  We review recent work on 111 Fe-rich impulsive solar energetic ($\sim$ 3
MeV/nuc) particle (SEP) events observed from 1994 to 2013. Strong elemental
abundance enhancements scale with A/Q, the ion mass-to-charge ratio, as
(A/Q)$^{\alpha}$, where 2 $< \alpha <$ 8 for different events. Most Fe-rich
events are associated with both flares and coronal mass ejections (CMEs), and
those with larger $\alpha$ are associated with smaller flares, slower and
narrower CMEs, and lower SEP event fluences. The narrow equilibrium temperature
range required to fit the observed A/Q enhancements is 2.5--3.2 MK, far below
the characteristic flare temperatures of $>$ 10 MK. Only a small number of SEP
events slightly outside this temperature range were found in an expanded search
of impulsive Fe-rich events. Event characteristics are similar for events
isolated in time and those occurring in clusters. The current challenge is to
determine the solar sources of the Fe-rich events. Ambient coronal regions in
the 2.5--3.2 MK range are broadly distributed both in and outside active
regions. We explore the possibility of acceleration from thermal plasmas at
reconnecting current sheets in the context of observed standard and blowout
jets. Recent current sheet reconnection modelling provides a basis for the A/Q
enhancements.


  The wide luminosity dispersion seen for stars at a given effective
temperature in the H-R diagrams of young clusters and star forming regions is
often interpreted as due to significant (~10 Myr) spreads in stellar
contraction age. In the scenario where most stars are born with circumstellar
discs, and that disc signatures decay monotonically (on average) over
timescales of only a few Myr, then any such age spread should lead to clear
differences in the age distributions of stars with and without discs. We have
investigated large samples of stars in the Orion Nebula Cluster (ONC) using
three methods to diagnose disc presence from infrared measurements. We find no
significant difference in the mean ages or age distributions of stars with and
without discs, consistent with expectations for a coeval population. Using a
simple quantitative model we show that any real age spread must be smaller than
the median disc lifetime. For a log-normal age distribution, there is an upper
limit of <0.14 dex (at 99% confidence) to any real age dispersion, compared to
the ~=0.4 dex implied by the H-R diagram. If the mean age of the ONC is 2.5
Myr, this would mean at least 95% of its low-mass stellar population has ages
between 1.3--4.8 Myr. We suggest that the observed luminosity dispersion is
caused by a combination of observational uncertainties and physical mechanisms
that disorder the conventional relationship between luminosity and age for pre
main-sequence stars. This means that individual stellar ages from the H-R
diagram are unreliable and cannot be used to directly infer a star formation
history. Irrespective of what causes the wide luminosity dispersion, the
finding that any real age dispersion is less than the median disc lifetime
argues strongly against star formation scenarios for the ONC lasting longer
than a few Myr.


  In this paper, performance of cognitive transmission over time-selective flat
fading channels is studied under quality of service (QoS) constraints and
channel uncertainty. Cognitive secondary users (SUs) are assumed to initially
perform channel sensing to detect the activities of the primary users, and then
attempt to estimate the channel fading coefficients through training. Energy
detection is employed for channel sensing, and different minimum
mean-square-error (MMSE) estimation methods are considered for channel
estimation. In both channel sensing and estimation, erroneous decisions can be
made, and hence, channel uncertainty is not completely eliminated. In this
setting, performance is studied and interactions between channel sensing and
estimation are investigated.
  Following the channel sensing and estimation tasks, SUs engage in data
transmission. Transmitter, being unaware of the channel fading coefficients, is
assumed to send the data at fixed power and rate levels that depend on the
channel sensing results. Under these assumptions, a state-transition model is
constructed by considering the reliability of the transmissions, channel
sensing decisions and their correctness, and the evolution of primary user
activity which is modeled as a two-state Markov process. In the data
transmission phase, an average power constraint on the secondary users is
considered to limit the interference to the primary users, and statistical
limitations on the buffer lengths are imposed to take into account the QoS
constraints of the secondary traffic. The maximum throughput under these
statistical QoS constraints is identified by finding the effective capacity of
the cognitive radio channel. Numerical results are provided for the power and
rate policies.


  Multifluid simulations of plasma sheaths are increasingly used to model a
wide variety of problems in plasma physics ranging from global magnetospheric
flows around celestial bodies to plasma-wall interactions in thrusters and
fusion devices. For multifluid problems, accurate boundary conditions to model
an absorbing wall that resolves a classical sheath remains an open research
area. This work justifies the use of vacuum boundary conditions for absorbing
walls to show comparable accuracy between a multifluid sheath and lower moments
of a continuum-kinetic sheath.


  We consider a finite volume scheme with two-point flux approximation (TPFA)
to approximate a Laplace problem when the solution exhibits no more regularity
than belonging to $H^1_0(\Omega)$. We establish in this case some error bounds
for both the solution and the approximation of the gradient component
orthogonal to the mesh faces. This estimate is optimal, in the sense that the
approximation error has the same order as that of the sum of the interpolation
error and a conformity error. A numerical example illustrates the error
estimate in the context of a solution with minimal regularity. This result is
extended to evolution problems discretized via the implicit Euler scheme in an
appendix.


  We show that the subcritical $d$-dimensional nonlinear Schr\"odinger equation
$i \psi_t + \Delta \psi + |\psi|^{2 \sigma} \psi = 0$, where $1<\sigma d<2$,
admits smooth solutions that become singular in~$L^p$ for $p^*<p \le \infty$,
where $p^*:=\frac{\sigma d}{\sigma d -1}$. Since $\lim_{\sigma d \to 2-} p^* =
2$, these solutions can collapse at any $2<p \le \infty$, and in particular for
$p = 2 \sigma+2$.


  We study the spectral properties of Schr\"odinger operators on a compact
connected Riemannian manifold $M$ without boundary in case that the underlying
Hamiltonian system possesses certain symmetries. More precisely, if $M$ carries
an isometric and effective action of a compact connected Lie group $G$, we
prove a generalized equivariant version of the semiclassical Weyl law with an
estimate for the remainder, using a semiclassical functional calculus for
$h$-dependent functions and relying on recent results on singular equivariant
asymptotics. These results will be used to derive an equivariant quantum
ergodicity theorem in Part II of this work. When $G$ is trivial, one recovers
the classical results.


  Let $F\subseteq\mathbb P ^{a+1}$ be a non-degenerate $K3$ surface of degree
$2a$, where $a\ge2$. In this paper we deal with Ulrich bundles on $F$ of rank
$2$. We deal with their stability and we construct $K3$ surfaces endowed with
families of non-special Ulrich bundles of rank $2$ for each $a\ge2$.


  We present a statistical analysis of turbulent convection in stars within our
Reynolds-Averaged Navier Stokes (RANS) framework in spherical geometry which we
derived from first principles. The primary results reported in this document
include: (1) an extensive set of mean-field equations for compressible,
multi-species hydrodynamics, and (2) corresponding mean-field data computed
from various simulation models. Some supplementary scale analysis data is also
presented.
  The simulation data which is presented includes: (1) shell convection during
oxygen burning in a 23 solar mass supernova progenitor, (2) envelope convection
in a 5 solar mass red giant, (3) shell convection during the helium flash, and
(4) a hydrogen injection flash in a 1.25 solar mass star. These simulations
have been partially described previously in Meakin [2006], Meakin and Arnett
[2007a,b, 2010], Arnett et al. [2009, 2010], Viallet et al. [2011, 2013a,b] and
Mocak et al. [2009, 2011]. New data is also included in this document with
several new domain and resolution configurations as well as some variations in
the physical model such as convection zone depth and driving source term.
  The long term goal of this work is to aid in the development of more
sophisticated models for treating hydrodynamic phenomena (e.g., turbulent
convection) in the field of stellar evolution by providing a direct link
between 3D simulation data and the mean fields which are modeled by 1D stellar
evolution codes. As such, this data can be used to test previously proposed
turbulence models found in the literature and sometimes used in stellar
modeling. This data can also serve to test basic physical principles for model
building and inspire new prescriptions for use in 1D evolution codes.


  We introduce a family of exactly-solvable two-dimensional Hamiltonians whose
wave functions are given in terms of Laguerre and exceptional Jacobi
polynomials. The Hamiltonians contain purely quantum terms which vanish in the
classical limit leaving only a previously known family of superintegrable
systems. Additional, higher-order integrals of motion are constructed from
ladder operators for the considered orthogonal polynomials proving the quantum
system to be superintegrable.


  Neuroscientists postulate 3D representations in the brain in a variety of
different coordinate frames (e.g. 'head-centred', 'hand-centred' and
'world-based'). Recent advances in reinforcement learning demonstrate a quite
different approach that may provide a more promising model for biological
representations underlying spatial perception and navigation. In this paper, we
focus on reinforcement learning methods that reward an agent for arriving at a
target image without any attempt to build up a 3D 'map'. We test the ability of
this type of representation to support geometrically consistent spatial tasks
such as interpolating between learned locations using decoding of feature
vectors. We introduce a hand-crafted representation that has, by design, a high
degree of geometric consistency and demonstrate that, in this case, information
about the persistence of features as the camera translates (e.g. distant
features persist) can improve performance on the geometric tasks. These
examples avoid Cartesian (in this case, 2D) representations of space.
Non-Cartesian, learned representations provide an important stimulus in
neuroscience to the search for alternatives to a 'cognitive map'.


  Carbon, capture, and storage (CCS) is an important bridging technology to
combat climate change in the transition towards net-zero. The FluidFlower
concept has been developed to visualize and study CO$_2$ flow and storage
mechanisms in sedimentary systems in a laboratory setting. Meter-scale
multiphase flow in two geological geometries, including normal faults with and
without smearing, is studied. The experimental protocols developed to provide
key input parameters for numerical simulations are detailed, including an
evaluation of operational parameters for the FluidFlower benchmark study.
Variability in CO$_2$ migration patterns for two different geometries is
quantified, both between 16 repeated laboratory runs and between
history-matched models and a CO$_2$ injection experiment. The predicative
capability of a history-matched model is then evaluated in a different
geological setting.


  We prove that, up to isometric congruence, there are exactly 2n+1 homogeneous
polar foliations of the complex hyperbolic space. We also give an explicit
description of each of these foliations.


