  Testing 3D hydrodynamic models of stellar atmospheres is feasible by
retrieving spectral line shapes across stellar disks, using differential
spectroscopy during exoplanet transits. From synthetic data at hyper-high
spectral resolution, characteristic patterns for FeI and FeII lines were
identified in Paper IV from 3D models spanning T=3964-6726K (spectral types
approx. K8V-F3V). The observability of patterns among lines of different
strength, excitation potential and ionization level are now examined, as
observed at ordinary spectral resolutions and in the presence of noise. Time
variability in 3D atmospheres induces changes in spectral-line parameters, some
of which are correlated. An adequate calibration could identify proxies for the
jitter in apparent radial velocity to enable adjustments to actual stellar
radial motion. We also examined the center-to-limb temporal variability.
Recovery of spatially resolved line profiles with fitted widths and depths is
shown for various noise levels. Signals during exoplanet transit are simulated.
In addition to Rossiter-McLaughlin type signatures in apparent radial velocity,
analogous effects are shown for line depths and widths. From exoplanet
transits, overall stellar line parameters of width, depth and wavelength
position can be retrieved already with moderate efforts, but a very good
signal-to-noise ratio is required to reveal the more subtle signatures between
subgroups of spectral lines, where finer details of atmospheric structure are
encoded. In a solar model, temporal variability shows correlations between
jittering in apparent radial velocity and fluctuations in line depth. Since
both fluctuations in line depth and jittering in wavelength can be measured
from the ground, searches for low-mass exoplanets should explore these to
adjust apparent radial velocities to actual stellar motion.


  This volume presents an overview of selected aspects of physical processes
occurring in the inner regions of Active Galactic Nuclei (AGN). The
observational evidence suggests that strong gravitational fields play a
significant role in governing the energy output of AGN and their influence on
the surrounding medium, possibly due to the presence of a supermassive black
hole. In order to reduce an unnecessary overlap with numerous reviews on the
subject of AGN, here we focus on several selected topics.


  We consider the energy spectrum of cosmic-rays (CRs) from a purely
phenomenological point of view and investigate the possibility that they all be
produced by the same type of sources with a single power-law spectrum, in
E^{-x}, from thermal to ultra-high energies. We show that the relative fluxes
of the Galactic (GCR) and extra-galactic (EGCR) components are compatible with
such a holistic model, provided that the index of the source spectrum be x
\simeq 2.23\pm 0.07. This is compatible with the best-fit indices for both GCRs
and EGCRs, assuming that their source composition is the same, which is indeed
the case in a holistic model. It is also compatible with theoretical
expectations for particle acceleration at relativistic shocks.


  It may appear that the recently found resonance at 125 GeV is not the only
Higgs boson. We point out the possibility that the Higgs bosons appear in
models of top-quark condensation, where the masses of the bosonic excitations
are related to the top quark mass by the sum rule similar to the Nambu sum rule
of the NJL models \cite{Nambu}. This rule was originally considered by Nambu
for superfluid $^3$He-B and for the BCS model of superconductivity. It relates
the two masses of bosonic excitations existing in each channel of Cooper
pairing to the fermion mass. An example of the Nambu partners is provided by
the amplitude and the phase modes in the BCS model describing Cooper pairing in
the s-wave channel. This sum rule suggests the existence of the Nambu partners
for the 125 GeV Higgs boson. Their masses can be predicted by the Nambu sum
rule under certain circumstances. For example, if there are only two states in
the given channel, the mass of the Nambu partner is $\sim$ 325 GeV. They
together satisfy the Nambu sum rule $M_1^2 + M_2^2 = 4 M_t^2$, where $M_t \sim
$174 GeV is the mass of the top quark. If there are two doubly degenerated
states, then the second mass is $\sim$ 210 GeV. In this case the Nambu sum rule
is $2 M_1^2 + 2 M_2^2 = 4 M_t^2$. In addition, the properties of the Higgs
modes in superfluid $^3$He-A, where the symmetry breaking is similar to that of
the Standard Model of particle physics, suggest the existence of two
electrically charged Higgs particles with masses around 245 GeV, which together
also obey the Nambu sum rule $M_+^2 + M_-^2 = 4 M_t^2$.


  Before taking actions in an environment with more than one intelligent agent,
an autonomous agent may benefit from reasoning about the other agents and
utilizing a notion of a guarantee or confidence about the behavior of the
system. In this article, we propose a novel multi-agent reinforcement learning
(MARL) algorithm CAMMARL, which involves modeling the actions of other agents
in different situations in the form of confident sets, i.e., sets containing
their true actions with a high probability. We then use these estimates to
inform an agent's decision-making. For estimating such sets, we use the concept
of conformal predictions, by means of which, we not only obtain an estimate of
the most probable outcome but get to quantify the operable uncertainty as well.
For instance, we can predict a set that provably covers the true predictions
with high probabilities (e.g., 95%). Through several experiments in two fully
cooperative multi-agent tasks, we show that CAMMARL elevates the capabilities
of an autonomous agent in MARL by modeling conformal prediction sets over the
behavior of other agents in the environment and utilizing such estimates to
enhance its policy learning.


  Many candidate models for dark energy are based on the existence of a
classical scalar field. In the context of Quantum Field Theory (QFT), we
briefly discus the condensation of such a field from a light quantum scalar
field produced by gradual decay of a heavy particle during cosmological time.
We obtain the necessary conditions for survival of the condensate in an
expanding universe and show that this process is directly related to quantum
nature of the field which preserves the coherence of the condensate at
cosmological distances. We also suggest a new interpretation of {\it vacuum
energy} in QFT in curved space time which can potentially solve the puzzle of
huge deviation of what is considered to be the vacuum energy from observations
of dark energy.


  The recent progress in formation of two-dimensional (2D) GaN by a
migration-enhanced encapsulated technique opens up new possibilities for group
III-V 2D semiconductors with a band gap within the visible energy spectrum.
Using first-principles calculations we explored alloying of 2D-GaN to achieve
an optically active material with a tuneable band gap. The effect of
isoelectronic III-V substitutional elements on the band gaps, band offsets, and
spatial electron localization is studied. In addition to optoelectronic
properties, the formability of alloys is evaluated using impurity formation
energies. A dilute highly-mismatched solid solution 2D-GaN$_{1-x}$P$_x$
features an efficient band gap reduction in combination with a moderate energy
penalty associated with incorporation of phosphorous in 2D-GaN, which is
substantially lower than in the case of the bulk GaN. The group-V alloying
elements also introduce significant disorder and localization at the valence
band edge that facilitates direct band gap optical transitions thus implying
the feasibility of using III-V alloys of 2D-GaN in light-emitting devices.


  The classification of the X-ray sources into classes (such as extragalactic
sources, background stars, ...) is an essential task in astronomy. Typically,
one of the classes corresponds to extragalactic radiation, whose photon
emission behaviour is well characterized by a homogeneous Poisson process. We
propose to use normalized versions of the Wasserstein and Zolotarev distances
to quantify the deviation of the distribution of photon interarrival times from
the exponential class. Our main motivation is the analysis of a massive dataset
from X-ray astronomy obtained by the Chandra Orion Ultradeep Project (COUP).
This project yielded a large catalog of 1616 X-ray cosmic sources in the Orion
Nebula region, with their series of photon arrival times and associated
energies. We consider the plug-in estimators of these metrics, determine their
asymptotic distributions, and illustrate their finite-sample performance with a
Monte Carlo study. We estimate these metrics for each COUP source from three
different classes. We conclude that our proposal provides a striking amount of
information on the nature of the photon emitting sources. Further, these
variables have the ability to identify X-ray sources wrongly catalogued before.
As an appealing conclusion, we show that some sources, previously classified as
extragalactic emissions, have a much higher probability of being young stars in
Orion Nebula.


  We investigate a potential of the higher multipole power spectra of the
galaxy distribution in redshift space as a cosmological probe on halo scales.
Based on the fact that a halo model explains well the multipole power spectra
of the luminous red galaxy (LRG) sample in the Sloan Digital Sky Survey (SDSS),
we focus our investigation on the random motions of the satellite LRGs that
determine the higher multipole spectra at large wavenumbers. We show that our
theoretical model fits the higher multipole spectra at large wave numbers from
N-body numerical simulations and we apply these results for testing the gravity
theory and the velocity structure of galaxies on the halo scales. In this
analysis, we use the multipole spectra P_4(k) and P_6(k) on the small scales of
the range of wavenumber 0.3<k/[h{Mpc}^{-1}]<0.6, which is in contrast to the
usual method of testing gravity by targeting the linear growth rate on very
large scales. We demonstrate that our method could be useful for testing
gravity on the halo scales.


  In this paper we introduce invariants of semi-free Hamiltonian actions of
$S\sp 1$ on compact symplectic manifolds (which satisfy some technical
conditions related to positivity) using the space of solutions to certain gauge
theoretical equations. These equations generalize at the same time the vortex
equations and the holomorphicity equation used in Gromov-Witten theory. In the
definition of the invariants we combine ideas coming from gauge theory and the
ideas underlying the construction of Gromov-Witten invariants. This paper is
based on a part of my PhD Thesis (see math/9912150).


  This paper proposes an adaptive neural network-based backstepping controller
that uses rigid graph theory to address the distance-based formation control
problem and target tracking for nonlinear multi-agent systems with bounded
time-delay and disturbance. The radial basis function neural network (RBFNN) is
used to overcome and compensate for the unknown nonlinearity and disturbance in
the system dynamics. The effect of the state time-delay of the agents is
alleviated by using an appropriate control signal that is designed based on
specific Lyapunov function and Young's inequality. The adaptive neural network
(NN) weights tuning law is derived using this Lyapunov function. An upper bound
for the singular value of the normalized rigidity matrix is introduced, and
uniform ultimate boundedness (UUB) of the formation distance error is
rigorously proven based on the Lyapunov stability theory. Finally, the
performance and effectiveness of the proposed method are validated through the
simulation results on nonlinear multi-agent systems. Comparisons between the
proposed distance-based method and an existing, displacement-based method are
provided to evaluate the performance of the suggested method.


