  We investigate whether the globular clusters (GCs) in the recently published
sample of GCs in the Fornax cluster by Bergond and coworkers are indeed
intra-cluster objects. We combine the catalogue of radial velocity measurements
by Bergond et al. with our CTIO MOSAIC photometry in the Washington system and
analyse the relation of metal-poor and metal-rich GCs with their host galaxies.
The metal-rich GCs appear to be kinematically associated with their respective
host galaxies. The vast majority of the metal-poor GCs found in between the
galaxies of the Fornax cluster have velocities which are consistent with them
being members of the very extended NGC 1399 GC system. We find that when the
sample is restricted to the most accurate velocity measurements, the GC
velocity dispersion profile can be described with a mass model derived for the
NGC 1399 GC system within 80 kpc. We identify one ``vagrant'' GC whose radial
velocity suggests that it is not bound to any galaxy unless its orbit has a
very large apogalactic distance.


  We do a complete calculation of the stochastic gravitational wave background
to be expected from cosmic strings. We start from a population of string loops
taken from simulations, smooth these by Lorentzian convolution as a model of
gravitational back reaction, calculate the average spectrum of gravitational
waves emitted by the string population at any given time, and propagate it
through a standard model cosmology to find the stochastic background today. We
take into account all known effects, including changes in the number of
cosmological relativistic degrees of freedom at early times and the possibility
that some energy is in rare bursts that we might never have observed.


  A tree with at most k leaves is called k-ended tree, and a tree with exactly
k leaves is called k-end tree, where a leaf is a vertex of degree one.
Contraction of a graph G along the edge e means deleting the edge e and
identifying its end vertices and deleting all edges between every two vertex
except one edge to gain again a simple graph and is denoted bye G/e. In this
paper we prove some theorems related to a graph and its contraction. For
example we prove the following theorem. If G is a connected graph that has a
spanning k-end tree and |V (G)| > K + 1 then there exist an edge e such G/e has
a spanning k-end tree.


  Linear algebra computations are foundational for neural networks and machine
learning, often handled through arrays. While many functional programming
languages feature lists and recursion, arrays in linear algebra demand
constant-time access and bulk operations. To bridge this gap, some languages
represent arrays as (eager) functions instead of lists. In this paper, we
connect this idea to a formal logical foundation by interpreting functions as
the usual negative types from polarized type theory, and arrays as the
corresponding dual positive version of the function type. Positive types are
defined to have a single elimination form whose computational interpretation is
pattern matching. Just like (positive) product types bind two variables during
pattern matching, (positive) array types bind variables with multiplicity
during pattern matching. We follow a similar approach for Booleans by
introducing conditionally-defined variables.
  The positive formulation for the array type enables us to combine typed
partial evaluation and common subexpression elimination into an elegant
algorithm whose result enjoys a property we call maximal fission, which we
argue can be beneficial for further optimizations. For this purpose, we present
the novel intermediate representation indexed administrative normal form
(AiNF), which relies on the formal logical foundation of the positive
formulation for the array type to facilitate maximal loop fission and
subsequent optimizations. AiNF is normal with regard to commuting conversion
for both let-bindings and for-loops, leading to flat and maximally fissioned
terms. We mechanize the translation and normalization from a simple surface
language to AiNF, establishing that the process terminates, preserves types,
and produces maximally fissioned terms.


  We study the dual linear code of points and generators on a non-singular
Hermitian variety $\mathcal{H}(2n+1,q^2)$. We improve the earlier results for
$n=2$, we solve the minimum distance problem for general $n$, we classify the
$n$ smallest types of code words and we characterize the small weight code
words as being a linear combination of these $n$ types.


  Trusted Execution Environments (TEEs) have been proposed as a solution to
protect code confidentiality in scenarios where computation is outsourced to an
untrusted operator. We study the resilience of such solutions to side-channel
attacks in two commonly deployed scenarios: when a confidential code is a
native binary that is shipped and executed within a TEE and when the
confidential code is an intermediate representation (IR) executed on top of a
runtime within a TEE. We show that executing IR code such as WASM bytecode on a
runtime executing in a TEE leaks most IR instructions with high accuracy and
therefore reveals the confidential code. Contrary to IR execution, native
execution is much less susceptible to leakage and largely resists even the most
powerful side-channel attacks. We evaluate native execution leakage in Intel
SGX and AMD SEV and experimentally demonstrate end-to-end instruction
extraction on Intel SGX, with WASM bytecode as IR executed within WAMR, a
hybrid between a JIT compiler and interpreter developed by Intel. Our
experiments show that IR code leakage from such systems is practical and
therefore question the security claims of several commercial solutions which
rely on TEEs+WASM for code confidentiality.


  The task of Named Entity Recognition (NER) is an important component of many
natural language processing systems, such as relation extraction and knowledge
graph construction. In this work, we present a simple and effective approach
for Named Entity Recognition. The main idea of our approach is to encode the
input subword sequence with a pre-trained transformer such as BERT, and then,
instead of directly classifying the word labels, another layer of transformer
is added to the subword representation to better encode the word-level
interaction. We evaluate our approach on three benchmark datasets for
scientific NER, particularly in the computer science and biomedical domains.
Experimental results show that our model outperforms the current
state-of-the-art on SciERC and TDM datasets without requiring external
resources or specific data augmentation. Code is available at
\url{https://github.com/urchade/HNER}.


  The clumpy stellar wind from the companion star in high mass X-ray binaries
causes variable, partial absorption of the emission from the X-ray source. We
studied XMM-Newton observations from the 7.22 d-long "Cyg X-1 Hard state
Observations of a Complete Binary Orbit in X-rays" (CHOCBOX) monitoring
campaign, in order to constrain the effects of the stellar wind on the
short-timescale X-ray spectral-timing properties of the source. We find these
properties to change significantly in the presence of the wind. In particular,
the longest sampled timescales (corresponding to temporal frequencies of
$\nu\sim$ 0.1-1 Hz) reveal an enhancement of the fractional variability power,
while on the shortest sampled timescales ($\nu\sim$ 1-10 Hz) the variability is
suppressed. In addition, we observe a reduction (by up to a factor of $\sim$
1.8) of the otherwise high coherence between soft and hard band light curves,
as well as of the amplitude of the hard X-ray lags intrinsic to the X-ray
continuum. The observed increase of low frequency variability power can be
explained in terms of variations of the wind column density as a consequence of
motions of the intervening clumps. In this scenario (and assuming a terminal
velocity of $v_{\infty}=2400\ {\rm km\ s^{-1}}$), we obtain an estimate of $l
\sim$ 0.5-1.5 $\times 10^{-4} R_{\ast}$ for the average radial size of a clump.
On the other hand, we suggest the behaviour at high frequencies to be due to
scattering in an optically thicker medium, possibly formed by collision of the
stellar wind with the edge of the disc.


  Surface reconstruction has traditionally relied on the Multi-View Stereo
(MVS)-based pipeline, which often suffers from noisy and incomplete geometry.
This is due to that although MVS has been proven to be an effective way to
recover the geometry of the scenes, especially for locally detailed areas with
rich textures, it struggles to deal with areas with low texture and large
variations of illumination where the photometric consistency is unreliable.
Recently, Neural Implicit Surface Reconstruction (NISR) combines surface
rendering and volume rendering techniques and bypasses the MVS as an
intermediate step, which has emerged as a promising alternative to overcome the
limitations of traditional pipelines. While NISR has shown impressive results
on simple scenes, it remains challenging to recover delicate geometry from
uncontrolled real-world scenes which is caused by its underconstrained
optimization. To this end, the framework PSDF is proposed which resorts to
external geometric priors from a pretrained MVS network and internal geometric
priors inherent in the NISR model to facilitate high-quality neural implicit
surface learning. Specifically, the visibility-aware feature consistency loss
and depth prior-assisted sampling based on external geometric priors are
introduced. These proposals provide powerfully geometric consistency
constraints and aid in locating surface intersection points, thereby
significantly improving the accuracy and delicate reconstruction of NISR.
Meanwhile, the internal prior-guided importance rendering is presented to
enhance the fidelity of the reconstructed surface mesh by mitigating the biased
rendering issue in NISR. Extensive experiments on the Tanks and Temples dataset
show that PSDF achieves state-of-the-art performance on complex uncontrolled
scenes.


  We establish the existence of wave-like solutions to spatially coupled
graphical models which, in the large size limit, can be characterized by a
one-dimensional real-valued state. This is extended to a proof of the threshold
saturation phenomenon for all such models, which includes spatially coupled
irregular LDPC codes over the BEC, but also addresses hard-decision decoding
for transmission over general channels, the CDMA multiple-access problem,
compressed sensing, and some statistical physics models.
  For traditional uncoupled iterative coding systems with two components and
transmission over the BEC, the asymptotic convergence behavior is completely
characterized by the EXIT curves of the components. More precisely, the system
converges to the desired fixed point, which is the one corresponding to perfect
decoding, if and only if the two EXIT functions describing the components do
not cross. For spatially coupled systems whose state is one-dimensional a
closely related graphical criterion applies. Now the curves are allowed to
cross, but not by too much. More precisely, we show that the threshold
saturation phenomenon is related to the positivity of the (signed) area
enclosed by two EXIT-like functions associated to the component systems, a very
intuitive and easy-to-use graphical characterization.
  In the spirit of EXIT functions and Gaussian approximations, we also show how
to apply the technique to higher dimensional and even infinite-dimensional
cases. In these scenarios the method is no longer rigorous, but it typically
gives accurate predictions. To demonstrate this application, we discuss
transmission over general channels using both the belief-propagation as well as
the min-sum decoder.


  In this paper, we revisit some classical and recent works on modelling
slide-contact with wear and propose their generalisation. Namely, we upgrade
the relation between the pressure and the wear rate by incorporating some
non-local time-dependence. To this effect, we use a combination of fractional
calculus and relaxation effects. Moreover, we consider a possibility when the
load is not constant in time. The proposed model is analysed and solved. The
results are illustrated numerically and comparison with similar models is
discussed.


  The Orion-Eridanus superbubble, formed by the nearby Orion high mass
star-forming region, contains multiple bright H$\alpha$ filaments on the
Eridanus side of the superbubble. We examine the implications of the H$\alpha$
brightnesses and sizes of these filaments, the Eridanus filaments. We find that
either the filaments must be highly elongated along the line of sight or they
cannot be equilibrium structures illuminated solely by the Orion star-forming
region. The Eridanus filaments may, instead, have formed when the
Orion-Eridanus superbubble encountered and compressed a pre-existing, ionized
gas cloud, such that the filaments are now out of equilibrium and slowly
recombining.


