  Cosmological information from forthcoming galaxy surveys, such as LSST and
Euclid, will soon exceed that available from the CMB. Higher order correlation
functions, like the bispectrum, will be indispensable for realising this
potential. The interpretation of this data faces many challenges because
gravitational collapse of matter is a complex non-linear process, typically
modelled by computationally expensive N-body simulations. Proposed alternatives
using fast dark matter codes (e.g. 2LPT or particle-mesh) are primarily
evaluated on their ability to reproduce clustering statistics linked to the
matter power spectrum. The accuracy of these codes can be tested in more detail
by looking at higher-order statistics, and in this paper we will present an
efficient and optimal methodology (MODAL-LSS) to reconstruct the full
bispectrum of any 3D density field. We make quantitative comparisons between a
number of fast dark matter codes and Gadget at redshift $z=0.5$. This will
serve as an important diagnostic tool for dark matter/halo mock catalogues and
lays the foundation for realistic high precision analysis with the galaxy
bispectrum. In particular, we show that the lack of small-scale power in the
bispectrum of fast codes can be ameliorated by a simple `boosting' technique
for the power spectrum. We also investigate the covariance of the MODAL-LSS
bispectrum estimator, demonstrating the plateauing of non-Gaussian errors in
contrast to simple Gaussian extrapolations. This has important consequences for
the extraction of information from the bispectrum and hence parameter
estimation. Finally we make quantitative comparisons of simulation bispectra
with theoretical models, discussing the initial parameters required to create
mock catalogues with accurate bispectra.


  In this paper, we present recent results in harmonic analysis in the real
line R and in the half-line R^+, which show a closed relation between Hermite
and Laguerre functions, respectively, their symmetry groups and Fourier
analysis. This can be done in terms of a unified framework based in the use of
rigged Hilbert spaces. We find a relation between the universal enveloping
algebra of the symmetry groups with the fractional Fourier transform. The
results obtained are relevant in quantum mechanics as well as in signal
processing as Fourier analysis has a close relation with signal filters. Also,
we introduce some new results concerning a discretized Fourier transform on the
circle. We introduce new functions on the circle constructed with the use of
Hermite functions with interesting properties under Fourier transformations.


  Applying standard statistical methods after model selection may yield
inefficient estimators and hypothesis tests that fail to achieve nominal type-I
error rates. The main issue is the fact that the post-selection distribution of
the data differs from the original distribution. In particular, the observed
data is constrained to lie in a subset of the original sample space that is
determined by the selected model. This often makes the post-selection
likelihood of the observed data intractable and maximum likelihood inference
difficult. In this work, we get around the intractable likelihood by generating
noisy unbiased estimates of the post-selection score function and using them in
a stochastic ascent algorithm that yields correct post-selection maximum
likelihood estimates. We apply the proposed technique to the problem of
estimating linear models selected by the lasso. In an asymptotic analysis the
resulting estimates are shown to be consistent for the selected parameters and
to have a limiting truncated normal distribution. Confidence intervals
constructed based on the asymptotic distribution obtain close to nominal
coverage rates in all simulation settings considered, and the point estimates
are shown to be superior to the lasso estimates when the true model is sparse.


  Dynamic Occupancy Grid Mapping is a technique used to generate a local map of
the environment containing both static and dynamic information. Typically,
these maps are primarily generated using lidar measurements. However, with
improvements in radar sensing, resulting in better accuracy and higher
resolution, radar is emerging as a viable alternative to lidar as the primary
sensor for mapping. In this paper, we propose a radar-centric dynamic occupancy
grid mapping algorithm with adaptations to the state computation, inverse
sensor model, and field-of-view computation tailored to the specifics of radar
measurements. We extensively evaluate our approach using real data to
demonstrate its effectiveness and establish the first benchmark for radar-based
dynamic occupancy grid mapping using the publicly available Radarscenes
dataset.


  Weakly-supervised audio-visual violence detection aims to distinguish
snippets containing multimodal violence events with video-level labels. Many
prior works perform audio-visual integration and interaction in an early or
intermediate manner, yet overlooking the modality heterogeneousness over the
weakly-supervised setting. In this paper, we analyze the modality asynchrony
and undifferentiated instances phenomena of the multiple instance learning
(MIL) procedure, and further investigate its negative impact on
weakly-supervised audio-visual learning. To address these issues, we propose a
modality-aware contrastive instance learning with self-distillation (MACIL-SD)
strategy. Specifically, we leverage a lightweight two-stream network to
generate audio and visual bags, in which unimodal background, violent, and
normal instances are clustered into semi-bags in an unsupervised way. Then
audio and visual violent semi-bag representations are assembled as positive
pairs, and violent semi-bags are combined with background and normal instances
in the opposite modality as contrastive negative pairs. Furthermore, a
self-distillation module is applied to transfer unimodal visual knowledge to
the audio-visual model, which alleviates noises and closes the semantic gap
between unimodal and multimodal features. Experiments show that our framework
outperforms previous methods with lower complexity on the large-scale
XD-Violence dataset. Results also demonstrate that our proposed approach can be
used as plug-in modules to enhance other networks. Codes are available at
https://github.com/JustinYuu/MACIL_SD.


  A model of genome evolution is proposed. Based on three assumptions the
evolutionary theory of a genome is formulated. The general law on the direction
of genome evolution is given. Both the deterministic classical equation and the
stochastic quantum equation are proposed. It is proved that the classical
equation can be put in a form of the least action principle and the latter can
be used for obtaining the quantum generalization of the evolutionary law. The
wave equation and uncertainty relation for the quantum evolution are deduced
logically. It is shown that the classical trajectory is a limiting case of the
general quantum evolution depicted in the coarse-grained time. The observed
smooth/sudden evolution is interpreted by the alternating occurrence of the
classical and quantum phases. The speciation event is explained by the quantum
transition in quantum phase. Fundamental constants of time dimension, the
quantization constant and the evolutionary inertia, are introduced for
characterizing the genome evolution. The size of minimum genome is deduced from
the quantum uncertainty lower bound. The present work shows the quantum law may
be more general than thought, since it plays key roles not only in atomic
physics, but also in genome evolution.


  Superoxide dismutase-1 (SOD1) is a ubiquitous, Cu and Zn binding, free
radical defense enzyme whose misfolding and aggregation play a potential key
role in amyotrophic lateral sclerosis, an invariably fatal neurodegenerative
disease. Over 150 mutations in SOD1 have been identified with a familial form
of the disease, but it is presently not clear what unifying features, if any,
these mutants share to make them pathogenic. Here, we develop several new
computational assays for probing the thermo-mechanical properties of both
ALS-associated and rationally-designed SOD1 variants. Allosteric interaction
free energies between residues and metals are calculated, and a series of
atomic force microscopy experiments are simulated with variable tether
positions, to quantify mechanical rigidity "fingerprints" for SOD1 variants.
Mechanical fingerprinting studies of a series of C-terminally truncated
mutants, along with an analysis of equilibrium dynamic fluctuations while
varying native constraints, potential energy change upon mutation,
frustratometer analysis, and analysis of the coupling between local frustration
and metal binding interactions for a glycine scan of 90 residues together
reveal that the apo protein is internally frustrated, that these internal
stresses are partially relieved by mutation but at the expense of metal-binding
affinity, and that the frustration of a residue is directly related to its role
in binding metals. This evidence points to apo SOD1 as a strained intermediate
with "self-allostery" for high metal-binding affinity. Thus, the prerequisites
for the function of SOD1 as an antioxidant compete with apo state
thermo-mechanical stability, increasing the susceptibility of the protein to
misfold in the apo state.


  A strongly special subvariety of a Shimura variety $S$ is (essentially) a
subvariety associated to a semi-simple sub-Shimura datum. We prove that the set
of probability measures canonically associated to to strongly special
subvarieties is compact. More precisely: If $\mu_n$ is a sequence of such
probability measures associated to strongly special subvarieties $Z_n$ of $S$
there exists a subsequence $\mu_{n_k}$ which converge to a measure $\mu_Z$
canonically associated to a strongly special subvariety $Z$ and for all $k>>0$
$Z_{n_k}$ is contained in $Z$.
  We give some application to the Andre-Oort conjecture: If $X$ is a subvariety
of $S$ then there exists at most finitely many maximal (amongs subvarieties of
$X$) strongly special subvarieties of $X$ as predicted by the Andre-Oort
Conjecture. The proof uses Ratner's theory, some results of Mozes-Shah and
Dani-Margulis.


  We study the entanglement between a qubit and its environment from the
spin-boson model with Ohmic dissipation. Through a mapping to the anisotropic
Kondo model, we derive the entropy of entanglement of the spin
$E(\alpha,\Delta,h)$, where $\alpha$ is the dissipation strength, $\Delta$ is
the tunneling amplitude between qubit states, and $h$ is the level asymmetry.
For $1-\alpha \gg \Delta/\omega_c$ and $(\Delta,h) \ll \omega_c$, we show that
the Kondo energy scale $T_K$ controls the entanglement between the qubit and
the bosonic environment ($\omega_c$ is a high-energy cutoff). For $h\ll T_K$,
the disentanglement proceeds as $(h/T_K)^2$; for $h\gg T_K$, $E$ vanishes as
$(T_K/h)^{2-2\alpha}$, up to a logarithmic correction. For a given $h$, the
maximum entanglement occurs at a value of $\alpha$ which lies in the crossover
regime $h\sim T_K$. We emphasize the possibility of measuring this entanglement
using charge qubits subject to electromagnetic noise.


  In this paper, we study a realistic model of quintessential inflation with
radiation and matter. By the analysis of the dynamical system and numerical
work about the evolution of the equation of state and cosmic density parameter,
we show that this model is a good match for the current astronomical
observation. The conclusion we obtain is in favor of the model where the
modular part of complex field plays the role of the inflaton whereas the
argument part is the quintessence field. The numerical calculation shows that a
heteroclinic orbit (solution of dynamical system) which interpolates between
early-time de Sitter phase (an unstable critical point) and a late-time de
Sitter attractor.


