  The steady state propagation of a phase transition front is classified,
according to hydrodynamics, as a deflagration or a detonation, depending on its
velocity with respect to the fluid. These propagation modes are further divided
into three types, namely, weak, Jouguet, and strong solutions, according to
their disturbance of the fluid. However, some of these hydrodynamic modes will
not be realized in a phase transition. One particular cause is the presence of
instabilities. In this work we study the linear stability of weak detonations,
which are generally believed to be stable. After discussing in detail the weak
detonation solution, we consider small perturbations of the interface and the
fluid configuration. When the balance between the driving and friction forces
is taken into account, it turns out that there are actually two different kinds
of weak detonations, which behave very differently as functions of the
parameters. We show that the branch of stronger weak detonations are unstable,
except very close to the Jouguet point, where our approach breaks down.


  Magnetic fields on a range of scales play a large role in the ecosystems of
galaxies, both in the galactic disk and in the extended layers of gas away from
the plane. Observing magnetic field strength, structure and orientation is
complex, and necessarily indirect. Observational data of magnetic fields in the
halo of the Milky Way are scarce, and non-conclusive about the large-scale
structure of the field. In external galaxies, various large-scale
configurations of magnetic fields are measured, but many uncertainties about
exact configurations and their origin remain. There is a strong interaction
between magnetic fields and other components in the interstellar medium such as
ionized and neutral gas and cosmic rays. The energy densities of these
components are comparable on large scales, indicating that magnetic fields are
not passive tracers but that magnetic field feedback on the other interstellar
medium components needs to be taken into account.


  We examine the procedure to construct the variables of use for the momentum
representation in quantum mechanics. The momentum variables must be chosen
properly conjugate to the corresponding position space variables, such that
valid uncertainty relationships are maintained. We then apply such
considerations to the hydrogen atom to obtain the momentum space wave functions
corresponding to the position space functions in paraboloidal coordinates. The
advantages and disadvantages of employing the momentum representation are
explored.


  Two dimensional (2D) crystal heterostructures are shown to possess a unique
opportunity for novel THz nonlinear devices. In contrast to the oxide tunneling
barrier, the uniformity of 2D insulators in the thickness control provides an
ideal condition for tunneling barriers in the atomic scale. Numerical
calculations based on a first principles method clearly indicate the
feasibility of diode operation with barriers as thin as two monolayers of
hexagonal boron nitride or molybdenum disulfide when placed between
graphene-metal asymmetric electrodes. Further analysis predicts the cut-off
frequencies of the proposed device over 10 THz while maintaining strong
nonlinearity for zero-bias rectification. Application of the tunneling
structure to hot electron transistors is also investigated, illustrating the
THz operation with superior power performance. The proposed concept provides an
excellent opportunity for realizing active nonlinear devices in the frequency
range inaccessible thus far.


  The aim of this paper is to investigate weakly developable spaces. For a
comparison with semi-metrizable spaces, we introduce and study a class of
spaces among those of weakly developable spaces, semimetrizable spaces and
first countable spaces having a G_delta-diagonal. Some results are obtained and
applications to the problem of extending continuous functions are discussed.


  This article explores how to effectively incorporate curvature information
generated using SIMD-parallel forward-mode Algorithmic Differentiation (AD)
into unconstrained Quasi-Newton (QN) minimization of a smooth objective
function, $f$. Specifically, forward-mode AD can be used to generate block
Hessian samples $Y=\nabla^2 f(x)\,S$ whenever the gradient is evaluated. Block
QN algorithms then update approximate inverse Hessians, $H_k \approx \nabla^2
f(x_k)$, with these Hessian samples. Whereas standard line-search based BFGS
algorithms carefully filter and correct secant-based approximate curvature
information to maintain positive definite approximations, our algorithms
directly incorporate Hessian samples to update indefinite inverse Hessian
approximations without filtering. The sampled directions supplement the
standard QN two-dimensional trust-region sub-problem to generate a moderate
dimensional subproblem which can exploit negative curvature. The resulting
quadratically-constrained quadratic program is solved accurately with a
generalized eigenvalue algorithm and the step advanced using standard trust
region step acceptance and radius adjustments. The article aims to avoid serial
bottlenecks, exploit accurate positive and negative curvature information, and
conduct a preliminary evaluation of selection strategies for $S$.


  In this paper, we study the singularities of two extended Ricci flow systems
--- connection Ricci flow and Ricci harmonic flow using newly-defined curvature
quantities. Specifically, we give the definition of three types of
singularities and their corresponding singularity models, and then prove the
convergence. In addition, for Ricci harmonic flow, we use the monotonicity of
functional $\nu_\alpha$ to show the connection between finite-time singularity
and shrinking Ricci harmonic soliton. At last, we explore the property of
ancient solutions for Ricci harmonic flow.


  Graph-structured data commonly have node annotations. A popular approach for
inference and learning involving annotated graphs is to incorporate annotations
into a statistical model or algorithm. By contrast, we consider a more direct
method named scotch-taping, in which the structural information in a graph and
its node annotations are encoded as a factor graph. Specifically, we establish
the mathematical basis of this method in the spectral framework.


  The Hypercat Database is developed at Observatoire de Lyon and is distributed
on the WEB through different mirrors in Europe. The goal of Hypercat is to
gather data necessary for studying the evolution of galaxies (dynamics and
stellar contains) and particularly for providing a z=0 reference for these
studies.


  In the summer of 1918, Emmy Noether published the theorem that now bears her
name, establishing a profound two-way connection between symmetries and
conservation laws. The influence of this insight is pervasive in physics; it
underlies all of our theories of the fundamental interactions and gives meaning
to conservation laws that elevates them beyond useful empirical rules.
Noether's papers, lectures, and personal interactions with students and
colleagues drove the development of abstract algebra, establishing her in the
pantheon of twentieth-century mathematicians. This essay traces her path from
Erlangen through G\"ottingen to a brief but happy exile at Bryn Mawr College in
Pennsylvania, illustrating the importance of "Noether's Theorem" for the way we
think today. The text draws on a colloquium presented at Fermilab on 15 August
2018.


  We develop an algorithm to solve the Bottleneck Assignment Problem (BAP) that
is amenable to having computation distributed over a network of agents. This
consists of exploring how each component of the algorithm can be distributed,
with a focus on one component in particular, i.e., the function to search for
an augmenting path. An augmenting path is a common tool used in most BAP
algorithms and poses a particular challenge for this distributed approach.
Given this significance, we compare two different methods to search for an
augmenting path in a bipartite graph. We also exploit properties of the
augmenting paths to formalise conditions for which the solution from subsets of
the sets of agents and tasks can be used to solve the BAP with the full sets of
agents and tasks. In the end, we evaluate and compare the derived approaches
with a numerical analysis.


  An intriguing connection between extreme value statistics and traveling
fronts has been found recently in a number of diverse problems. In this brief
review we outline a few such problems and consider their various applications.


  Whether the massive neutron star PSR J0348+0432 can become a hyperon star is
examined in the framework of the relativistic mean field theory by adjusting
the hyperon coupling constants. It is found that at the central baryon number
density of the massive neutron star PSR J0348+0432, the relative particle
number density of hyperons is smaller than those of neutrons and so it can not
change into a hyperon star. In its center, it is mainly composed of $\Lambda$,
$\Xi^{-}$ and a few $\Xi^{0}$. We also found that for the neutron star with a
maximum mass of 1.4 M$_{\odot}$, it can change into a hyperon star and the
hyperon star transition density is 0.668 fm$^{-3}$, at which the hyperons are
only composed of $\Lambda$. At its center, the hyperons are also only composed
of $\Lambda$ and the ratio of the hyperons is a little larger than that of the
neutrons. This illustrates that the NS1.4M$_{\odot}$ has just changed into a
hyperon star.


  In this paper we show the application of the new robotic multi-platform
system HSURF to a specific use case of teleoperation, aimed at monitoring and
inspection. The HSURF system, consists of 3 different kinds of platforms:
floater, sinker and robotic fishes. The collaborative control of the 3
platforms allows a remotely based operator to control the fish in order to
visit and inspect several targets underwater following a complex trajectory. A
shared autonomy solution shows to be the most suitable, in order to minimize
the effect of limited bandwidth and relevant delay intrinsic to acoustic
communications. The control architecture is described and preliminary results
of the acoustically teleoperated visits of multiple targets in a testing pool
are provided.


  In a wireless system with a large number of distributed nodes, the quality of
communication can be greatly improved by pooling the nodes to perform joint
transmission/reception. In this paper, we consider the problem of optimally
selecting a subset of nodes from potentially a large number of candidates to
form a virtual multi-antenna system, while at the same time designing their
joint linear transmission strategies. We focus on two specific application
scenarios: 1) multiple single antenna transmitters cooperatively transmit to a
receiver; 2) a single transmitter transmits to a receiver with the help of a
number of cooperative relays. We formulate the joint node selection and
beamforming problems as cardinality constrained optimization problems with both
discrete variables (used for selecting cooperative nodes) and continuous
variables (used for designing beamformers). For each application scenario, we
first characterize the computational complexity of the joint optimization
problem, and then propose novel semi-definite relaxation (SDR) techniques to
obtain approximate solutions. We show that the new SDR algorithms have a
guaranteed approximation performance in terms of the gap to global optimality,
regardless of channel realizations. The effectiveness of the proposed
algorithms is demonstrated via numerical experiments.


  We obtain a 1.5-approximation algorithm for the metric uncapacitated facility
location problem (UFL), which improves on the previously best known
1.52-approximation algorithm by Mahdian, Ye and Zhang. Note, that the
approximability lower bound by Guha and Khuller is 1.463.
  An algorithm is a {\em ($\lambda_f$,$\lambda_c$)-approximation algorithm} if
the solution it produces has total cost at most $\lambda_f \cdot F^* +
\lambda_c \cdot C^*$, where $F^*$ and $C^*$ are the facility and the connection
cost of an optimal solution. Our new algorithm, which is a modification of the
$(1+2/e)$-approximation algorithm of Chudak and Shmoys, is a
(1.6774,1.3738)-approximation algorithm for the UFL problem and is the first
one that touches the approximability limit curve $(\gamma_f, 1+2e^{-\gamma_f})$
established by Jain, Mahdian and Saberi. As a consequence, we obtain the first
optimal approximation algorithm for instances dominated by connection costs.
When combined with a (1.11,1.7764)-approximation algorithm proposed by Jain et
al., and later analyzed by Mahdian et al., we obtain the overall approximation
guarantee of 1.5 for the metric UFL problem. We also describe how to use our
algorithm to improve the approximation ratio for the 3-level version of UFL.