  In this paper laser cooling of atoms with a narrow-line optical transition,
i.e. in regimes of quantum nature of laser-light interactions resulting in a
significant recoil effect, is studied. It is demonstrated that a minimum laser
cooling temperature for two-level atom in standing wave reached for red
detuning close to 3 recoil frequency greatly different from the theory used for
a semiclassical description of Doppler cooling. A set of dimensionless
parameters uniquely characterizing the time evolution and the steady state of
different atoms with narrow-line optical transitions in the laser field is
introduced. The results can be used for analysis of optimal conditions for
laser cooling of atoms with narrow lines such as $Ca$, $Sr$, and $Mg$, which
are of great interest for atomic clocks.


  The control of optical fields is usually achieved through the electro-optic
or acousto-optic effect in single-crystal ferroelectric or polar compounds such
as LiNbO3 or quartz. In recent years, tremendous progress has been made in
ferroelectric oxide thin film technology - a field which is now a strong
driving force in areas such as electronics, spintronics and photovoltaics.
Here, we apply epitaxial strain engineering to tune the optical response of
BiFeO3 thin films, and find a very large variation of the optical index with
strain, corresponding to an effective elasto-optic coefficient larger than that
of quartz. We observe a concomitant strain-driven variation in light absorption
- reminiscent of piezochromism - which we show can be manipulated by an
electric field. This constitutes an electrochromic effect that is reversible,
remanent and not driven by defects. These findings broaden the potential of
multiferroics towards photonics and thin film acousto-optic devices, and
suggest exciting device opportunities arising from the coupling of ferroic,
piezoelectric and optical responses.


  The main purpose of this paper is to establish the existence, nonexistence
and symmetry of nontrivial solutions to the higher order Brezis-Nirenberg
problems associated with the GJMS operators $P_k$ on bounded domains in the
hyperbolic space $\mathbb{H}^n$ and as well as on the entire hyperbolic space
$\mathbb{H}^n$. Among other techniques, one of our main novelties is to use
crucially the Helgason-Fourier analysis on hyperbolic spaces and the higher
order Hardy-Sobolev-Maz'ya inequalities and careful study of delicate
properties of Green's functions of $P_k-\lambda$ on hyperbolic spaces which are
of independent interests in dealing with such problems. Such Green's functions
allow us to obtain the integral representations of solutions and thus to avoid
using the maximum principle to establish the symmetry of solutions.


  Entanglement entropy is one of the most prominent measures in quantum
physics. We show that it has an interesting ergotropic interpretation in terms
of unitarily extracted work. It determines how much energy one can extract from
a source of pure unknown states by applying unitary operations when only local
measurements can be performed to characterize this source. Additionally,
entanglement entropy sets a limit on the minimal temperature to which these
partially characterized states can be cooled down, by using only unitary
operations.


  Thermal fusion plasmas initiated by standing whistler waves are investigated
numerically by two- and one-dimensional Particle-in-Cell simulations. When a
standing whistler wave collapses due to the wave breaking of ion plasma waves,
the energy of the electromagnetic waves transfers directly to the ion kinetic
energy. Here we find that the ion heating by the standing whistler wave is
operational even in multi-dimensional simulations of multi-ion species targets,
such as deuterium-tritium (DT) ices and solid ammonia borane (H$_6$BN). The
energy conversion efficiency to ions becomes as high as 15% of the injected
laser energy, which depends significantly on the target thickness and laser
pulse duration. The ion temperature could reach a few tens of keV or much
higher if appropriate laser-plasma conditions are selected. DT fusion plasmas
generated by this method must be useful as efficient neutron sources. Our
numerical simulations suggest that the neutron generation efficiency exceeds
10$^9$ n/J per steradian, which is beyond the current achievements of the
state-of-the-art laser experiments. The standing whistler wave heating would
expand the experimental possibility for an alternative ignition design of
magnetically confined laser fusion, and also for more difficult fusion
reactions including the aneutronic proton-boron reaction.


  The phenomenological theory of the flexomagnetoelectric coupling in crystals
of the cubic, tetragonal and orthorhombic crystal systems has been suggested.
Secondary role of the crystal structure chirality was shown. Oppositely,
significant role of the crystallographic point group type (symmetric,
alternating, dihedral or cyclic) in the flexomagnetoelectric coupling has been
derived. It was shown, that conceptually new features of the
flexomagnetoelectric effects are expected in the crystals of the cyclic groups
(crystal classes 4/m, 4^- and 4). Proposed verification of the theory is
investigation of the domain wall bend details (changes of the effect symmetry).
Special case of such verification near the compensation point is suggested.
First-principles mechanisms of the flexomagnetoelectric interaction were
discussed.


  Recently, the KOTO experiment at J-PARC has observed three anomalous events
in the flavor-changing rare decay $K_L \to \pi^0 \nu \bar\nu$, which indicates
that the corresponding branching ratio is almost two orders of magnitude larger
than the Standard Model (SM) prediction. Taking this intriguing result at face
value, we explore model implications of its viable explanation by a long-lived
light SM-singlet scalar ($S$) emission, i.e. $K_L \to \pi^0 S$, with $S$
decaying outside the KOTO detector. We derive constraints on the parameter
space of such a light scalar in the context of three simple models: (i) a real
singlet scalar extension of the SM; (ii) a $B-L$ extension where neutrino
masses arise via type-I seesaw mechanism from $B-L$ breaking; and (iii) a
TeV-scale left-right symmetric model. The flavor-changing couplings needed to
explain the KOTO excess in models (i) and (ii) originate from tree-level mixing
of the scalar with SM Higgs field ($h$), and in model (iii), from the mixing of
$S$ and $h$ with the neutral component of the heavy bidoublet Higgs field.
After taking into account the stringent constraints from high-precision
searches for flavor-changing charged and neutral kaon decays at NA62, E949,
KOTO and CHARM experiments, as well as the astrophysical and cosmological
constraints on a light scalar, such as those from supernova energy loss, big
bang nucleosynthesis and relativistic degrees of freedom, we find that the
light scalar interpretation of the KOTO excess is allowed in all these models.
Parts of the parameter range can be tested in future NA62 and DUNE experiments.


  In this paper, we propose to use a Conditional Generative Adversarial Network
(CGAN) for distilling (i.e. transferring) knowledge from sensor data and
enhancing low-resolution target detection. In unconstrained surveillance
settings, sensor measurements are often noisy, degraded, corrupted, and even
missing/absent, thereby presenting a significant problem for multi-modal
fusion. We therefore specifically tackle the problem of a missing modality in
our attempt to propose an algorithm based on CGANs to generate representative
information from the missing modalities when given some other available
modalities. Despite modality gaps, we show that one can distill knowledge from
one set of modalities to another. Moreover, we demonstrate that it achieves
better performance than traditional approaches and recent teacher-student
models.


  In this paper we investigate pre-derivations of filiform Leibniz algebras.
Recall that the set of filiform Leibniz algebras of fixed dimension can be
decomposed into three non-intersected families. We describe the pre-derivation
of filiform Leibniz algebras for the first and second families. We found
sufficient conditions under which filiform Leibniz algebras are strongly
nilpotent. Moreover, for the first and second families, we give the description
of characteristically nilpotent algebras which are non-strongly nilpotent.


  Adding photovoltaic (PV) systems in distribution networks, while desirable
for reducing the carbon footprint, can lead to voltage violations under high
solar-low load conditions. The inability of traditional volt-VAr control in
eliminating all the violations is also well-known. This paper presents a novel
coordinated inverter control methodology that leverages system-wide situational
awareness to significantly improve hosting capacity (HC). The methodology
employs a real-time voltage-reactive power (VQ) sensitivity matrix in an
iterative linear optimizer to calculate the minimum reactive power intervention
from PV inverters needed for mitigating over-voltage without resorting to
active power curtailing or requiring step voltage regulator setting changes.
The algorithm is validated using the EPRI J1 feeder under an extensive set of
realistic use cases and is shown to provide 3x improvement in HC under all
scenarios.


  While the distribution of spin periods of High Mass X-ray Binaries (HMXBs)
spans more than four orders of magnitude (69ms - 25min), the few known X-ray
pulsars accreting from very low mass companions (<1 Msun) have very similar
periods between 5.4 and 8.7s . These pulsars display also several other
similarities and they are probably members of a subclass of Low Mass X-ray
Binaries (LMXBs) with similar magnetic field (a few 10^11 G), companion stars
and, possibly, evolutionary histories. If they are rotating at, or close to,
the equilibrium period, their properties are consistent with luminosities of
the order of a few 10^35 erg/s. These pulsars might represent the closest
members of a subclass of LMXBs characterized by lower luminosities, higher
magnetic fields and smaller ages than non-pulsating LMXBs.


  We address representation learning for large-scale instance-level image
retrieval. Apart from backbone, training pipelines and loss functions, popular
approaches have focused on different spatial pooling and attention mechanisms,
which are at the core of learning a powerful global image representation. There
are different forms of attention according to the interaction of elements of
the feature tensor (local and global) and the dimensions where it is applied
(spatial and channel). Unfortunately, each study addresses only one or two
forms of attention and applies it to different problems like classification,
detection or retrieval.
  We present global-local attention module (GLAM), which is attached at the end
of a backbone network and incorporates all four forms of attention: local and
global, spatial and channel. We obtain a new feature tensor and, by spatial
pooling, we learn a powerful embedding for image retrieval. Focusing on global
descriptors, we provide empirical evidence of the interaction of all forms of
attention and improve the state of the art on standard benchmarks.


  Deep Convolutional Neural Networks (CNNs) are the state-of-the-art in image
classification. Since CNN feed forward propagation involves highly regular
parallel computation, it benefits from a significant speed-up when running on
fine grain parallel programmable logic devices. As a consequence, several
studies have proposed FPGA-based accelerators for CNNs. However, because of the
large computationalpower required by CNNs, none of the previous studies has
proposed a direct mapping of the CNN onto the physical resources of an FPGA,
allocating each processing actor to its own hardware instance.In this paper, we
demonstrate the feasibility of the so called direct hardware mapping (DHM) and
discuss several tactics we explore to make DHM usable in practice. As a proof
of concept, we introduce the HADDOC2 open source tool, that automatically
transforms a CNN description into a synthesizable hardware description with
platform-independent direct hardware mapping.


