  We show that the standard Fermi--Pasta--Ulam system, with a suitable choice
for the interparticle potential, constitutes a model for glasses, and indeed an
extremely simple and manageable one. Indeed, it allows one to describe the
landscape of the minima of the potential energy and to deal concretely with any
one of them, determining the spectrum of frequencies and the normal modes. A
relevant role is played by the harmonic energy $\mathcal E$ relative to a given
minimum, i.e., the expansion of the Hamiltonian about the minimum up to second
order. Indeed we find that there exists an energy threshold in $\mathcal E$
such that below it the harmonic energy $\mathcal E$ appears to be an
approximate integral of motion for the whole observation time. Consequently,
the system remains trapped near the minimum, in what may be called a vitreous
or glassy state. Instead, for larger values of $\mathcal E$ the system rather
quickly relaxes to a final equilibrium state. Moreover we find that the
vitreous states present peculiar statistical behaviors, still involving the
harmonic energy $\mathcal E$. Indeed, the vitreous states are described by a
Gibbs distribution with an effective Hamiltonian close to $\mathcal E$ and with
a suitable effective inverse temperature. The final equilibrium state presents
instead statistical properties which are in very good agreement with the Gibbs
distribution relative to the full Hamiltonian of the system.


  Counterfactual Regret Minimization (CFR)} is the popular method for finding
approximate Nash equilibrium in two-player zero-sum games with imperfect
information. CFR solves games by travsersing the full game tree iteratively,
which limits its scalability in larger games. When applying CFR to solve
large-scale games in previously, large-scale games are abstracted into
small-scale games firstly. Secondly, CFR is used to solve the abstract game.
And finally, the solution strategy is mapped back to the original large-scale
game. However, this process requires considerable expert knowledge, and the
accuracy of abstraction is closely related to expert knowledge. In addition,
the abstraction also loses certain information, which will eventually affect
the accuracy of the solution strategy. Towards this problem, a recent method,
\textit{Deep CFR} alleviates the need for abstraction and expert knowledge by
applying deep neural networks directly to CFR in full games. In this paper, we
introduces \textit{Neural Network Counterfactual Regret Minimization (NNCFR)},
an improved variant of \textit{Deep CFR} that has a faster convergence by
constructing a dueling netwok as the value network. Moreover, an evaluation
module is designed by combining the value network and Monte Carlo, which
reduces the approximation error of the value network. In addition, a new loss
function is designed in the procedure of training policy network in the
proposed \textit{NNCFR}, which can be good to make the policy network more
stable. The extensive experimental tests are conducted to show that the
\textit{NNCFR} converges faster and performs more stable than \textit{Deep
CFR}, and outperforms \textit{Deep CFR} with respect to exploitability and
head-to-head performance on test games.


  Mathematical modeling of disease spreading plays a crucial role in
understanding, controlling and preventing epidemic outbreaks. In a microscopic
description of the propagation of a disease over the complex network of human
contacts, the probability that an individual is in a given state (susceptible,
infectious, recovered etc) depends on the state of its neighbors in the
network. Thus it depends on the state of pairs of nodes, which in turns depends
on triples, in a hierarchy of dynamical dependencies. In order to produce
models that are at the same time reliable and manageable, one has to understand
how to truncate such a hierarchy, and how the chosen order of approximation
affects the ability of the model to forecast the real temporal evolution of an
epidemics. In this paper we provide a systematic analysis of the reliability
(under different hypotheses on the quantity and quality of available data) of
the predictions obtained by truncating the hierarchy either at the level of
individuals or at the level of pairs. We find that pair-based models are
reliable tools both for estimating the epidemiological parameters and for
forecasting the temporal evolution of the epidemics, under all conditions taken
into account in our work. However, a pair-based approach provides a much better
prediction of an individual-based one, only if better data, namely information
on the state of node pairs, are available. Overall, our results suggest that
more refined mathematical models need to be informed by improved contact
tracing techniques to better support decision on policies and containment
measures to adopt.


  In this paper, we attempt to solve a long-lasting open question for
non-positive definite (non-PD) kernels in machine learning community: can a
given non-PD kernel be decomposed into the difference of two PD kernels (termed
as positive decomposition)? We cast this question as a distribution view by
introducing the \emph{signed measure}, which transforms positive decomposition
to measure decomposition: a series of non-PD kernels can be associated with the
linear combination of specific finite Borel measures. In this manner, our
distribution-based framework provides a sufficient and necessary condition to
answer this open question. Specifically, this solution is also computationally
implementable in practice to scale non-PD kernels in large sample cases, which
allows us to devise the first random features algorithm to obtain an unbiased
estimator. Experimental results on several benchmark datasets verify the
effectiveness of our algorithm over the existing methods.


  The $\gamma-\alpha$ transition in Ce$_{0.8}$La$_{0.1}$Th$_{0.1}$ is measured
as a function of applied magnetic field using both resistivity and
magnetization. The $\gamma - \alpha$ transition temperature decreases with
increasing magnetic field, reaching zero temperature at around 56 T. The
magnetic-field dependence of the transition temperature may be fitted using a
model that invokes the field and temperature dependence of the entropy of the
$4f$-electron moments of the $\gamma$ phase, suggesting that the volume
collapse in Ce and its alloys is primarily driven by entropic considerations.


  We consider radial solutions of the slightly subcritical problem $-\Delta
u_\varepsilon = |u_\varepsilon|^{\frac{4}{n-2}-\varepsilon}u_\varepsilon$
either on $\mathbb R^n$ ($n\geq 3$) or in a ball $B$ satisfying Dirichlet or
Neumann boundary conditions. In particular, we provide sharp rates and
constants describing the asymptotic behavior (as $\varepsilon\to 0$) of all
local minima and maxima of $u_\varepsilon$ as well as its derivative at roots.
Our proof is done by induction and uses energy estimates, blow-up/normalization
techniques, a radial pointwise Pohozaev identity, and some ODE arguments. As
corollaries, we complement a known asymptotic approximation of the Dirichlet
nodal solution in terms of a tower of bubbles and present a similar formula for
the Neumann problem.


  The microwave sky shows unexpected features at the largest angular scales,
among them the alignments of the dipole, quadrupole and octopole. Motivated by
recent X-ray cluster studies, we investigate the possibility that local
structures at the 100 h^(-1) Mpc scale could be responsible for such
correlations. These structures give rise to a local Rees-Sciama contribution to
the microwave sky that may amount to Delta T/T ~ 10^(-5) at the largest angular
scales. We model local structures by a spherical overdensity
(Lemaitre-Tolman-Bondi model) and assume that the Local Group is falling toward
the centre. We superimpose the local Rees-Sciama effect on a statistically
isotropic, gaussian sky. As expected we find alignments among low multipoles,
but a closer look reveals that they do not agree with the type of correlations
revealed by the data.


  We study travelling waves on a two--dimensional lattice with linear and
nonlinear coupling between nearest particles and a periodic nonlinear substrate
potential. Such a discrete system can model molecules adsorbed on a substrate
crystal surface. We show the existence of both uniform sliding states and
periodic travelling waves as well in a two-dimensional sine-Gordon lattice
equation using topological and variational methods.


  The use of predator-prey models in theoretical ecology has a long history,
and the model equations have largely evolved since the original Lotka-Volterra
system towards more realistic descriptions of the processes of predation,
reproduction and mortality. One important aspect is the recognition of the fact
that the growth of a population can be subject to an Allee effect, where the
per capita growth rate increases with the population density. Including an
Allee effect has been shown to fundamentally change predator-prey dynamics and
strongly impact species persistence, but previous studies mostly focused on
scenarios of an Allee effect in the prey population. Here we explore a
predator-prey model with an ecologically important case of the Allee effect in
the predator population where it occurs in the numerical response of predator
without affecting its functional response. Biologically, this can result from
various scenarios such as a lack of mating partners, sperm limitation and
cooperative breeding mechanisms, among others. Unlike previous studies, we
consider here a generic mathematical formulation of the Allee effect without
specifying a concrete parameterisation of the functional form, and analyse the
possible local bifurcations in the system. Further, we explore the global
bifurcation structure of the model and its possible dynamical regimes for three
different concrete parameterisations of the Allee effect. The model possesses a
complex bifurcation structure: there can be multiple coexistence states
including two stable limit cycles. Inclusion of the Allee effect in the
predator generally has a destabilising effect on the coexistence equilibrium.
We also show that regardless of the parametrisation of the Allee effect,
enrichment of the environment will eventually result in extinction of the
predator population.


  We introduce the notion of a Bishop topological group i.e., a group X
equipped with a Bishop topology of functions F such that the group operations
of X are Bishop morphisms with respect to F. A closed subset in the
neighborhood structure of X induced by its Bishop topology F is defined in a
positive way i.e., not as the complement of an open subset in X. The
corresponding closure operator, although it is not topological, in the
classical sense, does not involve sequences. As countable choice (CC) is
avoided, and in agreement with Richman's critique on the use of CC in
constructive mathematics, the fundamental facts on closed subsets in Bishop
topological groups shown here have a clear algorithmic content. We work within
Bishop's informal system of constructive mathematics BISH, without countable
choice, equipped with inductive definitions with rules of countably many
premises.


  We explore the significance of bars in triggering central star formation (SF)
and AGN activity for spiral galaxy evolution using a volume-limited sample with
$0.020<z<0.055$, $M_{\rm r}<-19.5$, and $\sigma>70\rm km s^{-1}$ selected from
SDSS DR7. On a central SF rate-$\sigma$ plane, we measure the fraction of
galaxies with strong bars in our sample and also the AGN fractions for barred
and non-barred galaxies, respectively. The comparison between the bar and AGN
fractions reveals a causal connection between the two phenomena of SF quenching
and AGN activity. A massive BH and abundant gas fuels are sufficient conditions
to trigger AGNs. We infer that the AGNs triggered by satisfying the two
conditions drive the strong AGN feedback, suddenly suppressing the central SF
and leaving the SF sequence. We find that in galaxies where either of the two
conditions is not sufficient, bars are a great help for the AGN triggering,
accelerating the entire process of evolution, which is particularly evident in
pseudo-bulge galaxies. All of our findings are obtained only when plotted in
terms of their central velocity dispersion and central SFR (not galactic scale
SFR), indicating that the AGN-driven SF quenching is confined in the central
kpc region.


