  The cut polytope of a graph $G$ is the convex hull of the indicator vectors
of all cuts in $G$ and is closely related to the MaxCut problem. We give the
facet-description of cut polytopes of $K_{3,3}$-minor-free graphs and introduce
an algorithm solving MaxCut on those graphs, which only requires the running
time of planar MaxCut. Moreover, starting a systematic geometric study of cut
polytopes, we classify graphs admitting a simple or simplicial cut polytope.


  A geometrical invariant for regular asymptotically Euclidean data for the
vacuum Einstein field equations is constructed. This invariant vanishes if and
only if the data correspond to a slice of the Kerr black hole spacetime --thus,
it provides a measure of the non-Kerr-like behavior of generic data. In order
to proceed with the construction of the geometric invariant, we introduce the
notion of approximate Killing spinors.


  Classically, the optimal control problem in the presence of an adversary is
formulated as a two-player zero-sum differential game or an $H_\infty$ control
problem. The solution to these problems can be obtained by solving the
Hamilton-Jacobi-Issac equation (HJIE). We provide a novel Koopman-based
expression of the HJIE, where the solutions can be obtained through the
approximation of the Koopman operator itself. In particular, we developed a
data-driven and model based policy iteration algorithm for approximating the
optimal value function using a finite-dimensional approximation of the Koopman
operator and generator.


  The mixed-alkali effect on the cation dynamics in silicate glasses is
analyzed via molecular dynamics simulations. Observations suggest a description
of the dynamics in terms of stable sites mostly specific to one ionic species.
As main contributions to the mixed--alkali slowdown longer residence times and
an increased probability of correlated backjumps are identified. The slowdown
is related to the limited accessibility of foreign sites. The mismatch
experienced in a foreign site is stronger and more retarding for the larger
ions, the smaller ions can be temporarily accommodated. Also correlations
between unlike as well as like cations are demonstrated that support
cooperative behavior.


  We study two body dipolar scattering with one dimension of confinement. We
include the effects of confinement by expanding this degree of freedom in
harmonic oscillator states. We then study the properties of the resulting
multi-channel system. We study the adiabatic curves as a function of D/l, the
ratio of the dipolar and confinement length scales. There is no dipolar barrier
for this system when D/l < 0.34. We also study the WKB tunneling probability as
a function of D/l and scattering energy. This can be used to estimate the
character of the scattering.


  We introduce a new class of scalar-tensor theories that extend Horndeski, or
"generalized galileon", models. Despite possessing equations of motion of
higher order in derivatives, we show that the true propagating degrees of
freedom obey well-behaved second-order equations and are thus free from
Ostrogradski instabilities, in contrast to the standard lore. Remarkably, the
covariant versions of the original galileon Lagrangians-obtained by direct
replacement of derivatives with covariant derivatives-belong to this class of
theories. These extensions of Horndeski theories exhibit an uncommon,
interesting phenomenology: the scalar degree of freedom affects the speed of
sound of matter, even when the latter is minimally coupled to gravity.


  Real-space entanglement spectra (RSES) capture characteristic features of the
topological order encoded in the fractional quantum Hall (FQH) states. In this
work, we numerically compute, using Monte Carlo methods, the RSES and the
counting of edge excitations of non-Abelian FQH states constructed using the
parton theory. Efficient numerical computation of RSES of parton states is
possible, thanks to their product-of-Slater-determinant structure, allowing us
to compute the spectra in systems of up to 80 particles. Specifically, we
compute the RSES of the parton states $\phi_2^2$, $\phi_2^3$, and $\phi_3^2$,
where $\phi_n$ is the wave function of $n$ filled Landau levels, in the ground
state as well as in the presence of bulk quasihole states. We then explicitly
demonstrate a one-to-one correspondence of RSES of the parton states with
representations of the Kac-Moody algebras satisfied by their edge currents. We
also show that for the lowest Landau level projected version of these parton
states, the spectra match with that obtained from the edge current algebra. We
also perform a computation of spectra of the overlap matrices corresponding to
the edge excitations of the parton states with a constrained number of
particles in the different parton Landau levels. Counting in these matches the
individual branches present in RSES, providing insight about how different
branches are formed.


  In this article we propose a new design methodology allowing us to control
both ampli- tude and phase of electromagnetic waves from a cylindrical incident
wave. This results in isotropic materials and does not resort to transformation
optics or its quasi-conformal approximations. Our method leads to
two-dimensional isotropic, inhomogeneous material profiles of permittivity and
permeability, to which a general class of scattering-free wave solutions arise.
Our design is based on the separation of the complex wave solution into
amplitude and phase. We give two types of examples to validate our methodology.


  Using Laplace transform techniques, we describe the evolution of the color
dipole cross section, at the leading-order and next-to-leading order
approximations, from the Bartels-Golec-Biernat-Kowalski model in a kinematical
region of low values of the Bjorken variable $x$ and a wide range of transverse
dipole size $r$. This evolution method shows that the saturation scale and
geometric scaling are retained. We derived analytical results for the
integrated and unintegrated color dipole gluon distribution functions and
compared them with the CJ15 parametrization group and the unintegrated color
dipole gluon distribution models respectively. The Sudakov form factor into the
evolution of the unintegrated color dipole gluon distribution is incorporated
and the results are considered at small and large values of $k_{t}^{2}$


  The ground state fidelity per lattice site is shown to be able to detect
quantum phase transitions for the Kitaev model on the honeycomb lattice, a
prototypical example of quantum lattice systems with topological order. It is
found that, in the thermodynamic limit, the ground state fidelity per lattice
site is non-analytic at the phase boundaries: the second-order derivative of
its logarithmic function with respect to a control parameter describing the
interaction between neighboring spins is logarithmically divergent. A finite
size scaling analysis is performed, which allows us to extract the correlation
length critical exponent from the scaling behaviors of the ground state
fidelity per lattice site.


  Optimal Transport (OT) has recently emerged as a central tool in data
sciences to compare in a geometrically faithful way point clouds and more
generally probability distributions. The wide adoption of OT into existing data
analysis and machine learning pipelines is however plagued by several
shortcomings. This includes its lack of robustness to outliers, its high
computational costs, the need for a large number of samples in high dimension
and the difficulty to handle data in distinct spaces. In this review, we detail
several recently proposed approaches to mitigate these issues. We insist in
particular on unbalanced OT, which compares arbitrary positive measures, not
restricted to probability distributions (i.e. their total mass can vary). This
generalization of OT makes it robust to outliers and missing data. The second
workhorse of modern computational OT is entropic regularization, which leads to
scalable algorithms while lowering the sample complexity in high dimension. The
last point presented in this review is the Gromov-Wasserstein (GW) distance,
which extends OT to cope with distributions belonging to different metric
spaces. The main motivation for this review is to explain how unbalanced OT,
entropic regularization and GW can work hand-in-hand to turn OT into efficient
geometric loss functions for data sciences.


  We study the interaction effect in a three dimensional Dirac semimetal and
find that two competing orders, charge-density-wave orders and nematic orders,
can be induced to gap the Dirac points. Applying a magnetic field can further
induce an instability towards forming these ordered phases. The charge density
wave phase is similar as that of a Weyl semimetal while the nematic phase is
unique for Dirac semimetals. Gapless zero modes are found in the vortex core
formed by nematic order parameters, indicating the topological nature of
nematic phases. The nematic phase can be observed experimentally using scanning
tunnelling microscopy.


  Structural and magnetic properties of the doped terbium manganites (Tb,A)MnO3
(A = Gd, Dy and Ho) have been investigated using first-principles calculations
and further confirmed by subse- quent experimental studies. Both computational
and experimental studies suggest that compared to the parent material, namely,
TbMnO3 (with a magnetic moment of 9.7 /muB for Tb3+) Dy- and Ho- ion
substituted TbMnO3 results in an increase in the magnetic moment (< 10.6/muB
for Dy3+ and Ho3+). The observed spiral-spin AFM order in TbMnO3 is stable with
respect to the dopant substitutions, which modify the Mn-O-Mn bond angles and
lead to stronger the ferromagnetic component of the magnetic moment. Given the
fact that magnetic ordering in TbMnO3 causes the ferroelectricity, this is an
important step in the field of the magnetically driven ferroelectricity in the
class of magnetoelectric multiferroics, which traditionally have low magnetic
moments due to the predominantly antiferromagnetic order. In addition, the
present study reveals important insights on the phenomenological coupling
mechanism in detail, which is essential in order to design new materials with
enhanced magneto-electric effects at higher temperatures.


  In the present study, we developed a fabrication process of an electrically
driven single-photon LED based on InP QDs emitting in the red spectral range,
the wavelength of interest coinciding with the high efficiency window of Si
APDs. A deterministic lithography technique allowed for the pre-selection of a
suitable QD, here exclusively operated under electrical carrier injection. The
final device was characterized under micro-electroluminescence in direct
current, as well as in pulsed excitation mode. In particular, under pulsed
excitation of one device, single-photon emission of a spectral line, identified
as an exciton, has been observed with $g^{(2)}_\mathrm{raw}(0)=0.42\pm0.02$,
where the non-zero $g^{(2)}$-value is mainly caused by background contribution
in the spectrum and re-excitation processes due to the electrical pulse length.
The obtained results constitute an important step forward in the fabrication of
electrically driven single-photon sources, where deterministic lithography
techniques can be used to sensibly improve the device performances. In
principle, the developed process can be extended to any desired emitter
wavelength above $600\,\mathrm{nm}$ up to the telecom bands.


  Anarchic warped extra dimensional models provide a solution to the hierarchy
problem. They can also account for the observed flavor hierarchies, but only at
the expense of little hierarchy and CP problems, which naturally require a
Kaluza-Klein (KK) scale beyond the LHC reach. We have recently shown that when
flavor issues are decoupled, and assumed to be solved by UV physics, the
framework's parameter space greatly opens. Given the possibility of a lower KK
scale and composite light quarks, this class of flavor triviality models enjoys
a rather exceptional phenomenology, which is the focus of this letter. We also
revisit the anarchic RS EDM problem, which requires m_{KK} > 8 TeV, and show
that it is solved within flavor triviality models. Interestingly, our framework
can induce a sizable differential t \bar{t} forward-backward asymmetry, and
leads to an excess of massive boosted di-jet events, which may be linked to the
recent findings of the CDF collaboration. This feature may be observed by
looking at the corresponding planar flow distribution, which is presented here.
Finally we point out that the celebrated standard model preference towards a
light Higgs is significantly reduced within our framework.


