  We provide estimates of volcanism versus time for planets with Earth-like
composition and masses from 0.25 to 25 times Earth, as a step toward predicting
atmospheric mass on extrasolar rocky planets. Volcanism requires melting of the
silicate mantle. We use a thermal evolution model, calibrated against Earth, in
combination with standard melting models, to explore the dependence of
convection-driven decompression mantle melting on planet mass. Here we show
that (1) volcanism is likely to proceed on massive planets with plate tectonics
over the main-sequence lifetime of the parent star; (2) crustal thickness (and
melting rate normalized to planet mass) is weakly dependent on planet mass; (3)
stagnant lid planets live fast (they have higher rates of melting than their
plate tectonic counterparts early in their thermal evolution) but die young
(melting shuts down after a few Gyr); (4) plate tectonics may not operate on
high mass planets because of the production of buoyant crust which is difficult
to subduct; and (5) melting is necessary but insufficient for efficient
volcanic degassing - volatiles partition into the earliest, deepest melts,
which may be denser than the residue and sink to the base of the mantle on
young, massive planets. Magma must also crystallize at or near the surface, and
the pressure of overlying volatiles must be fairly low, if volatiles are to
reach the surface. If volcanism is detected in the Tau Ceti system, and tidal
forcing can be shown to be weak, this would be evidence for plate tectonics.


  In the framework of perturbative QCD approach, we calculate the branching
ratio and CP asymmetry for $B_{s}^0(\bar{B}_{s}) \to \pi^{\pm} K^\mp$ and
$B_{s}(\bar{B}_{s})\to \pi^{0}\bar{K}^{0}(K^{0})$ decays. Besides the usual
factorizable diagrams, both non-factorizable and annihilation type
contributions are taken into account. We find that (a) the branching ratio of
$B_{s}^0(\bar{B}_{s}) \to \pi^{\pm} K^\mp$ is about $(6-10) \times 10^{-6}$;
$Br(B_{s}(\bar{B}_{s})\to \pi^{0}\bar{K}^{0}(K^{0}))$ about $ (1-3) \times
10^{-7}$; and (b) there are large CP asymmetries in the two processes, which
can be tested in the near future LHC-b experiments at CERN and BTeV experiments
at Fermilab.


  In this paper our objective is to investigate the existence of multiple
normalized solutions to the logarithmic Schr\"{o}dinger equation given by
\begin{align*}
  \left\{ \begin{aligned} &-\epsilon^2 \Delta u+V( x)u=\lambda u+u \log u^2,
\quad \quad \hbox{in }\mathbb{R}^N,\\
&\int_{\mathbb{R}^{N}}|u|^{2}dx=a^{2}\epsilon^N, \end{aligned} \right.
\end{align*} where $a, \epsilon>0, \lambda \in \mathbb{R}$ is an unknown
parameter that appears as a Lagrange multiplier and $V: \mathbb{R}^N
\rightarrow[-1, \infty)$ is a continuous function. Our analysis demonstrates
that the number of normalized solutions of the equation is associated with the
topology of the set where the potential function $V$ attains its minimum value.
To prove the main result, we employ minimization techniques and use the
Lusternik-Schnirelmann category. Additionally, we introduce a new function
space where the energy functional associated with the problem is of class
$C^1$.


  The discovery of disease subtypes is an essential step for developing
precision medicine, and disease subtyping via omics data has become a popular
approach. While promising, subtypes obtained from existing approaches are not
necessarily associated with clinical outcomes. With the rich clinical data
along with the omics data in modern epidemiology cohorts, it is urgent to
develop an outcome-guided clustering algorithm to fully integrate the
phenotypic data with the high-dimensional omics data. Hence, we extended a
sparse K-means method to an outcome-guided sparse K-means (GuidedSparseKmeans)
method. An unified objective function was proposed, which was comprised of (i)
weighted K-means to perform sample clusterings; (ii) lasso regularizations to
perform gene selection from the high-dimensional omics data; (iii)
incorporation of a phenotypic variable from the clinical dataset to facilitate
biologically meaningful clustering results. By iteratively optimizing the
objective function, we will simultaneously obtain a phenotype-related sample
clustering results and gene selection results. We demonstrated the superior
performance of the GuidedSparseKmeans by comparing with existing clustering
methods in simulations and applications of high-dimensional transcriptomic data
of breast cancer and Alzheimer's disease. Our algorithm has been implemented
into an R package, which is publicly available on GitHub
(https://github.com/LingsongMeng/GuidedSparseKmeans).


  We present first-principles total-energy electronic-structure calculations
that provide the microscopic mechanism of the adatom interchange reaction on
the Sn- and Pb-covered Ge(111)-(2x8) and the Sb-covered Si(111)-(7x7) surfaces
with and without the tip of the atomic force microscope (AFM). We find that,
without the presence of the AFM tip on the Ge surface, the adatom interchange
occurs through the migration of the adatom, the spontaneous formation of the
dimer structures of the two adatoms, the dimer-dimer structural transitions
that induce the exchange of the positions of the two adatoms, and then the
backward migration of the adatom. We also find that the dimer structure is
unfeasible at room temperature on the Si surface and the adatom interchange are
hereby unlikely. With the presence of the tip, we find that the reaction
pathways are essentially the same for the Ge surface but that the energy
barriers of the migration and the exchange processes are substantially reduced
by the AFM tip. We further find that the AFM tip induces the spontaneous
formation of the dimer structure even on the Si surface, hereby opening a
channel of the interchange of the adatoms. Our calculations show that the bond
formation between the AFM tip atom and the surface adatom is essential for the
atom manipulation using the AFM tip.


  Experiments on $^4$He films reveal an attractive Casimir-like force at the
bulk $\lambda$-point, and in the superfluid regime. Previous work has explained
the magnitude of this force at the $\lambda$ transition and deep in the
superfluid region but not the substantial attractive force immediately below
the $\lambda$-point. Utilizing a simple mean-field calculation renormalized by
critical fluctuations we obtain an effective Casimir force that is
qualitatively consistent with the scaling function $\vartheta$ obtained by
collapse of experimental data.


  In this paper, we address the problem of finding the optimal trajectory for
an unmanned aerial vehicle (UAV) for improving the wireless coverage of a
terrestrial cellular network. In particular, we consider a UAV that is tasked
to travel from one point to another within a given time constraint, and it can
also simultaneously assist the cellular network by providing wireless coverage
during its mission. Considering an interference limited downlink of a cellular
network, we formulate an optimization problem for maximizing the
proportional-fair (PF) data rate of the cellular network and explore dynamic
programming (DP) technique for finding the optimum UAV trajectory. We also
explore the optimal UAV trajectories associated with maximum sum-rate and 5th
percentile spectral efficiency (5pSE) rate and compare the capacity and
coverage performance of the three approaches. Numerical simulations show that
the maximum sum-rate trajectory provides the best per user capacity whereas,
the optimal PF trajectory yields higher coverage probability than the other two
trajectories. The optimal trajectories are generally infeasible to follow
exactly as the UAVs can not take sharp turns due to kinematic constraints.
Hence, we generate smooth trajectories using Bezier curve.


  Let $\Omega$ be a smooth bounded domain in $\R^n$, $n\ge 5$. We consider the
semilinear heat equation at the critical Sobolev exponent $$ u_t = \Delta u +
u^{\frac{n+2}{n-2}} \inn \Omega\times (0,\infty), \quad u =0 \onn
\pp\Omega\times (0,\infty). $$
  Let $G(x,y)$ be the Dirichlet Green's function of $-\Delta$ in $\Omega$ and
$H(x,y)$ its regular part. Let $q_j\in \Omega$, $j=1,\ldots,k$, be points such
that the matrix $$
  \left [ \begin{matrix} H(q_1, q_1) & -G(q_1,q_2) &\cdots & -G(q_1, q_k)
-G(q_1,q_2) & H(q_2,q_2) & -G(q_2,q_3) \cdots & -G(q_3,q_k) \vdots & & \ddots&
\vdots -G(q_1,q_k) &\cdots& -G(q_{k-1}, q_k) & H(q_k,q_k) \end{matrix} \right ]
$$ is positive definite. For any $k\ge 1$ such points indeed exist. We prove
the existence of a positive smooth solution $u(x,t)$ which blows-up by bubbling
in infinite time near those points. More precisely, for large time $t$, $u$
takes the approximate form $$ u(x,t) \approx \sum_{j=1}^k \alpha_n \left (
\frac { \mu_j(t)} { \mu_j(t)^2 + |x-\xi_j(t)|^2 } \right )^{\frac {n-2}2} . $$
Here $\xi_j(t) \to q_j$ and $0<\mu_j(t) \to 0$, as $t \to \infty$. We find that
$\mu_j(t) \sim t^{-\frac 1{n-4}} $ as $t\to +\infty$, when $n\geq 5$.


  A successor-invariant first-order formula is a formula that has access to an
auxiliary successor relation on a structure's universe, but the model relation
is independent of the particular interpretation of this relation. It is well
known that successor-invariant formulas are more expressive on finite
structures than plain first-order formulas without a successor relation. This
naturally raises the question whether this increase in expressive power comes
at an extra cost to solve the model-checking problem, that is, the problem to
decide whether a given structure together with some (and hence every) successor
relation is a model of a given formula. It was shown earlier that adding
successor-invariance to first-order logic essentially comes at no extra cost
for the model-checking problem on classes of finite structures whose underlying
Gaifman graph is planar [Engelmann et al., 2012], excludes a fixed minor
[Eickmeyer et al., 2013] or a fixed topological minor [Eickmeyer and
Kawarabayashi, 2016; Kreutzer et al., 2016]. In this work we show that the
model-checking problem for successor-invariant formulas is fixed-parameter
tractable on any class of finite structures whose underlying Gaifman graphs
form a class of bounded expansion. Our result generalises all earlier results
and comes close to the best tractability results on nowhere dense classes of
graphs currently known for plain first-order logic.


  We explain new developments in classical knot theory in 3 and 4~dimensions,
i.e. we study knots in 3-space, up to isotopy as well as up to concordance. In
dimension~3 we give a geometric interpretation of the Kontsevich integral
(joint with Jim Conant), and in dimension 4 we introduce new concordance
invariants using von Neumann signatures (joint with Tim Cochran and Kent Orr).
The common geometric feature of our results is the notion of a grope cobordism.