  Supersymmetric solutions, such as BPS domain walls or black holes, in four-
and five-dimensional supergravity theories with eight supercharges can be
described by effective quantum mechanics with a potential term. We show how
properties of the latter theory can help us to learn about the physics of
supersymmetric vacua and BPS solutions in these supergravity theories. The
general approach is illustrated in a number of specific examples where scalar
fields of matter multiplets take values in symmetric coset spaces.


  Let $\mathbb{F}$ be a field and $\mathsf{G}$ a group. We study the following
problem: how to describe the $\mathsf{G}$-graded associative
$\mathbb{F}$-algebras whose neutral components satisfy some polynomial identity
of degree $2$? We presented a description of these (graded) polynomial
identities and their consequences. Later, for $\mathsf{G}$ finite abelian and
$\mathbb{F}$ algebraically closed with $\mathsf{char}(\mathbb{F})=0$, we proved
that, given a finitely generated $\mathsf{G}$-graded $\mathbb{F}$-algebra
$\mathfrak{A}$, if $\mathfrak{A}_e$ satisfies a polynomial identity
$g\in\mathbb{F}\langle X^{\mathsf{G}} \rangle$ of degree $2$, then
$\mathfrak{A}$ either is nilpotent or has the commutative neutral component.
Furthermore, we proved that, in characteristic zero, if $\mathsf{G}$ is finite
cyclic and $\mathfrak{A}$ is finitely generated such that $\mathfrak{A}_e$ is
central, then the Lie algebra $\mathfrak{A}^{(-)}$ is solvable. In addition,
when the support of grading of $\mathfrak{A}$ has at most $3$ elements, then
$\mathfrak{A}^{(-)}$ is a nilpotent Lie algebra.


  In order to investigate the evolution of E+A galaxies, we observed a galaxy
SDSS J160241.00+521426.9, a possible E+A progenitor which shows both emission
and strong Balmer absorptions, and its neighbor galaxy. We used the integral
field spectroscopic mode of the Kyoto Tridimensional Spectrograph (Kyoto3DII),
mounted on the University of Hawaii 88-inch telescope located on Mauna Kea, and
the slit-spectroscopic mode of the Faint Object Camera and Spectrograph (FOCAS)
on the Subaru Telescope. We found a strong Balmer absorption region in the
center of the galaxy and an emission-line region located 2 kpc from the center,
in the direction of its neighbor galaxy. The recession velocities of the galaxy
and its neighbor galaxy differ only by 100 km s^-1, which suggests that they
are a physical pair and would have been interacting. Comparing observed Lick
indices of Balmer lines and color indices with those predicted from stellar
population synthesis models, we find that a suddenly quenched star-formation
scenario is plausible for the star-formation history of the central region. We
consider that star formation started in the galaxy due to galaxy interactions
and was quenched in the central region, whereas star formation in a region
offset from the center still continues or has begun recently. This work is the
first study of a possible E+A progenitor using spatially resolved spectroscopy.


  Since twelve years the researchers of the Roman area organize the European
Researchers' Night, a project funded by European Commission to discover science
and meet researchers through an Europe-wide public event dedicated to fun
learning. Since the first edition in 2006, when the National Laboratory of
INFN's in Frascati hosted 4000 visitors the project is always grown up to
50,000 attendees and more than 50 scientific partners. In the last edition, The
Frascati Scienza association, which was born to coordinate the event, operated
in over 30 Italian cities from south to north of the peninsula. In addition,
the Made in Science project - European Research Week 2016/17 - has been the one
of the largest project funded by the European Commission and it's often
referred to as a model for organization and communication to the general
public. The 12 yeas data collected and results obtained, as well as some of the
most important experiences in public communication of science will be shown.


  Self-heating effects of picosecond optoelectronic switches based on vertical
high-voltage structures with p-n-junctions (VPSS) operating in a high-frequency
mode were theoretically studied for the first time. It is shown that strong
temperature dependence of the control radiation absorption coefficient $k(T)$
is the main factor determining the maximum switching frequency $f_{max}$ and
the corresponding maximum crystal temperature $T_{max}$, as well as
distributions of temperature $T$ and current density $j$ over a device area. A
two-dimensional analysis of the simplest electrothermal model of VPSS embedded
into a double coaxial forming line showed that an increase in the switching
frequency $f$ leads to displacement of current to device periphery, where the
temperature is minimal. However, distributions of $T$ and $j$ over the device
area remain stable if $f < f_{max}$ and $T < T_{max}$. Of course, the values
$f_{max}$ and $T_{max}$ depend on the energy of control radiation pulses, pulse
switching power and heat sink conditions. For VPSS based on nondirect-gap
semiconductors (Si, SiC), they varies within 20-120 kHz and 120-160 $^o C$,
quite sufficient for practical application. However, VPSS based on direct-gap
semiconductors (GaAs, InP) are not actually suitable for operation in
high-frequency modes due to too sharp dependence $k(T)$.


  Genome-wide association studies have proven to be essential for understanding
the genetic basis of disease. However, many complex traits---personality
traits, facial features, disease subtyping---are inherently high-dimensional,
impeding simple approaches to association mapping. We developed a nonparametric
Bayesian reduced rank regression model for multi-SNP, multi-trait association
mapping that does not require the rank of the linear subspace to be specified.
We show in simulations and real data that our model shares strength over SNPs
and over correlated traits, improving statistical power to identify genetic
associations with an interpretable, SNP-supervised low-dimensional linear
projection of the high-dimensional phenotype. On the HapMap phase 3 gene
expression QTL study data, we identify pleiotropic expression QTLs that
classical univariate tests are underpowered to find and that two step
approaches cannot recover. Our Python software, BERRRI, is publicly available
at GitHub: https://github.com/ashlee1031/BERRRI.


  We present bound state spectra of the 3D rational potential, $V(r)=r^2 +
\lambda r^2/(1+gr^2)$, $g>0$, by means of the generalized pseudospectral
method. All the thirty states corresponding to $n$=0--9 are considered for the
first time for a broad range of coupling parameters. These results surpass the
accuracy of \emph{all} other existing calculations published so far except the
finite-difference method, which yields similar accuracy as ours. Variation of
energies and radial distribution functions is followed with respect to the
interaction parameters. Special emphasis has been laid on \emph{higher}
excitations and \emph{negative} values of the interaction, where relatively
less work has been reported. The energy sequence is found to be different for
positive and negative interaction; numerically following a mirror-image
relationship \emph{usually}, if not always. Additionally, twenty energy
splittings arising from certain levels belonging to $n$=0--9 are systematically
studied as functions of the potential parameters. Several new states (including
the higher ones) are presented.


  Scientific workflows are powerful tools for management of scalable
experiments, often composed of complex tasks running on distributed resources.
Existing cyberinfrastructure provides components that can be utilized within
repeatable workflows. However, data and computing advances continuously change
the way scientific workflows get developed and executed, pushing the scientific
activity to be more data-driven, heterogeneous and collaborative. Workflow
development today depends on the effective collaboration and communication of a
cross-disciplinary team, not only with humans but also with analytical systems
and infrastructure. This paper presents a collaboration-centered reference
architecture to extend workflow systems with dynamic, predictable and
programmable interfaces to systems and infrastructure while bridging the
exploratory and scalable activities in the scientific process. We also present
a conceptual design towards the development of methodologies and tools for
effective workflow-driven collaborations, namely the PPoDS methodology and the
SmartFlows Toolkit for smart utilization of workflows in a rapidly evolving
cyberinfrastructure ecosystem.


  The electrical, magnetic, thermal and optical characteristics of Gallium (Ga)
doped silicene are investigated using density functional theory (DFT). The
effect of doping is studied by tuning dopant concentrations as well as
examining varied doping distances, and atomic dopant interactions for the same
substitutional doping concentration. The results indicate that the Ga atoms
alter the band structure and the band gap in the silicene monolayer at various
concentrations, which can be referred back to to the repulsive interaction of
Ga-Ga atoms. The band gap is determined by the interaction strength of the
Ga-Ga atoms, the Coulomb repulsive force, and it does not always widen as
doping concentration increases. In addition, our spin-polarized DFT
calculations show that these monolayers behave like nonmagnetic semiconductors,
exhibiting symmetric spin-up and spin-down channels. The repulsive interaction
between the Ga atoms causes a symmetry breaking of the monolayers. As a
consequence, a Ga dopant can open the band gap, leading to better
thermoelectric properties such as the Seebeck coefficient and the figure of
merit, as well as an increase in the optical response. As a result of our
estimates, Ga doped silicene monolayers could be advantageous in thermoelectric
and optoelectronic devices.


  Recent experimental and theoretical (both improved semiclassical and fully
quantum-mechanical) results for B III and Ne VII delta n = 0 transitions with n
= 2 or 3, respectively, are discussed. The probable reasons for disagreements
by about a factor of 2 between the fully quantum-mechanically calculated and
both measured and semiclassically calculated widths can be explained in terms
of violation of validity criteria and non-thermal Doppler effects. More
independent determinations of line widths for multiply-ionized non-hydrogenic
ions are called for, but meanwhile caution should be exercised in the use of
corresponding semiclassically calculated widths, e.g., in opacity calculations
or for plasma density diagnostics. Only the quantum calculations allow a clear
separation of elastic and inelastic scattering contributions to the width. For
B III, elastic scattering contributes about 30% whereas for Ne VII inelastic
scattering dominates. This allows rather direct comparisons with benchmark
electron-ion scattering experiments.


  The Oslo method comprises a set of analysis techniques designed to extract
nuclear level density and average $\gamma$-decay strength function from a set
of excitation-energy tagged $\gamma$-ray spectra. Here we present a new
software implementation of the entire Oslo method, called OMpy. We provide a
summary of the theoretical basis and derive the essential equations used in the
Oslo method. In addition to the functionality of the original analysis code,
the new implementation includes novel components such as a rigorous method to
propagate uncertainties throughout all steps of the Oslo method using a Monte
Carlo approach. The resulting level density and $\gamma$-ray strength function
have to be normalized to auxiliary data. The normalization is performed
simultaneously for both quantities, thus preserving all correlations. The
software is verified by the analysis of a synthetic spectrum and compared to
the results of the previous implementation, the oslo-method-software.