  We construct the second quantized action for sub-critical closed string field
theory with zero cosmological constant in dimensions $ 2 \leq D < 26$,
generalizing the non-polynomial closed string field theory action proposed by
the author and the Kyoto and MIT groups for $D = 26$. The proof of gauge
invariance is considerably complicated by the presence of the Liouville field
$\phi$ and the non-polynomial nature of the action. However, we explicitly show
that the polyhedral vertex functions obey BRST invariance to all orders. By
point splitting methods, we calculate the anomaly contribution due to the
Liouville field, and show in detail that it cancels only if $D - 26 + 1 + 3 Q ^
2 = 0 $, in both the bosonized and unbosonized polyhedral vertex functions. We
also show explicitly that the four point function generated by this action
reproduces the shifted Shapiro-Virasoro amplitude found from $c=1$ matrix
models and Liouville theory in two dimensions. LATEX file.


  The outer regions of disk galaxies show a drop-off in optical and Halpha
emission, suggesting a star formation threshold radius, assumed to owe to a
critical surface density below which star formation does not take place. Signs
of filamentary star formation beyond this threshold radius have been observed
in individual galaxies in the Halpha and recent GALEX surveys have discovered
that 30% of disk galaxies show UV emission out to 2-3 times the optical radius
of the galaxy. We run smooth particle hydrodynamics simulations of disk
galaxies with constant density extended gas disks to test whether
over-densities owing to spiral structure in the outer disk can reproduce the
observed star formation. We indeed find that spiral density waves from the
inner disk propagate into the outer gas disk and raise local gas regions above
the star formation density threshold, yielding features similar to those
observed. Because the amount of star formation is low, we expect to see little
optical emission in outer disks, as observed. Our results indicate that XUV
disks can be simulated simply by adding an extended gas disk with a surface
density near the threshold density to an isolated galaxy and evolving it with
fiducial star formation parameters.


  We propose gauge theories in which the unstable branes and the fundamental
string are realized as classical solutions. While the former are represented by
domain wall like configurations of a scalar field coupled to the gauge field,
the latter is by a confined flux tube in the bulk. It is shown that the
confined flux tube is really a source of the bulk B-field. Our model also
provides a natural scenario of the confinement on the brane in the context of
the open string tachyon condensation. It is also argued that the fundamental
string can be realized as a classical solution in a certain IIB matrix model as
in our model.


  We investigate the existence of minisuperspace description for the
homogeneous cosmological field equations within the framework of symmetric
teleparallel $f(Q)$-gravity. We consider the background space to be described
by the isotropic Friedmann--Lema\^{\i}tre--Robertson--Walker geometry, the
anisotropic Kantowski-Sachs and the anisotropic Bianchi III geometries. Across
all these models, we establish that the field equations in $f(Q)$-cosmology
exhibit second-order characteristics in the coincident gauge and those of a
sixth-order theory in the non-coincident gauge. Specifically, within the latter
scenario, the dynamic degrees of freedom are attributed to two scalar fields.
Finally, as an example of integrability, we derive a vacuum cosmological
solution within the non-coincident gauge.


  Deep Neural Networks (DNNs) are commonly used for various traffic analysis
problems, such as website fingerprinting and flow correlation, as they
outperform traditional (e.g., statistical) techniques by large margins.
However, deep neural networks are known to be vulnerable to adversarial
examples: adversarial inputs to the model that get labeled incorrectly by the
model due to small adversarial perturbations. In this paper, for the first
time, we show that an adversary can defeat DNN-based traffic analysis
techniques by applying \emph{adversarial perturbations} on the patterns of
\emph{live} network traffic.


  Defect-based quantum emitters in solid state materials offer a promising
platform for quantum communication and sensing. Confocal fluorescence
microscopy techniques have revealed quantum emitters in a multitude of host
materials. In some materials, however, optical properties vary widely between
emitters, even within the same sample. In these cases, traditional ensemble
fluorescence measurements are confounded by heterogeneity, whereas individual
defect-by-defect studies are impractical. Here, we develop a method to
quantitatively and systematically analyze the properties of heterogeneous
emitter ensembles using large-area photoluminescence maps. We apply this method
to study the effects of sample treatments on emitters in hexagonal boron
nitride, and we find that low-energy (3 keV) electron irradiation creates
emitters, whereas high-temperature (850 $^\circ$C) annealing in an inert gas
environment brightens emitters.


  This paper introduces a feedback-based temperature controller design for
intelligent regulation of food internal temperature inside of standard
convection ovens. Typical convection ovens employ an open-loop control system
that requires a person to estimate the amount of time needed to cook foods in
order to achieve desired internal temperatures. This approach, however, can
result in undesired results with the final food temperatures being too high or
too low due to the inherent difficulty in accurately predicting required
cooking times without continuously measuring internal states and accounting for
noise in the system. By implementing and introducing a feedback controller with
a full-order Luenberger observer to create a closed-loop system, an oven can be
instrumented to measure and regulate the internal temperatures of food in order
to automatically control oven heat output and confidently achieve desired
results.


  We report that under some specific conditions a single qubit model weakly
interacting with information environments can be referred to as a quantum
classifier. We exploit the additivity and the divisibility properties of the
completely positive (CP) quantum dynamical maps in order to obtain an open
quantum classifier. The steady state response of the system with respect to the
input parameters was numerically investigated and it's found that the response
of the open quantum dynamics at steady state acts non-linearly with respect to
the input data parameters. We also demonstrate the linear separation of the
quantum data instances that reflects the success of the functionality of the
proposed model both for ideal and experimental conditions. Superconducting
circuits were pointed out as the physical model to implement the theoretical
model with possible imperfections.


  This comprehensive survey explored the evolving landscape of generative
Artificial Intelligence (AI), with a specific focus on the transformative
impacts of Mixture of Experts (MoE), multimodal learning, and the speculated
advancements towards Artificial General Intelligence (AGI). It critically
examined the current state and future trajectory of generative Artificial
Intelligence (AI), exploring how innovations like Google's Gemini and the
anticipated OpenAI Q* project are reshaping research priorities and
applications across various domains, including an impact analysis on the
generative AI research taxonomy. It assessed the computational challenges,
scalability, and real-world implications of these technologies while
highlighting their potential in driving significant progress in fields like
healthcare, finance, and education. It also addressed the emerging academic
challenges posed by the proliferation of both AI-themed and AI-generated
preprints, examining their impact on the peer-review process and scholarly
communication. The study highlighted the importance of incorporating ethical
and human-centric methods in AI development, ensuring alignment with societal
norms and welfare, and outlined a strategy for future AI research that focuses
on a balanced and conscientious use of MoE, multimodality, and AGI in
generative AI.


  The glassy state is known to undergo slow structural relaxation, where the
system progressively explores lower free-energy minima which are either
amorphous (ageing) or crystalline (devitrification). Recently, there is growing
interest in the unusual intermittent collective displacements of a large number
of particles known as "avalanches". However, their structural origin and
dynamics are yet to be fully addressed. Here, we study hard-sphere glasses
which either crystallise or age depending on the degree of size polydispersity,
and show that a small number of particles are thermodynamically driven to
rearrange in regions of low density and bond orientational order. This causes a
transient loss of mechanical equilibrium which facilitates a large cascade of
motion. Combined with previously identified phenomenology, we have a complete
kinetic pathway for structural change which is common to both ageing and
crystallisation. Furthermore, this suggests that transient force balance is
what distinguishes glasses from supercooled liquids.


  We highlight the progress in our understanding of how neutrinos change their
flavor in astrophysical environments, in particular effects from the neutrino
self-interaction. We emphasize extended descriptions of neutrino propagation in
massive stars that are beyond the current one based on the mean-field
approximation. The extended equations include, in particular, corrections from
(anti)neutrino-(anti)neutrino pairing correlations and from the neutrino mass.
We underline open issues and challenges.


  An analysis of the IRAS 1.2 Jy redshift catalogue with emphasis on the
separate examination of northern and southern parts (in galactic coordinates)
is performed using a complete set of morphological descriptors (Minkowski
functionals), nearest neighbour distributions and the variance of the galaxy
counts. We find large fluctuations in the clustering properties as seen in a
large difference between the northern and southern parts of the catalogue on
scales of 100Mpc/h. These fluctuations remain discernible even on the scale of
200Mpc/h. We also identify sparse sampling as a major source of ``apparent
homogenization''. Tests on observational selection effects concerning
luminosity, colour and redshift-space distortion support the significance of
these large-scale fluctuations.


  Chaos often represents a severe obstacle for the set-up of many-body
experiments, e.g., in fusion plasmas or turbulent flows. We propose a strategy
to control chaotic diffusion in conservative systems. The core of our approach
is a small apt modification of the system which channels chaos by building
barriers to diffusion. It leads to practical prescriptions for an experimental
apparatus to operate in a regular regime (drastic enhancement of confinement).
The experimental realization of this control on a Travelling Wave Tube opens
the possibility to practically achieve the control of a wide range of systems
at a low additional cost of energy.


  We prove that the profinite completion of the fundamental group of a compact
3-manifold $M$ satisfies a Tits alternative: if a closed subgroup $H$ does not
contain a free pro-$p$ subgroup for any $p$, then $H$ is virtually soluble, and
furthermore of a very particular form. In particular, the profinite completion
of the fundamental group of a closed, hyperbolic 3-manifold does not contain a
subgroup isomorphic to $\hat{\mathbb{Z}}^2$. This gives a profinite
characterization of hyperbolicity among irreducible 3-manifolds. We also
characterize Seifert fibred 3-manifolds as precisely those for which the
profinite completion of the fundamental group has a non-trivial procyclic
normal subgroup. Our techniques also apply to hyperbolic, virtually special
groups, in the sense of Haglund and Wise. Finally, we prove that every finitely
generated pro-$p$ subgroup of the profinite completion of a torsion-free,
hyperbolic, virtually special group is free pro-$p$.


  We investigate the impact of big bang nucleosynthesis (BBN) on the Hubble
tension, focusing on how the treatment of the reaction rate and observational
data affect the evaluation of the tension. We show that the significance of the
tension can vary by $0.8 \sigma$ in some early dark energy model, depending on
the treatment of the reaction rate and observational data. This indicates that
how we include the BBN data in the analysis can give a significant impact on
the Hubble tension, and we need to carefully consider the assumptions of the
analysis to evaluate the significance of the tension when the BBN data is used.


