  Depletion studies provide a way to understand the chemical composition of
interstellar dust grains. We here examine 23 gamma-ray bursts (GRB) optical
afterglow spectra (spanning 0.6<z<5.0) and compare their silicon and iron
dust-phase column densities with different extinction curve parameters to study
the composition of the interstellar dust grains in these high-redshift GRB host
galaxies. The majority of our sample (87%) show featureless extinction curves
and only vary in shape. We observe strong correlations (with >96% significance)
between the total-to-selective extinction, R_V, and the dust-phase column
densities of Si and Fe. Since a large fraction of interstellar iron is locked
in silicate grains, this indicates that high Si and Fe depletion leads to an
increase in the fraction of large silicate grains and vice versa. This suggests
that silicates play a vital role to induce the entire extinction at any
wavelength. On the other hand, the far-UV extinction is usually attributed to
the presence of small silicates. However, we find no trend between the far-UV
parameter of the extinction curve, c_4, and the abundance of Si and Fe in the
dust phase. We, therefore, propose that the far-UV extinction could be a
combined effect of small (probably nanoparticles) dust grains from various
species.


  In this paper we obtain lower bounds on the radius of spatial analyticity of
solutions to the Kawahara equation $u_t + uu_x + \alpha u_{xxx} + \beta
u_{xxxxx} = 0$, $\beta\neq0$, given initial data which is analytic with a fixed
radius. It is shown that the uniform radius of spatial analyticity of solutions
at later time $t$ can decay no faster than $1/|t|$ as $|t|\rightarrow\infty$.


  A megascopic revalidation is offered providing responses and resolutions of
current inconsistencies and existing contradictions in present-day quantum
theory. As the core of this study we present an independent proof of the
Goldstone theorem for a quantum field formulation of molecules and solids.
Along with phonons two types of new quasiparticles appear: rotons and
translons. In full analogy with Lorentz covariance, combining space and time
coordinates, a new covariance is necessary, binding together the internal and
external degrees of freedom, without explicitly separating the centre-of-mass,
which normally applies in both classical and quantum formulations. The
generally accepted view regarding the lack of a simple correspondence between
the Goldstone modes and broken symmetries, has significant consequences: an
ambiguous BCS theory as well as a subsequent Higgs mechanism. The application
of the archetype of the classical spontaneous symmetry breaking, i.e. the
Mexican hat, as compared to standard quantum relations, i.e. the Jahn-Teller
effect, superconductivity or the Higgs mechanism, becomes a disparity. In
short, symmetry broken states have a microscopic causal origin, but transitions
between them have a teleological component. The different treatments of the
problem of the centre of gravity in quantum mechanics and in field theories
imply a second type of Bohr complementarity on the many-body level opening the
door for megascopic representations of all basic microscopic quantum axioms
with further readings for teleonomic megascopic quantum phenomena, which have
no microscopic rationale: isomeric transitions, Jahn-Teller effect, chemical
reactions, Einstein-de Haas effect, superconductivity-superfluidity, and
brittle fracture.


  For nearly a century, the Stoner model has dominated research in itinerant
ferromagnetism, yet recent work on ultracold, optically trapped Fermi gases
suggests that phase separation of spins occurs independent of long-range
magnetic order. In this paper, we consider the breakdown of the Stoner
criterion in a Landau-Fermi liquid with weak non-zero gauge field. Due to a
process analogous to Kohn's theory of a metal-insulator transition, we find the
stability of a Fermi liquid phase in the absence of non-quasiparticle
contributions to the response is strongly dependent on Landau parameters of
mixed partial waves. Our work paves the way for the description of novel
spintronic hardware in the language of Landau-Fermi liquid transport.


  In semiconductor spintronics, the generation of highly spin-polarized
carriers and the efficient probe of spin order (due to strong ferromagnetism)
-- at or above room temperature -- are crucial because it allows for the design
of spin-based semiconductor devices. Usually, such goals were fulfilled in
room-temperature ferromagnetic semiconductors, being rare materials in nature.
While room-temperature antiferromagnetic semiconductors are plentiful, the
possibility for creating highly spin-polarized carriers and strong
ferromagnetism in these materials remain to be unraveled. Here, we explore such
a possibility by first-principles simulations, working with CaTcO$_3$ and
NaOsO$_3$ perovskites -- being room-temperature antiferromagnetic
semiconductors. We find that doping them by electrons or holes results in these
materials to be highly spin-polarized, carrying enormous ferromagnetic moments.
Doping electrons with moderate carrier density can yield strong ferromagnetism
in them, with the ferromagnetic moments being comparable to that in typical
ferromagnetic semiconductors. Our work thus indicates the merit of perovskite
antiferromagnetic semiconductors in spintronics -- for a possible replacement
of ferromagnetic semiconductors.


  Many patients with chronic diseases resort to multiple medications to relieve
various symptoms, which raises concerns about the safety of multiple medication
use, as severe drug-drug antagonism can lead to serious adverse effects or even
death. This paper presents a Decision Support System, called DSSDDI, based on
drug-drug interactions to support doctors prescribing decisions. DSSDDI
contains three modules, Drug-Drug Interaction (DDI) module, Medical Decision
(MD) module and Medical Support (MS) module. The DDI module learns safer and
more effective drug representations from the drug-drug interactions. To capture
the potential causal relationship between DDI and medication use, the MD module
considers the representations of patients and drugs as context, DDI and
patients' similarity as treatment, and medication use as outcome to construct
counterfactual links for the representation learning. Furthermore, the MS
module provides drug candidates to doctors with explanations. Experiments on
the chronic data collected from the Hong Kong Chronic Disease Study Project and
a public diagnostic data MIMIC-III demonstrate that DSSDDI can be a reliable
reference for doctors in terms of safety and efficiency of clinical diagnosis,
with significant improvements compared to baseline methods.


  We study a stochastic differential equation with an unbounded drift and
general H\"older continuous noise of an arbitrary order. The corresponding
equation turns out to have a unique solution that, depending on a particular
shape of the drift, either stays above some continuous function or has
continuous upper and lower bounds. Under some additional assumptions on the
noise, we prove that the solution has moments of all orders. We complete the
study providing a numerical scheme for the solution. As an illustration of our
results and motivation for applications, we suggest two stochastic volatility
models which we regard as generalizations of the CIR and CEV processes.


  Species tree estimation is a complex problem, due to the fact that different
parts of the genome can have different evolutionary histories than the genome
itself. One of the causes for this discord is incomplete lineage sorting (also
called deep coalescence), which is a population-level process that produces
gene trees that differ from the species tree. The last decade has seen a large
number of new methods developed to estimate species trees from multi-locus
datasets, specifically addressing this cause of gene tree heterogeneity. In
this paper, we review these methods, focusing mainly on issues that relate to
analyses of datasets containing large numbers of species or loci (or both). We
also discuss divide-and-conquer strategies for enabling species tree estimation
methods to run on large datasets, including new approaches that are based on
algorithms (such as TreeMerge) for the Disjoint Tree Merger problem.


  In the d=3 gluon mass problem in pure-glue non-Abelian $SU(N)$ gauge theory
we pay particular attention to the observed (in Landau gauge) violation of
positivity for the spectral function of the gluon propagator. This causes a
large bulge in the propagator at small momentum. Mass is defined through
$m^{-2}=\Delta (p=0)$, where $\Delta(p)$ is the scalar function for the gluon
propagator in some chosen gauge, it is not a pole mass and is generally
gauge-dependent, except in the gauge-invariant Pinch Technique (PT). We
truncate the PT equations with a new method called the vertex paradigm that
automatically satisfies the QED-like Ward identity relating the 3-gluon PT
vertex function with the PT propagator. The mass is determined by a homogeneous
Bethe-Salpeter equation involving this vertex and propagator. This gap equation
also encapsulates the Bethe-Salpeter equation for the massless scalar
excitations, essentially Nambu-Goldstone fields, that necessarily accompany
gauge-invariant gluon mass. The problem is to find a good approximate value for
$m$ and at the same time explain the bulge, which by itself leads, in the gap
equation for the gluon mass, to excessively large values for the mass. Our
point is not to give a high-accuracy determination of $m$ but to clarify the
way in which the propagator bulge and a fairly accurate estimate of $m$ can
co-exist, and we use various approximations that illustrate the underlying
mechanisms. The most critical point is to satisfy the Ward identity. In the PT
we estimate a gauge-invariant dynamical gluon mass of $m \approx Ng^2/(2.48
\pi)$. We translate these results to the Landau gauge using a
background-quantum identity involving a dynamical quantity $\kappa$ such that
$m=\kappa m_L$, where $m_L^{-2}\equiv \Delta_L(p=0)$. Given our estimates for
$m,\kappa$ the relation is fortuitously well-satisfied for $SU(2)$ lattice
data.


  In previous papers, we studied the asymptotic behaviour of
$S_N(A,X)=(2N+1)^{-d/2}\sum_{n \in A_N} X_n,$ where $X$ is a centered,
stationary and weakly dependent random field, and $A_N=A \cap [-N,N]^d$, $A
\subset \mathbb{Z}^d$. This leads to the definition of asymptotically
measurable sets, which enjoy the property that $S_N(A;X)$ has a Gaussian weak
limit for any $X$ belonging to a certain class. Here we extend this type of
results to the case of weakly dependent triangular arrays and present an
application of this technique to regression models. Indeed, we prove that CLT
and related results hold for $X_n^N=\varphi(\xi_n^N,Y_n^N), n \in
\mathbb{Z}^d$, where $\varphi$ satisfies certain regularity conditions, $\xi$
and $Y$ are independent random fields, $\xi$ is weakly dependent and $Y$
satisfies some Strong Law of Large Numbers.


  We construct uncountably categorical 3-nilpotent groups of exponent p > 3.
They are not one-based and do not allow the interpretation of an infinite
field. Therefore they are counterexamples to Zilbers Conjecture. First
2-nilpotent new uncoutably categorical groups were contructed in [3]. Here we
use the method of the additive Collapse developed in [5]. Essentially we work
with 3-nilpotent graded Lie algebras over the field with p elements.


  We show how Alesker's theory of valuations on manifolds gives rise to an
algebraic picture of the integral geometry of any Riemannian isotropic space.
We then apply this method to give a thorough account of the integral geometry
of the complex space forms, i.e. complex projective space, complex hyperbolic
space and complex euclidean space. In particular, we compute the family of
kinematic formulas for invariant valuations and invariant curvature measures in
these spaces. In addition to new and more efficient framings of the tube
formulas of Gray and the kinematic formulas of Shifrin, this approach yields a
new formula expressing the volumes of the tubes about a totally real
submanifold in terms of its intrinsic Riemannian structure. We also show by
direct calculation that the Lipschitz-Killing valuations stabilize the subspace
of invariant angular curvature measures, suggesting the possibility that a
similar phenomenon holds for all Riemannian manifolds. We conclude with a
number of open questions and conjectures.