  The accurate determination of the lowest electron attachment ($EA$) and
ionization ($IP$) energies for molecules embedded in molecular junctions is
important for correctly estimating, \emph{e.g.}, the magnitude of the currents
($I$) or the biases ($V$) where an $I-V$-curve exhibits a significant non-Ohmic
behavior. Benchmark calculations for the lowest electron attachment and
ionization energies of several typical molecules utilized to fabricate
single-molecule junctions characterized by n-type conduction (4,4'-bipyridine,
1,4-dicyanobenzene, and 4,4'-dicyano-1,1'-biphenyl) and p-type conduction
(benzenedithiol, biphenyldithiol, hexanemonothiol, and hexanedithiol] based on
the EOM-CCSD (equation-of-motion coupled-cluster singles and doubles)
state-of-the-art method of quantum chemistry are presented. They indicate
significant differences from the results obtained within current approaches to
molecular transport. The present study emphasizes that, in addition to a
reliable quantum chemical method, basis sets much better than the ubiquitous
double-zeta set employed for transport calculations are needed. The latter is a
particularly critical issue for correctly determining $EA$'s, which is
impossible without including sufficient diffuse basis functions. The spatial
distribution of the dominant molecular orbitals (MO's) is another important
issue, on which the present study draws attention, because it sensitively
affects the MO-energy shifts $\Phi$ due to image charges formed in electrodes.
The present results cannot substantiate the common assumption of a point-like
MO midway between electrodes, which substantially affects the actual
$\Phi$-values.


  Non-perturbative preheating decay of post-inflationary condensates often
results in a high density, low momenta, non-thermal gas. In the case where the
non-perturbative classical evolution also leads to Q-balls, this effect shields
them from instant dissociation, and may radically change the thermal history of
the universe. For example, in a large class of inflationary scenarios,
motivated by the MSSM and its embedding in string theory, the reheat
temperature changes by a multiplicative factor of $10^{12}$.


  The problem of maximizing non-negative monotone submodular functions under a
certain constraint has been intensively studied in the last decade. In this
paper, we address the problem for functions defined over the integer lattice.
  Suppose that a non-negative monotone submodular function $f:\mathbb{Z}_+^n
\to \mathbb{R}_+$ is given via an evaluation oracle. Assume further that $f$
satisfies the diminishing return property, which is not an immediate
consequence of submodularity when the domain is the integer lattice. Given
this, we design polynomial-time $(1-1/e-\epsilon)$-approximation algorithms for
a cardinality constraint, a polymatroid constraint, and a knapsack constraint.
For a cardinality constraint, we also provide a
$(1-1/e-\epsilon)$-approximation algorithm with slightly worse time complexity
that does not rely on the diminishing return property.


  In this paper, we present a new embedding model, called M3-Embedding, which
is distinguished for its versatility in Multi-Linguality, Multi-Functionality,
and Multi-Granularity. It can support more than 100 working languages, leading
to new state-of-the-art performances on multi-lingual and cross-lingual
retrieval tasks. It can simultaneously perform the three common retrieval
functionalities of embedding model: dense retrieval, multi-vector retrieval,
and sparse retrieval, which provides a unified model foundation for real-world
IR applications. It is able to process inputs of different granularities,
spanning from short sentences to long documents of up to 8192 tokens. The
effective training of M3-Embedding involves the following technical
contributions. We propose a novel self-knowledge distillation approach, where
the relevance scores from different retrieval functionalities can be integrated
as the teacher signal to enhance the training quality. We also optimize the
batching strategy, enabling a large batch size and high training throughput to
ensure the discriminativeness of embeddings. To the best of our knowledge,
M3-Embedding is the first embedding model which realizes such a strong
versatility. The model and code will be publicly available at
https://github.com/FlagOpen/FlagEmbedding.


  The general problem of representing the Greens function $G(k,z)$ in terms of
self energy, in field theories lacking Wick's theorem, is considered. A simple
construction shows that a Dyson like representation with a self energy
$\Sigma(k,z)$ is always possible, provided we start with a spectral
representation for $G(k,z)$ for finite sized systems and take the thermodynamic
limit. The self energy itself can then be iteratively expressed in terms of
another higher order self energy, capturing the spirit of Mori's formulation.
  We further discuss alternative and more general forms of $G(k,z)$ that are
possible. In particular, a recent theory by the author of extremely correlated
Fermi liquids at density "$n$", for Gutzwiller projected non canonical Fermi
operators obtains a new form of the Greens function: $$G(k,z)= \frac{\{1-
\frac{n}{2}\} + \Psi(k,z)}{z - \hat{E}_k - \Phi(k,z)}, $$ with {\em a pair of
self energies} $\Phi(z)$ and $\Psi(z)$. Its relationship with the Dyson form is
explored. A simple version of the two self energy model was shown recently to
successfully fit several data sets of photoemission line shapes in cuprates. We
provide details of the unusual spectral line shapes that arise in this model,
with the characteristic skewed shape depending upon a single parameter. The EDC
and MDC line shapes are shown to be skewed in opposite directions, and provide
a testable prediction of the theory.


  We propose the suppression of dispersive spreading of wave packets governed
by the free-space Schr\"odinger equation with a periodically pulsed nonlinear
term. Using asymptotic analysis, we construct stroboscopically-dispersionless
quantum states that are physically reminiscent of, but mathematically different
from, the well-known one-soliton solutions of the nonlinear Schr\"odinger
equation with a constant (time-independent) nonlinearity. Our analytics are
strongly supported by full numerical simulations. The predicted dispersionless
wave packets can move with arbitrary velocity and can be realized in
experiments involving ultracold atomic gases with temporally controlled
interactions.


  Neutron stars are associated with diverse physical phenomena that take place
in conditions characterized by ultrahigh densities as well as intense
gravitational, magnetic, and radiation fields. Understanding the properties and
interactions of matter in these regimes remains one of the challenges in
compact object astrophysics. Photons emitted from the surfaces of neutron stars
provide direct probes of their structure, composition, and magnetic fields. In
this review, I discuss in detail the physics that governs the properties of
emission from the surfaces of neutron stars and their various observational
manifestations. I present the constraints on neutron star radii, core and crust
composition, and magnetic field strength and topology obtained from studies of
their broadband spectra, evolution of thermal luminosity, and the profiles of
pulsations that originate on their surfaces.


  Directed Energy Deposition (DED) processes offer one of the most versatile
current techniques to additively manufacture and repair metallic components
that have generatively designed complex geometries, and with compositional
control. When compared to powder bed fusion (PBF), its applicability and
adoption has been limited because several issues innate to the process are yet
to be suitably understood and resolved. This work catalogs and delineates these
issues and anomalies in the DED process along with their causes and solutions,
based on a state-of-the-art literature review. This work also serves to
enumerate and associate the underlying causes to the detrimental effects which
manifest as undesirable part/process outcomes. These DED-specific anomalies are
categorized under groups related to the part, process, material, productivity,
safety, repair, and functional gradients. Altogether, this primer acts as a
guide to best prepare for and mitigate the problems that are encountered in
DED, and also to lay the groundwork to inspire novel solutions to further
advance DED into mainstream manufacturing.


  Disorder-free localization has been recently introduced as a mechanism for
ergodicity breaking in low-dimensional homogeneous lattice gauge theories
caused by local constraints imposed by gauge invariance. We show that also
genuinely interacting systems in two spatial dimensions can become nonergodic
as a consequence of this mechanism. Specifically, we prove nonergodic behavior
in the quantum link model by obtaining a rigorous bound on the
localization-delocalization transition through a classical correlated
percolation problem implying a fragmentation of Hilbert space on the nonergodic
side of the transition. We study the quantum dynamics in this system by means
of an efficient and perturbatively controlled representation of the
wavefunction in terms of a variational network of classical spins akin to
artificial neural networks. We identify a distinguishing dynamical signature by
studying the propagation of line defects, yielding different light cone
structures in the localized and ergodic phases, respectively. The methods we
introduce in this work can be applied to any lattice gauge theory with
finite-dimensional local Hilbert spaces irrespective of spatial dimensionality.


  Free Fermions on vertices of distance-regular graphs are considered.
Bipartition are defined by taking as one part all vertices at a given distance
from a reference vertex. The ground state is constructed by filling all states
below a certain energy. Borrowing concepts from time and band limiting
problems, algebraic Heun operators and Terwilliger algebras, it is shown how to
obtain, quite generally, a block tridiagonal matrix that commutes with the
entanglement Hamiltonian. The case of the Hadamard graphs is studied in details
within that framework and the existence of the commuting matrix is shown to
allow for an analytic diagonalization of the restricted two-point correlation
matrix and hence for an explicit determination of the entanglement entropy.


  High-quality video inpainting that completes missing regions in video frames
is a promising yet challenging task. State-of-the-art approaches adopt
attention models to complete a frame by searching missing contents from
reference frames, and further complete whole videos frame by frame. However,
these approaches can suffer from inconsistent attention results along spatial
and temporal dimensions, which often leads to blurriness and temporal artifacts
in videos. In this paper, we propose to learn a joint Spatial-Temporal
Transformer Network (STTN) for video inpainting. Specifically, we
simultaneously fill missing regions in all input frames by self-attention, and
propose to optimize STTN by a spatial-temporal adversarial loss. To show the
superiority of the proposed model, we conduct both quantitative and qualitative
evaluations by using standard stationary masks and more realistic moving object
masks. Demo videos are available at https://github.com/researchmm/STTN.


  Hyperbolic plasmonic metamaterials provide numerous opportunities for
designing unusual linear and nonlinear optical properties. We show that the
modal overlap of fundamental and second-harmonic light in an anisotropic
plasmonic metamaterial slab results in the broadband enhancement of radiated
second-harmonic intensity by up to 2 orders of magnitudes for TM- and
TE-polarized fundamental light, compared to a smooth Au film under TM-polarised
illumination. The results open up possibilities to design tuneable
frequency-doubling metamaterial with the goal to overcome limitations
associated with classical phase matching conditions in thick nonlinear
crystals.


