  P. Deligne defined interpolations of the tensor category of representations
of the symmetric group S_n to complex values of n. Namely, he defined tensor
categories Rep(S_t) for any complex t. This construction was generalized by F.
Knop to the case of wreath products of S_n with a finite group. Generalizing
these results, we propose a method of interpolating representations categories
of various algebras containing S_n (such as degenerate affine Hecke algebras,
symplectic reflection algebras, rational Cherednik algebras, etc.) to complex
values of n. We also define the group algebra of S_n for complex n, study its
properties, and propose a Schur-Weyl duality for Rep(S_t). In version 2, same
more details have been added.


  We present first results from the third GRavitational lEnsing Accuracy
Testing (GREAT3) challenge, the third in a sequence of challenges for testing
methods of inferring weak gravitational lensing shear distortions from
simulated galaxy images. GREAT3 was divided into experiments to test three
specific questions, and included simulated space- and ground-based data with
constant or cosmologically-varying shear fields. The simplest (control)
experiment included parametric galaxies with a realistic distribution of
signal-to-noise, size, and ellipticity, and a complex point spread function
(PSF). The other experiments tested the additional impact of realistic galaxy
morphology, multiple exposure imaging, and the uncertainty about a
spatially-varying PSF; the last two questions will be explored in Paper II. The
24 participating teams competed to estimate lensing shears to within systematic
error tolerances for upcoming Stage-IV dark energy surveys, making 1525
submissions overall. GREAT3 saw considerable variety and innovation in the
types of methods applied. Several teams now meet or exceed the targets in many
of the tests conducted (to within the statistical errors). We conclude that the
presence of realistic galaxy morphology in simulations changes shear
calibration biases by $\sim 1$ per cent for a wide range of methods. Other
effects such as truncation biases due to finite galaxy postage stamps, and the
impact of galaxy type as measured by the S\'{e}rsic index, are quantified for
the first time. Our results generalize previous studies regarding sensitivities
to galaxy size and signal-to-noise, and to PSF properties such as seeing and
defocus. Almost all methods' results support the simple model in which additive
shear biases depend linearly on PSF ellipticity.


  The concept of a 'Ballmer Peak' was first proposed in 2007, postulating that
there exists a very specific blood alcohol content which confers superhuman
programming ability. More generally, there is a commonly held belief among
software engineers that coding is easier and more productive after a few
drinks. Using the industry standard for assessment of coding ability, we
conducted a search for such a peak and more generally investigated the effect
of different amounts of alcohol on performance. We conclusively refute the
existence of a specific peak with large magnitude, but with p < 0.001 find that
there was a significant positive effect to a low amount of alcohol - slightly
less than two drinks - on programming ability.


  The evolution and propagation of a partially coherent matter wave (PCMW) is
investigated theoretically by the correlation function method. The ABCD matrix
formalism previously used for a fully coherent matter wave is extended to the
PCMW domain. A new ABCD law is derived, using a tensor method to describe the
evolution of a PCMW. An analytical solution of the first-order correlation
function is obtained that makes the propagation and evolution of a PCMW very
simple and clear. As an example, the propagation of a PCMW in a gravitational
field is calculated numerically.


  Workflow support typically focuses on single simulation experiments. This is
also the case for simulation based on finite element methods. If entire
simulation studies shall be supported, flexible means for intertwining revising
the model, collecting data, executing and analyzing experiments are required.
Artifact-based workflows present one means to support entire simulation
studies, as has been shown for stochastic discrete-event simulation. To adapt
the approach to finite element methods, the set of artifacts, i.e., conceptual
model, requirement, simulation model, and simulation experiment, and the
constraints that apply are extended by new artifacts, such as geometrical
model, input data, and simulation data. Artifacts, their life cycles, and
constraints are revisited revealing features both types of simulation studies
share and those they vary in. Also, the potential benefits of exploiting an
artifact-based workflow approach are shown based on a concrete simulation
study. To those benefits belong guidance to systematically conduct simulation
studies, reduction of effort by automatically executing specific steps, e.g.,
generating and executing convergence tests, and support for the automatic
reporting of provenance.


  Local density fluctuations are expected to scale as a universal power-law
when the system approaches critical point. Such power-law fluctuations are
studied within the framework of intermittency through the measurement of
normalized factorial moments in ($\eta$, $\phi$) phase space. Observations and
results from the intermittency analysis performed for charged particles in
Pb-Pb collisions using PYTHIA8/Angantyr at 2.76 TeV and 5.02 TeV are reported.
We observe no scaling behaviour in the particle generation for any of the
centrality studied in narrow p$_T$ bins. The scaling exponent $\nu$ shows no
dependence on the centrality ranges.


  Discontinuities in relativistic hydrodynamics - shock waves and freeze-out
shocks - are considered across both space-like and time-like hypersurfaces. We
analyze the peculiar features of the freeze-out discontinuities and their
connection to the shock-wave phenomena.


  Recent developments in offline reinforcement learning have uncovered the
immense potential of diffusion modeling, which excels at representing
heterogeneous behavior policies. However, sampling from diffusion policies is
considerably slow because it necessitates tens to hundreds of iterative
inference steps for one action. To address this issue, we propose to extract an
efficient deterministic inference policy from critic models and pretrained
diffusion behavior models, leveraging the latter to directly regularize the
policy gradient with the behavior distribution's score function during
optimization. Our method enjoys powerful generative capabilities of diffusion
modeling while completely circumventing the computationally intensive and
time-consuming diffusion sampling scheme, both during training and evaluation.
Extensive results on D4RL tasks show that our method boosts action sampling
speed by more than 25 times compared with various leading diffusion-based
methods in locomotion tasks, while still maintaining state-of-the-art
performance.


  In some areas of supersymmetry parameter space, sneutrinos are lighter than
the charginos and the next-to-lightest neutralino, and they decay into the
invisible neutrino plus lightest-neutralino channel with probability one. In
such a scenario they can be searched for in decays of charginos that are
pair-produced in e+e- collisions, and in associated sneutrino-chargino
production in photon-electron collisions. The sneutrino properties can be
determined with high accuracy from the edges of the decay energy spectra in the
first case and from threshold scans in the second. In the final part of the
report we investigate the mass difference of sneutrinos and charged sleptons
between the third and the first two generations in seesaw-type models of the
neutrino/sneutrino sector. For a wide range these mass differences are
sensitive to the seesaw scale.


  We study a modified bosonic string theory that has a pressureless ``dust''
field on the string worldsheet. The dust is a real scalar field with unit
gradient which breaks conformal invariance. Hamiltonian analysis reveals a time
reparametrization constraint linear in the dust field momentum and a spatial
diffeomorphism constraint. This feature provides a natural ``dust time" gauge
in analogy with the parametrized particle. In this gauge we give a Fock
quantization of the theory, which is complete and self-consistent in d<26. The
Hamiltonian of the theory is not a constraint; as a consequence the Hilbert
space and mass spectrum are characterized by an additional parameter, and
includes the usual string spectrum as a special case. The other sectors provide
new particle spectra, some of which do not have tachyons.


  We determine the radio size distribution of a large sample of 152 SMGs in
COSMOS that were detected with ALMA at 1.3 mm. For this purpose, we used the
observations taken by the VLA-COSMOS 3 GHz Large Project. One hundred and
fifteen of the 152 target SMGs were found to have a 3 GHz counterpart. The
median value of the major axis FWHM at 3 GHz is derived to be $4.6\pm0.4$ kpc.
The radio sizes show no evolutionary trend with redshift, or difference between
different galaxy morphologies. We also derived the spectral indices between 1.4
and 3 GHz, and 3 GHz brightness temperatures for the sources, and the median
values were found to be $\alpha=-0.67$ and $T_{\rm B}=12.6\pm2$ K. Three of the
target SMGs, which are also detected with the VLBA, show clearly higher
brightness temperatures than the typical values. Although the observed radio
emission appears to be predominantly powered by star formation and supernova
activity, our results provide a strong indication of the presence of an AGN in
the VLBA and X-ray-detected SMG AzTEC/C61. The median radio-emitting size we
have derived is 1.5-3 times larger than the typical FIR dust-emitting sizes of
SMGs, but similar to that of the SMGs' molecular gas component traced through
mid-$J$ line emission of CO. The physical conditions of SMGs probably render
the diffusion of cosmic-ray electrons inefficient, and hence an unlikely
process to lead to the observed extended radio sizes. Instead, our results
point towards a scenario where SMGs are driven by galaxy interactions and
mergers. Besides triggering vigorous starbursts, galaxy collisions can also
pull out the magnetised fluids from the interacting disks, and give rise to a
taffy-like synchrotron-emitting bridge. This provides an explanation for the
spatially extended radio emission of SMGs, and can also cause a deviation from
the well-known IR-radio correlation.


  We determine fundamental systems of invariants for complex solvable rigid Lie
algebras having nonsplit nilradicals of characteristic sequence $(3,1,..,1)$,
these algebras being the natural followers of solvable algebras having
Heisenberg nilradicals. A special case of this allows us to obtain a criterion
to determine the number of functionally independent invariants of rank one
subalgebras of (real or complex) solvable Lie algebras. Finally, we give
examples of the inverse procedure, obtaining fundamental systems of an algebra
starting from rank one subalgebras.


  This is the written version of a talk given by S.K. at the $10^{th}$
International Conference on High Energy and Astroparticle, Constantine,
Algeria. We briefly review the Standard Model (SM) and the major evidences and
main direction of physics beyond the SM (BSM). We introduce supersymmetry, as
one of the well-motivated BSM. Basic introduction to Minimal Supersymmetric
Standard Model (MSSM) is given. We analyze the thermal relic abundance of
lightest neutralino, which is the Lightest Supersymmetric Particle (LSP) in the
MSSM. We show that the combined Large Hadron Collider (LHC) and relic abundance
constraints rule out most of the MSSM parameter space except a very narrow
region. We also review non-minimal SUSY model, based on the gauge group
$SU(3)_C \times SU(2)_L \times U(1)_Y \times U(1)_{B-L}$ (BLSSM), where an
Inverse Seesaw mechanism of light neutrino mass generation is naturally
implemented. The phenomenological implications of this type of model at the
Large Hadron Collider (LHC) are analyzed.


  We decompose U(1) gauge fields into a monopole and photon part across the
phase transition from the confinement to the Coulomb phase. We analyze the
leading Lyapunov exponents of such gauge field configurations on the lattice
which are initialized by quantum Monte Carlo simulations. It turns out that
there is a strong relation between the sizes of the monopole density and the
Lyapunov exponent.


