  Malaria is the leading cause of death globally, especially in sub-Saharan
African countries claiming over 400,000 deaths globally each year, underscoring
the critical need for continued efforts to combat this preventable and
treatable disease. The objective of this study is to provide statistical
guidance on the optimal preventive and control measures against malaria. Data
have been collected from reliable sources, such as World Health Organization,
UNICEF, Our World in Data, and STATcompiler. Data were categorized according to
the factors and sub-factors related to deaths caused by malaria. These factors
and sub-factors were determined based on root cause analysis and data sources.
Using JMP 16 Pro software, both linear and multiple linear regression were
conducted to analyze the data. The analyses aimed to establish a linear
relationship between the dependent variable (malaria deaths in the overall
population) and independent variables, such as life expectancy, malaria
prevalence in children, net usage, indoor residual spraying usage, literate
population, and population with inadequate sanitation in each selected sample
country. The statistical analysis revealed that using insecticide treated nets
(ITNs) by children and individuals significantly decreased the death count, as
1,000 individuals sleeping under ITNs could reduce the death count by eight.
Based on the statistical analysis, this study suggests more rigorous research
on the usage of ITNs.


  The problem of identifying models of post-disaster reconstruction is an issue
that has been dealt with in depth in a number of works, mostly dedicated to
individual cases or to the comparison of models. There are also a number of
works that have attempted a systematisation on an historiographic basis. To
date, however, there is no overall work aimed at constructing a quantitative
method for evaluating and comparing reconstruction experiences. This article
proposes to establish a scientific method for the systematic classification of
post-disaster reconstructions, based on data analysis. The method consists of
four phases: the redrawing of cases with a precise replicable technique; the
choice of indicators; the measurement of urban development; the classification
of cases. The method is applied to cases that are comparable with each other in
terms of type of event and period: we have chosen post-World War II
reconstructions in Europe given the larger availability of documentation. The
paper leads both to the consolidation of the model as effective and replicable
and to the construction of the application, which revises the qualitative
classification of most of the addressed cases.


  This paper is concerned with the lower bounds for the principal frequency of
the $p$-Laplacian on $n$-dimensional Euclidean domains. In particular, we
extend the classical results involving the inner radius of a domain and the
first eigenvalue of the Laplace operator to the case $p\neq2$. As a by-product,
we obtain a lower bound on the size of the nodal set of an eigenfunction of the
$p$-Laplacian on planar domains.


  An axion can make the electroweak phase transition strongly first-order as
required for electroweak baryogenesis even if it is weakly coupled to the Higgs
sector. This is essentially because the axion periodicity naturally allows the
structure of phase transition to be insensitive to the axion decay constant
that determines the strength of axion interactions. Furthermore, the axion can
serve as a CP phase relevant to electroweak baryogenesis if one introduces an
effective axion coupling to the top quark Yukawa operator. Then, for $f$
between about TeV and order $10$~TeV, the observed baryon asymmetry can be
explained while avoiding current experimental constraints. It will be possible
to probe the axion window for baryogenesis in future lepton colliders and
beam-dump experiments.


  We study the Renormalization Group evolution of the couplings in a model with
a real SU(2) triplet in the Higgs sector. Insisting that the model remain valid
up to 1 TeV we show that it is possible for there to be no light Higgs bosons
without any otherwise dramatic deviation from the physics of the Standard
Model.


  According to the 'old view', proteins fold along well-defined sequential
pathways, whereas the 'new view' sees protein folding as a highly parallel
stochastic process on funnel-shaped energy landscapes. We have analyzed
parallel and sequential processes on a large number of Molecular Dynamics
unfolding trajectories of the protein CI2 at high temperatures. Using rigorous
statistical measures, we quantify the degree of sequentiality on two structural
levels. The unfolding process is highly parallel on the microstructural level
of individual contacts. On a coarser, macrostructural level of contact
clusters, characteristic parallel and sequential events emerge. These
characteristic events can be understood from loop-closure dependencies between
the contact clusters. A correlation analysis of the unfolding times of the
contacts reveals a high degree of substructural cooperativity within the
contact clusters.


  We address the issue of unbiased model selection and propose a methodology
based on Bayesian inference to extract physical information from kaon
photoproduction $p(\gamma,K^+)\Lambda$ data. We use the single-channel
Regge-plus-resonance (RPR) framework for $p(\gamma,K^+)\Lambda$ to illustrate
the proposed strategy. The Bayesian evidence Z is a quantitative measure for
the model's fitness given the world's data. We present a numerical method for
performing the multidimensional integrals in the expression for the Bayesian
evidence. We use the $p(\gamma,K^+)\Lambda$ data with an invariant energy W >
2.6 GeV in order to constrain the background contributions in the RPR framework
with Bayesian inference. Next, the resonance information is extracted from the
analysis of differential cross sections, single and double polarization
observables. This background and resonance content constitutes the basis of a
model which is coined RPR-2011. It is shown that RPR-2011 yields a
comprehensive account of the kaon photoproduction data and provides reasonable
predictions for $p(e,e' K^+)\Lambda$ observables.


  There are many ways to upsample functions from multivariate scattered data
locally, using only a few neighbouring data points of the evaluation point. The
position and number of the actually used data points is not trivial, and many
cases like Moving Least Squares require point selections that guarantee local
recovery of polynomials up to a specified order. This paper suggests a
kernel-based greedy local algorithm for point selection that has no such
constraints. It realizes the optimal $L_\infty$ convergence rates in Sobolev
spaces using the minimal number of points necessary for that purpose. On the
downside, it does not care for smoothness, relying on fast $L_\infty$
convergence to a smooth function. The algorithm ignores near-duplicate points
automatically and works for quite irregularly distributed point sets by proper
selection of points. Its computational complexity is constant for each
evaluation point, being dependent only on the Sobolev space parameters. Various
numerical examples are provided. As a byproduct, it turns out that the
well-known instability of global kernel-based interpolation in the standard
basis of kernel translates arises already locally, independent of global kernel
matrices and small separation distances.


  Recently, many approaches have been proposed through single or multiple
representations to improve the performance of point cloud semantic
segmentation. However, these works do not maintain a good balance among
performance, efficiency, and memory consumption. To address these issues, we
propose DRINet++ that extends DRINet by enhancing the sparsity and geometric
properties of a point cloud with a voxel-as-point principle. To improve
efficiency and performance, DRINet++ mainly consists of two modules: Sparse
Feature Encoder and Sparse Geometry Feature Enhancement. The Sparse Feature
Encoder extracts the local context information for each point, and the Sparse
Geometry Feature Enhancement enhances the geometric properties of a sparse
point cloud via multi-scale sparse projection and attentive multi-scale fusion.
In addition, we propose deep sparse supervision in the training phase to help
convergence and alleviate the memory consumption problem. Our DRINet++ achieves
state-of-the-art outdoor point cloud segmentation on both SemanticKITTI and
Nuscenes datasets while running significantly faster and consuming less memory.


  Light field cameras capture the 3D information in a scene with a single
exposure. This special feature makes light field cameras very appealing for a
variety of applications: from post-capture refocus, to depth estimation and
image-based rendering. However, light field cameras suffer by design from
strong limitations in their spatial resolution, which should therefore be
augmented by computational methods. On the one hand, off-the-shelf single-frame
and multi-frame super-resolution algorithms are not ideal for light field data,
as they do not consider its particular structure. On the other hand, the few
super-resolution algorithms explicitly tailored for light field data exhibit
significant limitations, such as the need to estimate an explicit disparity map
at each view. In this work we propose a new light field super-resolution
algorithm meant to address these limitations. We adopt a multi-frame alike
super-resolution approach, where the complementary information in the different
light field views is used to augment the spatial resolution of the whole light
field. We show that coupling the multi-frame approach with a graph regularizer,
that enforces the light field structure via nonlocal self similarities, permits
to avoid the costly and challenging disparity estimation step for all the
views. Extensive experiments show that the new algorithm compares favorably to
the other state-of-the-art methods for light field super-resolution, both in
terms of PSNR and visual quality.


  The quantum conductance of flat (Euclidean) circuits subject to Rashba
spin-orbit coupling shows a symmetric response to the inversion of the
spin-orbit field in Aharonov-Casher interference patterns. Here, we show that
this symmetry breaks down in curved (non-Euclidean) circuits defined on a
spherical two-dimensional electron gas. We demonstrate that this is a
consequence of parallel spin transport and holonomy on the surface of the
sphere, and that a symmetric response can be recovered when considering the
parallel transport condition as an offset. We discuss triangular circuits
defined along geodesic arcs on the sphere as a case study, and generalize it to
regular polygons and parallel curves of given latitude.


  Heterogeneous sonochemical synthesis was used to modify superconducting
properties of granular YBa2Ca3CuO7-y and Bi2Sr2CaCu2O8+x. Sonication of
liquid-powder alkane slurries produces material with enhanced intergrain
coupling and improved current-carrying capabilities. Co-sonication with metals
and organometallics results in highly compact nanocomposites with increased
magnetic irreversibility. Ultrasonic irradiation of YBa2Ca3CuO7-y carried under
partial oxygen atmosphere produces similar morphological effects and increases
superconducting transition temperature due to effective surface saturation with
oxygen. Detailed chemical and physical characterization of sonochemically
prepared high-Tc nanocomposites is presented.


  We study the problem of learning robust acoustic models in adverse
environments, characterized by a significant mismatch between training and test
conditions. This problem is of paramount importance for the deployment of
speech recognition systems that need to perform well in unseen environments.
First, we characterize data augmentation theoretically as an instance of
vicinal risk minimization, which aims at improving risk estimates during
training by replacing the delta functions that define the empirical density
over the input space with an approximation of the marginal population density
in the vicinity of the training samples. More specifically, we assume that
local neighborhoods centered at training samples can be approximated using a
mixture of Gaussians, and demonstrate theoretically that this can incorporate
robust inductive bias into the learning process. We then specify the individual
mixture components implicitly via data augmentation schemes, designed to
address common sources of spurious correlations in acoustic models. To avoid
potential confounding effects on robustness due to information loss, which has
been associated with standard feature extraction techniques (e.g., FBANK and
MFCC features), we focus on the waveform-based setting. Our empirical results
show that the approach can generalize to unseen noise conditions, with 150%
relative improvement in out-of-distribution generalization compared to training
using the standard risk minimization principle. Moreover, the results
demonstrate competitive performance relative to models learned using a training
sample designed to match the acoustic conditions characteristic of test
utterances.