  Optical emission line diagnostics, which are a common tool to constrain the
properties of the interstellar medium (ISM) of galaxies, become progressively
inaccessible at higher redshifts for ground-based facilities. Far-infrared
(FIR) emission lines, which are redshifted into atmospheric windows accessible
by ground-based sub-millimeter facilities, could provide alternative ISM
diagnostics to optical emission lines. We investigate FIR line ratios involving
[CII]$\lambda 158 \mu$m, [OIII]$\lambda 88 \mu$m, [OIII]$\lambda 52 \mu$m,
[NII]$\lambda 122 \mu$m and [NIII$\lambda 57 \mu$m, using synthetic emission
lines applied to a high-resolution (m$_{\rm gas}$= 883.4 M$_{\odot}$)
cosmological zoom-in simulation, including radiative-transfer post processing
with KramsesRT at z = 6.5. We find that the [CII]/[NII]122 ratio is sensitive
to the temperature and density of photo-dissociation regions, and thus could be
a useful tool to trace the properties of this gas phase in galaxies. We also
find that [NII]/[NIII] is a good tracer of the temperature and
[OIII]52/[OIII]88 a good tracer of the gas density of HII regions. Emission
line ratios containing the [OIII]$\lambda 88 \mu$m line are sensitive to high
velocity outflowing gas.


  We study multistage distributionally robust linear optimization, where the
uncertainty set is defined as a ball of distribution centered at a scenario
tree using the nested distance. The resulting minimax problem is notoriously
difficult to solve due to its inherent non-convexity. In this paper, we
demonstrate that, under mild conditions, the robust risk evaluation of a given
policy can be expressed in an equivalent recursive form. Furthermore, assuming
stagewise independence, we derive equivalent dynamic programming reformulations
to find an optimal robust policy that is time-consistent and well-defined on
unseen sample paths. Our reformulations reconcile two modeling frameworks: the
multistage-static formulation (with nested distance) and the multistage-dynamic
formulation (with one-period Wasserstein distance). Moreover, we identify
tractable cases when the value functions can be computed efficiently using
convex optimization techniques.


  We classify various types of graded extensions of a finite braided tensor
category $\cal B$ in terms of its $2$-categorical Picard groups. In particular,
we prove that braided extensions of $\cal B$ by a finite group $A$ correspond
to braided monoidal $2$-functors from $A$ to the braided $2$-categorical Picard
group of $\cal B$ (consisting of invertible central $\cal B$-module
categories). Such functors can be expressed in terms of the Eilnberg-Mac~Lane
cohomology. We describe in detail braided $2$-categorical Picard groups of
symmetric fusion categories and of pointed braided fusion categories.


  A variational framework, initially developed for high-order mesh
optimisation, is being extended for r-adaptation. The method is based on the
minimisation of a functional of the mesh deformation. To achieve adaptation,
elements of the initial mesh are manipulated using metric tensors to obtain
target elements. The nonlinear optimisation in turns adapts the final
high-order mesh to best fit the description of the target elements by
minimising the element distortion. Encouraging preliminary results prove that
the method behaves well and can be used in the future for more extensive work
which shall include the use of error indicators from CFD simulations.


  A gauged $SU_q(2)$ theory is characterized by two dual algebras, the first
lying close to the Lie algebra of SU(2) while the second introduces new degrees
of freedom that may be associated with non-locality or solitonic structure. The
first and second algebras, here called the external and internal algebras
respectively, define two sets of fields, also called external and internal. The
gauged external fields agree with the Weinberg-Salam model at the level of the
doublet representation but differ at the level of the adjoint representation.
For example the g-factor of the charged W-boson differs in the two models. The
gauged internal fields remain speculative but are analogous to color fields.


  In this paper, we study an unmanned aerial vehicle (UAV)-aided non-orthogonal
multiple access (NOMA) multi-way relaying networks (MWRNs). Multiple
terrestrial users aim to exchange their mutual information via an
amplify-and-forward (AF) UAV relay. Specifically, the realistic assumption of
the residual hardware impairments (RHIs) at the transceivers is taken into
account. To evaluate the performance of the considered networks, we derive the
analytical expressions for the achievable sum-rate (ASR). In addition, we carry
out the asymptotic analysis by invoking the affine expansion of the ASR in
terms of \emph{high signal-to-noise ratio (SNR) slope} and \emph{high SNR power
offset}. Numerical results show that: 1) Compared with orthogonal multiple
access (OMA), the proposed networks can significantly improve the ASR since it
can reduce the time slots from $\left[ {\left( {M - 1} \right)/2} \right] + 1$
to 2; and 2) RHIs of both transmitter and receiver have the same effects on the
ASR of the considered networks.


  A set of quantum protocols for online shopping is proposed and analyzed to
establish that it is possible to perform secure online shopping using different
types of quantum resources. Specifically, a single photon based, a Bell state
based and two 3-qubit entangled state based quantum online shopping schemes are
proposed. The Bell state based scheme, being a completely orthogonal state
based protocol, is fundamentally different from the earlier proposed schemes
which were based on conjugate coding. One of the 3-qubit entangled state based
scheme is build on the principle of entanglement swapping which enables us to
accomplish the task without transmission of the message encoded qubits through
the channel. Possible ways of generalizing the entangled state based schemes
proposed here to the schemes which use multiqubit entangled states is also
discussed. Further, all the proposed protocols are shown to be free from the
limitations of the recently proposed protocol of Huang et al. (Quantum Inf.
Process. 14, 2211-2225, 2015) which allows the buyer (Alice) to change her
order at a later time (after initially placing the order and getting it
authenticated by the controller). The proposed schemes are also compared with
the existing schemes using qubit efficiency.


  We report the first study of the glueball properties at finite temperatures
below T_c using SU(3) anisotropic lattice QCD with beta=6.25, the renormalized
anisotropy xi \equiv a_s/a_t = 4 and 20^3 \times N_t
(N_t=35,36,37,38,40,43,45,50,72) at the quenched level. From the temporal
correlation analysis with the smearing method, about 20 % mass reduction is
observed for the lowest scalar glueball as m_G(T)=1250 \pm 50MeV for 0.8 T_c <
T < T_c in comparison with m_G \simeq 1500 \sim 1700MeV at T \simeq 0.


  The Standard Model is in good shape, apart possibly from g_\mu - 2 and some
niggling doubts about the electroweak data. Something like a Higgs boson is
required to provide particle masses, but theorists are actively considering
alternatives. The problems of flavour, unification and quantum gravity will
require physics beyond the Standard Model, and astrophysics and cosmology also
provide reasons to expect physics beyond the Standard Model, in particular to
provide the dark matter and explain the origin of the matter in the Universe.
Personally, I find supersymmetry to be the most attractive option for new
physics at the TeV scale. The LHC should establish the origin of particle
masses has good prospects for discovering dark matter, and might also cast
light on unification and even quantum gravity. Important roles may also be
played by lower-energy experiments, astrophysics and cosmology in the searches
for new physics beyond the Standard Model.


  In software industries, individuals at different levels from customer to an
engineer apply diverse mechanisms to detect to which class a particular bug
should be allocated. Sometimes while a simple search in Internet might help, in
many other cases a lot of effort is spent in analyzing the bug report to
classify the bug. So there is a great need of a structured mining algorithm -
where given a crash log, the existing bug database could be mined to find out
the class to which the bug should be allocated. This would involve Mining
patterns and applying different classification algorithms. This paper focuses
on the feature extraction, noise reduction in data and classification of
network bugs using probabilistic Na\"ive Bayes approach. Different event models
like Bernoulli and Multinomial are applied on the extracted features. When new,
unseen bugs are given as input to the algorithms, the performance comparison of
different algorithms is done on the basis of accuracy and recall parameters.


  Networked systems that occur in various domains, such as the power grid, the
brain, and opinion networks, are known to obey conservation laws. For instance,
electric networks obey Kirchoff's laws, and social networks display opinion
consensus. Such conservation laws are often modeled as balance equations that
relate appropriate injected flows and potentials at the nodes of the networks.
A recent line of work considers the problem of estimating the unknown structure
of such networked systems from observations of node potentials (and only the
knowledge of the statistics of injected flows). Given the dynamic nature of the
systems under consideration, an equally important task is estimating the change
in the structure of the network from data -- the so called differential network
analysis problem. That is, given two sets of node potential observations, the
goal is to estimate the structural differences between the underlying networks.
We formulate this novel differential network analysis problem for systems
obeying conservation laws and devise a convex estimator to learn the edge
changes directly from node potentials. We derive conditions under which the
estimate is unique in the high-dimensional regime and devise an efficient
ADMM-based approach to perform the estimation. Finally, we demonstrate the
performance of our approach on synthetic and benchmark power network data.


  The objective of this paper is to develop diassociative analogues of
Lie-theoretic results from Peggy Batten's 1993 dissertation. We first prove
that covers of diassociative algebras are unique. Second, we show that the
multiplier of a diassociative algebra is characterized by the second cohomology
group with coefficients in the field. Third, we establish criteria for when the
center of a cover maps onto the center of the algebra. Along the way, we obtain
a collection of exact sequences, characterizations, and a brief theory of
unicentral diassociative algebras and stem extensions. This paper is part of an
ongoing project to advance extension theory in the context of several Loday
algebras.


  This tutorial review provides a guiding reference to researchers who want to
have an overview of the large body of literature about graph spanners. It
reviews the current literature covering various research streams about graph
spanners, such as different formulations, sparsity and lightness results,
computational complexity, dynamic algorithms, and applications. As an
additional contribution, we offer a list of open problems on graph spanners.


  Inspired by RNA-editing as occurs in transcriptional processes in the living
cell, we introduce an abstract notion of string adjustment, called guided
rewriting. This formalism allows simultaneously inserting and deleting
elements. We prove that guided rewriting preserves regularity: for every
regular language its closure under guided rewriting is regular too. This
contrasts an earlier abstraction of RNA-editing separating insertion and
deletion for which it was proved that regularity is not preserved. The
particular automaton construction here relies on an auxiliary notion of slice
sequence which enables to sweep from left to right through a completed rewrite
sequence.


  It is well known that the dependence structure for jointly Gaussian variables
can be fully captured using correlations, and that the conditional dependence
structure in the same way can be described using partial correlations. The
partial orrelation does not, however, characterize conditional dependence in
many non-Gaussian populations. This paper introduces the local Gaussian partial
correlation (LGPC), a new measure of conditional dependence. It is a local
version of the partial correlation coefficient that characterizes conditional
dependence in a large class of populations. It has some useful and novel
properties besides: The LGPC reduces to the ordinary partial correlation for
jointly normal variables, and it distinguishes between positive and negative
conditional dependence. Furthermore, the LGPC can be used to study departures
from conditional independence in specific parts of the distribution. We provide
several examples of this, both simulated and real, and derive estimation theory
under a local likelihood framework. Finally, we indicate how the LGPC can be
used to construct a powerful test for conditional independence, which, again,
can be used to detect Granger causality in time series.


