  We investigate the condensate wave function and elementary excitations of
strongly interacting bosonic polar molecules in a harmonic trap, treating the
scattering amplitude beyond the standard first Born approximation (FBA). By
using an appropriate trial wave function in the variational method, effects of
the leading order correction beyond the FBA have been investigated and shown to
be significantly enhanced when the system is close to the phase boundary of
collapse. How such leading order effect of going beyond the FBA can be observed
in a realistic experiment is also discussed.


  We introduce a new distributional invariance principle, called `partial
spreadability', which emerges from the representation theory of the Thompson
monoid $F^+$ in noncommutative probability spaces. We show that a partially
spreadable sequence of noncommutative random variables is adapted to a local
Markov filtration. Conversely we show that a large class of noncommutative
stationary Markov sequences provides representations of the Thompson monoid
$F^+$. In the particular case of a classical probability space, we arrive at a
de Finetti theorem for stationary Markov sequences with values in a standard
Borel space.


  We describe effects of anisotropy caused by the crystal lattice in d-wave
superconductors with s-wave mixing using the effective free energy approach.
Only the d-wave order parameter field $d$ is introduced, while the effect of
the s wave mixing as well as other effects breaking the rotational symmetry
down to the fourfold symmetry of the crystal are represented by a single four
(covariant) derivative term: $\eta d^{*}(\Pi _{y}^{2}-\Pi_{x}^{2})^{2}d $. The
single vortex solution in a phenomenologically interesting range of parameters
is almost identical to the two order parameters approach. We analytically
consider the most general oblique lattice and orientation, but find that only
rectangular body centered lattices are realized. A critical value $\eta _{c} $
at which a phase transition from the rectangular lattice to the square lattice
takes place. The influence on the phase transition line is discussed. The
formalism is extended to the time dependent anisotropic Ginzburg-Landau
equations in order to calculate the effect of the anisotropy on the flux flow.
The moving vortex structure is established and the magnetization as function of
the current is calculated. Although the linear conductivity tensor is
rotationally invariant due to the fourfold symmetry, the nonlinear one shows
anisotropy. We calculate dependence of both direct and Hall I-V curves on the
angle between the current and the crystal lattice orientation.


  We investigate the structure and the nonlinear dynamics of two rigid polar
rotors coupled through the dipole-dipole interaction in an external homogeneous
electric field. In the field-free stable head-tail configuration, an excess
energy is provided to one of the dipoles, and we explore the resulting
three-dimensional classical dynamics. This dynamics is characterized in terms
of the kinetic energy transfer between the dipoles, their orientation along the
electric field, as well as their chaotic behavior.
  The field-free energy transfer mechanism shows an abrupt transition between
equipartition and non-equipartition regimes, which
  is independent of the initial direction of rotation due to the existence of
an infinite set of equivalent manifolds. The field-dressed dynamics is highly
complex and strongly depends on the electric field strength and on the initial
conditions. In the strong field regime, the energy equipartition and chaotic
behavior dominate the dynamics.


  In this paper, we propose two families of nonconforming finite elements on
$n$-rectangle meshes of any dimension to solve the sixth-order elliptic
equations. The unisolvent property and the approximation ability of the new
finite element spaces are established. A new mechanism, called the exchange of
sub-rectangles, for investigating the weak continuities of the proposed
elements is discovered. With the help of some conforming relatives for the
$H^3$ problems, we establish the quasi-optimal error estimate for the
tri-harmonic equation in the broken $H^3$ norm of any dimension. The
theoretical results are validated further by the numerical tests in both 2D and
3D situations.


  The one-loop effective action corresponding the general model of dilaton
gravity given by the Lagrangian $L=-\sqrt{g} \left[ \frac{1}{2}Z(\Phi )
g^{\mu\nu} \partial_\mu \Phi \partial_\nu \Phi + C(\Phi ) R + V (\Phi
)\right]$, where $Z(\Phi )$, $ C(\Phi )$ and $V (\Phi )$ are arbitrary
functions of the dilaton field, is found. The question of the quantum
equivalence of classically equivalent dilaton gravities is studied. By specific
calculation of explicit examples it is shown that classically equivalent
quantum gravities are also perturbatively equivalent at the quantum level, but
only on-shell. The renormalization group equations for the generalized
effective couplings $Z(\Phi )$, $ C(\Phi )$ and $V (\Phi )$ are written. An
analysis of the equations shows, in particular, that the
Callan-Giddings-Harvey-Strominger model is not a fixed point of these
equations.


  We discuss the procedure to resum large logarithms to all orders for DIS
event shape variable distributions.
  Results are described for two variants of the thrust variable, both defined
wrt the boson axis in the current hemisphere of the Breit frame, but with
different normalisations.


  We experimentally study the behavior of orbital angular momentum (OAM) of
light in a noncollinear second harmonic generation (SHG) process. The
experiment is performed by using a type I BBO crystal under phase matching
conditions with femtosecond pumping fields at 830 nm. Two specular off-axis
vortex beams carrying fractional orbital angular momentum at the fundamental
frequency (FF) are used. We analyze the behavior of the OAM of the SH signal
when the optical vortex of each input field at the FF is displaced from the
beam's axis. We obtain different spatial configurations of the SH field, always
carrying the same zero angular momentum.


  Singularly perturbed dynamical systems, commonly known as fast-slow systems,
play a crucial role in various applications such as plasma physics. They are
closely related to reduced order modeling, closures, and structure-preserving
numerical algorithms for multiscale modeling. A powerful and well-known tool to
address these systems is the Fenichel normal form, which significantly
simplifies fast dynamics near slow manifolds through a transformation. However,
the Fenichel normal form is difficult to realize in conventional numerical
algorithms. In this work, we explore an alternative way of realizing it through
structure-preserving machine learning. Specifically, a fast-slow neural network
(FSNN) is proposed for learning data-driven models of singularly perturbed
dynamical systems with dissipative fast timescale dynamics. Our method enforces
the existence of a trainable, attracting invariant slow manifold as a hard
constraint. Closed-form representation of the slow manifold enables efficient
integration on the slow time scale and significantly improves prediction
accuracy beyond the training data. We demonstrate the FSNN on several examples
that exhibit multiple timescales, including the Grad moment system from
hydrodynamics, two-scale Lorentz96 equations for modeling atmospheric dynamics,
and Abraham-Lorentz dynamics modeling radiation reaction of electrons in a
magnetic field.


  The layer dependent structural, electronic and vibrational properties of SnS2
and SnSe2 are investigated using first-principles density functional theory
(DFT). The in-plane lattice constants, interlayer distances and binding
energies are found to be layer-independent. Bulk SnS2 and SnSe2 are both
indirect band gap semiconductors with Eg = 2.18 eV and 1.07 eV, respectively.
Few-layer and monolayer 2D systems also possess an indirect band gap, which is
increased to 2.41 eV and 1.69 eV for single layers of SnS2 and SnSe2. The
effective mass theory of 2D excitons, which takes into account the combined
effect of the anisotropy, non-local 2D screening and layer-dependent 3D
screening, predicts strong excitonic effects. The binding energy of indirect
excitons in monolayer samples, Ex~0.9 eV, is substantially reduced to Ex = 0.14
eV in bulk SnS2 and Ex = 0.09 eV in bulk SnSe2. The layer-dependent Raman
spectra display a strong decrease of intensities of the Raman active A1g mode
upon decreasing the number of layers down to a monolayer, by a factor of 7 in
the case of SnS2 and a factor of 20 in the case of SnSe2 which can be used to
identify number of layers in a 2D sample.


  Using angle-resolved photoelectron spectroscopy (ARPES), we investigate the
surface electronic structure of the magnetic van der Waals compounds
MnBi$_4$Te$_7$ and MnBi$_6$Te$_{10}$, the $n=$~1 and 2 members of a modular
(Bi$_2$Te$_3$)$_n$(MnBi$_2$Te$_4$) series, which have attracted recent interest
as intrinsic magnetic topological insulators. Combining circular dichroic,
spin-resolved and photon-energy-dependent ARPES measurements with calculations
based on density functional theory, we unveil complex momentum-dependent
orbital and spin textures in the surface electronic structure and disentangle
topological from trivial surface bands. We find that the Dirac-cone dispersion
of the topologial surface state is strongly perturbed by hybridization with
valence-band states for Bi$_2$Te$_3$-terminated surfaces but remains preserved
for MnBi$_2$Te$_4$-terminated surfaces. Our results firmly establish the
topologically non-trivial nature of these magnetic van der Waals materials and
indicate that the possibility of realizing a quantized anomalous Hall
conductivity depends on surface termination.


  We study the effect of correlation on the direction of particle exchange
between local thermal sub-systems where the total system is isolated. Our focus
is the situation where both sub-systems have the same temperature but different
chemical potentials to eliminate the effect of energy transfer due to the
temperature difference. The analysis is done in two limits; in the short time
scale where the final state of each sub-system is close to its initial thermal
state and in a longer time scale where each sub-system's final state can be
arbitrary. The results indicate that the conventional flow of particles from a
higher chemical potential to a lower one occurs when the correlation which is
quantified by mutual information increases. In contrast, an anomalous flow of
particles in the reverse direction has a chance to happen when the correlation
goes down. Our findings show that the direction of the particle exchange cannot
be predetermined by the chemical potential difference in the presence of
correlation.


  In this paper, we study scenarios of the super-Eddington accretion onto black
holes at high redshifts $z > 10$, which are expected to be seeds to evolve to
supermassive black holes until redshift $z \sim 7$. For an initial mass,
$M_{\rm BH, ini} \lesssim 2 \times 10^{3} M_{\odot}$ of a seed BH, we
definitely need the super-Eddington accretion, which can be applicable to both
astrophysical and primordial origins. Such an accretion disk inevitably emitted
high-energy photons which had heated the cosmological plasma of the
inter-galactic medium continuously from high redshifts. In this case, the
cosmic history of cosmological gas temperature is modified, by which the
absorption feature of the cosmological 21 cm lines is suppressed. By comparing
theoretical predictions of the 21cm line absorption with the observational data
at $z\sim17$, we obtain a cosmological upper bound on the mass-accretion rate
as a function of the seed BH masses. In order to realize $M_{\rm BH} \sim 10^9
M_{\odot}$ at $z \sim 7$ by a continuous mass-accretion on to a seed BH, to be
consistent with the cosmological 21cm line absorption at $z \sim 17$, we
obtained an severe upper bound on the initial mass of the seed BH to be $M_{\rm
BH, ini} \lesssim 10^2 M_{\odot}$ ($M_{\rm BH, ini} \lesssim 10^6 M_{\odot}$)
when we assume a seed BH with its comoving number density $n_{\rm seed,0} \sim
10^{-3} {\rm Mpc}^{-3}$ ($n_{\rm seed,0} \sim 10^{-7} {\rm Mpc}^{-3}$). We also
discuss some implications for application to primordial black holes as the seed
black holes.