  The binary black holes (BBHs) formed near the supermassive black holes
(SMBHs) in the galactic nuclei would undergo eccentricity excitation due to the
gravitational perturbations from the SMBH and therefore merger more
efficiently. In this paper, we study the coupling of the three body 1st
post-Newtonian (PN) effects with the spin effects from the SMBH in the
hierarchical triple system. We extend previous work by including the coupling
between the de Sitter precession and the Lense-Thirring precession from the
SMBH spin. This coupling includes both the precessions of the inner orbit
angular momentum and the Runge-Lenz vector around the outer orbit angular
momentum in a general reference frame. We find the change of the (maximal)
eccentricity in the neighboring Kozai-Lidov cycles due to spin effects is
detectable by LISA in the future. Our general argument on the coupling of the
three body 1PN effects in three body systems could be extended to any other
situation as long as the outer orbital plane evolves.


  The existence of a primordial magnetic field (PMF) would affect both the
temperature and polarization anisotropies of the cosmic microwave background
(CMB). It also provides a plausible explanation for the possible disparity
between observations and theoretical fits to the CMB power spectrum. Here we
report on calculations of not only the numerical CMB power spectrum from the
PMF, but also the correlations between the CMB power spectrum from the PMF and
the primary curvature perturbations. We then deduce a precise estimate of the
PMF effect on all modes of perturbations. We find that the PMF affects not only
the CMB TT and TE modes on small angular scales, but also on large angular
scales. The introduction of a PMF leads to a better fit to the CMB power
spectrum for the higher multipoles, and the fit at lowest multipoles can be
used to constrain the correlation of the PMF with the density fluctuations for
large negative values of the spectral index. Our prediction for the BB mode for
a PMF average field strength $|B_\lambda| =4.0$ nG is consistent with the upper
limit on the BB mode deduced from the latest CMB observations. We find that the
BB mode is dominated by the vector mode of the PMF for higher multipoles. We
also show that by fitting the complete power spectrum one can break the
degeneracy between the PMF amplitude and its power spectral index.


  Personalized virtual heart models have demonstrated increasing potential for
clinical use, although the estimation of their parameters given
patient-specific data remain a challenge. Traditional physics-based modeling
approaches are computationally costly and often neglect the inherent structural
errors in these models due to model simplifications and assumptions. Modern
deep learning approaches, on the other hand, rely heavily on data supervision
and lacks interpretability. In this paper, we present a novel hybrid modeling
framework to describe a personalized cardiac digital twin as a combination of a
physics-based known expression augmented by neural network modeling of its
unknown gap to reality. We then present a novel meta-learning framework to
enable the separate identification of both the physics-based and neural
components in the hybrid model. We demonstrate the feasibility and generality
of this hybrid modeling framework with two examples of instantiations and their
proof-of-concept in synthetic experiments.


  In this paper, we propose a class of median-based matrix information geometry
(MIG) detectors with a manifold filter and apply them to signal detection in
nonhomogeneous environments. As customary, the sample data is assumed to be
modeled as Hermitian positive-definite (HPD) matrices, and the geometric median
of a set of HPD matrices is interpreted as an estimate of the clutter
covariance matrix (CCM). Then, the problem of signal detection can be
reformulated as discriminating two points on the manifold of HPD matrices, one
of which is the HPD matrix in the cell under test while the other represents
the CCM. By manifold filter, we map a set of HPD matrices to another set of HPD
matrices by weighting them, that consequently improves the discriminative power
by reducing the intra-class distances while increasing the inter-class
distances. Three MIG median detectors are designed by resorting to three
geometric measures on the matrix manifold, and the corresponding geometric
medians are shown to be robust to outliers. Numerical simulations show the
advantage of the proposed MIG median detectors in comparison with their
state-of-the-art counterparts as well as the conventional detectors in
nonhomogeneous environments.


  COVID-19, since emerged in Wuhan, China, has been a major concern due to its
high infection rate, leaving more than one million infected people around the
world. Huge number of studies tried to reveal the structure of the SARS-CoV-2
compared to the SARS-CoV-1, in order to suppress this high infection rate. Some
of these studies showed that the mutations in the SARS-CoV-1 Spike protein
might be responsible for its higher affinity to the ACE2 human cell receptor.
In this work, we used molecular dynamics simulations and Monte Carlo sampling
to compare the binding affinities of the spike proteins of SARS-CoV and
SARS-CoV-2 to the ACE2. We found that the SARS-CoV-2 binds to ACE2 stronger
than SARS-CoV by 7 kcal/mol, due to enhanced electrostatic interactions. The
major contributions to the electrostatic binding energies are resulting from
the salt-bridges formed between R426 and ACE2-E329 in case of SARS-CoV and K417
and ACE2-D30 for SARS-CoV2. In addition, there is no significant contribution
from a single mutant to the binding energies. However, these mutations induce
sophisticated structural changes that enhance the binding energies. Our results
also indicate that the SARS-CoV-2 is unlikely a lab engineered virus.


  With the growing data consumption of emerging video applications and users
requirement for higher resolutions, up to 8K, a huge effort has been made in
video compression technologies. Recently, versatile video coding (VVC) has been
standardized by the moving picture expert group (MPEG), providing a significant
improvement in compression performance over its predecessor high efficiency
video coding (HEVC). In this paper, we provide a comparative subjective quality
evaluation between VVC and HEVC standards for 8K resolution videos. In
addition, we evaluate the perceived quality improvement offered by 8K over UHD
4K resolution. The compression performance of both VVC and HEVC standards has
been conducted in random access (RA) coding configuration, using their
respective reference software, VVC test model (VTM-11) and HEVC test model
(HM-16.20). Objective measurements, using PSNR, MS-SSIM and VMAF metrics have
shown that the bitrate gains offered by VVC over HEVC for 8K video content are
around 31%, 26% and 35%, respectively. Subjectively, VVC offers an average of
40% of bitrate reduction over HEVC for the same visual quality. A compression
gain of 50% has been reached for some tested video sequences regarding a
Student t-test analysis. In addition, for most tested scenes, a significant
visual difference between uncompressed 4K and 8K has been noticed.


  It has been suggested that chondrules and calcium-aluminum-rich inclusions
(CAIs) were formed at the inner edge of the protoplanetary disk and then
entrained in magnetocentrifugal X-winds. We study trajectories of such solid
bodies with the consideration of the central star gravity, the protoplanetary
disk gravity, and the gas drag of the wind. The efficiency of the gas drag
depends on a parameter $\eta$, which is the product of the solid body size and
density. We find that the gravity of the protoplanetary disk has a
non-negligible effect on the trajectories. If a solid body re-enters the flared
disk, the re-entering radius depends on the stellar magnetic dipole moment, the
disk's gravity, the parameter $\eta$, and the initial launching angle. The
disk's gravity can make the re-entering radius lower by up to 30%. We find a
threshold $\eta$, denoted as $\eta_t$, for any particular configuration of the
X-wind, below which the solid bodies will be expelled from the planetary
system. $\eta_t$ sensitively depends on the initial launching angle, and also
depends on the mass of the disk. Only the solid bodies with a $\eta$ larger
than but very close to $\eta_t$ can be launched to a re-entering radius larger
than 1 AU. This size-sorting effect may explain why chondrules come with a
narrow range of sizes within each chondritic class. In general, the size
distributions of CAIs and chondrules in chondrites can be determined from the
initial size distribution as well as the distribution over the initial
launching angle.


  Appropriately normalized square random Vandermonde matrices based on
independent random variables with uniform distribution on the unit circle are
studied. It is shown that as the matrix sizes increases without bound, with
respect to the expectation of the trace there is an asymptotic *-distribution,
equal to that of a C[0,1]-valued R-diagonal element.


  Electrical resistivity, magnetoresistivity, and the Hall effect have been
studied in a topological semimetal WTe2 single crystal in the temperature range
from 12 to 200 K under magnetic fields up to 9 T. It has been found that
quadratic temperature dependences of the electrical resistivity in the absence
of a magnetic field and the conductivity in a magnetic field are observed at
low temperatures, which is apparently associated with contributions from
various scattering mechanisms. Single-band and two-band models were used to
analyze data on the Hall effect and magnetoresistivity. These results indicate
electron-hole compensation with a slight predominance of electron charge
carriers.


  Many real-world networks are embedded in space, and their resilience in the
presence of reinforced nodes has not been studied. Here we model such networks
using a spatial network model that have an exponential distribution of link
length $r$ having a characteristic length $\zeta$. We find that reinforced
nodes can significantly increase the resilience of the networks which varies
with strength of spatial embedding. We also study different reinforced node
distribution strategies for improving the network resilience. Interestingly, we
find that the best strategy is highly dependent on the stage of the percolation
process, i.e., the expected fraction of failures. Finally, we show that the
reinforced nodes are analogous to an external field in percolation phase
transition i.e., having the same critical exponents and that the critical
exponents satisfy Widom's relation.


  Young stars show a variety of highly energetic phenomena, from accretion and
outflow processes to hot coronal plasmas confined in their outer atmosphere,
all regulated by the intense stellar magnetic fields. Many aspects on each of
these phenomena are debated, but, most notably, their complex mutual
interaction remains obscure. In this work I report how these phenomena are
simultaneously responsible for the high-energy emission from young stars, with
a special focus on the expected and observed variability in the X-ray band.
Investigating variations in the X-ray emission from young stars allows us to
pose constraints on flare and coronal plasma properties, coronal heating,
accretion stream properties, and accretion geometries. All these results are
important building blocks for constructing a comprehensive picture of the
complex magnetosphere of young stars.


  A novel framework of optical image hiding based on deep learning (DL) is
proposed in this paper, and hidden information can be reconstructed from an
interferogram by using an end to end network with high-quality. By using the
prior data between the hidden image and the object image, a generative
adversarial network was trained so that it can learn the hiding model, which
resulting in only an interferogram needs to be transmitted and recorded to
reconstruct image. Moreover, reconstruction process can be obtained without the
parameters in optical inverse diffraction and the reconstruction result will
not be affected by the phase shifts deviation and noise, which is convenient
for practical application. The feasibility and security of the proposed method
are demonstrated by the optical experiment results.


  We have obtained high-quality magnetic field measurements of 19 sharp-lined
B-type stars with precisely-measured N/C abundance ratios. Our primary goal is
to test the idea that a magnetic field may explain extra drag (through the
wind) on the surface rotation, thus producing more internal shear and mixing,
and thus could provide an explanation for the appearance of slowly rotating
N-rich main sequence B stars.


