  The Ordered Upwind Method (OUM) is used to approximate the viscosity solution
of the static Hamilton-Jacobi-Bellman (HJB) with direction-dependent weights on
unstructured meshes. The method has been previously shown to provide a solution
that converges to the exact solution, but no convergence rate has been
theoretically proven. In this paper, it is shown that the solutions produced by
the OUM in the boundary value formulation converge at a rate of at least the
square root of the largest edge length in the mesh in terms of maximum error.
An example with similar order of numerical convergence is provided.


  Through the introduction of a class of trial wave functions portraying
combined rotations and vibrations of molecules formed through particle
localization in concentric polygonal rings, a correlated basis is constructed
that spans the translationally invariant part of the lower-Landau-level (LLL)
spectra. These trial functions, referred to as rovibrational molecular (RVM)
functions, generalize our previous work which focused exclusively on electronic
cusp states, describing them as pure vibrationless rotations. From a
computational viewpoint, the RVM correlated basis enables controlled and
systematic improvements of the original strongly-correlated variational wave
function. Conceptually, it provides the basis for the development of a quantal
molecular description for the full LLL spectra. This quantal molecular
description is universal, being valid for both bosons and fermions, for both
the yrast and excited states of the LLL spectra, and for both low and high
angular momenta. Furthermore, it follows that all other translationally
invariant trial functions (e.g., the Jastrow-Laughlin, compact
composite-fermion, or Moore-Read functions) are reducible to a description in
terms of an excited rotating/vibrating quantal molecule.


  This paper studies a class of nonlinear Dirac equations with cubic terms in
$R^{1+1}$, which include the equations for the massive Thirring model and the
massive Gross-Neveu model. Under the assumptions that the initial data has
small charge, the global existence of the solution in $H^1$ are proved. The
proof is given by introducing some Bony functional to get the uniform estimates
on the nonlinear terms and the uniform bounds on the local smooth solution,
which enable us to extend the local solution globally in time. Then
$L^2$-stability estimates for these solutions are also established by a
Lyapunov functional and the global existence of weak solution in $L^2$ is
obtained.


  This paper studies the super-twisting algorithm (STA) for adaptive sliding
mode design. The proposed method tunes the two gains of STA on line
simultaneously such that a second order sliding mode can take place with small
rectifying gains. The perturbation magnitude is obtained exactly by employing a
third-order sliding mode observer in opposition to the conventional
approximations by using a first order low pass filter. While driving the
sliding variable to the sliding mode surface, one gain of the STA automatically
converges to an adjacent area of the perturbation magnitude in finite time. The
other gain is adjusted by the above gain to guarantee the robustness of the
STA. This method requires only one parameter to be adjusted. The adjustment is
straightforward because it just keeps increasing until it fulfills the
convergence constraints. For large values of the parameter, chattering in the
update law of the two gains is avoided by employing a geometry based backward
Euler integration method. The usefulness is illustrated by an example of
designing an equivalent control based sliding mode control (ECBC-SMC) with the
proposed adaptive STA for a perturbed LTI system.


  We study smoothed analysis of distributed graph algorithms, focusing on the
fundamental minimum spanning tree (MST) problem. With the goal of studying the
time complexity of distributed MST as a function of the "perturbation" of the
input graph, we posit a {\em smoothing model} that is parameterized by a
smoothing parameter $0 \leq \epsilon(n) \leq 1$ which controls the amount of
{\em random} edges that can be added to an input graph $G$ per round.
Informally, $\epsilon(n)$ is the probability (typically a small function of
$n$, e.g., $n^{-\frac{1}{4}}$) that a random edge can be added to a node per
round. The added random edges, once they are added, can be used (only) for
communication.
  We show upper and lower bounds on the time complexity of distributed MST in
the above smoothing model. We present a distributed algorithm that, with high
probability,\footnote{Throughout, with high probability (whp) means with
probability at least $1 - n^{-c}$, for some fixed, positive constant $c$.}
computes an MST and runs in $\tilde{O}(\min\{\frac{1}{\sqrt{\epsilon(n)}}
2^{O(\sqrt{\log n})}, D + \sqrt{n}\})$ rounds\footnote{The notation $\tilde{O}$
hides a $\polylog(n)$ factor and $\tilde{\Omega}$ hides a
$\frac{1}{\polylog{(n)}}$ factor, where $n$ is the number of nodes of the
graph.} where $\epsilon$ is the smoothing parameter, $D$ is the network
diameter and $n$ is the network size. To complement our upper bound, we also
show a lower bound of $\tilde{\Omega}(\min\{\frac{1}{\sqrt{\epsilon(n)}},
D+\sqrt{n}\})$. We note that the upper and lower bounds essentially match
except for a multiplicative $2^{O(\sqrt{\log n})} \polylog(n)$ factor.
  Our work can be considered as a first step in understanding the smoothed
complexity of distributed graph algorithms.


  We present an open-source database of superconducting quantum device designs
that may be used as the starting point for customized devices. Each design can
be generated programmatically using the open-source Qiskit Metal package, and
simulated using finite-element electromagnetic solvers. We present a robust
workflow for achieving high accuracy on design simulations. Many designs in the
database are experimentally validated, showing excellent agreement between
simulated and measured parameters. Our database includes a front-end interface
that allows users to generate ``best-guess'' designs based on desired circuit
parameters. This project lowers the barrier to entry for research groups
seeking to make a new class of devices by providing them a well-characterized
starting point from which to refine their designs.


  Strong cavity coupling of gas-phase molecules will enable studies of
benchmark chemical processes under strong light-matter interactions with a high
level of experimental control and no solvent effects. We recently demonstrated
the formation of gas-phase molecular polaritons by strongly coupling the bright
$\nu_3$, $J=3 \rightarrow 4$ rovibrational transitions of methane (CH$_4$) to a
Fabry-P\'{e}rot optical cavity mode inside a cryogenic buffer gas cell. Here,
we further explore the flexible capabilities of this infrastructure. We show
that we can greatly increase the collective coupling strength of the molecular
ensemble to the cavity by increasing the intracavity CH$_4$ number density. In
doing so, we can tune from the single-mode coupling regime to the multimode
coupling regime in which many nested polaritonic states arise as the Rabi
splitting approaches the cavity mode spacing. We explore polariton formation
for cavity geometries of varying length, finesse, and mirror radius of
curvature. We also report a proof-of-principle demonstration of rovibrational
gas-phase polariton formation at room temperature. This experimental
flexibility affords a great degree of control over the properties of molecular
polaritons and opens up a wider range of simple molecular processes to future
interrogation under strong cavity-coupling. We anticipate that ongoing work in
gas-phase polaritonics will facilitate convergence between experimental results
and theoretical models of cavity-altered chemistry and physics.


  We present analysis and photoionization modeling of the Chandra high
resolution spectrum of Mrk 279. There is clear evidence of an absorbing outflow
which is best fit by a two component model, one with a low ionization parameter
and one with a higher ionization parameter. The column density of the X-ray
warm absorber, about log N_H=20, is the smallest known of all AGNs in which
X-ray absorbing outflows are observed. We find that the X-ray and UV/FUV
absorbers are part of the same overall outflow. There is some evidence of
super-solar carbon, nitrogen, oxygen and iron in the Chandra spectrum of Mrk
279. While this is not a robust result in itself, Chandra data in combination
with the UV data and the pressure equilibrium between two phases of the
outflow, support the scenario of super-solar abundances. This the first case
where super-solar abundances are reported in the nucleus of a normal Seyfert
galaxy. The data suggest that the outflow originates from a compact region
around the nuclear black hole and that it carries insignificant amount of mass
and energy.


  In this paper, we analyze vertex-centered finite volume method (FVM) of any
order for elliptic equations on rectangular meshes. The novelty is a unified
proof of the inf-sup condition, based on which, we show that the FVM
approximation converges to the exact solution with the optimal rate in the
energy norm. Furthermore, we discuss superconvergence property of the FVM
solution. With the help of this superconvergence result, we find that the FVM
solution also converges to the exact solution with the optimal rate in the
$L^2$-norm. Finally, we validate our theory with several numerical experiments.


  Delattre et al. (2013) investigated asymptotic properties of the maximum
likelihood estimator of the population parameters of the random effects
associated with n independent stochastic differential equations (SDEs) assuming
that the SDEs are independent and identical (iid).
  In this article, we consider the Bayesian approach to learning about the
population parameters, and prove consistency and asymptotic normality of the
corresponding posterior distribution in the iid set-up as well as when the SDEs
are independent but non-identical.


  A transversely holomorphic foliation on a compact complex manifold, exhibits
a compact stable leaf if and only if the set of compact leaves is not a zero
measure subset of the manifold.


  A Luttinger liquid (LL) describes low energy excitations of many interacting
one dimensional systems, and exhibits universal response both in and out of
equilibrium. We analyze its behaviour in the non-hermitian realm after quantum
quenching to a PT-symmetric LL by focusing on the fermionic single particle
density matrix. For short times, we demonstrate the emergence of unique
phenomena, characteristic to non-hermitian systems, that correlations propagate
faster than the conventional maximal speed, known as the Lieb-Robinson bound.
These emergent supersonic modes travel with velocities that are multiples of
the conventional light-cone velocity. This behaviour is argued to be generic
for correlators in non-hermitian systems. In the long time limit, we find
typical LL behaviour, extending the LL universality to the non-equilibrium
non-hermitian case. Our analytical results are benchmarked numerically and
indicate that the dispersal of quantum information is much faster in
non-hermitian systems.


  We give a realization of crystal graphs for basic representations of the
quantum affine algebra $U_q(C_2^{(1)})$ in terms of new combinatorial objects
called the Young walls.


  In organic semiconductors working under ambient circumstance, there are
remarkable quantum effects lack of comprehensive understanding, and an exotic
composite particle named charge transfer (CT) exciton is normally regarded as
the key ingredient. Another essential substance is the phonons stemming from
intra- and inter-molecular vibrations, and the relevant diagonal
electron-phonon couplings give rise to spatial localization and the
off-diagonal couplings refer to the dispersion of electron wavefunctions. In
this work, we first propose a toy model based upon the fracton physics to
phenomenologically unveil the coherent motion of CT excitons followed by
resonant phonons in the aggregates. Based on this model, a generic scenario of
hierarchical quantum effects is described in various material systems. To
examine whether the fracton model can be applicable in practice, we calculate
the out-of-time-ordered correlator (OTOC), a quantum dynamic measurement of the
entanglement entropy, of CT excitons by the adaptive time-dependent density
matrix renormalization group algorithm. On the basis of three commonly-used
realistic models in organic materials with two competing interactions taking
into account, we investigate the irreducible roles of CT excitons and aggregate
phonons in the ultrafast charge transfer, the coherent polaron hopping, and the
dissociation of triplet pairs, respectively. Our theory unifies the charge,
exciton, spin and phonons into a single framework, which may help clarify the
complicated and diverse quantum effects in organic semiconductors.


