  The vortex electromagnetic wave carried by multiple orthogonal orbital
angular momentum (OAM) modes in the same frequency band can be applied to the
field of wireless communications, which greatly increases the spectrum
efficiency. The uniform circular array (UCA) is widely used to generate and
receive vortex electromagnetic waves with multiple OAM-modes. However, the
maximum number of orthogonal OAM-modes based on UCA is usually limited to the
number of array-elements of the UCA antenna, leaving how to utilize more
OAM-modes to achieve higher channel capacity with a fixed number of
arrayelements as an intriguing question. In this paper, we propose an
N-dimensional quasi-fractal UCA (ND QF-UCA) antenna structure in different
fractal geometry layouts to break through the limits of array-elements number
on OAM-modes number. We develop the N-dimensional OAM modulation (NOM) and
demodulation (NOD) schemes for OAM multiplexing transmission with the OAM-modes
number exceeding the array-elements number, which is beyond the traditional
concept of multiple antenna based wireless communications. Then, we investigate
different dimensional multiplexing transmission schemes based on the
corresponding QF-UCA antenna structure with various array-element layouts and
evaluate the optimal layout type and dimension to obtain the highest channel
capacity with a fixed number of array-elements. Simulation results show that
our proposed schemes can obtain a higher spectrum efficiency, surpassing those
of alternative array-element layouts of QF-UCA and the traditional multiple
antenna systems.


  We perform a detailed finite-size scaling analysis of the sheet resistance in
Bi-films and the LaAlO$_{3}$/SrTiO$_{3}$ interface in the presence and absence
of a magnetic field applied perpendicular to the system. Our main aim is to
explore the occurrence of Berezinskii-Kosterlitz-Thouless (BKT) and quantum
phase transition behavior in the presence of limited size, stemming from the
finite extent of the homogeneous domains or the magnetic field. Moreover we
explore the implications thereof. Above an extrapolated BKT transition
temperature, modulated by the thickness $d$, gate voltage $%V_{g}$ or magnetic
field $H$, we identify a temperature range where BKT behavior occurs. Its range
is controlled by the relevant limiting lengths,which are set by the extent of
the homogeneous domains or the magnetic field. The extrapolated BKT transition
lines $T_{c}\left(d,V_{g},H\right) $ uncover compatibility with the occurrence
of a quantum phase transition where $T_{c}\left( d_{c},V_{gc},H_{c}\right) =0$.
However, an essential implication of the respective limiting length is that the
extrapolated phase transition lines $T_{c}\left( d,V_{g},H\right) $ are
unattainable. Consequently, given a finite limiting length, BKT and quantum
phase transitions do not occur. Nevertheless, BKT and quantum critical behavior
is observable, controlled by the extent of the relevant limiting length.
Additional results and implications include: the magnetic field induced finite
size effect generates a flattening out of the sheet resistance in the
$T\rightarrow 0$ limit, while in zero field it exhibits a characteristic
temperature dependence and vanishes at $T=0$ only. The former prediction is
confirmed in both, the Bi-films and the LaAlO$_{3}$/SrTiO$_{3}$ interface, as
well as in previous studies. The latter is consistent with the
LaAlO$_{3}$/SrTiO$_{3}$ interface data, while the Bi-films exhibit a flattening
out.


  Motivated by the paradigm of reservoir computing, we consider randomly
initialized controlled ResNets defined as Euler-discretizations of neural
controlled differential equations (Neural CDEs), a unified architecture which
enconpasses both RNNs and ResNets. We show that in the infinite-width-depth
limit and under proper scaling, these architectures converge weakly to Gaussian
processes indexed on some spaces of continuous paths and with kernels
satisfying certain partial differential equations (PDEs) varying according to
the choice of activation function, extending the results of Hayou (2022); Hayou
& Yang (2023) to the controlled and homogeneous case. In the special,
homogeneous, case where the activation is the identity, we show that the
equation reduces to a linear PDE and the limiting kernel agrees with the
signature kernel of Salvi et al. (2021a). We name this new family of limiting
kernels neural signature kernels. Finally, we show that in the infinite-depth
regime, finite-width controlled ResNets converge in distribution to Neural CDEs
with random vector fields which, depending on whether the weights are shared
across layers, are either time-independent and Gaussian or behave like a
matrix-valued Brownian motion.


  We compute the Hausdorff dimension of the closure of the generalized
Brunner-Sidki-Vieira group acting on the $m$-adic tree for $m\ge 2$, providing
the first examples of self-similar topologically finitely generated closed
subgroups of transcendental Hausdorff dimension in the group of $m$-adic
automorphisms.


  Reduction of the inter-probe distance in multi-probe and double-tip STM down
to the nanometer scale has been a longstanding and technically difficult
challenge. Recent multi-probe systems have allowed for significant progress by
achieving distances of around 30 nm using two individually driven, traditional
metal wire tips. For situations where simple alignment and a fixed separation
can be advantageous, we here present the fabrication of on-chip double-tip
devices that incorporate two mechanically fixed gold tips with a tip separation
of only 35 nm. We utilize the excellent mechanical, insulating and dielectric
properties of high quality SiN as a base material to realize easy-to-implement,
lithographically defined and mechanically stable tips. With their large contact
pads and adjustable footprint these novel tips can be easily integrated with
most existing commercial combined STM/AFM systems.


  The Dark Energy Spectroscopic Instrument (DESI) collaboration recently
released its first year of data (DR1) on baryon acoustic oscillations (BAO) in
galaxy, quasar, and Lyman-$\alpha$ forest tracers. When combined with CMB and
SNIa data, DESI BAO results suggest potential thawing behavior in dark energy.
Cosmological analyses utilize comoving distances along ($D_H$) and
perpendicular to ($D_M$) the line of sight. Notably, there are $1\sim2\sigma$
deviations in $D_M$ and $D_H$ from Planck cosmology values in the luminous red
galaxies (LRG) bins LRG1 and LRG2.This study examines the role of LRG1 and LRG2
in diverging DESI 2024 BAO cosmology from Planck cosmology. We use
angle-averaged distance $D_V$ and the ratio $F_{\rm AP}=D_M/D_H$, which are
more directly related to the measured monopole and quadrupole components of the
galaxy power spectrum or correlation function, instead of the officially
adopted $D_M$ and $D_H$. This transformation aims to isolate the influence of
monopoles in LRG1 and LRG2 on deviations from $w=-1$. Our findings indicate
that removing the $D_V$ data point in LRG2 aligns DESI + CMB + SNIa data
compilation with $w=-1$ within a $2\sigma$ contour and reduces the $H_0$
discrepancy from the Planck 2018 results from $0.63\sigma$ to $0.31\sigma$.
Similarly, excluding the $D_V$ data point from LRG1 shifts the $w_0/w_a$
contour toward $w=-1$, although no intersection occurs. This highlights the
preference of both LRG1 and LRG2 BAO monopole components for the thawing dark
energy model, with LRG2 showing a stronger preference. We provide the $D_V$ and
$F_{\rm AP}$ data and their covariance alongside this paper.


  In this paper, we establish the following version at infinity of Whitney's
theorem [6, 7]: Geometric and algebraic tangent cones at infinity of complex
algebraic varieties coincide. The proof of this fact is based on a geometric
characterization of geometric tangent cones at infinity and using the global \L
ojasiewicz inequality with explicit exponents for complex algebraic varieties.
We also show that tangent cones at infinity of complex algebraic varieties can
be computed using Gr\"obner bases.


  Information and communication technologies (ICT) can make existing products
and activities more efficient or substitute them altogether and could thus
become crucial for the mitigation of climate change. In this context,
individual ICT companies, industry organizations and international initiatives
have started to estimate the environmental effects of ICT services. Often such
assessments rely on crude assumptions and methods, yielding inaccurate or even
misleading results. The few existing methodological attempts are too general to
provide guidance to practitioners. The starting points of this paper are i) a
high level standard from the European Telecommunication Standardisation
Institute (ETSI) and the International Telecommunication Union (ITU), and ii)
its suggested enhancements for single service assessment outlined in "A
Methodology for Assessing the Environmental Effects Induced by ICT Services
Part I: Single services" (Part I in short). Building on the assessment of
single services, the current article identifies and addresses shortcomings of
existing methodologies and industry practices with regard to multiple services
assessment. For a collection of services, it addresses the goal and scope
definition, the so far ignored aggregation of effects among several services,
and the allocation between several companies contributing to one or more
services. The article finally brings these considerations together with those
of Part I into a workflow for performing such assessments in practice.


  We propose dynamical systems trees (DSTs) as a flexible class of models for
describing multiple processes that interact via a hierarchy of aggregating
parent chains. DSTs extend Kalman filters, hidden Markov models and nonlinear
dynamical systems to an interactive group scenario. Various individual
processes interact as communities and sub-communities in a tree structure that
is unrolled in time. To accommodate nonlinear temporal activity, each
individual leaf process is modeled as a dynamical system containing discrete
and/or continuous hidden states with discrete and/or Gaussian emissions.
Subsequent higher level parent processes act like hidden Markov models and
mediate the interaction between leaf processes or between other parent
processes in the hierarchy. Aggregator chains are parents of child processes
that they combine and mediate, yielding a compact overall parameterization. We
provide tractable inference and learning algorithms for arbitrary DST
topologies via an efficient structured mean-field algorithm. The diverse
applicability of DSTs is demonstrated by experiments on gene expression data
and by modeling group behavior in the setting of an American football game.


  In this paper, the existence of weak solutions of a convective Cahn-Hilliard
equation with degenerate mobility is studied. We first define a notion of weak
solutions and establish a regularized problems. The existence of such solutions
is obtained by considered the limits of the regularized problems.


  A geometric graph is a simple graph G together with a straight line drawing
of G in the plane with the vertices in general position. Two geometric
realizations of a simple graph are geo-isomorphic if there is a vertex
bijection between them that preserves vertex adjacencies and non-adjacencies,
as well as edge crossings and non-crossings. A natural extension of graph
homomorphisms, geo-homomorphisms, can be used to define a partial order on the
set of geo-isomorphism classes of realizations of a given simple graph. In this
paper, the homomorphism poset of the complete bipartite graph K_{2,n} is
determined by establishing a correspondence between realizations of K_{2,n} and
permutations of S_n, in which crossing edges correspond to inversions. Through
this correspondence, geo-isomorphism defines an equivalence relation on S_n,
which we call geo-equivalence. The number of geo-isomorphism classes is
provided for all n <= 9. The modular decomposition tree of permutation graphs
is used to prove some results on the size of geo-equivalence classes. A
complete list of geo-equivalence classes and a Hasse diagrams of the poset
structure are given for n <= 5.