  Federated learning (FL) on heterogeneous data (non-IID data) has recently
received great attention. Most existing methods focus on studying the
convergence guarantees for the global objective. While these methods can
guarantee the decrease of the global objective in each communication round,
they fail to ensure risk decrease for each client. In this paper, to address
the problem,we propose FedCOME, which introduces a consensus mechanism to
enforce decreased risk for each client after each training round. In
particular, we allow a slight adjustment to a client's gradient on the server
side, which generates an acute angle between the corrected gradient and the
original ones of other clients. We theoretically show that the consensus
mechanism can guarantee the convergence of the global objective. To generalize
the consensus mechanism to the partial participation FL scenario, we devise a
novel client sampling strategy to select the most representative clients for
the global data distribution. Training on these selected clients with the
consensus mechanism could empirically lead to risk decrease for clients that
are not selected. Finally, we conduct extensive experiments on four benchmark
datasets to show the superiority of FedCOME against other state-of-the-art
methods in terms of effectiveness, efficiency and fairness. For
reproducibility, we make our source code publicly available at:
\url{https://github.com/fedcome/fedcome}.


  CO observations of the interacting galaxies IC 2163 and NGC 2207 are combined
with HI, Halpha and 24 microns to study the star formation rate (SFR) surface
density as a function of the gas surface density. More than half of the high
SFR regions are HI dominated. When compared to other galaxies, these
HI-dominated regions have excess SFRs relative to their molecular gas surface
densities but normal SFRs relative to their total gas surface densities. The
HI-dominated regions are mostly located in the outer part of NGC 2207, where
the HI velocity dispersion is high, 40 - 50 km/s. We suggest that the
star-forming clouds in these regions have envelopes at lower densities than
normal, making them predominantly atomic, and cores at higher densities than
normal because of the high turbulent Mach numbers. This is consistent with
theoretical predictions of a flattening in the density probability distribution
function for compressive, high Mach number turbulence.


  We explore the relation between the topological relevance of a node in a
complex network and the individual dynamics it exhibits. When the system is
weakly coupled, the effect of the coupling strength against the dynamical
complexity of the nodes is found to be a function of their topological role,
with nodes of higher degree displaying lower levels of complexity. We provide
several examples of theoretical models of chaotic oscillators, pulse-coupled
neurons and experimental networks of nonlinear electronic circuits evidencing
such a hierarchical behavior. Importantly, our results imply that it is
possible to infer the degree distribution of a network only from individual
dynamical measurements.


  With the H1 detector at the ep collider HERA, D* meson production cross
sections have been measured in deep inelastic scattering with four-momentum
transfers Q^2>2 GeV2 and in photoproduction at energies around W(gamma p)~ 88
GeV and 194 GeV. Next-to-Leading Order QCD calculations are found to describe
the differential cross sections within theoretical and experimental
uncertainties. Using these calculations, the NLO gluon momentum distribution in
the proton, x_g g(x_g), has been extracted in the momentum fraction range
7.5x10^{-4}< x_g <4x10^{-2} at average scales mu^2 =25 to 50 GeV2. The gluon
momentum fraction x_g has been obtained from the measured kinematics of the
scattered electron and the D* meson in the final state. The results compare
well with the gluon distribution obtained from the analysis of scaling
violations of the proton structure function F_2.


  We evaluate all two-point correlation functions of the Curci-Ferrari (CF)
model in four dimensions and in the presence of mass-degenerate fundamental
quark flavors, as a natural extension of an earlier investigation in the
quenched approximation. In principle, the proper account of chiral symmetry
breaking ($\chi$SB) and the corresponding dynamical generation of a quark mass
function within the CF model requires one to go beyond perturbation theory
\cite{Pelaez:2020ups}. However, it is interesting to assess whether a
perturbative description applies to correlation functions that are not directly
sensitive to $\chi$SB, such as the gluon, ghost and quark dressing functions.
We compare our two-loop results for these form factors to QCD lattice data in
the two flavor case for two different values of the pion mass, one that is
relatively far from the chiral limit, and one that is closer to the physical
value. Our results confirm that the QCD gluon and ghost dressing functions are
well described by a perturbative approach within the CF model, as already
observed at one-loop order in Ref. \cite{Pelaez:2014mxa}. Our new main result
is that the quark dressing function is also well captured by the perturbative
approach, but only starting at two-loop order, as also anticipated in Ref.
\cite{Pelaez:2014mxa}. The quark mass function predicted by the CF model at
two-loop order is in good agreement with the data if the quarks are not too
light but shows some clear tension with respect to the two-loop CF dressing
functions in the close to physical case, as expected. Interestingly, however,
we find that there is much less tension between the non-perturbative quark mass
function, as it can be obtained from lattice simulations or from
\cite{Pelaez:2020ups}, and the two-loop CF dressing functions, which confirms
the perturbative nature of the latter.


  We propose a novel technique to refine the modelling of galaxy clusters mass
distribution using gravitational lensing. The idea is to combine the strengths
of both "parametric" and "non-parametric" methods to improve the quality of the
fit. We develop a multi-scale model that allows sharper contrast in regions of
higher density where the number of constraints is generally higher. Our model
consists of (i) a multi-scale grid of radial basis functions with physically
motivated profiles and (ii) a list of galaxy-scale potentials at the location
of the cluster member galaxies. This arrangement of potentials of different
sizes allows to reach a high resolution for the model with a minimum number of
parameters. We apply our model to the well studied cluster Abell 1689. We
estimate the quality of our mass reconstruction with a Bayesian MCMC sampler.
For a selected subset of multiple images, we manage to halve the errors between
the predicted and observed image positions compared to previous studies. This
owes to the flexibility of multi-scale models at intermediate scale between
cluster and galaxy scale. The software developed for this paper is part of the
public lenstool package which can be found at www.oamp.fr/cosmology/lenstool.


  The paper analyzes the socio-economic impacts of dropshipping - a new form of
organization of sales, is rapidly gaining the Russian market. Dropshipping
opens up tremendous prospects not only for ordinary people, but also for the
Russian manufacturers, which if used properly can dropshipping opportunities
with minimal direct access to the world market.


  In these lectures I will discuss the following topics:
  (1) Twistors in 4 flat dimensions: Massless particles; constrained phase
space (x,p) versus twistors; Physical states in twistor space.
  (2) Introduction to 2T-physics and derivation of 1T-physics holographs and
twistors: Emergent spacetimes & dynamics, holography, duality; Sp(2,R) gauge
symmetry, constraints, solutions and (d,2); Global symmetry, quantization and
the SO(d,2) singleton.
  (3) Twistors for particle dynamics in d dimensions, particles with mass,
relativistic, non-relativistic, in curved spaces, with interactions.
  (4)Supersymmetric 2T-physics, gauge symmetries & twistor gauge: Coupling
(X,P,g), gauge symmetries, global symmetries; Covariant quantization,
constrained generators & representations of G_(super); Twistor gauge,
supertwistors dual to super phase space, examples in d=4,6,10,11.
  (5) Supertwistors and some field theory spectra in d=4,6: Super Yang-Mills
d=4, N=4; Supergravity d=4, N=8; Self-dual tensor supermultiplet and conformal
theory in d=6.
  (6) Twistor superstrings: d+2 view of twistor superstring in d=4; Worldsheet
anomalies and quantization of twistor superstring; Open problems.


  We propose new planar X-junctions and multi-port devices written by spatial
solitons, which are composed of two (or more) nonlinearly coupled components in
Kerr-type media. Such devices have no radiation losses at a given wavelength.
We demonstrate that, for the same relative angle between the channels of the
X-junctions, one can vary the transmission coefficients into the output
channels by adjusting the polarizations of multi-component solitons. We
determine analytically the transmission properties and suggest two types of
experimental embodiments of the proposed device.


  The inelastic scattering of neutrons from magnetic excitations in the
antiferromagnetic phase of the langasite compound Ba3NbFe3Si2O14 is analyzed
theoretically. In the calculations presented, the strongly coupled spin-5/2 Fe
triangles are accounted for as trimerized units. The weaker interactions
between the trimers are included within the mean-field/random-phase
approximation. The theory is compared with linear spin-wave theory, and a model
is developed which leads to good agreement with the published results from
unpolarized and polarized neutron-scattering experiments.


  Applications such as Magnetic Resonance Tomography acquire imaging data by
point samples of their Fourier transform. This raises the question of balancing
the efficiency of the sampling strategies with the approximation accuracy of an
associated reconstruction procedure. In this paper, we introduce a novel
sampling-reconstruction scheme based on a random anisotropic sampling pattern
and a compressed sensing type reconstruction strategy with a variant of
dualizable shearlet frames as sparsifying representation system. For this
scheme, we prove asymptotic optimality in an approximation theoretic sense for
cartoon-like functions as a model class for the imaging data. Finally, we
present numerical experiments showing the superiority of our scheme over other
approaches.


  This paper studies two classes of sampling methods for the solution of
inverse problems, namely Randomize-Then-Optimize (RTO), which is rooted in
sensitivity analysis, and Langevin methods, which are rooted in the Bayesian
framework. The two classes of methods correspond to different assumptions and
yield samples from different target distributions. We highlight the main
conceptual and theoretical differences between the two approaches and compare
them from a practical point of view by tackling two classical inverse problems
in imaging: deblurring and inpainting. We show that the choice of the sampling
method has a significant impact on the quality of the reconstruction and that
the RTO method is more robust to the choice of the parameters.


  The internal conversion coefficients (ICC) were calculated for all atomic
subshells of the elements with 104<=Z<=126, the E1...E4, M1...M4
multipolarities and the transition energies between 10 and 1000 keV. The atomic
screening was treated in the relativistic Hartree-Fock-Slater model. The Tables
comprising almost 90000 subshell and total ICC were recently deposited at LANL
preprint server.


  The existence of initial singularities in expanding universes is proved
without assuming the timelike convergence condition. The assumptions made in
the proof are ones likely to hold both in open universes and in many closed
ones. (It is further argued that at least some of the expanding closed
universes that do not obey a key assumption of the theorem will have initial
singularities on other grounds.) The result is significant for two reasons:
(a)~previous closed-universe singularity theorems have assumed the timelike
convergence condition, and (b)~the timelike convergence condition is known to
be violated in inflationary spacetimes. An immediate consequence of this
theorem is that a recent result on initial singularities in open,
future-eternal, inflating spacetimes may now be extended to include many closed
universes. Also, as a fringe benefit, the time-reverse of the theorem may be
applied to gravitational collapse.