  Several recent works [40, 24] observed an interesting phenomenon in neural
network pruning: A larger finetuning learning rate can improve the final
performance significantly. Unfortunately, the reason behind it remains elusive
up to date. This paper is meant to explain it through the lens of dynamical
isometry [42]. Specifically, we examine neural network pruning from an unusual
perspective: pruning as initialization for finetuning, and ask whether the
inherited weights serve as a good initialization for the finetuning? The
insights from dynamical isometry suggest a negative answer. Despite its
critical role, this issue has not been well-recognized by the community so far.
In this paper, we will show the understanding of this problem is very important
-- on top of explaining the aforementioned mystery about the larger finetuning
rate, it also unveils the mystery about the value of pruning [5, 30]. Besides a
clearer theoretical understanding of pruning, resolving the problem can also
bring us considerable performance benefits in practice.


  Sylvester equations $AX-XB=C$ have unique solutions for all $C$ when the
spectra of $A$ and $B$ are disjoint. Here $A$ and $B$ are bounded operators in
Banach spaces. We discuss the existence of polynomials $p$ such that the
spectra of $p(A)$ and $p(B)$ are well separated, either inside and outside of a
circle or separated into different half planes. Much of the discussion is based
on the following inclusion sets for the spectrum: $V_p(T)=\{\lambda \in \mathbb
C \ : \ |p(\lambda)| \le \|p(T)\| \}$ where $T$ is a bounded operator. We also
give an explicit series expansion for the solution in terms of $p(M)$, where
$M=\begin{pmatrix} A&C\\ &B\end{pmatrix}$, in the case where the spectra of $A$
and $B$ lie in different components of $V_p(M)$ .


  We consider the Coulomb drag between two two-dimensional electron layers at
filling factor \nu = 1/2 each, using a strong coupling approach within the
composite fermion picture. Due to an attractive interlayer interaction,
composite fermions are expected to form a paired state below a critical
temperature T_c. We find that above T_c pairing fluctuations make the
longitudinal transresistivity \rho_D increase with decreasing temperature. The
pairing mechanism we study is very sensitive to density variations in the two
layers, and to an applied current. We discuss possible relation to an
experiment by Lilly et al. [Phys. Rev. Lett. 80, 1714 (1998)].


  Simulation-based imaging (SBI) is a blood flow imaging technique that
optimally fits a computational fluid dynamics (CFD) simulation to
low-resolution, noisy magnetic resonance (MR) flow data to produce a
high-resolution velocity field. In this work, we study the effectivity of SBI
in predicting wall shear stress (WSS) relative to standard magnetic resonance
imaging (MRI) postprocessing techniques using two synthetic numerical
experiments: flow through an idealized, two-dimensional stenotic vessel and a
model of an adult aorta. In particular, we study the sensitivity of these two
approaches with respect to the Reynolds number of the underlying flow, the
resolution of the MRI data, and the noise in the MRI data. We found that the
SBI WSS reconstruction: 1) is insensitive to Reynolds number over the range
considered (Re $\leq$ 1000), 2) improves as the amount of MRI data increases
and provides accurate reconstructions with as little as three MRI voxels per
diameter, and 3) degrades linearly as the noise in the data increases with a
slope determined by the resolution of the MRI data. We also consider the
sensitivity of SBI to the resolution of the CFD mesh and found there is
flexibility in the mesh used for SBI, although the WSS reconstruction becomes
more sensitive to other parameters, particularly the resolution of the MRI
data, for coarser meshes. This indicates a fundamental trade-off between scan
time (i.e., MRI data quality and resolution) and reconstruction time using SBI,
which is inherently different than the trade-off between scan time and
reconstruction quality observed in standard MRI postprocessing techniques.


  Latent force models are a class of hybrid models for dynamic systems,
combining simple mechanistic models with flexible Gaussian process (GP)
perturbations. An extension of this framework to include multiplicative
interactions between the state and GP terms allows strong a priori control of
the model geometry at the expense of tractable inference. In this paper we
consider two methods of carrying out inference within this broader class of
models. The first is based on an adaptive gradient matching approximation, and
the second is constructed around mixtures of local approximations to the
solution. We compare the performance of both methods on simulated data, and
also demonstrate an application of the multiplicative latent force model on
motion capture data.


  Infrared divergences have long been heralded to cancel in sufficiently
inclusive cross-sections, according to the famous Kinoshita-Lee-Nauenberg
theorem which mandates an initial and final state sum. While well-motivated,
this theorem is much weaker than necessary: for finiteness, one need only sum
over initial $\textit{or}$ final states. Moreover, the cancellation generically
requires the inclusion of the forward scattering process. We provide a number
of examples showing the importance of this revised understanding: in $e^+e^-
\to Z$ at next-to-leading order, one can sum over certain initial and final
states with an arbitrary number of extra photons, or only over final states
with a finite number of photons, if forward scattering is included. For Compton
scattering, infrared finiteness requires the indistinguishability of hard
forward-scattered electrons and photons. This implies that in addition to
experimental limits on the energy and angular resolution, there must also be an
experimental limit on the momentum at which electric charge can be observed.
Similar considerations are required to explain why the rate for $\gamma \gamma$
to scatter into photons alone is infrared divergent but the rate for $\gamma
\gamma$ to scatter into photons or charged particles is finite. This new
understanding sheds light on the importance of including degenerate initial
states in physical predictions, the relevance of disconnected Feynman diagrams,
the importance of dressing initial or final-state charged particles, and the
quest to properly define the $S$ matrix.


  Tensor network states have enjoyed great success at capturing aspects of
strong correlation physics. However, obtaining dynamical correlators at
non-zero temperatures is generically hard even using these methods. Here, we
introduce a practical approach to computing such correlators using minimally
entangled typical thermal states (METTS). While our primary method directly
computes dynamical correlators of physical operators in real time, we propose
extensions where correlations are evaluated in the complex-time plane. The
imaginary time component bounds the rate of entanglement growth and strongly
alleviates the computational difficulty allowing the study of larger system
sizes. To extract the physical correlator one must take the limit of purely
real-time evolution. We present two routes to obtaining this information (i)
via an analytic correlation function in complex time combined with a stochastic
analytic continuation method to obtain the real-time limit and (ii) a hermitian
correlation function that asymptotically captures the desired correlation
function quantitatively without requiring effort of numerical analytic
continuation. We show that these numerical techniques capture the
finite-temperature dynamics of the Shastry-Sutherland model - a model of
interacting spin one-half in two dimensions.


  A new class of asynchronous discrete-event simulation schemes for
advection-diffusion-reaction equations are introduced, which is based on the
principle of allowing quanta of mass to pass through faces of a Cartesian
finite volume grid. The timescales of these events are linked to the flux on
the the face, and the schemes are self-adaptive, local in time and space.
Experiments are performed on realistic physical systems related to porous media
flow applications, including a large 3D advection diffusion equation and
advection diffusion reaction systems. The results are compared to highly
accurate results where the temporal evolution is computed with exponential
integrator schemes using the same finite volume discretisation. This allows a
reliable estimation of the solution error. Our results indicate a first order
convergence of the error as a control parameter is decreased.


  We introduce the notion of Stokes filtered quasi-local systems. It is proved
that the category of Stokes filtered quasi-local systems is abelian. We also
give a geometric way to construct Stokes filtered quasi-local systems, which
describe the asymptotic behavior of certain classes of solutions to some
differential-difference modules.


  Compressed sensing (CS) has become a popular field in the last two decades to
represent and reconstruct a sparse signal with much fewer samples than the
signal itself. Although regular images are not sparse on their own, many can be
sparsely represented in wavelet transform domain. Therefore, CS has also been
widely applied to represent digital images. However, an alternative approach,
adaptive sampling such as mesh-based image representation (MbIR), has not
attracted as much attention. MbIR works directly on image pixels and represents
the image with fewer points using a triangular mesh. In this paper, we perform
a preliminary comparison between the CS and a recently developed MbIR method,
AMA representation. The results demonstrate that, at the same sample density,
AMA representation can provide better reconstruction quality than CS based on
the tested algorithms. Further investigation with recent algorithms is needed
to perform a thorough comparison.


  Building on a recently introduced model for non-volatile resistive switching,
we propose a mechanism for unipolar resistance switching in
metal-insulator-metal sandwich structures. The commutation from the high to low
resistance state and back can be achieved with successive voltage sweeps of the
same polarity. Electronic correlation effects at the metal-insulator interface
are found to play a key role to produce a resistive commutation effect in
qualitative agreement with recent experimental reports on binary transition
metal oxide based sandwich structures.


  In this paper we extend the reduced-form setting under model uncertainty
introduced in [5] to include intensities following an affine process under
parameter uncertainty, as defined in [15]. This framework allows to introduce a
longevity bond under model uncertainty in a consistent way with the classical
case under one prior, and to compute its valuation numerically. Moreover, we
are able to price a contingent claim with the sublinear conditional operator
such that the extended market is still arbitrage-free in the sense of "No
Arbitrage of the first kind" as in [6].


  Transmission spectroscopy of exoplanets has the potential to provide precise
measurements of atmospheric chemical abundances, in particular of hot Jupiters
whose large sizes and high temperatures make them conducive to such
observations. To date, several transmission spectra of hot Jupiters have
revealed low amplitude features of water vapour compared to expectations from
cloud-free atmospheres of solar metallicity. The low spectral amplitudes in
such atmospheres could either be due to the presence of aerosols that obscure
part of the atmosphere or due to inherently low abundances of H$_2$O in the
atmospheres. A recent survey of transmission spectra of ten hot Jupiters used
empirical metrics to suggest atmospheres with a range of cloud/haze properties
but with no evidence for H$_2$O depletion. Here, we conduct a detailed and
homogeneous atmospheric retrieval analysis of the entire sample and report the
H$_2$O abundances, cloud properties, terminator temperature profiles, and
detection significances of the chemical species. Our present study finds that
the majority of hot Jupiters have atmospheres consistent with sub-solar H$_2$O
abundances at their day-night terminators. The best constrained abundances
range from $\mathrm{log(H_2O)}$ of $-5.04^{+0.46}_{-0.30}$ to
$-3.16^{+0.66}_{-0.69}$, which compared to expectations from solar-abundance
equilibrium chemistry correspond to $0.018^{+0.035}_{-0.009}\times$ solar to
$1.40^{+4.97}_{-1.11}\times$ solar. Besides H$_2$O we report statistical
constraints on other chemical species and cloud/haze properties, including
cloud/haze coverage fractions which range from $0.18^{+0.26}_{-0.12}$ to
$0.76^{+0.13}_{-0.15}$. The retrieved H$_2$O abundances suggest sub-solar
oxygen and/or super-solar C/O ratios, and can provide important constraints on
the formation and migration pathways of hot giant exoplanets.


