  Current cameras are capable of recording high resolution video. While viewing
on a mobile device, a user can manually zoom into this high resolution video to
get more detailed view of objects and activities. However, manual zooming is
not suitable for surveillance and monitoring. It is tiring to continuously keep
zooming into various regions of the video. Also, while viewing one region, the
operator may miss activities in other regions. In this paper, we propose sZoom,
a framework to automatically zoom into a high resolution surveillance video.
The proposed framework selectively zooms into the sensitive regions of the
video to present details of the scene, while still preserving the overall
context required for situation assessment. A multi-variate Gaussian penalty is
introduced to ensure full coverage of the scene. The method achieves near
real-time performance through a number of timing optimizations. An extensive
user study shows that, while watching a full HD video on a mobile device, the
system enhances the security operator's efficiency in understanding the details
of the scene by 99% on the average compared to a scaled version of the original
high resolution video. The produced video achieved 46% higher ratings for
usefulness in a surveillance task.


  We study the Casimir-Polder force arising between two identical two-level
atoms and mediated by a massless scalar field propagating in a black-hole
background. We study the interplay of Hawking radiation and Casimir-Polder
forces and find that, when the atoms are placed near the event horizon, the
scaling of the Casimir-Polder interaction energy as a function of interatomic
distance displays a transition from a thermallike character to a nonthermal
behavior. We corroborate our findings for a quantum field prepared in the
Boulware, Hartle-Hawking, and Unruh vacua. Our analysis is consistent with the
nonthermal character of the Casimir-Polder interaction of two-level atoms in a
relativistic accelerated frame [J. Marino et al., Phys. Rev. Lett. 113, 020403
(2014)], where a crossover from thermal scaling, consistent with the Unruh
effect, to a nonthermal scaling has been observed. The two crossovers are a
consequence of the noninertial character of the background where the field
mediating the Casimir interaction propagates. While in the former case the
characteristic crossover length scale is proportional to the inverse of the
surface gravity of the black hole, in the latter it is determined by the
inverse of the proper acceleration of the atoms.


  An enduring challenge for contemporary physics is to experimentally observe
and control quantum behavior in macroscopic systems. We show that a single
trapped atomic ion could be used to probe the quantum nature of a mesoscopic
mechanical oscillator precooled to 4K, and furthermore, to cool the oscillator
with high efficiency to its quantum ground state. The proposed experiment could
be performed using currently available technology.


  Flow-based super-resolution (SR) models have demonstrated astonishing
capabilities in generating high-quality images. However, these methods
encounter several challenges during image generation, such as grid artifacts,
exploding inverses, and suboptimal results due to a fixed sampling temperature.
To overcome these issues, this work introduces a conditional learned prior to
the inference phase of a flow-based SR model. This prior is a latent code
predicted by our proposed latent module conditioned on the low-resolution
image, which is then transformed by the flow model into an SR image. Our
framework is designed to seamlessly integrate with any contemporary flow-based
SR model without modifying its architecture or pre-trained weights. We evaluate
the effectiveness of our proposed framework through extensive experiments and
ablation analyses. The proposed framework successfully addresses all the
inherent issues in flow-based SR models and enhances their performance in
various SR scenarios. Our code is available at:
https://github.com/liyuantsao/BFSR


  Complex networks analyses of many physical, biological and social phenomena
show remarkable structural regularities, yet, their application in studying
human past interaction remains underdeveloped. Here, we present an innovative
method for identifying community structures in the archaeological record that
allow for independent evaluation of the copper using societies in the Balkans,
from c. 6200 to c. 3200 BC. We achieve this by exploring modularity of
networked systems of these societies across an estimated 3000 years. We employ
chemical data of copper-based objects from 79 archaeological sites as the
independent variable for detecting most densely interconnected sets of nodes
with a modularity maximization method. Our results reveal three dominant
modular structures across the entire period, which exhibit strong spatial and
temporal significance. We interpret patterns of copper supply among prehistoric
societies as reflective of social relations, which emerge as equally important
as physical proximity. Although designed on a variable isolated from any
archaeological and spatiotemporal information, our method provides
archaeologically and spatiotemporally meaningful results. It produces models of
human interaction and cooperation that can be evaluated independently of
established archaeological systematics, and can find wide application on any
quantitative data from archaeological and historical record.


  We report single-crystal growth of La$_{0.34}$Na$_{0.66}$Fe$_2$As$_2$
iron-based superconductor with the size of several millimeters. The samples
were accidentally obtained in trying to grow LaFeAsO$_{1-y}$F$_y$ ( $y \geq$
0.8 ) single crystals with NaAs and NaF flux. The sample shows both
antiferromagnetic and structural transitions at 106 K. The superconducting
transition temperature is about 27 K with the superconducting anisotropy of
about 1.9. These values and the temperature dependence of the Hall coefficient
suggest that La$_{0.34}$Na$_{0.66}$Fe$_2$As$_2$ belongs to hole-doped "122"
families of iron pnictides with the doping level slightly lower than optimal
doping. Compared with previous reports on the polycrystalline samples, our
results suggest that either $T_c$ of the this system can be further increased,
or the superconducting dome may not be well formed in this system. In either
case, the La$_{0.5-x}$Na$_{0.5+x}$Fe$_2$As$_2$ system provides a new platform
to study the antiferromagnetic and superconducting properties of iron-based
superconductors.


  Arrays of optically trapped nanoparticles have emerged as a promising
platform for the study of complex non-equilibrium phenomena. Analogous to
atomic many-body systems, one of the crucial ingredients is the ability to
precisely control the interactions between particles. However, the optical
interactions studied thus far only provide conservative optical binding forces
of limited tunability. Here we demonstrate a coupling mechanism that is orders
of magnitude stronger and has new qualitative features. These effects arise
from the previously unexplored phase coherence between the optical fields that
drive the light-induced dipole-dipole interaction. In addition, polarization
control allows us to observe electrostatic coupling between charged particles
in the array. Our results pave the way for a fully programmable many-body
system of interacting nanoparticles with tunable dissipative and nonreciprocal
interactions, which are instrumental for exploring entanglement and topological
phases in arrays of levitated nanoparticles.


  Semiclassical methods are used to study the nonlinear interaction of light in
vacuum in the context of four wave mixing. This study is motivated by a desire
to investigate the possibility of using recently developed powerful ultrashort
(femtosecond) laser pulses to demonstrate the existence of nonlinear effects in
vacuum, predicted by quantum electrodynamics (QED). An approach, similar to
classical nonlinear optics in a medium, is developed in this article. A third
order nonlinear effective susceptibility of vacuum is then introduced .


  Learning neural subset selection tasks, such as compound selection in
AI-aided drug discovery, have become increasingly pivotal across diverse
applications. The existing methodologies in the field primarily concentrate on
constructing models that capture the relationship between utility function
values and subsets within their respective supersets. However, these approaches
tend to overlook the valuable information contained within the superset when
utilizing neural networks to model set functions. In this work, we address this
oversight by adopting a probabilistic perspective. Our theoretical findings
demonstrate that when the target value is conditioned on both the input set and
subset, it is essential to incorporate an \textit{invariant sufficient
statistic} of the superset into the subset of interest for effective learning.
This ensures that the output value remains invariant to permutations of the
subset and its corresponding superset, enabling identification of the specific
superset from which the subset originated. Motivated by these insights, we
propose a simple yet effective information aggregation module designed to merge
the representations of subsets and supersets from a permutation invariance
perspective. Comprehensive empirical evaluations across diverse tasks and
datasets validate the enhanced efficacy of our approach over conventional
methods, underscoring the practicality and potency of our proposed strategies
in real-world contexts.


  A model-independent irreducible tensor formalism is developed to analyse
$\bar{\Omega}\Omega$ production in $\bar{p}p$ collisions and its subsequent
decay via the triple-strange decay process, $\bar{\Omega}^{+} \Omega^{-}
\rightarrow K^{+} \bar{\Lambda} K^{-} \Lambda \rightarrow K^{+} \bar{p} \pi^{+}
K^{-} p \pi^{-}$. These processes are relevant for the upcoming experiments at
PANDA. We not only provide expressions for the density matrix of the
$\Omega\bar{\Omega}$ system but also for the products at each stage of the
decay. The Fano statistical tensors so obtained not only completely
characterize the relevant final systems but also provide expressions for joint
angular distributions. Finally, we show which of the Fano statistical tensors
characterizing the $\bar{\Omega}\Omega$ system can be inferred from the Fano
statistical tensors characterizing the final $\bar{p}p$ system, wherein we also
obtain the relation between the production cross sections for
$\Omega\bar{\Omega}$ and the final $p\bar{p}$ system.


  We consider the mean-field game where each agent determines the optimal time
to exit the game by solving an optimal stopping problem with reward function
depending on the density of the state processes of agents still present in the
game. We place ourselves in the framework of relaxed optimal stopping, which
amounts to looking for the optimal occupation measure of the stopper rather
than the optimal stopping time. This framework allows us to prove the existence
of the relaxed Nash equilibrium and the uniqueness of the associated value of
the representative agent under mild assumptions. Further, we prove a rigorous
relation between relaxed Nash equilibria and the notion of mixed solutions
introduced in earlier works on the subject, and provide a criterion, under
which the optimal strategies are pure strategies, that is, behave in a similar
way to stopping times. Finally, we present a numerical method for computing the
equilibrium in the case of potential games and show its convergence.


  We investigate ergodic theory of Poisson suspensions. In the process, we
establish close connections between finite and infinite measure preserving
ergodic theory. Poisson suspensions thus provide a new approach to infinite
measure preserving ergodic theory. Fields investigated here are mixing
properties, spectral theory, joinings. We also compare Poisson suspensions to
the apparently similar looking Gaussian dynamical systems.


  Anomalous Cepheids are a rather rare family of pulsating variables preferably
found in dwarf galaxies. Attempts to model these variable stars via single-star
evolution scenarios still leave space for improvements to better grasp their
origin. Focusing on the LMC with its rich population of Anomalous Cepheids to
compare against we probe the role binary stars might play to understand the
nature of Anomalous Cepheids. The evolution of donors and accretors undergoing
Case-B mass transfer along the first red-giant branch as well as merger-like
models were calculated. First results show that in binary scenarios a larger
range of star masses and metallicities up to Z < 0.008, higher than deemed
possible hitherto, enter and pass through the instability strip. If binary
stars play a role in Anomalous Cepheid populations, mass donors, mass
accretors, or even mergers are potential candidates to counteract constraints
imposed by the single-star approach.