  Recommender systems are widely used in industry to improve user experience.
Despite great success, they have recently been criticized for collecting
private user data. Federated Learning (FL) is a new paradigm for learning on
distributed data without direct data sharing. Therefore, Federated Recommender
(FedRec) systems are proposed to mitigate privacy concerns to non-distributed
recommender systems. However, FedRec systems have a performance gap to its
non-distributed counterpart. The main reason is that local clients have an
incomplete user-item interaction graph, thus FedRec systems cannot utilize
indirect user-item interactions well. In this paper, we propose the Federated
Graph Recommender System (FedGRec) to mitigate this gap. Our FedGRec system can
effectively exploit the indirect user-item interactions. More precisely, in our
system, users and the server explicitly store latent embeddings for users and
items, where the latent embeddings summarize different orders of indirect
user-item interactions and are used as a proxy of missing interaction graph
during local training. We perform extensive empirical evaluations to verify the
efficacy of using latent embeddings as a proxy of missing interaction graph;
the experimental results show superior performance of our system compared to
various baselines. A short version of the paper is presented in
\href{https://federated-learning.org/fl-neurips-2022/}{the FL-NeurIPS'22
workshop}.


  Oxygen and zinc in the Galactic bulge are key elements for the understanding
of the bulge chemical evolution. Oxygen-to-iron abundance ratios provide a most
robust indicator of the star formation rate and chemical evolution of the
bulge. Zinc is enhanced in metal-poor stars, behaving as an $\alpha$-element,
and its production may require nucleosynthesis in hypernovae. Most of the
neutral gas at high redshift is in damped Lyman-alpha systems (DLAs), where Zn
is also observed to behave as an alpha-element. The aim of this work is the
derivation of the alpha-element oxygen, together with nitrogen, and the
iron-peak element zinc abundances in 417 bulge giants, from moderate resolution
(R~22,000) FLAMES-GIRAFFE spectra. For stars in common with a set of UVES
spectra with higher resolution (R~45,000), the data are intercompared. The
results are compared with literature data and chemodynamical models.


  Information-Centric Networking (ICN) specifically Name Data Networking (NDN)
is the name-base (content-base) networking and takes named-contents as "first
class citizen", being considered as the ideal candidate to form the Future
Internet basis. NDN striking features like named-data self-secured contents,
name-base-forwarding, in-network caching and mobility support suits the
Internet of Things (IoT) environment, which aims to enable communication among
smart devices and to combine all Internet-based smart applications under the
one roof. With these aims, IoT put many research challenges regarding its
network architecture as it should support heterogeneous devices and offer
scalability. IoT may depend on the names and addresses of billions of the
devices and should smartly manage the bulk of data produced every second. IoT
application smart campus has gained a lot of attention in both industry and
academia due to many reasons. Therefore, to design NDN for IoT, a sophisticated
naming scheme is needed to explore and it is the main motivation for this work.
In this paper, we study NDN-IoT smart campus (in terms of connected devices and
contents) and find that it lacks in a reasonable naming and addressing
mechanism; and thus we propose NDN based Hybrid Naming Scheme (NDN-HNS) for IoT
based Smart Campus (IoTSC).


  We address the cosmological moduli/gravitino problems and the issue of too
little thermal but excessive non-thermal dark matter from the decays of moduli.
The main examples we study are the G2-MSSM models arising from M theory
compactifications, which allow for a precise calculation of moduli decay rates
and widths. We find that the late decaying moduli satisfy both BBN constraints
and avoid the gravitino problem. The non-thermal production of wino LSPs, which
is a prediction of G2-MSSM models, gives a relic density of about the right
order of magnitude.


  A gauge invariant metric fluctuations formalism from a non-compact
Kaluza-Klein (NKK) theory of gravity is presented in this talk notes. In this
analysis we recover the well-known result $\frac{delta \rho}{\rho}\simeq 2\Phi$
obtained typically in the standard 4D semiclassical approach to inflation and
also the spectrum of this fluctuations becomes dependent of the fifth
(space-like) coordinate. This fact allows to establish an interval of values
for the wave number associated with the fifth dimension.


  The combination of conduct, emotion, motivation, and thinking is referred to
as personality. To shortlist candidates more effectively, many organizations
rely on personality predictions. The firm can hire or pick the best candidate
for the desired job description by grouping applicants based on the necessary
personality preferences. A model is created to identify applicants' personality
types so that employers may find qualified candidates by examining a person's
facial expression, speech intonation, and resume. Additionally, the paper
emphasises detecting the changes in employee behaviour. Employee attitudes and
behaviour towards each set of questions are being examined and analysed. Here,
the K-Modes clustering method is used to predict employee well-being, including
job pressure, the working environment, and relationships with peers, utilizing
the OCEAN Model and the CNN algorithm in the AVI-AI administrative system.
Findings imply that AVIs can be used for efficient candidate screening with an
AI decision agent. The study of the specific field is beyond the current
explorations and needed to be expanded with deeper models and new
configurations that can patch extremely complex operations.


  Contracting Universe (including bouncing models) solution generally depends
on the initial conditions and hence possesses an extreme fine-tuning problem.
In order to probe the stability of those solutions, in this work, we consider
the Brans-Dicke theory with the power law potential in the presence of an
additional barotropic matter in the homogeneous and isotropic background. We
study the phase space and obtain critical points. We find that the quadratic
potential is a special case where one of the solutions always gives rise to
de-Sitter solution in all conformally connected frame. We generalize the
condition for arbitrary power law potential and find that contracting Universe
solution can indeed lead to an attractor solution. In doing so, we also provide
an example of a matter contracting Universe that leads to near scale-invariant
spectra and study the behavior near the fixed point. In the vicinity of this
point, the system behaves as the Universe contains three different types of
matter. Amongst them, with time, energy densities of two effective fluids decay
down and only the leading order solution survives. Therefore, the non-minimal
coupling can address and solve the problem of fine-tuning of the contraction
models and may open a different outlook.


  Many real-world experimental design problems (a) evaluate multiple
experimental conditions in parallel and (b) replicate each condition multiple
times due to large and heteroscedastic observation noise. Given a fixed total
budget, this naturally induces a trade-off between evaluating more unique
conditions while replicating each of them fewer times vs. evaluating fewer
unique conditions and replicating each more times. Moreover, in these problems,
practitioners may be risk-averse and hence prefer an input with both good
average performance and small variability. To tackle both challenges, we
propose the Batch Thompson Sampling for Replicable Experimental Design
(BTS-RED) framework, which encompasses three algorithms. Our BTS-RED-Known and
BTS-RED-Unknown algorithms, for, respectively, known and unknown noise
variance, choose the number of replications adaptively rather than
deterministically such that an input with a larger noise variance is replicated
more times. As a result, despite the noise heteroscedasticity, both algorithms
enjoy a theoretical guarantee and are asymptotically no-regret. Our
Mean-Var-BTS-RED algorithm aims at risk-averse optimization and is also
asymptotically no-regret. We also show the effectiveness of our algorithms in
two practical real-world applications: precision agriculture and AutoML.


  The concept of arithmetic root systems is introduced. It is shown that there
is a one-to-one correspondence between arithmetic root systems and Nichols
algebras of diagonal type having a finite set of (restricted)
Poincare'-Birkhoff-Witt generators. This has strong consequences for both
objects. As an application all rank 2 Nichols algebras of diagonal type having
a finite set of (restricted) Poincare'-Birkhoff-Witt generators are determined.
  Key Words: Brandt groupoid, Hopf algebra, pseudo-reflections, Weyl group


  Let $X$ be a smooth projective real algebraic variety. We give new positive
and negative results on the problem of approximating a submanifold of the real
locus of $X$ by real loci of subvarieties of $X$, as well as on the problem of
determining the subgroups of the Chow groups of $X$ generated by subvarieties
with nonsingular real loci, or with empty real loci.


  Impactful applications such as materials discovery, hardware design, neural
architecture search, or portfolio optimization require optimizing
high-dimensional black-box functions with mixed and combinatorial input spaces.
While Bayesian optimization has recently made significant progress in solving
such problems, an in-depth analysis reveals that the current state-of-the-art
methods are not reliable. Their performances degrade substantially when the
unknown optima of the function do not have a certain structure. To fill the
need for a reliable algorithm for combinatorial and mixed spaces, this paper
proposes Bounce that relies on a novel map of various variable types into
nested embeddings of increasing dimensionality. Comprehensive experiments show
that Bounce reliably achieves and often even improves upon state-of-the-art
performance on a variety of high-dimensional problems.


  Recent 3D face reconstruction methods have made remarkable advancements, yet
there remain huge challenges in monocular high-quality facial reflectance
reconstruction. Existing methods rely on a large amount of light-stage captured
data to learn facial reflectance models. However, the lack of subject diversity
poses challenges in achieving good generalization and widespread applicability.
In this paper, we learn the reflectance prior in image space rather than UV
space and present a framework named ID2Reflectance. Our framework can directly
estimate the reflectance maps of a single image while using limited reflectance
data for training. Our key insight is that reflectance data shares facial
structures with RGB faces, which enables obtaining expressive facial prior from
inexpensive RGB data thus reducing the dependency on reflectance data. We first
learn a high-quality prior for facial reflectance. Specifically, we pretrain
multi-domain facial feature codebooks and design a codebook fusion method to
align the reflectance and RGB domains. Then, we propose an identity-conditioned
swapping module that injects facial identity from the target image into the
pre-trained autoencoder to modify the identity of the source reflectance image.
Finally, we stitch multi-view swapped reflectance images to obtain renderable
assets. Extensive experiments demonstrate that our method exhibits excellent
generalization capability and achieves state-of-the-art facial reflectance
reconstruction results for in-the-wild faces. Our project page is
https://xingyuren.github.io/id2reflectance/.


