges.


  Hyper-Positive real, matrix-valued, rational functions are associated with
absolute stability (the Lurie problem). Here, quantitative subsets of
Hyper-positive functions, related through nested inclusions, are introduced.
Structurally, this family of functions turns out to be matrix-convex and closed
under inversion.
  A state-space characterization of these functions, through a corresponding
Kalman-Yakubovich-Popov Lemma is given. Technically, the classical Linear
Matrix Inclusions, associated with passive systems, are here substituted by
Quadratic Matrix Inclusions.


  We analyze the symmetry breaking of matter-wave solitons in a pair of
cigar-shaped traps coupled by tunneling of atoms. The model is based on a
system of linearly coupled nonpolynomial Schr\"odinger equations (NPSEs).
Unlike the well-known spontaneous-symmetry-breaking (SSB) bifurcation in
coupled cubic equations, in the present model the SSB competes with the onset
of collapse in this system. Stability regions of symmetric and asymmetric
solitons, as well as the collapse region, are identified in the parameter space
of the system.


  We analytically investigate the ground-state properties of two-component
Bose-Einstein condensates with few ⁸⁷Rb atoms inside a high-quality
cavity quantum electrodynamics. In the SU(2) representation for atom, this
quantum system can be realized a generalized Dicke model with a quadratic term
arising from the interatomic interactions, which can be controlled
experimentally by Feshbach resonance technique. Moreover, this weak
interspecies interaction can give rise to an important zero-temperature quantum
phase transition from the normal to the superradiant phases, where the atomic
ensemble in the normal phase is collectively unexcited while is macroscopically
excited with coherent radiations in the superradiant phase. Finally, we propose
to observe this predicted quantum phase transition by measuring the direct and
striking signatures of the photon field in terms of a heterodyne detector out
of the cavity.


  CASP is an extension of ASP that allows for numerical constraints to be added
in the rules. PDDL+ is an extension of the PDDL standard language of automated
planning for modeling mixed discrete-continuous dynamics.
  In this paper, we present CASP solutions for dealing with PDDL+ problems,
i.e., encoding from PDDL+ to CASP, and extensions to the algorithm of the EZCSP
CASP solver in order to solve CASP programs arising from PDDL+ domains. An
experimental analysis, performed on well-known linear and non-linear variants
of PDDL+ domains, involving various configurations of the EZCSP solver, other
CASP solvers, and PDDL+ planners, shows the viability of our solution.


  The proportional fair resource allocation problem is a major problem studied
in flow control of networks, operations research, and economic theory, where it
has found numerous applications. This problem, defined as the constrained
maximization of $\sum_i \log x_i$, is known as the packing proportional
fairness problem when the feasible set is defined by positive linear
constraints and $x \in \mathbb{R}^{n}_{\geq 0}$. In this work, we present a
distributed accelerated first-order method for this problem which improves upon
previous approaches. We also design an algorithm for the optimization of its
dual problem. Both algorithms are width-independent. Finally, we show the
latter problem has applications to the volume reduction of bounding simplices
in an old linear programming algorithm of (YL82), and we obtain some
improvements as a result.


  We investigated the low-temperature properties of polycrystalline
HoNi_2^11B_2C by means of ac-susceptibility and neutron powder diffraction in
the temperature range of 1.5 to 10 K and zero magnetic field. A sample with
pronounced re-entrant behaviour was chosen since it exhibits a superconducting
state which is strongly affected by the intrinsic magnetism, the formation of
long range magnetic order, via pair-breaking. The evolution and volume
fractions of the three different magnetic structures were observed and
correlated to the superconducting behaviour.


  An MV-module is an MV-algebra endowed with a scalar multiplication with
scalars in a PMV-algebra (i.e. an MV-algebra endowed with a binary "ring-like"
product). We investigate the class of semisimple MV-modules over a semisimple
and totally ordered integral domain, and we prove an adjunction with a special
class of linear spaces.


  The article explains on a non-expert level how triaxial rotating nuclei may
attain a chiral structure.