  Water and water-mediated interactions determine thermodynamic and kinetics of
protein folding, protein aggregation and self-assembly in confined spaces. To
obtain insights into the role of water in the context of folding problems, we
describe computer simulations of a few related model systems. The dynamics of
collapse of eicosane shows that upon expulsion of water the linear hydrocarbon
chain adopts an ordered helical hairpin structure with 1.5 turns. The structure
of dimer of eicosane molecules has two well ordered helical hairpins that are
stacked perpendicular to each other. As a prelude to studying folding in
confined spaces we used simulations to understand changes in hydrophobic and
ionic interactions in nano droplets. Solvation of hydrophobic and charged
species change drastically in nano water droplets. Hydrophobic species are
localized at the boundary. The tendency of ions to be at the boundary where
water density is low increases as the charge density decreases. Interaction
between hydrophobic, polar, and charged residue are also profoundly altered in
confined spaces. Using the results of computer simulations and accounting for
loss of chain entropy upon confinement we argue and then demonstrate, using
simulations in explicit water, that ordered states of generic amphiphilic
peptide sequences should be stabilized in cylindrical nanopores.


  Datasets are crucial when training a deep neural network. When datasets are
unrepresentative, trained models are prone to bias because they are unable to
generalise to real world settings. This is particularly problematic for models
trained in specific cultural contexts, which may not represent a wide range of
races, and thus fail to generalise. This is a particular challenge for Driver
drowsiness detection, where many publicly available datasets are
unrepresentative as they cover only certain ethnicity groups. Traditional
augmentation methods are unable to improve a model's performance when tested on
other groups with different facial attributes, and it is often challenging to
build new, more representative datasets. In this paper, we introduce a novel
framework that boosts the performance of detection of drowsiness for different
ethnicity groups. Our framework improves Convolutional Neural Network (CNN)
trained for prediction by using Generative Adversarial networks (GAN) for
targeted data augmentation based on a population bias visualisation strategy
that groups faces with similar facial attributes and highlights where the model
is failing. A sampling method selects faces where the model is not performing
well, which are used to fine-tune the CNN. Experiments show the efficacy of our
approach in improving driver drowsiness detection for under represented
ethnicity groups. Here, models trained on publicly available datasets are
compared with a model trained using the proposed data augmentation strategy.
Although developed in the context of driver drowsiness detection, the proposed
framework is not limited to the driver drowsiness detection task, but can be
applied to other applications.


  In this work we study the interactions between stabilized Townes solitons. By
means of effective Lagrangian methods, we have found that the interactions
between these solitons are governed by central forces, in a first
approximation. In our numerical simulations we describe different types of
orbits, deflections, trapping and soliton splitting. Splitting phenomena are
also described by finite dimensional reduced models. All these effects could be
used for potential applications of stabilized solitons.


  High-frequency electron paramagnetic resonance (EPR) studies of the
antiferromagnetic Mn-$[3\times 3]$ molecular grid clearly reveal a breaking of
the $\Delta S = 0$ selection rule, providing direct evidence for the mixing of
spin wavefunctions ($S$-mixing) induced by the comparable exchange and
magneto-anisotropy energy scales within the grid. This finding highlights the
potential utility of EPR for studies of exchange splittings in molecular
nanomagnets, which is normally considered the sole domain of inelastic neutron
scattering, thereby offering improved sensitivity and energy resolution.


  We here give polynomial realizations of various Hopf algebras or bialgebras
on Feynman graphs, graphs, posets or quasi-posets, that it to say injections of
these objects into polynomial algebras generated by an alphabet. The alphabet
here considered are totally quasi-ordered. The coproducts are given by doubling
the alphabets; a second coproduct is defined by squaring the alphabets, and we
obtain cointeracting bialgebras in the commutative case.


  For noncooperative games the mean field (MF) methodology provides
decentralized strategies which yield Nash equilibria for large population
systems in the asymptotic limit of an infinite (mass) population. The MF
control laws use only the local information of each agent on its own state and
own dynamical parameters, while the mass effect is calculated offline using the
distribution function of (i) the population's dynamical parameters, and (ii)
the population's cost function parameters, for the infinite population case.
These laws yield approximate equilibria when applied in the finite population.
  In this paper, these a priori information conditions are relaxed, and
incrementally the cases are considered where, first, the agents estimate their
own dynamical parameters, and, second, estimate the distribution parameter in
(i) and (ii) above.
  An MF stochastic adaptive control (SAC) law in which each agent observes a
random subset of the population of agents is specified, where the ratio of the
cardinality of the observed set to that of the number of agents decays to zero
as the population size tends to infinity. Each agent estimates its own
dynamical parameters via the recursive weighted least squares (RWLS) algorithm
and the distribution of the population's dynamical parameters via maximum
likelihood estimation (MLE). Under reasonable conditions on the population
dynamical parameter distribution, the MF-SAC Law applied by each agent results
in (i) the strong consistency of the self parameter estimates and the strong
consistency of the population distribution function parameters; (ii) the long
run average stability of all agent systems; (iii) a (strong) e-Nash equilibrium
for the population of agents; and (iv) the a.s. equality of the long run
average cost and the non-adaptive cost in the population limit.


  We derive a tensorial formula for a fourth-order conformally invariant
differential operator on conformal 4-manifolds. This operator is applied to
algebraic Weyl tensor densities of a certain conformal weight, and takes its
values in algebraic Weyl tensor densities of another weight. For oriented
manifolds, this operator reverses duality: For example in the Riemannian case,
it takes self-dual to anti-self-dual tensors and vice versa. We also examine
the place that this operator occupies in known results on the classification of
conformally invariant operators, and we examine some related operators.


  In this publication we describe the extrusion process and the properties of
polymer-bonded anisotropic SrFe$_\text{12}$O$_\text{19}$ filaments for fused
filament fabrication (FFF). Highly filled polyamide 12 filaments with a filling
fraction from 40 vol.% to 55 vol.% are mixed and extruded into filaments with a
diameter of 1.75 mm. Such filaments are processable with a conventional FFF 3D
printer. No modifications of the 3D printer are necessary. Detailed mechanical
and magnetic investigations of printed samples are performed and discussed. In
the presence of an external alignment field, the Sr ferrite particles inside
the PA12 matrix can be aligned along an external magnetic field. The remanence
can be increased by 40 % by printing anisotropic structures. For the 55 vol.%
filled filament, a remanence of 212.8 mT and a coercivity of 307.4 mT are
measured. The capabilities of printing magnetic anisotropic structures in a
complex external field are presented with a Halbach-array arrangement. By the
aim of an inverse field model, based on a finite element method, the
orientation of the particles and the quality of the print can be estimated by a
nondestructive method.


  A mass of traces of human activities show rich dynamic patterns. In this
article, we comprehensively investigate the dynamic patterns of 50 thousands of
researchers' activities in Sciencenet, the largest multi-disciplinary academic
community in China. Through statistical analyses, we found that (i) there
exists a power-law scaling between the frequency of visits to an academic forum
and the number of corresponding visitors, with the exponent being about 1.33;
(ii) the expansion process of academic forums obeys the Heaps' law, namely the
number of distinct visited forums to the number of visits grows in a power-law
form with exponent being about 0.54; (iii) the probability distributions of
time intervals and the number of visits taken to revisit the same academic
forum both follow power-laws, indicating the existence of memory effect in
academic forum activities. On the basis of these empirical results, we propose
a dynamic model that incorporates the exploration, preferential return and
memory effect, which can well reproduce the observed scaling laws.


  Recent and preliminary single-particle data are presented from the AGS
Experiment 866 at BNL. Emphasis is put on the transverse mass as well as the
rapidity distributions of charged pions, kaons, protons, deuterons and
anti-protons measured in the most central Au+Au collisions at an incident
kinetic energy of 10.8 AGeV. The data suggest a high degree of stopping power
present in these reactions. Applying an expanding fireball scenario to describe
the experimental distributions substantial transverse and longitudinal flow
velocities result.


  6D object pose estimation is a prerequisite for many applications. In recent
years, monocular pose estimation has attracted much research interest because
it does not need depth measurements. In this work, we introduce ConvPoseCNN, a
fully convolutional architecture that avoids cutting out individual objects.
Instead we propose pixel-wise, dense prediction of both translation and
orientation components of the object pose, where the dense orientation is
represented in Quaternion form. We present different approaches for aggregation
of the dense orientation predictions, including averaging and clustering
schemes. We evaluate ConvPoseCNN on the challenging YCB-Video Dataset, where we
show that the approach has far fewer parameters and trains faster than
comparable methods without sacrificing accuracy. Furthermore, our results
indicate that the dense orientation prediction implicitly learns to attend to
trustworthy, occlusion-free, and feature-rich object regions.


  We introduce \textcolor{red}{general} new techniques for computing the
geometric index of a link $L$ in the interior of a solid torus $T$. These
techniques simplify and unify previous ad hoc methods used to compute the
geometric index in specific examples \textcolor{red}{ and allow the simple
computation of geometric index for new examples where the index was not
previously known}. The geometric index measures the minimum number of times any
meridional disc of $T$ must intersect $L$. It is related to the algebraic index
in the sense that adding up signed intersections of an interior simple closed
curve $C$ in $T$ with a meridional disc gives $\pm$ the algebraic index of $C$
in $T$. One key idea is introducing the notion of geometric index for solid
chambers of the form $B^2\times I$ in $T$. After that we prove that if a solid
torus can be divided into solid chambers by meridional discs in a specific
\textcolor{red}{(and often easy to obtain)} way, then the geometric index can
be easily computed.


  The ubiquity of connecting technologies in smart vehicles and the incremental
automation of its functionalities promise significant benefits, including a
significant decline in congestion and road fatalities. However, increasing
automation and connectedness broadens the attack surface and heightens the
likelihood of a malicious entity successfully executing an attack. In this
paper, we propose a Blockchain based Framework for sEcuring smaRt vehicLes
(B-FERL). B-FERL uses permissioned blockchain technology to tailor information
access to restricted entities in the connected vehicle ecosystem. It also uses
a challenge-response data exchange between the vehicles and roadside units to
monitor the internal state of the vehicle to identify cases of in-vehicle
network compromise. In order to enable authentic and valid communication in the
vehicular network, only vehicles with a verifiable record in the blockchain can
exchange messages. Through qualitative arguments, we show that B-FERL is
resilient to identified attacks. Also, quantitative evaluations in an emulated
scenario show that B-FERL ensures a suitable response time and required storage
size compatible with realistic scenarios. Finally, we demonstrate how B-FERL
achieves various important functions relevant to the automotive ecosystem such
as trust management, vehicular forensics and secure vehicular networks.