  Deep image prior (DIP) has recently attracted attention owing to its
unsupervised positron emission tomography (PET) image reconstruction, which
does not require any prior training dataset. In this paper, we present the
first attempt to implement an end-to-end DIP-based fully 3D PET image
reconstruction method that incorporates a forward-projection model into a loss
function. To implement a practical fully 3D PET image reconstruction, which
could not be performed due to a graphics processing unit memory limitation, we
modify the DIP optimization to block-iteration and sequentially learn an
ordered sequence of block sinograms. Furthermore, the relative difference
penalty (RDP) term was added to the loss function to enhance the quantitative
PET image accuracy. We evaluated our proposed method using Monte Carlo
simulation with [$^{18}$F]FDG PET data of a human brain and a preclinical study
on monkey brain [$^{18}$F]FDG PET data. The proposed method was compared with
the maximum-likelihood expectation maximization (EM), maximum-a-posterior EM
with RDP, and hybrid DIP-based PET reconstruction methods. The simulation
results showed that the proposed method improved the PET image quality by
reducing statistical noise and preserved a contrast of brain structures and
inserted tumor compared with other algorithms. In the preclinical experiment,
finer structures and better contrast recovery were obtained by the proposed
method. This indicated that the proposed method can produce high-quality images
without a prior training dataset. Thus, the proposed method is a key enabling
technology for the straightforward and practical implementation of end-to-end
DIP-based fully 3D PET image reconstruction.


  We prove that $n$-sphere $\mathbb{S}^n$, $n\geq 2$, admits structurally
stable diffeomorphisms $\mathbb{S}^n\to\mathbb{S}^n$ with non-orientable
expanding attractors of any topological dimension
$d\in\{1,\ldots,[\frac{n}{2}]\}$ where $[x]$ is an integer part of $x$. One
proves that $n$-torus $\mathbb{T}^n$, $n\geq 2$, admits structurally stable
diffeomorphisms $\mathbb{T}^n\to\mathbb{T}^n$ with orientable expanding
attractors of any topological dimension $1\leq q\leq n-1$. We also prove that
given any closed $n$-manifold $M^n$, $n\geq 2$, and any
$d\in\{1,\ldots,[\frac{n}{2}]\}$, there is an axiom A diffeomorphism $f: M^n\to
M^n$ with a $d$-dimensional non-orientable expanding attractor. Similar
statements hold for axiom A flows.


  With the decline of fossil fuel reserves and the escalating global average
temperature, the quest for environmentally friendly and renewable energy
sources has gained significant momentum. Focus has turned to wind and
photovoltaic energy, but their variable inputs necessitate energy storage for
reliable power. Economic viability of hybrid renewable power requires
meticulous optimization of generating units to ensure uninterrupted and
efficient energy production. This paper presents an optimal sizing approach for
a Wind-Photovoltaic-Biogas-Battery system using a single objective optimization
(SOO) method. A comprehensive comparative analysis is conducted, evaluating the
convergence speed and objective mean (for minimization) of seven metaheuristic
optimizers: Particle Swarm Optimization (PSO), Aquila Optimizer (AO), Pelican
Optimization Algorithm (POA), Dandelion Optimizing Algorithm (DOA), Gazelle
Optimization Algorithm (GOA), Zebra Optimization Algorithm (ZOA), and Osprey
Optimization Algorithm (OOA). The results demonstrate that the Pelican
Optimization Algorithm (POA) outperforms other existing algorithms, exhibiting
faster convergence and lower objective mean.


  Objective: To develop an algorithm that can infer the severity level of a
COPD patient's airflow limitation from tidal breathing data that is collected
by a wearable device.
  Methods: Data was collected from 25 single visit adult volunteers with a
confirmed or suspected diagnosis of chronic obstructive pulmonary disease
(COPD). The ground truth airflow limitation severity of each subject was
determined by applying the Global Initiative for Chronic Obstructive Lung
Disease (GOLD) staging criteria to the subject's spirometry results. Spirometry
was performed in a pulmonary function test laboratory under the supervision of
trained clinical staff. Separately, the subjects' respiratory signal was
measured during quiet breathing, and a classification model was built to infer
the subjects' level of airflow limitation from the measured respiratory signal.
The classification model was evaluated against the ground truth using
leave-one-out testing.
  Results: Severity of airway obstruction was classified as either
mild/moderate or severe/very severe with an accuracy of 96.4%.
  Conclusion: Tidal breathing parameters that are measured with a wearable
device can be used to distinguish between different levels of airflow
limitation in COPD patients.


  We consider a gradient flow associated to the mean field equation on $(M,g)$
a compact riemanniann surface without boundary. We prove that this flow exists
for all time. Moreover, letting $G$ be a group of isometry acting on $(M,g)$,
we obtain the convergence of the flow to a solution of the mean field equation
under suitable hypothesis on the orbits of points of $M$ under the action of
$G$.


  Real-time systems are a set of programs, a scheduling policy and a system
architecture, constrained by timing requirements. Most of daily embedded
devices are real-time systems, e.g. airplanes, cars, trains, spatial probes,
etc. The time required by a program for its end-to-end execution is called its
response time. Usually, upper-bounds of response times are computed in order to
provide safe deadline miss probabilities. In this paper, we propose a suited
re-parametrization of the inverse Gaussian mixture distribution adapted to
response times of real-time systems and the estimation of deadline miss
probabilities. The parameters and their associated deadline miss probabilities
are estimated with an adapted Expectation-Maximization algorithm.


  We show the following bounds on the prime counting function $\pi(x)$ using
principles from analytic number theory, giving an estimate: $$2 \log 2 \geq
\limsup_{x \rightarrow \infty} \frac{\pi(x)}{x / \log x} \geq \liminf_{x
\rightarrow \infty} \frac{\pi(x)}{x / \log x} \geq \log 2$$ for all $x$
sufficiently large. We also conjecture about the bounding of $\pi((x+1)^{2}) -
\pi(x^{2})$, as is relevant to Legendre's conjecture about the number of primes
in the aforementioned interval such that: $$ \left
\lfloor\frac{1}{2}\left(\frac{\left(x+1\right)^{2}}{\log\left(x+1\right)}-\frac{x^{2}}{\log
x}\right)-\frac{\left(\log x\right)^{2}}{\log\left(\log x\right)}\right \rfloor
\leq \pi((x+1)^{2}) - \pi(x^{2}) \leq $$ $$ \left
\lfloor\frac{1}{2}\left(\frac{\left(x+1\right)^{2}}{\log\left(x+1\right)}-\frac{x^{2}}{\log
x}\right) + \log^{2}x\log\log x \right \rfloor$$


  In this study, we obtained the position-momentum uncertainties and some
uncertainty relations for the P\"oschl-Teller-type potential for any $\ell$.
The radial expectation values of $r^{-2}$, $r^{2}$ and $p^{2}$ are obtained
from which the Heisenberg Uncertainty principle holds for the potential model
under consideration. The Fisher information is then obtained and it is observed
that the Fisher-information-based uncertainty relation and the Cramer-Rao
inequality hold for this even power potential. Some numerical and graphical
results are displayed.


  There are many recent research efforts to fine-tune a pre-trained generator
with a few target images to generate images of a novel domain. Unfortunately,
these methods often suffer from overfitting or under-fitting when fine-tuned
with a single target image. To address this, here we present a novel
single-shot GAN adaptation method through unified CLIP space manipulations.
Specifically, our model employs a two-step training strategy: reference image
search in the source generator using a CLIP-guided latent optimization,
followed by generator fine-tuning with a novel loss function that imposes CLIP
space consistency between the source and adapted generators. To further improve
the adapted model to produce spatially consistent samples with respect to the
source generator, we also propose contrastive regularization for patchwise
relationships in the CLIP space. Experimental results show that our model
generates diverse outputs with the target texture and outperforms the baseline
models both qualitatively and quantitatively. Furthermore, we show that our
CLIP space manipulation strategy allows more effective attribute editing.


  Rydberg atoms, with one highly-excited, nearly-ionized electron, have extreme
sensitivity to electric fields, including microwave fields ranging from 100 MHz
to over 1 THz. Here we show that room-temperature Rydberg atoms can be used as
sensitive, high bandwidth, microwave communication antennas. We demonstrate
near photon-shot-noise limited readout of data encoded in amplitude-modulated
17 GHz microwaves, using an electromagnetically-induced-transparency (EIT)
probing scheme. We measure a photon-shot-noise limited channel capacity of up
to 8.2 Mbit/s and implement an 8-state phase-shift-keying digital communication
protocol. The bandwidth of the EIT probing scheme is found to be limited by the
available coupling laser power and the natural linewidth of the rubidium D2
transition. We discuss how atomic communications receivers offer several
opportunities to surpass the capabilities of classical antennas.


  The CUPID-Mo experiment to search for 0$\nu\beta\beta$ decay in $^{100}$Mo
has been recently completed after about 1.5 years of operation at Laboratoire
Souterrain de Modane (France). It served as a demonstrator for CUPID, a next
generation 0$\nu\beta\beta$ decay experiment. CUPID-Mo was comprised of 20
enriched Li$_2$$^{100}$MoO$_4$ scintillating calorimeters, each with a mass of
$\sim$ 0.2 kg, operated at $\sim$20 mK. We present here the final analysis with
the full exposure of CUPID-Mo ($^{100}$Mo exposure of 1.47 kg$\times$yr) used
to search for lepton number violation via 0$\nu\beta\beta$ decay. We report on
various analysis improvements since the previous result on a subset of data,
reprocessing all data with these new techniques. We observe zero events in the
region of interest and set a new limit on the $^{100}$Mo 0$\nu\beta\beta$ decay
half-life of $T^{0\nu}_{1/2} > 1.8 \times 10^{24}$ year (stat.+syst.) at 90%
CI. Under the light Majorana neutrino exchange mechanism this corresponds to an
effective Majorana neutrino mass of $\left<m_{\beta \beta}\right> <
(0.28$--$0.49)$ eV, dependent upon the nuclear matrix element utilized.


  We describe the calculation of the two--loop massive operator matrix elements
for massive external fermions. These matrix elements are needed for the
calculation of the $O(\alpha^2)$ initial state radiative corrections to
$e^+e^-$ annihilation into a neutral virtual gauge boson, based on the
renormalization group technique.


  We propose a new spectral method, based on two classes of hat functions, for
solving systems of fractional differential equations. The fractional derivative
is considered in the Caputo sense. Properties of the basis functions, Caputo
derivatives, and Riemann-Liouville fractional integrals, are used to reduce the
main problem to a system of nonlinear algebraic equations. By analyzing in
detail the resulting system, we show that the method needs few computational
efforts. Two test problems are considered to illustrate the efficiency and
accuracy of the proposed method. Finally, an application to a recent
mathematical model in epidemiology is given, precisely to a system of
fractional differential equations modeling the respiratory syncytial virus
infection.