  We have theoretically studied vortex waves of Bose-Einstein condensates in
elongated harmonic traps. Our focus is on the axisymmetric varicose waves and
helical Kelvin waves of singly quantized vortex lines. Growth and decay
dynamics of both types of vortex waves are discussed. We propose a method to
experimentally create these vortex waves on demand.


  We propose a vector-valued regression problem whose solution is equivalent to
the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior
distribution. This equivalence provides a new understanding of kernel Bayesian
inference. Moreover, the optimization problem induces a new regularization for
the posterior embedding estimator, which is faster and has comparable
performance to the squared regularization in kernel Bayes' rule. This
regularization coincides with a former thresholding approach used in kernel
POMDPs whose consistency remains to be established. Our theoretical work solves
this open problem and provides consistency analysis in regression settings.
Based on our optimizational formulation, we propose a flexible Bayesian
posterior regularization framework which for the first time enables us to put
regularization at the distribution level. We apply this method to nonparametric
state-space filtering tasks with extremely nonlinear dynamics and show
performance gains over all other baselines.


  Using Chandra observations, we study the X-ray emission of the stellar
population in the compact dwarf elliptical galaxy M32. The proximity of M32
allows one to resolve all bright point sources with luminosities higher than
8e33 erg/s in the 0.5--7 keV band. The remaining (unresolved) emission closely
follows the galaxy's optical light and is characterized by an emissivity per
unit stellar mass of ~4.3e27 erg/s/M_sun in the 2--10 keV energy band. The
spectrum of the unresolved emission above a few keV smoothly joins the X-ray
spectrum of the Milky Way's ridge measured with RXTE and INTEGRAL. These
results strongly suggest that weak discrete X-ray sources (accreting white
dwarfs and active binary stars) provide the bulk of the ``diffuse'' emission of
this gas-poor galaxy. Within the uncertainties, the average X-ray properties of
the M32 stars are consistent with those of the old stellar population in the
Milky Way. The inferred cumulative soft X-ray (0.5--2 keV) emissivity is
however smaller than is measured in the immediate Solar vicinity in our Galaxy.
This difference is probably linked to the contribution of young (age <1Gyr)
stars, which are abundant in the Solar neighborhood but practically absent in
M32. Combining Chandra, RXTE and INTEGRAL data, we obtain a broad-band (0.5--60
keV) X-ray spectrum of the old stellar population in galaxies.


  We study the acceleration of ultra-high-energy cosmic rays (UHECRs) at FR-II
radio galaxies by performing Monte Carlo simulations for the transport,
scattering, and energy change of the CR particles injected into the
time-evolving jet flows that are realized through relativistic hydrodynamic
(RHD) simulations. Toward that end, we adopt physically motivated models for
the magnetic field and particle scattering. By identifying the primary
acceleration process among diffusive shock acceleration (DSA), turbulent shear
acceleration (TSA), and relativistic shear acceleration (RSA), we find that CRs
of $E\lesssim1$ EeV gain energy mainly through DSA in the jet-spine flow and
the backflow containing many shocks and turbulence. After they attain
$E\gtrsim$ a few EeV, CRs are energized mostly via RSA at the jet-backflow
interface, reaching energies well above $10^{20}$ eV. TSA makes a relatively
minor contribution. The time-asymptotic energy spectrum of escaping particles
is primarily governed by the jet power, shifting to higher energies at more
powerful jets. The UHECR spectrum fits well to the double-power-law form, whose
break energy, $E_{\rm break}$, corresponds to the size-limited maximum energy.
It is close to $d\mathcal{N}/dE\propto E^{-0.5}$ below $E_{\rm break}$, while
it follows $d\mathcal{N}/dE\propto E^{-2.6}$ above $E_{\rm break}$, decreasing
more gradually than the exponential. The power-law slope of the high-energy end
is determined by the energy boosts via non-gradual shear acceleration across
the jet-backflow interface and the confinement by the elongated cocoon. We
conclude that giant radio galaxies could be major contributors to the observed
UHECRs.


  Resource theories are broad frameworks that capture how useful objects are in
performing specific tasks. In this paper we devise a formal resource theory
quantum measurements, focusing on the ability of a measurement to acquire
information. The objects of the theory are equivalence classes of positive
operator-valued measures (POVMs), and the free transformations are changes to a
measurement device that can only deteriorate its ability to report information
about a physical system. We show that catalysis and purification, protocols
that are possible in other resource theories, are impossible in our resource
theory for quantum measurements. Standard measures of information gain are
shown to be resource monotones, and the resource theory is applied to the task
of quantum state discrimination.


  The concept of nimbers--a.k.a. Grundy-values or nim-values--is fundamental to
combinatorial game theory. Nimbers provide a complete characterization of
strategic interactions among impartial games in their disjunctive sums as well
as the winnability. In this paper, we initiate a study of nimber-preserving
reductions among impartial games. These reductions enhance the
winnability-preserving reductions in traditional computational
characterizations of combinatorial games. We prove that Generalized Geography
is complete for the natural class, $\cal{I}^P$ , of polynomially-short
impartial rulesets under nimber-preserving reductions, a property we refer to
as Sprague-Grundy-complete. In contrast, we also show that not every
PSPACE-complete ruleset in $\cal{I}^P$ is Sprague-Grundy-complete for
$\cal{I}^P$ .
  By considering every impartial game as an encoding of its nimber, our
technical result establishes the following striking cryptography-inspired
homomorphic theorem: Despite the PSPACE-completeness of nimber computation for
$\cal{I}^P$ , there exists a polynomial-time algorithm to construct, for any
pair of games $G_1$, $G_2$ of $\cal{I}^P$ , a prime game (i.e. a game that
cannot be written as a sum) $H$ of $\cal{I}^P$ , satisfying: nimber($H$) =
nimber($G_1$) $\oplus$ nimber($G_2$).


  Systematic investigations of dilepton production are performed at the SIS
accelerator of GSI with the HADES spectrometer. The goal of this program is a
detailed understanding of di-electron emission from hadronic systems at
moderate temperatures and densities. New results obtained in HADES experiments
focussing on electron pair production in elementary collisions are reported
here. They pave the way to a better understanding of the origin of the
so-called excess pairs earlier on observed in heavy-ion collisions by the DLS
collaboration and lately confirmed in two measurements of the HADES
collaboration using C+C and Ar+KCl collisions. Results of these studies are
discussed.


  Transformer-based acoustic modeling has achieved great suc-cess for both
hybrid and sequence-to-sequence speech recogni-tion. However, it requires
access to the full sequence, and thecomputational cost grows quadratically with
respect to the in-put sequence length. These factors limit its adoption for
stream-ing applications. In this work, we proposed a novel augmentedmemory
self-attention, which attends on a short segment of theinput sequence and a
bank of memories. The memory bankstores the embedding information for all the
processed seg-ments. On the librispeech benchmark, our proposed
methodoutperforms all the existing streamable transformer methods bya large
margin and achieved over 15% relative error reduction,compared with the widely
used LC-BLSTM baseline. Our find-ings are also confirmed on some large internal
datasets.


  The rare kaon decay program at BNL is summarized. A brief review of recent
results is provided along with a discussion of prospects for the future of this
program. The primary focus is the two golden modes: k+->pnn and kl->pnn. The
first step in an ambitious plan to precisely measure both branching ratios has
been successfully completed with the observation of two k+->pnn events by E787.
The E949 experiment is poised to reach an order of magnitude further in
sensitivity and to observe ~10 Standard Model events.


  Recently, there have been significant advancements in Image Restoration based
on CNN and transformer. However, the inherent characteristics of the Image
Restoration task are often overlooked in many works. They, instead, tend to
focus on the basic block design and stack numerous such blocks to the model,
leading to parameters redundant and computations unnecessary. Thus, the
efficiency of the image restoration is hindered. In this paper, we propose a
Lightweight Baseline network for Image Restoration called LIR to efficiently
restore the image and remove degradations. First of all, through an ingenious
structural design, LIR removes the degradations existing in the local and
global residual connections that are ignored by modern networks. Then, a
Lightweight Adaptive Attention (LAA) Block is introduced which is mainly
composed of proposed Adaptive Filters and Attention Blocks. The proposed
Adaptive Filter is used to adaptively extract high-frequency information and
enhance object contours in various IR tasks, and Attention Block involves a
novel Patch Attention module to approximate the self-attention part of the
transformer. On the deraining task, our LIR achieves the state-of-the-art
Structure Similarity Index Measure (SSIM) and comparable performance to
state-of-the-art models on Peak Signal-to-Noise Ratio (PSNR). For denoising,
dehazing, and deblurring tasks, LIR also achieves a comparable performance to
state-of-the-art models with a parameter size of about 30\%. In addition, it is
worth noting that our LIR produces better visual results that are more in line
with the human aesthetic.


  Toroidal nematics are nematic liquid crystals confined within a circular
torus and subject to planar degenerate anchoring on the boundary of the torus.
They may be droplets floating in an isotropic environment or cavities carved
out of a solid substrate. A universal solution of Frank's elastic free energy
is an equilibrium configuration for the nematic director field, irrespective of
the values of the elastic constants, whose vector lines are the coaxial
parallels of the torus. We explore the local stability of this configuration
and identify a range of parameters where the main drive towards instability
does not come from the surface-like elastic constant $K_{24}$ being large, but
from the the ratio $K_2/K_3$ of the twist to bend elastic constants being
small, which also makes our study relevant to chromonic liquid crystals.


  We study an asset allocation stochastic problem with restriction for a
defined-contribution pension plan during the accumulation phase. We consider a
financial market with stochastic interest rate, composed of a risk-free asset,
a real zero coupon bond price, the inflation-linked bond and the risky asset. A
plan member aims to maximize the expected power utility derived from the
terminal wealth. In order to protect the rights of a member who dies before
retirement, we introduce a clause which allows to withdraw his premiums and the
difference is distributed among the survival members. Besides the mortality
risk, the fund manager takes into account the salary and the inflation risks.
We then obtain closed form solutions for the asset allocation problem using a
sufficient maximum principle approach for the problem with partial information.
Finally, we give a numerical example.


