  The superconducting and structural properties of S/F/S
(Superconductor/Ferromagnet/Superconductor) heterostructures have been studied
by means of microwave measurements (1-20 GHz) and x-ray absorption fine
structure (XAFS) spectroscopy. Nb/PdNi/Nb trilayers have been studied as a
function of F layer thicness. With respect to pure Nb, XAFS analysis shows that
the heterostructures exhibit larger structural disorder in the S layers.
Microwave measurements show evidence for a progressively weaker vortex pinning
with increasing F thickness. However, no clear correlation is found with the
local disorder in Nb: the weakest pinning is not in the most disordered
trilayer. Therefore the structural disorder in the superconducting material
cannot explain on its own the changes in vortex pinning. We argue that the F
layer acts on the superconducting state itself. We propose possible
explanations for the observed behavior.


  We have observed the reflection nebula NGC 7023, with the Short-High module
and long-slit Short-Low and Long-Low modules of the Infrared Spectrograph on
the Spitzer Space Telescope. We also present Infrared Array Camera and
Multiband Imaging Photometer for Spitzer images of NGC 7023 at 3.6, 4.5, 8.0,
and 24 microns. We observe the aromatic emission features (AEFs) at 6.2, 7.7,
8.6, 11.3, and 12.7 microns, plus a wealth of weaker features. We find new
unidentified interstellar emission features at 6.7, 10.1, 15.8, 17.4, and 19.0
microns. Possible identifications include aromatic hydrocarbons or
nanoparticles of unknown mineralogy. We see variations in relative feature
strengths, central wavelengths, and feature widths, in the AEFs and weaker
emission features, depending on both distance from the star and nebular
position (southeast vs. northwest).


  An overview of the measurements of b->s\gamma, b->d\gamma and b->sll penguin
transitions at the B Factories is presented.


  Deep generative models have been successfully applied to many applications.
However, existing works experience limitations when generating large images
(the literature usually generates small images, e.g. 32 * 32 or 128 * 128). In
this paper, we propose a novel scheme, called deep tensor adversarial
generative nets (TGAN), that generates large high-quality images by exploring
tensor structures. Essentially, the adversarial process of TGAN takes place in
a tensor space. First, we impose tensor structures for concise image
representation, which is superior in capturing the pixel proximity information
and the spatial patterns of elementary objects in images, over the
vectorization preprocess in existing works. Secondly, we propose TGAN that
integrates deep convolutional generative adversarial networks and tensor
super-resolution in a cascading manner, to generate high-quality images from
random distributions. More specifically, we design a tensor super-resolution
process that consists of tensor dictionary learning and tensor coefficients
learning. Finally, on three datasets, the proposed TGAN generates images with
more realistic textures, compared with state-of-the-art adversarial
autoencoders. The size of the generated images is increased by over 8.5 times,
namely 374 * 374 in PASCAL2.


  Recently, it has been shown that it is possible to reconstruct the projected
mass distribution of a cluster from weak lensing provided that both the
geometry of the universe and the probability distribution of galaxy redshifts
are known; actually, when additional photometric data are taken to be
available, the galaxy redshift distribution could be determined jointly with
the cluster mass from the weak lensing analysis. In this paper we develop, in
the spirit of a ``thought experiment,'' a method to constrain the geometry of
the universe from weak lensing, provided that the redshifts of the source
galaxies are measured. The quantitative limits and merits of the method are
discussed analytically and with a set of simulations, in relation to point
estimation, interval estimation, and test of hypotheses for homogeneous
Friedmann-Lemaitre models. The constraints turn out to be significant when a
few thousand source galaxies are used.


  In this extended abstract, we computationally check and list the
CCZ-inequivalent APN functions from infinite families on $\mathbb{F}_2^n$ for n
from 6 to 11. These functions are selected with simplest coefficients from
CCZ-inequivalent classes. This work can simplify checking CCZ-equivalence
between any APN function and infinite APN families.


  1 - Introduction
  2 - Small-Angle Bhabha Scattering and the Luminosity Measurement
  3 - Z^0 Physics
  4 - Fits to Precision Data
  5 - Physics at LEP2
  6 - Conclusions


  Hotel bathrooms are one of the most important places in terms of customer
satisfaction, and where the most complaints are reported. To share their
experiences, guests rate hotels, comment, and share images of their positive or
negative ratings. An important part of the room images shared by guests is
related to bathrooms. Guests tend to prove their satisfaction or
dissatisfaction with the bathrooms with images in their comments. These
Positive or negative comments and visuals potentially affect the prospective
guests. In this study, two different versions of a deep learning algorithm were
designed to classify hotel bathrooms as satisfactory (good) or unsatisfactory
(bad, when any defects such as dirtiness, deficiencies, malfunctions were
present) by analyzing images. The best-performer between the two models was
determined as a result of a series of extensive experimental studies. The
models were trained for each of 144 combinations of 5 hyper-parameter sets with
a data set containing more than 11 thousand bathroom images, specially created
for this study. The "HotelBath" data set was shared also with the community
with this study. Four different image sizes were taken into consideration: 128,
256, 512 and 1024 pixels in both directions. The classification performances of
the models were measured with several metrics. Both algorithms showed very
attractive performances even with many combinations of hyper-parameters. They
can classify bathroom images with very high accuracy. Suh that the top
algorithm achieved an accuracy of 92.4% and an AUC (area under the curve) score
of 0.967. In addition, other metrics also proved the success...


  Both dissipation of helicity and it spectrum we are study on the basis of
asymptotic model. Introduction into model dependence of angle between turbulent
components vorticity and velocity on the governing parameters leads to the
spectra of helicity observed experimentally and obtained by DNS model
computations by various authors. At the same time, it settles the problem of
helicity dissipation divergence with growing Reynolds number.


  The post-main sequence eclipsing binary NN Serpentis was recently announced
as the potential host of at least two massive planetary companions. In that
work, the authors put forward two potential architectures that fit the
observations of the eclipsing binary with almost identical precision. In this
work, we present the results of a dynamical investigation of the orbital
stability of both proposed system architectures, finding that they are only
stable for scenarios in which the planets are locked in mutual mean motion
resonance. In the discovery work, the authors artificially fixed the orbital
eccentricity of the more massive planet, NN Ser(AB) c, at 0. Here, we reanalyse
the observational data on NN Serpentis without this artificial constraint, and
derive a new orbital solution for the two proposed planets. We detail the
results of further dynamical simulations investigating the stability of our new
orbital solution, and find that allowing a small non-zero eccentricity for the
outer planet renders the system unstable. We conclude that, although the
original orbits proposed for the NN Serpentis planetary system prove
dynamically feasible, further observations of the system are vital in order to
better constrain the system's true architecture.


  We review the Dudley integral for the Belyaev dichotomy applied to Gaussian
processes on spheres, and discuss the approximate (or restricted) continuity of
paths in the discontinuous case. We discuss also the spatio-temporal case, of
sphere cross line. In the continuous case, we investigate the link between the
smoothness of paths and the decay rate of the angular power spectrum, following
Tauberian work of the first author, Malyarenko, and Lang and Schwab.


  Functions of one or more variables are usually approximated with a basis: a
complete, linearly-independent system of functions that spans a suitable
function space. The topic of this paper is the numerical approximation of
functions using the more general notion of frames: that is, complete systems
that are generally redundant but provide infinite representations with bounded
coefficients. While frames are well-known in image and signal processing,
coding theory and other areas of applied mathematics, their use in numerical
analysis is far less widespread. Yet, as we show via a series of examples,
frames are more flexible than bases, and can be constructed easily in a range
of problems where finding orthonormal bases with desirable properties (rapid
convergence, high resolution power, etc.) is difficult or impossible.
  A key concern when using frames is that computing a best approximation
requires solving an ill-conditioned linear system. Nonetheless, we construct a
frame approximation via regularization with bounded condition number (with
respect to perturbations in the data), and which approximates any function up
to an error of order $\sqrt{\epsilon}$, or even of order $\epsilon$ with
suitable modifications. Here $\epsilon$ is a threshold value that can be chosen
by the user. Crucially, rate of decay of the error down to this level is
determined by the existence of approximate representations of $f$ in the frame
possessing small-norm coefficients. We demonstrate the existence of such
representations in all of our examples. Overall, our analysis suggests that
frames are a natural generalization of bases in which to develop numerical
approximation. In particular, even in the presence of severely ill-conditioned
linear systems, the frame condition imposes sufficient mathematical structure
in order to give rise to accurate, well-conditioned approximations.


  We report on the mass measurements of several neutron-rich $\mathrm{Rb}$ and
$\mathrm{Sr}$ isotopes in the $A \approx 100$ region with the TITAN
Penning-trap mass spectrometer. Using highly charged ions in the charge state
$q=10+$, the masses of $^{98,99}\mathrm{Rb}$ and $^{98-100}\mathrm{Sr}$ have
been determined with a precision of $6 - 12\ \mathrm{keV}$, making their
uncertainty negligible for r-process nucleosynthesis network calculations. The
mass of $^{101}\mathrm{Sr}$ has been determined directly for the first time
with a precision eight times higher than the previous indirect measurement and
a deviation of $3\sigma$ when compared to the Atomic Mass Evaluation. We also
confirm the mass of $^{100}\mathrm{Rb}$ from a previous measurement.
Furthermore, our data indicates the existance of a low-lying isomer with $80\
\mathrm{keV}$ excitation energy in $^{98}\mathrm{Rb}$. We show that our updated
mass values lead to minor changes in the r-process by calculating fractional
abundances in the $A\approx 100$ region of the nuclear chart.


  In Hanbury-Brown-Twiss interferometry measurements using identical bosons,
the chaoticity parameter lambda has been introduced phenomenologically to
represent the momentum correlation function at zero relative momentum. It is
useful to study an exactly solvable problem in which the lambda parameter and
its dependence on the coherence properties of the boson system can be worked
out in great detail. We are therefore motivated to study the state of a gas of
noninteracting identical bosons at various temperatures held together in a
harmonic oscillator potential that arises either externally or from bosons' own
mean fields. We determine the degree of Bose-Einstein condensation and its
momentum correlation function as a function of the attributes of the boson
environment. The parameter lambda can then be evaluated from the momentum
correlation function. We find that the lambda(p,T) parameter is a sensitive
function of both the average pair momentum p and the temperature T, and the
occurrence of lambda=1 is not a consistent measure of the absence of a coherent
condensate fraction. In particular, for large values of p, the lambda parameter
attains the value of unity even for significantly coherent systems with large
condensate fractions. We find that if a pion system maintains a static
equilibrium within its mean field, and if it contains a root-mean-squared
radius, a pion number, and a temperature typical of those in high-energy
heavy-ion collisions, then it will contain a large fraction of the
Bose-Einstein pion condensate.