  We present a classification of all global solutions for generalized 2D
dilaton gravity models (with Lorentzian signature). While for some of the
popular choices of potential-like terms in the Lagrangian, describing, e.g.,
string inspired dilaton gravity or spherically reduced gravity, the possible
topologies of the resulting spacetimes are restricted severely, we find that
for generic choices of these `potentials' there exist maximally extended
solutions to the field equations on all non-compact two-surfaces.


  We present a method that learns to answer visual questions by selecting image
regions relevant to the text-based query. Our method exhibits significant
improvements in answering questions such as "what color," where it is necessary
to evaluate a specific location, and "what room," where it selectively
identifies informative image regions. Our model is tested on the VQA dataset
which is the largest human-annotated visual question answering dataset to our
knowledge.


  The structural default model of Lipton and Sepp, 2009 is generalized for a
set of banks with mutual interbank liabilities whose assets are driven by
correlated Levy processes with idiosyncratic and common components. The
multi-dimensional problem is made tractable via a novel computational method,
which generalizes the one-dimensional fractional partial differential equation
method of Itkin, 2014 to the two- and three-dimensional cases. This method is
unconditionally stable and of the second order of approximation in space and
time; in addition, for many popular Levy models it has linear complexity in
each dimension. Marginal and joint survival probabilities for two and three
banks with mutual liabilities are computed. The effects of mutual liabilities
are discussed, and numerical examples are given to illustrate these effects.


  Let $$
  S_{m,n}(q):=\sum_{k=1}^{n}\frac{1-q^{2k}}{1-q^2}
  (\frac{1-q^k}{1-q})^{m-1}q^{\frac{m+1}{2}(n-k)}.
  $$ Generalizing the formulas of Warnaar and Schlosser, we prove that there
exist polynomials $P_{m,k}(q)\in\mathbb{Z}[q]$ such that $$
  S_{2m+1,n}(q) =\sum_{k=0}^{m}(-1)^kP_{m,k}(q)
  \frac{(1-q^n)^{m+1-k}(1-q^{n+1})^{m+1-k}q^{kn}}
  {(1-q^2)(1-q)^{2m-3k}\prod_{i=0}^{k}(1-q^{m+1-i})}, $$ and solve a problem
raised by Schlosser. We also show that there is a similar formula for the
following $q$-analogue of alternating sums of powers:
  $$
  T_{m,n}(q):=\sum_{k=1}^{n}(-1)^{n-k}
  (\frac{1-q^k}{1-q})^{m}q^{\frac{m}{2}(n-k)}.
  $$


  Signs of the different contributions to the isotope shift of an atomic line
are discussed in details to clarify some confusing differences between the
electronic parameters calculated with RIS (Naz\'e et al. Comput. Phys. Commun.
184 (2013) 2187 ; Ekman et al. Comput. Phys. Commun. 235 (2019) 433) and those
appearing in other commonly used expressions.


  The classical Friedman equations of time-varying Hubble function $H$,
dark-energy and matter densities couple to quantised field equations for
massive modes $M\gg H$. Numerically solving these equations, we show the
particle-antiparticle pairs production and oscillation in microscopic time
scale ${\mathcal O}(M^{-1})$. A massive pair plasma state is formed in
macroscopic time scale ${\mathcal O}(H^{-1})$. Its density and pressure
introduce the interaction of matter and dark energy densities in the Friedman
equations. Focusing on epochs after reheating, we show that the negative dark
energy tracks down the radiation energy in the radiation epoch. Such tracking
dynamics ends, and dark energy becomes positive in the matter epoch. The matter
converts to dark energy, and their present values are comparable, explaining
the cosmic coincidence. As a result, a class of effective interacting dark
energy models is advocated to confront cosmological observations.


  We introduce the concept of quantum reliability as an extension of the
concept of network reliability in the context of quantum networks. We show that
this concept is intimately related to the concept of quantum reliability
operator that we also introduce and show a Negami like splitting formula for
it. Considering that the simple factorization formula for classical networks
which is the basis of most of the calculation algorithms does not hold in the
quantum context due to entanglement, a Negami like splitting for the quantum
reliability operator becomes relevant.


  This work presents Past as a Guide (PaG), a simple approach for Large
Language Models (LLMs) to improve the coding capabilities by integrating the
past history with interactive and iterative code refinements. To be specific,
inspired by human cognitive processes, the proposed method enables LLMs to
utilize previous programming and debugging experiences to enhance the Python
code completion tasks. The framework facilitates LLMs to iteratively refine the
Python code based on previous execution and debugging results and optimize
learning and reasoning capabilities. The proposed methodology achieved a 92\%
pass@1 on HumanEval, demonstrating the potential to advance the field by
leveraging retrospection from past experiences and interactive and iterative
refinement processes without external correctness indicators.


  The present work deals with the global solvability as well as asymptotic
analysis of stochastic generalized Burgers-Huxley (SGBH) equation perturbed by
space-time white noise in a bounded interval of $\mathbb{R}$. We first prove
the existence of unique mild as well as strong solution to SGBH equation and
then obtain the existence of an invariant measure. Later, we establish two
major properties of the Markovian semigroup associated with the solutions of
SGBH equation, that is, irreducibility and strong Feller property. These two
properties guarantees the uniqueness of invariant measures and ergodicity also.
Then, under further assumptions on the noise coefficient, we discuss the
ergodic behavior of the solution of SGBH equation by providing a Large
Deviation Principle (LDP) for the occupation measure for large time
(Donsker-Varadhan), which describes the exact rate of exponential convergence.


  Deep learning models have been criticized for their lack of easy
interpretation, which undermines confidence in their use for important
applications. Nevertheless, they are consistently utilized in many
applications, consequential to humans' lives, mostly because of their better
performance. Therefore, there is a great need for computational methods that
can explain, audit, and debug such models. Here, we use flip points to
accomplish these goals for deep learning models with continuous output scores
(e.g., computed by softmax), used in social applications. A flip point is any
point that lies on the boundary between two output classes: e.g. for a model
with a binary yes/no output, a flip point is any input that generates equal
scores for "yes" and "no". The flip point closest to a given input is of
particular importance because it reveals the least changes in the input that
would change a model's classification, and we show that it is the solution to a
well-posed optimization problem. Flip points also enable us to systematically
study the decision boundaries of a deep learning classifier. The resulting
insight into the decision boundaries of a deep model can clearly explain the
model's output on the individual-level, via an explanation report that is
understandable by non-experts. We also develop a procedure to understand and
audit model behavior towards groups of people. Flip points can also be used to
alter the decision boundaries in order to improve undesirable behaviors. We
demonstrate our methods by investigating several models trained on standard
datasets used in social applications of machine learning. We also identify the
features that are most responsible for particular classifications and
misclassifications.


  Visual Question Answering (VQA) is challenging due to the complex cross-modal
relations. It has received extensive attention from the research community.
From the human perspective, to answer a visual question, one needs to read the
question and then refer to the image to generate an answer. This answer will
then be checked against the question and image again for the final
confirmation. In this paper, we mimic this process and propose a fully
attention based VQA architecture. Moreover, an answer-checking module is
proposed to perform a unified attention on the jointly answer, question and
image representation to update the answer. This mimics the human answer
checking process to consider the answer in the context. With answer-checking
modules and transferred BERT layers, our model achieves the state-of-the-art
accuracy 71.57\% using fewer parameters on VQA-v2.0 test-standard split.


  The time-dependent cosmological term arises from the energy-momentum tensor
calculated in a state different from the ground state. We discuss the
expectation value of the energy-momentum tensor on the rhs of Einstein
equations in various (approximate)pure as well as mixed states. We apply the
classical slow-roll field evolution as well as the Starobinsky and warm
inflation stochastic equations in order to calculate the expectation value. We
show that in a state concentrated at the local maximum of the double-well
potential the expectation value is decreasing exponentially. We confirm the
descend of the expectation value in the stochastic inflation model. We
calculate the cosmological constant $\Lambda$ at large time as the expectation
value of the energy density with respect to the stationary probability
distribution. We show that $\Lambda\simeq \gamma^{\frac{4}{3}} where $\gamma$
is the thermal dissipation rate.


  We propose a method to determine the solvability of the diophantine equation
$x^2-Dy^2=n$ for the following two cases:
  $(1)$ $D=pq$, where $p,q\equiv 1 \mod 4$ are distinct primes with
$(\frac{q}{p})=1$ and $(\frac{p}{q})_4(\frac{q}{p})_4=-1$.
  $(2)$ $D=2p_1p_2... p_m$, where $p_i\equiv 1 \mod 8,1\leq i\leq m$ are
distinct primes and $D=r^2+s^2$ with $r,s \equiv \pm 3 \mod 8$.


  We construct a class of quantum field theories depending on the data of a
holomorphic Poisson structure on a piece of the underlying spacetime. The main
technical tool relies on a characterization of deformations and anomalies of
such theories in terms of the Gelfand-Fuchs cohomology of formal Hamiltonian
vector fields. In the case that the Poisson structure is non-degenerate such
theories are topological in a certain weak sense, which we refer to as "de Rham
topological". While the Lie algebra of translations acts in a homotopically
trivial way, we will show that the space of observables of such a theory does
not define an E_n-algebra. Additionally, we will highlight a conjectural
relationship to theories of supergravity in four and five dimensions.


  An important class of three-manifolds are L-spaces, which are rational
homology spheres with the smallest possible Floer homology. For knots with an
instanton L-space surgery, we compute the framed instanton Floer homology of
all integral surgeries. As a consequence, if a knot has a Heegaard Floer and
instanton Floer L-space surgery, then the theories agree for all integral
surgeries. In order to prove the main result, we prove that the Baldwin-Sivek
contact invariant in framed instanton Floer homology is homogeneous with
respect to the absolute $\mathbb{Z}/2$-grading, but not the
$\mathbb{Z}/4$-grading.


  The observation of new suppressed Bs decays, Bs-> J/Psi K* (892)0 and
Bs->J/Psi Ks, and the measurement of their branching ratios are presented. This
measurement is based on an integrated luminosity of 5.9 fb-1 of CDF data
collected by a dedicated di-muon trigger. A cut based optimization is carried
out for the observation of Bs -> J/Psi K*, while a neural network is used for
the Bs->J/Psi Ks. In addition to the observation of the new decay modes, the
ratios of branching fractions to the reference B0 decays are measured.