  A poset can be regarded as a category in which there is at most one morphism
between objects, and such that at most one of Hom(c,c') and Hom(c',c) is
nonempty for distinct objects c,c'. If we keep in place the latter axiom but
allow for more than one morphism between objects, we have a sort of generalized
poset in which there are multiplicities attached to covering relations, and
possibly nontrivial automorphism groups. We call such a category an "updown
category". In this paper we give a precise definition of such categories and
develop a theory for them. We also give a detailed account of ten examples,
including updown categories of integer partitions, integer compositions, planar
rooted trees, and rooted trees.


  The universality of intermittency in hydrodynamic turbulence is considered
based on a recent model for the velocity gradient tensor evolution. Three
possible versions of the model are investigated differing in the assumed
correlation time-scale and forcing strength. Numerical tests show that the same
(universal) anomalous relative scaling exponents are obtained for the three
model variants. It is also found that transverse velocity gradients are more
intermittent than longitudinal ones, whereas dissipation and enstrophy scale
with the same exponents. The results are consistent with the universality of
intermittency and relative scaling exponents, and suggest that these are
dictated by the self-stretching terms that are the same in each variant of the
model.


  We predict that initially produced chi_cJ mesons at low transverse momentum
in the central rapidity region are almost dissociated by nucleons and
antinucleons in hadronic matter produced in central Au+Au collisions at RHIC
energies sqrt {s_{NN}}= 130 and 200 GeV. In calculations the nucleon and
antinucleon distributions in hadronic matter are results of evolution from
their freeze-out distributions which well fit the experimental p_T spectra of
proton and antiproton. Any measured chi_cJ mesons at low p_T are generated from
deconfined matter and give an explicit proof of regeneration mechanism
(recombination mechanism).


  We seek to quantify non-normality of the most amplified resolvent modes and
predict their features based on the characteristics of the base or mean
velocity profile. A 2-by-2 model linear Navier-Stokes (LNS) operator
illustrates how non-normality from mean shear distributes perturbation energy
in different velocity components of the forcing and response modes. The inverse
of their inner product, which is unity for a purely normal mechanism, is
proposed as a measure to quantify non-normality. In flows where there is
downstream spatial dependence of the base/mean, mean flow advection separates
the spatial support of forcing and response modes which impacts the inner
product. Success of mean stability analysis depends on the normality of
amplification. If the amplification is normal, the resolvent operator written
in its dyadic representation reveals that the adjoint and forward stability
modes are proportional to the forcing and response resolvent modes. If the
amplification is non-normal, then resolvent analysis is required to understand
the origin of observed flow structures. Eigenspectra and pseudospectra are used
to characterize these phenomena. Two test cases are studied: low Reynolds
number cylinder flow and turbulent channel flow. The first deals mainly with
normal mechanisms and quantification of non-normality using the inverse inner
product of the leading forcing and response modes agrees well with the product
of the resolvent norm and distance between the imaginary axis and least stable
eigenvalue. In turbulent channel flow, structures result from both normal and
non-normal mechanisms. Mean shear is exploited most efficiently by stationary
disturbances while bounds on the pseudospectra illustrate how non-normality is
responsible for the most amplified disturbances at spatial wavenumbers and
temporal frequencies corresponding to well-known turbulent structures.


  Wireless communication systems must increasingly support a multitude of
machine-type communications (MTC) devices, thus calling for advanced strategies
for active user detection (AUD). Recent literature has delved into AUD
techniques based on compressed sensing, highlighting the critical role of
signal sparsity. This study investigates the relationship between frequency
diversity and signal sparsity in the AUD problem. Single-antenna users transmit
multiple copies of non-orthogonal pilots across multiple frequency channels and
the base station independently performs AUD in each channel using the
orthogonal matching pursuit algorithm. We note that, although frequency
diversity may improve the likelihood of successful reception of the signals, it
may also damage the channel sparsity level, leading to important trade-offs. We
show that a sparser signal significantly benefits AUD, surpassing the
advantages brought by frequency diversity in scenarios with limited temporal
resources and/or high numbers of receive antennas. Conversely, with longer
pilots and fewer receive antennas, investing in frequency diversity becomes
more impactful, resulting in a tenfold AUD performance improvement.


  The classical Mercer's theorem claims that a continuous positive definite
kernel $K({\mathbf x}, {\mathbf y})$ on a compact set can be represented as
$\sum_{i=1}^\infty \lambda_i\phi_i({\mathbf x})\phi_i({\mathbf y})$ where
$\{(\lambda_i,\phi_i)\}$ are eigenvalue-eigenvector pairs of the corresponding
integral operator. This infinite representation is known to converge uniformly
to the kernel $K$. We estimate the speed of this convergence in terms of the
decay rate of eigenvalues and demonstrate that for $2m$ times differentiable
kernels the first $N$ terms of the series approximate $K$ as
$\mathcal{O}\big((\sum_{i=N+1}^\infty\lambda_i)^{\frac{m}{m+n}}\big)$ or
$\mathcal{O}\big((\sum_{i=N+1}^\infty\lambda^2_i)^{\frac{m}{2m+n}}\big)$.
Finally, we demonstrate some applications of our results to a spectral
charaterization of integral operators with continuous roots and other powers.


  Copulas, generalized estimating equations, and generalized linear mixed
models promote the analysis of grouped data where non-normal responses are
correlated. Unfortunately, parameter estimation remains challenging in these
three frameworks. Based on prior work of Tonda, we derive a new class of
probability density functions that allow explicit calculation of moments,
marginal and conditional distributions, and the score and observed information
needed in maximum likelihood estimation. Unlike true copulas, our quasi-copula
model only approximately preserves marginal distributions. Simulation studies
with Poisson, negative binomial, Bernoulli, and Gaussian bases demonstrate the
computational and statistical virtues of the quasi-copula model and its
limitations.


  We present the first protocol allowing a classical computer to interactively
verify the result of an efficient quantum computation. We achieve this by
constructing a measurement protocol, which enables a classical verifier to use
a quantum prover as a trusted measurement device. The protocol forces the
prover to behave as follows: the prover must construct an n qubit state of his
choice, measure each qubit in the Hadamard or standard basis as directed by the
verifier, and report the measurement results to the verifier. The soundness of
this protocol is enforced based on the assumption that the learning with errors
problem is computationally intractable for efficient quantum machines.


  Recent works in open-domain question answering (QA) have explored generating
context passages from large language models (LLMs), replacing the traditional
retrieval step in the QA pipeline. However, it is not well understood why
generated passages can be more effective than retrieved ones. This study
revisits the conventional formulation of QA and introduces the concept of
knowledge corpus error. This error arises when the knowledge corpus used for
retrieval is only a subset of the entire string space, potentially excluding
more helpful passages that exist outside the corpus. LLMs may mitigate this
shortcoming by generating passages in a larger space. We come up with an
experiment of paraphrasing human-annotated gold context using LLMs to observe
knowledge corpus error empirically. Our results across three QA benchmarks
reveal an increased performance (10% - 13%) when using paraphrased passage,
indicating a signal for the existence of knowledge corpus error. Our code is
available at https://github.com/xfactlab/emnlp2023-knowledge-corpus-error


  In this work we studied the combined action of chemical and electrical
synapses in small networks of Hindmarsh-Rose (HR) neurons on the synchronous
behaviour and on the rate of information produced (per time unit) by the
networks. We show that if the chemical synapse is excitatory, the larger the
chemical synapse strength used the smaller the electrical synapse strength
needed to achieve complete synchronisation, and for moderate synaptic strengths
one should expect to find desynchronous behaviour. Otherwise, if the chemical
synapse is inhibitory, the larger the chemical synapse strength used the larger
the electrical synapse strength needed to achieve complete synchronisation, and
for moderate synaptic strengths one should expect to find synchronous
behaviours. Finally, we show how to calculate semi-analytically an upper bound
for the rate of information produced per time unit (Kolmogorov-Sinai entropy)
in larger networks. As an application, we show that this upper bound is
linearly proportional to the number of neurons in a network whose neurons are
highly connected.


  The restricted planar elliptic three body problem (RPETBP) describes the
motion of a massless particle (a comet) under the gravitational field of two
massive bodies (the primaries, say the Sun and Jupiter) revolving around their
center of mass on elliptic orbits with some positive eccentricity. The aim of
this paper is to show the existence of orbits whose angular momentum performs
arbitrary excursions in a large region. In particular, there exist diffusive
orbits, that is, with a large variation of angular momentum.
  The leading idea of the proof consists in analysing parabolic motions of the
comet. By a well-known result of McGehee, the union of future (resp. past)
parabolic orbits is an analytic manifold. In a properly chosen coordinate
system these manifolds are stable (resp. unstable) manifolds of a manifold at
infinity $P_\infty$, which we call manifold at parabolic infinity.
  On this manifold, it is possible to define two scattering maps, which contain
the map structure of the homoclinic trajectories to it, i.e. orbits parabolic
both in the future and the past. Since the inner dynamics inside $P_\infty$ is
trivial, two different scattering maps are used. The combination of these two
scattering maps permits the design of the desired diffusive pseudo-orbits.
Using shadowing techniques and these pseudo orbits we show the existence of
true trajectories of the RPETBP whose angular momentum varies in any
predetermined fashion.


  The Slepian-Wolf (SW) coding system is a source coding system with two
encoders and a decoder, where these encoders independently encode source
sequences from two correlated sources into codewords, and the decoder
reconstructs both source sequences from the codewords. In this paper, we
consider the situation in which the SW coding system is asynchronous, i.e.,
each encoder samples a source sequence with some unknown delay. We assume that
delays are unknown but maximum and minimum values of possible delays are known
to encoders and the decoder. We also assume that sources are discrete
stationary memoryless and the probability mass function (PMF) of the sources is
unknown but the system knows that it belongs to a certain set of PMFs. For this
asynchronous SW coding system, we clarify the achievable rate region which is
the set of rate pairs of encoders such that the decoding error probability
vanishes as the blocklength tends to infinity. We show that this region does
not always coincide with that of the synchronous SW coding system in which each
encoder samples a source sequence without any delay.


  The nuclear $\alpha$ decay of heavy nuclei is investigated based on the
nuclear energy density functional, which leads to the $\alpha$ potential inside
the parent nucleus in terms of the proton and neutron density profiles of the
daughter nucleus. We use the Skyrme force model, Gogny force model, and
relativistic mean field model to get the nucleon density profiles inside heavy
nuclei. Once the nucleon density profiles are determined, the parameters of the
nuclear $\alpha$ potential are fitted to the observed $\alpha$ decay half-lives
of heavy nuclei. This approach is then applied to predict unknown $\alpha$
decay half-lives of heavy nuclei. To estimate the $Q$ values of unobserved
$\alpha$ decays, we make use of the liquid droplet model.