  Hierarchical problem abstraction, when applicable, may offer exponential
reductions in computational complexity. Previous work on coarse-to-fine dynamic
programming (CFDP) has demonstrated this possibility using state abstraction to
speed up the Viterbi algorithm. In this paper, we show how to apply temporal
abstraction to the Viterbi problem. Our algorithm uses bounds derived from
analysis of coarse timescales to prune large parts of the state trellis at
finer timescales. We demonstrate improvements of several orders of magnitude
over the standard Viterbi algorithm, as well as significant speedups over CFDP,
for problems whose state variables evolve at widely differing rates.


  We report the detection of magnesium dicarbide, MgC$_2$, in the laboratory at
centimeter wavelengths and assign $^{24}$MgC$_2$, $^{25}$MgC$_2$, and
$^{26}$MgC$_2$ to 14 unidentified lines in the radio spectrum of the
circumstellar envelope of the evolved carbon star IRC+10216. The structure of
MgC$_2$ is found to be T-shaped with a highly ionic bond between the metal atom
and the C$_2$ unit, analogous to other dicarbides containing electropositive
elements. A two-temperature excitation model of the MgC$_2$ emission lines
observed in IRC+10216 yields a very low rotational temperature of $6\pm1$ K, a
kinetic temperature of $22\pm13$ K, and a column density of $(1.0 \pm 0.3)
\times 10^{12}$ cm$^{-2}$. The abundance of MgC$_2$ relative to the
magnesium-carbon chains MgCCH, MgC$_4$H, and MgC$_6$H is $1{:}2{:}22{:}20$ and
provides a new constraint on the sequential radiative association-dissociative
recombination mechanisms implicated in the production of metal-bearing
molecules in circumstellar environments.


  The task of algorithm selection involves choosing an algorithm from a set of
algorithms on a per-instance basis in order to exploit the varying performance
of algorithms over a set of instances. The algorithm selection problem is
attracting increasing attention from researchers and practitioners in AI. Years
of fruitful applications in a number of domains have resulted in a large amount
of data, but the community lacks a standard format or repository for this data.
This situation makes it difficult to share and compare different approaches
effectively, as is done in other, more established fields. It also
unnecessarily hinders new researchers who want to work in this area. To address
this problem, we introduce a standardized format for representing algorithm
selection scenarios and a repository that contains a growing number of data
sets from the literature. Our format has been designed to be able to express a
wide variety of different scenarios. Demonstrating the breadth and power of our
platform, we describe a set of example experiments that build and evaluate
algorithm selection models through a common interface. The results display the
potential of algorithm selection to achieve significant performance
improvements across a broad range of problems and algorithms.


  The recent progress in chip-scale integrated photonics has stimulated the
rapid development of material platforms with desired optical properties. Among
the different material platforms that are currently investigated, the
third-generation semiconductor, silicon carbide (SiC), offers the broadest
range of functionalities, including wide bandgap, high optical nonlinearities,
high refractive index, and CMOS-compatible device fabrication process. Here, we
provide an overview of SiC-based integrated photonics, presenting the latest
progress on investigating its basic optical and optoelectronic properties, as
well as the recent developments in the fabrication of several typical
approaches for light confinement structures that form the basic building blocks
for low-loss, high functional and industry-compatible integrated photonic
platform. Moreover, recent works employing SiC as optically-readable spin hosts
for quantum information applications are also summarized and discussed. As a
still-developing integrated photonic platform, the prospects and challenges of
SiC material platform in the field of integrated photonics are also discussed,
followed by potential solutions.


  Photocontrol of reversibly switchable fluorescent proteins (RSFPs) was used
to program optoacoustic signal time courses that were temporally unmixed to
increase the proteins contrast-to-noise-ratios (CNRs) in optoacoustic imaging.
In this way, two variants of the RSFP Dronpa with very similar optoacoustic
spectra could be readily discriminated in the presence of highly absorbing
blood. Addition of temporal unmixing to multispectral optoacoustic tomography
(tuMSOT) in conjunction with synthetic or genetically controlled photochromic
contrast agents and customized photoswitching schedules can increase the
performance of multiplexed and high contrast molecular optoacoustic imaging.


  The state of many physical, biological and socio-technical systems evolves by
combining smooth local transitions and abrupt resetting events to a set of
reference values. The inclusion of the resetting mechanism not only provides
the possibility of modeling a wide variety of realistic systems but also leads
to interesting novel phenomenology not present in reset-free cases. However,
most models where stochastic resetting is studied address the case of a finite
number of uncorrelated variables, commonly a single one, such as the position
of non-interacting random walkers. Here we overcome this limitation by framing
the process of network growth with node deletion as a stochastic resetting
problem where an arbitrarily large number of degrees of freedom are coupled and
influence each other, both in the resetting and non-resetting (growth) events.
We find the exact, full-time solution of the model, and several
out-of-equilibrium properties are characterized as function of the growth and
resetting rates, such as the emergence of a time-dependent percolation-like
phase transition, and first-passage statistics. Coupled multiparticle systems
subjected to resetting are a necessary generalization in the theory of
stochastic resetting, and the model presented herein serves as an illustrative,
natural and solvable example of such a generalization.


  The evolution between Fermi liquid and non-Fermi-liquid states in correlated
electron systems has been a central subject in condensed matter physics because
of the coupled intriguing magnetic and electronic states. An effective pathway
to explore the nature of non-Fermi liquid behavior is to approach its phase
boundary. Here we report a crossover from non-Fermi liquid to Fermi-liquid
state in metallic CaRuO3 through ionic liquid gating induced protonation with
electric field. This electronic transition subsequently triggers a reversible
magnetic transition with the emergence of an exotic ferromagnetic state from
this paramagnetic compound. Our theoretical analysis reveals that hydrogen
incorporation plays a critical role in both the electronic and magnetic phase
transitions via structural distortion and electron doping. These observations
not only help understand the correlated magnetic and electronic transitions in
perovskite ruthenate systems, but also provide novel pathways to design
electronic phases in correlated materials.


  Most of current models of TeV blazars emission assume a Synchrotron
Self-Compton mechanism where relativistic particles emit both synchrotron
radiation and Inverse Compton photons. For sake of simplicity, these models
usually consider only steady state emission. The spectral features are thus
only related to the shape of the particle distribution, and do not depend on
the timing of observations. In this letter, we study the effect of, firstly,
the lag between the beginning of the injection of the fresh particles and the
trigger of the observation, and secondly, of a finite injection duration. We
illustrate these effects considering an analytical time-dependent model of the
synchrotron emission by a monoenergetic distribution of leptons. We point out
that the spectral shape can be in fact very dependent on observational
conditions if the particle injection term is time-dependent, particularly
taking into account the effect of the time averaging procedure on the final
shape of the SED. Consequences on the acceleration process are also discussed.


  In this paper we study CAT(0) groups and their splittings as graphs of
groups. For one-ended CAT(0) groups with isolated flats we prove a theorem
characterizing exactly when the visual boundary is locally connected. This
characterization depends on whether the group has a certain type of splitting
over a virtually abelian subgroup. In the locally connected case, we describe
the boundary as a tree of metric spaces in the sense of \'Swi\k{a}tkowski.
  A significant tool used in the proofs of the above results is a general
convex splitting theorem for arbitrary CAT(0) groups. If a CAT(0) group splits
as a graph of groups with convex edge groups, then the vertex groups are also
CAT(0) groups.


  A determination of the hadronic vacuum polarization contribution to the
anomalous magnetic moment of the muon from lattice QCD aiming at a precision of
$1\%$ requires to include isospin breaking corrections in the computation. We
present a lattice calculation of the QED and strong isospin breaking
corrections to the hadronic vacuum polarization with Domain Wall fermions. The
results are obtained using quark masses which are tuned such that pion and kaon
masses agree with their physical values including isospin breaking corrections.


  We estimate average responses curves for treatment time in the Emergency
Department (ED). Extending treatment time is considered a promising solution
for improving admission decisions. Providing empirical support for this
solution, however, is difficult because this intervention (treatment) is a
continuous time-to-event; is strongly influenced by unmeasured patient health
needs and is jointly determined with the admission decision (admit vs.
discharge); and may be only modifiable up to a shift in the realized time. We
formalize the admission process as a directed acyclic graph and show that
average responses curves for treatment time cannot be identified
nonparametrically due to unmeasured confounding from patient health needs. We
thus use a parametric model that includes a latent variable for health needs
and a threshold regression model for the admission process. We fit this model
to observational data (n = 28,862) from abdominal pain patients at a large
tertiary teaching hospital. We estimate that fixing ED treatment time to 2
hours rather than 1 hour decreases admission rates from 41.6% (95% CI: [40.6,
42.7]) to 32.7% (95% CI: [32.2, 33.2]) and that increasing the realized
treatment time by 30 minutes can reduce admission rates by 1.1% (95% CI: [-1.1,
3.2]), with little change to 30-day revisit and readmission rates.


  We consider piecewise $C^2$ non-flat maps of the interval and show that, for
Lebesgue almost every point, its omega-limit set is either a periodic orbit, a
cycle of intervals or the closure of the orbits of a subset of the critical
points. In particular, every piecewise $C^2$ non-flat map of the interval
displays only a finite number of non-periodic attractors.


  We discern hydration geometries around the sugar-phosphate-backbone of an RNA
double helix at the molecular level. RNA disordering upon melting is connected
with a transition from ordered water structures towards local phosphate group
hydration shells.


  Classical first-passage times under restart are used in a wide variety of
models, yet the quantum version of the problem still misses key concepts. We
study the quantum hitting time with restart using a monitored quantum walk. The
restart strategy eliminates the problem of dark states, i.e. cases where the
particle evades detection, while maintaining the ballistic propagation which is
important for fast search. We find profound effects of quantum oscillations on
the restart problem, namely a type of instability of the mean detection time,
and optimal restart times that form staircases, with sudden drops as the rate
of sampling is modified. In the absence of restart and in the Zeno limit, the
detection of the walker is not possible and we examine how restart overcomes
this well-known problem, showing that the optimal restart time becomes
insensitive to the sampling period.