  In an influential 1981 paper, Guibas and Odlyzko constructed a generating
function for the number of length n strings over a finite alphabet that avoid
all members of a given set of forbidden substrings. Here we extend this result
to the case in which the strings are weighted. This investigation was inspired
by the problem of counting compositions of an integer n that avoid all
compositions of a smaller integer m, a notion which arose from the
consideration of one-sided random walks.


  The equations for the electromagnetic two-body problem are neutral-delay
equations that for generic initial data have solutions with discontinuous
derivatives. If one wants to use these neutral-delay equations with arbitrary
initial data, solutions with discontinuous derivatives must be allowed.
Surprisingly, this same neutrality is compatible with the recently developed
variational method with mixed-type boundaries for the Wheeler-Feynman
electrodynamics. We show that two-body electromagnetic orbits with
discontinuous velocities are physically necessary by showing that orbits with
vanishing far-fields amost everywhere must have some discontinuous velocities
on a few points. We generalize the Wheeler-Feynman electrodynamics with the
variational method to include all continuous trajectories, allowing
piecewise-differentiable weak solutions represented by trajectories with fields
defined almost everywhere (but on a set of points of zero measure where
velocities jump). Along with this generalization we formulate the generalized
absorber hypothesis that the far-fields vanish asymptotically almost everywhere
and show that bounded two-body orbits satisfying the generalized absorber
hypothesis need to have discontinuous derivatives on a few points. We also give
the general solution for the family of bounded non-radiating two-body orbits.
We discuss the physics of orbits with discontinuous derivatives and show that
these conserve the physical momentum, stressing the differences to classical
variational methods. Last, we discuss how the electromagnetic variational
method with mixed-type boundaries is well-posed but lacks reversibilty.


  Classical T Tauri stars are low mass young forming stars that are surrounded
by a circumstellar accretion disc from which they gain mass. Despite this
accretion and their own contraction that should both lead to their spin up,
these stars seem to conserve instead an almost constant rotational period as
long as the disc is maintained. Several scenarios have been proposed in the
literature in order to explain this puzzling "disc-locking" situation: either
deposition in the disc of the stellar angular momentum by the stellar
magnetosphere or its ejection through winds, providing thereby an explanation
of jets from Young Stellar Objects.
  In this lecture, these various mechanisms will be critically detailed, from
the physics of the star-disc interaction to the launching of self-confined jets
(disc winds, stellar winds, X-winds, conical winds). It will be shown that no
simple model can account alone for the whole bulk of observational data and
that "disc locking" requires a combination of some of them.


  In our former study (J. Phys. A: Math. Theor. 43, (2010) 325210 or
arXiv:1002.0999v1 [math-ph]) we introduced a modified Fourier-Cattaneo law and
derived a non-autonomous telegraph-type heat conduction equation which has
desirable self-similar solution. Now we present a detailed in-depth analysis of
this model and discuss additional analytic solutions for different parameters.
The solutions have a very rich and interesting mathematical structure due to
various special functions.


  This paper presents a speech recognition system developed by the Transsion
Speech Understanding Processing Team (TSUP) for the ASRU 2023 MADASR Challenge.
The system focuses on adapting ASR models for low-resource Indian languages and
covers all four tracks of the challenge. For tracks 1 and 2, the acoustic model
utilized a squeezeformer encoder and bidirectional transformer decoder with
joint CTC-Attention training loss. Additionally, an external KenLM language
model was used during TLG beam search decoding. For tracks 3 and 4, pretrained
IndicWhisper models were employed and finetuned on both the challenge dataset
and publicly available datasets. The whisper beam search decoding was also
modified to support an external KenLM language model, which enabled better
utilization of the additional text provided by the challenge. The proposed
method achieved word error rates (WER) of 24.17%, 24.43%, 15.97%, and 15.97%
for Bengali language in the four tracks, and WER of 19.61%, 19.54%, 15.48%, and
15.48% for Bhojpuri language in the four tracks. These results demonstrate the
effectiveness of the proposed method.


  Estimating the occurrence of packet losses in a networked control systems
(NCS) can be used to improve the control performance and to detect failures or
cyber-attacks. This study considers simultaneous estimation of the plant state
and the packet loss occurrences at each time step. After formulation of the
problem, two solutions are proposed. In the first one, an input-output
representation of the NCS model is used to design a recursive filter for
estimation of the packet loss occurrences. This estimation is then used for
state estimation through Kalman filtering. In the second solution, a state
space model of NCS is used to design an estimator for both the plant state and
the packet loss occurrences which employs a Kalman filter. The effectiveness of
the solutions is shown during an example and comparisons are made between the
proposed solutions and another solution based on the interacting multiple model
estimation method.


  A systematic rotation of the plane of polarization of electromagnetic
radiation propagating over cosmological distances has been claimed to be
detected by Nodland and Ralston.Taking the finite rotating universe of Oszvath
and Sch\"ucking as a toy model for the actual universe,we calculate the
rotation of the plane of polarization of electromagnetic waves in this
universe.It turns out that the observed data are consistent with the
Oszvath-Sch\"ucking parameter $k=0.39$.


  This issue surveys some of the activities in the field since the previous
issue, and announces a conference fully dedicated to the topic of selection
principles.


  In increasingly autonomous and highly distributed multi-agent systems,
centralized coordination becomes impractical and raises the need for governance
and enforcement mechanisms from an agent-centric perspective. In our conceptual
view, sanctioning norm enforcement is part of this agent-centric approach and
they aim at promoting norm compliance while preserving agents' autonomy. The
few works dealing with sanctioning norm enforcement and sanctions from the
agent-centric perspective present limitations regarding the representation of
sanctions and the comprehensiveness of their norm enforcement process. To
address these drawbacks, we propose the NPL(s), an extension of the NPL
normative programming language enriched with the representation of norms and
sanctions as first-class abstractions. We also propose a BDI normative agent
architecture embedding an engine for processing the NPL(s) language and a set
of capabilities for approaching more comprehensively the sanctioning norm
enforcement process. We apply our contributions in a case study for improving
the robustness of agents' decision-making in a production automation system.


  We present a memory and computation efficient ternary weight networks (TWNs)
- with weights constrained to +1, 0 and -1. The Euclidian distance between full
(float or double) precision weights and the ternary weights along with a
scaling factor is minimized in training stage. Besides, a threshold-based
ternary function is optimized to get an approximated solution which can be fast
and easily computed. TWNs have shown better expressive abilities than binary
precision counterparts. Meanwhile, TWNs achieve up to 16$\times$ model
compression rate and need fewer multiplications compared with the float32
precision counterparts. Extensive experiments on MNIST, CIFAR-10, and ImageNet
datasets show that the TWNs achieve much better result than the
Binary-Weight-Networks (BWNs) and the classification performance on MNIST and
CIFAR-10 is very close to the full precision networks. We also verify our
method on object detection task and show that TWNs significantly outperforms
BWN by more than 10\% mAP on PASCAL VOC dataset. The pytorch version of source
code is available at: https://github.com/Thinklab-SJTU/twns.


  Membrane-type Acoustic Metamaterials (MAMs) have demonstrated unusual
capacity in controlling low-frequency sound transmission/reflection. In this
paper, an analytical vibroacoustic membrane model is developed to study sound
transmission behavior of the MAM under a normal incidence. The MAM is composed
of a prestretched elastic membrane with attached rigid masses. To accurately
capture finite-dimension rigid mass effects on the membrane deformation, the
point matching approach is adopted by applying a set of distributed point
forces along the interfacial boundary between masses and the membrane. The
accuracy and capability of the theoretical model is verified through the
comparison with the finite element method. In particular, microstructure
effects such as weight, size and eccentricity of the attached mass, pretension
and thickness of the membrane on the resulting transmission peak and dip
frequencies of the MAM are quantitatively investigated. New peak and dip
frequencies are found for the MAM with one and multiple eccentric attached
masses. The developed model can be served as an efficient tool for design of
such membrane-type metamaterials.


  Extragalactic globular clusters (GCs) are key objects for studying the
history of galaxies. The arrival of wide-field surveys such as the Javalambre
Photometric Local Universe Survey (J-PLUS) offers new possibilities for the
study of these systems. We perform the first study of GCs in J-PLUS to recover
information about the history of NGC 1023 taking advantage of wide-field images
and 12 filters. We develop the semiautomatic pipeline GCFinder that detects GC
candidates in J-PLUS images and can also be adapted to similar surveys. We
study the stellar population properties of a sub-sample of GC candidates using
spectral energy distribution (SED) fitting. We find 523 GC candidates in NGC
1023, of which $\sim$300 are new. We identify subpopulations of GC candidates,
where age and metallicity distributions have multiple peaks. By comparing our
results with simulations, we report a possible broad age-metallicity relation,
evidence that NGC 1023 experienced accretion events in the past. The dominating
age peak is at $10^{10}$ yr. We report a correlation between masses and ages
that suggests that massive GC candidates are more likely to survive the
turbulent history of the host galaxy. Modeling the light of NGC 1023, we find
two spiral-like arms and detect a displacement of the galaxy's photometric
center with respect to the outer isophotes and center of GC distribution
($\sim$700 pc and $\sim$1600 pc, respectively), which could be the result of
ongoing interaction between NGC 1023 and NGC 1023A. By studying the GC system
of NGC 1023 with J-PLUS we showcase the power of multi-band surveys for this
kind of study and find evidence of a complex accretion history of the host
galaxy.


  We obtain a complete asymptotic expansion of the integrated density of states
of operators of the form H =(-\Delta)^w +B in R^d. Here w >0, and B belongs to
a wide class of almost-periodic self-adjoint pseudo-differential operators of
order less than 2w. In particular, we obtain such an expansion for magnetic
Schr\"odinger operators with either smooth periodic or generic almost-periodic
coefficients.


  We show that the 2d Poisson Sigma Model on a Poisson groupoid arises as an
effective theory of the 3d Courant Sigma Model associated to the double of the
underlying Lie bialgebroid. This field-theoretic result follows from a
Lie-theoretic one involving a coisotropic reduction of the odd cotangent bundle
by a generalized space of algebroid paths. We also provide several examples,
including the case of symplectic groupoids in which we relate the symplectic
realization construction of Crainic-Marcut to a particular gauge fixing of the
3d theory.