  In this paper, we study the long time asymptotic behavior for the initial
value problem of the modified Camassa-Holm (mCH) equation in the solitonic
region \begin{align}
  &m_{t}+\left(m\left(u^{2}-u_{x}^{2}\right)\right)_{x}+\kappa u_{x}=0, \quad
m=u-u_{x x}, \nonumber
  &u(x, 0)=u_{0}(x),\nonumber \end{align} where $\kappa$ is a positive
constant. Based on the spectral analysis of the Lax pair associated with the
mCH equation and scattering matrix, the solution of the Cauchy problem is
characterized via the solution of a Riemann-Hilbert (RH) problem. Further using
the $\overline\partial$ generalization of Deift-Zhou steepest descent method,
we derive different long time asymptotic expansion of the solution $u(x,t)$ in
different space-time solitonic region of $x/t$. These asymptotic approximations
can be characterized with an $N(\Lambda)$-soliton whose parameters are
modulated by a sum of localized soliton-soliton interactions as one moves
through the region with diverse residual error order from $\overline\partial$
equation: $\mathcal{O}(|t|^{-1+2\rho})$ for
$\xi=\frac{y}{t}\in(-\infty,-0.25)\cup(2,+\infty)$ and
$\mathcal{O}(|t|^{-3/4})$ for $\xi=\frac{y}{t}\in(-0.25,2)$. Our results also
confirm the soliton resolution conjecture and asymptotically stability of
N-soliton solutions for the mCH equation.


  Whether we recognize it or not, the Internet is rife with exciting and
original institutional forms that are transforming social organization on and
offline. Issues of governance in these Internet platforms and other digital
institutions have posed a challenge for software engineers, many of whom have
little exposure to the relevant history or theory of institutional design.
Here, we offer one useful framework with an aim to stimulate dialogue between
computer scientists and political scientists. The dominant guiding practices
for the design of digital institutions to date in human-computer interaction,
computer-supported cooperative work, and the tech industry at large have been
an incentive-focused behavioral engineering paradigm, a collection of
atheoretical approaches such as A/B-testing, and incremental issue-driven
software engineering. One institutional analysis framework that has been useful
in the design of traditional institutions is the body of resource governance
literature known as the "Ostrom Workshop". A key finding of this literature
that has yet to be broadly incorporated in the design of many digital
institutions is the importance of including participatory change process
mechanisms in what is called a "constitutional layer" of institutional
design---in other words, defining rules that allow and facilitate diverse
stakeholder participation in the ongoing process of institutional design
change. We explore to what extent this consideration is met or could be better
met in three varied cases of digital institutions: cryptocurrencies, cannabis
informatics, and amateur Minecraft server governance. Examining such highly
varied cases allows us to demonstrate the broad relevance of constitutional
layers in many different types of digital institutions.


  Affine W-algebras are a somewhat complicated family of (topological)
associative algebras associated with a semisimple Lie algebra, quantizing
functions on the algebraic loop space of Kostant's slice. They have attracted a
great deal of attention in geometric representation theory because of
Feigin-Frenkel's duality theorem for them, which identifies W-algebras for a
Lie algebra and its Langlands dual through a subtle construction.
  The main result of this paper is an affine version of Skryabin's theorem,
describing the category of modules over the W-algebra in simpler categorical
terms. But unlike the classical story, it is essential to work with derived
categories in the affine setting.
  One novel feature is the use of geometric techniques to study W-algebras: the
theory of D-modules on the loop group and the geometry of the affine
Grassmannian are indispensable tools. These are used to give an infinite family
of affine analogues of the Bezrukavnikov-Braverman-Mirkovic theorem, providing
a geometric version of Rodier's compact approximation to the Whittaker model
from the arithmetic setting. We also use these methods to generalize Beraldo's
theorem identifying Whittaker invariants and Whittaker coinvariants, extending
his result from GL_n to a general reductive group. At integral level, these
methods seem to have deep intrinsic meaning in the local geometric Langlands
program.
  The theory developed here provides systematic proofs of many classical
results in the subject. In particular, we clarify the exactness properties of
the quantum Drinfeld-Sokolov functor.


  The Kepler mission was launched in 2009 and has discovered thousands of
planet candidates. In a recent paper, Esteves et al. (2013) found a periodic
signal in the light curves of KOI-13 and HAT-P-7, with a frequency triple the
orbital frequency of a transiting planet. We found similar harmonics in many
systems with a high occurrence rate. At this time, the origins of the signal
are not entirely certain.
  We look carefully at the possibility of errors being introduced through our
data processing routines but conclude that the signal is real. The harmonics on
multiples of the orbital frequency are a result of non-sinusoidal periodic
signals. We speculate on their origin and generally caution that these
harmonics could lead to wrong estimates of planet albedos, beaming mass
estimates, and ellipsoidal variations.


  We revise the conventional nuclear effects of Fermi motion, binding and
pionic effects in deep inelastic lepton scattering using a relativistic
formalism for an interacting Fermi sea and the local density approximation to
translate results from nuclear matter to finite nuclei. In addition we also
consider effects from rho-meson renormalization in the nucleus. The use of
nucleon Green's functions in terms of their spectral functions offers a precise
way to account for Fermi motion and binding. On the other hand the use of many
body Feynman diagrams in a relativistic framework allows one to avoid using
prescriptions given in the past to introduce relativistic corrections in a non
relativistic formalism. We show that with realistic nucleon spectral functions
and meson nucleus selfenergies one can get a reasonable description of the EMC
effect for x > 0.15, outside the shadowing region.


  Let $\mathfrak{G}$ be the subgroup $\mathfrak{S}_{n-q} \times
\mathfrak{S}_{q}$ of the $n$-th symmetric group $\mathfrak{S}_{n}$ for $n-q
\geq q$. In this paper, we study the $\mathfrak{G}$-invariant part of the
rational cohomology group of the pure braid group $P_{n}$. The invariant part
includes the rational cohomology of a spin hyperelliptic mapping class group of
genus $g$ as a subalgebra when $n=2g+2$, denoted by
$H^*(P_{n})^{\mathfrak{G}}$. Based on the study of Lehrer-Solomon, we prove
that they are independent of $n$ and $q$ in degree $*\leq q-1$. We also give a
formula to calculate the dimension of $H^*(P_{n})^{\mathfrak{G}}$ and calculate
it in all degree for $q\leq 3$.


  We discuss the deep galaxy counts from the Hubble Deep Field (HDF) imaging
survey. At faint magnitudes, the slope of the differential number-magnitude
relation is flatter than 0.2 in all four HDF bandpasses. In the ultraviolet, a
fluctuation analysis shows that the flattening observed below U=26 mag is not
due to incompleteness and is more pronounced than in the other bands,
consistent with the idea that a redshift limit has been reached in the galaxy
distribution. A reddening trend of about 0.5 magnitude is observed at faint
fluxes in the colour-magnitude diagram, (U-V)_{eff} vs. V. We interpret these
results as the effect of intergalactic attenuation on distant galaxies. At flux
levels of AB=27 mag and in agreement with the fluctuation analysis and the
colour-magnitude relation, about 7% of the sources in U, 30% in B and 35% in V
are Lyman-break ``dropouts'', i.e. candidate star-forming galaxies at z>2. By
integrating the number counts to the limits of the HDF survey we find that the
mean surface brightness of the extragalactic sky is dominated by galaxies that
are relatively bright and are known to have <z>=0.6. To AB=29 mag, the
integrated light from resolved galaxies in the I-band is 2.1\pm 0.4 \times
10^{-20} erg/cm^2/s/Hz/sr, and its spectrum is well described by a broken
power-law. We discuss the predictions for the counts, colours, and luminosity
densities from standard low-q_0 pure-luminosity-evolution models without dust
obscuration, and find that they are unable to reproduce all the observed
properties of faint field galaxies.


  Concept of the topological order is useful to characterize anisotropic
superconductivities. The spin Hall conductance distinguishes
superconductivities with the same symmetry. The Chern number for the spin Hall
conductance is given by the covering degree of a closed surface around the
Dirac monopole. It gives a clear illustration for the on-critical condition for
the $d_{x^2-y^2}$ supreconductivitiy with non zero chemical potential. Non
trivial topological orders on the triangular lattice are also presented and
demonstrated by the topological objects.


  We propose an inexpensive scalable approach for achieving extremely high
values of Seebeck coefficient ($\alpha$) by exploiting the natural superlattice
structure in Aurivillius phase oxides. In particular, we report an $\alpha
\approx $ 319\,mV/K at 300\,K in a composite of Aurivillius phase compound
SrBi$_4$Ti$_4$O$_{15}$ (as a matrix) and a perovskite phase material (e.g.,
La$_{0.7}$Sr$_{0.3}$MnO$_3$ or, La$_{0.7}$Sr$_{0.3}$CoO$_3$ as filler). Such a
colossal value of $\alpha$ can be attributed to contributions from the enhanced
density of states due to the effective low dimensional character of Bi$_2$O$_2$
layer. The corresponding thermal conductivity ($\kappa$) and the electrical
conductivity ($\sigma$) lies in the range 0.7 - 1.25 W/m-K and 10 - 100
$\mu$S/m, respectively at 300\,K. Attributed to the high $\alpha$ values, such
oxide composites can be used as thermopile sensors and highly sensitive
bolometric applications. We anticipate that the demonstration of colossal
$\alpha$ in oxide composites using a simple synthesis strategy also sets the
stage for future material innovations for high temperature thermoelectric
applications.


  We develop statistical mechanics for stochastic growth processes as applied
to Laplacian growth by using its remarkable connection with a random matrix
theory. The Laplacian growth equation is obtained from the variation principle
and describes adiabatic (quasi-static) thermodynamic processes in the
two-dimensional Dyson gas. By using Einstein's theory of thermodynamic
fluctuations we consider transitional probabilities between thermodynamic
states, which are in a one-to-one correspondence with planar domains.
Transitions between these domains are described by the stochastic Laplacian
growth equation, while the transitional probabilities coincide with the
free-particle propagator on the infinite dimensional complex manifold with the
K\"ahler metric.