  We study distributed optimization to minimize a global objective that is a
sum of smooth and strongly-convex local cost functions. Recently, several
algorithms over undirected and directed graphs have been proposed that use a
gradient tracking method to achieve linear convergence to the global minimizer.
However, a connection between these different approaches has been unclear. In
this paper, we first show that many of the existing first-order algorithms are
in fact related with a simple state transformation, at the heart of which lies
the $\mathcal{AB}$ algorithm. We then describe \textit{distributed heavy-ball},
denoted as $\mathcal{AB}m$, i.e., $\mathcal{AB}$ with momentum, that combines
gradient tracking with a momentum term and uses nonidentical local step-sizes.
By simultaneously implementing both row- and column-stochastic weights,
$\mathcal{AB}m$ removes the conservatism in the related work due to
doubly-stochastic weights or eigenvector estimation. $\mathcal{AB}m$ thus
naturally leads to optimization and average-consensus over both undirected and
directed graphs, casting a unifying framework over several well-known consensus
algorithms over arbitrary strongly-connected graphs. We show that
$\mathcal{AB}m$ has a global $R$-linear rate when the largest step-size is
positive and sufficiently small. Following the standard practice in the
heavy-ball literature, we numerically show that $\mathcal{AB}m$ achieves
accelerated convergence especially when the objective function is
ill-conditioned.


  Here we understand \textit{dimensional reduction} as a procedure to obtain an
effective model in $D-1$ dimensions that is related to the original model in
$D$ dimensions. To explore this concept we use both a self-interacting
fermionic model and self-interacting bosonic model. Furthermore, in both cases,
we consider different boundary conditions in space: periodic, antiperiodic,
Dirichlet and Neumann. For bosonic fields, we get the so defined dimensional
reduction. Taking the simple example of a quartic interaction, we obtain that
the boundary condition (periodic, Dirichlet, Neumann) influence the new
coupling of the reduced model. For fermionic fields, we get the curious result
that the model obtained reducing from $D$ dimensions to $D-1$ dimensions is
distinguishable from taking into account a fermionic field originally in $D-1$
dimensions. Moreover, when one considers antiperiodic boundary condition in
space (both for bosons or fermions) it is found that the dimensional reduction
is not allowed.


  A pressure jump has been found at the onset of the dissolution of bcc
inclusions in separated solid 3He-4He mixture if the crystal is overheated
above a certain critical value. This effect can be explained in the framework
of a multistage dissolution process model.


  Let a three-dimensional isotropic elastic body be described by the Lam\'e
system with the body force of the form $F(x,t)=\phi(t)f(x)$, where $\phi$ is
known. We consider the problem of determining the unknown spatial term $f(x)$
of the body force where the surface stress history is given as the
overdetermination. This inverse problem is ill-posed. Using the interpolation
method and truncated Fourier series, we construct a regularized solution from
approximate data and provide explicit error estimates.
  AMS 2010 Subject Classification: 35L20, 35R30.
  Keywords: Body force, elastic, ill$-$posed problem, interpolation, Fourier
series.


  The antiferromagnetic kagome material Na2Ti3Cl8 exhibits a first-order phase
transition; the low-temperature phase is characterized by the trimerizations of
Ti ions. In this work, we carry out first-principles calculations on the
crystal and electronic structure of Na$_2$Ti$_3$Cl$_8$ at the high- and
low-temperature phases. The crystal structures, including the lattice constant
and the trimerization of Ti ions, are well reproduced by taking account a small
Hubbard correction of 1 eV. The calculated total energy landscape reveals a
first-order phase transition with the total energy barrier of 80 meV per
formula unit. Analysis of the electronic structure indicates a direct metal
bonding among Ti in the trimierized low-temperature phase.


  The problem of universal outlying sequence detection is studied, where the
goal is to detect outlying sequences among $M$ sequences of samples. A sequence
is considered as outlying if the observations therein are generated by a
distribution different from those generating the observations in the majority
of the sequences. In the universal setting, we are interested in identifying
all the outlying sequences without knowing the underlying generating
distributions. In this paper, a class of tests based on distribution clustering
is proposed. These tests are shown to be exponentially consistent with linear
time complexity in $M$. Numerical results demonstrate that our clustering-based
tests achieve similar performance to existing tests, while being considerably
more computationally efficient.


  In this article we explore an algorithm for diffeomorphic random sampling of
nonuniform probability distributions on Riemannian manifolds. The algorithm is
based on optimal information transport (OIT)---an analogue of optimal mass
transport (OMT). Our framework uses the deep geometric connections between the
Fisher-Rao metric on the space of probability densities and the right-invariant
information metric on the group of diffeomorphisms. The resulting sampling
algorithm is a promising alternative to OMT, in particular as our formulation
is semi-explicit, free of the nonlinear Monge--Ampere equation. Compared to
Markov Chain Monte Carlo methods, we expect our algorithm to stand up well when
a large number of samples from a low dimensional nonuniform distribution is
needed.


  Convolutional neural networks (CNNs) are very popular nowadays for image
processing. CNNs allow one to learn optimal filters in a (mostly) supervised
machine learning context. However this typically requires abundant labelled
training data to estimate the filter parameters. Alternative strategies have
been deployed for reducing the number of parameters and / or filters to be
learned and thus decrease overfitting. In the context of reverting to preset
filters, we propose here a computationally efficient harmonic block that uses
Discrete Cosine Transform (DCT) filters in CNNs. In this work we examine the
performance of harmonic networks in limited training data scenario. We validate
experimentally that its performance compares well against scattering networks
that use wavelets as preset filters.


  The emergence of CsCl bulk structure in (CsCl)nCs+ cluster ions is
investigated using a mixed quantum-mechanical/semiempirical theoretical
approach. We find that rhombic dodecahedral fragments (with bulk CsCl symmetry)
are more stable than rock-salt fragments after the completion of the fifth
rhombic dodecahedral atomic shell. From this size (n=184) on, a new set of
magic numbers should appear in the experimental mass spectra. We also propose
another experimental test for this transition, which explicitely involves the
electronic structure of the cluster. Finally, we perform more detailed
calculations in the size range n=31--33, where recent experimental
investigations have found indications of the presence of rhombic dodecahedral
(CsCl)32Cs+ isomers in the cluster beams.


  We present the results of a systematic, unbiased search for subpulse
modulation of 187 pulsars performed with the Westerbork Synthesis Radio
Telescope (WSRT) in the Netherlands at an observing wavelength of 21 cm. Using
new observations and archival WSRT data we have expanded the list of pulsars
which show the drifting subpulse phenomenon by 42, indicating that at least one
in three pulsars exhibits this phenomenon. The real fraction of pulsars which
show the drifting phenomenon is likely to be larger than some 55%. The majority
of the analysed pulsars show subpulse modulation (170), of which the majority
were not previously known to show subpulse modulation and 30 show clear
systematic drifting. The large number of new drifters we have found allows us,
for the first time, to do meaningful statistics on the drifting phenomenon. We
find that the drifting phenomenon is correlated with the pulsar age such that
drifting is more likely to occur in older pulsars. Pulsars which drift more
coherently seem to be older and have a lower modulation index. There is no
significant correlation found between P3 and other pulsar parameters (such as
the pulsar age), as has been reported in the past. There is no significant
preference of drift direction and the drift direction is not found to be
correlated with pulsar parameters. None of the four complexity parameters
predicted by different emission models (Jenet & Gil 2003) are shown to be
inconsistent with the set of modulation indices of our sample of pulsars.
Therefore none of the models can be ruled out based on our observations. We
also present results on some interesting new individual sources like a pulsar
which shows similar subpulse modulation in both the main- and interpulse and
six pulsars with opposite drift senses in different components.


  The integration of sensor data is crucial in the field of robotics to take
full advantage of the various sensors employed. One critical aspect of this
integration is determining the extrinsic calibration parameters, such as the
relative transformation, between each sensor. The use of data fusion between
complementary sensors, such as radar and LiDAR, can provide significant
benefits, particularly in harsh environments where accurate depth data is
required. However, noise included in radar sensor data can make the estimation
of extrinsic calibration challenging. To address this issue, we present a novel
framework for the extrinsic calibration of radar and LiDAR sensors, utilizing
CycleGAN as amethod of image-to-image translation. Our proposed method employs
translating radar bird-eye-view images into LiDAR-style images to estimate the
3-DOF extrinsic parameters. The use of image registration techniques, as well
as deskewing based on sensor odometry and B-spline interpolation, is employed
to address the rolling shutter effect commonly present in spinning sensors. Our
method demonstrates a notable improvement in extrinsic calibration compared to
filter-based methods using the MulRan dataset.


  We systematically construct vector solitary waves in harmonically trapped
one-dimensional two-component Bose-Einstein condensates with unequal dispersion
coefficients by a numerical continuation in chemical potentials from the
respective analytic low-density linear limits to the high-density nonlinear
Thomas-Fermi regime. The main feature of the linear states herein is that the
component with the larger quantum number has instead a smaller linear
eigenenergy, enabled by suitable unequal dispersion coefficients, leading to
new series of solutions compared with the states similarly obtained in the
equal dispersion setting. Particularly, the lowest-lying series gives the
well-known dark-anti-dark waves, and the second series yields the
dark-multi-dark states, and the following series become progressively more
complex in their wave structures. The Bogoliubov-de Gennes spectra analysis
shows that most of these states are typically unstable, but they can be
long-lived and most of them can be fully stabilized in suitable parameter
regimes.