  From a handlebody-theoretic perspective, the simplest compact, contractible
4-manifolds, other than the 4-ball, are Mazur manifolds. We produce the first
pairs of Mazur manifolds that are homeomorphic but not diffeomorphic. Our
diffeomorphism obstruction comes from our proof that the knot Floer homology
concordance invariant $\nu$ is an invariant of the smooth 4-manifold associated
to a knot in the 3-sphere by attaching an n-framed 2-handle to the 4-ball along
the knot. In contrast, we also show (modulo forthcoming work of Ozsv\'ath and
Szab\'o) that the concordance invariants $\tau$ and $\epsilon$ are not
invariants of such 4-manifolds. As a corollary to the existence of exotic Mazur
manifolds, we produce integer homology 3-spheres admitting two distinct $S^1
\times S^2$ surgeries, resolving a question from Problem 1.16 in Kirby's list.


  Many of the mathematical frameworks describing natural selection are
equivalent to Bayes Theorem, also known as Bayesian updating. By definition, a
process of Bayesian Inference is one which involves a Bayesian update, so we
may conclude that these frameworks describe natural selection as a process of
Bayesian inference. Thus natural selection serves as a counter example to a
widely-held interpretation that restricts Bayesian Inference to human mental
processes (including the endeavors of statisticians). As Bayesian inference can
always be cast in terms of (variational) free energy minimization, natural
selection can be viewed as comprising two components: a generative model of an
"experiment" in the external world environment, and the results of that
"experiment" or the "surprise" entailed by predicted and actual outcomes of the
"experiment". Minimization of free energy implies that the implicit measure of
"surprise" experienced serves to update the generative model in a Bayesian
manner. This description closely accords with the mechanisms of generalized
Darwinian process proposed both by Dawkins, in terms of replicators and
vehicles, and Campbell, in terms of inferential systems. Bayesian inference is
an algorithm for the accumulation of evidence-based knowledge. This algorithm
is now seen to operate over a wide range of evolutionary processes, including
natural selection, the evolution of mental models and cultural evolutionary
processes, notably including science itself. The variational principle of free
energy minimization may thus serve as a unifying mathematical framework for
universal Darwinism, the study of evolutionary processes operating throughout
nature.


  We study inclusive semi-leptonic (B -> X_c \ell \nu) decay using the power
counting m_c ~ \sqrt{Lambda_{QCD} m_b}. Assuming this scaling for the
charm-quark mass, the decay kinematics can be chosen to access the
shape-function region even in b -> c transitions. To apply effective field
theory methods in this region we extend SCET to describe massive collinear
quarks. We calculate the tree-level decay rate, including O(Lambda_{QCD}/m_b)
power corrections, and show that it factorizes into a convolution of jet and
shape functions. We identify a certain kinematical variable whose decay
spectrum is proportional to the universal leading-order shape function familiar
from b -> u decay, and speculate as to whether information about this shape
function can be extracted from data on b -> c decay.


  We construct an effective action describing brane-antibrane system containing
N D-branes and N \bar{D}-branes. BPS equations for remaining D-branes after
tachyon condensation are derived and their properties are investigated. The
value of the D-brane tension and the number of brane bound states are
discussed.


  Disc truncations are the closest feature to an edge that galaxies have, but
the nature of this phenomena is not yet understood. In this paper, we explore
the truncations in two nearby (D ~15 Mpc) Milky Way-like galaxies: NGC 4565 and
NGC 5907. We cover a wide wavelength range from the NUV and optical, to 3.6
{\mu}m. We find that the radius of the truncation (26+/-0.5 kpc) is independent
of wavelength. Surprisingly, we identify (at all wavelengths) the truncation at
altitudes as high as 3 kpc above the mid-plane, which implies that the thin
disc in those outer regions has a width of at least this value. We find the
characteristic U-shape radial colour profile associated with a star formation
threshold at the location of the truncation. Further supporting such an origin,
the stellar mass density at the position of the truncation is ~1-2 M_sun pc^-2,
in good agreement with the critical gas density for transforming gas into
stars. Beyond the truncation, the stellar mass in the mid-plane of the disc
drops to just 0.1-0.2% of the total stellar mass of the galaxies. The detection
of the truncation at high altitude in combination with the U shape of the
radial colour profile allows us to establish, for the first time, an upper
limit to the present-day growth rate of galactic discs. We find that, if the
discs of the galaxies are growing inside-out, their growth rate is less than
0.6-0.9 kpc Gyr^-1.


  The conditional variance, skewness, and kurtosis play a central role in time
series analysis. These three conditional moments (CMs) are often studied by
some parametric models but with two big issues: the risk of model
mis-specification and the instability of model estimation. To avoid the above
two issues, this paper proposes a novel method to estimate these three CMs by
the so-called quantiled CMs (QCMs). The QCM method first adopts the idea of
Cornish-Fisher expansion to construct a linear regression model, based on $n$
different estimated conditional quantiles. Next, it computes the QCMs simply
and simultaneously by using the ordinary least squares estimator of this
regression model, without any prior estimation of the conditional mean. Under
certain conditions, the QCMs are shown to be consistent with the convergence
rate $n^{-1/2}$. Simulation studies indicate that the QCMs perform well under
different scenarios of Cornish-Fisher expansion errors and quantile estimation
errors. In the application, the study of QCMs for three exchange rates
demonstrates the effectiveness of financial rescue plans during the COVID-19
pandemic outbreak, and suggests that the existing ``news impact curve''
functions for the conditional skewness and kurtosis may not be suitable.


  We analyse the local discontinuous Galerkin (LDG) method for two-dimensional
singularly perturbed reaction-diffusion problems. A class of layer-adapted
meshes, including Shishkin- and Bakhvalov-type meshes, is discussed within a
general framework. Local projections and their approximation properties on
anisotropic meshes are used to derive error estimates for energy and "balanced"
norms. Here, the energy norm is naturally derived from the bilinear form of LDG
formulation and the "balanced" norm is artifically introduced to capture the
boundary layer contribution. We establish a uniform convergence of order $k$
for the LDG method using the balanced norm with the local weighted $L^2$
projection as well as an optimal convergence of order $k+1$ for the energy norm
using the local Gauss-Radau projections. Numerical experiments are presented.


  Given a lattice $\mathbb{L}$ and a class $K$ of algebraic structures, we say
that $\mathbb{L}$ \emph{forces nilpotency} in $K$ if every algebra $\mathbf{A}
\in K$ whose congruence lattice $\mathrm{Con} (\mathbf{A})$ is isomorphic to
$\mathbb{L}$ is nilpotent. We describe congruence lattices that force
nilpotency, supernilpotency or solvability for some classes of algebras. For
this purpose, we investigate which commutator operations can exist on a given
congruence lattice.


  We study tidal dissipation in hot Jupiter host stars due to the nonlinear
damping of tidally driven $g$-modes, extending the calculations of Essick &
Weinberg (2016) to a wide variety of non-solar type hosts. This process causes
the planet's orbit to decay and has potentially important consequences for the
evolution and fate of hot Jupiters. Previous studies either only accounted for
linear dissipation processes or assumed that the resonantly excited primary
mode becomes strongly nonlinear and breaks as it approaches the stellar center.
However, the great majority of hot Jupiter systems are in the weakly nonlinear
regime in which the primary mode does not break but instead excites a sea of
secondary modes via three-mode interactions. We simulate these nonlinear
interactions and calculate the net mode dissipation for stars that range in
mass from $0.5 M_\odot \le M_\star \le 2.0 M_\odot$ and in age from the early
main sequence to the subgiant phase. For stars with $M_\star \lesssim 1.0
M_\odot$ of nearly any age, we find that the orbital decay time is $\lesssim
100 \textrm{ Myr}$ for orbital periods $P_{\rm orb} \lesssim 1 \textrm{ day}$.
For $M_\star \gtrsim 1.2 M_\odot$, the orbital decay time only becomes short on
the subgiant branch, where it can be $\lesssim 10 \textrm{ Myr}$ for $P_{\rm
orb} \lesssim 2 \textrm{ days}$ and result in significant transit time shifts.
We discuss these results in the context of known hot Jupiter systems and
examine the prospects for detecting their orbital decay with transit timing
measurements.


  We examine the structure of the underlying event in neutral Higgs production
at the Superconducting-Supercollider (SSC). Gaps, regions of rapidity
containing no soft particle production, can provide a clean signature for $W$
boson fusion to the heavy Higgs. We first examine the physical basis of gap
production and estimate the survival probability of gaps in the minijet model.
Then, using PYTHIA, and HERWIG we compare gap events to $W$ pair production
from top decay and $q\bar{q}$ fusion. We find that, if experimental problems
can be overcome, gaps should provide a small, but clean, signal for heavy Higgs
production at the SSC.


  The techniques of low-rank matrix recovery were adapted for Quantum State
Tomography (QST) previously by D. Gross et al. [Phys. Rev. Lett. 105, 150401
(2010)], where they consider the tomography of $n$ spin-$1/2$ systems. For the
density matrix of dimension $d = 2^n$ and rank $r$ with $r \ll 2^n$, it was
shown that randomly chosen Pauli measurements of the order $O(dr \log(d)^2)$
are enough to fully reconstruct the density matrix by running a specific convex
optimization algorithm. The result utilized the low operator-norm of the Pauli
operator basis, which makes it `incoherent' to low-rank matrices. For quantum
systems of dimension $d$ not a power of two, Pauli measurements are not
available, and one may consider using SU($d$) measurements. Here, we point out
that the SU($d$) operators, owing to their high operator norm, do not provide a
significant savings in the number of measurement settings required for
successful recovery of all rank-$r$ states. We propose an alternative strategy,
in which the quantum information is swapped into the subspace of a power-two
system using only $\textrm{poly}(\log(d)^2)$ gates at most, with QST being
implemented subsequently by performing $O(dr \log(d)^2)$ Pauli measurements. We
show that, despite the increased dimensionality, this method is more efficient
than the one using SU($d$) measurements.


  In recent years, multi-view subspace clustering has achieved impressive
performance due to the exploitation of complementary imformation across
multiple views. However, multi-view data can be very complicated and are not
easy to cluster in real-world applications. Most existing methods operate on
raw data and may not obtain the optimal solution. In this work, we propose a
novel multi-view clustering method named smoothed multi-view subspace
clustering (SMVSC) by employing a novel technique, i.e., graph filtering, to
obtain a smooth representation for each view, in which similar data points have
similar feature values. Specifically, it retains the graph geometric features
through applying a low-pass filter. Consequently, it produces a
``clustering-friendly" representation and greatly facilitates the downstream
clustering task. Extensive experiments on benchmark datasets validate the
superiority of our approach. Analysis shows that graph filtering increases the
separability of classes.