  We advocate the use of on-shell constrained $M_2$ variables in order to
mitigate the combinatorial problem in SUSY-like events with two invisible
particles at the LHC. We show that in comparison to other approaches in the
literature, the constrained $M_2$ variables provide superior ansatze for the
unmeasured invisible momenta and therefore can be usefully applied to
discriminate combinatorial ambiguities. We illustrate our procedure with the
example of dilepton $t\bar{t}$ events. We critically review the existing
methods based on the Cambridge $M_{T2}$ variable and MAOS-reconstruction of
invisible momenta, and show that their algorithm can be simplified without loss
of sensitivity, due to a perfect correlation between events with complex
solutions for the invisible momenta and events exhibiting a kinematic endpoint
violation. Then we demonstrate that the efficiency for selecting the correct
partition is further improved by utilizing the $M_2$ variables instead.
Finally, we also consider the general case when the underlying mass spectrum is
unknown, and no kinematic endpoint information is available.


  In the late stage of terrestrial planet formation, planets are predicted to
undergo pairwise collisions known as giant impacts. Here we present a
high-resolution database of giant impacts for differentiated colliding bodies
of iron-silicate composition, with target masses ranging from 10^-4 M_Earth up
to super-Earths (5 M_Earth). We vary impactor-to-target mass ratio, core-mantle
(iron-silicate) fraction, impact velocity, and impact angle. Strength in the
form of friction is included in all simulations. We find that due to strength,
collisions with bodies smaller than about 2*10^-3 M_Earth can result in
irregular shapes, compound core structures, and captured binaries. We observe
that the characteristic escaping velocity of smaller remnants (debris) is
approximately half of the impact velocity, significantly faster than currently
assumed in N-body simulations of planet formation. Incorporating these results
in N-body planet formation studies would provide more realistic debris-debris
and debris-planet interactions.


  In this paper, we present a parallel numerical algorithm for solving the
phase field crystal equation. In the algorithm, a semi-implicit finite
difference scheme is derived based on the discrete variational derivative
method. Theoretical analysis is provided to show that the scheme is
unconditionally energy stable and can achieve second-order accuracy in both
space and time. An adaptive time step strategy is adopted such that the time
step size can be flexibly controlled based on the dynamical evolution of the
problem. At each time step, a nonlinear algebraic system is constructed from
the discretization of the phase field crystal equation and solved by a domain
decomposition based, parallel Newton--Krylov--Schwarz method with improved
boundary conditions for subdomain problems. Numerical experiments with several
two and three dimensional test cases show that the proposed algorithm is
second-order accurate in both space and time, energy stable with large time
steps, and highly scalable to over ten thousands processor cores on the Sunway
TaihuLight supercomputer.


  The radiative decay $\Lambda_{b}^{0} \to \Lambda \gamma$ is observed for the
first time using a data sample of proton-proton collisions corresponding to an
integrated luminosity of $1.7\,fb^{-1}$ collected by the LHCb experiment at a
center-of-mass energy of $13\,TeV$. Its branching fraction is measured
exploiting the $B^{0} \to K^{*0} \gamma$ decay as a normalization mode and is
found to be $\mathcal{B}(\Lambda_{b}^{0} \to \Lambda \gamma)= (7.1 \pm 1.5 \pm
0.6 \pm 0.7) \times 10^{-6}$, where the quoted uncertainties are statistical,
systematic and systematic from external inputs, respectively. This is the first
observation of a radiative decay of a beauty baryon.


  This paper is devoted to deformations of Lagrangian submanifolds contained in
the singular locus of a log-symplectic manifold. We prove a normal form result
for the log-symplectic structure around such a Lagrangian, which we use to
extract algebraic and geometric information about the Lagrangian deformations.
We show that the deformation problem is governed by a DGLA, we discuss whether
the Lagrangian admits deformations not contained in the singular locus, and we
give precise criteria for unobstructedness of first order deformations. We also
address equivalences of deformations, showing that the gauge equivalence
relation of the DGLA corresponds with the geometric notion of equivalence by
Hamiltonian isotopies. We discuss the corresponding moduli space, and we prove
a rigidity statement for the more flexible equivalence relation by Poisson
isotopies.


  It is shown that a pair of identical emitters (e.g. wire dipole antennas) in
the focal points of a disc, made of left-handed metamaterial (a "perfect"
lens), form a non-radiating electromagnetic configuration. The emitters are fed
with voltages of equal magnitude and pi-out-of-phase. Detailed
finite-difference time-domain (FDTD) modeling shows that there are
non-propagating electromagnetic fields generated - fields that remain confined
within the region between the emitters and the lens. The energy balance of the
system shows that the radiation resistance of the system is very low. This
means that the input power is converted to heat in the volume of the lens and
only a small fraction of it is radiated. The system performance shows that
disturbing the configuration of the non-propagating electromagnetic fields with
the presence of an externally introduced object stimulates radiation. This
suggests possible detector applications. In-phase feeding voltages are also
studied with the consequence that the radiation resistance of the antennae is
increased.


  The two matrix model is considered, with measure given by the exponential of
a sum of polynomials in two different variables. It is shown how to derive a
sequence of pairs of ``dual'' finite size systems of ODEs for the corresponding
biorthonormal polynomials. An inverse theorem is proved showing how to
reconstruct such measures from pairs of semi-infinite finite band matrices
defining the recursion relations and satisfying the string equation. A proof is
given in the $N\to \infty$ limit that the dual systems obtained share the same
spectral curve.


  In high-stakes applications of machine learning models, interpretability
methods provide guarantees that models are right for the right reasons. In
medical imaging, saliency maps have become the standard tool for determining
whether a neural model has learned relevant robust features, rather than
artefactual noise. However, saliency maps are limited to local model
explanation because they interpret predictions on an image-by-image basis. We
propose aggregating saliency globally, using semantic segmentation masks, to
provide quantitative measures of model bias across a dataset. To evaluate
global saliency methods, we propose two metrics for quantifying the validity of
saliency explanations. We apply the global saliency method to skin lesion
diagnosis to determine the effect of artefacts, such as ink, on model bias.


  The punctured binary Reed-Muller code is cyclic and was generalized into the
punctured generalized Reed-Muller code over $\gf(q)$ in the literature. The
major objective of this paper is to present another generalization of the
punctured binary Reed-Muller code. Another objective is to construct a family
of reversible cyclic codes that are related to the newly generalized
Reed-Muller codes.


  We demonstrate for the first time using a robust Bayesian approach to analyse
the populations of radio-quiet (RQ) and radio-loud (RL) gamma-ray pulsars. We
quantify their differences and obtain their distributions of the radio-cone
opening half-angle $\delta$ and the magnetic inclination angle $\alpha$ by
Bayesian inference. In contrast to the conventional frequentist point
estimations that might be non-representative when the distribution is highly
skewed or multi-modal, which is often the case when data points are scarce,
Bayesian statistics displays the complete posterior distribution that the
uncertainties can be readily obtained regardless of the skewness and modality.
We found that the spin period, the magnetic field strength at the light
cylinder, the spin-down power, the gamma-ray-to-X-ray flux ratio, and the
spectral curvature significance of the two groups of pulsars exhibit
significant differences at the 99\% level. Using Bayesian inference, we are
able to infer the values and uncertainties of $\delta$ and $\alpha$ from the
distribution of RQ and RL pulsars. We found that $\delta$ is between $10^\circ$
and $35^\circ$ and the distribution of $\alpha$ is skewed towards large values.


  A partition of the set of unary pp formulas into four regions is presented,
which has a bearing on various structural properties of modules. The machinery
developed allows for applications to IF, weakly coherent, nonsingular, and
reduced rings, as well as domains, specifically Ore domains. One of the four
types of formula are called high. These are used to define Ulm submodules and
Ulm length of modules over any associative ring. It is shown that pure
injective modules have Ulm length at most 1. As a consequence, pure injective
modules over RD domains (in particular, pure injective modules over the first
Weyl algebra over a field of characteristic 0) are shown to decompose into a
largest injective and a reduced submodule. This study serves as preparation for
forthcoming work with A. Martsinkovsky on injective torsion.


  Suppose the spaces X and X cross A have the same Lusternik-Schnirelmann
category: cat(X cross A)= cat(X). Then there is a strict inequality cat(X cross
(A halfsmash B)) < cat (X) + cat(A halfsmash B) for every space B, provided the
connectivity of A is large enough (depending only on X). This is applied to
give a partial verification of a conjecture of Iwase on the category of
products of spaces with spheres.


  Central Bank Digital Currency (CBDC) is an emerging trend in digital
payments, with the vast majority of central banks around the world researching,
piloting, or even operating a digital version of cash. While design choices
differ broadly, such as accounts vs. tokens, the wallets are generally
protected through cryptographic algorithms that safeguard against double
spending and ensure non-repudiation. With the advent of quantum computing,
these algorithms are threatened by new attack vectors. To better understand
those threats, we conducted a study of typical assets in a CBDC system,
describe which ones are most amenable to post-quantum cryptography, and propose
an upgrade strategy.


  The one-dimensional quantum sine-Gordon system with a linear spatial
modulation is investigated in a special case, $\beta ^{2}$ =4$\pi $. The model
is tranformed into a massive Thirring model and then is exactly diagonalized,
the energy spetrum of the model is obtained. Our result clearly demonstrates
that cancelling the cosine term without any considering is unadvisable.


  This paper presents an analysis of various forms of articulation between
graphico-gestural and verbal modalities in parallel interactions between
designers in a collaborative design situation. Based on our methodological
framework, we illustrate several forms of multimodal articulations, that is,
integrated and non-integrated, through extracts from a corpus on an
architectural design meeting. These modes reveal alignment or disalignment
between designers, with respect to the focus of their activities. They also
show different forms of coalition.


  We propose a method for increasing purity of interacting quantum systems that
takes advantage of correlations present due to the internal interaction. In
particular we show that by using the system's quantum correlations one can
achieve cooling beyond established limits of previous conventional algorithmic
cooling proposals which assume no interaction.


  In this work, the microstructure of charged AdS black holes under minimal
length effects is investigated. We study the thermodynamics of black holes in
the extended phase space, where the cosmological constant is regarded as the
thermodynamic pressure. The modified Hawking temperature and phase transition
are obtained based on the generalized uncertainty principle (GUP). Then, using
thermodynamic geometry, we show that the microstructure of black holes can be
determined by the ratio of GUP parameter to charge. For a small ratio, the
black hole exhibits the typical RN-AdS microstructure with van der Waals phase
transition and repulsive/attractive interactions. As the ratio increases, the
reentrant phase transition takes place, and both the repulsion-attraction
coexisted black hole and the attraction dominated black hole can be found in
this case. For a large ratio, the black hole behaves like a Schwarzchild-AdS
black hole in which neither phase transition nor repulsive interaction exists.
These results suggest that the GUP effect will reduce the repulsive interaction
presented by the charged AdS black hole, which can also be qualitatively
understood from the perspective of black hole molecules.