  Microscopic biological systems operate far from equilibrium, are subject to
strong fluctuations, and are composed of many coupled components with
interactions varying in nature and strength. Researchers are actively
investigating the general design principles governing how biomolecular machines
achieve effective free-energy transduction in light of these challenges. We use
a model of two strongly coupled stochastic rotary motors to explore the effect
of coupling strength between components of a molecular machine. We observe
prominent thermodynamic characteristics at intermediate coupling strength, near
that which maximizes output power: a maximum in power and information
transduced from the upstream to the downstream system, and equal subsystem
entropy production rates. These observations are unified through a bound on the
machine's input and output power, which accounts for both the energy and
information transduced between subsystems.


  We report the existence of two new limiting turbulent regimes in horizontal
convection (HC) using direct numerical simulations at intermediate to low
Prandtl numbers. The flow driven by a horizontal gradient along a horizontal
surface, perpendicular to the acceleration of gravity is shown to transition to
turbulence in the plume and the core, modifying the rate of heat and momentum
transport. These transitions set a sequence of scaling laws blending the
theoretical arguments from both the Shishkina, Grossmann & Lohse (SGL) theory
with the Hughes, Griffiths & Mullarney (HGM) regime. These results embed the
HGM model in the SGL theory, agree, and extend the known regime diagram of
horizontal convection at high Rayleigh numbers. In particular, we show that HC
and Rayleigh-B\'enard share similar turbulent characteristics at low-Prandtl
numbers, where HC is shown for the first time to be ruled by its core dynamics
and turbulent boundary layers. This new scenario confirms that fully turbulent
HC enhances the transport of heat and momentum with respect to previously
reported regimes at high Rayleigh numbers. This work provides new insights on
the applicability of horizontal convection for geophysical flows such as
overturning circulations found in the atmosphere, the oceans, and flows near
the earth's inner core.


  The application of high-performance computing (HPC) processes, tools, and
technologies to Controlled Unclassified Information (CUI) creates both
opportunities and challenges. Building on our experiences developing,
deploying, and managing the Research Environment for Encumbered Data (REED)
hosted by AWS GovCloud, Research Computing at Purdue University has recently
deployed Weber, our locally-sited HPC solution for the storage and analysis of
CUI data. Weber presents our customer base with advances in data access,
portability, and usability at a low, stable cost while reducing administrative
overhead for our information technology support team.


  Synchrotron x-ray reflectivity is used to study ion distributions at the
liquid-liquid interface between a nitrobenzene solution of tetrabutylammonium
tetraphenylborate (TBATPB) and a water solution of tetrabutylammonium bromide
(TBABr). The concentration of TBABr is varied to alter the ion distribution.
Our x-ray measurements are inconsistent with several commonly used theories of
ion distributions, including Gouy-Chapman, modified Verwey-Niessen, and the
MPB5 version of the Poisson-Boltzmann equation. These structural measurements
are described well by ion distributions predicted by a version of the
Poisson-Boltzmann equation that explicitly includes a free energy profile for
ion transfer across the interface when this profile is described by a simple
analytic form or by a potential of mean force from molecular dynamics
simulations. These x-ray measurements from the liquid-liquid interface provide
evidence for the importance of interfacial liquid structure in determining
interfacial ion distributions.


  In this paper we continue the work on implicit-explicit (IMEX) time
discretizations for the incompressible Oseen equations that we started in
\cite{BGG23} (E. Burman, D. Garg, J. Guzm\`an, {\emph{Implicit-explicit time
discretization for Oseen's equation at high Reynolds number with application to
fractional step methods}}, SIAM J. Numer. Anal., 61, 2859--2886, 2023). The
pressure velocity coupling and the viscous terms are treated implicitly, while
the convection term is treated explicitly using extrapolation. Herein we focus
on the implicit-explicit Crank-Nicolson method for time discretization. For the
discretization in space we consider finite element methods with stabilization
on the gradient jumps. The stabilizing terms ensures inf-sup stability for
equal order interpolation and robustness at high Reynolds number. Under
suitable Courant conditions we prove stability of the implicit-explicit
Crank-Nicolson scheme in this regime. The stabilization allows us to prove
error estimates of order $O(h^{k+\frac12} + \tau^2)$. Here $h$ is the mesh
parameter, $k$ the polynomial order and $\tau$ the time step. Finally we
discuss some fractional step methods that are implied by the IMEX scheme.
Numerical examples are reported comparing the different methods when applied to
the Navier-Stokes' equations.


  Together with the recent CLIC detector model CLICdet a new software suite was
introduced for the simulation and reconstruction of events in this detector.
This note gives a brief introduction to CLICdet and describes the CLIC
experimental conditions at 380 GeV and 3 TeV, including beam-induced
backgrounds. The simulation and reconstruction tools are introduced, and the
physics performance obtained is described in terms of single particles,
particles in jets, jet energy resolution and flavour tagging. The performance
of the very forward electromagnetic calorimeters is also discussed.


  The internal (or residual) stress is among the key notions to describe the
state of the systems far from equilibrium. Such stress is invisible on the
macroscopic scale where the system is regarded as a blackbox. Yet
nonequilibrium macroscopic operations allow to create and observe the internal
stress. We present in this lecture some examples of the internal stress and its
operations. We describe the memory effect in some detail, the process in which
the history of past operations is recalled through the relaxation of internal
stress.


  We explore the use of correlation with simple functions to get lower bounds
for arithmetic quantities. In particular, we apply this idea to the power
moments of the error term when counting visible lattice points in large
spheres.


  We constrain Galactic foreground contamination of the Python V cosmic
microwave background anisotropy data by cross correlating it with foreground
contaminant emission templates. To model foreground emission we use 100 and 12
$\mu$m dust emission templates and two point source templates based on the PMN
survey. The analysis takes account of inter-modulation correlations in 8
modulations of the data that are sensitive to a large range of angular scales
and also densely sample a large area of sky. As a consequence the analysis here
is highly constraining. We find little evidence for foreground contamination in
an analysis of the whole data set. However, there is indication that
foregrounds are present in the data from the larger-angular-scale modulations
of those Python V fields that overlap the region scanned earlier by the UCSB
South Pole 1994 experiment. This is an independent consistency cross-check of
findings from the South Pole 1994 data.


  Cylindrical Algebraic Decomposition (CAD) has long been one of the most
important algorithms within Symbolic Computation, as a tool to perform
quantifier elimination in first order logic over the reals. More recently it is
finding prominence in the Satisfiability Checking community as a tool to
identify satisfying solutions of problems in nonlinear real arithmetic.
  The original algorithm produces decompositions according to the signs of
polynomials, when what is usually required is a decomposition according to the
truth of a formula containing those polynomials. One approach to achieve that
coarser (but hopefully cheaper) decomposition is to reduce the polynomials
identified in the CAD to reflect a logical structure which reduces the solution
space dimension: the presence of Equational Constraints (ECs).
  This paper may act as a tutorial for the use of CAD with ECs: we describe all
necessary background and the current state of the art. In particular, we
present recent work on how McCallum's theory of reduced projection may be
leveraged to make further savings in the lifting phase: both to the polynomials
we lift with and the cells lifted over. We give a new complexity analysis to
demonstrate that the double exponent in the worst case complexity bound for CAD
reduces in line with the number of ECs. We show that the reduction can apply to
both the number of polynomials produced and their degree.


  In this paper we investigate to what extent the results of Z. Wang and D.
Daigle on nice derivations of the polynomial ring in three variables over a
field k of characteristic zero extend to the polynomial ring over a PID R,
containing the field of rational numbers. One of our results shows that the
kernel of a nice derivation on the polynomial ring in four variables over k of
rank at most three is a polynomial ring over k.


  We describe a class of asymptotically AdS scalar field spacetimes, and
calculate the associated conserved charges for three, four and five spacetime
dimensions using the conformal and counter-term prescriptions. The energy
associated with the solutions in each case is proportional to $\sqrt{M^2 -
k^2}$, where $M$ is a constant and $k$ is a scalar charge. In five spacetime
dimensions, the counter-term prescription gives an additional vacuum (Casimir)
energy, which agrees with that found in the context of AdS/CFT correspondence.
We find a surprising degeneracy: the energy of the ``extremal'' scalar field
solution $M=k$ equals the energy of pure AdS. This result is discussed in light
of the AdS/CFT conjecture.


  This paper presents a Hoare-style calculus for formal reasoning about
reconfiguration programs of distributed systems. Such programs create and
delete components and/or interactions (connectors) while the system components
change state according to their internal behaviour. Our proof calculus uses a
resource logic, in the spirit of Separation Logic, to give local specifications
of reconfiguration actions. Moreover, distributed systems with an unbounded
number of components are described using inductively defined predicates. The
correctness of reconfiguration programs relies on havoc invariants, that are
assertions about the ongoing interactions in a part of the system that is not
affected by the structural change caused by the reconfiguration. We present a
proof system for such invariants in an assume/rely-guarantee style. We
illustrate the feasibility of our approach by proving the correctness of
real-life distributed systems with reconfigurable (self-adjustable) tree
architectures.


  The representation is essentially the same as that given by J.P.Nagle in J.
Comb. Theory (B), 1971, 10:1, 42--59. The distinction is in the definition of
the weighting function via the number of flows. This new definition allows one
to deduce a number of corollaries, in particular, the following.
  A) The chromatic polynomial of a connected planar graph G can be uniquely
determined from its combinatory dual graph G^* (although the graph G itself
isn't, in general, determined uniquely by G^*).
  B) If a planar graph G is different from the full graph K_3 and has exactly
one (up to renaming of colors) proper coloring of vertices in three colors,
then the graph G^* dual to graph G is also vertex colorable in three colors.