  We review the present status of gauge theories built on various quantum
space-times described by noncommutative space-times. The mathematical tools and
notions underlying their construction are given. Different formulations of
gauge theory models on Moyal spaces as well as on quantum spaces whose
coordinates form a Lie algebra are covered, with particular emphasis on some
explored quantum properties. Recent attempts aiming to include gravity dynamics
within a noncommutative framework are also considered.


  In this paper we study the problem of the convergence in variation for the
generalized sampling series based upon averaged-type kernels in the
multidimensional setting. As a crucial tool, we introduce a family of operators
of sampling-Kantorovich type for which we prove convergence in L^p on a
subspace of L^p(R^N): therefore we obtain the convergence in variation for the
multidimensional generalized sampling series by means of a relation between the
partial derivatives of such operators acting on an absolutely continuous
function f and the sampling-Kantorovich type operators acting on the partial
derivatives of f. Applications to digital image processing are also furnished.


  Neural networks with random weights appear in a variety of machine learning
applications, most prominently as the initialization of many deep learning
algorithms and as a computationally cheap alternative to fully learned neural
networks. In the present article, we enhance the theoretical understanding of
random neural networks by addressing the following data separation problem:
under what conditions can a random neural network make two classes
$\mathcal{X}^-, \mathcal{X}^+ \subset \mathbb{R}^d$ (with positive distance)
linearly separable? We show that a sufficiently large two-layer ReLU-network
with standard Gaussian weights and uniformly distributed biases can solve this
problem with high probability. Crucially, the number of required neurons is
explicitly linked to geometric properties of the underlying sets
$\mathcal{X}^-, \mathcal{X}^+$ and their mutual arrangement. This
instance-specific viewpoint allows us to overcome the usual curse of
dimensionality (exponential width of the layers) in non-pathological situations
where the data carries low-complexity structure. We quantify the relevant
structure of the data in terms of a novel notion of mutual complexity (based on
a localized version of Gaussian mean width), which leads to sound and
informative separation guarantees. We connect our result with related lines of
work on approximation, memorization, and generalization.


  Fusion rules among irreducible modules of the free bosonic orbifold vertex
operator algebra are completely determined.


  Ferroelectric films usually have phase states and physical properties very
different from those of bulk ferroelectrics. Here we propose free-standing
ferroelectric-elastic multilayers as a bridge between these two material
systems. Using a nonlinear thermodynamic theory, we determine phase states of
such multilayers as a function of temperature, misfit strain, and volume
fraction fi of ferroelectric material. The numerical calculations performed for
two classical ferroelectrics - PbTiO3 and BaTiO3 - demonstrate that
polarization states of multilayers in the limiting cases fi -> 0 and fi -> 1
coincide with those of thin films and bulk crystals. At intermediate volume
fractions, however, the misfit strain-temperature phase diagrams of multilayers
differ greatly from those of epitaxial films. Remarkably, a ferroelectric phase
not existing in thin films and bulk crystals can be stabilized in BaTiO3
multilayers. Owing to additional tunable parameter and reduced clamping,
ferroelectric multilayers may be superior for a wide range of device
applications.


  Understanding player strategies is a key question when analyzing player
behavior both for academic researchers and industry practitioners. For game
designers and game user researchers, it is important to gauge the distance
between intended strategies and emergent strategies; this comparison allows
identification of glitches or undesirable behaviors. For academic researchers
using games for serious purposes such as education, the strategies adopted by
players are indicative of their cognitive progress in relation to serious
goals, such as learning process. Current techniques and systems created to
address these needs present a few drawbacks. Qualitative methods are difficult
to scale upwards to include large number of players and are prone to subjective
biases. Other approaches such as visualization and analytical tools are either
designed to provide an aggregated overview of the data, losing the nuances of
individual player behaviors, or, in the attempt of accounting for individual
behavior, are not specifically designed to reduce the visual cognitive load. In
this work, we propose a novel visualization technique that specifically
addresses the tasks of comparing behavior sequences in order to capture an
overview of the strategies enacted by players and at the same time examine
individual player behaviors to identify differences and outliers. This approach
allows users to form hypotheses about player strategies and verify them. We
demonstrate the effectiveness of the technique through a case study: utilizing
a prototype system to investigate data collected from a commercial educational
puzzle game. While the prototype's usability can be improved, initial testing
results show that core features of the system proved useful to our potential
users for understanding player strategies.


  Horn-satisfiability or Horn-SAT is the problem of deciding whether a
satisfying assignment exists for a Horn formula, a conjunction of clauses each
with at most one positive literal (also known as Horn clauses). It is a
well-known P-complete problem, which implies that unless P = NC, it is a hard
problem to parallelize. In this paper, we empirically show that, under a known
simple random model for generating the Horn formula, the ratio of
hard-to-parallelize instances (closer to the worst-case behavior) is
infinitesimally small. We show that the depth of a parallel algorithm for
Horn-SAT is polylogarithmic on average, for almost all instances, while keeping
the work linear. This challenges theoreticians and programmers to look beyond
worst-case analysis and come up with practical algorithms coupled with
respective performance guarantees.


  "Evolution behaves like a tinkerer" (Francois Jacob, Science, 1977). Software
systems provide a unique opportunity to understand biological processes using
concepts from network theory. The Debian GNU/Linux operating system allows us
to explore the evolution of a complex network in a novel way. The modular
design detected during its growth is based on the reuse of existing code in
order to minimize costs during programming. The increase of modularity
experienced by the system over time has not counterbalanced the increase in
incompatibilities between software packages within modules. This negative
effect is far from being a failure of design. A random process of package
installation shows that the higher the modularity the larger the fraction of
packages working properly in a local computer. The decrease in the relative
number of conflicts between packages from different modules avoids a failure in
the functionality of one package spreading throughout the entire system. Some
potential analogies with the evolutionary and ecological processes determining
the structure of ecological networks of interacting species are discussed.


  The Soreq Applied Research Accelerator Facility (SARAF) is under construction
in the Soreq Nuclear Research Center at Yavne, Israel. When completed at the
beginning of the next decade, SARAF will be a user facility for basic and
applied nuclear physics, based on a 40 MeV, 5 mA CW proton/deuteron
superconducting linear accelerator. Phase I of SARAF (SARAF-I, 4 MeV, 2 mA CW
protons, 5 MeV 1 mA CW deuterons) is already in operation, generating
scientific results in several fields of interest. The main ongoing program at
SARAF-I is the production of 30 keV neutrons and measurement of Maxwellian
Averaged Cross Sections (MACS), important for the astrophysical s-process. The
world leading Maxwellian epithermal neutron yield at SARAF-I ($5\times 10^{10}$
epithermal neutrons/sec), generated by a novel Liquid-Lithium Target (LiLiT),
enables improved precision of known MACSs, and new measurements of
low-abundance and radioactive isotopes. Research plans for SARAF-II span
several disciplines: Precision studies of beyond-Standard-Model effects by
trapping light exotic radioisotopes, such as $^6$He, $^8$Li and
$^{18,19,23}$Ne, in unprecedented amounts (including meaningful studies already
at SARAF-I); extended nuclear astrophysics research with higher energy
neutrons, including generation and studies of exotic neutron-rich isotopes
relevant to the rapid (r-) process; nuclear structure of exotic isotopes; high
energy neutron cross sections for basic nuclear physics and material science
research, including neutron induced radiation damage; neutron based imaging and
therapy; and novel radiopharmaceuticals development and production. In this
paper we present a technical overview of SARAF-I and II, including a
description of the accelerator and its irradiation targets; a survey of
existing research programs at SARAF-I; and the research potential at the
completed facility (SARAF-II).


  The statistically steady humidity distribution resulting from an interaction
of advection, modeled as an uncorrelated random walk of moist parcels on an
isentropic surface, and a vapour sink, modeled as immediate condensation
whenever the specific humidity exceeds a specified saturation humidity, is
explored with theory and simulation. A source supplies moisture at the
deep-tropical southern boundary of the domain, and the saturation humidity is
specified as a monotonically decreasing function of distance from the boundary.
The boundary source balances the interior condensation sink, so that a
stationary spatially inhomogeneous humidity distribution emerges. An exact
solution of the Fokker-Planck equation delivers a simple expression for the
resulting probability density function (PDF) of the water vapour field and also
of the relative humidity. This solution agrees completely with a numerical
simulation of the process, and the humidity PDF exhibits several features of
interest, such as bimodality close to the source and unimodality further from
the source. The PDFs of specific and relative humidity are broad and
non-Gaussian. The domain averaged relative humidity PDF is bimodal with
distinct moist and dry peaks, a feature which we show agrees with middleworld
isentropic PDFs derived from the ERA interim dataset.


  Electrostatic correlations and variable permittivity of electrolytes are
essential for exploring many chemical and physical properties of interfaces in
aqueous solutions. We propose a continuum electrostatic model for the treatment
of these effects in the framework of the self-consistent field theory. The
model incorporates a space-or field-dependent dielectric permittivity and an
excluded ion-size effect for the correlation energy. This results in a
self-energy modified Poisson-Nernst-Planck or Poisson-Boltzmann equation
together with state equations for the self energy and the dielectric function.
We show that the ionic size is of significant importance in predicting a finite
self energy for an ion in an inhomogeneous medium. Asymptotic approximation is
proposed for the solution of a generalized Debye-Huckel equation, which has
been shown to capture the ionic correlation and dielectric self energy. Through
simulating ionic distribution surrounding a macroion, the modified
self-consistent field model is shown to agree with particle-based Monte Carlo
simulations. Numerical results for symmetric and asymmetric electrolytes
demonstrate that the model is able to predict the charge inversion at high
correlation regime in the presence of multivalent interfacial ions which is
beyond the mean-field theory, and also show strong effect to double layer
structure due to the space- or field-dependent dielectric permittivity.