  The signal-to-noise ratio of a multistage cascade network is often estimated
using Friis formulas for noise factors (or the noise figures in decibel). In
this letter, the correct formulas to calculate the stage-wise noise factors and
the total noise factor in terms of the stage-wise noise factors of an n-stage
cascade network are derived. A comparison of our derived formulas for noise
factors with Friis's formulas is presented. Contrary to Friis's total noise
factor in terms of the stage-wise noise factors, we define the actual total
noise factor of the n-stage cascade network as the product of its stage-wise
noise factors.


  We study residually finite-dimensional (or RFD) operator algebras which may
not be self-adjoint. An operator algebra may be RFD while simultaneously
possessing completely isometric representations whose generating C*-algebra is
not RFD. This has provided many hurdles in characterizing residual
finite-dimensionality for operator algebras. To better understand the elusive
behaviour, we explore the C*-covers of an operator algebra. First, we equate
the collection of C*-covers with a complete lattice arising from the spectrum
of the maximal C*-cover. This allows us to identify a largest RFD C*-cover
whenever the underlying operator algebra is RFD. The largest RFD C*-cover is
shown to be similar to the maximal C*-cover in several different facets and
this provides supporting evidence to a previous query of whether an RFD
operator algebra always possesses an RFD maximal C*-cover. In closing, we
present a non self-adjoint version of Hadwin's characterization of separable
RFD C*-algebras.


  In this work, we show that if $f$ is a uniformly continuous map defined over
a Polish metric space, then the set of $f$-invariant measures with zero metric
entropy is a $G_\delta$ set (in the weak topology). In particular, this set is
generic if the set of $f$-periodic measures is dense in the set of
$f$-invariant measures. This settles a conjecture posed by Sigmund (Sigmund, K.
On dynamical systems with the specification property. Trans. Amer. Math. Soc.
190 (1974), 285-299) which states that the metric entropy of an invariant
measure of a topological dynamical system that satisfies the periodic
specification property is typically zero.
  We also show that if $X$ is compact and if $f$ is an expansive or a Lipschitz
map with a dense set of periodic measures, typically the lower correlation
entropy for $q\in(0,1)$ is equal to zero. Moreover, we show that if $X$ is a
compact metric space and if $f$ is an expanding map with a dense set of
periodic measures, then the set of invariant measures with packing dimension,
upper rate of recurrence and upper quantitative waiting time indicator equal to
zero is residual.
  Finally, we present an alternative proof of the fact that the set of
expansive measures is a $G_{\delta\sigma}$ set in the set of probability
measures $\M(X)$, if $X$ is a Polish metric space and if $f$ is uniformly
continuous; this result was originally proved by Lee, Morales and Shin (Lee,
K., Morales, C. A., and Shin, B. On the set of expansive measures. Commun.
Contemp. Math. 20, 7 (2018), 1750086, 10) for compact metric spaces.


  Nonlinear photocurrent in time-reversal invariant noncentrosymmetric systems
have attracted substantial interest. Here we propose two new types of
second-order nonlinear direct photocurrent as the counterpart of normal shift
photocurrent (NSC) and normal injection photocurrent (NIC), namely magnetic
shift photocurrent (MSC) and magnetic injection photocurrent (MIC) in
time-reversal symmetry and inversion symmetry broken system. We show that MSC
is mainly governed by shift vector and interband Berry curvature, and MIC is
dominated by absorption strength and asymmetry of the group velocity difference
at time-reversed $\pm$$\textbf{k}$ points. MSC and MIC can be induced by
circularly and linearly polarized light, respectively, in
$\mathcal{PT}$-symmetric systems with $\mathcal{P}$ and $\mathcal{T}$ being
individually broken. Taking $\mathcal{PT}$-symmetric magnetic topological
quantum material bilayer antiferromagnetic (AFM) MnBi$_2$Te$_4$ as an example,
we predict the presence of large MIC in the terahertz frequency regime which
can be magnetically switched between two AFM states with time-reversed spin
orderings. While NSC vanishes in $\mathcal{T}$-symmetric systems, external
electric field breaks $\mathcal{PT}$ symmetry and enables large NSC response
which can be electrically switched. MIC and NSC are perpendicular to each other
upon linearly $x$/$y$-polarized light, and are highly tunable under electric
field, resulting in giant nonlinear photocurrent response down to a few THz
regime. It suggests bilayer AFM MnBi$_2$Te$_4$ as a tunable platform with rich
THz and magneto-optoelectronic applications. The present work reveals that
nonlinear photocurrent provides a powerful tool for deciphering magnetic
structures and interactions, particularly fruitful for probing and
understanding magnetic topological quantum materials.


  If known, the spectrum of heavy-hadron molecules will be a key tool to
disentangle the nature of the exotic states that are being discovered in
experiments. Here we argue that the general features of the molecular spectrum
can be deduced from the idea that the short-range interaction between the heavy
hadrons is effectively described by scalar and vector meson exchange, i.e. the
$\sigma$, $\omega$ and $\rho$ mesons. By means of a contact-range theory where
the couplings are saturated by the aforementioned light mesons we are indeed
able to postdict the $X(3872)$ (as a $D^* \bar{D}$ molecule) from the three
$P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ pentaquarks (as $\bar{D}\Sigma_c$ and
$\bar{D}^* \Sigma_c$ molecules). We predict a $J^{PC} = 1^{--}$ $D \bar{D}_1$
molecule at $4240-4260\,{\rm MeV}$ which might support the hypothesis that the
$Y(4260)$ is at least partly molecular. The extension of these ideas to the
light baryons requires minor modifications, after which we recover approximate
SU(4)-Wigner symmetry in the two-nucleon system and approximately reproduce the
masses of the deuteron and the virtual state.


  The relation between the covariant Euclidean free-energy $F^E$ and the
canonical statistical-mechanical free energy $F^C$ in the presence of the
Killing horizons is studied. $F^E$ is determined by the covariant Euclidean
effective action. The definition of $F^C$ is related to the Hamiltonian which
is the generator of the evolution along the Killing time. At arbitrary
temperatures $F^E$ acquires additional ultraviolet divergences because of
conical singularities. The divergences of $F^C$ are different and occur since
the density ${dn \over d\omega}$ of the energy levels of the system blows up
near the horizon in an infrared way. We show that there are regularizations
that make it possible to remove the infrared cutoff in ${dn \over d\omega}$.
After that the divergences of $F^C$ become identical to the divergences of
$F^E$. The latter property turns out to be crucial to reconcile the covariant
Euclidean and the canonical formulations of the theory. The method we use is
new and is based on a relation between ${dn \over d\omega}$ and heat kernels on
hyperbolic-like spaces. Our analysis includes spin 0 and spin 1/2 fields on
arbitrary backgrounds. For these fields the divergences of ${dn \over
d\omega}$, $F^C$ and $F^E$ are presented in the most complete form.


  Understanding and identifying musical shape plays an important role in music
education and performance assessment. To simplify the otherwise time- and
cost-intensive musical shape evaluation, in this paper we explore how
artificial intelligence (AI) driven models can be applied. Considering musical
shape evaluation as a classification problem, a light-weight Siamese residual
neural network (S-ResNN) is proposed to automatically identify musical shapes.
To assess the proposed approach in the context of piano musical shape
evaluation, we have generated a new dataset, containing 4116 music pieces
derived by 147 piano preparatory exercises and performed in 28 categories of
musical shapes. The experimental results show that the S-ResNN significantly
outperforms a number of benchmark methods in terms of the precision, recall and
F1 score.


  It is widely recognized that the structure of porous media is of relevance
for a variety of mechanical and physical phenomena. The focus of the present
work is on capillarity, a pore-scale process occurring at the micron scale. We
attempt to characterize the influence of pore shape for capillary infiltration
by means of Lattice Boltzmann simulations in 2D with reactive boundaries
leading to surface growth and ultimately to pore closure. The systems under
investigation consist of single channels with different simplified
morphologies: namely, periodic profiles with sinusoidal, step-shaped and
zig-zag walls, as well as constrictions and expansions with rectangular, convex
and concave steps. This is a useful way to decompose the complexity of typical
porous media into basic structures. The simulations show that the minimum
radius alone fails to characterize properly the infiltration dynamics. The
structure of the channels emerge as the dominant property controlling the
process. A factor responsible for this behavior is identified as being the
occurrence of pinning of the contact line. It turns out that the optimal
configuration for the pore structure arises from the packing of large particles
with round shapes. In this case, the probability to have flow paths wide and
straight is higher. Faceted surfaces presenting sharp edges should be avoided
because of the phenomenon of pinning near narrow-to-wide parts. This study is
motivated by the infiltration of molten metals into carbon preforms. This is a
manufacturing technique for ceramic components devised to advanced
applications. Guidelines for experimental work are discussed.


  Numerical approximation of the Boltzmann equation is a challenging problem
due to its high-dimensional, nonlocal, and nonlinear collision integral. Over
the past decade, the Fourier-Galerkin spectral method has become a popular
deterministic method for solving the Boltzmann equation, manifested by its high
accuracy and potential of being further accelerated by the fast Fourier
transform. Albeit its practical success, the stability of the method is only
recently proved by Filbet, F. & Mouhot, C. in [$ Trans. Amer. Math. Soc.$ 363,
no. 4 (2011): 1947-1980.] by utilizing the "spreading" property of the
collision operator. In this work, we provide a new proof based on a careful
$L^2$ estimate of the negative part of the solution. We also discuss the
applicability of the result to various initial data, including both continuous
and discontinuous functions.


  We employ the twistor approach to the construction of U(2) multi-instantons
`a la 't Hooft on noncommutative R^4. The noncommutative deformation of the
Corrigan-Fairlie-'t Hooft-Wilczek ansatz is derived. However, naively
substituting into it the 't Hooft-type solution is unsatisfactory because the
resulting gauge field fails to be self-dual on a finite-dimensional subspace of
the Fock space. We repair this deficiency by a suitable Murray-von Neumann
transformation after a specific projection of the gauge potential. The proper
noncommutative 't Hooft multi-instanton field strength is given explicitly, in
a singular as well as in a regular gauge.