  We present a solution to an optimal stopping problem for a process with a
wide-class of novel dynamics. The dynamics model the support/resistance line
concept from financial technical analysis.


  We consider a bi-Lagrangian manifold
$(M,\omega,\mathcal{F}_{1},\mathcal{F}_{2})$. That is, $\omega$ is a 2-form,
closed and non-degenerate (called symplectic form) on $M$, and
$(\mathcal{F}_{1},\mathcal{F}_{2})$ is a pair of transversal Lagrangian
foliations on the symplectic manifold $(M,\omega)$. In this case, $(\omega,
\mathcal{F}_{1},\mathcal{F}_{2})$ is a bi-Lagrangian structure on $M$. In this
paper, we prolong a bi-Lagrangian structure on $M$ on its tangent bundle $TM$
and its cotangent bundle $T^{*}M$ in different ways. As a consequence some
dynamics on the bi-Lagrangian structure of $M$ can be prolonged as dynamics on
the bi-Lagrangian structure of $TM$ and $T^{*}M$. Observe that a pair of
transversal vector fields without singularity on the 2-torus
$\mathbb{T}^2=\mathbb{S}^1\times\mathbb{S}^1$ endowed with a symplectic form
defines a bi-Lagrangian structure on $\mathbb{T}^2$. This sparked our
curiosity. By studying the dynamic of pairs of vector fields on $\mathbb{T}^2$,
we found that some circle maps with a flat piece (called Cherry maps) can be
generated by a pair of vector fields. Moreover, the push forward action of the
set of diffeomorphisms $\mathbb{T}^2$ on the set of its vector fields induces a
conjugation action on the set of generated Cherry maps.


  Empirical risk minimization (ERM), with proper loss function and
regularization, is the common practice of supervised classification. In this
paper, we study training arbitrary (from linear to deep) binary classifier from
only unlabeled (U) data by ERM. We prove that it is impossible to estimate the
risk of an arbitrary binary classifier in an unbiased manner given a single set
of U data, but it becomes possible given two sets of U data with different
class priors. These two facts answer a fundamental question---what the minimal
supervision is for training any binary classifier from only U data. Following
these findings, we propose an ERM-based learning method from two sets of U
data, and then prove it is consistent. Experiments demonstrate the proposed
method could train deep models and outperform state-of-the-art methods for
learning from two sets of U data.


  The study of Chow varieties of decomposable forms lies at the confluence of
algebraic geometry, commutative algebra, representation theory and
combinatorics. There are many open questions about homological properties of
Chow varieties and interesting classes of modules supported on them. The goal
of this note is to survey some fundamental constructions and properties of
these objects, and to propose some new directions of research. Our main focus
will be on the study of certain maximal Cohen-Macaulay modules of covariants
supported on Chow varieties, and on defining equations and syzygies. We also
explain how to assemble Tor groups over Veronese subalgebras into modules over
a Chow variety, leading to a result on the polynomial growth of these groups.


  This paper is concerned with weighted energy estimates and diffusion
phenomena for the initial-boundary problem of the wave equation with
space-dependent damping term in an exterior domain. In this analysis, an
elliptic problem was introduced by Todorova and Yordanov. This attempt was
quite useful when the coefficient of the damping term is radially symmetric. In
this paper, by modifying their elliptic problem, we establish weighted energy
estimates and diffusion phenomena even when the coefficient of the damping term
is not radially symmetric.


  A simple mechanism for the generation of electromagnetic Zebra pattern
emission is proposed. The mechanism is based on the generation of an ion-ring
distribution in a magnetic mirror geometry in the presence of a properly
directed field-aligned electric potential field. The ion-cyclotron maser then
generates a number of electromagnetic ion-cyclotron harmonics which modulate
the electron maser emission. The mechanism is capable of switching the emission
on and off or amplifying it quasi-periodically which is a main feature of the
observations.


  A folded resonant Fabry-Perot cavity has the potential to significantly
reduce the impact of coating thermal noise on the performance of kilometer
scale gravitational wave detectors. When constructed using only spherical
mirror surfaces it is possible to utilize the extremely robust $TEM_{00}$ mode
optical mode. In this paper we investigate the potential thermal noise
improvements that can be achieved for third generation gravitational wave
detectors using realistic constraints. Comparing the previously proposed beam
configurations such as e.g. higher order Laguerre-Gauss modes, we find that
similar or better thermal noise improvement factors can be achieved, while
avoiding degeneracy issues associated with those beams.


  We present static solutions of the 5-dimensional Einstein equations in the
brane-world scenario by using two different approaches for the stabilization of
the extra dimension. Assuming a ``phenomenological'' stabilization mechanism,
that creates a non-vanishing $\hat T^5_5$ in the bulk, we construct a two-brane
model, which allows both branes to have positive self-energies. We then
consider a candidate theory for the dynamical stabilization, through the
introduction of a massless scalar field in the bulk, which interacts with the
branes. We find exact static solutions for the metric and scalar field in the
bulk and demonstrate that the inter-brane distance is determined by the
parameters of scalar field-brane interactions. However, these solutions are
always accompanied by a correlation between the bulk cosmological constant, the
brane self-energies and the interaction terms of the scalar field with the
branes and thus cannot be considered as candidates for the phenomenologically
viable stabilized geometry. We find that the aforementioned correlation cannot
be avoided even in the case of a single-brane solution with positive
self-energy where the fifth dimension ends on a singularity.


  Several investigations on the complete-incomplete fusion (CF-ICF) dynamics of
$\alpha$-cluster well-bound nuclei has been contemplated above the Coulomb
barrier ($\sim$ 4-7 MeV/nucleon) in recent years. It is therefore expected to
observe significant ICF over CF in the reactions induced by a weakly bound
$\alpha$-cluster nucleus at slightly above the barrier. In order to investigate
CF-ICF in the loosely bound system, $^{\text{7}}$Li beam was bombarded on the
$^{\text{nat}}$Mo foils, separated by the aluminium (Al) catcher foils
alternatively, within $\sim$ 3-6.5 MeV/nucleon. Evaporation residues produced
in each foil were identified by the $\gamma$-ray spectrometry. Measured cross
section data of the residues were compared with the theoretical model
calculations based on the equilibrium (EQ) and preequilibrium (PEQ) reaction
mechanisms. The experimental cross section of $^{\text{101m,100,99m,97}}$Rh,
$^{\text{97,95}}$Ru, $^{\text{99m,96,95,94,93m+g}}$Tc and $^{\text{93m}}$Mo
residues measured at various projectile energies were satisfactorily reproduced
by the simplified coupled channel approach in comparison to single barrier
penetration model calculation. Significant cross section enhancement in the
$\alpha$-emitting channels was observed compared to EQ and PEQ model
calculations throughout observed energy region. The ICF process over CF was
analyzed by comparing with EMPIRE. The increment of the incomplete fusion
fraction was observed with increasing projectile energies. Theoretical model
calculations reveal that compound reaction mechanism is the major contributor
to the production of residues. Theoretical evaluations substantiate the
contribution of ICF over the CF in $\alpha$-emitting channels.


  We consider a Josephson junction formed by a quantum dot connected to two
bulk superconductors in presence of Coulomb interaction and coupling to both an
electromagnetic environment and a finite density of electronic quasi-particles.
In the limit of large superconducting gap we obtain a Born-Markov description
of the system dynamics. We calculate the current-phase relation and we find
that the experimentally unavoidable presence of quasi-particles can
dramatically modify the 0-pi standard transition picture. We show that
photon-assisted quasi-particles absorption allows the dynamic switching from
the 0- to the pi-state and vice-versa, washing out the 0-pi transition
predicted by purely thermodynamic arguments.


  We present an organic compound exhibiting a spin-Peierls (SP) transition to
an effective spin-1 antiferromagnetic uniform chain, that is, the Haldane
chain. The clear disappearance of magnetization, accompanied by a structural
phase transition, is well explained by the deformation to an effective spin-1
Haldane chain. The flexibility of the molecular orbitals in the organic radical
compound allows the transformation of the exchange interactions into the
Haldane state with different topologies. The SP transition in the present
compound demonstrates a mechanism different from that of the conventional
systems, paving another path for research in quantum phenomena originating from
spin-lattice couplings.


  Now Standard $\Lambda$CDM cosmology is based on physics Beyond the Standard
Model (BSM), which in turn needs cosmological probes for its study. This
vicious circle of problems can be resolved by methods of cosmoparticle physics,
in which cosmological messengers of new physics provide sensitive model
dependent probes for BSM physics. Such messengers, which are inevitably present
in any BSM basis for now Standard cosmology, lead to deviations from the
Standard cosmological paradigm. We give brief review of some possible
cosmological features and messengers of BSM physics, which include balancing of
baryon asymmetry and dark matter by sphaleron transitions, hadronic dark matter
and exotic cosmic ray components, a solution for puzzles of direct dark matter
searches in dark atom model, antimatter in baryon asymmetrical Universe as
sensitive probe for models of inflation and baryosynthesis and its possible
probe in AMS02 experiment, PBH and GW messengers of BSM models and phase
transitions in early Universe. These aspects are discussed in the general
framework of methods of cosmoparticle physics.


  This study analyzes the problem of a constant height hydraulic fracture. It
is assumed that the fracture is driven by Newtonian fluid, and the effects of
fracture toughness and leak-off are included in the model as well. Analysis of
the tip region for such a fracture is presented first. The limiting solutions
and their locations in the two-dimensional parametric space are investigated.
In addition, an approximate solution for the problem is constructed and its
accuracy is examined in the whole parametric space. Then, analysis of the
finite fracture is presented. Analytic expressions for the limiting solutions
are obtained. Full numerical solution is constructed, as well as an
approximation, which is based on the solution for the tip region and the global
volume balance, is developed. The numerical solution is used to check accuracy
of the approximation, while the latter is used to investigate the whole
parametric space for the problem. This in turn allows determining zones of
applicability of the limiting solutions that can be further used to quantify
which problem parameters dominate fracture dynamics.


  In this paper, we are concerned with the following prey-taxis system with
fluid surrounding describing by the incompressible Navier-Stokes equations in a
bounded domain with smooth boundary. We show that it has global classical
solutions and give decay properties of these solutions.