  We consider the one-dimensional XY quantum spin chain in a transverse
magnetic field. We are interested in the Renyi entropy of a block of L
neighboring spins at zero temperature on an infinite lattice. The Renyi entropy
is essentially the trace of some power $\alpha$ of the density matrix of the
block. We calculate the asymptotic for $L \to \infty$ analytically in terms of
Klein's elliptic $\lambda$ - function. We study the limiting entropy as a
function of its parameter $\alpha$. We show that up to the trivial addition
terms and multiplicative factors, and after a proper re-scaling, the Renyi
entropy is an automorphic function with respect to a certain subgroup of the
modular group; moreover, the subgroup depends on whether the magnetic field is
above or below its critical value. Using this fact, we derive the
transformation properties of the Renyi entropy under the map $\alpha \to
\alpha^{-1}$ and show that the entropy becomes an elementary function of the
magnetic field and the anisotropy when $\alpha$ is a integer power of 2, this
includes the purity $tr \rho^2$. We also analyze the behavior of the entropy as
$\alpha \to 0$ and $\infty$ and at the critical magnetic field and in the
isotropic limit [XX model].


  We present a detailed asymptotic analysis of correlation functions for the
two component spanning tree on the two-dimensional lattice when one component
contains three paths connecting vicinities of two fixed lattice sites at large
distance $s$ apart. We extend the known result for correlations on the plane to
the case of the upper half-plane with closed and open boundary conditions. We
found asymptotics of correlations for distance $r$ from the boundary to one of
the fixed lattice sites for the cases $r\gg s \gg 1$ and $s \gg r \gg 1$.


  This paper discusses the relevance and potential impact of both RFID and
reverse engineering of RFID technology, followed by a discussion of common
protocols and internals of RFID technology. The focus of the paper is on
providing an overview of the different approaches to reverse engineering RFID
technology and possible countermeasures that could limit the potential of such
reverse engineering attempts.


  We present the first statistical analysis of 27 UVOT optical/ultra-violet
lightcurves of GRB afterglows. We have found, through analysis of the
lightcurves in the observer's frame, that a significant fraction rise in the
first 500s after the GRB trigger, that all lightcurves decay after 500s,
typically as a power-law with a relatively narrow distribution of decay
indices, and that the brightest optical afterglows tend to decay the quickest.
We find that the rise could either be produced physically by the start of the
forward shock, when the jet begins to plough into the external medium, or
geometrically where an off-axis observer sees a rising lightcurve as an
increasing amount of emission enters the observers line of sight, which occurs
as the jet slows. We find that at 99.8% confidence, there is a correlation, in
the observed frame, between the apparent magnitude of the lightcurves at 400s
and the rate of decay after 500s. However, in the rest frame a Spearman Rank
test shows only a weak correlation of low statistical significance between
luminosity and decay rate. A correlation should be expected if the afterglows
were produced by off-axis jets, suggesting that the jet is viewed from within
the half-opening angle theta or within a core of uniform energy density
theta_c. We also produced logarithmic luminosity distributions for three rest
frame epochs. We find no evidence for bimodality in any of the distributions.
Finally, we compare our sample of UVOT lightcurves with the XRT lightcurve
canonical model. The range in decay indices seen in UVOT lightcurves at any
epoch is most similar to the range in decay of the shallow decay segment of the
XRT canonical model. However, in the XRT canonical model there is no indication
of the rising behaviour observed in the UVOT lightcurves.


  In this paper, we define time-independent modifiers to construct a long-range
scattering theory for discrete schr\"odinger operators on the square lattice
$\mathbb{Z}^N$. We prove the existence and completeness of modified wave
operators in terms of the above mentioned time-independent modifiers.


  Orbital degree of freedom of electrons and its interplay with spin, charge
and lattice degrees of freedom are one of the central issues in colossal
magnetoresistive manganites. The orbital degree of freedom has until recently
remained hidden, since it does not couple directly to most of experimental
probes. Development of synchrotron light sources has changed the situation; by
the resonant x-ray scattering (RXS) technique the orbital ordering has
successfully been observed . In this article, we review progress in the recent
studies of RXS in manganites. We start with a detailed review of the RXS
experiments applied to the orbital ordered manganites and other correlated
electron systems. We derive the scattering cross section of RXS where the
tensor character of the atomic scattering factor (ASF) with respect to the
x-ray polarization is stressed. Microscopic mechanisms of the anisotropic
tensor character of ASF is introduced and numerical results of ASF and the
scattering intensity are presented. The azimuthal angle scan is a unique
experimental method to identify RXS from the orbital degree of freedom. A
theory of the azimuthal angle and polarization dependence of the RXS intensity
is presented. The theoretical results show good agreement with the experiments
in manganites. Apart from the microscopic description of ASF, a theoretical
framework of RXS to relate directly to the 3d orbital is presented. The
scattering cross section is represented by the correlation function of the
pseudo-spin operator for the orbital degree of freedom. A theory is extended to
the resonant inelastic x-ray scattering and methods to observe excitations of
the orbital degree of freedom are proposed.


  Deep neural networks (DNN) have achieved remarkable performance in various
fields. However, training a DNN model from scratch requires a lot of computing
resources and training data. It is difficult for most individual users to
obtain such computing resources and training data. Model copyright infringement
is an emerging problem in recent years. For instance, pre-trained models may be
stolen or abuse by illegal users without the authorization of the model owner.
Recently, many works on protecting the intellectual property of DNN models have
been proposed. In these works, embedding watermarks into DNN based on backdoor
is one of the widely used methods. However, when the DNN model is stolen, the
backdoor-based watermark may face the risk of being detected and removed by an
adversary. In this paper, we propose a scheme to detect and remove watermark in
deep neural networks via generative adversarial networks (GAN). We demonstrate
that the backdoor-based DNN watermarks are vulnerable to the proposed GAN-based
watermark removal attack. The proposed attack method includes two phases. In
the first phase, we use the GAN and few clean images to detect and reverse the
watermark in the DNN model. In the second phase, we fine-tune the watermarked
DNN based on the reversed backdoor images. Experimental evaluations on the
MNIST and CIFAR10 datasets demonstrate that, the proposed method can
effectively remove about 98% of the watermark in DNN models, as the watermark
retention rate reduces from 100% to less than 2% after applying the proposed
attack. In the meantime, the proposed attack hardly affects the model's
performance. The test accuracy of the watermarked DNN on the MNIST and the
CIFAR10 datasets drops by less than 1% and 3%, respectively.


  Ancilla systems are often indispensable to universal control of a nearly
isolated quantum system. However, ancilla systems are typically more vulnerable
to environmental noise, which limits the performance of such ancilla-assisted
quantum control. To address this challenge of ancilla-induced decoherence, we
propose a general framework that integrates quantum control and quantum error
correction, so that we can achieve robust quantum gates resilient to ancilla
noise. We introduce the path independence criterion for fault-tolerant quantum
gates against ancilla errors. As an example, a path-independent gate is
provided for superconducting circuits with a hardware-efficient design.


  An oriented hypergraph is an oriented incidence structure that extends the
concept of a signed graph. We introduce hypergraphic structures and techniques
central to the extension of the circuit classification of signed graphs to
oriented hypergraphs. Oriented hypergraphs are further decomposed into three
families -- balanced, balanceable, and unbalanceable -- and we obtain a
complete classification of the balanced circuits of oriented hypergraphs.


  The main idea in this paper is merging two techniques that have been recently
developed. On the one hand, we consider MCCGS, standing for Minimal Canonical
Comprehensive Groebner Systems, a recently introduced computational tool
yielding "good" bases for ideals of polynomials over a field depending on
several parameters, that specialize "well", for instance, regarding the number
of solutions for the given ideal, for different values of the parameters. The
second ingredient concerns automatic theorem discovery in elementary geometry.
Automatic discovery aims to obtain complementary hypotheses for a (generally
false) geometric statement to become true. The paper shows how to use MCCGS for
automatic discovering of theorems and gives relevant examples.


  Using ideas due to Jean-Luc Sauvageot, we prove the existence of a continuous
unital dilation of a CP$_0$-semigroup on a separable W$^*$-algebra. This paper
presents the material in the author's Ph. D. thesis (arXiv.org:1304.0134.pdf)
with some generalizations and an improved exposition.


  Two-component second and third-order Burgers type systems with nondiagonal
constant matrix of leading order terms are classified for higher symmetries.
New symmetry integrable systems with their master symmetries are obtained. Some
third order systems are observed to possess conservation laws. Bi-Poisson
structures of systems possessing conservation laws are given.


  In the 1920's, Ritt studied the operation of functional composition g o h(x)
= g(h(x)) on complex rational functions. In the case of polynomials, he
described all the ways in which a polynomial can have multiple `prime
factorizations' with respect to this operation. Despite significant effort by
Ritt and others, little progress has been made towards solving the analogous
problem for rational functions. In this paper we use results of Avanzi--Zannier
and Bilu--Tichy to prove analogues of Ritt's results for decompositions of
Laurent polynomials, i.e., rational functions with denominator a power of x.


  We have carried out an analysis of helicity and partial-wave amplitudes for
the process D -> K^* \rho in the factorization approximation using several
models for the form factors. All the models, with the exception of one,
generate partial-wave amplitudes with the hierarchy $\mid S\mid >\mid P\mid
>\mid D\mid$. The one exception gives $\mid S \mid >\mid D \mid >\mid P \mid$.
Even though in most models the D-wave amplitude is an order of magnitude
smaller than the S-wave amplitude, its effect on the longitudinal polarization
could be as large as 30%. Due to a misidentification of the partial-wave
amplitudes in terms of the Lorentz structures in the relevant literature, we
cast doubt on the veracity of the listed data, particularly the partial-wave
branching ratios.
  (PACS numbers: 13.25.-k, 13.25.Ft)


  A proper or singular abelian mapping from $C^n$ to $\bar\C^n$ is parametrized
by $n$ meromorphic functions with at most $2n$ periods. We develop the
existence and structure theorems of the classical theory of an abelian mapping
purely on the basis of its defining functional equation, the so-called
algebraic addition theorem (AAT), with no appeal to any representation as
quotients of theta functions. We offer two new proofs of the periodicity of a
nonrational mapping admitting an AAT. We also prove by new arguments the
existence of a rational group law on an associated algebraic variety, and that
all proper and singular abelian mappings do admit an AAT.