  In this paper we analyze the rogue wave spectra of the Kundu-Eckhaus equation
(KEE). We compare our findings with their nonlinear Schrodinger equation (NLSE)
analogs and show that the spectra of the individual rogue waves significantly
differ from their NLSE analogs. A remarkable difference is the one-sided
development of the triangular spectrum before the rogue wave becomes evident in
time. Also we show that increasing the skewness of the rogue wave results in
increased asymmetry in the triangular Fourier spectra. Additionally, the
triangular spectra of the rogue waves of the KEE begin to develop at earlier
stages of the their development compared to their NLSE analogs, especially for
larger skew angles. This feature may be used to enhance the early warning times
of the rogue waves. However we show that in a chaotic wavefield with many
spectral components the triangular spectra remains as the main attribute as a
universal feature of the typical wavefields produced through modulation
instability and characteristic features of the KEE's analytical rogue wave
spectra may be suppressed in a realistic chaotic wavefield.


  The Chiral Magnetic Effect (CME) is the phenomenon of electric charge
separation along the external magnetic field that is induced by the chirality
imbalance. The CME is a macroscopic quantum effect - it is a manifestation of
the chiral anomaly creating a collective motion in Dirac sea. Because the
chirality imbalance is related to the global topology of gauge fields, the CME
current is topologically protected and hence non-dissipative even in the
presence of strong interactions. As a result, the CME and related quantum
phenomena affect the hydrodynamical and transport behavior of systems
possessing chiral fermions, from the quark-gluon plasma to chiral materials.
The goal of the present review is to provide an elementary introduction into
the main ideas underlying the physics of CME, a historical perspective, and a
guide to the rapidly growing literature on this topic.


  According to astrophysical observations value of recession velocity in a
certain point is proportional to a distance to this point. The proportionality
coefficient is the Hubble constant measured with 5% accuracy. It is used in
many cosmological theories describing dark energy, dark matter, baryons, and
their relation with the cosmological constant introduced by Einstein.
  In the present work we have determined a limit value of the global Hubble
constant (in a big distance from a point of observations) theoretically without
using any empirical constants on the base of our own fractal model used for the
description a relation between distance to an observed galaxy and coordinate of
its center. The distance has been defined as a nonlinear fractal measure with
scale of measurement corresponding to a deviation of the measure from its fixed
value (zero-gravity radius). We have suggested a model of specific anisotropic
fractal for simulation a radial Universe expansion. Our theoretical results
have shown existence of an inverse proportionality between accuracy of
determination the Hubble constant and accuracy of calculation a coordinates of
galaxies leading to ambiguity results obtained at cosmological observations.


  We introduce an adversarial sample detection algorithm based on image
residuals, specifically designed to guard against patch-based attacks. The
image residual is obtained as the difference between an input image and a
denoised version of it, and a discriminator is trained to distinguish between
clean and adversarial samples. More precisely, we use a wavelet domain
algorithm for denoising images and demonstrate that the obtained residuals act
as a digital fingerprint for adversarial attacks. To emulate the limitations of
a physical adversary, we evaluate the performance of our approach against
localized (patch-based) adversarial attacks, including in settings where the
adversary has complete knowledge about the detection scheme. Our results show
that the proposed detection method generalizes to previously unseen, stronger
attacks and that it is able to reduce the success rate (conversely, increase
the computational effort) of an adaptive attacker.


  As medium-scale quantum computers progress, the application of quantum
algorithms across diverse fields like simulating physical systems, chemistry,
optimization, and cryptography becomes more prevalent. However, these quantum
computers, known as Noisy Intermediate Scale Quantum (NISQ), are susceptible to
noise, prompting the search for applications that can capitalize on quantum
advantage without extensive error correction procedures. Since, Machine
Learning (ML), particularly Deep Learning (DL), faces challenges due to
resource-intensive training and algorithmic opacity. Therefore, this study
explores the intersection of quantum computing and ML, focusing on computer
vision tasks. Specifically, it evaluates the effectiveness of hybrid
quantum-classical algorithms, such as the data re-uploading scheme and the
patch Generative Adversarial Networks (GAN) model, on small-scale quantum
devices. Through practical implementation and testing, the study reveals
comparable or superior performance of these algorithms compared to classical
counterparts, highlighting the potential of leveraging quantum algorithms in ML
tasks.


  Finding a parking space nowadays becomes an issue that is not to be
neglected, it consumes time and energy. We have used computer vision techniques
to infer the state of the parking lot given the data collected from the
University of The Witwatersrand. This paper presents an approach for a
real-time parking space classification based on Convolutional Neural Networks
(CNN) using Caffe and Nvidia DiGITS framework. The training process has been
done using DiGITS and the output is a caffemodel used for predictions to detect
vacant and occupied parking spots. The system checks a defined area whether a
parking spot (bounding boxes defined at initialization of the system) is
containing a car or not (occupied or vacant). Those bounding box coordinates
are saved from a frame of the video of the parking lot in a JSON format, to be
later used by the system for sequential prediction on each parking spot. The
system has been trained using the LeNet network with the Nesterov Accelerated
Gradient as solver and the AlexNet network with the Stochastic Gradient Descent
as solver. We were able to get an accuracy on the validation set of 99\% for
both networks. The accuracy on a foreign dataset(PKLot) returned as well 99\%.
Those are experimental results based on the training set shows how robust the
system can be when the prediction has to take place in a different parking
space.


  We have developed a model for the variability of gamma ray emission in jets
of active galactic nuclei in which the variability arises as a result of
photon-photon pair production interactions with X-rays emitted by a hot spot in
the inner part of the accretion disk. As the hot spot orbits around the central
engine, the amount of absorption varies periodically. Our model may account for
the observed variability of TeV emission from Markarian 421 and other blazars
detected by the EGRET instrument on the Compton Gamma Ray Observatory, as well
as correlated variations of X-ray and TeV gamma flux from Markarian 421.
Quasi-periodic variations observed in Markarian 421 enable us to place an upper
limit on the black hole mass of (2-30) times 10^8 solar masses.


  In this paper, we investigate the anomalous planets precession in the
nearly-newtonian gravitational regime. This limit is obtained from the
application of the slow motion condition to the geodesic equations without
altering the geodesic deviation equations. Using a non-standard expression for
the perihelion advance from the Weyl conformastatic vacuum solution as a model,
we can describe the anomaly in planets precession compared with different
observational data from Ephemerides of the Planets and the Moon (EPM2008 and
EPM2011) and Planetary and Lunar Ephemeris (INPOP10a). As a result, using the
Levenberg-Marquardt algorithm and calculating the related Chi-squared
statistic, we find that the anomaly is statistical irrelevant in accordance
with INPOP10a observations. As a complement to this work, we also do an
application to the relativistic precession of giant planets using observational
data calibrated with the EPM2011.


  We answer affirmatively a question of Srinivas--Trivedi: in a Noetherian
local ring $(R,\mathfrak{m})$, if $I=(f_1,\dots,f_r)$ is an ideal generated by
a filter-regular sequence and $J$ is an ideal such that $I+J$ is
$\mathfrak{m}$-primary, then there exists $N>0$ such that for any
$\varepsilon_1,\dots,\varepsilon_r \in \mathfrak{m}^N$, we have an equality of
Hilbert functions: $H(J, R/(f_1,\dots,f_r))(n)=H(J, R/(f_1+\varepsilon_1,\dots,
f_r+\varepsilon_r))(n)$ for all $n\geq 0$. We also prove that the dimension of
the non Cohen--Macaulay locus does not increase under small perturbations.


  We give a new formula for $p$-typical real topological cyclic homology that
refines the fiber sequence formula discovered by Nikolaus and Scholze for
$p$-typical topological cyclic homology to one involving genuine $C_2$-spectra.
To accomplish this, we give a new definition of the $\infty$-category of real
$p$-cyclotomic spectra that replaces the usage of genuinely equivariant
dihedral spectra with the parametrized Tate construction $(-)^{t_{C_2} \mu_p}$
associated to the dihedral group $D_{2p} = \mu_p \rtimes C_2$. We then define a
$p$-typical and $\infty$-categorical version of H{\o}genhaven's
$O(2)$-orthogonal cyclotomic spectra, construct a forgetful functor relating
the two theories, and show that this functor restricts to an equivalence
between full subcategories of appropriately bounded below objects.


  Honey consumption in Russia has been actively growing in recent years due to
the increasing interest in healthy and environment-friendly food products.
However, it remains an open question which characteristics of honey are the
most significant for consumers and, more importantly, from an economic point of
view, for which of them consumers are willing to pay. The purpose of this study
was to investigate the role of sensory characteristics in assessing consumers'
willingness to pay for honey and to determine which properties and
characteristics "natural" honey should have to encourage repeated purchases by
target consumers. The study involved a behavioral experiment that included a
pre-test questionnaire, blind tasting of honey samples, an in-room test to
assess perceived quality, and a closed auction using the
Becker-DeGroote-Marschak method. As the result, it was revealed that the
correspondence of the expected sensations to the actual taste, taste intensity,
duration of the aftertaste and the sensations of tickling in the throat had a
positive effect on both the perceived quality of the product and the
willingness to pay for it, while perception of off-flavors or added sugar had a
negative impact. Using factor analysis, we have combined 21 sensory
characteristics of honey into eight components that were sufficient to obtain
the flavor portrait of honey by Russian consumers.


  We prove new one shot achievability results for measurement compression of
quantum instruments with side information at the receiver. Unlike previous one
shot results for this problem, our one shot bounds are nearly optimal and do
not need catalytic randomness. In fact, we state a more general problem called
centralised multi link measurement compression with quantum side information
and provide one shot achievability results for it. As a simple corollary, we
obtain one shot measurement compression results for quantum instruments with
side information that we mentioned earlier. All our one shot results lead to
the standard results for this problem in the asymptotic iid setting. We prove
our achievability bounds by first proving a novel sequential classical quantum
multipartite covering lemma, which should be of independent interest.


  We propose a new scheme to control the shape of the Autler-Townes (AT)
doublet in the photoelectron spectrum from atomic resonance-enhanced
multiphoton ionization (REMPI). The scheme is based on the interference of two
AT doublets created by ionization of the strongly driven atom from the ground
and the resonantly excited state using tailored bichromatic femtosecond (fs)
laser pulses. In this scheme, the quantum phase of the photoelectrons is
crucial for the manipulation of the AT doublet. The laser polarization state
and the relative optical phase between the two colors are used to manipulate
the interference pattern. We develop an analytical model to describe the
bichromatic REMPI process and provide a physical picture of the control
mechanism. To validate the model, the results are compared to an ab initio
calculation based on the solution of the 2D time-dependent Schr\"odinger
equation for the non-perturbative interaction of an atom with intense
polarization-shaped bichromatic fs-laser pulses. Our results indicate that the
control mechanism is robust with respect to the laser intensity facilitating
its experimental observation.