  The hydronium cation plays a crucial role in interstellar oxygen and water
chemistry. While its spectroscopy was extensively investigated earlier, the
collisional excitation of H$_3$O$^+$ is not well studied yet. In this work we
present state-to-state collisional data for rotational de-excitation of both
ortho- and para-H$_3$O$^+$ due to para-H$_2$ impact. The cross sections are
calculated within the close-coupling formalism using our recent, highly
accurate rigid-rotor potential energy surface for this collision system. The
corresponding thermal rate coefficients are calculated up to 100 K. For
para-H$_3$O$^+$ the lowest 20 rotation-inversion states were considered in the
calculations, while for ortho-H$_3$O$^+$ the lowest 11 states are involved (up
to $j\leq5$), so all levels with rotational energy below 420 K (292 cm$^{-1}$)
are studied. In order to analyse the impact of the new collisional rates on the
excitation of H$_3$O$^+$ in astrophysical environments radiative transfer
calculations are also provided. The most relevant emission lines from an
astrophysical point of view are studied, taking into account the transitions at
307, 365, 389 and 396 GHz. We show that our new collisional data have a
non-negligible impact (from a few percents up to about a factor of 3) on the
brightness and excitation temperatures of H$_3$O$^+$, justifying the revision
of the physical conditions in the appropriate astrophysical observations. The
calculated rate coefficients allow one to recalculate the column density of
hydronium in interstellar clouds, which can lead to a better understanding of
interstellar water and oxygen chemistry.


  We construct a family of homomorphisms between Weyl modules for affine Lie
algebras in characteristic p, which supports our conjecture on the strong
linkage principle in this context. We also exhibit a large class of reducible
Weyl modules beyond level one, for p not necessarily small.


  I review the present status of measurements at RHIC and suggest possible
upgrades which will be necessary to answer some of the most critical questions
in Relativistic Heavy Ion Physics.


  We study the cosmological evolution of a scalar field in Horndeski gravity,
assuming that the scalar field is subdominant with respect to the cosmic fluid.
We first analyse the most general shift-symmetric action that respects local
Lorentz symmetry. We show that the bound on the speed of gravitational waves
set by GW170817+GRB170817A imposes a constraint only on the linear coupling
between the scalar and the Gauss-Bonnet invariant and this constraint is rather
mild. Then, we consider some interesting examples of theories that break
shift-symmetry, such as the Damour-Esposito-Far\`ese model of spontaneous
scalarization and a theory with a quadratic coupling to the Gauss-Bonnet
invariant that can lead to black hole scalarization. In both cases, tuning of
cosmological initial conditions is necessary to keep the scalar field dormant
during cosmic evolution.


  Given any two Einstein (pseudo-)metrics, with scalar curvatures suitably
related, we give an explicit construction of a Poincar\'e-Einstein
(pseudo-)metric with conformal infinity the conformal class of the product of
the initial metrics. We show that these metrics are equivalent to ambient
metrics for the given conformal structure. The ambient metrics have holonomy
that agrees with the conformal holonomy. In the generic case the ambient metric
arises directly as a product of the metric cones over the original Einstein
spaces. In general the conformal infinity of the Poincare metrics we construct
is not Einstein, and so this describes a class of non-conformally Einstein
metrics for which the (Fefferman-Graham) obstruction tensor vanishes.


  Small-angle scattering (SAS) techniques, which utilize neutrons and X-rays,
are employed in various scientific fields, including materials science,
biochemistry, and polymer physics. During the analysis of SAS data, model
parameters that contain information about the sample are estimated by fitting
the observational data to a model of sample. Previous research has demonstrated
the effectiveness of Bayesian inference in analyzing SAS data using a sphere
model. However, compared with the sphere model, the core-shell model, which
represents functional nanoparticles, offers higher application potential and
greater analytical value. Therefore, in this study, we propose an analytical
method for the more complex and practical core-shell model based on Bayesian
inference. Through numerical experiments, we evaluated the performance of this
method under different conditions, including measurement times, number of data
points, and differences in scattering length density. As a result, we clarify
the conditions under which accurate estimations are possible.


  Self-consistent equations for intrinsic rotation in tokamaks with small
poloidal magnetic field $B_p$ compared to the total magnetic field $B$ are
derived. The model gives the momentum redistribution due to turbulence,
collisional transport and energy injection. Intrinsic rotation is determined by
the balance between the momentum redistribution and the turbulent diffusion and
convection. Two different turbulence regimes are considered: turbulence with
characteristic perpendicular lengths of the order of the ion gyroradius,
$\rho_i$, and turbulence with characteristic lengths of the order of the
poloidal gyroradius, $(B/B_p) \rho_i$. Intrinsic rotation driven by gyroradius
scale turbulence is mainly due to the effect of neoclassical corrections and of
finite orbit widths on turbulent momentum transport, whereas for the intrinsic
rotation driven by poloidal gyroradius scale turbulence, the slow variation of
turbulence characteristics in the radial and poloidal directions and the
turbulent particle acceleration can be become as important as the neoclassical
and finite orbit width effects. The magnetic drift is shown to be indispensable
for the intrinsic rotation driven by the slow variation of turbulence
characteristics and the turbulent particle acceleration. The equations are
written in a form conducive to implementation in a flux tube code, and the
effect of the radial variation of the turbulence is included in a novel way
that does not require a global gyrokinetic formalism.


  Medical image segmentation is one of the most fundamental tasks concerning
medical information analysis. Various solutions have been proposed so far,
including many deep learning-based techniques, such as U-Net, FC-DenseNet, etc.
However, high-precision medical image segmentation remains a highly challenging
task due to the existence of inherent magnification and distortion in medical
images as well as the presence of lesions with similar density to normal
tissues. In this paper, we propose TFCNs (Transformers for Fully Convolutional
denseNets) to tackle the problem by introducing ResLinear-Transformer
(RL-Transformer) and Convolutional Linear Attention Block (CLAB) to
FC-DenseNet. TFCNs is not only able to utilize more latent information from the
CT images for feature extraction, but also can capture and disseminate semantic
features and filter non-semantic features more effectively through the CLAB
module. Our experimental results show that TFCNs can achieve state-of-the-art
performance with dice scores of 83.72\% on the Synapse dataset. In addition, we
evaluate the robustness of TFCNs for lesion area effects on the COVID-19 public
datasets. The Python code will be made publicly available on
https://github.com/HUANGLIZI/TFCNs.


  We report on the high-pressure growth, structural characterization, and
investigation of the electronic properties of single-crystalline LaFeAsO
co-substituted by Sm and P, in both its normal- and superconducting states.
Here, the appearance of superconductivity is attributed to the inner chemical
pressure induced by the smaller-size isovalent substituents. X-ray structural
refinements show that the partial substitution of La by Sm and As by P in the
parent LaFeAsO compound leads to a contraction in both the conducting
Fe2(As,P)2 layers and the interlayer spacing. The main parameters of the
superconducting state, including the critical temperature, the lower- and upper
critical fields, as well as the coherence length, the penetration depth, and
their anisotropy, were determined from magnetometry measurements on a
single-crystalline La0.87Sm0.13FeAs0.91P0.09O sample. The critical current
density (jc), as resulting from loops of magnetization hysteresis in the
self-generated magnetic field, is 2 x 106 A/cm2 at 2 K. Overall, our findings
illustrate a rare and interesting case of how superconductivity can be induced
by co-substitution in the 1111 family. Such approach delineates new
possibilities in the creation of superconductors by design, thus stimulating
the exploration of related systems under multi-chemical pressure conditions.


  Just as the Temperley-Lieb algebra is a good place to compute the Jones
polynomial, the Kauffman bracket skein algebra of a disk with $2k$ colored
points on the boundary, each with color $n$, is a good place to compute the
$n^{th}$ colored Jones polynomial. Here, this colored skein algebra is shown to
be a cellular algebra and a set of separating Jucys-Murphy elements is
provided. This is done by explicitly providing the cellular basis and the
JM-elements. Having done this several results of Mathas on such algebras are
considered, including the construction of pairwise non-isomorphic irreducible
submodules and their corresponding primitive idempotents. These idempotents are
then used to define recursive elements of the colored skein algebra. Recursive
elements are of particular interest as they have been used to relate geometric
properties of link diagrams to the Mahler measure of the Jones polynomial. In
particular, a single proof is given for the result of Champanerkar and Kofman,
that the Mahler measure of the Jones and colored Jones polynomial converges
under twisting on some number of strands.


  We give an exact spectral equivalence between the quantum group invariant XXZ
chain with arbitrary left boundary term and the same XXZ chain with purely
diagonal boundary terms.
  This equivalence, and a further one with a link pattern Hamiltonian, can be
understood as arising from different representations of the one-boundary
Temperley-Lieb algebra. For a system of size L these representations are all of
dimension 2^L and, for generic points of the algebra, equivalent. However at
exceptional points they can possess different indecomposable structures.
  We study the centralizer of the one-boundary Temperley-Lieb algebra in the
'non-diagonal' spin-1/2 representation and find its eigenvalues and
eigenvectors. In the exceptional cases the centralizer becomes indecomposable.
We show how to get a truncated space of 'good' states. The indecomposable part
of the centralizer leads to degeneracies in the three mentioned Hamiltonians.


  In this paper, we introduce a novel approach for active contours with free
endpoints. A scheme is presented for image segmentation and restoration based
on a discrete version of the Mumford-Shah functional where the contours can be
both closed and open curves. Additional to a flow of the curves in normal
direction, evolution laws for the tangential flow of the endpoints are derived.
Using a parametric approach to describe the evolving contours together with an
edge-preserving denoising, we obtain a fast method for image segmentation and
restoration. The analytical and numerical schemes are presented followed by
numerical experiments with artificial test images and with a real medical
image.