  The evolution of dispersal is a classical question in evolutionary biology,
and it has been studied in a wide range of mathematical models. A
selection-mutation model, in which the population is structured by space and a
phenotypic trait, with the trait acting directly on the dispersal (diffusion)
rate, was formulated by Perthame and Souganidis [Math. Model. Nat. Phenom. 11
(2016), 154-166] to study the evolution of random dispersal towards the
evolutionarily stable strategy. For the rare mutation limit, it was shown that
the equilibrium population concentrates on a single trait associated to the
smallest dispersal rate. In this paper, we consider the corresponding evolution
equation and characterize the asymptotic behaviors of the time-dependent
solutions in the rare mutation limit, under mild convexity assumptions on the
underlying Hamiltonian function.


  All current techniques for showing that a number field has an infinite
p-class field tower depend on one of various forms of the Golod-Shafarevich
inequality. Such techniques can also be used to restrict the types of p-groups
which can occur as Galois groups of finite p-class field towers. In the case
that the base field is a quadratic imaginary number field, the theory
culminates in showing that a finite such group must be of one of three possible
presentation types. By keeping track of the error terms arising in standard
proofs of Golod-Shafarevich type inequalities, we prove a Golod-Shafarevich
equality for analytic pro-p-groups. As an application, we further work of
Skopin, showing that groups of the third of the three types mentioned above are
necessarily tremendously large.


  Segmentation of medical images is a critical issue: several process of
analysis and classification rely on this segmentation. With the growing number
of people presenting back pain and problems related to it, the automatic or
semi-automatic segmentation of fractured vertebral bodies became a challenging
task. In general, those fractures present several regions with non-homogeneous
intensities and the dark regions are quite similar to the structures nearby.
Aimed at overriding this challenge, in this paper we present a semi-automatic
segmentation method, called Balanced Growth (BGrowth). The experimental results
on a dataset with 102 crushed and 89 normal vertebrae show that our approach
significantly outperforms well-known methods from the literature. We have
achieved an accuracy up to 95% while keeping acceptable processing time
performance, that is equivalent to the state-of-the-artmethods. Moreover,
BGrowth presents the best results even with a rough (sloppy) manual annotation
(seed points).


  We prove that the Bourgain slicing conjecture and the
Kannan-Lov\'asz-Simonovits (KLS) isoperimetric conjecture in $\mathbb{R}^n$
hold true up to a factor of $\sqrt{\log n}$. A new ingredient used in the proof
is an improved log-concave Lichnerowicz inequality.


  In this paper we study finite monoids M such that the group algebras over a
domain R for all Schutzenberger groups of M are cell algebras. We show that for
any such M the monoid algebra A over R has a standard cell algebra structure.
Using properties of cell algebras we then find conditions for A to be
quasi-hereditary and we show that if such an M is an inverse semi-group and R
is a field k, then A is semi-simple if and only if the group algebras over k
for all maximal subgroups of M are semi-simple. Finally, we show that for any
"compatible" twisting of M into R the twisted monoid algebra is also a cell
algebra and can thus be analyzed using cell algebra properties.


  We discuss multichannel inelastic rescatterring effects in B decays into a
pair $PP$ of pseudoscalar mesons ($PP = \pi \pi$ or $K\bar{K}$). In agreement
with short-distance models it is assumed that initially $B$ meson decays
dominantly into jet-like states composed of two flying-apart low-mass
resonances $M_1 M_2$ which rescatter into $PP$. Since from all S-matrix
elements $<i|S|PP>$ involving $PP$ only some ($i = M_1 M_2$) contribute to the
final state rescatterring, the latter is treated as a correction only. The
rescatterring of resonance pair $M_1 M_2$ into the final $PP$ state is assumed
to proceed through Regge exchange. Although effects due to a single
intermediate state $M_1 M_2$ are small, it is shown that the combined effect of
all such states should be large. In particular, amplitudes of B decays into
$K\bar{K}$ become significantly larger than those estimated through
short-distance penguin diagrams, to the point of being comparable to the $B\to
\pi \pi$ amplitudes.


  We prove new results on the existence of positive radial solutions of the
elliptic equation $-\Delta u= \lambda h(|x|,u)$ in an annular domain in
$\mathbb{R}^{N}, N\geq 2$. Existence of positive radial solutions are
determined under the conditions that the nonlinearity function $h(t,u)$ is
either superlinear or sublinear growth in $u$ or satisfies some upper and lower
inequalities on $h$. Our discussion is based on a fixed point theorem due to a
revised version of a fixed point theorem of Gustafson and Schmitt.


  Some classical and recent results on the Euler equations governing perfect
(incompressible and inviscid) fluid motion are collected and reviewed, with
some small novelties scattered throughout. The perspective and emphasis will be
given through the lens of infinite-dimensional dynamical systems, and various
open problems are listed and discussed.


  The observed branching ratios for $B\to K \eta'$ decays are much larger than
factorization predictions in the Standard Model (SM). Many proposals have been
made to reconcile the data and theoretical predictions. In this paper we study
these decays within the SM using flavor U(3) symmetry. If small annihilation
amplitudes are neglected, one needs 11 hadronic parameters to describe $B\to
PP$ decays where $P$ can be one of the $\pi$, $K$, $\eta$ and $\eta'$ nonet
mesons. We find that existing data are consistent with SM with flavor U(3)
symmetry. We also predict several measurable branching ratios and CP
asymmetries for $B \to K (\pi) \eta(\eta')$, $\eta(\eta')\eta(\eta')$ decays.
Near future experiments can provide important tests for the Standard Model with
flavor U(3) symmetry.


  In this work we provide the best constants of the multiple Khintchine
inequality. This allows us, among other results, to obtain the best constants
of the mixed $\left( \ell_{\frac{p}{p-1}},\ell_{2}\right) $-Littlewood
inequality, thus ending completely a work started by Pellegrino in \cite{pell}.


  Using an apparatus that allows superfluid liquid 4He to be in contact with
hcp solid \4he at pressures greater than the bulk melting pressure of the
solid, we have performed experiments that show evidence for 4He mass flux
through the solid and the likely presence of superfluid inside the solid. We
present results that show that a thermomechanical equilibrium in quantitative
agreement with the fountain effect exists between two liquid reservoirs
connected to each other through two superfluid-filled Vycor rods in series with
a chamber filled with solid 4He. We use the thermomechanical effect to induce
flow through the solid and measure the flow rate. On cooling, mass flux appears
near T = 600 mK and rises smoothly as the temperature is lowered. Near T = 75
mK a sharp drop in the flux is present. The flux increases as the temperature
is reduced below 75 mK. We comment on possible causes of this flux minimum.


  Einstein-aether theory is general relativity coupled to a dynamical, unit
timelike vector. If this vector is restricted in the action to be hypersurface
orthogonal, the theory is identical to the IR limit of the extension of Horava
gravity proposed by Blas, Pujol\`{a}s and Sibiryakov. Hypersurface orthogonal
solutions of Einstein-aether theory are solutions to the IR limit of this
theory, hence numerous results already obtained for Einstein-aether theory
carry over.


  Optical microscopy is an essential tool in biology and medicine. Imaging
thin, yet non-flat objects in a single shot (without relying on more
sophisticated sectioning setups) remains challenging as the shallow depth of
field that comes with high-resolution microscopes leads to unsharp image
regions and makes depth localization and quantitative image interpretation
difficult.
  Here, we present a method that improves the resolution of light microscopy
images of such objects by locally estimating image distortion while jointly
estimating object distance to the focal plane. Specifically, we estimate the
parameters of a spatially-variant Point-Spread function (PSF) model using a
Convolutional Neural Network (CNN), which does not require instrument- or
object-specific calibration. Our method recovers PSF parameters from the image
itself with up to a squared Pearson correlation coefficient of 0.99 in ideal
conditions, while remaining robust to object rotation, illumination variations,
or photon noise. When the recovered PSFs are used with a spatially-variant and
regularized Richardson-Lucy deconvolution algorithm, we observed up to 2.1 dB
better signal-to-noise ratio compared to other blind deconvolution techniques.
Following microscope-specific calibration, we further demonstrate that the
recovered PSF model parameters permit estimating surface depth with a precision
of 2 micrometers and over an extended range when using engineered PSFs. Our
method opens up multiple possibilities for enhancing images of non-flat objects
with minimal need for a priori knowledge about the optical setup.


  We consider a magnetic configuration consisting of an arcade structure and a
detached plasmoid, resulting from a magnetic reconnection process, as is
typically found in connection with solar flares. We study spontaneous current
fragmentation caused by shear and vortex plasma flows. An exact analytical
transformation method was applied to calculate self-consistent solutions of the
nonlinear stationary MHD equations. The assumption of incompressible
field-aligned flows implies that both the Alfven Mach number and the mass
density are constant on field lines. We first calculated nonlinear MHS
equilibria with the help of the Liouville method, emulating the scenario of a
solar eruptive flare configuration with plasmoids and flare arcade. Then a Mach
number profile was constructed that describes the upflow along the open
magnetic field lines and implements a vortex flow inside the plasmoid. This
Mach number profile was used to map the MHS equilibrium to the stationary one.
We find that current fragmentation takes place at different locations within
our configuration. Steep gradients of the Alfven Mach number are required,
implying the strong influence of shear flows on current amplification and
filamentation of the MHS current sheets. Crescent- or ring-like structures
appear along the outer separatrix, butterfly structures between the upper and
lower plasmoids, and strong current peaks close the lower boundary. Impressing
an intrinsic small-scale structure on the upper plasmoid results in strong
fragmentation of the plasmoid. Hence fragmentation of current sheets and
plasmoids is an inherent property of MHD theory. Transformations from MHS into
MHD steady-states deliver fine-structures needed for plasma heating and
acceleration of particles and bulk plasma flows in dissipative events that are
typically connected to magnetic reconnection processes in flares and coronal
mass ejections.


  The doctrinal paradox is analysed from a probabilistic point of view assuming
a simple parametric model for the committee's behaviour. The well known
issue-by-issue and case-by-case majority rules are compared in this model, by
means of the concepts of false positive rate (FPR), false negative rate (FNR)
and Receiver Operating Characteristics (ROC) space. We introduce also a new
rule that we call path-by-path, which is somehow halfway between the other two.
Under our model assumptions, the issue-by-issue rule is shown to be the best of
the three according to an optimality criterion based in ROC maps, for all
values of the model parameters (committee size and competence of its members),
when equal weight is given to FPR an FNR. For unequal weights, the relative
goodness of the rules depends on the values of the competence and the weights,
in a way which is precisely described. The results are illustrated with some
numerical examples.