  In order to generalize finite element methods to differential forms, Arnold,
Falk, and Winther constructed two families of spaces of polynomial differential
forms on a simplex $T$, the $\mathcal P_r\Lambda^k(T)$ spaces and the $\mathcal
P_r^-\Lambda^k(T)$ spaces, where $k$ is the degree of the form and $r$ is the
degree of its coefficients. The geometric decomposition for these finite
element spaces hinges on a duality relationship between the $\mathcal P$ and
$\mathcal P^-$ spaces proved by Arnold, Falk, and Winther. In this article, we
give a natural alternate construction of the $\mathcal P_r\Lambda^k(T)$ and
$\mathcal P_r^-\Lambda^k(T)$ spaces, leading to a new basis-free proof of this
duality relationship using a modified Hodge star operator.


  Accurate deposition of nanoparticles at defined positions on a substrate is
still a challenging task, because it requires simultaneously stable long-range
transport and attraction to the target site and precise short-range orientation
and deposition. Here we present a method based on geometry-induced energy
landscapes in a nanofluidic slit for particle manipulation: Brownian motors or
electro-osmotic flows are used for particle delivery to the target area. At the
target site, electrostatic trapping localizes and orients the particles.
Finally, reducing the gap distance of the slit leads sequentially to a focusing
of the particle position and a jump into adhesive contact by several
nanometers. For 60 nm gold spheres, we obtain a placement accuracy of 8 nm. The
versatility of the method is demonstrated further by a stacked assembly of
nanorods and the directed deposition of InAs nanowires.


  This paper proposes a novel method for deep learning based on the analytical
convolution of multidimensional Gaussian mixtures. In contrast to tensors,
these do not suffer from the curse of dimensionality and allow for a compact
representation, as data is only stored where details exist. Convolution kernels
and data are Gaussian mixtures with unconstrained weights, positions, and
covariance matrices. Similar to discrete convolutional networks, each
convolution step produces several feature channels, represented by independent
Gaussian mixtures. Since traditional transfer functions like ReLUs do not
produce Gaussian mixtures, we propose using a fitting of these functions
instead. This fitting step also acts as a pooling layer if the number of
Gaussian components is reduced appropriately. We demonstrate that networks
based on this architecture reach competitive accuracy on Gaussian mixtures
fitted to the MNIST and ModelNet data sets.


  For the zone of moderate deviation probabilities the local asymptotic minimax
lower bound of asymptotic efficiency of estimators is established. The
estimation parameter is multidimensional. The lower bound admits the
interpretation as the lower bound of asymptotic efficiency in confidence
estimation.


  We propose a class of scalar models that, once coupled to gravity, lead to
cosmologies that smoothly and stably connect an inflationary quasi-de Sitter
universe to a low, or even zero-curvature, maximally symmetric spacetime in the
asymptotic past, strongly violating the null energy condition ($\dot H\gg H^2$)
at intermediate times. The models are deformations of the conformal galileon
lagrangian and are therefore based on symmetries, both exact and approximate,
that ensure the quantum robustness of the whole picture. The resulting
cosmological backgrounds can be viewed as regularized extensions of the
galilean genesis scenario, or, equivalently, as `early-time-complete'
realizations of inflation. The late-time inflationary dynamics possesses
phenomenologically interesting properties: it can produce a large
tensor-to-scalar ratio within the regime of validity of the effective field
theory and can lead to sizeable equilateral nongaussianities.


  Petabytes of data are to be processed and stored requiring millions of
CPU-years in high energy particle (HEP) physics event simulation. This enormous
demand is handled in worldwide distributed computing centers as part of the LHC
computing grid. These significant resources require a high quality and
efficient production and the early detection of potential errors. In this
article we present novel monitoring techniques in a Grid environment to collect
quality measures during job execution. This allows online assessment of data
quality information to avoid configuration errors or inappropriate settings of
simulation parameters and therefore is able to save time and resources.


  X-ray diffraction (XRD) data acquisition and analysis is among the most
time-consuming steps in the development cycle of novel thin-film materials. We
propose a machine-learning-enabled approach to predict crystallographic
dimensionality and space group from a limited number of thin-film XRD patterns.
We overcome the scarce-data problem intrinsic to novel materials development by
coupling a supervised machine learning approach with a model agnostic,
physics-informed data augmentation strategy using simulated data from the
Inorganic Crystal Structure Database (ICSD) and experimental data. As a test
case, 115 thin-film metal halides spanning 3 dimensionalities and 7
space-groups are synthesized and classified. After testing various algorithms,
we develop and implement an all convolutional neural network, with cross
validated accuracies for dimensionality and space-group classification of 93%
and 89%, respectively. We propose average class activation maps, computed from
a global average pooling layer, to allow high model interpretability by human
experimentalists, elucidating the root causes of misclassification. Finally, we
systematically evaluate the maximum XRD pattern step size (data acquisition
rate) before loss of predictive accuracy occurs, and determine it to be
0.16{\deg}, which enables an XRD pattern to be obtained and classified in 5.5
minutes or less.


  In this paper we give an overview of different Morse-theoretic methods used
to study the topology of moduli spaces of Higgs bundles.


  A less studied numerical characteristic of periodic orbits of area preserving
twist maps of the annulus is the twist or torsion number, called initially the
amount of rotation. It measures the average rotation of tangent vectors under
the action of the derivative of the map along that orbit, and characterizes the
degree of complexity of the dynamics. The aim of this paper is to give new
insights into the definition and properties of the twist number, and to relate
its range to the order properties of periodic orbits. We derive an algorithm to
deduce the exact value or a demi--unit interval containing the exact value of
the twist number. We prove that at a period-doubling bifurcation threshold of a
mini-maximizing periodic orbit, the new born doubly periodic orbit has the
absolute twist number larger than the absolute twist of the original orbit
after bifurcation. We give examples of periodic orbits having large absolute
twist number, that are badly ordered, and illustrate how characterization of
these orbits only by their residue can lead to incorrect results. In connection
to the study of the twist number of periodic orbits of standard--like maps we
introduce a new tool, called 1-cone function. We prove that the location of
minima of this function with respect to the vertical symmetry lines of a
standard-like map encodes a valuable information on the symmetric periodic
orbits and their twist number.


  An excess in gamma-rays from the galactic center observed by the Fermi Large
Area Telescope has been proposed as a possible signal of dark matter
annihilation. Recently, the Fermi collaboration showed that systematic errors
broaden the range of spectral shapes for this excess. We demonstrate fits to
this range for (1) flavor-violating annihilations to top-charm pairs and (2)
annihilations to on-shell bosonic mediators which decay to Standard Model
quarks in a boosted frame. Annihilation of 40 - 100 GeV DM to pairs of spin-1
mediators provide a good fit to the Fermi-LAT spectrum with a normalization
consistent with a thermal relic. Top-charm modes and annihilation to three
pseudoscalar mediators can fit the spectral shape but typically require
non-thermal annihilation cross sections.


  Solving the algebraic dichotomy conjecture for constraint satisfaction
problems over structures first-order definable in countably infinite finitely
bounded homogeneous structures requires understanding the applicability of
local-consistency methods in this setting. We study the amount of consistency
(measured by relational width) needed to solve CSP for first-order expansions S
of countably infinite homogeneous graphs that additionally have bounded strict
width, i.e., for which establishing local consistency of an instance of the CSP
not only decides if there is a solution but also ensures that every solution
may be obtained from a locally consistent instance by greedily assigning values
to variables, without backtracking.
  Our main result is that the structures S under consideration have relational
width exactly (2, L) where L is the maximal size of a forbidden subgraph of a
homogeneous graph under consideration, but not smaller than 3. It beats the
upper bound (2m, 3m) where m = max(arity(S)+1, L, 3) and arity(S) is the
largest arity of a relation in S, which follows from a sufficient condition
implying bounded relational width from the literature. Since L may be
arbitrarily large, our result contrasts the collapse of the relational bounded
width hierarchy for finite structures , whose relational width, if finite, is
always at most (2,3).


  Leveraging knowledge from electronic health records (EHRs) to predict a
patient's condition is essential to the effective delivery of appropriate care.
Clinical notes of patient EHRs contain valuable information from healthcare
professionals, but have been underused due to their difficult contents and
complex hierarchies. Recently, hypergraph-based methods have been proposed for
document classifications. Directly adopting existing hypergraph methods on
clinical notes cannot sufficiently utilize the hierarchy information of the
patient, which can degrade clinical semantic information by (1) frequent
neutral words and (2) hierarchies with imbalanced distribution. Thus, we
propose a taxonomy-aware multi-level hypergraph neural network (TM-HGNN), where
multi-level hypergraphs assemble useful neutral words with rare keywords via
note and taxonomy level hyperedges to retain the clinical semantic information.
The constructed patient hypergraphs are fed into hierarchical message passing
layers for learning more balanced multi-level knowledge at the note and
taxonomy levels. We validate the effectiveness of TM-HGNN by conducting
extensive experiments with MIMIC-III dataset on benchmark in-hospital-mortality
prediction.


  The search for faint emission or absorption lines in astronomical spectra has
received considerable attention in recent years, especially in the X-ray
wavelength range. These features usually appear as a deficit or excess of
counts in a single resolution element of the detector, and as such they are
referred to as unresolved fluctuations. The general problem under investigation
is the probability of occurrence of chance fluctuations. A quantitative answer
is necessary to determine whether detected fluctuations are a real
(astronomical, in this case) signal, or if they can be attributed to chance.
This application note provides a new comprehensive method to answer this
question as function of the instrument's resolution, the wavelength coverage of
the spectrum, the number of fluctuations of interest, and the confidence level
chosen. The method is based on the binomial distribution, and addresses also
the probability of multiple simultaneous fluctuations. A critical aspect of the
model is the a priori knowledge of the location of possible fluctuations, which
significantly affects the probability of detection. In fact, a wider wavelength
range for the 'blind' search of possible fluctuations results in a larger
number of 'tries' for the detection of a fluctuation, lowering the overall
significance of a specific feature. The method is illustrated with a case study
and examples using X-ray data.