  Inspired by the Turing mechanism for pattern formation, we propose a simple
self-propelled particle model with short-ranged alignment and anti-alignment at
larger distances. It is able to produce orientationally ordered states,
periodic vortex patterns as well as meso-scale turbulence. The latter phase
resembles observations in dense bacterial suspensions. The model allows a
systematic derivation and analysis of a kinetic theory as well as hydrodynamic
equations for density and momentum fields. A phase diagram with regions of such
pattern formation as well as spatially homogeneous orientational order and
disorder is obtained from a linear stability analysis of these continuum
equations. Microscopic Langevin simulations of the self-propelled particle
system are in agreement with these findings.


  We report the discovery of new Herbig-Haro (HH) jets in the Carina Nebula,
and we discuss the protostellar outflow activity of a young OB association.
These are the first results of an HST/ACS H-alpha imaging survey of Carina.
Adding to the one previously known example (HH666), we detect 21 new HH jets,
plus 17 new candidate jets, ranging in length from 0.005 to 3 pc. We derive jet
mass-loss rates ranging from 8e-9 to 1e-6 Msun/yr, but a comparison to the
distribution of jet mass-loss rates in Orion suggests that we may be missing a
large fraction of the jets below 1e-8 Msun/yr. A key qualitative result is that
even some of the smallest dark globules with sizes of 0.01pc are active sites
of ongoing star formation because we see HH jets emerging from them, and that
these offer potential analogs to the cradle of our Solar System because of
their proximity to dozens of imminent supernovae that will enrich them with
radioactive nuclides like 60Fe. HST images reveal proplyd structures in the
core of the Tr14 cluster, only 0.1-0.2 pc from several O-type stars. Many
examples of bent jets serve as "wind socks"; strong photoevaporative flows can
shape the jets, competing with the direct winds and radiation from massive
stars. Finally, even allowing for a large number of jets that may escape
detection, we find that HH jets are negligible to the global turbulence of the
surrounding region, which is driven by massive star feedback.


  The Banach-Mazur problem, which asks if every infinite-dimensional Banach
space has an infinite-dimensional separable quotient space, has remained
unsolved for 85 years, but has been answered in the affirmative for special
cases such as reflexive Banach spaces. It is also known that every
infinite-dimensional non-normable Fr\'{e}chet space has an infinite-dimensional
separable quotient space, namely $\mathbb{R}^\omega $. It is proved in this
paper that every infinite-dimensional Fr\'{e}chet space (including every
infinite-dimensional Banach space), indeed every locally convex space which has
a subspace which is an infinite-dimensional Fr\'{e}chet space, has an
infinite-dimensional (in the topological sense) separable metrizable quotient
group, namely $\mathbb{T}^\omega$, where $\mathbb{T}$ denotes the compact unit
circle group.


  We present a spectroscopic survey of over 3400 potential members in the North
America and Pelican nebulae (NAP) using several low-resolution ($R\approx$
1300-2000) spectrographs: Palomar/Norris, WIYN/HYDRA, Keck/DEIMOS, and
MMT/Hectospec. We identify 580 young stars as likely members of the NAP region
based on criteria involving infrared excess, Li I 6708 absorption, X-ray
emission, parallax, and proper motions. The spectral types of individual
spectra are derived by fitting them with templates that are either empirical
spectra of pre-main sequence stars, or model atmospheres. The templates are
artificially veiled, and a best-fit combination of spectral type and veiling
parameter is derived for each star. We use the spectral types with archival
photometry to derive $V$-band extinction and stellar luminosity. From the H-R
diagram, the median age of the young stars is about 1 Myr, with a luminosity
dispersion of $\sim$0.3--0.4 dex. We investigate the photometric variability of
the spectroscopic member sample using ZTF data, and conclude that photometric
variability, while present, does not significantly contribute to the luminosity
dispersion. While larger than the formal errors, the luminosity dispersion is
smaller than if veiling were not taken into account in our spectral typing
process. The measured ages of stellar kinematic groups, combined with inferred
ages for embedded stellar populations revealed by Spitzer, suggests a
sequential history of star formation in the NAP region.


  We consider some probabilistic and analytic realizations of Virasoro
highest-weight representations. Specifically, we consider measures on paths
connecting points marked on the boundary of a (bordered) Riemann surface. These
Schramm-Loewner Evolution (SLE)- type measures are constructed by the method of
localization in path space. Their partition function (total mass) is the
highest-weight vector of a Virasoro representation, and the action is given by
Virasoro uniformization.
  We review the formalism of Virasoro uniformization, which allows to define a
canonical action of Virasoro generators on functions (or sections) on a -
suitably extended - Teichm\"uller space. Then we describe the construction of
families of measures on paths indexed by marked bordered Riemann surfaces.
Finally we relate these two notions by showing that the partition functions of
the latter generate a highest-weight representation - the quotient of a
reducible Verma module - for the former.


  One of the main objectives of the ANTARES telescope is the search for
point-like neutrino sources. Both the pointing accuracy and the angular
resolution of the detector are important in this context and a reliable way to
evaluate this performance is needed. In order to measure the pointing accuracy
of the detector, one possibility is to study the shadow of the Moon, i.e. the
deficit of the atmospheric muon flux from the direction of the Moon induced by
the absorption of cosmic rays. Analysing the data taken between 2007 and 2016,
the Moon shadow is observed with $3.5\sigma$ statistical significance. The
detector angular resolution for downward-going muons is
0.73$^{\circ}\pm0.14^{\circ}.$ The resulting pointing performance is consistent
with the expectations. An independent check of the telescope pointing accuracy
is realised with the data collected by a shower array detector onboard of a
ship temporarily moving around the ANTARES location.


  We define the concept of a flat pseudo-Riemannian $F$-Lie algebra and
construct its corresponding double extension. This algebraic structure can be
interpreted as the infinitesimal analogue of a Frobenius Lie group devoid of
Euler vector fields. We show that the double extension provides a framework for
generating all weakly flat Lorentzian non-abelian bi-nilpotent $F$-Lie algebras
possessing one dimensional light-cone subspaces. A similar result can be
established for nilpotent Lie algebras equipped with flat scalar products of
signature $(2,n-2)$ where $n\geq 4$. Furthermore, we use this technique to
construct Poisson algebras exhibiting compatibility with flat scalar products.


  With information from multiple input modalities, sensor fusion-based
algorithms usually out-perform their single-modality counterparts in robotics.
Camera and LIDAR, with complementary semantic and depth information, are the
typical choices for detection tasks in complicated driving environments. For
most camera-LIDAR fusion algorithms, however, the calibration of the sensor
suite will greatly impact the performance. More specifically, the detection
algorithm usually requires an accurate geometric relationship among multiple
sensors as the input, and it is often assumed that the contents from these
sensors are captured at the same time. Preparing such sensor suites involves
carefully designed calibration rigs and accurate synchronization mechanisms,
and the preparation process is usually done offline. In this work, a
segmentation-based framework is proposed to jointly estimate the geometrical
and temporal parameters in the calibration of a camera-LIDAR suite. A semantic
segmentation mask is first applied to both sensor modalities, and the
calibration parameters are optimized through pixel-wise bidirectional loss. We
specifically incorporated the velocity information from optical flow for
temporal parameters. Since supervision is only performed at the segmentation
level, no calibration label is needed within the framework. The proposed
algorithm is tested on the KITTI dataset, and the result shows an accurate
real-time calibration of both geometric and temporal parameters.


  Using radiation-hydrodynamic cosmological simulations, we present a detailed
($0.1$ pc resolution), physically motivated portrait of a typical-mass dwarf
galaxy before the epoch of reionization, resolving the formation and evolution
of star clusters into individual $10\:\mathrm{M_{\odot}}$ star particles. In
the rest-frame UV, the galaxy has an irregular morphology with no bulge or
galactic disk, dominated by light emitted from numerous, compact, and
gravitationally-bound star clusters. This is especially interesting in light of
recent HST and JWST observations that -- aided by the magnifying power of
gravitational lenses -- have imaged, at parsec-scale resolution, individual
young star clusters in the process of forming in similar galaxies at $z>6$.
Because of their low metallicities and high temperatures, star-forming gas
clouds in this galaxy have densities $\sim 100$ times higher than typical giant
molecular clouds; hence, their star formation efficiencies are high enough
($f_*\sim10-70$ per cent) to produce a sizeable population of potential
globular cluster progenitors but typically smaller (between a few $100\:-\:
2\times10^4\:\mathrm{M_{\odot}}$, sizes of $0.1-3$ pc) and of lower
metallicities ($10^{-3.5}-10^{-2.5}\:\mathrm{Z_{\odot}}$). The initial mass
function of the star-forming clouds is log-normal while the bound star cluster
mass function is a power-law with a slope that depends mainly on $f_*$ but also
on the temporal proximity to a major starburst. We find slopes between $-0.5$
and $-2.5$ depending on the assumed sub-grid $f_*$. Star formation is
self-regulated on galactic scales; however, the multi-modal metallicity
distribution of the star clusters and the fraction of stars locked into
surviving bound star clusters depends on $f_*$.


  We study the nontrivial dispersion relation of mesons resulting from the
splitting of the transversal and longitudinal mesonic wave function
renormalizations, and its influences on the QCD phase transition, equation of
state, and the fluctuations of baryon number. The calculations are performed in
a two-flavor low energy effective model within the functional renormalization
group approach. We find that influences of the splitting mesonic wave function
renormalizations on the equilibrium thermodynamical bulk properties are mild.
Furthermore, we have compare the fixed and running expansion for the effective
potential in detail, through which the role of the field-dependent meson and
quark wave function renormalizations could be inferred.


  The principal aim of the present paper is to establish the uniqueness and
Ulam-Hyers Mittag-Leffler (UHML) stability of solutions for a new class of
multi-terms fractional time-delay differential equations in the context of the
$\Phi$-Caputo fractional derivative. To achieve this purpose, the generalized
Laplace transform method alongside facet with properties of the Mittag-Leffler
functions (M-LFs), are utilized to give a new representation formula of the
solutions for the aforementioned problem. Besides that, the uniqueness of the
solutions of the considered problem is also proved by applying the well-known
Banach contraction principle coupled with the $\Phi$-fractional Bielecki-type
norm. While the $\Phi$-fractional Gronwall type inequality and the Picard
operator (PO) technique combined with abstract Gronwall lemma are used to prove
the UHML stability results for the proposed problem. Lastly, an example is
offered to assure the validity of the obtained theoretical results.


