  We delve into the first-order thermodynamics of Horndeski gravity, focusing
on spatially flat, homogeneous, and isotropic cosmologies. Our exploration
begins with a comprehensive review of the effective fluid representation within
viable Horndeski gravity. Notably, we uncover a surprising alignment between
the constitutive relations governing the "Horndeski fluid" and those of
Eckart's thermodynamics. Narrowing our focus, we specialize our discussion to
spatially flat Friedmann-Lema{\^i}tre-Robertson-Walker spacetimes. Within this
specific cosmological framework, we systematically analyze two classes of
theories: shift-symmetric and asymptotically shift-symmetric. These theories
are characterized by a non-vanishing braiding parameter, adding a nuanced
dimension to our investigation. On the one hand, unlike the case of the
"traditional" scalar-tensor gravity, these peculiar subclasses of viable
Horndeski gravity never relax to General Relativity (seen within this formalism
as an equilibrium state at zero temperature), but give rise to additional
equilibrium states with non-vanishing viscosity. On the other hand, this
analysis further confirms previous findings according to which curvature
singularities are "hot" and exhibit a diverging temperature, which suggests
that deviations of scalar-tensor theories from General Relativity become
extreme at spacetime singularities. Furthermore, we provide a novel exact
cosmological solution for an asymptotically shift-symmetric theory as a toy
model for our thermodynamic analysis.


  Distributed quantum sensing can provide quantum-enhanced sensitivity beyond
the shot-noise limit (SNL) for sensing spatially distributed parameters. To
date, distributed quantum sensing experiments have been mostly accomplished in
laboratory environments without a real space separation for the sensors. In
addition, the post-selection is normally assumed to demonstrate the sensitivity
advantage over the SNL. Here, we demonstrate distributed quantum sensing in
field and show the unconditional violation (without post-selection) of SNL up
to 0.916 dB for the field distance of 240 m. The achievement is based on a
loophole free Bell test setup with entangled photon pairs at the averaged
heralding efficiency of 73.88%. Moreover, to test quantum sensing in real life,
we demonstrate the experiment for long distances (with 10-km fiber) together
with the sensing of a completely random and unknown parameter. The results
represent an important step towards a practical quantum sensing network for
widespread applications.


  To define a minimal mathematical framework for isolating some of the
characteristic properties of quantum entanglement, we introduce a
generalization of the tensor product of graphs. Inspired by the notion of a
density matrix, the generalization is a simple one: every graph can be obtained
by addition modulo two, possibly with many summands, of tensor products of
adjacency matrices. In this picture, we are still able to prove a combinatorial
analogue of the Peres-Horodecki criterion for testing separability.


  We describe an atom interferometric gravitational wave detector design that
can operate in a resonant mode for increased sensitivity. By oscillating the
positions of the atomic wavepackets, this resonant detection mode allows for
coherently enhanced, narrow-band sensitivity at target frequencies. The
proposed detector is flexible and can be rapidly switched between broadband and
narrow-band detection modes. For instance, a binary discovered in broadband
mode can subsequently be studied further as the inspiral evolves by using a
tailored narrow-band detector response. In addition to functioning like a
lock-in amplifier for astrophysical events, the enhanced sensitivity of the
resonant approach also opens up the possibility of searching for important
cosmological signals, including the stochastic gravitational wave background
produced by inflation. We give an example of detector parameters which would
allow detection of inflationary gravitational waves down to $\Omega_\text{GW}
\sim 10^{-14}$ for a two satellite space-based detector.


  The spatially uniaxially anisotropic d=3 Ising spin glass is solved exactly
on a hierarchical lattice. Five different ordered phases, namely ferromagnetic,
columnar, layered, antiferromagnetic, and spin-glass phases, are found in the
global phase diagram. The spin-glass phase is more extensive when randomness is
introduced within the planes than when it is introduced in lines along one
direction. Phase diagram cross-sections, with no Nishimori symmetry, with
Nishimori symmetry lines, or entirely imbedded into Nishimori symmetry, are
studied. The boundary between the ferromagnetic and spin-glass phases can be
either reentrant or forward, that is either receding from or penetrating into
the spin-glass phase, as temperature is lowered. However, this boundary is
always reentrant when the multicritical point terminating it is on the
Nishimori symmetry line.


