  We report the serendipitous discovery of a nitrogen-rich, mildly metal-poor
([Fe/H]=-1.08) giant star in a single-lined spectroscopic binary system found
in the SDSS-IV Apache Point Observatory Galactic Evolution Experiment
(APOGEE-2) survey, Data Release 14 (DR14). Previous work has assumed that the
two percent of halo giants with unusual elemental abundances have been
evaporated from globular clusters, but other origins for their abundance
signatures, including binary mass transfer, must also be explored. We present
the results of an abundance re-analysis of the APOGEE-2 high-resolution
near-infrared spectrum of 2M12451043+1217401 with the Brussels Automatic
Stellar Parameter (BACCHUS) automated spectral analysis code, and re-derive
manually the main element families, namely the light elements (C, N), elements
(O, Mg, Si), iron-peak element (Fe), \textit{s}-process element (Ce), and the
light odd-Z element (Al). Our analysis confirm the N-rich nature of
2M12451043+1217401, which has a [N/Fe] ratio of $+0.69$, and shows that the
abundances of C and Al are slightly discrepant from that of a typical mildly
metal-poor RGB star, but exhibit Mg, Si, O and \textit{s}-process abundances
(Ce) of typical field stars. We also detect a particularly large variability in
its radial velocity over the period of the APOGEE-2 observations, and the most
likely orbit fit to the radial velocity data has a period of $730.89\pm106.86$
days, a velocity semi-amplitude of $9.92 \pm 0.14$ km s$^{-1}$, and an
eccentricity of $\sim 0.1276 \pm0.1174$, which support the hypothesis of a
binary companion, and that has probably been polluted by a now-extinct AGB
star.


  In this paper we examine the Riemannian geometry of the group of
contactomorphisms of a compact contact manifold. We compute the sectional
curvature of $\mathcal{D}_\theta(M)$ in the sections containing the Reeb field
and show that it is non-negative. We also solve explicitly the Jacobi equation
along the geodesic corresponding to the flow of the Reeb field and determine
the conjugate points. Finally, we show that the Riemannian exponential map is a
non-linear Fredholm map of index zero.


  The CUbesat Solar Polarimeter (CUSP) project aims to develop a constellation
of two CubeSats orbiting the Earth to measure the linear polarization of solar
flares in the hard X-ray band by means of a Compton scattering polarimeter on
board of each satellite. CUSP will allow to study the magnetic reconnection and
particle acceleration in the flaring magnetic structures. CUSP is a project
approved for a Phase B study by the Italian Space Agency in the framework of
the Alcor program aimed to develop CubeSat technologies and missions. In this
paper we describe the a method for a multi-physical simulation analysis while
analyzing some possible design optimization of the payload design solutions
adopted. In particular, we report the mechanical design for each structural
component, the results of static and dynamic finite element analysis, the
preliminary thermo-mechanical analysis for two specific thermal cases (hot and
cold orbit) and a topological optimization of the interface between the
platform and the payload.


  Ray tracing algorithm simulates the physical movements of a huge amount of
rays to render a high quality image, in which the tracing procedure for each
ray can be implemented in parallel. By leveraging the inherent parallelism of
quantum computing, we propose a quantum ray tracing algorithm, which is proved
to have a quadratic speedup over the classical path tracing.


  An elegant procedure which characterizes a decomposition of some class of
binomial configurations into two other, resembling a definition of Pascal's
Triangle, was given in \cite{gevay}. In essence, this construction was already
presented in \cite{perspect}. We show that such a procedure is a result of
fixing in configurations in some class $\mathcal K$ suitable hyperplanes which
both: are in this class, and deleting such a hyperplane results in a
configuration in this class. By a way of example we show two more (added to
that of \cite{gevay}) natural classes of such configurations, discuss some
other, and propose some open questions that seem also natural in this context.


  What kinds of motion can occur in classical mechanics? We address this
question by looking at the structures traced out by trajectories in phase
space; the most orderely, completely integrable systems, are charactrized by
phase trajectories confined to low-dimensional, invariant tori. The KAM theory
examines what happens to the tori when an integrable system is subjected to a
small perturbation and finds that, for small enough perturbations, most of them
survive.
  The KAM theory is mute on the suject of the disrupted tori, but, for two
dimensional systems, Aubry and Mather discovered an astonishing picture: the
broken tori are replaced by "cantori", tattered, Cantor-set remnants of the
original invariant curves. We seek to extend Aubry and Mather's picture to
higher dimensional systems and report two kinds of studies; both concern
perturbations of a completely integrable, four-dimensional symplectic map. In
the first study we compute some numerical approximations to Birkhoff periodic
orbits; sequences of such orbits should approximate any higher dimensional
analogs of the cantori. In the second study we prove converse KAM theorems;
that is, we use a combination of analytic arguments and rigorous,
machine-assisted computations to find perturbations so large that no KAM tori
survive. We are able to show that the last few of our Birkhoff orbits exist in
a regime where there are no tori.


  Quasicrystals and their periodic approximants are complex phases, which have
by now been observed in many metallic alloys, soft matter systems, and particle
simulations. In recent experiments of thin-film perovskites on solid
substrates, the type of complex phase was found to change depending on
thermodynamic conditions and the type of substrate used. Here, we investigate
the effect of a substrate on the relative stability of a two-dimensional model
quasicrystal and its approximants. Our numerical methods are molecular dynamics
simulations and free energy calculations that take into account phason flips
explicitly. For weak substrates, we observe an incommensurate-commensurate
transition, in which a continuous series of QC approximants locks into a
discrete number of approximants. For stronger substrates, an enhancement of the
stability of the dodecagonal quasicrystal and a variants of square lattices
were found. All phenomena can be explained by the interplay of the model system
with the substrate. Our results demonstrate that designing novel complex
periodic and quasiperiodic structures by choice of suitable substrates is a
promising strategy.


  In this article, we investigate an artificial traffic model on scale-free
networks. Instead of using the routing strategy of the shortest path, a
generalized routing algorithm is introduced to improve the transportation
throughput, which is measured by the value of the critical point disjoining the
free-flow phase and the congested phase. By using the detrended fluctuation
analysis, we found that the traffic rate fluctuation near the critical point
exhibits the $1/f$-type scaling in the power spectrum. The simulation results
agree very well with the empirical data, thus the present model may contribute
to the understanding of the underlying mechanism of network traffics.


  Consider the problem of approximating the optimal policy of a Markov decision
process (MDP) by sampling state transitions. In contrast to existing
reinforcement learning methods that are based on successive approximations to
the nonlinear Bellman equation, we propose a Primal-Dual $\pi$ Learning method
in light of the linear duality between the value and policy. The $\pi$ learning
method is model-free and makes primal-dual updates to the policy and value
vectors as new data are revealed. For infinite-horizon undiscounted Markov
decision process with finite state space $S$ and finite action space $A$, the
$\pi$ learning method finds an $\epsilon$-optimal policy using the following
number of sample transitions $$ \tilde{O}( \frac{(\tau\cdot t^*_{mix})^2 |S|
|A| }{\epsilon^2} ),$$ where $t^*_{mix}$ is an upper bound of mixing times
across all policies and $\tau$ is a parameter characterizing the range of
stationary distributions across policies. The $\pi$ learning method also
applies to the computational problem of MDP where the transition probabilities
and rewards are explicitly given as the input. In the case where each state
transition can be sampled in $\tilde{O}(1)$ time, the $\pi$ learning method
gives a sublinear-time algorithm for solving the averaged-reward MDP.


  We present state-of-the-art predictions for the ultra-high energy (UHE)
neutrino-nucleus cross-sections in charged- and neutral-current scattering. The
calculation is performed in the framework of collinear factorisation at NNLO,
extended to include the resummation of small-$x$ BFKL effects. Further
improvements are made by accounting for the free-nucleon PDF constraints
provided by $D$-meson data from LHCb and assessing the impact of nuclear
corrections and heavy-quark mass effects. The calculations presented here
should play an important role in the interpretation of future data from
neutrino telescopes such as IceCube and KM3NET, and highlight the opportunities
that astroparticle experiments offer to study the strong interactions.


  We present results of experiments in superfluid phases of 3He confined in
aerogel which strands are nearly parallel to one another. High temperature
superfluid phases of 3He in this aerogel (ESP1 and ESP2) are chiral phases and
have polar distorted ABM order parameter which orbital part forms 2D
Larkin-Imry-Ma state. We demonstrate that this state can be anisotropic if the
aerogel is squeezed in direction transverse to the strands. Values of this
anisotropy in ESP1 and ESP2 phases are different, what leads to different NMR
properties.


  We present the first direct evidence that quenched QCD differs from full QCD
in the chiral ($m_q \rightarrow 0$) limit, as predicted by chiral perturbation
theory, from our quenched lattice QCD simulations at $\beta = 6/g^2 = 6.0$. We
measured the spectrum of light hadrons on $16^3 \times 64$, $24^3 \times 64$
and $32^3 \times 64$, using staggered quarks of masses $m_q=0.01$, $m_q=0.005$
and $m_q=0.0025$. The pion masses showed clear evidence for logarithmic
violations of the PCAC relation $m_{\pi}^2 \propto m_q$, as predicted by
quenched chiral perturbation theory. The dependence on spatial lattice volume
precludes this being a finite size effect. No evidence was seen for such chiral
logarithms in the behaviour of the chiral condensate
$\langle\bar{\psi}\psi\rangle$.


  The emergence and development of cancer is a consequence of the accumulation
over time of genomic mutations involving a specific set of genes, which
provides the cancer clones with a functional selective advantage. In this work,
we model the order of accumulation of such mutations during the progression,
which eventually leads to the disease, by means of probabilistic graphic
models, i.e., Bayesian Networks (BNs). We investigate how to perform the task
of learning the structure of such BNs, according to experimental evidence,
adopting a global optimization meta-heuristics. In particular, in this work we
rely on Genetic Algorithms, and to strongly reduce the execution time of the
inference -- which can also involve multiple repetitions to collect
statistically significant assessments of the data -- we distribute the
calculations using both multi-threading and a multi-node architecture. The
results show that our approach is characterized by good accuracy and
specificity; we also demonstrate its feasibility, thanks to a 84x reduction of
the overall execution time with respect to a traditional sequential
implementation.