  We study the global existence and regularity of solutions for a system
describing the evolution of a nematic liquid crystal fluid. The fluid is
described by a system that couples a forced Navier-Stokes system with a
parabolic-type system. In our previous work, \cite{pz1}, we assumed that a
certain parameter, $\xi$, is zero, which had the effect of cancelling certain
terms. In the current work we do not make this assumption and study the full
system, observing that the presence of these additional terms has a non-trivial
effect, namely the quadruply exponential increase of the high norms. We also
estimate differently certain terms already existent in the simplified system
and improve the estimates in \cite{pz1}. We prove the existence of global weak
solutions in dimensions two and three. In dimension two we prove the higher
regularity of solutions and show that the high norms increase in time at most
quadruply exponential. We also show the weak-strong uniqueness in dimension
two.


  The three dimensional rotation group, SO(3), is a symmetry group of the
normal hydrogen atom. Each reducible representation of this group can be
associated with a degenerate energy level. If this atom is placed in an
external magnetic field, the interaction between the orbital magnetic moment
with this field will lead to a symmetry breaking where the symmetry group of
the atom is a new group distinct from the SO(3) group. This phenomenon
describes the normal Zeeman effect, where a degenerate energy level splits into
several new energy levels. It is explicitly shown that each of the new energy
levels can be associated with an irreducible representation of the new symmetry
group.


  Uranium and thorium within the Earth produce a major portion of terrestrial
heat along with a measurable flux of electron antineutrinos. These elements are
key components in geophysical and geochemical models. Their quantity and
distribution drive the dynamics, define the thermal history, and are a
consequence of the differentiation of the Earth. Knowledge of uranium and
thorium concentrations in geological reservoirs relies largely on geochemical
model calculations. This research report describes the methods and criteria to
experimentally determine average concentrations of uranium and thorium in the
continental crust and in the mantle using site-specific measurements of the
terrestrial antineutrino flux. Optimal, model-independent determinations
involve significant exposures of antineutrino detectors remote from nuclear
reactors at both a mid-continental and a mid-oceanic site. This would require
major, new antineutrino detection projects. The results of such projects could
yield a greatly improved understanding of the deep interior of the Earth.


  The objective of this work is to analyze the usefulness to transform the
information to measure sports performance. This analysis is carried out within
the field of basketball due to the existing tradition in this sport in data
collection, although it is easily adaptable to any other sport. As a result, a
modification of the Performance Index Rating (PIR) is proposed to measure
sports performance. The results obtained are illustrated from the statistics of
Larry Bird, Earvin Johnson, Michael Jordan and Kobe Bryant throughout their
careers and can serve to optimize the process of player renewal/firing/hiring
in the design of a roster or to aid decision-making in awarding individual
awards as best player of a season.


  A neural net model for forecasting the prices of Venezuelan crude oil is
proposed. The inputs of the neural net are selected by reference to a dynamic
system model of oil prices by Mashayekhi (1995, 2001) and its performance is
evaluated using two criteria: the Excess Profitability test by Anatoliev and
Gerko (2005) and the characteristics of the equity curve generated by a trading
strategy based on the neural net predictions.
  -----
  Se introduce aqui un modelo no parametrico para pronosticar los precios del
petroleo Venezolano cuyos insumos son seleccionados en base a un sistema
dinamico que explica los precios en terminos de dichos insumos. Se describe el
proceso de recoleccion y pre-procesamiento de datos y la corrida de la red y se
evaluan sus pronosticos a traves de un test estadistico de predictibilidad y de
las caracteristicas del Equity Curve inducido por la estrategia de compraventa
bursatil generada por dichos pronosticos.


  We study the homogeneous equation (*) $ u' = \Delta u$, $t > 0$, $u(0)=f\in
wX$, where $wX$ is a weighted Banach space, $w(x)= (1+||x||)^k$, $x\in \r^n$
with $k\ge 0$, $ \Delta$ is the Laplacian, $Y$ a complex Banach space and $X$
one of the spaces $ BUC (\r^n,Y)\} $, $ C_0 (\r^n,Y)$, $ L^p (\r^n,Y)$, $1 \le
p < \infty$. It is shown that the mild solutions of (*) are still given by the
classical Gauss-Poisson formula, a holomorphic $C_0$-semigroup.


  We consider extra dimensional descriptions of models where there are two
separate strongly interacting sectors contributing to electroweak symmetry
breaking (``topcolor'' type models). In the extra dimensional picture there
would be two separate (anti-de Sitter) bulks meeting on the Planck brane, with
each bulk having its own corresponding IR (TeV) brane. Sources for electroweak
symmetry breaking can then be localized on both of these IR branes, while the
different generations of fermions may be separated from each other. We describe
the modes propagating in such a setup, and consider the cases where the
electroweak symmetry breaking on either of the two IR branes come either from a
higgsless scenario (via boundary conditions) or a (top-)Higgs. We show that the
tension that exists between obtaining a large top quark mass and the correct
value of the Zb\bar{b} couplings in ordinary higgsless models can be largely
relieved in the higgsless--top-Higgs versions of the two IR brane models. This
may also be true in the purely higgsless--higgsless case, however since that
model is necessarily in the strongly coupled regime the tree-level results for
the properties of the third generation may get large corrections. A necessary
consequence of such models is the appearance of additional pseudo-Goldstone
bosons (``top-pions''), which would be strongly coupled to the third
generation.


  We study transient work Fluctuation Relations (FRs) for Gaussian stochastic
systems generating anomalous diffusion. For this purpose we use a Langevin
approach by employing two different types of additive noise: (i) internal noise
where the Fluctuation-Dissipation Relation of the second kind (FDR II) holds,
and (ii) external noise without FDR II. For internal noise we demonstrate that
the existence of FDR II implies the existence of the Fluctuation-Dissipation
Relation of the first kind (FDR I), which in turn leads to conventional
(normal) forms of transient work FRs. For systems driven by external noise we
obtain violations of normal FRs, which we call anomalous FRs. We derive them in
the long-time limit and demonstrate the existence of logarithmic factors in FRs
for intermediate times. We also outline possible experimental verifications.


  A novel equation of state used for analysis of the heavy ion collision
experimental data is generalized to also describe the matter inside neutron
stars. This approach differs from others by including an induced surface
tension caused by the short range repulsion between particles accounted by
presence of their hard cores. This new equation of state respects thermodynamic
consistency and is free from the usual causality problems. This makes it
applicable over a wide range of temperatures and baryon densities, including
the ones inside neutron stars. Despite small number of parameters the present
equation of state reproduces properties of the saturated nuclear matter and is
consistent with the proton flow constraint as well as with astrophysical data
obtained from neutron star observations. Accordingly, we found the sets of
parameters that agree with the same ones obtained from the heavy ion collision
data analysis.


  Recently evidence has emerged for enormous features in the gamma-ray sky
observed by the Fermi-LAT instrument: bilateral `bubbles' of emission centered
on the core of the Galaxy and extending to around 10 kpc above and below the
Galactic plane. These structures are coincident with a non-thermal microwave
`haze' found in WMAP data and an extended region of X-ray emission detected by
ROSAT. The bubbles' gamma-ray emission is characterised by a hard and
relatively uniform spectrum, relatively uniform intensity, and an overall
luminosity ~4 x 10^37 erg/s, around one order of magnitude larger than their
microwave luminosity while more than order of magnitude less than their X-ray
luminosity. Here we show that the bubbles are naturally explained as due to a
population of relic cosmic ray protons and heavier ions injected by processes
associated with extremely long timescale (>~8 Gyr) and high areal density
star-formation in the Galactic center.


  Caching of popular content closer to the mobile user can significantly
increase overall user experience as well as network efficiency by decongesting
backbone network segments in the case of congestion episodes. In order to find
the optimal caching locations, many conventional approaches rely on solving a
complex optimization problem that suffers from the curse of dimensionality,
which may fail to support online decision making. In this paper we propose a
framework to amalgamate model based optimization with data driven techniques by
transforming an optimization problem to a grayscale image and train a
convolutional neural network (CNN) to predict optimal caching location
policies. The rationale for the proposed modelling comes from CNN's superiority
to capture features in grayscale images reaching human level performance in
image recognition problems. The CNN is trained with optimal solutions and
numerical investigations reveal that the performance can increase by more than
400% compared to powerful randomized greedy algorithms. To this end, the
proposed technique seems as a promising way forward to the holy grail aspect in
resource orchestration which is providing high quality decision making in real
time.


  Rich out of equilibrium collective dynamics of strongly interacting large
assemblies emerge in many areas of science. Some intriguing and not fully
understood examples are the glassy arrest in atomic, molecular or colloidal
systems, flocking in natural or artificial active matter, and the organization
and subsistence of ecosystems. The learning process, and ensuing amazing
performance, of deep neural networks bears resemblance with some of the
before-mentioned examples. Quantum mechanical extensions are also of interest.
In exact or approximate manner the evolution of these systems can be expressed
in terms of a dynamical mean-field theory which not only captures many of their
peculiar effects but also has predictive power. This short review presents a
summary of recent developments of this approach with emphasis on applications
on the examples mentioned above.