  In photoelectron spectroscopy, the measured electron momentum range is
intrinsically related to the excitation photon energy. Low photon energies
$<10$ eV are commonly encountered in laser-based photoemission and lead to a
momentum range that is smaller than the Brillouin zones of most materials. This
can become a limiting factor when studying condensed matter with laser-based
photoemission. An additional restriction is introduced by widely used
hemispherical analyzers that record only electrons photoemitted in a solid
angle set by the aperture size at the analyzer entrance. Here, we present an
upgrade to increase the effective solid angle that is measured with a
hemispherical analyzer. We achieve this by accelerating the photoelectrons
towards the analyzer with an electric field that is generated by a bias voltage
on the sample. Our experimental geometry is comparable to a parallel plate
capacitor and, therefore, we approximate the electric field to be uniform along
the photoelectron trajectory. With this assumption, we developed an analytic,
parameter-free model that relates the measured angles to the electron momenta
in the solid and verify its validity by comparing with experimental results on
the charge density wave material TbTe$_3$. By providing a larger field of view
in momentum space, our approach using a bias potential considerably expands the
flexibility of laser-based photoemission setups.


  We report the first direct detection of an exoplanet in the visible polarized
light. The transiting planet HD189733b is one of the very hot Jupiters with
shortest periods and, thus, smallest orbits, which makes them ideal candidates
for polarimetric detections. We obtained polarimetric measurements of HD189733
in the $B$ band well distributed over the orbital period and detected two
polarization maxima near planetary elongations with a peak amplitude of
$\sim2\cdot10^{-4}$. Assuming Rayleigh scattering, we estimated the effective
size of the scattering atmosphere (Lambert sphere) to be 1.5$\pm$0.2 $R_{\rm
J}$, which is 30% larger than the radius of the opaque body previously inferred
from transits. If the scattering matter fills the planetary Roche lobe, the
lower limit of the geometrical albedo can be estimated as 0.14. The phase
dependence of polarization indicates that the planetary orbit is oriented
almost in a north-south direction with a longitude of ascending node
$\Omega$=(16\degr or 196\degr)$\pm$8\degr. We obtain independent estimates of
the orbit inclination $i$=98\degr$\pm$8\degr and eccentricity $e$=0.0 (with an
uncertainty of 0.05) which are in excellent agreement with values determined
previously from transits and radial velocities. Our findings clearly
demonstrate the power of polarimetry and open a new dimension in exploring
exoplanetary atmospheres even for systems without transits.


  Forecasting speculative stock prices is essential for effective investment
risk management that drives the need for the development of innovative
algorithms. However, the speculative nature, volatility, and complex sequential
dependencies within financial markets present inherent challenges which
necessitate advanced techniques. This paper proposes a novel framework, CAB-XDE
(customized attention BiLSTM-XGB decision ensemble), for predicting the daily
closing price of speculative stock Bitcoin-USD (BTC-USD). CAB-XDE framework
integrates a customized bi-directional long short-term memory (BiLSTM) with the
attention mechanism and the XGBoost algorithm. The customized BiLSTM leverages
its learning capabilities to capture the complex sequential dependencies and
speculative market trends. Additionally, the new attention mechanism
dynamically assigns weights to influential features, thereby enhancing
interpretability, and optimizing effective cost measures and volatility
forecasting. Moreover, XGBoost handles nonlinear relationships and contributes
to the proposed CAB-XDE framework robustness. Additionally, the weight
determination theory-error reciprocal method further refines predictions. This
refinement is achieved by iteratively adjusting model weights. It is based on
discrepancies between theoretical expectations and actual errors in individual
customized attention BiLSTM and XGBoost models to enhance performance. Finally,
the predictions from both XGBoost and customized attention BiLSTM models are
concatenated to achieve diverse prediction space and are provided to the
ensemble classifier to enhance the generalization capabilities of CAB-XDE. The
proposed CAB-XDE framework is empirically validated on volatile Bitcoin market,
sourced from Yahoo Finance and outperforms state-of-the-art models with a MAPE
of 0.0037, MAE of 84.40, and RMSE of 106.14.


  This paper establishes a uniform procedure to split the operations in any
algebraic operad, generalizing previous known notions of splitting algebraic
structures from the dendriform algebra of Loday that splits the associative
operation to the successors that split any binary operad. Examples are provided
for various $n$-associative algebras, $n$-Lie algebras, $A_\infty$ algebras and
$L_\infty$ algebras. Further, the concept of a Rota-Baxter operator, first
showing its importance in the associative and Lie algebra context and then
generalized to any binary operads, is generalized to arbitrary operads. The
classical links from the Rota-Baxter associative algebra to the dendriform
algebra and its numerous generalizations are further generalized and unified as
the link from the Rota-Baxter operator on an operad to the splitting of the
operad. Finally, the remarkable fact that any dendriform algebra can be
recovered from a relative Rota-Baxter operator is generalized to the context of
operads with the generalized notion of a relative Rota-Baxter operator for any
operad.


  The modeling and prediction of the ultrafast nonlinear dynamics in the
optical fiber are essential for the studies of laser design, experimental
optimization, and other fundamental applications. The traditional propagation
modeling method based on the nonlinear Schr\"odinger equation (NLSE) has long
been regarded as extremely time-consuming, especially for designing and
optimizing experiments. The recurrent neural network (RNN) has been implemented
as an accurate intensity prediction tool with reduced complexity and good
generalization capability. However, the complexity of long grid input points
and the flexibility of neural network structure should be further optimized for
broader applications. Here, we propose a convolutional feature separation
modeling method to predict full-field ultrafast nonlinear dynamics with low
complexity and high flexibility, where the linear effects are firstly modeled
by NLSE-derived methods, then a convolutional deep learning method is
implemented for nonlinearity modeling. With this method, the temporal relevance
of nonlinear effects is substantially shortened, and the parameters and scale
of neural networks can be greatly reduced. The running time achieves a 94%
reduction versus NLSE and an 87% reduction versus RNN without accuracy
deterioration. In addition, the input pulse conditions, including grid point
numbers, durations, peak powers, and propagation distance, can be flexibly
changed during the predicting process. The results represent a remarkable
improvement in the ultrafast nonlinear dynamics prediction and this work also
provides novel perspectives of the feature separation modeling method for
quickly and flexibly studying the nonlinear characteristics in other fields.


  In this paper we give a metric construction of a tree which correctly
identifies connected components of superlevel sets of $\mathbb{R}$-valued
continuous functions $f$ on $X$ and show that it is possible to retrieve the
$H_0$-persistent diagram from this tree. We revisit the notion of homological
dimension previously introduced by Schweinhart and give some bounds for the
latter in terms of the upper-box dimension of $X$, thereby partially answering
a question of the same author. We prove a quantitative version of the
Wasserstein stability theorem valid for regular enough $X$ and
$\alpha$-H\"older functions and discuss some applications of this theory to
random fields and the topology of their superlevel sets.


  We introduce a new class of generalised quadratic forms over totally real
number fields, which is rich enough to capture the arithmetic of arbitrary
systems of quadrics over the rational numbers. We explore this connection
through a version of the Hardy-Littlewood circle method over number fields.


  Understanding the query complexity for testing linear-invariant properties
has been a central open problem in the study of algebraic property testing.
Triangle-freeness in Boolean functions is a simple property whose testing
complexity is unknown. Three Boolean functions $f_1$, $f_2$ and $f_3:
\mathbb{F}_2^k \to \{0, 1\}$ are said to be triangle free if there is no $x, y
\in \mathbb{F}_2^k$ such that $f_1(x) = f_2(y) = f_3(x + y) = 1$. This property
is known to be strongly testable (Green 2005), but the number of queries needed
is upper-bounded only by a tower of twos whose height is polynomial in $1 /
\epsislon$, where $\epsislon$ is the distance between the tested function
triple and triangle-freeness, i.e., the minimum fraction of function values
that need to be modified to make the triple triangle free. A lower bound of $(1
/ \epsilon)^{2.423}$ for any one-sided tester was given by Bhattacharyya and
Xie (2010). In this work we improve this bound to $(1 / \epsilon)^{6.619}$.
Interestingly, we prove this by way of a combinatorial construction called
\emph{uniquely solvable puzzles} that was at the heart of Coppersmith and
Winograd's renowned matrix multiplication algorithm.


  We consider a toric degeneration of Calabi--Yau complete intersections of
Batyrev--Borisov in the Gross--Siebert program. The author showed in his
previous work that there exists an integral affine contraction map called a
tropical contraction, from the tropical variety obtained as its tropicalization
to the dual intersection complex of the toric degeneration. In this article, we
prove that the dual intersection complex is isomorphic to the essential
skeleton of the Berkovich analytification as piecewise integral affine
manifolds, and the composition of the tropicalization map and the tropical
contraction is an affinoid torus fibration with a discriminant of codimension
$2$, which induces the same integral affine structure as the one coming from
the toric degeneration. This is a generalization of the earlier work by
Pille-Schneider for a specific degeneration of Calabi--Yau hypersurfaces in
projective spaces.


  We review some recent developments in string theory, emphasizing the
importance of vacuum instabilities, their relation to the density of states,
and the role of space-time fermions in non-critical string theory. We also
discuss the classical dynamics of two dimensional string theory.


  We explore galaxy properties in general and properties of host galaxies of
gamma-ray bursts (GRBs) in particular, using N-body/Eulerian hydrodynamic
simulations and the stellar population synthesis model, Starburst99, to infer
observable properties. We identify simulated galaxies that have optical star
formation rate (SFR) and SFR-to-luminosity ratio similar to those observed in a
well-defined sample of ten host galaxies. Each of the numerical counterparts
are found in catalogs at the same redshifts as the observed hosts. The
counterparts are found to be low-mass galaxies, with low mass-to-light ratio,
recent epoch of formation, and high ratio between the SFR and the average of
the SFR. When compared to the overall galaxy population, they have colors much
bluer than the high-mass star-forming galaxy population. Although their SFRs
span a range of values, the specific rates of the numerical counterparts are
equal to or higher than the median values estimated at the different redshifts.
We also emphasize the strong relationships between the specific star formation
rate (SFR) and quantities known to reflect the star formation history of
galaxies, i.e. color and mass-to-light ratio: At intermediate redshift, the
faintest and bluest galaxies are also the objects with the highest specific
rates. These results suggest that GRB host galaxies are likely to be drawn from
the high specific SFR sub-population of galaxies, rather than the high SFR
galaxy population. Finally, as indicated by our catalogs, in an extended
sample, the majority of GRB host galaxies is expected to have specific SFRs
higher than found in the magnitude-limited sample studied here.