  The utilization of traffic conflict indicators is crucial for assessing
traffic safety, especially when the crash data is unavailable. To identify
traffic conflicts based on traffic flow characteristics across various traffic
states, we propose a framework that utilizes unsupervised learning to
automatically establish surrogate safety measures (SSM) thresholds. Different
traffic states and corresponding transitions are identified with the
three-phase traffic theory using high-resolution trajectory data. Meanwhile,
the SSMs are mapped to the corresponding traffic states from the perspectives
of time, space, and deceleration. Three models, including k-means, GMM, and
Mclust, are investigated and compared to optimize the identification of traffic
conflicts. It is observed that Mclust outperforms the others based on the
evaluation metrics. According to the results, there is a variation in the
distribution of traffic conflicts among different traffic states, wide moving
jam (phase J) has the highest conflict risk, followed by synchronous flow
(phase S), and free flow (phase F). Meanwhile, the thresholds of traffic
conflicts cannot be fully represented by the same value through different
traffic states. It reveals that the heterogeneity of thresholds is exhibited
across traffic state transitions, which justifies the necessity of dynamic
thresholds for traffic conflict analysis.


  We report on the structural and magnetic characterization of Co0.1Zn0.9O and
Mn0.1Zn0.9O nanopowders obtained by a soft chemistry route. We show that those
samples fired at low temperatures display a ferromagnetic interaction that can
not be attributed to the presence of impurities. A magnetic aging mechanism is
observed, reflecting the key role played by defects in the stabilization of
ferromagnetism in this kind of diluted magnetic semiconductors.


  We recover the spatially resolved star formation history across the entire
main body and Wing of the Small Magellanic Cloud (SMC), using fourteen deep
tile images from the VISTA survey of the Magellanic Clouds (VMC), in the YJKs
filters. The analysis is performed on 168 subregions of size 0.143 deg2,
covering a total contiguous area of 23.57 deg2. We apply a colour-magnitude
diagram (CMD) reconstruction method that returns the best-fitting star
formation rate SFR(t), age--metallicity relation, distance and mean reddening,
together with their confidence intervals, for each subregion. With respect to
previous analyses, we use a far larger set of VMC data, updated stellar models,
and fit the two available CMDs (Y-Ks versus Ks and J-Ks versus Ks)
independently. The results allow us to derive a more complete and more reliable
picture of how the mean distances, extinction values, star formation rate, and
metallicities vary across the SMC, and provide a better description of the
populations that form its Bar and Wing. We conclude that the SMC has formed a
total mass of (5.31+-0.05)x10^8 Msun in stars over its lifetime. About two
thirds of this mass is expected to be still locked in stars and stellar
remnants. 50 per cent of the mass was formed prior to an age of 6.3 Gyr, and 80
per cent was formed between 8 and 3.5 Gyr ago. We also illustrate the likely
distribution of stellar ages and metallicities in different parts of the CMD,
to aid the interpretation of data from future astrometric and spectroscopic
surveys of the SMC.


  We present a simple choice of integration variables that can be used to
exploit the near-integrable character of problems in celestial mechanics. The
approach is based on the well-known principle of variation of parameters:
instead of orbital elements, we use the phase-space coordinates the object
would have at a given point in its (Keplerian) orbit if the perturbing forces
were removed. This formulation is suitable for almost any numerical integrator;
thus, multistep schemes are easy to build, stepsize can be adjusted, and
dissipative forces are allowed. Compared with traditional non-symplectic N-body
integrators, the approach often offers increase in speed or accuracy if
perturbations are small.


  We show that the odd-primary Brown-Peterson spectrum $\mathrm{BP}$ does not
admit the structure of an $\mathbb{E}_{2(p^2+2)}$ ring spectrum and that there
can be no map $\mathrm{MU} \to \mathrm{BP}$ of $\mathbb{E}_{2p+3}$ ring
spectra. We also prove the same results for truncated Brown-Peterson spectra
$\mathrm{BP} \langle n \rangle$ of height $n \geq 4$. This extends results of
Lawson at the prime $2$.


  Measurements of time delays between multiple quasar images produced by strong
lensing are reaching a sensitivity that makes them a promising cosmological
probe. Future surveys will provide significantly more measurements, reaching
unprecedented depth in redshift, making strong lensing time delay (SLTD)
observations competitive with other background probes. We forecast constraints
on the nature of dark energy from upcoming SLTD surveys, simulating future
catalogues with different numbers of lenses distributed up to redshift $z\sim
1$ and focusing on cosmological parameters such as the Hubble constant $H_0$
and parametrisations of the dark energy equation of state. We also explore the
impact of our ability to precisely model the lens mass profile and its
environment, on the forecasted constraints. We find that in the most optimistic
cases, SLTD will constrain $H_0$ at the level of $\sim 0.1\%$, while the CPL
equation of state parameters, $w_0$ and $w_a$, can be determined with errors
$\sigma_{w_0}\sim 0.05$ and $\sigma_{w_a}\sim 0.3$, respectively. Furthermore,
we investigate the bias introduced when a wrong cosmological model is assumed
for the analysis. We find that the value of $H_0$ could be biased up to $10
\sigma$, assuming a perfect knowledge of the lens profile, when a $\Lambda$CDM
model is used to analyse data that really belong to a $w$CDM cosmology with
$w=-0.9$. Based on these findings, we identify a consistency check of the
assumed cosmological model in future SLTD surveys, by splitting the dataset in
several redshift bins. Depending on the characteristics of the survey, this
could provide a smoking gun for dark energy.


  We present the full magnetic g tensors of the $^{6}$H$_{5/2}$Z$_{1}$ and
$^{4}$G$_{5/2}$A$_{1}$ electronic states for both crystallographic sites in
Sm$^{3+}$:Y$_{2}$SiO$_{5}$, deduced through the use of Raman heterodyne
spectroscopy performed along 9 different crystallographic directions. The
maximum principle g values were determined to be 0.447 (site 1) and 0.523 (site
2) for the ground state and 2.490 (site 1) and 3.319 (site 2) for the excited
state. The determination of these g tensors provide essential spin Hamiltonian
parameters that can be utilized in future magnetic and hyperfine studies of
Sm$^{3+}$:Y$_{2}$SiO$_{5}$, with applications in quantum information storage
and communication devices.


  It is shown that the functional determinant ($\sim$ effective action) for a
scalar field propagating on the mixed signature product of unit spheres,
S$^q\times$S$^p$, according to the GJMS operator, depends, if $d$ is odd, only
on $d=p+q$ and on whether $p$ is even or odd. In the first case the effective
action equals twice the standard quantity on S$^d$ and vanishes in the second.


  We consider the loop-induced production of a single Higgs boson from direct
photon-photon scattering at a photon collider. A dedicated analysis of the
total cross section and the relative strength of the effective $h\gamma\gamma$
coupling is carried out within the general Two-Higgs-Doublet Model (2HDM) and
the Minimal Supersymmetric Standard Model (MSSM). We systematically survey
representative regions over the parameter space, in full agreement with
brought-to-date theoretical and phenomenological restrictions, and obtain
production rates up to $10^4$ Higgs boson events per $500 fb^{-1}$ of
integrated luminosity. We identify trademark phenomenological profiles for the
different $\gamma\gamma \to h$ channels and trace them back to the distinctive
dynamical features characterizing each of these models -- most significantly,
the enhancement potential of the Higgs self-interactions in the general 2HDM.
The upshot of our results illustrates the possibilities of
$\gamma\gamma$-physics and emphasizes the relevance of linear colliders for the
Higgs boson research program.


  A fraction of young neutron stars, magnetars, have ultra-strong magnetic
fields. Models invoked for their strong fields require highly specific
conditions with extreme parameters which are incompatible with the inference
that the magnetar birth rate is comparable to the rate of core-collapse
supernovae. We suggest that these seemingly contradictory trends can be
reconciled if the toroidal magnetic fields are subject to oscillations
following the proto-neutron star (PNS) dynamo stage. Depending on the phase of
the oscillation at which the oscillations are terminated, the neutron star can
have a very high ($\gtrsim 10^{15}\,{\rm G}$) or relatively small ($\sim
10^{14}\,{\rm G}$) toroidal field. As an example, we invoke a shear-driven
dynamo model for the generation of PNS magnetic fields and show that the
toroidal field indeed exhibits oscillations following the dynamo stage. We
argue that these Alfv\'enic oscillations can lead to the formation of both
magnetars and ordinary neutron stars depending on at what phase of the
oscillation the fields froze.


  We give examples of real Banach spaces with exactly infinite countably many
complex structures and with $\omega_1$ many complex structures.


  We investigate self-contracted curves, arising as (discrete or continuous
time) gradient curves of quasi-convex functions, and their rectifiability
(finiteness of the lengths) in Euclidean spaces, Hadamard manifolds and
CAT(0)-spaces. In the Hadamard case, we give a quantitative refinement of the
original proof of the rectifiability of bounded self-contracted curves (in
general Riemannian manifolds) by Daniilidis et al. Our argument leads us to a
generalization to CAT(0)-spaces satisfying several uniform estimates on their
local structures. Upon these conditions, we show the rectifiability of bounded
self-contracted curves in trees, books and CAT(0)-simplicial complexes.


  In this paper we discuss the asymptotic entropy for ancient solutions to the
Ricci flow. We prove a gap theorem for ancient solutions, which could be
regarded as an entropy counterpart of Yokota's work. In addition, we prove that
under some assumptions on one time slice of a complete ancient solution with
nonnegative curvature operator, finite asymptotic entropy implies
kappa-noncollapsing on all scales. This provides an evidence for Perelman's
more general assertion that on a complete ancient solution with nonnegative
curvature operator, bounded entropy is equivalent to kappa-noncollapsing.


  Surface reconstruction from point clouds is a crucial task in the fields of
computer vision and computer graphics. SDF-based methods excel at
reconstructing smooth meshes with minimal error and artefacts but struggle with
representing open surfaces. On the other hand, UDF-based methods can
effectively represent open surfaces but often introduce noise, leading to
artefacts in the mesh. In this work, we propose a novel approach that directly
predicts the intersection points between line segment of point pairs and
implicit surfaces. To achieve it, we propose two modules named Relative
Intersection Module and Sign Module respectively with the feature of point pair
as input. To preserve the continuity of the surface, we also integrate symmetry
into the two modules, which means the position of predicted intersection will
not change even if the input order of the point pair changes. This method not
only preserves the ability to represent open surfaces but also eliminates most
artefacts on the mesh. Our approach demonstrates state-of-the-art performance
on three datasets: ShapeNet, MGN, and ScanNet. The code will be made available
upon acceptance.