  The rapid analysis of ongoing gravitational microlensing events has been
integral to the successful detection and characterisation of cool planets
orbiting low mass stars in the Galaxy. In this paper we present an
implementation of search and fit techniques on Graphical Processing Unit
hardware. The method allows for the rapid identification of candidate planetary
microlensing events and their subsequent followup for detailed
characterisation.


  Extending earlier results of Godsil and of Dobson and Malnic on Johnson
graphs, we characterise those merged Johnson graphs $J=J(n,k)_I$ which are
Cayley graphs, that is, which are connected and have a group of automorphisms
acting regularly on the vertices. We also characterise the merged Johnson
graphs which are not Cayley graphs but which have a transitive group of
automorphisms with vertex-stabilisers of order $2$. Even though these merged
Johnson graphs are all vertex-transitive, we show that only relatively few of
them are Cayley graphs or have a transitive group of automorphisms with
vertex-stabilisers of order $2$.


  This volume contains the proceedings of EXPRESS/SOS 2019: the Combined 26th
International Workshop on Expressiveness in Concurrency and the 16th Workshop
on Structural Operational Semantics, which was held on August 26, 2019, in
Amsterdam (The Netherlands), as an affiliated workshop of CONCUR 2019, the 30th
International Conference on Concurrency Theory.
  The EXPRESS/SOS workshop series aims at bringing together researchers
interested in the formal semantics of systems and programming concepts, and in
the expressiveness of computational models.


  Dense molecular gas tracers in the central 1 kpc region of the superwind
galaxy NGC 1808 have been imaged by ALMA at a resolution of 1" (~50 pc).
Integrated intensities and line intensity ratios of HCN (1-0), H$^{13}$CN
(1-0), HCO$^+$ (1-0), H$^{13}$CO$^+$ (1-0), HOC$^+$ (1-0), HCO$^+$ (4-3), CS
(2-1), C$_2$H (1-0), and previously detected CO (1-0) and CO (3-2) are
presented. SiO (2-1) and HNCO (4-3) are detected toward the circumnuclear disk
(CND), indicating the presence of shocked dense gas. There is evidence that an
enhanced intensity ratio of HCN(1-0)/HCO$^+$(1-0) reflects star formation
activity, possibly in terms of shock heating and electron excitation in the CND
and a star-forming ring at radius ~300 pc. A non-LTE analysis indicates that
the molecular gas traced by HCN, H$^{13}$CN, HCO$^+$, and H$^{13}$CO$^+$ in the
CND is dense ($n_{\mathrm{H}_2}$~$10^5$ cm$^{-3}$) and warm (20
K$<T_\mathrm{k}$<100 K). The calculations yield a low average gas density of
$n_{\mathrm{H}_2}$~$10^2\mathrm{-}10^3$ cm$^{-3}$ for a temperature of
$T_\mathrm{k}\geq30$ K in the nuclear outflow. Dense gas tracers HCN (1-0),
HCO$^+$ (1-0), CS (2-1), and C$_2$H (1-0) are detected for the first time in
the superwind of NGC 1808, confirming the presence of a velocity gradient in
the outflow direction.


  In this work a novel approach is presented for the isogeometric Boundary
Element analysis of domains that contain inclusions with different elastic
properties than the ones used for computing the fundamental solutions. In
addition the inclusion may exhibit inelastic material behavior. In this paper
only plane stress/strain problems are considered.
  In our approach the geometry of the inclusion is described using NURBS basis
functions. The advantage over currently used methods is that no discretization
into cells is required in order to evaluate the arising volume integrals. The
other difference to current approaches is that Kernels of lower singularity are
used in the domain term. The implementation is verified on simple finite and
infinite domain examples with various boundary conditions. Finally a practical
application in geomechanics is presented.