  In this paper, we consider compressive sensing (CS)-based recovery of delays
and Doppler frequencies of targets in high resolution radars. We propose a
novel sub-Nyquist sampling method in the Fourier domain based on difference
sets (DS), called DS-sampling, to create dictionaries with highly incoherent
atoms. The coherence of the dictionary reaches the Welch minimum bound if the
DS-sampling is employed. This property let us to implement sub-Nyquist high
resolution radars with minimum number of samples. We also develop a low
complexity recovery method, based on structured CS and propose a new waveform,
called difference set--frequency coded modulated (DS-FCM) waveform, to boost
the recovery performance of the sub-Nyquist radar in noisy environments. The
proposed method solves some of the common problems in many CS-based radars and
overcome disadvantages of the conventional Nyquist processing, i.e. matched
filtering in high resolution radar systems. The proposed method allows us to
design sub-Nyquist radars, which require less than 2% of Nyquist samples and
recover targets without resolution degradation in comparison to the
conventional Nyquist processing.


  Some Besov-type spaces $B^{s,\tau}_{p,q}(\mathbb{R}^n)$ can be characterized
in terms of the behavior of the Fourier--Haar coefficients. In this article,
the authors discuss some necessary restrictions for the parameters $s$, $\tau$,
$p$, $q$ and $n$ of this characterization. Therefore, the authors measure the
regularity of the characteristic function $\mathcal X$ of the unit cube in
$\mathbb{R}^n$ via the Besov-type spaces $B^{s,\tau}_{p,q}(\mathbb{R}^n)$.
Furthermore, the authors study necessary and sufficient conditions such that
the operation $\langle f, \mathcal{X} \rangle$ generates a continuous linear
functional on $B^{s,\tau}_{p,q}(\mathbb{R}^n)$.


  We generalize recent analysis of the dynamics of point particle in
Horava-Lifshitz background to the case of string probe when we replace the
Hamiltonian constraint of the Polyakov string with the constraint that breaks
Lorentz invariance of target space-time. Then we find corresponding Lagrangian
and argue that the world-sheet theory is invariant under foliation preserving
diffeomorphism. Finally we discuss the Hamiltonian dynamics and show that this
is well defined on condition that the world-sheet lapse function obeys the
projectability condition.


  Active galactic nuclei (AGN) found at the centers of clusters of galaxies are
a possible source for weak cluster-wide magnetic fields. To evaluate this
scenario, we present 3D adaptive mesh refinement MHD simulations of a cool-core
cluster that include injection of kinetic, thermal, and magnetic energy via an
AGN-powered jet. Using the MHD solver in FLASH 2, we compare several
sub-resolution approaches that link the estimated accretion rate as measured on
the simulation mesh to the accretion rate onto the central black hole and the
resulting feedback. We examine the effects of magnetized outflows on the
accretion history of the black hole and discuss the ability of these models to
magnetize the cluster medium.


  This paper introduces to the calculus of regular expressions a replace
operator, ->, and defines a set of replacement expressions that concisely
encode several alternate variations of the operation.
  The basic case is unconditional obligatory replacement:
  UPPER -> LOWER
  Conditional versions of replacement, such as,
  UPPER -> LOWER || LEFT _ RIGHT constrain the operation by left and right
contexts. UPPER, LOWER, LEFT, and RIGHT may be regular expressions of any
complexity.
  Replace expressions denote regular relations. The replace operator is defined
in terms of other regular expression operators using techniques introduced by
Ronald M. Kaplan and Martin Kay in "Regular Models of Phonological Rule
Systems" (Computational Linguistics 20:3 331-378. 1994).


  We have one more look at the (homological) perturbation lemma and we point
out some non-standard consequences, including the relevance to deformations.


  We analyze the quantum chaotic behavior of the Yukawa-SYK model as a function
of filling and temperature, which describes random Yukawa interactions between
$N$ complex fermions and $M$ bosons in zero spatial dimensions, for both the
non-Fermi liquid and insulating states at finite temperature and chemical
potential. We solve the ladder equations for the out-of-time-order correlator
(OTOC) for both the bosons and fermions. Despite the appearance of the chemical
potential in the Hamiltonian, which explicitly introduces an additional energy
scale, the OTOCs for the fermions and bosons in the non-Fermi liquid state turn
out to be unaffected, and the Lyapunov exponents that diagnose chaos remain
maximal. As the chemical potential increases, the system is known to experience
a first-order transition from a critical phase to a gapped insulating phase. We
postulate that the boundary of the region in parameter space where each phase
is (meta)stable coincides with the curve on which the Lyapunov exponent is
maximal. By calculating the exponent in the insulating phase and comparing to
numerical results on the boundaries of stability, we show that this is
plausible.


  A major disagreement between different views about the foundations of quantum
mechanics concerns whether for a theory to be intelligible as a fundamental
physical theory it must involve a "primitive ontology" (PO), i.e., variables
describing the distribution of matter in 4-dimensional space-time. In this
paper, we illustrate the value of having a PO. We do so by focussing on the
role that the PO plays for extracting predictions from a given theory and
discuss valid and invalid derivations of predictions. To this end, we
investigate a number of examples based on toy models built from the elements of
familiar interpretations of quantum theory.


  Pole-skipping refers to the special phenomenon that the pole and the zero of
a retarded two-point Green's function coincide at certain points in momentum
space. We study the pole-skipping phenomenon in holographic Green's functions
of boundary operators that are dual to massive $p$-form fields and the dRGT
massive gravitational fields in the AdS black hole background. Pole-skipping
points for these systems are computed using the near horizon method. The
relation between the pole-skipping points of massive fields and their massless
counterparts is revealed. In particular, as the field mass $m$ is varied from
zero to non-zero, the pole-skipping phenomenon undergoes an abrupt change with
doubled pole-skipping points found in the massive case. This arises from the
breaking of gauge invariance due to the mass term and the consequent appearance
of more degrees of freedom. We recover the gauge invariance using the
Stueckelberg formalism by introducing auxiliary dynamical fields. The extra
pole-skipping points are identified to be associated with the Stueckelberg
fields. We also observe that, as the mass varies, some pole-skipping points of
the wave number $q$ may move from a non-physical region with complex $q$ to a
physical region with real $q$.


  We study some Hardy-type inequalities involving a general norm in $R^n$ and
an anisotropic distance function to the boundary. The case of the optimality of
the constants is also addressed.


  Instruction-tuned Large Language Models (LLMs) excel at many tasks and will
even explain their reasoning, so-called self-explanations. However, convincing
and wrong self-explanations can lead to unsupported confidence in LLMs, thus
increasing risk. Therefore, it's important to measure if self-explanations
truly reflect the model's behavior. Such a measure is called
interpretability-faithfulness and is challenging to perform since the ground
truth is inaccessible, and many LLMs only have an inference API. To address
this, we propose employing self-consistency checks to measure faithfulness. For
example, if an LLM says a set of words is important for making a prediction,
then it should not be able to make its prediction without these words. While
self-consistency checks are a common approach to faithfulness, they have not
previously been successfully applied to LLM self-explanations for
counterfactual, feature attribution, and redaction explanations. Our results
demonstrate that faithfulness is explanation, model, and task-dependent,
showing self-explanations should not be trusted in general. For example, with
sentiment classification, counterfactuals are more faithful for Llama2, feature
attribution for Mistral, and redaction for Falcon 40B.


  We consider testing for presence of a signal in Gaussian white noise with
intensity 1/sqrt(n), when the alternatives are given by smoothness ellipsoids
with an L2-ball of (squared) radius rho removed. It is known that, for a fixed
Sobolev type ellipsoid of smoothness beta and size M, a rho which is of order n
to the power -4 beta/(4 beta+1)} is the critical separation rate, in the sense
that the minimax error of second kind over alpha-tests stays asymptotically
between 0 and 1 strictly (Ingster, 1982). In addition, Ermakov (1990) found the
sharp asymptotics of the minimax error of second kind at the separation rate.
For adaptation over both beta and M in that context, it is known that a
loglog-penalty over the separation rate for rho is necessary for a nonzero
asymptotic power. Here, following an example in nonparametric estimation
related to the Pinsker constant, we investigate the adaptation problem over the
ellipsoid size M only, for fixed smoothness degree beta. It is established that
the sharp risk asymptotics can be replicated in that adaptive setting, if rho
tends to zero slower than the separation rate. The penalty for adaptation here
turns out to be a sequence tending to infinity arbitrarily slowly.


  Aims: We present POLARIS (POLArized RadIation Simulator), a newly developed
three-dimensional Monte-Carlo radiative transfer code. POLARIS was designed to
calculate dust temperature, polarization maps, and spectral energy
distributions. It is optimized to handle data that results from sophisticated
magneto-hydrodynamic simulations. The main purpose of the code is to prepare
and analyze multi-wavelength continuum polarization measurements in the context
of magnetic field studies in the interstellar medium. An exemplary application
is the investigation of the role of magnetic fields in star formation
processes.
  Methods: We combine currently discussed state-of-the-art grain alignment
theories with existing dust heating and polarization algorithms. We test the
POLARIS code on multiple scales in complex astrophysical systems that are
associated with different stages of star formation. POLARIS uses the full
spectrum of dust polarization mechanisms to trace the underlying magnetic field
morphology.
  Results: Resulting temperature distributions are consistent with the density
and position of radiation sources resulting from magneto-hydrodynamic (MHD) -
collapse simulations. The calculated layers of aligned dust grains in the
considered cirumstellar disk models are in excellent agreement with theoretical
predictions. Finally, we compute unique patterns in synthetic multi-wavelength
polarization maps that are dependent on applied dust-model and grain-alignment
theory in analytical cloud models.


  One salient characteristic of Quantum Cascade Laser (QCL) is its very shor
gain recovery time that so far thwarted the attempts to achieve self-mode
locking of the device into a train of single pulses. We show theoretically that
four wave mixing, combined with the short gain recovery time causes QCL to
operate in the self-frequency-modulated regime characterized by a constant
power in time domain and stable coherent comb in the frequency domain.Coherent
frequency comb may enable many potential applications of QCL in sensing and
measurement.