  We use the cosmological semi-analytic model (SAM) for galaxy formation
presented in Paper I to study the metallicities and abundance ratios of the
intracluster medium (ICM) within the hierarchical structure formation paradigm.
By requiring a slightly flat IMF (x=1.15) and a two-population
delay-time-distribution (DTD) for SN Ia explosions we found previously that
this model is able to reproduce the abundance ratios and supernova rates of
early-type galaxies in the local Universe. Predictions for elemental abundances
in the ICM pose a further test of the model. We find that with the fiducial
model from Paper I the overall metal content of the ICM is too low, although
the abundance ratios are in good agreement with the data. However, we find that
allowing a fraction of the metal-enriched material ejected by stars to be
deposited directly into the hot ICM, instead of being deposited into the cold
ISM, appears to be a plausible and physically-motivated solution.


  Here we report the development of high-efficiency microscale GaAs laser power
converters, and their successful transfer printing onto silicon substrates,
presenting a unique, high power, low-cost and integrated power supply solution
for implantable electronics, autonomous systems and internet of things
applications. We present 300 {\mu}m diameter single-junction GaAs laser power
converters and successfully demonstrate the transfer printing of these devices
to silicon using a PDMS stamp, achieving optical power conversion efficiencies
of 48% and 49% under 35 and 71 W/cm2 808 nm laser illumination respectively.
The transferred devices are coated with ITO to increase current spreading and
are shown to be capable of handling very high short-circuit current densities
up to 70 A/cm2 under 141 W/cm2 illumination intensity (~1400 Suns), while their
open circuit voltage reaches 1235 mV, exceeding the values of pre-transfer
devices indicating the presence of photon-recycling. These optical power
sources could deliver Watts of power to sensors and systems in locations where
wired power is not an option, while using a massively parallel, scalable, and
low-cost fabrication method for the integration of dissimilar materials and
devices.


  We study the nonlinear dynamics of a completely inhomogeneous DNA chain which
is governed by a perturbed sine-Gordon equation. A multiple scale perturbation
analysis provides perturbed kink-antikink solitons to represent open state
configuration with small fluctuation. The perturbation due to inhomogeneities
changes the velocity of the soliton. However, the width of the soliton remains
constant.


  Cloud computing is a web-based utility model that is becoming popular every
day with the emergence of 4th Industrial Revolution, therefore, cybercrimes
that affect web-based systems are also relevant to cloud computing. In order to
conduct a forensic investigation into a cyber-attack, it is necessary to
identify and locate the source of the attack as soon as possible. Although
significant study has been done in this domain on obstacles and its solutions,
research on approaches and strategies is still in its development stage. There
are barriers at every stage of cloud forensics, therefore, before we can come
up with a comprehensive way to deal with these problems, we must first
comprehend the cloud technology and its forensics environment. Although there
are articles that are linked to cloud forensics, there is not yet a paper that
accumulated the contemporary concerns and solutions related to cloud forensic.
Throughout this chapter, we have looked at the cloud environment, as well as
the threats and attacks that it may be subjected to. We have also looked at the
approaches that cloud forensics may take, as well as the various frameworks and
the practical challenges and limitations they may face when dealing with cloud
forensic investigations.


  The extent to which a magnetosphere protects its planetary atmosphere from
stellar wind ablation depends upon how well it prevents energy and momentum
exchange with the atmosphere and how well it traps otherwise escaping plasma.
We focus on the former, and provide a formalism for estimating approximate
upper limits on mass, energy, and momentum capture, and use them to constrain
loss rates. Our approach quantifies a competition between the local deflection
of incoming plasma by a planetary magnetic field and the increase in area for
solar wind mass capture provided by this magnetosphere when the wind and
planetary fields incur magnetic reconnection. Solar wind capture can be larger
for a magnetized planet versus an unmagnetized planet with small ionosphere,
even if the rate of energy transfer is less. We find this to be the case
throughout Earth's history since the lunar forming impact-- the likely start of
the geodynamo. Focusing of incoming charged particles near the magnetic poles
can increase the local energy flux for a strong enough planetary field and weak
enough wind, and we find that this may be the case for Earth's future. The
future protective role of Earth's magnetic field would then depend on its
ability to trap outgoing plasma. This competition between increased collection
area and reduced inflow speed from a magnetosphere is likely essential in
determining the net protective role of planetary fields and its importance in
sustaining habitability, and can help explain the current ion loss rates from
Mars, Venus and Earth.


  We report on a detailed numerical study of the evolution of semilocal string
networks, based on the largest and most accurate field theory simulations of
these objects to date. We focus on the large-scale network properties,
confirming earlier indications (coming from smaller simulations) that linear
scaling is the attractor solution for the entire parameter space of initial
conditions that we are able to probe. We also provide a brief comparison of our
numerical results with the predictions of a previously developed one-scale
model for the overall evolution of these networks. Two subsequent papers will
discuss in more detail the analytic modeling of the semilocal segment
populations as well as optimized numerical diagnostics.


  In a spacetime with nonvanishing torsion there can occur topologically stable
configurations associated with the frame bundle which are independent of the
curvature. The relevant topological invariants are integrals of local scalar
densities first discussed by Nieh and Yan (N-Y). In four dimensions, the N-Y
form $N= (T^a \wedge T_a - R_{ab} \wedge e^a \wedge e^b)$ is the only closed
4-form invariant under local Lorentz rotations associated with the torsion of
the manifold. The integral of $N$ over a compact D-dimensional (Euclidean)
manifold is shown to be a topological invariant related to the Pontryagin
classes of SO(D+1) and SO(D). An explicit example of a topologically nontrivial
configuration carrying nonvanishing instanton number proportional to $\int N$
is costructed. The chiral anomaly in a four-dimensional spacetime with torsion
is also shown to contain a contribution proportional to $N$, besides the usual
Pontryagin density related to the spacetime curvature. The violation of chiral
symmetry can thus depend on the instanton number of the tangent frame bundle of
the manifold. Similar invariants can be constructed in D>4 dimensions and the
existence of the corresponding nontrivial excitations is also discussed.


  In this paper we present SynKB, an open-source, automatically extracted
knowledge base of chemical synthesis protocols. Similar to proprietary
chemistry databases such as Reaxsys, SynKB allows chemists to retrieve
structured knowledge about synthetic procedures. By taking advantage of recent
advances in natural language processing for procedural texts, SynKB supports
more flexible queries about reaction conditions, and thus has the potential to
help chemists search the literature for conditions used in relevant reactions
as they design new synthetic routes. Using customized Transformer models to
automatically extract information from 6 million synthesis procedures described
in U.S. and EU patents, we show that for many queries, SynKB has higher recall
than Reaxsys, while maintaining high precision. We plan to make SynKB available
as an open-source tool; in contrast, proprietary chemistry databases require
costly subscriptions.


  The purpose of this study is to find evidence for supporting the hypothesis
that language is the mirror of our thinking, our prejudices and cultural
stereotypes. In this analysis, a questionnaire was administered to 537 people.
The answers have been analysed to see if gender stereotypes were present such
as the attribution of psychological and behavioural characteristics. In
particular, the aim was to identify, if any, what are the stereotyped images,
which emerge in defining the roles of men and women in modern society.
Moreover, the results given can be a good starting point to understand if
gender stereotypes, and the expectations they produce, can result in
penalization or inequality. If so, the language and its use would create
inherently a gender bias, which influences evaluations both in work settings
both in everyday life.


  We present a coarse-grained two dimensional mechanical model for the
microtubule-tau bundles in neuronal axons in which we remove taus, as can
happen in various neurodegenerative conditions such as Alzheimer's disease,
tauopathies, and chronic traumatic encephalopathy. Our simplified model
includes (i) taus modeled as entropic springs between microtubules, (ii)
removal of taus from the bundles due to phosphorylation, and (iii) a possible
depletion force between microtubules due to these dissociated phosphorylated
taus. We equilibrate upon tau removal using steepest descent relaxation. In the
absence of the depletion force, the transverse rigidity to radial compression
of the bundle falls to zero at about 60% tau occupancy, in agreement with
standard percolation theory results. However, with the attractive depletion
force, spring removal leads to a first order collapse of the bundles over a
wide range of tau occupancies for physiologically realizable conditions. While
our simplest calculations assume a constant concentration of microtubule
intercalants to mediate the depletion force, including a dependence that is
linear in the detached taus yields the same collapse. Applying percolation
theory to removal of taus at microtubule tips, which are likely to be the
protective sites against dynamic instability, we argue that the microtubule
instability can only obtain at low tau occupancy, from 0.06-0.30 depending upon
the tau coordination at the microtubule tips. Hence, the collapse we discover
is likely to be more robust over a wide range of tau occupancies than the
dynamic instability. We suggest in vitro tests of our predicted collapse.


  Prototyping of van der Waals materials on dense nanophotonic devices requires
high-precision monolayer discrimination to avoid bulk material contamination.
We use the glass transition temperature of polycarbonate, used in the standard
dry transfer process, to draw an in situ point for the precise pickup of two
dimensional materials. We transfer transition metal dichalcogenide monolayers
onto a large-area silicon nitride spiral waveguide and silicon nitride ring
resonators to demonstrate the high-precision contamination-free nature of the
modified dry transfer method. Our improved local transfer technique is a
necessary step for the deterministic integration of high-quality van der Waals
materials onto nanocavities for the exploration of few-photon nonlinear optics
on a high-throughput, nanofabrication-compatible platform.


  In two-dimensional electron systems (2DES) the breaking of the inversion,
time-reversal and bulk crystal-field symmetries is interlaced with the effects
of spin-orbit coupling (SOC) triggering exotic quantum phenomena. Here, we used
epitaxial engineering to design and realize a 2DES characterized simultaneously
by ferromagnetic order, large Rashba SOC and hexagonal band warping at the
(111) interfaces between LaAlO$_{3}$, EuTiO$_{3}$ and SrTiO$_{3}$ insulators.
The 2DES displays anomalous quantum corrections to the magneto-conductance
driven by the time-reversal-symmetry breaking occurring below the magnetic
transition temperature. The results are explained by the emergence of a
non-trivial Berry phase and competing weak anti-localization / weak
localization back-scattering of Dirac-like fermions, mimicking the
phenomenology of gapped topological insulators. These findings open
perspectives for the engineering of novel spin-polarized functional 2DES
holding promises in spin-orbitronics and topological electronics.