  Several attempts to solve the cosmological constant problem, which concerns
the value of the cosmological constant being extremely smaller than the
Standard Model mass scales, have introduced a scalar field with a very flat
potential that can be approximated as linear around any given position. The
scalar field scans the cosmological constant in such a way that the current
small value is explained. Recently, Dark Energy Spectroscopic Instrument (DESI)
reported the results of the first year. Combining the data with CMB, Pantheon,
Union3, and/or DES-SN5YR, there is a preference or anomaly, indicating that the
dark energy in the current Universe slightly deviates from that in the
$\Lambda$CDM model and varies over time. In this paper, I show that the simple
linear potential of a scalar field that may explain the small cosmological
constant can explain the DESI anomaly. In particular, the model proposed by the
present author in 2108.04246, which relaxes the cosmological constant by the
condition that inflation ends, predicts a time-dependence of the dark energy
close to the one favored by the data.


  Quantifying and estimating wildlife population sizes is a foundation of
wildlife management. However, many carnivore species are cryptic, leading to
innate difficulties in estimating their populations. We evaluated the potential
for using more rigorous statistical models to estimate the populations of black
bears (Ursus americanus) in Wisconisin, and their applicability to other
furbearers such as bobcats (Lynx rufus). To estimate black bear populations, we
developed an AAH state-space model in a Bayesian framework based on Norton
(2015) that can account for variation in harvest and population demographics
over time. Our state-space model created an accurate estimate of the black bear
population in Wisconsin based on age-at-harvest data and improves on previous
models by using little demographic data, no auxiliary data, and not being
sensitive to initial population size. The increased accuracy of the AAH
state-space models should allow for better management by being able to set
accurate quotas to ensure a sustainable harvest for the black bear population
in each zone. We also evaluated the demography and annual harvest data of
bobcats in Wisconsin to determine trends in harvest, method, and hunter
participation in Wisconsin. Each trait of harvested bobcats that we tested
(mass, male:female sex ratio, and age) changed over time, and because these
were interrelated, and we inferred that harvest selection for larger size
biased harvests in favor of a) larger, b) older, and c) male bobcats by hound
hunters. We also found an increase in the proportion of bobcats that were
harvested by hound hunting compared to trapping, and that hound hunters were
more likely to create taxidermy mounts than trappers. We also found that
decreasing available bobcat tags and increasing success have occurred over
time, and correlate with substantially increasing both hunter populations and
hunter interest.


  Vendors in the Android ecosystem typically customize their devices by
modifying Android Open Source Project (AOSP) code, adding in-house developed
proprietary software, and pre-installing third-party applications. However,
research has documented how various security problems are associated with this
customization process.
  We develop a model of the Android ecosystem utilizing the concepts of game
theory and product differentiation to capture the competition involving two
vendors customizing the AOSP platform. We show how the vendors are incentivized
to differentiate their products from AOSP and from each other, and how prices
are shaped through this differentiation process. We also consider two types of
consumers: security-conscious consumers who understand and care about security,
and na\"ive consumers who lack the ability to correctly evaluate security
properties of vendor-supplied Android products or simply ignore security. It is
evident that vendors shirk on security investments in the latter case.
  Regulators such as the U.S. Federal Trade Commission have sanctioned Android
vendors for underinvestment in security, but the exact effects of these
sanctions are difficult to disentangle with empirical data. Here, we model the
impact of a regulator-imposed fine that incentivizes vendors to match a minimum
security standard. Interestingly, we show how product prices will decrease for
the same cost of customization in the presence of a fine, or a higher level of
regulator-imposed minimum security.


  Feature attribution methods are widely used to explain neural models by
determining the influence of individual input features on the models' outputs.
We propose a novel feature attribution method, CAFE (Conflict-Aware
Feature-wise Explanations), that addresses three limitations of the existing
methods: their disregard for the impact of conflicting features, their lack of
consideration for the influence of bias terms, and an overly high sensitivity
to local variations in the underpinning activation functions. Unlike other
methods, CAFE provides safeguards against overestimating the effects of neuron
inputs and separately traces positive and negative influences of input features
and biases, resulting in enhanced robustness and increased ability to surface
feature conflicts. We show experimentally that CAFE is better able to identify
conflicting features on synthetic tabular data and exhibits the best overall
fidelity on several real-world tabular datasets, while being highly
computationally efficient.


  Objective: Multi-modal functional magnetic resonance imaging (fMRI) can be
used to make predictions about individual behavioral and cognitive traits based
on brain connectivity networks. Methods: To take advantage of complementary
information from multi-modal fMRI, we propose an interpretable multi-modal
graph convolutional network (MGCN) model, incorporating the fMRI time series
and the functional connectivity (FC) between each pair of brain regions.
Specifically, our model learns a graph embedding from individual brain networks
derived from multi-modal data. A manifold-based regularization term is then
enforced to consider the relationships of subjects both within and between
modalities. Furthermore, we propose the gradient-weighted regression activation
mapping (Grad-RAM) and the edge mask learning to interpret the model, which is
used to identify significant cognition-related biomarkers. Results: We validate
our MGCN model on the Philadelphia Neurodevelopmental Cohort to predict
individual wide range achievement test (WRAT) score. Our model obtains superior
predictive performance over GCN with a single modality and other competing
approaches. The identified biomarkers are cross-validated from different
approaches. Conclusion and Significance: This paper develops a new
interpretable graph deep learning framework for cognitive ability prediction,
with the potential to overcome the limitations of several current data-fusion
models. The results demonstrate the power of MGCN in analyzing multi-modal fMRI
and discovering significant biomarkers for human brain studies.


  Infinite population models are important tools for studying population
dynamics of evolutionary algorithms. They describe how the distributions of
populations change between consecutive generations. In general, infinite
population models are derived from Markov chains by exploiting symmetries
between individuals in the population and analyzing the limit as the population
size goes to infinity. In this paper, we study the theoretical foundations of
infinite population models of evolutionary algorithms on continuous
optimization problems. First, we show that the convergence proofs in a widely
cited study were in fact problematic and incomplete. We further show that the
modeling assumption of exchangeability of individuals cannot yield the
transition equation. Then, in order to analyze infinite population models, we
build an analytical framework based on convergence in distribution of random
elements which take values in the metric space of infinite sequences. The
framework is concise and mathematically rigorous. It also provides an
infrastructure for studying the convergence of the stacking of operators and of
iterating the algorithm which previous studies failed to address. Finally, we
use the framework to prove the convergence of infinite population models for
the mutation operator and the $k$-ary recombination operator. We show that
these operators can provide accurate predictions for real population dynamics
as the population size goes to infinity, provided that the initial population
is identically and independently distributed.


  Temperature effects on the electromagnetic couplings of pions in hot hadronic
matter are studied with an effective chiral Lagrangian. We show that the
Ward-Takahashi identity is satisfied at non-zero temperature in the soft pion
limit. The in-medium electromagnetic form factor of the pion is obtained in the
time-like region and shown to be reduced in magnitude, especially near the
vector-meson resonance region. Finally, we discuss the consequences of this
medium effect on dilepton production from hot hadronic matter.


  We present a minimal phase oscillator model for learning quadrupedal
locomotion. Each of the four oscillators is coupled only to itself and its
corresponding leg through local feedback of the ground reaction force, which
can be interpreted as an observer feedback gain. We interpret the oscillator
itself as a latent contact state-estimator. Through a systematic ablation
study, we show that the combination of phase observations, simple phase-based
rewards, and the local feedback dynamics induces policies that exhibit emergent
gait preferences, while using a reduced set of simple rewards, and without
prescribing a specific gait. The code is open-source, and a video synopsis
available at https://youtu.be/1NKQ0rSV3jU.


  Selective forgetting or removing information from deep neural networks (DNNs)
is essential for continual learning and is challenging in controlling the DNNs.
Such forgetting is crucial also in a practical sense since the deployed DNNs
may be trained on the data with outliers, poisoned by attackers, or with
leaked/sensitive information. In this paper, we formulate selective forgetting
for classification tasks at a finer level than the samples' level. We specify
the finer level based on four datasets distinguished by two conditions: whether
they contain information to be forgotten and whether they are available for the
forgetting procedure. Additionally, we reveal the need for such formulation
with the datasets by showing concrete and practical situations. Moreover, we
introduce the forgetting procedure as an optimization problem on three
criteria; the forgetting, the correction, and the remembering term.
Experimental results show that the proposed methods can make the model forget
to use specific information for classification. Notably, in specific cases, our
methods improved the model's accuracy on the datasets, which contains
information to be forgotten but is unavailable in the forgetting procedure.
Such data are unexpectedly found and misclassified in actual situations.


  $k$-means clustering is a fundamental problem in unsupervised learning. The
problem concerns finding a partition of the data points into $k$ clusters such
that the within-cluster variation is minimized. Despite its importance and wide
applicability, a theoretical understanding of the $k$-means problem has not
been completely satisfactory. Existing algorithms with theoretical performance
guarantees often rely on sophisticated (sometimes artificial) algorithmic
techniques and restricted assumptions on the data. The main challenge lies in
the non-convex nature of the problem; in particular, there exist additional
local solutions other than the global optimum. Moreover, the simplest and most
popular algorithm for $k$-means, namely Lloyd's algorithm, generally converges
to such spurious local solutions both in theory and in practice.
  In this paper, we approach the $k$-means problem from a new perspective, by
investigating the structures of these spurious local solutions under a
probabilistic generative model with $k$ ground truth clusters. As soon as
$k=3$, spurious local minima provably exist, even for well-separated and
balanced clusters. One such local minimum puts two centers at one true cluster,
and the third center in the middle of the other two true clusters. For general
$k$, one local minimum puts multiple centers at a true cluster, and one center
in the middle of multiple true clusters. Perhaps surprisingly, we prove that
this is essentially the only type of spurious local minima under a separation
condition. Our results pertain to the $k$-means formulation for mixtures of
Gaussians or bounded distributions. Our theoretical results corroborate
existing empirical observations and provide justification for several improved
algorithms for $k$-means clustering.