  Stars form in embedded star clusters which play a key role in determining the
properties of a galaxy's stellar population. Physical mechanisms discussed in
this paper are runaway stars shot out from young clusters, binary-star
disruption in clusters, gas blow-out from clusters and the origin of thick
galactic disks. I emphasise that the SNIa rate per low-mass star depends on the
star-clusters formed in a galaxy and I discuss the IGIMF theory. Based on the
IGIMF theory, the re-calibrated Halpha-luminosity--SFR relation implies dwarf
irregular galaxies to have the same gas-depletion time-scale as major disk
galaxies, suggesting a major change in our understanding of dwarf-galaxy
evolution. The IGIMF-theory also naturally leads to the observed radial Halpha
cutoff in disk galaxies without a radial star-formation cutoff. It emerges that
the thorough understanding of the physics and distribution of star clusters may
be leading to a major paradigm shift in our understanding of galaxy evolution.


  We present an original multi-state projective diabatization scheme based on
the Green's function formalism that allows the systematic mapping of many-body
ab initio calculations onto effective excitonic models. This method inherits
the ability of the Bethe-Salpeter equation to describe Frenkel molecular
excitons and intermolecular charge-transfer states equally well, as well as the
possibility for an effective description of environmental effects in a QM/MM
framework. The latter is found to be a crucial element in order to obtain
accurate model parameters for condensed phases and to ensure their
transferability to excitonic models for extended systems. The method is
presented through a series of examples illustrating its quality, robustness,
and internal consistency.


  Super-Kamiokande has reported the results for the lepton events in the
atmospheric neutrino experiment. These results have been presented for a 22.5kT
water fiducial mass on an exposure of 1489 days, and the events are divided
into sub-GeV, multi-GeV and PC events. We present a study of nuclear medium
effects in the sub-GeV energy region of atmospheric neutrino events for the
quasielastic scattering, incoherent and coherent pion production processes, as
they give the most dominant contribution to the lepton events in this energy
region. We have used the atmospheric neutrino flux given by Honda et al. These
calculations have been done in the local density approximation. We take into
account the effect of Pauli blocking, Fermi motion, Coulomb effect,
renormalization of weak transition strengths in the nuclear medium in the case
of the quasielastic reactions. The inelastic reactions leading to production of
leptons along with pions is calculated in a $\Delta $- dominance model by
taking into account the renormalization of $\Delta$ properties in the nuclear
medium and the final state interaction effects of the outgoing pions with the
residual nucleus. We present the results for the lepton events obtained in our
model with and without nuclear medium effects, and compare them with the Monte
Carlo predictions used in the simulation and the experimentally observed events
reported by the Super-Kamiokande collaboration.


  Surfaces of carbonaceous asteroids (C-complex) have shown diverse contrasting
spectral variations, which may be related to space weathering. We performed
laser irradiation experiments on CI and CM simulant material under vacuum to
mimic the spectral alteration induced by micrometeorite impacts. We used in
situ ultraviolet-visible and near-infrared reflectance spectroscopy to analyze
spectral alterations in response to pulsed laser irradiation, as well as
scanning electron microscopy and x-ray photoelectron spectroscopy to search for
microstructural and compositional changes. Laser irradiation causes an increase
in spectral slope (reddening) and a decrease in the albedo (darkening), and
these changes are stronger in the ultraviolet-visible region. These spectral
changes are likely driven by the excess iron found in the altered surface
region, although other factors, such as the observed structural changes, may
also contribute. Additionally, while the 0.27~${\mu}m$ band appears relatively
stable under laser irradiation, a broad feature at 0.6~${\mu}m$ rapidly
disappears with laser irradiation, suggesting that space weathering may inhibit
the detection of any feature in this spectral region, including the
0.7~${\mu}m$ band, which has typically been used an indicator of hydration.
Comparing our laboratory results with optical spectrophotometry observations of
C-complex asteroids, we find that the majority of objects are spectrally red
and possess colors that are similar to our irradiated material rather than our
fresh samples. Furthermore, we also find that ``younger'' and ``older''
C-complex families have similar colors, suggesting that the space weathering
process is near-equal or faster than the time it takes to refresh the surfaces
of these airless bodies.


  The zero modes of closed strings on a torus --the torus coordinates plus dual
coordinates conjugate to winding number-- parameterize a doubled torus. In
closed string field theory, the string field depends on all zero-modes and so
can be expanded to give an infinite set of fields on the doubled torus. We use
the string field theory to construct a theory of massless fields on the doubled
torus. Key to the consistency is a constraint on fields and gauge parameters
that arises from the L_0 - \bar L_0=0 condition in closed string theory. The
symmetry of this double field theory includes usual and 'dual diffeomorphisms',
together with a T-duality acting on fields that have explicit dependence on the
torus coordinates and the dual coordinates. We find that, along with gravity, a
Kalb-Ramond field and a dilaton must be added to support both usual and dual
diffeomorphisms. We construct a fully consistent and gauge invariant action on
the doubled torus to cubic order in the fields. We discuss the challenges
involved in the construction of the full nonlinear theory. We emphasize that
the doubled geometry is physical and the dual dimensions should not be viewed
as an auxiliary structure or a gauge artifact.


  In this paper, we elaborate analytical theory of domain wall dynamics close
to the angular momentum compensation point based on non-linear dynamic
equations derived from the effective Lagrangian of a ferrimagnet. Analysis of
the precession angle and domain wall velocity oscillations in post Walker
regime in a ferrimagnet is performed. In the framework of the proposed model,
we explore dynamic processes in the Walker and post Walker regimes. We show
that although spin oscillations quench the dynamics of domain walls near the
Walker breakdown field, a further increase of the driving magnetic field
increases domain wall speed and mobility. An anomalous behavior of domain wall
dynamic properties near the angular momentum compensation point in ferrimagnets
is discussed.


  We consider all genus 2 curves over Q given by an equation y^2 = f(x) with f
a squarefree polynomial of degree 5 or 6, with integral coefficients of
absolute value at most 3. For each of these roughly 200000 isomorphism classes
of curves, we decide if there is a rational point on the curve or not, by a
combination of techniques. For a small number of curves, our result is
conditional on the BSD conjecture or on GRH.


  The Gaussian state description of continuous variables is adapted to describe
the quantum interaction between macroscopic atomic samples and continuous-wave
light beams. The formalism is very efficient: a non-linear differential
equation for the covariance matrix of the atomic system explicitly accounts for
both the unitary evolution, the dissipation and noise due to the atom-light
interaction, and the back-action due to homodyne optical detection on the beam
after its interaction with the atoms. Applications to atomic spin squeezing and
estimation of unknown classical parameters are presented, and extensions beyond
the Gaussian states are discussed.


  We show how a candidate mean-field amplitude can be constructed from the
exact wave function of an externally forced $N$-Boson system. The construction
makes use of subsidiary $(N-1)$-particle states which are propagated in time in
addition to the true $N$-particle state, but does not involve spontaneous
breaking of the $U(1)$ symmetry associated with particle number conservation.
Provided the flow in Fock space possesses a property which we call maximum
stiffness, or $t$-coherence, the candidate amplitude actually satisfies the
time-dependent Gross-Pitaevskii equation, and then serves as macroscopic wave
function of the forced $N$-particle system. The general procedure is
illustrated in detail by numerical calculations performed for the model of a
driven bosonic Josephson junction, which allows one to keep track of all
contributions which usually are subject to uncontrolled assumptions. These
calculations indicate that macroscopic wave functions can persist even under
conditions of strong forcing, but are rapidly destroyed upon entering a regime
of chaotic dynamics. Our results provide a foundation for future attempts to
manipulate, and actively control, macroscopic wave functions by means of
purposefully designed force protocols.


  We investigate the attractor solution in the coupled Yang-Mills field dark
energy models with the general interaction term, and obtain the constraint
equations for the interaction if the attractor solution exists. The research
also shows that, if the attractor solution exists, the equation-of-state of the
dark energy must evolve from $w_y>0$ to $w_y\le-1$, which is slightly suggested
by the observation. At the same time, the total equation-of-state in the
attractor solution is $w_{tot}=-1$, the universe is a de Sitter expansion, and
the cosmic big rip is naturally avoided. These features are all independent of
the interacting forms.


  This is a slightly expanded version of the talk given by Ch.O. at the
conference "Instantons in complex geometry", at the Steklov Institute in
Moscow. The purpose of this talk was to explain the algebraic results of our
paper "Abelian Yang-Mills theory on Real tori and Theta divisors of Klein
surfaces".
  In this paper we compute determinant index bundles of certain families of
Real Dirac type operators on Klein surfaces as elements in the corresponding
Grothendieck group of Real line bundles in the sense of Atiyah. On a Klein
surface these determinant index bundles have a natural holomorphic description
as theta line bundles. In particular we compute the first Stiefel-Whitney
classes of the corresponding fixed point bundles on the real part of the Picard
torus. The computation of these classes is important, because they control to a
large extent the orientability of certain moduli spaces in Real gauge theory
and Real algebraic geometry.


  High-frequency financial data can be collected as a sequence of curves over
time; for example, as intra-day price, currently one of the topics of greatest
interest in finance. The Functional Data Analysis framework provides a suitable
tool to extract the information contained in the shape of the daily paths,
often unavailable from classical statistical methods. In this paper, a novel
goodness-of-fit test for autoregressive Hilbertian (ARH) models, with unknown
and general order, is proposed. The test imposes just the Hilbert-Schmidt
assumption on the functional form of the autocorrelation operator, and the test
statistic is formulated in terms of a Cram\'er-von Mises norm. A wild bootstrap
resampling procedure is used for calibration, such that the finite sample
behavior of the test, regarding power and size, is checked via a simulation
study. Furthermore, we also provide a new specification test for diffusion
models, such as Ornstein-Uhlenbeck processes, illustrated with an application
to intra-day currency exchange rates. In particular, a two-stage methodology is
proffered: firstly, we check if functional samples and their past values are
related via ARH(1) model; secondly, under linearity, we perform a functional
F-test.