  Monotone inclusions involving the sum of three maximally monotone operators
or more have received much attention in recent years. In this paper, we propose
three splitting algorithms for finding a zero of the sum of four monotone
operators, which are two maximally monotone operators, one monotone Lipschitz
operator, and one cocoercive operator. These three splitting algorithms are
based on the forward-reflected-Douglas-Rachford splitting algorithm,
backward-forward-reflected-backward splitting algorithm, and
backward-reflected-forward-backward splitting algorithm, respectively. As
applications, we apply the proposed algorithms to solve the monotone inclusions
problem involving a finite sum of maximally monotone operators. Numerical
results on the Projection on Minkowski sums of convex sets demonstrate the
effectiveness of the proposed algorithms.


  We have developed a semi-analytic method of parameterizing N-body simulations
of self-gravity wakes in Saturn's rings, describing their properties by means
of only 6 numbers: 3 optical depths and 3 weighting factors. These numbers are
obtained using a density-estimation procedure that finds the frequencies of
various values of local density within a simulated ring patch.
  Application of our parameterization to a suite of N-body simulations implies
that the distribution of local optical depths is trimodal, rather than bimodal
as previous authors have assumed. Rings dominated by self-gravity wakes appear
to be mostly empty space.
  The implications of this result for the analysis of occultation data are more
conceptual than practical. The only adjustment needed is that the model
parameter $\tau_{gap}$ should be interpreted as representing the area-weighted
average optical depth within the gaps (or inter-wake regions).
  The most significant consequence of our results applies to the question of
why "propeller" structures observed in the mid-A ring are seen as
relative-bright features, even though the most prominent features of simulated
propellers are regions of relatively low density. We find preliminary
quantitative support for the hypothesis that propellers would be bright if they
involve a local and temporary disruption of self-gravity wakes, flooding the
region with more "photometrically active" material (i.e., material that can
contribute to the rings' local optical depth) even though the overall density
is lower, and thus raising their apparent brightnesses in agreement with
observations. We suggest that this mechanism be tested by future detailed
numerical models.


  Local translational and scaling symmetries in space-time is exploited for
modelling ductile damage in metals and alloys over wide ranges of strain rate
and temperature. The invariant energy density corresponding to the ductile
deformation is constructed through the gauge invariant curvature tensor by
imposing the Weyl like condition. The energetics of the plastic deformation is
brought in through the gauge compensating field emerged due to local
translation. Invariance of the energy density under the local action of
translation and scaling is preserved through minimally replaced space-time
gauge covariant operators. Minimal replacement introduces two non-trivial gauge
compensating fields pertaining to local translation and scaling. These are used
to describe ductile damage, including plastic flow and micro-crack evolution in
the material. A space-time pseudo-Riemannian metric is used to lay out the
kinematics in a finite-deformation setting. Recognizing the available insights
in classical theories of viscoplasticity, we also establish a correspondence of
the gauge compensating field due to spatial translation with Kr\"{o}ner's
multiplicative decomposition of the deformation gradient. Thermodynamically
consistent coupling between viscoplasticity and ductile damage is ensured
through an appropriate degradation function. Non-ordinary state-based (NOSB)
peridynamics (PD) discretization of the model is used for numerical
implementation. The model's viability is tested in reproducing a few
experimentally known facts, viz., strain rate locking in the stress-strain
response, whose origin is traced to a nonlinear microscopic inertia term
arising out of the space-time translation symmetry. Finally, we solved 2D and
axisymmetric deformation problems for qualitatively validating the model's
viability. NOSB peridynamics axisymmetric formulation in finite deformation
setup is also presented.


  Let $\Omega$ be a bounded domain with $C^2$-smooth boundary in an
$n$-dimensional oriented Riemannian manifold. It is well-known that for the
bi-harmonic equation $\Delta^2 u=0$ in $\Omega$ with the $0$-Dirichlet boundary
condition, there exists an infinite set $\{u_k\}$ of biharmonic functions in
$\Omega$ with positive eigenvalues $\{\lambda_k\}$ satisfying $\Delta u_k+
\lambda_k \varrho \frac{\partial u_k}{\partial \nu}=0$ on the boundary
$\partial \Omega$. In this paper, by a new method we establish the Weyl-type
asymptotic formula for the counting function of the biharmonic Stekloff
eigenvalues $\lambda_k$.


  We present new and accurate near-infrared (NIR) J, K-band time series data
for the Galactic globular cluster (GC) M5 = NGC5904. Data were collected with
SOFI at the NTT (71 J + 120 K images) and with NICS at the TNG (25 J + 22 K
images) and cover two orthogonal strips across the center of the cluster of
\approx 5 \times 10 arcmin^{2} each. These data allowed us to derive accurate
mean K-band magnitudes for 52 fundamental (RR_{ab}) and 24 first overtone
(RR_{c}) RR Lyrae stars. Using this sample of RR Lyrae stars, we find that the
slope of the K-band Period Luminosity (PLK) relation (-2.33 \pm 0.08) agrees
quite well with similar estimates available in the literature. We also find,
using both theoretical and empirical calibrations of the PLK relation, a true
distance to M5 of (14.44 \pm 0.02) mag. This distance modulus agrees very well
(1\sigma) with distances based on main sequence fitting method and on kinematic
method (14.44 \pm 0.41 mag, \citealt{rees_1996}), while is systematically
smaller than the distance based on the white dwarf cooling sequence (14.67 \pm
0.18 mag, \citealt{layden2005}), even if with a difference slightly larger than
1\sigma. The true distance modulus to M5 based on the PLJ relation (14.50 \pm
0.08 mag) is in quite good agreement with the distance based on the PLK
relation further supporting the use of NIR PL relations for RR Lyrae stars to
improve the precision of the GC distance scale.


  The occurrence of the low-lying charge-exchange non spin-flip dipole modes
below the giant resonance in neutron-rich nuclei is predicted on the basis of
nuclear density functional theory. The ground and excited states are described
in the framework of the self-consistent Hartree-Fock-Bogoliubov and the
proton-neutron quasiparticle-random-phase approximation employing a Skyrme-type
energy density functional. The model calculations are performed for the
spherical neutron-rich Ca, Ni, and Sn isotopes. It is found that the low-lying
states appear sensitively to the shell structure associated with the $-1 \hbar
\omega_0$ excitation below the Gamow-Teller states. Furthermore, the pygmy
resonance emerges below the giant resonance when the neutrons occupy the
low-$\ell (\ell \leq 2 -3)$ orbitals analogous to the pygmy resonance seen in
the electric dipole response.


  We report first-principle atomistic simulations on the effect of local strain
gradients on the nanoscale domain morphology of free-standing PbTiO$_3$
ultrathin films. First, the ferroelectric properties of free films at the
atomic level are reviewed. For the explored thicknesses (10 to 23 unit cells),
we find flux-closure domain structures whose morphology is thickness dependent.
A critical value of 20 unit cells is observed: thinner films show structures
with 90$^\circ$ domain loops, whereas thicker ones develop, in addition,
180$^\circ$ domain walls, giving rise to structures of the Landau-Lifshitz
type. When a local and compressive strain gradient at the top surface is
imposed, the gradient is able to switch the polarization of the downward
domains, but not to the opposite ones. The evolution of the domain pattern as a
function of the strain gradient strength consequently depends on the film
thickness. Our simulations indicate that in thinner films, first the 90$^\circ$
domain loops migrate towards the strain-gradient region, and then the
polarization in that zone is gradually switched. In thicker films, instead, the
switching in the strain-gradient region is progressive, not involving
domain-wall motion, which is attributed to less mobile 180$^\circ$ domain
walls. The ferroelectric switching is understood based on the knowledge of the
local atomic properties, and the results confirm that mechanical
flexoelectricity provides a means to control the nanodomain pattern in
ferroelectric systems.


  This paper is concerned with the computation of an optimal matching between
two manifold-valued curves. Curves are seen as elements of an
infinite-dimensional manifold and compared using a Riemannian metric that is
invariant under the action of the reparameterization group. This group induces
a quotient structure classically interpreted as the ''shape space''. We
introduce a simple algorithm allowing to compute geodesics of the quotient
shape space using a canonical decomposition of a path in the associated
principal bundle. We consider the particular case of elastic metrics and show
simulations for open curves in the plane, the hyperbolic plane and the sphere.


  In this letter, a novel variation of sparse code multiple access (SCMA),
called codeword position index based SCMA (CPI-SCMA), is proposed. In this
scheme, the information is transmitted not only by the codewords in M point
SCMA codebook, but also by the indices of the codeword positions in a data
block. As such, both the power and transmission efficiency (TE) can be
improved, moreover, CPI-SCMA can achieve a better error rate performance
compare to conventional SCMA (C-SCMA).


  Image galleries provide a rich source of diverse information about a product
which can be leveraged across many recommendation and retrieval applications.
We study the problem of building a universal image gallery encoder through
multi-task learning (MTL) approach and demonstrate that it is indeed a
practical way to achieve generalizability of learned representations to new
downstream tasks. Additionally, we analyze the relative predictive performance
of MTL-trained solutions against optimal and substantially more expensive
solutions, and find signals that MTL can be a useful mechanism to address
sparsity in low-resource binary tasks.


  The renormalization group flow in the theory space of a BRST invariant string
$\sigma$-model is investigated. For the open bosonic string the
non-perturbative off-shell effective action and its gauge symmetry properties
are determined from $\beta$-functions defined by the local Weyl anomaly. The
interactions are shown to explicitly break the free theory BRST invariance
generating new non-linear gauge symmetries of the type present in Witten's
string field theory. In the Feynman-Siegel gauge the $\sigma$-model is shown to
generate Witten's structure of vertex couplings.


  We consider the mass critical NLS on $\mathbb{T}$ and $\mathbb{T}^2$. In the
$\mathbb{R}^d$ case the Strichartz estimates enable us to show well-posedness
of the IVP in $L^2$ (at least for small data) via the Picard iteration method.
However, counterexamples to the $L^6$ Strichartz on $\mathbb{T}$ and the $L^4$
Strichartz on $\mathbb{T}^2$ were given by Bourgain (1993) and Takaoka-Tzvetkov
(2001), respectively, which means that the Strichartz spaces are not suitable
for iteration in these problems. In this note, we show a slightly stronger
result, namely, that the IVP on $\mathbb{T}$ and $\mathbb{T}^2$ cannot have a
smooth data-to-solution map in $L^2$ even for small initial data. The same
results are also obtained for most of the two dimensional irrational tori.