  We evaluate the coupling constant for the lightest scalar glueball to decay
to pseudoscalar meson pairs. The calculation is done in the valence
approximation on a $16^3 \times 24$ lattice at $\beta = 5.70$ for two different
values of pseudoscalar meson mass.


  We provide bounds linear in the rank for the generalized conjugacy diameters,
introduced by Kedra, Libman and Martin, for the special linear and symplectic
groups defined over the rings of integers of global fields by way of using
certain stability considerations familiar from classical algebraic K-theory.
This determines the growth rates of these generalized conjugacy diameters.


  Binary neural networks (BNNs) represent original full-precision weights and
activations into 1-bit with sign function. Since the gradient of the
conventional sign function is almost zero everywhere which cannot be used for
back-propagation, several attempts have been proposed to alleviate the
optimization difficulty by using approximate gradient. However, those
approximations corrupt the main direction of factual gradient. To this end, we
propose to estimate the gradient of sign function in the Fourier frequency
domain using the combination of sine functions for training BNNs, namely
frequency domain approximation (FDA). The proposed approach does not affect the
low-frequency information of the original sign function which occupies most of
the overall energy, and high-frequency coefficients will be ignored to avoid
the huge computational overhead. In addition, we embed a noise adaptation
module into the training phase to compensate the approximation error. The
experiments on several benchmark datasets and neural architectures illustrate
that the binary network learned using our method achieves the state-of-the-art
accuracy. Code will be available at
\textit{https://gitee.com/mindspore/models/tree/master/research/cv/FDA-BNN}.


  We develop a general theory for percolation in directed random networks with
arbitrary two point correlations and bidirectional edges, that is, edges
pointing in both directions simultaneously. These two ingredients alter the
previously known scenario and open new views and perspectives on percolation
phenomena. Equations for the percolation threshold and the sizes of the giant
components are derived in the most general case. We also present simulation
results for a particular example of uncorrelated network with bidirectional
edges confirming the theoretical predictions.


  Visible-light-absorbing carbonaceous aerosols within the boundary layer
affect the radiance and polarization states of the radiation at the top of the
atmosphere. Remote sensing from suborbital and satellite-based platforms
utilizes these radiance and polarization signals to retrieve the key properties
of these aerosols. Recent retrieval algorithms have shown a progressive trend
toward including multi-angular and multi-spectral polarimetric measurements to
produce better retrieval accuracy in comparison to those using measurements
based on a single viewing angle. Here, we perform a theoretical investigation
of the top of atmosphere (TOA) radiance-related reflectance factor
(bidirectional reflectance factor (BRF)) and the two types of
polarimetry-related factors (polarized bidirectional reflectance factor (pBRF)
and the degree of linear polarization (DoLP)) for different types of
atmospheric light-absorbing carbonaceous aerosols as a function of particle
size distribution. We selected three polarimetric bands corresponding to those
utilized by NASA Airborne Multiangle SpectroPolarimetric Imager (AirMSPI) --
near-UV (470 nm), visible (660 nm), and near-infrared (865 nm) -- for our
simulations which were performed over ocean surface using the successive order
of scattering (SOS) algorithm coupled to a Lorenz-Mie aerosol optics model. The
analysis of particle phase matrix elements indicates a close relationship
between the angular dependencies of DoLP and associated phase matrix components
at the shortest polarimetric band (470 nm). Using Jacobian analysis, we find
that the radiance- and polarimetry-related reflectance factors of weakly
light-absorbing aerosols, such as brown carbon, are more sensitive to changes
in particle size and imaginary refractive index in comparison with those of
black carbon, which is strongly light-absorbing.


  In the category of semisimple Hopf algebras the Hopf kernels introduced by
Andruskiewitsch and Devoto in \cite{AD} coincide with kernels of representation
as introduced in \cite{Bker}. Some new results concerning the normality of
kernels are also presented. It is proven that the property for Hopf algebras to
have all kernels normal Hopf subalgebras is a self dual property.


  By applying quantum chemical calculation, interstellar infrared spectrum was
categorized to three classes. Type-A show unusual feature of strong peaks at
11.3,12.9, and 14.0 micrometer. Usually observed 6.2, 7.7, and 8.6 micrometer
bands are weak or not recognized. Typical examples are NGC1316 and NGC4589.
Such spectrum could be identified for the first time by pure carbon molecule
(C23)2+ (dication) having two carbon pentagons combined with five hexagons.
Calculated spectrum coincided well at 11.3, 13.0, and 14.0 micrometer. Also we
could find more coincidence at 5.2, 5.6, 7.6, 8.8,10.6,15.7 and 17.2
micrometer. Type-B is ubiquitously observed IR, but show medium strength at
11.3 micrometer. Examples are NGC6946 and the red triangle nebula. Coronene
modified PAH (C23H12)2+ show best coincidence for both wavelength and strength.
Type-C is usualy observed one featuring very strong peak at 11.3 micrometer.
Examples are NGC7023, NGC2023 and M17SW. One capable expanation of large 11.3
micrometer band is a mixture of Type-A and Type-B. Combination of polycyclic
pure-carbon-molecule and hydrocarbon-molecule may give a variety of IR
spectrum.


  We study the anomalous normal state properties of a simple two-dimensional
model whose ground state is a d-wave superconductor. Using a self-consistent,
conserving formulation, we show that pairing correlations above T_c lead to the
appearance of a highly anisotropic pseudogap in the electronic spectral
function and the destruction of the Fermi surface. We discuss the similarities
and differences between our results and ARPES experiments on underdoped
cuprates.


  In this paper we show that a process modeled by a strongly continuous
real-valued semigroup (that has a space convolution operator as infinitesimal
generator) cannot satisfy causality. We present and analyze a causal model of
diffusion that satisfies the semigroup property at a discrete set of time
points $M:=\{\tau_m\,|\,m\in\N_0\}$ and that is in contrast to the classical
diffusion model not smooth. More precisely, if $v$ denotes the concentration of
a substance diffusing with constant speed, then $v$ is continuous but its time
derivative is discontinuous at the discrete set $M$ of time points. It is this
property of diffusion that forbids the classical limit procedure that leads to
the noncausal diffusion model in Stochastics. Furthermore, we show that
diffusion with constant speed satisfies an inhomogeneous wave equation with a
time dependent coefficient.


  In this paper, we propose a generic framework that enables game developers
without knowledge of machine learning to create bot behaviors with playstyles
that align with their preferences. Our framework is based on interactive
reinforcement learning (RL), and we used it to create a behavior authoring tool
called MarioMix. This tool enables non-experts to create bots with varied
playstyles for the game titled Super Mario Bros. The main interaction procedure
of MarioMix consists of presenting short clips of gameplay displaying
precomputed bots with different playstyles to end-users. Then, end-users can
select the bot with the playstyle that behaves as intended. We evaluated
MarioMix by incorporating input from game designers working in the industry.


  We consider the hydrogen molecular ion $H^+_2$ in the presence of a strong
homogeneous magnetic field. In this regime, the effective Hamiltonian is almost
one dimensional with a potential energy which looks like a sum of two Dirac
delta functions. This model is solvable, but not close enough to our exact
Hamiltonian for relevant strenght of the magnnetic field. However we show that
the correct values of the equilibrium distance as well as the binding energy of
the ground state of the ion, can be obtained when incorporating perturbative
corrections up to second order. Finally, we show that $ He_2^{3+}$ exists for
sufficiently large magnetic fields.


  It has been assumed until very recently that all long-range correlations are
screened in three-dimensional melts of linear homopolymers on distances beyond
the correlation length $\xi$ characterizing the decay of the density
fluctuations. Summarizing simulation results obtained by means of a variant of
the bond-fluctuation model with finite monomer excluded volume interactions and
topology violating local and global Monte Carlo moves, we show that due to an
interplay of the chain connectivity and the incompressibility constraint, both
static and dynamical correlations arise on distances $r \gg \xi$. These
correlations are scale-free and, surprisingly, do not depend explicitly on the
compressibility of the solution. Both monodisperse and (essentially)
Flory-distributed equilibrium polymers are considered.


  Facial actions are spatio-temporal signals by nature, and therefore their
modeling is crucially dependent on the availability of temporal information. In
this paper, we focus on inferring such temporal dynamics of facial actions when
no explicit temporal information is available, i.e. from still images. We
present a novel approach to capture multiple scales of such temporal dynamics,
with an application to facial Action Unit (AU) intensity estimation and
dimensional affect estimation. In particular, 1) we propose a framework that
infers a dynamic representation (DR) from a still image, which captures the
bi-directional flow of time within a short time-window centered at the input
image; 2) we show that we can train our method without the need of explicitly
generating target representations, allowing the network to represent dynamics
more broadly; and 3) we propose to apply a multiple temporal scale approach
that infers DRs for different window lengths (MDR) from a still image. We
empirically validate the value of our approach on the task of frame ranking,
and show how our proposed MDR attains state of the art results on BP4D for AU
intensity estimation and on SEMAINE for dimensional affect estimation, using
only still images at test time.


  This extended abstract introduces a class of graph learning applicable to
cases where the underlying graph has polytopic uncertainty, i.e., the graph is
not exactly known, but its parameters or properties vary within a known range.
By incorporating this assumption that the graph lies in a polytopic set into
two established graph learning frameworks, we find that our approach yields
better results with less computation.


  We study noncommutative principal bundles (Hopf-Galois extensions) in the
context of coquasitriangular Hopf algebras and their monoidal category of
comodule algebras. When the total space is quasi-commutative, and thus the base
space subalgebra is central, we define the gauge group as the group of vertical
automorphisms or equivalently as the group of equivariant algebra maps. We
study Drinfeld twist (2-cocycle) deformations of Hopf-Galois extensions and
show that the gauge group of the twisted extension is isomorphic to the gauge
group of the initial extension. In particular, noncommutative principal bundles
arising via twist deformation of commutative principal bundles have classical
gauge group. We illustrate the theory with a few examples.