  This paper presents a neural incremental Structure-from-Motion (SfM)
approach, Level-S$^2$fM, which estimates the camera poses and scene geometry
from a set of uncalibrated images by learning coordinate MLPs for the implicit
surfaces and the radiance fields from the established keypoint correspondences.
Our novel formulation poses some new challenges due to inevitable two-view and
few-view configurations in the incremental SfM pipeline, which complicates the
optimization of coordinate MLPs for volumetric neural rendering with unknown
camera poses. Nevertheless, we demonstrate that the strong inductive basis
conveying in the 2D correspondences is promising to tackle those challenges by
exploiting the relationship between the ray sampling schemes. Based on this, we
revisit the pipeline of incremental SfM and renew the key components, including
two-view geometry initialization, the camera poses registration, the 3D points
triangulation, and Bundle Adjustment, with a fresh perspective based on neural
implicit surfaces. By unifying the scene geometry in small MLP networks through
coordinate MLPs, our Level-S$^2$fM treats the zero-level set of the implicit
surface as an informative top-down regularization to manage the reconstructed
3D points, reject the outliers in correspondences via querying SDF, and refine
the estimated geometries by NBA (Neural BA). Not only does our Level-S$^2$fM
lead to promising results on camera pose estimation and scene geometry
reconstruction, but it also shows a promising way for neural implicit rendering
without knowing camera extrinsic beforehand.


  The issue of giving an explicit description of the flow of information
concerning the time of bankruptcy of a company (or a state) arriving on the
market is tackled by defining a bridge process starting from zero and
conditioned to be equal to zero when the default occurs. This enables to catch
some empirical facts on the behavior of financial markets: when the bridge
process is away from zero, investors can be relatively sure that the default
will not happen immediately. However, when the information process is close to
zero, market agents should be aware of the risk of an imminent default. In this
sense the bridge process leaks information concerning the default before it
occurs. The objective of this first paper on Brownian bridges on stochastic
intervals is to provide the basic properties of these processes.


  I present a novel equivariant neural network architecture for the large-scale
spin dynamics simulation of the Kondo lattice model. This neural network mainly
consists of tensor-product-based convolution layers and ensures two
equivariances: translations of the lattice and rotations of the spins. I
implement equivariant neural networks for two Kondo lattice models on
two-dimensional square and triangular lattices, and perform training and
validation. In the equivariant model for the square lattice, the validation
error (based on root mean squared error) is reduced to less than one-third
compared to a model using invariant descriptors as inputs. Furthermore, I
demonstrate the ability to reproduce phase transitions of skyrmion crystals in
the triangular lattice, by performing dynamics simulations using the trained
model.


  Single-molecule microscopy has become an indispensable tool for biochemical
analysis. The capability of characterizing distinct properties of individual
molecules without averaging has provided us with a different perspective for
the existing scientific issues and phenomena. Recently, the super-resolution
fluorescence microscopy techniques have overcome the optical diffraction limit
by the localization of molecule positions. However, the labelling process can
potentially modify the intermolecular dynamics. Based on the highly-sensitive
nanomechanical photothermal microscopy reported previously, we propose
optimizations on this label-free microscopy technique towards localization
microscopy. A localization precision of 3 $\unicode{x212B}$ is achieved with
gold nanoparticles, and the detection of polarization-dependent absorption is
demonstrated, which opens the door for further improvement with polarization
modulation imaging.


  Perceptual aliasing is one of the main causes of failure for Simultaneous
Localization and Mapping (SLAM) systems operating in the wild. Perceptual
aliasing is the phenomenon where different places generate a similar visual
(or, in general, perceptual) footprint. This causes spurious measurements to be
fed to the SLAM estimator, which typically results in incorrect localization
and mapping results. The problem is exacerbated by the fact that those outliers
are highly correlated, in the sense that perceptual aliasing creates a large
number of mutually-consistent outliers. Another issue stems from the fact that
most state-of-the-art techniques rely on a given trajectory guess (e.g., from
odometry) to discern between inliers and outliers and this makes the resulting
pipeline brittle, since the accumulation of error may result in incorrect
choices and recovery from failures is far from trivial. This work provides a
unified framework to model perceptual aliasing in SLAM and provides practical
algorithms that can cope with outliers without relying on any initial guess. We
present two main contributions. The first is a Discrete-Continuous Graphical
Model (DC-GM) for SLAM: the continuous portion of the DC-GM captures the
standard SLAM problem, while the discrete portion describes the selection of
the outliers and models their correlation. The second contribution is a
semidefinite relaxation to perform inference in the DC-GM that returns
estimates with provable sub-optimality guarantees. Experimental results on
standard benchmarking datasets show that the proposed technique compares
favorably with state-of-the-art methods while not relying on an initial guess
for optimization.


  Fast evolution of Internet technologies has led to an explosive growth of
video data available in the public domain and created unprecedented challenges
in the analysis, organization, management, and control of such content. The
problems encountered in video analysis such as identifying a video in a large
database (e.g. detecting pirated content in YouTube), putting together video
fragments, finding similarities and common ancestry between different versions
of a video, have analogous counterpart problems in genetic research and
analysis of DNA and protein sequences. In this paper, we exploit the analogy
between genetic sequences and videos and propose an approach to video analysis
motivated by genomic research. Representing video information as video DNA
sequences and applying bioinformatic algorithms allows to search, match, and
compare videos in large-scale databases. We show an application for
content-based metadata mapping between versions of annotated video.


  For the initial boundary problem of the incompressible MHD equations in a
bounded domain with general curved boundary in 3D with the general Navier-slip
boundary conditions for the velocity field and the perfect conducting condition
for the magnetic field, we establish the uniform regularity of conormal Sobolev
norms and Lipschitz norms to addressing the anisotropic regularity of
tangential and normal directions, which enable us to prove the vanishing
dissipation limit as the viscosity and the magnetic diffusion coefficients tend
to zero. We overcome the difficulties caused by the intricate interaction of
boundary curvature, velocity field, and magnetic fields and resolve the issue
caused by the problem that the viscosity and the magnetic diffusion
coefficients are not required to be equal.


  Background: Given the importance of relation or event extraction from
biomedical research publications to support knowledge capture and synthesis,
and the strong dependency of approaches to this information extraction task on
syntactic information, it is valuable to understand which approaches to
syntactic processing of biomedical text have the highest performance. Results:
We perform an empirical study comparing state-of-the-art traditional
feature-based and neural network-based models for two core natural language
processing tasks of part-of-speech (POS) tagging and dependency parsing on two
benchmark biomedical corpora, GENIA and CRAFT. To the best of our knowledge,
there is no recent work making such comparisons in the biomedical context;
specifically no detailed analysis of neural models on this data is available.
Experimental results show that in general, the neural models outperform the
feature-based models on two benchmark biomedical corpora GENIA and CRAFT. We
also perform a task-oriented evaluation to investigate the influences of these
models in a downstream application on biomedical event extraction, and show
that better intrinsic parsing performance does not always imply better
extrinsic event extraction performance. Conclusion: We have presented a
detailed empirical study comparing traditional feature-based and neural
network-based models for POS tagging and dependency parsing in the biomedical
context, and also investigated the influence of parser selection for a
biomedical event extraction downstream task. Availability of data and material:
We make the retrained models available at
https://github.com/datquocnguyen/BioPosDep


  The phase transition to a deconfined phase is studied and the consequences in
the formation of neutron stars are investigated. We use the
quark-meson-coupling model for the hadron matter and the MIT Bag model for the
quark matter in order to build the appropriate equations of state for the
hybrid stars. The properties of the stars are then calculated. The differences
between unpaired and color-flavor locked quark matter are discussed.


  We study the time evolution of different Laponite suspensions from a
low-viscosity ergodic state to a viscoelastic non-ergodic state over a wide
range of volume fractions and salt contents. We find that the evolution of
non-ergodicity parameter (Debye-Waller factor) splits into two branches for all
the samples, which correspond to two distinct dynamically arrested states. At
moderately high salt concentrations, on the other hand, a third and new
nonergodic state appears that are different from the above two nonergodic
states. Measurement of the conductivity of Laponite solutions in pure water
shows that the contribution of counterions in the ionic strength is
considerable and their role should be taken into account in interpretations of
aging dynamics and the phase diagram. Based on these data and available data in
the literature, we propose a new (non-equilibrium) phase diagram for Laponite
suspensions.


  The annual number of publications at scientific venues, for example,
conferences and journals, is growing quickly. Hence, even for researchers it
becomes harder and harder to keep track of research topics and their progress.
In this task, researchers can be supported by automated publication analysis.
Yet, many such methods result in uninterpretable, purely numerical
representations. As an attempt to support human analysts, we present topic
space trajectories, a structure that allows for the comprehensible tracking of
research topics. We demonstrate how these trajectories can be interpreted based
on eight different analysis approaches. To obtain comprehensible results, we
employ non-negative matrix factorization as well as suitable visualization
techniques. We show the applicability of our approach on a publication corpus
spanning 50 years of machine learning research from 32 publication venues. Our
novel analysis method may be employed for paper classification, for the
prediction of future research topics, and for the recommendation of fitting
conferences and journals for submitting unpublished work.


  Duality games are a way of looking at wave-particle duality. In these games.
Alice and Bob together are playing against the House. The House specifies, at
random, which of two sub-games Alice and Bob will play. One game, Ways,
requires that they obtain path information about a particle going through an
$N$-path interferometer and the other, Phases, requires that they obtain phase
information. In general, because of wave-particle duality, Alice and Bob cannot
always win the overall game. However, if the required amount of path and phase
information is not too great, for example specifying a set of paths or phases,
one of which is the right one, then they can always win. Here we study examples
of duality games that can always be won, and develop a wave-particle duality
relation expressed only in terms of mutual information to help analyze these
games.


  We discuss the applicability of the energy density formalism (EDF) for
heavy-ion fusion reactions at sub-barrier energies. For this purpose, we
calculate the fusion excitation function and the fusion barrier distribution
for the reactions of $^{16}$O with $^{154,}$$^{144}$Sm,$^{186}$W and $^{208}$Pb
with the coupled-channels method. We also discuss the effect of saturation
property on the fusion cross section for the reaction between two $^{64}$Ni
nuclei, in connection to the so called steep fall-off phenomenon of fusion
cross sections at deep sub-barrier energies.