  The electronic structure of BaTi2As2O, a parent compound of the newly
discovered titanium-based oxypnictide superconductors, is studied by
angle-resolved photoemission spectroscopy. The electronic structure shows
multi-orbital nature and possible three-dimensional character. An anomalous
temperature-dependent spectral weight redistribution and broad lineshape
indicate the incoherent nature of the spectral function. At the
density-wave-like transition temperature around 200 K, a partial gap opens at
the Fermi patches. These findings suggest that BaTi2As2O is likely a charge
density wave material in the strong interaction regime.


  In many practical applications of learning algorithms, unlabeled data is
cheap and abundant whereas labeled data is expensive. Active learning
algorithms developed to achieve better performance with lower cost. Usually
Representativeness and Informativeness are used in active learning algoirthms.
Advanced recent active learning methods consider both of these criteria.
Despite its vast literature, very few active learning methods consider noisy
instances, i.e. label noisy and outlier instances. Also, these methods didn't
consider accuracy in computing representativeness and informativeness. Based on
the idea that inaccuracy in these measures and not taking noisy instances into
consideration are two sides of a coin and are inherently related, a new loss
function is proposed. This new loss function helps to decrease the effect of
noisy instances while at the same time, reduces bias. We defined "instance
complexity" as a new notion of complexity for instances of a learning problem.
It is proved that noisy instances in the data if any, are the ones with maximum
instance complexity. Based on this loss function which has two functions for
classifying ordinary and noisy instances, a new classifier, named
"Simple-Complex Classifier" is proposed. In this classifier there are a simple
and a complex function, with the complex function responsible for selecting
noisy instances. The resulting optimization problem for both learning and
active learning is highly non-convex and very challenging. In order to solve
it, a convex relaxation is proposed.


  It is shown that the Einstein-Podolsky-Rosen conclusion concerning the
`incompleteness' of Quantum Mechanics does not follow from the results of their
proposed gedanken experiment, but is rather stated as a premise. If it were
possible to perform the experiment it would, in fact, show that Quantum
  Mechanics is `complete' for the observables discussed.
  Because, however, of the non square-integrable nature of the wave function,
the proposed experiment gives vanishing probabilities for measurements
performed in finite intervals of configuration or momentum space. Hence no
conclusion as to the `completeness', or otherwise, of Quantum Mechanics can be
drawn from the experiment.


  We generalize Richardson-Lucy (RL) deblurring to 4-D light fields by
replacing the convolution steps with light field rendering of motion blur. The
method deals correctly with blur caused by 6-degree-of-freedom camera motion in
complex 3-D scenes, without performing depth estimation. We introduce a novel
regularization term that maintains parallax information in the light field
while reducing noise and ringing. We demonstrate the method operating
effectively on rendered scenes and scenes captured using an off-the-shelf light
field camera. An industrial robot arm provides repeatable and known
trajectories, allowing us to establish quantitative performance in complex 3-D
scenes. Qualitative and quantitative results confirm the effectiveness of the
method, including commonly occurring cases for which previously published
methods fail. We include mathematical proof that the algorithm converges to the
maximum-likelihood estimate of the unblurred scene under Poisson noise. We
expect extension to blind methods to be possible following the generalization
of 2-D Richardson-Lucy to blind deconvolution.


  Fractional nonlinear differential equations present an interplay between two
common and important effective descriptions used to simplify high dimensional
or more complicated theories: nonlinearity and fractional derivatives. These
effective descriptions thus appear commonly in physical and mathematical
modeling. We present a new series method providing systematic controlled
accuracy for solutions of fractional nonlinear differential equations. The
method relies on spatially iterative use of power series expansions. Our
approach permits an arbitrarily large radius of convergence and thus solves the
typical divergence problem endemic to power series approaches. We apply our
method to the fractional nonlinear Schr\"odinger equation and its imaginary
time rotation, the fractional nonlinear diffusion equation. For the fractional
nonlinear Schr\"odinger equation we find fractional generalizations of cnoidal
waves of Jacobi elliptic functions as well as a fractional bright soliton. For
the fractional nonlinear diffusion equation we find the combination of
fractional and nonlinear effects results in a more strongly localized solution
which nevertheless still exhibits power law tails, albeit at a much lower
density.


  We study semiparametric time series models with innovations following a
log-concave distribution. We propose a general maximum likelihood framework
which allows us to estimate simultaneously the parameters of the model and the
density of the innovations. This framework can be easily adapted to many
well-known models, including ARMA, GARCH and ARMA-GARCH. Furthermore, we show
that the estimator under our new framework is consistent in both ARMA and
ARMA-GARCH settings. We demonstrate its finite sample performance via a
thorough simulation study and apply it to model the daily log-return of FTSE
100 index and the rabbit population.


  We present a deep Graph Convolutional Kernel Machine (GCKM) for
semi-supervised node classification in graphs. The method is built of two main
types of blocks: (i) We introduce unsupervised kernel machine layers
propagating the node features in a one-hop neighborhood, using implicit node
feature mappings. (ii) We specify a semi-supervised classification kernel
machine through the lens of the Fenchel-Young inequality. We derive an
effective initialization scheme and efficient end-to-end training algorithm in
the dual variables for the full architecture. The main idea underlying GCKM is
that, because of the unsupervised core, the final model can achieve higher
performance in semi-supervised node classification when few labels are
available for training. Experimental results demonstrate the effectiveness of
the proposed framework.


  We study a tendency to orientational symmetry breaking of the square lattice
t-J model by applying the exact diagonalization technique. We introduce a small
external anisotropy to t and J, and calculate the induced anisotropy of
hole-hole correlations as a response. It is found that the response is strongly
enhanced for particular band parameters, meaning that the system has a strong
tendency to orientational symmetry breaking. The analysis of the momentum
distribution function indicates that the correlation develops when the Fermi
surface is close to (pi,0) and (0,pi). Some properties of high-Tc cuprates
previously attributed to stripes can also be understood from orientational
symmetry breaking alone.


  Recently, linear codes constructed by defining sets have attracted a lot of
study, and many optimal linear codes with a few weights have been produced. The
objective of this paper is to present a class of binary linear codes with three
weights.


  Motivated by Exel's inverse semigroup approach to combinatorial C*-algebras,
in a previous work the authors defined an inverse semigroup associated with a
labelled space. We construct a representation of the C*-algebra of a labelled
space, inspired by how one might cut or glue labelled paths together, that
proves that non-zero elements in the inverse semigroup correspond to non-zero
elements in the C*-algebra. We also show that the spectrum of its diagonal
C*-subalgebra is homeomorphic to the tight spectrum of the inverse semigroup
associated with the labelled space.


  Using the relativistic coupled-cluster method, we have calculated ionization
potentials, E1 matrix elements and dipole polarizabilities of many low-lying
states of Ca$^+$. Contributions from the Breit interaction are given explicitly
for these properties. Polarizabilities of the ground and the first excited
d-states are determined by evaluating the wave functions that are perturbed to
first order by the electric dipole operator and the black-body radiation shifts
are estimated from these results. We also report the results of branching
ratios and lifetimes of the first excited p-states using both the calculated
and experimental wavelengths and compare them with their measured values.


  MXenes are a family two-dimensional transition metal carbide and nitride
materials, which often exhibit very good metallic conductivity and are thus of
great interest for applications in, e.g., flexible electronics,
electrocatalysis, and electromagnetic interference shielding. However,
surprisingly little is known about the fermiology of MXenes, i.e, the shape and
size of their Fermi-surfaces, and its effect on the material properties. One
reason for this may be that MXene surfaces are almost always covered by a
mixture of functional groups, and studying Fermi-surfaces of disordered systems
is cumbersome. Here, we study fermiology of four common Ti-based MXenes as a
function of the surface functional group composition. We first calculate the
effective band structures of systems with explicit mixed surfaces and observe
gradual evolution in the filling of the Ti-d band and resulting shift of
Fermi-level. We then demonstrate that these band structures can be closely
approximated by using pseudohydrogenated surfaces, and also compare favorably
to the experimental angle-resolved photoemission spectroscopy results. By
modifying the pseudohydrogen charge we then proceed to plot Fermi-surfaces for
all systems and extract their properties, such as the Fermi-surface area and
average Fermi-velocity. These are in turn used to evaluate the electrical
conductivity with the relaxation time fitted to experimentally measured
conductivities.


  We propose a novel efficient and robust Wavelet-based Edge Multiscale Finite
Element Method (WEMsFEM) motivated by \cite{MR3980476,GL18} to solve the
singularly perturbed convection-diffusion equations. The main idea is to first
establish a local splitting of the solution over a local region by a local
bubble part and local Harmonic extension part, and then derive a global
splitting by means of Partition of Unity. This facilitates a representation of
the solution as a summation of a global bubble part and a global Harmonic
extension part, where the first part can be computed locally in parallel. To
approximate the second part, we construct an edge multiscale ansatz space
locally with hierarchical bases as the local boundary data that has a
guaranteed approximation rate \noteLg{both inside and outside of the layers}.
The key innovation of this proposed WEMsFEM lies in a provable convergence rate
with little restriction on the mesh size. Its convergence rate with respect to
the computational degree of freedom is rigorously analyzed, which is verified
by extensive 2-d and 3-d numerical tests.


  We prove that the spaces $\ell_p$, $1<p<\infty, p\ne 2$, and all
infinite-dimensional subspaces of their quotient spaces do not admit equivalent
almost transitive renormings. This is a step towards the solution of the
Banach-Mazur rotation problem, which asks whether a separable Banach space with
a transitive norm has to be isometric or isomorphic to a Hilbert space. We
obtain this as a consequence of a new property of almost transitive spaces with
a Schauder basis, namely we prove that in such spaces the unit vector basis of
$\ell_2^2$ belongs to the two-dimensional asymptotic structure and we obtain
some information about the asymptotic structure in higher dimensions.
  Further, we prove that the spaces $\ell_p$, $1<p<\infty$, $p\ne 2$, have
continuum different renormings with 1-unconditional bases each with a different
maximal isometry group, and that every symmetric space other than $\ell_2$ has
at least a countable number of such renormings. On the other hand we show that
the spaces $\ell_p$, $1<p<\infty$, $p\ne 2$, have continuum different
renormings each with an isometry group which is not contained in any maximal
bounded subgroup of the group of isomorphisms of $\ell_p$.