  The directed-loop quantum Monte Carlo method is generalized to the case of
retarded interactions. Using the path integral, fermion-boson or spin-boson
models are mapped to actions with retarded interactions by analytically
integrating out the bosons. This yields an exact algorithm that combines the
highly-efficient loop updates available in the stochastic series expansion
representation with the advantages of avoiding a direct sampling of the bosons.
The application to electron-phonon models reveals that the method overcomes the
previously detrimental issues of long autocorrelation times and exponentially
decreasing acceptance rates. For example, the resulting dramatic speedup allows
us to investigate the Peierls quantum phase transition on chains of up to
$1282$ sites.


  A theoretical study is given for the self-oscillation excited in a spin
torque oscillator (STO) consisting of an in-plane magnetized free layer and a
perpendicularly magnetized pinned layer in the presence of a perpendicular
magnetic field. This type of STO is a potential candidate for a microwave
source of microwave assisted magnetization reversal (MAMR). It is, however,
found that the self-oscillation applicable to MAMR disappears when the
perpendicular field is larger than a critical value, which is much smaller than
a demagnetization field. This result provides a condition that the reversal
field of a magnetic recording bit by MAMR in nanopillar structure should be
smaller than the critical value. The analytical formulas of currents
determining the critical field are obtained, which indicate that a material
with a small damping is not preferable to acheive a wide range of the
self-oscillation applicable to MAMR, although such a material is preferable
from the view point of the reduction of the power consumption.


  In this work we intend to report on some results obtained by an analytical
modelling of biomacromolecular structures as driven by the study of Steiner
points and Steiner trees with an Euclidean definition of distance.


  We study the global well-posedness of the two-dimensional defocusing
fourth-order Schr\"odinger initial value problem with power type nonlinearities
$\vert u\vert^{2k}u$ where $k$ is a positive integer. By using the $I$-method,
we prove that global well-posedness is satisfied in the Sobolev spaces
$H^{s}(\mathbb{R}^{2})$ for $2-\frac{3}{4k}<s<2$.


  We consider a widely used form of models for ship maneuvering, whose
nonlinearities entail continuous but nonsmooth second-order modulus terms. For
such models bifurcations of straight motion are not amenable to standard center
manifold reduction and normal forms. Based on a recently developed analytical
approach, we nevertheless determine the character of local bifurcations when
stabilizing the straight motion course with standard proportional control. For
a specific model class we perform a detailed analysis of the linearization to
determine the location of these bifurcations in the control parameter space and
its dependence on selected design parameters. By computing the analytically
derived characteristic parameters, we find that `safe' supercritical
Andronov--Hopf bifurcations are typical. Through numerical continuation we
provide a more global bifurcation analysis, which identifies the arrangement
and relative location of stable and unstable equilibria and periodic orbits.


  We have considered the results of solar and atmospheric neutrino oscillation
experiments in the scheme of mixing of three neutrinos with a mass hierarchy.
It is shown that the recent results of the CHOOZ experiment imply that
|U_{e3}|^2<<1 (U is the neutrino mixing matrix), that the oscillations of solar
neutrinos are described by the two-generation formalism and that the
oscillations of solar and atmospheric neutrinos decouple. It is also shown that
if not only |U_{e3}|^2<<1 but also |U_{e3}|<<1, then the oscillations of
atmospheric neutrinos do not depend on matter effects and are described by the
two-generation formalism. In this case, with an appropriate identification of
the mixing parameters, the two-generation analyses of solar and atmospheric
neutrino data provide direct information on the mixing parameters of three
neutrinos. We discuss the possibility to get information on |U_{e3}|^2 in
long-baseline neutrino oscillation experiments.


  With the boom in the development of computer hardware and software, social
media, IoT platforms, and communications, there has been an exponential growth
in the volume of data produced around the world. Among these data, relational
datasets are growing in popularity as they provide unique insights regarding
the evolution of communities and their interactions. Relational datasets are
naturally non-negative, sparse, and extra-large. Relational data usually
contain triples, (subject, relation, object), and are represented as
graphs/multigraphs, called knowledge graphs, which need to be embedded into a
low-dimensional dense vector space. Among various embedding models, RESCAL
allows learning of relational data to extract the posterior distributions over
the latent variables and to make predictions of missing relations. However,
RESCAL is computationally demanding and requires a fast and distributed
implementation to analyze extra-large real-world datasets. Here we introduce a
distributed non-negative RESCAL algorithm for heterogeneous CPU/GPU
architectures with automatic selection of the number of latent communities
(model selection), called pyDRESCALk. We demonstrate the correctness of
pyDRESCALk with real-world and large synthetic tensors, and the efficacy
showing near-linear scaling that concurs with the theoretical complexities.
Finally, pyDRESCALk determines the number of latent communities in an
11-terabyte dense and 9-exabyte sparse synthetic tensor.


  Fuzzing has emerged as a powerful technique for finding security bugs in
complicated real-world applications. American fuzzy lop (AFL), a leading
fuzzing tool, has demonstrated its powerful bug finding ability through a vast
number of reported CVEs. However, its random mutation strategy is unable to
generate test inputs that satisfy complicated branching conditions (e.g.,
magic-byte comparisons, checksum tests, and nested if-statements), which are
commonly used in image decoders/encoders, XML parsers, and checksum tools.
Existing approaches (such as Steelix and Neuzz) on addressing this problem
assume unrealistic assumptions such as we can satisfy the branch condition
byte-to-byte or we can identify and focus on the important bytes in the input
(called hot-bytes) once and for all. In this work, we propose an approach
called \tool~which is designed based on the following principles. First, there
is a complicated relation between inputs and branching conditions and thus we
need not only an expressive model to capture such relationship but also an
informative measure so that we can learn such relationship effectively. Second,
different branching conditions demand different hot-bytes and we must adjust
our fuzzing strategy adaptively depending on which branches are the current
bottleneck. We implement our approach as an open source project and compare its
efficiency with other state-of-the-art fuzzers. Our evaluation results on 10
real-world programs and LAVA-M dataset show that \tool~achieves sustained
increases in branch coverage and discovers more bugs than other fuzzers.


  We define reduced and essential Banach algebras associated to a twisted
\'{e}tale (not necessarily Hausdorff) groupoid $(\mathcal{G},\mathcal{L})$ and
extend some fundamental results from $C^*$-algebras to this context. For
instance, we prove that for topologically free and minimal groupoids every
essential Banach algebra is simple, and we give conditions under which reduced
algebras are essential (for example Hausdorffness of $\mathcal{G}$ is
sufficient). This in particular solves the simplicity problem posed recently by
Gardella-Lupini for $L^p$-operator algebras associated to $\mathcal{G}$. In
addition, using either the $n$-filling or locally contracting condition we give
pure infiniteness criteria for essential simple Banach algebras associated to
$(\mathcal{G},\mathcal{L})$. This extends the corresponding $C^*$-algebraic
results that were previously known to hold in the untwisted Hausdorff case. The
results work nicely, and allow for characterisation of the generalized
intersection property, in the realm of $L^P$-operator algebras where $P
\subseteq [1,\infty]$ is a non-empty set of parameters. Such algebras cover in
particular $L^p$-operator algebras, for $p\in [1,\infty]$, and their Banach
$*$-algebra versions.
  We apply our results to Banach algebra crossed products by twisted partial
group actions, Roe-type Banach algebras with coefficients in finite-rank
operators on a Banach space, twisted tight $L^P$-operator algebras of inverse
semigroups, graph $L^P$-operator algebras, and algebras associated to
self-similar group actions on graphs. We also interpret our results in terms of
twisted inverse semigroup actions and their crossed products.


  The main interest of the Science Team for the exploitation of the MEGARA
instrument at the 10.4m Gran Telescopio Canarias (GTC hereafter) is devoted to
the study of nearby galaxies, with focus on the research of the history of star
formation, and chemical and kinematical properties of disc systems. We refer to
this project as MEGADES: MEGARA Galaxy Discs Evolution Survey. The initial goal
of MEGADES is to provide a detailed study of the inner regions of nearby disc
galaxies, both in terms of their spectrophotometric and chemical evolution, and
their dynamical characterisation, by disentangling the contribution of in-situ
and ex-situ processes to the history of star formation and effective chemical
enrichment of these regions. In addition, the dynamical analysis of these inner
regions naturally includes the identification and characterization of galactic
winds potentially present in these regions. At a later stage, we will extend
this study further out in galactocentric distance. The first stage of this
project encompasses the analysis of the central regions of a total of 43 nearby
galaxies observed with the MEGARA Integral Field Unit for 114 hours, including
both Guaranteed Time and Open Time observations. In this paper we provide a set
of all the processed data products available to the community and early results
from the analysis of these data regarding stellar continuum, ionized and
neutral gas features.


  We study the proposal that a $d+1$ dimensional induced metric is constructed
from a $d$ dimensional field theory using gradient flow. Applying the idea to
the O($N$) $\varphi^4$ model and normalizing the flow field, we have shown in
the large $N$ limit that the induced metric is finite and universal in the
sense that it does not depend on the details of the flow equation and the
original field theory except for the renormalized mass, which is the only
relevant quantity in this limit. We have found that the induced metric
describes Euclidean Anti-de-Sitter (AdS) space in both ultra-violet (UV) and
infra-red (IR) limits of the flow direction, where the radius of the AdS is
bigger in the IR than in the UV.


  We study a general class of line-soliton solutions of the
Kadomtsev-Petviashvili II (KPII) equation by investigating the Wronskian form
of its tau-function. We show that, in addition to previously known line-soliton
solutions, this class also contains a large variety of new multi-soliton
solutions, many of which exhibit nontrivial spatial interaction patterns. We
also show that, in general, such solutions consist of unequal numbers of
incoming and outgoing line solitons. From the asymptotic analysis of the
tau-function, we explicitly characterize the incoming and outgoing
line-solitons of this class of solutions. We illustrate these results by
discussing several examples.


  This Reply to preceding Comment of arXiv:1909.09867 shows why the statements
in the Comment are misleading. We point out that our physical picture and
theirs are fundamentally different, therefore the claim of using their
correlation to include ours shows a very limited physical relevance, which
instead may impede the precise understanding of either of the two pictures.