  Despite various playful and educational tools have been developed to support
children's learning abilities, limited work focuses on tangible toys designed
to improve and maintain children's hygiene perception, habits and awareness, as
well as fostering their collaboration and social abilities in home education
contexts. We developed \textbf{Awayvirus} to address this research and design
gap, aiming to help children gain hygiene habits knowledge through tangible
blocks. Our findings indicate that a playful tangible interaction method can
effectively increase children's interest in learning and encourage parents to
become actively involved in their children's hygiene and health education.
Additionally, Awayvirus seeks to build a collaborative bridge between children
and parents, promoting communication strategies while mitigating the adverse
effects of the challenging the post-pandemic period.


  We present the asymptotic formula for the Wigner 9j-symbol, valid when all
quantum numbers are large, in the classically allowed region. As in the
Ponzano-Regge formula for the 6j-symbol, the action is expressed in terms of
lengths of edges and dihedral angles of a geometrical figure, but the angles
require care in definition. Rules are presented for converting spin networks
into the associated geometrical figures. The amplitude is expressed as the
determinant of a 2x2 matrix of Poisson brackets. The 9j-symbol possesses
caustics associated with the fold and elliptic and hyperbolic umbilic
catastrophes. The asymptotic formula obeys the exact symmetries of the
9j-symbol.


  We study a bound system of N identical bosons interacting by model pair
potentials of the form V(r) = A sgn(p)r^p + B/r^2, A > 0, B >= 0. By using a
variational trial function and the `equivalent 2-body method', we find explicit
upper and lower bound formulas for the N-particle ground-state energy in
arbitrary spatial dimensions d > 2 for the two cases p = 2 and p = -1. It is
demonstrated that the upper bound can be systematically improved with the aid
of a special large-N limit in collective field theory.


  In the framework of Wilson Chiral Perturbation Theory, we study the effect
induced by a twisted Wilson term, as it appears in Twisted Mass QCD (with 2
degenerate quarks). In particular we consider the vacuum orientation and the
pion masses. The computations are done to NLO both in the mass and in the
lattice spacing (i.e. to O(a^2)). There are no restrictions on the relative
size of lattice artifacts with respect to the physical mass, thus allowing, in
principle, to bridge between the physical regime and the unphysical one, where
lattice artifacts tend to dominate. The inclusion of O(a^2) lattice artifacts
can account for the splitting of degeneracy of the three pion masses. Moreover
O(a^2) terms are necessary to model non trivial behaviors of the vacuum
orientation such as possible Aoki phases. It turns out that these last two
phenomena are determined by the same constant.


  Attaching attributes (such as color, shape, state, action) to object
categories is an important computer vision problem. Attribute prediction has
seen exciting recent progress and is often formulated as a multi-label
classification problem. Yet significant challenges remain in: 1) predicting
diverse attributes over multiple categories, 2) modeling attributes-category
dependency, 3) capturing both global and local scene context, and 4) predicting
attributes of objects with low pixel-count. To address these issues, we propose
a novel multi-category attribute prediction deep architecture named GlideNet,
which contains three distinct feature extractors. A global feature extractor
recognizes what objects are present in a scene, whereas a local one focuses on
the area surrounding the object of interest. Meanwhile, an intrinsic feature
extractor uses an extension of standard convolution dubbed Informed Convolution
to retrieve features of objects with low pixel-count. GlideNet uses gating
mechanisms with binary masks and its self-learned category embedding to combine
the dense embeddings. Collectively, the Global-Local-Intrinsic blocks
comprehend the scene's global context while attending to the characteristics of
the local object of interest. Finally, using the combined features, an
interpreter predicts the attributes, and the length of the output is determined
by the category, thereby removing unnecessary attributes. GlideNet can achieve
compelling results on two recent and challenging datasets -- VAW and CAR -- for
large-scale attribute prediction. For instance, it obtains more than 5\% gain
over state of the art in the mean recall (mR) metric. GlideNet's advantages are
especially apparent when predicting attributes of objects with low pixel counts
as well as attributes that demand global context understanding. Finally, we
show that GlideNet excels in training starved real-world scenarios.


  The discrepancy between dynamical mass measures of objects such as galaxies
and the observed distribution of luminous matter in the universe is typically
explained by invoking an unseen ``dark matter'' component. Dark matter must
necessarily be non-baryonic. We introduce a simple hypothesis to do away with
the necessity for dark matter by introducing an additional non-gravitational
force coupled to baryon number as a charge. We compare this hypothesis to
Milgrom's Modified Newtonian Dynamics. The model ultimately fails when
confronted with observation, but it fails in an interesting way.


  We find significant differences between degradation and healing at the
surface or in the bulk for each of the different APbBr3 single crystals
(A=CH3NH3+, methylammonium (MA); HC(NH2)2+, formamidinium (FA); and cesium,
Cs+). Using 1- and 2-photon microscopy and photobleaching we conclude that
kinetics dominate the surface, and thermodynamics the bulk stability.
Fluorescence-lifetime imaging microscopy, as well as results from several other
methods, relate the (damaged) state of the halide perovskite (HaP) after
photobleaching to its modified optical and electronic properties. The A cation
type strongly influences both the kinetics and the thermodynamics of recovery
and degradation: FA heals best the bulk material with faster self-healing; Cs+
protects the surface best, being the least volatile of the A cations and
possibly through O-passivation; MA passivates defects via methylamine from
photo-dissociation, which binds to Pb2+. DFT simulations not only provide
insight into the latter conclusion, but also show the importance and stability
of the Br3- defect. These results rationalize the use of mixed A-cation
materials for optimizing both solar cell stability and overall performance of
HaP-based devices, and provide a basis for designing new HaP variants.


  Quantum computers are expected to be able to solve mathematical problems that
cannot be solved using conventional computers. Many of these problems are of
practical importance, especially in the areas of cryptography and secure
communications. APL is developing an optical approach to quantum computing in
which the bits, or "qubits", are represented by single photons. Our approach
allows the use of ordinary (linear) optical elements that are available for the
most part as off-the-shelf components. Recent experimental demonstrations of a
variety of logic gates for single photons, a prototype memory device, and other
devices will be described.


  We completely characterize General Gauge Mediation (GGM) at the weak scale by
solving all IR constraints over the full parameter space. This is made possible
through a combination of numerical and analytical methods, based on a set of
algebraic relations among the IR soft masses derived from the GGM boundary
conditions in the UV. We show how tensions between just a few constraints
determine the boundaries of the parameter space: electroweak symmetry breaking
(EWSB), the Higgs mass, slepton tachyons, and left-handed stop/sbottom
tachyons. While these constraints allow the left-handed squarks to be
arbitrarily light, they place strong lower bounds on all of the right-handed
squarks. Meanwhile, light EW superpartners are generic throughout much of the
parameter space. This is especially the case at lower messenger scales, where a
positive threshold correction to $m_h$ coming from light Higgsinos and winos is
essential in order to satisfy the Higgs mass constraint.


  We propose a simple scheme for complete Bell-state measurement of photons
using hyperentangled states - entangled in multiple degrees of freedom. In
addition to hyperentanglement, our scheme requires only linear optics and
single photon detectors, and is realizable with current technology. At the cost
of additional classical communication, our Bell-state measurement can be
implemented non-locally. We discuss the possible application of these results
to quantum dense coding and quantum teleportation.


  We experimentally study the effects of coupling one-dimensional Many-Body
Localized (MBL) systems with identical disorder. Using a gas of ultracold
fermions in an optical lattice, we artifically prepare an initial charge
density wave in an array of 1D tubes with quasi-random onsite disorder and
monitor the subsequent dynamics over several thousand tunneling times. We find
a strikingly different behavior between MBL and Anderson Localization. While
the non-interacting Anderson case remains localized, in the interacting case
any coupling between the tubes leads to a delocalization of the entire system.


  Using an NMR quantum computer, we experimentally simulate the quantum phase
transition of a Heisenberg spin chain. The Hamiltonian is generated by a
multiple pulse sequence, the nuclear spin system is prepared in its
(pseudo-pure) ground state and the effective Hamiltonian varied in such a way
that the Heisenberg chain is taken from a product state to an entangled state
and finally to a different product state.


  As the rate of content production grows, we must make a staggering number of
daily decisions about what information is worth acting on. For any flourishing
online social media system, users can barely keep up with the new content
shared by friends. How does the user-interface design help or hinder users'
ability to find interesting content? We analyze the choices people make about
which information to propagate on the social media sites Twitter and Digg. We
observe regularities in behavior which can be attributed directly to cognitive
limitations of humans, resulting from the different visibility policies of each
site. We quantify how people divide their limited attention among competing
sources of information, and we show how the user-interface design can mediate
information spread.


  Automatic summarisation has the potential to aid physicians in streamlining
clerical tasks such as note taking. But it is notoriously difficult to evaluate
these systems and demonstrate that they are safe to be used in a clinical
setting. To circumvent this issue, we propose a semi-automatic approach whereby
physicians post-edit generated notes before submitting them. We conduct a
preliminary study on the time saving of automatically generated consultation
notes with post-editing. Our evaluators are asked to listen to mock
consultations and to post-edit three generated notes. We time this and find
that it is faster than writing the note from scratch. We present insights and
lessons learnt from this experiment.


  We report on hydrogen adsorption and desorption on titanium-covered graphene
in order to test theoretical proposals to use of graphene functionalized with
metal atoms for hydrogen storage. At room temperature titanium islands grow
with an average diameter of about 10 nm. Samples were then loaded with
hydrogen, and its desorption kinetics was studied by thermal desorption
spectroscopy. We observe the desorption of hydrogen in the temperature range
between 400K and 700 K. Our results demonstrate the stability of hydrogen
binding at room temperature and show that hydrogen desorbs at moderate
temperatures in line with what required for practical hydrogen-storage
applications.