  Single photon emitters (SPEs) in low-dimensional layered materials have
recently gained a large interest owing to the auspicious perspectives of
integration and extreme miniaturization offered by this class of materials.
However, accurate control of both the spatial location and the emission
wavelength of the quantum emitters is essentially lacking to date, thus
hindering further technological steps towards scalable quantum photonic
devices. Here, we evidence SPEs in high purity synthetic hexagonal boron
nitride (hBN) that can be activated by an electron beam at chosen locations.
SPE ensembles are generated with a spatial accuracy better than the cubed
emission wavelength, thus opening the way to integration in optical
microstructures. Stable and bright single photon emission is subsequently
observed in the visible range up to room temperature upon non-resonant laser
excitation. Moreover, the low-temperature emission wavelength is reproducible,
with an ensemble distribution of width 3 meV, a statistical dispersion that is
more than one order of magnitude lower than the narrowest wavelength spreads
obtained in epitaxial hBN samples. Our findings constitute an essential step
towards the realization of top-down integrated devices based on identical
quantum emitters in 2D materials.


  Large field excursions are required in a number of axion models of inflation.
These models also possess global cosmic strings, around which the axion follows
a path mirroring the inflationary trajectory. Cosmic strings are thus an
interesting theoretical laboratory for the study of transplanckian field
excursions. We describe connections between various effective field theory
models of axion monodromy and study the classical spacetimes around their
supercritical cosmic strings. For small decay constants $f<M_p$ and large
winding numbers $n>M_p/f$, the EFT is under control and the string cores
undergo topological inflation, which may be either of exponential or power-law
type. We show that the exterior spacetime is nonsingular and equivalent to a
decompactifying cigar geometry, with the radion rolling in a potential
generated by axion flux. Signals are able to circumnavigate infinite straight
strings in finite but exponentially long time, $t\sim e^{\Delta a/M_p}$. For
finite loops of supercritical string in asymptotically flat space, we argue
that if topological inflation occurs, then topological censorship implies
transplanckian censorship, or that external observers are forbidden from
threading the loop and observing the full excursion of the axion.


  We introduce the class of projective reflection groups which includes all
complex reflection groups. We show that several aspects involving the
combinatorics and the representation theory of all non exceptional irreducible
complex reflection groups find a natural description in this wider setting.


  Genome-wide association studies (GWAS) are used to identify relationships
between genetic variations and specific traits. When applied to
high-dimensional medical imaging data, a key step is to extract
lower-dimensional, yet informative representations of the data as traits.
Representation learning for imaging genetics is largely under-explored due to
the unique challenges posed by GWAS in comparison to typical visual
representation learning. In this study, we tackle this problem from the mutual
information (MI) perspective by identifying key limitations of existing
methods. We introduce a trans-modal learning framework Genetic InfoMax (GIM),
including a regularized MI estimator and a novel genetics-informed transformer
to address the specific challenges of GWAS. We evaluate GIM on human brain 3D
MRI data and establish standardized evaluation protocols to compare it to
existing approaches. Our results demonstrate the effectiveness of GIM and a
significantly improved performance on GWAS.


  We introduce a new multimode cavity QED architecture for superconducting
circuits which can be used to implement photonic memories, more efficient
Purcell filters, and quantum simulations of photonic materials. We show that
qubit interactions mediated by multimode cavities can have exponentially
improved contrast for two qubit gates without sacrificing gate speed. Using
two-qubits coupled via a three-mode cavity system we spectroscopically observe
multimode strong couplings up to 102MHz and demonstrate suppressed interactions
off-resonance of 10kHz when the qubits are ~600MHz detuned from the cavity
resonance. We study Landau-Zener transitions in our multimode systems and
demonstrate quasi-adiabatic loading of single photons into the multimode cavity
in 25ns. We introduce an adiabatic gate protocol to realize a controlled-Z gate
between the qubits in 95ns and create a Bell state with 94.7% fidelity. This
corresponds to an on/off ratio (gate contrast) of 1000.


  The complex geometry underlying the Schr\"odinger dynamics of coherent states
for non-Hermitian Hamiltonians is investigated. In particular two seemingly
contradictory approaches are compared: (i) a complex WKB formalism, for which
the centres of coherent states naturally evolve along complex trajectories,
which leads to a class of complexified coherent states; (ii) the investigation
of the dynamical equations for the real expectation values of position and
momentum, for which an Ehrenfest theorem has been derived in a previous paper,
yielding real but non-Hamiltonian classical dynamics on phase space for the
real centres of coherent states. Both approaches become exact for quadratic
Hamiltonians. The apparent contradiction is resolved building on an observation
by Huber, Heller and Littlejohn, that complexified coherent states are
equivalent if their centres lie on a specific complex Lagrangian manifold. A
rich underlying complex symplectic geometry is unravelled. In particular a
natural complex structure is identified that defines a projection from complex
to real phase space, mapping complexified coherent states to their real
equivalents.


  We present an extensive analysis on several string solutions in AdS_5 x Ypq
and find some interesting properties of their energy-spin relations. Their
energy depends always on the parameter a(p,q) which characterizes these
manifolds. The range of this parameter for the string solutions is constrained
by the Sasaki-Einstein constraints that the solutions should satisfy. Hence
some string solutions we find are not valid for the whole class of Ypq
manifolds. For some of our solutions, when the maximum allowed value of a(p,q)
corresponds to the string approaching the poles of the squashed sphere in Ypq,
their energy at this limit approaches the BPS one. Thus certain non-BPS string
solutions in the whole class of Sasaki-Einstein manifolds, can become BPS in
particular manifolds. For the solutions with this property we point out that
this behavior is independent of the string motion in the other directions on
the manifold. We expect that in the field theory the corresponding generic
operators to these semi-classical strings, become BPS at certain quivers.


  We prove a nonequilibirum central limit theorem for the position of a tagged
particle in the one-dimensional nearest-neighbor symmetric simple exclusion
process under diffusive scaling starting from a Bernoulli product measure
associated to a smooth profile $\rho_0:\bb R\to [0,1]$.


  Series elastic actuators (SEA) are playing an increasingly important role in
the fields of physical human-robot interaction. This paper focuses on the
modeling and control of a cable-driven SEA. First, the scheme of the
cable-driven SEA has been proposed, and a velocity controlled DC motor has been
used as its power source. Based on this, the model of the cable-driven SEA has
been built up. Further, a two degrees of freedom (2-DOF) control approach has
been employed to control the output torque. Simulation results have shown that
the 2-DOF method has achieved better robust performance than the PD method.


  We study the regularity of the viscosity solution $u$ of the
$\sigma_k$-Loewner-Nirenberg problem on a bounded smooth domain $\Omega \subset
\mathbb{R}^n$ for $k \geq 2$. It was known that $u$ is locally Lipschitz in
$\Omega$. We prove that, with $d$ being the distance function to
$\partial\Omega$ and $\delta > 0$ sufficiently small, $u$ is smooth in $\{0 <
d(x) < \delta\}$ and the first $(n-1)$ derivatives of $d^{\frac{n-2}{2}} u$ are
H\"older continuous in $\{0 \leq d(x) < \delta\}$. Moreover, we identify a
boundary invariant which is a polynomial of the principal curvatures of
$\partial\Omega$ and its covariant derivatives and vanishes if and only if
$d^{\frac{n-2}{2}} u$ is smooth in $\{0 \leq d(x) < \delta\}$. Using a relation
between the Schouten tensor of the ambient manifold and the mean curvature of a
submanifold and related tools from geometric measure theory, we further prove
that, when $\partial\Omega$ contains more than one connected components, $u$ is
not differentiable in $\Omega$.


  The survey is devoted to algebraic structures related to integrable ODEs and
evolution PDEs. A description of Lax representations is given in terms of
vector space decomposition of loop algebras into a direct sum of Taylor series
and a complementary subalgebra. Examples of complementary subalgebras and
corresponding integrable models are presented. In the framework of the
bi-Hamiltonian approach compatible associative algebras related affine Dynkin
diagrams are considered. A bi-Hamiltonian origin of the classical elliptic
Calogero-Moser models is revealed.


  We discuss the physics of the high temperature superconductivity in hole
doped copper oxide ceramics in the pseudogap region. Starting from an effective
reduced Hamiltonian relevant to the dynamics of holes injected into the copper
oxide layers proposed in a previous paper, we determine the superconductive
condensate wavefunction. We show that the low-lying elementary condensate
excitations are analogous to the rotons in superfluid $^4He$. We argue that the
rotons-like excitations account for the specific heat anomaly at the critical
temperature. We discuss and compare with experimental observations the London
penetration length, the Abrikosov vortices, the upper and lower critical
magnetic fields, and the critical current density. We give arguments to explain
the origin of the Fermi arcs and Fermi pockets. We investigate the nodal gap in
the cuprate superconductors and discuss both the doping and temperature
dependence of the nodal gap. We suggest that the nodal gap is responsible for
the doping dependence of the so-called nodal Fermi velocity detected in angle
resolved photoemission spectroscopy studies. We discuss the thermodynamics of
the nodal quasielectron liquid and their role in the low temperature specific
heat. We propose that the ubiquitous presence of charge density wave in hole
doped cuprate superconductors in the pseudogap region originates from
instabilities of the nodal quasielectrons driven by the interaction with the
planar $CuO_2$ lattice. We investigate the doping dependence of the charge
density wave gap and the competition between charge order and
superconductivity. We discuss the effects of external magnetic fields on the
charge density wave gap and elucidate the interplay between charge density wave
and Abrikosov vortices. Finally, we examine the physics underlying quantum
oscillations in the pseudogap region.


  A numerical method is presented for first-principle simulations of charged
colloidal dispersions in electrolyte solutions. Utilizing a smoothed profile
for colloid-solvent boundaries, efficient mesoscopic simulations are enabled
for modeling dispersions of many colloidal particles exhibiting many-body
electrostatic interactions. The validity of the method was examined for simple
colloid geometries, and the efficiency was demonstrated by calculating stable
structures of two-dimensional dispersions, which resulted in the formation of
colloidal crystals.


  Compressed sensing (CS) has been playing a key role in accelerating the
magnetic resonance imaging (MRI) acquisition process. With the resurgence of
artificial intelligence, deep neural networks and CS algorithms are being
integrated to redefine the state of the art of fast MRI. The past several years
have witnessed substantial growth in the complexity, diversity, and performance
of deep learning-based CS techniques that are dedicated to fast MRI. In this
meta-analysis, we systematically review the deep learning-based CS techniques
for fast MRI, describe key model designs, highlight breakthroughs, and discuss
promising directions. We have also introduced a comprehensive analysis
framework and a classification system to assess the pivotal role of deep
learning in CS-based acceleration for MRI.