  The presence of defects in solids formed by active particles breaks their
discrete translational symmetry. As a consequence, many of their properties
become space-dependent and different from those characterizing perfectly
ordered structures. Motivated by recent numerical investigations concerning the
nonuniform distribution of entropy production and its relation to the
configurational properties of active systems, we study theoretically and
numerically the spatial profile of the entropy production rate when an active
solid contains an isotopic mass defect. The theoretical study of such an
imperfect active crystal is conducted by employing a perturbative analysis that
considers the perfectly ordered harmonic solid as a reference system. The
perturbation theory predicts a nonuniform profile of the entropy production
extending over large distances from the position of the impurity. The entropy
production rate decays exponentially to its bulk value with a typical healing
length that coincides with the correlation length of the spatial velocity
correlations characterizing the perfect active solids in the absence of
impurities. The theory is validated against numerical simulations of an active
Brownian particle crystal in two dimensions with Weeks-Chandler-Andersen
repulsive interparticle potential.


  We ask whether Krylov complexity is mutually compatible with the circuit and
Nielsen definitions of complexity. We show that the Krylov complexities between
three states fail to satisfy the triangle inequality and so cannot be a measure
of distance: there is no possible metric for which Krylov complexity is the
length of the shortest path to the target state or operator. We show this
explicitly in the simplest example, a single qubit, and in general.


  We investigate the transmission properties of quasiperiodic or aperiodic
structures based on graphene arranged according to the Cantor sequence. In
particular, we have found self-similar behaviour in the transmission spectra,
and most importantly, we have calculated the scalability of the spectra. To do
this, we implement and propose scaling rules for each one of the fundamental
parameters: generation number, height of the barriers and length of the system.
With this in mind we have been able to reproduce the reference transmission
spectrum, applying the appropriate scaling rule, by means of the scaled
transmission spectrum. These scaling rules are valid for both normal and
oblique incidence, and as far as we can see the basic ingredients to obtain
self-similar characteristics are: relativistic Dirac electrons, a self-similar
structure and the non-conservation of the pseudo-spin. This constitutes a
reduction of the number of conditions needed to observe self-similarity in
graphene-based structures, see D\'iaz-Guerrero et al. [D. S. D\'iaz-Guerrero,
L. M. Gaggero-Sager, I. Rodr\'iguez-Vargas, and G. G. Naumis,
arXiv:1503.03412v1, 2015].


  In this article we discuss the presentation of a random binary matrix using
sequence of whole nonnegative numbers. We examine some advantages and
disadvantages of this presentation as an alternative of the standard
presentation using two-dimensional array. It is shown that the presentation of
binary matrices using ordered n-tuples of natural numbers makes the algorithms
faster and saves a lot of memory. In this work we use object-oriented
programming using the syntax and the semantic of C++ programming language.


  Hyaluronic acid is an abundant polyelectrolyte in the human body that forms
extracellular hydrogels in connective tissues. It is essential for regulating
tissue biomechanics and cell-cell communication, yet hyaluronan overexpression
is associated with pathological situations such as cancer and multiple
sclerosis. Due to its enormous molecular weight (in the range of millions of
Daltons), accumulation of hyaluronan hinders transport of macromolecules
including nutrients and growth factors through tissues and also hampers drug
delivery. However, the exact contribution of hyaluronan to tissue penetrability
is poorly understood due to the complex structure and molecular composition of
tissues. Here we reconstitute biomimetic hyaluronan gels and systematically
investigate the effects of gel composition and crosslinking on the diffusion of
microscopic tracer particles. We combine ensemble-averaged measurements via
differential dynamic microscopy with single-particle tracking. We show that the
particle diffusivity depends on the particle size relative to the network pore
size and also on the stress relaxation dynamics of the network. We furthermore
show that addition of collagen, the other major biopolymer in tissues, causes
the emergence of caged particle dynamics, which is not present in the
one-component systems. Our findings are useful for understanding macromolecular
transport in tissues and for designing biomimetic extracellular matrix
hydrogels for drug delivery and tissue regeneration.


  Big models are widely used by online recommender systems to boost
recommendation performance. They are usually learned on historical user
behavior data to infer user interest and predict future user behaviors (e.g.,
clicks). In fact, the behaviors of heavy users with more historical behaviors
can usually provide richer clues than cold users in interest modeling and
future behavior prediction. Big models may favor heavy users by learning more
from their behavior patterns and bring unfairness to cold users. In this paper,
we study whether big recommendation models are fair to cold users. We
empirically demonstrate that optimizing the overall performance of big
recommendation models may lead to unfairness to cold users in terms of
performance degradation. To solve this problem, we propose a BigFair method
based on self-distillation, which uses the model predictions on original user
data as a teacher to regularize predictions on augmented data with randomly
dropped user behaviors, which can encourage the model to fairly capture
interest distributions of heavy and cold users. Experiments on two datasets
show that BigFair can effectively improve the performance fairness of big
recommendation models on cold users without harming the performance on heavy
users.


  The fundamental optical effects that are at basis of giant reflection band
and anomalous negative transmission in a self-sustained rectangular dielectric
grating slab in P polarization and for incidence angle not very far from the
Brewster's angle of the equivalent slab, are investigated. Notice, that the
self sustained dielectric grating slab is the simplest system that, due to the
Bragg diffraction, can show both the former optical effects. A systematic study
of its optical response is performed by an analytical exact solution of the
Maxwell equations for a general incidence geometry. At variance of the well
known broad reflection bands in high contrast dielectric grating slab in the
sub-wavelength regime, obtained by the destructive interference between the
travelling fundamental wave and the first diffracted wave (a generalization of
the so called second kind Wood's anomalies), the giant reflection band is a
subtle effect due to the interplay, as well as among the travelling fundamental
wave and the first quasi-guided diffracted one, also among the higher in-plane
wave- vector components of the evanescent/divergent waves. To better describe
this effect we will compare the optical response of the self-sustained high
contrast dielectric grating slab with a system composed by an equivalent
homogeneous slab with a thin rectangular high contrast dielectric grating
engraved in one of the two surfaces, usually taken as a prototype for the
second kind Wood's anomalies generation. Finally, the electromagnetic field
confinement in a patterned planar cavity, where the mirrors are two
self-sustained rectangular dielectric grating slabs, is briefly discussed.


  In the minimal Universal Extra Dimension model, single production of n = 2
gauge bosons provides a unique discriminating feature from supersymmetry. We
discuss how the proposed International Linear Collider can act as a n = 2
factory, much in the same vein as LEP. We also touch upon the potential of the
gamma-gamma mode of the collider to study the production and the decay of an
intermediate mass Higgs boson and its KK excitations.


  Rascal is a high-level transformation language that aims to simplify software
language engineering tasks like defining program syntax, analyzing and
transforming programs, and performing code generation. The language provides
several features including built-in collections (lists, sets, maps), algebraic
data-types, powerful pattern matching operations with backtracking, and
high-level traversals supporting multiple strategies. Interaction between
different language features can be difficult to comprehend, since most features
are semantically rich. The report provides a well-defined formal semantics for
a large subset of Rascal, called Rascal Light, suitable for developing formal
techniques, e.g., type systems and static analyses. Additionally, the report
states and proofs a series of interesting properties of the semantics,
including purity of backtracking, strong typing, partial progress and the
existence of a terminating subset.


  The main goal of this paper is to prove existence and non-existence results
for deterministic Kardar-Parisi-Zhang type equations involving non-local
"gradient terms". More precisely, let $\Omega \subset \mathbb{R}^N$, $N \geq
2$, be a bounded domain with boundary $\partial \Omega$ of class $C^2$. For $s
\in (0,1)$, we consider problems of the form \[ \tag{KPZ} \left\{
\begin{aligned} (-\Delta)^s u & = \mu(x) |\mathbb{D}(u)|^q + \lambda f(x),
\quad && \mbox{ in } \Omega,\\ u & = 0, && \mbox{ in } \mathbb{R}^N \setminus
\Omega, \end{aligned} \right. \] where $q > 1$ and $\lambda > 0$ are real
parameters, $f$ belongs to a suitable Lebesgue space, $\mu$ belongs to
$L^{\infty}(\Omega)$ and $\mathbb{D}$ represents a nonlocal "gradient term".
Depending on the size of $\lambda > 0$, we derive existence and non-existence
results. In particular, we solve several open problems posed in [4, Section 6]
and [2, Section 7].


  Social media has become an important communication channel during high impact
events, such as the COVID-19 pandemic. As misinformation in social media can
rapidly spread, creating social unrest, curtailing the spread of misinformation
during such events is a significant data challenge. While recent solutions that
are based on machine learning have shown promise for the detection of
misinformation, most widely used methods include approaches that rely on either
handcrafted features that cannot be optimal for all scenarios, or those that
are based on deep learning where the interpretation of the prediction results
is not directly accessible. In this work, we propose a data-driven solution
that is based on the ICA model, such that knowledge discovery and detection of
misinformation are achieved jointly. To demonstrate the effectiveness of our
method and compare its performance with deep learning methods, we developed a
labeled COVID-19 Twitter dataset based on socio-linguistic criteria.


  A method for designing transformation electromagnetics devices using tensor
impedance surfaces (TISs) is presented. The method is first applied to
idealized tensor impedance boundary conditions (TIBCs), and later to
printed-circuit tensor impedance surfaces (PCTISs). A PCTIS is a practical
realization of a TIBC. It consists of a tensor impedance sheet, which models a
subwavelength patterned metallic cladding, over a grounded dielectric
substrate. The method outlined in this paper allows anisotropic TIBCs and
PCTISs to be designed that support tangential wave vector distributions and
power flow directions specified by a coordinate transformation. As an example,
beamshifting devices are designed, using TIBCs and PCTISs, that allow a surface
wave to be shifted laterally. The designs are verified with a commercial
full-wave electromagnetic solver. This work opens new opportunities for the
design and implementation of anisotropic and inhomogeneous printed-circuit or
graphene based surfaces that can guide or radiate electromagnetic fields.


  Optical properties of a series of Gd2O3 doped sodium zinc tellurite
[xGd2O3-(0.8-x) TeO2-0.1Na2O-0.1ZnO] glasses prepared by conventional melt
quenching method have been studied. UV-Vis spectrophotometer was used in the
integrating sphere mode at room temperature to study the effect of Gd2O3 doping
on the optical band gap, refractive index, dielectric constant and
susceptibility within the wavelength range from 230-800 nm. Density is measured
using Archimedes principle for the calculation of molar volume, molar
refraction, polarizability and metallization criterion of the glasses.