  We report results of large scale ground state density matrix renormalization
group(DMRG) calculations on $t$-$t'$-$J$ cylinders with circumferences 6 and 8.
We determine a rough phase diagram which appears to approximate the 2D system.
While for many properties, positive and negative $t'$ values ($t'/t = \pm 0.2$)
appear to correspond to electron and hole doped cuprate systems, respectively,
the behavior of superconductivity itself shows an inconsistency between the
model and the materials. The $t'<0$ (hole doped) region shows
antiferromagnetism limited to very low doping, stripes more generally, and the
familiar Fermi-surface of the hole doped cuprates. However, we find $t'<0$
strongly suppresses superconductivity. The $t'>0$ (electron doped) region shows
the expected circular Fermi pocket of holes around the $(\pi,\pi)$ point and a
broad low-doped region of coexisting antiferromagnetism and $d$-wave pairing
with a strong triplet $p$ component at wave-vector $(\pi,\pi)$ induced by the
antiferromagnetism and $d$-wave pairing. The pairing for the electron low-doped
system with $t'>0$ is strong and unambiguous in the DMRG simulations. At larger
doping another broad region with stripes in addition to weaker $d$-wave pairing
and striped $p$-wave pairing appears. In a small doping region near $x=0.08$
for $t'\sim-0.2$, we find a new type of stripe involving unpaired holes located
predominantly on chains spaced three lattice spacings apart. The undoped
two-leg ladder regions in between mimic the short-ranged spin correlations seen
in two-leg Heisenberg ladders.


  Reliable knowledge of road boundaries is critical for autonomous vehicle
navigation. We propose a robust curb detection and filtering technique based on
the fusion of camera semantics and dense lidar point clouds. The lidar point
clouds are collected by fusing multiple lidars for robust feature detection.
The camera semantics are based on a modified EfficientNet architecture which is
trained with labeled data collected from onboard fisheye cameras. The point
clouds are associated with the closest curb segment with $L_2$-norm analysis
after projecting into the image space with the fisheye model projection. Next,
the selected points are clustered using unsupervised density-based spatial
clustering to detect different curb regions. As new curb points are detected in
consecutive frames they are associated with the existing curb clusters using
temporal reachability constraints. If no reachability constraints are found a
new curb cluster is formed from these new points. This ensures we can detect
multiple curbs present in road segments consisting of multiple lanes if they
are in the sensors' field of view. Finally, Delaunay filtering is applied for
outlier removal and its performance is compared to traditional RANSAC-based
filtering. An objective evaluation of the proposed solution is done using a
high-definition map containing ground truth curb points obtained from a
commercial map supplier. The proposed system has proven capable of detecting
curbs of any orientation in complex urban road scenarios comprising straight
roads, curved roads, and intersections with traffic isles.


  A prominent continuum steepening is observed in quasar energy distributions
near 1100A. We review possible interpretations for the physical origin of this
so-called far-UV break.


  We report the observation of stationary turbulence in antiferromagnetic
spin-1 Bose-Einstein condensates driven by a radio-frequency magnetic field.
The magnetic driving injects energy into the system by spin rotation and the
energy is dissipated via dynamic instability, resulting in the emergence of an
irregular spin texture in the condensate. Under continuous driving, the spinor
condensate evolves into a nonequilibrium steady state with characteristic spin
turbulence, while the low energy scale of spin excitations ensures that the
sample's lifetime is minimally affected. When the driving strength is on par
with the system's spin interaction energy and the quadratic Zeeman energy,
remarkably, the stationary turbulent state exhibits spin-isotropic features in
spin composition and spatial spin texture. We numerically show that ambient
field fluctuations play a crucial role in sustaining the turbulent state within
the system. These results open up new avenues for exploring quantum turbulence
in spinor superfluid systems.


  We have developed an analytical formulation to calculate the plasmon
dispersion relation for a two-dimensional layer which is encapsulated within a
narrow spatial gap between two bulk half-space plasmas. This is based on a
solution of the inverse dielectric function integral equation within the
random-phase approximation (RPA). We take into account the nonlocality of the
plasmon dispersion relation for both gapped and gapless graphene as the
sandwiched two-dimensional (2D) semiconductor plasma. The associated nonlocal
graphene plasmon spectrum coupled to the "sandwich" system is exhibited in
density plots, which show a linear mode and a pair of depolarization modes
shifted from the bulk plasma frequency.