  We study the problem of the damping of collective modes close to a
Pomeranchuk quantum critical point in a Fermi liquid. In analogy with problems
in dissipative open quantum systems, we derive the Landau damping of a Fermi
liquid by integrating out a macroscopic number of degrees of freedom from a
generating functional. Being a reformulation of the linearized Boltzmann
equation this approach reproduces well-known results from the theory of Fermi
liquids. We also study the Bethe-Salpeter equations within the Landau theory
and discuss the implications of these results on quantum phase transitions of
the Pomeranchuk type and its dynamical exponent, z. We apply our results to the
electronic nematic instability and find z=3 in the collisionless limit.


  This paper introduces a new stochastic hybrid system (SHS) framework for
contingency detection in modern power systems (MPS). The framework uses
stochastic hybrid system representations in state space models to expand and
facilitate capability of contingency detection. In typical microgrids (MGs),
buses may contain various synchronous generators, renewable generators,
controllable loads, battery systems, regular loads, etc. For development of SHS
models in power systems, this paper introduces the concept of dynamic and
non-dynamic buses. By converting a physical power grid into a virtual
linearized state space model and representing contingencies as random switching
of system structures and parameters, this paper formulates the contingency
detection problem as a joint estimation problem of discrete event and
continuous states in stochastic hybrid systems. This method offers unique
advantages, including using common measurement signals on voltage and current
synchrophasors to detect different types and locations of contingencies,
avoiding expensive local direct fault measurements and detecting certain
contingencies that cannot be directly measured. The method employs a small and
suitably-designed probing signal to sustain the ability of persistent
contingency detection. Joint estimation algorithms are presented with their
proven convergence and reliability properties. Examples that use an IEEE 5-bus
system demonstrate the main ideas and derivation steps. Simulation case studies
on an IEEE 33-bus system are used for detecting transmission line faults and
sensor interruptions.


  Jackknife empirical likelihood (JEL) is an effective modified version of
empirical likelihood method (EL). Through the construction of the jackknife
pseudo-values, JEL overcomes the computational difficulty of EL method when its
constraints are nonlinear while maintaining the same asymptotic results for one
sample and two-sample U statistics. In this paper, we propose an adjusted
version of JEL to guarantee that the adjusted jackknife empirical likelihood
(AJEL) statistic is well-defined for all the values of the parameter, instead
of restricting on the convex hull of the estimation equation. The properties of
JEL have been preserved for AJEL.


  We study the effects of temperature on the band structure of the Bi$_2$Se$_3$
family of topological insulators using first-principles methods. Increasing
temperature drives these materials towards the normal state, with similar
contributions from thermal expansion and from electron-phonon coupling. The
band gap changes with temperature reach $0.3$ eV at $600$ K, of similar size to
the changes caused by electron correlation. Our results suggest that
temperature-induced topological phase transitions should be observable near
critical points of other external parameters.


  We construct a metamaterial from radio-frequency harmonic oscillators, and
find two topologically distinct phases resulting from dissipation engineered
into the system. These phases are distinguished by a quantized value of bulk
energy transport. The impulse response of our circuit is measured and used to
reconstruct the band structure and winding number of circuit eigenfunctions
around a dark mode. Our results demonstrate that dissipation can lead to
topological transport in a much wider class of physical systems than considered
before.


  In the summarization domain, a key requirement for summaries is to be
factually consistent with the input document. Previous work has found that
natural language inference (NLI) models do not perform competitively when
applied to inconsistency detection. In this work, we revisit the use of NLI for
inconsistency detection, finding that past work suffered from a mismatch in
input granularity between NLI datasets (sentence-level), and inconsistency
detection (document level). We provide a highly effective and light-weight
method called SummaCConv that enables NLI models to be successfully used for
this task by segmenting documents into sentence units and aggregating scores
between pairs of sentences. On our newly introduced benchmark called SummaC
(Summary Consistency) consisting of six large inconsistency detection datasets,
SummaCConv obtains state-of-the-art results with a balanced accuracy of 74.4%,
a 5% point improvement compared to prior work. We make the models and datasets
available: https://github.com/tingofurro/summac


  Edge theories of symmetry-protected topological phases are well-known to
possess global symmetry anomalies. In this work we focus on two-dimensional
bosonic phases protected by an on-site symmetry and analyse the corresponding
edge anomalies in more detail. Physical interpretations of the anomaly in terms
of an obstruction to orbifolding and constructing symmetry-preserving
boundaries are connected to the cohomology classification of symmetry-protected
phases in two dimensions. Using the tensor network and matrix product state
formalism we numerically illustrate our arguments and discuss computational
detection schemes to identify symmetry-protected order in a ground state wave
function.


  The invariant differential cross section of inclusive $\omega(782)$ meson
production at midrapidity ($|y|<0.5$) in pp collisions at $\sqrt{s}$ = 7 TeV
was measured with the ALICE detector at the LHC over a transverse momentum
range of 2 < $p_{\rm{T}}$ < 17 GeV/$c$. The $\omega$ meson was reconstructed
via its $\omega\rightarrow\pi^+\pi^-\pi^0$ decay channel. The measured $\omega$
production cross section is compared to various calculations: PYTHIA 8.2 Monash
2013 describes the data, while PYTHIA 8.2 Tune 4C overestimates the data by
about 50%. A recent NLO calculation, which includes a model describing the
fragmentation of the whole vector-meson nonet, describes the data within
uncertainties below 6 GeV/$c$, while it overestimates the data by up to 50% for
higher $p_{\rm{T}}$. The $\omega/\pi^0$ ratio is in agreement with previous
measurements at lower collision energies and the PYTHIA calculations. In
addition, the measurement is compatible with transverse mass scaling within the
measured $p_{\rm{T}}$ range and the ratio is constant with $C^{\omega/\pi^{0}}$
= 0.67 $\pm$ 0.03 (stat) $\pm$ 0.04 (sys) above a transverse momentum of 2.5
GeV/$c$.


  Cerebral arterial blood flow (CABF) can be investigated in few seconds
without any synchronization by Real-Time phase contrast. Significant changes in
CABF were found between expiration and inspiration during normal breathing of
healthy volunteers. Synopsis (100/100) Real-time phase contrast MRI has been
applied to investigate cerebral arterial blood flow (CABF) during normal
breathing of healthy volunteers. We developed a novel time-domain analysis
method to quantify the effect of normal breathing on several parameters of
CABF. We found the existence of a delay between the recorded respiratory signal
from the belt sensor and the breathing frequency component present in the
reconstructed arterial blood flows. During the expiratory, the mean flow rate
of CABF increased by 4.4$\pm$1.7%, stroke volume of CABF increased by
9.8$\pm$3.1% and the duration of the cardiac period of CABF increased by
8.1$\pm$3%.


  To verify safety and robustness of neural networks, researchers have
successfully applied abstract interpretation, primarily using the interval
abstract domain. In this paper, we study the theoretical power and limits of
the interval domain for neural-network verification.
  First, we introduce the interval universal approximation (IUA) theorem. IUA
shows that neural networks not only can approximate any continuous function $f$
(universal approximation) as we have known for decades, but we can find a
neural network, using any well-behaved activation function, whose interval
bounds are an arbitrarily close approximation of the set semantics of $f$ (the
result of applying $f$ to a set of inputs). We call this notion of
approximation interval approximation. Our theorem generalizes the recent result
of Baader et al. (2020) from ReLUs to a rich class of activation functions that
we call squashable functions. Additionally, the IUA theorem implies that we can
always construct provably robust neural networks under $\ell_\infty$-norm using
almost any practical activation function.
  Second, we study the computational complexity of constructing neural networks
that are amenable to precise interval analysis. This is a crucial question, as
our constructive proof of IUA is exponential in the size of the approximation
domain. We boil this question down to the problem of approximating the range of
a neural network with squashable activation functions. We show that the range
approximation problem (RA) is a $\Delta_2$-intermediate problem, which is
strictly harder than $\mathsf{NP}$-complete problems, assuming
$\mathsf{coNP}\not\subset \mathsf{NP}$. As a result, IUA is an inherently hard
problem: No matter what abstract domain or computational tools we consider to
achieve interval approximation, there is no efficient construction of such a
universal approximator.


  B[e] type stars are characterised by strong emission lines, photometric $\&$
spectroscopic variabilities and unsteady mass-loss rates. MWC 137 is a galactic
B[e] type star situated in the constellation Orion. Recent photometric
observation of MWC 137 by TESS has revealed variabilities with a dominant
period of 1.9 d. The origin of this variability is not known but suspected to
be from stellar pulsation. To understand the nature and origin of this
variability, we have constructed three different set of models of MWC 137 and
performed non-adiabatic linear stability analysis. Several low order modes are
found to be unstable in which models having mass in the range of 31 to 34
M$_{\odot}$ and 43 to 46 M$_{\odot}$ have period close to 1.9 d. The evolution
of instabilities in the non-linear regime for model having solar chemical
composition and mass of 45 M$_{\odot}$ leads to finite amplitude pulsation with
a period of 1.9 d. Therefore in the present study we confirm that this
variability in MWC 137 is due to pulsation. Evolutionary tracks passing through
the location of MWC 137 in the HR diagram indicate that the star is either in
post main sequence evolutionary phase or about to enter in this evolutionary
phase.


  Customer data typically is held in database systems, which can be seen as
rule-based knowledge base, whereas businesses increasingly want to benefit from
the capabilities of large, pre-trained language models.
  In this technical report, we describe a case study of how a commercial rule
engine and an integrated neural chatbot may be integrated, and what level of
control that particular integration mode leads to. We also discuss alternative
ways (including past ways realized in other systems) how researchers strive to
maintain control and avoid what has recently been called model "hallucination".


  We investigate the deformation of an $L_\infty$ structure that encodes the
geometric information about a smooth vector bundle. We establish that this
specific type of deformation endows the bundle with a Lie algebroid structure.
Additionally, we compute the Atiyah class and Atiyah-Chern classes in the
geometrically deformed case. The precise relationship between the first
Atiyah-Chern class and the modular class is shown. In the case of action Lie
algebroids, the Atiyah-Chern classes at the leading order are given by the
equivariant Chern characters.