  We establish necessary and sufficient conditions for complex potentials in
the Schr\"odinger equation to enable spectral singularities (SSs) and show that
such potentials have the universal form $U(x) = -w^2(x) - iw_x(x) + k_0^2$,
where $w(x)$ is a differentiable function, such that $\lim_{x\to \pm
\infty}w(x)=\mp k_0$, and $k_0$ is a nonzero real. We also find that when $k_0$
is a complex number, then the eigenvalue of the corresponding Shr\"odinger
operator has an exact solution which, depending on $k_0$, represents a coherent
perfect absorber (CPA), laser, a localized bound state, a quasi bound state in
the continuum (a quasi-BIC), or an exceptional point (the latter requiring
additional conditions). Thus, $k_0$ is a bifurcation parameter that describes
transformations among all those solutions. Additionally, in a more specific
case of a real-valued function $w(x)$ the resulting potential, although not
being $PT$ symmetric, can feature a self-dual spectral singularity associated
with the CPA-laser operation. In the space of the system parameters, the
transition through each self-dual spectral singularity corresponds to a
bifurcation of a pair of complex-conjugate propagation constants from the
continuum. The bifurcation of a first complex-conjugate pair corresponds to the
phase transition from purely real to complex spectrum.


  The development of sources delivering non-classical states of light is one of
the main needs for applications of optical quantum information science. Here,
we demonstrate the generation of non-classical states of light using
strong-laser fields driving a solid-state system, by using the process of
high-order harmonic generation, where an electron tunnels out of the parent
site and, later on, recombines on it emitting high-order harmonic radiation, at
the expense of affecting the driving laser field. Since in solid-state systems
the recombination of the electron can be delocalized along the material, the
final state of the electron determines how the electromagnetic field gets
affected because of the laser-matter interaction, leading to the generation of
entanglement between the electron and the field. These features can be enhanced
by applying conditioning operations, i.e., quantum operations based on the
measurement of high-harmonic radiation. We study non-classical features present
in the final quantum optical state, and characterize the amount of entanglement
between the light and the electrons in the solid. The work sets the foundation
for the development of compact solid-state-based non-classical light sources
using strong-field physics.


  Laser-plasma accelerators have become compact sources of ultrashort electron
bunches at energies up to the gigaelectronvolt range thanks to the remarkable
progress made over the past decade. A direct application of these electron
bunches is the production of short pulse x-ray radiation sources. In this
letter, we study a fully optically driven x-ray source based on the combination
of a laser-plasma accelerator and a plasma wave undulator. The longitudinal
electric field of a laser-generated plasma wave is used to wiggle electrons
transversally. The period of this plasma undulator being equal to the plasma
wavelength, tunable photon energies in the 10 keV range can be achieved with
electron energies in the 100-200 MeV range. Considering a 10s TW class
femtosecond laser system, undulators with a strength parameter K~0.5 and with
about ten periods can be combined with a laser-plasma accelerator, resulting in
several 10^-2 emitted x-ray photons per electron.


  We present a method for predicting the linear response deformation of finite
and semi-infinite 2D solid structures with circular holes and inclusions by
employing the analogies with image charges and induction in electrostatics.
Charges in electrostatics induce image charges near conductive boundaries and
an external electric field induces polarization (dipoles, quadrupoles, and
other multipoles) of conductive and dielectric objects. Similarly, charges in
elasticity induce image charges near boundaries and external stress induces
polarization (quadrupoles and other multipoles) inside holes and inclusions.
Stresses generated by these induced elastic multipoles as well as stresses
generated by their images near boundaries then lead to interactions between
holes and inclusions and with their images, which induce additional
polarization and thus additional deformation of holes and inclusions. We
present a method that expands induced polarization in a series of elastic
multipoles, which systematically takes into account the interactions of
inclusions and holes with the external field, between them, and with their
images. The results of our method for linear deformation of circular holes and
inclusions near straight and curved boundaries show good agreement with both
linear finite element simulations and experiments.


  Discovering and characterizing exoplanets at the outer edge of the transit
method's sensitivity has proven challenging owing to geometric biases and the
practical difficulties associated with acquiring long observational baselines.
Nonetheless, a sample of giant exoplanets on orbits longer than 100 days has
been identified by transit hunting missions. We present long-term Doppler
spectroscopy for 11 such systems with observation baselines spanning a few
years to a decade. We model these radial velocity observations jointly with
transit photometry to provide initial characterizations of these objects and
the systems in which they exist. Specifically, we make new precise mass
measurements for four long-period giant exoplanets (Kepler-111 c, Kepler-553 c,
Kepler-849 b, and PH-2 b), we place new upper limits on mass for four others
(Kepler-421 b, KOI-1431.01, Kepler-1513 b, and Kepler-952 b), and we show that
several "confirmed" planets are in fact not planetary at all. We present these
findings to complement similar efforts focused on closer-in short-period giant
planets, and with the hope of inspiring future dedicated studies of cool giant
exoplanets.


  We consider pressure-driven, steady state Poiseuille flow in straight
channels with various cross-sectional shapes: elliptic, rectangular,
triangular, and harmonic-perturbed circles. A given shape is characterized by
its perimeter P and area A which are combined into the dimensionless
compactness number C = P^2/A, while the hydraulic resistance is characterized
by the well-known dimensionless geometrical correction factor alpha. We find
that alpha depends linearly on C, which points out C as a single dimensionless
measure characterizing flow properties as well as the strength and
effectiveness of surface-related phenomena central to lab-on-a-chip
applications. This measure also provides a simple way to evaluate the hydraulic
resistance for the various shapes.


  We theoretically consider superconducting proximity effect, using the
Bogoliubov-de Gennes theory, in heterostructure sandwich-type geometries
involving a normal s-wave superconductor and a non-superconducting material
with the proximity effect being driven by Cooper pairs tunneling from the
superconducting slab to the non-superconducting slab. Applications of the
superconducting proximity effect may rely on an induced spectral gap or induced
pairing correlations without any spectral gap. We clarify that in a
non-superconducting material the induced spectral gap and pairing correlations
are independent physical quantities arising from the proximity effect. This is
a crucial issue in proposals to create topological superconductivity through
the proximity effect. Heterostructures of 3D topological insulator (TI) slabs
on conventional s-wave superconductor (SC) substrates provide a platform, with
proximity-induced topological superconductivity expected to be observed on the
"naked" top surface of a thin TI slab. We theoretically study the induced
superconducting gap on this naked surface. In addition, we compare against the
induced spectral gap in heterostructures of SC with a normal metal or a
semiconductor with strong spin orbit coupling and a Zeeman splitting potential
(another platform for topological superconductivity). We find that for any
model for the non-SC metal (including metallic TI) the induced spectral gap on
the naked surface decays as $L^{-3}$ as the thickness ($L$) of the non-SC slab
is increased in contrast to the slower $1/L$ decay of the pairing correlations.
Our distinction between proximity-induced spectral gap (with its faster spatial
decay) and pairing correlation (with its slower spatial decay) has important
implications for the currently active search for topological superconductivity
and Majorana fermions in various superconducting heterostructures.


  In the framework of the Chandrasekhar-mass deflagration model for Type Ia
supernovae (SNe Ia), a persisting free parameter is the initial morphology of
the flame front, which is linked to the ignition process in the progenitor
white dwarf. Previous analytical models indicate that the thermal runaway is
driven by temperature perturbations (''bubbles'') that develop in the white
dwarf's convective core. In order to probe the conditions at ignition
(diameters, temperatures and evolutionary timescales), we have performed
hydrodynamical 2D simulations of buoyant bubbles in white dwarf interiors. Our
results show that fragmentation occurring during the bubble rise affects the
outcome of the bubble evolution. Possible implications for the ignition process
of SNe Ia are discussed.


  In this chapter, we reflect on the use of Artificial Intelligence (AI) and
its acceptance in clinical environments. We develop a general view of
hindrances for clinical acceptance in the form of a pipeline model combining AI
and clinical practise. We then link each challenge to the relevant stage in the
pipeline and discuss the necessary requirements in order to overcome each
challenge. We complement this discussion with an overview of opportunities for
AI, which we currently see at the periphery of clinical workflows.


  We demonstrate combined high-fidelity long-haul transfer of a linearly
chirped, optical frequency and time transfer. In a proof-of-principle
experiment we transfer an optical frequency with a linear chirp of around 238
kHz/s via a phase-stabilized underground fiber link of 150 km. We find a
fractional frequency transfer instability (Allan deviation, 18000 s averaging
time) and simultaneity of the chirped frequency between both ends on a level of
around $2\times10^{-19}$, where the active phase stabilization suppresses
cumulative, symmetrical effects. In a second step, we demonstrate the remote
measurement of synchronisation taking advantage of chirped-frequency transfer.
The uncertainty of time transfer here is around 500 ps.


  The continuous information explosion through the Internet and all information
sources makes it necessary to perform all information processing activities
automatically in quick and reliable manners. In this paper, we proposed and
implemented a method to automatically create and Index for books written in
Arabic language. The process depends largely on text summarization and
abstraction processes to collect main topics and statements in the book. The
process is developed in terms of accuracy and performance and results showed
that this process can effectively replace the effort of manually indexing books
and document, a process that can be very useful in all information processing
and retrieval applications.


  Meteorites with known orbital origins are key to our understanding of Solar
System formation and the source of life on Earth. However, these pristine
samples of space material are incredibly rare. Less than 40 of the 60,000
meteorites held in collections around the world have known dynamical origins.
Fireball networks have been developed globally in a unified effort to increase
this number by using multiple observatories to record, triangulate, and
dynamically analyse ablating meteoroids as they enter our atmosphere. The
accuracy of the chosen meteoroid triangulation method directly influences the
accuracy of the determined orbit and the likelihood of possible meteorite
recovery.
  There are three leading techniques for meteoroid triangulation discussed in
the literature: the Method of Planes, the Straight Line Least Squares method,
and the Multi-Parameter Fit method. Here we describe an alternative method to
meteoroid triangulation, called the Dynamic Trajectory Fit. This approach uses
the meteoroid's 3D dynamic equations of motion to fit a realistic trajectory
directly to multi-sensor line-of-sight observations. This method has the
ability to resolve fragmentation events, fit systematic observatory timing
offsets, and determine mass estimates of the meteoroid along its observable
trajectory.
  Through a comprehensive Monte-Carlo analysis of over 100,000 trajectory
simulations, we find this new method to more accurately estimate meteoroid
trajectories of slow entry events ($<$25\,km/s) and events observed from low
convergence angles ($<$10$^{\circ}$) compared to existing meteoroid
triangulation techniques. Additionally, we triangulate an observed fireball
event with visible fragmentation using the various triangulation methods to
show that the proposed Dynamic Trajectory Fit implementing fragmentation to
best match the captured multi-sensor line-of-sight data.