  Current satellite precipitation retrievals like GPROF assume that brightness
temperature is sufficient to constrain rainfall. This information, however,
often represents multiple rain states, resulting in rainfall estimate
uncertainties. These uncertainties, while dominated by random variability, can
also exhibit substantial regional biases, complicating the use of traditional
ground validation techniques which seek to understand these uncertainties. This
study aims to characterize the physical contributors to these biases for use in
uncertainty quantification. To do this, coincident GPROF Version 7, GMI, and
GPM Combined observations were examined over three tropical land regions, the
Amazon, Congo, and Southeast Asia, which are known to exhibit distinct biases
relative to one another when comparing GPROF with GPM Combined. Rain intensity
and ice-rain ratio were identified as the primary sources of GPROF regional
biases. By incorporating the information from these sources, the
self-similarity between these three regions was brought from within 13 percent
to within 7 percent, reducing the interregional bias by half. Including a third
constraint based on the polarization-corrected 37-GHz brightness temperature
further improved this self-similarity to within 4 percent by accounting for
second-order hydrometeor profile differences which were underutilized by GPROF.
Comparing the effects of these three constraints between GPROF Version 7 with
the 1D version of GPROF-NN showed similar improvements, indicating the utility
of this uncertainty quantification and adjustment method across precipitation
products. With these constraints, regional GPROF biases can be made more
consistent, improving the fidelity of the precipitation climate data records
and operational precipitation products which utilize this information.


  It is shown that quantum logic is a logic in the very same way in which
classical logic is a logic. Soundness and completeness of both quantum and
classical logics have been proved for novel lattice models that are not
orthomodular and therefore cannot be distributive either - as opposed to the
standard lattice models that are orthomodular and distributive for the
respective logics. Hence, we cannot attribute the orthomodularity to quantum
logic itself, and we cannot attribute the distributivity to classical logic
itself. The valuations of logics with respect of novel models turn out to be
non-numerical, and therefore truth values and truth tables cannot in general be
ascribed to the propositions of logics themselves but only to the variables of
some of their models -for example, the two-valued Boolean algebra. Logics are,
first of all, axiomatic deductive systems, and if we stop short of considering
their semantics (models, valuations, etc.), then both quantum and classical
logics will have a completely equal footing in the sense of being two deductive
systems that differ from each other in a few axioms and nothing else. There is
no ground for considering either of the two logics more "proper" than the
other. Semantics of these logics belong to their models, and we show that there
are bigger differences between the two aforementioned classical models than
between two corresponding quantum and classical models.


  Decision making in uncertain and risky environments is a prominent area of
research. Standard economic theories fail to fully explain human behaviour,
while a potentially promising alternative may lie in the direction of
Reinforcement Learning (RL) theory. We analyse data for 46 players extracted
from a financial market online game and test whether Reinforcement Learning
(Q-Learning) could capture these players behaviour using a risk measure based
on financial modeling. Moreover we test an earlier hypothesis that players are
"na\"ive" (short-sighted). Our results indicate that a simple Reinforcement
Learning model which considers only the selling component of the task captures
the decision-making process for a subset of players but this is not sufficient
to draw any conclusion on the population. We also find that there is not a
significant improvement of fitting of the players when using a full RL model
against a myopic version, where only immediate reward is valued by the players.
This indicates that players, if using a Reinforcement Learning approach, do so
na\"ively


  We briefly summarize the BRITE observations of classical Cepheids. Possible
detection of modulation in a fundamental mode Cepheid, T Vul, and of additional
non-radial modes in first overtone Cepheids, DT Cyg and V1334 Cyg, are
reported.


  We review some properties of quasi-one-dimensional organic conductors, such
as the Bechgaard salts, with an emphasis on aspects related to the crossovers
between a Mott insulating state to a metallic state, and crossovers between
different metallic behaviors. We discuss why a theoretical description of these
issues is a particularly challenging problem, and describe a recent
non-perturbative approach designed to deal with systems of coupled chains. This
method, dubbed "chain-DMFT", is a generalization of dynamical mean field theory
that treats both, one-dimensional and higher dimensional physics, in a unified
manner. We present numerical results for a system of coupled Hubbard chains.
Chain-DMFT indeed captures the metal-insulator transition and the dimensional
crossover from a high temperature Luttinger liquid to a low temperature Fermi
liquid phase, and allows to access the properties of these phases. Based on
these results perspectives for a theoretical understanding of the physics of
the Bechgaard salts are discussed.


  A sequence of pure-hydrogen CO5BOLD 3D model atmospheres of DA white dwarfs
is presented for a surface gravity of log g = 8 and effective temperatures from
6000 to 13,000 K. We show that convective properties, such as flow velocities,
characteristic granulation size and intensity contrast of the granulation
patterns, change significantly over this range. We demonstrate that these 3D
simulations are not sensitive to numerical parameters unlike the 1D structures
that considerably depend on the mixing-length parameters. We conclude that 3D
spectra can be used directly in the spectroscopic analyses of DA white dwarfs.
We confirm the result of an earlier preliminary study that 3D model spectra
provide a much better characterization of the mass distribution of white dwarfs
and that shortcomings of the 1D mixing-length theory are responsible for the
spurious high-log g determinations of cool white dwarfs. In particular, the 1D
theory is unable to account for the cooling effect of the convective overshoot
in the upper atmospheres.


  In a recent paper [arXiv:1506.06649 [nlin.CG]], we presented an example of a
3-state cellular automaton which exhibits behaviour analogous to degenerate
hyperbolicity often observed in finite-dimensional dynamical systems. We also
calculated densities of 0, 1 and 2 after n iterations of this rule, using
finite state machines to conjecture patterns present in preimage sets. Here, we
re-derive the same formulae in a rigorous way, without resorting to any
semi-empirical methods. This is done by analysing the behaviour of continuous
clusters of symbols and by considering their interactions.


  Momentum distributions of particles from fast three-body halo fragmentation
reactions with polarized beams and outgoing fragments are analyzed by use of
the sudden approximation. The final state interaction between the two
non-disturbed particles is considered. We first give a general and detailed
description of the method. We introduce observable quantities that emphasize
the two-body correlations in the initial three-body structure as well as in the
final two-body system. Using neutron removal from 11Li as an example we
investigate the dependence of the polarization observables on the properties of
the low-lying resonances and virtual states of the 10Li subsystem. These
observables are very sensitive to the l > 0-waves in the wave functions, and
they provide detailed information on the resonance structure of the
neutron-core subsystem.


  We study qualitative and quantitative properties of local weak solutions of
the fast $p$-Laplacian equation, $\partial_t u=\Delta_{p}u$, with $1<p<2$. Our
main results are quantitative positivity and boundedness estimates for locally
defined solutions in domains of $\RR^n\times [0,T]$. We combine these lower and
upper bounds in different forms of intrinsic Harnack inequalities, which are
new in the very fast diffusion range, that is when $1<p \le 2n/(n+1)$. The
boundedness results may be also extended to the limit case $p=1$, while the
positivity estimates cannot.
  We prove the existence as well as sharp asymptotic estimates for the
so-called large solutions for any $1<p<2$, and point out their main properties.
  We also prove a new local energy inequality for suitable norms of the
gradients of the solutions. As a consequence, we prove that bounded local weak
solutions are indeed local strong solutions, more precisely $\partial_t u\in
L^2_{\rm loc}$.


  We study stability conditions on the Calabi-Yau-$N$ categories associated to
an affine type $A_n$ quiver which can be constructed from certain meromorphic
quadratic differentials with zeroes of order $N-2$. We follow Ikeda's work to
show that this moduli space of quadratic differentials is isomorphic to the
space of stability conditions quotient by the spherical subgroup of the
autoequivalence group. We show that the spherical subgroup is isomorphic to the
braid group of affine type $A$ based on Khovanov-Seidel-Thomas method.


  A key building block in the design of ultra-reliable communication systems is
a wireless channel model that captures the statistics of rare events occurring
due to significant fading. In this paper, we propose a novel methodology based
on extreme value theory (EVT) to statistically model the behavior of extreme
events in a wireless channel for ultra-reliable communication. This methodology
includes techniques for fitting the lower tail distribution of the received
power to the generalized Pareto distribution (GPD), determining the optimum
threshold over which the tail statistics are derived, ascertaining the optimum
stopping condition on the number of samples required to estimate the tail
statistics by using GPD, and finally, assessing the validity of the derived
Pareto model. Based on the data collected within the engine compartment of Fiat
Linea under various engine vibrations and driving scenarios, we demonstrate
that the proposed methodology provides the best fit to the collected data,
significantly outperforming the conventional extrapolation-based methods.
Moreover, the usage of the EVT in the proposed method decreases the required
number of samples for estimating the tail statistics by about $7 \times 10^5$.


  Phase transition in spherically symmetric collapse of a massless scalar field
is studied in 4-d Einstein gravity. A class of exact solutions that show the
evolution of a constant incoming energy flux turned on at a point in the past
null infinity are constructed to serve as an explicit example. The recently
discovered phase transition in this system via numerical methods
\cite{choptuik} is manifest; above a threshold value of the incooming energy
flux, a black hole is dynamically formed and below that, the incoming flux is
reflected forward into the future null infinity. The critical exponent is
evaluated and discussed using the solutions.


  In this paper we prove the existence of a positive solution to the equation
$-\Delta u + V(x)u=g(u)$ in $R^N,$ assuming the general hypotheses on the
nonlinearity introduced by Berestycki & Lions. Moreover we show that a
minimizing problem, related to the existence of a ground state, has no
solution.


  When building a new application we are increasingly confronted with the need
of reusing and integrating pre-existing knowledge. Nevertheless, it is a fact
that this prior knowledge is virtually impossible to reuse as-is. This is true
also in domains, e.g., eHealth, where a lot of effort has been put into
developing high-quality standards and reference ontologies, e.g. FHIR1. In this
paper, we propose an integrated methodology, called iTelos, which enables data
and knowledge reuse towards the construction of Interoperable Electronic Health
Records (iEHR). The key intuition is that the data level and the schema level
of an application should be developed independently, thus allowing for maximum
flexibility in the reuse of the prior knowledge, but under the overall guidance
of the needs to be satisfied, formalized as competence queries. This intuition
is implemented by codifying all the requirements, including those concerning
reuse, as part of a purpose defined a priori, which is then used to drive a
middle-out development process where the application schema and data are
continuously aligned. The proposed methodology is validated through its
application to a large-scale case study.