  We give a new proof of the sharp one weight $L^p$ inequality for any operator
$T$ that can be approximated by Haar shift operators such as the Hilbert
transform, any Riesz transform, the Beurling-Ahlfors operator. Our proof avoids
the Bellman function technique and two weight norm inequalities. We use instead
a recent result due to A. Lerner to estimate the oscillation of dyadic
operators. Our method is flexible enough to prove the corresponding sharp
one-weight norm inequalities for some operators of harmonic analysis: the
maximal singular integrals associated to $T$, Dyadic square functions and
paraproducts, and the vector-valued maximal operator of C. Fefferman-Stein.
Also we can derive a very sharp two-weight bump type condition for $T$.


  Two new proofs are provided, offering two new perspectives on Godbersen's
conjecture. One of the proofs utilizes Helly's theorem to provide a concise and
elegant proof of the inequality in Godbersen's conjecture. The other proof
utilizes the Brunn-Minkowski inequality to provide a completely new proof of
the inclusion $-K\subset nK$ for convex bodies $K$ with centroid at the origin,
thereby proving Godbersen's conjecture.


  Two new sufficient conditions for generalized cycles (including Hamilton and
dominating cycles as special cases) in an arbitrary k-connected graph
(k=1,2,...) are derived, which prove the truth of Bondy's (1980) famous
conjecture for some variants significantly improving the result expected by the
given hypothesis. Similarly, two new lower bounds for the circumference (the
length of a longest cycle) are established for the reverse hypothesis proposed
by Jung (2001).


  We revisit low-temperature optical spectra of transition-metal dichalcogenide
monolayers and point to a possible crystallization of electrons (or holes) at
low to moderate charge densities. To calculate the excitonic spectra under such
conditions, we introduce the recursion method and compute how the charge
density affects the energies, linewidths, and oscillator strengths of exciton
and trion complexes. Equally important, we study how excitons and trions in the
monolayer evolve when the charge particles gradually transition to a periodic
Wigner lattice. The results provide valuable information on the ability to
detect whether the particles are ordered through the exciton spectrum. Finally,
we calculate the change in exciton energy in cases that the added charge
particles have similar and dissimilar quantum numbers (spin and valley) to
those of the electron or hole in the exciton. The results of this work shed new
light on important optical properties of monolayer semiconductors.


  Social network research has begun to take advantage of fine-grained
communications regarding coordination, decision-making, and knowledge sharing.
These studies, however, have not generally analyzed how external events are
associated with a social network's structure and communicative properties.
Here, we study how external events are associated with a network's change in
structure and communications. Analyzing a complete dataset of millions of
instant messages among the decision-makers in a large hedge fund and their
network of outside contacts, we investigate the link between price shocks,
network structure, and change in the affect and cognition of decision-makers
embedded in the network. When price shocks occur the communication network
tends not to display structural changes associated with adaptiveness. Rather,
the network "turtles up". It displays a propensity for higher clustering,
strong tie interaction, and an intensification of insider vs. outsider
communication. Further, we find changes in network structure predict shifts in
cognitive and affective processes, execution of new transactions, and local
optimality of transactions better than prices, revealing the important
predictive relationship between network structure and collective behavior
within a social network.


  In a self-consistent semi-empirical numerical approach based on
ab-initio-calculations for small samples, we evaluate the GMR effect for
disordered (001)-(3--Fe/3--V)$_\infty$ multilayers by means of a Kubo
formalism. We consider four different types of disorder arrangements: In case
(i) and (ii), the disorder consists in the random interchange of some Fe and V
atoms, respectively, at interface layers; in case (iii) in the formation of
small groups of three substitutional Fe atoms in a V interface layer and a
similar V group in a Fe layer at a different interface; and for case (iv) in
the substitution of some V atoms in the innermost V layers by Fe. For cases (i)
and (ii), depending on the distribution of the impurities, the GMR effect is
enhanced or reduced by increasing disorder, in case (iii) the GMR effect is
highest, whereas finally, in case (iv), a negative GMR is obtained (''inverse
GMR'').


  Recent methods have significantly reduced the performance degradation of
Binary Neural Networks (BNNs), but guaranteeing the effective and efficient
training of BNNs is an unsolved problem. The main reason is that the estimated
gradients produced by the Straight-Through-Estimator (STE) mismatches with the
gradients of the real derivatives. In this paper, we provide an explicit convex
optimization example where training the BNNs with the traditionally adaptive
optimization methods still faces the risk of non-convergence, and identify that
constraining the range of gradients is critical for optimizing the deep binary
model to avoid highly suboptimal solutions. For solving above issues, we
propose a BAMSProd algorithm with a key observation that the convergence
property of optimizing deep binary model is strongly related to the
quantization errors. In brief, it employs an adaptive range constraint via an
errors measurement for smoothing the gradients transition while follows the
exponential moving strategy from AMSGrad to avoid errors accumulation during
the optimization. The experiments verify the corollary of theoretical
convergence analysis, and further demonstrate that our optimization method can
speed up the convergence about 1:2x and boost the performance of BNNs to a
significant level than the specific binary optimizer about 3:7%, even in a
highly non-convex optimization problem.


  The phase diagram of isospin-symmetric chemically equilibrated mixture of
alpha particles and nucleons is studied in the mean-field approximation.
Skyrme-like parametrization is used for the mean-field potentials as functions
of partial densities of nucleons and alphas. We find that there is a threshold
value a* of the parameter a(N-alpha) which describes the attractive interaction
between alpha-particles and nucleons. At a(N-alpha)<a* the ground state of
nuclear matter at zero temperature behaves as a pure system of interacting
nucleons, whereas at a(N-alpha)>a* the nuclear ground state includes also a
nonzero fraction of alphas. We demonstrate that the equation of state of such
alpha-N system includes both the first-order liquid-gas phase transitions and
the Bose-Einstein condensation of alpha particles.


  We analyze the method of encoding pairwise interactions of higher-than-binary
discrete variables (these models are sometimes referred to as discrete
quadratic models) into binary variables based on domain walls on one
dimensional Ising chains. We discuss how this is relevant to quantum annealing,
but also many gate model algorithms such as VQE and QAOA. We theoretically show
that for problems of practical interest for quantum computing and assuming only
quadratic interactions are available between the binary variables, it is not
possible to have a more efficient general encoding in terms of number of binary
variables per discrete variable. We furthermore use a D-Wave Advantage 1.1 flux
qubit quantum annealing computer to show that the dynamics effectively freeze
later for a domain-wall encoding compared to a traditional one-hot encoding.
This second result could help explain the dramatic performance improvement of
domain wall over one hot which has been seen in a recent experiment on D-Wave
hardware. This is an important result because usually problem encoding and the
underlying physics are considered separately, our work suggests that
considering them together may be a more useful paradigm. We argue that this
experimental result is also likely to carry over to a number of other settings,
we discuss how this has implications for gate-model and quantum-inspired
algorithms.


  The near-isotropy of the cosmic microwave background (CMB) is considered to
be the strongest indication for the homogeneity and isotropy of the universe, a
cornerstone of most cosmological analysis. We derive new theorems which extend
the Ehlers-Geren-Sachs result that an isotropic CMB implies that the universe
is either stationary or homogeneous and isotropic, and its generalisation to
the almost isotropic case. We discuss why the theorems do not apply to the real
universe, and why the CMB observations do not imply that the universe would be
nearly homogeneous and isotropic.


  The paper tries to extend results of the classical Descriptive Set Theory to
as many countably based T_0-spaces (cb_0-spaces) as possible. Along with
extending some central facts about Borel, Luzin and Hausdorff hierarchies of
sets we consider also the more general case of k-partitions. In particular, we
investigate the difference hierarchy of k-partitions and the fine hierarchy
closely related to the Wadge hierarchy.


  In this article, we study the final-state rescattering effects in the decays
$B^0\to \chi_{c0}K^{*0}$ and $B^+ \to \chi_{c0}K^{*+}$, and observe the
corrections are zero in the SU(3) limit, which is warranted by the heavy quark
symmetry. It is difficult to accommodate the experimental data without
fine-tuning.


  Consider the motion of a Brownian particle in $n$ dimensions, whose
coordinate processes are standard Brownian motions with zero drift initially,
and then at some random/unobservable time, exactly $k$ of the coordinate
processes get a (known) non-zero drift permanently. Given that the position of
the Brownian particle is being observed in real time, the problem is to detect
the time at which the $k$ coordinate processes get the drift as accurately as
possible. We solve this problem in the most uncertain scenario when the
random/unobservable time is (i) exponentially distributed and (ii) independent
from the initial motion without drift. The solution is expressed in terms of a
stopping time that minimises the probability of a false early detection and the
expected delay of a missed late detection. The elliptic case $k=1$ has been
settled in Ernst and Peskir (2022) where the hypoelliptic case $1 < k < n$
resolved in the present paper was left open (the case $k = n$ reduces to the
classic case $n=1$ having a known solution). We also show that the methodology
developed solves the problem in the general case where exactly $k$ is relaxed
to any number of the coordinate processes getting the drift. To our knowledge
this is the first time that such a multi-dimensional hypoelliptic problem has
been solved exactly in the literature.


  Predicting and discovering drug-drug interactions (DDIs) is an important
problem and has been studied extensively both from medical and machine learning
point of view. Almost all of the machine learning approaches have focused on
text data or textual representation of the structural data of drugs. We present
the first work that uses drug structure images as the input and utilizes a
Siamese convolutional network architecture to predict DDIs.


  We consider the quantum mechanics of a charged particle in the presence of
Dirac's magnetic monopole. Wave functions are sections of a complex line bundle
and the magnetic potential is a connection on the bundle. We use a continuum
eigenfunction expansion to find an invariant domain of essential
self-adjointness for the Hamiltonian. This leads to a proof of the a
Feynman-Kac formula expressing solutions of the imaginary time Schrodinger
equation as stochastic integrals.


  We compute and analyze the Flavor-Changing Neutral Current (FCNC)
interactions of Minimal Supersymmetric Standard Model Higgs bosons (h = h0, H0,
A0) with heavy quarks (top and bottom), focusing on the strongly-interacting
sector. We correlate the Higgs bosons production cross-section at the LHC with
the FCNC decay branching ratios and find the maximum allowed values of the
production rates, sigma(pp -> h -> qq') = sigma(pp -> h) x B(h -> qq') (qq'= tc
or bs) after taking into account limits from low energy data on flavor-changing
interactions. We single out the top channel, with a maximum production rate of
sigma^max(pp -> h -> tc) =~ 10^-3 - 10^-2 pb, as the most promising FCNC
channel to be detected at the LHC.