  We propose a framework for the analysis of transmission channels in a large
class of dynamic models. To this end, we formulate our approach both using
graph theory and potential outcomes, which we show to be equivalent. Our
method, labelled Transmission Channel Analysis (TCA), allows for the
decomposition of total effects captured by impulse response functions into the
effects flowing along transmission channels, thereby providing a quantitative
assessment of the strength of various transmission channels. We establish that
this requires no additional identification assumptions beyond the
identification of the structural shock whose effects the researcher wants to
decompose. Additionally, we prove that impulse response functions are
sufficient statistics for the computation of transmission effects. We
demonstrate the empirical relevance of TCA for policy evaluation by decomposing
the effects of policy shocks arising from a variety of popular macroeconomic
models.


  Supersymmetric compactification with moderately large radius (${\rm Re}< T >
\sim {\cal O}(10)$ or more) not only accommodates supersymmetric unification,
but also provides candidates for an inflaton in the form of geometric moduli;
the value of ${\rm Re}< T > > 1$ may be used as a parameter that brings
corrections to the inflaton potential under control. Motivated by a bottom-up
idea "right-handed sneutrino inflation" scenario, we study whether complex
structure moduli can play some role during the slow-roll inflation and/or
reheating process in this moderately large radius regime. Even when we allow a
tuning introduced by Kallosh and Linde, the barrier of volume stabilization
potential from gaugino condensation racetrack superpotential can hardly be as
high as $(10^{16} \; {\rm GeV})^4$ for generic choice of parameters in this
regime. It is also found that even very small deformation of complex structure
during inflation/reheating distorts the volume stabilization potential, so that
the volume stabilization imposes tight constraints on large-field inflation
scenario involving evolution of complex structure moduli. A few ideas of
satisfying those constraints in string theory are also discussed.


  With the increasing emphasis on the safe autonomy for robots, model-based
safe control approaches such as Control Barrier Functions have been extensively
studied to ensure guaranteed safety during inter-robot interactions. In this
paper, we introduce the Parametric Control Barrier Function (Parametric-CBF), a
novel variant of the traditional Control Barrier Function to extend its
expressivity in describing different safe behaviors among heterogeneous robots.
Instead of assuming cooperative and homogeneous robots using the same safe
controllers, the ego robot is able to model the neighboring robots' underlying
safe controllers through different Parametric-CBFs with observed data. Given
learned parametric-CBF and proved forward invariance, it provides greater
flexibility for the ego robot to better coordinate with other heterogeneous
robots with improved efficiency while enjoying formally provable safety
guarantees. We demonstrate the usage of Parametric-CBF in behavior prediction
and adaptive safe control in the ramp merging scenario from the applications of
autonomous driving. Compared to traditional CBF, Parametric-CBF has the
advantage of capturing varying drivers' characteristics given richer
description of robot behavior in the context of safe control. Numerical
simulations are given to validate the effectiveness of the proposed method.


  The intent of this short note is to provide context for and an independent
proof of the discovery of Klaus Kroencke that complex projective space with its
canonical Fubini--Study metric is dynamically unstable under Ricci flow in all
complex dimensions N>1. The unstable perturbation is not Kaehler. This provides
a counterexample to a well known conjecture widely attributed to Hamilton.
Moreover, it shows that the expected stability of the subspace of Kaehler
metrics under Ricci flow, another conjecture believed by several experts, needs
to be interpreted in a more nuanced way than some may have expected.


  Index modulation (IM) techniques can be applied to the different media in
order to achieve spectral- and energy-efficient communication as well as to the
indices of the subcarriers of a generalized frequency division multiplexing
(GFDM) data block. In this work, a novel transceiver architecture for
multi-user GFDM-IM system is introduced. The performance of the GFDM-IM is
studied by considering the bit error rate (BER) as performance metric. It is
shown that better BER performance than the classical GFDM and the orthogonal
frequency division multiplexing (OFDM) with IM can be achieved by employing IM
to the GFDM.


  Let $F\subseteq\mathbb{P}^3$ be a smooth quartic surface and let
$\mathcal{O}_F(h):=\mathcal{O}_{\mathbb{P}^3}(1)\otimes\mathcal{O}_F$. In the
present paper we classify locally free sheaves $\mathcal{E}$ of rank $2$ on $F$
such that $c_1(\mathcal{E})=\mathcal{O}_F(2h)$, $c_2(\mathcal{E})=8$ and
$h^1\big(F,\mathcal{E}(th)\big)=0$ for $t\in\mathbb{Z}$. We also deal with
their stability.


  We demonstrate the use of Langevin spin dynamics for studying dynamical
properties of an archetypical spin glass system. Simulations are performed on
CuMn (20% Mn) where we study the relaxation that follows a sudden quench of the
system to the low temperature phase. The system is modeled by a Heisenberg
Hamiltonian where the Heisenberg interaction parameters are calculated by means
of first-principles density functional theory. Simulations are performed by
numerically solving the Langevin equations of motion for the atomic spins. It
is shown that dynamics is governed, to a large degree, by the damping parameter
in the equations of motion and the system size. For large damping and large
system sizes we observe the typical aging regime.


  It is shown that formulas for the radiative power loss and radiation reaction
from a charge can be derived in a heuristic manner from the kinetic power (rate
of change of the kinetic energy) of its electric inertial mass. The derivation
assumes a non-relativistic but otherwise an arbitrary motion of the charge. We
exploit the fact that as the charge velocity changes because of a constant
acceleration, there are accompanying modifications in its electromagnetic
fields which can remain concurrent with the charge motion because the velocity
as well as acceleration information enters into the field expression. However,
if the acceleration of the charge is varying, information about that being not
present in the field expressions, the electromagnetic fields get `out of step'
with the actual charge motion. Accordingly we arrive at a radiation reaction
formula for an arbitrarily moving charge, obtained hitherto in literature from
the self-force, derived in a rather cumbersome way from the detailed mutual
interaction between various constituents of a small charged sphere. This way we
demonstrate that a power loss from a charge occurs only when there is a change
in its acceleration and the derived instantaneous power loss is directly
proportional to the scalar product of the velocity and the rate of change of
the acceleration of the charge.


  Networks in nature possess a remarkable amount of structure. Via a series of
data-driven discoveries, the cutting edge of network science has recently
progressed from positing that the random graphs of mathematical graph theory
might accurately describe real networks to the current viewpoint that networks
in nature are highly complex and structured entities. The identification of
high order structures in networks unveils insights into their functional
organization. Recently, Clauset, Moore, and Newman, introduced a new algorithm
that identifies such heterogeneities in complex networks by utilizing the
hierarchy that necessarily organizes the many levels of structure. Here, we
anchor their algorithm in a general community detection framework and discuss
the future of community detection.


  Can we obtain insights about the brain using AI models? How is the
information in deep learning models related to brain recordings? Can we improve
AI models with the help of brain recordings? Such questions can be tackled by
studying brain recordings like functional magnetic resonance imaging (fMRI). As
a first step, the neuroscience community has contributed several large
cognitive neuroscience datasets related to passive reading/listening/viewing of
concept words, narratives, pictures, and movies. Encoding and decoding models
using these datasets have also been proposed in the past two decades. These
models serve as additional tools for basic cognitive science and neuroscience
research. Encoding models aim at generating fMRI brain representations given a
stimulus automatically. They have several practical applications in evaluating
and diagnosing neurological conditions and thus may also help design therapies
for brain damage. Decoding models solve the inverse problem of reconstructing
the stimuli given the fMRI. They are useful for designing brain-machine or
brain-computer interfaces. Inspired by the effectiveness of deep learning
models for natural language processing, computer vision, and speech, several
neural encoding and decoding models have been recently proposed. In this
survey, we will first discuss popular representations of language, vision and
speech stimuli, and present a summary of neuroscience datasets. Further, we
will review popular deep learning based encoding and decoding architectures and
note their benefits and limitations. Finally, we will conclude with a summary
and discussion about future trends. Given the large amount of recently
published work in the computational cognitive neuroscience (CCN) community, we
believe that this survey enables an entry point for DNN researchers to
diversify into CCN research.


  On a n-dimensional connected compact manifold with non-empty boundary
equipped with a Riemannian metric, a spin structure and a chirality operator,
we study some properties of a spin conformal invariant defined from the first
eigenvalue of the Dirac operator under the chiral bag boundary condition. More
precisely, we show that we can derive a spinorial analogue of Aubin's
inequality.


  Second-order spin-wave expansions are used to compute the ground-state energy
and sublattice magnetizations of the quantum one-dimensional Heisenberg
ferrimagnet with nearest-neighbor antiferromagnetic interactions and two types
of alternating sublattice spins $S_1>S_2$. It is found that in the extreme
quantum cases $(S_1,S_2)=(1,1/2)$, $(3/2,1)$, and $(3/2,1/2)$, the estimates
for the ground-state energy and sublattice magnetizations differ less than
0.03% for the energy and 0.2% for the sublattice magnetizations from the
recently published density matrix renormalization group numerical calculations.
  The reported results strongly suggest that the quantum Heisenberg
ferrimagnetic chains give another example of a low-dimensional quantum spin
system where the spin-wave approach demonstrates a surprising efficiency.


  The amoeba of a Laurent polynomial $f \in \C[z_1^{\pm 1},\ldots,z_n^{\pm 1}]$
is the image of its zero set $\mathcal{V}(f)$ under the log-absolute-value map.
Understanding the space of amoebas (i.e., the decomposition of the space of all
polynomials, say, with given support or Newton polytope, with regard to the
existing complement components) is a widely open problem.
  In this paper we investigate the class of polynomials $f$ whose Newton
polytope $\New(f)$ is a simplex and whose support $A$ contains exactly one
point in the interior of $\New(f)$. Amoebas of polynomials in this class may
have at most one bounded complement component. We provide various results on
the space of these amoebas. In particular, we give upper and lower bounds in
terms of the coefficients of $f$ for the existence of this complement component
and show that the upper bound becomes sharp under some extremal condition. We
establish connections from our bounds to Purbhoo's lopsidedness criterion and
to the theory of $A$-discriminants.
  Finally, we provide a complete classification of the space of amoebas for the
case that the exponent of the inner monomial is the barycenter of the simplex
Newton polytope. In particular, we show that the set of all polynomials with
amoebas of genus 1 is path-connected in the corresponding space of amoebas,
which proves a special case of the question on connectivity (for general Newton
polytopes) stated by H. Rullg{\aa}rd.