  In Sgr A* at the Galactic center, by far the closest and easiest supermassive
black hole we can study, the observational evidence is increasingly pointing to
the presence of a compact, hot, magnetized disk feeding the accretor. In such
low-Mach-number plasmas, forces arising, e.g., from pressure gradients in the
plasma, can altogether negate the warping of disks around Kerr black holes
caused by the Bardeen-Petterson effect and can lead to coherent precession of
the entire disk. In this Letter, we present for the first time highly detailed
3D SPH simulations of the accretion disk evolution in Sgr A*, guided by
observational constraints on its physical characteristics, and conclude that
indeed the Bardeen-Petterson effect is probably absent in this source. Given
what we now understand regarding the emission geometry in this object, we
suggest that a ~ 50-500-day modulation in Sgr A*'s spectrum, arising from the
disk precession, could be an important observational signature; perhaps the ~
106-day period seen earlier in its radio flux, if confirmed, could be due to
this process. On the other hand, if future observations do not confirm this
long modulation in Sgr A*'s spectrum, this would be an indication that either
the disk size or orientation is very different from current estimates, or that
the black hole is not spinning at all (unlikely), or that our current
understanding of how it produces its radiative output is incorrect.


  We present the results of high-resolution spectropolarimetric observations of
the optically dominant component in the rare hydrogen-deficient binary system
upsilon Sgr. Only a small number of such systems in a very late phase of helium
shell burning are currently known. The mass transfer from the donor star in
binary systems usually leads to the stripping of its hydrogen envelope.
Consequently, since the mass of the secondary increases, it appears
rejuvenated. Using a few ESO FORS1 low-resolution spectropolarimetric
observations of this system, Hubrig et al. announced in 2009 the presence of a
magnetic field of the order of -70 - -80G. Here we report on more recent
high-resolution ESO HARPS spectropolarimetric observations showing that the
primary in upsilon Sgr is a spectrum variable star and possesses a weak
magnetic field of the order of a few tens of Gauss. The detection of a magnetic
field in this rare hydrogen-deficient binary is of particular interest, as such
systems are frequently discussed as probable progenitors of core-collapse
supernovae and gravitational-wave sources. Future magnetic studies of such
systems will be worthwhile to gain deeper insights into the role of magnetic
fields in the evolution of massive stars in binary systems.


  As software systems have grown in scale and complexity the test suites built
alongside those systems have also become increasingly complex. Understanding
key aspects of test suites, such as their coverage of production code, is
important when maintaining or reengineering systems. This work investigates the
distribution of unit tests in Open Source Software (OSS) systems through the
visualization of data obtained from both dynamic and static analysis. Our
long-term aim is to support developers in their understanding of test
distribution and the relationship of tests to production code. We first obtain
dynamic coupling information from five selected OSS systems and we then map the
test and production code results. The mapping is shown in graphs that depict
both the dependencies between classes and static test information. We analyze
these graphs using Centrality metrics derived from graph theory and SNA. Our
findings suggest that, for these five systems at least, unit test and dynamic
coupling information 'do not match', in that unit tests do not appear to be
distributed in line with the systems' dynamic coupling. We contend that, by
mapping dynamic coupling data onto unit test information, and through the use
of software metrics and visualization, we can locate central system classes and
identify to which classes unit testing effort has (or has not) been dedicated.


  This paper considers linear model selection when the response is
vector-valued and the predictors are randomly observed. We propose a new
approach that decouples statistical inference from the selection step in a
"post-inference model summarization" strategy. We study the impact of predictor
uncertainty on the model selection procedure. The method is demonstrated
through an application to asset pricing.


  We investigate the implications of intrinsic time deparameterization on the
phase space of the connection representation of canonical gravity in the form
of the Ashtekar variables. We find that, much like the metric representation of
this formalism, the Hamiltonian constraint now becomes a physical Hamiltonian
generating evolution with respect to an intrinsic time. The complete
observables for the theory are then constructed. Also, the dynamics in this
formulation is cast into a classical master constraint theory.


  New measurements of the coherent elastic neutrino-nucleus scattering (CEvNS)
are expected to be achieved in the near future by using two neutrino production
channels with different energy distributions: the very low energy electron
antineutrinos from reactor sources and the muon and electron neutrinos from
spallation neutron sources (SNS) with a relatively higher energy. Although
precise measurements of this reaction would allow an improved knowledge of
standard and beyond the Standard Model physics, it is important to distinguish
the different new contributions to the process. We illustrate this idea by
constraining the average neutron root mean square (rms) radius of the
scattering material, as a standard physics parameter, together with the
nonstandard interactions (NSI) contribution as the new physics formalism. We
show that the combination of experiments with different neutrino energy ranges
could give place to more robust constraints on these parameters as long as the
systematic errors are under control.


  We propose a second-order total generalized variation (TGV) regularization
for the reconstruction of the initial condition in variational data
assimilation problems. After showing the equivalence between TGV regularization
and the Bayesian method for the MAP estimator, we focus on the detailed study
of the inviscid Burgers' data assimilation problem. Due to the difficult
structure of the governing hyperbolic conservation law, we consider a
discretize-then-optimize approach and derive first-order optimality conditions
for the problem. For the numerical solution, we propose a globalized reduced
Newton-type method and prove convergence of the algorithm to stationary points.
The paper finishes with some numerical experiments where among others, the
performance of TGV-regularization compared to the TV-regularization is tested.


  We partition the fast escaping set of a transcendental entire function into
two subsets, the maximally fast escaping set and the non-maximally fast
escaping set. These sets are shown to have strong dynamical properties. We show
that the intersection of the Julia set with the non-maximally fast escaping set
is never empty. The proof uses a new covering result for annuli, which is of
wider interest.
  It was shown by Rippon and Stallard that the fast escaping set has no bounded
components. In contrast, by studying a function considered by Hardy, we give an
example of a transcendental entire function for which the maximally and
non-maximally fast escaping sets each have uncountably many singleton
components.


  The aim of this paper is to compare two asset allocation methods for a
pension scheme during the decumulation phase in the simplified portfolio
selection between a risky asset following a geometric Brownian motion and a
riskless asset. The two asset allocation criteria are the ruin probability of
the insurance company and the optimization of the economic capital. We first
solve the asset allocation problem with deterministic pension payments then
with stochastic mortality risk. We analyze the part of mortality risk in the
global risk of the company. Then we show the impact of the indexation of the
pensions to the inflation on the asset allocation.


  The GC problem is to identify a pre-determined number of center vertices such
that the distances or costs from (or to) the centers to (or from) other
vertices is minimized. The bottleneck of a path is the minimum capacity of
edges on the path. The Bottleneck Paths (BP) problem is to compute the paths
that give us the maximum bottleneck values between pairs of vertices. The Graph
Bottleneck (GB) problem is to find the minimum bottleneck value out of
bottleneck paths for all possible pairs of vertices. We give two similar
algorithms that are based on binary search to solve the 1-center GC problem and
the GB problem on directed graphs with unit edge costs. We achieve
$\tilde{O}(n^{2.373})$ worst case time complexity for both the 1-center GC
problem and the GB problem, where $n$ is the number of vertices in the graph.
This is better than the straightforward methods of solving the two problems in
$O(n^{2.575})$ and $O(n^{2.688})$ time bounds, respectively.
  We then combine the Bottleneck Paths (BP) problem with the well known
Shortest Paths (SP) problem to compute the shortest paths for all possible flow
values. We call this problem the Shortest Paths for All Flows (SP-AF) problem.
We show that if the flow demand is uncertain, but between two consecutive
capacity values, the unique shortest path can be computed to push that flow. If
the uncertainty stretches over two intervals, we need to prepare two shortest
paths to accommodate the uncertainty, etc. In introducing this new problem, we
define a new semi-ring called the distance/flow semi-ring, and show that the
well known algorithm by Floyd can be used over the distance/flow semi-ring to
solve the All Pairs Shortest Paths for All Flows (APSP-AF) problem.


  We predict a universal echo phenomenon present in the time evolution of
many-body states of interacting quantum systems described by Fermi-Hubbard
models. It consists of the coherent revival of transition probabilities echoing
a sudden flip of the spins that, contrary to its single-particle (Hahn)
version, is not dephased by interactions or spin-orbit coupling. The many-body
spin echo signal has a universal shape independent of the interaction strength,
and an amplitude and sign depending only on combinatorial relations between the
number of particles and the number of applied spin flips. Our analytical
predictions, based on semiclassical interfering amplitudes in Fock space
associated with chaotic mean-field solutions, are tested against extensive
numerical simulations confirming that the coherent origin of the echo lies in
the existence of anti-unitary symmetries.


  Location-Based Service (LBS) becomes increasingly popular with the dramatic
growth of smartphones and social network services (SNS), and its context-rich
functionalities attract considerable users. Many LBS providers use users'
location information to offer them convenience and useful functions. However,
the LBS could greatly breach personal privacy because location itself contains
much information. Hence, preserving location privacy while achieving utility
from it is still an challenging question now. This paper tackles this
non-trivial challenge by designing a suite of novel fine-grained
Privacy-preserving Location Query Protocol (PLQP). Our protocol allows
different levels of location query on encrypted location information for
different users, and it is efficient enough to be applied in mobile platforms.


  We present a Lagrangian description of the $SU(2)/U(1)$ coset model perturbed
by its first thermal operator. This is the simplest perturbation that changes
sign under Krammers--Wannier duality. The resulting theory, which is a
2--component generalization of the sine--Gordon model, is then taken in
Minkowski space. For negative values of the coupling constant $g$, it is
classically equivalent to the $O(4)$ non--linear $\s$--model reduced in a
certain frame. For $g > 0$, it describes the relativistic motion of vortices in
a constant external field. Viewing the classical equations of motion as a zero
curvature condition, we obtain recursive relations for the infinitely many
conservation laws by the abelianization method of gauge connections. The higher
spin currents are constructed entirely using an off--critical generalization of
the $W_{\infty}$ generators. We give a geometric interpretation to the
corresponding charges in terms of embeddings. Applications to the chirally
invariant $U(2)$ Gross--Neveu model are also discussed.


  We report on the fabrication of metasurface phase plates consisting of gold
nanoantenna arrays that generate Laguerre-Gaussian modes from a circularly
polarized Gaussian input beam. The corresponding helical phase profiles with
radial discontinuities are encoded in the metasurfaces by the orientation of
the nanoantennas. A common-path interferometer is used to determine the orbital
angular momentum of the generated beams. Additionally, we employ digital
holography to record detailed phase profiles of the Laguerre-Gaussian modes.
Experiments with different laser sources demonstrate the broadband operation of
the metasurfaces.