  $\textbf{Background:}$ The chiral magnetic effect (CME) is extensively
studied in heavy-ion collisions at RHIC and LHC. In the commonly used reaction
plane (RP) dependent, charge dependent azimuthal correlator ($\Delta\gamma$),
both the close and back-to-back pairs are included. Many backgrounds contribute
to the close pairs (e.g. resonance decays, jet correlations), whereas the
back-to-back pairs are relatively free of those backgrounds.
  $\textbf{Purpose:}$ In order to reduce those backgrounds, we propose a new
observable which only focuses on the back-to-back pairs, namely, the relative
back-to-back opposite-sign (OS) over same-sign (SS) pair excess
($r_{\text{BB}}$) as a function of the pair azimuthal orientation with respect
to the RP ($\varphi_{\text{BB}}$).
  $\textbf{Methods:}$ We use analytical calculations and toy model simulations
to demonstrate the sensitivity of $r_{\text{BB}}(\varphi_{\text{BB}})$ to the
CME and its insensitivity to backgrounds.
  $\textbf{Results:}$ With finite CME, the $\varphi_{\text{BB}}$ distribution
of $r_{\text{BB}}$ shows a clear characteristic modulation. Its sensitivity to
background is significantly reduced compared to the previous $\Delta\gamma$
observable. The simulation results are consistent with our analytical
calculations.
  $\textbf{Conclusions:}$ Our studies demonstrate that the
$r_{\text{BB}}(\varphi_{\text{BB}})$ observable is sensitive to the CME signal
and rather insensitive to the resonance backgrounds.


  Recent progress in understanding de Sitter spacetime in supergravity and
string theory has led to the development of a four dimensional supergravity
with spontaneously broken supersymmetry allowing for de Sitter vacua, also
called de Sitter supergravity. One approach makes use of constrained
(nilpotent) superfields, while an alternative one couples supergravity to a
locally supersymmetric generalization of the Volkov-Akulov goldstino action.
These two approaches have been shown to give rise to the same 4D action. A
novel approach to de Sitter vacua in supergravity involves the generalisation
of unimodular gravity to supergravity using a super-St\"uckelberg mechanism. In
this paper, we make a connection between this new approach and the previous two
which are in the context of nilpotent superfields and the goldstino brane. We
show that upon appropriate field redefinitions, the 4D actions match up to the
cubic order in the fields. This points at the possible existence of a more
general framework to obtain de Sitter spacetimes from high-energy theories.


  In this paper, we show that the etale index of a torsion cohomological Brauer
class is divisible by the period of the class. The tool used to make this
computation is the Cech approximation of the title. To create the
approximation, we use the folklore theorem that the homotopy limit and
Postnikov spectral sequences for a cosimplicial space agree beginning with the
E2-page. As far we know, this folklore theorem has no proof in the literature,
so we include a proof.


  While platial representations are being developed for sedentary entities, a
parallel and useful endeavour would be to consider time in so-called
"platio-temporal" representations that would also expand notions of mobility in
GIScience, that are solely dependent on Euclidean space and time. Besides
enhancing such aspects of place and mobility via spatio-temporal, we also
include human aspects of these representations via considerations of the
sociological notions of mobility via the mobilities paradigm that can
systematically introduce representation of both platial information along with
mobilities associated with 'moving places.' We condense these aspects into
'platial mobility,' a novel conceptual framework, as an integration in
GIScience and the mobilities paradigm in sociology, that denotes movement of
places in our platio-temporal and sociology-based representations. As
illustrative cases for further study using platial mobility as a framework, we
explore its benefits and methodological aspects toward developing better
understanding for disaster management, disaster risk reduction and pandemics.
We then discuss some of the illustrative use cases to clarify the concept of
platial mobility and its application prospects in the areas of disaster
management, disaster risk reduction and pandemics. These use cases, which
include flood events and the ongoing COVID-19 pandemic, have led to displaced
and restricted communities having to change practices and places, which would
be particularly amenable to the conceptual framework developed in our work.


  This paper investigates the dynamics of the net-baryon multiplicity
fluctuations near the QCD critical point, within the inhomogeneous temperature
and baryon chemical potential profile of quark-gluon plasma from the
hydrodynamics. We numerically solve the Langevin dynamics of conserved
net-baryon density and borrow the temperature and chemical potential profile
from hydrodynamic simulation. It is found that the local systems at different
rapidities reach the critical point at different proper times, owing to the
inhomogeneous temperature and chemical potential. As a result, we find the
pronounced enhancement of the magnitude for the net-baryon multiplicity
fluctuations with large rapidity acceptance at the freeze-out surface, which is
the consequence of the combined effect of critical slowing down and
inhomogeneous profile.


  The anisotropy parameter of two-dimensional equilibrium clusters of site
percolation process in long-range self-affine correlated structures are studied
numerically. We use a fractional Brownian Motion(FBM) statistic to produce both
persistent and anti-persistent long-range correlations in 2-D models. It is
seen that self affinity makes the shape of percolation clusters slightly more
isotropic. Moreover, we find that the sign of correction to scaling term is
determined by the nature of correlation. For persistent correlation the
correction to scaling term adds a negative contribution to the anisotropy of
percolation clusters, while for the anti-persistent case it is positive.


  We investigate two closely related LZ78-based compression schemes: LZMW (an
old scheme by Miller and Wegman) and LZD (a recent variant by Goto et al.).
Both LZD and LZMW naturally produce a grammar for a string of length $n$; we
show that the size of this grammar can be larger than the size of the smallest
grammar by a factor $\Omega(n^{\frac{1}3})$ but is always within a factor
$O((\frac{n}{\log n})^{\frac{2}{3}})$. In addition, we show that the standard
algorithms using $\Theta(z)$ working space to construct the LZD and LZMW
parsings, where $z$ is the size of the parsing, work in $\Omega(n^{\frac{5}4})$
time in the worst case. We then describe a new Las Vegas LZD/LZMW parsing
algorithm that uses $O (z \log n)$ space and $O(n + z \log^2 n)$ time w.h.p..


  [Methods]. We obtained high-precision radial velocities with HARPS on the ESO
3.6 m telescope and determined precise stellar elemental abundances (~0.01 dex)
using MIKE spectra on the Magellan 6.5m telescope. [Results]. Our data indicate
the presence of a planet with a minimum mass of 26 Earth masses around the
solar twin HIP 68468. The planet is a super-Neptune, but unlike the distant
Neptune in our solar system (30 AU), HIP 68468c is close-in, with a semi-major
axis of 0.66 AU, similar to that of Venus. The data also suggest the presence
of a super-Earth with a minimum mass of 2.9 Earth masses at 0.03 AU; if the
planet is confirmed, it will be the fifth least massive radial velocity planet
discovery to date and the first super-Earth around a solar twin. Both
isochrones (5.9 Gyr) and the abundance ratio [Y/Mg] (6.4 Gyr) indicate an age
of about 6 billion years. The star is enhanced in refractory elements when
compared to the Sun, and the refractory enrichment is even stronger after
corrections for Galactic chemical evolution. We determined a NLTE Li abundance
of 1.52 dex, which is four times higher than what would be expected for the age
of HIP 68468. The older age is also supported by the low log(R'HK) (-5.05) and
low jitter. Engulfment of a rocky planet of 6 Earth masses can explain the
enhancement in both lithium and the refractory elements. [Conclusions]. The
super-Neptune planet candidate is too massive for in situ formation, and
therefore its current location is most likely the result of planet migration
that could also have driven other planets towards its host star, enhancing thus
the abundance of lithium and refractory elements in HIP 68468. The intriguing
evidence of planet accretion warrants further observations to verify the
existence of the planets that are indicated by our data and to better constrain
the nature of the planetary system around this unique star.


  We reprove the results of Jordan [18] and Siebert [31] and show that the Lie
algebra of polynomial vector fields on an irreducible affine variety X is
simple if and only if X is a smooth variety. Given proof is self-contained and
does not depend on papers mentioned above. Besides, the structure of the module
of polynomial functions on an irreducible smooth affine variety over the Lie
algebra of vector fields is studied. Examples of Lie algebras of polynomial
vector fields on an N-dimensional sphere, non-singular hyperelliptic curves and
linear algebraic groups are considered.


  We propose a framework for analyzing classical sampling strategies for
estimating the Hamming weight of a large string, when applied to a multi-qubit
quantum system instead. The framework shows how to interpret such a strategy
and how to define its accuracy when applied to a quantum system. Furthermore,
we show how the accuracy of any strategy relates to its accuracy in its
classical usage, which is well understood for the important examples. We show
the usefulness of our framework by using it to obtain new and simple security
proofs for the following quantum-cryptographic schemes: quantum
oblivious-transfer from bit-commitment, and BB84 quantum-key-distribution.


  Does determinism (or even the incompleteness of quantum mechanics) follow
from locality and perfect correlations? In a 1964 paper John Bell gave the
first demonstration that quantum mechanics is incompatible with local hidden
variables. Since then a vigorous debate has rung out over whether he relied on
an assumption of determinism or instead, as he later claimed in a 1981 paper,
derived determinism from assumptions of locality and perfect correlation. This
paper aims to bring clarity to the debate via simple examples and rigorous
results. It is first recalled, via quantum and classical counterexamples, that
the weakest statistical form of locality consistent with Bell's 1964 paper
(parameter independence) is insufficient for the derivation of determinism.
Attention is then turned to critically assess Bell's appealing to the
Einstein-Rosen-Podolsky incompleteness argument to support his claim. It is
shown this argument is itself incomplete, via counterexamples that expose two
logical gaps. However, closing these gaps via a strong ``counterfactual''
reality criterion enables a rigorous derivation of each of quantum
incompleteness, determinism and parameter independence, and in this sense
justifies Bell's claim. Consequences for quantum interpretations are briefly
discussed.


  We have studied the IGM reionization process in its full cosmological context
including structure evolution and a realistic galaxy population. We have used a
combination of high-resolution N-body simulations (to describe the dark matter
and diffuse gas component), a semi-analytic model of galaxy formation (to track
the evolution of the sources of ionizing radiation) and the Monte Carlo
radiative transfer code CRASH (to follow the propagation of ionizing photons
into the IGM). The process has been followed in the largest volume ever used
for this kind of study, a field region of the universe with a comoving length
of L~20/h Mpc, embedded in a much larger cosmological simulation. To assess the
effect of environment on the reionization process, the same radiative transfer
simulations have been performed on a 10/h Mpc comoving box, centered on a
clustered region. We find that, to account for the all ionizing radiation,
objects with total masses of M~10^9 Msun must be resolved. In this case, the
simulated stellar population produces a volume averaged ionization fraction
x_v=0.999 by z~8, consistent with observations without requiring any additional
sources of ionization. We also find that environment substantially affects the
reionization process. In fact, although the simulated proto-cluster occupies a
smaller volume and produces a higher number of ionizing photons, it gets
totally ionized later. This is because high density regions, which are more
common in the proto-cluster, are difficult to ionize because of their high
recombination rates.