  Information-centric networking (ICN) facilitates content identification in
networks and offers parametric representation of content semantics. This work,
proposes an ICN/WDM network architecture that uses these features to offer
superior network utilization, in terms of performance and power consumption.
The architecture introduces an ICN publish/subscribe communication approach to
the wavelength layer, whereby, content is aggregated according to its
popularity rank into wavelength-size groups that can be published and
"subscribed to" by multiple nodes. Consequently, routing and wavelength
assignment (RWA) algorithms benefit from anycast to identify multiple sources
of aggregate content and allow optimization of the source selection of
light-paths. A power-aware algorithm, Maximum Degree of connectivity (MaxDeg),
has been developed with the objective of exploiting this flexibility to address
the trade-off between power consumption and network performance. The algorithm
is also applicable to IP architectures, albeit with less flexibility.
Evaluation results indicate the superiority of the proposed ICN architecture,
even when utilizing conventional routing methods, compared to its IP
counterpart. The results further highlight the performance improvement achieved
by the proposed algorithm, compared to conventional RWA methods such as
Shortest-path First Fit (SFF).


  High-energy muons generated from cosmic-ray particle showers have been shown
to exhibit properties ideal for imaging the interior of large structures. This
paper explores the possibility of using a single portable muon detector in
conjunction with image reconstruction methods used in nuclear medicine to
reconstruct a 3D image of the interior of critical infrastructure such as the
Zero Energy Deuterium (ZED-2) research reactor at Canadian Nuclear
Laboratories' Chalk River site. The ZED-2 reactor core and muon detector
arrangement are modeled in GEANT4 and Monte Carlo measurements of the resultant
muon throughput and angular distribution at several angles of rotation around
the reactor are generated. Statistical analysis is then performed on these
measurements based on the well-defined flux and angular distribution of muons
expected near the surface of the earth. The results of this analysis are shown
to produce reconstructed images of the spatial distribution of nuclear fuel
within the core for multiple fuel configurations. This one-sided tomography
concept is a possible candidate for examining the internal structure of larger
critical facilities, for example the Fukushima Daiichi power plant where the
integrity of the containment infrastructure and the location of the reactor
fuel is unknown.


  Diagrams enable the use of various algebraic and geometric tools for
analysing and classifying knots. In this paper we introduce a new diagrammatic
representation of triply-periodic entangled structures (TP tangles), which are
embeddings of simple curves in $\mathbb{R}^3$ that are invariant under
translations along three non-coplanar axes. As such, these entanglements can be
seen as lifts of links in the 3-torus $\mathbb{T}^3 = \mathbb{S}^1 \times
\mathbb{S}^1 \times \mathbb{S}^1$, where two non-isotopic links in
$\mathbb{T}^3$ may lift to the same TP tangle. We consider the equivalence of
TP tangles in $\mathbb{R}^3$ through the use of diagrams representing links in
$\mathbb{T}^3$. These diagrams require additional moves beyond the classical
Reidemeister moves, which we define and show that they preserve ambient
isotopies of links in $\mathbb{T}^3$. The final definition of a tridiagram of a
link in $\mathbb{T}^3$ allows us to then consider additional notions of
equivalence that encode global isotopies of a TP tangle, such as a change of
basis or lattice in $\mathbb{R}^3$.


  We describe the generation and properties of a cryogenic beam of $^7$Li$_2$
dimers from sublimation of a neon matrix where lithium atoms have been
implanted via laser ablation of solid precursors of metallic lithium or lithium
hydride (LiH). Different sublimation regimes lead to pulsed molecular beams
with different temperatures, densities and forward velocities. With laser
absorption spectroscopy these parameters were measured using the molecular
$^7$Li$_2$ (R) transitions A$^1\Sigma_u^+(v'=4,J'=J''+1)\leftarrow
$X$^1\Sigma_g^+ (v''=0,J''=0,1,3)$. In a typical regime, sublimating a matrix
at 16 K, translational temperatures of 6--8 K with a drift velocity of 130
m$\,$s$^{-1}$ in a free expanding pulsed beam with molecular density of 10$^9$
cm$^{-3}$, averaged along the laser axis, were observed. Rotational
temperatures around 5--7 K were obtained. In recent experiments we were able to
monitor the atomic Li signal -- in the D2 line -- concomitantly with the
molecular signal in order to compare them as a function of the number of
ablation pulses. Based on the data and a simple model, we discuss the
possibility that a fraction of these molecules are being formed in the matrix,
by mating atoms from different ablation pulses, which would open up the way to
formation of other more interesting and difficult molecules to be studied at
low temperatures. Such a source of cryogenic molecules have possible
applications encompassing fundamental physics tests, quantum information
studies, cold collisions, chemistry, and trapping.


  With the advent of numerous languages it is difficult to realize the edge of
one language in a particular scope over another one. We are making an effort,
realizing these few issues and comparing some main stream languages like Java,
Scala, C++, Haskell, VB .NET, AspectJ, Perl, Ruby, PHP and Scheme keeping in
mind some core issues in program development.


  Using the recent result of the SNO solar neutrino experiment, we have
demonstrated in a model independent way that the contribution of Be-7 and other
medium energy neutrinos to the event rate of the Homestake experiment is 4
sigma smaller than the BP2000 SSM prediction. We have considered the
implications of this result for the future BOREXINO experiment.


  We study the bi-Hamiltonian structures for the hierarchy of a 3-component
generalization of the Degasperis-Procesi (3-DP) equation. We show that all
Hamiltonian functionals in the hierarchy are homogenous, and Hamiltonian
functionals of the hierarchy in the negative direction are local. We construct
two different Liouville transformations by construct a reciprocal
transformation. The associated system for the first one is a reduction of a
negative flow in a modified Yajima-Oikawa hierarchy. The associated system for
the second one and the associated system for another 3-component CH type system
under a equivalent transformation are shown to be different reductions of a
negative generalized mKdV equation, besides the Hamiltonian structures of the
3-DP equation under this Liouville transformation are considered. In addition,
we consider a limit for the 3-DP equation.


  We prove the infinitude of shifted primes $p-1$ without prime factors above
$p^{0.2844}$. This refines $p^{0.2961}$ from Baker and Harman in 1998.
Consequently, we obtain an improved lower bound on the the distribution of
Carmichael numbers. Our main technical result is a new mean value theorem for
primes in arithmetic progressions to large moduli. Namely, we estimate primes
of size $x$ with quadrilinear forms of moduli up to $x^{17/32}$. This extends
moduli beyond $x^{11/21}$, recently obtained by Maynard, improving $x^{29/56}$
from well-known 1986 work of Bombieri, Friedlander, and Iwaniec.


  Simultaneous measurements, such as the combination of particle image
velocimetry (PIV) for velocity fields with planar laser induced fluorescence
(PLIF) for species fields, are widely used in experimental turbulent combustion
applications for the analysis of a plethora of complex physical processes. Such
physical analyses are driven by the interpretation of spatial correlations
between these fields by the experimenter. However, these correlations also
imply some amount of intrinsic redundancy; the simultaneous fields contain
overlapping information content. The goal of this work lies in the quantitative
extraction of this overlapping information content in simultaneous field
measurements. Specifically, the amount of PIV information contained in
simultaneously measured OH-PLIF fields in the domain of a swirl-stabilized
combustor is sought. This task is accomplished using machine learning
techniques based on artificial neural networks designed to optimize PLIF-to-PIV
mappings. It was found that most of the velocity information content could be
retrieved when considering linear combinations of neighborhoods of OH-PLIF
signal spanning roughly two integral lengthscales (half of the considered
domain), and that PLIF signal interactions contained in smaller, local regions
(less than half of the domain) contained no PIV information. Further, by
visualizing the coherent structures contained within the neural network
parameters, the role of multi-scale interactions related to velocity field
retrieval from the OH-PLIF signal became more apparent. Overall, this study
reveals a useful pathway (in the form of overlapping information content
extraction) to develop diagnostic tools that capture more information using the
same experimental resources by minimizing redundancy.


  In the framework of accurate and efficient segregated schemes for 3D cardiac
electromechanics and 0D cardiovascular models, we propose here a novel
numerical approach to address the coupled 3D-0D problem introduced in Part I of
this two-part series of papers. We combine implicit-explicit schemes to solve
the different cardiac models in a multiphysics setting. We properly separate
and manage the different time and space scales related to cardiac
electromechanics and blood circulation. We employ a flexible and scalable
intergrid transfer operator that enables to interpolate Finite Element
functions among different meshes and, possibly, among different Finite Element
spaces. We propose a numerical method to couple the 3D electromechanical model
and the 0D circulation model in a numerically stable manner within a fully
segregated fashion. No adaptations are required through the different phases of
the heartbeat. We also propose a robust algorithm to reconstruct the
stress-free reference configuration. Due to the computational cost associated
with the numerical solution of this inverse problem, the reference
configuration recovery algorithm comes along with a novel projection technique
to precisely recover the unloaded geometry from a coarser representation of the
computational domain. We show the convergence property of our numerical schemes
by performing an accuracy study through grid refinement. To prove the
biophysical accuracy of our computational model, we also address different
scenarios of clinical interest in our numerical simulations by varying preload,
afterload and contractility. Indeed, we simulate physiologically relevant
behaviors and we reproduce meaningful results in the context of cardiac
function.


  Based on the structure predicted in a ferroelectric tunnel junction in the
resent density functional theory study, we investigate the electron transport
through the FTJ with asymmetric interfaces, i.e., one interface dipole is
pinned and the other interface dipole is switchable. Tuneling electroresistance
can be induced due to the nonswitchable interface dipole in FTJs with symmetric
electrodes. Compared with the dependence relationship between TER and the
polarization of switchable interface, TER is not sensitive to the variation of
the polarization of pinned interface. A large TER can be achieved when the
pinned polarization points to the ferroelectric film and low interface
dielectric constants. In addition, effect of electrode on TER in the structure
is also discussed.