  We consider several transformation groups of a locally conformally K\"ahler
manifold and discuss their inter-relations. Among other results, we prove that
all conformal vector fields on a compact Vaisman manifold which is neither
locally conformally hyperk\"ahler nor a diagonal Hopf manifold are Killing,
holomorphic and that all affine vector fields with respect to the minimal Weyl
connection of a locally conformally K\"ahler manifold which is neither
Weyl-reducible nor locally conformally hyperk\"ahler are holomorphic and
conformal


  Event cameras are a paradigm shift in camera technology. Instead of full
frames, the sensor captures a sparse set of events caused by intensity changes.
Since only the changes are transferred, those cameras are able to capture quick
movements of objects in the scene or of the camera itself. In this work we
propose a novel method to perform camera tracking of event cameras in a
panoramic setting with three degrees of freedom. We propose a direct camera
tracking formulation, similar to state-of-the-art in visual odometry. We show
that the minimal information needed for simultaneous tracking and mapping is
the spatial position of events, without using the appearance of the imaged
scene point. We verify the robustness to fast camera movements and dynamic
objects in the scene on a recently proposed dataset and self-recorded
sequences.


  We consider the velocity fluctuations of a system of particles described by
the Inelastic Maxwell Model. The present work extends the methods, previously
employed to obtain the one-particle velocity distribution function, to the
study of the two particle correlations. Results regarding both the homogeneous
cooling process and the steady state driven regime are presented. In particular
we obtain the form of the pair correlation function in the scaling region of
the homogeneous cooling process and show that some of its moments diverge. This
fact has repercussions on the behavior of the energy fluctuations of the model.


  We combine MAP-Elites and highly parallelisable simulation to explore the
design space of a class of large legged robots, which stand at around 2m tall
and whose design and construction is not well-studied. The simulation is
modified to account for factors such as motor torque and weight, and presents a
reasonable fidelity search space. A novel robot encoding allows for
bio-inspired features such as legs scaling along the length of the body. The
impact of three possible control generation schemes are assessed in the context
of body-brain co-evolution, showing that even constrained problems benefit
strongly from coupling-promoting mechanisms. A two stage process in
implemented. In the first stage, a library of possible robots is generated,
treating user requirements as constraints. In the second stage, the most
promising robot niches are analysed and a suite of human-understandable design
rules generated related to the values of their feature variables. These rules,
together with the library, are then ready to be used by a (human) robot
designer as a Design Assist tool.


  Random population dynamics with catastrophes (events pertaining to possible
elimination of a large portion of the population) has a long history in the
mathematical literature. In this paper we study an ergodic model for random
population dynamics with linear growth and binomial catastrophes: in a
catastrophe, each individual survives with some fixed probability,
independently of the rest. Through a coupling construction, we obtain sharp
two-sided bounds for the rate of convergence to stationarity which are applied
to show that the model exhibits a cutoff phenomenon.


  The concept of friction-induced brake vibrations, commonly known as judder,
is investigated. Judder vibration is based on the class of geometrically
induced or kinematic constraint instability. After presenting the modal
coupling mechanism and the associated dynamic model, a stability analysis as
well as a sensitivity analysis have been conducted in order to identify
physical parameters for a brake design avoiding friction-induced judder
instability. Next, in order to reduce the size of the instability regions in
relation to possible system parameter combinations, robust stability via
\mu-synthesis is applied. By comparing the unstable regions between the initial
and controlled brake system, some general indications emerge and it appears
that robust stability via \mu-synthesis has some effect on the instability of
the brake system.


  We present Dynamics-Guided Diffusion Model, a data-driven framework for
generating manipulator geometry designs for a given manipulation task. Instead
of training different design models for each task, our approach employs a
learned dynamics network shared across tasks. For a new manipulation task, we
first decompose it into a collection of individual motion targets which we call
target interaction profile, where each individual motion can be modeled by the
shared dynamics network. The design objective constructed from the target and
predicted interaction profiles provides a gradient to guide the refinement of
finger geometry for the task. This refinement process is executed as a
classifier-guided diffusion process, where the design objective acts as the
classifier guidance. We evaluate our framework on various manipulation tasks,
under the sensor-less setting using only an open-loop parallel jaw motion. Our
generated designs outperform optimization-based and unguided diffusion
baselines relatively by 31.5% and 45.3% on average manipulation success rate.
With the ability to generate a design within 0.8 seconds, our framework could
facilitate rapid design iteration and enhance the adoption of data-driven
approaches for robotic mechanism design.