  We discuss the static and kinetic properties of a Ginzburg-Landau spherically
symmetric $O(N)$ model recently introduced (Phys. Rev. Lett. {\bf 75}, 2176,
(1995)) in order to generalize the so called Phase field model of Langer. The
Hamiltonian contains two $O(N)$ invariant fields $\phi$ and $U$ bilinearly
coupled. The order parameter field $\phi$ evolves according to a non conserved
dynamics, whereas the diffusive field $U$ follows a conserved dynamics. In the
limit $N \to \infty$ we obtain an exact solution, which displays an interesting
kinetic behavior characterized by three different growth regimes. In the early
regime the system displays normal scaling and the average domain size grows as
$t^{1/2}$, in the intermediate regime one observes a finite wavevector
instability, which is related to the Mullins-Sekerka instability; finally, in
the late stage the structure function has a multiscaling behavior, while the
domain size grows as $t^{1/4}$.


  Images of near-field SAR contains spatial-variant sidelobes and clutter,
subduing the image quality. Current image restoration methods are only suitable
for small observation angle, due to their assumption of 2D spatial-invariant
degradation operation. This limits its potential for large-scale objects
imaging, like the aircraft. To ease this restriction, in this work an image
restoration method based on the 2D spatial-variant deconvolution is proposed.
First, the image degradation is seen as a complex convolution process with 2D
spatial-variant operations. Then, to restore the image, the process of
deconvolution is performed by cyclic coordinate descent algorithm. Experiments
on simulation and measured data validate the effectiveness and superiority of
the proposed method. Compared with current methods, higher precision estimation
of the targets' amplitude and position is obtained.


  With the growing cosmopolitan culture of modern cities, the need of robust
Multi-Lingual scene Text (MLT) detection and recognition systems has never been
more immense. With the goal to systematically benchmark and push the
state-of-the-art forward, the proposed competition builds on top of the
RRC-MLT-2017 with an additional end-to-end task, an additional language in the
real images dataset, a large scale multi-lingual synthetic dataset to assist
the training, and a baseline End-to-End recognition method. The real dataset
consists of 20,000 images containing text from 10 languages. The challenge has
4 tasks covering various aspects of multi-lingual scene text: (a) text
detection, (b) cropped word script classification, (c) joint text detection and
script classification and (d) end-to-end detection and recognition. In total,
the competition received 60 submissions from the research and industrial
communities. This paper presents the dataset, the tasks and the findings of the
presented RRC-MLT-2019 challenge.


  We consider a single electron confined within a quantum wire in a system of
two electrostatically-induced QDs defined by nearby gates. The time-varying
electric field, of single GHz frequency, perpendicular to the quantum wire, is
used to induce the Rashba coupling and enable spin-dependent resonant tunneling
of the electron between two adjacent potential wells with fidelity over 99.5%.
This effect can be used for the high fidelity all-electrical electron-spin
initialization or readout in the spin-based quantum computer. In contrast to
other spin initialization methods, our technique can be performed adiabatically
without increase in the energy of the electron. Our simulations are supported
by a realistic self-consistent time-dependent Poisson-Schroedinger
calculations.


  In view of controlling finite dimensional open quantum systems, we provide a
unified Lie-semigroup framework describing the structure of completely positive
trace-preserving maps. It allows (i) to identify the Kossakowski-Lindblad
generators as the Lie wedge of a subsemigroup, (ii) to link properties of Lie
semigroups such as divisibility with Markov properties of quantum channels, and
(iii) to characterise reachable sets and controllability in open systems. We
elucidate when time-optimal controls derived for the analogous closed system
already give good fidelities in open systems and when a more detailed knowledge
of the open system (e.g., in terms of the parameters of its
Kossakowski-Lindblad master equation) is actually required for state-of-the-art
optimal-control algorithms. -- As an outlook, we sketch the structure of a new,
potentially more efficient numerical approach explicitly making use of the
corresponding Lie wedge.


  We study permutations $p$ such that both $p$ and $p^2$ avoid a given pattern
$q$. We obtain a generating function for the case of $q=312$ (equivalently,
$q=231$), we prove that if $q$ is monotone increasing, then above a certain
length, there are no such permutations, and we prove an upper bound for
$q=321$. We also present some intriguing questions in the case of $q=132$.


  Continual Knowledge Graph Embedding (CKGE) aims to efficiently learn new
knowledge and simultaneously preserve old knowledge. Dominant approaches
primarily focus on alleviating catastrophic forgetting of old knowledge but
neglect efficient learning for the emergence of new knowledge. However, in
real-world scenarios, knowledge graphs (KGs) are continuously growing, which
brings a significant challenge to fine-tuning KGE models efficiently. To
address this issue, we propose a fast CKGE framework (\model), incorporating an
incremental low-rank adapter (\mec) mechanism to efficiently acquire new
knowledge while preserving old knowledge. Specifically, to mitigate
catastrophic forgetting, \model\ isolates and allocates new knowledge to
specific layers based on the fine-grained influence between old and new KGs.
Subsequently, to accelerate fine-tuning, \model\ devises an efficient \mec\
mechanism, which embeds the specific layers into incremental low-rank adapters
with fewer training parameters. Moreover, \mec\ introduces adaptive rank
allocation, which makes the LoRA aware of the importance of entities and
adjusts its rank scale adaptively. We conduct experiments on four public
datasets and two new datasets with a larger initial scale. Experimental results
demonstrate that \model\ can reduce training time by 34\%-49\% while still
achieving competitive link prediction performance against state-of-the-art
models on four public datasets (average MRR score of 21.0\% vs.
21.1\%).Meanwhile, on two newly constructed datasets, \model\ saves 51\%-68\%
training time and improves link prediction performance by 1.5\%.


  The angular power spectrum estimator developed by Peebles (1973) and Hauser &
Peebles (1973) has been modified and applied to the 2 year maps produced by the
COBE DMR. The power spectrum of the real sky has been compared to the power
spectra of a large number of simulated random skies produced with noise equal
to the observed noise and primordial density fluctuation power spectra of power
law form, with $P(k) \propto k^n$. Within the limited range of spatial scales
covered by the COBE DMR, corresponding to spherical harmonic indices $3 \leq
\ell \lsim 30$, the best fitting value of the spectral index is $n =
1.25^{+0.4}_{-0.45}$ with the Harrison-Zeldovich value $n = 1$ approximately
0.5$\sigma$ below the best fit. For $3 \leq \ell \lsim 19$, the best fit is $n
= 1.46^{+0.39}_{-0.44}$. Comparing the COBE DMR $\Delta T/T$ at small $\ell$ to
the $\Delta T/T$ at $\ell \approx 50$ from degree scale anisotropy experiments
gives a smaller range of acceptable spectral indices which includes $n = 1$.


  We report on the experimental realization of an all optical router for
exciton-polaritons. This device is based on the design proposed by H. Flayac
and I.G. Savenko [APL 103, 201105 (2013)], in which a zero-dimensional island
is connected through tunnel barriers to two periodically modulated wires of
different periods. Selective transmission of polaritons injected in the island,
into either of the two wires, is achieved by tuning the energy of the island
state across the band structure of the modulated wires. We show such polariton
routing using an optical control beam which blueshifts the island quantum
states thanks to polariton-exciton interactions. Operation of the device is
demonstrated both under cw and pulsed operation.


  The moving sofa problem asks for the connected shape with the largest area
$\mu_{\text{max}}$ that can move around the right-angled corner of a hallway
$L$ with unit width. The best bounds currently known on $\mu_{\max}$ are
summarized as $2.2195\ldots \leq \mu_{\max} \leq 2.37$. The lower bound
$2.2195\ldots \leq \mu_{\max}$ comes from Gerver's sofa $S_G$ of area $\mu_G :=
2.2195\ldots$. The upper bound $\mu_{\max} \leq 2.37$ was proved by Kallus and
Romik using extensive computer assistance. It is conjectured that the equality
$\mu_{\max} = \mu_G$ holds at the lower bound.
  We develop a new approach to the moving sofa problem by approximating it as
an infinite-dimensional convex quadratic optimization problem. The problem is
then explicitly solved using a calculus of variation based on the
Brunn-Minkowski theory. Consequently, we prove that any moving sofa satisfying
a property named the injectivity condition has an area of at most $1 + \pi^2/8
= 2.2337\dots$. The new conditional bound does not rely on any computer
assistance, yet it is much closer to the lower bound $2.2195\ldots$ of Gerver
than the computer-assisted upper bound $2.37$ of Kallus and Romik. Gerver's
sofa $S_G$, the conjectured optimum, satisfies the injectivity condition in
particular.


  We study the normal state electronic structure of the recently discovered
infinite-layer nickelate superconductor, Nd$_{1-x}$Sr$_x$NiO$_2$. Using
SrNiO$_2$ as a reference, we find that Nd$_{1-x}$Sr$_x$NiO$_2$ is a
multi-orbital electronic system with characteristic Hund's metal behaviors,
such as metallicity, the importance of high-spin configurations, tendency
towards orbital differentiation, and the absence of magnetism in regimes which
are ordered according to static mean-field theories. In addition, our DFT+DMFT
calculations with exact double counting scheme show that despite large charge
carrier doping from SrNiO$_2$ to LaNiO$_2$, the Ni-$3d$ total occupancy is
barely changed due to the decreased hybridization with the occupied oxygen-2$p$
states, and increased hybridization with the unoccupied La-5$d$ states. Our
results are in good agreement with the existing resonant inelastic x-ray
scattering measurements and pave the way to understand the pairing mechanism of
Nd$_{1-x}$Sr$_x$NiO$_2$.


  In this paper we consider the unique determination of inhomogeneities
together with possible buried obstacles by scattering measurements. Under the
assumption that the buried obstacles have only planar contacts with the
inhomogeneities, we prove that one can recover both of them by knowing the
associated scattering amplitude at a fixed energy.


  Chimera states are dynamical states where regions of synchronous trajectories
coexist with incoherent ones. A significant amount of research has been devoted
to study chimera states in systems of identical oscillators, non-locally
coupled through pairwise interactions. Nevertheless, there is an increasing
evidence, also supported by available data, that complex systems are composed
by multiple units experiencing many-body interactions, that can be modeled by
using higher-order structures beyond the paradigm of classic pairwise networks.
In this work we investigate whether phase chimera states appear in this
framework, by focusing on a novel topology solely involving many-body,
non-local and non-regular interactions, hereby named non-local d-hyperring,
being (d+1) the order of the interactions. We present the theory by using the
paradigmatic Stuart-Landau oscillators as node dynamics, and show that phase
chimera states emerge in a variety of structures and with different coupling
functions. For comparison, we show that, when higher-order interactions are
"flattened" to pairwise ones, the chimera behavior is weaker and more elusive.