  We solve the RSOS($p$) models on the light--cone lattice with fixed boundary
conditions by disentangling the type II representations of $SU(2)_q$, at
$q=e^{i\pi/p}$, from the full SOS spectrum obtained through Algebraic Bethe
Ansatz. The rule which realizes the quantum group reduction to the RSOS states
is that there must not be {\it singular} roots in the solutions of the Bethe
Ansatz equations describing the states with quantum spin $J<(p-1)/2$. By
studying how this rule is active on the particle states, we are able to give a
microscopic derivation of the lattice $S-$matrix of the massive kinks. The
correspondence between the light--cone Six--Vertex model and the Sine--Gordon
field theory implies that the continuum limit of the RSOS($p+1$) model is to be
identified with the $p-$restricted Sine--Gordon field theory.


  We address the problem of reconstructing the phase-space distribution
function for an extended collisionless system, with known density profile and
in equilibrium within an axisymmetric gravitational potential. Assuming that it
depends on only two integrals of motion, namely the energy and the component of
the angular momentum along the axis of symmetry $L_z$, there is a one-to-one
correspondence between the density profile and the component of the
distribution function that is even in $L_z$, as well as between the weighted
azimuthal velocity profile and the odd component. This inversion procedure was
originally proposed by Lynden-Bell and later refined in its numerical
implementation by Hunter & Qian; after overcoming a technical difficulty, we
apply it here for the first time in presence of a strongly flattened component,
as a novel approach of extracting the phase-space distribution function for
dark matter particles in the halo of spiral galaxies. We compare results
obtained for realistic axisymmetric models to those in the spherical symmetric
limit as assumed in previous analyses, showing the rather severe shortcomings
in the latter. We then apply the scheme to the Milky Way and discuss the
implications for the direct dark matter searches. In particular, we reinterpret
the null results of the Xenon1T experiment for spin-(in)dependent interactions
and make predictions for the annual modulation of the signal for a set of
axisymmetric models, including a self-consistently defined co-rotating halo.


  We prove the Duality Theorems for the stochastic optimal transportation
problems with a convex cost function without a regularity assumption that is
often supposed in the proof of the lower semicontinuity of an action integral.
In our new approach, we prove that the stochastic optimal transportation
problems with a convex cost function are equivalent to a class of variational
problems for the Fokker-Planck equation, which lets us revisit them. It is done
by the so-called superposition principle and by an idea from the mather theory.
The superposition principle is the construction of a semimartingale from the
Fokker-Planck equation and can be considered a class of the so-called marginal
problems that construct stochastic processes from given marginal distributions.
It was first considered in stochastic mechanics by E. Nelson, called Nelson's
problem, and was proved by E. Carlen first. The semimartingale is called the
Nelson process, provided it is Markovian. We also consider the Markov property
of a minimizer of the stochastic optimal transportation problem with a
nonconvex cost in a one-dimensional case. In the proof, the superposition
principle and the minimizer of an optimal transportation problem with a concave
cost function play crucial roles. Lastly, we prove the semiconcavity and the
Lipschitz continuity of Schrodinger's problem that is a typical example of the
stochastic optimal transportation problem.


  The output of Deep Neural Networks (DNN) can be altered by a small
perturbation of the input in a black box setting by making multiple calls to
the DNN. However, the high computation and time required makes the existing
approaches unusable. This work seeks to improve the One-pixel (few-pixel)
black-box adversarial attacks to reduce the number of calls to the network
under attack. The One-pixel attack uses a non-gradient optimization algorithm
to find pixel-level perturbations under the constraint of a fixed number of
pixels, which causes the network to predict the wrong label for a given image.
We show through experimental results how the choice of the optimization
algorithm and initial positions to search can reduce function calls and
increase attack success significantly, making the attack more practical in
real-world settings.


  An approach to complex interpolation of compact subsets of $\Bbb C^n$,
including Brunn-Minkowski type inequalities for the capacities of the
interpolating sets, was developed recently by means of plurisubharmonic
geodesics between relative extremal functions of the given sets. Here we show
that a much better control can be achieved by means of the geodesics between
weighted relative extremal functions. In particular, we establish convexity
properties of the capacities that are stronger than those given by the
Brunn-Minkowski inequalities.


  Energy forecasting is pivotal in energy systems, by providing fundamentals
for operation, with different horizons and resolutions. Though energy
forecasting has been widely studied for capturing temporal information, very
few works concentrate on the frequency information provided by forecasts. They
are consequently often limited to single-resolution applications (e.g.,
hourly). Here, we propose a unified energy forecasting framework based on
Laplace transform in the multi-resolution context. The forecasts can be
seamlessly produced at different desired resolutions without re-training or
post-processing. Case studies on both energy demand and supply data show that
the forecasts from our proposed method can provide accurate information in both
time and frequency domains. Across the resolutions, the forecasts also
demonstrate high consistency. More importantly, we explore the operational
effects of our produced forecasts in the day-ahead and intra-day energy
scheduling. The relationship between (i) errors in both time and frequency
domains and (ii) operational value of the forecasts is analysed. Significant
operational benefits are obtained.


  Packing problems constitute an important class of optimization problems, both
because of their high practical relevance and theoretical appeal. However,
despite the large number of variants that have been studied in the literature,
most packing problems encompass a single tier of capacity restrictions only.
For example, in the Multiple Knapsack Problem, we assign items to multiple
knapsacks such that their capacities are not exceeded. But what if these
knapsacks are partitioned into clusters, each imposing an additional capacity
restriction on the knapsacks contained in that cluster? In this paper, we study
the Maximum Coverage Problem with Cluster Constraints (MCPC), which generalizes
the Maximum Coverage Problem with Knapsack Constraints (MCPK) by incorporating
cluster constraints. Our main contribution is a general LP-based technique to
derive approximation algorithms for cluster capacitated problems. Our technique
allows us to reduce the cluster capacitated problem to the respective original
packing problem. By using an LP-based approximation algorithm for the original
problem, we can then obtain an effective rounding scheme for the problem, which
only loses a small fraction in the approximation guarantee. We apply our
technique to derive approximation algorithms for MCPC. To this aim, we develop
an LP-based $\frac12(1-\frac1e)$-approximation algorithm for MCPK by adapting
the pipage rounding technique. Combined with our reduction technique, we obtain
a $\frac13(1-\frac1e)$-approximation algorithm for MCPC. We also derive
improved results for a special case of MCPC, the Multiple Knapsack Problem with
Cluster Constraints (MKPC). Based on a simple greedy algorithm, our approach
yields a $\frac13$-approximation algorithm. By combining our technique with a
more sophisticated iterative rounding approach, we obtain a
$\frac12$-approximation algorithm for certain special cases of MKPC.


  We extend ideas of Garling to consider the so called Hardy martingales in a
more general setting of H^p theory of compact abelian groups with ordered dual.
As a consequence, we obtain a new proof of a result of Helson and Lowdenslager
which generalizes Jensen's Inequality for H^1 functions.


  In natural languages, words are used in association to construct sentences.
It is not words in isolation, but the appropriate combination of hierarchical
structures that conveys the meaning of the whole sentence. Neural networks can
capture expressive language features; however, insights into the link between
words and sentences are difficult to acquire automatically. In this work, we
design a deep neural network architecture that explicitly wires lower and
higher linguistic components; we then evaluate its ability to perform the same
task at different hierarchical levels. Settling on broad text classification
tasks, we show that our model, MHAL, learns to simultaneously solve them at
different levels of granularity by fluidly transferring knowledge between
hierarchies. Using a multi-head attention mechanism to tie the representations
between single words and full sentences, MHAL systematically outperforms
equivalent models that are not incentivized towards developing compositional
representations. Moreover, we demonstrate that, with the proposed architecture,
the sentence information flows naturally to individual words, allowing the
model to behave like a sequence labeller (which is a lower, word-level task)
even without any word supervision, in a zero-shot fashion.


  Rejoinder to "Multiple Testing for Exploratory Research" by J. J. Goeman, A.
Solari [arXiv:1208.2841].


  Some topics concerning the Gould integral are presented here: new results of
integrability on finite measure spaces with values in an M-space are given,
together with a Radon-Nikodym theorem relative to a Gould-type integral of real
functions with respect to a multisubmeasure.


  Decentralized identity mechanisms endeavor to endow users with complete
sovereignty over their digital assets within the Web3 ecosystem. Unfortunately,
this benefit frequently comes at the expense of users' credential and identity
privacy. Additionally, existing schemes fail to resist Sybil attacks that have
long plagued Web3, and lack reasonable key recovery mechanisms to regain
control of digital assets after loss. In this work, we propose LinkDID, a
privacy-preserving, Sybil-resistant, and key-recoverable decentralized identity
scheme that supports selective disclosure of credentials for arbitrary
predicates while maintaining privacy for credentials and identities. Through an
identifier association mechanism, LinkDID can privately and forcibly aggregate
users' identifiers, providing Sybil resistance without relying on any external
data or collateral from benign users. To enable key recovery, LinkDID permits
users to establish proofs of ownership for identifiers with lost keys and
request an update of corresponding keys from the decentralized ledger. We
provide a detailed theoretical analysis and security proofs of LinkDID, along
with an exhaustive performance evaluation that shows its ability to complete
interactions in less than 10 seconds on consumer-grade devices.


  Collimated relativistic outflows, or jets, are amongst the most energetic and
relativistic phenomena in the Universe. They are associated with supermassive
black holes in distant active galactic nuclei (AGN), accreting black holes and
neutron stars in binary systems and are believed to be responsible for
gamma-ray bursts. The physics of these jets,however, remains something of a
mystery in that their bulk velocities, compositions and energetics remain
poorly determined. Here we report the discovery of an ultra-relativistic
outflow from a binary accreting neutron star accreting gas within a binary
system. The velocity of the outflow is comparable to the fastest-moving flows
observed from active galactic nuclei, and its strength is modulated by the rate
of accretion of material onto the neutron star. Shocks are energized further
downstream in the flow, which are themselves moving with mildly relativistic
bulk velocities and are the sites of the observed synchrotron emission from the
jet. We conclude that the generation of such highly relativistic outflows does
not require properties unique to black holes, such as an event horizon.