  We discuss the relation between the gravitational and electromagnetic fields
as governed by the Einstein-Maxwell field equations. It is emphasized that the
tendency of the gravitational field to induce electromagnetic effects increases
as the size of the system goes down. In particular, the gravitational field,
according to general relativity, tends to become dominated by the spin at
distances of the order of the Compton wavelength. The relevant quantity which
governs this behavior is the ratio S/M^2 where S is the (spin) angular
momentum. For an electron, S/M^2 ~ 10^44. Therefore, gravitomagnetic effects
will play a significant role in the subatomic domain. To analyze this situation
we use the asymptotic structure in the form of the multipole fields. Some
important consequences for the electromagnetic fields of charged particles with
spin are pointed out. In particular, the gravitational field may induce
corrections to the Coulomb field which can be tested experimentally.


  We present polaron effective masses and selected polaron band structures of
the Holstein molecular crystal model in 1-D as computed by the Global-Local
variational method over a wide range of parameters. These results are augmented
and supported by leading orders of both weak- and strong-coupling perturbation
theory. The description of the polaron effective mass and polaron band
distortion that emerges from this work is comprehensive, spanning weak,
intermediate, and strong electron-phonon coupling, and non-adiabatic, weakly
adiabatic, and strongly adiabatic regimes. Using the effective mass as the
primary criterion, the self-trapping transition is precisely defined and
located. Using related band-shape criteria at the Brillouin zone edge, the
onset of band narrowing is also precisely defined and located. These two lines
divide the polaron parameter space into three regimes of distinct polaron
structure, essentially constituting a polaron phase diagram. Though the
self-trapping transition is thusly shown to be a broad and smooth phenomenon at
finite parameter values, consistency with notion of self-trapping as a critical
phenomenon in the adiabatic limit is demonstrated. Generalizations to higher
dimensions are considered, and resolutions of apparent conflicts with
well-known expectations of adiabatic theory are suggested.


  We investigate the formation of spherical cosmological structures following
both dark matter and gas components. We focus on the dynamical aspect of the
collapse assuming an adiabatic, $\gamma = 5/3$, fully ionized primordial
plasma. We use for that purpose a fully Lagrangian hydrodynamical code designed
to describe highly compressible flows in spherical geometry. We investigate
also a "fluid approach" to describe the mean physical quantities of the dark
matter flow. We test its validity for a wide range of initial density contrast.
We show that an homogeneous isentropic core forms in the gas distribution,
surrounded by a self-similar hydrostatic halo, with much higher entropy
generated by shock dissipation. We derive analytical expressions for the size,
density and temperature of the core, as well as for the surrounding halo. We
show that, unless very efficient heating processes occur in the intergalactic
medium, we are unable to reproduce within adiabatic models the typical core
sizes in X-ray clusters. We also show that, for dynamical reasons only, the gas
distribution is naturally antibiased relative to the total mass distribution,
without invoking any reheating processes. This could explain why the gas
fraction increases with radius in very large X-ray clusters. As a preparation
for the next study devoted to the thermodynamical aspect of the collapse, we
investigate the initial entropy level required to solve the core problem in
X-ray clusters.


  Strong laser physics is a research direction that relies on the use of
high-power lasers and has led to fascinating achievements ranging from
relativistic particle acceleration to attosecond science. On the other hand,
quantum optics has been built on the use of low photon number sources and has
opened the way for groundbreaking discoveries in quantum technology, advancing
investigations ranging from fundamental tests of quantum theory to quantum
information processing. Despite the tremendous progress, until recently these
directions have remained disconnected. This is because, the majority of the
interactions in the strong-field limit have been successfully described by
semi-classical approximations treating the electromagnetic field classically,
as there was no need to include the quantum properties of the field to explain
the observations. The link between strong laser physics, quantum optics, and
quantum information science has been developed in the recent past. Studies
based on fully quantized and conditioning approaches have shown that intense
laser--matter interactions can be used for the generation of controllable
entangled and non-classical light states. This achievement opens the way for a
vast number of investigations stemming from the symbiosis of strong laser
physics, quantum optics, and quantum information science. Here, after an
introduction to the fundamentals of these research directions, we report on the
recent progress in the fully quantized description of intense laser--matter
interaction and the methods that have been developed for the generation of
non-classical light states and entangled states. Also, we discuss the future
directions of non-classical light engineering using strong laser fields, and
the potential applications in ultrafast and quantum information science.


  Solar S-bursts are short duration ($<1$ s at decameter wavelengths) radio
bursts that have been observed during periods of moderate solar activity, where
S stands for short. The frequency drift of S-bursts can reflect the density
variation and the motion state of the electron beams. In this work, we
investigate the frequency drift and the fine structure of the S-bursts with the
LOw Frequency ARray (LOFAR). We find that the average frequency drift rate of
the S-bursts within 110-180MHz could be described by $df/dt=-0.0077f^{1.59}$.
With the high time and frequency resolution of LOFAR, we can resolve the fine
structures of the observed solar S-bursts. A fine drift variation pattern was
found in the structure of S-bursts (referred to as solar Sb-bursts in this
paper) during the type-III storm on 2019 April 13, in the frequency band of
120-240 MHz. The Sb-bursts have a quasi-periodic segmented pattern, and the
relative flux intensity tends to be large when the frequency drift rate is
relatively large. This kind of structure exists in about 20\% of the solar
S-burst events within the observed frequency range. We propose that the fine
structure is due to the density fluctuations of the background coronal density.
We performed a simulation based on this theory which can reproduce the shape
and relative flux intensity of the Sb-bursts. This work shows that the fine
structure of solar radio bursts can be used to diagnose the coronal plasma.


  We report lifetimes, branching fractions, and the resulting oscillator
strengths for transitions within the P II multiplet (3s23p2 3P - 3s3p3 3Po) at
1308 {\AA}. These comprehensive beam-foil measurements, which are the most
precise set currently available experimentally, resolve discrepancies involving
earlier experimental and theoretical results. Interstellar phosphorus
abundances derived from {\lambda}1308 can now be interpreted with greater
confidence. In the course of our measurements, we also obtained an experimental
lifetime for the 3p4s 3P0o level of P IV. This lifetime agrees well with the
available theoretical calculation.


  We derive the planar dilatation operator in the closed subsector of scalar
composite operators of an N=2 superconformal quiver gauge theory to three
loops. By tuning the ratio of its two gauge couplings we interpolate between a
Z_2 orbifold of N=4 SYM theory and N=2 superconformal QCD. We find zeta(3)
contributions at three loops that disappear when the theory is at the orbifold
point. They are responsible for imaginary contributions to the dispersion
relation of a single scalar excitation in the spin-chain picture. This points
towards an interpretation of the individual scalar excitations as effective
rather than as elementary magnons. We argue that the elementary excitations
should be associated with certain fermions and covariant derivatives, and that
integrability in the respective subsectors should persist at least to two
loops.


  This paper investigates the role of tutor feedback in language learning using
computational models. We compare two dominant paradigms in language learning:
interactive learning and cross-situational learning - which differ primarily in
the role of social feedback such as gaze or pointing. We analyze the
relationship between these two paradigms and propose a new mixed paradigm that
combines the two paradigms and allows to test algorithms in experiments that
combine no feedback and social feedback. To deal with mixed feedback
experiments, we develop new algorithms and show how they perform with respect
to traditional knn and prototype approaches.


  Vertically stratified shearing box simulations of magnetorotational
turbulence commonly exhibit a so-called butterfly diagram of quasi-periodic
azimuthal field reversals. However, in the presence of hydrodynamic convection,
field reversals no longer occur. Instead, the azimuthal field strength
fluctuates quasi-periodically while maintaining the same polarity, which can
either be symmetric or antisymmetric about the disc midplane. Using data from
the simulations of Hirose et al. (2014), we demonstrate that the lack of field
reversals in the presence of convection is due to hydrodynamic mixing of
magnetic field from the more strongly magnetized upper layers into the
midplane, which then annihilate field reversals that are starting there. Our
convective simulations differ in several respects from those reported in
previous work by others, in which stronger magnetization likely plays a more
important role than convection.


  The risk of dying increases exponentially with age, in humans as well as in
many other species. This increase is often attributed to the "accumulation of
damage" known to occur in many biological structures and systems. The aim of
this paper is to describe a generic model of damage accumulation and death in
which mortality increases exponentially with age. The damage-accumulation
process is modeled by a stochastic process know as a queue, and risk of dying
is a function of the accumulated damage, i.e. length of the queue. The model
has four parameters and the main characteristics of the model are: (i) damage
occurs at random times with a constant high rate; (ii) the damage is repaired
at a limited rate, and consequently damage can accumulate; (iii) the efficiency
of the repair mechanism decays linearly with age; (iv) the risk of dying is a
function of the accumulated damage. Using standard results from the
mathematical theory of queues it is shown that there is an exponential
dependence between risk of dying and age in these models, and that this
dependency holds irrespective of how the damage-accumulation process is
modeled. Furthermore, the ways in which this exponential dependence is shaped
by the model parameters are also independent of the details of the damage
accumulation process. These generic features suggest that the model could be
useful when interpreting changes in the relation between age and mortality in
real data. To examplify, historical mortality data from Sweden are interpreted
in the light of the model. The decrease in mortality seen between cohorts born
in 1905, compared to those born in 1885, can be accounted for by higher
threshold to damage. This fits well with the many advances made in public
health during the 20th century.


  Let $\mathcal{T}$ be a triangular algebra over a commutative ring
$\mathcal{R}$ and $\varphi: \mathcal{T} \times \mathcal{T}\longrightarrow
\mathcal{T}$ be an arbitrary Lie biderivation of $\mathcal{T}$. We will address
the question of describing the form of $\varphi$ in the current work. It is
shown that under certain mild assumptions, $\varphi$ is the sum of an inner
biderivation and an extremal biderivation and a some central bilinear mapping.
Our results is immediately applied to block upper triangular algebras and
Hilbert space nest algebras .


  Two sinks drain precision from higher-order flow analyses: (1) merging of
argument values upon procedure call and (2) merging of return values upon
procedure return. To combat the loss of precision, these two sinks have been
addressed independently. In the case of procedure calls, abstract garbage
collection reduces argument merging; while in the case of procedure returns,
context-free approaches eliminate return value merging. It is natural to expect
a combined analysis could enjoy the mutually beneficial interaction between the
two approaches. The central contribution of this work is a direct product of
abstract garbage collection with context-free analysis. The central challenge
to overcome is the conflict between the core constraint of a pushdown system
and the needs of garbage collection: a pushdown system can only see the top of
the stack, yet garbage collection needs to see the entire stack during a
collection. To make the direct product computable, we develop "stack
summaries," a method for tracking stack properties at each control state in a
pushdown analysis of higher-order programs.