  An accreting system in two-temperature regime, admits multiple solutions for
the same set of constants of motion, producing widely different spectra.
Comparing observed spectrum with that derived from a randomly chosen accretion
solution, will give us a wrong estimation of the accretion parameters of the
system. The form of entropy measure obtained by us, have helped in removing the
degeneracy of the solutions, allowing us to understand the physics of the
system, shorn of arbitrary assumptions. In this work, we have shown how the
spectra and luminosities of an accreting system depends on the constants of
motion, producing solutions ranging from radiatively inefficient flows to
luminous flows. Increase in BH mass quantitatively changes the system, makes
the system more luminous and the spectral bandwidth also increases. Higher BH
mass system spans from radio to gamma-rays. However, increasing the accretion
rate around a BH of certain mass, has little influence in the frequency range
of the spectra.


  In this paper we consider the two component $b$-family of equations on
$\mathbb R$. We write the equations on a Sobolev type diffeomorphism group. As
an application of this formulation we show that the dependence on the initial
data is nowhere locally uniformly continuous. In particular it is nowhere
locally Lipschitz and nowhere locally H\"older continuous.


  The excess of solar-neutrino events above 13 MeV that has been recently
observed by Superkamiokande can be explained by vacuum oscillations (VO). If
the boron neutrino flux is 20% smaller than the standard solar model (SSM)
prediction and the chlorine signal is assumed 30% (or 3.5 sigmas) higher than
the measured one, there exists a VO solution that reproduces both the observed
boron neutrino spectrum, including the high energy distortion, and the other
measured neutrino rates. This solution might already be testable by the
predicted anomalous seasonal variation of the gallium signal. Its most distinct
signature, a large anomalous seasonal variation of Be7 neutrino flux, can be
easily observed by the future detectors, BOREXINO and LENS.


  In this paper, novel closed-form point estimators of the beta distribution
are proposed and investigated. The first estimators are a modified version of
Pearson's method of moments. The underlying idea is to involve the sufficient
statistics, i.e., log-moments in the moment estimation equations and solve the
mixed type of moment equations simultaneously. The second estimators are based
on an approximation to Fisher's likelihood principle. The idea is to solve two
score equations derived from the log-likelihood function of generalized beta
distributions. Both two resulted estimators are in closed forms, strongly
consistent and asymptotically normal. In addition, through extensive
simulations, the proposed estimators are shown to perform very close to the ML
estimators in both small and large samples, and they significantly outperform
the moment estimators.


  Let $\Sigma$ be a signed graph where two edges joining the same pair of
vertices with opposite signs are allowed. The zero-free chromatic number
$\chi^*(\Sigma)$ of $\Sigma$ is the minimum even integer $2k$ such that $G$
admits a proper coloring $f\colon\,V(\Sigma)\mapsto \{\pm 1,\pm 2,\ldots,\pm
k\}$. The zero-free list chromatic number $\chi^*_l(\Sigma)$ is the list
version of zero-free chromatic number. $\Sigma$ is called zero-free
chromatic-choosable if $\chi^*_l(\Sigma)=\chi^*(\Sigma)$. We show that if
$\Sigma$ has at most $\chi^*(\Sigma)+1$ vertices then $\Sigma$ is zero-free
chromatic-choosable. This result strengthens Noel-Reed-Wu Theorem which states
that every graph $G$ with at most $2\chi(G)+1$ vertices is chromatic-choosable,
where $\chi(G)$ is the chromatic number of $G$.


  End-to-end text-to-speech synthesis (TTS), which generates speech sounds
directly from strings of texts or phonemes, has improved the quality of speech
synthesis over the conventional TTS. However, most previous studies have been
evaluated based on subjective naturalness and have not objectively examined
whether they can reproduce pitch patterns of phonological phenomena such as
downstep, rhythmic boost, and initial lowering that reflect syntactic
structures in Japanese. These phenomena can be linguistically explained by
phonological constraints and the syntax$\unicode{x2013}$prosody mapping
hypothesis (SPMH), which assumes projections from syntactic structures to
phonological hierarchy. Although some experiments in psycholinguistics have
verified the validity of the SPMH, it is crucial to investigate whether it can
be implemented in TTS. To synthesize linguistic phenomena involving syntactic
or phonological constraints, we propose a model using phonological symbols
based on the SPMH and prosodic well-formedness constraints. Experimental
results showed that the proposed method synthesized similar pitch patterns to
those reported in linguistics experiments for the phenomena of initial lowering
and rhythmic boost. The proposed model efficiently synthesizes phonological
phenomena in the test data that were not explicitly included in the training
data.


  We investigate the discrete orbital angular momentum (OAM) of photoelectrons
freed in strongfield ionization. We use these `twisted' electrons to provide an
alternative interpretation on existing experimental work of vortex
interferences caused by strong field ionization mediated by two counterrotating
circularly polarized pulses separated by a delay. Using the strong field
approximation, we derive an interference condition for the vortices. In
computations for a neon target we find very good agreement of the vortex
condition with photoelectron momentum distributions computed with the strong
field approximation, as well as with the time-dependent methods Qprop and
R-Matrix. For each of these approaches we examine the OAM of the
photoelectrons, finding a small number of vortex states localized in separate
energy regions. We demonstrate that the vortices arise from the interference of
pairs of twisted electron states. The OAM of each twisted electron state can be
directly related to the number of arms of the spiral in that region. We gain
further understanding by recreating the vortices with pairs of twisted
electrons and use this to determine a semiclassical relation for the OAM. A
discussion is included on measuring the OAM in strong field ionization directly
or by employing specific laser pulse schemes as well as utilizing the OAM in
time-resolved imaging of photo-induced dynamics.


  Radiometer is a light-induced aerodynamic propulsive device under the
rarefied gas environment, which holds great potential for the next-gen
near-space flight. However, its practical applications are hindered by the weak
propulsion forces on the conventional radiometer vanes. Herein, this
material-aerodynamics cross-disciplinary study develops novel radiometer vanes
with graphene aerogel coatings, which for the first time realize an order of
magnitude enhancement in radiometric propulsion. The improvement is manifested
as up to 29.7 times faster rotation speed at a low pressure of 0.2 Pa, 13.8
times faster at the pressure (1.5 Pa) with maximum speeds, and 4 orders of
magnitude broader operating pressure range (10E-4 - 10E2 Pa). Direct Simulation
Monte Carlo calculations reveal that the outstanding performance is ascribed to
the improved temperature gradient and gas-solid momentum transfer efficiency
tailored by surface porous microstructures. Moreover, we demonstrate a stable
and long-term levitation prototype under both 1 sun irradiation and a rarefied
gas environment.


  Finite index subgroups of the modular group are of great arithmetic
importance. Farey symbols, introduced by Ravi Kulkarni in 1991, are a tool for
working with these groups. Given such a group $\Gamma$, a Farey symbol for
$\Gamma$ is a certain finite sequence of rational numbers (representing
vertices of a fundamental domain of $\Gamma$) together with pairing information
for the edges between the vertices. They are a compact way of encoding the
information about the group and they provide a simple way to do calculations
with the group. For example: calculating an independent set of generators and
decomposing group elements into a word in these generators, finding coset
representatives, elliptic points, and genus of the group, testing if the group
is congruence, etc. In this expository article, we will discuss Farey Symbols
and explicit algorithms for working with them.


  In the last years it has been shown that some properties of strongly coupled
superconductors can be potentially described by classical general relativity
living in one higher dimension, which is known as holographic superconductors.
This paper gives a quick and introductory overview of some holographic
superconductor models with s-wave, p-wave and d-wave orders in the literature
from point of view of bottom-up, and summarizes some basic properties of these
holographic models in various regimes. The competition and coexistence of these
superconductivity orders are also studied in these superconductor models.


  Multidimensional factorization method is formulated in arbitrary curvilinear
coordinates. Particular cases of polar and spherical coordinates are considered
and matrix potentials with separating variables are constructed. A new class of
matrix potentials is obtained which reveals a double degeneracy or equidistant
splitting of energy levels (hidden symmetry).


  We have investigated properties of the Quasi Periodic Oscillation (QPO)
features in the accretion powered X-ray pulsar Cen X-3 over a period of about
four years using observations carried out with the Proportional Counter Array
(PCA) of the {\it {Rossi X-ray Timing Explorer}}. The observations cover a wide
range of X-ray intensity of the source in excess of the binary intensity
modulation. We have detected QPOs in 11 out of a total 81 pointings with the
PCA with rms intensity fluctuation upto 10%. The QPO peak frequency shows
clustering around 40 and 90 mHz with the QPO frequency having no dependence on
X-ray intensity. This indicates that either (a) the observed X-ray luminosity
of the source is not related to the mass accretion rate or inner radius of the
accretion disk or (b) that the QPO generation mechanism in Cen X-3 is different
from the beat frequency model or Keplerian frequency model that is believed to
be operational in most other transient and persistent X-ray pulsars. We have
also found that, the rms variation in the 40 mHz QPO feature is not dependent
on the X-ray energy, indicating that disk absorption related origin for the QPO
is unlikely.


  In a seminal paper Richard Stanley derived Pieri rules for the Jack symmetric
function basis. These rules were extended by Macdonald to his now famous
symmetric function basis. The original form of these rules had a forbidding
complexity that made them difficult to use in explicit calculations. In the
early 90's it was discovered that, due to massive cancellations, the dual rule,
which expresses skewing by $e_1$ the modified Macdonald polynomial ${\tilde
H}_\mu[X;q,t]$, can be given a very simple combinatorial form in terms of
corner weights of the Ferrers' diagram of $\mu$. A similar formula was later
obtained by the last named author for the multiplication of ${\tilde
H}_\mu[X;q,t]$ by $e_1$, but never published. In the years that followed we
have seen some truly remarkable uses of these two Pieri rules in establishing
highly non trivial combinatorial results in the Theory of Macdonald
polynomials. This theory has recently been spectacularly enriched by various
Algebraic Geometrical results in the works of Hikita, Schiffmann,
Schiffmann-Vasserot, A. Negut and Gorsky-Negut. This development opens up the
challenging task of deriving their results by purely Algebraic Combinatorial
methods. In this paper we present the progress obtained by means of Pieri
rules.