  We theoretically calculate and experimentally measure the beyond-mean-field
(BMF) equation of state in a coherently-coupled two-component Bose-Einstein
condensate (BEC) in the regime where averaging of the interspecies and
intraspecies coupling constants over the hyperfine composition of the
single-particle dressed state predicts the exact cancellation of the two-body
interaction. We show that with increasing the Rabi-coupling frequency $\Omega$,
the BMF energy density crosses over from the nonanalytic Lee-Huang-Yang (LHY)
scaling $\propto n^{5/2}$ to an expansion in integer powers of density, where,
in addition to a two-body BMF term $\propto n^2 \sqrt{\Omega}$, there emerges a
repulsive three-body contribution $\propto n^3/\sqrt{\Omega}$. We
experimentally evidence this two contributions, thanks to their different
scaling with $\Omega$, in the expansion of a Rabi-coupled two-component
$^{39}$K condensate in a waveguide. By studying the expansion with and without
Rabi coupling, we reveal an important feature relevant for observing BMF
effects and associated phenomena in mixtures with spin-asymmetric losses: Rabi
coupling helps preserve the spin composition and thus prevents the system from
drifting away from the point of vanishing mean field.


  For positive integers $q$, Dirichlet's theorem states that there are
infinitely many primes in each reduced residue class modulo $q$. A stronger
form of the theorem states that the primes are equidistributed among the
$\varphi(q)$ reduced residue classes modulo $q$. This paper considers patterns
of sequences of consecutive primes $(p_n, p_{n+1}, \ldots, p_{n+k})$ modulo
$q$. Numerical evidence suggests a preference for certain prime patterns. For
example, computed frequencies of the pattern $(a,a)$ modulo $q$ up to $x$ are
much less than the expected frequency $\pi(x)/\varphi(q)^2$. We begin to
rigorously connect the Hardy-Littlewood prime $k$-tuple conjecture to a
conjectured asymptotic formula for the frequencies of prime patterns modulo
$q$.


  We present new HST WFC3 near-IR observations of the CMD's in two LSB
galaxies, F575-3 and F615-1, notable for having no current star formation based
on a lack of H$\alpha$ emission. Key features of the near-IR CMD's are
resolved, such as the red giant branch (RGB), the asymptotic giant branch (AGB)
region and the top of the blue main sequence (bMS). F575-3 has the bluest RGB
of any CMD in the literature, indicating an extremely low mean metallicity.
F615-1 has unusually wide RGB and AGB sequences suggesting multiple episodes of
star formation from metal-poor gas, possibly infalling material. Both galaxies
have an unusual population of stars to the red of the RGB and lower in
luminosity than typical AGB stars. These stars have normal optical colors but
abnormal near-IR colors. We suggest that this population of stars might be
analogous to local peculiar stars like Be stars with strong near-IR excesses
owing to a surrounding disk of hot gas.


  Most approaches to human attribute and action recognition in still images are
based on image representation in which multi-scale local features are pooled
across scale into a single, scale-invariant encoding. Both in bag-of-words and
the recently popular representations based on convolutional neural networks,
local features are computed at multiple scales. However, these multi-scale
convolutional features are pooled into a single scale-invariant representation.
We argue that entirely scale-invariant image representations are sub-optimal
and investigate approaches to scale coding within a Bag of Deep Features
framework.
  Our approach encodes multi-scale information explicitly during the image
encoding stage. We propose two strategies to encode multi-scale information
explicitly in the final image representation. We validate our two scale coding
techniques on five datasets: Willow, PASCAL VOC 2010, PASCAL VOC 2012,
Stanford-40 and Human Attributes (HAT-27). On all datasets, the proposed scale
coding approaches outperform both the scale-invariant method and the standard
deep features of the same network. Further, combining our scale coding
approaches with standard deep features leads to consistent improvement over the
state-of-the-art.


  The differential expansion is one of the key structures reflecting group
theory properties of colored knot polynomials, which also becomes an important
tool for evaluation of non-trivial Racah matrices. This makes highly desirable
its extension from knots to links, which, however, requires knowledge of the
$6j$-symbols, at least, for the simplest triples of non-coincident
representations. Based on the recent achievements in this direction, we
conjecture a shape of the differential expansion for symmetrically-colored
links and provide a set of examples. Within this study, we use a special
framing that is an unusual extension of the topological framing from knots to
links. In the particular cases of Whitehead and Borromean rings links, the
differential expansions are different from the previously discovered.


  The recoil properties of the product nuclei from the interaction of 2.2
GeV/nucleon 12-C ions from Nuclotron of the Laboratory of High Energies (LHE),
Joint Institute for Nuclear Research (JINR) at Dubna with a 118-Sn target have
been studied using catcher foils. The experimental data were analyzed using the
mathematical formalism of the standard two-step vector model. The results for
12-C ions are compared with those for deuterons and protons. Three different
Los Alamos versions of the Quark-Gluon String Model (LAQGSM) were used for
comparison with our experimental data.


  The entanglement entropy is a unique probe to reveal universal features of
strongly interacting many-body systems. In two or more dimensions these
features are subtle, and detecting them numerically requires extreme precision,
a notoriously difficult task. This is especially challenging in models of
interacting fermions, where many such universal features have yet to be
observed. In this paper we tackle this challenge by introducing a new method to
compute the R\'enyi entanglement entropy in auxiliary-field quantum Monte Carlo
simulations, where we treat the entangling region itself as a stochastic
variable. We demonstrate the efficiency of this method by extracting, for the
first time, universal subleading logarithmic terms in a two dimensional model
of interacting fermions, focusing on the half-filled honeycomb Hubbard model at
$T=0$. We detect the universal corner contribution due to gapless fermions
throughout the Dirac semi-metal phase and at the Gross-Neveu-Yukawa critical
point, where the latter shows a pronounced enhancement depending on the type of
entangling cut. Finally, we observe the universal Goldstone mode contribution
in the antiferromagnetic Mott insulating phase.


  Registration of longitudinal brain MRI scans containing pathologies is
challenging due to dramatic changes in tissue appearance. Although there has
been progress in developing general-purpose medical image registration
techniques, they have not yet attained the requisite precision and reliability
for this task, highlighting its inherent complexity. Here we describe the Brain
Tumor Sequence Registration (BraTS-Reg) challenge, as the first public
benchmark environment for deformable registration algorithms focusing on
estimating correspondences between pre-operative and follow-up scans of the
same patient diagnosed with a diffuse brain glioma. The BraTS-Reg data comprise
de-identified multi-institutional multi-parametric MRI (mpMRI) scans, curated
for size and resolution according to a canonical anatomical template, and
divided into training, validation, and testing sets. Clinical experts annotated
ground truth (GT) landmark points of anatomical locations distinct across the
temporal domain. Quantitative evaluation and ranking were based on the Median
Euclidean Error (MEE), Robustness, and the determinant of the Jacobian of the
displacement field. The top-ranked methodologies yielded similar performance
across all evaluation metrics and shared several methodological commonalities,
including pre-alignment, deep neural networks, inverse consistency analysis,
and test-time instance optimization per-case basis as a post-processing step.
The top-ranked method attained the MEE at or below that of the inter-rater
variability for approximately 60% of the evaluated landmarks, underscoring the
scope for further accuracy and robustness improvements, especially relative to
human experts. The aim of BraTS-Reg is to continue to serve as an active
resource for research, with the data and online evaluation tools accessible at
https://bratsreg.github.io/.


  It is known that some GIT compactifications associated to moduli spaces of
either points in the projective line or cubic surfaces are isomorphic to
Baily-Borel compactifications of appropriate ball quotients. In this paper, we
show that their respective toroidal compactifications are isomorphic to moduli
spaces of stable pairs as defined in the context of the MMP. Moreover, we give
a precise mixed-Hodge-theoretic interpretation of this isomorphism for the case
of eight labeled points in the projective line.


  The purpose of the present article is to examine the essence of what has
commonlybeen described as a "projective line", but which is here named a
"meridian". This shall be done in several papers: this first paper devoted to
the meridian itself, the second to the character and form of the family of
projective isomorphisms of one meridian onto another and the third to some
connections between meridians and higher dimensional projective space. Here we
view the meridian from various aspects:
  (1) as a set acted upon by a family of involutions;
  (2) as a set acted upon by a 3-transitive group of permutations;
  (3) as a set with a quinary operator;
  (4) as an equivalence class of quadruples, relating to the cross ratio.
  In the final section of this first paper we shall investigate how the
existence of a certain single-valued exponential on a meridian is
characteristic of the meridian corresponding to the field of real numbers.


  The occurrence of new events in a system is typically driven by external
causes and by previous events taking place inside the system. This is a general
statement, applying to a range of situations including, more recently, to the
activity of users in Online social networks (OSNs). Here we develop a method
for extracting from a series of posting times the relative contributions of
exogenous, e.g. news media, and endogenous, e.g. information cascade. The
method is based on the fitting of a generalized linear model (GLM) equipped
with a self-excitation mechanism. We test the method with synthetic data
generated by a nonlinear Hawkes process, and apply it to a real time series of
tweets with a given hashtag. In the empirical dataset, the estimated
contributions of exogenous and endogenous volumes are close to the amounts of
original tweets and retweets respectively. We conclude by discussing the
possible applications of the method, for instance in online marketing.


  We deal with a degenerate model describing the dynamics of a population
depending on time, on age and on space. We assume that the degeneracy can occur
at the boundary or in the interior of the space domain and we focus on null
controllability problem. To this aim, we prove first Carleman estimates for the
associated adjoint problem, then, via cut off functions, we prove the existence
of a null control function localized in the interior of the space domain.


  We use an AdS/QCD holographic wavefunction to generate predictions for the
rate of diffractive {\rho}-meson electroproduction that are in reasonable
agreement with data collected at the HERA electron-proton collider.


  If a locally cartesian closed category carries a weak factorisation system,
then the left maps are stable under pullback along right maps if and only if
the right maps are closed under pushforward along right maps. We refer to this
statement as the Frobenius equivalence and in this paper we state and prove an
analogical statement for algebraic weak factorisation systems. These algebraic
weak factorisation systems are an explicit variant of the more traditional weak
factorisation systems in that the factorisation and the lifts are part of the
structure of an algebraic weak factorisation system and are not merely required
to exist. Our work has been motivated by the categorical semantics of type
theory, where the Frobenius equivalence provides a useful tool for constructing
dependent function types. We illustrate our ideas using split fibrations of
groupoids, which are the backbone of the groupoid model of Hofmann and
Streicher.