  Spaces where each element describes a shape, so-called shape spaces, are of
particular interest in shape optimization and its applications. Theory and
algorithms in shape optimization are often based on techniques from
differential geometry. Challenges arise when an application demands a
non-smooth shape, which is commonly-encountered as an optimal shape for
fluid-mechanical problems. In order to avoid the restriction to
infinitely-smooth shapes of a commonly-used shape space, we construct a space
containing shapes in $\mathbb{R}^2$ that can be identified with a Riemannian
product manifold but at the same time admits piecewise-smooth curves as
elements. We combine the new product manifold with an approach for optimizing
multiple non-intersecting shapes. For the newly-defined shapes, adjustments are
made in the known shape optimization definitions and algorithms to ensure their
usability in applications. Numerical results regarding a fluid-mechanical
problem constrained by the Navier-Stokes equations, where the viscous energy
dissipation is minimized, show its applicability.


  External forces acting on a microswimmer can feed back on its self-propulsion
mechanism. We discuss this load response for a generic microswimmer that swims
by cyclic shape changes. We show that the change in cycle frequency is
proportional to the Lighthill efficiency of self-propulsion. As a specific
example, we consider Najafi's three-sphere swimmer. The force-velocity relation
of a microswimmer implies a correction for a formal superposition principle for
active and passive motion.


  We present BeppoSAX and XMM-Newton observations of MKN 231. These
observations and in particular the BeppoSAX PDS data allowed us to unveil, for
the first time, the highly absorbed (N$_H\sim 2\times10^{24}$ cm$^{-2}$) AGN
component. We find that: a) the AGN powering MKN231 has an intrinsic 2-10 keV
luminosity of $1^{+1}_{-0.5}\times 10^{44}$ erg/s; b) the strong starburst
activity contributes significantly in the 0.1-10 keV energy range. We propose
that the starburst activity strongly contributes to the far infrared luminosity
of MKN 231; this is also suggested by the multiwavelength properties of MKN
231.


  Research on crowdfunding success that incorporates CATA (computer-aided text
analysis) is quickly advancing to the big leagues (e.g., Parhankangas and
Renko, 2017; Anglin et al., 2018; Moss et al., 2018) and is often theoretically
based on information asymmetry, social capital, signaling or a combination
thereof. Yet, current papers that explore crowdfunding success criteria fail to
take advantage of the full breadth of signals available and only very few such
papers examine technology projects. In this paper, we compare and contrast the
strength of the entrepreneur's textual success signals to project backers
within this category. Based on a random sample of 1,049 technology projects
collected from Kickstarter, we evaluate textual information not only from
project titles and descriptions but also from video subtitles. We find that
incorporating subtitle information increases the variance explained by the
respective models and therefore their predictive capability for funding
success. By expanding the information landscape, our work advances the field
and paves the way for more fine-grained studies of success signals in
crowdfunding and therefore for an improved understanding of investor
decision-making in the crowd.


  Many physical and biological processes are stochastic in nature.
Computational models and simulations of such processes are a mathematical and
computational challenge. The basic stochastic simulation algorithm was
published by D. Gillespie about three decades ago [D.T. Gillespie, J. Phys.
Chem. {\bf 81}, 2340, (1977)]. Since then, intensive work has been done to make
the algorithm more efficient in terms of running time. All accelerated versions
of the algorithm are aimed at minimizing the running time required to produce a
stochastic trajectory in state space. In these simulations, a necessary
condition for reliable statistics is averaging over a large number of
simulations. In this study I present a new accelerating approach which does not
alter the stochastic algorithm, but reduces the number of required runs. By
analysis of collected data I demonstrate high precision levels with fewer
simulations. Moreover, the suggested approach provides a good estimation of
statistical error, which may serve as a tool for determining the number of
required runs.


  Aspect-oriented software development builds upon object-oriented development
by offering additional abstraction boundaries that help us separate different
types of requirements into so-called aspects. Given a legacy OO application, it
pays to identify existing aspects to help understand the structure of the
application and potentially to extract those aspects into separate software
modules that can be maintained and reused individually. We present an approach
to extract functional aspects using program slicing. We first characterize what
we mean by functional aspect, and explore the extent to which program slicing
techniques could improve over existing aspect mining and feature location
methods for such aspects. We then describe the results of applying our approach
to two medium-sized open source programs. Our preliminary results show that
program slicing can yield well-defined functional aspects when the appropriate
slicing criteria are used. Finally, we explore the effect of design quality on
the candidate functional aspects.


  This work describes the development and real-world deployment of a deep
learning-based AI system for evaluating canine and feline radiographs across a
broad range of findings and abnormalities. We describe a new semi-supervised
learning approach that combines NLP-derived labels with self-supervised
training leveraging more than 2.5 million x-ray images. Finally we describe the
clinical deployment of the model including system architecture, real-time
performance evaluation and data drift detection.


  In the context of the IRAM 30m Large Program GEMS, we present a study of
thioformaldehyde in several starless cores located in star-forming filaments of
Taurus, Perseus, and Orion. We investigate the influence of the environmental
conditions on the abundances of these molecules in the cores, and the effect of
time evolution. We have modelled the observed lines of H2CS, HDCS, and D2CS
using the radiative transfer code RADEX. We have also used the chemical code
Nautilus to model the evolution of these species depending on the
characteristics of the starless cores. We derive column densities and
abundances for all the cores. We also derive deuterium fractionation ratios,
Dfrac, to determine and compare the evolutionary stage between different parts
of each star-forming region. Our results indicate that the north region of the
B213 filament in Taurus is more evolved than the south, while the north-eastern
part of Perseus presents an earlier evolutionary stage than the south-western
zone. Model results also show that Dfrac decreases with the cosmic-ray
ionisation rate, while it increases with density and with the degree of sulphur
depletion. In particular, we only reproduce the observations when the initial
sulphur abundance in the starless cores is at least one order of magnitude
lower than the solar elemental sulphur abundance. The progressive increase in
HDCS/H2CS and D2CS/H2CS with time makes these ratios powerful tools for
deriving the chemical evolutionary stage of starless cores. However, they
cannot be used to derive the temperature of these regions, since both ratios
present a similar evolution at two different temperature ranges (7-11 K and
15-19 K). Regarding chemistry, (deuterated) thioformaldehyde is mainly formed
through gas-phase reactions (double-replacement and neutral-neutral
displacement reactions), while surface chemistry plays an important role as a
destruction mechanism.


  When analysing data from air-shower arrays, it has become common practice to
use the signal at a considerable distance from the shower axis ($r_\text{opt}$)
as a surrogate for the size of the shower. This signal, $S(r_\text{opt}$), can
then be related to the primary energy in a variety of ways. After a brief
review of the reasons behind the introduction of $r_\text{opt}$ laid out in a
seminal paper by Hillas in 1969, it will be shown that $r_\text{opt}$, is a
more effective tool when detectors are laid out on a triangular grid than when
detectors are deployed on a square grid. This result may have implications for
explaining the differences between the flux observed by the Auger and Telescope
collaborations above 10\,EeV and should be kept in mind when designing new
shower arrays.


  The question if a given partial solution to a problem can be extended
reasonably occurs in many algorithmic approaches for optimization problems. For
instance, when enumerating minimal dominating sets of a graph $G=(V,E)$, one
usually arrives at the problem to decide for a vertex set $U \subseteq V$, if
there exists a \textit{minimal} dominating set $S$ with $U\subseteq S$. We
propose a general, partial-order based formulation of such extension problems
and study a number of specific problems which can be expressed in this
framework. Possibly contradicting intuition, these problems tend to be NP-hard,
even for problems where the underlying optimisation problem can be solved in
polynomial time. This raises the question of how fixing a partial solution
causes this increase in difficulty. In this regard, we study the parameterised
complexity of extension problems with respect to parameters related to the
partial solution, as well as the optimality of simple exact algorithms under
the Exponential-Time Hypothesis. All complexity considerations are also carried
out in very restricted scenarios, be it degree restrictions or topological
restrictions (planarity) for graph problems or the size of the given partition
for the considered extension variant of Bin Packing.


  71Ga NQR, magnetization and specific heat measurements have been performed on
polycrystalline Ge doped FeGa3 samples. A crossover from an insulator to a
correlated local moment metal in the low doping regime and the evolution of
itinerant ferromagnet upon further doping is found. For the nearly critical
concentration at the threshold of ferromagnetic order, xC=0.15, (1/T1T)
exhibits a pronounced T4/3 power law over two orders of magnitude in
temperature which indicates 3D quantum critical ferromagnetic fluctuations.
Furthermore, for the ordered x = 0.2 sample (TC = 6 K) 1/T1T could be fitted
well in the frame of Moriya's SCR theory for weakly FM systems with 1/T1T
proportional to chi. In contrast to this, the low doping regime nicely displays
local moment behavior where 1/T1T proportional to chi2 is valid. For
temperature tending to zero the Sommerfeld ratio = (C/T) is enhanced (70
mJ/mole-K2 for x = 0.1) which indicates the formation of heavy 3d-electrons.


  Kernel-based learning algorithms are widely used in machine learning for
problems that make use of the similarity between object pairs. Such algorithms
first embed all data points into an alternative space, where the inner product
between object pairs specifies their distance in the embedding space. Applying
kernel methods to partially labeled datasets is a classical challenge in this
regard, requiring that the distances between unlabeled pairs must somehow be
learnt using the labeled data. In this independent study, I will summarize the
work of G. Lanckriet et al.'s work on "Learning the Kernel Matrix with
Semidefinite Programming" used in support vector machines (SVM) algorithms for
the transduction problem. Throughout the report, I have provide alternative
explanations / derivations / analysis related to this work which is designed to
ease the understanding of the original article.


  We generalize the analytic solutions presented in Pantoni et al. (2019) by
including a simple yet effective description of wind recycling and galactic
fountains, with the aim of self-consistently investigating the
spatially-averaged time evolution of the gas, stellar, metal, and dust content
in disc-dominated late-type galaxies (LTGs). Our analytic solutions, when
supplemented with specific prescriptions for parameter setting and with halo
accretion rates from $N-$body simulations, can be exploited to reproduce the
main statistical relationships followed by local LTGs; these involve, as a
function of the stellar mass, the star formation efficiency, the gas mass
fraction, the gas/stellar metallicity, the dust mass, the star formation rate,
the specific angular momentum, and the overall mass/metal budget. Our analytic
solutions allow to easily disentangle the diverse role of the main physical
processes ruling galaxy formation in LTGs; in particular, we highlight the
crucial relevance of wind recycling and galactic fountains in efficiently
refurnishing the gas mass, extending the star-formation timescale, and boosting
the metal enrichment in gas and stars. All in all, our analytic solutions
constitute a transparent, handy, and fast tool that can provide a basis for
improving the (subgrid) physical recipes presently implemented in more
sophisticated semi-analytic models and numerical simulations, and can offer a
benchmark for interpreting and forecasting current and future
spatially-averaged observations of local and higher redshift LTGs.