  Experimental bounds on induced vacuum magnetic birefringence can be used to
improve present photon-photon scattering limits in the electronvolt energy
range. Measurements with the PVLAS apparatus (E. Zavattini {\it et al.}, Phys.
Rev. D {\bf77} (2008) 032006) at both $\lambda = 1064$ nm and 532 nm lead to
bounds on the parameter {\it A$_{e}$}, describing non linear effects in QED, of
$A_{e}^{(1064)} < 6.6\cdot10^{-21}$ T$^{-2}$ @ 1064 nm and $A_{e}^{(532)} <
6.3\cdot10^{-21}$ T$^{-2}$ @ 532 nm, respectively, at 95% confidence level,
compared to the predicted value of $A_{e}=1.32\cdot10^{-24}$ T$^{-2}$. The
total photon-photon scattering cross section may also be expressed in terms of
$A_e$, setting bounds for unpolarized light of $\sigma_{\gamma\gamma}^{(1064)}
< 4.6\cdot10^{-62}$ m$^{2}$ and $\sigma_{\gamma\gamma}^{(532)} <
2.7\cdot10^{-60}$ m$^{2}$. Compared to the expected QED scattering cross
section these results are a factor of $\simeq2\cdot10^{7}$ higher and represent
an improvement of a factor about 500 on previous bounds based on ellipticity
measurements and of a factor of about $10^{10}$ on bounds based on direct
stimulated scattering measurements.


  We present a self-consistent Bayesian formalism to sample the primordial
density fields compatible with a set of dark matter density tracers after
cosmic evolution observed in redshift space. Previous works on density
reconstruction did not self-consistently consider redshift space distortions or
included an additional iterative distortion correction step. We present here
the analytic solution of coherent flows within a Hamiltonian Monte Carlo
posterior sampling of the primordial density field. We test our method within
the Zel'dovich approximation, presenting also an analytic solution including
tidal fields and spherical collapse on small scales using augmented Lagrangian
perturbation theory. Our resulting reconstructed fields are isotropic and their
power spectra are unbiased compared to the true one defined by our mock
observations. Novel algorithmic implementations are introduced regarding the
mass assignment kernels when defining the dark matter density field and
optimization of the time step in the Hamiltonian equations of motions. Our
algorithm, dubbed barcode, promises to be specially suited for analysis of the
dark matter cosmic web down to scales of a few Megaparsecs. This large scale
structure is implied by the observed spatial distribution of galaxy clusters
--- such as obtained from X-ray, SZ or weak lensing surveys --- as well as that
of the intergalactic medium sampled by the Lyman alpha forest or perhaps even
by deep hydrogen intensity mapping. In these cases, virialized motions are
negligible, and the tracers cannot be modeled as point-like objects. It could
be used in all of these contexts as a baryon acoustic oscillation
reconstruction algorithm.


  This paper provides further insight into the key concept of missing at random
(MAR) in incomplete data analysis. Following the usual selection modelling
approach we envisage two models with separable parameters: a model for the
response of interest and a model for the missing data mechanism
  (MDM). If the response model is given by a complete density family, then
frequentist inference from the likelihood function ignoring the MDM is valid if
and only if the MDM is MAR. This necessary and sufficient condition also holds
more generally for models for coarse data, such as censoring.
  Examples are given to show the necessity of the completeness of the
underlying model for this equivalence to hold.


  We present measurements of branching fractions and charge asymmetries for the
decays etaK*, where K* indicates a spin 0, 1, or 2 Kpi system. The data sample
corresponds to 344x10^6 BBbar pairs collected with the BABAR detector at the
PEP-II asymmetric-energy e+e- collider at SLAC. We measure the branching
fractions (in units of 10^-6): BR(B0->etaK*0)=16.5\pm1.1\pm0.8,
BR(B+->etaK*+)=18.9\pm1.8\pm1.3, BR(B0->eta(Kpi)_0*0)=11.0\pm1.6\pm1.5,
BR(B+->eta(Kpi)_0*+)=18.2\pm2.6\pm 2.6, BR(B0->etaK_2*0(1430))=9.6\pm1.8\pm1.1,
and BR(B+->etaK_2*+(1430))=9.1\pm2.7\pm 1.4. We also determine the charge
asymmetries for all decay modes.


  The differential cross section, $d\sigma/dt$ for $\omega$ meson exclusive
photoproduction on the proton above the resonance region ($2.6<W<2.9$ GeV) was
measured up to a momentum transfer $-t = 5$ GeV$^2$ using the CLAS detector at
Jefferson Laboratory. The $\omega$ channel was identified by detecting a proton
and $\pi^+$ in the final state and using the missing mass technique. While the
low momentum transfer region shows the typical diffractive pattern expected
from Pomeron and Reggeon exchange, at large $-t$ the differential cross section
has a flat behavior. This feature can be explained by introducing quark
interchange processes in addition to the QCD-inspired two-gluon exchange.


  The observed Galactic rate of stellar mergers or the initiation of common
envelope phases brighter than M_V=-3 (M_I=-4) is of order 0.5 (0.3)/year with
90% confidence statistical uncertainties of 0.24-1.1 (0.14-0.65) and factor of
2 systematic uncertainties. The (peak) luminosity function is roughly dN/dL
L^(-1.4+/-0.3), so the rates for events more luminous than V1309 Sco (M_V=-7
mag) or V838Mon (M_V=-10 mag) are lower at r~0.1/year and 0.03/year,
respectively. The peak luminosity is a steep function of progenitor mass, L
M^(2-3). This very roughly parallels the scaling of luminosity with mass on the
main sequence, but the transients are ~2000-4000 times more luminous at peak.
Combining these, the mass function of the progenitors, dN/dM M^(-2.0+/-0.8), is
consistent with the initial mass function, albeit with broad uncertainties.
These observational results are also broadly consistent with the estimates of
binary population synthesis models. While extragalactic variability surveys can
better define the rates and properties of the high luminosity events,
systematic, moderate depth (I>16 mag) surveys of the Galactic plane are needed
to characterize the low luminosity events. The existing Galactic samples are
only ~20% complete and Galactic surveys are (at best) reaching a typical
magnitude limit of <13 mag.


  These are the notes for my lecture ``Resolution of Sigularities in
Charcteristic 0" given at the AMS Summer Institute at Seattle. It gives a self
contained proof of the strong Hironaka resolution theorem.


  We generalise Zhang's and Pintz recent results on bounded prime gaps to give
a lower bound for the the number of prime pairs bounded by 6*10^7 in the short
interval $[x,x+x (\log x)^{-A}]$. Our result follows only by analysing Zhang's
proof of Theorem 1, but we also explain how a sharper variant of Zhang's
Theorem 2 would imply the same result for shorter intervals.


  Automorphic Lie Algebras arise in the context of reduction groups introduced
in the late 1970s in the field of integrable systems. They are subalgebras of
Lie algebras over a ring of rational functions, defined by invariance under the
action of a finite group, the reduction group. Since their introduction in 2005
a classification is pursued. Past work shows remarkable uniformity between the
Lie algebras associated to different reduction groups. That is, many
Automorphic Lie Algebras with nonisomorphic reduction groups are isomorphic. In
this thesis we set out to find the origin of these observations by searching
for properties that are independent of the reduction group, called invariants
of Automorphic Lie Algebras.
  Several invariants are obtained and used to set up a structure theory for
Automorphic Lie Algebras. This naturally leads to a cohomology theory for root
systems. A first exploration of this structure theory narrows down the search
for Automorphic Lie Algebras significantly. Various particular cases are fully
determined by their invariants, including most of the previously studied
Automorphic Lie Algebras, thereby providing an explanation for their
uniformity. In addition, the structure theory advances the classification
project. For example, it clarifies the effect of a change in pole orbit
resulting in various new Cartan-Weyl normal form generators for Automorphic Lie
Algebras. From a more general perspective, the success of the structure theory
and root cohomology in absence of a field promises interesting theoretical
developments for Lie algebras over a graded ring.


  We have developed a data reduction procedure to extract multiple spectra from
a single two-dimensional Space Telescope Imaging Spectrograph (STIS) image of a
crowded stellar field. This paper provides a description of our new technique,
utilizing a STIS ultraviolet spectral image, acquired with the G140L grating
and the 52 arcsec x 2 arcsec aperture, sampling a concentration of O and B
stars in the central region of the NGC 604 starburst in M33. The software
routines can disentangle and produce reliable ultraviolet spectra of stars with
angular separations as small as 0.055 arcsec. Use of the extraction slit, based
upon our model of the spectral cross dispersion profile, generates spectra with
slightly higher resolution than the STScI standard processing. Our results
clearly show that the spectral imaging capability of STIS represents a powerful
tool for studying luminous stars in the star-forming regions of the Local
Group.


  These are lecture notes of a course taken in Leipzig 2023, spring semester.
It deals with extremal combinatorics, algebraic methods and combinatorial
geometry. These are not meant to be exhaustive, and do not contain many proofs
that were presented in the course.


  Feedback from outflows driven by active galactic nuclei (AGN) can affect the
distribution and properties of the gaseous halos of galaxies. We study the
hydrodynamics and non-thermal emission from the forward outflow shock produced
by an AGN-driven outflow. We consider a few possible profiles for the halo gas
density, self-consistently constrained by the halo mass, redshift and the disk
baryonic concentration of the galaxy. We show that the outflow velocity levels
off at $\sim 10^3\,\rm km\, s^{-1}$ within the scale of the galaxy disk.
Typically, the outflow can reach the virial radius around the time when the AGN
shuts off. We show that the outflows are energy-driven, consistently with
observations and recent theoretical findings. The outflow shock lights up the
halos of massive galaxies across a broad wavelength range. For Milky Way (MW)
mass halos, radio observations by The Jansky Very Large Array (JVLA) and The
Square Kilometer Array (SKA) and infrared/optical observations by The James
Webb Space Telescope (JWST) and Hubble Space Telescope (HST) can detect the
emission signal of angular size $\sim 8"$ from galaxies out to redshift
$z\sim5$. Millimeter observations by The Atacama Large Millimeter/submillimeter
Array (ALMA) are sensitive to non-thermal emission of angular size $\sim 18"$
from galaxies at redshift $z\lesssim1$, while X-ray observations by Chandra,
XMM-Newton and The Advanced Telescope for High Energy Astrophysics (ATHENA) is
limited to local galaxies ($z\lesssim 0.1$) with an emission angular size of
$\sim2'$. Overall, the extended non-thermal emission provides a new way of
probing the gaseous halos of galaxies at high redshifts.