  We investigate adiabatic quantum pumping of chiral Majorana states in a
system composed of two Mach--Zehnder type interferometers coupled via a quantum
point contact. The pumped current is generated by periodic modulation of the
phases accumulated by traveling around each interferometer. Using scattering
matrix formalism we show that the pumped current reveals a definite signature
of the chiral nature of the Majorana states involved in transport in this
geometry. Furthermore, by tuning the coupling between the two interferometers
the pump can operate in a regime where finite pumped current and zero
two-terminal conductance is expected.


  In the present paper, we give the definition and properties of the multipoled
global Zhou weights. Some approximation and convergence results of multipoled
global Zhou weights are given. We also establish a semi-continuity result for
the Zhou numbers.


  Geometry of circumstellar (CS) medium around supernovae (SNe) provides
important diagnostics to understand the nature of their progenitors. In this
paper, properties of CS dust around SN 2012dn, a super-Chandrasekhar candidate
Type Ia supernova (SC-SN), have been studied through detailed three dimensional
radiation transfer simulations. With the detected near-infrared excess from SN
2012dn, we show that it has a disk-like dusty CS environment whose mass is
roughly consistent with a branch of an accreting white dwarf system (the single
degenerate scenario). We show that a similar system should produce polarization
signals up to $\sim 8$ \% in the $B$ band, depending on the viewing direction
if polarimetric observation is performed. We predict that the maximum
polarization is reached around $\sim 60$ days after the $B$-band maximum. We
show that the temporal and wavelength dependence of the polarization signals,
together with other unique features, can be easily distinguished from the
interstellar polarization and intrinsic SN polarization. Indeed, the small
polarization degree observed for normal Type Ia SNe (SNe Ia) can constrain a
parameter space in the CS dust mass and distribution. We thus encourage
multi-band polarimetric observations for SNe Ia, especially for outliers
including SC-SNe for which some arguments for the single degenerate scenario
exist but the polarization data are very rare so far.


  This work is motivated by the interest in determining the effect of the
micro-anatomy of the spinal subarachnoid space on the cerebrospinal fluid flow
and on the associated transport of solutes. To that aim, we focus on a
canonical model problem in which a circular post of radius $a$, confined
between two parallel plates separated by a distance $2h$, is subjected to an
oscillatory flow. In particular, we are concerned with the steady, viscous,
time-averaged flow that persists in the vicinity on the cylinder, when the
stroke length of the oscillating flow, $U_{\infty}/\omega$ is smaller or
comparable to the radius of the post, $a$, where $U_{\infty}$ and $\omega$ are
the mean velocity amplitude and the corresponding angular frequency,
respectively. First, we analyze the asymptotic limit of small values of the
stroke length varying the aspect ratio of the post $\lambda$ and the Womersley
number $M$. First-order steady-streaming corrections at leading order have been
computed, together with associated Stokes-drift component, the sum of both
yielding the mean Lagrangian velocity field. The confinement effect is seen to
induce the three-dimensionality of flow. Moreover, in the mid plane the
time-averaged steady flow exhibits a recirculating vortex attached to the wall
of the post that decreases as $M$ increases for low values of $M$. However, for
values of $M$ larger than a critical one, $M_{cr}(\lambda)$, a second, outer
vortex is also formed. The dependence $M_{cr}(\lambda)$ has been quantified.
The analysis has been corroborated experimentally for a fixed aspect ratio.
Consideration of an anharmonic oscillating flow shows the fort-and-aft symmetry
of the steady flow is broken. Finally, the analysis is experimentally extended
to consider an array of equally spaced posts.


  The ``evolving constants'' method of defining the quantum dynamics of
time-reparametrization-invariant theories is investigated for a particular
implementation of parametrized non-relativistic quantum mechanics (PNRQM). The
wide range of time functions that are available to define evolving constants
raises issues of interpretation, consistency, and the degree to which the
resulting quantum theory coincides with, or generalizes, the usual
non-relativistic theory. The allowed time functions must be restricted for the
predictions of PNRQM to coincide with those of usual quantum theory. They must
be restricted to have a notion of quantum evolution in a time-parameter
connected to spacetime geometry. They must be restricted to prevent the theory
from making inconsistent predictions for the probabilities of histories.
Suitable restrictions can be introduced in PNRQM but these seem unlikely to
apply to a reparametrization invariant theory like general relativity.


  The noiseless amplification or attenuation are two heralded filtering
operations that enable respectively to increase or decrease the mean field of
any quantum state of light with no added noise, at the cost of a small success
probability. We show that inserting such noiseless operations in a transmission
line improves the performance of continuous-variable quantum key distribution
over this line. Remarkably, these noiseless operations do not need to be
physically implemented but can simply be simulated in the data post-processing
stage. Hence, virtual noiseless amplification or attenuation amounts to perform
a Gaussian post-selection, which enhances the secure range or tolerable excess
noise while keeping the benefits of Gaussian security proofs.


  Medical images and radiology reports are crucial for diagnosing medical
conditions, highlighting the importance of quantitative analysis for clinical
decision-making. However, the diversity and cross-source heterogeneity of these
data challenge the generalizability of current data-mining methods. Multimodal
large language models (MLLMs) have recently transformed many domains,
significantly affecting the medical field. Notably, Gemini-Vision-series
(Gemini) and GPT-4-series (GPT-4) models have epitomized a paradigm shift in
Artificial General Intelligence (AGI) for computer vision, showcasing their
potential in the biomedical domain. In this study, we evaluated the performance
of the Gemini, GPT-4, and 4 popular large models for an exhaustive evaluation
across 14 medical imaging datasets, including 5 medical imaging categories
(dermatology, radiology, dentistry, ophthalmology, and endoscopy), and 3
radiology report datasets. The investigated tasks encompass disease
classification, lesion segmentation, anatomical localization, disease
diagnosis, report generation, and lesion detection. Our experimental results
demonstrated that Gemini-series models excelled in report generation and lesion
detection but faces challenges in disease classification and anatomical
localization. Conversely, GPT-series models exhibited proficiency in lesion
segmentation and anatomical localization but encountered difficulties in
disease diagnosis and lesion detection. Additionally, both the Gemini series
and GPT series contain models that have demonstrated commendable generation
efficiency. While both models hold promise in reducing physician workload,
alleviating pressure on limited healthcare resources, and fostering
collaboration between clinical practitioners and artificial intelligence
technologies, substantial enhancements and comprehensive validations remain
imperative before clinical deployment.


  The terms multi-task learning and multitasking are easily confused.
Multi-task learning refers to a paradigm in machine learning in which a network
is trained on various related tasks to facilitate the acquisition of tasks. In
contrast, multitasking is used to indicate, especially in the cognitive science
literature, the ability to execute multiple tasks simultaneously. While
multi-task learning exploits the discovery of common structure between tasks in
the form of shared representations, multitasking is promoted by separating
representations between tasks to avoid processing interference. Here, we build
on previous work involving shallow networks and simple task settings suggesting
that there is a trade-off between multi-task learning and multitasking,
mediated by the use of shared versus separated representations. We show that
the same tension arises in deep networks and discuss a meta-learning algorithm
for an agent to manage this trade-off in an unfamiliar environment. We display
through different experiments that the agent is able to successfully optimize
its training strategy as a function of the environment.


  An epoch of Higgs relaxation may occur in the early universe during or
immediately following postinflationary reheating. It has recently been pointed
out that leptogenesis may occur in minimal extensions of the Standard Model
during this epoch. We analyse Higgs relaxation taking into account the effects
of perturbative and non-perturbative decays of the Higgs condensate, and we
present a detailed derivation of the relevant kinetic equations and of the
relevant particle interaction cross sections. We identify the parameter space
in which a sufficiently large asymmetry is generated.


  In this paper, we present an approach to ultrasonic beam-forming and
beam-steering in structures based on the concept of embedded non-resonant
acoustic metamaterial lenses. The lens design exploits the principle of
acoustic drop-channel which enables the dynamic coupling of multiple ultrasonic
waveguides at selected frequencies. In contrast with currently available
technology, the embedded lens allows generating directional excitation by means
of a single ultrasonic transducer. The lens design and performance are
numerically investigated by using Plane Wave Expansion and Finite Difference
Time Domain techniques applied to bulk structures. Then, the design is
experimentally validated on a thin aluminum plate where the lens is implemented
by through-holes. The dynamic response of the embedded lens is estimated by
reconstructing, via Laser Vibrometry, the velocity field induced by a
piezoelectric shaker source.


  In this work, to limit the number of required attention inference hops in
memory-augmented neural networks, we propose an online adaptive approach called
A2P-MANN. By exploiting a small neural network classifier, an adequate number
of attention inference hops for the input query is determined. The technique
results in elimination of a large number of unnecessary computations in
extracting the correct answer. In addition, to further lower computations in
A2P-MANN, we suggest pruning weights of the final FC (fully-connected) layers.
To this end, two pruning approaches, one with negligible accuracy loss and the
other with controllable loss on the final accuracy, are developed. The efficacy
of the technique is assessed by using the twenty question-answering (QA) tasks
of bAbI dataset. The analytical assessment reveals, on average, more than 42%
fewer computations compared to the baseline MANN at the cost of less than 1%
accuracy loss. In addition, when used along with the previously published
zero-skipping technique, a computation count reduction of up to 68% is
achieved. Finally, when the proposed approach (without zero-skipping) is
implemented on the CPU and GPU platforms, up to 43% runtime reduction is
achieved.


  Let $M$ be a compact surface and $P$ be a one dimensional manifold without
boundary, that is the line $\mathbb{R}^1$ or a circle $S^1$. The classification
of path-components of the space of Morse maps from $M$ into $P$ was recently
obtained by S. V. Matveev and V. V. Sharko for the case $P=\mathbb{R}$. For
$P=S^1$ the classification was obtained by the author. All this results can be
reformulated as one theorem: "Two Morse maps $f,g:M \to P$ belong to the same
path component of a space of Morse mappings from $M$ into $P$ if and only if
they are homotopic and have the same number of crutucal points in each index
and the same sets of positive and negative boundary circles". Here we give
another independent proof of this theorem based on Lickorish's theorem on
generators of homeotopy group of surface.