  Unintended biases in machine learning (ML) models are among the major
concerns that must be addressed to maintain public trust in ML. In this paper,
we address process fairness of ML models that consists in reducing the
dependence of models on sensitive features, without compromising their
performance. We revisit the framework FixOut that is inspired in the approach
"fairness through unawareness" to build fairer models. We introduce several
improvements such as automating the choice of FixOut's parameters. Also, FixOut
was originally proposed to improve fairness of ML models on tabular data. We
also demonstrate the feasibility of FixOut's workflow for models on textual
data. We present several experimental results that illustrate the fact that
FixOut improves process fairness on different classification settings.


  Twitter is one of the most used applications in the current Internet with
more than 200M accounts created so far. As other large-scale systems Twitter
can obtain enefit by exploiting the Locality effect existing among its users.
In this paper we perform the first comprehensive study of the Locality effect
of Twitter. For this purpose we have collected the geographical location of
around 1M Twitter users and 16M of their followers. Our results demonstrate
that language and cultural characteristics determine the level of Locality
expected for different countries. Those countries with a different language
than English such as Brazil typically show a high intra-country Locality
whereas those others where English is official or co-official language suffer
from an external Locality effect. This is, their users have a larger number of
followers in US than within their same country. This is produced by two
reasons: first, US is the dominant country in Twitter counting with around half
of the users, and second, these countries share a common language and cultural
characteristics with US.


  Understanding the origin of electron incoherence is believed to be the first
step toward the resolution of the mysteries of the high-T$_{c}$ cuprate
superconductors. Such electron incoherence manifests itself most evidently in
the non-Drude form of the optical absorption spectrum of the system. The
spectral weight transfer related to such dissipative response, which is absent
in conventional Fermi liquid metal, has direct consequence on the dc transport
property of the system. However, a theoretical study of the optical
conductivity of a strongly correlated model is a formidable task. Here we
present an exact formula for the optical conductivity of the 2D Hubbard model
from the low energy effective theory perspective. We show that the optical
conductivity in Matsubara frequency of the 2D Hubbard model can be represented
as the ensemble average of the optical conductivity of non-interacting systems
in the background of fluctuating local moment. We find that such an ensemble
average can be done exactly with a sign-problem-free Monte Carlo simulation if
we assume the widely adopted Millis-Monien-Pines spin susceptibility for the
fluctuating local moment. For thermal fluctuation of the local moment, our
formula can be used to calculate directly the optical conductivity in real
frequency which can be compared with the result of optical measurements in the
cuprate superconductors.


  We study the young S-stars within a distance of 0.04 pc from the supermassive
black hole in the center of our Galaxy. Given how inhospitable the region is
for star formation, their presence is more puzzling the younger we estimate
their ages. In this study, we analyse the result of 12 years of high resolution
spectroscopy within the central arcsecond of the Galactic Center (GC). By
co-adding between 55 and 105 hours of spectra we have obtained high signal to
noise H- and K-band spectra of eight stars orbiting the central supermassive
black hole. Using deep H-band spectra, we show that these stars must be high
surface gravity (dwarf) stars. We compare these deep spectra to detailed model
atmospheres and stellar evolution models to infer the stellar parameters. Our
analysis reveals an effective temperature of 21000-28500 K, a rotational
velocity of 60-170 km/s, and a surface gravity of 4.1-4.2. These parameters
imply a spectral type of B0-B3V for these stars. The inferred masses lie within
8-14 Msun. We derive an age of 6.6^{+3.4}{-4.7} Myr for the star S2, which is
compatible with the age of the clockwise rotating young stellar disk in the GC.
We estimate the age of all other studied S-stars to be less than 15 Myr, which
are compatible with the age of S2 within the uncertainties. The relatively low
ages for these S-stars favor a scenario in which the stars formed in a local
disk rather than the field-binary-disruption scenario throughout a longer
period of time.


  To complement the IceCube neutrino telescope currently under construction at
the South Pole, the three Mediterranean neutrino telescope projects ANTARES,
NEMO and NESTOR have joined forces to develop, construct and operate a
km^3-scale neutrino telescope in the Mediterranean Sea. Since February 2006,
the technical specifications and performance of such a detector are studied in
the framework of a 3-year EU-funded Design Study. In 2009 a technical design
report will be released laying the foundations for the construction of the
detector. In the following, the current status of the Design Study is presented
and examples of solutions for the technical challenges are discussed.


  Human eyes can recognize person identities based on small salient regions,
i.e. human saliency is distinctive and reliable in pedestrian matching across
disjoint camera views. However, such valuable information is often hidden when
computing similarities of pedestrian images with existing approaches. Inspired
by our user study result of human perception on human saliency, we propose a
novel perspective for person re-identification based on learning human saliency
and matching saliency distribution. The proposed saliency learning and matching
framework consists of four steps: (1) To handle misalignment caused by drastic
viewpoint change and pose variations, we apply adjacency constrained patch
matching to build dense correspondence between image pairs. (2) We propose two
alternative methods, i.e. K-Nearest Neighbors and One-class SVM, to estimate a
saliency score for each image patch, through which distinctive features stand
out without using identity labels in the training procedure. (3) saliency
matching is proposed based on patch matching. Matching patches with
inconsistent saliency brings penalty, and images of the same identity are
recognized by minimizing the saliency matching cost. (4) Furthermore, saliency
matching is tightly integrated with patch matching in a unified structural
RankSVM learning framework. The effectiveness of our approach is validated on
the VIPeR dataset and the CUHK01 dataset. Our approach outperforms the
state-of-the-art person re-identification methods on both datasets.


  We study the operational regime of a noiseless linear amplifier based on
quantum scissors that can nondeterministically amplify the one photon component
of a quantum state with weak excitation. It has been shown that an arbitrarily
large quantum state can be amplified by first splitting it into weak excitation
states using a network of beamsplitters. The output states of the network can
then be coherently recombined. In this paper, we analyse the performance of
such a device for distilling entanglement after transmission through a lossy
quantum channel, and look at two measures to determine the efficacy of the
noiseless linear amplifier. The measures used are the amount of entanglement
achievable and the final purity of the output amplified entangled state. We
study the performances of both a single and a two-element noiseless linear
amplifier for amplifying weakly excited states. Practically, we show that it
may be advantageous to work with a limited number of stages.


  In vivo calcium imaging through microscopes has enabled deep brain imaging of
previously inaccessible neuronal populations within the brains of freely moving
subjects. However, microendoscopic data suffer from high levels of background
fluorescence as well as an increased potential for overlapping neuronal
signals. Previous methods fail in identifying neurons and demixing their
temporal activity because the cellular signals are often submerged in the large
fluctuating background. Here we develop an efficient method to extract cellular
signals with minimal influence from the background. We model the background
with two realistic components: (1) one models the constant baseline and slow
trends of each pixel, and (2) the other models the fast fluctuations from
out-of-focus signals and is therefore constrained to have low spatial-frequency
structure. This decomposition avoids cellular signals being absorbed into the
background term. After subtracting the background approximated with this model,
we use Constrained Nonnegative Matrix Factorization (CNMF, Pnevmatikakis et al.
(2016)) to better demix neural signals and get their denoised and deconvolved
temporal activity. We validate our method on simulated and experimental data,
where it shows fast, reliable, and high quality signal extraction under a wide
variety of imaging parameters.


  Machine learning (ML) in healthcare presents numerous opportunities for
enhancing patient care, population health, and healthcare providers' workflows.
However, the real-world clinical and cost benefits remain limited due to
challenges in data privacy, heterogeneous data sources, and the inability to
fully leverage multiple data modalities. In this perspective paper, we
introduce "patchwork learning" (PL), a novel paradigm that addresses these
limitations by integrating information from disparate datasets composed of
different data modalities (e.g., clinical free-text, medical images, omics) and
distributed across separate and secure sites. PL allows the simultaneous
utilization of complementary data sources while preserving data privacy,
enabling the development of more holistic and generalizable ML models. We
present the concept of patchwork learning and its current implementations in
healthcare, exploring the potential opportunities and applicable data sources
for addressing various healthcare challenges. PL leverages bridging modalities
or overlapping feature spaces across sites to facilitate information sharing
and impute missing data, thereby addressing related prediction tasks. We
discuss the challenges associated with PL, many of which are shared by
federated and multimodal learning, and provide recommendations for future
research in this field. By offering a more comprehensive approach to healthcare
data integration, patchwork learning has the potential to revolutionize the
clinical applicability of ML models. This paradigm promises to strike a balance
between personalization and generalizability, ultimately enhancing patient
experiences, improving population health, and optimizing healthcare providers'
workflows.


  A modified Borel transform of the Adler function is used to resum the
hadronic tau decay width ratio. In contrast to the ordinary Borel transform,
the integrand of the Borel integral is renormalization--scale invariant. We use
an ansatz which explicitly accounts for the structure of the leading infrared
renormalon. Further, we use judiciously chosen conformal transformations for
the Borel variable, in order to map sufficiently away from the origin the other
ultraviolet and infrared renormalon singularities. In addition, we apply Pade
approximants for the corresponding truncated perturbation series of the
modified Borel transform, in order to further accelerate the convergence.
Comparing the results with the presently available experimental data on the tau
hadronic decay width ratio, we obtain $\alpha_s(M^z) = 0.1192 +- 0.0007_{exp.}
+- 0.0010_{EW+CKM} +- 0.0009_{th.} +- 0.0003_{evol.}$. These predictions
virtually agree with those of our previous resummations where we used ordinary
Borel transforms instead.


  Of the light element abundances capable of testing standard big bang
nucleosynthesis, only He4 is measured with an accuracy of a few percent. Thus,
it is imperative to establish a comprehensive technique for determining He4
abundances and reliable estimates of the true systematic uncertainties. Helium
abundance determinations in H II regions are made from the observations of
several distinct He I emission lines and their strengths relative to H I
emission lines. With the general availability of large format, linear CCD
detectors, the accuracy of relative emission line ratios has improved to the
point where several terms in the error budget which were assumed to be
negligible may now be important. Here we investigate the estimation of errors
in deriving and reporting nebular helium abundances from optical emission line
spectra.