  Synthetic biology sets out to implement new functions in cells, and to
develop a deeper understanding of biological design principles. In 2000,
Elowitz and Leibler showed that by rational design of the reaction network, and
using existing biological components, they could create a network that exhibits
periodic gene expression, dubbed the repressilator (Elowitz and Leibler,
Nature, 2000). More recently, Stricker et al. presented another synthetic
oscillator, called the dual-feedback oscillator (Stricker et al., 2008), which
is more stable. How the stability of these oscillators is affected by the
intrinsic noise of the interactions between the components and the stochastic
expression of their genes, has been studied in considerable detail. However, as
all biological oscillators reside in growing and dividing cells, an important
question is how these oscillators are perturbed by the cell cycle. In previous
work we showed that the periodic doubling of the gene copy numbers due to DNA
replication can couple not only natural, circadian oscillators to the cell
cycle (Paijmans et al., PNAS, \textbf{113}, 4063, (2016)), but also these
synthetic oscillators. Here we expand this study. We find that the strength of
the locking between oscillators depends not only on the positions of the genes
on the chromosome, but also on the noise in the timing of gene replication:
noise tends to weaken the coupling. Yet, even in the limit of high levels of
noise in the replication times of the genes, both synthetic oscillators show
clear signatures of locking to the cell cycle. This work enhances our
understanding of the design of robust biological oscillators inside growing and
diving cells.


  We associate in a canonical way a substitution to any abstract numeration
system built on a regular language. In relationship with the growth order of
the letters, we define the notion of two independent substitutions. Our main
result is the following. If a sequence $x$ is generated by two independent
substitutions, at least one being of exponential growth, then the factors of
$x$ appearing infinitely often in $x$ appear with bounded gaps. As an
application, we derive an analogue of Cobham's theorem for two independent
substitutions (or abstract numeration systems) one with polynomial growth, the
other being exponential.


  All imaging modalities such as computed tomography (CT), emission tomography
and magnetic resonance imaging (MRI) require a reconstruction approach to
produce an image. A common image processing task for applications that utilise
those modalities is image segmentation, typically performed posterior to the
reconstruction. We explore a new approach that combines reconstruction and
segmentation in a unified framework. We derive a variational model that
consists of a total variation regularised reconstruction from undersampled
measurements and a Chan-Vese based segmentation. We extend the variational
regularisation scheme to a Bregman iteration framework to improve the
reconstruction and therefore the segmentation. We develop a novel alternating
minimisation scheme that solves the non-convex optimisation problem with
provable convergence guarantees. Our results for synthetic and real data show
that both reconstruction and segmentation are improved compared to the
classical sequential approach.


  In the Orthogonal Vectors (OV) problem, we wish to determine if there is an
orthogonal pair of vectors among $n$ Boolean vectors in $d$ dimensions. The OV
Conjecture (OVC) posits that OV requires $n^{2-o(1)}$ time to solve, for all
$d=\omega(\log n)$. Assuming the OVC, optimal time lower bounds have been
proved for many prominent problems in $P$.
  We prove that OVC is true in several computational models of interest:
  * For all sufficiently large $n$ and $d$, OV for $n$ vectors in $\{0,1\}^d$
has branching program complexity $\tilde{\Theta}(n\cdot \min(n,2^d))$. In
particular, the lower bounds match the upper bounds up to polylog factors.
  * OV has Boolean formula complexity $\tilde{\Theta}(n\cdot \min(n,2^d))$,
over all complete bases of $O(1)$ fan-in.
  * OV requires $\tilde{\Theta}(n\cdot \min(n,2^d))$ wires, in formulas
comprised of gates computing arbitrary symmetric functions of unbounded fan-in.
  Our lower bounds basically match the best known (quadratic) lower bounds for
any explicit function in those models. Analogous lower bounds hold for many
related problems shown to be hard under OVC, such as Batch Partial Match, Batch
Subset Queries, and Batch Hamming Nearest Neighbors, all of which have very
succinct reductions to OV.
  The proofs use a certain kind of input restriction that is different from
typical random restrictions where variables are assigned independently. We give
a sense in which independent random restrictions cannot be used to show
hardness, in that OVC is false in the "average case" even for $AC^0$ formulas:
  * For every fixed $p \in (0,1)$ there is an $\epsilon_p > 0$ such that for
every $n$ and $d$, OV instances where input bits are independently set to $1$
with probability $p$ (and $0$ otherwise) can be solved with $AC^0$ formulas of
size $O(n^{2-\epsilon_p})$, on all but a $o_n(1)$ fraction of instances.


  We define the (total) center of mass for suitably asymptotically hyperbolic
time-slices of asymptotically anti-de Sitter spacetimes in general relativity.
We do so in analogy to the picture that has been consolidated for the (total)
center of mass of suitably asymptotically Euclidean time-slices of
asymptotically Minkowskian spacetimes (isolated systems). In particular, we
unite -- an altered version of -- the approach based on Hamiltonian charges
with an approach based on CMC-foliations near infinity. The newly defined
center of mass transforms appropriately under changes of the asymptotic
coordinates and evolves in the direction of an appropriately defined linear
momentum under the Einstein evolution equations.


  We use the Lindblad equation approach to investigate topological phases
hosting more than one localized state at each side of a disordered SSH chain
with properly tuned long range hoppings. Inducing a non equilibrium steady
state across the chain, we probe the robustness of each phase and the fate of
the edge modes looking at the distribution of electrons along the chain and the
corresponding standard deviation in the presence of different kinds of disorder
either preserving, or not, the symmetries of the Hamiltonian.


  For the extrapolation of magnetic fields into the solar corona from
measurements taken in the photosphere (or chromosphere) force-free magnetic
fields are typically used. This does not take into account that the lower
layers of the solar atmosphere are not force-free. While some numerical
extrapolation methods using magnetohydrostatic magnetic fields have been
suggested, a complementary and numerically comparatively cheap method is to use
analytical magnetohydrostatic equilibria to extrapolate the magnetic field. In
this paper, we present a new family of solutions for a special class of
analytical three-dimensional magnetohydrostatic equilibria, which can be of use
for such magnetic field extrapolation. The new solutions allow for the more
flexible modelling of a transition from non-force-free to (linear) force-free
magnetic fields. In particular, the height and width of the region where this
transition takes place can be specified by choosing appropriate model
parameters.


  Spectroscopic observations of 32 HII regions in the spiral galaxy NGC 3963
and the barred irregular galaxy NGC 7292 were carried out with the 2.5-m
telescope of the Caucasus Mountain Observatory of the Sternberg Astronomical
Institute using the Transient Double-beam Spectrograph with a dispersion of
1A/pixel and a spectral resolution of 3A. These observations were used to
estimate the oxygen and nitrogen abundances and the electron temperatures in
HII regions through modern strong-line methods. In general, the galaxies have
oxygen and nitrogen abundances typical of stellar systems with similar
luminosities, sizes, and morphology. However, we have found some peculiarities
in chemical abundance distributions in both galaxies. The distorted outer
segment of the southern arm of NGC 3963 shows an excess oxygen and nitrogen
abundances. Chemical elements abundances in NGC 7292 are constant and do not
depend on the galactocentric distance. These peculiarities can be explained in
terms of external gas accretion in the case of NGC 3963 and major merging for
NGC 7292.


  Exclusive electroproduction of $\phi$ mesons has been studied in $e^\pm p$
collisions at $\sqrt{s}=318 \gev$ with the ZEUS detector at HERA using an
integrated luminosity of 65.1 pb$^{-1}$. The $\gamma^*p$ cross section is
presented in the kinematic range $2<Q^2<70 \gev^2$, $35<W<145 \gev$ and
${|t|}<0.6 \gev^2$. The cross sections as functions of $Q^2$, $W$, $t$ and
helicity angle $\theta_h$ are compared to cross sections for other vector
mesons. The ratios $R$ of the cross sections for longitudinally and
transversely polarized virtual photons are presented as functions of $Q^2$ and
$W$. The data are also compared to predictions from theoretical models.


  Comparator circuit model was originally introduced by Mayr and Subramanian
(1992) (and further studied by Cook, Filmus and Le (2012)) to capture problems
which are not known to be P-complete but still not known to admit efficient
parallel algorithms. The class CC is the complexity class of problems many-one
logspace reducible to the Comparator Circuit Value Problem and we know that NL
is contained in CC which is inturn contained in P. Cook, Filmus and Le (2012)
showed that CC is also the class of languages decided by polynomial size
comparator circuits.
  We study generalizations of the comparator circuit model that work over fixed
finite bounded posets. We observe that there are universal comparator circuits
even over arbitrary fixed finite bounded posets. Building on this, we show that
general (resp. skew) comparator circuits of polynomial size over fixed finite
distributive lattices characterizes CC (resp. L). Complementing this, we show
that general comparator circuits of polynomial size over arbitrary fixed finite
lattices exactly characterizes P even when the comparator circuit is skew. In
addition, we show a characterization of the class NP by a family of polynomial
sized comparator circuits over fixed {\em finite bounded posets}. These results
generalize the results by Cook, Filmus and Le (2012) regarding the power of
comparator circuits. As an aside, we consider generalizations of Boolean
formulae over arbitrary lattices. We show that Spira's theorem (1971) can be
extended to this setting as well and show that polynomial sized Boolean
formulae over finite fixed lattices capture exactly NC^1.


  The pandemic threat of COVID-19 with more than 37 million cases in which
about 5 percent entering critical stage characterized by cytokine storm and
hyperinflammatory condition, the state more often leads to admission to
intensive care unit with rapid mortality. Janus kinase enzymes of Jak-1, Jak-2,
Jak-3, and Tyk2 seem to be good targets for inhibition by medications to
control cytokine storm in this context. In the present work, the inhibitory
properties of different analgesic drugs on these targets are studied to assess
their ability for clinical application from different points of view. Our
docking results indicated that naproxen, methadone, and amitriptyline
considering their higher binding energy, lower energy variance, and higher
hydrophobicity, seem to express more inhibitory effects on Janus kinase enzymes
than thats for approved inhibitors i.e. baricitinib and ruxolitinib.
Accordingly, we suggest our wide list of candidate drugs including
indomethacin, etodolac, buprenorphine, rofecoxib, duloxetine, valdecoxib,
naproxen, methadone, and amitriptilin for clinical assessments for their
usefulness in COVID-19 treatment, especially taking into account that up to
now, there is no approved cure for this disease.