  This article gives a summary of the finite-dimesional irreducible
representations of the $q$-Onsager algebra, which are treated in detail in our
paper `The augmented tridiagonal algebra'.


  Using standard big-bang nucleosynthesis and present, high-precision
measurements of light element abundances, we place constraints on the
self-gravity of radiation pressure in the early universe. The self-gravity of
pressure is strictly non-Newtonian, and thus the constraints we set are a
direct test of this aspect of general relativity.


  In-context learning (ICL) using large language models for tasks with many
labels is challenging due to the limited context window, which makes it
difficult to fit a sufficient number of examples in the prompt. In this paper,
we use a pre-trained dense retrieval model to bypass this limitation, giving
the model only a partial view of the full label space for each inference call.
Testing with recent open-source LLMs (OPT, LLaMA), we set new state of the art
performance in few-shot settings for three common intent classification
datasets, with no finetuning. We also surpass fine-tuned performance on
fine-grained sentiment classification in certain cases. We analyze the
performance across number of in-context examples and different model scales,
showing that larger models are necessary to effectively and consistently make
use of larger context lengths for ICL. By running several ablations, we analyze
the model's use of: a) the similarity of the in-context examples to the current
input, b) the semantic content of the class names, and c) the correct
correspondence between examples and labels. We demonstrate that all three are
needed to varying degrees depending on the domain, contrary to certain recent
works.


  The aim of this paper is to describe the torus equivariant $K$-ring of
even-dimensional complex quadrics by studying the graph equivariant $K$-theory
of their corresponding GKM graphs. This involves providing a presentation for
its graph equivariant $K$- ring in terms of generators and relations. This
parallels the description of the equivariant cohomology ring of
even-dimensional complex quadrics due to Kuroki.


  Motivated by recent experimental results reporting giant coercive fields in
Co(II)-based molecular magnets we present a theory of hysteresis phenomena
based on the Glauber stochastic dynamics. Unusual form of hysteresis loops is
similar to those of found in Co-based quasi-one-dimensional ferrimagnet CoPhOMe
at low temperatures. Temperature dependence of the coercive field has a
characteristic form with an inflection that may serve as an indicator of the
Glauber dynamics in real compounds. A relevance of the model for other Co-based
molecular magnets is discussed.


  We present a scattering theory of transport through noncollinear disordered
magnetic insulators. For concreteness, we study and compare the random field
model (RFM) and the random anisotropy model (RAM). The RFM and RAM are used to
model random spin disorder systems and amorphous materials, respectively. We
utilize the Landauer-Buttiker formalism to compute the transmission probability
and spin conductance of one-dimensional disordered spin chains. The RFM and the
RAM both exhibit Anderson localization, which means that the transmission
probability and spin conductance decay exponentially with the system length. We
define two localization lengths based on the transmission probability and the
spin conductance, respectively. Next, we numerically determine the relationship
between the localization lengths and the strength of the disorder. In the limit
of weak disorder, we find that the localization lengths obey power laws and
determine the critical exponents. Our results are expressed via the universal
exchange length and are therefore expected to be general.


  We demonstrate nearly-spherical, strain-free, self-assembled Ge quantum dots
(QDs) fully encapsulated by AlAs, grown on (100) GaAs by molecular beam epitaxy
(MBE). The QDs were formed without a wetting layer using a high temperature,
in-situ anneal. Subsequent AlAs overgrowth was free from threading dislocations
and anti-phase domains. The straddling band alignment for Ge in AlAs promises
strong and tunable confinement for both electrons and holes. The reflection
high-energy electron diffraction (RHEED) pattern changed from 2x3 to 2x5 with
anneal, which can be explained by surface reconstructions based on the
electron-counting model.


  The structure of the densest crystal packings is determined for a variety of
concave shapes in 2D constructed by the overlap of two or three disks. The
maximum contact number per particle pair is defined and proposed as a useful
means of categorizing particle shape. We demonstrate that the densest packed
crystal exhibits a maximum in the number of contacts per particle but does not
necessarily include particle pairs with the maximum contact number. In
contrast, amorphous structures, generated by energy minimization of high
temperature liquids, typically do include maximum contact pairs. The amorphous
structures exhibit a large number of contacts per particle corresponding to
over-constrained structures. Possible consequences of this over-constraint are
discussed.


  We present a novel formulation of structural design optimization problems
specifically tailored to be solved by quantum annealing (QA). Structural design
optimization aims to find the best, i.e., material-efficient yet
high-performance, configuration of a structure. To this end, computational
optimization strategies can be employed, where a recently evolving strategy
based on quantum mechanical effects is QA. This approach requires the
optimization problem to be present, e.g., as a quadratic unconstrained binary
optimization (QUBO) model. Thus, we develop a novel formulation of the
optimization problem. The latter typically involves an analysis model for the
component. Here, we use energy minimization principles that govern the behavior
of structures under applied loads. This allows us to state the optimization
problem as one overall minimization problem. Next, we map this to a QUBO
problem that can be immediately solved by QA. We validate the proposed approach
using a size optimization problem of a compound rod under self-weight loading.
To this end, we develop strategies to account for the limitations of currently
available hardware and find that the presented formulation is suitable for
solving structural design optimization problems through QA and, for small-scale
problems, already works on today's hardware.


  Following analogous constructions for Lie algebras, we define Whittaker
modules and Whittaker categories for finite-dimensional simple Lie
superalgebras. Results include a decomposition of Whittaker categories for a
Lie superalgebra according to the action of an appropriate sub-superalgebra;
and, for basic classical Lie superalgebras of type I, a description of the
strongly typical simple Whittaker modules.


  From a fibered link in the 3-sphere may be constructed a field of not
everywhere tangent 2-planes; when the fibered link is the link of an isolated
critical point of a map from 4-space to the plane, the plane field is
essentially the field of kernels of the derivative of the map. Homotopically,
such a plane field determines two integers. I show that the sum of these
integers is the Milnor number of the fibered link. Taking the mirror image of a
link exchanges the integers. Various examples are computed. It is noted (proof
given elsewhere) that these integers are not determined by the algebraic
monodromy (or Seifert form) of the fibered link.


  How to determine the symmetry of the superconducting order parameter is one
of the important issues in novel superconductors, which include charge
conjugated organic superconductors. We have proposed that the angular
dependence of the thermal conductivity in a planar magnetic field provides a
new window to look at the symmetry of the order parameter. After a brief
summary of the quasiclassical approach we describe how the symmetry of the
superconducting order parameter in Sr$_2$RuO$_4$, CeCoIn$_5$ and
$\kappa$-(ET)$_2$Cu(NCS)$_2$ is determined. Also in some of experiments the
phononic thermal conductivity plays the crucial role.


  Human pose estimation has an important impact on a wide range of applications
from human-computer interface to surveillance and content-based video
retrieval. For human pose estimation, joint obstructions and overlapping upon
human bodies result in departed pose estimation. To address these problems, by
integrating priors of the structure of human bodies, we present a novel
structure-aware network to discreetly consider such priors during the training
of the network. Typically, learning such constraints is a challenging task.
Instead, we propose generative adversarial networks as our learning model in
which we design two residual multiple instance learning (MIL) models with the
identical architecture, one is used as the generator and the other one is used
as the discriminator. The discriminator task is to distinguish the actual poses
from the fake ones. If the pose generator generates the results that the
discriminator is not able to distinguish from the real ones, the model has
successfully learnt the priors. In the proposed model, the discriminator
differentiates the ground-truth heatmaps from the generated ones, and later the
adversarial loss back-propagates to the generator. Such procedure assists the
generator to learn reasonable body configurations and is proved to be
advantageous to improve the pose estimation accuracy. Meanwhile, we propose a
novel function for MIL. It is an adjustable structure for both instance
selection and modeling to appropriately pass the information between instances
in a single bag. In the proposed residual MIL neural network, the pooling
action adequately updates the instance contribution to its bag. The proposed
adversarial residual multi-instance neural network that is based on pooling has
been validated on two datasets for the human pose estimation task and
successfully outperforms the other state-of-arts models.


  The frontal structure of the Southern Ocean is investigated using a
sophisticated frontal detection methodology, the Wavelet/Higher Order
Statistics Enhancement (WHOSE) method, introduced in \cite{Chapman2014}. This
methodology is applied to 21 years of daily gridded sea-surface height (SSH)
data to obtain daily maps of the locations of the fronts. By forming
`heat-maps' of the frontal occurrence frequency and then approximating these
heat-maps by a superposition of simple functions, the time-mean locations of
the fronts, as well as a measure of their capacity to meander, are obtained and
related to the frontal locations found by previous studies.
  The spatial and temporal variability of the frontal structure is then
considered. The number of fronts is found to be highly variable throughout the
Southern Ocean, increasing (`splitting') downstream of large bathymetric
features and decreasing (`merging') in regions where the fronts are tightly
controlled by the underlying topography. In contrast, frontal meandering
remains relatively constant. Contrary to many previous studies, little no
southward migration of the fronts over the 1993-2014 time period is found, and
there is only weak sensitivity to atmospheric forcing related to SAM or ENSO.
The reasons for the discrepancy between this study and previous studies using
contour methods are investigated and it is shown that the spatial variability
of the frontal structure is not tied to the underlying sea-surface height. It
is argued that the results of studies using sea-surface height contours to
define front must be interpreted with care.


  Recently, Pomme et al did an analysis of $\rm{^{36}Cl} $ radioactive decay
data from measurements at the Physikalisch-Technische Bundesanstalt (PTB), in
order to verify the claims by Sturrock and collaborators of an influence on
beta-decay rates measured at Brookehaven National Lab (BNL) due to the
rotation-induced modulation of the solar neutrino flux. Their analysis excluded
any sinusoidal modulations in the frequency range from 0.2-20/year. We carry
out an independent analysis of the same PTB and BNL data using the generalized
Lomb-Scargle periodogram, to look for any statistically significant peaks in
the range from 0 to 14 per year, and by evaluating the significance of every
peak using multiple methods. Our results for the PTB data are in agreement with
those by Pomme et al. For BNL data, we do find peaks at some of the same
frequencies as Sturrock et al, but the significance is much lower. All our
analysis codes and datasets have been made publicly available.