  We present the detection of an absorpton feature at $E=8.77^{+0.05}_{-0.06}$
keV in the combined X-ray spectrum of the ultraluminous X-ray source NGC 1313
X-1 observed with XMM-Newton and NuSTAR, significant at the 3$\sigma$ level. If
associated with blueshifted ionized iron, the implied outflow velocity is
~0.2$c$ for Fe XXVI, or ~0.25$c$ for Fe XXV. These velocities are similar to
the ultrafast outflow seen in absorption recently discovered in this source at
lower energies by XMM-Newton, and we therefore conclude that this is an iron
component to the same outflow. Photoionization modeling marginally prefers the
Fe XXV solution, but in either case the outflow properties appear to be
extreme, potentially supporting a super-Eddington hypothesis for NGC 1313 X-1.


  One of the biggest challenges in understanding Magnetohydrodynamic (MHD)
turbulence is identifying the plasma mode components from observational data.
Previous studies on synchrotron polarization from the interstellar medium (ISM)
suggest that the dominant MHD modes can be identified via statistics of Stokes
parameters, which would be crucial for studying various ISM processes such as
the scattering and acceleration of cosmic rays, star formation, dynamo. In this
paper, we present a numerical study of the Synchrotron Polarization Analysis
(SPA) method through systematic investigation of the statistical properties of
the Stokes parameters. We derive the theoretical basis for our method from the
fundamental statistics of MHD turbulence, recognizing that the projection of
the MHD modes allows us to identify the modes dominating the energy fraction
from synchrotron observations. Based on the discovery, we revise the SPA method
using synthetic synchrotron polarization observations obtained from 3D ideal
MHD simulations with a wide range of plasma parameters and driving mechanisms,
and present a modified recipe for mode identification. We propose a
classification criterion based on a new SPA+ fitting procedure, which allows us
to distinguish between Alfv\'en mode and compressible/slow mode dominated
turbulence. We further propose a new method to identify fast modes by analyzing
the asymmetry of the SPA+ signature and establish a new asymmetry parameter to
detect the presence of fast mode turbulence. Additionally, we confirm through
numerical tests that the identification of the compressible and fast modes is
not affected by Faraday rotation in both the emitting plasma and the
foreground.


  It is pointed out that the concepts and methods introduced by Bachelier and
by Mandelbrot to Finance and Economics can be used to examine the fluctuations
observed in high-energy hadron production processes. Theoretical arguments and
experimental evidences are presented which show that the relative variations of
hadron-numbers between successive rapidity intervals are non-Gaussian stable
random variables, which exhibit stationarity and scaling. The implications of
the obtained results are discussed.


  We perform numerical simulations of athermal repulsive frictionless disks and
spheres in two and three spatial dimensions undergoing cyclic quasi-static
simple shear to investigate particle-scale reversible motion. We identify three
classes of steady-state dynamics as a function of packing fraction \phi and
maximum strain amplitude per cycle \gamma_{\rm max}. Point-reversible states,
where particles do not collide and exactly retrace their intra-cycle
trajectories, occur at low \phi and \gamma_{\rm max}. Particles in
loop-reversible states undergo numerous collisions and execute complex
trajectories, but return to their initial positions at the end of each cycle.
Loop-reversible dynamics represents a novel form of self-organization that
enables reliable preparation of configurations with specified structural and
mechanical properties over a broad range of \phi from contact percolation to
jamming onset at \phi_J. For sufficiently large \phi and \gamma_{\rm max},
systems display irreversible dynamics with nonzero self-diffusion.


  In this article we will construct the Liouville parametrization of the
triaxial ellipsoid. In the literature quadrics are given as examples of
Liouville surfaces, yet no one gives such a parametrization. For this we
introduce the generalized Jacobi amplitude as inverse of the elliptic integral
of the third kind.


  We prove that the isomorphism problem for group algebras reduces to group
algebras over finite extensions of the prime field. In particular, the modular
isomorphism problem reduces to finite modular group algebras.


  We focus on the problem of learning a single motor module that can flexibly
express a range of behaviors for the control of high-dimensional physically
simulated humanoids. To do this, we propose a motor architecture that has the
general structure of an inverse model with a latent-variable bottleneck. We
show that it is possible to train this model entirely offline to compress
thousands of expert policies and learn a motor primitive embedding space. The
trained neural probabilistic motor primitive system can perform one-shot
imitation of whole-body humanoid behaviors, robustly mimicking unseen
trajectories. Additionally, we demonstrate that it is also straightforward to
train controllers to reuse the learned motor primitive space to solve tasks,
and the resulting movements are relatively naturalistic. To support the
training of our model, we compare two approaches for offline policy cloning,
including an experience efficient method which we call linear feedback policy
cloning. We encourage readers to view a supplementary video (
https://youtu.be/CaDEf-QcKwA ) summarizing our results.


  We propose a new class of spontaneous baryogenesis models that does not
produce baryon isocurvature perturbations. The baryon chemical potential in
these models is independent of the field value of the baryon-generating scalar,
hence the scalar field fluctuations are blocked from propagating into the
baryon isocurvature. We demonstrate this mechanism in simple examples where
spontaneous baryogenesis is driven by a non-canonical scalar field. The
suppression of the baryon isocurvature allows spontaneous baryogenesis to be
compatible even with high-scale inflation.


  Using high-resolution Hubble Space Telescope data, we reexamine the
fundamental properties (ages, masses and extinction values) of the rich star
cluster population in the dwarf starburst galaxy NGC 5253. The gain in
resolution compared to previous studies is of order a factor of two in both
spatial dimensions, while our accessible wavelength range transcends previous
studies by incorporation of both near-ultraviolet and near-infrared (IR)
passbands. We apply spectral synthesis treatments based on two different simple
stellar population model suites to our set of medium-, broad-band and H-alpha
images to gain an improved physical understanding of the IR-excess flux found
for a subset of young clusters (30 of 149). With the caveat that our models are
based on fully sampled stellar mass functions, the NGC 5253 cluster population
is dominated by a significant number of relatively low-mass (M_cl <= a few 10^4
Msun) objects with ages ranging from a few x 10^6 to a few x 10^7 yr, which is
in excellent agreement with the starburst age of the host galaxy. The IR-excess
clusters are almost all found in this young age range and have masses of up to
a few x 10^4 Msun. The IR excess in the relatively low-mass NGC 5253 clusters
is most likely caused by a combination of stochastic sampling effects and
colour variations due to the presence of either luminous red or
pre-main-sequence stars. We also find a small number of intermediate-age (~ 1
Gyr-old), ~10^5 Msun clusters, as well as up to a dozen massive, ~10 Gyr-old
globular clusters. Their presence supports the notion that NGC 5253 is a very
active galaxy that has undergone multiple episodes of star cluster formation.


  In this paper, we consider the problem of remote vector Gaussian source
coding for a wireless acoustic sensor network. Each node receives messages from
multiple nodes in the network and decodes these messages using its own
measurement of the sound field as side information. The node's measurement and
the estimates of the source resulting from decoding the received messages are
then jointly encoded and transmitted to a neighboring node in the network. We
show that for this distributed source coding scenario, one can encode a
so-called conditional sufficient statistic of the sources instead of jointly
encoding multiple sources. We focus on the case where node measurements are in
form of noisy linearly mixed combinations of the sources and the acoustic
channel mixing matrices are invertible. For this problem, we derive the
rate-distortion function for vector Gaussian sources and under covariance
distortion constraints.


  Attention-based models have recently shown great performance on a range of
tasks, such as speech recognition, machine translation, and image captioning
due to their ability to summarize relevant information that expands through the
entire length of an input sequence. In this paper, we analyze the usage of
attention mechanisms to the problem of sequence summarization in our end-to-end
text-dependent speaker recognition system. We explore different topologies and
their variants of the attention layer, and compare different pooling methods on
the attention weights. Ultimately, we show that attention-based models can
improves the Equal Error Rate (EER) of our speaker verification system by
relatively 14% compared to our non-attention LSTM baseline model.


  In porous media physics, calibrating model parameters through experiments is
a challenge. This process is plagued with errors that come from modelling,
measurement and computation of the macroscopic observables through random
homogenization -- the forward problem -- as well as errors coming from the
parameters fitting procedure -- the inverse problem. In this work, we address
these issues by considering a least-square formulation to identify parameters
of the microscopic model on the basis on macroscopic observables. In
particular, we discuss the selection of the macroscopic observables which we
need to know in order to uniquely determine these parameters. To gain a better
intuition and explore the problem without a too high computational load, we
mostly focus on the one-dimensional case. We show that the Newton algorithm can
be efficiently used to robustly determine optimal parameters, even if some
small statistical noise is present in the system.


  We compute the ground-state properties of fully polarized, trapped,
one-dimensional fermionic systems interacting through a gaussian potential. We
use an antisymmetric artificial neural network, or neural quantum state, as an
ansatz for the wavefunction and use machine learning techniques to
variationally minimize the energy of systems from 2 to 6 particles. We provide
extensive benchmarks with other many-body methods, including exact
diagonalisation and the Hartree-Fock approximation. The neural quantum state
provides the best energies across a wide range of interaction strengths. We
find very different ground states depending on the sign of the interaction. In
the non-perturbative repulsive regime, the system asymptotically reaches
crystalline order. In contrast, the strongly attractive regime shows signs of
bosonization. The neural quantum state continuously learns these different
phases with an almost constant number of parameters and a very modest increase
in computational time with the number of particles.