  We define and analyze an inductive reasoning game of voluntary yearly
vaccination in order to establish whether or not a population of individuals
acting in their own self-interest would be able to prevent influenza epidemics.
We find that epidemics are rarely prevented. We also find that severe epidemics
may occur without the introduction of pandemic strains. We further address the
situation where market incentives are introduced to help ameliorating
epidemics. Surprisingly, we find that vaccinating families exacerbates
epidemics. However, a public health program requesting prepayment of
vaccinations may significantly ameliorate influenza epidemics.


  In this paper we consider a target-guarding differential game where the
defender must protect a linearly translating line-segment by intercepting an
attacker who tries to reach it. In contrast to common target-guarding problems,
we assume that the defender is attached to the target and moves along with it.
This assumption affects the defenders' maximum speed in inertial frame, which
depends on the target's direction of motion. Zero-sum differential game of
degree for both the attacker-win and defender-win scenarios are studied, where
the payoff is defined to be the distance between the two agents at the time of
game termination. We derive the equilibrium strategies and the Value function
by leveraging the solution for the infinite-length target scenario. The
zero-level set of this Value function provides the barrier surface that divides
the state space into defender-win and attacker-win regions. We present
simulation results to demonstrate the theoretical results.


  In this review, three subjects are discussed: a phenomenological application
of lattice predictions to $K^0$--$\bar K^0$ mixing in Super Symmetry; a
discussion of the non-perturbative renormalization methods for four-fermion
operators and a new approach to extract weak matrix elements in effective
theories denoted as OPE without OPE (operator product expansion without
operator product expansion)


  So far, the environment has been considered as a source of fading, clutter,
blockage, etc., with detrimental consequences for the efficiency and robustness
of communication systems. However, the intense research developed toward
beyond-5G communications is leading to a paradigm change, in which the
environment is exploited as a new degree of freedom and plays an active role in
achieving unprecedented system performances. For implementing this challenging
paradigm, it has been recently proposed the use of intelligent surfaces able to
control almost at will the propagation of electromagnetic waves. In this
framework, metasurfaces have emerged as a promising solution, thanks to their
field manipulation capabilities achieved through low-cost, lightweight, and
planar structures. The aim of this paper is to review some recent applications
of metasurfaces and cast them in the scenario of next-generation wireless
systems. In particular, we show their potentialities in overcoming some
detrimental effects presented by the environment in wireless communications,
and discuss their crucial role towards the practical implementation of a smart
electromagnetic environment.


  We investigate performing classical and quantum metrology and parameter
estimation by using interacting trapped bosons, which we theoretically treat by
a self-consistent many-body approach of the multiconfigurational Hartree type.
Focusing on a tilted double-well geometry, we compare a self-consistently
determined and monitored two-mode truncation, with dynamically changing
orbitals, to the conventional two-mode approach of fixed orbitals, where only
Fock space coefficients evolve in time. We demonstrate that, as a consequence,
various metrological quantities associated to a concrete measurement such as
the classical Fisher information and the maximum likelihood estimator are
deeply affected by the orbitals' change during the quantum evolution.
Self-consistency of the quantum many-body dynamics of interacting trapped
ultracold gases thus fundamentally affects the attainable parameter estimation
accuracy of a given metrological protocol.


  We study transport properties and topological phase transition in
two-dimensional interacting disordered systems. Within dynamical mean-field
theory, we derive the Hall conductance, which is quantized and serves as a
topological invariant for insulators, even when the energy gap is closed by
localized states. In the spinful Harper-Hofstadter-Hatsugai model, in the
trivial insulator regime, we find that the repulsive on-site interaction can
assist weak disorder to induce the integer quantum Hall effect, while in the
topologically non-trivial regime, it impedes Anderson localization. Generally,
the interaction broadens the regime of the topological phase in the disordered
system.


  We present the results of our calculations for the relative yields of
neutron-rich fission fragments emitted in $^{208}$Pb ($^{18}$O, fission)
reaction by using the concept of the conservation of isospin and compare with
the experimental data. We take into account a range of isospin values allowed
by the isospin algebra and assume that the fission fragments are formed in
Isobaric Analog States. We also take into account the neutron multiplicity data
for various neutron-emission channels in each partition, and use them to obtain
the weight factors in calculating the yields. We then calculate the relative
yields of the fission fragments. Our calculated results are able to reproduce
the experimental trends reasonably well. This is the first direct evidence of
the isospin conservation in neutron-rich systems and may prove a very useful
tool in their studies.


  We present a technique to extract radial velocity measurements from echelle
spectrograph observations of rapidly rotating stars ($V\sin{i} \gtrsim 50$ km
s$^{-1}$). This type of measurement is difficult because the line widths of
such stars are often comparable to the width of a single echelle order. To
compensate for the scarcity of lines and Doppler information content, we have
developed a process that forward-models the observations, fitting the radial
velocity shift of the star for all echelle orders simultaneously with the
echelle blaze function. We use our technique to extract radial velocity
measurements from a sample of rapidly rotating A- and B-type stars used as
calibrator stars observed by the California Planet Survey observations. We
measure absolute radial velocities with a precision ranging from 0.5-2.0 km
s$^{-1}$ per epoch for more than 100 A- and B-type stars. In our sample of 10
well-sampled stars with radial velocity scatter in excess of their measurement
uncertainties, three of these are single-lined binaries with long observational
baselines. From this subsample, we present detections of two previously unknown
spectroscopic binaries and one known astrometric system. Our technique will be
useful in measuring or placing upper limits on the masses of sub-stellar
companions discovered by wide-field transit surveys, and conducting future
spectroscopic binarity surveys and Galactic space-motion studies of massive
and/or young, rapidly-rotating stars.


  Motivated by recent progress on pricing in the AI literature, we study
marketplaces that contain multiple vendors offering identical or similar
products and unit-demand buyers with different valuations on these vendors. The
objective of each vendor is to set the price of its product to a fixed value so
that its profit is maximized. The profit depends on the vendor's price itself
and the total volume of buyers that find the particular price more attractive
than the price of the vendor's competitors. We model the behaviour of buyers
and vendors as a two-stage full-information game and study a series of
questions related to the existence, efficiency (price of anarchy) and
computational complexity of equilibria in this game. To overcome situations
where equilibria do not exist or exist but are highly inefficient, we consider
the scenario where some of the vendors are subsidized in order to keep prices
low and buyers highly satisfied.


  This paper is concerned with the detection and correction of sub-sentential
English text errors. Previous spelling programs, unless restricted to a very
small set of words, have operated as post-processors. And to date, grammar
checkers and other programs which deal with ill-formed input usually step
directly from spelling considerations to a full-scale parse, assuming a
complete sentence. Work described below is aimed at evaluating the
effectiveness of shallow (sub-sentential) processing and the feasibility of
cooperative error checking, through building and testing appropriately an
error-processing system. A system under construction is outlined which
incorporates morphological checks (using new two-level error rules) over a
directed letter graph, tag positional trigrams and partial parsing. Intended
testing is discussed.


  Pathologists routinely classify breast tumors according to recurring patterns
of nuclear grades, cytoplasmic coloration, and large-scale morphological
formations (i.e. streams of spindle cells, adenoid islands, etc.). The fact
that there are large-scale morphological formations suggest that tumor cells
still possess the genetic programming to arrange themselves in orderly
patterns. However, small regions of order or subtle patterns of order are
invisible to the human eye. The ability to detect subtle regions of order and
correlate them with clinical outcome and resistance to treatment can enhance
diagnostic efficacy. By measuring the acute angle that results when the line
extending from the longest length within a nucleus intersects with the
corresponding line of an adjacent nucleus, the degree of alignment between two
adjacent nuclei can be measured. Through a series of systematic
transformations, subtle regions of order and disorder within a tumor image can
be quantified and visualized in the form of a heat map. This numerical
transformation of spatial relationships between nuclei within tumors allows for
the detection of subtly ordered regions.


  Graph-based reaction systems were recently introduced as a generalization of
the intensely studied set-based reaction systems. They deal with simple
edge-labeled directed graphs, and dynamic semantics of graph-based reaction
systems is defined by graph surfing as a novel kind of graph transformation
where, in a single surf step, reactions are applied to a subgraph of a given
background graph yielding a successor subgraph. In this paper, we propose a
categorical approach to reaction systems so that a wider spectrum of data
structures becomes available on which reaction systems can be based. In this
way, many types of graphs, hypergraphs, and graph-like structures are covered.


  The baryon spectrum in the Sakai-Sugimoto model in the D4 background with
smeared D0 charges is studied. We follow the instanton description of baryons
by Hata et al.[Prog. Theor. Phys. 117, 1157]. The background corresponds to an
excited state with nonzero glue condensate $\langle {\rm tr} (F_{\mu\nu}\tilde
F^{\mu\nu})\rangle$ which is proportional to the D0 charge density. The baryon
size shrinks when we turn on small D0 charge density. But for larger D0 charge
density where massive modes in the gauge theory may also take effect, the size
of baryons will grow. The difference between baryon masses will become smaller
when D0 charge density increases. There may also be indications that the baryon
will become unstable and cannot exist for sufficiently large D0 density.


  This paper generalizes a result of Ogus that, under certain technical
conditions, the vanishing order of the Hasse invariant of a family $Y/X$ of
$n$-dimensional Calabi-Yau varieties in characteristic $p$ at a point $x$ of
$X$ equals the "conjugate line position" of $H^n_{\text{dR}}(Y/X)$ at $x$, i.e.
the largest $i$ such that the line of the conjugate filtration is contained in
$\text{Fil}^i$ of the Hodge filtration. For every triple $(G,\mu,r)$ consisting
of a connected, reductive $\mathbf{F}_p$-group $G$, a cocharacter $\mu \in
X_*(G)$ and an $\mathbf{F}_p$-representation $r$ of $G$, we state a generalized
Ogus Principle. If $\zeta:X \to \text{$G$-$\mathtt{Zip}$}^{\mu}$ is a smooth
morphism (=`Zip period map'), then the group theoretic Ogus Principle implies
an Ogus Principle on $X$. We deduce an Ogus Principle for several Hodge and
abelian-type Shimura varieties and the moduli space of K3 surfaces.