  The aim of this note is to provide a simple proof of some well-known
identities and recurrences relating classical Bernoulli and Euler numbers by
using the Abel sum of the divergent series $\sum_{n=0}^\infty (-1)^{n}
(n+1)^k$, $k$ a positive integers. Special attention is placed on the fact that
the numerical value of these sums is determined by the linearity of the
summation method involved.


  Tree-level color-ordered Yang-Mills (YM) amplitudes can be decomposed in
terms of $(n-2)!$ bi-scalar (BS) amplitudes, whose expansion coefficients form
a basis of Bern-Carrasco-Johansson (BCJ) numerators. By the help of the
recursive expansion of Einstein-Yang-Mills (EYM) amplitudes, the BCJ numerators
are given by polynomial functions of Lorentz contractions which are
conveniently described by graphic rule. In this work, we extend the expansion
of YM amplitudes to off-shell level. We define different types of off-shell
extended numerators that can be generated by graphs. By the use of these
extended numerators, we propose a general decomposition formula of off-shell
Berends-Giele currents in YM. This formula consists of three terms: (i). an
effective current which is expanded as a combination of the Berends-Giele
currents in BS theory (The expansion coefficients are one type of off-shell
extended numerators) (ii). a term proportional to the total momentum of
on-shell lines and (iii). a term expressed by the sum of lower point
Berends-Giele currents in which some polarizations and momenta are replaced by
vectors proportional to off-shell momenta appropriately. In the on-shell limit,
the last two terms vanish while the decomposition of effective current
precisely reproduces the decomposition of on-shell YM amplitudes with the the
expected coefficients (BCJ numerators in DDM basis). We further symmetrize
these coefficients such that the Lie symmetries are satisfied. These symmetric
BCJ numerators simultaneously satisfy the relabeling property of external lines
and the algebraic properties (antisymmetry and Jacobi identity).


  We investigate the electronic stress tensor of the hydrogen molecular ion for
the ground state using the exact wave function and wave functions approximated
by gaussian function basis set expansion. The spatial distribution of the
largest eigenvalue, corresponding eigenvectors, tension and kinetic energy
density are compared. We find that the cc-pV6Z basis set gives the spindle
structure very close to the one calculated from the exact wave function.
Similarly, energy density at the Lagrange point is very well approximated by
the cc-pV5Z or cc-pV6Z basis sets.


  Rotation is one of the key physical mechanisms that deeply impact the
evolution of stars. Helio- and asteroseismology reveal a strong extraction of
angular momentum from stellar radiation zones over the whole
Hertzsprung-Russell diagram. Turbulent transport in differentially rotating
stably stratified stellar radiation zones should be carefully modeled and its
strength evaluated. Stratification and rotation imply that this turbulent
transport is anisotropic. Only phenomenological prescriptions have been
proposed for the transport in the horizontal direction, which however
constitutes a cornerstone in current theoretical formalisms for stellar
hydrodynamics in evolution codes. We derive a new theoretical prescription for
the anisotropy of the turbulent transport in radiation zones using a spectral
formalism for turbulence that takes simultaneously stable stratification,
rotation, and a radial shear into account. Then, the horizontal turbulent
transport resulting from 3D turbulent motions sustained by the instability of
the radial differential rotation is derived. We implement this framework in the
stellar evolution code STAREVOL and quantify its impact on the rotational and
structural evolution of low-mass stars from the pre-main-sequence to the red
giant branch. The anisotropy of the turbulent transport scales as
$N^4\tau^2/\left(2\Omega^2\right)$, $N$ and $\Omega$ being the buoyancy and
rotation frequencies respectively and $\tau$ a time characterizing the source
of turbulence. This leads to a horizontal turbulent transport of similar
strength in average that those obtained with previously proposed prescriptions
even if it can be locally larger below the convective envelope. As a
consequence, a complementary transport mechanism like internal gravity waves or
magnetic fields is still needed to explain the observed strong transport of
angular momentum along stellar evolution.


  NullPointerExceptions (NPEs) are a key source of crashes in modern Java
programs. Previous work has shown how such errors can be prevented at compile
time via code annotations and pluggable type checking. However, such systems
have been difficult to deploy on large-scale software projects, due to
significant build-time overhead and / or a high annotation burden. This paper
presents NullAway, a new type-based null safety checker for Java that overcomes
these issues. NullAway has been carefully engineered for low overhead, so it
can run as part of every build. Further, NullAway reduces annotation burden
through targeted unsound assumptions, aiming for no false negatives in practice
on checked code. Our evaluation shows that NullAway has significantly lower
build-time overhead (1.15X) than comparable tools (2.8-5.1X). Further, on a
corpus of production crash data for widely-used Android apps built with
NullAway, remaining NPEs were due to unchecked third-party libraries (64%),
deliberate error suppressions (17%), or reflection and other forms of
post-checking code modification (17%), never due to NullAway's unsound
assumptions for checked code.


  The ability to incrementally learn new classes is vital to all real-world
artificial intelligence systems. A large portion of high-impact applications
like social media, recommendation systems, E-commerce platforms, etc. can be
represented by graph models. In this paper, we investigate the challenging yet
practical problem, Graph Few-shot Class-incremental (Graph FCL) problem, where
the graph model is tasked to classify both newly encountered classes and
previously learned classes. Towards that purpose, we put forward a Graph Pseudo
Incremental Learning paradigm by sampling tasks recurrently from the base
classes, so as to produce an arbitrary number of training episodes for our
model to practice the incremental learning skill. Furthermore, we design a
Hierarchical-Attention-based Graph Meta-learning framework, HAG-Meta. We
present a task-sensitive regularizer calculated from task-level attention and
node class prototypes to mitigate overfitting onto either novel or base
classes. To employ the topological knowledge, we add a node-level attention
module to adjust the prototype representation. Our model not only achieves
greater stability of old knowledge consolidation, but also acquires
advantageous adaptability to new knowledge with very limited data samples.
Extensive experiments on three real-world datasets, including Amazon-clothing,
Reddit, and DBLP, show that our framework demonstrates remarkable advantages in
comparison with the baseline and other related state-of-the-art methods.


  The Kepler-186 system consists of five planets orbiting an early-M dwarf. The
planets have physical radii of 1.0-1.50 R$_\oplus$ and orbital periods of 4 to
130 days. The $1.1~$R$_\oplus$ Kepler-186f with a period of 130 days is of
particular interest. Its insolation of roughly $0.32~S_\odot$places it within
the liquid water habitable zone. We present a multi-faceted study of the
Kepler-186 system. First, we show that the distribution of planet masses can be
roughly reproduced if the planets accreted from a high-surface density disk
presumably sculpted by an earlier phase of migration. However, our simulations
predict the existence of 1-2 undetected planets between planets e and f. Next,
we present a dynamical analysis of the system including the effect of tides.
The timescale for tidal evolution is short enough that the four inner planets
must have small obliquities and near-synchronous rotation rates. Tidal
evolution of Kepler-186f is slow enough that its current spin state depends on
a combination of its dissipation rate and the stellar age. Finally, we study
the habitability of Kepler-186f with a 1-D climate model. The planet's surface
temperature can be raised above 273 K with 0.5-5 bars of CO$_2$, depending on
the amount of N$_2$ present. Kepler-186f represents a case study of an
Earth-sized planet in the cooler regions of the habitable zone of a cool star.


  It is observed that the finite size of hadrons produced in high energy
collisions implies that their positions are correlated, since the probability
of finding two hadrons on top of each other is highly reduced. It is then shown
that this effect can naturally explain the values of the correlation function
below one, observed at LEP and LHC for pairs of identical pions.


  While deep learning has proven to be extremely successful at supervised
classification tasks at the LHC and beyond, for practical applications, raw
classification accuracy is often not the only consideration. One crucial issue
is the stability of network predictions, either versus changes of individual
features of the input data, or against systematic perturbations. We present a
new method based on a novel application of "distance correlation" (DisCo), a
measure quantifying non-linear correlations, that achieves equal performance to
state-of-the-art adversarial decorrelation networks but is much simpler and
more stable to train. To demonstrate the effectiveness of our method, we
carefully recast a recent ATLAS study of decorrelation methods as applied to
boosted, hadronic W-tagging. We also show the feasibility of DisCo
regularization for more powerful convolutional neural networks, as well as for
the problem of hadronic top tagging.


  We consider $n$-component fixed-length order parameter interacting with a
weak random field in $d=1,2,3$ dimensions. Relaxation from the initially
ordered state and spin-spin correlation functions have been studied on lattices
containing hundreds of millions sites. At $n-1<d$ presence of topological
structures leads to metastability, with the final state depending on the
initial condition. At $n-1>d$, when topological objects are absent, the final,
lowest-energy, state is independent of the initial condition. It is
characterized by the exponential decay of correlations that agrees
quantitatively with the theory based upon the Imry-Ma argument. In the
borderline case of $n-1=d$, when topological structures are non-singular, the
system possesses a weak metastability with the Imry-Ma state likely to be the
global energy minimum.


  We propose a novel mechanism for single spin detection based on the 1/f spin
current noise. We postulate the 1/f spin noise for the tunneling current,
similar to the ubiquitous 1/f noise in magnetic systems. Magnetic coupling
between tunneling electrons and localized spin S then leads to the peak at
Larmor frequency in the power spectrum of the electric current fluctuations
$I^2_{\omega}$. The elevated noise in the current spectrum will be spatially
localized near the magnetic site. The difference in the power spectra taken at
the Larmor frequency and elsewhere would reveal the peak in the spectrum. We
argue that signal to noise ratio for this mechanism is on the order one. In
addition we discuss the asymmetric lineshapes observed regularly with this
measurement. We show that such lineshapes are in accordance to the random
sampling done with the tunneling electrons. Yet, this predicts a linewidth at
least one order of magnitude larger than observed experimentally which is
likely to be due to electrostatic repulsion between the tunneling electrons and
temporal correlations in the tunneling process.