  The ordinary spectrum is restricted in its applications, since it is based on
the second order moments (auto and cross-covariances). Alternative approaches
to spectrum analysis have been investigated based on other measures of
dependence. One such approach was developed for univariate time series by the
authors of this paper using the local Gaussian auto-spectrum based on the local
Gaussian auto-correlations. This makes it possible to detect local structures
in univariate time series that looks like white noise when investigated by the
ordinary auto-spectrum. In this paper the local Gaussian approach is extended
to a local Gaussian cross-spectrum for multivariate time series. The local
Gaussian cross-spectrum has the desirable property that it coincides with the
ordinary cross-spectrum for Gaussian time series, which implies that it can be
used to detect non-Gaussian traits in the time series under investigation. In
particular: If the ordinary spectrum is flat, then peaks and troughs of the
local Gaussian spectrum can indicate nonlinear traits, which potentially might
reveal local periodic phenomena that goes undetected in an ordinary spectral
analysis.


  We study a renormalizable scalar singlet dark matter model based on $Z_4$
lepton flavor symmetry. A $\mu\tau$-philic scalar doublet is introduced to
explain the discrepancy between the experimental value and the theoretical
prediction of the muon anomalous magnetic moment. At the same time, these
flavored scalars play the role of a mediator which connects dark matter and
standard model particles. The observed relic abundance of the dark matter is
easily maintained while satisfying the current severe constraints on the dark
matter from various experiments and observations thanks to the flavor
off-diagonal interactions of scalar mediators. We also explore the possibility
of dark matter direct detection through the one-loop process.


  We present the discovery by the WASP-South survey, in close collaboration
with the Euler and TRAPPIST telescopes, of WASP-121 b, a new remarkable
short-period transiting hot Jupiter, whose planetary nature has been
statistically validated by the PASTIS software. The planet has a mass of
$1.183_{-0.062}^{+0.064}$ $M_{\mathrm{Jup}}$, a radius of 1.865 $\pm$ 0.044
$R_{\mathrm{Jup}}$, and transits every $1.2749255_{-0.0000025}^{+0.0000020}$
days an active F6-type main-sequence star ($V$=10.4, $1.353_{-0.079}^{+0.080}$
$M_{\odot}$, 1.458 $\pm$ 0.030 $R_{\odot}$, $T_{\mathrm{eff}}$ = 6460 $\pm$ 140
K). A notable property of WASP-121 b is that its orbital semi-major axis is
only $\sim$1.15 times larger than its Roche limit, which suggests that the
planet might be close to tidal disruption. Furthermore, its large size and
extreme irradiation ($\sim$$7.1\:10^{9}$ erg $\mathrm{s}^{-1}
\mathrm{cm}^{-2}$) make it an excellent target for atmospheric studies via
secondary eclipse observations. Using the TRAPPIST telescope, we indeed detect
its emission in the $z'$-band at better than $\sim$4$\sigma$, the measured
occultation depth being 603 $\pm$ 130 ppm. Finally, from a measurement of the
Rossiter-McLaughlin effect with the CORALIE spectrograph, we infer a
sky-projected spin-orbit angle of $257.8_{-5.5}^{+5.3}$ deg. This result
indicates a significant misalignment between the spin axis of the host star and
the orbital plane of the planet, the planet being in a nearly polar orbit. Such
a high misalignment suggests a migration of the planet involving strong
dynamical events with a third body.


  We show that A. Javanpeykar's proof of Belyi's theorem for smooth complete
intersections of general type in ordinary projective spaces can be generalized
to smooth complete intersections of general type in generalized Grassmannians
and weighted projective spaces.
  We also propose an explicit approach to the generalization of Belyi's theorem
to smooth complete intersections of general type in weighted generalized
Grassmannians.