  Optical Mie resonators based on silicon nanostructures allow tuning of
light-matter-interaction with advanced design concepts based on CMOS compatible
nanofabrication. Optically active materials such as transition-metal
dichalcogenide (TMD) monolayers can be placed in the near-field region of such
Mie resonators. Here, we experimentally demonstrate and verify by numerical
simulations coupling between a MoSe2 monolayer and the near-field of dielectric
nanoresonators. Through a comparison of dark-field (DF) scattering spectroscopy
and photoluminescence excitation experiments (PLE), we show that the MoSe2
absorption can be enhanced via the near-field of a nanoresonator. We
demonstrate spectral tuning of the absorption via the geometry of individual
Mie resonators. We show that we indeed access the optical near-field of the
nanoresonators, by measuring a spectral shift between the typical near-field
resonances in PLE compared to the far-field resonances in DF scattering. Our
results prove that using MoSe2 as an active probe allows accessing the optical
near-field above photonic nanostructures, without the requirement of highly
complex near-field microscopy equipment.


  Reinforcement learning with neural networks (RLNN) has recently demonstrated
great promise for many problems, including some problems in quantum information
theory. In this work, we apply RLNN to quantum hypothesis testing and determine
the optimal measurement strategy for distinguishing between multiple quantum
states $\{ \rho_{j} \}$ while minimizing the error probability. In the case
where the candidate states correspond to a quantum system with many qubit
subsystems, implementing the optimal measurement on the entire system is
experimentally infeasible.
  We use RLNN to find locally-adaptive measurement strategies that are
experimentally feasible, where only one quantum subsystem is measured in each
round. We provide numerical results which demonstrate that RLNN successfully
finds the optimal local approach, even for candidate states up to 20
subsystems. We additionally demonstrate that the RLNN strategy meets or exceeds
the success probability for a modified locally greedy approach in each random
trial.
  While the use of RLNN is highly successful for designing adaptive local
measurement strategies, in general a significant gap can exist between the
success probability of the optimal locally-adaptive measurement strategy and
the optimal collective measurement. We build on previous work to provide a set
of necessary and sufficient conditions for collective protocols to strictly
outperform locally adaptive protocols. We also provide a new example which, to
our knowledge, is the simplest known state set exhibiting a significant gap
between local and collective protocols. This result raises interesting new
questions about the gap between theoretically optimal measurement strategies
and practically implementable measurement strategies.


  Measurements of Bose-Einstein correlations played a crucial role in the
discovery and the subsequent detailed exploration of the Quark-Gluon-Plasma
(QGP) created in high-energy collisions of heavy nuclei. Such measurements gave
rise to femtoscopy, a flourishing sub-field of high-energy physics, and there
are important new directions to explore and discoveries to be made in the near
future. One of these important current topics is the precise investigation of
the shape of the correlation functions utilizing L\'evy-stable sources. In this
paper, we present a novel method of calculating the shape of the two-particle
correlation functions, including the Coulomb final-state interaction. This
method relies on an exact calculation of a large part of the necessary
integrals of the Coulomb wave function and can be utilized to calculate the
correlation function for any source function with an easily accessible Fourier
transform. In this way, it is eminently applicable to L\'evy-stable source
functions. In this particular case, we find that the new method is more robust
and allows the investigation of a wider parameter range than the previously
utilized techniques. We present an easily applicable software package that is
ready to use in experimental studies.


  A simple mechanism for SUSY breaking is proposed due to the coexistence of
BPS domain walls. It requires no messenger fields nor complicated SUSY breaking
sector on any of the walls. We assumed that our world is on a BPS domain wall
and that the other BPS wall breaks the SUSY preserved by our wall. We obtain an
${\cal N}=1$ model in four dimensions which admits an exact solution of a
stable non-BPS configuration of two walls. The stability is assured by a
topological quantum number associated with the winding on the field space of
the topology of $S^1$. We propose that the overlap of the wave functions of the
Nambu-Goldstone fermion and those of physical fields provides a practical
method to evaluate SUSY breaking mass splitting on our wall thanks to a
low-energy theorem. This is based on our recent works hep-th/0009023 and
hep-th/0107204.


  Recent observations suggest that gamma-ray bursts (GRBs) and their afterglows
are produced by jets of highly relativistic cannonballs (CBs), emitted in
supernova explosions. The fully ionized CBs cool to a temperature below 4500 K
within a day or two, at which point electron-proton recombination produces an
intense Lyman-$\alpha$ emission. The line energy is Doppler-shifted by the CBs'
motion to X-ray energies in the observer's frame. The measured line energies,
corrected for their cosmological redshift, imply Doppler factors in the range
600 to 1000, consistent with those estimated -in the CB model- from the
characteristics of the $\gamma$-ray bursts. All other observed properties of
the lines are also well described by the CB model. Scattering and
self-absorption of the recombination lines within the CB also produce a
wide-band flare-up in the GRB afterglow, as the observations indicate. A very
specific prediction of the CB model is that the X-ray lines ought to be narrow
and move towards lower line energies as they are observed: their current
apparently large widths would be the effect of time integration, and/or of the
blending of lines from CBs with different Doppler factors.


  We present a guiding principle for designing fermionic Hamiltonians and
quantum Monte Carlo (QMC) methods that are free from the infamous sign problem
by exploiting the Lie groups and Lie algebras that appear naturally in the
Monte Carlo weight of fermionic QMC simulations. Specifically, rigorous
mathematical constraints on the determinants involving matrices that lie in the
split orthogonal group provide a guideline for sign-free simulations of
fermionic models on bipartite lattices. This guiding principle not only unifies
the recent solutions of the sign problem based on the continuous-time quantum
Monte Carlo methods and the Majorana representation, but also suggests new
efficient algorithms to simulate physical systems that were previously
prohibitive because of the sign problem.


  Social networks have a scale-free property and community structure, and many
problems in life have the characteristic of public goods, such as resource
shortage. Due to different preferences of individuals, there exist individuals
who adopt heterogeneous strategies updating rules in the network. We
investigate the evolution of cooperation in the scale-free community network
with public goods games and the influence of multiple strategy updating rules.
Here, two types of strategy updating rules are considered which are pairwise
comparison rules and aspiration-driven rules. Numerical simulations are
conducted and presented corresponding results. We find that community structure
promotes the emergence of cooperation in public goods games. In the meantime,
there is a "U" shape relationship between the frequency of cooperators and the
proportion of the two strategy updating rules. With the variance in the
proportion of the two strategy updating rules, pairwise comparison rules seem
to be more sensitive. Compared with aspiration-driven rules, pairwise
comparison rules play a more important role in promoting cooperation. Our work
may be helpful to understand the evolution of cooperation in social networks.


  We implemented combination of DMFT and $GW$ in its fully self-consistent way,
one shot $GW$ approximation, and quasiparticle self-consistent scheme, and
studied how well these combined methods perform on H$_2$ molecule as compared
to more established methods such as LDA+DMFT. We found that most flavors of
$GW$+DMFT break down in strongly correlated regime due to causality violation.
Among $GW$+DMFT methods, only the self-consistent quasiparticle $GW$+DMFT with
static double-counting, and a new method with causal double-counting, correctly
recover the atomic limit at large H-atom separation. While some flavors of
$GW$+DMFT improve the single-electron spectra as compared to LDA+DMFT, the
total energy is best predicted by LDA+DMFT, for which the exact double-counting
is known, and is static.


  In this paper we develop a detailed analysis of critical prewetting in the
context of the two-dimensional Ising model. Namely, we consider a
two-dimensional nearest-neighbor Ising model in a $2N\times N$ rectangular box
with a boundary condition inducing the coexistence of the $+$ phase in the bulk
and a layer of $-$ phase along the bottom wall. The presence of an external
magnetic field of intensity $h=\lambda/N$ (for some fixed $\lambda>0$) makes
the layer of $-$ phase unstable. For any $\beta>\beta_{\rm c}$, we prove that,
under a diffusing scaling by $N^{-2/3}$ horizontally and $N^{-1/3}$ vertically,
the interface separating the layer of unstable phase from the bulk phase weakly
converges to an explicit Ferrari-Spohn diffusion.


  We study the asymptotic behavior of the volume preserving mean curvature and
the Mullins-Sekerka flat flow in three dimensional space. Motivated by this we
establish a 3D sharp quantitative version of the Alexandrov inequality for
$C^2$-regular sets with a perimeter bound.


  Precision measurements of the quantum Hall resistance with alternating
current (ac) in the kHz range were performed on epitaxial graphene in order to
assess its suitability as a quantum standard of impedance. The quantum Hall
plateaus measured with alternating current were found to be flat within one
part in 10^7. This is much better than for plain GaAs quantum Hall devices and
shows that the magnetic-flux-dependent capacitive ac losses of the graphene
device are less critical. The observed frequency dependence of about
-8x10^-8/kHz is comparable in absolute value to the positive frequency
dependence of plain GaAs devices, but the negative sign is attributed to stray
capacitances which we believe can be minimized by a careful design of the
graphene device. Further improvements thus may lead to a simpler and more
user-friendly quantum standard for both resistance and impedance.


  The task of controlling an underactuated robotic finger with a single tendon
and a single actuator is difficult. Methods for controlling the class of
underactuated systems are available in the literature. However, this particular
system does not fall into the class of underactuated system. This paper
presents a design change which introduces kinematic constraints into the
system, making the system controllable. Backstepping control strategy is used
to control the system. Simulation results are presented for single finger
driven by a single actuator.


  Data processing pipelines represent an important slice of the astronomical
software library that include chains of processes that transform raw data into
valuable information via data reduction and analysis. In this work we present
Corral, a Python framework for astronomical pipeline generation. Corral
features a Model-View-Controller design pattern on top of an SQL Relational
Database capable of handling: custom data models; processing stages; and
communication alerts, and also provides automatic quality and structural
metrics based on unit testing. The Model-View-Controller provides concept
separation between the user logic and the data models, delivering at the same
time multi-processing and distributed computing capabilities. Corral represents
an improvement over commonly found data processing pipelines in Astronomy since
the design pattern eases the programmer from dealing with processing flow and
parallelization issues, allowing them to focus on the specific algorithms
needed for the successive data transformations and at the same time provides a
broad measure of quality over the created pipeline. Corral and working examples
of pipelines that use it are available to the community at
https://github.com/toros-astro.