  A celebrated impossibility result by Myerson and Satterthwaite (1983) shows
that any truthful mechanism for two-sided markets that maximizes social welfare
must run a deficit, resulting in a necessity to relax welfare efficiency and
the use of approximation mechanisms. Such mechanisms in general make extensive
use of the Bayesian priors. In this work, we investigate a question of
increasing theoretical and practical importance: how much prior information is
required to design mechanisms with near-optimal approximations?
  Our first contribution is a more general impossibility result stating that no
meaningful approximation is possible without any prior information, expanding
the famous impossibility result of Myerson and Satterthwaite.
  Our second contribution is that one {\em single sample} (one number per
item), arguably a minimum-possible amount of prior information, from each
seller distribution is sufficient for a large class of two-sided markets. We
prove matching upper and lower bounds on the best approximation that can be
obtained with one single sample for subadditive buyers and additive sellers,
regardless of computational considerations.
  Our third contribution is the design of computationally efficient blackbox
reductions that turn any one-sided mechanism into a two-sided mechanism with a
small loss in the approximation, while using only one single sample from each
seller. On the way, our blackbox-type mechanisms deliver several interesting
positive results in their own right, often beating even the state of the art
that uses full prior information.


  We use the historic record of sunspot groups compiled by the Royal Greenwich
Observatory together with the sunspot number to derive the statistical
properties of sunspot group emergence in dependence of cycle phase and
strength. In particular we discuss the latitude, longitude, area and tilt angle
of sunspot groups as functions of the cycle strength and of time during the
solar cycle. Using these empirical characteristics the time-latitude diagram of
sunspot group emergence (butterfly diagram) is reconstructed from 1700 onward
on the basis of the Wolf and group sunspot numbers. This reconstruction will be
useful in studies of the long-term evolution of the Sun's magnetic field.


  In this note, we give a geometric characterization of the compact and totally
umbilical hypersurfaces that carry a non trivial locally static Killing Initial
Data (KID). More precisely, such compact hypersurfaces have constant mean
curvature and are isometric to one of the following manifolds: (i) Sn the
standard sphere, (ii) a finite quotient of a warped product of a circle with a
compact Einstein manifold of positive scalar curvature. In particular, these
hypersurfaces have harmonic curvature and strictly positive constant scalar
curvature.


  Recent observations indicate that in a large fraction of binary neutron star
(BNS) mergers a long-lived neutron star (NS) may be formed rather than a black
hole. Unambiguous electromagnetic (EM) signatures of such a scenario would
strongly impact our knowledge on how short gamma-ray bursts (SGRBs) and their
afterglow radiation are generated. Furthermore, such EM signals would have
profound implications for multimessenger astronomy with joint EM and
gravitational-wave (GW) observations of BNS mergers, which will soon become
reality with the ground-based advanced LIGO/Virgo GW detector network starting
its first science run this year. Here we explore such EM signatures based on
the model presented in a companion paper, which provides a self-consistent
evolution of the post-merger system and its EM emission starting from an early
baryonic wind phase and resulting in a final pulsar wind nebula that is
confined by the previously ejected material. Lightcurves and spectra are
computed for a wide range of post-merger physical properties and particular
attention is paid to the emission in the X-ray band. In the context of SGRB
afterglow modeling, we present X-ray lightcurves corresponding to the
'standard' and the recently proposed 'time-reversal' scenario (SGRB prompt
emission produced at the time of merger or at the time of collapse of the
long-lived NS). The resulting afterglow lightcurve morphologies include, in
particular, single and two-plateau features with timescales and luminosities
that are in good agreement with the observations by the Swift satellite.
Furthermore, we compute the X-ray signal that should precede the SGRB in the
time-reversal scenario. If found, such a signal would represent smoking-gun
evidence for this scenario. Finally, we find a bright, highly isotropic EM
transient signal peaking in the X-ray band ...


  We consider the Wiener integral with respect to a $d$-parameter Hermite
process with Hurst multi-index ${\bf H}= (H_{1},\ldots, H_{d}) \in \left(
\frac{1}{2}, 1\right) ^{d}$ and we analyze the limit behavior in distribution
of this object when the components of ${\bf H}$ tend to $1$ and/or
$\frac{1}{2}$. As examples, we focus on the solution to the stochastic heat
equation with additive Hermite noise and to the Hermite Ornstein-Uhlenbeck
process.


  We examine some common features of minimal surfaces, nonzero constant mean
curvature surfaces and marginally outer trapped surfaces, concerning their
stability and rigidity, and consider some applications to Riemannian geometry
and general relativity.


  I propose and briefly define the concept of Urban Isobenefit Lines by using
functions as easy as efficient, whose results can offer a rich tool to use into
spatial equilibrium analysis involving cities. They are line joining urban
points with equal level of positional advantage from city amenities. The
results which one obtain by implementing a chosen function, gave specific
scenarios: numerically described by indicators and graphically visualized by
efficient city matrix views. This is also a theoretical concept for the Urban
Economics theory and Spatial Equilibrium analysis in cities.


  It has been demonstrated that quantum vacuum energy gravitates according to
the equivalence principle, at least for the finite Casimir energies associated
with perfectly conducting parallel plates. We here add further support to this
conclusion by considering parallel semitransparent plates, that is,
delta-function potentials, acting on a massless scalar field, in a spacetime
defined by Rindler coordinates (tau,x,y,xi). Fixed xi in such a spacetime
represents uniform acceleration. We calculate the force on systems consisting
of one or two such plates at fixed values of xi. In the limit of large Rindler
coordinate xi (small acceleration), we recover (via the equivalence principle)
the situation of weak gravity, and find that the gravitational force on the
system is just Mg, where g is the gravitational acceleration and M is the total
mass of the system, consisting of the mass of the plates renormalized by the
Casimir energy of each plate separately, plus the energy of the Casimir
interaction between the plates. This reproduces the previous result in the
limit as the coupling to the delta-function potential approaches infinity.


  We introduce a simple and effective method for retrieval of videos showing a
specific event, even when the videos of that event were captured from
significantly different viewpoints. Appearance-based methods fail in such
cases, as appearances change with large changes of viewpoints.
  Our method is based on a pixel-based feature, "motion barcode", which records
the existence/non-existence of motion as a function of time. While appearance,
motion magnitude, and motion direction can vary greatly between disparate
viewpoints, the existence of motion is viewpoint invariant. Based on the motion
barcode, a similarity measure is developed for videos of the same event taken
from very different viewpoints. This measure is robust to occlusions common
under different viewpoints, and can be computed efficiently.
  Event retrieval is demonstrated using challenging videos from stationary and
hand held cameras.


  Topic modeling has been a widely used tool for unsupervised text analysis.
However, comprehensive evaluations of a topic model remain challenging.
Existing evaluation methods are either less comparable across different models
(e.g., perplexity) or focus on only one specific aspect of a model (e.g., topic
quality or document representation quality) at a time, which is insufficient to
reflect the overall model performance. In this paper, we propose WALM (Words
Agreement with Language Model), a new evaluation method for topic modeling that
comprehensively considers the semantic quality of document representations and
topics in a joint manner, leveraging the power of large language models (LLMs).
With extensive experiments involving different types of topic models, WALM is
shown to align with human judgment and can serve as a complementary evaluation
method to the existing ones, bringing a new perspective to topic modeling. Our
software package will be available at
https://github.com/Xiaohao-Yang/Topic_Model_Evaluation, which can be integrated
with many widely used topic models.


  Approximate linear programming (ALP) and its variants have been widely
applied to Markov Decision Processes (MDPs) with a large number of states. A
serious limitation of ALP is that it has an intractable number of constraints,
as a result of which constraint approximations are of interest. In this paper,
we define a linearly relaxed approximation linear program (LRALP) that has a
tractable number of constraints, obtained as positive linear combinations of
the original constraints of the ALP. The main contribution is a novel
performance bound for LRALP.


  It is well known that an (in general, non-commutative) set of non-Hermitian
operators $\Lambda_j$ with real eigenvalues need not necessarily represent
observables. We describe a specific class of quantum models in which these
operators plus the underlying physical Hilbert-space metric $\Theta$ are all
represented in terms of an auxiliary operator $(N+1)-$plet $Z_k$,
$k=0,1,\ldots,N$. Our formalism degenerates to the ${\cal PT}-$symmetric
quantum mechanics at $N=2$, with metric $\Theta=Z_2Z_1$, parity ${\cal P}=Z_2$,
charge ${\cal C}=Z_1$ and Hamiltonian $H=Z_0$.


  We study a percolation problem on a substrate formed by two-dimensional XY
spin configurations, using Monte Carlo methods. For a given spin configuration
we construct percolation clusters by randomly choosing a direction $x$ in the
spin vector space, and then placing a percolation bond between nearest-neighbor
sites $i$ and $j$ with probability $p_{ij} = \max (0,1-e^{-2K s^x_i s^x_j})$,
where $K > 0$ governs the percolation process. A line of percolation thresholds
$K_{\rm c} (J)$ is found in the low-temperature range $J \geq J_{\rm c}$, where
$J > 0$ is the XY coupling strength. Analysis of the correlation function $g_p
(r)$, defined as the probability that two sites separated by a distance $r$
belong to the same percolation cluster, yields algebraic decay for $K \geq
K_{\rm c}(J)$, and the associated critical exponent depends on $J$ and $K$.
Along the threshold line $K_{\rm c}(J)$, the scaling dimension for $g_p$ is,
within numerical uncertainties, equal to $1/8$. On this basis, we conjecture
that the percolation transition along the $K_{\rm c} (J)$ line is of the
Berezinskii-Kosterlitz-Thouless type.


  Phase transitions in dissipative quantum systems are intriguing because they
are induced by the interplay between coherent quantum and incoherent classical
fluctuations. Here, we investigate the crossover from a quantum to a classical
absorbing phase transition arising in the quantum contact process (QCP). The
Lindblad equation contains two parameters, $\omega$ and $\kappa$, which adjust
the contributions of the quantum and classical effects, respectively. We find
that in one dimension when the QCP starts from a homogeneous state with all
active sites, there exists a critical line in the region $0 \le \kappa <
\kappa_*$ along which the exponent $\alpha$ (which is associated with the
density of active sites) decreases continuously from a quantum to the classical
directed percolation (DP) value. This behavior suggests that the quantum
coherent effect remains to some extent near $\kappa=0$. However, when the QCP
in one dimension starts from a heterogeneous state with all inactive sites
except for one active site, all the critical exponents have the classical DP
values for $\kappa \ge 0$. In two dimensions, anomalous crossover behavior does
not occur, and classical DP behavior appears in the entire region of $\kappa
\ge 0$ regardless of the initial configuration. Neural network machine learning
is used to identify the critical line and determine the correlation length
exponent. Numerical simulations using the quantum jump Monte Carlo technique
and tensor network method are performed to determine all the other critical
exponents of the QCP.