  We propose a generalization of Quillen's exact category -- arithmetic exact
category and we discuss conditions on such categories under which one can
establish the notion of Harder-Narasimhan filtrations and Harder-Narsimhan
polygons. Furthermore, we show the functoriality of Harder-Narasimhan
filtrations (indexed by $\mathbb R$), which can not be stated in the classical
setting of Harder and Narasimhan's formalism.


  A major quest in cosmology is the understanding of the nature of dark energy.
It is now well known that a combination of cosmological probes is required to
break the underlying degeneracies on cosmological parameters. In this paper, we
present a method, based on a frequentist approach, to combine probes without
any prior constraints, taking full account of the correlations in the
parameters. As an application, a combination of current SNIa and CMB data with
an evolving dark energy component is first compared to other analyses. We
emphasise the consequences of the implementation of the dark energy
perturbations on the result for a time varying equation of state. The impact of
future weak lensing surveys on the measurement of dark energy evolution is then
studied in combination with future measurements of the cosmic microwave
background and type Ia supernovae. We present the combined results for future
mid-term and long-term surveys and confirm that the combination with weak
lensing is very powerful in breaking parameter degeneracies. A second
generation of experiment is however required to achieve a 0.1 error on the
parameters describing the evolution of dark energy.


  This paper explores the use of Control Affine Neural Nonlinear AutoRegressive
eXogenous (CA-NNARX) models for nonlinear system identification and model-based
control design. The idea behind this architecture is to match the known
control-affine structure of the system to achieve improved performance.
Coherently with recent literature of neural networks for data-driven control,
we first analyze the stability properties of CA-NNARX models, devising
sufficient conditions for their incremental Input-to-State Stability
($\delta$ISS) that can be enforced at the model training stage. The model's
stability property is then leveraged to design a stable Internal Model Control
(IMC) architecture. The proposed control scheme is tested on a simulated
Quadruple Tank benchmark system to address the output reference tracking
problem. The results achieved show that (i) the modeling accuracy of CA-NNARX
is superior to the one of a standard NNARX model for given weight size and
training epochs, and (ii) the proposed IMC law provides performance comparable
to the ones of a standard Model Predictive Controller (MPC) at a significantly
lower computational burden.


  The posterior matching scheme, for feedback encoding of a message point lying
on the unit interval over memoryless channels, maximizes mutual information for
an arbitrary number of channel uses. However, it in general does not always
achieve any positive rate; so far, elaborate analyses have been required to
show that it achieves any positive rate below capacity. More recent efforts
have introduced a random "dither" shared by the encoder and decoder to the
problem formulation, to simplify analyses and guarantee that the randomized
scheme achieves any rate below capacity. Motivated by applications (e.g.
human-computer interfaces) where (a) common randomness shared by the encoder
and decoder may not be feasible and (b) the message point lies in a higher
dimensional space, we focus here on the original formulation without common
randomness, and use optimal transport theory to generalize the scheme for a
message point in a higher dimensional space. By defining a stricter, almost
sure, notion of message decoding, we use classical probabilistic techniques
(e.g. change of measure and martingale convergence) to establish succinct
necessary and sufficient conditions on when the message point can be recovered
from infinite observations: Birkhoff ergodicity of a random process
sequentially generated by the encoder. We also show a surprising "all or
nothing" result: the same ergodicity condition is necessary and sufficient to
achieve any rate below capacity. We provide applications of this message point
framework in human-computer interfaces and multi-antenna communications.


  Galaxy clusters can play a key role in modern cosmology provided their
evolution is properly understood. However, observed clusters give us only a
single timeframe of their dynamical state. Therefore, finding present
observable data of clusters that are well correlated to their assembly history
constitutes an inestimable tool for cosmology. Former studies correlating
environmental descriptors of clusters to their formation history are dominated
by halo mass - environment relations. This paper presents a mass-free
correlation between the present neighbor distribution of cluster-size halos and
the latter mass assembly history. From the Big Multidark simulation, we extract
two large samples of random halos with masses ranging from Virgo to Coma
cluster sizes. Additionally, to find the main environmental culprit for the
formation history of the Virgo cluster, we compare the Virgo-size halos to 200
Virgo-like halos extracted from simulations that resemble the local Universe.
The number of neighbors at different cluster-centric distances permits
discriminating between clusters with different mass accretion histories.
Similarly to Virgo-like halos, clusters with numerous neighbors within a
distance of about 2 times their virial radius experience a transition at z~1
between an active period of mass accretion, relative to the mean, and a quiet
history. On the contrary, clusters with few neighbors share an opposite trend:
from passive to active assembly histories. Additionally, clusters with massive
companions within about 4 times their virial radius tend to have recent active
merging histories. Therefore, the radial distribution of cluster neighbors
provides invaluable insights into the past history of these objects.


  We analytically compute, to linear order in the mass-ratio, the "geodetic"
spin precession frequency of a small spinning body orbiting a large
(non-spinning) body to the eight-and-a-half post-Newtonian order, thereby
extending previous analytical knowledge which was limited to the third
post-Newtonian level. These results are obtained applying analytical
gravitational self-force theory to the first-derivative level generalization of
Detweiler's gauge-invariant redshift variable. We compare our analytic results
with strong-field numerical data recently obtained by S.~R.~Dolan et al.
[Phys.\ Rev.\ D {\bf 89}, 064011 (2014)]. Our new, high-post-Newtonian-order
results capture the strong-field features exhibited by the numerical data. We
argue that the spin-precession will diverge as $\approx -0.14/(1-3y)$ as the
light-ring is approached. We transcribe our kinematical spin-precession results
into a corresponding improved analytic knowledge of one of the two
(gauge-invariant) effective gyro-gravitomagnetic ratios characterizing
spin-orbit couplings within the effective-one-body formalism. We provide
simple, accurate analytic fits both for spin-precession and the effective
gyro-gravitomagnetic ratio. The latter fit predicts that the
linear-in-mass-ratio correction to the gyro-gravitomagnetic ratio changes sign
before reaching the light-ring. This strong-field prediction might be important
for improving the analytic modeling of coalescing spinning binaries.


  We study homogeneous nucleation from a deeply quenched metastable liquid to a
spatially modulated phase. We find, for a general class of density functional
theories, that the universally favored nucleating droplet in dimensions $d \geq
3$ is spherically symmetric with radial modulations resembling the layers of an
onion. The existence of this droplet has important implications for systems
with effective long-range interactions, and potentially applies to polymers,
plasmas, and metals.


  We give a fixed-parameter tractable (FPT) approximation algorithm computing
the path-width of a tournament, and more generally, of a semi-complete digraph.
Based on this result, we prove that topological containment and rooted
immersion problems are FPT on semi-complete digraphs.


  A cosmological constant, Lambda, is the most natural candidate to explain the
origin of the dark energy (DE) component in the Universe. However, due to
experimental evidence that the equation of state (EOS) of the DE could be
evolving with time/redshift (including the possibility that it might behave
phantom-like near our time) has led theorists to emphasize that there might be
a dynamical field (or some suitable combination of them) that could explain the
behavior of the DE. While this is of course one possibility, here we show that
there is no imperative need to invoke such dynamical fields and that a variable
cosmological constant (including perhaps a variable Newton's constant too) may
account in a natural way for all these features.


  We introduce three spectral sequences which give some expressions of colored
Jones polynomials. Each spectral sequence contains a Khovanov-type homology
groups. Two of them are derived from a bicomplex of the colored Jones
polynomial. The other is the spectral sequence that deduces a colored Rasmussen
invariant of links. We also introduce three functors between categories of
nanophrases, generalizations of links, and obtain their applications using
colored Jones polynomials and their categorifications.


  In this article, we consider the estimation of the structural change point in
the nonparametric model with dependent observations. We introduce a
maximum-CUSUM-estimation procedure, where the CUSUM statistic is constructed
based on the sum-of-squares aggregation of the difference of the two
Nadaraya-Watson estimates using the observations before and after a specific
time point. Under some mild conditions, we prove that the statistic tends to
zero almost surely if there is no change, and is larger than a threshold
asymptotically almost surely otherwise, which helps us to obtain a
threshold-detection strategy. Furthermore, we demonstrate the strong
consistency of the change point estimator. In the simulation, we discuss the
selection of the bandwidth and the threshold used in the estimation, and show
the robustness of our method in the long-memory scenario. We implement our
method to the data of Nasdaq 100 index and find that the relation between the
realized volatility and the return exhibits several structural changes in
2007-2009.


  Large language models of code (Code-LLMs) have recently brought tremendous
advances to code completion, a fundamental feature of programming assistance
and code intelligence. However, most existing works ignore the possible
presence of bugs in the code context for generation, which are inevitable in
software development. Therefore, we introduce and study the buggy-code
completion problem, inspired by the realistic scenario of real-time code
suggestion where the code context contains potential bugs -- anti-patterns that
can become bugs in the completed program. To systematically study the task, we
introduce two datasets: one with synthetic bugs derived from semantics-altering
operator changes (buggy-HumanEval) and one with realistic bugs derived from
user submissions to coding problems (buggy-FixEval). We find that the presence
of potential bugs significantly degrades the generation performance of the
high-performing Code-LLMs. For instance, the passing rates of CODEGEN-2B-MONO
on test cases of buggy-HumanEval drop more than 50% given a single potential
bug in the context. Finally, we investigate several post-hoc methods for
mitigating the adverse effect of potential bugs and find that there remains a
significant gap in post-mitigation performance.


  Analog In-Memory Computing (AIMC) is emerging as a disruptive paradigm for
heterogeneous computing, potentially delivering orders of magnitude better peak
performance and efficiency over traditional digital signal processing
architectures on Matrix-Vector multiplication. However, to sustain this
throughput in real-world applications, AIMC tiles must be supplied with data at
very high bandwidth and low latency; this poses an unprecedented pressure on
the on-chip communication infrastructure, which becomes the system's
performance and efficiency bottleneck. In this context, the performance and
plasticity of emerging on-chip wireless communication paradigms provide the
required breakthrough to up-scale on-chip communication in large AIMC devices.
This work presents a many-tile AIMC architecture with inter-tile wireless
communication that integrates multiple heterogeneous computing clusters,
embedding a mix of parallel RISC-V cores and AIMC tiles. We perform an
extensive design space exploration of the proposed architecture and discuss the
benefits of exploiting emerging on-chip communication technologies such as
wireless transceivers in the millimeter-wave and terahertz bands.