  Two-dimensional (2D) van der Waals (vdW) magnetic materials could be an ideal
platform for ultracompact spintronic applications. Among them, FeCl$_{2}$
monolayer in the triangular lattice is subject to a strong debate. Thus, we
critically examine its spin-orbital state, electronic structure, and magnetic
properties, using a set of delicate first-principles calculations, crystal
field level analyses, and Monte Carlo simulations. Our work reveals that
FeCl$_{2}$ monolayer is a ferromagnetic (FM) semiconductor in which the
electron correlation of the narrow Fe $3d$ bands determines the band gap of
about 1.2 eV. Note that only when the spin-orbit coupling (SOC) is properly
handled, the unique $d$$^{5\uparrow}$$l$$^\downarrow_{z+}$ electronic ground
state is achieved. Then, both the orbital and spin contributions (0.59
$\mu_{\rm B}$ plus 3.56 $\mu_{\rm B}$) to the total magnetic moment well
account for, for the first time, the experimental perpendicular moment of 4.3
$\mu_{\rm B}$/Fe. Moreover, we find that a compressive strain further
stabilizes the $d$$^{5\uparrow}$$l$$^\downarrow_{z+}$ ground state, and that
the enhanced magnetic anisotropy and exchange coupling would boost the Curie
temperature ($T_{\rm C}$) from 25 K for the pristine FeCl$_{2}$ monolayer to
69-102 K under 3$\%$-5$\%$ compressive strain. Therefore, FeCl$_{2}$ monolayer
is indeed an appealing 2D FM semiconductor.


  The influence of the weak gravitational wave on the light polarization is
considered. Oscillations in the direction of the polarization vector is found.


  Recently A.Galajinsky has suggested the N=1 supersymmetric extension of Euler
top and made a few interesting observations on its properties [arXiv:2111.06083
[hep-th]]. In this paper we use the formulation of the Euler top as a system on
complex projective plane, playing the role of phase space, i.e. as a
one-dimensional mechanical system.
  Then we suggest the supersymmetrization scheme of the generic one-dimensional
systems with positive Hamiltonian which yields a priori integrable family of
N=2k supersymmetric Hamiltonians parameterized by N/2 arbitrary real functions.


  We analyse the high temperature behaviour of softly broken supersymmetric
theories taking into account the role played by effective non-renormalizable
terms generated by the decoupling of superheavy degrees of freedom or the
Planck scale physics. It turns out that discrete or continuous symmetries,
spontaneously broken at intermediate scales, may never be restored, at least up
to temperatures of the cutoff scale. There are a few interesting differences
from the usual non-restoration in non-supersymmetric theories case where one
needs at least two Higgs fields and non-restoration takes place for a range of
parameters only. We show that with non-renormalizable interactions taken into
account the non-restoration can occur for any nonzero range of parameters even
for a single Higgs field. We show that such theories in general solve the
cosmological domain wall problem, since the thermal production of the dangerous
domain walls is enormously suppressed.


  We study the variation of the frequency splitting coefficients describing the
solar asphericity in both GONG and MDI data, and use these data to investigate
temporal sound-speed variations as a function of both depth and latitude during
the period from 1995-2000 and a little beyond. The temporal variations in even
splitting coefficients are found to be correlated to the corresponding
component of magnetic flux at the solar surface. We confirm that the
sound-speed variations associated with the surface magnetic field are
superficial. Temporally averaged results show a significant excess in sound
speed around 0.92 solar radii and latitude of 60 degrees.


  We describe the privatization method used in reporting labor market insights
from LinkedIn's Economic Graph, including the differentially private algorithms
used to protect member's privacy. The reports show who are the top employers,
as well as what are the top jobs and skills in a given country/region and
industry. We hope this data will help governments and citizens track labor
market trends during the COVID-19 pandemic while also protecting the privacy of
our members.


  This paper addresses the problem of mapping natural language text to
knowledge base entities. The mapping process is approached as a composition of
a phrase or a sentence into a point in a multi-dimensional entity space
obtained from a knowledge graph. The compositional model is an LSTM equipped
with a dynamic disambiguation mechanism on the input word embeddings (a
Multi-Sense LSTM), addressing polysemy issues. Further, the knowledge base
space is prepared by collecting random walks from a graph enhanced with textual
features, which act as a set of semantic bridges between text and knowledge
base entities. The ideas of this work are demonstrated on large-scale
text-to-entity mapping and entity classification tasks, with state of the art
results.


  In this paper, elliptic control problems with pointwise box constraints on
the state is considered, where the corresponding Lagrange multipliers in
general only represent regular Borel measure functions. To tackle this
difficulty, the Lavrentiev regularization is employed to deal with the state
constraints. To numerically discretize the resulted problem, since the weakness
of variational discretization in numerical implementation, full piecewise
linear finite element discretization is employed. Estimation of the error
produced by regularization and discretization is done. The error order of full
discretization is not inferior to that of variational discretization because of
the Lavrentiev-regularization. Taking the discretization error into account,
algorithms of high precision do not make much sense. Utilizing efficient
first-order algorithms to solve discretized problems to moderate accuracy is
sufficient. Then a heterogeneous alternating direction method of multipliers
(hADMM) is proposed. Different from the classical ADMM, our hADMM adopts two
different weighted norms in two subproblems respectively. Additionally, to get
more accurate solution, a two-phase strategy is presented, in which the
primal-dual active set (PDAS) method is used as a postprocessor of the hADMM.
Numerical results not only verify error estimates but also show the efficiency
of the hADMM and the two-phase strategy.


  An accurate calibration of the source redshift distribution $p(z)$ is a key
aspect in the analysis of cosmic shear data. This, one way or another, requires
the use of spectroscopic or high-quality photometric samples. However, the
difficulty to obtain colour-complete spectroscopic samples matching the depth
of weak lensing catalogs means that the analyses of different cosmic shear
datasets often use the same samples for redshift calibration. This introduces a
source of statistical and systematic uncertainty that is highly correlated
across different weak lensing datasets, and which must be accurately
characterised and propagated in order to obtain robust cosmological constraints
from their combination. In this paper we introduce a method to quantify and
propagate the uncertainties on the source redshift distribution in two
different surveys sharing the same calibrating sample. The method is based on
an approximate analytical marginalisation of the $p(z)$ statistical
uncertainties and the correlated marginalisation of residual systematics. We
apply this method to the combined analysis of cosmic shear data from the DESY1
data release and the HSC-DR1 data, using the COSMOS 30-band catalog as a common
redshift calibration sample. We find that, although there is significant
correlation in the uncertainties on the redshift distributions of both samples,
this does not change the final constraints on cosmological parameters
significantly. The same is true also for the impact of residual systematic
uncertainties from the errors in the COSMOS 30-band photometric redshifts.
Additionally, we show that these effects will still be negligible in Stage-IV
datasets. Finally, the combination of DESY1 and HSC-DR1 allows us to constrain
the ``clumpiness'' parameter to $S_8 = 0.768^{+0.021}_{-0.017}$. This
corresponds to a $\sim\sqrt{2}$ improvement in uncertainties with respect to
either DES or HSC alone.


  Planets and minor bodies such as asteroids, Kuiper-belt objects and comets
are integral components of a planetary system. Interactions among them leave
clues about the formation process of a planetary system. The signature of such
interactions is most prominent through observations of its debris disk at
millimeter wavelengths where emission is dominated by the population of large
grains that stay close to their parent bodies. Here we present ALMA 1.3 mm
observations of HD 95086, a young early-type star that hosts a directly imaged
giant planet b and a massive debris disk with both asteroid- and Kuiper-belt
analogs. The location of the Kuiper-belt analog is resolved for the first time.
The system can be depicted as a broad ($\Delta R/R \sim$0.84), inclined
(30\arcdeg$\pm$3\arcdeg) ring with millimeter emission peaked at 200$\pm$6 au
from the star. The 1.3 mm disk emission is consistent with a broad disk with
sharp boundaries from 106$\pm$6 to 320$\pm$20 au with a surface density
distribution described by a power law with an index of --0.5$\pm$0.2. Our deep
ALMA map also reveals a bright source located near the edge of the ring, whose
brightness at 1.3 mm and potential spectral energy distribution are consistent
with it being a luminous star-forming galaxy at high redshift. We set
constraints on the orbital properties of planet b assuming co-planarity with
the observed disk.


  Electrocardiograms (ECGs) are non-invasive diagnostic tools crucial for
detecting cardiac arrhythmic diseases in clinical practice. While ECG
Self-supervised Learning (eSSL) methods show promise in representation learning
from unannotated ECG data, they often overlook the clinical knowledge that can
be found in reports. This oversight and the requirement for annotated samples
for downstream tasks limit eSSL's versatility. In this work, we address these
issues with the Multimodal ECG Representation Learning (MERL}) framework.
Through multimodal learning on ECG records and associated reports, MERL is
capable of performing zero-shot ECG classification with text prompts,
eliminating the need for training data in downstream tasks. At test time, we
propose the Clinical Knowledge Enhanced Prompt Engineering (CKEPE) approach,
which uses Large Language Models (LLMs) to exploit external expert-verified
clinical knowledge databases, generating more descriptive prompts and reducing
hallucinations in LLM-generated content to boost zero-shot classification.
Based on MERL, we perform the first benchmark across six public ECG datasets,
showing the superior performance of MERL compared against eSSL methods.
Notably, MERL achieves an average AUC score of 75.2% in zero-shot
classification (without training data), 3.2% higher than linear probed eSSL
methods with 10\% annotated training data, averaged across all six datasets.
Code and models are available at https://github.com/cheliu-computation/MERL


  Multimodal multitask learning has attracted an increasing interest in recent
years. Singlemodal models have been advancing rapidly and have achieved
astonishing results on various tasks across multiple domains. Multimodal
learning offers opportunities for further improvements by integrating data from
multiple modalities. Many methods are proposed to learn on a specific type of
multimodal data, such as vision and language data. A few of them are designed
to handle several modalities and tasks at a time. In this work, we extend and
improve Omninet, an architecture that is capable of handling multiple
modalities and tasks at a time, by introducing cross-cache attention,
integrating patch embeddings for vision inputs, and supporting structured data.
The proposed Structured-data-enhanced Omninet (S-Omninet) is a universal model
that is capable of learning from structured data of various dimensions
effectively with unstructured data through cross-cache attention, which enables
interactions among spatial, temporal, and structured features. We also enhance
spatial representations in a spatial cache with patch embeddings. We evaluate
the proposed model on several multimodal datasets and demonstrate a significant
improvement over the baseline, Omninet.