  In this paper, we present the first results obtained using $\sim$ 50 ks
observations of the bright low-mass X-ray binary (LMXB) GX 17+2 with Large Area
X-ray Proportional Counter (LAXPC) onboard {\it AstroSat}. The source traced
out a complete Z-track in the hardness intensity diagram (HID). The spectra at
different sections of the Z-diagram are well described by either a combination
of a thermal Comptonization component, a power-law and a relativistic iron line
or a model consisting of a thermal disk component, a single temperature
blackbody, a power-law and a relativistic iron line. Fitting the spectra with
both phenomenological models suggests that the power-law component is strong in
the horizontal branch (HB), becomes weaker as the source moves down the normal
branch (NB) and then again becomes stronger as the sources moves up the flaring
branch (FB). However, we find that the strength of the power-law component is
model dependent, although the trend in the variation of the power-law strength
along the Z-track is similar. A simple model composed by a Comptonized emission
and power-law component, convolved with the ionized reflection, also describes
the spectra very well.
  A normal branch oscillation (NBO) with a centroid frequency 7.42$\pm$0.23 Hz,
quality factor (Q) $\sim$ 4.88, rms 1.41$\pm$0.29\% and significance
5.1$\sigma$ is detected at the middle of the NB. The parameters of the
Comptonized emission show a systematic evolution along the Z-diagram. The
optical depth of the corona increases as the source moves up along the FB,
suggesting possible trigger of an outflow or dumping of the disc material in to
the corona by radiation pressure.


  We present a novel strategy to systematically study complex-structure moduli
stabilization in Type IIB and F-theory flux compactifications. In particular,
we determine vacua in any asymptotic regime of the complex-structure moduli
space by exploiting powerful tools of asymptotic Hodge theory. In a leading
approximation the moduli dependence of the vacuum conditions are shown to be
polynomial with a dependence given by sl(2)-weights of the fluxes. This simple
algebraic dependence can be extracted in any asymptotic regime, even though in
nearly all asymptotic regimes essential exponential corrections have to be
present for consistency. We give a pedagogical introduction to the
sl(2)-approximation as well as a detailed step-by-step procedure for
constructing the corresponding Hodge star operator. To exemplify the
construction, we present a detailed analysis of several Calabi-Yau three- and
fourfold examples. For these examples we illustrate that the vacua in the
sl(2)-approximation match the vacua obtained with all polynomial and essential
exponential corrections rather well, and we determine the behaviour of the
tadpole contribution of the fluxes. Finally, we discuss the structure of vacuum
loci and their relations to several swampland conjectures. In particular, we
comment on the realization of the so-called linear scenario in view of the
tadpole conjecture.


  We analyze the open charm production in the binary $\pi p \to \bar{D}
\Lambda_c$ and $\pi(\rho) J/\psi$ reactions within the Regge theory including
the absorption corrections. The calculations show that the total cross section
is about a few $\mu$b for the first processes and a few mb for the second
reactions at energy close to the threshold. Then it decreases with increasing
energy according to the true Regge asymptotics.


  The central 2x1 kpc of the starburst galaxy NGC 253 has been imaged using the
Submillimeter Array at a 60 pc resolution in the J=2-1 transitions of 12CO,
13CO, and C18O as well as in the 1.3 mm continuum. Molecular gas and dust are
mainly in the circumnuclear disk of ~500 pc radius, with warm (~40 K) and high
area-filling factor gas in its central part. Two gas shells or cavities have
been discovered in the circumnuclear disk. They have ~100 pc diameters and have
large velocity widths of 80-100 km/s, suggestive of expansion at ~50 km/s.
Modeled as an expanding bubble, each shell has an age of ~0.5 Myr and needed
kinetic energy of ~1E46 J as well as mean mechanical luminosity of ~1E33 W for
its formation. The large energy allows each to be called a superbubble. A ~10^6
Msun super star cluster can provide the luminosity, and could be a building
block of the nuclear starburst in NGC 253. Alternatively, a hypernova can also
be the main source of energy for each superbubble, not only because it can
provide the mechanical energy and luminosity but also because the estimated
rate of superbubble formation and that of hypernova explosions are comparable.
Our observations indicate that the circumnuclear molecular disk harboring the
starburst is highly disturbed on 100 pc or smaller scales, presumably by
individual young clusters and stellar explosions, in addition to globally
disturbed in the form of the well-known superwind.


  Recently, Bai and Benzi proposed a class of regularized Hermitian and
skew-Hermitian splitting methods (RHSS) iteration methods for solving the
nonsingular saddle point problem. In this paper, we apply this method to solve
the singular saddle point problem from the Stokes equations. In the process of
the semi-convergence analysis, we get that the RHSS method and the HSS method
are unconditionally semi-convergent, which weaken the previous results. Then
some spectral properties of the corresponding preconditioned matrix and a class
of improved preconditioned matrix are analyzed. Finally, some numerical
experiments on linear systems arising from the discretization of the Stokes
equations are presented to illustrate the feasibility and effectiveness of this
method and preconditioners.


  Answer Set Programming (ASP) is a powerful declarative programming paradigm
commonly used for solving challenging search and optimization problems. The
modeling languages of ASP are supported by sophisticated solving algorithms
(solvers) that make the solution search efficient while enabling the programmer
to model the problem at a high level of abstraction. As an approach to
Knowledge Representation and Reasoning, ASP benefits from its simplicity,
conciseness and rigorously defined semantics. These characteristics make ASP a
straightforward way to develop formally verifiable programs. In the context of
artificial intelligence (AI), the clarity of ASP programs lends itself to the
construction of explainable, trustworthy AI. In support of these goals, my
research is concerned with extending the theory and tools supporting the
verification of ASP progams.


  The Fluctuation Relation (FR) is an asymptotic result on the distribution of
certain observables averaged over time intervals T as T goes to infinity and it
is a generalization of the fluctuation--dissipation theorem to far from
equilibrium systems in a steady state which reduces to the usual Green-Kubo
(GK) relation in the limit of small external non conservative forces. FR is a
theorem for smooth uniformly hyperbolic systems, and it is assumed to be true
in all dissipative ``chaotic enough'' systems in a steady state. In this paper
we develop a theory of finite time corrections to FR, needed to compare the
asymptotic prediction of FR with numerical observations, which necessarily
involve fluctuations of observables averaged over finite time intervals T. We
perform a numerical test of FR in two cases in which non Gaussian fluctuations
are observable while GK does not apply and we get a non trivial verification of
FR that is independent of and different from linear response theory. Our
results are compatible with the theory of finite time corrections to FR, while
FR would be observably violated, well within the precision of our experiments,
if such corrections were neglected.


  Approximate gravitational potentials are often used to describe analytically
the motion of particles near black holes (BHs), as well as to study the
structure of an accretion disk. Such 'pseudo-Newtonian' potentials are used
with the flat-metric equations. Here we consider the motion of a free particle
near a non-rotating BH in the context of an exact `logarithmic' gravitational
potential. We show how the logarithmic potential gives an exact solution for a
mechanical problem and present the relativistic Bernoulli equation for the
fluid in the Schwarzschild metric.


  The Dorokhov-Mello-Pereyra-Kumar (DMPK) equation for transmission eigenvalues
is derived for metallic carbon nanotubes with several conducting channels when
the potential range of scatterers is larger than the lattice constant. With
increasing system length L, the system approaches a fixed point, where only one
channel is perfectly conducting and other channels are completely closed. The
asymptotic behavior of the conductance in the long-L regime is investigated on
the basis of the DMPK equation. It is shown that the length scale for the
exponential decay of the typical conductance is reduced due to the presence of
the perfectly conducting channel. If a magnetic field is applied, the system
falls into the unitary class. It is pointed out that this transition is
characterized by the disappearance of the perfectly conducting channel and the
increase in decay length for the typical conductance.


  Video Anomaly Detection(VAD) has been traditionally tackled in two main
methodologies: the reconstruction-based approach and the prediction-based one.
As the reconstruction-based methods learn to generalize the input image, the
model merely learns an identity function and strongly causes the problem called
generalizing issue. On the other hand, since the prediction-based ones learn to
predict a future frame given several previous frames, they are less sensitive
to the generalizing issue. However, it is still uncertain if the model can
learn the spatio-temporal context of a video. Our intuition is that the
understanding of the spatio-temporal context of a video plays a vital role in
VAD as it provides precise information on how the appearance of an event in a
video clip changes. Hence, to fully exploit the context information for anomaly
detection in video circumstances, we designed the transformer model with three
different contextual prediction streams: masked, whole and partial. By learning
to predict the missing frames of consecutive normal frames, our model can
effectively learn various normality patterns in the video, which leads to a
high reconstruction error at the abnormal cases that are unsuitable to the
learned context. To verify the effectiveness of our approach, we assess our
model on the public benchmark datasets: USCD Pedestrian 2, CUHK Avenue and
ShanghaiTech and evaluate the performance with the anomaly score metric of
reconstruction error. The results demonstrate that our proposed approach
achieves a competitive performance compared to the existing video anomaly
detection methods.


  Recently, Ono and the third author discovered that the reciprocals of the
theta series $(q;q)_\infty^3$ and $(q^2;q^2)_\infty(q;q^2)_\infty^2$ have
infinitely many closed formulas in terms of MacMahon's quasimodular forms
$A_k(q)$ and $C_k(q)$. In this article, we use the well-known infinite product
identities due to Jacobi, Watson, and Hirschhorn to derive further such closed
formulas for reciprocals of other interesting infinite products. Moreover, with
these formulas, we approximate these reciprocals to arbitrary order simply
using MacMahon's functions and {\it MacMahon type} functions. For example, let
$\Theta_{6}(q):=\frac{1}{2}\sum_{n\in\mathbb{Z}} \chi_6(n) n
q^{\frac{n^2-1}{24}}$ be the theta function corresponding to the odd quadratic
character modulo $6$. Then for any positive integer $n$, we have
$$\frac{1}{\Theta_{6}(q)}= q^{-\frac{3n^2+n}{2}}\sum_{\substack{k=r_1\\ k\equiv
n\hspace{-0.2cm}\pmod{2}}}^{r_2}(-1)^{\frac{n-k}{2}}A_{k}(q)C_{\frac{3n-k}{2}}(q)+O(q^{n+1}),$$
where $r_1:=\lfloor\frac{3n-1-\sqrt{12n+13}}{3}\rfloor+1$ and
$r_2:=\lceil\frac{3n-1+\sqrt{12n+13}}{3}\rceil-1$.