  We present a collection of algorithms to filter a stream of documents in such
a way that the filtered documents will cover as well as possible the interest
of a person, keeping in mind that, at any given time, the offered documents
should not only be relevant, but should also be diversified, in the sense not
only of avoiding nearly identical documents, but also of covering as well as
possible all the interests of the person. We use a modification of the WEBSOM
algorithm, with limited architectural adaptation, to create a user model (which
we call the "user context" or simply the "context") based on a network of units
laid out in the word space and trained using a collection of documents
representative of the context.
  We introduce the concepts of novelty and coverage. Novelty is related to, but
not identical to, the homonymous information retrieval concept: a document is
novel it it belongs to a semantic area of interest to a person for which no
documents have been seen in the recent past. A group of documents has coverage
to the extent to which it is a good representation of all the interests of a
person.
  In order to increase coverage, we introduce an "interest" (or "urgency")
factor for each unit of the user model, modulated by the scores of the incoming
documents: the interest of a unit is decreased drastically when a document
arrives that belongs to its semantic area and slowly recovers its initial value
if no documents from that semantic area are displayed.
  Our tests show that these algorithms can effectively increase the coverage of
the documents that are shown to the user without overly affecting precision.


  We present observations of 25 transitions of 17 isotopologues of 9 molecules
toward B335. With a goal of constraining chemical models of collapsing clouds,
we compare our observations, along with data from the literature, to models of
chemical abundances. The observed lines are simulated with a Monte Carlo code,
which uses various physical models of density and velocity as a function of
radius. The dust temperature as a function of radius is calculated
self-consistently by a radiative transfer code. The gas temperature is then
calculated at each radius, including gas-dust collisions, cosmic rays,
photoelectric heating, and molecular cooling. The results provide the input to
the Monte Carlo code. We consider both {\it ad hoc} step function models for
chemical abundances and abundances taken from a self-consistent modeling of the
evolution of a star-forming core. The step function models can match the
observed lines reasonably well, but they require very unlikely combinations of
radial variations in chemical abundances. Among the self-consistent chemical
models, the observed lines are matched best by models with somewhat enhanced
cosmic-ray ionization rates and sulfur abundances. We discuss briefly the steps
needed to close the loop on the modeling of dust and gas, including off-center
spectra of molecular lines.


  We examine the spatial distribution of electrons generated by a fixed energy
point source in uniform, parallel electric and magnetic fields. This problem is
simple enough to permit analytic quantum and semiclassical solution, and it
harbors a rich set of features which find their interpretation in the unusual
and interesting properties of the classical motion of the electrons: For
instance, the number of interfering trajectories can be adjusted in this
system, and the turning surfaces of classical motion contain a complex array of
singularities. We perform a comprehensive analysis of both the semiclassical
approximation and the quantum solution, and we make predictions that should
serve as a guide for future photodetachment experiments.


  In this paper we study the geometry of the Severi varieties parametrizing
curves on the rational ruled surface $\fn$. We compute the number of such
curves through the appropriate number of fixed general points on $\fn$, and the
number of such curves which are irreducible. These numbers are known as Severi
degrees; they are the degrees of unions of components of the Hilbert scheme. As
(i) $\fn$ can be deformed to $\eff_{n+2}$, (ii) the Gromov-Witten invariants
are deformation-invariant, and (iii) the Gromov-Witten invariants of $\eff_0$
and $\eff_1$ are enumerative, Theorem \ref{irecursion} computes the genus $g$
Gromov-Witten invariants of all $\fn$. (The genus 0 case is well-known.) The
arguments are given in sufficient generality to also count plane curves in the
style of L. Caporaso and J. Harris and to lay the groundwork for computing
higher genus Gromov-Witten invariants of blow-ups of the plane at up to five
points (in a future paper).


  We discuss the four requirements for a real point-to-point quantum secure
direct communication (QSDC) first, and then present two efficient QSDC network
schemes with an N ordered Einstein-Podolsky-Rosen pairs. Any one of the
authorized users can communicate another one on the network securely and
directly.


  We consider the problem of determining the arrival statistics of unbiased
planar random walkers to complex target configurations. In contrast to problems
posed in finite domains, simple moments of the distribution, such as the mean
(MFPT) and variance, are not defined and it is necessary to obtain the full
arrival statistics. We describe several methods to obtain these distributions
and other associated quantities such as splitting probabilities. One approach
combines a Laplace transform of the underlying parabolic equation with matched
asymptotic analysis followed by numerical transform inversion. The second
approach is similar, but uses a boundary integral equation method to solve for
the Laplace transformed variable. To validate the results of this theory, and
to obtain the arrival time statistics in very general configurations of
absorbers, we introduce an efficient Kinetic Monte Carlo (KMC) method that
describes trajectories as a combination of large but exactly solvable
projection steps. The effectiveness of these methodologies is demonstrated on a
variety of challenging examples highlighting the applicability of these methods
to a variety of practical scenarios, such as source inference. A particularly
useful finding arising from these results is that homogenization theories, in
which complex configurations are replaced by equivalent simple ones, are
remarkably effective at describing arrival time statistics.