  The optimal multicast tree problem in the Software-Defined Networking (SDN)
multicast routing is an NP-hard combinatorial optimization problem. Although
existing SDN intelligent solution methods, which are based on deep
reinforcement learning, can dynamically adapt to complex network link state
changes, these methods are plagued by problems such as redundant branches,
large action space, and slow agent convergence. In this paper, an SDN
intelligent multicast routing algorithm based on deep hierarchical
reinforcement learning is proposed to circumvent the aforementioned problems.
First, the multicast tree construction problem is decomposed into two
sub-problems: the fork node selection problem and the construction of the
optimal path from the fork node to the destination node. Second, based on the
information characteristics of SDN global network perception, the multicast
tree state matrix, link bandwidth matrix, link delay matrix, link packet loss
rate matrix, and sub-goal matrix are designed as the state space of intrinsic
and meta controllers. Then, in order to mitigate the excessive action space,
our approach constructs different action spaces at the upper and lower levels.
The meta-controller generates an action space using network nodes to select the
fork node, and the intrinsic controller uses the adjacent edges of the current
node as its action space, thus implementing four different action selection
strategies in the construction of the multicast tree. To facilitate the
intelligent agent in constructing the optimal multicast tree with greater
speed, we developed alternative reward strategies that distinguish between
single-step node actions and multi-step actions towards multiple destination
nodes.


  We theoretically investigate the control of a magnetic Feshbach resonance
using a bound-to-bound molecular transition driven by spatially modulated laser
light. Due to the spatially periodic coupling between the ground and excited
molecular states, there exists a band structure of bound states, which can
uniquely be characterized by some extra bumps in radio-frequency spectroscopy.
With the increasing of coupling strength, the series of bound states will cross
zero energy and directly result in a number of scattering resonances, whose
position and width can be conveniently tuned by the coupling strength of the
laser light and the applied magnetic field (i.e., the detuning of the ground
molecular state). In the presence of the modulated laser light, universal
two-body bound states near zero-energy threshold still exist. However, compared
with the case without modulation, the regime for such universal states is
usually small. An unified formula which embodies the influence of the modulated
coupling on the resonance width is given. The spatially modulated coupling also
implies a local spatially varying interaction between atoms. Our work proposes
a practical way of optically controlling interatomic interactions with high
spatial resolution and negligible atomic loss.


  We study a dissipative variant of the Gross-Pitaevskii equation with
rotation. The model contains a nonlocal, nonlinear term that forces the
conservation of $L^2$-norm of solutions. We are motivated by several physical
experiments and numerical simulations studying the formation of vortices in
Bose-Einstein condensates. We show local and global well-posedness of this
model and investigate the asymptotic behavior of its solutions. In the linear
case, the solution asymptotically tends to the eigenspace associated with the
smallest eigenvalue in the decomposition of the initial datum. In the nonlinear
case, we obtain weak convergence to a stationary state. Moreover, for initial
energies in a specific range, we prove strong asymptotic stability of ground
state solutions.


  Solar jets are impulsive, collimated plasma ejections that are triggered by
magnetic reconnection. They are observed for many decades in various
temperatures and wavelengths, therefore their kinematic characteristics, such
as velocity and recurrence, have been extensively studied.Nevertheless, the
high spatial resolution of the Interface Region Imaging Spectrograph (IRIS)
launched in 2013 allowed us to make a step forward in the understanding of the
relationship between surges and hot jets. In this paper we report on several
results of recent studies of jets observed by IRIS. Cool and hot plasma have
been detected with ejections of cool blobs having a speed reaching 300 km/s
during the impulsive phase of jet formation and slow velocity surges
surrounding hot jets after the reconnection phase. Plasma characteristics of
solar jets, such as the emission measure, temperature, and density have been
quantified. A multi-layer atmosphere at the reconnection site based on observed
IRIS spectra has been proposed. IRIS evidenced bidirectional flows at
reconnection sites, and tilt along the spectra which were interpreted as the
signature of twist in jets. The search of possible sites for reconnection could
be achieved by the analysis of magnetic topology. Combining Solar Dynamics
Observatory/Helioseismic Magnetic Imager (SDO/HMI) vector magnetograms and IRIS
observations, it was found that reconnection site could be located at null
points in the corona as well as in bald patch regions low in the photosphere.
In one case study a magnetic sketch could explain the initiation of a jet
starting in a bald patch transformed to a current sheet in a dynamical way, and
the transfer of twist from a flux rope to the jet during the magnetic
reconnection process.


  We initiate a holographic model building approach to `strange metallic'
phenomenology. Our model couples a neutral Lifshitz-invariant quantum critical
theory, dual to a bulk gravitational background, to a finite density of gapped
probe charge carriers, dually described by D-branes. In the physical regime of
temperature much lower than the charge density and gap, we exhibit anomalous
scalings of the temperature and frequency dependent conductivity. Choosing the
dynamical critical exponent $z$ appropriately we can match the non-Fermi liquid
scalings, such as linear resistivity, observed in strange metal regimes. As
part of our investigation we outline three distinct string theory realizations
of Lifshitz geometries: from F theory, from polarised branes, and from a
gravitating charged Fermi gas. We also identify general features of
renormalisation group flow in Lifshitz theories, such as the appearance of
relevant charge-charge interactions when $z \geq 2$. We outline a program to
extend this model building approach to other anomalous observables of interest
such as the Hall conductivity.


  In the present work, we have used Tesseract 2.01 open source Optical
Character Recognition (OCR) Engine under Apache License 2.0 for recognition of
handwriting samples of lower case Roman script. Handwritten isolated and
free-flow text samples were collected from multiple users. Tesseract is trained
to recognize user-specific handwriting samples of both the categories of
document pages. On a single user model, the system is trained with 1844
isolated handwritten characters and the performance is tested on 1133
characters, taken form the test set. The overall character-level accuracy of
the system is observed as 83.5%. The system fails to segment 5.56% characters
and erroneously classifies 10.94% characters.


  We present a study of the metallicity and age of the globular clusters system
of M49 (NGC 4472), the most luminous galaxy in the Virgo cluster. We measure
Lick indices for 47 GCs in M49 from LRIS/Keck spectra and establish their
metallicity parameters qualitatively in comparison to the Galactic GCs and to
published data for 150 M87 GCs. We then compare our measurements with the
predictions of models for the integrated light of old single burst stellar
systems by Worthey and by Thomas, Maraston & Bender. We find that the
metallicity of the M49 GC system spans the range from [Fe/H]_Z = -2.0 to +0.4
dex. We show that the metallicity and age parameters for these two GC systems
are basically identical, except that the M49 GCs reach slightly higher
metallicities than do those of M87. We find that the GCs of both of these giant
elliptical galaxies are alpha-enhanced by a factor of about two above the Solar
value, as is also true of the Galactic GCs. While adoption of the
alpha-enhanced models of TMB has eliminated most of the previous discrepancies
with observations, the most metal rich M49 GCs have NaD lines which are still
considerably stronger than those predicted by any model, and there are still
issues involving the metallicity scale of these models. We find that in the
mean, the M49 GCs are at least 10 Gyr old. However, the grids of models we used
differ in how they treat the horizontal branch, and this perceptibly affects
the predicted Hbeta index. Hence our current incomplete understanding of the
role of the horizontal branch limits our ability to derive a more detailed
distribution for the ages of the GCs in M49 and in M87.


  We propose CAVIA for meta-learning, a simple extension to MAML that is less
prone to meta-overfitting, easier to parallelise, and more interpretable. CAVIA
partitions the model parameters into two parts: context parameters that serve
as additional input to the model and are adapted on individual tasks, and
shared parameters that are meta-trained and shared across tasks. At test time,
only the context parameters are updated, leading to a low-dimensional task
representation. We show empirically that CAVIA outperforms MAML for regression,
classification, and reinforcement learning. Our experiments also highlight
weaknesses in current benchmarks, in that the amount of adaptation needed in
some cases is small.


  In this paper we obtain the non - asymptotic estimations of Poincare type
between function and its gradient in the so - called Bilateral Grand Lebesgue
Spaces. We also give some examples to show the sharpness of these inequalities.


  We introduce auxiliary quantum master equation - dual fermion approach
(QME-DF) and argue that it presents a convenient way to describe steady-states
of correlated impurity systems. The combined scheme yields an expansion around
a reference much closer to the true nonequilibrium state than in the original
dual fermion formulation. In steady-state situations, the scheme is numerically
cheaper and allows to avoid long time propagation of previous considerations.
Anderson impurity is used as a test model. The QME-DF simulations are compared
with numerically exact tdDMRG results.


  We determine the nonlinear transformations between coordinate systems which
are mutually in a constant symmetrical accelerated motion. The maximal
acceleration limit follows from the kinematical origin and it is an analogue of
the maximal velocity in special relativity. We derive the dependence of mass,
length, time, Doppler effect, Cherenkov effect and transition radiation angle
on acceleration as an analogue phenomena in special theory of relativity. The
last application of our method is the Thomas precession by uniform acceleration
with the possible role in the modern physics and cosmology. The comparison of
derived results with other relativistic methods is necessary.


  We study coarea inequalities for metric surfaces -- metric spaces that are
topological surfaces, without boundary, and which have locally finite Hausdorff
2-measure $\mathcal{H}^2$. For monotone Sobolev functions $u\colon X \to
\mathbb{R} $, we prove the inequality
  \begin{equation*}
  \int_{ \mathbb{R} }^{*}
  \int_{ u^{-1}(t) }
  g
  \,d\mathcal{H}^{1}
  \,dt
  \leq
  \kappa
  \int_{ X }
  g \rho
  \,d\mathcal{H}^{2}
  \quad\text{for every Borel $g \colon X \rightarrow \left[0,\infty\right]$,}
\end{equation*} where $\rho$ is any integrable upper gradient of $u$. If $\rho$
is locally $L^2$-integrable, we obtain the sharp constant $\kappa=4/\pi$. The
monotonicity condition cannot be removed as we give an example of a metric
surface $X$ and a Lipschitz function $u \colon X \to \mathbb{R}$ for which the
coarea inequality above fails.