  We discuss the observability of the lightest neutral Higgs boson in the
constrained MSSM (CMSSM), with universal soft supersymmetry-breaking
parameters, at hadron colliders such as the Tevatron and the LHC. We take
account of the constraints on parameter space provided by LEP, the measured
rate of b to s gamma decay, the cosmological relic density Omega h^2, and the
recent measurement of g_mu - 2. We normalize products of the expected CMSSM
Higgs production cross sections and decay branching ratios (sigma B)_CMSSM
relative to those expected for a Standard Model Higgs boson of the same mass.
In the h to gamma gamma channel, we find that (sigma B)_CMSSM > 0.85 (sigma
B)_SM. In the W/t tbar + h, h to b bbar channels, we find that (sigma B)_CMSSM
\~ 1.05 (sigma B)_SM. We conclude that the lightest CMSSM Higgs boson should be
almost as easy to see as the Standard Model Higgs boson: in particular, it
should be discoverable with about 15/fb of luminosity at the Tevatron or 10/fb
of luminosity at the LHC.


  Context-based copresence detection schemes are a necessary prerequisite to
building secure and usable authentication systems in the Internet of Things
(IoT). Such schemes allow one device to verify proximity of another device
without user assistance utilizing their physical context (e.g., audio). The
state-of-the-art copresence detection schemes suffer from two major
limitations: (1) they cannot accurately detect copresence in low-entropy
context (e.g., empty room with few events occurring) and insufficiently
separated environments (e.g., adjacent rooms), (2) they require devices to have
common sensors (e.g., microphones) to capture context, making them impractical
on devices with heterogeneous sensors. We address these limitations, proposing
Next2You, a novel copresence detection scheme utilizing channel state
information (CSI). In particular, we leverage magnitude and phase values from a
range of subcarriers specifying a Wi-Fi channel to capture a robust wireless
context created when devices communicate. We implement Next2You on
off-the-shelf smartphones relying only on ubiquitous Wi-Fi chipsets and
evaluate it based on over 95 hours of CSI measurements that we collect in five
real-world scenarios. Next2You achieves error rates below 4%, maintaining
accurate copresence detection both in low-entropy context and insufficiently
separated environments. We also demonstrate the capability of Next2You to work
reliably in real-time and its robustness to various attacks.


  An approximation is derived for a Langevin equation with
distribution-dependent potential and state-dependent, randomly fast
oscillation. By some estimates and a diffusion approximation the limiting
equation is shown to be distribution-dependent stochastic differential equation
(SDEs) driven by white noise.


  In this short note, we show that any rational curve passing through the
generic point in a moduli space of stable bundles with rank $r$ and fixed
determinant on a smooth projective curve of genus $g\ge 4$ has degree (with
respect to the anti-canonical line bundle of the moduli space) at least $2r$.
It has degree $2r$ if and only if it is a Hecke curve.


  The hydrodynamic flow of the chiral electron fluid in a Weyl semimetal slab
of finite thickness is studied by using the consistent hydrodynamic theory. The
latter includes viscous, anomalous, and vortical effects, as well as accounts
for dynamical electromagnetism. The energy and momentum separations between the
Weyl nodes are taken into account via the topological Chern-Simons
contributions in the electric current and charge densities in Maxwell's
equations. When an external electric field is applied parallel to the slab, it
is found that the electron fluid velocity has a nonuniform profile determined
by the viscosity and the no-slip boundary conditions. Most remarkably, the
fluid velocity field develops a nonzero component across the slab that
gradually dissipates when approaching the surfaces. This abnormal component of
the flow arises due to the anomalous Hall voltage induced by the topological
Chern-Simons current. Another signature feature of the hydrodynamics in Weyl
semimetals is a strong modification of the anomalous Hall current along the
slab in the direction perpendicular to the applied electric field.
Additionally, it is found that the topological current induces an electric
potential difference between the surfaces of the slab that is strongly affected
by the hydrodynamic flow.


  We observed Hubble V, the brightest HII region complex in the dwarf irregular
galaxy NGC 6822, at near-infrared (1.8--2.4 um) wavelengths using the Cooled
Grating Spectrometer 4 (CGS4) at the United Kingdom Infra-Red Telescope
(UKIRT). The line emission maps of Hubble V show the typical structure of a
photo-dissociation region (PDR) where an ionized core, traced by compact He I
emission (2.0587 um) and Br_gamma emission (2.1661 um), is surrounded by an
outer layer traced by molecular hydrogen (H_2) emission. The measured line
ratios of H_2 2-1 S(1) (2.2477 um) / 1-0 S(1) (2.1218 um) from 0.2 to 0.6 and
the un-shifted and un-resolved line profiles suggest that the H_2 emission
originates purely from a PDR. By comparing the H_2 results with a PDR model, we
conclude that Hubble V includes dense (10^{4.5} cm^{-3}) and warm PDRs. In this
environment, most of the H_2 molecules are excited by far-UV photons (with a
field strength of 10^{2-4} times that of the average interstellar field),
although collisional processes de-excite H_2 and contribute significantly to
the excitation of the first vibrational level. We expect that Hubble V is in
the early stage of molecular cloud dissolution.


  A deep learning model, named IITNet, is proposed to learn intra- and
inter-epoch temporal contexts from raw single-channel EEG for automatic sleep
scoring. To classify the sleep stage from half-minute EEG, called an epoch,
sleep experts investigate sleep-related events and consider the transition
rules between the found events. Similarly, IITNet extracts representative
features at a sub-epoch level by a residual neural network and captures intra-
and inter-epoch temporal contexts from the sequence of the features via
bidirectional LSTM. The performance was investigated for three datasets as the
sequence length (L) increased from one to ten. IITNet achieved the comparable
performance with other state-of-the-art results. The best accuracy, MF1, and
Cohen's kappa ($\kappa$) were 83.9%, 77.6%, 0.78 for SleepEDF (L=10), 86.5%,
80.7%, 0.80 for MASS (L=9), and 86.7%, 79.8%, 0.81 for SHHS (L=10),
respectively. Even though using four epochs, the performance was still
comparable. Compared to using a single epoch, on average, accuracy and MF1
increased by 2.48%p and 4.90%p and F1 of N1, N2, and REM increased by 16.1%p,
1.50%p, and 6.42%p, respectively. Above four epochs, the performance
improvement was not significant. The results support that considering the
latest two-minute raw single-channel EEG can be a reasonable choice for sleep
scoring via deep neural networks with efficiency and reliability. Furthermore,
the experiments with the baselines showed that introducing intra-epoch temporal
context learning with a deep residual network contributes to the improvement in
the overall performance and has the positive synergy effect with the
inter-epoch temporal context learning.


  Our work proposes a novel deep learning framework for estimating crowd
density from static images of highly dense crowds. We use a combination of deep
and shallow, fully convolutional networks to predict the density map for a
given crowd image. Such a combination is used for effectively capturing both
the high-level semantic information (face/body detectors) and the low-level
features (blob detectors), that are necessary for crowd counting under large
scale variations. As most crowd datasets have limited training samples (<100
images) and deep learning based approaches require large amounts of training
data, we perform multi-scale data augmentation. Augmenting the training samples
in such a manner helps in guiding the CNN to learn scale invariant
representations. Our method is tested on the challenging UCF_CC_50 dataset, and
shown to outperform the state of the art methods.


  We study $\mathcal{N}=2$ supersymmetric Sachdev-Ye-Kitaev (SYK) models with
complex fermions at non-zero background charge. Motivated by multi-charge
supersymmetric black holes, we propose a new $\mathcal{N}=2$ SYK model with
multiple $U(1)$ symmetries, integer charges, and a non-vanishing supersymmetric
index, realizing features not present in known SYK models. In both models, a
conformal solution with a super-Schwarzian mode emerges at low temperatures,
signalling the appearance of nearly AdS$_2$/BPS physics. However, in contrast
to complex SYK, the fermion scaling dimension depends on the background charge
in the conformal limit. For a critical charge, we find a high to low entropy
phase transition in which the conformal solution ceases to be valid. This
transition has a simple interpretation: the fermion scaling dimension violates
the unitarity bound. We offer some comments on a holographic interpretation for
supersymmetric black holes.


  Particle-like excitations, or quasi-particles, emerging from interacting
fermionic and bosonic quantum fields underlie many intriguing quantum phenomena
in high energy and condensed matter systems. Computation of the properties of
these excitations is frequently intractable in the strong interaction regime.
Quantum degenerate Bose-Fermi mixtures offer promising prospects to elucidate
the physics of such quasi-particles. In this work, we investigate phonon
propagation in an atomic Bose-Einstein condensate immersed in a degenerate
Fermi gas with interspecies scattering length $a_\text{BF}$ tuned by a Feshbach
resonance. We observe sound mode softening with moderate attractive
interactions. For even greater attraction, surprisingly, stable sound
propagation re-emerges and persists across the resonance. The stability of
phonons with resonant interactions opens up opportunities to investigate novel
Bose-Fermi liquids and fermionic pairing in the strong interaction regime.


  The R-matrix of the symplecto-orthogonal quantum superalgebra U_q(spo(2n|2m))
in the vector representation is calculated, and its basic properties are
derived.


  Deformation of morphisms along leaves of foliations define the tangential
foliation on the corresponding space of morphisms. We prove that codimension
one fo-liations having a tangential foliation with at least one non-algebraic
leaf are transversely homogeneous with structure group determined by the
codimension of the non-algebraic leaf in its Zariski closure. As an
application, we provide a structure theorem for degree three foliations on
$P^3$ .


  This thesis looks at the electronic energy transfer in the
Fenna-Matthews-Olson complex, in which evidence of long-lived coherence has
been observed in 2-dimensional infrared experiments. I use three techniques:
the numerically exact Hierarchical Equations of Motion, and the perturbative
Redfield and Foerster theories, the latter of which ignores quantum coherence
in the transfer. Both of the approximate methods perform very well - and while
oscillations in site populations (a hallmark of coherence) are present in the
exact transfer dynamics and absent in the dynamics of Foerster theory, the
latter gives a reasonable prediction of transfer rates and steady-state
populations, despite being incoherent - suggesting that coherence is not vital
for the dynamics of transfer. Since Foerster theory is very inexpensive to run
and performs so well, I then apply it to calculate the effects of static
disorder in bacteriochlorophyll site energies and of a more structured spectral
density. Ultimately, the energy transfer in the complex is found to be very
robust to changes in its environment, which is advantageous for its biological
function.