  Transmission through photoexcited semiconductors is used to temporally and
spectrally shape a Terahertz pulse. By adjusting the optical pump-THz probe
delay, we experimentally introduce a polar asymmetry in the pulse profile as
high as 92%. To shape the spectrum, we apply the same technique after strongly
chirping the Terahertz pulse. This led to significant reshaping of the spectrum
with a 52% upshift of spectrum median. Pulse shaping techniques introduced here
are of particular importance for temporal and spectral shape-sensitive THz
nonlinear experiments.


  An elegant and convenient rigorous approach for solving circular open-ended
dielectric-loaded waveguide diffraction problems is presented. It uses the
solution of corresponding Wiener-Hopf-Fock equation and leads to an infinite
linear system for reflection coefficients (S-parameters) of the waveguide, the
latter can be efficiently solved numerically using the reducing technique. As a
specific example directly applicable to beam-driven radiation sources based on
dielectric-lined capillaries, diffraction of a slow TM symmetrical mode at the
open end of a circular waveguide with uniform dielectric filling is considered.
A series of such modes forms the wakefield (Cherenkov radiation field)
generated by a charged particle bunch during its passage along the waveguide
axis. Calculated S-parameters were compared with those obtained from COMSOL
simulation and an excellent agreement is shown. This method is expected to be
very convenient for analytical investigation of various electromagnetic
interactions of Terahertz (THz) waves (both free and guided) and charged
particle bunches with slow-wave structures prospective in context of modern
beam-driven THz emitters, THz accererators and THz-based bunch manipulation and
bunch diagnostic systems.


  The Boltzmann equation without Grad's angular cutoff assumption is believed
to have regularizing effect on the solution because of the non-integrable
angular singularity of the cross-section. However, even though so far this has
been justified satisfactorily for the spatially homogeneous Boltzmann equation,
it is still basically unsolved for the spatially inhomogeneous Boltzmann
equation. In this paper, by sharpening the coercivity and upper bound estimates
for the collision operator, establishing the hypo-ellipticity of the Boltzmann
operator based on a generalized version of the uncertainty principle, and
analyzing the commutators between the collision operator and some weighted
pseudo differential operators, we prove the regularizing effect in all (time,
space and velocity) variables on solutions when some mild regularity is imposed
on these solutions. For completeness, we also show that when the initial data
has this mild regularity and Maxwellian type decay in velocity variable, there
exists a unique local solution with the same regularity, so that this solution
enjoys the $C^\infty$ regularity for positive time.


  Effective hyper-parameter tuning is essential to guarantee the performance
that neural networks have come to be known for. In this work, a principled
approach to choosing the learning rate is proposed for shallow feedforward
neural networks. We associate the learning rate with the gradient Lipschitz
constant of the objective to be minimized while training. An upper bound on the
mentioned constant is derived and a search algorithm, which always results in
non-divergent traces, is proposed to exploit the derived bound. It is shown
through simulations that the proposed search method significantly outperforms
the existing tuning methods such as Tree Parzen Estimators (TPE). The proposed
method is applied to three different existing applications: a) channel
estimation in OFDM systems, b) prediction of the exchange currency rates and c)
offset estimation in OFDM receivers, and it is shown to pick better learning
rates than the existing methods using the same or lesser compute power.


  The abundance of primordial black holes is currently significantly
constrained in a wide range of masses. The weakest limits are established for
the small mass objects, where the small intensity of the associated physical
phenomenon provides a challenge for current experiments. We used gamma- ray
bursts with known redshifts detected by the Fermi Gamma-ray Burst Monitor (GBM)
to search for the femtolensing effects caused by compact objects. The lack of
femtolensing detection in the GBM data provides new evidence that primordial
black holes in the mass range 5 \times 10^{17} - 10^{20} g do not constitute a
major fraction of dark matter.


  While deep neural networks are capable of achieving state-of-the-art
performance in various domains, their training typically requires iterating for
many passes over the dataset. However, due to computational and memory
constraints and potential privacy concerns, storing and accessing all the data
is impractical in many real-world scenarios where the data arrives in a stream.
In this paper, we investigate the problem of one-pass learning, in which a
model is trained on sequentially arriving data without retraining on previous
datapoints. Motivated by the increasing use of overparameterized models, we
develop Orthogonal Recursive Fitting (ORFit), an algorithm for one-pass
learning which seeks to perfectly fit every new datapoint while changing the
parameters in a direction that causes the least change to the predictions on
previous datapoints. By doing so, we bridge two seemingly distinct algorithms
in adaptive filtering and machine learning, namely the recursive least-squares
(RLS) algorithm and orthogonal gradient descent (OGD). Our algorithm uses the
memory efficiently by exploiting the structure of the streaming data via an
incremental principal component analysis (IPCA). Further, we show that, for
overparameterized linear models, the parameter vector obtained by our algorithm
is what stochastic gradient descent (SGD) would converge to in the standard
multi-pass setting. Finally, we generalize the results to the nonlinear setting
for highly overparameterized models, relevant for deep learning. Our
experiments show the effectiveness of the proposed method compared to the
baselines.


  In this paper we will determine the NBB bases with respect to standard
ordering of coatoms (resp.atoms) of 123-132-213-avoiding (resp.321-avoiding)
lattices. Using these expression we will calculate the M\"obius numbers of
123-132-213-avoiding lattices and 321-avoiding lattices. These values become
some modification of fibonacci polynomials.


  For spectrally negative L\'evy processes, adapting an approach from
\cite{BoLi:sub1} we identify joint
  Laplace transforms involving local times evaluated at either the first
passage times, or independent exponential times, or inverse local times. The
Laplace transforms are expressed in terms of the associated scale functions.
  Connections are made with the permanental process and the Markovian loop soup
measure.


  In this paper, we consider the parameterized quantum query complexity for
graph problems. We design parameterized quantum query algorithms for $k$-vertex
cover and $k$-matching problems, and present lower bounds on the parameterized
quantum query complexity. Then, we show that our quantum query algorithms are
optimal up to a constant factor when the parameters are small.


  In this paper a detailed numerical study (in frames of the Slonczewski
formalism) of magnetization oscillations driven by a spin-polarized current
through a thin elliptical nanoelement is presented. We show that a
sophisticated micromagnetic model, where a polycrystalline structure of a
nanoelement is taken into account, can explain qualitatively all most important
features of the magnetization oscillation spectra recently observed
experimentally (S.I. Kiselev et al., Nature, vol. 425, p. 380 (2003), namely:
existence of several equidistant spectral bands, sharp onset and abrupt
disappearance of magnetization oscillations with increasing current, absence of
the out-of-plane regime predicted by a macrospin model and the relation between
frequencies of so called small-angle and quasichaotic oscillations. However, a
quantitative agreement with experimental results (especially concerning the
frequency of quasichaotic oscillations) could not be achieved in the region of
reasonable parameter values, indicating that further model refinement is
necessary for a complete understanding of the spin-driven magnetization
precession even in this relatively simple experimental situation.


  In high energy hadronic collisions a scalar or pseudoscalar Higgs boson,
Phi=H,A, can be efficiently produced via gluon fusion, which is mediated by
heavy quark loops. We here consider double real emission corrections to Phi=A
production, which lead to a Higgs plus two-jet final state, at order alpha_s^4.
Full quark mass effects are considered in the calculation of scattering
amplitudes for the CP-odd Higgs boson A, as induced by quark triangle-, box-
and pentagon-diagrams. They complement the analogous results for a CP-even
Higgs boson H in Ref.[1]. Interference effects between loops with top and
bottom quarks as well as between CP-even and CP-odd couplings of the heavy
quarks are fully taken into account.


  We present a computational technique to calculate time and momentum resolved
non-equilibrium spectral density of correlated systems using a tunneling
approach akin scanning tunneling spectroscopy. The important difference is that
our probe is extended, basically a copy of the sample, allowing one to extract
the momentum information of the excitations. We illustrate the method by
measuring the spectrum of a Mott-insulating extended Hubbard chain after a
sudden quench with the aid of time-dependent density matrix renormalization
group (tDMRG) calculations. We demonstrate that the system realizes a
non-thermal state that is an admixture of spin and charge density wave states,
with corresponding signatures that are recognizable as in-gap sub-bands. In
particular, we identify a band of excitons and one of stable anti-bound states
at high energies that gains enhanced visibility after the pump. We do not
appreciate noticeable relaxation within the time-scales considered, which is
attributed to the lack of decay channels due to spin-charge separation. These
ideas can be readily applied to study transient dynamics and spectral
signatures of correlation-driven non-equilibrium processes.


  Understanding the survival of gas within subhalos under various astrophysical
processes is crucial for elucidating cosmic structure formation and evolution.
We study the resilience of gas in subhalos, focusing on the impact of tidal and
ram pressure stripping through hydrodynamic simulations. Our results uncover
significant gas stripping primarily driven by ram pressure effects, which also
profoundly influence the gas distribution within these subhalos. Notably,
despite their vulnerability to ram pressure effects, the low-mass subhalos can
play a pivotal role in influencing the observable characteristics of cosmic
structures due to their large abundance. Specifically, we explore the
application of our findings to the 21 cm forest, showing how the survival
dynamics of gas in subhalos can modulate the 21 cm optical depth, a key probe
for detecting minihalos in the pre-reionization era. (abridged) In this work,
we further investigate the contribution of subhalos to the 21 cm optical depth
with hydrodynamics simulations, particularly highlighting the trajectories and
fates of subhalos within mass ranges of \(10^{4-6} M_{\odot}h^{-1}\) in a host
halo of \(10^7 M_{\odot}h^{-1}\). Despite their susceptibility to ram pressure
stripping, the contribution of abundant low-mass subhalos to the 21-cm optical
depth is more significant than that of their massive counterparts primarily due
to their greater abundance. We find that the 21-cm optical depth can be
increased by a factor of approximately two due to the abundant low-mass
subhalos. (abridged) Our work provides critical insights into the gas dynamics
within subhalos in the early Universe, highlighting their resilience against
environmental stripping effects, and their impact on observable 21-cm signals.