  Finding a well-performing architecture is often tedious for both DL
practitioners and researchers, leading to tremendous interest in the automation
of this task by means of neural architecture search (NAS). Although the
community has made major strides in developing better NAS methods, the quality
of scientific empirical evaluations in the young field of NAS is still lacking
behind that of other areas of machine learning. To address this issue, we
describe a set of possible issues and ways to avoid them, leading to the NAS
best practices checklist available at http://automl.org/nas_checklist.pdf.


  We study a class of procurement auctions with a budget constraint, where an
auctioneer is interested in buying resources or services from a set of agents.
Ideally, the auctioneer would like to select a subset of the resources so as to
maximize his valuation function, without exceeding a given budget. As the
resources are owned by strategic agents however, our overall goal is to design
mechanisms that are truthful, budget-feasible, and obtain a good approximation
to the optimal value. Budget-feasibility creates additional challenges, making
several approaches inapplicable in this setting. Previous results on
budget-feasible mechanisms have considered mostly monotone valuation functions.
In this work, we mainly focus on symmetric submodular valuations, a prominent
class of non-monotone submodular functions that includes cut functions. We
begin first with a purely algorithmic result, obtaining a
$\frac{2e}{e-1}$-approximation for maximizing symmetric submodular functions
under a budget constraint. We view this as a standalone result of independent
interest, as it is the best known factor achieved by a deterministic algorithm.
We then proceed to propose truthful, budget feasible mechanisms (both
deterministic and randomized), paying particular attention on the Budgeted Max
Cut problem. Our results significantly improve the known approximation ratios
for these objectives, while establishing polynomial running time for cases
where only exponential mechanisms were known. At the heart of our approach lies
an appropriate combination of local search algorithms with results for monotone
submodular valuations, applied to the derived local optima.


  Traditional UNIX time-share schedulers attempt to be fair to all users by
employing a round-robin style algorithm for allocating CPU time. Unfortunately,
a loophole exists whereby the scheduler can be biased in favor of a greedy user
running many short CPU-time processes. This loophole is not a defect but an
intrinsic property of the round-robin scheduler that ensures responsiveness to
the short CPU demands associated with multiple interactive users. A new
generation of UNIX system resource management software constrains the scheduler
to be equitable to all users regardless of the number of processes each may be
running. This "fair-share" scheduling draws on the concept of pro rating
resource "shares" across users and groups and then dynamically adjusting CPU
usage to meet those share proportions. The simple notion of statically
allocating these shares, however, belies the potential consequences for
performance as measured by user response time and service level targets. We
demonstrate this point by modeling several simple share allocation scenarios
and analyzing the corresponding performance effects. A brief comparison of
commercial system resource management implementations from HP, IBM, and SUN is
also given.


  Extrapolation in Large language models (LLMs) for open-ended inquiry
encounters two pivotal issues: (1) hallucination and (2) expensive training
costs. These issues present challenges for LLMs in specialized domains and
personalized data, requiring truthful responses and low fine-tuning costs.
Existing works attempt to tackle the problem by augmenting the input of a
smaller language model with information from a knowledge graph (KG). However,
they have two limitations: (1) failing to extract relevant information from a
large one-hop neighborhood in KG and (2) applying the same augmentation
strategy for KGs with different characteristics that may result in low
performance. Moreover, open-ended inquiry typically yields multiple responses,
further complicating extrapolation. We propose a new task, the extreme
multi-label KG link prediction task, to enable a model to perform extrapolation
with multiple responses using structured real-world knowledge. Our retriever
identifies relevant one-hop neighbors by considering entity, relation, and
textual data together. Our experiments demonstrate that (1) KGs with different
characteristics require different augmenting strategies, and (2) augmenting the
language model's input with textual data improves task performance
significantly. By incorporating the retrieval-augmented framework with KG, our
framework, with a small parameter size, is able to extrapolate based on a given
KG. The code can be obtained on GitHub:
https://github.com/exiled1143/Retrieval-Augmented-Language-Model-for-Multi-Label-Knowledge-Graph-Link-Prediction.git


  Comment on paper by P.W. Anderson is presented. This Anderson's work is shown
to contain a number of inaccurate and ungrounded statements. We point out, in
particular, that the total static dielectric function not only can be negative,
but inevitably has a minus sign in many stable systems. We also demonstrate
that in many metals, the effective electron-phonon interaction is stronger than
the direct Coulomb repulsion, without taking into account the ladder-sum
renormalization or pseudization of the Coulomb repulsion. Other issues touched
in Anderson's paper are also discussed.


  Calogero-Moser systems are classical and quantum integrable multi-particle
dynamics defined for any root system $\Delta$. The {\em quantum} Calogero
systems having $1/q^2$ potential and a confining $q^2$ potential and the
Sutherland systems with $1/\sin^2q$ potentials have "integer" energy spectra
characterised by the root system $\Delta$. Various quantities of the
corresponding {\em classical} systems, {\em e.g.} minimum energy, frequencies
of small oscillations, the eigenvalues of the classical Lax pair matrices, etc.
at the equilibrium point of the potential are investigated analytically as well
as numerically for all root systems. To our surprise, most of these classical
data are also "integers", or they appear to be "quantised". To be more precise,
these quantities are polynomials of the coupling constant(s) with integer
coefficients. The close relationship between quantum and classical
integrability in Calogero-Moser systems deserves fuller analytical treatment,
which would lead to better understanding of these systems and of integrable
systems in general.


  We show that the family of 21-dimensional intermediate jacobians of cubic
fivefolds containing a given cubic fourfold X is generically an algebraic
integrable system. In the proof we apply an integrability criterion, introduced
and used by Donagi and Markman to find a similar integrable system over the
family of cubic threefolds in X. To enter in the conditions of this criterion,
we write down explicitly the known by Beauville and Donagi symplectic structure
on the family F(X) of lines on the general cubic fourfold X, and prove that the
family of planes on a cubic fivefold containing X is embedded as a Lagrangian
surface in F(X). By a symplectic reduction we deduce that our integrable system
induces on the nodal boundary another integrable system, interpreted
generically as the family of 20-dimensional intermediate jacobians of Fano
threefolds of genus four contained in X. Along the way we prove an Abel-Jacobi
type isomorphism for the Fano surface of conics in the general Fano threefold
of genus 4, and compute the numerical invariants of this surface.


  This paper proposes a novel approach to regularize the ill-posed blind image
deconvolution (blind image deblurring) problem using deep generative networks.
We employ two separate deep generative models - one trained to produce sharp
images while the other trained to generate blur kernels from lower dimensional
parameters. To deblur, we propose an alternating gradient descent scheme
operating in the latent lower-dimensional space of each of the pretrained
generative models. Our experiments show excellent deblurring results even under
large blurs and heavy noise. To improve the performance on rich image datasets
not well learned by the generative networks, we present a modification of the
proposed scheme that governs the deblurring process under both generative and
classical priors.


  We perform a comprehensive study of the dark energy equation of state (EoS)
utilizing the model-independent Gaussian processes (GP). Using a combination of
the Union 2.1 data set, the 30 newly added H(z) cosmic chronometer data points
and Planck's shift parameter, we modify the usual GaPP code and provide a
tighter constraint on the dark energy EoS than the previous literature about GP
reconstructions. Subsequently, we take the "controlling variable method" to
investigate directly the effects of variable matter density parameter
$\Omega_{m0}$, variable cosmic curvature $\Omega_{k0}$ and variable Hubble
constant $H_0$ on the dark energy EoS, respectively. We find that too small or
large $\Omega_{m0}$, $\Omega_{k0}$ and $H_0$ are all disfavored by our GP
reconstructions based on current cosmological observations. Subsequently, we
find that variable $\Omega_{m0}$ and $\Omega_{k0}$ affect the reconstructions
of the dark energy EoS, but affect hardly the reconstructions of the normalized
comoving distance $D(z)$ and its derivatives $D'(z)$ and $D"(z)$. However,
variable $H_0$ affects the reconstructions of the dark energy EoS by affecting
obviously those of $D(z), D'(z)$ and $D"(z)$. Furthermore, we find that the
results of our reconstructions support substantially the recent local
measurement of $H_0$ reported by Riess et al.


  Graph transformation systems (GTS) have been successfully proposed as a
general, theoretically sound model for concurrency. Petri nets (PN), on the
other side, are a central and intuitive formalism for concurrent or distributed
systems, well supported by a number of analysis techniques/tools. Some PN
classes have been shown to be instances of GTS. In this paper, we change
perspective presenting an operational semantics of GTS in terms of Symmetric
Nets, a well-known class of Coloured Petri nets featuring a structured syntax
that outlines model symmetries. Some practical exploitations of the proposed
operational semantics are discussed. In particular, a recently developed
structural calculus for SN is used to validate graph rewriting rules in a
symbolic way.


  This paper reports the results of the numerical study of the formation of
aspherical Planetary Nebulae through the Generalised Interacting Winds Model,
taking into account the effects caused by the evolving central star and fast
wind. The results show for the first time that aspherical nebulae do form
within the required time scale. Consideration of the development of the nebula
shows that in the early stages it is the ionization of the aspherical AGB wind
that contributes considerably to the shaping of the nebula. Furthermore the
passing through of the ionization front may modifies the density distribution
in the slow wind, leading to the formation of a surrounding envelope, and
sometimes a different morphology for the nebula than was to be expected from
the initial conditions. I consider how the different phases of ionization
fronts and wind swept bubbles can be observationally distinguished.


  Synchronization of quantum nonlinear oscillators has attracted much attention
recently. To characterize the quantum oscillatory dynamics, we recently
proposed a fully quantum-mechanical definition of the asymptotic phase, which
is a key quantity in the synchronization analysis of classical nonlinear
oscillators (Kato and Nakao 2022 Chaos 32 063133). In this work, we further
extend this theory and introduce multiple asymptotic phases using the
eigenoperators of the adjoint Liouville superoperator of the quantum nonlinear
oscillator associated with different fundamental frequencies. We analyze a
quantum van der Pol oscillator with Kerr effect in the strong quantum regime
and show that the system has several different fundamental frequencies. By
introducing order parameters and power spectra in terms of the associated
quantum asymptotic phases, we reveal that phase locking of the system with a
harmonic drive at several different frequencies, an explicit quantum signature
observed only in the strong quantum regime, can be interpreted as
synchronization on a torus rather than a simple limit cycle.