  In this paper we review the most common descriptions for the first order
phase transition to deconfined quark matter in the core of neutron stars. We
also present a new description of these phase transitions in the core of
proto-neutron stars, in which more constraints are enforced so as to include
trapped neutrinos. Finally, we calculate the emission of gravitational waves
associated with deconfinement phase transitions, discuss the possibility of
their detection, and how this would provide information about the equation of
state of dense matter.


  Motivated by the need to model the dependence between regions of interest in
functional neuroconnectivity for efficient inference, we propose a new
sampling-based Bayesian clustering approach for covariance structures of
high-dimensional Gaussian outcomes. The key technique is based on a Dirichlet
process that clusters covariance sub-matrices into independent groups of
outcomes, thereby naturally inducing sparsity in the whole brain connectivity
matrix. A new split-merge algorithm is employed to achieve convergence of the
Markov chain that is shown empirically to recover both uniform and Dirichlet
partitions with high accuracy. We investigate the empirical performance of the
proposed method through extensive simulations. Finally, the proposed approach
is used to group regions of interest into functionally independent groups in
the Autism Brain Imaging Data Exchange participants with autism spectrum
disorder and and co-occurring attention-deficit/hyperactivity disorder.


  We obtain linear elasticity as $\Gamma$-limit of finite elasticity under
incompressibility assumption and Dirichlet boundary conditions. The result is
shown for a large class of energy densities for rubber-like materials.


  Safeguarding data from unauthorized exploitation is vital for privacy and
security, especially in recent rampant research in security breach such as
adversarial/membership attacks. To this end, \textit{unlearnable examples}
(UEs) have been recently proposed as a compelling protection, by adding
imperceptible perturbation to data so that models trained on them cannot
classify them accurately on original clean distribution. Unfortunately, we find
UEs provide a false sense of security, because they cannot stop unauthorized
users from utilizing other unprotected data to remove the protection, by
turning unlearnable data into learnable again. Motivated by this observation,
we formally define a new threat by introducing \textit{learnable unauthorized
examples} (LEs) which are UEs with their protection removed. The core of this
approach is a novel purification process that projects UEs onto the manifold of
LEs. This is realized by a new joint-conditional diffusion model which denoises
UEs conditioned on the pixel and perceptual similarity between UEs and LEs.
Extensive experiments demonstrate that LE delivers state-of-the-art countering
performance against both supervised UEs and unsupervised UEs in various
scenarios, which is the first generalizable countermeasure to UEs across
supervised learning and unsupervised learning. Our code is available at
\url{https://github.com/jiangw-0/LE_JCDP}.


  Spectral unmixing is one of the most important quantitative analysis tasks in
hyperspectral data processing. Conventional physics-based models are
characterized by clear interpretation. However they may not be suitable for
analyzing scenes with unknown complex physical characteristics. Data-driven
methods have developed rapidly in recent years, in particular deep learning
methods because they possess superior capability in modeling complex and
nonlinear systems. Simply transferring these methods as black-boxes to conduct
unmixing may lead to low physical interpretability and generalization ability.
This article reviews hyperspectral unmixing works that integrate advantages of
both physics-based models and data-driven methods by means of deep neural
network structures design, prior design and loss design. Most of these methods
derive from a common mathematical optimization framework, and combine good
interpretability with high accuracy.


  This paper summarizes recent developments in the study of the propagation of
ultra-high energy cosmic ray protons or nuclei in the Universe, with emphasis
on the consequences of energy losses and on the influence of extra-galactic
magnetic fields.


  The two dimensional Hasegawa-Mima (HM) equation $$ -\Delta u_t+u_t =
\{u,\Delta u\} + ku_y$$ describes the time evolution of drift waves in
magnetically-confined plasma. Several authors have treated the HM equation
theoretically and numerically, with difficulties arising when handling the
non-linear Poisson's bracket $\{u,\Delta u\}:=u_x\Delta u_u-u_y\Delta u_x $. In
this paper, we introduce a new decoupling approach that avoids the Poisson's
bracket term by reformulating the HM equation as a system of two linear PDEs, a
solution of which is a pair $(u,w)$ such that
$$(HM)\,\,\,\left\{\begin{array}{lll} w_t + \vec{V}(u) \cdot \nabla w = ku_y\\
-\Delta u+u=w, \\ \end{array}\right.$$ where $\vec{V}(u)= -u_y \vec{\textbf{i}}
+ u_x \vec{\textbf{j}}$ is a divergence-free vector field. Based on this
coupled hyperbolic-elliptic system, we derive several variational frames, all
propitious for finding weak solutions with spacial periodic boundary conditions
and lower regularity assumptions on the initial data. More precisely, for
initial data $u_0 \in H_P^2(\Omega)$ with $w_0:=(I-\Delta) u_0 \in
L^2(\Omega)$, we prove the existence of a weak solution that is global in time.
And for initial data $u_0 \in H_P^3(\Omega)$ with $w_0:=(I-\Delta) u_0 \in
H_P^1(\Omega) \cap L^\infty(\Omega)$, we prove the existence of a unique strong
solution that is local in time. Our proofs are based on the existence of
fixed-point ordered pairs $\{u_N,w_N\}$ that solve Petrov-Galerkin HM systems,
constructed using spacial Fourier basis. Through appropriate a-priori estimates
combined with compactness arguments, we reach when $N\to\infty$ limit point
solutions $(u,w)$ to the (HM) system.


  The observed abundance diversities among the CEMP stars can shed light on the
formation and evolution of elements in the early Galaxy. In this work, we
present results obtained from a detailed abundance analysis of a sample of
seven extrinsic carbon stars. The analysis is based on high-resolution spectra
obtained with
  HCT/HESP (R$\sim$60,000) and SUBARU/HDS (R$\sim$50,000). We present, for the
first time, the elemental abundance results for the objects BD$-$19 132,
BD$-$19 290, HE~1304$-$2111, HE~1354$-$2257, and BD+19 3109. Abundances of a
few elements are available in literature for HE~1157$-$0518 and HD~202851, we
present an update on the abundances of these elements along with new abundance
estimates for several other elements. Our analysis confirms the object
HD~202851 to be a CH star. While BD$-$19 132, HE~1354$-$2257, and BD+19 3109
are found to be CEMP-s stars, the objects BD$-$19 290, HE~1157$-$0518, and
HE~1304$-$2111 are found to belong to CEMP-r/s group. The observed abundance
patterns of the three CEMP-r/s stars are well reproduced with the i-process
model predictions. While the objects BD+19 3109 and HD~202851 are confirmed
binaries, the binary status of the remaining objects are not known. Analysis
based on different elemental abundance ratios confirms low-mass former AGB
companions for all the objects. Kinematic analysis shows that BD$-$19 290,
HE~1157$-$0518, HE~1354$-$2257, and BD+19 3109 belong to the Galactic halo,
whereas BD$-$19 132, HE~1304$-$2111, and HD~202851 are members of Galactic thin
disk.


  In 2013, Pak and Panova proved the strict unimodality property of
$q$-binomial coefficients $\binom{\ell+m}{m}_q$ (as polynomials in $q$) based
on the combinatorics of Young tableaux and the semigroup property of Kronecker
coefficients. They showed it to be true for all $\ell,m\geq 8$ and a few other
cases. We propose a different approach to this problem based on computer
algebra, where we establish a closed form for the coefficients of these
polynomials and then use cylindrical algebraic decomposition to identify
exactly the range of coefficients where strict unimodality holds. This strategy
allows us to tackle generalizations of the problem, e.g., to show unimodality
with larger gaps or unimodality of related sequences. In particular, we present
proofs of two additional cases of a conjecture by Stanley and Zanello.


  In this work, the stopping power of a partially ionized plasma is analyzed by
means of free electron stopping and bound electron stopping. For the first one,
the RPA dielectric function is used, and for the latter one, an interpolation
of high and low projectile velocity formulas is used. The dynamical energy loss
of an ion beam inside a plasma is estimated by using an iterative scheme of
calculation. The Abel inversion is also applied when we have a plasma with
radial symmetry. Finally, we compare our methods with two kind of plasmas. In
the first one, we estimate the energy loss in a plasma created by a laser
prepulse, whose density is approximated by a piecewise function. For the latter
one, a radial electron density is supposed and the stopping is obtained as
function of radius from the calculated lateral points. In both cases, the
dependence with the density profile is observed.


  We show that the Coulomb drag effect exhibits saturation at small
temperatures, when calculated to the third order in the interlayer
interactions. The zero-temperature transresistance is inversely proportional to
the third power of the dimensionless sheet conductance. The effect is therefore
the strongest in low mobility samples. This behavior should be contrasted with
the conventional (second order) prediction that the transresistance scales as a
certain power of temperature and is almost mobility-independent. The result
demonstrates that the zero-temperature drag is not an unambiguous signature of
a strongly-coupled state in double-layer systems.


  Analysis of time-domain profiles for gravitational perturbations shows that
Gauss-Bonnet black holes in a de Sitter world possess a new kind of dynamical
instability which does not take place for asymptotically flat
Einstein-Gauss-Bonnet black holes. The new instability is in the gravitational
perturbations of the scalar type and is due to the nonvanishing cosmological
constant. Analysis of the quasinormal spectrum in the stability sector shows
that although the scalar type of gravitational perturbations alone does not
obey Hod's conjectural bound, connecting the damping rate and the Hawking
temperature, the vector and tensor types (and thereby the gravitational
spectrum as a whole) do obey it.


  In the framework of the grand-canonical ensemble of statistical mechanics, we
give an exact diagrammatic representation of the density profiles in a
classical multicomponent plasma near a dielectric wall. By a reorganization of
Mayer diagrams for the fugacity expansions of the densities, we exhibit how the
long-range of both the self-energy and pair interaction are exponentially
screened at large distances from the wall. However, the self-energy due to
Coulomb interaction with images still diverges in the vicinity of the
dielectric wall and the variation of the density is drastically different at
short or large distances from the wall. This variation is involved in the
inhomogeneous Debye-H\"uckel equation obeyed by the screened pair potential.
Then the main difficulty lies in the determination of the latter potential at
every distance. We solve this problem by devising a systematic expansion with
respect to the ratio of the fundamental length scales involved in the two
coulombic effects at stake. (The application of this method to a plasma
confined between two ideally conducting plates and to a quantum plasma will be
presented elsewhere). As a result we derive the exact analytical perturbative
expressions for the density profiles up to first order in the coupling between
charges. The mean-field approach displayed in Paper I is then justified.