  Ensuring that large language models (LLMs) reflect diverse user values and
preferences is crucial as their user bases expand globally. It is therefore
encouraging to see the growing interest in LLM personalization within the
research community. However, current works often rely on the LLM-as-a-Judge
approach for evaluation without thoroughly examining its validity. In this
paper, we investigate the reliability of LLM-as-a-Personalized-Judge, asking
LLMs to judge user preferences based on personas. Our findings suggest that
directly applying LLM-as-a-Personalized-Judge is less reliable than previously
assumed, showing low and inconsistent agreement with human ground truth. The
personas typically used are often overly simplistic, resulting in low
predictive power. To address these issues, we introduce verbal uncertainty
estimation into the LLM-as-a-Personalized-Judge pipeline, allowing the model to
express low confidence on uncertain judgments. This adjustment leads to much
higher agreement (above 80%) on high-certainty samples for binary tasks.
Through human evaluation, we find that the LLM-as-a-Personalized-Judge achieves
comparable performance to third-party humans evaluation and even surpasses
human performance on high-certainty samples. Our work indicates that
certainty-enhanced LLM-as-a-Personalized-Judge offers a promising direction for
developing more reliable and scalable methods for evaluating LLM
personalization.


  In the framework of nonrelativistic QCD, the excited doubly heavy baryons are
thoroughly studied via the channel $e^{+} e^{-}\rightarrow \langle
QQ^{\prime}\rangle[n] \rightarrow \Xi_{QQ^{\prime}} +\bar{Q^{\prime}}
+\bar{Q}$, which takes place at the collision energy $Z$-pole. $Q^{(\prime)}$
represents $b$ or $c$ quark for the production of $\Xi_{cc}$, $\Xi_{bc}$, and
$\Xi_{bb}$, respectively. All of the intermediate diquark states $\langle
QQ'\rangle[n]$ in $P$-wave, $\langle cc\rangle[^{1}P_{1}]_{\mathbf{\bar 3}}$,
$\langle cc\rangle[^{3}P_{J}]_{\mathbf{6}}$, $\langle
bc\rangle[^{1}P_{1}]_{\mathbf{\bar 3}/ \mathbf{6}}$, $\langle
bc\rangle[^{3}P_{J}]_{\mathbf{\bar 3}/ \mathbf{6}}$, $\langle bb
\rangle[^{1}P_{1}]_{\mathbf{\bar 3}}$, and $\langle
bb\rangle[^{3}P_{J}]_{\mathbf{6}}$ with $J=0$, 1, or 2, are taken into account.
The cross sections and differential distributions, including the transverse
momentum, rapidity, angular, and invariant mass, are discussed for the excited
baryons production. We find that the contributions of $\langle cc \rangle$,
$\langle bc \rangle$, and $\langle bb \rangle$ in $P$-wave are found to be
3.97$\%$, 5.08$\%$, and 5.89$\%$, respectively, compared to $S$-wave. Supposing
that all excited states can decay into the ground state 100\%, the total events
$N_{\Xi_{cc}}=8.48 \times10^{4-6}$, $N_{\Xi_{bc}}=2.26\times10^{5-7}$, and
$N_{\Xi_{bb}}=4.12 \times10^{3-5}$ would be produced at the Super-$Z$ Factory
with a high luminosity up to ${\cal L} \simeq 10^{34-36}{\rm cm}^{-2} {\rm
s}^{-1}$.


  Social hierarchy in animal groups carries a crucial adaptive function by
reducing conflict and injury while protecting valuable group resources. Social
hierarchy is dynamic and can be altered by social conflict, agonistic
interactions, and aggression. Understanding social conflict and aggressive
behavior is of profound importance to our society and welfare. In this study,
we developed a quantitative theory of social conflict. We modeled individual
agonistic interactions as a normal-form game between two agents. We assumed
that the agents use Bayesian inference to update their beliefs about their
strength or their opponent's strength and to derive optimal actions. We
compared the results of our model to behavioral and whole-brain neural activity
data obtained for a large (n=116) population of mice engaged in agonistic
interactions. We find that both types of data are consistent with the
first-level Theory of Mind model (1-ToM) in which mice form both "primary"
beliefs about their and their opponent's strengths as well as the "secondary"
beliefs about the beliefs of their opponents. Our model helps identify brain
regions that carry information about these levels of beliefs. Overall, we both
propose a model to describe agonistic interactions and support our quantitative
results with behavioral and neural activity data.


  This article extends a paper of Abraham and Bonnet which generalised the
famous Hausdorff characterisation of the class of scattered linear orders.
Abraham and Bonnet gave a poset hierarchy that characterised the class of
scattered posets which do not have infinite antichains (abbreviated FAC for
finite antichain condition). An antichain here is taken in the sense of
incomparability. We define a larger poset hierarchy than that of Abraham and
Bonnet, to include a broader class of ``scattered'' posets that we call
$\kappa$-scattered. These posets cannot embed any order such that for every two
subsets of size $ < \kappa$, one being strictly less than the other, there is
an element in between. If a linear order has this property and has size
$\kappa$ we call this set $\qkappa$. Such a set only exists when
$\kappa^{<\kappa}=\kappa$. Partial orders with the property that for every
$a<b$ the set $\{x: a<x<b\}$ has size $\geq \kappa$ are called weakly
$\kappa$-dense, and partial orders that do not have a weakly $\kappa$-dense
subset are called strongly $\kappa$-scattered. We prove that our hierarchy
includes all strongly $\kappa$-scattered FAC posets, and that the hierarchy is
included in the class of all FAC $\kappa$-scattered posets. In addition, we
prove that our hierarchy is in fact the closure of the class of all
$\kappa$-well-founded linear orders under inversions, lexicographic sums and
FAC weakenings. For $\kappa=\aleph_0$ our hierarchy agrees with the one from
the Abraham-Bonnet theorem.


  Computing on graphics processors is maybe one of the most important
developments in computational science to happen in decades. Not since the
arrival of the Beowulf cluster, which combined open source software with
commodity hardware to truly democratize high-performance computing, has the
community been so electrified. Like then, the opportunity comes with
challenges. The formulation of scientific algorithms to take advantage of the
performance offered by the new architecture requires rethinking core methods.
Here, we have tackled fast summation algorithms (fast multipole method and fast
Gauss transform), and applied algorithmic redesign for attaining performance on
gpus. The progression of performance improvements attained illustrates the
exercise of formulating algorithms for the massively parallel architecture of
the gpu. The end result has been gpu kernels that run at over 500 Gigaflops on
one nvidia Tesla C1060 card, thereby reaching close to practical peak. We can
confidently say that gpu computing is not just a vogue, it is truly an
irresistible trend in high-performance computing.


  Let $S=\{x_1,x_2,\dots,x_n\}$ be a set of distinct positive integers, and let
$f$ be an arithmetical function. The GCD matrix $(S)_f$ on $S$ associated with
$f$ is defined as the $n\times n$ matrix having $f$ evaluated at the greatest
common divisor of $x_i$ and $x_j$ as its $ij$ entry. The LCM matrix $[S]_f$ is
defined similarly. We consider inertia, positive definiteness and $\ell_p$ norm
of GCD and LCM matrices and their unitary analogs. Proofs are based on matrix
factorizations and convolutions of arithmetical functions.


  As Large Language Models (LLMs) become widely used to model and simulate
human behavior, understanding their biases becomes critical. We developed an
experimental framework using Big Five personality surveys and uncovered a
previously undetected social desirability bias in a wide range of LLMs. By
systematically varying the number of questions LLMs were exposed to, we
demonstrate their ability to infer when they are being evaluated. When
personality evaluation is inferred, LLMs skew their scores towards the
desirable ends of trait dimensions (i.e., increased extraversion, decreased
neuroticism, etc). This bias exists in all tested models, including GPT-4/3.5,
Claude 3, Llama 3, and PaLM-2. Bias levels appear to increase in more recent
models, with GPT-4's survey responses changing by 1.20 (human) standard
deviations and Llama 3's by 0.98 standard deviations-very large effects. This
bias is robust to randomization of question order and paraphrasing.
Reverse-coding all the questions decreases bias levels but does not eliminate
them, suggesting that this effect cannot be attributed to acquiescence bias.
Our findings reveal an emergent social desirability bias and suggest
constraints on profiling LLMs with psychometric tests and on using LLMs as
proxies for human participants.


  Coronal mass ejections (CMEs) drive powerful shocks and thereby accelerate
solar energetic particles (SEPs) as they propagate from the corona into
interplanetary space. Here we present the processes of three-stage particle
acceleration by a CME-driven shock detected by the in situ spacecraft--Parker
Solar Probe (PSP) on 2022 August 27. The onset of SEPs is produced by a fast
CME with a speed of 1284 km/s when it propagates to $\sim$2.85 Rs. The second
stage of particle acceleration occurs when the fast CME catches up and
interacts with a preceding slow one in interplanetary space at $\sim$40 Rs
($\sim$0.19 au). The CME interaction is accompanied by an intense
interplanetary type II radio enhancement. Such direct measurement of particle
acceleration during interplanetary CME interaction/radio enhancement is rarely
recorded in previous studies. The third stage of energetic storm particles is
associated with the CME-driven shock passage of the PSP at $\sim$0.38 au.
Obviously, harder particle spectra are found in the latter two stages than the
first one, which can arise from a stronger shock produced by the CME
interaction and the enriched seed particles inside the preceding CME.


  In practice, since many communication networks are huge in scale, or
complicated in structure, or even dynamic, the predesigned linear network codes
based on the network topology is impossible even if the topological structure
is known. Therefore, random linear network coding has been proposed as an
acceptable coding technique for the case that the network topology cannot be
utilized completely. Motivated by the fact that different network topological
information can be obtained for different practical applications, we study the
performance analysis of random linear network coding by analyzing some failure
probabilities depending on these different topological information of networks.
We obtain some tight or asymptotically tight upper bounds on these failure
probabilities and indicate the worst cases for these bounds, i.e., the networks
meeting the upper bounds with equality. In addition, if the more topological
information of the network is utilized, the better upper bounds are obtained.
On the other hand, we also discuss the lower bounds on the failure
probabilities.


  We consider a scanning tunneling microscope (STM) such that tunneling occurs
through two atomically sharp protrusions on its tip. When the two protrusions
are separated by at least several atomic spacings, the differential conductance
of this STM depends on the electronic transport in the sample between the
protrusions. Furthermore two-protrusion tips commonly occur during STM tip
preparation. We explore possible applications to probing dynamical impurity
potentials on a metallic surface and local transport in an anisotropic
superconductor.