  Wolf-Rayet (WR) stars are evolved massive stars, presumably on their way to
becoming supernova. They are characterized by high luminosities and fast and
dense stellar winds. We have detected signs of a radio continuum pinwheel
associated with WR147, a nitrogen-rich WR star with spectral subtype WN8. These
structures are known around a handful of late-type carbon-rich WR stars with
massive companions were the dust formed at the zone where the two winds collide
produces a plume of dense gas and dust that is carried out with the WR wind. As
the binary system rotates, an Archimedean spiral detectable in the infrared is
formed. The resulting pinwheel contains information on wind speeds,
wind-momentum ratio and orbital parameters. However, WR147 is a WN star and the
formation of dust is unlikely so a different emission mechanism must be at
work. Our analysis of the data suggests that in this case the emission is
dominantly of non-thermal nature (synchrotron), although we cannot exclude that
some clumps could be brighter in free-free emission. It is possible that the
pinwheels associated with WN stars will be detectable only as non-thermal
emitters at radio wavelengths. From the characteristics of the pinwheel we
estimate a period of 1.7 years for the binary system (the WN8 star and a
companion yet undetected directly) responsible for the pinwheel.


  Digital evidence underpin the majority of crimes as their analysis is an
integral part of almost every criminal investigation. Even if we temporarily
disregard the numerous challenges in the collection and analysis of digital
evidence, the exchange of the evidence among the different stakeholders has
many thorny issues. Of specific interest are cross-border criminal
investigations as the complexity is significantly high due to the heterogeneity
of legal frameworks which beyond time bottlenecks can also become prohibiting.
The aim of this article is to analyse the current state of practice of
cross-border investigations considering the efficacy of current collaboration
protocols along with the challenges and drawbacks to be overcome. Further to
performing a legally-oriented research treatise, we recall all the challenges
raised in the literature and discuss them from a more practical yet global
perspective. Thus, this article paves the way to enabling practitioners and
stakeholders to leverage horizontal strategies to fill in the identified gaps
timely and accurately.


  Several novel statistical methods have been developed to estimate large
integrated volatility matrices based on high-frequency financial data. To
investigate their asymptotic behaviors, they require a sub-Gaussian or finite
high-order moment assumption for observed log-returns, which cannot account for
the heavy-tail phenomenon of stock-returns. Recently, a robust estimator was
developed to handle heavy-tailed distributions with some bounded fourth-moment
assumption. However, we often observe that log-returns have heavier tail
distribution than the finite fourth-moment and that the degrees of heaviness of
tails are heterogeneous across asset and over time. In this paper, to deal with
the heterogeneous heavy-tailed distributions, we develop an adaptive robust
integrated volatility estimator that employs pre-averaging and truncation
schemes based on jump-diffusion processes. We call this an adaptive robust
pre-averaging realized volatility (ARP) estimator. We show that the ARP
estimator has a sub-Weibull tail concentration with only finite 2$\alpha$-th
moments for any $\alpha>1$. In addition, we establish matching upper and lower
bounds to show that the ARP estimation procedure is optimal. To estimate large
integrated volatility matrices using the approximate factor model, the ARP
estimator is further regularized using the principal orthogonal complement
thresholding (POET) method. The numerical study is conducted to check the
finite sample performance of the ARP estimator.


  Mobile phones and smartphones have evolved to be very powerful devices that
have the potential to be utilized in many application areas apart from generic
communication. With each passing year, we see increasingly powerful smartphones
being manufactured, which have a plethora of powerful embedded sensors like
microphone, camera, digital compass, GPS, accelerometer, temperature sensors
and many more. Moreover, the ability to easily program today's smartphones,
enables us to exploit these sensors, in a wide variety of application such as
personal safety, emergency and calamity response, situation awareness, remote
activity monitoring, transportation and environment monitoring. In this paper,
we survey the existing mobile phone sensing methodologies and application
areas. We also formulate the architectural framework of our project,
SenseDroid, its utility, limitations and possible future applications.


  Drivers cognitive and physiological states affect their ability to control
their vehicles. Thus, these driver states are important to the safety of
automobiles. The design of advanced driver assistance systems (ADAS) or
autonomous vehicles will depend on their ability to interact effectively with
the driver. A deeper understanding of the driver state is, therefore,
paramount. EEG is proven to be one of the most effective methods for driver
state monitoring and human error detection. This paper discusses EEG-based
driver state detection systems and their corresponding analysis algorithms over
the last three decades. First, the commonly used EEG system setup for driver
state studies is introduced. Then, the EEG signal preprocessing, feature
extraction, and classification algorithms for driver state detection are
reviewed. Finally, EEG-based driver state monitoring research is reviewed
in-depth, and its future development is discussed. It is concluded that the
current EEG-based driver state monitoring algorithms are promising for safety
applications. However, many improvements are still required in EEG artifact
reduction, real-time processing, and between-subject classification accuracy.


  We present a systematic investigation of the possible locations for the
special point (SP), a unique feature of hybrid neutron stars in the
mass-radius. The study is performed within the two-phase approach where the
high-density (quark matter) phase is described by the constant-sound-speed
(CSS) equation of state (EoS) and the nuclear matter phase around saturation
density is varied from very soft (APR) to stiff (DD2 with excluded nucleon
volume. Different construction schemes for the deconfinement transition are
applied: Maxwell construction, mixed phase construction and parabolic
interpolation. We demonstrate for the first time that the SP is invariant not
only against changing the nuclear matter EoS, but also against variation of the
construction schemes for the phase transition. Since the SP serves as a proxy
for the maximum mass and accessible radii of massive hybrid stars, we draw
conclusions for the limiting masses and radii of hybrid neutron stars.


  Many commonsense reasoning NLP tasks involve choosing between one or more
possible answers to a question or prompt based on knowledge that is often
implicit. Large pretrained language models (PLMs) can achieve near-human
performance on such tasks, while providing little human-interpretable evidence
of the underlying reasoning they use. In this work, we show how to use these
same models to generate such evidence: inspired by the contrastive nature of
human explanations, we use PLMs to complete explanation prompts which contrast
alternatives according to the key attribute(s) required to justify the correct
answer (for example, peanuts are usually salty while raisins are sweet).
Conditioning model decisions on these explanations improves performance on two
commonsense reasoning benchmarks, as compared to previous non-contrastive
alternatives. These explanations are also judged by humans to be more relevant
for solving the task, and facilitate a novel method to evaluate explanation
faithfulfness.


  In this paper we present a novel mechanism for producing the observed Dark
Matter(DM) relic abundance during the First Order Phase Transition (FOPT) in
the early universe. We show that the bubble expansion with ultra-relativistic
velocities can lead to the abundance of DM particles with masses much larger
than the scale of the transition. We study this non-thermal production
mechanism in the context of a generic phase transition and the electroweak
phase transition. The application of the mechanism to the Higgs portal DM as
well as the signal in the Stochastic Gravitational Background are discussed.


  We do further investigation in a certain cosine function defined for smooth
Minkowski spaces. We prove that such function is symmetric if and only if the
referred space is Euclidean, and also that it can be given in terms of the
Gateaux derivative of the norm. As an application we use it to study the ratio
between the lengths of tangent segments drawn through an external point to the
unit circle of a Radon plane. We also give an easy characterization of such
planes in terms of signs of the cosine function.


  New photometry and spectroscopy for the two rich clusters Abell 665 and Abell
2218 are presented and used to establish the Fundamental Plane (FP) for the
clusters. The FP for these two clusters adds important knowledge about the
properties of E and S0 galaxies in the relatively unexplored redshift interval
0.05 to 0.3. We have compared the FP for A665 and A2218 with the FP for the
three clusters CL0024+16, CL1358+62 and MS2053-04 with redshifts between 0.33
and 0.58, and with the FP for the Coma cluster. The scatter around the FP is
similar for all six clusters. We find that the slope of the FP for the
intermediate redshift clusters is slightly different from the one found for the
Coma cluster and other nearby clusters. This may either be caused by selection
effects for the intermediate redshift clusters or by differences in the
evolution of low luminosity galaxies and high luminosity galaxies. The
mass-to-light (M/L) ratios, as measured from the FP, change with redshift.
Using the data for all five intermediate redshift clusters, we find that the
M/L ratios for photometry calibrated to Gunn r change with redshift as Delta
log M/L_r = (-0.26+-0.06) Delta z for q0=0.5. This is consistent with the
previously published analysis for CL0024+16, CL1358+62 and MS2053-04. For
q0=0.5 the results are consistent with passive evolution of a stellar
population which formed at a redshift larger than five. For q0=0.15 the
formation redshift must be larger than 1.7. Our new data for A665 and A2218
confirm the gradual and slow evolution of the bright E and S0 galaxies.
However, possible star formation in E and S0 galaxies during the last 3-4 Gyr
of the history of the Universe, as well as the selection effects complicate the
interpretation of the data.


  Transparent conductors (TC's) combine the usually contraindicated properties
of electrical conductivity with optical transparency and are generally made by
starting with a transparent insulator and making it conductive via heavy
doping, an approach that generally faces severe 'doping bottlenecks'. We
propose a different idea for TC design-starting with a metallic conductor and
designing transparency by control of intrinsic interband transitions and
intraband plasmonic frequency. We identify the specific design principles for
three such prototypical intrinsic TC classes and then search computationally
for materials that satisfy them. Remarkably, one of the intrinsic TC,
Ag3Al22O34, is predicted also to be a prototype 3D compounds that manifest
natural 2D electron gas (2DEG) regions with very high electron density and
conductivity.


  M85 is a peculiar S0 galaxy in Virgo and is a well-known merger remnant. In
this paper, we present the first spectroscopic study of globular clusters (GCs)
in M85. We obtain spectra for 21 GC candidates and the nucleus of M85 using the
Gemini Multi-Object Spectrograph on the Gemini North 8.1 m telescope. From
their radial velocities, 20 of the GCs are found to be members of M85. We find
a strong rotation signal of the M85 GC system with a rotation amplitude of 235
km s$^{-1}$. The rotation axis of the GC system has a position angle of about
161$^{\circ}$, which is 51$\rlap{.}{^\circ}$5 larger than that of the stellar
light. The rotation-corrected radial velocity dispersion of the GC system is
estimated to be $\sigma_{\rm r,cor} = $ 160 km s$^{-1}$. The rotation parameter
$\Omega R_{\rm icor}/\sigma_{\rm r,cor}$ of the GC system is derived to be
1.47$^{+1.05}_{-0.48}$, which is one of the largest among known early-type
galaxies. The ages and metallicities of the GCs, which show the same trend as
the results based on Lick indices, are derived from full spectrum fitting
(ULySS). About a half of the GCs are an intermediate-age population of which
the mean age is $\sim$ 3.7 $\pm$ 1.9 Gyr, having a mean [Fe/H] value of --0.26.
The other half are old and metal-poor. These results suggest that M85
experienced a wet merging event about 4 Gyr ago, forming a significant
population of star clusters. The strong rotational feature of the GC system can
be explained by an off-center major merging.