  In a recent paper [Phys. Rev. A 77, 062511 (2008)], it was advocated to
modify the variational principle for the action-integral functional in the
Runge-Gross foundation of time-dependent density-functional theory. This was
criticised in a subsequent paper [Phys. Rev. A 62, 052510 (2010)] by the
present author. In a Comment [Phys. Rev. A 83, 046501 (2011)], it is argued
that the criticism is unfounded. This is a response as given to the four
specific points raised in the Comment, clarifying and confirming the essence of
the original criticism.


  We introduce a new R package, BeSS, for solving the best subset selection
problem in linear, logistic and Cox's proportional hazard (CoxPH) models. It
utilizes a highly efficient active set algorithm based on primal and dual
variables, and supports sequential and golden search strategies for best subset
selection. We provide a C++ implementation of the algorithm using Rcpp
interface. We demonstrate through numerical experiments based on enormous
simulation and real datasets that the new BeSS package has competitive
performance compared to other R packages for best subset selection purpose.


  We present a registration algorithm which jointly estimates motion and the
ground truth image from a set of noisy frames under rigid, constant
translation. The algorithm is non-iterative and needs no hyperparameter tuning.
It requires a fixed number of FFT, multiplication, and downsampling operations
for a given input size, enabling fast implementation on embedded platforms like
cubesats where on-board image fusion can greatly save on limited downlink
bandwidth. The algorithm is optimal in the maximum likelihood sense for
additive white Gaussian noise and non-stationary Gaussian approximations of
Poisson noise. Accurate registration is achieved for very low SNR, even when
visible features are below the noise floor.


  We consider spatially coupled code ensembles. A particular instance are
convolutional LDPC ensembles. It was recently shown that, for transmission over
the memoryless binary erasure channel, this coupling increases the belief
propagation threshold of the ensemble to the maximum a-posteriori threshold of
the underlying component ensemble. This paved the way for a new class of
capacity achieving low-density parity check codes. It was also shown
empirically that the same threshold saturation occurs when we consider
transmission over general binary input memoryless channels.
  In this work, we report on empirical evidence which suggests that the same
phenomenon also occurs when transmission takes place over a class of channels
with memory. This is confirmed both by simulations as well as by computing EXIT
curves.


  Autonomous vehicles (AVs) are being rapidly introduced into our lives.
However, public misunderstanding and mistrust have become prominent issues
hindering the acceptance of these driverless technologies. The primary
objective of this study is to evaluate the effectiveness of a driving simulator
to help the public gain an understanding of AVs and build trust in them. To
achieve this aim, we built an integrated simulation platform, designed various
driving scenarios, and recruited 28 participants for the experiment. The study
results indicate that a driving simulator effectively decreases the
participants' perceived risk of AVs and increases perceived usefulness. The
proposed methodologies and findings of this study can be further explored by
auto manufacturers and policymakers to provide user-friendly AV design.


  In this paper we have studied a model for self-induced aggregation in
Brownian particle incorporating the non-Markovian and non-Gaussian character of
the associated random noise process. In this model the time evolution of each
individual is guided by an over-damped Langevin equation of motion with a
non-local drift resulting from the local unbalance distributions of the other
individuals. Our simulation result shows that colored nose can induce the
cluster formation even at large noise strength. Another observation is that
critical noise strength grows very rapidly with increase of noise correlation
time for Gaussian noise than non Gaussian one. However, at long time limit the
cluster number in aggregation process decreases with time following a power
law. The exponent in the power law increases remarkable for switching from
Markovian to non Markovian noise process.


  The role of the a_1(1420) resonance in the three-pion decays of the tau
lepton is investigated using a phenomenological model. For all data before
2008, roughly equal fit quality is achieved when the basic a_1(1260) resonance
is supplemented with either a_1(1640) or a_1(1420). However, two recent and
more precise data sets require resonances with masses that are not very far
from that of a_1(1420). This suggests that the axial-vector resonance that
accompanies the a_1(1260) in the three-pion decays of the tauon is a_1(1420),
not a_1(1640), as believed up to now. More data are needed to demonstrate this
definitely.


  Quantum low-density parity-check codes can be decoded using a syndrome based
$\mathrm{GF}(4)$ belief propagation decoder. However, the performance of this
decoder is limited both by unavoidable $4$-cycles in the code's factor graph
and the degenerate nature of quantum errors. For the subclass of CSS codes, the
number of $4$-cycles can be reduced by breaking an error into an $X$ and $Z$
component and decoding each with an individual $\mathrm{GF}(2)$ based decoder.
However, this comes at the expense of ignoring potential correlations between
these two error components. We present a number of modified belief propagation
decoders that address these issues. We propose a $\mathrm{GF}(2)$ based decoder
for CSS codes that reintroduces error correlations by reattempting decoding
with adjusted error probabilities. We also propose the use of an augmented
decoder, which has previously been suggested for classical binary low-density
parity-check codes. This decoder iteratively reattempts decoding on factor
graphs that have a subset of their check nodes duplicated. The augmented
decoder can be based on a $\mathrm{GF}(4)$ decoder for any code, a
$\mathrm{GF}(2)$ decoder for CSS code, or even a supernode decoder for a
dual-containing CSS code. For CSS codes, we further propose a $\mathrm{GF}(2)$
based decoder that combines the augmented decoder with error probability
adjustment. We demonstrate the performance of these new decoders on a range of
different codes, showing that they perform favorably compared to other decoders
presented in literature.


  We consider the terminal value problem (or called final value problem,
initial inverse problem, backward in time problem) of determining the initial
value, in a general class of time-fractional wave equations with Caputo
derivative, from a given final value. We are concerned with the existence,
regularity of solutions upon the terminal value. Under several assumptions on
the nonlinearity, we address and show the well-posedness (namely, the
existence, uniqueness, and continuous dependence) for the terminal value
problem. Some regularity results for the mild solution and its derivatives of
first and fractional orders are also derived. The effectiveness of our methods
are showed by applying the results to two interesting models: Time fractional
Ginzburg-Landau equation, and Time fractional Burgers equation, where time and
spatial regularity estimates are obtained.


  The celebrated BKK Theorem expresses the number of roots of a system of
generic Laurent polynomials in terms of the mixed volume of the corresponding
system of Newton polytopes.Pukhlikov and the second author noticed that the
cohomology ring of smooth projective toric varieties over $\mathbb{C}$ can be
computed via the BKK Theorem. This complemented the known descriptions of the
cohomology ring of toric varieties, like the one in terms of Stanley-Reisner
algebras.
  Sankaran and Uma generalized the "Stanley-Reisner description" to the case of
toric bundles, i.e. equivariant compactifications of (not necessarily
algebraic) torus principal bundles. We provide a description of the cohomology
ring of toric bundles which is based on a generalization of the \BKK Theorem,
and thus extends the approach by Pukhlikov and the second author. Indeed, for
every cohomology class of the base of the toric bundle, we obtain a BKK-type
theorem. Furthermore, our proof relies on a description of graded-commutative
algebras which satisfy Poincar\'e duality.
  From this computation of the cohomology ring of toric bundles, we obtain a
description of the ring of conditions of horospherical homogeneous spaces as
well as a version of Brion-Kazarnovskii theorem for them. We conclude the
manuscript with a number of examples. In particular, we apply our results to
toric bundles over a full flag variety $G/B$. The description that we get
generalizes the corresponding description of the cohomology ring of toric
varieties as well as the one of full flag varieties $G/B$ previously obtained
by Kaveh.


  Blind detection of the forged regions in digital images is an effective
authentication means to counter the malicious use of local image editing
techniques. Existing encoder-decoder forensic networks overlook the fact that
detecting complex and subtle tampered regions typically requires more feedback
information. In this paper, we propose a Progressive FeedbACk-enhanced
Transformer (ProFact) network to achieve coarse-to-fine image forgery
localization. Specifically, the coarse localization map generated by an initial
branch network is adaptively fed back to the early transformer encoder layers
for enhancing the representation of positive features while suppressing
interference factors. The cascaded transformer network, combined with a
contextual spatial pyramid module, is designed to refine discriminative
forensic features for improving the forgery localization accuracy and
reliability. Furthermore, we present an effective strategy to automatically
generate large-scale forged image samples close to real-world forensic
scenarios, especially in realistic and coherent processing. Leveraging on such
samples, a progressive and cost-effective two-stage training protocol is
applied to the ProFact network. The extensive experimental results on nine
public forensic datasets show that our proposed localizer greatly outperforms
the state-of-the-art on the generalization ability and robustness of image
forgery localization. Code will be publicly available at
https://github.com/multimediaFor/ProFact.


  Earlier work on program and thread algebra detailed the functional,
observable behavior of programs under execution. In this article we add the
modeling of unobservable, mechanistic processing, in particular processing due
to jump instructions. We model mechanistic processing preceding some further
behavior as a delay of that behavior; we borrow a unary delay operator from
discrete time process algebra. We define a mechanistic improvement ordering on
threads and observe that some threads do not have an optimal implementation.


  We report the results of the spectral and timing analysis of observations of
the Vela pulsar with the Chandra X-ray Observatory. The spectrum shows no
statistically significant spectral lines in the observed 0.25--8.0 keV band. It
consists of two distinct continuum components. The softer component can be
modeled as either a magnetic hydrogen atmosphere spectrum with kT = 59 +- 3 eV,
R = 15.5 +- 1.5 km, or a standard blackbody with kT = 129 +- 4 eV, R = 2.1 +-
0.2 km (the radii are for a distance of 250 pc). The harder component, modeled
as a power-law spectrum, gives photon indices depending on the model adopted
for the soft component: gamma = 1.5 +- 0.3 for the magnetic atmosphere soft
component, and gamma = 2.7 +- 0.4 for the blackbody soft component. Timing
analysis shows three peaks in the pulse profile, separated by about 0.3 in
phase. Energy-resolved timing provides evidence for pulse profile variation
with energy. The higher energy (E > 1.8 keV) profile shows significantly higher
pulsed fraction.