  Understanding the solar corona requires knowledge of its dynamics through its
various layers and subsequent connectivity to the heliosphere. This requires
understanding the nature of the outflows and the physical transitions through
the middle corona (~1.5-6.0 Rs). While this region is still inaccessible to in
situ measurements, remote sensing observations are available, but their
interpretation can be controversial due to line-of-sight effects and the
non-radial motion of outflowing structures close to the Sun (<3.0 Rs). In this
work, we describe a method to mitigate these challenges by generating
non-radial Height-Time profiles of outflows by using advanced image processing
techniques. The North and South boundaries of a large equatorial streamer
during the 2008 solar minimum were identified in STEREO/SECCHI solar images,
using two different methodologies based on thresholds of brightness and
piece-wise polynomial function fitting. To address line-of-sight issues, we
used tomographic reconstruction of the 3D distribution of the coronal electron
density based on SECCHI/COR2 images. Spectral analysis of the time series of
the position angle of the streamer boundary revealed its oscillatory nature at
some heights at 36-48 hours and 10.5-14.6 hours. Dividing the distance between
the North and South streamer boundaries in equal parts at each height, we
obtained non-radial Height-Time paths from which we generated non-radial
profiles of corona/solar wind plasma outflow. We tracked outflows as they moved
uninterruptedly from the Sun in EUVI, through COR1 and into COR2. Finally, we
discuss preliminary results of non-radial plane-of-sky velocities for a CME and
two small-scale features.


  In this paper, we present a computationally efficient technique based on the
\emph{Method of Lines} (MOL) for the approximation of the Bermudan option
values via the associated partial differential equations (PDEs). The MOL
converts the Black Scholes PDE to a system of ordinary differential equations
(ODEs). The solution of the system of ODEs so obtained only requires spatial
discretization and avoids discretization in time. Additionally, the exact
solution of the ODEs can be obtained efficiently using the exponential matrix
operation, making the method computationally attractive and straightforward to
implement. An essential advantage of the proposed approach is that the
associated Greeks can be computed with minimal additional computations. We
illustrate, through numerical experiments, the efficacy of the proposed method
in pricing and computation of the sensitivities for a European call,
cash-or-nothing, powered option, and Bermudan put option.


  The planned neutrino program at Fermilab requires large proton beam
intensities in excess of 2 MW. Measuring the transverse profiles of these high
intensity beams is challenging and often depends on non-invasive techniques.
One such technique involves measuring the deflection of a probe beam of
electrons with a trajectory perpendicular to the proton beam. A device such as
this is already in use at the Spallation Neutron Source at ORNL and a similar
device has been installed in the Main Injector at Fermilab. Commissioning of
the device is in progress with the goal of having it operational by the end of
the year. The status of the commissioning and initial results will be
presented.


  SNO+ is a large multipurpose neutrino detector situated 2km underground at
SNOLAB in Sudbury, Canada. It reuses the structure of the SNO experiment with
numerous infrastructure upgrades and with heavy water replaced by ultra-pure
liquid scintillator. The detector will be loaded with 0.5% natural tellurium in
order to search for neutrinoless double beta decay ($0\nu\beta\beta$). The
expected sensitivity after 5 years of data taking is T$^{0\nu} _{1/2} > 1.9
\times 10^{26}$ years (90% CL). A future increase in loading could achieve a
sensitivity of ${\sim}10^{27}$ years.


  We study the atom-light interaction in the fully quantum regime, with focus
on off-resonant light scattering into a cavity from ultracold atoms trapped in
an optical lattice. The detection of photons allows the quantum nondemolition
(QND) measurement of quantum correlations of the atomic ensemble,
distinguishing between different quantum states. We analyse the entanglement
between light and matter and show how it can be exploited for realising
multimode macroscopic quantum superpositions such as Schr\"odinger cat states,
for both bosons and fermions. We provide examples utilising different
measurement schemes, and study their robustness to decoherence. Finally, we
address the regime where the optical lattice potential is a quantum dynamical
variable and is modified by the atomic state, leading to novel quantum phases,
and significantly altering the phase diagram of the atomic system.


  We studied the magnetic properties of bulk LaCrO3; a GdFeO3-type distorted
perovskite, with a predominant antiferromagnetic phase transition at ~ 290 K.
The bulk LaCrO3 exhibits intrinsic weak ferromagnetism at room temperature,
which may arise due to the tilting of CrO6 octahedra, resulting in a non-zero
net magnetic moment, as confirmed from the magnetization measurements. A broad
magnetically-induced entropy change (-{\Delta}S) is observed with the maximum
at 290 K, close to room temperature in LaCrO3 system.


  We prove the equivalence of two classes of counter machines and one class of
distributed automata. Our counter machines operate on finite words, which they
read from left to right while incrementing or decrementing a fixed number of
counters. The two classes differ in the extra features they offer: one allows
to copy counter values, whereas the other allows to compute copyless sums of
counters. Our distributed automata, on the other hand, operate on directed path
graphs that represent words. All nodes of a path synchronously execute the same
finite-state machine, whose state diagram must be acyclic except for
self-loops, and each node receives as input the state of its direct
predecessor. These devices form a subclass of linear-time one-way cellular
automata.


  The comparison of specific interplanetary conditions for 798 magnetic storms
with Dst < -50 nT for the period 1976-2000 was made on the basis of the OMNI
archive data.We categorized various large-scale types of solar wind as
interplanetary drivers of storms: corotating interaction region (CIR), Sheath,
interplanetary CME (ICME) including magnetic cloud (MC) and Ejecta, separately
MC and Ejecta, and "Indeterminate" type. The data processing was carried out by
the method of double superposed epoch analysis which uses two reference times
(onset of storm and the minimum Dst index) and make a re-scaling of main phase
of storm a such way that after this transformation all storms have equal
durations of main phase in new time reference frame. This method reproduced
some well-known results and allowed us to obtain some new results.
Specifically, obtained results demonstrate high importance of Sheath in
generation of magnetic storms as well as a significant differences in
properties of MC and Ejecta and in their geoeffectiveness.


  In a previous work arXiv:physics/0611108v2, it was shown that the volume
spanned by a molecular system in its conformational space can be effectively
bounded by a polyhedral cone, this cone is described by means of a simple
combinatorial formula. On the other hand it was constructed a transversal graph
structure encoding the region of conformational space accessible to the system.
  From the information in this graph, it is possible to decompose the main cone
into a hierarchy of smaller ones that are more manageable, and are
progressively more tightly bound to the region in which the system evolves.


  In this paper a generalization of the Voronoi partition is used for optimal
deployment of autonomous agents carrying sensors with heterogeneous
capabilities, to maximize the sensor coverage. The generalized centroidal
Voronoi configuration, in which the agents are located at the centroids of the
corresponding generalized Voronoi cells, is shown to be a local optimal
configuration. Simulation results are presented to illustrate the presented
deployment strategy.


  We introduce signed exceptional sequences as factorizations of morphisms in
the cluster morphism category. The objects of this category are wide
subcategories of the module category of a hereditary algebra. A morphism
$[T]:\mathcal A\to \mathcal B$ is the equivalence class of a rigid object $T$
in the cluster category of $\mathcal A$ so that $\mathcal B$ is the right
hom-ext perpendicular category of the underlying object $|T|\in \mathcal A$.
Factorizations of a morphism $[T]$ are given by total orderings of the
components of $T$. This is equivalent to a "signed exceptional sequence." For
an algebra of finite representation type, the geometric realization of the
cluster morphism category is an Eilenberg-MacLane space with fundamental group
equal to the "picture group" introduced by the authors in [IOTW4].


  The online assignment problem plays an important role in operational research
and computer science which is why immense attention has been given to improving
its solution quality. Due to the incomplete information about the input, it is
difficult for online algorithms to produce the optimal solution. The quality of
the solution of an online algorithm is measured using a competitive ratio. No
online deterministic algorithm can achieve a competitive ratio better than
(2n-1). It has been shown that advice in online computation improves the lower
bound of the competitive ratio of online problems. Advice in online computation
can be interpreted as additional information for the online algorithm to
compensate for the lack of information about the whole input sequence. In this
study, we investigate how introducing machine-learned advice could improve the
competitive ratio for this problem. We provide an online algorithm for the
online assignment problem by simulating a machine learning algorithm that
predicts the whole input in advance. We utilize an optimal offline algorithm to
provide a matching solution from the predicted input. Furthermore, we
investigate how the prediction error of machine learning affects the
competitive ratio of the online algorithm. We utilize a benchmark data set to
perform our empirical analysis. We show that as the Machine Learning prediction
error increases, the solution quality decreases. Moreover, the magnitude of
error is directly proportional to the size of the input. This result is
analogous to the competitive ratio of the best deterministic algorithm for the
online assignment problem which is dependent also on the parameter n.


  We study the spin-$1$ Heisenberg model on the square lattice with the
antiferromagnetic nearest-neighbor $J_1$ and the next-nearest-neighbor $J_2$
couplings by using the infinite projected entangled-pair state (iPEPS) ansatz
and density matrix renormalization group (DMRG) calculation. The iPEPS
simulation, which studies the model directly in the thermodynamic limit, finds
a crossing of the ground state from the N\'eel magnetic state to the stripe
magnetic state at $J_2/J_1 \simeq 0.549$, showing a direct phase transition. In
the finite-size DMRG calculation on the cylinder geometry up to the cylinder
width $L_y = 10$, we find a very small intermediate regime $\sim 0.005 J_1$
between the two magnetic order phases, which may imply the absent intermediate
phase. Both calculations identify that the stripe order comes with a
first-order transition at $J_2/J_1 \simeq 0.549$. Our results indicate that
unlike the spin-$1/2$ $J_1-J_2$ square model, quantum fluctuations in the
spin-$1$ model may be not strong enough to stabilize an intermediate
non-magnetic phase.