  In this paper, we present DEMC, a deep Dual-Encoder network to remove Monte
Carlo noise efficiently while preserving details. Denoising Monte Carlo
rendering is different from natural image denoising since inexpensive
by-products (feature buffers) can be extracted in the rendering stage. Most of
them are noise-free and can provide sufficient details for image
reconstruction. However, these feature buffers also contain redundant
information, which makes Monte Carlo denoising different from natural image
denoising. Hence, the main challenge of this topic is how to extract useful
information and reconstruct clean images. To address this problem, we propose a
novel network structure, Dual-Encoder network with a feature fusion
sub-network, to fuse feature buffers firstly, then encode the fused feature
buffers and a noisy image simultaneously, and finally reconstruct a clean image
by a decoder network. Compared with the state-of-the-art methods, our model is
more robust on a wide range of scenes and is able to generate satisfactory
results in a significantly faster way.


  Health-related mobile applications are known as eHealth apps. These apps make
people more aware of their health, help during critical situations, provide
home-based disease management, and monitor/support personalized care through
sensing/interaction. eHealth app usage is rapidly increasing with a large
number of new apps being developed. Unfortunately, many eHealth apps do not
successfully adopt Human-Centric Issues (HCI) in the app development process
and its deployment stages, leading them to become ineffective and not inclusive
of diverse end-users. This paper provides an initial assessment of key human
factors related to eHealth apps by literature review, existing guidelines
analysis, and user studies. Preliminary results suggest that Usability,
Accessibility, Reliability, Versatility, and User Experience are essential HCIs
for eHealth apps, and need further attention from researchers and
practitioners. Therefore, outcomes of this research will look to amend support
for users, developers, and stakeholders of eHealth apps in the form of improved
actionable guidelines, best practice examples, and evaluation techniques. The
research also aims to trial the proposed solutions on real-world projects.


  We prove, assuming Greenberg's conjecture, that the ordinary eigencurve is
Gorenstein at an intersection point between the Eisenstein family and the
cuspidal locus. As a corollary, we obtain new results on Sharifi's conjecture.
This result is achieved by constructing a universal ordinary pseudodeformation
ring and proving an $R = \mathbb T$ result.


  Observational and theoretical arguments support the idea that violent events
connected with $AGN$ activity and/or intense star forming episodes have played
a significant role in the early phases of galaxy formation at high red shifts.
Being old stellar systems, globular clusters seem adequate candidates to search
for the eventual signatures that might have been left by those energetic
phenomena. The analysis of the colour distributions of several thousands of
globular clusters in the Virgo and Fornax galaxy clusters reveals the existence
of some interesting and previously undetected features. A simple pattern
recognition technique, indicates the presence of "colour modulations",
distinctive for each galaxy cluster. The results suggest that the globular
cluster formation process has not been completely stochastic but, rather,
included a significant fraction of globulars that formed in a synchronized way
and over supra-galactic spatial scales.


  Field emission from nano-structured emitters primarily takes place from the
tips. Using recent results on the variation of enhancement factor around the
apex (Biswas et al, Ultramicroscopy 185, 1-4 (2018)), analytical expressions
for surface distribution of net emitted electrons as well as the total and
normal energy distributions are derived in terms of the apex radius $R_a$ and
the local electric field at the apex $E_a$. Formulae for the net emitted
current and effective emission area in terms of these quantities are also
obtained.


  Distinguishing conformally coupled frames from the tree-level perturbative
observables (scalar spectral index $n_{\rm s}$ and tensor-to-scalar ratio $r$)
is challenging in cosmology as they are nearly identical. However, since the
background evolution in these two frames differs significantly, we can look for
potential signatures in the reheating constraints to discriminate these frames.
In this work, we study the reheating phase in these frames and find that the
difference in the inflationary energy scales in these frames contributes to a
significant difference in the reheating e-folding number and hence, different
reheating temperature. This difference will eventually lead to a contrasting
thermal history in the two frames, which may have a potential observational
signature in future observations. This study will open up an avenue for
distinguishing various conformally connected otherwise indistinguishable frames
and may finally lead us to the correct theory of gravity for our Universe.


  Auscultation for neonates is a simple and non-invasive method of providing
diagnosis for cardiovascular and respiratory disease. Such diagnosis often
requires high-quality heart and lung sounds to be captured during auscultation.
However, in most cases, obtaining such high-quality sounds is non-trivial due
to the chest sounds containing a mixture of heart, lung, and noise sounds. As
such, additional preprocessing is needed to separate the chest sounds into
heart and lung sounds. This paper proposes a novel deep-learning approach to
separate such chest sounds into heart and lung sounds. Inspired by the
Conv-TasNet model, the proposed model has an encoder, decoder, and mask
generator. The encoder consists of a 1D convolution model and the decoder
consists of a transposed 1D convolution. The mask generator is constructed
using stacked 1D convolutions and transformers. The proposed model outperforms
previous methods in terms of objective distortion measures by 2.01 dB to 5.06
dB in the artificial dataset, as well as computation time, with at least a
17-time improvement. Therefore, our proposed model could be a suitable
preprocessing step for any phonocardiogram-based health monitoring system.


  Many systems, ranging from biological and engineering systems to social
systems, can be modeled as directed networks, with links representing directed
interaction between two nodes. To assess the importance of a node in a directed
network, various centrality measures based on different criteria have been
proposed. However, calculating the centrality of a node is often difficult
because of the overwhelming size of the network or the incomplete information
about the network. Thus, developing an approximation method for estimating
centrality measures is needed. In this study, we focus on modular networks;
many real-world networks are composed of modules, where connection is dense
within a module and sparse across different modules. We show that ranking-type
centrality measures including the PageRank can be efficiently estimated once
the modular structure of a network is extracted. We develop an analytical
method to evaluate the centrality of nodes by combining the local property
(i.e., indegree and outdegree of nodes) and the global property (i.e.,
centrality of modules). The proposed method is corroborated with real data. Our
results provide a linkage between the ranking-type centrality values of modules
and those of individual nodes. They also reveal the hierarchical structure of
networks in the sense of subordination (not nestedness) laid out by
connectivity among modules of different relative importance. The present study
raises a novel motive of identifying modules in networks.


  The concentration dependence of the excluded volume effects in polymer
solutions is investigated. Through thermodynamic arguments for the
interpenetration of polymer segments and the free energy change, we show that
the disappearance of the excluded volume effects should occur at medium
concentration. The result is in accord with the recent experimental
observations.


  The Born effective charge tensors of Barium Titanate have been calculated for
each of its 4 phases. Large effective charges of Ti and O, also predicted by
shell model calculations and made plausible by a simplified model, reflect the
partial covalent character of the chemical bond. A band by band decomposition
confirms that orbital hybridization is not restricted to Ti and O atoms but
also involves Ba which appears more covalent than generally assumed. Our
calculations reveal a strong dependence of the effective charges on the atomic
positions contrasting with a relative insensitivity on isotropic volume
changes.


  The pursuit of experimental precision in the $CP$-violating weak phase
$\phi_2$ ($\alpha$) is not without its challenges, in part due to the need to
combine multiple physical observables from various related decay channels, and
therein lies a fundamental issue. Similarities in analysis procedures give rise
to systematic correlations between the measured inputs constraining $\phi_2$
that must be taken into account to avoid bias. Specifically, in the case of the
irreducible model uncertainty accompanying analyses involving the $\rho$ meson,
it is demonstrated that ignoring correlations derived from its pole parameters,
or indeed even treating correlations individually contained within each decay
channel, can ultimately lead to a bias in $\phi_2$ of $\mathcal{O}(1^\circ)$.
Correct treatment on the other hand, markedly reduces wandering of its central
value as a function of the model uncertainty strength with the added dividend
of a further improved overall uncertainty. Bias in the combination of $B^0 \to
(\rho \pi)^0$ and $B \to \rho \rho$ is also seen to depend on the statistical
strength of the former in relation to that of the model uncertainty in the
latter. This work can inspire other studies into the points at which systematic
correlations beyond those determined in single measurements matter in
combinations leading to other $CP$-violating weak phases such as $\phi_1$
($\beta$), $\phi_3$ ($\gamma$) and $\phi_s$.


  In this paper, we investigate geometric properties of monotone systems by
studying their isostables and basins of attraction. Isostables are boundaries
of specific forward-invariant sets defined by the so-called Koopman operator,
which provides a linear infinite-dimensional description of a nonlinear system.
First, we study the spectral properties of the Koopman operator and the
associated semigroup in the context of monotone systems. Our results generalize
the celebrated Perron-Frobenius theorem to the nonlinear case and allow us to
derive geometric properties of isostables and basins of attraction.
Additionally, we show that under certain conditions we can characterize the
bounds on the basins of attraction under parametric uncertainty in the vector
field. We discuss computational approaches to estimate isostables and basins of
attraction and illustrate the results on two and four state monotone systems.


  Lensed billiards are an extension of the notion of billiard dynamical systems
obtained by adding a potential function of the form $C1_{\mathcal{A}}$, where
$C$ is a real valued constant and $1_{\mathcal{A}}$ is the indicator function
of an open subset $\mathcal{A}$ of the billiard table whose boundaries (of
$\mathcal{A}$ and the table) are piecewise smooth. Trajectories are polygonal
lines that undergo either reflection or refraction at the boundary of
$\mathcal{A}$ depending on the angle of incidence. After laying out some basic
concepts and general facts, in particular reviewing the optical/mechanical
analogy that motivates these billiard models, we explore how their dynamical
properties depend on the potential parameter $C$ using a number of families of
examples. In particular, we explore numerically the Lyapunov exponents for
these parametric families and highlight the more salient common properties that
distinguish them from standard billiard systems. We further justify some of
these properties by characterizing lensed billiards in terms of switching
dynamics between two open (standard) billiard subsystems and obtaining mean
values associated to orbit sojourn in each subsystem.