  The possibility of determining the value of the Hubble constant using
observations of galaxy clusters in X-ray and microwave wavelengths through the
Sunyaev Zel\'dovich (SZ) effect has long been known. Previous measurements have
been plagued by relatively large errors in the observational data and severe
biases induced, for example, by cluster triaxiality and clumpiness. The advent
of \textit{Planck} allows us to map the Compton parameter y, that is, the
amplitude of the SZ effect, with unprecedented accuracy at intermediate
cluster-centric radii, which in turn allows performing a detailed spatially
resolved comparison with X-ray measurements. Given such higher quality
observational data, we developed a Bayesian approach that combines informed
priors on the physics of the intracluster medium obtained from hydrodynamical
simulations of massive clusters with measurement uncertainties.
  We apply our method to a sample of 61 galaxy clusters with redshifts up to z
< 0.5 observed with Planck and XMM-Newton observations and find H_0=67 \pm 3 km
s^{-1} Mpc^{-1}.


  We present new linear relations among the masses of S-wave tetraquarks with
either one flavour ($QQ \bar Q \bar Q$) or two ($QQ\bar q \bar q$). Because the
relations are sensitive to the hidden-colour, spin, and spatial degrees of
freedom, comparison to experimental data can help to reveal the internal
structure of tetraquarks, and discriminate among different theoretical models.
Depending on the model, the relations are either exact, or valid in
perturbation theory, and a thorough comparison with existing literature
confirms their validity at the MeV level. Additionally, we explore the
connections among tetraquark models, and show how those with effective (quark
or diquark) masses are related to dynamical potential models. We also show how
the spectrum of diquark models is effectively a limiting case of (more general)
quark models, and in particular, that the diquark concept is most relevant in
the particular combination $QQ\bar q \bar q$, where $Q$ is much heavier than
$\bar q$.


  Free words are elements of a free monoid, generated over an alphabet via the
binary operation of concatenation. Casually speaking, a free word is a finite
string of letters. Henceforth, we simply refer to them as words. Motivated by
recent advances in the combinatorial limit theory of graphs-notably those
involving flag algebras, graph homomorphisms, and graphons-we investigate the
extremal and asymptotic theory of pattern containment and avoidance in words.
Word V is a factor of word W provided V occurs as consecutive letters within W.
W is an instance of V provided there exists a nonerasing monoid homomorphsism
{\phi} with {\phi}(V) = W. For example, using the homomorphism {\phi} defined
by {\phi}(P) = Ror, {\phi}(h) = a, and {\phi}(D) = baugh, we see that Rorabaugh
is an instance of PhD.
  W avoids V if no factor of W is an instance of V. V is unavoidable provided,
over any finite alphabet, there are only finitely many words that avoid V.
Unavoidable words were classified by Bean, Ehrenfeucht, and McNulty (1979) and
Zimin (1982). We briefly address the following Ramsey-theoretic question: For
unavoidable word V and a fixed alphabet, what is the longest a word can be that
avoids V? The density of V in W is the proportion of nonempty substrings of W
that are instances of V. Since there are 45 substrings in Rorabaugh and 28 of
them are instances of PhD, the density of PhD in Rorabaugh is 28/45. We
establish a number of asymptotic results for word densities, including the
expected density of a word in arbitrarily long, random words and the minimum
density of an unavoidable word over arbitrarily long words.
  This is joint work with Joshua Cooper.


  We study the linear stability of the Peregrine breather both numerically and
with analytical arguments based on its derivation as the singular limit of a
single-mode spatially periodic breather as the spatial period becomes infinite.
By constructing solutions of the linearization of the nonlinear Schr\"odinger
equation in terms of quadratic products of components of the eigenfunctions of
the Zakharov-Shabat system, we show that the Peregrine breather is linearly
unstable. A numerical study employing a highly accurate Chebychev
pseudo-spectral integrator confirms exponential growth of random initial
perturbations of the Peregrine breather.


  As Graph Neural Networks (GNNs) become increasingly prevalent in a variety of
fields, from social network analysis to protein-protein interaction studies,
growing concerns have emerged regarding the unauthorized utilization of
personal data. Recent studies have shown that imperceptible poisoning attacks
are an effective method of protecting image data from such misuse. However, the
efficacy of this approach in the graph domain remains unexplored. To bridge
this gap, this paper introduces GraphCloak to safeguard against the
unauthorized usage of graph data. Compared with prior work, GraphCloak offers
unique significant innovations: (1) graph-oriented, the perturbations are
applied to both topological structures and descriptive features of the graph;
(2) effective and stealthy, our cloaking method can bypass various inspections
while causing a significant performance drop in GNNs trained on the cloaked
graphs; and (3) stable across settings, our methods consistently perform
effectively under a range of practical settings with limited knowledge. To
address the intractable bi-level optimization problem, we propose two
error-minimizing-based poisoning methods that target perturbations on the
structural and feature space, along with a subgraph injection poisoning method.
Our comprehensive evaluation of these methods underscores their effectiveness,
stealthiness, and stability. We also delve into potential countermeasures and
provide analytical justification for their effectiveness, paving the way for
intriguing future research.


  We formulate in terms of the quantum inverse scattering method the exact
solution of a $spl(2|1)$ invariant vertex model recently introduced in the
literature. The corresponding transfer matrix is diagonalized by using the
algebraic (nested) Bethe ansatz approach. The ground state structure is
investigated and we argue that a Pokrovsky-Talapov transition is favored for
certain value of the 4-dimensional $spl(2|1)$ parameter.


  The rapid development of deep learning techniques has created new challenges
in identifying the origin of digital images because generative adversarial
networks and variational autoencoders can create plausible digital images whose
contents are not present in natural scenes. In this paper, we consider the
origin that can be broken down into three categories: natural photographic
image (NPI), computer generated graphic (CGG), and deep network generated image
(DGI). A method is presented for effectively identifying the origin of digital
images that is based on a convolutional neural network (CNN) and uses a
local-to-global framework to reduce training complexity. By feeding labeled
data, the CNN is trained to predict the origin of local patches cropped from an
image. The origin of the full-size image is then determined by majority voting.
Unlike previous forensic methods, the CNN takes the raw pixels as input without
the aid of "residual map". Experimental results revealed that not only the
high-frequency components but also the middle-frequency ones contribute to
origin identification. The proposed method achieved up to 95.21% identification
accuracy and behaved robustly against several common post-processing operations
including JPEG compression, scaling, geometric transformation, and contrast
stretching. The quantitative results demonstrate that the proposed method is
more effective than handcrafted feature-based methods.


  We present a theoretical analysis of a possible route for directly detecting
Kondo resonances in local density of states (LDOS) of an interacting quantum
dot. By very weakly couple a third and/or a fourth lead to a two-probe quantum
dot and measuring differential conductance through these extra links, we show
that Kondo peaks directly map onto the differential conductance measured from
the third link. We analyze the conditions by which this detection of Kondo
peaks in LDOS is possible.


  Using an 185-kg NaI[Tl] array, COHERENT has measured the inclusive
electron-neutrino charged-current cross section on ${}^{127}$I with pion
decay-at-rest neutrinos produced by the Spallation Neutron Source at Oak Ridge
National Laboratory. Iodine is one the heaviest targets for which low-energy
($\leq$ 50 MeV) inelastic neutrino-nucleus processes have been measured, and
this is the first measurement of its inclusive cross section. After a five-year
detector exposure, COHERENT reports a flux-averaged cross section for electron
neutrinos of $9.2^{+2.1}_{-1.8} \times 10^{-40}$ cm$^2$. This corresponds to a
value that is $\sim$41% lower than predicted using the MARLEY event generator
with a measured Gamow-Teller strength distribution. In addition, the observed
visible spectrum from charged-current scattering on $^{127}$I has been measured
between 10 and 55 MeV, and the exclusive zero-neutron and one-or-more-neutron
emission cross sections are measured to be $5.2^{+3.4}_{-3.1} \times 10^{-40}$
and $2.2^{+3.5}_{-2.2} \times 10^{-40}$ cm$^2$, respectively.


  We provide a physical explanation for enhancement of the low-energy electron
production by sensitizing nanoparticles due to irradiation by fast ions. It is
demonstrated that a significant increase in the number of emitted electrons
arises from the collective electron excitations in the nanoparticle. We predict
a new mechanism of the yield enhancement due to the plasmon excitations and
quantitatively estimate its contribution to the electron production. Revealing
the nanoscale mechanism of the electron yield enhancement, we provide an
efficient tool for evaluating the yield of emitted electron from various
sensitizers. It is shown that the number of low-energy electrons generated by
the gold and platinum nanoparticles of a given size exceeds that produced by
the equivalent volume of water and by other metallic (e.g., gadolinium)
nanoparticles by an order of magnitude. This observation emphasizes the
sensitization effect of the noble metal nanoparticles and endorses their
application in novel technologies of cancer therapy with ionizing radiation.


  We consider in detail an approach (proposed by the author earlier) where
quantum states are described by elements of a linear space over a Galois field,
and operators of physical quantities - by linear operators in this space. The
notion of Galois fields (which is extremely simple and elegant) is discussed in
detail and we also discuss the conditions when our description gives the same
predictions as the conventional one. In quantum theory based on a Galois field,
all operators are well defined and divergencies cannot not exist in principle.
A particle and its antiparticle are described by the same modular irreducible
representation of the symmetry algebra. This automatically explains the
existence of antiparticles and shows that a particle and its antiparticle are
the different states of the same object. As a consequence, a new symmetry
arises, and the structure of the theory is considerably simplified. In
particular, one can work with only creation operators or only annihilation ones
since they are no more independent. In our approach the problem arises whether
the existence of neutral elementary particles (e.g. the photon) is compatible
with the usual relation between spin and statistics, or in other words whether
neutral particles can be elementary or only composite.


  We start with a noncommutative version of the Jackiw-Teitelboim gravity in
two dimensions which has a linear potential for the dilaton fields. We study
whether it is possible to deform this model by adding quadratic terms to the
potential but preserving the number of gauge symmetries. We find that no such
deformation exists (provided one does not twist the gauge symmetries).