  We present a study of the evolved stellar populations in the dwarf spheroidal
galaxy LeoII, based on JHKs observations obtained with the near-infrared array
WFCAM at the UKIRT telescope. Combining the new data with optical data, we
derived photometric estimates of the distribution of global metallicity [M/H]
of individual red giant stars from their V-Ks colours. We used the new data to
derive the properties of a nearly complete sample of asymptotic giant branch
(AGB) stars in LeoII. Using a near-infrared two-colour diagram, we were able to
obtain a clean separation from Milky Way foreground stars and discriminate
between carbon- and oxygen-rich AGB stars. We simulate the JHKs data with the
TRILEGAL population synthesis code together with the most updated thermally
pulsing AGB models, and using the star formation histories derived from
independent work based on deep HST photometry. After scaling the mass of LeoII
models to the observed number of upper RGB stars, we find that present models
predict too many O-rich TP-AGB stars of higher luminosity due to a likely
under-estimation of either their mass-loss rates at low metallicity, and/or
their degree of obscuration by circumstellar dust. On the other hand, the
TP-AGB models are able to reproduce the observed number and luminosities of
carbon stars satisfactorily well, indicating that in this galaxy the least
massive stars that became carbon stars should have masses as low as ~1 M_sun.


  We study in details the distribution of mass in galaxy cluster CL0024+1654
inferred using the method of strong gravitational lensing by Tyson {\it et al.}
(1998). We show that a linear correlation exists between total, visible and
dark matter distributions on log-log scale with consistent coefficients. The
shape and parameters of log-log-linear correlation are not affected
significantly whether one uses projected or volume mass densities but is
consistent with $\kappa=2-5$ visible/dark ratio. We also show and analyze in
depth so called alignment properties of the above-mentioned profiles. We show
that log-log-linear correlation and alignments can all be understood in terms
of thermodynamic/hydrodynamic equilibrium with gravitational potential growing
almost linearly in the region of interest. We then analyze the hypothesis of
thermal equilibrium on the base of the existing data about CL0024 cluster. If
the presence of log-log-linear correlation and alignments were interpreted
thermodynamically, this would indicate the mass of the dark matter particle 2-5
times smaller than that of atomic hydrogen, thus giving range for the mass of
dark matter particle between 200MeV and 1000MeV.


  We introduce the post-processing preorder and equivalence relations for
general measurements on a possibly infinite-dimensional general probabilistic
theory described by an order unit Banach space $E$ with a Banach predual. We
define the measurement space $\mathfrak{M}(E)$ as the set of post-processing
equivalence classes of continuous measurements on $E .$ We define the weak
topology on $\mathfrak{M} (E)$ as the weakest topology in which the state
discrimination probabilities for any finite-label ensembles are continuous and
show that $\mathfrak{M}(E)$ equipped with the convex operation corresponding to
the probabilistic mixture of measurements can be regarded as a compact convex
set regularly embedded in a locally convex Hausdorff space. We also prove that
the measurement space $\mathfrak{M}(E) $ is infinite-dimensional except when
the system is $1$-dimensional and give a characterization of the
post-processing monotone affine functional. We apply these general results to
the problems of simulability and incompatibility of measurements. We show that
the robustness measures of unsimulability and incompatibility coincide with the
optimal ratio of the state discrimination probability of measurement(s)
relative to that of simulable or compatible measurements, respectively. The
latter result for incompatible measurements generalizes the recent result for
finite-dimensional quantum measurements. Throughout the paper, the fact that
any weakly$\ast$ continuous measurement can be arbitrarily approximated in the
weak topology by a post-processing increasing net of finite-outcome
measurements is systematically used to reduce the discussions to finite-outcome
cases.


  We study the quench dynamics of a topologically trivial one-dimensional
gapless wire following its sudden coupling to topological bound states. We find
that as the bound states leak into and propagate through the wire, signatures
of their topological nature survive and remain measurable over a long lifetime.
Thus, the quench dynamically induces topological properties in the gapless
wire. Specifically, we study a gapless wire coupled to fractionally charged
solitons or Majorana fermions and characterize the dynamically induced topology
in the wire, in the presence of disorder and short-range interactions, by
analytical and numerical calculations of the dynamics of fractional charge,
fermion parity, entanglement entropy, and fractional exchange statistics. In a
dual effective description, this phenomenon is described by correlators of
boundary changing operators, which, remarkably, generate topologically
non-trivial monodromies in the gapless wire, both for abelian and non-abelian
quantum statistics of the bound states.


  We consider the Schr\"{o}dinger operator $\mathcal{L}=-\Delta+V$ on $\mathbb
R^d$, $d\geq3$, where the nonnegative potential $V$ belongs to the reverse
H\"{o}lder class $RH_s$ for some $s\geq d/2$. A real-valued function $f\in
L^1_{\mathrm{loc}}(\mathbb R^d)$ belongs to the (BMO) space
$\mathrm{BMO}_{\rho,\theta}(\mathbb R^d)$ with $0<\theta<\infty$ if
\begin{equation*} \|f\|_{\mathrm{BMO}_{\rho,\theta}}
:=\sup_{B(x_0,r)}\bigg(1+\frac{r}{\rho(x_0)}\bigg)^{-\theta}\bigg(\frac{1}{|B(x_0,r)|}\int_{B(x_0,r)}\big|f(x)-f_{B}\big|\,dx\bigg),
\end{equation*} where the supremum is taken over all balls
$B(x_0,r)\subset\mathbb R^d$, $\rho(\cdot)$ is the critical radius function in
the Schr\"{o}dinger context and \begin{equation*}
f_{B}:=\frac{1}{|B(x_0,r)|}\int_{B(x_0,r)}f(y)\,dy. \end{equation*} A
real-valued function $f\in L^1_{\mathrm{loc}}(\mathbb R^d)$ belongs to the
(Lipschitz) space $\mathrm{Lip}_{\beta}^{\rho,\theta}(\mathbb R^d)$ with
$0<\beta<1$ and $0<\theta<\infty$ if \begin{equation*}
\|f\|_{\mathrm{Lip}_{\beta}^{\rho,\theta}}
:=\sup_{B(x_0,r)}\bigg(1+\frac{r}{\rho(x_0)}\bigg)^{-\theta}
\bigg(\frac{1}{|B(x_0,r)|^{1+\beta/d}}\int_{B(x_0,r)}\big|f(x)-f_{B}\big|\,dx\bigg).
\end{equation*} It can be easily seen that $\mathrm{BMO}_{\rho,\theta}(\mathbb
R^d)$ (or $\mathrm{Lip}_{\beta}^{\rho,\theta}(\mathbb R^d)$) is a function
space which is larger than the classical BMO (or Lipschitz) space. In this
paper, we give some new characterizations of BMO and Lipschitz spaces
associated with the Schr\"{o}dinger operator $\mathcal{L}$. We extend some
previous works of Bongioanni--Harboure--Salinas and Liu--Sheng to the weighted
case. The classes of weights considered here are larger than the classical
Muckenhoupt classes.


  We here present an investigation of the ringing effect observed on the VIRGO
mode-cleaner prototype MC30. The results of a numerical calculation show how a
simple empirical formula can determine the cavity expansion rate from the
oscillatory behavior. We also show how the simulation output can be adjusted to
estimate the finesse value of the suspended cavity.


  A periodic long slot leaky-wave antenna (LWA) based on a ridged substrate
integrated waveguide (RSIW) is proposed. To reduce the cross polarization, the
long slot is placed on the SIW centerline, and a sinusoidal ridge is used to
produce a controllable asymmetric electric field around the long slot. Also,
only a small stopband occurs when the beam is scanned through the broadside.
Varying the amplitude and width of the sinusoidal ridge provides a fixed phase
constant and controllable leakage rate to achieve the desired sidelobe level of
less than 30 dB. Measurement results are consistent with the simulation
results.


  We formulate a new class of fractional difference and sum operators, study
their fundamental properties, and find their discrete Laplace transforms. The
method depends on iterating the fractional sum operators corresponding to
fractional differences with discrete Mittag-Leffler kernels. The iteration
process depends on the binomial theorem. We note in particular the fact that
the iterated fractional sums have a certain semigroup property and hence the
new introduced iterated fractional difference-sum operators have this semigroup
property as well.


  We introduce an alternative approach to the third order helicity of a volume
preserving vector field $B$, which leads us to a lower bound for the
$L^2$-energy of $B$. The proposed approach exploits correspondence between the
Milnor $\bar{\mu}_{123}$-invariant for 3-component links and the homotopy
invariants of maps to configuration spaces, and we provide a simple geometric
proof of this fact in the case of Borromean links. Based on these connections
we develop a formulation for the third order helicity of $B$ on invariant
\emph{unlinked} domains of $B$, and provide Arnold's style ergodic
interpretation of this invariant as an average asymptotic
$\bar{\mu}_{123}$-invariant of orbits of $B$.


  This note describes an algorithm for enumerating all the elements in a finite
set based on uniformly random sampling from the set. This algorithm can be used
for enumeration by fair sampling with quantum annealing. Our algorithm is based
on a lemma of the coupon collector's problem and is an improved version of the
algorithm described in arXiv:2007.08487 (2020). We provide a mathematical
analysis and a numerical demonstration of our algorithm.


  We present a complete morphologically classified sample of 144 faint field
galaxies from the HST Medium Deep Survey with 20.0 < I <22.0 mag. We compare
the global properties of the ellipticals, early and late-type spirals, and find
a non-negligible fraction (13/144) of compact blue [(V-I) < 1.0 mag] systems
with $r^{1/4}$-profiles. We give the differential galaxy number counts for
ellipticals and early-type spirals independently, and find that the data are
consistent with no-evolution predictions based on conventional flat Schechter
luminosity functions (LF's) and a standard cosmology.
  Conversely, late-type/Irregulars show a steeply rising differential number
count with slope $(\frac{\delta log N}{\delta m}) = 0.64\pm 0.1$. No-evolution
models based on the Loveday et al. (1992) and Marzke et al. (1994b) {\it local}
luminosity functions under-predict the late-type/Irregular counts by 1.0 and
0.5 dex, respectively, at I = 21.75 mag. Examination of the Irregulars alone
shows that $\sim 50$% appear inert and the remainder have multiple cores. If
the inert galaxies represent a non-evolving late-type population, then a
Loveday-like LF ($\alpha\simeq -1.0$) is ruled out for these types, and a LF
with a steep faint-end ($\alpha\simeq -1.5$) is suggested. If multiple core
structure indicates recent star-formation, then the observed excess of faint
blue field galaxies is likely due to {\it evolutionary} processes acting on a
{\it steep} field LF for late-type/Irregulars. The evolutionary mechanism is
unclear, but 60% of the multiple-core Irregulars show close companions. To
reconcile a Marzke-like LF with the faint redshift surveys, this evolution must
be preferentially occurring in the brightest late-type galaxies with z > 0.5 at
I = 21.75 mag.