  Determining the properties of the warm ionized medium (WIM) at the leading
edge of spiral arms is important for understanding its dynamics and cloud
formation. The inner edge of the Scutum arm tangency is a unique location in
which to disentangle the WIM from other components. We use high spectral
resolution [C II] 158 micron and [N II] 205 micron fine structure line
observations taken with the upGREAT and GREAT instruments on SOFIA, along with
auxiliary HI and 13CO observations. The observations were in and out of the
Galactic plane along 18 lines of sight between longitude 30deg and 32deg. We
detect strong [N II] emission throughout the Scutum tangency. At VLSR = 110 to
125 km/s, where there is little, if any, 13CO, we could disentangle the [N II]
and [C II] emission that arises from the WIM at the inner edge. We find an
average electron density, <n(e)> about 0.9 cm{-3} in the plane, and about 0.4
cm{-3} above the plane. For VLSR < 110 km/s there is [N II] emission tracing
highly ionized gas throughout the arm's molecular layer. This ionized gas has a
high density, n(e) ~ 30 cm{-3}, and a few percent filling factor. Thus, [N II]
and [C II] at the Scutum arm tangency reveal a highly ionized gas with <n(e)>
about 10 to 20 times those of the interarm WIM, which is best explained by a
model in which the interarm WIM is compressed as it falls into the potential
well of the arm. The widespread distribution of [N II] in the molecular layers
shows that high density ionized gas is distributed throughout the Scutum arm.
The n(e) derived from [N II] for these molecular cloud regions are about 30
cm{-3}, and probably arise in the ionized boundary layers of clouds. This [N
II] emission from the ionized boundary layers is probably the result of the
shock compression of the WIM as it impacts the arm's neutral gas, but some
could arise from extended HII regions.


  Fusing abundant satellite data with sparse ground measurements constitutes a
major challenge in climate modeling. To address this, we propose a strategy to
augment the training dataset by introducing unlabeled satellite images paired
with pseudo-labels generated through a spatial interpolation technique known as
ordinary kriging, thereby making full use of the available satellite data
resources. We show that the proposed data augmentation strategy helps enhance
the performance of the state-of-the-art convolutional neural network-random
forest (CNN-RF) model by a reasonable amount, resulting in a noteworthy
improvement in spatial correlation and a reduction in prediction error.


  We obtain the mass parameter for a class of static and spherically symmetric
regular black holes (BHs) (namely Bardeen, Hayward and
Ay\'{o}n-Beato-Garc\'{i}a BHs) which are solutions of Einstein's field
equations coupled to nonlinear electrodynamics (NED) in terms of redshifts and
blueshifts of photons emitted by geodesic particles (for instance, stars)
orbiting around these BHs. The motion of photons is not governed by null
geodesics for these type of spacetime geometries which reflects the direct
effects of the electrodynamic nonlinearities in the photon motion; hence, an
effective geometry needs to be constructed to study null trajectories [Phys.
Rev. D61, 045001 (2000)]. To achieve the above, we first study the constants of
motion from the analysis of the motion of both geodesic particles moving in
stable circular orbits and photons ejected from them and reaching a distant
observer (or detector) in the equatorial plane for the above mentioned regular
BHs. The relationship between red/blueshifts of photons and the regular BH
observables is presented. We also numerically find the bounds on the photon
shifts for these regular BH cases.


  The concepts of negative refractive index and near-field imaging are
explained in the form of a tutorial.


  We conducted a panoramic spectroscopic campaign with MOSCA at the Calar Alto
observatory. We acquired spectra of more than 500 objects. Approximately 150 of
these spectra were of galaxies that are members of six different clusters,
which differ in intrinsic X-ray luminosity. The wavelength range allows us to
quantify the star formation activity by using the OII and the Halpha lines.
This activity is examined in terms of the large-scale environment expressed by
the clustercentric distance of the galaxies as well as on local scales given by
the spatial galaxy densities. A global suppression of star-formation is
detected in the outskirts of clusters, at about 3Rvir. Galaxies with ongoing
star-formation have similar activity, regardless of the environment. Therefore,
the decline of the star-formation activity inside the investigated clusters is
driven mainly by the significant change in the fraction of active versus
passive populations. This suggests that the suppression of the star-formation
activity occurs on short timescales. We detect a significant population of red
star-forming galaxies whose colors are consistent with the red-sequence of
passive galaxies. They appear to be in an intermediate evolutionary stage
between active and passive types. Since a suppression of star-formation
activity is measured at large clustercentric distances and low projected
densities, purely cluster-specific phenomena cannot fully explain the observed
trends. Therefore, as suggested by other studies, group preprocessing may play
an important role in transforming galaxies before they enter into the cluster
environment. Since models predict that a significant fraction of galaxies
observed in the outskirts may have already transversed through the cluster
center, the effects of ram-pressure stripping cannot be neglected. (ABRIDGED)


  We argue that it is a fluctuational underpinning of the Quantum vacuum which
on the one hand gives a stochastic character to the conservation laws, and on
the other is required for explaining the recently observed acceleration of the
universe. This also provides us with the arrow of time, in a consistent
cosmology.


  Markov Decision Processes and Dynamic Treatment Regimes have grown
increasingly popular in the treatment of diseases, including cancer. However,
cancer treatment often impacts quality of life drastically, and people often
fail to take treatments that are sustainable, affordable and can be adhered to.
In this paper, we emphasize the usage of ambient factors like profession,
radioactive exposure, food habits on the treatment choice, keeping in mind that
the aim is not just to relieve the patient of his disease, but rather to
maximize his overall physical, social and mental well being. We delineate a
general framework which can directly incorporate a net benefit function from a
physician as well as patient's utility, and can incorporate the varying
probabilities of exposure and survival of patients of varying medical profiles.
We also show by simulations that the optimal choice of actions often is
sensitive to extraneous factors, like the financial status of a person (as a
proxy for the affordability of treatment), and that these actions should be
welcome keeping in mind the overall quality of life.


  Double-diffusive convection driven by both thermal and compositional buoyancy
in a rotating spherical shell can exhibit a rather large number of behaviours
often distinct from that of the single diffusive system. In order to understand
how the differences in thermal and compositional molecular diffusivities
determine the dynamics of thermo-compositional convection we investigate
numerically the linear onset of convective instability in a double-diffusive
setup. We construct an alternative equivalent formulation of the
non-dimensional equations where the linearised double-diffusive problem is
described by an effective Rayleigh number, $\text{Ra}$, measuring the amplitude
of the combined buoyancy driving, and a second parameter, $\alpha$, measuring
the mixing of the thermal and compositional contributions. This formulation is
useful in that it allows for the analysis of several limiting cases and reveals
dynamical similarities in the parameters space which are not obvious otherwise.
We analyse the structure of the critical curves in this $\text{Ra}-\alpha$
space, explaining asymptotic behaviours in $\alpha$, transitions between
inertial and diffusive regimes, and transitions between large scale (fast
drift) and small scale (slow drift) convection. We perform this analysis for a
variety of diffusivities, rotation rates and shell aspect ratios showing where
and when new modes of convection take place.


  We discuss the relation between the Wasserstein distance of order 1 between
probability distributions on a metric space, arising in the study of
Monge-Kantorovich transport problem, and the spectral distance of
noncommutative geometry. Starting from a remark of Rieffel on compact
manifolds, we first show that on any - i.e. non-necessary compact - complete
Riemannian spin manifolds, the two distances coincide. Then, on convex
manifolds in the sense of Nash embedding, we provide some natural upper and
lower bounds to the distance between any two probability distributions.
Specializing to the Euclidean space $R^n$, we explicitly compute the distance
for a particular class of distributions generalizing Gaussian wave packet.
Finally we explore the analogy between the spectral and the Wasserstein
distances in the noncommutative case, focusing on the standard model and the
Moyal plane. In particular we point out that in the two-sheet space of the
standard model, an optimal-transport interpretation of the metric requires a
cost function that does not vanish on the diagonal. The latest is similar to
the cost function occurring in the relativistic heat equation.


  With the rapid advancement of autonomous driving technology, self-driving
cars have become a central focus in the development of future transportation
systems. Scenario generation technology has emerged as a crucial tool for
testing and verifying the safety performance of autonomous driving systems.
Current research in scenario generation primarily focuses on open roads such as
highways, with relatively limited studies on underground parking garages. The
unique structural constraints, insufficient lighting, and high-density
obstacles in underground parking garages impose greater demands on the
perception systems, which are critical to autonomous driving technology.
  This study proposes an accelerated generation method for perception failure
scenarios tailored to the underground parking garage environment, aimed at
testing and improving the safety performance of autonomous vehicle (AV)
perception algorithms in such settings. The method presented in this paper
generates an intelligent testing environment with a high density of perception
failure scenarios by learning the interactions between background vehicles
(BVs) and autonomous vehicles (AVs) within perception failure scenarios.
Furthermore, this method edits the Markov process within the perception failure
scenario data to increase the density of critical information in the training
data, thereby optimizing the learning and generation of perception failure
scenarios. A simulation environment for an underground parking garage was
developed using the Carla and Vissim platforms, with Bevfusion employed as the
perception algorithm for testing. The study demonstrates that this method can
generate an intelligent testing environment with a high density of perception
failure scenarios and enhance the safety performance of perception algorithms
within this experimental setup.


  We study electronic structure of vortex core states of FeSe superconductors
based on a t$_{2g}$ three-orbital model by solving the Bogoliubov-de
Gennes(BdG) equation self-consistently. The orbital-resolved vortex core states
of different pairing symmetries manifest themselves as distinguishable
structures due to different quasi-particle wavefunctions. The obtained vortices
are classified in terms of the invariant subgroups of the symmetry group of the
mean-field Hamiltonian in the presence of magnetic field. Isotropic $s$ and
anisotropic $s$ wave vortices have $G_5$ symmetry for each orbital, whereas
$d_{x^2-y^2}$ wave vortices show $G^{*}_{6}$ symmetry for $d_{xz/yz}$ orbitals
and $G^{*}_{5}$ symmetry for $d_{xy}$ orbital. In the case of $d_{x^2-y^2}$
wave vortices, hybridized-pairing between $d_{xz}$ and $d_{yz}$ orbitals gives
rise to a relative phase difference in terms of gauge transformed pairing order
parameters between $d_{xz/yz}$ and $d_{xy}$ orbitals, which is essentially
caused by a transformation of co-representation of $G^{*}_{5}$ and $G^{*}_{6}$
subgroup. The calculated local density of states(LDOS) of $d_{x^2-y^2}$ wave
vortices show qualitatively similar pattern with experiment results. The phase
difference of $\frac{\pi}{4}$ between $d_{xz/yz}$ and $d_{xy}$ orbital-resolved
$d_{x^2-y^2}$ wave vortices can be verified by further experiment observation.