  The constant introduction of standardized benchmarks in the literature has
helped accelerating the recent advances in meta-learning research. They offer a
way to get a fair comparison between different algorithms, and the wide range
of datasets available allows full control over the complexity of this
evaluation. However, for a large majority of code available online, the data
pipeline is often specific to one dataset, and testing on another dataset
requires significant rework. We introduce Torchmeta, a library built on top of
PyTorch that enables seamless and consistent evaluation of meta-learning
algorithms on multiple datasets, by providing data-loaders for most of the
standard benchmarks in few-shot classification and regression, with a new
meta-dataset abstraction. It also features some extensions for PyTorch to
simplify the development of models compatible with meta-learning algorithms.
The code is available here: https://github.com/tristandeleu/pytorch-meta


  We present the confirmation of the eccentric warm giant planet TOI-201 b,
first identified as a candidate in \textit{TESS} photometry (Sectors 1-8,
10-13, and 27-28) and confirmed using ground-based photometry from NGTS and
radial velocities from FEROS, HARPS, CORALIE, and \textsc{Minerva}-Australis.
TOI-201 b orbits a young ($\mathrm{0.87^{+0.46}_{-0.49} \, Gyr}$) and
bright(V=9.07 mag) F-type star with a $\mathrm{52.9781 \, d}$ period. The
planet has a mass of $\mathrm{0.42^{+0.05}_{-0.03}\, M_J}$, a radius of
$\mathrm{1.008^{+0.012}_{-0.015}\, R_J}$, and an orbital eccentricity of
$0.28^{+0.06}_{-0.09}$; it appears to still be undergoing fairly rapid cooling,
as expected given the youth of the host star. The star also shows long-term
variability in both the radial velocities and several activity indicators,
which we attribute to stellar activity. The discovery and characterization of
warm giant planets such as TOI-201 b is important for constraining formation
and evolution theories for giant planets.


  We describe and evaluate the algorithmic techniques that are used in the FF
planning system. Like the HSP system, FF relies on forward state space search,
using a heuristic that estimates goal distances by ignoring delete lists.
Unlike HSP's heuristic, our method does not assume facts to be independent. We
introduce a novel search strategy that combines hill-climbing with systematic
search, and we show how other powerful heuristic information can be extracted
and used to prune the search space. FF was the most successful automatic
planner at the recent AIPS-2000 planning competition. We review the results of
the competition, give data for other benchmark domains, and investigate the
reasons for the runtime performance of FF compared to HSP.


  We investigate the mechanics of bistable, hard-magnetic, elastic beams,
combining experiments, finite element modeling (FEM), and a reduced-order
theory. The beam is made of a hard magneto-rheological elastomer, comprising
two segments with antiparallel magnetization along the centerline, and is set
into a bistable curved configuration by imposing an end-to-end shortening.
Reversible snapping is possible between these two stable states. First, we
experimentally characterize the critical field strength for the onset of
snapping, at different levels of end-to-end shortening. Second, we perform 3D
FEM simulations using the Riks method to analyze high-order deformation modes
during snapping. Third, we develop a reduced-order centerline-based beam theory
to rationalize the observed magneto-elastic response. The theory and
simulations are validated against experiments, with an excellent quantitative
agreement. Finally, we consider the case of combined magnetic and
mechanical-indentation loading, examining how the applied field affects the
bistability and quantifying the maximum load-bearing capacity. Our work
provides a set of predictive tools for the rational design of one-dimensional,
bistable, magneto-elastic structural elements.


  The Schwarz or Bayesian information criterion (BIC) is one of the most widely
used tools for model comparison in social science research. The BIC however is
not suitable for evaluating models with order constraints on the parameters of
interest. This paper explores two extensions of the BIC for evaluating order
constrained models, one where a truncated unit information prior is used under
the order-constrained model, and the other where a truncated local unit
information prior is used. The first prior is centered around the maximum
likelihood estimate and the latter prior is centered around a null value.
Several analyses show that the order-constrained BIC based on the local unit
information prior works better as an Occam's razor for evaluating
order-constrained models and results in lower error probabilities. The
methodology based on the local unit information prior is implemented in the R
package `BICpack' which allows researchers to easily apply the method for
order-constrained model selection. The usefulness of the methodology is
illustrated using data from the European Values Study.


  In this paper we study the parameterized complexity of two well-known
permutation group problems which are NP-complete. 1. Given a permutation group
G=<S>, subgroup of $S_n$, and a parameter $k$, find a permutation $\pi$ in G
such that $|{i\in [n]\mid \pi(i)\ne i}|$ is at least $k$. This generalizes the
well-known NP-complete problem of finding a fixed-point free permutation in G.
(this is the case when $k=n$). We show that this problem with parameter $k$ is
fixed parameter tractable. In the process, we give a simple deterministic
polynomial-time algorithm for finding a fixed point free element in a
transitive permutation group, answering an open question of Cameron. 2. Next we
consider the problem of computing a base for a permutation group G=<S>. A base
for G is a subset B of $[n]$ such that the subgroup of G that fixes B pointwise
is trivial. This problem is known to be NP-complete. We show that it is fixed
parameter tractable for the case of cyclic permutation groups and for
permutation groups of constant orbit size. For more general classes of
permutation groups we do not know whether the problem is in FPT or is
W[1]-hard.


  We study the Frequency Resolved Spectra of the Seyfert galaxy MCG -6-30-15
obtained during two recent XMM-Newton observations. Splitting the Fourier
spectra in soft (<2 keV) and hard (>2 keV) bands, we find that the soft band
has a variability amplitude larger than the hard one on time scales longer than
10 ksec, while the opposite is true on time scales shorter than 3 ksec. Both
the soft and hard band spectra are well fitted by power laws of different
indices. The spectra of the hard band become clearly softer as the Fourier
Frequency decreases from 7x10^{-4} Hz to 10^{-5} Hz, while the spectral slope
of the soft band power law component is independent of the Fourier frequency.
The well known broad Fe Ka feature is absent at all frequency bins; this result
implies that this feature is not variable on time scales shorter than ~10^5
sec, in agreement with recent line variability studies. Strong spectral
features are also present in the soft X-ray band (at E~0.7), clearly
discernible in all Fourier Frequency bins. This fact is consistent with the
assumption that they are due to absorption by intervening matter within the
source.


  Let G = Z2 act freely on a nitistic space X. If the mod 2 cohomology of X is
isomorphic to the real projective space RP^{2n+1} (resp. complex projective
space
  CP^{2n+1}) then the mod 2 cohomology of orbit spaces of these free actions
are RP1 x CPn (resp. RP2 x HPn) [7]. In this paper, we have discussed converse
of these results. We have showed that if the mod 2 cohomology of the orbit
space X/G is RP1 x CPn (resp. RP2 x HPn) then the mod 2 cohomology of X is
RP^{2n+1} or S1 x CPn (resp. CP^{2n+1} or
  S2 x HPn). A partial converse of free involutions on the product of
projective spaces RPn x RP2m+1 (resp. CPn x CP2m+1) are also discussed.


  Although the Blandford-Payne process, the standard model for the production
of AGN jet outflow, has been fully acknowledged and long-known in both the
theoretical Astrophysics and observational Astronomy communities, subsequent
research works to gain observational supports have been quite rare. In the
present work, therefore, we would like to suggest a likely event and encourage
its observation which demonstrates observational supports for the
Blandford-Payne process. That is, we propose the coupling of it to the
well-known Bardeen-Petterson effect. In order for this set-up to comply with
our objective stated above, however, the two coupled processes need to be
well-resolved. We, therefore, carefully study and present the condition for
this to take place. We also point out that this major concern of our present
work allows us to measure the strength of the intra-galactic magnetic field
which has been known to be uneasy and unclear even in the galaxy observation
Astronomy community for a long time.


  The matrix $S = [1+x_i y_j]_{i,j=1}^{n}, 0<x_1<\cdots<x_n,\,
0<y_1<\cdots<y_n$, has gained importance lately due to its role in powers
preserving total nonnegativity. We give an explicit decomposition of $S$ in
terms of elementary bidiagonal matrices, which is analogous to the Neville
decomposition. We give a bidiagonal decomposition of $S^{\circ
m}=[(1+x_iy_j)^m]$ for positive integers $1\leq m \leq n-1$. We also explore
the total positivity of Hadamard powers of another important class of matrices
called mean matrices.


  This work introduces an efficient power management approach for shipboard
microgrids that integrates diesel generators, a fuel cell, and battery energy
storage system. This strategy addresses both unit commitment and power
dispatch, considering the zero-emission capability of the ship, as well as
optimizing the ship's speed. The optimization is done through mixed integer
linear programming with the objective of minimizing the operational cost of all
the power resources. Evaluations are conducted on a notional all-electric ship,
with electrical load simulated using a Markov chain based on actual measurement
data. The findings underscore the effectiveness of the proposed strategy in
optimizing fuel consumption while ensuring protection against blackout
occurrences.


  We show an improvement of Bray sharp mass-capacity inequality and Bray-Miao
sharp upper bound of the capacity of the boundary in terms of its area, for
three-dimensional, complete, one-ended asymptotically flat manifolds with
compact, connected boundary and with nonnegative scalar curvature, under
appropriate assumptions on the topology and on the mean curvature of the
boundary. Our arguments relies on two monotonicity formulas holding along level
sets of a suitable harmonic potential, associated to the boundary of the
manifold. This work is an expansion of the results contained in the PhD thesis
of the author.


  We investigate the relationship between the quasi-thermal baryon-related
photosphere in relativistic outflows, and the internal shocks arising outside
them, which out to a limiting radius may be able to create enough pairs to
extend the optically thick region. Variable gamma-ray light curves are likely
to arise outside this limiting pair-forming shock radius, while X-ray excess
bursts may arise from shocks occurring below it; a possible relation to X-ray
flashes is discussed. This model leads to a simple physical interpretation of
the observational gamma-ray variability-luminosity relation.


  In this work, we make a theoretical study on the $p \bar p \rightarrow
\Lambda \bar\Lambda \eta$ reaction for antiproton beam energy from threshold to
4GeV within an effective Lagrangian approach and isobar model. By assuming this
reaction is dominated by the excitation of $\Lambda$ and $\bar \Lambda$
resonances in intermediate states, we calculate the total cross sections and
give the predictions of the angular distribution and invariant mass spectrum of
final particles. In particular, we discuss the possibility to verify the
existence of a narrow $\Lambda$ resonance found in the process of $K^- p\to
\eta \Lambda$ in the present reaction. It shows that the $p \bar p \rightarrow
\bar \Lambda \Lambda \eta$ reaction can provide us with valuable information
about the $\Lambda$ resonances having significant couplings to $\bar K N$ and
$\Lambda\eta$ channels. Thus the experimental data of this reaction will be a
good supplement to the $\bar K N\to\eta \Lambda$ scattering data for studying
$\Lambda$ resonances.