  An efficient first principles approach to calculate X-ray magnetic circular
dichroism (XMCD) and X-ray natural circular dichroism (XNCD) is developed and
applied in the near edge region at the K-and L1-edges in solids. Computation of
circular dichroism requires precise calculations of X-ray absorption spectra
(XAS) for circularly polarized light. For the derivation of the XAS cross
section, we used a relativistic description of the photon-electron interaction
that results in an additional term in the cross-section that couples the
electric dipole operator with an operator $\mathbf{\sigma}\cdot
(\mathbf{\epsilon} \times \mathbf{r})$ that we name spin-position. The
numerical method relies on pseudopotentials, on the gauge including projected
augmented wave method and on a collinear spin relativistic description of the
electronic structure. We apply the method to the calculations of K-edge XMCD
spectra of ferromagnetic iron, cobalt and nickel and of I L1-edge XNCD spectra
of $\alpha$-LiIO3, a compound with broken inversion symmetry. For XMCD spectra
we find that, even if the electric dipole term is the dominant one, the
electric quadrupole term is not negligible (8% in amplitude in the case of
iron). The term coupling the electric dipole operator with the spin-position
operator is significant (28% in amplitude in the case of iron). We obtain a
sum-rule relating this new term to the spin magnetic moment of the p-states. In
$\alpha$-LiIO3 we recover the expected angular dependence of the XNCD spectra.


  Multiferroics with coexistent ferroelectric and magnetic orders can provide
an interesting laboratory to test unprecedented magnetoelectric responses and
their possible applications. One such example is the dynamical and/or resonant
coupling between magnetic and electric dipoles in a solid. As the examples of
such dynamical magnetoelectric effects, (1) the multiferroic domain wall
dynamics and (2) the electric-dipole active magnetic responses are discussed
with the overview of recent experimental observations.


  In the present paper, we obtain an explicit product formula for products of
multiple integrals w.r.t. a random measure associated with a L\'evy process. As
a building block, we use a representation formula for products of martingales
from a compensated-covariation stable family. This enables us to consider
L\'evy processes with both jump and Gaussian part. It is well known that for
multiple integrals w.r.t. the Brownian motion such product formulas exist
without further integrability conditions on the kernels. However, if a jump
part is present, this is, in general, false. Therefore, we provide here
sufficient conditions on the kernels which allow us to establish product
formulas. As an application, we obtain explicit expressions for the expectation
of products of iterated integrals, as well as for the moments and the cumulants
for stochastic integrals w.r.t. the random measure. Based on these expressions,
we show a central limit theorem for the long time behaviour of a class of
stochastic integrals. Finally, we provide methods to calculate the number of
summands in the product formula.


  Several novel frameworks for hyperparameter search have emerged in the last
decade, but most rely on strict, often normal, distributional assumptions,
limiting search model flexibility. This paper proposes a novel optimization
framework based on upper confidence bound sampling of conformal confidence
intervals, whose weaker assumption of exchangeability enables greater choice of
search model architectures. Several such architectures were explored and
benchmarked on hyperparameter search of random forests and convolutional neural
networks, displaying satisfactory interval coverage and superior tuning
performance to random search.


  We present observations of the intermediate to massive star-forming region
I05345+3157 using the molecular line tracer CS(2-1) with CARMA to reveal the
properties of the dense gas cores. Seven gas cores are identified in the
integrated intensity map of CS(2-1). Among these, core 1 and core 3 have
counterparts in the 2.7 millimeter continuum data. We suggest that core 1 and
core 3 are star-forming cores that may already or will very soon harbor young
massive protostars. The total masses of core 1 estimated from the LTE method
and dust emission by assuming a gas-to-dust ratio are 5 +- 1 solar masses and
18 +- 6 solar masses, and that of core 3 are 15 +- 7 solar masses and 11 +- 3
solar masses. The spectrum of core 3 shows blue-skewed self-absorption, which
suggests gas infall -- a collapsing core. The observed broad linewidths of the
seven gas cores indicate non-thermal motions. These non-thermal motions can be
interactions with nearby outflows or due to the initial turbulence; the former
is observed, while the role of initial turbulence is less certain. Finally, the
virial masses of the gas cores are larger than the LTE masses, which for a
bound core implies a requirement on the external pressure of ~ 10^8 K/cm^3. The
cores have the potential to further form massive stars.


  We consider families of Dirac operators on the unit interval which depend on
parameters via boundary conditions. We study the associated eta forms and
Maslov cocyles. With this simple example we show how previous results of
Lesch/Woiciechowski and the first author on the eta invariant of cylinders
generalize to the family case.


  Quantum systems in Fock states do not have a phase. When two or more
Bose-Einstein condensates are sent into interferometers, they nevertheless
acquire a relative phase under the effect of quantum measurements. The usual
explanation relies on spontaneous symmetry breaking, where phases are ascribed
to all condensates and treated as unknown classical quantities. However, this
image is not always sufficient: when all particles are measured, quantum
mechanics predicts probabilities that are sometimes in contradiction with it,
as illustrated by quantum violations of local realism. In this letter, we show
that interferometers can be used to demonstrate a large variety of violations
with an arbitrarily large number of particles. With two independent
condensates, we find violations of the BCHSH inequalities, as well as new
N-body Hardy impossibilities. With three condensates, we obtain new GHZ
(Greenberger, Horne and Zeilinger) type contradictions.


  A new set of projection operators is constructed to suitably handle
non-relativistic theories of gravity with anisotropic scaling, including the
ones with parity-violating terms. This alternative procedure allows us to
discuss unitarity and spectral properties for different formulations of the
Horava-Lifshitz gravity. This task, that generally involves lengthy algebraic
steps, becomes more systematic and greatly simplified in terms of the
projectors we work out. Moreover, this procedure allows us to fix the number of
propagating degrees of freedom and the structure of gauge symmetries is readily
determined. In order to test the efficacy of the technique at hand, the
unitarity and low-energy regime of a general Horava-Lifshitz Gravity model are
investigated.


  We report the recent progress in the studies of D-wave heavy quarkonia
production from gluon fragmentation at the Tevatron and in Z^0 decays, and the
D-wave charmonia production in B decays. We show that the color-octet
contributions are of crucial importance to the production of D-wave quarkonia.
Signals, as strong as that for J/\psi and \psi^\prime, should be seen for the
D-wave charmonium in the processes. These will provide a test of the
color-octet production mechanism.


  For situations where we are trying to decide which of two hypotheses $H_{0}$
and $H_{1}$ provides a better description of some data, we discuss the
usefulness of plots of $p_{0}$ versus $p_{1}$, where $p_{i}$ is the $p$-value
for testing $H_{i}$. They provide an interesting way of understanding the
difference between the standard way of excluding $H_{1}$ and the $CL_{s}$
approach; the Punzi definition of sensitivity; the relationship between
$p$-values and likelihood ratios; and the probability of observing misleading
evidence. They also help illustrate the Law of the Iterated Logarithm and the
Jeffreys-Lindley paradox.


  Over the past decade, distributed CSMA, which forms the basis for WiFi, has
been deployed ubiquitously to provide seamless and high-speed mobile internet
access. However, distributed CSMA might not be ideal for future IoT/M2M
applications, where the density of connected devices/sensors/controllers is
expected to be orders of magnitude higher than that in present wireless
networks. In such high-density networks, the overhead associated with
completely distributed MAC protocols will become a bottleneck. Moreover, IoT
communications are likely to have strict QoS requirements, for which the
`best-effort' scheduling by present WiFi networks may be unsuitable. This calls
for a clean-slate redesign of the wireless MAC taking into account the
requirements for future IoT/M2M networks. In this paper, we propose a
reservation-based (for minimal overhead) wireless MAC designed specifically
with IoT/M2M applications in mind. The key features include: (i) flow-level,
rather than packet level contention to minimize overhead, (ii) deadline aware,
reservation based scheduling, and (iii) the ability to dynamically adapt the
MAC parameters with changing workload.


  The purpose of this letter is to compare the quality of different methods for
estimating stellar masses of galaxies. We compare the results of (a) fitting
stellar population synthesis models to broad band colors from SDSS and 2MASS,
(b) the analysis of spectroscopic features of SDSS galaxies (Kauffmann et al.
2003), and, (c) a simple dynamical mass estimate based on SDSS velocity
dispersions and effective radii. Knowing that all three methods can have
significant biases, a comparison can help to establish their (relative)
reliability. In this way, one can also probe the quality of the observationally
cheap broadband color mass estimators for galaxies at higher redshift.
Generally, masses based on broad-band colors and spectroscopic features agree
reasonably well, with a rms scatter of only ~ 0.25 dex over almost 4 decades in
mass. However, as may be expected, systematic differences do exist and have an
amplitude of ~ 0.15 dex, corrleting with Halpha emission strength.
Interestingly, masses from broad-band color fitting are in better agreement
with dynamical masses than masses based on the analysis of spectroscopic
features. In addition, the differences between the latter and the dynamical
masses correlate with Halpha equivalent width, while this much less the case
for the broad-band masses. We conclude that broad band color mass estimators,
provided they are based on a large enough wavelength coverage and use an
appropriate range of ages, metallicities and dust extinctions, can yield fairly
reliable stellar masses for galaxies. This is a very encouraging result as such
mass estimates are very likely the only ones available at significant redshifts
for some time to come.


  For analyzing quantum transport in semiconductor devices, accurate electronic
structures are critical for quantitative predictions. Here we report
theoretical analysis of electronic structures of all III-V zinc-blende
semiconductor compounds. Our calculations are from density functional theory
with the semi-local exchange proposed recently [F. Tran and P. Blaha, Phys.
Rev. Lett. 102, 226401 (2009)], within the linear muffin tin orbital scheme.
The calculated band gaps and effective masses are compared to experimental data
and good quantitative agreement is obtained. Using the theoretical scheme
presented here, quantum transport in nanostructures of III-V compounds can be
confidently predicted.


  This note provides a set of separating invariants for the ring of vector
invariants $K[V^2]^{S_n}$ of two copies of the natural $S_n$-representation $V
= K^n$ over a field of characteristic 0. This set is much smaller than
generating sets of $K[V^2]^{S_n}$.
  For $n \leq 4$ we show that this set is minimal with respect to inclusion
among all separating sets.