  Based on the q-exponential distribution which has been observed in more and
more physical systems, the varentropy method is used to derive the uncertainty
measure of such an abnormal distribution function. The uncertainty measure
obtained here can be considered as a new entropic form for the abnormal
physical systems with complex interaction. The entropy obtained here also
presents non-additive property for two independent subsystems and it will tend
to the Boltzmann-Gibbs entropy when the nonextensive parameter q->1. It is very
important to find that for different systems with any q, this entropic form is
always concave and the systemic entropy is maximizable.


  Traditional blockchains grant the miner of a block full control not only over
which transactions but also their order. This constitutes a major flaw
discovered with the introduction of decentralized finance and allows miners to
perform MEV attacks. In this paper, we address the issue of sandwich attacks by
providing a construction that takes as input a blockchain protocol and outputs
a new blockchain protocol with the same security but in which sandwich attacks
are not profitable. Furthermore, our protocol is fully decentralized with no
trusted third parties or heavy cryptography primitives and carries a linear
increase in latency and minimum computation overhead.


  Integral equations for thermodynamic quantities are derived in the framework
of the non-crossing approximation (NCA). Entropy and specific heat of 4f
contribution are calculated without numerical differentiations of thermodynamic
potential. The formulation is applied to systems such as PrFe4P12 with
singlet-triplet crystalline electric field (CEF) levels.


  Serum albumin, recognized mainly for its capacity to act as a carrier protein
for many compounds, can also actively transform some organic molecules. As a
starting point in this study we consider esterase-like activity of bovine serum
albumin (BSA) toward p-nitrophenyl acetate (p-NPA). Our results reveal that the
reaction goes beyond ester hydrolysis step. In fact the transformation product,
p-nitrophenol (p-NP), becomes a substrate for further reaction with BSA in
which its nitro group in subtracted and released in the form of HNO2. Spectral
data indicate that this cascade of events proceeds through formation of
phenoxyl radical via proton coupled electron transport (PCET) between OH group
of p-NP and imidazole ring of histidine from the protein. Furthermore, the
effect of application of electromagnetic radiation in the infrared range,
suggests that this remote physical trigger can support interactions based on
PCET mechanism by acting on polarization and mutual alignment of water dipoles
serving as effective water wires.


  We use high accuracy photometric data obtained with the Kepler satellite to
monitor the activity modulations of the Kepler-210 planet host star over a time
span of more than four years. Following the phenomenology of the star's light
curve in combination with a five spot model, we identify six different
so-called spot seasons. A characteristic, which is common in the majority of
the seasons, is the persistent appearance of spots in a specific range of
longitudes on the stellar surface. The most prominent period of the observed
activity modulations is different for each season and appears to evolve
following a specific pattern, resembling the changes in the sunspot periods
during the solar magnetic cycle. Under the hypothesis that the star exhibits
solar-like differential rotation, we suggest differential rotation values of
Kepler-210 that are similar to or smaller than that of the Sun. Finally, we
estimate spot life times between 60 days and 90 days, taking into consideration
the evolution of the total covered stellar surface computed from our model.


  In a supersymmetric model with hierarchical squark masses we analyze a
pattern of flavour symmetry breaking centered on the special role of the top
Yukawa coupling and, by extension, of the full Yukawa couplings for the up-type
quarks. For sufficiently heavy squarks of the first and second generation this
leads to effective Minimal Flavour Violation of the Flavour Changing Neutral
Current amplitudes. For this to happen we determine the bounds on the masses of
the heavy squarks with QCD corrections taken into account, properly including
previously neglected effects. We believe that the view presented in this paper
altogether strengthens the case for hierarchical sfermions.


  In this article, we present a cognitive architecture that is built from
powerful yet simple neural models. Specifically, we describe an implementation
of the common model of cognition grounded in neural generative coding and
holographic associative memory. The proposed system creates the groundwork for
developing agents that learn continually from diverse tasks as well as model
human performance at larger scales than what is possible with existant
cognitive architectures.


  Numerical modelling is performed for extreme relativistic parallel shocks
with upstream Lorentz factor $\Gamma=50$. Assuming the scattering is either
large angle or over pitch angles $\sim \Gamma^{-1}$, spectral flattening and
shock aaceleration speed-up is found. The energy gain for the first shock cycle
is $\sim \Gamma^{2}$. The likely output from relativistic shocks due to the
infall from the accretion disk to the AGN black hole is computed. Neutrinos
from proton-gamma interactions may be detectable with planned neutrino
telescopes.


  We study first-order spatial coherence for interacting polar bosons trapped
in triple-well potentials. It is argued that besides the well-known coherence
produced by couplings related to tunneling between the sites, there exists a
nonlocal coherence predominantly determined by intersite interactions, which
prevails between the outer sites of the triple well when their total filling is
odd. We find that the nonlocal interaction-induced coherence originates from
the superposition of degenerate many-body states in symmetric triple wells, and
demonstrate its robustness against perturbations due to various tunneling
mechanisms and thermal fluctuations.


  We consider an agent who is involved in a Markov decision process and
receives a vector of outcomes every round. Her objective is to maximize a
global concave reward function on the average vectorial outcome. The problem
models applications such as multi-objective optimization, maximum entropy
exploration, and constrained optimization in Markovian environments. In our
general setting where a stationary policy could have multiple recurrent
classes, the agent faces a subtle yet consequential trade-off in alternating
among different actions for balancing the vectorial outcomes. In particular,
stationary policies are in general sub-optimal. We propose a no-regret
algorithm based on online convex optimization (OCO) tools (Agrawal and Devanur
2014) and UCRL2 (Jaksch et al. 2010). Importantly, we introduce a novel
gradient threshold procedure, which carefully controls the switches among
actions to handle the subtle trade-off. By delaying the gradient updates, our
procedure produces a non-stationary policy that diversifies the outcomes for
optimizing the objective. The procedure is compatible with a variety of OCO
tools.


  Participation incentives a well-known issue inhibiting randomized clinical
trials (RCTs). We frame this issue as a non-standard exploration-exploitation
tradeoff: an RCT would like to explore as uniformly as possible, whereas each
patient prefers "exploitation", i.e., treatments that seem best. We incentivize
participation by leveraging information asymmetry between the trial and the
patients. We measure statistical performance via worst-case estimation error
under adversarially generated outcomes, a standard objective for RCTs. We
obtain a near-optimal solution in terms of this objective: an
incentive-compatible mechanism with a particular guarantee, and a nearly
matching impossibility result for any incentive-compatible mechanism. We
consider three model variants: homogeneous patients (of the same "type"
comprising preferences and medical histories), heterogeneous agents, and an
extension with estimated type frequencies.


  We solve the stabilization problem on the $n-$sphere in the presence of conic
constraints. We use the stereographic projection to map this problem to the
classical navigation problem on $\mathbb{R}^n$ in the presence of spherical
obstacles. As a consequence, any obstacle avoidance algorithm for navigation in
the Euclidean space can be used to solve the given problem on the $n-$sphere.
We illustrate the effectiveness of the approach using the kinematics of the
reduced attitude model on the $2-$sphere.


  Let $N\geq 3$ be a composite, odd, and square-free integer and let $\Gamma$
be the principal congruence subgroup of level $N$. Let $X(N)$ be the modular
curve of genus $g_{\Gamma}$ associated to $\Gamma$. In this article, we study
the Arakelov invariant $e(\Gamma)=\bar{\omega}^2/\varphi(N)$, with
$\bar{\omega}^2$ denoting the self-intersection of the relative dualizing sheaf
for the minimal regular model of $X(N)$, equipped with the Arakelov metric, and
$\varphi(N)$ is the Euler's phi function. Our main result is the asymptotics
$e(\Gamma) = 2g_{\Gamma}\log(N) + o(g_{\Gamma}\log(N))$, as the level $N$ tends
to infinity.


  Raven's Progressive Matrices are a benchmark originally designed to test the
cognitive abilities of humans. It has recently been adapted to test relational
reasoning in machine learning systems. For this purpose the so-called
Procedurally Generated Matrices dataset was set up, which is so far one of the
most difficult relational reasoning benchmarks. Here we show that deep neural
networks are capable of solving this benchmark, reaching an accuracy of 98.0
percent over the previous state-of-the-art of 62.6 percent by combining Wild
Relation Networks with Multi-Layer Relation Networks and introducing Magnitude
Encoding, an encoding scheme designed for late fusion architectures.


  Trusted Execution Environment, or enclave, promises to protect data
confidentiality and execution integrity of an outsourced computation on an
untrusted host. Extending the protection to distributed applications that run
on physically separated hosts, however, remains non-trivial. For instance, the
current enclave provisioning model hinders elasticity of cloud applications.
Furthermore, it remains unclear how an enclave process could verify if there
exists another concurrently running enclave process instantiated using the same
codebase, or count a number of such processes. In this paper, we seek an
autonomous membership service for enclave applications. The application owner
only needs to partake in instantiating the very first process of the
application, whereas all subsequent process commission and decommission will be
administered by existing and active processes of that very application. To
achieve both safety and liveness, our protocol design admits unjust
excommunication of a non-faulty process from the membership group. We implement
the proposed membership service in a system called AMES. Our experimental study
shows that AMES incurs an overhead of 5% - 16% compared to vanilla enclave
execution.


  Radiative corrections to electronic structure are characterized by
perturbative expansions in $\alpha$ and $Z\alpha$, where $\alpha$ is the
fine-structure constant and $Z$ is the nuclear charge. A formulation of the
leading-order $\alpha(Z\alpha)$ Uehling contribution to the renormalized vacuum
polarization is reported in a form that is convenient for implementation in
computational studies of the relativistic electronic structures of molecules.
Benchmark calculations based on these methods are reported that include the
leading-order vacuum polarization effects within relativistic mean-field
methods for the E119$^+$ ion and the closed-shell diatomic species E119F.