  Urban commuting data has long been a vital source of understanding population
mobility behaviour and has been widely adopted for various applications such as
transport infrastructure planning and urban anomaly detection. While
individual-specific transaction records (such as smart card (tap-in, tap-out)
data or taxi trip records) hold a wealth of information, these are often
private data available only to the service provider (e.g., taxicab operator).
In this work, we explore the utility in harnessing publicly available, albeit
noisy, transportation datasets, such as noisy "Estimated Time of Arrival" (ETA)
records (commonly available to commuters through transit Apps or electronic
signages). We first propose a framework to extract accurate individual bus
trajectories from such ETA records, and present results from both a primary
city (Singapore) and a secondary city (London) to validate the techniques.
Finally, we quantify the upper bound on the spatiotemporal resolution, of the
reconstructed trajectory outputs, achieved by our proposed technique.


  We investigate if the super-saturation phenomenon observed at X-ray
wavelengths for the corona, exists in the chromosphere for rapidly rotating
late-type stars. Moderate resolution optical spectra of fast rotating EUV- and
X-ray- selected late-type stars were obtained. Stars in alpha Per were observed
in the northern hemisphere with the Isaac Newton 2.5 m telescope and IDS
spectrograph. Selected objects from IC 2391 and IC 2602 were observe in the
southern hemisphere with the Blanco 4m telescope and R-C spectrograph at CTIO.
Ca II H & K fluxes were measured for all stars in our sample. We find the
saturation level for Ca II K at log(L_CaK/L_bol) = -4.08. The Ca II K flux does
not show a decrease as a function of increased rotational velocity or smaller
Rossby number as observed in the X-ray. This lack of "super-saturation"
supports the idea of coronal-stripping as the cause of saturation and
super-saturation in stellar chromospheres and corona, but the detailed
underlying mechanism is still under investigation.


  Diagnostic and prognostic models are increasingly important in medicine and
inform many clinical decisions. Recently, machine learning approaches have
shown improvement over conventional modeling techniques by better capturing
complex interactions between patient covariates in a data-driven manner.
However, the use of machine learning introduces a number of technical and
practical challenges that have thus far restricted widespread adoption of such
techniques in clinical settings. To address these challenges and empower
healthcare professionals, we present a machine learning framework,
AutoPrognosis 2.0, to develop diagnostic and prognostic models. AutoPrognosis
leverages state-of-the-art advances in automated machine learning to develop
optimized machine learning pipelines, incorporates model explainability tools,
and enables deployment of clinical demonstrators, without requiring significant
technical expertise. Our framework eliminates the major technical obstacles to
predictive modeling with machine learning that currently impede clinical
adoption. To demonstrate AutoPrognosis 2.0, we provide an illustrative
application where we construct a prognostic risk score for diabetes using the
UK Biobank, a prospective study of 502,467 individuals. The models produced by
our automated framework achieve greater discrimination for diabetes than expert
clinical risk scores. Our risk score has been implemented as a web-based
decision support tool and can be publicly accessed by patients and clinicians
worldwide. In addition, AutoPrognosis 2.0 is provided as an open-source python
package. By open-sourcing our framework as a tool for the community, clinicians
and other medical practitioners will be able to readily develop new risk
scores, personalized diagnostics, and prognostics using modern machine learning
techniques.


  Addressing the challenge of scaling-up epidemiological inference to complex
and heterogeneous models, we introduce Poisson Approximate Likelihood (PAL)
methods. In contrast to the popular ODE approach to compartmental modelling, in
which a large population limit is used to motivate a deterministic model, PALs
are derived from approximate filtering equations for finite-population,
stochastic compartmental models, and the large population limit drives
consistency of maximum PAL estimators. Our theoretical results appear to be the
first likelihood-based parameter estimation consistency results which apply to
a broad class of partially observed stochastic compartmental models and address
the large population limit. PALs are simple to implement, involving only
elementary arithmetic operations and no tuning parameters, and fast to
evaluate, requiring no simulation from the model and having computational cost
independent of population size. Through examples we demonstrate how PALs can be
used to: fit an age-structured model of influenza, taking advantage of
automatic differentiation in Stan; compare over-dispersion mechanisms in a
model of rotavirus by embedding PALs within sequential Monte Carlo; and
evaluate the role of unit-specific parameters in a meta-population model of
measles.