  We report on the design and performance of the LUX-ZEPLIN (LZ) "Screener", a
small liquid scintillator detector consisting of $\approx 23$ kg of LAB-based
gadolinium-loaded liquid scintillator (GdLS) to be used in the LZ Outer
Detector. The Outer Detector will be filled with 17.3 tonnes of GdLS and will
surround the central liquid xenon time projection chamber of LZ. Its primary
function will be to veto neutron single-scatter events in the liquid xenon
which could mimic a WIMP dark matter signal. To meet the requirements for the
Outer Detector, the radioimpurity levels in the GdLS must be kept below
$\lesssim0.07$ mBq/kg. This background level corresponds to a rate of
$\approx50$ Hz above an energy threshold of 100 keV.
  The Screener was operated in the ultra-low-background environment of the
former LUX water shield in the Davis Laboratory at the Sanford Underground
Research Facility for radioassay of the GdLS. Careful selection of detector
materials and use of ultra-low-background PMTs allows the measurement of a
variety of radioimpurities. The $^{14}\textrm{C}$/$^{12}\textrm{C}$ ratio in
the scintillator is measured to be
$(2.83\pm0.06\textrm{(stat.)}\pm0.01\textrm{(sys.)}) \times 10^{-17}$. Use of
pulse shape discrimination allows the concentration of isotopes throughout the
$^{238}\textrm{U}$, $^{235}\textrm{U}$, and $^{232}\textrm{Th}$ chains to be
measured by fitting the collected spectra from $\alpha$ and $\beta$ events. We
find that equilibrium is broken in the $^{238}\textrm{U}$ and
$^{232}\textrm{Th}$ chains and that a significant portion of the contamination
in the GdLS results from decays in the $^{227}\textrm{Ac}$ subchain of the
$^{235}\textrm{U}$ series.
  Predictions for the singles rate in the Outer Detector are presented. The
rate from radioimpurities above 100 keV in the GdLS is estimated to be
$97.9\pm6.4$ Hz, with $65.5\pm1.9$ Hz resulting from $\alpha$-decays.


  The importance of the excitation bandwidth is well known in diagnostic
ultrasound imaging. However, the effect of excitation bandwidth in therapeutic
applications of microbubbles has been mostly overlooked. A majority of contrast
agent production techniques generate polydisperse microbubble populations, so a
wide range of resonance frequencies exist. Therefore, wideband excitation is
necessary to fully utilize microbubble resonance behavior and maximize the
reradiated energy from a microbubble population, both for imaging and therapy.
  Oscillations of sixty SonoVue microbubbles in proximity of a rigid boundary
were captured on a high speed camera at 3 Mfps, excited with a peak negative
pressure of 50 kPa at 1 MHz. Measurements were analyzed according to their peak
radiated pressure, radial oscillations, root mean squared pressure, and shear
stress generated by microbubbles. Results showed that long duration and
wideband excitation at low intensity levels was preferable for sonoporation,
where microbubbles can be driven in a stable oscillation state without
experiencing inertial cavitation or destruction.


  The effects of a variable amount of random dilution of the synaptic couplings
in Q-Ising multi-state neural networks with Hebbian learning are examined. A
fraction of the couplings is explicitly allowed to be anti-Hebbian. Random
dilution represents the dying or pruning of synapses and, hence, a static
disruption of the learning process which can be considered as a form of
multiplicative noise in the learning rule. Both parallel and sequential
updating of the neurons can be treated. Symmetric dilution in the statics of
the network is studied using the mean-field theory approach of statistical
mechanics. General dilution, including asymmetric pruning of the couplings, is
examined using the generating functional (path integral) approach of disordered
systems. It is shown that random dilution acts as additive gaussian noise in
the Hebbian learning rule with a mean zero and a variance depending on the
connectivity of the network and on the symmetry. Furthermore, a scaling factor
appears that essentially measures the average amount of anti-Hebbian couplings.


  Synthetic microswimmers offer models for cell motility and their tunability
makes them promising candidates for biomedical applications. Here we measure
the acoustic propulsion of bimetallic micro-rods that, when trapped at the
nodal plane of a MHz acoustic resonator, swim with speeds of up to 300 microns
per second. While past acoustic streaming models predict speeds that are more
than one order of magnitude smaller than our measurements, we demonstrate that
the acoustic locomotion of the rods is driven by a viscous, non-reciprocal
mechanism relying on shape anisotropy akin to that used by swimming cells and
that reproduces our data with no adjustable parameters.


  Despite great progress achieved by transformer in various vision tasks, it is
still underexplored for skeleton-based action recognition with only a few
attempts. Besides, these methods directly calculate the pair-wise global
self-attention equally for all the joints in both the spatial and temporal
dimensions, undervaluing the effect of discriminative local joints and the
short-range temporal dynamics. In this work, we propose a novel Focal and
Global Spatial-Temporal Transformer network (FG-STFormer), that is equipped
with two key components: (1) FG-SFormer: focal joints and global parts coupling
spatial transformer. It forces the network to focus on modelling correlations
for both the learned discriminative spatial joints and human body parts
respectively. The selective focal joints eliminate the negative effect of
non-informative ones during accumulating the correlations. Meanwhile, the
interactions between the focal joints and body parts are incorporated to
enhance the spatial dependencies via mutual cross-attention. (2) FG-TFormer:
focal and global temporal transformer. Dilated temporal convolution is
integrated into the global self-attention mechanism to explicitly capture the
local temporal motion patterns of joints or body parts, which is found to be
vital important to make temporal transformer work. Extensive experimental
results on three benchmarks, namely NTU-60, NTU-120 and NW-UCLA, show our
FG-STFormer surpasses all existing transformer-based methods, and compares
favourably with state-of-the art GCN-based methods.


  Scanning probe microscopy and spectroscopy, and more recently in combination
with electron spin resonance, have allowed the direct observation of electron
dynamics on the single-atom limit. The interpretation of data is strongly
depending on model Hamiltonians. However, fitting effective spin Hamiltonians
to experimental data lacks the ability to explore a vast number of potential
systems of interest. By using plane-wave density functional theory (DFT) as
starting point, we build a multiplet Hamiltonian making use of
maximally-localized Wannier functions. The Hamiltonian contains spin-orbit and
electron-electron interactions needed to obtain the relevant spin dynamics. The
resulting reduced Hamiltonian is solved by exact diagonalization. We compare
three prototypical cases of 3d transition metals Mn (total spin $S=5/2$), Fe
($S=2$) and Co ($S=3/2$) on MgO with experimental data and find that our
calculations can accurately predict the spin orientation and anisotropy of the
magnetic adatom. Our method does not rely on experimental input and permits us
to explore and predict the fundamental magnetic properties of adatoms on
surfaces.


  The dual axion model (DAM), yielding bot DM and DE form a PQ-like scalar
field solving the strong CP problem, is known to allow a fair fit of CMB data.
Recently, however, it was shown that its transfer function exhibits significant
anomalies, causing difficulties to fit deep galaxy sample data. Here we show
how DAM can be modified to agree with the latter data set. The modification
follows the pattern suggested to reconcile any PQ-like approach with gravity.
Modified DAM allows precise predictions which can be testable against future
CMB and/or deep sample data.


  We study the fundamental plane relation in high redshift clusters using a
sample of 26 galaxies in MS 2053-04 (z=0.583) and 22 galaxies in MS 1054-03
(z=0.83). The zeropoint and scatter are compared to results for lower redshift
clusters in order to trace evolutionary effects. Furthermore, our large sample
enables us to investigate correlations between residuals from the fundamental
plane and other characteristics of the galaxies, such as color, $H\beta$
linestrength, spatial distribution, and mass. The observed scatter of the
early-type galaxies with sigma > 100 km/s around the fundamental plane is 0.134
and 0.106 in log r_e for MS 2053-04 and MS 1054-03 respectively. The residuals
from the fundamental plane of MS 2053-04 are correlated with residuals from the
$H\beta - \sigma$ relation, suggesting that stellar populations are playing a
role in shaping the fundamental plane. The measured evolution in log M/L is
influenced by selection effects, as galaxies with lower M/L in the Johnson
B-band enter a magnitude-limited sample more easily. When we select high mass
early-type galaxies to avoid this bias, we find $\log M/L_B \sim -0.47 z$ and a
formation redshift $z_{form} \sim 2.95$, similar to earlier results.


  In deformation-rigidity theory it is often important to know whether certain
bimodules are weakly contained in the coarse bimodule. Consider a bimodule $H$
over the group algebra $\mathbb{C}[\Gamma]$, with $\Gamma$ a discrete group.
The starting point of this paper is that if a dense set of the so-called
coefficients of $H$ is contained in the Schatten $\mathcal{S}_p$ class $p \in
[2, \infty)$ then the $n$-fold tensor power $H^{\otimes n}_\Gamma$ for $n \geq
p/2$ is quasi-contained in the coarse bimodule. We apply this to gradient
bimodules associated with the carr\'e du champ of a symmetric quantum Markov
semi-group.
  For Coxeter groups we give a number of characterizations of having
coefficients in $\mathcal{S}_p$ for the gradient bimodule constructed from the
word length function. We get equivalence of: (1) the gradient-$\mathcal{S}_p$
property introduced by the second named author, (2) smallness at infinity of a
natural compactification of the Coxeter group, and for a large class of Coxeter
groups: (3) walks in the Coxeter diagram called parity paths.
  We derive several strong solidity results. In particular, we extend current
strong solidity results for right-angled Hecke von Neumann algebras beyond
right-angled Coxeter groups that are small at infinity. Our general methods
also yield a concise proof of a result by T. Sinclair for discrete groups
admitting a proper cocycle into a $p$-integrable representation.


  We introduce two simple models of forward-backward stochastic differential
equations with a singular terminal condition and we explain how and why they
appear naturally as models for the valuation of CO2 emission allowances. Single
phase cap-and-trade schemes lead readily to terminal conditions given by
indicator functions of the forward component, and using fine partial
differential equations estimates, we show that the existence theory of these
equations, as well as the properties of the candidates for solution, depend
strongly upon the characteristics of the forward dynamics. Finally, we give a
first order Taylor expansion and show how to numerically calibrate some of
these models for the purpose of CO2 option pricing.


  We address the problem of decomposing a single image into reflectance and
shading. The difficulty comes from the fact that the components of image---the
surface albedo, the direct illumination, and the ambient illumination---are
coupled heavily in observed image. We propose to infer the shading by ordering
pixels by their relative brightness, without knowing the absolute values of the
image components beforehand. The pairwise shading orders are estimated in two
ways: brightness order and low-order fittings of local shading field. The
brightness order is a non-local measure, which can be applied to any pair of
pixels including those whose reflectance and shading are both different. The
low-order fittings are used for pixel pairs within local regions of smooth
shading. Together, they can capture both global order structure and local
variations of the shading. We propose a Consistency-aware Selective Fusion
(CSF) to integrate the pairwise orders into a globally consistent order. The
iterative selection process solves the conflicts between the pairwise orders
obtained by different estimation methods. Inconsistent or unreliable pairwise
orders will be automatically excluded from the fusion to avoid polluting the
global order. Experiments on the MIT Intrinsic Image dataset show that the
proposed model is effective at recovering the shading including deep shadows.
Our model also works well on natural images from the IIW dataset, the UIUC
Shadow dataset and the NYU-Depth dataset, where the colors of direct lights and
ambient lights are quite different.