  The WKB equations for dynamics of the surface plasmon polariton (SPP)
wavepacket are studied. The dispersion law for the SPP in the metal-dielectric
heterostructure with varying thickness of a perforated dielectric layer is
rigorously calculated and investigated using the scattering matrix method. Two
channels of the SPP wavepacket optical losses related to the absorption in a
metal and to the SPP leakage are analyzed. It is shown that change of the
dielectric layer thickness acts on the SPP as an external force leading to
evolution of its quasimomentum and to the wavepacket reversal or even to the
optical Bloch oscillations (BO). Properties of these phenomena are investigated
and discussed. Typical values of the BO amplitude are about tens of microns and
the period is around tens or hundreds of femtoseconds.


  We analyze how the crust equation of state affects several neutron star
properties and how it impacts on possible constraints inferred from
astrophysical observations. Using three distinct crusts, we generate three sets
of model-independent equations of state describing stellar matter from a Taylor
expansion around saturation density. The equations of state are
thermodynamically consistent, causal, and compatible with astrophysical
observations. The relations between the tidal deformability $\Lambda$ and
compactness $C$, Love number $k_2$ and radius of neutron star with mass $M$ are
studied, and the effect of the crust equation of state on these relations
analyzed. In most of the relations, the impact of the crust equation of state
is not larger that 2\%. If, however, a fixed neutron star mass is considered,
the relation between the tidal deformability and the radius depends on the
crust. We have found that the relation $\Lambda_{M_i} = \alpha R_{M_i}^{\beta}$
becomes almost exact and crust independent for massive neutron stars. It is
shown that it is possible to determine the tidal deformability of an
1.4$M_\odot$ star from the GW179817 effective tidal deformability
$\tilde\Lambda$ with an accuracy of at least $\approx 10\%$. A high correlation
between $\tilde\Lambda$ and the radius of the most massive star of the neutron
star binary was confirmed, however, it was demonstrated that the crust has an
effect of $\approx 14\%$ on this relation. We have found that the relation
$\Lambda_1/\Lambda_2=q^a$ depends on $M_{\text{chirp}}$ as $a\sim
\sqrt{M_{\text{chirp}}}$.


  Satellite imagery analysis plays a pivotal role in remote sensing; however,
information loss due to cloud cover significantly impedes its application.
Although existing deep cloud removal models have achieved notable outcomes,
they scarcely consider contextual information. This study introduces a
high-performance cloud removal architecture, termed Progressive Multi-scale
Attention Autoencoder (PMAA), which concurrently harnesses global and local
information to construct robust contextual dependencies using a novel
Multi-scale Attention Module (MAM) and a novel Local Interaction Module (LIM).
PMAA establishes long-range dependencies of multi-scale features using MAM and
modulates the reconstruction of fine-grained details utilizing LIM, enabling
simultaneous representation of fine- and coarse-grained features at the same
level. With the help of diverse and multi-scale features, PMAA consistently
outperforms the previous state-of-the-art model CTGAN on two benchmark
datasets. Moreover, PMAA boasts considerable efficiency advantages, with only
0.5% and 14.6% of the parameters and computational complexity of CTGAN,
respectively. These comprehensive results underscore PMAA's potential as a
lightweight cloud removal network suitable for deployment on edge devices to
accomplish large-scale cloud removal tasks. Our source code and pre-trained
models are available at https://github.com/XavierJiezou/PMAA.


  We have analyzed the influence of the stellar populations, from which SN
progenitors come from, on the observational outcome, including the metal free
Pop. III. We use our models to study the evolution of the progenitor, the
subsequent explosion and the light curves.
  For Type Ia, the variation of the main sequence mass of the progenitor of the
exploding WD, produces an offset in the maximum-decline relation of 0.2 mag.
This effect is critical for the use of high redshift Type Ia SNe as
cosmological standard candles. In contrast, the metallicity does not change the
above relation (at maximum, Delta M_V < 0.06 mag).
  For Type II, we find a dependence of the light curve properties with both,
main sequence mass and metallicity of the progenitor, and we identify a rather
homogeneous subclass, {\it Extreme} II-P, that may be used as a quasi-standard
candle. Note that, although not as good as Type Ia for distance determinations,
Type II are expected to occur since the first stars were formed.