  The pionic contribution to the g-2 of the muon involves a certain integral
over the the modulus squared of F_\pi(t), the pion electromagnetic form factor.
We extend techniques that use cut-plane analyticity properties of F_\pi(t) in
order to account for present day estimates of the pionic contribution and
experimental information at a finite number of points in the space-like region.
Using data from several experiments over a large kinematic range for |t|, we
find bounds on the expansion coefficients of F_\pi(t), sub-leading to the
charge radius. The value of one of these coefficients in chiral perturbation
theory respects these bounds. Furthermore, we present a sensitivity analysis to
the inputs. A brief comparison with results in the literature that use
observables other than the g-2 and timelike data is presented.


  This paper introduces a new loss function, OSM (One-Sided Margin), to solve
maximum-margin classification problems effectively. Unlike the hinge loss, in
OSM the margin is explicitly determined with corresponding hyperparameters and
then the classification problem is solved. In experiments, we observe that
using OSM loss leads to faster training speeds and better accuracies than
binary and categorical cross-entropy in several commonly used deep models for
classification and optical character recognition problems.
  OSM has consistently shown better classification accuracies over
cross-entropy and hinge losses for small to large neural networks. it has also
led to a more efficient training procedure. We achieved state-of-the-art
accuracies for small networks on several benchmark datasets of
CIFAR10(98.82\%), CIFAR100(91.56\%), Flowers(98.04\%), Stanford Cars(93.91\%)
with considerable improvements over other loss functions. Moreover, the
accuracies are rather better than cross-entropy and hinge loss for large
networks. Therefore, we strongly believe that OSM is a powerful alternative to
hinge and cross-entropy losses to train deep neural networks on classification
tasks.


  We present ALMA band 3 observations of the CO(6-5), CO(7-6), and [CI]
369micron emission lines in three of the highest redshift quasar host galaxies
at 6.6<z<6.9. These measurements constitute the highest-redshift CO detections
to date. The target quasars have previously been detected in [CII] 158micron
emission and the underlying far-infrared (FIR) dust continuum. We detect
(spatially unresolved, at a resolution of >2", or >14kpc) CO emission in all
three quasar hosts. In two sources, we detect the continuum emission around
400micron (rest-frame), and in one source we detect [CI] at low significance.
We derive molecular gas reservoirs of (1-3)x10^10 M_sun in the quasar hosts,
i.e. approximately only 10 times the mass of their central supermassive black
holes. The extrapolated [CII]-to-CO(1-0) luminosity ratio is 2500-4200,
consistent with measurements in galaxies at lower redshift. The detection of
the [CI] line in one quasar host galaxy and the limit on the [CI] emission in
the other two hosts enables a first characterization of the physical properties
of the interstellar medium in z~7 quasar hosts. In the sources, the derived
global CO/[CII]/[CI] line ratios are consistent with expectations from
photodissociation regions (PDR), but not X-ray dominated regions (XDR). This
suggest that quantities derived from the molecular gas and dust emission are
related to ongoing star-formation activity in the quasar hosts, providing
further evidence that the quasar hosts studied here harbor intense starbursts
in addition to their active nucleus.


  In this work, we explore the charmed pentaquarks, where the relativistic
five-quark equations are obtained by the dispersion relation technique. By
solving these equations with the method based on the extraction of the leading
singularities of the amplitudes, we predict the mass spectrum of charmed
pentaquarks with $J^P=1/2^{\pm}$ and $3/2^{\pm}$, which is valuable to further
experimental study of charmed pentaquark.


  We study the characteristics of moving type IV radio bursts which extend to
the hectometric wavelengths (interplanetary type IV or type IV IP bursts) and
their relationship with energetic phenomena on the Sun. Our dataset comprises
48 interplanetary type IV bursts observed with Wind/WAVES in the 13.825 MHz-20
kHz frequency range. The dynamic spectra of the RSTN, the Nancay Decametric
Array (DAM), the ARTEMIS-IV, the Culgoora, Hiraiso and Izmiran Radio
Spectrographs were used to track the evolution of the events in the low corona.
These were supplemented with SXR flux data from the GOES and CME data from the
SOHO/LASCO. Positional information of the coronal bursts was obtained by the
NRH. We examined the relationship of the type IV events with coronal radio
bursts, CMEs and SXR flares. The majority of the events (45) were characterized
as compact; their duration was on average 106 minutes. This type of events was,
mostly, associated with M-and X-class flares (40 out of 45) and fast CMEs; 32
of these events had CMEs faster than 1000 km/s. Furthermore, in 43 compact
events the CME was, possibly, subjected to reduced aerodynamic drag as it was
propagating in the wake of a previous CME. A minority (three) of long lived
type IV IP bursts was detected, with duration from 960 minutes to 115 hours.
These events are referred to as extended or long duration and appear to
replenish their energetic electron content, possibly from electrons escaping
from the corresponding coronal type IV bursts. The latter were found to persist
on the disk, for tens of hours to days. Prominent among them was the unusual
interplanetary type IV burst of 18--23 May 2002, which is the longest event in
the Wind/WAVES catalog. The three extended events were, usually, accompanied by
a number of flares, of GOES class C in their majority, and of CMEs, many of
which were slow and narrow.


  Conventional methods of wavefront reconstruction from the raw data of the
Shack-Hartmann sensor use the focal spot shifts and discard the high-frequency
information about the wavefront. Phase-retrieval-based methods treat the
Hartmann pattern as the diffraction image and use the Rayleigh-Sommerfeld
propagation to estimate the wavefront with greater accuracy and resolution. In
this Letter, we propose a novel approach to the phase-retrieval-based
reconstruction by considering the Hartmann pattern as a point-spread function
of a general imaging system with an introduced phase diversity of a special
type. This model allows one not only to use any phase retrieval algorithm to
reconstruct the wavefront but also to analyse the limitations of the
phase-retrieval-based methods. We demonstrate the validity of this approach
both on the simulated and experimental data.


  We examine consequences of non-trivial topology in background spacetimes and
super-spacetimes: It is shown how the semi-invariance of a brane Lagrangian
under supertranslations gives rise to topological extensions of the Noether
charge algebra carried by D-branes. We investigate how isometry groups of
lightlike compactified spacetimes admit an extension to a semigroup. It is
shown how the splitting of classical multiplets caused by
multiply-connectedness of a phase space can be described in the framework of
Symplectic Geometry, based on the concept of symplectic covering spaces and
local moment maps.


  This paper considers the mean-reverting portfolio design problem arising from
statistical arbitrage in the financial markets. The problem is formulated by
optimizing a criterion characterizing the mean-reversion strength of the
portfolio and taking into consideration the variance of the portfolio and an
investment budget constraint at the same time. An efficient algorithm based on
the majorization-minimization (MM) method is proposed to solve the problem.
Numerical results show that our proposed mean-reverting portfolio design method
can significantly outperform every underlying single spread and the benchmark
method in the literature.


  We propose Diverse Restormer (DART), a novel image restoration method that
effectively integrates information from various sources (long sequences, local
and global regions, feature dimensions, and positional dimensions) to address
restoration challenges. While Transformer models have demonstrated excellent
performance in image restoration due to their self-attention mechanism, they
face limitations in complex scenarios. Leveraging recent advancements in
Transformers and various attention mechanisms, our method utilizes customized
attention mechanisms to enhance overall performance. DART, our novel network
architecture, employs windowed attention to mimic the selective focusing
mechanism of human eyes. By dynamically adjusting receptive fields, it
optimally captures the fundamental features crucial for image resolution
reconstruction. Efficiency and performance balance are achieved through the
LongIR attention mechanism for long sequence image restoration. Integration of
attention mechanisms across feature and positional dimensions further enhances
the recovery of fine details. Evaluation across five restoration tasks
consistently positions DART at the forefront. Upon acceptance, we commit to
providing publicly accessible code and models to ensure reproducibility and
facilitate further research.


  In order to reconcile the wave-function collapse in quantum mechanics with
the finiteness of signals' propagation in general relativity, we delve into a
stochastic version of the Ricci flow and study its non-relativistic limit in
presence of matter. We hence derive the Di\'osi-Penrose collapse model for the
wave-function of a quantum gas. The procedure entails additional parameters
with respect to phenomenological models hitherto accounted for, including the
temperature of the gas and the cosmological constant, in turn related to the
stochastic gravitational noise responsible for the collapse.


  A routing algorithm is the most fundamental problem in complex network
communication. In complex networks, the amount of computation increases as the
number of nodes increases which reduces routing performance. In this paper, we
propose a routing algorithm for software-defined networking (SDN) based on a
box-covering (BC) algorithm. It is known that using the BC algorithm it is
possible to increase performance in complex SDN. We partition the entire SDN
network into subnets using three existing box-covering methods such as MEMB,
GC, and CIEA, then we use Dijkstra\textquotesingle s algorithm to find the
shortest path between subnets and within each subnet. We compared all
box-covering algorithms and found that the GC algorithm has the highest
performance for SDN routing.


  The quantum relative entropy is a measure of the distinguishability of two
quantum states, and it is a unifying concept in quantum information theory:
many information measures such as entropy, conditional entropy, mutual
information, and entanglement measures can be realized from it. As such, there
has been broad interest in generalizing the notion to further understand its
most basic properties, one of which is the data processing inequality. The
quantum f-divergence of Petz is one generalization of the quantum relative
entropy, and it also leads to other relative entropies, such as the Petz-Renyi
relative entropies. In this paper, I introduce the optimized quantum
f-divergence as a related generalization of quantum relative entropy. I prove
that it satisfies the data processing inequality, and the method of proof
relies upon the operator Jensen inequality, similar to Petz's original
approach. Interestingly, the sandwiched Renyi relative entropies are particular
examples of the optimized f-divergence. Thus, one benefit of this paper is that
there is now a single, unified approach for establishing the data processing
inequality for both the Petz-Renyi and sandwiched Renyi relative entropies, for
the full range of parameters for which it is known to hold. This paper
discusses other aspects of the optimized f-divergence, such as the classical
case, the classical-quantum case, and how to construct optimized f-information
measures.