  We investigate the quantum entropy, its power spectrum, and the excitation
inversion of a Cooper pair box interacting with a nanomechanical resonator, the
first initially prepared in its excited state, the second prepared in a
"cat"-state. The method uses the Jaynes-Cummings model with damping, with
different decay rates of the Cooper pair box and distinct detuning conditions,
including time dependent detunings. Concerning the entropy, it is found that
the time dependent detuning turns the entanglement more stable in comparison
with previous results in literature. With respect to the Cooper pair box
excitation inversion, while the presence of detuning destroys the its collapses
and revivals, it is shown that with a convenient time dependent detuning one
recovers such events in a nice way.


  Space-time in quantum mechanics is about bridging Hilbert and configuration
space. Thereby, an entirely new perspective is obtained by replacing the
Newtonian space-time theater with the image of a presumably high-dimensional
Hilbert space, through which space-time becomes an epiphenomenon construed by
internal observers.


  We study elliptic and parabolic problems governed by the singular elliptic
operators \begin{equation*} \mathcal L =y^{\alpha_1}\Delta_{x}
+y^{\alpha_2}\left(D_{yy}+\frac{c}{y}D_y -\frac{b}{y^2}\right), \qquad\alpha_1,
\alpha_2 \in\mathbb R \end{equation*} in the half-space $\mathbb
R^{N+1}_+=\{(x,y): x \in \mathbb R^N, y>0\}$.


  We consider the Josephson vortex motion in a long one--dimensional Josephson
junction in a thin film. We show that this Josephson vortex is similar to a
mesoscopic capacitor. We demonstrate that a single Cooper pair tunneling
results in nonlinear Bloch--type oscillations of a Josephson vortex in a
current-biased Josephson junction. We find the frequency and the amplitude of
this motion.


  We investigate the interior structure, perturbations, and the associated
quasinormal modes of a quantum black hole model recently proposed by
Bodendorfer, Mele, and M\"unch (BMM). Within the framework of loop quantum
gravity, the quantum parameters in the BMM model are introduced through
polymerization, consequently replacing the Schwarzschild singularity with a
spacelike transition surface. By treating the quantum geometry corrections as
an `effective' matter contribution, we first prove the violation of energy
conditions (in particular the null energy condition) near the transition
surface and then investigate the required junction conditions on it. In
addition, we study the quasinormal modes of massless scalar field
perturbations, electromagnetic perturbations, and axial gravitational
perturbations in this effective model. As expected, the quasinormal spectra
deviate from their classical counterparts in the presence of quantum
corrections. Interestingly, we find that the quasinormal frequencies of
perturbations with different spins share the same qualitative tendency with
respect to the change of the quantum parameters in this model.


  We introduce a novel and extensible benchmark for large language models
(LLMs) through grid-based games such as Tic-Tac-Toe, Connect Four, and Gomoku.
The open-source game simulation code, available on GitHub, allows LLMs to
compete and generates detailed data files in JSON, CSV, TXT, and PNG formats
for leaderboard rankings and further analysis. We present the results of games
among leading LLMs, including Claude 3.5 Sonnet and Claude 3 Sonnet by
Anthropic, Gemini 1.5 Pro and Gemini 1.5 Flash by Google, GPT-4 Turbo and
GPT-4o by OpenAI, and Llama3-70B by Meta. We also encourage submissions of
results from other LLMs. In total, we simulated 2,310 matches (5 sessions for
each pair among 7 LLMs and a random player) across three types of games, using
three distinct prompt types: list, illustration, and image. The results
revealed significant variations in LLM performance across different games and
prompt types, with analysis covering win and disqualification rates, missed
opportunity analysis, and invalid move analysis. The details of the leaderboard
and result matrix data are available as open-access data on GitHub. This study
enhances our understanding of LLMs' capabilities in playing games they were not
specifically trained for, helping to assess their rule comprehension and
strategic thinking. On the path to Artificial General Intelligence (AGI), this
study lays the groundwork for future exploration into their utility in complex
decision-making scenarios, illuminating their strategic thinking abilities and
offering directions for further inquiry into the limits of LLMs within
game-based frameworks.


  It is generally assumed that quantum field theory (QFT) is gauge invariant.
However it is well known that non-gauge invariant terms appear in various
calculations. This problem was examined in Refs. [3] and [4] and it was shown
that at the formal level QFT in the Schroedinger picture is not, in fact, gauge
invariant. It was determined that this problem was due to a mathematical
inconsistency related to the way the vacuum state is defined. In order to shed
further light on this problem we consider a simple field theory in 1-1D
space-time consisting of a quantized fermion field with zero mass in the
presence of a classical electromagnetic potential. It can easily be shown that
for this situation the equations of motion can be solved exactly in both the
Heisenberg and Schroedinger pictures. This allows us to easily identify the
source of the mathematical inconsistency that appears in QFT.