  Context: Software development is human-centric and vulnerable to human error.
Human errors are errors in the human thought process. To ensure software
quality, practitioners must understand how to manage these human errors.
Organizations often change the requirements engineering process to prevent
human errors from occurring or to mitigate the harm caused when those errors do
occur. While there are studies on human error management in other disciplines,
research on the prevention and mitigation of human errors in software
engineering, and requirements engineering specifically, are limited. The
software engineering studies do not provide strong results about the types of
changes that are most effective in requirements engineering. Objective: The
goal of this paper is to develop a taxonomy of human error prevention and
mitigation strategies based on data from requirements engineering
professionals. Method: We performed a qualitative analysis of two practitioner
surveys on requirements engineering practices to identify and classify
strategies for the prevention and mitigation of human errors. Results: We
organized the human error management strategies into a taxonomy based on
whether they primarily affect People, Processes, or the Environment. Inside
each high-level category, we further organized the strategies into low-level
classes. More than 50% of the reported strategies require a change in Process,
23% require a change in Environment, 21% require a change in People, with the
remaining 5% too ambiguous to classify. In addition, more than 50\% of the
strategies focus on Management activities. Conclusions: The Human Error
Management Taxonomy provides a systematic classification and organization of
strategies for prevention and mitigation of human errors in requirements
engineering. This systematic organization provides a foundation upon which
research can build.


  This paper considers Einstein-Brans-Dicke action being coupled with a Higgs
sector. It is shown that classically graceful exit from inflation is not
possible in principle, rejecting the claim of La and Steinhardt. Further,
wormhole solutions with and without conserved charges are explored. Finally,
the wavefunction of the universe in this model is constructed with the boundary
condition, as proposed by Vilenkin. The interesting feature of the wavefunction
is that it has been constructed for an arbitrary factor-ordering index.


  Relativistic calculations for the quasifree electron scattering process (e,
e'p) and the direct knockout contribution to (gamma, p) reactions are
presented. The spectroscopic factors determined from the former reaction are
used to fix the magnitude of the knockout contribution to the (gamma, p)
reaction at 60 MeV. The results obtained for several nuclei indicate that the
knockout contributions are much larger in magnitude and hence closer to the
data than predicted in an earlier comparison based on non-relativistic
calculations. We discuss the sensitivity of the results to the choice of
parameters for the binding and final state interactions. We find these
uncertainties to be more pronounced at the larger missing momenta explored by
the (gamma, p) reaction. The implications of the present results for the size
of contributions due to meson exchange currents are discussed.


  Recently, Social Network Analysis studies have led to an improvement and to a
generalization of existing tools to networks with multiple subsystems and
layers of connectivity. These kind of networks are usually called multilayer
networks. Multilayer networks in which each layer shares at least one node with
some other layer in the network are called multiplex networks. Being a
multiplex network does not require all nodes to exist on every layer. In this
paper, we built a criminal multiplex network which concerns an anti-mafia
operation called "Montagna" and it is based on the examination of a pre-trial
detention order issued on March 14, 2007 by the judge for preliminary
investigations of the Court of Messina (Sicily). "Montagna" focus on two Mafia
families called "Mistretta" and "Batanesi" who infiltrated several economic
activities including the public works in the north-eastern part of Sicily,
through a cartel of entrepreneurs close to the Sicilian Mafia. Originally we
derived two single-layer networks, the former capturing meetings between
suspected individuals and the latter recording phone calls. But some networked
systems can be better modeled by multilayer structures where the individual
nodes develop relationships in multiple layers. For this reason we built a
two-layer network from the single-layer ones. These two layers share 47 nodes.
We followed three different approaches to measure the importance of nodes in
multilayer networks using degree as descriptor. Our analysis can aid in the
identification of key players in criminal networks.


  Some works have appeared in recent accredited literature considering the
possibility of macroscopic violations of the second law in simulated as well as
really executed experiments. We argue the inexistence of such violations in
experiments based on the so-called nonbias diode, demonstrating that the
interpretation of the authors is flawed by a confusion between the concepts of
thermal equilibrium and thermodynamic equilibrium. We also discuss an
isomorphic experimental set up based on the evaporation-condensation of a
liquid in a closed atmosphere. Some critical observations are then made
concerning recent attempts to reformulate classical equilibrium thermodynamics.


  Brane-like states are defined by physical vertex operators in NSR superstring
theory, existing at nonzero pictures only. These states exist both in open and
closed string theories, in the NS and NS-NS sectors respectively. In this paper
we present a detailed analysis of their BRST properties, giving a proof that
these vertex operators are physical, i.e. BRST invariant and BRST non-trivial.


  The chromatic symmetric function $X_G$ is a sum of monomials corresponding to
proper vertex colorings of a graph $G$. Crew, Pechenik, and Spirkl (2023)
recently introduced a $K$-theoretic analogue $\overline{X}_G$ called the
Kromatic symmetric function, where each vertex is instead assigned a nonempty
set of colors such that adjacent vertices have nonoverlapping color sets. $X_G$
does not distinguish all graphs, but a longstanding open question is whether it
distinguishes all trees. We conjecture that $\overline{X}_G$ does distinguish
all graphs. As evidence towards this conjecture, we show that $\overline{X}_G$
determines the number of copies in $G$ of certain induced subgraphs on 4 and 5
vertices as well as the number of induced subgraphs isomorphic to each graph
consisting of a star plus some number of isolated vertices.


  This note is a response to one of problems posed by A.K. Kwasniewski in one
of his recent papers. Namely for the sequence of finite cobweb subposets, the
looked for explicit formulas for corresponding sequence of characteristic
polynomials are discovered and delivered here. The recurrence relation defining
arbitrary family of charactristic polynomials of finite cobweb posets is also
derived.


  Stochastic multiplicative dynamics characterize many complex natural
phenomena such as selection and mutation in evolving populations, and the
generation and distribution of wealth within social systems. Population
heterogeneity in stochastic growth rates has been shown to be the critical
driver of diversity dynamics and of the emergence of wealth inequality over
long time scales. However, we still lack a general statistical framework that
systematically explains the origins of these heterogeneities from the
adaptation of agents to their environment. In this paper, we derive population
growth parameters resulting from the interaction between agents and their
knowable environment, conditional on subjective signals each agent receives. We
show that average growth rates converge, under specific conditions, to their
maximal value as the mutual information between the agent's signal and the
environment, and that sequential Bayesian learning is the optimal strategy for
reaching this maximum. It follows that when all agents access the same
environment using the same inference model, the learning process dynamically
attenuates growth rate disparities, reversing the long-term effects of
heterogeneity on inequality. Our approach lays the foundation for a unified
general quantitative modeling of social and biological phenomena such as the
dynamical effects of cooperation, and the effects of education on life history
choices.


  Given a suitable link map f into a manifold M, we constructed, in [10], link
homotopy invariants kappa(f) and mu(f). In the present paper we study the case
M=S^n x R^{m - n} in detail. Here mu(f) turns out to be the starting term of a
whole sequence mu^(s)(f), s = 0, 1, ..., of higher mu-invariants which together
capture all the information contained in kappa(f). We discuss the geometric
significance of these new invariants. In several instances we obtain complete
classification results. A central ingredient of our approach is the homotopy
theory of wedges of spheres.


  The candidate of supersolid-like state, cnoidal wave, is investigated in
finite temperature holographic superfluid model for the first time. We find by
giving different source $a_x$ for the particle current density $\langle
j^{x}\rangle$, different kinds of superflow states can be obtained numerically.
And based on $a_x$, three limiting cases of cnoidal waves can be found easily
as well as the general cnoidal wave solution. The chemical potential $\mu$ and
particle current density $\langle j^x \rangle$, as functions of source $a_x$,
are calculated for these superflow states and are compared with homogeneous
superflow. We find as we increasing $a_x$, cnoidal waves will enter into the
uniform limit, which reflects in the confluence of the behavior of $\mu(a_x)$
and $\langle j^x(a_x) \rangle$ between cnoidal wave and homogeneous superflow.
Based on the quasi-normal modes, we show the cnodial waves are always
dynamically unstable due to the finite temperature, while the energetic
stability is influenced by the particle current density. All these evidences
manifest that the cnoidal wave can be seen as an \textcolor{black}{unstable
excited states} with supersolidity in finite temperature superfluid system.


  While most power system small-signal stability assessments rely on the
reduced Jacobian, which depends non-linearly on the states, uncertain operating
points introduce nontrivial hurdles in certifying the system's stability. In
this paper, a novel probabilistic robust small-signal stability (PRS) framework
is developed for a power system based on Gaussian process (GP) learning. The
proposed PRS assessment provides a robust stability certificate for a state
subspace, such as that specified by the error bounds of the state estimation,
with a given probability. With such a PRS certificate, all inner points of the
concerned subspace will be stable with at least the corresponding confidence
level. To this end, the behavior of the critical eigenvalue of the reduced
Jacobian with state points in a state subspace is learned using GP. The
proposed PRS certificate along with the Subspace-based Search and
Confidence-based Search mechanisms constitute a holistic framework catering to
all scenarios. The proposed framework is a powerful approach to assess the
stability under uncertainty because it does not require input uncertainty
distributions and other state-specific input-to-output approximations. Further,
the critical eigenvalue behavior in a state subspace is analyzed using an upper
bound of the eigenvalue variations and their inferences are discussed in
detail. The results on three-machine nine-bus WSCC system show that the
proposed certificate can find the robust stable state subspace with a given
probability.


  The approach the first-passage time (FPT) of a random process to a certain
level is applied to the description of radiation-enhanced diffusion. This is an
integral approach to describing the problem of radiation-enhanced diffusion,
which does not specify the details of the process but takes into account the
overall change in entropy during the process. Relationships are obtained to
take into account the influence of radiation effects on the diffusion
coefficient. The theoretical results obtained are compared with the
experimental ones.


  A novel overlap histogramming method based on Dual-Topology
Hamiltonian-Replica-Exchange simulation technique is presented to efficiently
calculate relative free energy difference in rough energy landscape, in which
multiple conformers coexist and are separated by large energy barriers. The
proposed method is based on the realization that both DT-HERM exchange
efficiency and confidence of free energy determination in overlap histogramming
method depend on the same criteria: neighboring states' energy derivative
distribution overlap. In this paper, we demonstrate this new methodology by
calculating free energy difference between amino acids: Leucine and Asparagine,
which is an identified chanllenging system for free energy simulations.


  We investigate the aggregation of amphiphilic molecules by adapting the
two-state Muller-Lee-Graziano model for water, in which a solvent-induced
hydrophobic interaction is included implicitly. We study the formation of
various types of micelle as a function of the distribution of hydrophobic
regions at the molecular surface. Successive substitution of non-polar surfaces
by polar ones demonstrates the influence of hydrophobicity on the upper and
lower critical solution temperatures. Aggregates of lipid molecules, described
by a refinement of the model in which a hydrophobic tail of variable length
interacts with different numbers of water molecules, are stabilized as the
length of the tail increases. We demonstrate that the essential features of
micelle formation are primarily solvent-induced, and are explained within a
model which focuses only on the alteration of water structure in the vicinity
of the hydrophobic surface regions of amphiphiles in solution.