  Currently, agriculture in Africa contributes only a tenth to global Green
House Gas (GHG) emissions from agriculture. Despite its relatively low
contribution to GHG, a conundrum of "climate justice", adverse impacts of
climate change disproportionately threaten Africa's agriculture, the
Continent's main economic sector. Consequently, we seek to review the effects
of climate change on Agriculture.


  Measures of tail dependence between random variables aim to numerically
quantify the degree of association between their extreme realizations. Existing
tail dependence coefficients (TDCs) are based on an asymptotic analysis of
relevant conditional probabilities, and do not provide a complete framework in
which to compare extreme dependence between two random variables. In fact, for
many important classes of bivariate distributions, these coefficients take on
non-informative boundary values. We propose a new approach by first considering
global measures based on the surface area of the conditional cumulative
probability in copula space, normalized with respect to departures from
independence and scaled by the difference between the two boundary copulas of
co-monotonicity and counter-monotonicity. The measures could be approached by
cumulating probability on either the lower left or upper right domain of the
copula space, and offer the novel perspective of being able to differentiate
asymmetric dependence with respect to direction of conditioning. The resulting
TDCs produce a smoother and more refined taxonomy of tail dependence. The
empirical performance of the measures is examined in a simulated data context,
and illustrated through a case study examining tail dependence between stock
indices.


  The goal of quantum metrology is the precise estimation of parameters using
quantum properties such as entanglement. This estimation usually consists of
three steps: state preparation, time evolution during which information of the
parameters is encoded in the state, and readout of the state. Decoherence
during the time evolution typically degrades the performance of quantum
metrology and is considered to be one of the major obstacles to realizing
entanglement-enhanced sensing. We show, however, that under suitable
conditions, this decoherence can be exploited to improve the sensitivity.
Assume that we have two axes, and our aim is to estimate the relative angle
between them. Our results reveal that the use of Markvoian collective dephasing
to estimate the relative angle between the two directions affords
Heisenberg-limited sensitivity. Moreover, our scheme based on Markvoian
collective dephasing is robust against environmental noise, and it is possible
to achieve the Heisenberg limit even under the effect of independent dephasing.
Our counterintuitive results showing that the sensitivity is improved by using
the decoherence pave the way to novel applications in quantum metrology.


  In this paper we consider D=4 NCSYM theories with 8 supercharges. We study
these theories through a proper type IIA (and M-theory) brane configuration. We
find the one loop beta function of these theories and show that there is an
elliptic curve describing the moduli space of the theory, which is in principle
the same as the curve for the commutative counter-part of our theory. We study
some other details of the dynamics by means of this brane configuration.


  The Fisher matrix formalism has in recent times become the standard method
for predicting the precision with which various cosmological parameters can be
extracted from future data. This approach is fast, and generally returns
accurate estimates for the parameter errors when the individual parameter
likelihoods approximate a Gaussian distribution. However, where Gaussianity is
not respected (due, for instance, to strong parameter degeneracies), the Fisher
matrix formalism loses its reliability. In this paper, we compare the results
of the Fisher matrix approach with those from Monte Carlo simulations. The
latter method is based on the publicly available CosmoMC code, but uses
synthetic realisations of data sets anticipated for future experiments. We
focus on prospective cosmic microwave background (CMB) data from the Planck
satellite, with or without CMB lensing information, and its implications for a
minimal cosmological scenario with eight parameters and an extended model with
eleven parameters. We show that in many cases, the projected sensitivities from
the Fisher matrix and the Monte Carlo methods differ significantly,
particularly in models with many parameters. Sensitivities to the neutrino mass
and the dark matter fraction are especially susceptible to change.


  The purpose of this paper is to review some elasticity effects in epitaxial
growth. We start by a description of the main ingredients needed to describe
elasticity effects (elastic interactions, surface stress, bulk and surface
elasticity, thermodynamics of stressed solids). Then we describe how bulk and
surface elasticity affect growth mode and surface morphology by means of
stress-driven instability. At last stress-strain evolution during crystal
growth is reported.


  Movable antenna (MA) is an emerging technology which enables a local movement
of the antenna in the transmitter/receiver region for improving the channel
condition and communication performance. In this paper, we study the deployment
of multiple MAs at the base station (BS) for enhancing the multiuser
communication performance. First, we model the multiuser channel in the uplink
to characterize the wireless channel variation due to MAs' movements at the BS.
Then, an optimization problem is formulated to maximize the minimum achievable
rate among multiple users for MA-aided uplink multiuser communications by
jointly optimizing the MAs' positions, their receive combining at the BS, and
the transmit power of users, under the constraints of finite moving region for
MAs, minimum inter-MA distance, and maximum transmit power of each user. To
solve this challenging non-convex optimization problem, a two-loop iterative
algorithm is proposed by leveraging the particle swarm optimization (PSO)
method. Specifically, the outer-loop updates the positions of a set of
particles, where each particle's position represents one realization of the
antenna position vector (APV) of all MAs. The inner-loop implements the fitness
evaluation for each particle in terms of the max-min achievable rate of
multiple users with its corresponding APV, where the receive combining matrix
of the BS and the transmit power of each user are optimized by applying the
block coordinate descent (BCD) technique. Simulation results show that the
antenna position optimization for MAs-aided BSs can significantly improve the
rate performance as compared to conventional BSs with fixed-position antennas
(FPAs).


  In this paper, we present several algorithms for dealing with graded
components of Laurent polynomial rings. To be more precise, let $S$ be the
Laurent polynomial ring $k[x_1,...,x_{r},x_{r+1}^{\pm 1},..., x_n^{\pm 1}]$,
$k$ algebraicaly closed field of characteristic 0. We define the multigrading
of $S$ by an arbitrary finitely generated abelian group $A$. We construct a set
of fans compatible with the multigrading and use this fans to compute the
graded components of $S$ using polytopes. We give an algorithm to check whether
the graded components of $S$ are finite dimensional. Regardless of the
dimension, we determine a finite set of generators of each graded component as
a module over the component of homogeneous polynomials of degree 0.


  We propose a holographic version of a reconfigurable intelligent surface
(RIS) and investigate its application to terahertz (THz) massive multiple-input
multiple-output systems. Capitalizing on the miniaturization of THz electronic
components, RISs can be implemented by densely packing sub-wavelength unit
cells, so as to realize continuous or quasi-continuous apertures and to enable
holographic communications. In this paper, in particular, we derive the beam
pattern of a holographic RIS. Our analysis reveals that the beam pattern of an
ideal holographic RIS can be well approximated by that of an ultra-dense RIS,
which has a more practical hardware architecture. In addition, we propose a
closed-loop channel estimation (CE) scheme to effectively estimate the
broadband channels that characterize THz massive MIMO systems aided by
holographic RISs. The proposed CE scheme includes a downlink coarse CE stage
and an uplink finer-grained CE stage. The uplink pilot signals are judiciously
designed for obtaining good CE performance. Moreover, to reduce the pilot
overhead, we introduce a compressive sensing-based CE algorithm, which exploits
the dual sparsity of THz MIMO channels in both the angular domain and delay
domain. Simulation results demonstrate the superiority of holographic RISs over
the non-holographic ones, and the effectiveness of the proposed CE scheme.


  Existing unconditional generative models mainly focus on modeling general
objects, such as faces and indoor scenes. Fashion textures, another important
type of visual elements around us, have not been extensively studied. In this
work, we propose an effective generative model for fashion textures and also
comprehensively investigate the key components involved: internal
representation, latent space sampling and the generator architecture. We use
Gram matrix as a suitable internal representation for modeling realistic
fashion textures, and further design two dedicated modules for modulating Gram
matrix into a low-dimension vector. Since fashion textures are scale-dependent,
we propose a recursive auto-encoder to capture the dependency between multiple
granularity levels of texture feature. Another important observation is that
fashion textures are multi-modal. We fit and sample from a Gaussian mixture
model in the latent space to improve the diversity of the generated textures.
Extensive experiments demonstrate that our approach is capable of synthesizing
more realistic and diverse fashion textures over other state-of-the-art
methods.


  The report demonstrates the benefits (in terms of improved claims loss
modeling) of harnessing the value of Federated Learning (FL) to learn a single
model across multiple insurance industry datasets without requiring the
datasets themselves to be shared from one company to another. The application
of FL addresses two of the most pressing concerns: limited data volume and data
variety, which are caused by privacy concerns, the rarity of claim events, the
lack of informative rating factors, etc.. During each round of FL,
collaborators compute improvements on the model using their local private data,
and these insights are combined to update a global model. Such aggregation of
insights allows for an increase to the effectiveness in forecasting claims
losses compared to models individually trained at each collaborator.
Critically, this approach enables machine learning collaboration without the
need for raw data to leave the compute infrastructure of each respective data
owner. Additionally, the open-source framework, OpenFL, that is used in our
experiments is designed so that it can be run using confidential computing as
well as with additional algorithmic protections against leakage of information
via the shared model updates. In such a way, FL is implemented as a
privacy-enhancing collaborative learning technique that addresses the
challenges posed by the sensitivity and privacy of data in traditional machine
learning solutions. This paper's application of FL can also be expanded to
other areas including fraud detection, catastrophe modeling, etc., that have a
similar need to incorporate data privacy into machine learning collaborations.
Our framework and empirical results provide a foundation for future
collaborations among insurers, regulators, academic researchers, and InsurTech
experts.


  We describe a successful effort to produce a laser comb around 1.55 $\mu$m in
the astronomical H band using a method based on a line-referenced,
electro-optical-modulation frequency comb. We discuss the experimental setup,
laboratory results, and proof of concept demonstrations at the NASA Infrared
Telescope Facility (IRTF) and the Keck-II telescope. The laser comb has a
demonstrated stability of $<$ 200 kHz, corresponding to a Doppler precision of
~0.3 m/s. This technology, when coupled with a high spectral resolution
spectrograph, offers the promise of $<$1 m/s radial velocity precision suitable
for the detection of Earth-sized planets in the habitable zones of cool M-type
stars.