  We consider the problem of bounding CFT correlators on the Euclidean section.
By reformulating the question as an optimization problem, we construct
functionals numerically which determine upper and lower bounds on correlators
under several circumstances. A useful outcome of our analysis is that the gap
maximization bootstrap problem can be reproduced by a numerically easier
optimization problem. We find that the 3d Ising spin correlator takes the
minimal possible allowed values on the Euclidean section. Turning to the
maximization problem we find that for d > 2 there are gap-independent maximal
bounds on CFT correlators. Under certain conditions we show that the maximizing
correlator is given by the generalized free boson for general Euclidean
kinematics. In our explorations we also uncover an intriguing 3d CFT which
saturates gap, OPE maximization and correlator value bounds. Finally we comment
on the relation between our functionals and the Polyakov bootstrap.


  Many planet candidates have been detected by radial velocity variations of
the primary star; they are planet candidates, because of the unknown orbit
inclination. Detection of the wobble in the two other dimensions, to be
measured by astrometry, would yield the inclination and, hence, true mass of
the companions. We aim to show that planets can be confirmed or discovered in a
close visual stellar binary system by measuring the astrometric wobble of the
exoplanet host star as periodic variation of the separation, even from the
ground. We test the feasibility with HD 19994, a visual binary with one radial
velocity planet candidate. We use the adaptive optics camera NACO at the VLT
with its smallest pixel scale (13 mas) for high precision astrometric
measurements. The separations measured in single 120 images taken within one
night are shown to follow white noise, so that the standard deviation can be
devided by the square root of the number of images to obtain the precision. In
this paper we present the first results and investigate the achievable
precision in relative astrometry with adaptive optics. With a careful data
reduction it is possible to achieve a relative astrometric precision as low as
50 micro arc sec for a 0.6 arc sec, binary with VLT/NACO observations in one
hour, the best relative astrometric precision ever achieved with a single
telescope from the ground. The relative astrometric precision demonstrated here
with AO at an 8-m mirror is sufficient to detect the astrometric signal of the
planet HD 19994 Ab as periodic variation of the separation between HD 19994 A
and B.


  Thermalization in closed quantum systems can be explained either by means of
the eigenstate thermalization hypothesis or the concept of canonical
typicality. Both concepts are based on quantum mechanical formalism such as
spectral properties of the eigenstates or entanglement between subsystems
respectively. Here we study the onset of thermalization of Bose particles in a
two-band double well potential using the truncated Wigner approximation. This
allows us to use the familiar classical formalism to explain quantum
thermalization in this system. In particular, we demonstrate that sampling of
an initial quantum state plays the role of a statistical mechanical ensemble,
while subsequent chaotic classical evolution turns the initial quantum state
into the thermal state.


  With the increasing number of data collectors such as smartphones, immense
amounts of data are available. Federated learning was developed to allow for
distributed learning on a massive scale whilst still protecting each users'
privacy. This privacy is claimed by the notion that the centralized server does
not have any access to a client's data, solely the client's model update. In
this paper, we evaluate a novel attack method within regular federated learning
which we name the First Dense Layer Attack (Fidel). The methodology of using
this attack is discussed, and as a proof of viability we show how this attack
method can be used to great effect for densely connected networks and
convolutional neural networks. We evaluate some key design decisions and show
that the usage of ReLu and Dropout are detrimental to the privacy of a client's
local dataset. We show how to recover on average twenty out of thirty private
data samples from a client's model update employing a fully connected neural
network with very little computational resources required. Similarly, we show
that over thirteen out of twenty samples can be recovered from a convolutional
neural network update. An open source implementation of this attack can be
found here https://github.com/Davidenthoven/Fidel-Reconstruction-Demo


  The applications of Artificial Intelligence (AI) methods especially machine
learning techniques have increased in recent years. Classification algorithms
have been successfully applied to different problems such as requirement
classification. Although these algorithms have good performance, most of them
cannot explain how they make a decision. Explainable Artificial Intelligence
(XAI) is a set of new techniques that explain the predictions of machine
learning algorithms. In this work, the applicability of XAI for software
requirement classification is studied. An explainable software requirement
classifier is presented using the LIME algorithm. The explainability of the
proposed method is studied by applying it to the PROMISE software requirement
dataset. The results show that XAI can help the analyst or requirement
specifier to better understand why a specific requirement is classified as
functional or non-functional. The important keywords for such decisions are
identified and analyzed in detail. The experimental study shows that the XAI
can be used to help analysts and requirement specifiers to better understand
the predictions of the classifiers for categorizing software requirements.
Also, the effect of the XAI on feature reduction is analyzed. The results
showed that the XAI model has a positive role in feature analysis.


  We point out that the standard chromomagnetic penguin dipole operator has a
counterpart corresponding to off-shell momenta for external quarks. By
employing the chiral quark model, we show that this new dipole penguin operator
has the same bosonisation as the standard Q_6 operator. Accordingly, this new
operator enlarges by ~ 5 % the referent Q_6 contribution, which gives the
dominant contribution to the CP-violating ratio epsilon'/epsilon and also gives
an important contribution to the Delta I = 1/2 amplitude.


  In the standard entropic mechanism adopted in the simple Ekpyrotic models to
generate the nearly scale-invariant and Gaussian primordial perturbation, the
entropy direction is tachyonically unstable. In this paper, we consider the
stable production of the scale-invariant entropy perturbation in the Ekpyrotic
universe via non-minimal couplings. In this model the non-minimally coupled
massless scalar field serves as a spectator and is stabilized by the introduced
non-minimal couplings. It always corresponds to the entropy field during the
contraction and with appropriate couplings can obtain a scale-invariant
spectrum. This scenario requires additional mechanisms such as curvaton or
modulated preheating to convert the entropy perturbation to the curvature
perturbation after the bounce.


  After a brief review of the motivations for grand unification, I discuss the
main challenges facing realistic SUSY GUT model building. Achieving
doublet-triplet splitting without fine--tuning is chief among them. Symmetry
breaking should occur consistently without unwanted Goldston bosons, \mu-term
of order TeV for the MSSM Higgs fileds should emerge naturally, and realistic
fermion masses with small quark mixing angles and large lepton mixing angles
should be generated with some predictivity. Significant progress has been made
over the years towards achieving these goals in the context of supersymmetric
SO(10) GUT. A complete SO(10) model is presented along this line wherein,
somewhat surprisingly, the GUT scale threshold corrections to the gauge
couplings are found to be small. This results in a predictive scenario for
proton lifetime. An interesting correlation between the d=6 (p\to e^+\pi^0) and
d=5 (p\to \nu-bar K^+) decay amplitudes is observed. This class of models
predicts that both proton decay modes should be observable with an improvement
in the current sensitivity by about a factor of five to ten.


  We report on a nanoscale quantum-sensing protocol which tracks a free
precession of a single nuclear spin and is capable of estimating an azimuthal
angle---a parameter which standard multipulse protocols cannot determine---of
the target nucleus. Our protocol combines pulsed dynamic nuclear polarization,
a phase-controlled radiofrequency pulse, and a multipulse AC sensing sequence
with a modified readout pulse. Using a single nitrogen-vacancy center as a
solid-state quantum sensor, we experimentally demonstrate this protocol on a
single 13C nuclear spin in diamond and uniquely determine the lattice site of
the target nucleus. Our result paves the way for magnetic resonance imaging at
the single-molecular level.


  One of the main tasks of Natural Language Processing (NLP), is Named Entity
Recognition (NER). It is used in many applications and also can be used as an
intermediate step for other tasks. We present ANER, a web-based named entity
recognizer for the Arabic, and Arabizi languages. The model is built upon BERT,
which is a transformer-based encoder. It can recognize 50 different entity
classes, covering various fields. We trained our model on the WikiFANE\_Gold
dataset which consists of Wikipedia articles. We achieved an F1 score of
88.7\%, which beats CAMeL Tools' F1 score of 83\% on the ANERcorp dataset,
which has only 4 classes. We also got an F1 score of 77.7\% on the
NewsFANE\_Gold dataset which contains out-of-domain data from News articles.
The system is deployed on a user-friendly web interface that accepts users'
inputs in Arabic, or Arabizi. It allows users to explore the entities in the
text by highlighting them. It can also direct users to get information about
entities through Wikipedia directly. We added the ability to do NER using our
model, or CAMeL Tools' model through our website. ANER is publicly accessible
at \url{http://www.aner.online}. We also deployed our model on HuggingFace at
https://huggingface.co/boda/ANER, to allow developers to test and use it.


  By relying on recently improved Hipparcos parallaxes for the Hyades, Pleiades
and Ursa Major clusters we find that stellar models with updated physical
inputs nicely reproduce the location in the color magnitude diagram of main
sequence stars of different metallicities. Stars in the helium burning phase
are also discussed, showing that the luminosity of giants in the Hyades,
Praesepe and Ursa Major clusters appears to be in reasonable agreement with
theoretical predictions. A short discussion concerning the current evolutionary
scenarios closes the paper.


  In this paper we give a new proof of Riemann's well known mapping theorem.
The suggested method permits to prove an analog of that theorem for the three
dimensional case.


  Multi principal element alloys (MPEAs) comprise a unique class of metal
alloys. MPEAs have been demonstrated to possess several exceptional properties,
including, as most relevant to the present study, a high corrosion resistance.
In the context of MPEA design, the vast number of potential alloying elements
and the staggering number of elemental combinations favours a computational
alloy design approach. In order to computationally assess the prospective
corrosion performance of MPEA, an approach was developed in this study. A
density functional theory (DFT) based Monte Carlo method was used for the
development of MPEA structure, with the AlCrTiV alloy used as a model.
High-throughput DFT calculations were performed to create training datasets for
surface activity towards different adsorbate species: O2-, Cl- and H+. Machine
learning (ML) with combined representation was then utilised to predict the
adsorption and vacancy energies as descriptors for surface activity. The
capability of the combined computational methods of MC, DFT and ML, as a
virtual electrochemical performance simulator for MPEAs was established and may
be useful in exploring other MPEAs.