  Nuclei segmentation is a crucial task for whole slide image analysis in
digital pathology. Generally, the segmentation performance of fully-supervised
learning heavily depends on the amount and quality of the annotated data.
However, it is time-consuming and expensive for professional pathologists to
provide accurate pixel-level ground truth, while it is much easier to get
coarse labels such as point annotations. In this paper, we propose a
weakly-supervised learning method for nuclei segmentation that only requires
point annotations for training. First, coarse pixel-level labels are derived
from the point annotations based on the Voronoi diagram and the k-means
clustering method to avoid overfitting. Second, a co-training strategy with an
exponential moving average method is designed to refine the incomplete
supervision of the coarse labels. Third, a self-supervised visual
representation learning method is tailored for nuclei segmentation of pathology
images that transforms the hematoxylin component images into the H&E stained
images to gain better understanding of the relationship between the nuclei and
cytoplasm. We comprehensively evaluate the proposed method using two public
datasets. Both visual and quantitative results demonstrate the superiority of
our method to the state-of-the-art methods, and its competitive performance
compared to the fully-supervised methods. Code:
https://github.com/hust-linyi/SC-Net


  The observed evolution of the galaxy cluster X-ray integral temperature
distribution function between $z=0.05$ and $z=0.32$ is used in an attempt to
constrain the value of the density parameter, $\Omega_{0}$, for both open and
spatially-flat universes. We estimate the overall uncertainty in the
determination of both the observed and the predicted galaxy cluster X-ray
integral temperature distribution functions at $z=0.32$ by carrying out Monte
Carlo simulations, where we take into careful consideration all the most
important sources of possible error. We include the effect of the formation
epoch on the relation between virial mass and X-ray temperature, improving on
the assumption that clusters form at the observed redshift which leads to an
{\em overestimate} of $\Omega_0$. We conclude that at present both the
observational data and the theoretical modelling carry sufficiently large
associated uncertainties to prevent an unambiguous determination of
$\Omega_{0}$. We find that values of $\Omega_{0}$ around 0.75 are most
favoured, with $\Omega_{0}<0.3$ excluded with at least 90 per cent confidence.
In particular, the $\Omega_{0}=1$ hypothesis is found to be still viable as far
as this dataset is concerned. As a by-product, we also use the revised data on
the abundance of galaxy clusters at $z=0.05$ to update the constraint on
$\sigma_8$ given by Viana & Liddle 1996, finding slightly lower values than
before.


  We derive a measurement-independent asymptotic continuity bound on the
observational entropy for general POVM measurements, making essential use of
its property of bounded concavity. The same insight is used to obtain
continuity bounds for other entropic quantities, including the measured
relative entropy distance to a convex a set of states under a general set of
measurements. As a special case, we define and study conditional observational
entropy, which is an observational entropy in one (measured) subsystem
conditioned on the quantum state in another (unmeasured) subsystem. We also
study continuity of relative entropy with respect to a jointly applied channel,
finding that observational entropy is uniformly continuous as a function of the
measurement. But we show by means of an example that this continuity under
measurements cannot have the form of a concrete asymptotic bound.


  Strongly correlated amorphous solids are a class of glass-formers whose
inter-particle potential admits an approximate inverse power-law form in a
relevant range of inter-particle distances. We study the steady-state plastic
flow of such systems, firstly in the athermal, quasi-static limit, and secondly
at finite temperatures and strain rates. In all cases we demonstrate the
usefulness of scaling concepts to reduce the data to universal scaling
functions where the scaling exponents are determined a-priori from the
inter-particle potential. In particular we show that the steady plastic flow at
finite temperatures with efficient heat extraction is uniquely characterized by
two scaled variables; equivalently, the steady state displays an equation of
state that relates one scaled variable to the other two. We discuss the range
of applicability of the scaling theory, and the connection to density scaling
in supercooled liquid dynamics. We explain that the description of transient
states calls for additional state variables whose identity is still far from
obvious.


  Large language models (LLMs), like ChatGPT and GPT-4, have demonstrated
remarkable abilities in natural language understanding and generation. However,
alongside their positive impact on our daily tasks, they can also produce
harmful content that negatively affects societal perceptions. To systematically
assess the safety of Chinese LLMs, we introduce SuperCLUE-Safety (SC-Safety) -
a multi-round adversarial benchmark with 4912 open-ended questions covering
more than 20 safety sub-dimensions. Adversarial human-model interactions and
conversations significantly increase the challenges compared to existing
methods. Experiments on 13 major LLMs supporting Chinese yield the following
insights: 1) Closed-source models outperform open-sourced ones in terms of
safety; 2) Models released from China demonstrate comparable safety levels to
LLMs like GPT-3.5-turbo; 3) Some smaller models with 6B-13B parameters can
compete effectively in terms of safety. By introducing SC-Safety, we aim to
promote collaborative efforts to create safer and more trustworthy LLMs. The
benchmark and findings provide guidance on model selection. Our benchmark can
be found at https://www.CLUEbenchmarks.com


  We present the result of a Chandra ACIS observation of the pulsar PSR
B1853+01 and its associated pulsar wind nebula (PWN), embedded within the
supernova remnant W44. A hard band ACIS map cleanly distinguishes the PWN from
the thermal emission of W44. The nebula is extended in the north-south
direction, with an extent about half that of the radio emission. Morphological
differences between the X-ray and radio images are apparent. Spectral fitting
reveals a clear difference in spectral index between the hard emission from PSR
B1853+01 (Gamma ~ 1.4) and the extended nebula (Gamma ~ 2.2). The more accurate
values for the X-ray flux and spectral index are used refine estimates for PWN
parameters, including magnetic field strength, the average Lorentz factor,
gamma, of the particles in the wind, the magnetization parameter, sigma, and
the ratio k of electrons to other particles.


  We have obtained spectropolarimetric observations of the four images of the
gravitationally lensed broad absorption line quasar H1413+117. The polarization
of the microlensed image D is significantly different both in the continuum and
in the broad lines from the polarization of image A which is essentially
unaffected by microlensing. The observations suggest that the continuum is
scattered off two regions spatially separated and producing roughly
perpendicular polarizations. These results are compatible with a model in which
the microlensed polarized continuum comes from a compact region located in the
equatorial plane close to the accretion disk and the non-microlensed continuum
from an extended region located along the polar axis.


  We use a frequentist statistical approach to set confidence intervals on the
values of cosmological parameters using the MAXIMA-1 and COBE measurements of
the angular power spectrum of the cosmic microwave background. We define a
$\Delta \chi^{2}$ statistic, simulate the measurements of MAXIMA-1 and COBE,
determine the probability distribution of the statistic, and use it and the
data to set confidence intervals on several cosmological parameters. We compare
the frequentist confidence intervals to Bayesian credible regions. The
frequentist and Bayesian approaches give best estimates for the parameters that
agree within 15%, and confidence interval-widths that agree within 30%. The
results also suggest that a frequentist analysis gives slightly broader
confidence intervals than a Bayesian analysis. The frequentist analysis gives
values of \Omega=0.89{+0.26\atop -0.19}, \Omega_{\rm B}h^2=0.026{+0.020\atop
-0.011} and n=1.02{+0.31\atop -0.10}, and the Bayesian analysis gives values of
\Omega=0.98{+0.14\atop -0.19}, \Omega_{\rm B}h^2=0.0.029{+0.015\atop-0.010},
and $n=1.18{+0.10\atop -0.23}$, all at the 95% confidence level.


  Discrete-time quantum walks allow Floquet topological insulator materials to
be explored using controllable systems such as ultracold atoms in optical
lattices. By numerical simulations, we study the robustness of topologically
protected edge states in the presence of decoherence in one- and
two-dimensional discrete-time quantum walks. We also develop a simple
analytical model quantifying the robustness of these edge states against either
spin or spatial dephasing, predicting an exponential decay of the population of
topologically protected edge states. Moreover, we present an experimental
proposal based on neutral atoms in spin-dependent optical lattices to realize
spatial boundaries between distinct topological phases. Our proposal relies on
a new scheme to implement spin-dependent discrete shift operations in a
two-dimensional optical lattice. We analyze under realistic decoherence
conditions the experimental feasibility of observing unidirectional,
dissipationless transport of matter waves along boundaries separating distinct
topological domains.


  We show that the supersymmetric partition function of three-dimensional N=2
R-symmetric Chern-Simons-matter theories on the squashed S^3 and on S^2 x S^1
can be computed with the so-called Higgs branch localization method,
alternative to the more standard Coulomb branch localization. For theories that
could be completely Higgsed by Fayet-Iliopoulos terms, the path integral is
dominated by BPS vortex strings sitting at two circles in the geometry. In this
way, the partition function directly takes the form of a sum, over a finite
number of points on the classical Coulomb branch, of a vortex-string times an
antivortex-string partition functions.


  An excess of $\gamma$-ray emission from the Galactic Center (GC) region with
respect to predictions based on a variety of interstellar emission models and
$\gamma$-ray source catalogs has been found by many groups using data from the
{\it Fermi} Large Area Telescope (LAT). Several interpretations of this excess
have been invoked. In this paper we search for members of an unresolved
population of $\gamma$-ray pulsars located in the inner Galaxy that are
predicted by the interpretation of the GC excess as being due to a population
of such sources. We use cataloged LAT sources to derive criteria that
efficiently select pulsars with very small contamination from blazars. We
search for point sources in the inner $40^\circ\times40^\circ$ region of the
Galaxy, derive a list of approximately 400 sources, and apply pulsar selection
criteria to extract pulsar candidates among our source list. We performed the
entire data analysis chain with two different interstellar emission models
(IEMs), and found a total of 135 pulsar candidates, of which 66 were selected
with both IEMs.


  We introduce the generic Lah polynomials $L_{n,k}(\phi)$, which enumerate
unordered forests of increasing ordered trees with a weight $\phi_i$ for each
vertex with $i$ children. We show that, if the weight sequence $\phi$ is
Toeplitz-totally positive, then the triangular array of generic Lah polynomials
is totally positive and the sequence of row-generating polynomials
$L_n(\phi,y)$ is coefficientwise Hankel-totally positive. Upon specialization
we obtain results for the Lah symmetric functions and multivariate Lah
polynomials of positive and negative type. The multivariate Lah polynomials of
positive type are also given by a branched continued fraction. Our proofs use
mainly the method of production matrices; the production matrix is obtained by
a bijection from ordered forests of increasing ordered trees to labeled partial
Lukasiewicz paths. We also give a second proof of the continued fraction using
the Euler--Gauss recurrence method.