  We consider equivalence relations among smooth map germs with respect to
geometry of G-structures on the target space germ. These equivalence relations
are natural generalization of right-left equivalence (i.e., A-equivalence) in
the sense of Thom-Mather depending on geometric structures on the target space
germ. Unfortunately, these equivalence relations are not necessarily geometric
subgroups in the sense of Damon (1984). However, we have interesting
applications of these equivalence relations.


  We study the trade-off relations given by the l_1-norm coherence of general
multipartite states. Explicit trade-off inequalities are derived with lower
bounds given by the coherence of either bipartite or multipartite reduced
density matrices. In particular, for pure three-qubit states, it is explicitly
shown that the trade-off inequality is lower bounded by the three tangle of
quantum entanglement.


  We propose Bayesian nonparametric Weibull delegate racing (WDR) for survival
analysis with competing events and achieve both model interpretability and
flexibility. Utilizing a natural mechanism of surviving competing events, we
assume a race among a potentially infinite number of sub-events. In doing this,
WDR accommodates nonlinear covariate effects with no need of data
transformation. Moreover, WDR is able to handle left truncation, time-varying
covariates, different types of censoring, and missing event times or types. We
develop an efficient MCMC algorithm based on Gibbs sampling for Bayesian
inference and provide an \texttt{R} package. Synthetic data analysis and
comparison with benchmark approaches demonstrate WDR's outstanding performance
and parsimonious nonlinear modeling capacity. In addition, we analyze two real
data sets and showcase advantages of WDR. Specifically, we study time to death
of three types of lymphoma and show the potential of WDR in modeling nonlinear
covariate effects and discovering new diseases. We also use WDR to investigate
the age at onset of mild cognitive impairment and interpret the accelerating or
decelerating effects of biomarkers on the progression of Alzheimer's disease.


  We consider representations of the free group $F_2$ on two generators such
that the norm of the sum of the generators and their inverses is bounded by
$\mu\in[0,4]$. These $\mu$-constrained representations determine a C*-algebra
$A_{\mu}$ for each $\mu\in[0,4]$. We prove that these C*-algebras form a
continuous bundle of C*-algebras over $[0,4]$ and calculate their K-groups.


  The classic result of Bulow and Klemperer \cite{BK96} says that in a
single-item auction recruiting one more bidder and running the Vickrey auction
achieves a higher revenue than the optimal auction's revenue on the original
set of bidders, when values are drawn i.i.d. from a regular distribution. We
give a version of Bulow and Klemperer's result in settings where bidders'
values are drawn from non-i.i.d. irregular distributions. We do this by
modeling irregular distributions as some convex combination of regular
distributions. The regular distributions that constitute the irregular
distribution correspond to different population groups in the bidder
population. Drawing a bidder from this collection of population groups is
equivalent to drawing from some convex combination of these regular
distributions. We show that recruiting one extra bidder from each underlying
population group and running the Vickrey auction gives at least half of the
optimal auction's revenue on the original set of bidders.


  A practical notation can convey valuable intuitions and concisely express new
ideas. Information theory is of importance to machine learning, but the
notation for information-theoretic quantities is sometimes opaque. We propose a
practical and unified notation and extend it to include information-theoretic
quantities between observed outcomes (events) and random variables. This
includes the point-wise mutual information known in NLP and mixed quantities
such as specific surprise and specific information in the cognitive sciences
and information gain in Bayesian optimal experimental design. We apply our
notation to prove a version of Stirling's approximation for binomial
coefficients mentioned by MacKa (2003) using new intuitions. We also concisely
rederive the evidence lower bound for variational auto-encoders and variational
inference in approximate Bayesian neural networks. Furthermore, we apply the
notation to a popular information-theoretic acquisition function in Bayesian
active learning which selects the most informative (unlabelled) samples to be
labelled by an expert and extend this acquisition function to the core-set
problem with the goal of selecting the most informative samples given the
labels.


  Let $Q$ be an acyclic quiver. Associated with any element $w$ of the Coxeter
group of $Q$, triangulated categories $\underline{\Sub}\Lambda_w$ were
introduced in \cite{Bua2}. There are shown to be triangle equivalent to
generalized cluster categories $\Cc_{\Gamma_w}$ associated to algebras
$\Gamma_w$ of global dimension $\leq 2$ in \cite{ART}. For $w$ satisfying a
certain property, called co-$c$-sortable, other algebras $A_w$ of global
dimension $\leq 2$ are constructed in \cite{AIRT} with a triangle equivalence
$\Cc_{A_w}\simeq \underline{\Sub}\Lambda_w$. The main result of this paper is
to prove that the algebras $\Gamma_w$ and $A_w$ are derived equivalent when $w$
is co-$c$-sortable. The proof uses the 2-APR-tilting theory introduced in
\cite{IO}.


  Few-shot classification aims to recognize unlabeled samples from unseen
classes given only few labeled samples. The unseen classes and low-data problem
make few-shot classification very challenging. Many existing approaches
extracted features from labeled and unlabeled samples independently, as a
result, the features are not discriminative enough. In this work, we propose a
novel Cross Attention Network to address the challenging problems in few-shot
classification. Firstly, Cross Attention Module is introduced to deal with the
problem of unseen classes. The module generates cross attention maps for each
pair of class feature and query sample feature so as to highlight the target
object regions, making the extracted feature more discriminative. Secondly, a
transductive inference algorithm is proposed to alleviate the low-data problem,
which iteratively utilizes the unlabeled query set to augment the support set,
thereby making the class features more representative. Extensive experiments on
two benchmarks show our method is a simple, effective and computationally
efficient framework and outperforms the state-of-the-arts.


  Recent work on curvilinear structure segmentation has mostly focused on
backbone network design and loss engineering. The challenge of collecting
labelled data, an expensive and labor intensive process, has been overlooked.
While labelled data is expensive to obtain, unlabelled data is often readily
available. In this work, we propose SemiCurv, a semi-supervised learning (SSL)
framework for curvilinear structure segmentation that is able to utilize such
unlabelled data to reduce the labelling burden. Our framework addresses two key
challenges in formulating curvilinear segmentation in a semi-supervised manner.
First, to fully exploit the power of consistency based SSL, we introduce a
geometric transformation as strong data augmentation and then align
segmentation predictions via a differentiable inverse transformation to enable
the computation of pixel-wise consistency. Second, the traditional mean square
error (MSE) on unlabelled data is prone to collapsed predictions and this issue
exacerbates with severe class imbalance (significantly more background pixels).
We propose a N-pair consistency loss to avoid trivial predictions on unlabelled
data. We evaluate SemiCurv on six curvilinear segmentation datasets, and find
that with no more than 5% of the labelled data, it achieves close to 95% of the
performance relative to its fully supervised counterpart.


  Understanding the non-Markovian mechanisms underlying the revivals of quantum
entanglement in the presence of classical environments is central in the theory
of quantum information. Tentative interpretations have been given by either the
role of the environment as a control device or the concept of hidden
entanglement. We address this issue from an information-theoretic point of
view. To this aim, we consider a paradigmatic tripartite system, already
realized in the laboratory, made of two independent qubits and a random
classical field locally interacting with one qubit alone. We study the
dynamical relationship between the two-qubit entanglement and the genuine
tripartite correlations of the overall system, finding that collapse and
revivals of entanglement correspond, respectively, to raise and fall of the
overall tripartite correlations. Interestingly, entanglement dark periods can
enable plateaux of nonzero tripartite correlations. We then explain this
behavior in terms of information flows among the different parties of the
system. Besides showcasing the phenomenon of the freezing of overall
correlations, our results provide new insights on the origin of retrieval of
entanglement within a hybrid quantum-classical system.


  Computer-aided assessment of physical rehabilitation entails evaluation of
patient performance in completing prescribed rehabilitation exercises, based on
processing movement data captured with a sensory system. Despite the essential
role of rehabilitation assessment toward improved patient outcomes and reduced
healthcare costs, existing approaches lack versatility, robustness, and
practical relevance. In this paper, we propose a deep learning-based framework
for automated assessment of the quality of physical rehabilitation exercises.
The main components of the framework are metrics for quantifying movement
performance, scoring functions for mapping the performance metrics into
numerical scores of movement quality, and deep neural network models for
generating quality scores of input movements via supervised learning. The
proposed performance metric is defined based on the log-likelihood of a
Gaussian mixture model, and encodes low-dimensional data representation
obtained with a deep autoencoder network. The proposed deep spatio-temporal
neural network arranges data into temporal pyramids, and exploits the spatial
characteristics of human movements by using sub-networks to process joint
displacements of individual body parts. The presented framework is validated
using a dataset of ten rehabilitation exercises. The significance of this work
is that it is the first that implements deep neural networks for assessment of
rehabilitation performance.


  We propose that wave propagation through a class of mechanical metamaterials
opens unprecedented avenues in seismic wave protection based on spectral
properties of auxetic-like metamaterials. The elastic parameters of these
metamaterials like the bulk and shear moduli, the mass density, and even the
Poisson ratio, can exhibit negative values in elastic stop bands. We show here
that the propagation of seismic waves with frequencies ranging from 1Hz to 40Hz
can be influenced by a decameter scale version of auxetic-like metamaterials
buried in the soil, with the combined effects of impedance mismatch, local
resonances and Bragg stop bands. More precisely, we numerically examine and
illustrate the markedly different behaviors between the propagation of seismic
waves through a homogeneous isotropic elastic medium (concrete) and an
auxetic-like metamaterial plate consisting of 64 cells (40mx40mx40m), utilized
here as a foundation of a building one would like to protect from seismic site
effects. This novel class of seismic metamaterials opens band gaps at
frequencies compatible with seismic waves when they are designed appropriately,
what makes them interesting candidates for seismic isolation structures.