  While label fusion from multiple noisy annotations is a well understood
concept in data wrangling (tackled for example by the Dawid-Skene (DS) model),
we consider the extended problem of carrying out learning when the labels
themselves are not consistently annotated with the same schema. We show that
even if annotators use disparate, albeit related, label-sets, we can still draw
inferences for the underlying full label-set. We propose the Inter-Schema
AdapteR (ISAR) to translate the fully-specified label-set to the one used by
each annotator, enabling learning under such heterogeneous schemas, without the
need to re-annotate the data. We apply our method to a mouse behavioural
dataset, achieving significant gains (compared with DS) in out-of-sample
log-likelihood (-3.40 to -2.39) and F1-score (0.785 to 0.864).


  We re-analyze all archival Chandra/ACIS observations of the Orion Nebula
Cluster (ONC) to study the X-ray properties of a large sample of
pre--main-sequence (PMS) stars with optically determined rotation periods. Our
goal is to elucidate the origins of X-rays in PMS stars by seeking out
connections between the X-rays and the mechanisms most likely driving their
production--rotation and accretion. In our sample X-ray luminosity is
significantly correlated with stellar rotation, in the sense of decreasing
Lx/Lbol with more rapid rotation, suggesting that these stars are in the
"super-saturated" regime of the rotation-activity relationship. However, we
also find that stars with optical rotation periods are significantly biased to
high Lx. This is not the result of magnitude bias in the optical
rotation-period sample but rather to the diminishingly small amplitude of
optical variations in stars with low Lx. Evidently, there exists in the ONC a
population of stars whose rotation periods are unknown and that possess lower
average X-ray luminosities than those of stars with known rotation periods.
These stars may sample the linear regime of the rotation-activity relationship.
Accretion also manifests itself in X-rays, though in a somewhat
counterintuitive fashion: While stars with spectroscopic signatures of
accretion show harder X-ray spectra than non-accretors, they show lower X-ray
luminosities and no enhancement of X-ray variability. We interpret these
findings in terms of a common origin for the X-ray emission observed from both
accreting and non-accreting stars, with the X-rays from accreting stars simply
being attenuated by magnetospheric accretion columns. This suggests that X-rays
from PMS stars have their origins primarily in chromospheres, not accretion.


  Gradient jet tomography in high-energy heavy-ion collisions utilizes the
asymmetric transverse momentum broadening of a propagating parton in an
inhomogeneous medium. Such broadening is studied within a path integral
description of the evolution of the Wigner distribution for a propagating
parton in medium. Going beyond the eikonal approximation of multiple
scattering, the evolution operator in the transverse direction can be expressed
as the functional integration over all classical trajectories of a massive
particle with the light-cone momentum $\omega$ as its mass. With a dipole
approximation of the Wilson line correlation function, evolution with the
light-cone time $t$ is determined by the jet transport coefficient $\hat q$
that can vary with space and time. In a uniform medium with a constant $\hat
q_0$, the analytical solution to the Wigner distribution becomes a typical
drifted Gaussian in both transverse momentum and coordinate with the diffusion
width $\sqrt{\hat q_0t}$ and $\sqrt{\hat q_0t^3/3\omega^2}$, respectively. In
the case of a simple Gaussian-like transverse inhomogeneity with a spatial
width $\sigma$ on top of a uniform medium, the final asymmetrical momentum
distribution can be calculated semi-analytically. The transverse asymmetry
defined for jet gradient tomography that characterizes the asymmetrical
distribution is found to linearly correlate with the initial transverse
position of the propagating parton within the domain of the inhomogeneity. It
decreases with the parton energy $\omega$, increases with the propagation time
initially and saturates when the diffusion distance is much larger than the
size of the inhomogeneity or $t^3\gg 3\omega^2\sigma^2/\hat q_0$. The
transverse momentum broadening due to the inhomogeneity also saturates at late
time in contrast to the continued increase with time if the drifted diffusion
in space is ignored.


  MoonBEAM is a SmallSat concept placed in cislunar orbit developed to study
the progenitors and multimessenger/multiwavelength signals of transient
relativistic jets and outflows and determine the conditions that lead to the
launching of a transient relativistic jet. The advantage of MoonBEAM is the
instantaneous all-sky coverage due to its orbit, which maximizes the
gamma-raytransient observations and provides upperlimits for non-detections.
Earth blockage and detector downtime from the high particle activity in the
South Atlantic Anomaly region prevent gamma-ray observatories in low Earth
orbit from surveying the entire sky at a given time. In addition, the long
baseline provided from a cislunar orbit allows MoonBEAM to constrain the
localization annulus when combined with a gamma-ray instrument in low Earth
orbit utilizing the timing triangulation technique. We present the scientific
performance of MoonBEAM including the expected effective area, localization
ability and duty cycle. MoonBEAM provides many advantages to the gamma-ray and
gravitational-wave follow up community by reducing the search region needed to
identify the afterglow and kilanova emission. In addition, the all-sky coverage
will provide insight into the conditions that lead to a successful relativistic
jet, instead of a shock breakout event, or a completely failed jet in the case
of core collapse supernovae.


  We present COVID-Q, a set of 1,690 questions about COVID-19 from 13 sources,
which we annotate into 15 question categories and 207 question clusters. The
most common questions in our dataset asked about transmission, prevention, and
societal effects of COVID, and we found that many questions that appeared in
multiple sources were not answered by any FAQ websites of reputable
organizations such as the CDC and FDA. We post our dataset publicly at
https://github.com/JerryWeiAI/COVID-Q. For classifying questions into 15
categories, a BERT baseline scored 58.1% accuracy when trained on 20 examples
per category, and for a question clustering task, a BERT + triplet loss
baseline achieved 49.5% accuracy. We hope COVID-Q can help either for direct
use in developing applied systems or as a domain-specific resource for model
evaluation.


  We consider the long time limit theorems for the solutions of a discrete wave
equation with a weak stochastic forcing. The multiplicative noise conserves the
energy and the momentum. We obtain a time-inhomogeneous Ornstein-Uhlenbeck
equation for the limit wave function that holds both for square integrable and
statistically homogeneous initial data. The limit is understood in the
point-wise sense in the former case, and in the weak sense in the latter. On
the other hand, the weak limit for square integrable initial data is
deterministic.


  Tree decompositions of graphs are of fundamental importance in structural and
algorithmic graph theory. Planar decompositions generalise tree decompositions
by allowing an arbitrary planar graph to index the decomposition. We prove that
every graph that excludes a fixed graph as a minor has a planar decomposition
with bounded width and a linear number of bags.
  The crossing number of a graph is the minimum number of crossings in a
drawing of the graph in the plane. We prove that planar decompositions are
intimately related to the crossing number. In particular, a graph with bounded
degree has linear crossing number if and only if it has a planar decomposition
with bounded width and a linear number of bags. It follows from the above
result about planar decompositions that every graph with bounded degree and an
excluded minor has linear crossing number.
  Analogous results are proved for the convex and rectilinear crossing numbers.
In particular, every graph with bounded degree and bounded tree-width has
linear convex crossing number, and every $K_{3,3}$-minor-free graph with
bounded degree has linear rectilinear crossing number.


  Many practical machine learning tasks can be framed as Structured prediction
problems, where several output variables are predicted and considered
interdependent. Recent theoretical advances in structured prediction have
focused on obtaining fast rates convergence guarantees, especially in the
Implicit Loss Embedding (ILE) framework. PAC-Bayes has gained interest recently
for its capacity of producing tight risk bounds for predictor distributions.
This work proposes a novel PAC-Bayes perspective on the ILE Structured
prediction framework. We present two generalization bounds, on the risk and
excess risk, which yield insights into the behavior of ILE predictors. Two
learning algorithms are derived from these bounds. The algorithms are
implemented and their behavior analyzed, with source code available at
\url{https://github.com/theophilec/PAC-Bayes-ILE-Structured-Prediction}.


  E-commerce companies deal with a high volume of customer service requests
daily. While a simple annotation system is often used to summarize the topics
of customer contacts, thoroughly exploring each specific issue can be
challenging. This presents a critical concern, especially during an emerging
outbreak where companies must quickly identify and address specific issues. To
tackle this challenge, we propose a novel machine learning algorithm that
leverages natural language techniques and topological data analysis to monitor
emerging and trending customer issues. Our approach involves an end-to-end deep
learning framework that simultaneously tags the primary question sentence of
each customer's transcript and generates sentence embedding vectors. We then
whiten the embedding vectors and use them to construct an undirected graph.
From there, we define trending and emerging issues based on the topological
properties of each transcript. We have validated our results through various
methods and found that they are highly consistent with news sources.


  Nanostructuring on length scales corresponding to phonon mean free paths
provides control over heat flow in semiconductors and makes it possible to
engineer their thermal properties. However, the influence of boundaries limits
the validity of bulk models, while first principles calculations are too
computationally expensive to model real devices. Here we use extreme
ultraviolet beams to study phonon transport dynamics in a 3D nanostructured
silicon metalattice with deep nanoscale feature size, and observe dramatically
reduced thermal conductivity relative to bulk. To explain this behavior, we
develop a predictive theory wherein thermal conduction separates into a
geometric permeability component and an intrinsic viscous contribution, arising
from a new and universal effect of nanoscale confinement on phonon flow. Using
experiments and atomistic simulations, we show that our theory applies to a
general set of highly-confined silicon nanosystems, from metalattices,
nanomeshes, porous nanowires to nanowire networks, of great interest for
next-generation energy-efficient devices.


  Rate theory of the radiation-induced precipitation in solids is modified with
account of non-equilibrium fluctuations driven by the gas of lattice solitons
(a.k.a. quodons) produced by irradiation. According to quantitative
estimations, a steady-state density of the quodon gas under sufficiently
intense irradiation can be as high as the density of phonon gas. The quodon gas
may be a powerful driver of the chemical reaction rates under irradiation, the
strength of which exponentially increases with irradiation flux and may be
comparable with strength of the phonon gas that exponentially increases with
temperature. The modified rate theory is applied to modelling of copper
precipitation in FeCu binary alloys under electron irradiation. In contrast to
the classical rate theory, which disagrees strongly with experimental data on
all precipitation parameters, the modified rate theory describes quite well
both the evolution of precipitates and the matrix concentration of copper
measured by different methods