  We study the dynamics of topological defects in continuum theories governed
by a free energy minimization principle, building on our recently developed
framework [Romano J, Mahault B and Golestanian R 2023 J. Stat. Mech.: Theory
Exp. 083211]. We show how the equation of motion of point defects, domain
walls, disclination lines and any other singularity can be understood with one
unifying mathematical framework. For disclination lines, this also allows us to
study the interplay between the internal line tension and the interaction with
other lines. This interplay is non-trivial, allowing defect loops to expand,
instead of contracting, due to external interaction. We also use this framework
to obtain an analytical description of two long-lasting problems in point
defect motion, namely the scale dependence of the defect mobility and the role
of elastic anisotropy in the motion of defects in liquid crystals. For the
former, we show that the effective defect mobility is strongly
problem-dependent, but it can be computed with high accuracy for a pair of
annihilating defects. For the latter, we show that at the first order in
perturbation theory, anisotropy causes a non-radial force, making the
trajectory of annihilating defects deviate from a straight line. At higher
orders, it also induces a correction in the mobility, which becomes
non-isotropic for the $+1/2$ defect. We argue that, due to its generality, our
method can help to shed light on the motion of singularities in many different
systems, including driven and active non-equilibrium theories.


  Controlled organic functionalization of silicon surfaces as integral part of
semiconductor technology offers new perspectives for a wide range of
applications. The high reactivity of the silicon dangling bonds, however,
presents a major hindrance for the first basic reaction step of such a
functionalization, i.e., the chemoselective attachment of bifunctional organic
molecules on the pristine silicon surface. We overcome this problem by
employing cyclooctyne as the major building block of our strategy.
Functionalized cyclooctynes are shown to react on Si(001) selectively via the
strained cyclooctyne triple bond while leaving the side groups intact. The
achieved selectivity originates from the distinctly different adsorption
dynamics of the separate functionalities: A direct adsorption pathway is
demonstrated for cyclooctyne as opposed to the vast majority of other organic
functional groups. The latter ones react on Si(001) via a metastable
intermediate which makes them effectively unreactive in competition with the
direct pathway of cyclooctyne's strained triple bond.


  It is shown that the order and the lower order of growth are equal for all
non-trivial solutions of $f^{(k)}+A f=0$ if and only if the coefficient $A$ is
analytic in the unit disc and $\log^+ M(r,A)/\log(1-r)$ tends to a finite limit
as $r\to 1^-$. A family of concrete examples is constructed, where the order of
solutions remain the same while the lower order may vary on a certain interval
depending on the irregular growth of the coefficient. These coefficients emerge
as the logarithm of their modulus approximates smooth radial subharmonic
functions of prescribed irregular growth on a sufficiently large subset of the
unit disc. A result describing the phenomenon behind these highly non-trivial
examples is also established. En route to results of general nature, a new
sharp logarithmic derivative estimate involving the lower order of growth is
discovered. In addition to these estimates, arguments used are based, in
particular, on the Wiman-Valiron theory adapted for the lower order, and on a
good understanding of the right-derivative of the logarithm of the maximum
modulus.


  The running coupling constants (in particular, the gravitational one) are
studied in asymptotically free GUTs and in finite GUTs in curved spacetime,
with explicit examples. The running gravitational coupling is used to calculate
the leading quantum GUT corrections to the Newtonian potential, which turn out
to be of logarithmic form in asymptotically free GUTs. A comparison with the
effective theory for the conformal factor ---where leading quantum corrections
to the Newtonian potential are again logarithmic--- is made. A totally
asymptotically free $O(N)$ GUT with quantum higher derivative gravity is then
constructed, using the technique of introducing renormalization group (RG)
potentials in the space of couplings. RG equations for the cosmological and
gravitational couplings in this theory are derived, and solved numerically,
showing the influence of higher-derivative quantum gravity on the Newtonian
potential. The RG-improved effective gravitational Lagrangian for
asymptotically free massive GUTs is calculated in the strong (almost constant)
curvature regime, and the non-singular De Sitter solution to the quantum
corrected gravitational equations is subsequently discussed. Finally, possible
extensions of the results here obtained are briefly outlined.


  The Hodge numerical invariants of a variation of Hodge structure over a
smooth quas--projective variety are a measure of complexity for the global
twisting of the limit mixed Hodge structure when it degenerates. These
invariants appear in inequalities which they may have correction terms, called
Arakelov inequalities. One may investigate the correction term to make them
into equalities, also called Arakelov equalities. We investigate numerical
Arakelov type (in)equilities for a family of surfaces fibered by curves. Our
method uses Arakelov identities in a weight 1 and also in a weight 2 variations
of Hodge structure (cf. \cite{GGK}), in a commutative triangle of fibrations.
We have proposed to relate the degrees of the Hodge bundles in the two
families. We also compare the Fujita decomposition of Hodge bundles in these
fibrations. We examine various identities and relations between Hodge numbers
and degrees of the Hodge bundles in different levels.


  We present results for the hadronic running of the electromagnetic coupling
and the weak mixing angle from simulations of lattice QCD with $N_f=2+1$
flavours of $O(a)$-improved Wilson fermions. Using two different
discretisations of the vector current, we compute the quark-connected and
-disconnected contributions to the hadronic vacuum polarisation (HVP) functions
$\bar{\Pi}^{\gamma\gamma}$ and $\bar{\Pi}^{Z\gamma}$ for spacelike squared
momenta $Q^2\leq 7$ $\mathrm{GeV}^2$. Our results are extrapolated to the
physical point using ensembles at four lattice spacings, with pion masses
ranging from 130 to 420 MeV. We observe a tension of up to 3.5 standard
deviations between our lattice results for $\Delta\alpha_{\rm had}^{(5)}(-Q^2)$
and estimates based on the $\textit{R}$-ratio for space-like momenta in the
range $Q^2=3-7\,\rm GeV^2$. To obtain an estimate for
$\Delta\alpha_\mathrm{had}^{(5)}(M_Z^2)$, we employ the Euclidean split
technique. The implications for comparison with global electroweak fits are
assessed.


  We discuss a relationship between rate-distortion and optimal transport (OT)
theory, even though they seem to be unrelated at first glance. In particular,
we show that a function defined via an extremal entropic OT distance is
equivalent to the rate-distortion function. We numerically verify this result
as well as previous results that connect the Monge and Kantorovich problems to
optimal scalar quantization. Thus, we unify solving scalar quantization and
rate-distortion functions in an alternative fashion by using their respective
optimal transport solvers.


  Catalytic prior distributions provide general, easy-to-use, and interpretable
specifications of prior distributions for Bayesian analysis. They are
particularly beneficial when the observed data are inadequate to stably
estimate a complex target model. A catalytic prior distribution is constructed
by augmenting the observed data with synthetic data that are sampled from the
predictive distribution of a simpler model estimated from the observed data. We
illustrate the usefulness of the catalytic prior approach using an example from
labor economics. In the example, the resulting Bayesian inference reflects many
important aspects of the observed data, and the estimation accuracy and
predictive performance of the inference based on the catalytic prior are
superior to, or comparable to, that of other commonly used prior distributions.
We further explore the connection between the catalytic prior approach and a
few popular regularization methods. We expect the catalytic prior approach to
be useful in many applications.


  The operator product expansion (OPE) for heavy-light-quark pseudoscalar
mesons (D-mesons and B-mesons) in medium is determined, both for a moving meson
with respect to the surrounding medium as well as for a meson at rest. First of
all, the OPE is given in terms of normal-ordered operators up to mass dimension
5, and the mass of the heavy-quark and the mass of the light-quark are kept
finite. The Wilson coefficients of such an expansion are infrared (IR)
divergent in the limit of a vanishing light-quark mass. A consistent separation
of scales necessitates an OPE in terms of non-normal-ordered operators, which
implies operator mixing, where the IR-divergences are absorbed into the
operators. It is shown that the Wilson coefficients of such an expansion are
IR-stable, and the limit of a vanishing light-quark mass is perfomed. Details
of the major steps for the calculation of the Wilson coefficients are
presented. By a comparison with previous results obtained by other theoretical
groups we have found serious disagreements.


  In this paper, we prove two results: first, we use crystalline cohomology of
classifying stacks to directly reconstruct the classical Dieudonn\'e module of
a finite, $p$-power rank, commutative group scheme $G$ over a perfect field $k$
of characteristic $p>0$. As a consequence, we give a new proof of the
isomorphism $\sigma^* M(G) \simeq \mathrm{Ext}^1 (G,
\mathcal{O}^{\mathrm{crys}})$ due to Berthelot--Breen--Messing using stacky
methods combined with the theory of de Rham--Witt complexes. Additionally, we
show that finite locally free commutative group schemes of $p$-power rank over
a quasisyntomic base ring embed fully faithfully into the category of prismatic
$F$-gauges, which extends the work of Ansch\"utz and Le Bras on prismatic
Dieudonn\'e theory.


  In this paper, we analyze the relationship between generation dispatch
solutions produced by the DC optimal power flow (DC OPF) problem by the AC
optimal power flow (AC OPF) problem. While there has been much previous work in
analyzing the approximation error of the DC assumption, the AC feasibility has
not been fully explored, although difficulty achieving AC feasibility is known
in practice. Here, we consider the set of feasible points in a standard DC OPF
problem and the set of feasible points in a standard AC OPF problem. Under some
very light assumptions, we show that the intersection of these sets is the
empty set; i.e., that no solution to the DC OPF problem will satisfy the AC
power flow constraints. Then, it is demonstrated that even with generation
adjustments in DC OPF to account for losses, DC OPF solutions are still not AC
feasible.


  The rapid development of robotics has benefited by more and more people
putting their attention to it. With the demand for robots is growing for the
purpose of fulfilling tasks instead of humans, how to control the robot better
is becoming a hot topic. For obstacle avoidance, we proposed algorithms for
both 2D planar environments and 3D space environments. The example cases we
raise are those that need to be addressed but have always been ignored. In
addition, we put efforts into trajectory planning for robots. The two scenarios
we set are self-driving cars on the road and reconnaissance and surveillance of
drones. For future expectations, there are some possible directions. How to
combine traditional navigation algorithms and high-tech algorithms together so
as to fulfill the tasks perfectly while the computational efficiency is not too
high is a worthy topic. In addition, extending the obstacle avoidance
algorithms to more competitive situations. Moreover, cooperation among multi
robots are worth attention by researchers. All in all, there is still a long
way to go for the development of navigation and control of mobile robots.
Despite this, we believe we do not need to wait for too long time to see the
revolution of robots.