  This paper studies the sharp interface limit for a mass conserving Allen-Cahn
equation added an external noise and derives a stochastically perturbed mass
conserving mean curvature flow in the limit. The stochastic term destroys the
precise conservation law, instead the total mass changes like a Brownian motion
in time. For our equation, the comparison argument does not work, so that to
study the limit we adopt the asymptotic expansion method, which extends that
for deterministic equations used in Chen et al. [3]. Differently from the
deterministic case, each term except the leading term appearing in the
expansion of the solution in a small parameter $\epsilon$ diverges as
$\epsilon$ tends to $0$, since our equation contains the noise which converges
to a white noise and the products or the powers of the white noise diverge. To
derive the error estimate for our asymptotic expansion, we need to establish
the Schauder estimate for a diffusion operator with coefficients determined
from higher order derivatives of the noise and their powers. We show that one
can choose the noise sufficiently mild in such a manner that it converges to
the white noise and at the same time its diverging speed is slow enough for
establishing a necessary error estimate.


  We investigate the power of quantum systems for the simulation of Hamiltonian
time evolutions on a cubic lattice under the constraint of translational
invariance. Given a set of translationally invariant local Hamiltonians and
short range interactions we determine time evolutions which can and those that
can not be simulated. Whereas for general spin systems no finite universal set
of generating interactions is shown to exist, universality turns out to be
generic for quadratic bosonic and fermionic nearest-neighbor interactions when
supplemented by all translationally invariant on-site Hamiltonians.


  An \emph{additive coloring} of a graph $G$ is an assignment of positive
integers $\{1,2,...,k\}$ to the vertices of $G$ such that for every two
adjacent vertices the sums of numbers assigned to their neighbors are
different. The minimum number $k$ for which there exists an additive coloring
of $G$ is denoted by $\eta (G)$. We prove that $\eta (G)\leqslant 468$ for
every planar graph $G$. This improves a previous bound $\eta (G)\leqslant 5544$
due to Norin. The proof uses Combinatorial Nullstellensatz and coloring number
of planar hypergrahs. We also demonstrate that $\eta (G)\leqslant 36$ for
3-colorable planar graphs, and $\eta (G)\leqslant 4$ for every planar graph of
girth at least 13. In a group theoretic version of the problem we show that for
each $r\geqslant 2$ there is an $r$-chromatic graph $G_{r}$ with no additive
coloring by elements of any Abelian group of order $r$.


  We introduce a spectral embedding algorithm for finding proximal
relationships between nodes in signed graphs, where edges can take either
positive or negative weights. Adopting a physical perspective, we construct a
Hamiltonian which is dependent on the distance between nodes, such that
relative embedding distance results in a similarity metric between nodes. The
Hamiltonian admits a global minimum energy configuration, which can be
reconfigured as an eigenvector problem, and therefore is computationally
efficient to compute. We use matrix perturbation theory to show that the
embedding generates a ground state energy, which can be used as a statistical
test for the presence of strong balance, and to develop an energy-based
approach for locating the optimal embedding dimension. Finally, we show through
a series of experiments on synthetic and empirical networks, that the resulting
position in the embedding can be used to recover certain continuous node
attributes, and that the distance to the origin in the optimal embedding gives
a measure of node extremism.


  A solution to energy-efficient magnetization switching in a nanoparticle with
biaxial anisotropy is presented. Optimal control paths minimizing the energy
cost of magnetization reversal are calculated numerically as functions of the
switching time and materials properties, and used to derive energy-efficient
switching pulses of external magnetic field. Hard-axis anisotropy reduces the
minimum energy cost of magnetization switching due to the internal torque in
the desired switching direction. Analytical estimates quantifying this effect
are obtained based on the perturbation theory. The optimal switching time
providing a tradeoff between fast switching and energy efficiency is obtained.
The energy cost of switching and the energy barrier between the stable states
can be controlled independently in a biaxial nanomagnet. This provides a
solution to the dilemma between energy-efficient writability and good thermal
stability of magnetic memory elements.


  Variational and Bayesian methods are two approaches that have been widely
used to solve image reconstruction problems. In this paper, we propose original
connections between Hamilton--Jacobi (HJ) partial differential equations and a
broad class of Bayesian methods and posterior mean estimators with Gaussian
data fidelity term and log-concave prior. Whereas solutions to certain
first-order HJ PDEs with initial data describe maximum a posteriori estimators
in a Bayesian setting, here we show that solutions to some viscous HJ PDEs with
initial data describe a broad class of posterior mean estimators. These
connections allow us to establish several representation formulas and optimal
bounds involving the posterior mean estimate. In particular, we use these
connections to HJ PDEs to show that some Bayesian posterior mean estimators can
be expressed as proximal mappings of twice continuously differentiable
functions, and furthermore we derive a representation formula for these
functions.