  We propose a new task to benchmark scene understanding of embodied agents:
Situated Question Answering in 3D Scenes (SQA3D). Given a scene context (e.g.,
3D scan), SQA3D requires the tested agent to first understand its situation
(position, orientation, etc.) in the 3D scene as described by text, then reason
about its surrounding environment and answer a question under that situation.
Based upon 650 scenes from ScanNet, we provide a dataset centered around 6.8k
unique situations, along with 20.4k descriptions and 33.4k diverse reasoning
questions for these situations. These questions examine a wide spectrum of
reasoning capabilities for an intelligent agent, ranging from spatial relation
comprehension to commonsense understanding, navigation, and multi-hop
reasoning. SQA3D imposes a significant challenge to current multi-modal
especially 3D reasoning models. We evaluate various state-of-the-art approaches
and find that the best one only achieves an overall score of 47.20%, while
amateur human participants can reach 90.06%. We believe SQA3D could facilitate
future embodied AI research with stronger situation understanding and reasoning
capability.


  We propose thin single-layer grating waveguide structures to be used as
high-reflectivity, but low thermal noise, alternative to conventional coatings
for gravitational wave detector test mass mirrors. Grating waveguide (GWG)
coatings can show a reflectivity of up to 100% with an overall thickness of
less than a wavelength. We theoretically investigate GWG coatings for 1064nm
based on tantala (Ta2O5) on a Silica substrate focussing on broad spectral
response and low thickness.


  Suppose X,Y are manifolds, f,g:X->Y are maps. The well-known Coincidence
Problem studies the coincidence set C={x:f(x)=g(x)}. The number m=dimX-dimY is
called the codimension of the problem. More general is the Preimage Problem.
For a map f:X->Z and a submanifold Y of Z, it studies the preimage set
C={x:f(x) in Y}, and the codimension is m=dimX+dimY-dimZ. In case of
codimension 0, the classical Nielsen number N(f,Y) is a lower estimate of the
number of points in C changing under homotopies of f, and for an arbitrary
codimension, of the number of components of C. We extend this theory to take
into account other topological characteristics of C. The goal is to find a
"lower estimate" of the bordism group Omega_{p}(C) of C. The answer is the
Nielsen group S_{p}(f,Y) defined as follows. In the classical definition the
Nielsen equivalence of points of C based on paths is replaced with an
equivalence of singular submanifolds of C based on bordisms. We let
S_{p}^{prime}(f,Y) be the quotient group of Omega_{p}(C) with respect to this
equivalence relation, then the Nielsen group of order p is the part of this
group preserved under homotopies of f. The Nielsen number N_{p}(f,Y) of order p
is the rank of this group (then N(f,Y)=N_{0}(f,Y)). These numbers are new
obstructions to removability of coincidences and preimages. Some examples and
computations are provided.


  Safety alignment of Large Language Models (LLMs) can be compromised with
manual jailbreak attacks and (automatic) adversarial attacks. Recent studies
suggest that defending against these attacks is possible: adversarial attacks
generate unlimited but unreadable gibberish prompts, detectable by
perplexity-based filters; manual jailbreak attacks craft readable prompts, but
their limited number due to the necessity of human creativity allows for easy
blocking. In this paper, we show that these solutions may be too optimistic. We
introduce AutoDAN, an interpretable, gradient-based adversarial attack that
merges the strengths of both attack types. Guided by the dual goals of
jailbreak and readability, AutoDAN optimizes and generates tokens one by one
from left to right, resulting in readable prompts that bypass perplexity
filters while maintaining high attack success rates. Notably, these prompts,
generated from scratch using gradients, are interpretable and diverse, with
emerging strategies commonly seen in manual jailbreak attacks. They also
generalize to unforeseen harmful behaviors and transfer to black-box LLMs
better than their unreadable counterparts when using limited training data or a
single proxy model. Furthermore, we show the versatility of AutoDAN by
automatically leaking system prompts using a customized objective. Our work
offers a new way to red-team LLMs and understand jailbreak mechanisms via
interpretability.


  We summarize the results of the New Gauge Boson Subgroup on the physics of
extended gauge sectors at future colliders as presented at the 1996 Snowmass
workshop. We discuss the direct and indirect search reaches for new gauge
bosons at both hadron and lepton colliders as well as the ability of such
machines to extract detailed information on the couplings of these particles to
the fermions and gauge bosons of the Standard Model. [To appear in the
Proceedings of the 1996 DPF/DPB Summer Study on New Directions for High Energy
Physics-Snowmass96, Snowmass, CO, 25 June-12 July, 1996.]


  Navigating the challenges of data-driven speech processing, one of the
primary hurdles is accessing reliable pathological speech data. While public
datasets appear to offer solutions, they come with inherent risks of potential
unintended exposure of patient health information via re-identification
attacks. Using a comprehensive real-world pathological speech corpus, with over
n=3,800 test subjects spanning various age groups and speech disorders, we
employed a deep-learning-driven automatic speaker verification (ASV) approach.
This resulted in a notable mean equal error rate (EER) of 0.89% with a standard
deviation of 0.06%, outstripping traditional benchmarks. Our comprehensive
assessments demonstrate that pathological speech overall faces heightened
privacy breach risks compared to healthy speech. Specifically, adults with
dysphonia are at heightened re-identification risks, whereas conditions like
dysarthria yield results comparable to those of healthy speakers. Crucially,
speech intelligibility does not influence the ASV system's performance metrics.
In pediatric cases, particularly those with cleft lip and palate, the recording
environment plays a decisive role in re-identification. Merging data across
pathological types led to a marked EER decrease, suggesting the potential
benefits of pathological diversity in ASV, accompanied by a logarithmic boost
in ASV effectiveness. In essence, this research sheds light on the dynamics
between pathological speech and speaker verification, emphasizing its crucial
role in safeguarding patient confidentiality in our increasingly digitized
healthcare era.


  Network models are widely used as structural summaries of biochemical
systems. Statistical estimation of networks is usually based on linear or
discrete models. However, the dynamics of these systems are generally
nonlinear, suggesting that suitable nonlinear formulations may offer gains with
respect to network inference and associated prediction problems. We present a
general framework for both network inference and dynamical prediction that is
rooted in nonlinear biochemical kinetics. This is done by considering a
dynamical system based on a chemical reaction graph and associated kinetics
parameters. Inference regarding both parameters and the reaction graph itself
is carried out within a fully Bayesian framework. Prediction of dynamical
behavior is achieved by averaging over both parameters and reaction graphs,
allowing prediction even when the underlying reactions themselves are unknown
or uncertain. Results, based on (i) data simulated from a mechanistic model of
mitogen-activated protein kinase signaling and (ii) phosphoproteomic data from
cancer cell lines, demonstrate that nonlinear formulations can yield gains in
network inference and permit dynamical prediction in the challenging setting
where the reaction graph is unknown.


  The elementary resolution of singularities algorithm of the author's earlier
paper (math.CA/0609217) is developed further, replacing the quasibump functions
in the blown up coordinates with the characteristic function of a rectangle
times a smooth function. Such functions are easier to deal with, and as
application the existence of asymptotic expansions for oscillatory integrals
and related objects is given an elementary proof. In addition, some more
detailed information about these expansions is given.


  We have retrieved high-resolution UV spectra of 69 hot stars from the HST
archive and determined the strengths of the interstellar Ni II absorption
features at 1317.217A. We then compared them to absorptions from either the
transitions at 1741.553A (covered in the spectra of 21 of the stars) or the one
at 1370.132A (seen for the remaining 48 stars). All spectra were recorded by
the either the E140M, E140H, or E230H gratings of STIS. By comparing the
strengths of the two lines in each spectrum and evaluating a weighted average
of all such comparisons, we have found that the f-value of the 1317A line is
1.34 +/-0.019 times the one at 1741A and 0.971 +/-0.014 times that of the one
at 1370A. We adopt as a comparison standard an experimentally determined
f-value for the 1741A line (known to 10% accuracy), so that f(1317A) = 0.0571
+/-0.006. It follows from this f-value and our measured line-strength ratios
that f(1370A) = 0.0588 +/-0.006. As an exercise to validate our methodology, we
compared the 1317A transition to another Ni II line at 1454.842A and arrived at
an f-value for the latter that is consistent with a previously measured
experimental value to within the expected error.


  In (Kabanets, Impagliazzo, 2004) it is shown how to decide the circuit
polynomial identity testing problem (CPIT) in deterministic subexponential
time, assuming hardness of some explicit multilinear polynomial family for
arithmetical circuits. In this paper, a special case of CPIT is considered,
namely low-degree non-singular matrix completion (NSMC). For this subclass of
problems it is shown how to obtain the same deterministic time bound, using a
weaker assumption in terms of determinantal complexity.
  Hardness-randomness tradeoffs will also be shown in the converse direction,
in an effort to make progress on Valiant's VP versus VNP problem. To separate
VP and VNP, it is known to be sufficient to prove that the determinantal
complexity of the m-by-m permanent is $m^{\omega(\log m)}$. In this paper it is
shown, for an appropriate notion of explicitness, that the existence of an
explicit multilinear polynomial family with determinantal complexity
m^{\omega(\log m)}$ is equivalent to the existence of an efficiently computable
generator $G_n$ for multilinear NSMC with seed length $O(n^{1/\sqrt{\log n}})$.
The latter is a combinatorial object that provides an efficient deterministic
black-box algorithm for NSMC. ``Multilinear NSMC'' indicates that $G_n$ only
has to work for matrices $M(x)$ of $poly(n)$ size in $n$ variables, for which
$det(M(x))$ is a multilinear polynomial.


  We analyze robustness of correlations of the $N$-qubit GHZ and Dicke states
against white noise admixture. For sufficiently large $N$, the Dicke states
(for any number of excitations) lead to more robust violation of local realism
than the GHZ states (e.g. for $N=9$ for the W state). We also identify states
that are the most resistant to white noise. Surprisingly, it turns out that
these states are partially product. As a by-product, we obtain a simple
three-setting Bell inequality which is violated by any pure entangled state.


  Given $[n]=\{1,2,\ldots,n\}$, a poset order $\preceq$ on $[n]$, a label map
$\pi : [n] \rightarrow \mathbb{N}$ defined by $\pi(i)=k_i$ with
$\sum_{i=1}^{n}\pi (i) = N$, and a weight function $w$ on $\mathbb{F}_{q}$, let
$\mathbb{F}_{q}^N$ be the vector space of $N$-tuples over the field
$\mathbb{F}_{q}$ equipped with $(P,w,\pi)$-metric where $ \mathbb{F}_q^N $ is
the direct sum of spaces $ \mathbb{F}_{q}^{k_1}, \mathbb{F}_{q}^{k_2}, \ldots,
\mathbb{F}_{q}^{k_n} $. In this paper, we determine the groups of linear
isometries of $(P,w,\pi)$-metric spaces in terms of a semi-direct product,
which turns out to be similar to the case of poset (block) metric spaces. In
particular, we re-obtain the group of linear isometries of the $(P,w)$-mertic
spaces and $(P,\pi)$-mertic spaces.