  Physics-informed neural networks (PINN) is a extremely powerful paradigm used
to solve equations encountered in scientific computing applications. An
important part of the procedure is the minimization of the equation residual
which includes, when the equation is time-dependent, a time sampling. It was
argued in the literature that the sampling need not be uniform but should
overweight initial time instants, but no rigorous explanation was provided for
these choice. In this paper we take some prototypical examples and, under
standard hypothesis concerning the neural network convergence, we show that the
optimal time sampling follows a truncated exponential distribution. In
particular we explain when the time sampling is best to be uniform and when it
should not be. The findings are illustrated with numerical examples on linear
equation, Burgers' equation and the Lorenz system.


  This work presents a new tool to verify the correctness of cryptographic
implementations with respect to cache attacks. Our methodology discovers
vulnerabilities that are hard to find with other techniques, observed as
exploitable leakage. The methodology works by identifying secret dependent
memory and introducing forced evictions inside potentially vulnerable code to
obtain cache traces that are analyzed using Mutual Information. If dependence
is observed, the cryptographic implementation is classified as to leak
information.
  We demonstrate the viability of our technique in the design of the three main
cryptographic primitives, i.e., AES, RSA and ECC, in eight popular up to date
cryptographic libraries, including OpenSSL, Libgcrypt, Intel IPP and NSS. Our
results show that cryptographic code designers are far away from incorporating
the appropriate countermeasures to avoid cache leakages, as we found that 50%
of the default implementations analyzed leaked information that lead to key
extraction. We responsibly notified the designers of all the leakages found and
suggested patches to solve these vulnerabilities.


  Previous researches on high-energy photon events from gamma-ray bursts~(GRBs)
suggest a light speed variation $v(E)=c(1-E/E_{\mathrm{LV}})$ with
$E_{\mathrm{LV}}=3.6\times10^{17}~\mathrm{ GeV}$, together with a pre-burst
scenario that hight-energy photons come out about 10 seconds earlier than
low-energy photons at the GRB source. However, in the Lorentz invariance
violating scenario with an energy dependent light speed considered here,
high-energy photons travel slower than low-energy photons due to the light
speed variation, so that they are usually detected after low-energy photons in
observed GRB data. Here we find four high-energy photon events which were
observed earlier than low-energy photons from Fermi Gamma-ray Space
Telescope~(FGST), and analysis on these photon events supports the pre-burst
scenario of high energy photons from GRBs and the energy dependence of light
speed listed above.


  An infinite family of exact solutions of the two-photon Rabi model was found
by investigating the differential algebraic properties of the Hamiltonian. This
family corresponds to energy level crossings not covered by the Juddian class,
which is given by elemetary functions. In contrast, the new states are
expressible in terms of parabolic cylinder or Bessel functions. We discuss
three approaches for discovering this hidden structure: factorization of
differential equations, Kimura transformation, and a doubly-infinite,
transcendental basis of the Bargmann space.


  Balancing computational efficiency with recognition accuracy is one of the
major challenges in real-world video-based face recognition. A significant
design decision for any such system is whether to process and use all possible
faces detected over the video frames, or whether to select only a few "best"
faces. This paper presents a video face recognition system based on
probabilistic Multi-Region Histograms to characterise performance trade-offs
in: (i) selecting a subset of faces compared to using all faces, and (ii)
combining information from all faces via clustering. Three face selection
metrics are evaluated for choosing a subset: face detection confidence, random
subset, and sequential selection. Experiments on the recently introduced MOBIO
dataset indicate that the usage of all faces through clustering always
outperformed selecting only a subset of faces. The experiments also show that
the face selection metric based on face detection confidence generally provides
better recognition performance than random or sequential sampling. Moreover,
the optimal number of faces varies drastically across selection metric and
subsets of MOBIO. Given the trade-offs between computational effort,
recognition accuracy and robustness, it is recommended that face feature
clustering would be most advantageous in batch processing (particularly for
video-based watchlists), whereas face selection methods should be limited to
applications with significant computational restrictions.


  Internal jet structure in dijet production in deep-inelastic scattering is
measured with the H1 detector at HERA. Jets with transverse energies ET,Breit >
5 GeV are selected in the Breit frame employing k_perp and cone jet algorithms.
In the kinematic region of squared momentum transfers 10 < Q2 <~ 120 GeV2 and
x-Bjorken values 2.10^-4 <~ xBj <~ 8.10^-3, jet shapes and subjet
multiplicities are measured as a function of a resolution parameter.
Distributions of both observables are corrected for detector effects and
presented as functions of the transverse jet energy and jet pseudo-rapidity.
Dependences of the jet shape and the average number of subjets on the
transverse energy and the pseudo-rapidity of the jet are observed. With
increasing transverse jet energies and decreasing pseudo-rapidities,
i.e.towards the photon hemisphere, the jets are more collimated. QCD models
give a fair description of the data.


  In pioneering work from 2019, Barcel\'o and coauthors identified logics that
precisely match the expressive power of constant iteration-depth graph neural
networks (GNNs) relative to properties definable in first-order logic. In this
article, we give exact logical characterizations of recurrent GNNs in two
scenarios: (1) in the setting with floating-point numbers and (2) with reals.
For floats, the formalism matching recurrent GNNs is a rule-based modal logic
with counting, while for reals we use a suitable infinitary modal logic, also
with counting. These results give exact matches between logics and GNNs in the
recurrent setting without relativising to a background logic in either case,
but using some natural assumptions about floating-point arithmetic. Applying
our characterizations, we also prove that, relative to graph properties
definable in monadic second-order logic (MSO), our infinitary and rule-based
logics are equally expressive. This implies that recurrent GNNs with reals and
floats have the same expressive power over MSO-definable properties and shows
that, for such properties, also recurrent GNNs with reals are characterized by
a (finitary!) rule-based modal logic. In the general case, in contrast, the
expressive power with floats is weaker than with reals. In addition to
logic-oriented results, we also characterize recurrent GNNs, with both reals
and floats, via distributed automata, drawing links to distributed computing
models.


  As a promising quantum key distribution (QKD), most of the existing
round-robin differential-phase-shift quantum key distribution (RRDPS-QKD)
protocols have adopted the decoy-state method and have assumed the source
states are exactly controlled. However, the precise manipulation of source
states is impossible for any practical experiment, and the RRDPS-QKD with
source errors has an unignorable impact on the performance of the protocol. In
the paper, we study the three-intensity decoy-state RRDPS-QKD protocol with
source errors, formulate the secure generation key rate of the proposed
protocol, do the numerical simulations to testify the deductions. The results
show that our evaluation can estimate the influence of source errors.


  We provide a one-to-one correspondence between line operators and states in
four-dimensional CFTs with continuous 1-form symmetries. In analogy with 0-form
symmetries in two dimensions, such CFTs have a free photon realisation and
enjoy an infinite-dimensional current algebra that generalises the familiar
Kac-Moody algebras. We construct the representation theory of this current
algebra, which allows for a full description of the space of states on an
arbitrary closed spatial slice. On $\mathbb{S}^2\times\mathbb{S}^1$, we
rederive the spectrum by performing a path integral on
$\mathbb{B}^3\times\mathbb{S}^1$ with insertions of line operators. This leads
to a direct and explicit correspondence between the line operators of the
theory and the states on $\mathbb{S}^2\times\mathbb{S}^1$. Interestingly, we
find that the vacuum state is not prepared by the empty path integral but by a
squeezing operator. Additionally, we generalise some of our results in two
directions. Firstly, we construct current algebras in $(2p+2)$-dimensional
CFTs, that are universal whenever the theory has a $p$-form symmetry, and
secondly we provide a non-invertible generalisation of those higher-dimensional
current algebras.


  Understanding the crystal field splitting and orbital polarization in
non-centrosymmetric systems such as ferroelectric materials is fundamentally
important. In this study, taking BaTiO$_3$ (BTO) as a representative material
we investigate titanium crystal field splitting and orbital polarization in
non-centrosymmetric TiO$_6$ octahedra with resonant X-ray linear dichroism at
Ti $L_{2,3}$-edge. The high-quality BaTiO$_3$ thin films were deposited on
DyScO$_3$ (110) single crystal substrates in a layer-by-layer way by pulsed
laser deposition. The reflection high-energy electron diffraction (RHEED) and
element specific X-ray absorption spectroscopy (XAS) were performed to
characterize the structural and electronic properties of the films. In sharp
contrast to conventional crystal field splitting and orbital configuration
($d_{xz}$/$d_{yz}$ $<$ $d_{xy}$ $<$ $d_{3z^2-r^2}$ $<$ $d_{x^2-y^2}$ or
$d_{xy}$ $<$ $d_{xz}$/$d_{yz}$ $<$ $d_{x^2-y^2}$ $<$ $d_{3z^2-r^2}$) according
to Jahn-Teller effect, it is revealed that $d_{xz}$, $d_{yz}$, and $d_{xy}$
orbitals are nearly degenerate, whereas $d_{3z^2-r^2}$ and $d_{x^2-y^2}$
orbitals are split with an energy gap $\sim$ 100 meV in the epitaxial BTO
films. The unexpected degenerate states $d_{xz}$/$d_{yz}$/$d_{xy}$ are coupled
to Ti-O displacements resulting from competition between polar and Jahn-Teller
distortions in non-centrosymmetric TiO$_6$ octhedra of BTO films. Our results
provide a route to manipulate orbital degree of freedom by switching electric
polarization in ferroelectric materials.


  This paper presents a novel automatic face recognition approach based on
local binary patterns. This descriptor considers a local neighbourhood of a
pixel to compute the feature vector values. This method is not very robust to
handle image noise, variances and different illumination conditions. We address
these issues by proposing a novel descriptor which considers more pixels and
different neighbourhoods to compute the feature vector values. The proposed
method is evaluated on two benchmark corpora, namely UFI and FERET face
datasets. We experimentally show that our approach outperforms state-of-the-art
methods and is efficient particularly in the real conditions where the above
mentioned issues are obvious. We further show that the proposed method handles
well one training sample issue and is also robust to the image resolution.