  Let $p$ be an odd prime and $q=p^r$, $r\geq 1$. For positive integers $n$,
let ${_n}G_n[\cdots]_q$ denote McCarthy's $p$-adic hypergeometric functions. In
this article, we prove an identity expressing a ${_4}G_4[\cdots]_q$
hypergeometric function as a sum of two ${_2}G_2[\cdots]_q$ hypergeometric
functions. This identity generalizes some known identities satisfied by the
finite field hypergeometric functions. We also prove a transfomation that
relates ${_{n+2}}G_{n+2}[\cdots]_q$ and ${_n}G_n[\cdots]_q$ hypergeometric
functions. Next, we express the trace of Frobenius of elliptic curves in terms
of special values of ${_4}G_4[\cdots]_q$ and ${_6}G_6[\cdots]_q$ hypergeometric
functions. Our results extend the recent works of Tripathi and Meher on the
finite field hypergeometric functions to wider classes of primes.


  We discuss factorization of the Dyson--Schwinger equations using the Lie- and
Hopf algebra of graphs. The structure of those equations allows to introduce a
commutative associative product on 1PI graphs. In scalar field theories, this
product vanishes if and only if one of the factors vanishes. Gauge theories are
more subtle: integrality relates to gauge symmetries.


  Internet of Things (IoT) has catapulted human ability to control our
environments through ubiquitous sensing, communication, computation, and
actuation. Over the past few years, IoT has joined forces with Machine Learning
(ML) to embed deep intelligence at the far edge. TinyML (Tiny Machine Learning)
has enabled the deployment of ML models for embedded vision on extremely lean
edge hardware, bringing the power of IoT and ML together. However, TinyML
powered embedded vision applications are still in a nascent stage, and they are
just starting to scale to widespread real-world IoT deployment. To harness the
true potential of IoT and ML, it is necessary to provide product developers
with robust, easy-to-use software engineering (SE) frameworks and best
practices that are customized for the unique challenges faced in TinyML
engineering. Through this systematic literature review, we aggregated the key
challenges reported by TinyML developers and identified state-of-art SE
approaches in large-scale Computer Vision, Machine Learning, and Embedded
Systems that can help address key challenges in TinyML based IoT embedded
vision. In summary, our study draws synergies between SE expertise that
embedded systems developers and ML developers have independently developed to
help address the unique challenges in the engineering of TinyML based IoT
embedded vision.


  We propose a deep learning method for the numerical solution of partial
differential equations that arise as gradient flows. The method relies on the
Brezis--Ekeland principle, which naturally defines an objective function to be
minimized, and so is ideally suited for a machine learning approach using deep
neural networks. We describe our approach in a general framework and illustrate
the method with the help of an example implementation for the heat equation in
space dimensions two to seven.


  We consider electrons in a quantum wire interacting via a long-range Coulomb
potential screened by a nearby gate. We focus on the quantum phase transition
from a strictly one-dimensional to a quasi-one-dimensional electron liquid,
that is controlled by the dimensionless parameter $n x_0$, where $n$ is the
electron density and $x_0$ is the characteristic length of the transverse
confining potential. If this transition occurs in the low-density limit, it can
be understood as the deformation of the one-dimensional Wigner crystal to a
zigzag arrangement of the electrons described by an Ising order parameter. The
critical properties are governed by the charge degrees of freedom and the spin
sector remains essentially decoupled. At large densities, on the other hand,
the transition is triggered by the filling of a second one-dimensional subband
of transverse quantization. Electrons at the bottom of the second subband
interact strongly due to the diverging density of states and become
impenetrable. We argue that this stabilizes the electron liquid as it
suppresses pair-tunneling processes between the subbands that would otherwise
lead to an instability. However, the impenetrable electrons in the second band
are screened by the excitations of the first subband, so that the transition is
identified as a Lifshitz transition of impenetrable polarons. We discuss the
resulting phase diagram as a function of $n x_0$.


  This paper tries to discuss two strategies of dealing with this complex
passenger demand from two aspects: transit train formation and real-time
holding control. The genetic algorithm (GA) is designed to solve the integrated
two-stage model of optimizing the number, timetable and real-time holding
control of the multi-marshalling operated trains. The numerical results show
that the combined two-stage model of multi-marshalling operation and holding
control at stations can better deal with the demand fluctuation of urban rail
transit connecting with the comprehensive transportation hub.


  We consider 3- and 6-vector deformations of 11-dimensional supergravity
backgrounds of the form $M_5\times M_6$ admitting at least 3 Killing vectors.
Using flux formulation of the E${}_{6(6)}$ exceptional field theory we derive
(sufficient) conditions for the deformations to generate a solution. In the
group manifold case these generalisations of the classical Yang-Baxter equation
for the case of r-matrices with 3 and 6 indices are shown to reproduce those
obtained from exceptional Drinfeld algebra for E${}_{6(6)}$. In general we see
an additional constraint, which might be related to higher exceptional Drinfeld
algebras.


  In the present paper it is considered space time manifold with four
commutative coordinates with Poinc\'are group of motion but different from
Poinc\'are Minkowski space time of the modern physics.


  We present a comprehensive X-ray study of the population of supernova
remnants (SNRs) in the LMC. Using primarily XMM-Newton, we conduct a systematic
spectral analysis of LMC SNRs to gain new insights on their evolution and the
interplay with their host galaxy. We combined all the archival XMM observations
of the LMC with those of our Very Large Programme survey. We produced X-ray
images and spectra of 51 SNRs, out of a list of 59. Using a careful modelling
of the background, we consistently analysed all the X-ray spectra and measure
temperatures, luminosities, and chemical compositions. We investigated the
spatial distribution of SNRs in the LMC and the connection with their
environment, characterised by various SFHs. We tentatively typed all LMC SNRs
to constrain the ratio of core-collapse to type Ia SN rates in the LMC. We
compared the X-ray-derived column densities to HI maps to probe the
three-dimensional structure of the LMC. This work provides the first
homogeneous catalogue of X-ray spectral properties of LMC SNRs. It offers a
complete census of LMC SNRs exhibiting Fe K lines (13% of the sample), or
revealing contribution from hot SN ejecta (39%). Abundances in the LMC ISM are
found to be 0.2-0.5 solar, with a lower [$\alpha$/Fe] than in the Milky Way.
The ratio of CC/type Ia SN in the LMC is $N_{\mathrm{CC}}/N_{\mathrm{Ia}} =
1.35(_{-0.24}^{+0.11})$, lower than in local SN surveys and galaxy clusters.
Comparison of X-ray luminosity functions of SNRs in Local Group galaxies
reveals an intriguing excess of bright objects in the LMC. We confirm that 30
Doradus and the LMC Bar are offset from the main disc of the LMC, to the far
and near sides, respectively. (abridged)


  The beam-beam interaction is one of the most critical factors determining the
luminosity performance of colliders. As a circular collider utilizing the
crab-waist scheme, multiple factors, such as beam-beam, crab waist, impedances,
etc., interact to determine the luminosity of SuperKEKB. The interplay of these
factors makes it challenging to predict luminosity via simulations. This paper
presents recent advances in understanding the luminosity performance of
SuperKEKB from beam-beam simulations and experiments. The key aspects affecting
the luminosity of SuperKEKB, as well as the areas where further research is
needed, are highlighted.


  We use gauge/gravity duality to study simultaneously the mass spectrum and
the thermodynamics of a generic quasi-conformal gauge theory, specified by its
beta function. The beta function of a quasi-conformal theory almost vanishes,
and the coupling is almost constant between two widely separated energy scales.
Depending on whether the gravity dual has a black hole or not, the mass
spectrum is either a spectrum of quasinormal oscillations or a normal T=0 mass
spectrum. The mass spectrum is quantitatively correlated with the thermal
properties of the system. As the theory approaches conformality, the masses
have to vanish. We show that in this limit, the masses calculated via
gauge/gravity duality satisfy expected scaling properties.


  We present a microwave realization of a reflective topological limiter based
on an explicit self-induced violation of a charge-conjugation (CT) symmetry.
The starting point is a bipartite structure created by coupled dielectric
resonators with a topological defect placed at the center and two lossy
resonators placed on the neighboring sites of the defect. This defect supports
a resonant mode if the CT-symmetry is present, while it is suppressed once the
symmetry is violated due to permittivity changes of the defect resonator
associated with high irradiances of the incident radiation. This destruction
leads to a suppression of transmittance and a subsequent increase of the
reflectance while the absorption is also suppressed.


  In a 1937 paper B.H. Neumann constructed an uncountable family of
$2$-generated groups. We prove that all of his groups are permutation stable by
analyzing the structure of their invariant random subgroups.


  Self-Organized Criticality (SOC) phenomena could have a significant effect on
the dynamics of ecosystems. The Bak-Sneppen (BS) model is a simple and robust
model of biological evolution that exhibits punctuated equilibrium behavior.
Here we will introduce random version of BS model. Also we generalize the
single objective BS model to a multiobjective one.


  This paper presents our research on leveraging social media Big Data and AI
to support hurricane disaster emergency response. The current practice of
hurricane emergency response for rescue highly relies on emergency call
centres. The more recent Hurricane Harvey event reveals the limitations of the
current systems. We use Hurricane Harvey and the associated Houston flooding as
the motivating scenario to conduct research and develop a prototype as a
proof-of-concept of using an intelligent agent as a complementary role to
support emergency centres in hurricane emergency response. This intelligent
agent is used to collect real-time streaming tweets during a natural disaster
event, to identify tweets requesting rescue, to extract key information such as
address and associated geocode, and to visualize the extracted information in
an interactive map in decision supports. Our experiment shows promising
outcomes and the potential application of the research in support of hurricane
emergency response.