  One of the major barriers that CMOS devices face at nanometer scale is
increasing parameter variation due to manufacturing imperfections. Process
variations severely inhibit the reliable operation of circuits, as the
operational frequency at the nominal process corner is insufficient to suppress
timing violations across the entire variability spectrum. To avoid
variability-induced timing errors, previous efforts impose pessimistic and
performance-degrading timing guardbands atop the operating frequency. In this
work, we employ approximate computing principles and propose a circuit-agnostic
automated framework for generating variability-aware approximate circuits that
eliminate process-induced timing guardbands. Variability effects are accurately
portrayed with the creation of variation-aware standard cell libraries, fully
compatible with standard EDA tools. The underlying transistors are fully
calibrated against industrial measurements from Intel 14nm FinFET in which both
electrical characteristics of transistors and variability effects are
accurately captured. In this work, we explore the design space of approximate
variability-aware designs to automatically generate circuits of reduced
variability and increased performance without the need for timing guardbands.
Experimental results show that by introducing negligible functional error of
merely $5.3\times 10^{-3}$, our variability-aware approximate circuits can be
reliably operated under process variations without sacrificing the application
performance.


  In this paper we prove the existence of infinitely many nontrivial solutions
for the class of $(p,\, q)$ fractional elliptic equations involving
concave-critical nonlinearities in bounded domains in $\mathbb{R}^N$. Further,
when the nonlinearity is of convex-critical type, we establish the multiplicity
of nonnegative solutions using variational methods. In particular, we show the
existence of at least $cat_{\Omega}(\Omega)$ nonnegative solutions.


  Motivated by recent developments in the fields of large deviations for
interacting particle system and mean field control, we establish a comparison
principle for the Hamilton--Jacobi equation corresponding to linearly
controlled gradient flows of an energy function $\cE$ defined on a metric space
$(E,d)$. Our analysis is based on a systematic use of the regularizing
properties of gradient flows in evolutional variational inequality (EVI)
formulation, that we exploit for constructing rigorous upper and lower bounds
for the formal Hamiltonian at hand and, in combination with the use of the
Tataru's distance, for establishing the key estimates needed to bound the
difference of the Hamiltonians in the proof of the comparison principle. Our
abstract results apply to a large class of examples only partially covered by
the existing theory, including gradient flows on Hilbert spaces and the
Wasserstein space equipped with a displacement convex energy functional $\cE$
satisfying McCann's condition.


  We show that a right artinian ring $R$ is right self-injective if and only if
$\psi(M)=0$ (or equivalently $\phi(M)=0$) for all finitely generated right
$R$-modules $M$, where $\psi, \phi : \mod R \to \mathbb N$ are functions
defined by Igusa and Todorov. In particular, an artin algebra $\Lambda$ is
self-injective if and only if $\phi(M)=0$ for all finitely generated right
$\Lambda$-modules $M$.


  We show that a collection of three-sorted set-theoretic formulae, denoted
TLQSR and which admits a restricted form of quantification over individual and
set variables, has a solvable satisfiability problem by proving that it enjoys
a small model property, i.e., any satisfiable TLQSR-formula psi has a finite
model whose size depends solely on the size of psi itself. We also introduce
the sublanguages (TLQSR)^h of TLQSR, whose formulae are characterized by having
quantifier prefixes of length bounded by h \geq 2 and some other syntactic
constraints, and we prove that each of them has the satisfiability problem
NP-complete. Then, we show that the modal logic S5 can be formalized in
(TLQSR)^3.


  In this paper we we will argue against the orthodox definition of quantum
entanglement which has been implicitly grounded on several widespread
(metaphysical) presuppositions which have no relation whatsoever to the
formalism of QM. We will show how these presuppositions have been introduced
through a naive interpretation of the quantum mathematical structure which
assumes dogmatically that the theory talks about "small particles" represented
by pure states (in general, superpositions) which suddenly "collapse" when a
measurement takes place. In the second part of this paper we will present a
non-collapse approach to QM which makes no use whatsoever of particle
metaphysics, escaping the need to make reference to space-time separability or
the restriction to certain predictions of definite valued binary properties.
Our paper ends up concluding the essential need to redefine the notion of
quantum entanglement, at least in the cases of: i) non-collapse interpretations
of QM; or, ii) any other interpretation which abandons the idea that QM makes
reference to "small particles".


  We consider a large number of Bosons with interaction potential $v_N(x)=N^{3
\beta}v(N^{\beta}x)$. In earlier papers we considered a set of equations for
the condensate $\phi$ and pair excitation function $k$ and proved that they
provide a Fock space approximation to the exact evolution of the condensate for
$\beta <\frac{1}{3}$. This result was extended to the case $\beta<\frac{1}{2}$
by E. Kuz, where it was also argued informally that the equations of our
earlier work do not provide an approximation for $\beta>\frac{1}{2}$. In 2013,
we introduced a coupled refinement of our original equations and conjectured
that they provide a Fock space approximation in the range $0 \le \beta < 1$. In
the current paper we prove that this is indeed the case for $\beta <
\frac{2}{3}$, at least locally in time. In order to do that, we re-formulate
the equations of \cite{GMM} in a way reminiscent of BBGKY and apply harmonic
analysis techniques in the spirit of X. Chen and J. Holmer to prove the
necessary estimates. In turn, these estimates provide bounds for the pair
excitation function $k$.


  The central equations in classical general relativity are the Einstein Field
Equations, which accurately describe not only the generation of
pseudo-Riemannian curvature by matter and radiation manifesting as
gravitational effects, but more importantly mass-energy dynamics, evolution and
distribution on the space-time manifold. Herein, we introduce a geometric phase
in general relativity corresponding to Schwarzschild black hole information
content. This quantity appropriately satisfies a local conservation law subject
to minimal coupling, with other desirable properties such as the quantization
of the black hole horizon in units of Planck area. The local conservation law
is imposed by field equations, which not only contain the trace of Einstein
Field Equations, but also a complex-valued function with properties analogous
to the quantum-mechanical wave function. Such success attests to the utility of
the proposed field equations in capturing key aspects of quantum gravity
theories.


  We study quantum noise and decoherence induced by gravitons. We derive a
Langevin equation of geodesic deviation in the presence of gravitons. The
amplitude of noise correlations tells us that large squeezing is necessary to
detect the noise. We also consider the decoherence of spatial superpositions of
two massive particles caused by gravitons in the vacuum state and find that
gravitons could give a relevant contribution to the decoherence. The
decoherence induced by gravitons would offer new vistas to test quantum gravity
in tabletop experiments.


  We analyse the topology of photospheric magnetic fields and sub-photospheric
flows of several active regions (ARs) that are observed during the peak to
descending phase of the solar cycle 23. Our analysis shows clear evidence of
hemispheric preferences in all the topological parameters such as the magnetic,
current and kinetic helicities, and the 'curl-divergence'. We found that
68\%(67\%) ARs in the northern (southern) hemisphere with negative (positive)
magnetic helicities. Same hemispheric preference sign is found for the current
helicities in 68\%(68\%) ARs. The hemispheric preferences are found to exist
statistically for all the time except in few ARs observed during the peak and
the end phases of the solar cycle. This means that magnetic fields are
dominantly left(right)-helical in scales smaller than individual ARs of
northern(southern) hemisphere. We found that magnetic and current helicities
parameters show equator-ward propagation similar to the sunspot cycle. The
kinetic helicity showed similar hemispheric trend to that of magnetic and
current helicity parameters. There are 65\%(56\%) ARs with negative (positive)
kinetic helicity as well as divergence-curl, at the depth of 2.4\,Mm, in the
northern (southern) hemisphere. The hemispheric distribution of the kinetic
helicity becomes more evident at larger depths, e.g., 69\%(67\%) at the depth
of 12.6\,Mm. Similar hemispheric trend of kinetic helicity to that of the
current helicity supports the mean field dynamo model. We also found that the
hemispheric distribution of all the parameters increases with the field
strength of ARs. The topology of photospheric magnetic fields and near surface
sub-photospheric flow fields did not show good association but the correlation
between them enhances with depths which could be indicating more aligned flows
at deeper layers of ARs.


  Commercial refrigeration systems consume 7% of the total commercial energy
consumption in the United States. Improving their energy efficiency contributes
to the sustainability of global energy systems and the supermarket business
sector. This paper proposes a new control method that can save the energy
consumption of multi-case supermarket refrigerators by explicitly taking into
account their interconnected and switched system dynamics. Its novelty is a
bilevel combinatorial optimization formulation to generate ON/OFF control
actions for expansion valves and compressors. The inner optimization module
keeps display case temperatures in a desirable range and the outer optimization
module minimizes energy consumption. In addition to its energy-saving
capability, the proposed controller significantly reduces the frequency of
compressor switchings by employing a conservative compressor control strategy.
However, solving this bilevel optimization problem associated with
interconnected and switched systems is a computationally challenging task. To
solve the problem in near real time, we propose two approximation algorithms
that can solve both the inner and outer optimization problems at once. The
first algorithm uses a linear approximation, and the second is based on the
submodular structure of the optimization problem. Both are (polynomial-time)
scalable algorithms and generate near-optimal solutions with performance
guarantees. Our work complements existing optimization-based control methods
(e.g., MPC) for supermarket refrigerators, as our algorithms can be adopted as
a tool for solving combinatorial optimization problems arising in these
methods.


  Through the direct study of the analysis estimator we derive oracle
inequalities with fast and slow rates by adapting the arguments involving
projections by Dalalyan, Hebiri and Lederer (2017). We then extend the theory
to the square root analysis estimator. Finally, we focus on (square root) total
variation regularized estimators on graphs and obtain constant-friendly rates,
which, up to log-terms, match previous results obtained by entropy
calculations. We also obtain an oracle inequality for the (square root) total
variation regularized estimator over the cycle graph.


  Optimal quasiconformal dimension distortions bounds for subsets of the
complex plane have been established by Astala. We show that these estimates can
be improved when one considers subsets of the real line of arbitrary Hausdorff
dimension. We present some explicit numerical bounds.


  We show that the sum of the Morse indices of the Willmore spheres realising
the width of Willmore type sweep-outs is bounded by the number of the
parameters of the min-max. As an application, we deduce that among the true
Willmore spheres realising the min-max sphere eversion, at most one of them one
has index 1, while the others must be stable.