  Leveraging Artificial Intelligence (AI) in decision support systems has
disproportionately focused on technological advancements, often overlooking the
alignment between algorithmic outputs and human expectations. A human-centered
perspective attempts to alleviate this concern by designing AI solutions for
seamless integration with existing processes. Determining what information AI
should provide to aid humans is vital, a concept underscored by explainable
AI's efforts to justify AI predictions. However, how the information is
presented, e.g., the sequence of recommendations and solicitation of
interpretations, is equally crucial as complex interactions may emerge between
humans and AI. While empirical studies have evaluated human-AI dynamics across
domains, a common vocabulary for human-AI interaction protocols is lacking. To
promote more deliberate consideration of interaction designs, we introduce a
taxonomy of interaction patterns that delineate various modes of human-AI
interactivity. We summarize the results of a systematic review of AI-assisted
decision making literature and identify trends and opportunities in existing
interactions across application domains from 105 articles. We find that current
interactions are dominated by simplistic collaboration paradigms, leading to
little support for truly interactive functionality. Our taxonomy offers a tool
to understand interactivity with AI in decision-making and foster interaction
designs for achieving clear communication, trustworthiness, and collaboration.


  We present three giant stars from the ongoing Penn State-Toru\'n Planet
Search with the Hobby-Eberly Telescope, which exhibit radial velocity
variations that point to a presence of planetary --mass companions around them.
BD+49 828 is a $M=1.52 \pm 0.22$ $M_{\odot}$ K0 giant with a $m
sini$=$1.6^{+0.4}_{-0.2}$ $M_{J}$ minimum mass companion in
$a=4.2^{+0.32}_{-0.2}$ AU ($2590^{+300}_{-180}$d), $e=0.35^{+0.24}_{-0.10}$
orbit. HD 95127, a log$L$/$L_{\odot}$=$2.28 \pm 0.38$, $R = 20\pm 9$
$R_{\odot}$, $M=1.20 \pm 0.22$ $M_{\odot}$ K0 giant has a $m
sini$=$5.01^{+0.61}_{-0.44}$ $M_{J}$ minimum mass companion in
$a=1.28^{+0.01}_{-0.01}$ AU ($482^{+5}_{-5}$d), $e=0.11^{+0.15}_{-0.06}$ orbit.
Finally, HD 216536, is a $M=1.36 \pm 0.38$ $M_{\odot}$ K0 giant with a $m sin
i=1.47^{+0.20}_{-0.12}$ $M_{J}$ minimum mass companion in
$a=0.609^{+0.002}_{-0.002}$ AU ($148.6^{+0.7}_{-0.7}$d),
$e=0.38^{+0.12}_{-0.10}$ orbit. Both, HD 95127 b and HD 216536 b in their
compact orbits, are very close to the engulfment zone and hence prone to
ingestion in the near future. BD+49 828 b is among the longest period planets
detected with the radial velocity technique until now and it will remain
unaffected by stellar evolution up to a very late stage of its host. We discuss
general properties of planetary systems around evolved stars and planet
survivability using existing data on exoplanets in more detail.


  In this paper, we solve the existence problem of telescopers for rational
functions in three discrete variables. We reduce the problem to that of
deciding the summability of bivariate rational functions, which has been solved
recently. The existence criteria we present is needed for detecting the
termination of Zeilberger's algorithm to the function classes studied in this
paper.


  We introduce a new notion of conditional nonlinear expectation under
probability distortion. Such a distorted nonlinear expectation is not
sub-additive in general, so it is beyond the scope of Peng's framework of
nonlinear expectations. A more fundamental problem when extending the distorted
expectation to a dynamic setting is time-inconsistency, that is, the usual
"tower property" fails. By localizing the probability distortion and
restricting to a smaller class of random variables, we introduce a so-called
distorted probability and construct a conditional expectation in such a way
that it coincides with the original nonlinear expectation at time zero, but has
a time-consistent dynamics in the sense that the tower property remains valid.
Furthermore, we show that in the continuous time model this conditional
expectation corresponds to a parabolic differential equation whose coefficient
involves the law of the underlying diffusion. This work is the first step
towards a new understanding of nonlinear expectations under probability
distortion, and will potentially be a helpful tool for solving
time-inconsistent stochastic optimization problems.


  With the development of neural networks and the increasing popularity of
automatic driving, the calibration of the LiDAR and the camera has attracted
more and more attention. This calibration task is multi-modal, where the rich
color and texture information captured by the camera and the accurate
three-dimensional spatial information from the LiDAR is incredibly significant
for downstream tasks. Current research interests mainly focus on obtaining
accurate calibration results through information fusion. However, they seldom
analyze whether the calibrated results are correct or not, which could be of
significant importance in real-world applications. For example, in large-scale
production, the LiDARs and the cameras of each smart car have to get
well-calibrated as the car leaves the production line, while in the rest of the
car life period, the poses of the LiDARs and cameras should also get
continually supervised to ensure the security. To this end, this paper proposes
a self-checking algorithm to judge whether the extrinsic parameters are
well-calibrated by introducing a binary classification network based on the
fused information from the camera and the LiDAR. Moreover, since there is no
such dataset for the task in this work, we further generate a new dataset
branch from the KITTI dataset tailored for the task. Our experiments on the
proposed dataset branch demonstrate the performance of our method. To the best
of our knowledge, this is the first work to address the significance of
continually checking the calibrated extrinsic parameters for autonomous
driving. The code is open-sourced on the Github website at
https://github.com/OpenCalib/LiDAR2camera_self-check.


  We present observations of CO, 13CO and of H2O in the middle and far-infrared
taken with the ISO-SWS and ISO-LWS spectrometers toward two positions in the
Galactic Center region (Sgr A* and GCS-3). Both ice and gas phase molecules are
detected. The ISO data have been complemented with observations of the J=3-2
and J=7-6 lines of CO carried out at the Caltech Submillimeter Observatory. The
ISO and CSO data indicate that the absorbing gas is extremely cold, T_K ~ 10 K,
suggesting that it is located in the dark clouds of the different spiral arms
that intersect the line of sight towards the Galactic Center. From the analysis
of the CO absorption we derive 13CO gas phase column densities of 1.1 and
0.7E17 cm-2 towards Sgr A* and GCS-3, respectively. The H2O gas column density
in the direction of Sgr A* is ~ 2E16 cm-2. The derived CO/H2O and gas/solid
abundance ratios corresponding to these cold clouds are remarkably similar
along the two lines of sight. We find that nearly all the CO is in the gas
phase, while the H2O is almost entirely frozen onto the surfaces of cold dust
grains. Finally, the N_{gas+ice}(CO)/N_{gas+ice}(H2O) abundance ratio is ~5
implying that H2O formation processes are highly efficient.


  Bayesian optimization (BO) is an efficient method to optimize expensive
black-box functions. It has been generalized to scenarios where objective
function evaluations return stochastic binary feedback, such as success/failure
in a given test, or preference between different parameter settings. In many
real-world situations, the objective function can be evaluated in controlled
'contexts' or 'environments' that directly influence the observations. For
example, one could directly alter the 'difficulty' of the test that is used to
evaluate a system's performance. With binary feedback, the context determines
the information obtained from each observation. For example, if the test is too
easy/hard, the system will always succeed/fail, yielding uninformative binary
outputs. Here we combine ideas from Bayesian active learning and optimization
to efficiently choose the best context and optimization parameter on each
iteration. We demonstrate the performance of our algorithm and illustrate how
it can be used to tackle a concrete application in visual psychophysics:
efficiently improving patients' vision via corrective lenses, using
psychophysics measurements.


  The dependence of the superconducting proximity effect on the amount of
magnetic impurities in the normal part of Andreev interferometers has been
studied experimentally. The dephasing rates obtained from fitting experimental
data to quasiclassical theory of the proximity effect are consistent with the
spin flip scattering from Cr impurities forming a local moment in the Cu host.
In contrast, Ni impurities do not form a local moment in Cu and as a result
there is no extra dephasing from Ni as long as Cu/Ni alloy remain paramagnetic.


  Unlike flat space quantum field theories that focus on scattering amplitudes,
the main observables in quantum cosmology are correlation functions. The
systematic way of calculating correlators is called in-in formalism, which
requires only a single asymptotic region, i.e. past infinity. The rules in
perturbation theory and the path integral measure are very different for in-in
and in-out formalisms, and thus the results which are standard in one approach
may not necessarily hold in the other one. We show that stationary phase
approximation works completely different for a scalar in-in path integral.
Hence, in a cosmological background there are solutions, pseudo-instantons,
that allow tunneling between locally stable vacua even in infinite volume,
which is counterintuitive from an in-out perspective. We argue that various
familiar notions of in-out formalism must be reexamined in the in-in formalism,
which might have important consequences for quantum cosmology.


  This paper presents an innovative approach, called credal wrapper, to
formulating a credal set representation of model averaging for Bayesian neural
networks (BNNs) and deep ensembles, capable of improving uncertainty estimation
in classification tasks. Given a finite collection of single distributions
derived from BNNs or deep ensembles, the proposed approach extracts an upper
and a lower probability bound per class, acknowledging the epistemic
uncertainty due to the availability of a limited amount of sampled predictive
distributions. Such probability intervals over classes can be mapped on a
convex set of probabilities (a 'credal set') from which, in turn, a unique
prediction can be obtained using a transformation called 'intersection
probability transformation'. In this article, we conduct extensive experiments
on multiple out-of-distribution (OOD) detection benchmarks, encompassing
various dataset pairs (CIFAR10/100 vs SVHN/Tiny-ImageNet, CIFAR10 vs CIFAR10-C,
CIFAR100 vs CIFAR100-C and ImageNet vs ImageNet-O) and using different network
architectures (such as VGG16, Res18/50, EfficientNet B2, and ViT Base).
Compared to BNN and deep ensemble baselines, the proposed credal representation
methodology exhibits superior performance in uncertainty estimation and
achieves lower expected calibration error on OOD samples.


  We develop a notion of causal order on a generic manifold as independent of
the underlying differential and topological structure. We show that
sufficiently regular causal orders can be recovered from a distinguished
algebra of sets, which plays a role analogous to that of topologies and
$\sigma$ algebras. We then discuss how a natural notion of measure can be
associated to the algebra of causal sets.