  We present results showing the capability of concrete-based information
processing substrate in the signal classification task in accordance with in
materio computing paradigm. As the Reservoir Computing is a suitable model for
describing embedded in materio computation, we propose that this type of
presented basic construction unit can be used as a source for "reservoir of
states" necessary for simple tuning of the readout layer. In that perspective,
buildings constructed from computing concrete could function as a highly
parallel information processor for smart architecture. We present an electrical
characterization of the set of samples with different additive concentrations
followed by a dynamical analysis of selected specimens showing fingerprints of
memfractive properties. Moreover, on the basis of obtained parameters,
classification of the signal waveform shapes can be performed in scenarios
explicitly tuned for a given device terminal.


  We analyze PLANET photometric observations of the caustic-crossing
binary-lens microlensing event, EROS BLG-2000-5, and find that modeling the
observed light curve requires incorporation of the microlens parallax and the
binary orbital motion. The projected Einstein radius (~r_E = 3.61 +/- 0.11 AU)
is derived from the measurement of the microlens parallax, and we are also able
to infer the angular Einstein radius (theta_E = 1.38 +/- 0.12 mas) from the
finite source effect on the light curve, combined with an estimate of the
angular size of the source given by the source position in a color-magnitude
diagram. The lens mass, M = 0.612 +/- 0.057 M_sun, is found by combining these
two quantities. This is the first time that parallax effects are detected for a
caustic-crossing event and also the first time that the lens mass degeneracy
has been completely broken through photometric monitoring alone. The
combination of the projected Einstein radius and the angular Einstein radius
also allows us to conclude that the lens lies in the near side of the disk,
within 2.6 kpc of the Sun, while the radial velocity measurement indicates that
the source is a Galactic bulge giant.


  The extraction of spectral features from a music clip is a computationally
expensive task. As in order to extract accurate features, we need to process
the clip for its whole length. This preprocessing task creates a large overhead
and also makes the extraction process slower. We show how formatting a dataset
in a certain way, can help make the process more efficient by eliminating the
need for processing the clip for its whole duration, and still extract the
features accurately. In addition, we discuss the possibility of defining set
generic durations for analyzing a certain type of music clip while training.
And in doing so we cut down the need of processing the clip duration to just
10% of the global average.


  A recent neutron interferometry experiment claims to demonstrate a
paradoxical phenomena dubbed the "quantum Cheshire Cat" \cite{Denkmayr2014}. We
have reproduced and extended these results with an equivalent optical
interferometer. The results suggest that the photon travels through one arm of
the interferometer, while its polarization travels through the other. However,
we show that these experimental results belong to the domain where quantum and
classical wave theories coincide; there is nothing uniquely quantum about the
illusion of this cheshire cat.


  For structured-light range imaging, color stripes can be used for increasing
the number of distinguishable light patterns compared to binary BW stripes.
Therefore, an appropriate use of color patterns can reduce the number of light
projections and range imaging is achievable in single video frame or in "one
shot". On the other hand, the reliability and range resolution attainable from
color stripes is generally lower than those from multiply projected binary BW
patterns since color contrast is affected by object color reflectance and
ambient light. This paper presents new methods for selecting stripe colors and
designing multiple-stripe patterns for "one-shot" and "two-shot" imaging. We
show that maximizing color contrast between the stripes in one-shot imaging
reduces the ambiguities resulting from colored object surfaces and limitations
in sensor/projector resolution. Two-shot imaging adds an extra video frame and
maximizes the color contrast between the first and second video frames to
diminish the ambiguities even further. Experimental results demonstrate the
effectiveness of the presented one-shot and two-shot color-stripe imaging
schemes.


  In this article, we present a dual-band 28/38-GHz power amplifier (PA) with
inter-band suppression for millimeter-wave 5G communications. The dual-band
operation is achieved using a center-tapped transformer network with an extra
resonator which can provide optimum load impedance of the transistor in the two
bands and synthesize a short-circuit between the two bands. This feature
suppresses the PA signal emissions in the inter band, commonly allocated for
other applications. A design procedure is developed for the proposed matching
network including physical limits on the quality factor and the coupling
coefficient of the transformer. The PA is designed using a 22-nm fully-depleted
silicon-on-insulator (FD-SOI) CMOS process. The transistor stacking and a
four-path transformer parallel-series power combining techniques are used to
achieve high output power using the low-voltage process. The PA achieves
simulated performance of 22.6/22.0 dBm saturated output power, 19.8/20.0 dBm
output power at 1-dB gain compression, and 33/32 % maximum power-added
efficiency (PAE) at 28/38 GHz. The inter-band suppression is 6 dB at 33 GHz.


  The flow-based generative model is a deep learning generative model, which
obtains the ability to generate data by explicitly learning the data
distribution. Theoretically its ability to restore data is stronger than other
generative models. However, its implementation has many limitations, including
limited model design, too many model parameters and tedious calculation. In
this paper, a bi-parallel linear flow model for facial emotion generation from
emotion set images is constructed, and a series of improvements have been made
in terms of the expression ability of the model and the convergence speed in
training. The model is mainly composed of several coupling layers superimposed
to form a multi-scale structure, in which each coupling layer contains 1*1
reversible convolution and linear operation modules. Furthermore, this paper
sorted out the current public data set of facial emotion images, made a new
emotion data, and verified the model through this data set. The experimental
results show that, under the traditional convolutional neural network, the
3-layer 3*3 convolution kernel is more conducive to extracte the features of
the face images. The introduction of principal component decomposition can
improve the convergence speed of the model.


  The study of collaborative multi-agent bandits has attracted significant
attention recently. In light of this, we initiate the study of a new
collaborative setting, consisting of $N$ agents such that each agent is
learning one of $M$ stochastic multi-armed bandits to minimize their group
cumulative regret. We develop decentralized algorithms which facilitate
collaboration between the agents under two scenarios. We characterize the
performance of these algorithms by deriving the per agent cumulative regret and
group regret upper bounds. We also prove lower bounds for the group regret in
this setting, which demonstrates the near-optimal behavior of the proposed
algorithms.


  The Cherenkov Telescope Array (CTA) is planned to serve as a ground-based
observatory for (very-)high-energy gamma-ray astronomy, open to a wide
astrophysics community, providing a deep insight into the non-thermal
high-energy universe. It foresees a factor of ~10 improvement in sensitivity
above 100 GeV, with substantially better angular and spectral resolutions and
wider field-of-view in comparison with currently operational experiments. The
CTA consortium is investigating the different physics cases for different
proposed array configurations and subsets. Pulsar Wind Nebulae (PWNe), the most
numerous VHE Galactic sources, and Supernova Remnants (SNRs), believed to be
the acceleration sites of the bulk of cosmic rays, will be two of the main
observation targets for CTA. In this contribution, the main scientific goals
regarding PWNe and SNRs are discussed, and quantitative examples of the
capability of CTA to achieve these objectives are presented.


  We show how direct integration can be used to solve the closed amplitudes of
multi-cut matrix models with polynomial potentials. In the case of the cubic
matrix model, we give explicit expressions for the ring of non-holomorphic
modular objects that are needed to express all closed matrix model amplitudes.
This allows us to integrate the holomorphic anomaly equation up to holomorphic
modular terms that we fix by the gap condition up to genus four. There is an
one-dimensional submanifold of the moduli space in which the spectral curve
becomes the Seiberg--Witten curve and the ring reduces to the non-holomorphic
modular ring of the group $\Gamma(2)$. On that submanifold, the gap conditions
completely fix the holomorphic ambiguity and the model can be solved explicitly
to very high genus. We use these results to make precision tests of the
connection between the large order behavior of the 1/N expansion and
non-perturbative effects due to instantons. Finally, we argue that a full
understanding of the large genus asymptotics in the multi-cut case requires a
new class of non-perturbative sectors in the matrix model.


  We present new simulations of decaying hydromagnetic turbulence for a
relativistic equation of state relevant to the early universe. We compare
helical and nonhelical cases either with kinetically or magnetically dominated
initial fields. Both kinetic and magnetic initial helicities lead to maximally
helical magnetic fields after some time, but with different temporal decay
laws. Both are relevant to the early universe, although no mechanisms have yet
been identified that produce magnetic helicity with strengths comparable to the
big bang nucleosynthesis limit at scales comparable to the Hubble horizon at
the electroweak phase transition. Nonhelical magnetically dominated fields
could still produce picoGauss magnetic fields under most optimistic conditions.
Only helical magnetic fields can potentially have nanoGauss strengths at scales
up to 30 kpc today.


  We formulate the dynamics for the NS5-brane of the A-model, via the 'maximal
form' method, which couples all background fields to the world-volume. This
procedure provides the extra one- and five-forms fields of the extended Hitchin
model. The generalised B-model emerges as the world-volume theory of this
brane. The starting point of the construction is an embedding of the brane in a
superspace geometry with 16 fermionic directions. The correspondence with
Hitchin's formulation in terms of pure spinors is explained.


  In multi-agent informative path planning (MAIPP), agents must collectively
construct a global belief map of an underlying distribution of interest (e.g.,
gas concentration, light intensity, or pollution levels) over a given domain,
based on measurements taken along their trajectory. They must frequently replan
their path to balance the exploration of new areas with the exploitation of
known high-interest areas, to maximize information gain within a predefined
budget. Traditional approaches rely on reactive path planning conditioned on
other agents' predicted future actions. However, as the belief is continuously
updated, the predicted actions may not match the executed actions, introducing
noise and reducing performance. We propose a decentralized, deep reinforcement
learning (DRL) approach using an attention-based neural network, where agents
optimize long-term individual and cooperative objectives by sharing their
intent, represented as a distribution of medium-/long-term future positions
obtained from their own policy. Intent sharing enables agents to learn to claim
or avoid broader areas, while the use of attention mechanisms allows them to
identify useful portions of imperfect predictions, maximizing cooperation even
based on imperfect information. Our experiments compare the performance of our
approach, its variants, and high-quality baselines across various MAIPP
scenarios. We finally demonstrate the effectiveness of our approach under
limited communication ranges, towards deployments under realistic communication
constraints.