  The shear stress relaxation modulus $G(t)$ may be determined from the shear
stress $\tau(t)$ after switching on a tiny step strain $\gamma$ or by inverse
Fourier transformation of the storage modulus $G^{\prime}(\omega)$ or the loss
modulus $G^{\prime\prime}(\omega)$ obtained in a standard oscillatory shear
experiment at angular frequency $\omega$. It is widely assumed that $G(t)$ is
equivalent in general to the equilibrium stress autocorrelation function $C(t)
= \beta V \langle \delta \tau(t) \delta \tau(0)\rangle$ which may be readily
computed in computer simulations ($\beta$ being the inverse temperature and $V$
the volume). Focusing on isotropic solids formed by permanent spring networks
we show theoretically by means of the fluctuation-dissipation theorem and
computationally by molecular dynamics simulation that in general $G(t) = G_{eq}
+ C(t)$ for $t > 0$ with $G_{eq}$ being the static equilibrium shear modulus. A
similar relation holds for $G^{\prime}(\omega)$. $G(t)$ and $C(t)$ must thus
become different for a solid body and it is impossible to obtain $G_{eq}$
directly from $C(t)$.


  We have produced an atlas of the Th-Ar hollow-cathode lamp used with the
2dcoude spectrograph at McDonald Observatory. The atlas covers from 3611.9 to
10596.4 A at a resolving power of 52,000. We have determined the wavelenghts of
1483 emission lines in the spectrum with a median precision of 0.00023 A. A
web-based interface is offered for interactive visualization of segments of the
atlas or spectral orders.


  We shall show that the Picard number of the generic fiber, in the sense of
scheme, of an abelian fibered hyperk\"ahler manifold over the projective space
is always one. We then give a few applications for the Mordell-Weil group. In
particular, by deforming O'Grady's 10-dimensional manifold, we construct an
abelian fibered hyperk\"ahler manifold of Mordell-Weil rank 20, which is the
maximum possible among all known ones.


  We exhibit a particular free subarrangement of a certain restriction of the
Weyl arrangement of type $E_7$ and use it to give an affirmative answer to a
recent conjecture by T.~Abe on the nature of additionally free and stair-free
arrangements.


  Multiple perspectives on the nonlinear processes of medical innovations can
be distinguished and combined using the Medical Subject Headings (MeSH) of the
Medline database. Focusing on three main branches-"diseases," "drugs and
chemicals," and "techniques and equipment"-we use base maps and overlay
techniques to investigate the translations and interactions and thus to gain a
bibliometric perspective on the dynamics of medical innovations. To this end,
we first analyze the Medline database, the MeSH index tree, and the various
options for a static mapping from different perspectives and at different
levels of aggregation. Following a specific innovation (RNA interference) over
time, the notion of a trajectory which leaves a signature in the database is
elaborated. Can the detailed index terms describing the dynamics of research be
used to predict the diffusion dynamics of research results? Possibilities are
specified for further integration between the Medline database, on the one
hand, and the Science Citation Index and Scopus (containing citation
information), on the other.


  Bour's minimal surface has remarkable properties in three dimensional
Minkowski space. We reveal the definite and indefinite cases of the Bour's
surface using Weierstrass representations, and give some differential geometric
properties of the astonishing maximal and minimal surfaces.


  As the next generation of diverse workloads like autonomous driving and
augmented/virtual reality evolves, computation is shifting from cloud-based
services to the edge, leading to the emergence of a cloud-edge compute
continuum. This continuum promises a wide spectrum of deployment opportunities
for workloads that can leverage the strengths of cloud (scalable
infrastructure, high reliability) and edge (energy efficient, low latencies).
Despite its promises, the continuum has only been studied in silos of various
computing models, thus lacking strong end-to-end theoretical and engineering
foundations for computing and resource management across the continuum.
Consequently, developers resort to ad hoc approaches to reason about
performance and resource utilization of workloads in the continuum. In this
work, we conduct a first-of-its-kind systematic study of various computing
models, identify salient properties, and make a case to unify them under a
compute continuum reference architecture. This architecture provides an
end-to-end analysis framework for developers to reason about resource
management, workload distribution, and performance analysis. We demonstrate the
utility of the reference architecture by analyzing two popular continuum
workloads, deep learning and industrial IoT. We have developed an accompanying
deployment and benchmarking framework and first-order analytical model for
quantitative reasoning of continuum workloads. The framework is open-sourced
and available at https://github.com/atlarge-research/continuum.


  Far-from-equilibrium dynamics of SU(2) gauge theory with Wilson fermions is
studied in 1+1 space-time dimensions using a real-time lattice approach.
Lattice improved Hamiltonians are shown to be very efficient in simulating
Schwinger pair creation and emergent phenomena such as plasma oscillations. As
a consequence, significantly smaller lattices can be employed to approach
continuum physics in the infinite-volume limit as compared to unimproved
implementations. This allows us to compute also higher-order correlation
functions including four fermion fields, which give unprecedented insights into
the real-time dynamics of the fragmentation process of strings between fermions
and antifermions.


  Ab initio calculations within the density-functional theory formalism are
performed to investigate the ground state, electric charge doping, and
electronic properties of titanium and titanium dioxide monolayers adsorbed on a
graphene surface. A new ground state structrure of Ti monolayer adsorbed on
graphene is reported which is shown to be stable up to T = 500 K. Effects due
to lower and higher Ti adatoms coverage are studied. We find that the adsorbed
Ti provides a strong n-type doping which supports recent experimental
observations. On the other hand, TiO_2 can induce both p- and n-type doping in
the carbon monolayer depending on whether oxygen or titanium atoms are closest
to the substrate. We identify the structures which are responsible for the
experimentally observed autocompensation mechanism that leads to the reversion
of adsorbate effects after oxidation of the adsorbed Ti.


  In general relativity, gravitational waves (GWs) exhibit two tensor modes,
while alternative theories predict up to six polarization modes. We investigate
GW polarization constraints using a model-independent parametrized
post-Einsteinian framework with space- and ground-based detectors. Evaluating
LISA, Taiji, TianQin, LIGO, Virgo, KAGRA, and Einstein Telescope (ET), we
analyze their capabilities and network performance. Taiji provides the best
constraints among space-based detectors, with LISA outperforming TianQin. Among
ground-based detectors, LIGO excels in vector modes, while ET offers the most
comprehensive constraints. In network scenarios, LISA+TJm performs best, and ET
surpasses second-generation detector combinations. Multiband observations
alleviate scalar mode degeneracies, significantly enhancing ground-based
detector performance. Combined space- and ground-based observations yield
robust constraints on GW polarization, advancing tests of deviations from
general relativity. Our findings highlight the potential of future GW missions
to refine our understanding of gravitational physics through precise
polarization measurements.


  In recent years studying the content of the World Wide Web became a very
important yet rather difficult task. There is a need for a compression
technique that would allow a web graph representation to be put into the memory
while maintaining random access time competitive to the time needed to access
uncompressed web graph on a hard drive.
  There are already available techniques that accomplish this task, but there
is still room for improvements and this thesis attempts to prove it. It
includes a comparison of two methods contained in state of art of this field
(BV and k2partitioned) to two already implemented algorithms (rewritten,
however, in C++ programming language to maximize speed and resource management
efficiency), which are LM and 2D, and introduces the new variant of the latter
one, called 2D stripes.
  This thesis serves as well as a proof of concept. The final considerations
show positive and negative aspects of all presented methods, expose the
feasibility of the new variant as well as indicate future direction for
development.


  Weather disaster related emergency operations pose a great challenge to air
mobility in both aircraft and airport operations, especially when the impact is
gradually approaching. We propose an optimized framework for adjusting airport
operational schedules for such pre-disaster scenarios. We first, aggregate
operational data from multiple airports and then determine the optimal count of
evacuation flights to maximize the impacted airport's outgoing capacity without
impeding regular air traffic. We then propose a novel Neural Network (NN)
accelerated Genetic Algorithm(GA) for evacuation planning. Our experiments show
that integration yielded comparable results but with smaller computational
overhead. We find that the utilization of a NN enhances the efficiency of a GA,
facilitating more rapid convergence even when operating with a reduced
population size. This effectiveness persists even when the model is trained on
data from airports different from those under test.


  We present a method to differentiate organisms solely by their motion based
on the generalized Langevin equation (GLE) and use it to distinguish two
different swimming modes of strongly confined unicellular microalgae
Chlamydomonas reinhardtii (CR). The GLE is the most general model for active or
passive motion of organisms and particles and in particular includes
non-Markovian effects, i.e., the trajectory memory of its past. We extract all
GLE parameters from individual cell trajectories and perform an unbiased
cluster analysis to group them into different classes. For the specific cell
population employed in the experiments, the GLE-based assignment into the two
different swimming modes works perfectly, as checked by control experiments.
The classification and sorting of single cells and organisms is important in
different areas, our method that is based on motion trajectories offers
wide-ranging applications in biology and medicine.


  Let $(M^{n+1},g)$ be a closed Riemannian manifold, $n+1\geq 3$. We will prove
that for all $m \in \mathbb{N}$, there exists $c^{*}(m)>0$, which depends on
$g$, such that if $0<c<c^{*}(m)$, $(M,g)$ contains at least $m$ many closed
$c$-CMC hypersurfaces with optimal regularity. More quantitatively, there
exists a constant $\gamma_0$, depending on $g$, such that for all $c>0$, there
exist at least $\gamma_0c^{-\frac{1}{n+1}}$ many closed $c$-CMC hypersurfaces
(with optimal regularity) in $(M,g)$. This extends the theorem of Zhou and Zhu,
where they proved the existence of at least one closed $c$-CMC hypersurface in
$(M,g)$.