  In this letter we study the eccentricity evolution of a massive black hole
(MBH) binary (MBHB) embedded in a rotating stellar cusp. Following the
observation that stars on counter-rotating (with respect to the MBHB) orbits
extract angular momentum from the binary more efficiently then their
co-rotating counterparts, the eccentricity evolution of the MBHB must depend on
the degree of co-rotation (counter-rotation) of the surrounding stellar
distribution. Using an hybrid scheme that couples numerical three-body
scatterings to an analytical formalism for the cusp-binary interaction, we
verify this hypothesis by evolving the MBHB in spherically symmetric cusps with
different fractions F of co-rotating stars. Consistently with previous works,
binaries in isotropic cusps (F=0.5) tend to increase their eccentricity, and
when F approaches zero (counter-rotating cusps) the eccentricity rapidly
increases to almost unity. Conversely, binaries in cusps with a significant
degree of co-rotation (F>0.7) tend to become less and less eccentric,
circularising quite quickly for F approaching unity. Direct N-body integrations
performed to test the theory, corroborate the results of the hybrid scheme, at
least at a qualitative level. We discuss quantitative differences, ascribing
their origin to the oversimplified nature of the hybrid approach.


  The fast radio burst (FRB) population is observationally divided into sources
that have been observed to repeat and those that have not. There is tentative
evidence that the bursts from repeating sources have different properties than
the non-repeating ones. In order to determine the occurrence rate of repeating
sources and characterize the nature of repeat emission, we have been conducting
sensitive searches for repetitions from bursts detected with the Australian
Square Kilometre Array Pathfinder (ASKAP) with the 64-m Parkes radio telescope,
using the recently commissioned Ultra-wideband Low (UWL) receiver system, over
a band spanning 0.7$-$4.0 GHz. We report the detection of a repeat burst from
the source of FRB 20190711A. The detected burst is 1 ms wide and has a
bandwidth of just 65 MHz. We find no evidence of any emission in the remaining
part of the 3.3 GHz UWL band. While the emission bandwidths of the ASKAP and
UWL bursts show $\nu^{-4}$ scaling consistent with a propagation effect, the
spectral occupancy is inconsistent with diffractive scintillation. This
detection rules out models predicting broad-band emission from the FRB
20190711A source and puts stringent constraints on the emission mechanism. The
low spectral occupancy highlights the importance of sub-banded search methods
in detecting FRBs.


  We show that the third order optical nonlinearity of 15-atom gold clusters is
significantly enhanced when in contact with indium tin oxide (ITO) conducting
film. Open and close aperture z-scan experiments together with non-degenerate
pump-probe differential transmission experiments were done using 80 fs laser
pulses centered at 395 nm and 790 nm on gold clusters encased inside
cyclodextrin cavities. We show that two photon absorption coefficient is
enhanced by an order of magnitude as compared to that when the clusters are on
pristine glass plate. The enhancement for the nonlinear optical refraction
coefficient is ~3 times. The photo-induced excited state absorption using
pump-probe experiments at pump wavelength of 395 nm and probe at 790 nm also
show an enhancement by an order of magnitude. These results attributed to the
excited state energy transfer in the coupled gold cluster-ITO system are
different from the enhancement seen so far in charge donor-acceptor complexes
and nanoparticle-conjugate polymer composites.


  In this paper, we prove a general halfspace theorem for constant mean
curvature surfaces. Under certain hypotheses, we prove that, in an ambient
space M^3, any constant mean curvature H_0 surface on one side of a constant
mean curvature H_0 surface \Sigma_0 is an equidistant surface to \Sigma_0. The
main hypotheses of the theorem are that \Sigma_0 is parabolic and the mean
curvature of the equidistant surfaces to \Sigma_0 evolves in a certain way.


  In this paper, we study the Cauchy problem of a weakly dissipative $\mu$HS
equation. We first establish the local well-posedness for the weakly
dissipative $\mu$HS equation by Kato's semigroup theory. Then, we derive the
precise blow-up scenario for strong solutions to the equation. Moreover, we
present some blow-up results for strong solutions to the equation. Finally, we
give two global existence results to the equation.