  We combine our compilation of photometry of M31 globular cluster and probable
cluster candidates with new near-infrared photometry for 30 objects. Using
these data we determine the globular cluster luminosity function (GCLF) in
multiple filters for the M31 halo clusters. We find a GCLF peak and dispersion
of V_0^0=16.84 +/-0.11, sigma_t=0.93 +/- 0.13 (Gaussian sigma = 1.20 +/- 0.14),
consistent with previous results. The halo GCLF peak colors (e.g., B^0_0 -
V^0_0) are consistent with the average cluster colors. We also measure V-band
GCLF parameters for several other subsamples of the M31 globular cluster
population. The inner third of the clusters have a GCLF peak significantly
brigher than that of the outer clusters (delta V =~ 0.5mag). Dividing the
sample by both galacticentric distance and metallicity, we find that the GCLF
also varies with metallicity, as the metal-poor clusters are on average 0.36
mag fainter than the metal-rich clusters. Our modeling of the catalog selection
effects suggests that they are not the cause of the measured differences, but a
more complete, less-contaminated M31 cluster catalog is required for
confirmation. Our results imply that dynamical destruction is not the only
factor causing variation in the M31 GCLF: metallicity, age, and cluster initial
mass function may also be important.


  In this paper, we consider the $(L,1)$ state-dependent reflecting random walk
(RW) on the half line, which is a RW allowing jumps to the left at a maxial
size $L$. For this model, we provide an explicit criterion for (positive)
recurrence and an explicit expression for the stationary distribution.As an
application, we prove the geometric tail asymptotic behavior of the stationary
distribution under certain conditions. The main tool employed in the paper is
the intrinsic branching structure within the $(L,1)$-random walk.


  A linear equation L is called k-regular if every k-coloring of the positive
integers contains a monochromatic solution to L. Richard Rado conjectured that
for every positive integer k, there exists a linear equation that is
(k-1)-regular but not k-regular. We prove this conjecture by showing that the
equation $\sum_{i=1}^{k-1} \frac{2^i}{2^i-1} x_i = (-1 + \sum_{i=1}^{k-1}
\frac{2^i}{2^i-1}) x_0$ has this property.
  This conjecture is part of problem E14 in Richard K. Guy's book "Unsolved
problems in number theory", where it is attributed to Rado's 1933 thesis,
"Studien zur Kombinatorik".


  In the Standard Model Effective Field Theory (SMEFT), the $SU(2)_L\times
U(1)_Y$ symmetry of the Standard Model is linearly realized. However, it is
possible that more general effective field theories, such as the Higgs
Effective Field Theory (HEFT) where this symmetry is realized non-linearly, are
needed to describe the data. Identifying physics beyond SMEFT could shed light
on the nature of Higgs and the realization of the electroweak symmetry. We
explore the possibility of such an identification by studying the effects of
scalar and vector new-physics operators on the angular distribution of
$\Lambda_b\rightarrow \Lambda_c(\rightarrow\Lambda\pi)\tau\bar\nu_\tau$. This
decay is sensitive to the 6-dimensional effective operator
$O_V^{LR}\equiv(\bar{\tau}\gamma^\mu P_L\nu_\tau)(\bar{c}\gamma_\mu P_R b)$,
which is present in HEFT but suppressed in SMEFT. We identify the angular
observables that can have significant contributions from $O_V^{LR}$, and hence
would be useful for probing not only BSM physics but also physics beyond SMEFT.
We further find that constraining the branching ratio of $B_c\rightarrow \tau
\bar \nu_\tau$ would be crucial for performing this task.


  We introduce a multimodal dataset where users express preferences through
images. These images encompass a broad spectrum of visual expressions ranging
from landscapes to artistic depictions. Users request recommendations for books
or music that evoke similar feelings to those captured in the images, and
recommendations are endorsed by the community through upvotes. This dataset
supports two recommendation tasks: title generation and multiple-choice
selection. Our experiments with large foundation models reveal their
limitations in these tasks. Particularly, vision-language models show no
significant advantage over language-only counterparts that use descriptions,
which we hypothesize is due to underutilized visual capabilities. To better
harness these abilities, we propose the chain-of-imagery prompting, which
results in notable improvements. We release our code and datasets.


  Let $F$ be a non-Archimedean local field with the ring of integers
$\mathcal{O}$ and the prime ideal $\mathfrak{p}$ and let $G={\bf
G}\left(\mathcal{O}/\mathfrak{p}^n\right)$ be the adjoint Chevalley group. Let
$m_f(G)$ denote the smallest possible dimension of a faithful representation of
$G$. Using the Stone-von Neumann theorem, we determine a lower bound for
$m_f(G)$ which is asymptotically the same as the results of Landazuri, Seitz
and Zalesskii for split Chevalley groups over $\mathbb{F}_q$. Our result yields
a conceptual explanation of the exponents that appear in the aforementioned
results


  2. In Section 3, we used some vague statements to affirm the training process
of the neural network, which cannot support others to reproduce the results of
the paper. In addition, this section does not show the difference between this
paper and other work, nor does it reflect innovation. 3. In Section 5, the
numerical examples are not compared with other multi-resolution methods, which
is not enough to explain the superiority of the method proposed in this paper.
Figure 10 also fails to show that this method is significantly improved
compared to the traditional method. Thanks for your understanding.
  Topology optimization is a pioneering design method that can provide various
candidates with high mechanical properties. However, the high-resolution for
the optimum structures is highly desired, normally in turn leading to
computationally intractable puzzle, especially for the famous Solid Isotropic
Material with Penalization (SIMP) method. In this paper, we introduce the
Super-Resolution Convolutional Neural Network (SRCNN) technique into topology
optimization framework to improve the resolution of topology solutions with
extremely high computational efficiency. Additionally, a pooling strategy is
established to balance the number of finite element analysis (FEA) and the
output mesh in optimization process. Considering the high training cost of 3D
neural networks, several 2D neural networks are combined to deal with 3D
topology optimization design problems. The combined treatment method used in 3D
topology optimization design eliminates the expense of retraining 3D
convolutional neural network and guarantees the quality of 3D design. Some
typical examples justify that the high-resolution topology optimization method
adopting SRCNN has excellent applicability and high efficiency.


  We determine the dynamical attractors associated with anisotropic
hydrodynamics (aHydro) and the DNMR equations for a 0+1d conformal system using
kinetic theory in the relaxation time approximation. We compare our results to
the non-equilibrium attractor obtained from exact solution of the 0+1d
conformal Boltzmann equation, Navier-Stokes theory, and second-order
Mueller-Israel-Stewart theory. We demonstrate that the aHydro attractor
equation resums an infinite number of terms in the inverse Reynolds number. The
resulting resummed aHydro attractor possesses a positive longitudinal to
transverse pressure ratio and is virtually indistinguishable from the exact
attractor. This suggests that kinetic theory involves not only a resummation in
gradients (Knudsen number) but also a novel resummation in inverse Reynolds
number. We also demonstrate that the DNMR result provides a better
approximation to the exact kinetic theory attractor than Mueller-Israel-Stewart
theory. Finally, we introduce a new method for obtaining approximate aHydro
equations which relies solely on an expansion in inverse Reynolds number, carry
out this expansion to third order, and compare these third-order results to the
exact kinetic theory solution.


  A systematic analysis of resonant x-ray Bragg diffraction data for UPd$_3$,
with signal enhancement at the U M$_{IV}$ edge, including possible structural
phase-transitions leads to a new determination of the space groups of the
material in the phases between $T_0 = 7.8$ K and $T_{+1}$ = 6.9 K as P222$_1$
and between $T_{-1}$ = 6.7 K and $T_{2}$ = 4.4 K as space group P2$_1$. In
addition, the quadrupolar order-parameters, $<Q_{ab}>$, inferred from
diffraction data in the phase between $T_{-1}$ and $T_{2}$, are $<Q_{xz}>$ and
$<Q_{yz}>$ at the (103) Bragg reflection, and $<Q_{xy}>$ at the (104)
reflection.


  We implement the theory of resonant scattering in the context of Cosmic
Microwave Background (CMB) polarisation anisotropies. We compute the changes in
the E-mode polarisation (EE) and Temperature E-mode (TE) CMB power spectra
introduced by the scattering on a resonant transition with a given optical
depth $\tau_X$ and polarisation coefficient $E_1$. The latter parameter,
accounting for how anisotropic the scattering is, depends on the exchange of
angular momentum in the transition and enables, {\it a priori}, to distinguish
among different possible resonances. We use this formalism in two different
scenarios: cosmological recombination and cosmological reionisation. In the
context of cosmological recombination, we compute predictions in frequency and
multipole space for the change in the TE and EE power spectra introduced by
scattering on the $H_{\alpha}$ and $P_{\alpha}$ lines of Hydrogen. This
constitutes a fundamental test for the standard model of recombination, and the
sensitivity it requires is comparable to that needed in measuring the
primordial CMB B-mode polarisation component. In the context of reionisation,
we study the scattering off metals and ions produced by the first stars, and
find that polarisation anisotropies, apart from providing a consistency test
for intensity measurements, give some insight on how reionisation evolved:
since they keep memory of how anisotropic the line scattering is, they should
be able to discern the OI 63.2$\mu$m transition from other possible transitions
associated to OIII, NII, NIII, etc. The amplitude of these signals are,
however, between 10 to 100 times below the (already challenging) level of CMB
B-mode polarisation anisotropies.


  We study combinatorial Dyson Schwinger equations, expressed in the Hopf
algebra of words with a quasi shuffle product. We map them into an algebra of
polynomials in one indeterminate L and show that the leading log expansion one
obtains with such a mapping are simple power law like expression


  These are lecture notes from a series of three lectures given at the summer
school "Geometric and Computational Spectral Theory" in Montreal in June 2015.
The aim of the lecture was to explain the mathematical theory behind
computations of eigenvalues and spectral determinants in geometrically
non-trivial contexts.


  Stationary wave functions at the transition between plateaus of the integer
quantum Hall effect are known to exhibit multi-fractal statistics. Here we
explore this critical behavior for the case of scattering states of the
Chalker-Coddington model with point contacts. We argue that moments formed from
the wave amplitudes of critical scattering states decay as pure powers of the
distance between the points of contact and observation. These moments in the
continuum limit are proposed to be correlations functions of primary fields of
an underlying conformal field theory. We check this proposal numerically by
finite-size scaling. We also verify the CFT prediction for a 3-point function
involving two primary fields.