  In this paper, we give a generalized Cline's formula for the generalized
Drazin inverse. Let $R$ be a ring, and let $a,b,c,d\in R$ satisfying
$$\begin{array}{c} (ac)^2 = (db)(ac), (db)^2 = (ac)(db);\\ b(ac)a = b(db)a,
c(ac)d = c(db)d.\end{array}$$ Then $ac\in R^d$ if and only if $bd\in R^d$. In
this case, $(bd)^d = b((ac)^d)^2 d$. We also present generalized Cline's
formulas for Drazin and group inverses. Some weaker conditions in a Banach
algebra are also investigated. These extend the main results of Cline's formula
on g-Drazin inverse of Liao, Chen and Cui (Bull. Malays. Math. Soc., 37 (2014),
37-42), Lian and Zeng (Turk. J. Math., 40 (2016), 161-165) and Miller and
Zguitti (Rend. Circ. Mat. Palermo, II. Ser., 67 (2018), 105-114). As an
application, new common spectral property of bounded linear operators over
Banach spaces are obtained.


  We prove, as claimed by A.Carboni and P.T.Johnstone, that the category of
non-unital polygraphs, i.e. polygraphs where the source and target of each
generator are not identity arrows, is a presheaf category. More generally we
develop a new criterion for proving that certain classes of polygraphs are
presheaf categories. This criterion also applies to the larger class of
polygraphs where only the source of each generator is not an identity, and to
the class of "many-to-one polygraphs", producing a new, more direct, proof that
this is a presheaf category. The criterion itself seems to be extendable to
more general type of operads over possibly different combinatorics, but we
leave this question for future work. In an appendix we explain why this result
is relevant if one wants to fix the arguments of a famous paper of M.Kapranov
and V.Voevodsky and make them into a proof of C.Simpson's semi-strictification
conjecture. We present a program aiming at proving this conjecture, which will
be continued in subsequent papers.


  In this paper, we show how to extend the notion of reducibility introduced by
Girard for proving the termination of $\beta$-reduction in the polymorphic
$\lambda$-calculus, to prove the termination of various kinds of rewrite
relations on $\lambda$-terms, including rewriting modulo some equational theory
and rewriting with matching modulo $\beta$$\eta$, by using the notion of
computability closure. This provides a powerful termination criterion for
various higher-order rewriting frameworks, including Klop's Combinatory
Reductions Systems with simple types and Nipkow's Higher-order Rewrite Systems.


  We study phase transitions in five-dimensional Einstein Gravity with a
negative cosmological constant, coupled to a Skyrme matter field. These
transitions are topological generalizations of the Hawking-Page transition
between thermal Anti de Sitter (AdS) spacetime and an AdS black hole. Phases
are characterized by a topological number associated with the Skyrme field
configuration. Depending on that topological number and on the Skyrme coupling
strength, there occur transitions between those phases at two, one, or no
value(s) of the temperature. Through the holographic (AdS/CFT) correspondence,
these solutions are dual to topologically non-trivial states in a conformal
field theory (CFT) with an SU(2)-symmetry, which support either confined or
deconfined (quasi-)particles at strong coupling. We compare to similar known
phase transitions, and discuss potential applications to confinement in
topological phases of condensed matter and the quark-gluon plasma.


  Primordial chemistry began in the recombination epoch when the adiabatic
expansion caused the temperature of the radiation to fall below 4000 K. The
chemistry of the early Universe involves the elements hydrogen, its isotope
deuterium, helium with its isotopic forms and lithium. In this communication I
will present results on the evolution of the primordial $H_2$ abundance for
different cosmological models and the influence on the thermal decoupling.


  Smooth entropies are a tool for quantifying resource trade-offs in (quantum)
information theory and cryptography. In typical bi- and multi-partite problems,
however, some of the sub-systems are often left unchanged and this is not
reflected by the standard smoothing of information measures over a ball of
close states. We propose to smooth instead only over a ball of close states
which also have some of the reduced states on the relevant sub-systems fixed.
This partial smoothing of information measures naturally allows to give more
refined characterizations of various information-theoretic problems in the
one-shot setting. In particular, we immediately get asymptotic second-order
characterizations for tasks such as privacy amplification against classical
side information or classical state splitting. For quantum problems like state
merging the general resource trade-off is tightly characterized by partially
smoothed information measures as well.


  With extensive variational Monte Carlo simulation, we show that the uniform
resonating valence bond state(U-RVB) on square lattice is actually
antiferromagnetic long range ordered. The ordered moment is estimated to be
$m\approx 0.17$. Finite size scaling analysis on lattice up to lattice size of
$50\times 50$ shows that the spin structure factor at the antiferromagnetic
ordering wave vector follows perfectly the $\mathrm{S}_{\mathrm{q}=(\pi,\pi)}
\simeq S_{0}+\alpha (1/L)^{5/4}$ behavior, where $L$ is linear scale of the
lattice. Such a behavior is quite unexpected from the slave Boson mean field
treatment or the Gutzwiller approximation of the uniform RVB state.


  In medical imaging, there are clinically relevant segmentation tasks where
the output mask is a projection to a subset of input image dimensions. In this
work, we propose a novel convolutional neural network architecture that can
effectively learn to produce a lower-dimensional segmentation mask than the
input image. The network restores encoded representation only in a subset of
input spatial dimensions and keeps the representation unchanged in the others.
The newly proposed projective skip-connections allow linking the encoder and
decoder in a UNet-like structure. We evaluated the proposed method on two
clinically relevant tasks in retinal Optical Coherence Tomography (OCT):
geographic atrophy and retinal blood vessel segmentation. The proposed method
outperformed the current state-of-the-art approaches on all the OCT datasets
used, consisting of 3D volumes and corresponding 2D en-face masks. The proposed
architecture fills the methodological gap between image classification and ND
image segmentation.


  We reformulate the proof of the renormalization of a spontaneously broken
gauge theory by multiplicatively renormalizing the vacuum expectation value of
the Higgs field in the $SU(2)$~Higgs model.


  In this paper, we propose a probabilistic framework for solving the task of
`Visual Dialog'. Solving this task requires reasoning and understanding of
visual modality, language modality, and common sense knowledge to answer.
Various architectures have been proposed to solve this task by variants of
multi-modal deep learning techniques that combine visual and language
representations. However, we believe that it is crucial to understand and
analyze the sources of uncertainty for solving this task. Our approach allows
for estimating uncertainty and also aids a diverse generation of answers. The
proposed approach is obtained through a probabilistic representation module
that provides us with representations for image, question and conversation
history, a module that ensures that diverse latent representations for
candidate answers are obtained given the probabilistic representations and an
uncertainty representation module that chooses the appropriate answer that
minimizes uncertainty. We thoroughly evaluate the model with a detailed
ablation analysis, comparison with state of the art and visualization of the
uncertainty that aids in the understanding of the method. Using the proposed
probabilistic framework, we thus obtain an improved visual dialog system that
is also more explainable.


  We are interested in random uniform minimal factorizations of the $n$-cycle
which are factorizations of $(1~2\dots n)$ into a product of $n-1$
transpositions. Our main result is an explicit formula for the joint
probability that 1 and 2 appear a given number of times in a uniform minimal
factorization. For this purpose, we combine bijections with Cayley trees
together with explicit computations of multivariate generating functions.


  I comment on a number of theoretical issues related to magnetobremsstrahlung,
and especially on synchrotron radiation and Unruh (temperature) radiation, that
I consider of importance for the current progress towards a better
understanding of the stationary features of such fundamental radiation patterns
both in an accelerator context and, more generally, in the physical world


  The theory of integral quadratic constraints (IQCs) allows verification of
stability and gain-bound properties of systems containing nonlinear or
uncertain elements. Gain bounds often imply exponential stability, but it can
be challenging to compute useful numerical bounds on the exponential decay
rate. This work presents a generalization of the classical IQC results of
Megretski and Rantzer that leads to a tractable computational procedure for
finding exponential rate certificates that are far less conservative than ones
computed from $L_2$ gain bounds alone. An expanded library of IQCs for
certifying exponential stability is also provided and the effectiveness of the
technique is demonstrated via numerical examples.


  In the extra U(1) superstring inspired model, we examine the electroweak and
U(1)-prime symmetry breaking with the singlet and exotic quark D, D+{\c}along
with the study of heavy Z-prime boson in accordance with the top quark mass
region. For this, we have done the analysis of complete renormalization group
equations (RGEs)pertaining to the anomaly free E-{\6}-Eta model of rank 5. The
Z-prime is found to the order of TeV or above with allowed small Z-Zprime
mixing angle, for which the large singlet VEV is required. This is done by
considering the only non-universality of Yukawa couplings at GUT scale because
these do not obey the E-{\6}relationship and also satisfies the unitarity
constraints both at GUT and weak scale, where rest of the parameters, i.e.,
gaugino masses, tri-linear couplings, and soft supersymmetric breaking masses
are kept universal at GUT scale with the gauge couplings unification. The large
value of Yukawa couplings (order of 1) triggered the symmetry breaking
radiatively and induces the effective-Mu parameter at the electroweak scale and
lead to a viable low energy spectrum at weak scale.


  We discuss growing evidence that pulsar high energy is emission is generated
via Inverse Compton mechanism. We reproduce the broadband spectrum of Crab
pulsar, from UV to very high energy gamma-rays - nearly ten decades in energy,
within the framework of the cyclotron-self-Compton model. Emission is produced
by two counter-streaming beams within the outer gaps, at distances above ~ 20
NS radii. The outward moving beam produces UV-X-ray photons via Doppler-booster
cyclotron emission, and GeV photons by Compton scattering the cyclotron photons
produced by the inward going beam. The scattering occurs in the deep
Klein-Nishina regime, whereby the IC component provides a direct measurement of
particle distribution within the magnetosphere. The required plasma
multiplicity is high, ~ 10^6-10^7, but is consistent with the average particle
flux injected into the pulsar wind nebula.