  We analyze the stochastic evolution and dephasing of a qubit within the
quantum jump (QJ) approach. It allows one to treat individual realizations of
inelastic processes, and in this way it provides solutions, for instance, to
problems in quantum thermodynamics and distributions in statistical mechanics.
As a solvable example, we study a qubit in the weak dissipation limit, and
demonstrate that dephasing and relaxation render the Jarzynski and Crooks
fluctuation relations (FRs) of non-equilibrium thermodynamics intact. On the
contrary, the standard two-measurement protocol, taking into account only the
fluctuations of the internal energy $U$, leads to deviations in FRs under the
same conditions. We relate the average $\langle e^{-\beta U} \rangle $ (where
$\beta$ is the inverse temperature) with the qubit's relaxation and dephasing
rates, and discuss this relationship for different mechanisms of decoherence.


  Future astrometric satellites, such as SIM (NASA's Space Interferometric
Mission) and GAIA (ESA's Global Astrometric Interferometer for Astrophysics),
hold the promise of mapping out the detailed phase space structure of the
Galactic halo by providing unprecedented annual proper motion and parallax of
$1-10\mu$as astrometric accuracy. Here we show that proper motions of hundred
or so giant branch stars in a tidal debris torn from a small satellite (a
$10^{5-7}L_\odot$ Galactic dwarf galaxy or globular cluster) in the halo is
sensitive to the current Galactic potential and its past evolution. We follow
the evolution of a cold (velocity dispersion of 10 km/s) stream on a nearby
(between 8-50 kpc) polar orbit in a variety of histories of the potential of
the Galaxy, and observe the bright ($V<18$mag) members of the debris tail with
GAIA accuracy. We simulate effects due to the growing or flipping of the
Galactic disk over the past 4 Gyrs or the perturbation from a massive accreted
lump such as the progenitor of the Magellanic Clouds. We study various factors
influencing our ability to identify streams, including contamination from field
stars, accuracy of radial velocity and distance data and evolution and
non-axial symmetry of the potential. Our simulations suggest that nearby, cold
streams could be detected with GAIA if these cousins of the Sagittarius stream
exist. Results of Johnston, Zhao, Spergel & Hernquist (1999) and Helmi, Zhao &
de Zeeuw (1999) for static Galactic potentials are likely to be largely
generalizable to moderately time-evolving potentials. SIM and GAIA measurements
of debris stars might be used to probe both Galactic structure and Galactic
history.


  Let $F$ be a free non-abelian group. We show that for any group word $w$ the
set $w[F]$ of all values of $w$ in $F$ is rational in $F$ if and only if $w[F]
= 1$ or $w[F] = F.$ We generalize this to a wide class of free products of
groups.


  Despite their deterministic nature, dynamical systems often exhibit seemingly
random behaviour. Consequently, a dynamical system is usually represented by a
probabilistic model of which the unknown parameters must be estimated using
statistical methods. When measuring the uncertainty of such parameter
estimation, the bootstrap stands out as a simple but powerful technique. In
this paper, we develop the bootstrap for dynamical systems and establish not
only its consistency but also its second-order efficiency via a novel
\textit{continuous} Edgeworth expansion for dynamical systems. This is the
first time such continuous Edgeworth expansions have been studied. Moreover, we
verify the theoretical results about the bootstrap using computer simulations.


  Due to the explosion in the size of the training datasets, distributed
learning has received growing interest in recent years. One of the major
bottlenecks is the large communication cost between the central server and the
local workers. While error feedback compression has been proven to be
successful in reducing communication costs with stochastic gradient descent
(SGD), there are much fewer attempts in building communication-efficient
adaptive gradient methods with provable guarantees, which are widely used in
training large-scale machine learning models. In this paper, we propose a new
communication-compressed AMSGrad for distributed nonconvex optimization
problem, which is provably efficient. Our proposed distributed learning
framework features an effective gradient compression strategy and a worker-side
model update design. We prove that the proposed communication-efficient
distributed adaptive gradient method converges to the first-order stationary
point with the same iteration complexity as uncompressed vanilla AMSGrad in the
stochastic nonconvex optimization setting. Experiments on various benchmarks
back up our theory.


  We present the analysis of the stationary equilibria and their stability in
case of an opinion formation process in presence of binary opposite opinions
evolving according to majority-like rules on social networks. The starting
point is a kinetic Boltzmann-type model derived from microscopic interactions
rules for the opinion exchange among individuals holding a certain degree of
connectivity. The key idea is to derive from the kinetic model an Allen-Cahn
type equation for the fraction of individuals holding one of the two opinions.
The latter can be studied by means of a linear stability analysis and by
exploiting integral operator analysis. While this is true for ternary
interactions, for binary interactions the derived equation of interest is a
linear scattering equation, that can be studied by means of General Relative
Entropy tools and integral operators.


  Efficient verification of pure quantum states in the adversarial scenario is
crucial to many applications in quantum information processing, such as blind
measurement-based quantum computation and quantum networks. However, little is
known about this topic so far. Here we establish a general framework for
verifying pure quantum states in the adversarial scenario and clarify the
resource cost. Moreover, we propose a simple and general recipe to constructing
efficient verification protocols for the adversarial scenario from protocols
for the nonadversarial scenario. With this recipe, arbitrary pure states can be
verified in the adversarial scenario with almost the same efficiency as in the
nonadversarial scenario. Many important quantum states can be verified in the
adversarial scenario using local projective measurements with unprecedented
high efficiencies.


  The structural, magnetic, magnetocaloric and Griffiths phase (GP) disorder of
non-stoichiometric perovskite manganites La_(0.8-x) Sr_(0.2-y) Mn_(1+x+y) O_3
are reported here. Determination of valence states and structural phases
evidenced that the smaller cations Mn2+ and Mn3+ will not occupy the A-site of
a perovskite under atmospheric synthesis conditions. The same analysis also
supports that the vacancy in the A-site of a perovskite induces a similar
vacancy in the B-site. The La3+ and Sr2+ cation substitutions in the A-site
with vacancy influences the magnetic phase transition temperature (TC)
inversely, which is explained in terms of the electronic bandwidth change. An
anomalous non-linear change of the GP has been observed in the Sr-substituted
compounds. The agglomeration of Mn3+-Mn4+ pairs (denoted as dimerons), into
small ferromagnetic clusters, has been identified as the reason for the
occurrence of the GP. A threshold limit of the dimeron formation explains the
observed non-linear behaviour of the GP formation. The Sr-substituted compounds
show a relatively large value of isothermal entropy change (maximum 3.27 J/kgK
at {\mu}_0 H=2T) owing to its sharp magnetic transition, while the broad change
of magnetization in the La-substituted compound enhances the relative cooling
power (maximum 98 J/kg at {\mu}_0 H=2T).


  We study inverse spectral problems for ordinary differential equations with
regular singularities on compact star-type graphs when differential equations
have different orders on diferent edges. As the main spectral characteristics
we introduce and study the so-called Weyl-type matrices which are
generalizations of the Weyl function for the classical Sturm-Liouville
operator. We provide a procedure for constructing the solution of the inverse
problem and prove its uniqueness.


  We investigate a special sequence of random variables $A(N)$ defined by an
exponential power series with independent standard complex Gaussians $(X(k))_{k
\geq 1}$. Introduced by Hughes, Keating, and O'Connell in the study of random
matrix theory, this sequence relates to Gaussian multiplicative chaos (in
particular "holomorphic multiplicative chaos'' per Najnudel, Paquette, and
Simm) and random multiplicative functions. Soundararajan and Zaman recently
determined the order of $\mathbb{E}[|A(N)|]$. By constructing an algorithm to
calculate $A(N)$ in $O(N^2 \log N)$ steps, we produce computational evidence
that their result can likely be strengthened to an asymptotic result with a
numerical estimate for the asymptotic constant. We also obtain similar
conclusions when $A(N)$ is defined using standard real Gaussians or uniform
$\pm 1$ random variables. However, our evidence suggests that the asymptotic
constants do not possess a natural product structure.


  In many medical and business applications, researchers are interested in
estimating individualized treatment effects using data from a randomized
experiment. For example in medical applications, doctors learn the treatment
effects from clinical trials and in technology companies, researchers learn
them from A/B testing experiments. Although dozens of machine learning models
have been proposed for this task, it is challenging to determine which model
will be best for the problem at hand because ground-truth treatment effects are
unobservable. In contrast to several recent papers proposing methods to select
one of these competing models, we propose an algorithm for aggregating the
estimates from a diverse library of models. We compare ensembling to model
selection on 43 benchmark datasets, and find that ensembling wins almost every
time. Theoretically, we prove that our ensemble model is (asymptotically) at
least as accurate as the best model under consideration, even if the number of
candidate models is allowed to grow with the sample size.


  We characterize the metallic structure on the product of two metallic
manifolds in terms of metallic maps and provide a necessary and sufficient
condition for the warped product of two locally metallic Riemannian manifolds
to be locally metallic. The particular case of product manifolds is discussed
and an example of metallic warped product Riemannian manifold is provided.


  Diffusing-Wave Spectroscopy (DWS) allows for the direct measurement of the
squared strain-rate tensor. When combined with commonly available high-speed
cameras, we show that DWS gives direct access to the spatio-temporal variations
of the viscous dissipation rate of a Newtonian fluid flow. The method is
demonstrated using a Taylor-Couette (TC) cell filled with a lipid emulsion or a
\ch{TiO2} suspension. We image the boundary dissipation rate in a quantitative
and time-resolved fashion by shining coherent light at the experimental cell
and measuring the local correlation time of the speckle pattern. The results
are validated by comparison with the theoretical prediction for an ideal TC
flow and with global measurements using a photomultiplier tube and a photon
correlator. We illustrate the method by characterizing the spatial organization
of the boundary dissipation rate past the Taylor-Couette instability threshold,
and its spatio-temporal dynamics in the wavy vortex flow that arises beyond a
secondary instability threshold. This study paves the way for direct imaging of
the dissipation rate in a large variety of flows, including turbulent ones.