  When a deep learning model is deployed in the wild, it can encounter test
data drawn from distributions different from the training data distribution and
suffer drop in performance. For safe deployment, it is essential to estimate
the accuracy of the pre-trained model on the test data. However, the labels for
the test inputs are usually not immediately available in practice, and
obtaining them can be expensive. This observation leads to two challenging
tasks: (1) unsupervised accuracy estimation, which aims to estimate the
accuracy of a pre-trained classifier on a set of unlabeled test inputs; (2)
error detection, which aims to identify mis-classified test inputs. In this
paper, we propose a principled and practically effective framework that
simultaneously addresses the two tasks. The proposed framework iteratively
learns an ensemble of models to identify mis-classified data points and
performs self-training to improve the ensemble with the identified points.
Theoretical analysis demonstrates that our framework enjoys provable guarantees
for both accuracy estimation and error detection under mild conditions readily
satisfied by practical deep learning models. Along with the framework, we
proposed and experimented with two instantiations and achieved state-of-the-art
results on 59 tasks. For example, on iWildCam, one instantiation reduces the
estimation error for unsupervised accuracy estimation by at least 70% and
improves the F1 score for error detection by at least 4.7% compared to existing
methods.


  We prove that subsets of ${\Bbb R}^d$, $d \ge 4$ of large enough Hausdorff
dimensions contain vertices of an equilateral triangle. It is known that
additional hypotheses are needed to assure the existence of equilateral
triangles in two dimensions (see \cite{CLP14}). We show that no extra
conditions are needed in dimensions four and higher. The three dimensional case
remains open.
  Some interesting parallels exist between the triangle problem in Euclidean
space and its counter-part in vector spaces over finite fields. We shall
outline these similarities in hopes of eventually achieving a comprehensive
understanding of this phenomenon in the setting of locally compact abelian
groups.


  In Turkey the increasing tension, due to the presence of 3.4 million Syrian
refugees, demands the formulation of effective integration policies. Moreover,
their design requires tools aimed at understanding the integration of refugees
despite the complexity of this phenomenon. In this work, we propose a set of
metrics aimed at providing insights and assessing the integration of Syrians
refugees, by analyzing a real-world Call Details Records (CDRs) dataset
including calls from refugees and locals in Turkey throughout 2017.
Specifically, we exploit the similarity between refugees' and locals' spatial
and temporal behaviors, in terms of communication and mobility in order to
assess integration dynamics. Together with the already known methods for data
analysis, we use a novel computational approach to analyze spatiotemporal
patterns: Computational Stigmergy, a bio-inspired scalar and temporal
aggregation of samples. Computational Stigmergy associates each sample to a
virtual pheromone deposit (mark). Marks in spatiotemporal proximity are
aggregated into functional structures called trails, which summarize the
spatiotemporal patterns in data and allows computing the similarity between
different patterns. According to our results, collective mobility and
behavioral similarity with locals have great potential as measures of
integration, since they are: (i) correlated with the amount of interaction with
locals; (ii) an effective proxy for refugee's economic capacity, thus refugee's
potential employment; and (iii) able to capture events that may disrupt the
integration phenomena, such as social tensions.


  We analyze a model of interacting agents (e.g. prebiotic chemical species)
which are represended by nodes of a network, whereas their interactions are
mapped onto directed links between these nodes. On a fast time scale, each
agent follows an eigendynamics based on catalytic support from other nodes,
whereas on a much slower time scale the network evolves through selection and
mutation of its nodes-agent. In the first part of the paper, we explain the
dynamics of the model by means of characteristic snapshots of the network
evolution and confirm earlier findings on crashes an recoveries in the network
structure. In the second part, we focus on the aggregate behavior of the
network dynamics. We show that the disruptions in the network structure are
smoothed out, so that the average evolution can be described by a growth regime
followed by a saturation regime, without an initial random regime. For the
saturation regime, we obtain a logarithmic scaling between the average
connectivity per node $\mean{l}_{s}$ and a parameter $m$, describing the
average incoming connectivity, which is independent of the system size $N$.


  We consider quantum spin ice in a temperature regime in which its response is
dominated by the coherent motion of a dilute gas of monopoles. The hopping
amplitude of a monopole is sensitive to the configuration of its surrounding
spins, taken to be quasi-static on the relevant timescales. This leads to
well-known blocked directions in the monopole motion; we find that these are
sufficient to reduce the coherent propagation of monopoles to quantum
diffusion. This result is robust against disorder, as a direct consequence of
the ground-state degeneracy, which disrupts the quantum interference processes
needed for weak localization. Moreover, recent work [Tomasello et al., Phys.
Rev. Lett. 123, 067204 (2019)] has shown that the monopole hopping amplitudes
are roughly bimodal: for $\approx 1/3$ of the flippable spins surrounding a
monopole, these amplitudes are extremely small. We exploit this structure to
construct a theory of quantum monopole motion in spin ice. In the limit where
the slow hopping terms are set to zero, the monopole wavefunctions appear to be
fractal; we explain this observation via a mapping to quantum percolation on
trees. The fractal, non-ergodic nature of monopole wavefunctions manifests
itself in the low-frequency behavior of monopole spectral functions, and is
consistent with experimental observations.


  Using the Caldirola-Kanai Hamiltonian, we study the time evolution of the
wave function of a particle whose classical motion is governed by the Langevin
equation. We show, in particular, that if the initial wave function is
Gaussian, then (i) it remains Gaussian for all times, (ii) its width grows,
approaching a finite value when t->infinity, and (iii) its center describes a
Brownian motion, and so the uncertainty in the position of the particle grows
without limit.


  Phenomenology of relic neutralinos is analyzed in an effective supersymmetric
scheme at the electroweak scale. It is shown that current direct experiments
for WIMPs, when interpreted in terms of relic neutralinos, are indeed probing
regions of supersymmetric parameter space compatible with all present
experimental bounds.


  Fits to the transverse momentum distributions of charged particles produced
in p - p collisions at LHC energies based on the Tsallis distribution have been
shown to work over 14 orders of magnitude. Two versions of the Tsallis
distribution are compared and discussed, the thermodynamically consistent
version leads to a temperature of T = 74 +/- 13 MeV at the highest beam energy,
a result which is in agreement with previous analyses done with lower
transverse momentum data.


  With the recent experimental hint of new physics from flavor physics
anomalies, combined with the evidence from neutrino mass and dark matter, we
consider a minimal extension of SM with a scalar leptoquark and a fermion
triplet. The scalar leptoquark with couplings to leptons and quarks can explain
lepton flavor non-universality observables $R_K$, $R_{K^{(*)}}$, $R_{D^{(*)}}$
and $R_{J/\psi}$. Neutral component of fermion triplet provides current
abundance of dark matter in the Universe. The interesting feature of the
proposal is that the minimal addition of these phenomenologically rich
particles (scalar leptoquark and fermion triplet) assist in realizing the
unification of the gauge couplings associated with the strong and electroweak
forces of standard model when embedded in the non-supersymmetric $SO(10)$ grand
unified theory. We discuss on unification mass scale and the corresponding
proton decay constraints while taking into account the GUT threshold
corrections.


  In this paper, we introduce DiarizationLM, a framework to leverage large
language models (LLM) to post-process the outputs from a speaker diarization
system. Various goals can be achieved with the proposed framework, such as
improving the readability of the diarized transcript, or reducing the word
diarization error rate (WDER). In this framework, the outputs of the automatic
speech recognition (ASR) and speaker diarization systems are represented as a
compact textual format, which is included in the prompt to an optionally
finetuned LLM. The outputs of the LLM can be used as the refined diarization
results with the desired enhancement. As a post-processing step, this framework
can be easily applied to any off-the-shelf ASR and speaker diarization systems
without retraining existing components. Our experiments show that a finetuned
PaLM 2-S model can reduce the WDER by rel. 55.5% on the Fisher telephone
conversation dataset, and rel. 44.9% on the Callhome English dataset.


  Phase-resolved VLT spectroscopy of the bursting Low Mass X-ray Binaries 4U
1636-536/V801 Ara and 4U 1735-444/V926 Sco is presented. Doppler images of the
NIII 4640 Bowen transition reveal compact spots which we attribute to
fluorescent emission from the donor star and enable us to define a new set of
spectroscopic ephemerides. We measure Kem=277+-22 km/s and Kem=226+-22 km/s
from the NIII spots in V801 Ara and V926 Sco respectively which represent
strict lower limits to the radial velocity semi-amplitude of the donor stars.
Our new ephemerides provide confirmation that lightcurve maxima in V801 Ara and
likely V926 Sco occur at superior conjunction of the donor star and hence
photometric modulation is caused by the visibility of the X-ray heated donor.
The velocities of HeII 4686 and the broad Bowen blend are strongly modulated
with the orbital period, with phasing supporting emission dominated by the disc
bulge. In addition, a reanalysis of burst oscillations in V801 Ara, using our
spectroscopic T0, leads to K1=90-113 km/s. We also estimate the K-corrections
for all possible disc flaring angles and present the first dynamical
constraints on the masses of these X-ray bursters. These are K2=360+-74 km/s,
f(M)=0.76+-0.47 Msun and q=0.21-0.34 for V801 Ara and K2=298+-83 km/s,
f(M)=0.53+-0.44 Msun and q=0.05-0.41 for V926 Sco. Disc flaring angles alpha>12
deg and q~0.26-0.34 are favoured for V801 Ara whereas the lack of K1 constraint
for V926 Sco prevents tight constraints on this system. Although both binaries
seem to have intermediate inclinations, the larger equivalent width of the
narrrow NIII line in V801 Ara at phase 0.5 relative to phase 0 suggests that it
has the higher inclination of the two.


  The effect of spatially modulated interaction on quantum phase transition in
one-dimensional interacting spinless fermion system is theoretically
investigated by exact diagonalization and density matrix renormalization group
method. Our calculations show that the periodically modulated interaction can
drive the spinless fermion system into topological charge density wave state.
The topological state is encoded by quasiparticle end states and the fractional
quantized $e/2$ end charges, and characterized by Berry phase and Chern number.
The quasiparticle energy spectra as a function of modulated interaction period
appears a stunning fractal-like structure. For the quasi-periodic case, the
topological phase transition can also occur. In a word, the spatially modulated
interaction can be a new simple and elegant avenue towards realizing to
interacting topological phases.


  Here we propose a technique that successfully reconstructs ocean bathymetry
from the free surface velocity and elevation data. This technique is based on
the principles of open-channel hydraulics, according to which a sub-critical
flow over a seamount creates a free surface dip. The proposed method recognizes
that such free surface dip contains the signature of the bottom topography,
hence inverts the free surface to reconstruct the topography accurately. We
applied our inversion technique on re-analysis data, and reconstructed the
Mediterranean and the Red sea bathymetries of $1/12\degree$ resolution with
approximately $90$\% accuracy.