  Given graphs $H$ and $F$, a subgraph $G\subseteq H$ is an $F$-saturated
subgraph of $H$ if $F\nsubseteq G$, but $F\subseteq G+e$ for all $e\in
E(H)\setminus E(G)$. The saturation number of $F$ in $H$, denoted
$\text{sat}(H,F)$, is the minimum number of edges in an $F$-saturated subgraph
of $H$. In this paper we study saturation numbers of tripartite graphs in
tripartite graphs. For $\ell\ge 1$ and $n_1$, $n_2$, and $n_3$ sufficiently
large, we determine $\text{sat}(K_{n_1,n_2,n_3},K_{\ell,\ell,\ell})$ and
$\text{sat}(K_{n_1,n_2,n_3},K_{\ell,\ell,\ell-1})$ exactly and
$\text{sat}(K_{n_1,n_2,n_3},K_{\ell,\ell,\ell-2})$ within an additive constant.
We also include general constructions of $K_{\ell,m,p}$-saturated subgraphs of
$K_{n_1,n_2,n_3}$ with few edges for $\ell\ge m\ge p>0$.


  Bochner's theorem says that if $M$ is a compact Riemannian manifold with
negative Ricci curvature, then the isometry group $\operatorname{Iso}(M)$ is
finite. In this article, we show that if $(X,d,m)$ is a compact metric measure
space with synthetic negative Ricci curvature in Sturm's sense, then the
measure preserving isometry group $\operatorname{Iso}(X,d,m)$ is finite. We
also give an effective estimate on the order of the measure preserving isometry
group for a compact weighted Riemannian manifold with negative Bakry-\'Emery
Ricci curvature except for small portions.


  We show that simple coverings of B^4 branched over ribbon surfaces up to
certain local ribbon moves bijectively represent orientable 4-dimensional
2-handlebodies up to handle sliding and addition/deletion of cancelling
handles. As a consequence, we obtain an equivalence theorem for simple
coverings of S^3 branched over links, in terms of local moves. This result
generalizes to coverings of any degree results by the second author and
Apostolakis, concerning respectively the case of degree 3 and 4. We also
provide an extension of our equivalence theorem to possibly non-simple
coverings of S^3 branched over embedded graphs. This work represents the first
part of our study of 4-dimensional 2-handlebodies. In the second part
(arXiv:math.GT/0612806), we factor such bijective correspondence between simple
coverings of B^4 branched over ribbon surfaces and orientable 4-dimensional
2-handlebodies through a map onto the closed morphisms in a universal braided
category freely generated by a Hopf algebra object.


  We show that the four-wave mixing can restrict spectral broadening. This is a
general physical phenomenon that occurs in one-dimensional systems of four wave
packets that resonantly interact "2-to-2": $
\omega_1+\omega_2=\omega_3+\omega_4,\; k_1+k_2=k_3+k_4$, when an annihilation
of one pair of waves results in the creation of another pair. In addition, for
this phenomenon to occur, the group velocities $C_1,C_2,C_3,C_4$ of the packets
should be in a certain order: The extreme value (max or min) of the four group
velocities should be in the same pair with the middle value of the remaining
three, e.g. $C_1<C_3<C_2<C_4$. This phenomenon is due to the presence of an
extra invariant, in addition to the energy, momentum, and Manley-Rowe
relations.


  We prove that if the geodesic flow on a surface has an integral,
fractional-linear in momenta, then the dimension of the space of such integrals
is either 3 or 5, the latter case corresponding to constant gaussian curvature.
We give also a geometric criterion for existence of fractional-linear
integrals: such integral exists if and only if the surface carries a geodesic
4-web with constant cross-ratio of the four directions tangent to the web
leaves.


  By June of 2020, the extended ROentgen Survey with an Imaging Telescope Array
(eROSITA) on board the Spectrum Roentgen Gamma observatory had completed its
first of the planned eight X-ray all-sky survey (eRASS1). The large effective
area of the X-ray telescope makes it ideal for a survey of the faint X-ray
diffuse emission over half of the sky with an unprecedented energy resolution
and position accuracy. In this work, we produce the X-ray diffuse emission maps
of the eRASS1 data with a current calibration, covering the energy range from
0.2 to 8.0 keV. We validated these maps by comparison with X-ray background
maps derived from the ROSAT All Sky Survey (RASS). We generated X-ray images
with a pixel area of 9 arcmin$^2$ using the observations available to the
German eROSITA consortium. The contribution of the particle background to the
photons was subtracted from the final maps. We also subtracted all the point
sources above a flux threshold dependent on the goal of the subtraction,
exploiting the eRASS1 catalog that will soon be available. The accuracy of the
eRASS1 maps is shown by a flux match to the RASS X-ray maps, obtained by
converting the eROSITA rates into equivalent ROSAT count rates in the standard
ROSAT energy bands R4, R5, R6, and R7, within 1.25$\sigma$. We find small
residual deviations in the R4, R5, and R6 bands, where eROSITA tends to observe
lower flux than ROSAT (~11%), while a better agreement is achieved in the R7
band (~1%). The eRASS maps exhibit lower noise levels than RASS maps at the
same resolution above 0.3 keV. We report the average surface brightness and
total flux of different large sky regions as a reference. The detection of
faint emission from diffuse hot gas in the Milky Way is corroborated by the
consistency of the eRASS1 and RASS maps shown in this paper and by their
comparable flux dynamic range.


  We study numerical restricted volumes of (1,1) classes on compact Kahler
manifolds, as introduced by Boucksom. Inspired by work of
Ein-Lazarsfeld-Mustata-Nakamaye-Popa on restricted volumes of line bundles on
projective manifolds, we pose a natural conjecture to the effect that
irreducible components of the non-Kahler locus of a big class should have
vanishing numerical restricted volume. We prove this conjecture when the class
has a Zariski decomposition, and give several applications.


  We introduce new complex analytic integral transforms, the Lisbon Integrals,
which naturally arise in the study of the affine space $\mathbb{C}^k$ of
unitary polynomials $P_s(z)$ where $s\in\mathbb{C}^k$ and $z\in \mathbb{C}$,
$s_i$ identified to the $i-$th symmetric function of the roots of $P_s(z)$. We
completely determine the $\mathcal{D}$-modules (or systems of partial
differential equations) the Lisbon Integrals satisfy and prove that they are
their unique global solutions. If we specify a holomorphic function $f$ in the
$z$-variable, our construction induces an integral transform which associates a
regular holonomic module quotient of the sub-holonomic module we computed. We
illustrate this correspondence in the case of a $1$-parameter family of
exponentials $f_t(z) = exp(t z)$ with $t$ a complex parameter.


  The attributes of object contours has great significance for instance
segmentation task. However, most of the current popular deep neural networks do
not pay much attention to the object edge information. Inspired by the human
annotation process when making instance segmentation datasets, in this paper,
we propose Mask Point R-CNN aiming at promoting the neural network's attention
to the object boundary. Specifically, we innovatively extend the original human
keypoint detection task to the contour point detection of any object. Based on
this analogy, we present an contour point detection auxiliary task to Mask
R-CNN, which can boost the gradient flow between different tasks by effectively
using feature fusion strategies and multi-task joint training. As a
consequence, the model will be more sensitive to the edges of the object and
can capture more geometric features. Quantitatively, the experimental results
show that our approach outperforms vanilla Mask R-CNN by 3.8\% on Cityscapes
dataset and 0.8\% on COCO dataset.


  The classical definition of the virial temperature of a galaxy halo excludes
a fundamental contribution to the energy partition of the halo: the kinetic
energy of non-thermal gas motions. Using simulations of low-redshift, $\sim
L^*$ galaxies from the FOGGIE project (Figuring Out Gas & Galaxies In Enzo)
that are optimized to resolve low-density gas, we show that the kinetic energy
of non-thermal motions is roughly equal to the energy of thermal motions. The
simulated FOGGIE halos have $\sim 2\times$ lower bulk temperatures than
expected from a classical virial equilibrium, owing to significant non-thermal
kinetic energy that is formally excluded from the definition of
$T_\mathrm{vir}$. We derive a modified virial temperature explicitly including
non-thermal gas motions that provides a more accurate description of gas
temperatures for simulated halos in virial equilibrium. Strong bursts of
stellar feedback drive the simulated FOGGIE halos out of virial equilibrium,
but the halo gas cannot be accurately described by the standard virial
temperature even when in virial equilibrium. Compared to the standard virial
temperature, the cooler modified virial temperature implies other effects on
halo gas: (i) the thermal gas pressure is lower, (ii) radiative cooling is more
efficient, (iii) O VI absorbing gas that traces the virial temperature may be
prevalent in halos of a higher mass than expected, (iv) gas mass estimates from
X-ray surface brightness profiles may be incorrect, and (v) turbulent motions
make an important contribution to the energy balance of a galaxy halo.


  We present a theoretical framework for a quantitative understanding of the
full doping dependence of the optical spectra of the cuprates. In accord with
experimental observations, the computed spectra show how the high-energy Mott
features continue to persist in the overdoped regime even after the
mid-infrared (MIR) peak originating from the pseudogap has collapsed in a
quantum critical point. In this way, we reconcile the opposing tendencies of
the MIR and Mott peaks to shift in opposite directions in the optical spectra
with increasing doping. The competition between the pseudogap and the Mott gap
also results in rapid loss of spectral weight in the high energy region with
doping.


  The present paper is devoted to modelling of a probability measure of logical
connectives on a quantum logic (QL), via a $G$-map, which is a special map on
it. We follow the work in which the probability of logical conjunction,
disjunction and symmetric difference and their negations for non-compatible
propositions are studied.
  We study such a $ G $-map on quantum logics, which is a probability measure
of a projection and show, that unlike classical (Boolean) logic, probability
measure of projections on a quantum logic are not necessarilly pure
projections.
  We compare properties of a $G$-map on QLs with properties of a probability
measure related to logical connectives on a Boolean algebra.


  OHANA is an interferometric snapshot survey of the gaseous circumstellar
environments of hot stars, carried out by the VLTI group at the Paranal
observatory. It aims to characterize the mass-loss dynamics (winds/disks) at
unexplored spatial scales for many stars. The survey employs the unique
combination of AMBER's high spectral resolution with the unmatched spatial
resolution provided by the VLTI. Because of the spatially unresolved central
OBA-type star, with roughly neutral colour terms, their gaseous environments
are among the easiest objects to be observed with AMBER, yet the extent and
kinematics of the line emission regions are of high astrophysical interest.


  We prove that, for every odd prime number $p$, there are $2p-1$ paramedial
quasigroups of order $p$ and $6p^2-p-1$ paramedial quasigroups of order $p^2$,
up to isomorphism. We present a complete list of those which are simple.