  This paper focuses on the modeling of musical melodies as networks. Notes of
a melody can be treated as nodes of a network. Connections are created whenever
notes are played in sequence. We analyze some main tracks coming from different
music genres, with melodies played using different musical instruments. We find
out that the considered networks are, in general, scale free networks and
exhibit the small world property. We measure the main metrics and assess
whether these networks can be considered as formed by sub-communities. Outcomes
confirm that peculiar features of the tracks can be extracted from this
analysis methodology. This approach can have an impact in several multimedia
applications such as music didactics, multimedia entertainment, and digital
music generation.


  A modular object in a symmetric monoidal bicategory is a Frobenius algebra
object whose product and coproduct are biadjoint, equipped with a braided
structure and a compatible twist, satisfying rigidity, ribbon, pivotality, and
modularity conditions. We prove that the oriented 3-dimensional bordism
bicategory of 1-, 2-, and 3-manifolds is the free symmetric monoidal bicategory
on a single anomaly-free modular object.


  In an age of voice-enabled technology, voice anonymization offers a solution
to protect people's privacy, provided these systems work equally well across
subgroups. This study investigates bias in voice anonymization systems within
the context of the Voice Privacy Challenge. We curate a novel benchmark dataset
to assess performance disparities among speaker subgroups based on sex and
dialect. We analyze the impact of three anonymization systems and attack models
on speaker subgroup bias and reveal significant performance variations.
Notably, subgroup bias intensifies with advanced attacker capabilities,
emphasizing the challenge of achieving equal performance across all subgroups.
Our study highlights the need for inclusive benchmark datasets and
comprehensive evaluation strategies that address subgroup bias in voice
anonymization.


  Carbon nanotubes are of central importance for applications in
nano-electronics thanks to their exceptional transport properties. They can be
used as sensors, for example in biological applications, provided that they are
functionalized to detect specific molecules. Due to their one-dimensional
geometry the carbon nanotubes are very sensitive to the phenomenon of Anderson
localization and it is therefore essential to know how the functionalization
modifies their conduction properties and if they remain good conductors. Here
we present a study of the quantum localization induced by functionalization in
metallic single walled carbon nanotubes (SWCNT) with circumferences up to $
15\; nm $. We consider resonant and non-resonant adsorbates that represent two
types of covalently functionalized groups with moderate and strong scattering
properties. The present study provides a detailed analysis of the localization
behaviour and shows that the localization length can decrease down to $ 20-50\;
nm $ at concentrations of about 1 percent of adsorbates. On this basis we
discuss the possible electronic transport mechanisms which can be either
metallic like or insulating like with variable range hopping.


  We propose to detect quadrupole interactions of neutral ultra-cold atoms via
their induced mean-field shift. We consider a Mott insulator state of
spin-polarized atoms in a two-dimensional optical square lattice. The
quadrupole moments of the atoms are aligned by an external magnetic field. As
the alignment angle is varied, the mean-field shift shows a characteristic
angular dependence, which constitutes the defining signature of the quadrupole
interaction. For the $^{3}P_{2}$ states of Yb and Sr atoms, we find a frequency
shift of the order of tens of Hertz, which can be realistically detected in
experiment with current technology. We compare our results to the mean-field
shift of a spin-polarized quasi-2D Fermi gas in continuum.


  We discuss the role of orbital degeneracy in the transport properties of
perovskite manganites, focusing in particular on the optical conductivity in
the metallic ferromagnetic phase at low temperatures. Orbital degeneracy and
strong correlations are described by an orbital t-J model which we treat in a
slave-boson approach. Employing the memory-function formalism we calculate the
optical conductivity, which is found to exhibit a broad incoherent component
extending up to bare bandwidth accompanied by a strong suppression of the Drude
weight. Further, we calculate the constant of T-linear specific heat. Our
results are in overall agreement with experiment and suggest low-energy orbital
fluctuations as the origin of the strongly correlated nature of the metallic
phase of manganites.


  The quantum phase transition of the system of N radiators in case of
two-photon exchange interaction with cavity electromagnetic field is
considered. It is shown that for this system the atom-field exchange integral
increases with the increase of temperature. This effect generates peculiarities
in phase transition picture. The process of nonlinear exchange between the
quasi-spins leads to the increase of critical temperature as compared to
traditional second order phase transition of quasi-spin system.


  We propose a method for building an interpretable recommender system for
personalizing online content and promotions. Historical data available for the
system consists of customer features, provided content (promotions), and user
responses. Unlike in a standard multi-class classification setting,
misclassification costs depend on both recommended actions and customers. Our
method transforms such a data set to a new set which can be used with standard
interpretable multi-class classification algorithms. The transformation has the
desirable property that minimizing the standard misclassification penalty in
this new space is equivalent to minimizing the custom cost function.


  We have investigated the present renormalization prescriptions of the
Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix. Based on one prescription
which is formulated by comparing with the fictitious case of no mixing of quark
generations, we propose a new prescription which can make the physical
amplitude involving quark's mixing gauge independent and ultraviolet finite.
Compared with the previous prescriptions this prescription is very simple and
suitable for actual calculations. Through analytical calculations we also give
a strong Proof for the important hypothesis that in order to keep the CKM
matrix gauge independent the unitarity of the CKM matrix must be preserved.


  Microlensed double-image quasars have sent a consistent message that the
baryonic dark matter consists of a population of free-roaming planet mass
objects, as summarized previously. These were previously predicted to have
formed at the time of recombination, 300,000 years after the Big Bang, whence
they collapsed on a Kelvin Helmholz time scale. Today they are glimpsed as the
cometary knots in planetary nebulae. But they probably also nucleate the
mysterious Lyman-alpha clouds and cause a reduction in the transparency of the
universe to distant quasars and supernovae.


  Auto-oscillations of magnetization driven by direct spin current have been
previously observed in multiple quasi-zero-dimensional (0D) ferromagnetic
systems such as nanomagnets and nanocontacts. Recently, it was shown that pure
spin Hall current can excite coherent auto-oscillatory dynamics in
quasi-one-dimensional (1D) ferromagnetic nanowires but not in
quasi-two-dimensional (2D) ferromagnetic films. Here we study the 1D to 2D
dimensional crossover of current-driven magnetization dynamics in wire-based
Pt/$\mathrm{Ni}_{80}\mathrm{Fe}_{20}$ bilayer spin Hall oscillators via varying
the wire width. We find that increasing the wire width results in an increase
of the number of excited auto-oscillatory modes accompanied by a decrease of
the amplitude and coherence of each mode. We also observe a crossover from a
hard to a soft onset of the auto-oscillations with increasing the wire width.
The amplitude of auto-oscillations rapidly decreases with increasing
temperature suggesting that interactions of the phase-coherent auto-oscillatory
modes with incoherent thermal magnons plays an important role in suppression of
the auto-oscillatory dynamics. Our measurements set the upper limit on the
dimensions of an individual spin Hall oscillator and elucidate the mechanisms
leading to suppression of coherent auto-oscillations with increasing oscillator
size.


  An axion-like particle (ALP) offers a new direction in electroweak
baryogenesis because the periodic nature enables it to trigger a strong
first-order phase transition insensitively to the decay constant $f$. For $f$
much above TeV, the ALP-induced electroweak phase transition is approximately
described by adiabatic processes, distinguishing our scenario for electroweak
baryogenesis from the conventional ones. We show that, coupled to the
electroweak anomaly, the ALP can naturally realize spontaneous electroweak
baryogenesis to solve the matter-antimatter asymmetry problem for $f$ in the
range between about $10^5$ GeV and $10^7$ GeV. In such an ALP window, the $CP$
violation for baryogenesis is totally free from the experimental constraints,
especially from the recently improved limit on the electron electric dipole
moment. Future searches for ALPs could probe our scenario while revealing the
connection between electroweak symmetry breaking and baryogenesis.


  Estimating the predictive uncertainty of a Bayesian learning model is
critical in various decision-making problems, e.g., reinforcement learning,
detecting adversarial attack, self-driving car. As the model posterior is
almost always intractable, most efforts were made on finding an accurate
approximation the true posterior. Even though a decent estimation of the model
posterior is obtained, another approximation is required to compute the
predictive distribution over the desired output. A common accurate solution is
to use Monte Carlo (MC) integration. However, it needs to maintain a large
number of samples, evaluate the model repeatedly and average multiple model
outputs. In many real-world cases, this is computationally prohibitive. In this
work, assuming that the exact posterior or a decent approximation is obtained,
we propose a generic framework to approximate the output probability
distribution induced by model posterior with a parameterized model and in an
amortized fashion. The aim is to approximate the true uncertainty of a specific
Bayesian model, meanwhile alleviating the heavy workload of MC integration at
testing time. The proposed method is universally applicable to Bayesian
classification models that allow for posterior sampling. Theoretically, we show
that the idea of amortization incurs no additional costs on approximation
performance. Empirical results validate the strong practical performance of our
approach.


  Xiong and Liu [L. Xiong and Z. Liu, Hamiltonian iterated line graphs,
Discrete Math. 256 (2002) 407-422] gave a characterization of the graphs $G$
for which the $n$-th iterated line graph $L^n(G)$ is hamiltonian, for $n\ge2$.
In this paper, we study the existence of a hamiltonian path in $L^n(G)$, and
give a characterization of $G$ for which $L^n(G)$ has a hamiltonian path. As
applications, we use this characterization to give several upper bounds on the
hamiltonian path index of a graph.


  We consider the time dependent Schr\"odinger equation with a coupling
spin-orbit in the semi-classical regime $\hbar\searrow 0$ and large spin number
$\spin\rightarrow +\infty$ such that $\hbar^\delta\spin=c$ where $c>0$ and
$\delta>0$ are constant. The initial state $\Psi(0)$ is a product of an orbital
coherent state in $L^2(\R^d)$ and a spin coherent state in a spin irreducible
representation space ${\mathcal H}_{2\spin +1}$. For $\delta <1$, at the
leading order in $\hbar$, the time evolution $\Psi(t)$ of $ \Psi(0)$ is well
approximated by the product of an orbital and a spin coherent state.
Nevertheless for $1/2<\delta<1$ the quantum orbital leaves the classical
orbital. For $\delta=1$ we prove that this last claim is no more true when the
interaction depends on the orbital variables.
  For the Dicke model, we prove that the orbital partial trace of the projector
on $\Psi(t)$ is a mixed state in $L^2(\R)$ for small $t>0$.