  Overfitting negatively impacts the generalization ability of deep neural
networks (DNNs) in both natural and adversarial training. Existing methods
struggle to consistently address different types of overfitting, typically
designing strategies that focus separately on either natural or adversarial
patterns. In this work, we adopt a unified perspective by solely focusing on
natural patterns to explore different types of overfitting. Specifically, we
examine the memorization effect in DNNs and reveal a shared behaviour termed
over-memorization, which impairs their generalization capacity. This behaviour
manifests as DNNs suddenly becoming high-confidence in predicting certain
training patterns and retaining a persistent memory for them. Furthermore, when
DNNs over-memorize an adversarial pattern, they tend to simultaneously exhibit
high-confidence prediction for the corresponding natural pattern. These
findings motivate us to holistically mitigate different types of overfitting by
hindering the DNNs from over-memorization training patterns. To this end, we
propose a general framework, Distraction Over-Memorization (DOM), which
explicitly prevents over-memorization by either removing or augmenting the
high-confidence natural patterns. Extensive experiments demonstrate the
effectiveness of our proposed method in mitigating overfitting across various
training paradigms.


  We design and implement an efficient parallel algorithm for finding a perfect
matching in a weighted bipartite graph such that weights on the edges of the
matching are large. This problem differs from the maximum weight matching
problem, for which scalable approximation algorithms are known. It is primarily
motivated by finding good pivots in scalable sparse direct solvers before
factorization. Due to the lack of scalable alternatives, distributed solvers
use sequential implementations of maximum weight perfect matching algorithms,
such as those available in MC64. To overcome this limitation, we propose a
fully parallel distributed memory algorithm that first generates a perfect
matching and then iteratively improves the weight of the perfect matching by
searching for weight-increasing cycles of length four in parallel. For most
practical problems the weights of the perfect matchings generated by our
algorithm are very close to the optimum. An efficient implementation of the
algorithm scales up to 256 nodes (17,408 cores) on a Cray XC40 supercomputer
and can solve instances that are too large to be handled by a single node using
the sequential algorithm.


  We turn the stochastic critical forest-fire model introduced by Drossel and
Schwabl (PRL 69, 1629, 1992) into a deterministic threshold model. This new
model has many features in common with sandpile and earthquake models of
Self-Organized Criticality. Nevertheless our deterministic forest-fire model
exhibits in detail the same macroscopic statistical properties as the original
Drossel and Schwabl model. We use the deterministic model and a related
semi-deterministic version of the model to elaborate on the relation between
forest-fire, sandpile and earthquake models.


  We build a SAT solver implementing the DPLL algorithm in the
verification-enabled programming language Dafny. The resulting solver is fully
verified (soundness, completeness and termination are computer checked). We
benchmark our Dafny solver and we show that it is just as efficient as an
equivalent DPLL solver implemented in C# and roughly two times less efficient
than an equivalent solver written in C++. We conclude that auto-active
verification is a promising approach to increasing trust in SAT solvers, as it
combines a good trade-off between execution speed and degree of trustworthiness
of the final product.


  Liquid metals (LM) are embedded in an elastomer matrix to obtain soft
composites with unique thermal, dielectric, and mechanical properties. They
have applications in soft robotics, biomedical engineering, and wearable
electronics. By linking the structure to the properties of these materials, it
is possible to perform material design rationally. Liquid-metal embedded
elastomers (LMEEs) have been designed for targeted electro-thermo-mechanical
properties by semi-supervised learning of structure-property (SP) links in a
variational autoencoder network (VAE). The design parameters are the
microstructural descriptors that are physically meaningful and have affine
relationships with the synthetization of the studied particulate composite. The
machine learning (ML) model is trained on a generated dataset of
microstructural descriptors with their multifunctional property quantities as
their labels. Sobol sequence is used for in-silico Design of Experiment (DoE)
by sampling the design space to generate a comprehensive dataset of 3D
microstructure realizations via a packing algorithm. The mechanical responses
of the generated microstructures are simulated using a previously developed
Finite Element (FE) model, considering the surface tension induced by LM
inclusions, while the linear thermal and dielectric constants are homogenized
with the help of our in-house Fast Fourier Transform (FFT) package. Following
the training by minimization of an appropriate loss function, the VAE encoder
acts as the surrogate of numerical solvers of the multifunctional
homogenizations, and its decoder is used for the material design. Our results
indicate the satisfactory performance of the surrogate model and the inverse
calculator with respect to high-fidelity numerical simulations validated with
LMEE experimental results.


  In the paper it is shown that, even without a knowledge of the concrete form
of the equations of mathematical physics and field theories, with the help of
skew-symmetric differential forms one can see specific features of the
equations of mathematical physics, the relation between mathematical physics
and field theory, to understand the mechanism of evolutionary processes that
develop in material media and lead to emergency of physical structures forming
physical fields. This discloses a physical meaning of such concepts like
"conservation laws", "postulates" and "causality" and gives answers to many
principal questions of mathematical physics and general field theory.
  In present paper, beside the exterior forms, the skew-symmetric differential
forms, whose basis (in contrast to the exterior forms) are deforming manifolds,
are used. Mathematical apparatus of such differential forms(which were named
evolutionary ones) includes nontraditional elements like nonidentical relations
and degenerate transformations and this enables one to describe discrete
transitions, quantum steps, evolutionary processes, and generation of various
structures.


  This paper presents some new Lie groups preserving fixed subspaces of
geometric algebras (or Clifford algebras) under the twisted adjoint
representation. We consider the cases of subspaces of fixed grades and
subspaces determined by the grade involution and the reversion. Some of the
considered Lie groups can be interpreted as generalizations of Lipschitz groups
and spin groups. The Lipschitz groups and the spin groups are subgroups of
these Lie groups and coincide with them in the cases of small dimensions. We
study the corresponding Lie algebras.


  Exceptional points with coalescence of eigenvalues and eigenvectors are
spectral singularities in the parameter space, achieving which often needs
fine-tuning of parameters in quantum systems. We predict a persistent
realization of nodal magnon-photon polariton, i.e., a polariton without any gap
splitting in a thin ferromagnetic insulator film sandwiched by two normal
metals, which persistently exists when the ferromagnet is sufficiently thick
$\sim 100$~nm. We perform the model calculation beyond the perturbation theory
using a classical approach, develop a quantum scheme able to account for the
Ohmic dissipation, and find ultrastrong coupling with coupling strength
comparable to the bare magnon frequency. Via revealing a simple conversion
relation we extend this formalism to superconductors and predict the gap opened
by the ultrastrong coupling strongly depends on the direction of polariton
propagation. Our findings may help search for robust non-Hermitian topological
phases in magnonic and spintronic devices.


  Spin-polarized band calculations for LaSr_7B_{48} show a weak ferro-magnetic
state. This is despite a low density-of-states (DOS) and a low Stoner factor.
The reason for the magnetic state is found to be associated with a gain in
potential energy in addition to the exchange energy, as a spin-splitting is
imposed. An impurity like La DOS is essential for this effect. It makes a
correction to the Stoner factor, and provides an explanation of the recently
observed weak ferro-magnetism in doped hexaborides.


  A factorized Regge-pole model for deeply virtual Compton scattering is
suggested. The use of an effective logarithmic Regge-Pomeron trajectory
provides for the description of both ``soft'' (small $|t|$) and ``hard'' (large
$|t|$) dynamics. The model contains explicitly the photoproduction and the DIS
limits and fits the existing HERA data on deeply virtual Compton scattering.


  A 10.24 days Neptune-mass planet was recently announced to orbit the nearby
M2 dwarf Gl 176, based on 28 radial velocities measured with the HRS
spectrograph on the Hobby-Heberly Telescope (HET). We obtained 57 radial
velocities of Gl 176 with the ESO 3.6m telescope and the HARPS spectrograph,
which is known for its sub-m/s stability. The median photon-noise standard
error of our measurements is 1.1 m/s, significantly lower than the 4.7 m/s of
the HET velocities, and the 4 years period over which they were obtained has
much overlap with the epochs of the HET measurements. The HARPS measurements
show no evidence for a signal at the period of the putative HET planet,
suggesting that its detection was spurious. We do find, on the other hand,
strong evidence for a lower mass 8.4 Mearth planet, in a quasi-circular orbit
and at the different period of 8.78 days. The host star has moderate magnetic
activity and rotates on a 39-days period, which we confirm through modulation
of both contemporaneous photometry and chromospheric indices. We detect that
period as well in the radial velocities, but it is well removed from the
orbital period and no cause for confusion. This new detection of a super-Earth
(2 Mearth < M sin(i) < 10 Mearth) around an M dwarf adds to the growing
evidence that such planets are common around very low mass stars: a third of
the 20 known planets with M sin(i) < 0.1 Mjup and 3 of the 7 known planets with
M sin(i) < 10 Mearth orbit an M dwarf, in contrast to just 4 of the ~300 known
Jupiter-mass planets.


  The general structure of trace anomaly, suggested recently by Deser and
Shwimmer, is argued to be the consequence of the Wess-Zumino consistency
condition. The response of partition function on a finite Weyl transformation,
which is connected with the cocycles of the Weyl group in $d=2k$ dimensions is
considered, and explicit answers for $d=4,6$ are obtained. Particularly, it is
shown, that addition of the special combination of the local counterterms leads
to the simple form of that cocycle, quadratic over Weyl field $\sigma$, i.e.
the form, similar to the two-dimensional Lioville action. This form also
establishes the connection of the cocycles with conformal-invariant operators
of order $d$ and zero weight. Beside that, the general rule for transformation
of that cocycles into the cocycles of diffeomorphisms group is presented.


  We investigated the cause of optical transmittance degradation in tapered
fibers. Degradation commences immediately after fabrication and it eventually
reduces the transmittance to almost zero. It is a major problem that limits
applications of tapered fibers. We systematically investigated the effect of
the dust-particle density and the humidity on the degradation dynamics. The
results clearly show that the degradation is mostly due to dust particles and
that it is not related to the humidity. In a dust free environment it is
possible to preserve the transmittance with a degradation of less than the
noise (+/- ?0.02) over 1 week.