  We derive an uncertainty principle for Lipschitz maps acting on subsets of
Banach spaces. We show that this nonlinear uncertainty principle reduces to the
Heisenberg-Robertson-Schrodinger uncertainty principle for linear operators
acting on Hilbert spaces.


  The exact number of CNOT and single qubit gates needed to implement a Quantum
Algorithm in a given architecture is one of the central problems of Quantum
Computation. In this work we study the importance of concise realizations of
Partially defined Unitary Transformations for better circuit construction using
the case study of Dicke State Preparation. The Dicke States $(\left|D^n_k
\right>)$ are an important class of entangled states with uses in many branches
of Quantum Information. In this regard we provide the most efficient
Deterministic Dicke State Preparation Circuit in terms of CNOT and single qubit
gate counts in comparison to existing literature. We further observe that our
improvements also reduce architectural constraints of the circuits. We
implement the circuit for preparing $\left| D^4_2 \right>$ on the "ibmqx2"
machine of the IBM QX service and observe that the error induced due to noise
in the system is lesser in comparison to the existing circuit descriptions. We
conclude by describing the CNOT map of the generic $\left| D^n_k \right>$
preparation circuit and analyze different ways of distributing the CNOT gates
in the circuit and its affect on the induced error.


  We derive a priori $C^2$ estimates for the $\chi$-plurisubharmonic solutions
of general complex Hessian equations with right-hand side depending on
gradients.


  At present, there are several measurements of $B$ decays that exhibit
discrepancies with the predictions of the Standard Model, and suggest the
presence of new physics in $b\to s$ and $b \to c(u)$ quark level transitions.
Motivated by the prospects of the ongoing high-luminosity $B$ factories, we
study the exclusive $B \to a_1 (1260) \ell^- \bar{\nu}_\ell$ process within the
Standard Model Effective Field Theory (SMEFT) formalism, to understand the
sensitivity of new physics. The new physics parameters are constrained by using
the experimental branching fractions of the (semi)leptonic $B \to \ell
\bar{\nu}$ and $B \to (\pi, \rho, \omega) \ell \bar{\nu}$ processes (where
$\ell = e, \mu, \tau$) which undergo $b \to u \ell \bar{\nu}$ quark level
transitions. We then perform a comprehensive angular analysis of the exclusive
$B \to a_1 (1260) \ell^- \bar{\nu}_\ell$ process in the Standard Model and in
the presence of various new physics operators. We also provide the predictions
and comment on various observables, such as branching ratio, forward-backward
asymmetry, and the test of lepton flavor non universality of the $B \to a_1
(1260) \ell^- \bar{\nu}_\ell$ channel.


  The Gaia space astrometry mission is measuring accurate distances and space
motions of more than two billion stars throughout our Galaxy and beyond. This
is a first look at how Gaia is contributing to fundamental physics, and in
particular to our understanding of dark matter, for which a few examples are
given from the current literature.
  One of our goals is to illustrate how deep, and often surprising, insight
into very diverse areas of fundamental physics can be extracted from this new
and enormous high-accuracy stellar data set. In this spirit, we finish by
suggesting a search for a connection between stellar activity, dark matter
streams, and planetary configuration in nearby exoplanetary systems, as has
been tentatively proposed in the case of the solar system.


  In this paper, we present a framework for getting a series of exact vacuum
solutions to the Einstein equation. This procedure of resolution is based on a
canonical form of the metric. According to this procedure, the Einstein
equation can be reduced to some 2-dimensional Laplace-like equations or
rotation and divergence equations, which are much convenient for the
resolution.


  We consider continuous quantum measurement of a superconducting qubit in the
circuit QED setup with a moderate bandwidth of the measurement resonator, i.e.,
when the "bad cavity" limit is not applicable. The goal is a simple description
of the quantum evolution due to measurement, i.e., the measurement back-action.
Extending the quantum Bayesian approach previously developed for the "bad
cavity" regime, we show that the evolution equations remain the same, but now
they should be applied to the entangled qubit-resonator state, instead of the
qubit state alone. The derivation uses only elementary quantum mechanics and
basic properties of coherent states, thus being accessible to non-experts.


  Disordered systems are interesting for many physical reasons. In this
article, we study the renormalization group property of quenched disorder
systems in the presence of a boundary. We construct examples of scalar field
theories in various dimensions with both classical and quantum disorder
localized at the boundary. We study these theories in $\e$-expansion and
discuss properties of fixed points of the renormalization group flow.


  Influence maximization is among the most fundamental algorithmic problems in
social influence analysis. Over the last decade, a great effort has been
devoted to developing efficient algorithms for influence maximization, so that
identifying the ``best'' algorithm has become a demanding task. In SIGMOD'17,
Arora, Galhotra, and Ranu reported benchmark results on eleven existing
algorithms and demonstrated that there is no single state-of-the-art offering
the best trade-off between computational efficiency and solution quality.
  In this paper, we report a high-level experimental study on three
well-established algorithmic approaches for influence maximization, referred to
as Oneshot, Snapshot, and Reverse Influence Sampling (RIS). Different from
Arora et al., our experimental methodology is so designed that we examine the
distribution of random solutions, characterize the relation between the sample
number and the actual solution quality, and avoid implementation dependencies.
Our main findings are as follows: 1. For a sufficiently large sample number, we
obtain a unique solution regardless of algorithms. 2. The average solution
quality of Oneshot, Snapshot, and RIS improves at the same rate up to scaling
of sample number. 3. Oneshot requires more samples than Snapshot, and Snapshot
requires fewer but larger samples than RIS. We discuss the time efficiency when
conditioning Oneshot, Snapshot, and RIS to be of identical accuracy. Our
conclusion is that Oneshot is suitable only if the size of available memory is
limited, and RIS is more efficient than Snapshot for large networks; Snapshot
is preferable for small, low-probability networks.


  While artificial-intelligence-based methods suffer from lack of transparency,
rule-based methods dominate in safety-critical systems. Yet, the latter cannot
compete with the first ones in robustness to multiple requirements, for
instance, simultaneously addressing safety, comfort, and efficiency. Hence, to
benefit from both methods they must be joined in a single system. This paper
proposes a decision making and control framework, which profits from advantages
of both the rule- and machine-learning-based techniques while compensating for
their disadvantages. The proposed method embodies two controllers operating in
parallel, called Safety and Learned. A rule-based switching logic selects one
of the actions transmitted from both controllers. The Safety controller is
prioritized every time, when the Learned one does not meet the safety
constraint, and also directly participates in the safe Learned controller
training. Decision making and control in autonomous driving is chosen as the
system case study, where an autonomous vehicle learns a multi-task policy to
safely cross an unprotected intersection. Multiple requirements (i.e., safety,
efficiency, and comfort) are set for vehicle operation. A numerical simulation
is performed for the proposed framework validation, where its ability to
satisfy the requirements and robustness to changing environment is successfully
demonstrated.


  Nous d\'efinissons et \'etudions les d\'evissages des $F$-complexes de
$\mathcal{D}$-modules arithm\'etiques en $F$-isocristaux surconvergents. Nous
prouvons que les $F$-complexes surholonomes sont d\'evissables en
$F$-isocristaux surconvergents. On \'etablit ensuite une formule cohomologique,
\'etendant celle d'\'Etesse et Le Stum, des fonctions $L$ associ\'ees aux duaux
des $F$-complexes de $\mathcal{D}$-modules arithm\'etiques d\'evissables en
$F$-isocristaux surconvergents. Puis, nous obtenons un analogue $p$-adique de
Weil II \'etendant celui de Kedlaya.


  We introduce the concept of matching connectivity as a notion of connectivity
in graph admitting perfect matchings which heavily relies on the structural
properties of those matchings. We generalise a result of Robertson, Seymour and
Thomas for bipartite graphs with perfect matchings (see [Neil Roberts, Paul D
Seymour, and Robin Thomas. Permanents, pfaffian orientations, and even directed
curcuits. Annals of Mathematics, 150(2):929-975, 1999]) in order to obtain a
concept of alternating paths that turns out to be sufficient for the
description of our connectivity parameter. We introduce some basic properties
of matching connectivity and prove a Menger-type result for matching
n-connected graphs. Furthermore, we show that matching connectivity fills a gap
in the investigation of n-extendable graphs and their connectivity properties.
To be more precise we show that every n-extendable graph is matching
n-connected and for the converse every matching (n+1)-connected graph either is
n-extendable, or belongs to a well described class of graphs: the brace
h-critical graphs.


  Intertwining charge density wave (CDW) with spin and pairing order parameters
is a major focus of contemporary condensed matter physics. Lattice distortions
and local symmetry breaking resulted from CDWs are crucial for the emergence of
correlated and topological states in quantum materials in general. While the
presence of CDWs can be detected by diffraction or spectroscopic techniques,
atomic visualization of the CDW induced lattice distortions remains limited to
CDW with short wavelengths. In this letter, we realized the imaging of
incommensurate long-wavelength CDWs based on cryogenic four-dimensional
scanning transmission electron microscopy (cryo-4DSTEM). By visualizing the
incommensurate CDW induced lattice modulations in a skyrmion magnet EuAl4, we
discover two out-of-phase intra-unit cell shear modulations that specifically
break the local inversion-symmetry. Our results provide direct evidence for the
intertwined spin and charge orders in EuAl4 and key information about local
symmetry. Furthermore, we establish cryo-4DSTEM as an indispensable approach to
understand CDW induced new quantum states of matter.


  In this paper, we design and train a Generative Image-to-text Transformer,
GIT, to unify vision-language tasks such as image/video captioning and question
answering. While generative models provide a consistent network architecture
between pre-training and fine-tuning, existing work typically contains complex
structures (uni/multi-modal encoder/decoder) and depends on external modules
such as object detectors/taggers and optical character recognition (OCR). In
GIT, we simplify the architecture as one image encoder and one text decoder
under a single language modeling task. We also scale up the pre-training data
and the model size to boost the model performance. Without bells and whistles,
our GIT establishes new state of the arts on 12 challenging benchmarks with a
large margin. For instance, our model surpasses the human performance for the
first time on TextCaps (138.2 vs. 125.5 in CIDEr). Furthermore, we present a
new scheme of generation-based image classification and scene text recognition,
achieving decent performance on standard benchmarks. Codes are released at
\url{https://github.com/microsoft/GenerativeImage2Text}.