  Stochastic models that incorporate birth, death and immigration (also called
birth-death and innovation models) are ubiquitous and applicable to many
research topics such as quantifying species sizes in ecological populations,
describing gene family sizes, modeling lymphocyte evolution in the body, and
modeling the evolution of firm sizes. Many of these applications involve the
immigration of new species into the system. We develop the full
high-dimensional stochastic process associated with multispecies
birth-death-immigration processes and present a number of exact and asymptotic
results for the steady-state solutions to these types of processes. We
considered models that include carrying capacity and random mutations and find
analytic and approximate results for the statistics of the total number of
individuals, the total number of species, the species size distribution, and
various diversity indices. Our results include a rigorous analysis of the
behavior of these systems in the fast immigration limit which shows that of the
different diversity indices, the species richness is best able to distinguish
different types of birth-death-immigration models. Surprisingly, we also find
that detailed balance is preserved in all of our neutral
birth-death-immigration models, except for those that incorporate carrying
capacity through the birth rate.


  The ac response of self-sustained current oscillations (SSCOs) in GaAs/AlAs
superlattices (SLs) is derived based on the deformation of a limit cycle under
an external ac driving force. Frequency locking into an integer fraction of the
ac frequency is obtained in a periodic response in which a limit cycle deforms
either with or without a topological change. This frequency locking is robust
against the ac bias because a limit cycle can adjust itself. The results are
verified both numerically and experimentally, indicating that SSCOs in SLs can
be understood within the framework of the general concepts and principles of
nonlinear physics.


  This paper is concerned with the derivation and analysis of hydrodynamic
models for systems of self-propelled particles subject to alignment interaction
and attraction-repulsion. The starting point is the kinetic model considered in
earlier work of Degond & Motsch with the addition of an attraction-repulsion
interaction potential. Introducing different scalings than in Degond & Motsch,
the non-local effects of the alignment and attraction-repulsion interactions
can be kept in the hydrodynamic limit and result in extra pressure, viscosity
terms and capillary force. The systems are shown to be symmetrizable hyperbolic
systems with viscosity terms. A local-in-time existence result is proved in the
2D case for the viscous model and in the 3D case for the inviscid model. The
proof relies on the energy method.


  While machine learning is traditionally a resource intensive task, embedded
systems, autonomous navigation, and the vision of the Internet of Things fuel
the interest in resource-efficient approaches. These approaches aim for a
carefully chosen trade-off between performance and resource consumption in
terms of computation and energy. The development of such approaches is among
the major challenges in current machine learning research and key to ensure a
smooth transition of machine learning technology from a scientific environment
with virtually unlimited computing resources into everyday's applications. In
this article, we provide an overview of the current state of the art of machine
learning techniques facilitating these real-world requirements. In particular,
we focus on resource-efficient inference based on deep neural networks (DNNs),
the predominant machine learning models of the past decade. We give a
comprehensive overview of the vast literature that can be mainly split into
three non-mutually exclusive categories: (i) quantized neural networks, (ii)
network pruning, and (iii) structural efficiency. These techniques can be
applied during training or as post-processing, and they are widely used to
reduce the computational demands in terms of memory footprint, inference speed,
and energy efficiency. We also briefly discuss different concepts of embedded
hardware for DNNs and their compatibility with machine learning techniques as
well as potential for energy and latency reduction. We substantiate our
discussion with experiments on well-known benchmark data sets using compression
techniques (quantization, pruning) for a set of resource-constrained embedded
systems, such as CPUs, GPUs and FPGAs. The obtained results highlight the
difficulty of finding good trade-offs between resource efficiency and
prediction quality.


  Extending a previous result of the authors, we classify globally generated
vector bundles on projective spaces with first Chern class equal to three.


  Force estimation using neural networks is a promising approach to enable
haptic feedback in minimally invasive surgical robots without end-effector
force sensors. Various network architectures have been proposed, but none have
been tested in real time with surgical-like manipulations. Thus, questions
remain about the real-time transparency and stability of force feedback from
neural network-based force estimates. We characterize the real-time impedance
transparency and stability of force feedback rendered on a da Vinci Research
Kit teleoperated surgical robot using neural networks with vision-only,
state-only, and state and vision inputs. Networks were trained on an existing
dataset of teleoperated manipulations without force feedback. To measure
real-time stability and transparency during teleoperation with force feedback
to the operator, we modeled a one-degree-of-freedom human and surgeon-side
manipulandum that moved the patient-side robot to perform manipulations on
silicone artificial tissue over various robot and camera configurations, and
tools. We found that the networks using state inputs displayed more transparent
impedance than a vision-only network. However, state-based networks displayed
large instability when used to provide force feedback during lateral
manipulation of the silicone. In contrast, the vision-only network showed
consistent stability in all the evaluated directions. We confirmed the
performance of the vision-only network for real-time force feedback in a
demonstration with a human teleoperator.


  In this paper we investigated the influence of the rare-earth ionic radii on
the spin-phonon coupling in RE2NiMnO6 double perovskites by Raman spectroscopy.
Spin-phonon in dense Nd2NiMnO6 and Gd2NiMnO6 ceramics were investigated by
Raman spectroscopy at low temperatures. The magnitude of the coupling observed
in comparison with other isostructural compounds shows that it is not
influenced by the rare-earth ionic radius, as well as the deviation of the
position of the stretching phonon in the ferromagnetic phase with relation to
the anharmonic contributions follows a power law.


  We prove a conjecture by Aboulker, Charbit and Naserasr by showing that every
oriented graph in which the out-neighborhood of every vertex induces a
transitive tournament can be partitioned into two acyclic induced subdigraphs.
We prove multiple extensions of this result to larger classes of digraphs
defined by a finite list of forbidden induced subdigraphs. We thereby resolve
several special cases of an extension of the famous Gy\'{a}rf\'{a}s-Sumner
conjecture to directed graphs by Aboulker et al.


  We present a sample of 18 optically-selected and X-ray detected spatially
offset active galactic nuclei (AGN) from the Sloan Digital Sky Survey (SDSS).
In 9 systems, the X-ray AGN is spatially offset from the galactic stellar core
that is located within the 3'' diameter SDSS spectroscopic fiber. In 11
systems, the X-ray AGN is spatially offset from a stellar core that is located
outside the fiber, with an overlap of 2. To build the sample, we cross-matched
Type II AGN selected from the SDSS galaxy catalogue with archival Chandra
imaging and employed our custom astrometric and registration procedure. The
projected angular (physical) offsets span a range of 0."6 (0.8 kpc) to 17."4
(19.4 kpc), with a median value of 2."7 (4.6 kpc). The offset nature of an AGN
is an unambiguous signature of a galaxy merger, and these systems can be used
to study the properties of AGN in galaxy mergers without the biases introduced
by morphological merger selection techniques. In this paper (Paper I), we use
our sample to assess the kinematics of AGN photoionized gas in galaxy mergers.
We find that spectroscopic offset AGN selection may be up to 89% incomplete due
to small projected velocity offsets. We also find that the magnitude of the
velocity offsets are generally larger than expected if our spatial selection
introduces a bias toward face-on orbits, suggesting the presence of complex
kinematics in the emission line gas of AGN in galaxy mergers.


  We consider the occupation area of spherical (fractional) Brownian motion,
i.e. the area where the process is positive, and show that it is uniformly
distributed. For the proof, we introduce a new simple combinatorial view on
occupation times of stochastic processes that turns out to be surprisingly
effective. A sampling method is used to relate the moments of occupation times
to persistence probabilities of random walks that again relate to combinatorial
factors in the moments of beta distributions. Our approach also yields a new
and completely elementary proof of L\'evy's second arcsine law for Brownian
motion. Further, combined with Spitzer's formula and the use of Bell
polynomials, we give a characterisation of the distribution of the occupation
times for all L\'evy processes.


  Aims: We study the distribution of Wolf-Rayet (WR) stars and their subtypes
with respect to their host galaxy light distribution. We thus want to
investigate whether WR stars are potential progenitors of stripped-envelope
core-collapse supernovae (SNe) and/or long-duration gamma-ray bursts (LGRBs).
Methods: We derived the relative surface brightness (fractional flux) at the
locations of WR stars and compared with similar results for LGRBs and SNe. We
examined two nearby galaxies, M 83 and NGC 1313, for which a comprehensive
study of the WR population exists. These two galaxies contain a sufficiently
large number of WR stars and sample different metallicities. To enable the
comparison, the images of the galaxies were processed to make them appear as
they would look at a higher redshift. The robustness of our results against
several sources of uncertainty was investigated with the aid of Monte Carlo
simulations. Results: We find that the WC star distribution favours brighter
pixels than the WN star population. WC stars are more likely drawn from the
same distribution as SNe Ic than from other SN distributions, while WN stars
show a higher degree of association with SNe Ib. It can also not be excluded
that WR (especially WC) stars are related to LGRBs. Some differences between
the two galaxies do exist, especially in the subtype distributions, and may
stem from differences in metallicity. Conclusions: Although a conclusive answer
is not possible, the expectation that WR stars are the progenitors of SNe Ib/c
and LGRBs survives this test. The trend observed between the distributions of
WN and WC stars, as compared to those of SNe Ib and Ic, is consistent with the
theoretical picture that SNe Ic result from progenitors that have been stripped
of a larger part of their envelope.


  Momentum sum rule can be used as an inequality to estimate the lower and
upper bounds of the momentum fractions of quarks and gluons in a model of
proton valid in a limited \textit{x} range. We compute such bounds in a
self-similarity based model of proton structure function valid in the range $
6.2\times 10^{-7} \leq x \leq 10^{-2} $. The results conform to the asymptotic
QCD expectations.


  Recently, instant level labeling for supervised machine learning requires a
considerable number of filled masks. In this paper, we propose an efficient
automatic region filling algorithm for complicated regions. Distinguishing
between adjacent connected regions, the Main Filling Process scans through all
pixels and fills all the pixels except boundary ones with either exterior or
interior label color. In this way, we succeed in classifying all the pixels
inside the region except boundary ones in the given image to form two groups: a
background group and a mask group. We then set all exterior label pixels to
background color, and interior label pixels to mask color. With this algorithm,
we are able to generate output masks precisely and efficiently even for
complicated regions as long as boundary pixels are given. Experimental results
show that the proposed algorithm can generate precise masks that allow for
various machine learning tasks such as supervised training. This algorithm can
effectively handle multiple regions, complicated `holes' and regions whose
boundaries touch the image border. By testing the algorithm on both toy and
practical images, we show that the performance of Scan-flood Fill(SCAFF) has
achieved favorable results.