  The type of decision dependent uncertainties (DDUs) imposes a great challenge
in decision making, while existing methodologies are not sufficient to support
many real practices. In this paper, we present a systematic study to handle
this challenge in two-stage robust optimization~(RO). Our main contributions
include three sophisticated variants of column-and-constraint generation method
to exactly compute DDU-based two-stage RO. By a novel application of core
concepts of linear programming, we provide rigorous analyses on their
computational behaviors. Interestingly, in terms of the iteration complexity of
those algorithms, DDU-based two-stage RO is not more demanding than its
decision independent uncertainty (DIU) based counterpart. It is worth
highlighting a counterintuitive discovery that converting a DIU set into a DDU
set by making use of "deep knowledge" and then computing the resulting
DDU-based formulation may lead to a significant improvement. Indeed, as shown
in this paper, in addition to capturing the actual dependence existing in the
real world, DDU is a powerful and flexible tool to represent and leverage
analytical properties or simply domain expertise to achieve a strong solution
capacity. So, we believe it will open a new direction to solve large-scale DIU-
or DDU-based RO. Other important results include basic structural properties
for two-stage RO, an approximation scheme to deal with mixed integer recourse,
and a couple of enhancement techniques for the developed algorithms, as well as
an organized numerical study to help us appreciate all algorithms and
enhancement techniques' computational performances.


  The Time-of-Flight and Neutron-Spin-Echo techniques have been applied for the
research of ultrasonic effect at the cold neutron diffraction in mosaic single
crystals (KBr and mica). It was found that h.f. ultrasound intensifies
quasi-elastic neutron scattering and this effect cannot be explained as a
result of neutron scattering by thermal phonons in a sample heated by
ultrasound; neither can it be interpreted in the context of standard secondary
extinction theory. A new modified model is proposed based on the assumption
that the angular distribution function describing mosaic block disorientation
is not smooth but contains deep narrow troughs. This model is qualitatively
equivalent to the preposition about existence large block structure of sample.
The corresponding kinetic equations are formulated and exactly solved. The
results obtained correlate well with experimental data. Our results evidence
that such an approach is applicable for studying the ultrasonic effect at
neutron diffraction in different technologies dealing with mosaic single
crystals. PACS: 61.05F-,62.65, 63.20.dd Keywords: neutron, ultrasound, mosaic,
time-of-flight, spin-echo


  States of Low Energy are a class of exact Hadamard states for free quantum
fields on cosmological spacetimes whose structure is fixed at {\it all} scales
by a minimization principle. The original construction was for
Friedmann-Lema\^{i}tre geometries and is here generalized to anisotropic
Bianchi I geometries relevant to primordial cosmology. In addition to proving
the Hadamard property, systematic series expansions in the infrared and
ultraviolet are developed. The infrared expansion is convergent and induces in
the massless case a leading spatial long distance decay that is always
Minkowski-like but anisotropy modulated. The ultraviolet expansion is shown to
be equivalent to the Hadamard property, and a non-recursive formula for its
coefficients is presented.


  This research proposes a distributed switching control to secure multi-robot
systems in the presence of cyberattacks. Two major types of cyberattack are
considered: deception attack and denial of service (DoS) attack, which
compromise the integrity and availability of resources, respectively. First, a
residual-based attack detection scheme is introduced to identify the type of
attacks. Then, a switching control is designed to neutralize the effect of the
identified attacks, satisfying the performance guarantees required for state
consensus among robots. For the type of a deception attack, coordination-free
consensus protocols are designed to tune the weights of each robot in a way
that uncompromised robots gain more weight than compromised robots. For the
type of a DoS attack, leader-follower protocols that reconfigure the
communication topology are utilized to transform the compromised robots into
sub-robots following the leaders. The performance of the proposed approach is
evaluated on the Robotarium multi-robot testbed. A full demonstration with
extensive cases is available at https://youtu.be/eSj0XS2pdxI.


  The geometry of small causal diamonds is systematically studied, based on
three distinct constructions that are common in the literature, namely the
geodesic ball, the Alexandrov interval and the lightcone cut. The causal
diamond geometry is calculated perturbatively using Riemann normal coordinate
expansion up to the leading order in both vacuum and non-vacuum. We provide a
collection of results including the area of the codimension-two edge, the
maximal hypersurface volume and their isoperimetric ratio for each
construction, which will be useful for any applications involving the
quantitative properties of causal diamonds. In particular, by solving the
dynamical equations of the expansion and the shear on the lightcone, we find
that intriguingly only the light-cone cut construction yields an area deficit
proportional to the Bel-Robinson superenergy density W in four dimensional
spacetime, but such a direct connection fails to hold in any other dimension.
We also compute the volume of the Alexandrov interval causal diamond in vacuum,
which we believe is important but missing from the literatures. Our work
complements and extends the earlier works on the causal diamond geometry by
Gibbons and Solodukhin, Jacobson, Senovilla and Speranza and others. Some
potential applications of our results in mathematical general relativity and
quantum gravity are discussed.


  Ultra-faint dwarf galaxies (UFDs) are promising observable proxies to
building blocks of galaxies formed in the early Universe. We study the
formation and evolution of UFDs using cosmological hydrodynamic simulations. In
particular, we show that a major merger of two building block galaxies with
3,900 Msun and 7,500 Msun at the cosmic age of 510 Myr results in a system with
an extended stellar distribution consistent with the de Vaucouleurs profile.
The simulated galaxy has an average stellar metallicity of [Fe/H]=-2.7 and
features a metallicity gradient. These results closely resemble the properties
of a recently discovered UFD, Tucana II, which is extremely metal-poor and has
a spatially extended stellar halo with the more distant stars being more
metal-poor. Our simulation suggests that the extended stellar halo of Tucana II
may have been formed through a past major merger. Future observational searches
for spatially extended structures around other UFDs, combined with further
theoretical studies, will provide tangible measures of the evolutionary history
of the ancient, surviving satellite galaxies.


  This note is a somewhat-lighthearted comment on a recent paper by David
Wallace, arXiv:0906.2718[quant-ph] entitled "A formal proof of the Born rule
from decision-theoretic assumptions".


  The hierarchical cold dark matter (CDM) model for structure formation is a
well defined and testable model. Direct detection is the best technique for
confirming the model yet predictions for the energy and density distribution of
particles on earth remain inadequate. Axially symmetric collapse of
collisionless dark matter can leave observable caustic rings in phase space and
this model is frequently used to make experimental predictions (Sikivie 1999).
Such cold collapses inevitably suffer from radial orbit instabilities that
produce unrealistic bar-like halos. Moreover, this model bears no relation to
the hierarchical growth of CDM galactic halos which form via a complicated
sequence of mergers and violent relaxation. This process destroys any symmetry
and phase wraps existing caustics on a scale comparable to the first objects to
collapse. Since axions can cluster on microscopic scales and free streaming of
neutralinos only erases structure smaller than \sim 100 (GeV/m_{CDM}) A.U., the
dynamical effects of caustics in the Galactic halo are expected to be
negligible.


  Thermal (<1 eV) electron density measurements, derived from the Mars
Atmosphere and Volatile Evolution's (MAVEN) Langmuir Probe and Waves (LPW)
instrument, are analyzed to produce the first statistical study of the thermal
electron population in the Martian magnetotail. Coincident measurements of the
local magnetic field are used to demonstrate that close to Mars, the thermal
electron population is most likely to be observed at a cylindrical distance of
~1.1 Mars radii (RM) from the central tail region during times when the
magnetic field flares inward toward the central tail, compared to ~1.3 RM
during times when the magnetic field flares outward away from the central tail.
Similar patterns are observed further down the magnetotail with greater
variability. Thermal electron densities are highly variable throughout the
magnetotail; average densities are typically ~20-50 /cc within the optical
shadow of Mars and can peak at ~100 /cc just outside of the optical shadow.
Standard deviations of 100% are observed for average densities measured
throughout the tail. Analysis of the local magnetic field topology suggests
that thermal electrons observed within the optical shadow of Mars are likely
sourced from the nightside ionosphere, whereas electrons observed just outside
of the optical shadow are likely sourced from the dayside ionosphere. Finally,
thermal electrons within the optical shadow of Mars are up to 20% more likely
to be observed when the strongest crustal magnetic fields point sunward than
when they point tailward.


  We study complex plane projective sextic curves with simple singularities up
to equisingular deformations. It is shown that two such curves are deformation
equivalent if and only if the corresponding pairs are diffeomorphic. A way to
enumerate all deformation classes is outlined, and a few examples are
considered, including classical Zariski pairs.


  The propagation of terahertz waves in a dust acoustic wave is investigated
numerically. By assuming a sinus profile of the dust number density in the dust
acoustic waves, the transmission properties are calculated using finite
difference time domain method. It shows that the dust acoustic wave can
function similarly as a Bragg filter to block the terahertz waves of a certain
wavelength. The bandwidth of the filter depends on the density profile of the
dust acoustic wave.


  We consider the question of how geometric structures of a Deligne-Mumford
stack affect its Gromov-Witten invariants. The two geometric structures studied
here are {\em gerbes} and {\em root constructions}. In both cases, we explain
conjectures on Gromov-Witten theory for these stacks and survey some recent
progress on these conjectures.


  In this paper, we consider a finite difference grid-based semi-Lagrangian
approach in solving the Vlasov-Poisson (VP) system. Many of existing methods
are based on dimensional splitting, which decouples the problem into solving
linear advection problems, see {\em Cheng and Knorr, Journal of Computational
Physics, 22(1976)}. However, such splitting is subject to the splitting error.
If we consider multi-dimensional problems without splitting, difficulty arises
in tracing characteristics with high order accuracy. Specifically, the
evolution of characteristics is subject to the electric field which is
determined globally from the distribution of particle densities via the
Poisson's equation. In this paper, we propose a novel strategy of tracing
characteristics high order in time via a two-stage multi-derivative
prediction-correction approach and by using moment equations of the VP system.
With the foot of characteristics being accurately located, we proposed to use
weighted essentially non-oscillatory (WENO) interpolation to recover function
values between grid points, therefore to update solutions at the next time
level. The proposed algorithm does not have time step restriction as Eulerian
approach and enjoys high order spatial and temporal accuracy. However, such
finite difference algorithm does not enjoy mass conservation; we discuss one
possible way of resolving such issue and its potential challenge in numerical
stability. The performance of the proposed schemes are numerically demonstrated
via classical test problems such as Landau damping and two stream
instabilities.