  Verifying mathematical proofs is difficult, but can be automated with the
assistance of a computer. Autoformalization is the task of automatically
translating natural language mathematics into a formal language that can be
verified by a program. This is a challenging task, and especially for
higher-level mathematics found in research papers. Research paper mathematics
requires large amounts of background and context. In this paper, we propose an
avenue towards tackling autoformalization for research-level mathematics, by
breaking the task into easier and more approachable subtasks: unlinked
formalization (formalization with unlinked definitions and theorems), entity
linking (linking to the proper theorems and definitions), and finally adjusting
types so it passes the type checker. In addition, we present arXiv2Formal, a
benchmark dataset for unlinked formalization consisting of 50 theorems
formalized for the Lean theorem prover sampled from papers on arXiv.org. We
welcome any contributions from the community to future versions of this
dataset.


  After showing that a covering space of surface bundles over $S^1$ factors as
a `covering of fibers' followed by a `power covering', we prove that, for torus
bundles, power coverings do not lower Heegaard genus, and that fiber coverings
lower the genus only in special cases.


  Generative adversarial networks (GANs) are able to model the complex
highdimensional distributions of real-world data, which suggests they could be
effective for anomaly detection. However, few works have explored the use of
GANs for the anomaly detection task. We leverage recently developed GAN models
for anomaly detection, and achieve state-of-the-art performance on image and
network intrusion datasets, while being several hundred-fold faster at test
time than the only published GAN-based method.


  We present a framework for expressing bottom-up algorithms to compute the
well-founded model of non-disjunctive logic programs. Our method is based on
the notion of conditional facts and elementary program transformations studied
by Brass and Dix for disjunctive programs. However, even if we restrict their
framework to nondisjunctive programs, their residual program can grow to
exponential size, whereas for function-free programs our program remainder is
always polynomial in the size of the extensional database (EDB).
  We show that particular orderings of our transformations (we call them
strategies) correspond to well-known computational methods like the alternating
fixpoint approach, the well-founded magic sets method and the magic alternating
fixpoint procedure. However, due to the confluence of our calculi, we come up
with computations of the well-founded model that are provably better than these
methods.
  In contrast to other approaches, our transformation method treats magic set
transformed programs correctly, i.e. it always computes a relevant part of the
well-founded model of the original program.


  Our goal of this note is to give an easy proof that spaces of predictable
processes with values in a Banach space are isomorphic to spaces of progressive
resp. adapted, measurable processes. This provides a straightforward extension
of the It\^{o} integral in infinite dimensions. We also outline an application
to stochastic partial differential equations.


  Dynamical mean field theory (DMFT) combined with the local density
approximation (LDA) is widely used in solids to predict properties of
correlated systems. In this paper, its application to one of the simplest
strongly correlated systems, the hydrogen molecule H$_2$, is demonstrated to
develop a parameter-free LDA+DMFT framework. We propose a method to calculate
the exact intersection of LDA and DMFT that leads to highly accurate
subtraction of the doubly counted correlation in both methods. When the exact
double-counting treatment and a good projector to the correlated subspace are
used, LDA+DMFT yields very accurate total energy and excitation spectrum of the
H$_2$ molecule. We also discuss how this double-counting scheme can be extended
to solid state calculations.


  In practice, the parameters of control policies are often tuned manually.
This is time-consuming and frustrating. Reinforcement learning is a promising
alternative that aims to automate this process, yet often requires too many
experiments to be practical. In this paper, we propose a solution to this
problem by exploiting prior knowledge from simulations, which are readily
available for most robotic platforms. Specifically, we extend Entropy Search, a
Bayesian optimization algorithm that maximizes information gain from each
experiment, to the case of multiple information sources. The result is a
principled way to automatically combine cheap, but inaccurate information from
simulations with expensive and accurate physical experiments in a
cost-effective manner. We apply the resulting method to a cart-pole system,
which confirms that the algorithm can find good control policies with fewer
experiments than standard Bayesian optimization on the physical system only.


  This study examines nonnegative solutions to the problem
\begin{equation*}\left\{\arraycolsep=1.5pt \begin {array}{lll} \Delta
u=\displaystyle\frac{\lambda|x|^{\alpha}}{u^p} \ \ &\hbox{ in} \,\ \R
^2\setminus \{0\},\\[2mm] u(0)=0 \ \text{and}\ u> 0 \ \ &\hbox{ in} \,\ \R
^2\setminus \{0\},\\ \end{array}\right. \label{eqn} \end{equation*} where $\lam
>0,$ $\alp>-2$, and $p>0$ are constants. The possible asymptotic behaviors of
$u(x)$ at $|x|=0$ and $|x|=\infty$ are classified according to $(\alpha,p)$. In
particular, the results show that for some $(\alpha,p)$, $u(x)$ exhibits only
``isotropic" behavior at $|x|=0$ and $|x|=\infty$. However, in other cases,
$u(x)$ may exhibit the "anisotropic" behavior at $|x|=0$ or $|x|=\infty$.
Furthermore, the relation between the limit at $|x|=0$ and the limit at
$|x|=\infty$ for a global solution is investigated.


  We introduce an infinite-dimensional version of the Christoffel function,
where now (i) its argument lies in a Hilbert space of functions, and (ii) its
associated underlying measure is supported on a compact subset of the Hilbert
space. We show that it possesses the same crucial property as its
finite-dimensional version to identify the support of the measure (and so to
detect outliers). Indeed, the growth of its reciprocal with respect to its
degree is at least exponential outside the support of the measure and at most
polynomial inside. Moreover, for a fixed degree, its computation mimics that of
the finite-dimensional case, but now the entries of the moment matrix
associated with the measure are moments of moments. To illustrate the potential
of this new tool, we consider the following application. Given a data base of
registered reference trajectories, we consider the problem of detecting whether
a newly acquired trajectory is abnormal (or out of distribution) with respect
to the data base. As in the finite-dimensional case, we use the
infinite-dimensional Christoffel function as a score function to detect
outliers and abnormal trajectories. A few numerical examples are provided to
illustrate the theory.


  Layered cuprates offer a preferential playground for optical non-linearity
thanks to the emergence, below Tc, of soft out-of-plane Josephson plasmons. The
hallmark of such a non-linearity is the observation of Third Harmonic
Generation, that has been theoretically understood as a sum-frequency process
involving a two-plasmon excitation. However, recent experiments in cuprates
with two planes per unit cell challenge this interpretation, due to the lack of
resonant response at the temperature where the driving frequency matches the
plasma energy scale, as observed instead in single-layer cuprates. Here we show
that such an apparent discrepancy in bilayer systems can be resolved by taking
into account the combined effect of light polarization and Josephson-coupling
anisotropy on setting the energy range where three-dimensional layered plasma
modes can be resonantly excited. Our results offer a novel perspective on the
possibility to tune on demand high-harmonic generation by artificially
designing Josephson heterostructures.


  Loss tomography has received considerable attention in recent years and a
number of estimators have been proposed. Although most of the estimators claim
to be the maximum likelihood estimators, the claim is only partially true since
the maximum likelihood estimate can be obtained at most for a class of data
sets. Unfortunately, few people are aware of this restriction that leads to a
misconception that an estimator is applicable to all data sets as far as it
returns a unique solution. To correct this, we in this paper point out the risk
of this misconception and illustrate the inconsistency between data and model
in the most influential estimators. To ensure the model used in estimation
consistent with the data collected from an experiment, the data sets used in
estimation are divided into 4 classes according to the characteristics of
observations. Based on the classification, the validity of an estimator is
defined and the validity of the most influential estimators is evaluated. In
addition, a number of estimators are proposed, one for a class of data sets
that have been overlooked. Further, a general estimator is proposed that is
applicable to all data classes. The discussion starts from the tree topology
and end at the general topology.


  Researchers have proposed hardware, software, and algorithmic optimizations
to improve the computational performance of deep learning. While some of these
optimizations perform the same operations faster (e.g., increasing GPU clock
speed), many others modify the semantics of the training procedure (e.g.,
reduced precision), and can impact the final model's accuracy on unseen data.
Due to a lack of standard evaluation criteria that considers these trade-offs,
it is difficult to directly compare these optimizations. To address this
problem, we recently introduced DAWNBench, a benchmark competition focused on
end-to-end training time to achieve near-state-of-the-art accuracy on an unseen
dataset---a combined metric called time-to-accuracy (TTA). In this work, we
analyze the entries from DAWNBench, which received optimized submissions from
multiple industrial groups, to investigate the behavior of TTA as a metric as
well as trends in the best-performing entries. We show that TTA has a low
coefficient of variation and that models optimized for TTA generalize nearly as
well as those trained using standard methods. Additionally, even though
DAWNBench entries were able to train ImageNet models in under 3 minutes, we
find they still underutilize hardware capabilities such as Tensor Cores.
Furthermore, we find that distributed entries can spend more than half of their
time on communication. We show similar findings with entries to the MLPERF v0.5
benchmark.


  Ultrafast strengthening or quenching of the ferromagnetic order of
semiconducting Eu1-xGdxO was achieved by resonant photoexcitation. The
modification of the magnetic order is established within 3 ps as revealed by
optical second harmonic generation. A theoretical analysis shows that the
response is determined by the interplay of chemically and optically generated
carriers in a nonequilibrium scenario beyond the three-temperature model.
General criteria for the design of spintronics materials with tunable ultrafast
spin dynamics are given.


  Optical flow techniques are becoming increasingly performant and robust when
estimating motion in a scene, but their performance has yet to be proven in the
area of facial expression recognition. In this work, a variety of optical flow
approaches are evaluated across multiple facial expression datasets, so as to
provide a consistent performance evaluation. The aim of this work is not to
propose a new expression recognition technique, but to understand better the
adequacy of existing state-of-the art optical flow for encoding facial motion
in the context of facial expression recognition. Our evaluations highlight the
fact that motion approximation methods used to overcome motion discontinuities
have a significant impact when optical flows are used to characterize facial
expressions.


  The construction of a universal static quantum computer actually provides
another proof of the NP-hardness of spin-glass problems.