  There is a resurgence of interest in the electronic structure of perylene for
its applications in molecular devices such as organic photovoltaics and organic
light emitting diodes. In this study, we have obtained the low-lying singlet
states of perylene by exactly solving the Parisar-Parr-Pople model Hamiltonian
of this system with 20 sites and 20 electrons, in the VB basis where
dimensionality is $\sim$ 5.92 billion. The triplet states of perylene are
obtained using a DMRG scheme with symmetry adaptation. The one and two photon
states are very close in energy $\sim$ 3.2 eV while the lowest triplet state is
slightly below 1.6 eV indicating that perylene is a good candidate for singlet
fission. To explore the tunability of the electronic states, we have studied
donor-acceptor substituted perylenes. The two donors and two acceptors are
substituted symmetrically either at the four bay sites or four peri sites. In
all the bay substitution and one peri substitution at moderate D/A strength,
the optical gap is lowered to about 2.8 eV. These molecules can be used as blue
emitters. We have also reported bond orders in all the cases and perylene as
well as substituted perylenes can be viewed as two weakly coupled naphthalene
in the singlet states but in triplets these bonds tend to be comparable to
other bonds in strength. The charge densities in substituted perylenes are
mostly localized around the substitution sites in the ground state. The
positive spin densities in triplets are concentrated around the peri and bay
sites with the remaining sites having small spin densities of either sign.


  We consider an example of a quantum algorithm from the point of view of the
de Broglie-Bohm formulation of quantum mechanics. For concreteness we look at
two particular implementations: one using spin-1/2 particles as described by a
simple model due to Bell and the other as energy states in an infinite-well
potential. We extend the analysis to encompass a complete set of quantum gates.
We conclude by discussing the relevance of our investigations for the debate
about the origin of the quantum-computational speed-up.


  Transport events in turbulent tokamak plasmas often exhibit non-local or
non-diffusive action at a distance features that so far have eluded a
conclusive theoretical description. In this paper a theory of non-local
transport is investigated through a Fokker-Planck equation with fractional
velocity derivatives. A dispersion relation for density gradient driven linear
drift modes is derived including the effects of the fractional velocity
derivative in the Fokker-Planck equation. It is found that a small deviation (a
few percent) from the Maxwellian distribution function alters the dispersion
relation such that the growth rates are substantially increased and thereby may
cause enhanced levels of transport.


  We reconsider the minimal SU(5) Grand Unified Theory (GUT) in the context of
no-scale supergravity, assuming that the soft supersymmetry-breaking parameters
satisfy universality conditions at some input scale M_in above the GUT scale
M_GUT. When setting up such a no-scale super-GUT model, special attention must
be paid to avoiding the Scylla of rapid proton decay and the Charybdis of an
excessive density of cold dark matter, while also having an acceptable mass for
the Higgs boson. We do not find consistent solutions if none of the matter and
Higgs fields are assigned to twisted chiral supermultiplets, even in the
presence of Giudice-Masiero terms. However, consistent solutions may be found
if at least one fiveplet of GUT Higgs fields is assigned to a twisted chiral
supermultiplet, with a suitable choice of modular weights. Spin-independent
dark matter scattering may be detectable in some of these consistent solutions.


  We consider a single outbreak susceptible-infected-recovered (SIR) model and
corresponding estimation procedures for the effective reproductive number
$\mathcal{R}(t)$. We discuss the estimation of the underlying SIR parameters
with a generalized least squares (GLS) estimation technique. We do this in the
context of appropriate statistical models for the measurement process. We use
asymptotic statistical theories to derive the mean and variance of the limiting
(Gaussian) sampling distribution and to perform post statistical analysis of
the inverse problems. We illustrate the ideas and pitfalls (e.g., large
condition numbers on the corresponding Fisher information matrix) with both
synthetic and influenza incidence data sets.


  We study the propagation of a linearly polarized laser beam in the external
transverse magnetic field taking into consideration the vacuum polarization by
arbitrary spin particles. Induced ellipticity of the beam are evaluated using
the effective Lagrangian. With the help of the PVLAS experimental data, we
obtain bounds on masses of charged higher spin particles contributed to
ellipticity.


  Studies of dynamics on temporal networks often represent the network as a
series of "snapshots," static networks active for short durations of time. We
argue that successive snapshots can be aggregated if doing so has little effect
on the overlying dynamics. We propose a method to compress network chronologies
by progressively combining pairs of snapshots whose matrix commutators have the
smallest dynamical effect. We apply this method to epidemic modeling on real
contact tracing data and find that it allows for significant compression while
remaining faithful to the epidemic dynamics.


  We have studied the chromospheric evaporation flow during the impulsive phase
of the flare by using the Hinode/EIS observation and 1D hydrodynamic numerical
simulation coupled to the time-dependent ionization. The observation clearly
shows that the strong redshift can be observed at the base of the flaring loop
only during the impulsive phase. We performed two different numerical
simulations to reproduce the strong downflows in FeXII and FeXV during the
impulsive phase. By changing the thermal conduction coefficient, we carried out
the numerical calculation of chromospheric evaporation in the thermal
conduction dominant regime (conductivity coefficient kappa0 = classical value)
and the enthalpy flux dominant regime (kappa0 = 0.1 x classical value). The
chromospheric evaporation calculation in the enthalpy flux dominant regime
could reproduce the strong redshift at the base of the flare during the
impulsive phase. This result might indicate that the thermal conduction can be
strongly suppressed in some cases of flare. We also find that time-dependent
ionization effect is importance to reproduce the strong downflows in Fe XII and
Fe XV.


  The RF stabilization of tearing modes with current condensation has the
potential to increase stabilization efficiency and loosen power localization
requirements. Such benefits stem from the cooperative feedback between the RF
deposition and resulting island temperature perturbation governed by diffusion.
A self consistent treatment of the damping of an rf ray as it traverses the
island shows that low damping scenarios can require unfavorably high powers to
overcome initial power leakage and effectively capitalize on the nonlinear
effect. In this work it is demonstrated that for such regimes,modulated
stabilization schemes can achieve significant improvements in heating and
current drive contributions to stabilization for the same average power as a
continuous wave scheme. The impact of modulation frequency and duty cycle on
the performance is explored, the results of which suggest modulation strategies
in which the pulsing periods are kept on the order of a diffusive time.


  In this paper, we show that coherence witness for a single qubit itself
yields conditions for nonlocality and entanglement inequalities for multiqubit
systems. It also yields a condition for quantum discord in two--qubit systems.
It is shown by employing homomorphism among the stabiliser group of a single
qubit and those of multi--qubit states. Interestingly, globally commuting
homomorphic images of single qubit stabilisers do not allow for consistent
assignments of outcomes of local observables. As an application, we show that
CHSH inequality can be straightforwardly generalised to nonlocality
inequalities for multiqubit GHZ states. It also reconfirms the fact that
quantumness prevails even in the large $N$--limit, if coherence is sustained.
The mapping provides a way to construct many nonlocality inequalities, given a
{\it seed} inequality. This study gives us a motivation to gain a better
control over multiple degrees of freedom and multi-party systems. It is because
in multi-party systems, the same nonclassical feature, {\it viz.}, coherence
may appear in many avatars.


  Semileptonic B decays into excited charmed mesons $D'_0$ and $D'_1$ are
studied in the framework of heavy quark effective field theory (HQEFT) up to
order $1/m_Q$. They are characterized by a single leading Isgur-Wise function
$\tau$ and several wave functions arising at $1/m_Q$ order. $\tau$ and the
$1/m_Q$ order functions $\chi^b_0$, $\chi^c_0$ related to the kinetic energy
operators are evaluated through QCD sum rule approach; zero recoil values of
the $1/m_Q$ order functions $\kappa_1$, $\kappa_2$, $\kappa'_1$ and $\kappa'_2$
are extracted from the meson masses; and the branching ratios are found to be
suppressed by the $1/m_Q$ corrections. It is concluded that the next leading
order wave functions can be significant. However it does not change the
previous prediction that the production rate of $j_l^P=3/2^+$ charmed mesons
dominates over that of $1/2^+$ doublets.


  We consider the heat transfer problem associated with a periodic array of
extended surfaces (fins) subjected to convection heat transfer with a uniform
heat transfer coefficient. Our analysis differs from the classical approach as
(i) we consider two-dimensional heat conduction and (ii) the base of the fin is
included in the heat transfer process. The problem is modeled as an arbitrary
two-dimensional channel whose upper surface is flat and isothermal, while the
lower surface has a periodic array of extensions/fins which are subjected to
heat convection with a uniform heat transfer coefficient. Using the generalized
Schwarz-Christoffel transformation the domain is mapped onto a straight channel
where the heat conduction problem is solved using the boundary element method.
The boundary element solution is subsequently used to pose a shape optimization
problem, i.e. an inverse problem, where the objective function is the
normalized Shape Factor and the variables of the optimization are the
parameters of the Schwarz-Christoffel transformation. Numerical optimization
suggests that the optimum fin is infinitely thin and that there exists a
critical Biot number that characterizes whether the addition of the fin would
result in an enhancement of heat transfer. The existence of a critical Biot
number was investigated for the case of rectangular fins. {\bf It is concluded
that a rectangular fin is effective if its thickness is less than} $1.64 k/h$,
where the $h$ is the heat transfer coefficient and $k$ is the thermal
conductivity. This result is independent of both the thickness of the base and
the length of the fin.


  Complex question answering over knowledge base (Complex KBQA) is challenging
because it requires various compositional reasoning capabilities, such as
multi-hop inference, attribute comparison, set operation. Existing benchmarks
have some shortcomings that limit the development of Complex KBQA: 1) they only
provide QA pairs without explicit reasoning processes; 2) questions are poor in
diversity or scale. To this end, we introduce KQA Pro, a dataset for Complex
KBQA including ~120K diverse natural language questions. We introduce a
compositional and interpretable programming language KoPL to represent the
reasoning process of complex questions. For each question, we provide the
corresponding KoPL program and SPARQL query, so that KQA Pro serves for both
KBQA and semantic parsing tasks. Experimental results show that SOTA KBQA
methods cannot achieve promising results on KQA Pro as on current datasets,
which suggests that KQA Pro is challenging and Complex KBQA requires further
research efforts. We also treat KQA Pro as a diagnostic dataset for testing
multiple reasoning skills, conduct a thorough evaluation of existing models and
discuss further directions for Complex KBQA. Our codes and datasets can be
obtained from https://github.com/shijx12/KQAPro_Baselines.