  Very recently, a new decay framework has been given by [51] for linearized
dissipative hyperbolic systems satisfying the Kawashima-Shizuta condition on
the framework of Besov spaces, which allows to pay less attention on the
traditional spectral analysis. However, owing to interpolation techniques, the
analysis remains valid only for nonlinear systems in higher dimensions
$(n\geq3)$ and the corresponding case of low dimensions was left open, which
provides the main motivation of this work. Firstly, we develop new time-decay
properties on the frequency-localization Duhamel principle. Furthermore, it is
shown that the classical solution and its derivatives of fractional order decay
at the optimal algebraic rate in dimension 1, by time-weighted energy
approaches in terms of low-frequency and high-frequency decompositions.
Finally, as applications, decay results for several concrete systems subjected
to the same dissipative structure as general hyperbolic systems, for instance,
damped compressible Euler equations, thermoelasticity with second sound and
Timoshenko systems with equal wave speeds, are also obtained.


  This paper examines the dynamics of policy implementation and how policy
contradicts reality on the ground when it comes to practice. The paper finds
that despite having well-laid out policy; the actual practice is contrary.
Taking data storage policy within the Ministry of Health in Malawi as a case
study, the paper highlights that the contextual realities of where Ministry of
Health (MoH) data is stored depends on a number of
Technology-Organizational-Environmental (TOE) factors. In the wake of cloud
computing; some of these factors act as causative factors for data to be stored
in the cloud; contradicting the data storage policy.


  In the era of large language models (LLMs), in-context learning (ICL) stands
out as an effective prompting strategy that explores LLMs' potency across
various tasks. However, applying LLMs to grammatical error correction (GEC) is
still a challenging task. In this paper, we propose a novel
ungrammatical-syntax-based in-context example selection strategy for GEC.
Specifically, we measure similarity of sentences based on their syntactic
structures with diverse algorithms, and identify optimal ICL examples sharing
the most similar ill-formed syntax to the test input. Additionally, we carry
out a two-stage process to further improve the quality of selection results. On
benchmark English GEC datasets, empirical results show that our proposed
ungrammatical-syntax-based strategies outperform commonly-used word-matching or
semantics-based methods with multiple LLMs. This indicates that for a
syntax-oriented task like GEC, paying more attention to syntactic information
can effectively boost LLMs' performance. Our code will be publicly available
after the publication of this paper.


  Gaussian Markov random fields (GMRFs) are probabilistic graphical models
widely used in spatial statistics and related fields to model dependencies over
spatial structures. We establish a formal connection between GMRFs and
convolutional neural networks (CNNs). Common GMRFs are special cases of a
generative model where the inverse mapping from data to latent variables is
given by a 1-layer linear CNN. This connection allows us to generalize GMRFs to
multi-layer CNN architectures, effectively increasing the order of the
corresponding GMRF in a way which has favorable computational scaling. We
describe how well-established tools, such as autodiff and variational
inference, can be used for simple and efficient inference and learning of the
deep GMRF. We demonstrate the flexibility of the proposed model and show that
it outperforms the state-of-the-art on a dataset of satellite temperatures, in
terms of prediction and predictive uncertainty.


  JPEG is one of the most commonly used standards among lossy image compression
methods. However, JPEG compression inevitably introduces various kinds of
artifacts, especially at high compression rates, which could greatly affect the
Quality of Experience (QoE). Recently, convolutional neural network (CNN) based
methods have shown excellent performance for removing the JPEG artifacts. Lots
of efforts have been made to deepen the CNNs and extract deeper features, while
relatively few works pay attention to the receptive field of the network. In
this paper, we illustrate that the quality of output images can be
significantly improved by enlarging the receptive fields in many cases. One
step further, we propose a Dual-domain Multi-scale CNN (DMCNN) to take full
advantage of redundancies on both the pixel and DCT domains. Experiments show
that DMCNN sets a new state-of-the-art for the task of JPEG artifact removal.


  Recent advances in machine learning-aided lossy compression are incorporating
perceptual fidelity into the rate-distortion theory. In this paper, we study
the rate-distortion-perception trade-off when the perceptual quality is
measured by the total variation distance between the empirical and product
distributions of the discrete memoryless source and its reconstruction. We
consider the general setting, where two types of resources are available at
both the encoder and decoder: a common side information sequence, correlated
with the source sequence, and common randomness. We consider both the strong
perceptual constraint and the weaker empirical perceptual constraint. The
required communication rate for achieving the distortion and empirical
perceptual constraint is the minimum conditional mutual information, and
similar result holds for strong perceptual constraint when sufficient common
randomness is provided and the output along with the side information is
constraint to an independent and identically distributed sequence.


  We deal with a mechanism of generating distributional chaos in planar
nonautonomous ODEs and try to measure chaosity in terms of topological entropy.
It is based on the interplay between simple periodic solutions. We prove the
existence of infinitely many heteroclinic solutions betwen the periodic ones.


  In this paper we review the observational results on Relic radio sources in
clusters of galaxies. We discuss their observational properties, structures and
radio spectra. We will show that Relics can be divided according to their size,
morphology, and location in the galaxy cluster. These differences could be
related to physical properties of Relic sources. The comparison with cluster
conditions suggests that Relics could be related to shock waves originated by
cluster mergers.


  We report the direct detection of a binary/disk system towards the high-mass
(proto)stellar object IRAS20126+4104 at infrared wavengths. The presence of a
multiple system had been indicated by the precession of the outflow and the
double jet system detected earlier at cm-wavelengths. Our new K, L' & M' band
infrared images obtained with the UKIRT under exceptional seeing conditions on
Mauna Kea are able to resolve the central source for the first time, and we
identify two objects separated by ~ 0.5'' (850 AU). The K and L' images also
uncover features characteristic of a nearly edge-on disk, similar to many low
mass protostars with disks: two emission regions oriented along an outflow axis
and separated by a dark lane. The peaks of the L' & M' band and mm-wavelength
emission are on the dark lane, presumably locating the primary young star. The
thickness of the disk is measured to be ~ 850 AU for radii < 1000 AU.
Approximate limits on the NIR magnitudes of the two young stars indicate a
high-mass system, although with much uncertainty. These results are a
demonstration of the high-mass nature of the system, and the similarities of
the star-formation process in the low-mass and high-mass regimes viz. the
presence of a disk-accretion stage. The companion is located along the dark
lane, consistent with it being in the equatorial/disk plane, indicating a
disk-accretion setting for massive, multiple, star-formation.


  Angular dispersion is the effect of a multi-path propagation observed in
received signals. An assessment of this phenomenon is particularly important
from the viewpoint of emerging fifth generation (5G) communication systems. In
these systems, using the beam-forming and massive multiple-input
multiple-output antenna arrays are planned. This phenomenon also has a negative
impact on direction finding and older generation communication systems used in
an urban environment. In this paper, we present the angular dispersion
evaluation for various propagation environments based on simulation studies.
This analysis is carried out for different environment types defined in the
3GPP standard model for a selected frequency. In this case, the angular spread
is determinated based on the power angular spectrum. This parameter is the
basis for the influence evaluation of the propagation environment on the
received signal angular dispersion.


  Given a collection of videos, how to detect content-based copies efficiently
with high accuracy? Detecting copies in large video collections still remains
one of the major challenges of multimedia retrieval. While many video copy
detection approaches show high computation times and insufficient quality, we
propose a new efficient content-based video copy detection algorithm improving
both aspects. The idea of our approach consists in utilizing self-similarity
matrices as video descriptors in order to capture different visual properties.
We benchmark our algorithm on the MuscleVCD ST1 benchmark dataset and show that
our approach is able to achieve a score of 100\% and a score of at least 93\%
in a wide range of parameters.


  Importance sampling (IS) represents a fundamental technique for a large surge
of off-policy reinforcement learning approaches. Policy gradient (PG) methods,
in particular, significantly benefit from IS, enabling the effective reuse of
previously collected samples, thus increasing sample efficiency. However,
classically, IS is employed in RL as a passive tool for re-weighting historical
samples. However, the statistical community employs IS as an active tool
combined with the use of behavioral distributions that allow the reduction of
the estimate variance even below the sample mean one. In this paper, we focus
on this second setting by addressing the behavioral policy optimization (BPO)
problem. We look for the best behavioral policy from which to collect samples
to reduce the policy gradient variance as much as possible. We provide an
iterative algorithm that alternates between the cross-entropy estimation of the
minimum-variance behavioral policy and the actual policy optimization,
leveraging on defensive IS. We theoretically analyze such an algorithm, showing
that it enjoys a convergence rate of order $O(\epsilon^{-4})$ to a stationary
point, but depending on a more convenient variance term w.r.t. standard PG
methods. We then provide a practical version that is numerically validated,
showing the advantages in the policy gradient estimation variance and on the
learning speed.


  We use Voiculescu's concept of free probability to construct a completely
isomorphic embedding of the operator space OH in the predual of a von Neumann
algebra. We analyze the properties of this embedding and determine the operator
space projection constant of OH_n: It is of the order (n/1+ln n)^{1/2} The
lower estimate is a recent result of Pisier and Shlyakhtenko that improves an
estimate of order 1/(1+ln n) of the author. The additional factor 1/(1+ln
n)^{1/2} indicates that the operator space OH_n behaves differently than its
classical counterpart l_2^n. We give an application of this formula to positive
sesquilinear forms on B(H). This leads to logarithmic characterization of
C*-algebras with the weak expectation property introduced by Lance.


  We describe a $O(\log n )$-approximation algorithm for computing the
homotopic \Frechet distance between two polygonal curves that lie on the
boundary of a triangulated topological disk. Prior to this work, algorithms
were known only for curves on the Euclidean plane with polygonal obstacles.
  A key technical ingredient in our analysis is a $O(\log n)$-approximation
algorithm for computing the minimum height of a homotopy between two curves. No
algorithms were previously known for approximating this parameter.
Surprisingly, it is not even known if computing either the homotopic \Frechet
distance, or the minimum height of a homotopy, is in NP.