  Online sparse linear regression is an online problem where an algorithm
repeatedly chooses a subset of coordinates to observe in an adversarially
chosen feature vector, makes a real-valued prediction, receives the true label,
and incurs the squared loss. The goal is to design an online learning algorithm
with sublinear regret to the best sparse linear predictor in hindsight. Without
any assumptions, this problem is known to be computationally intractable. In
this paper, we make the assumption that data matrix satisfies restricted
isometry property, and show that this assumption leads to computationally
efficient algorithms with sublinear regret for two variants of the problem. In
the first variant, the true label is generated according to a sparse linear
model with additive Gaussian noise. In the second, the true label is chosen
adversarially.


  Riemann surfaces are geometric constructions in complex analysis that may
represent multi-valued holomorphic functions using multiple sheets of the
complex plane. We show that the energy dispersion of surface states in
topological semimetals can be represented by Riemann surfaces generated by
holomorphic functions in the two-dimensional momentum space, whose constant
height contours correspond to Fermi arcs. This correspondence is demonstrated
in the recently discovered Weyl semimetals and leads us to predict new types of
topological semimetals, whose surface states are represented by double- and
quad-helicoid Riemann surfaces. The intersection of multiple helicoids, or the
branch cut of the generating function, appears on high-symmetry lines in the
surface Brillouin zone, where surface states are guaranteed to be doubly
degenerate by a glide reflection symmetry. We predict the heterostructure
superlattice [(SrIrO$_3$)$_2$(CaIrO$_3$)$_2$] to be a topological semimetal
with double-helicoid Riemann surface states.


  In a recent series of papers Endean examines the properties of spatially
homogeneous and isotropic (FLRW) cosmological models filled with dust in the
``conformally flat spacetime presentation of cosmology'' (CFS cosmology). This
author claims it is possible to resolve a certain number of the difficulties
the standard model exhibits when confronted to observations, if the theoretical
predictions are obtained in the special framework of CFS cosmology. As a
by-product of his analysis Endean claims that no initial (big-bang) nor final
(big-crunch) singularities occur in the closed FLRW model. In this paper we
show up the fallacious arguments leading to Endean's conclusions and we
consistently reject his CFS cosmology.


  We study a variant of the chip-firing game called \emph{diffusion}. In
diffusion on a graph, each vertex of the graph is initially labelled with an
integer interpreted as the number of chips at that vertex, and at each
subsequent step, each vertex simultaneously fires one chip to each of its
neighbours with fewer chips. Since this firing rule may result in negative
labels, diffusion, unlike the parallel chip-firing game, is not obviously
periodic. In 2016, Duffy, Lidbetter, Messinger and Nowakowski nevertheless
conjectured that diffusion is always eventually periodic, and moreover, that
the process eventually has period either 1 or 2. Here, we establish this
conjecture.


  In search of materials with three-dimensional flat band dispersions, using
{\em ab-initio} computations, we investigate how topological phases evolve as a
function of hydrostatic pressure and uniaxial strain in two types of
superlattices: HgTe/CdTe and HgTe/HgSe. In short-period HgTe/CdTe
superlattices, our analysis unveils the presence of isoenergetic nodal lines,
which could host strain-induced three-dimensional flat bands at the Fermi level
without requiring doping, when fabricated, for instance, as core-shell
nanowires. In contrast, HgTe/HgSe short-period superlattices are found to
harbor a rich phase diagram with a plethora of topological phases. Notably, the
unstrained superlattice realizes an ideal Weyl semimetal with Weyl points
situated at the Fermi level. A small-gap topological insulator with multiple
band inversions can be obtained by tuning the volume: under compressive
uniaxial strain, the material transitions sequentially into a Dirac semimetal
to a nodal-line semimetal, and finally into a topological insulator with a
single band inversion.


  Virtualization technology allows currently any application run any
application complex and expensive computational (the scientific applications
are a good example) on heterogeneous distributed systems, which make regular
use of Grid and Cloud technologies, enabling significant savings in computing
time. This model is particularly interesting for the mass execution of
scientific simulations and calculations, allowing parallel execution of
applications using the same execution environment (unchanged) used by the
scientist as usual. However, the use and distribution of large virtual images
can be a problem (up to tens of GBytes), which is aggravated when attempting a
mass mailing on a large number of distributed computers. This work has as main
objective to present an analysis of how implementation and a proposal for the
improvement (reduction in size) of the virtual images pretending reduce
distribution time in distributed systems. This analysis is done very specific
requirements that need an operating system (guest OS) on some aspects of its
execution.


  In this paper, a symplectic structure on a Leibniz algebra is defined to be a
{\em symmetric} nondegenerate bilinear form satisfying certain compatibility
condition, and a phase space of a Leibniz algebra is defined to be a symplectic
Leibniz algebra satisfying certain conditions. We show that a Leibniz algebra
has a phase space if and only if there is a compatible Leibniz-dendriform
algebra, and phase spaces of Leibniz algebras one-to-one corresponds to Manin
triples of Leibniz-dendriform algebras. Product (paracomplex) structures and
complex structures on Leibniz algebras are studied in terms of decompositions
of Leibniz algebras. A para-K\"{a}hler structure on a Leibniz algebra is
defined to be a symplectic structure and a paracomplex structure satisfying a
compatibility condition. We show that a symplectic Leibniz algebra admits a
para-K\"{a}hler structure if and only if the Leibniz algebra is the direct sum
of two isotropic subalgebras as vector spaces. A complex product structure on a
Leibniz algebra consists of a complex structure and a product structure
satisfying a compatibility condition. A pseudo-K\"{a}hler structure on a
Leibniz algebra is defined to be a symplectic structure and a complex structure
satisfying a compatibility condition. Various properties and relations of
complex product structures and pseudo-K\"{a}hler structures are studied. In
particular, Leibniz-dendriform algebras give rise to complex product structures
and pseudo-K\"{a}hler structures naturally.


  Cosmological LCDM simulations of 12 M_vir~10^14 Msun galaxy groups have been
performed, invoking star formation, chemical evolution with non-instantaneous
recycling, metallicity dependent radiative cooling, strong star-burst driven
galactic super-winds and effects of a meta-galactic UV field. At z=0,
intra-group light (IGL) fractions are found to be 12-45%. Low values refer to
groups with only a small difference between the R-band magnitudes of the first
and second ranked group galaxy, large are typical of "fossil" groups (FGs). The
IG stars in the 4 FGs are 0.3-0.5 Gyr older than in the 8 nonFGs. For the IGL,
B-R=~1.4, in good agreement with observations. For FGs/nonFGs the iron
abundance of the IG stars is slightly sub-solar in the central parts (r~100
kpc) decreasing to about 40% solar at about 0.5 r_vir The IG stars are
alpha-element enhanced with [O/Fe] increasing with r, and an overall
[O/Fe]~0.45, indicating predominant SNII enrichment. The velocity distributions
of the IG stars and group galaxies are, at r>~30 kpc, significantly more
radially anisotropic for FGs than for nonFGs. So a characteristic of FG
formation, apart from formation time (D'Onghia et al.), may be the "initial"
velocity distribution of the group galaxies. For FGs one can dynamically infer
the (dark matter dominated) mass distribution of the groups all the way to
r_vir, from the kinematics of the IG stars or group galaxies. For the nonFGs
this method overestimates the group mass at r>~200 kpc, by up to a factor of
two at r_vir. This is interpreted as FGs being, in general, more relaxed than
nonFGs. Finally, FGs of the above M_vir should host ~500 planetary nebulae at
projected distances between 100 and 1000 kpc from the first ranked galaxy. All
results appear consistent with the FG formation scenario of D'Onghia et al.


  Generation of pseudo random sequences by cellular automata, as well as by
hybrid cellular automata is surveyed. An application to the fast evaluation and
FPGA implementation of some classes of boolean functions is sketched out.


  Cold dust grains emission in the FIR/submm is usually expressed as a modified
black body law in which the dust mass absorption coefficient (MAC), is
described with a temperature- and wavelength-independent emissivity spectral
index, beta. However, numerous data from space and balloon-born missions and
recently from Herschel and Planck show that dust emission is not well
understood, as revealed by the observed anti-correlation of beta with the grain
temperature. In order to give astronomers the necessary data to interpret
FIR/submm observations, we synthesised analogues of interstellar amorphous and
crystalline silicate grains, rich in Mg and Ca, and having stiochiometry of
olivine and pyroxene and measured their MAC, in the 100-1000/1500 \mum range
for grain temperatures varying from 300 to 10 K. We find that the grain MAC
decreases when the grain temperature decreases and that the local spectral
index, beta, defined as the slope of the MAC curve, is anti-correlated with the
grain temperature. These variations, which are not observed in the crystallised
samples, are related to the amorphous nature of the samples. In addition, the
spectral shape of the MAC is complex: at short wavelengths (lambda < 500/700
\mum), beta is in the range 1.6 - 2.1 for all grain temperature and grain
composition whereas at longer wavelengths (lambda > 500/700 \mum), beta < 2 for
samples with a pyroxene stoichiometry and beta > 2 for samples with an olivine
stoichiometry. Hence, the simplifying asymptotic expression based on a single
temperature- and wavelength-independent spectral index used by astronomers is
not appropriate to describe the dust MAC and thus the dust emission, and may
induce significant errors on the derived parameters such as the dust mass and
the dust physical and chemical properties. Instead, dust emission models should
use the dust MAC as a function of wavelength and temperature.


  We study a family of Teichm\"uller curves T(n,m) constructed by Bouw and
M\"oller, and previously by Veech and Ward in the cases n=2,3. We simplify the
proof that T(n,m) is a Teichm\"uller curve, avoiding the use M\"oller's
characterization of Teichm\"uller curves in terms of maximally Higgs bundles.
Our key tool is a description of the period mapping of T(n,m) in terms of
Schwarz triangle mappings.
  We prove that T(n,m) is always generated by Hooper's lattice surface with
semiregular polygon decomposition. We compute Lyapunov exponents, and determine
algebraic primitivity in all cases. We show that frequently, every point
(Riemann surface) on T(n,m) covers some point on some distinct T(n',m').
  The T(n,m) arise as fiberwise quotients of families of abelian covers of CP^1
branched over four points. These covers of CP^1 can be considered as abelian
parallelogram-tiled surfaces, and this viewpoint facilitates much of our study.