  The ability to automatically identify industry sector coverage in articles on
legal developments, or any kind of news articles for that matter, can bring
plentiful of benefits both to the readers and the content creators themselves.
By having articles tagged based on industry coverage, readers from all around
the world would be able to get to legal news that are specific to their region
and professional industry. Simultaneously, writers would benefit from
understanding which industries potentially lack coverage or which industries
readers are currently mostly interested in and thus, they would focus their
writing efforts towards more inclusive and relevant legal news coverage. In
this paper, a Machine Learning-powered industry analysis approach which
combined Natural Language Processing (NLP) with Statistical and Machine
Learning (ML) techniques was investigated. A dataset consisting of over 1,700
annotated legal articles was created for the identification of six industry
sectors. Text and legal based features were extracted from the text. Both
traditional ML methods (e.g. gradient boosting machine algorithms, and
decision-tree based algorithms) and deep neural network (e.g. transformer
models) were applied for performance comparison of predictive models. The
system achieved promising results with area under the receiver operating
characteristic curve scores above 0.90 and F-scores above 0.81 with respect to
the six industry sectors. The experimental results show that the suggested
automated industry analysis which employs ML techniques allows the processing
of large collections of text data in an easy, efficient, and scalable way.
Traditional ML methods perform better than deep neural networks when only a
small and domain-specific training data is available for the study.


  We study the influence of mobility of the confining media in the structural
and dynamical properties of a core-softened fluid under confinement. The fluid
is modeled using a two-length scale potential, which reproduces in bulk the
anomalous behavior observed in water. We perform simulations in the $NVT$
ensemble with fixed flat walls and in the $NpT$ ensemble using a fluctuating
wall control of pressure to study how the fluid behavior is affected by fixed
and non-fixed walls. Our results indicate that the fluid dynamical and
structural properties are strongly affected by the wall mobility. The distinct
observed behavior are explained in the framework of the two length scale
potential.


  The transmission dynamics of Tuberculosis (TB) involve complex
epidemiological and socio-economical interactions between individuals living in
highly distinct regional conditions. The level of exogenous reinfection and
first time infection rates within high-incidence settings may influence the
impact of control programs on TB prevalence. This study aims at enhancing the
understanding of TB dynamics via the study of scenarios, within {\it
simplified}, two patch, risk-defined environments, in the presence of short
term mobility and variations in reinfection and infection rates. The modeling
framework captures the role of individuals' `daily' dynamics within and between
places of residency, work or business via the proportion of time spent in
residence and as visitors to TB-risk environments (patches). As a result, the
{\it effective population size} of Patch $i$ (home of $i$-residents) at time
$t$ must account for visitors and residents of Patch $i$, at time $t$. The
impact that {\it effective population size} and the distribution of {\it
individuals' residence times} in different patches have on TB transmission and
control are studied using selected scenarios where risk is defined by the
estimated or perceive first time infection and/or exogenous re-infection rates.
Our results suggest that, under certain conditions, allowing infected
individuals to move from high to low TB prevalence areas (for example via the
sharing of treatment and isolation facilities) may lead to a reduction in the
total TB prevalence in the overall, here two-patch, population.


  We present a new definition of influences in product spaces of continuous
distributions. Our definition is geometric, and for monotone sets it is
identical with the measure of the boundary with respect to uniform enlargement.
We prove analogs of the Kahn-Kalai-Linial (KKL) and Talagrand's influence sum
bounds for the new definition. We further prove an analog of a result of
Friedgut showing that sets with small "influence sum" are essentially
determined by a small number of coordinates. In particular, we establish the
following tight analog of the KKL bound: for any set in $\mathbb{R}^n$ of
Gaussian measure $t$, there exists a coordinate $i$ such that the $i$th
geometric influence of the set is at least $ct(1-t)\sqrt{\log n}/n$, where $c$
is a universal constant. This result is then used to obtain an isoperimetric
inequality for the Gaussian measure on $\mathbb{R}^n$ and the class of sets
invariant under transitive permutation group of the coordinates.


  This work proposes a continuum-based approach for the propagation of
uncertainties in the initial conditions and parameters for the analysis and
prediction of spacecraft re-entries. Using the continuity equation together
with the re-entry dynamics, the joint probability distribution of the
uncertainties is propagated in time for specific sampled points. At each time
instant, the joint probability distribution function is then reconstructed from
the scattered data using a gradient-enhanced linear interpolation based on a
simplicial representation of the state space. Uncertainties in the initial
conditions at re-entry and in the ballistic coefficient for three
representative test cases are considered: a three-state and a six-state steep
Earth re-entry and a six-state unguided lifting entry at Mars. The paper shows
the comparison of the proposed method with Monte Carlo based techniques in
terms of quality of the obtained marginal distributions and runtime as a
function of the number of samples used.


  We study branes moving in an AdS Schwarzschild black hole background. When
the brane tension exceeds a critical value, the induced metric on the brane is
of FRW type and asymptotically de Sitter. We discuss the relevance of such
configurations to dS/CFT correspondence. When the black hole mass reaches a
critical value that depends on the brane tension, the brane interpolates in the
infinite past and future between a dS space and a finite space of zero Hubble
constant. This corresponds to a cosmological evolution without a Big Bang or a
Big Crunch. Moreover, the central charge of the CFT dual to the dS brane enters
the Cardy-Verlinde formula that gives the entropy of the thermal CFT dual to
the bulk AdS black hole.


  Assessing the similarity of matrices is valuable for analyzing the extent to
which data sets exhibit common features in tasks such as data clustering,
dimensionality reduction, pattern recognition, group comparison, and graph
analysis. Methods proposed for comparing vectors, such as cosine similarity,
can be readily generalized to matrices. However, this approach usually neglects
the inherent two-dimensional structure of matrices. Here, we propose singular
angle similarity (SAS), a measure for evaluating the structural similarity
between two arbitrary, real matrices of the same shape based on singular value
decomposition. After introducing the measure, we compare SAS with standard
measures for matrix comparison and show that only SAS captures the
two-dimensional structure of matrices. Further, we characterize the behavior of
SAS in the presence of noise and as a function of matrix dimensionality.
Finally, we apply SAS to two use cases: square non-symmetric matrices of
probabilistic network connectivity, and non-square matrices representing neural
brain activity. For synthetic data of network connectivity, SAS matches
intuitive expectations and allows for a robust assessment of similarities and
differences. For experimental data of brain activity, SAS captures differences
in the structure of high-dimensional responses to different stimuli. We
conclude that SAS is a suitable measure for quantifying the shared structure of
matrices with arbitrary shape.


  A pictorial atlas of the spectroscopic evolution at optical wavelengths is
presented for the first 18 days of the 2021 outburst of the recurrent nova RS
Oph, prior to the emergence of high ionization emission lines. The spectra
presented here have been obtained at daily cadence with the Asiago 1.22m + B&C
(3200-7900 Ang, 2.3 \AA/pix) and Varese 0.84m + Echelle telescopes (4250-8900
\AA, resolving power 18,000). The spectra have been fully calibrated in IRAF,
absolutely fluxed, and heliocentric corrected. The Echelle spectra have been
also corrected for telluric absorptions.


  Starting from an axisymmetric equilibrium distribution function (DF) in
action space, representing a Milky Way thin disc stellar population, we use the
linearized Boltzmann equation to explicitly compute the response to a
three-dimensional spiral potential in terms of the perturbed DF. This DF, valid
away from the main resonances, allows us to investigate a snapshot of the
velocity distribution at any given point in three-dimensional configuration
space. Moreover, the first order moments of the DF give rise to non-zero radial
and vertical bulk flows -- namely breathing modes -- qualitatively similar to
those recently observed in the extended Solar neighbourhood. We show that these
analytically predicted mean stellar motions are in agreement with the outcome
of test-particle simulations. Moreover, we estimate for the first time the
reduction factor for the vertical bulk motions of a stellar population compared
to the case of a cold fluid. Such an explicit expression for the full perturbed
DF of a thin disc stellar population in the presence of spiral arms will be
helpful in order to dynamically interpret the detailed information on the Milky
Way disc stellar kinematics that will be provided by upcoming large astrometric
and spectroscopic surveys of the Galaxy.


  With the rapid development of neural network applications in NLP, model
robustness problem is gaining more attention. Different from computer vision,
the discrete nature of texts makes it more challenging to explore robustness in
NLP. Therefore, in this paper, we aim to connect discrete perturbations with
continuous perturbations, therefore we can use such connections as a bridge to
help understand discrete perturbations in NLP models. Specifically, we first
explore how to connect and measure the correlation between discrete
perturbations and continuous perturbations. Then we design a regression task as
a PerturbScore to learn the correlation automatically. Through experimental
results, we find that we can build a connection between discrete and continuous
perturbations and use the proposed PerturbScore to learn such correlation,
surpassing previous methods used in discrete perturbation measuring. Further,
the proposed PerturbScore can be well generalized to different datasets,
perturbation methods, indicating that we can use it as a powerful tool to study
model robustness in NLP.


  We introduce the concept of Automated Causal Discovery (AutoCD), defined as
any system that aims to fully automate the application of causal discovery and
causal reasoning methods. AutoCD's goal is to deliver all causal information
that an expert human analyst would and answer a user's causal queries. We
describe the architecture of such a platform, and illustrate its performance on
synthetic data sets. As a case study, we apply it on temporal telecommunication
data. The system is general and can be applied to a plethora of causal
discovery problems.


  In this paper we establish a precise comparison between vanishing cycles and
the singularity category of Landau-Ginzburg models over a complete discrete
valuation ring. By using noncommutative motives, we first construct a motivic
$\ell$-adic realization functor for dg-categories. Our main result, then
asserts that, given a Landau-Ginzburg model over a complete discrete valuation
ring with potential induced by a uniformizer, the $\ell$-adic realization of
its singularity category is given by the inertia-invariant part of vanishing
cohomology. We also prove a functorial and $\infty$-categorical version of
Orlov's comparison theorem between the derived category of singularities and
the derived category of matrix factorizations for a Landau-Ginzburg model over
a noetherian regular local ring.