  Neutral pion transverse momentum (pT) spectra at mid-rapidity (|y| < 0.35)
were measured in Cu+Cu collisions at \sqrt s_NN = 22.4, 62.4, and 200 GeV.
Relative to pi -zero yields in p+p collisions scaled by the number of inelastic
nucleon-nucleon collisions (Ncoll) at the respective energies, the pi-zero
yields for pT \ge 2 GeV/c in central Cu+Cu collisions at 62.4 and 200 GeV are
suppressed, whereas an enhancement is observed at 22.4 GeV. A comparison with a
jet quenching model suggests that final state parton energy loss dominates in
central Cu+Cu collisions at 62.4 GeV and 200 GeV, while the enhancement at 22.4
GeV is consistent with nuclear modifications in the initial state alone.


  We report an experimental and numerical investigation of the fragmentation
mechanisms of micrometer-sized metal droplet irradiated by ultrashort laser
pulses. The results of the experiment show that the fast one-side heating of
such a droplet may lead to either symmetric or asymmetric expansion followed by
different fragmentation scenarios. To unveil the underlying processes leading
to fragmentation we perform simulation of liquid-tin droplet expansion produced
by the initial conditions similar to those in experiment using the smoothed
particle hydrodynamics (SPH) method. Simulation demonstrates that a thin heated
surface layer generates a ultrashort shock wave propagating from the frontal
side to rear side of the droplet. Convergence of such shock wave followed by a
rarefaction tale to the droplet center results in the cavitation of material
inside the central region by the strong tensile stress. Reflection of the shock
wave from the rear side of droplet produces another region of highly stretched
material where the spallation may occur producing a thin spallation layer
moving with a velocity higher than expansion of the central shell after
cavitation. It is shown both experimentally and numerically that the threshold
laser intensity necessary for the spallation is higher than the threshold
required to induce cavitation in the central region of droplet. Thus, the
regime of asymmetrical expansion is realized if the laser intensity exceeds the
spallation threshold. The transverse and longitudinal expansion velocities
obtained in SPH simulations of different regimes of expansion are agreed well
with our experimental data.


  Contextualized word embeddings derived from pre-trained language models (LMs)
show significant improvements on downstream NLP tasks. Pre-training on
domain-specific corpora, such as biomedical articles, further improves their
performance. In this paper, we conduct probing experiments to determine what
additional information is carried intrinsically by the in-domain trained
contextualized embeddings. For this we use the pre-trained LMs as fixed feature
extractors and restrict the downstream task models to not have additional
sequence modeling layers. We compare BERT, ELMo, BioBERT and BioELMo, a
biomedical version of ELMo trained on 10M PubMed abstracts. Surprisingly, while
fine-tuned BioBERT is better than BioELMo in biomedical NER and NLI tasks, as a
fixed feature extractor BioELMo outperforms BioBERT in our probing tasks. We
use visualization and nearest neighbor analysis to show that better encoding of
entity-type and relational information leads to this superiority.


  A triangle-path in a graph $G$ is a sequence of distinct triangles
$T_1,T_2,\ldots,T_m$ in $G$ such that for any $i, j$ with $1\leq i < j \leq m$,
$|E(T_i)\cap E(T_{i+1})|=1$ and $E(T_i)\cap E(T_j)=\emptyset$ if $j > i+1$. A
connected graph $G$ is triangularly connected if for any two nonparallel edges
$e$ and $e'$ there is a triangle-path $T_1T_2\cdots T_m$ such that $e\in
E(T_1)$ and $e'\in E(T_m)$. For ordinary graphs, Fan {\it et al.}~(J. Combin.
Theory Ser. B 98 (2008) 1325-1336) characterize all triangularly connected
graphs that admit nowhere-zero $3$-flows or $4$-flows. Corollaries of this
result include integer flow of some families of ordinary graphs, such as,
locally connected graphs due to Lai (J. Graph Theory 42 (2003) 211-219) and
some types of products of graphs due to Imrich et al.(J. Graph Theory 64 (2010)
267-276). In this paper, Fan's result for triangularly connected graphs is
further extended to signed graphs. We proved that every flow-admissible
triangularly connected signed graph admits a nowhere-zero $4$-flow if and only
if it is not the wheel $W_5$ associated with a specific signature. Moreover,
this result is sharp since there are infinitely many unbalanced triangularly
connected signed graphs admitting a nowhere-zero $4$-flow but not $3$-flow.


  Nodal loops in two-dimensional (2D) systems are typically vulnerable against
spin-orbit coupling (SOC). Here, we explore 2D systems with a type of doubly
degenerate nodal loops that are robust under SOC and feature an hourglass type
dispersion. We present symmetry conditions for realizing such hourglass Weyl
loops, which involve nonsymmorphic lattice symmetries. Depending on the
symmetry, the loops may exhibit different patterns in the Brillouin zone. Based
on first-principles calculations, we identify the monolayer GaTeI-family
materials as a realistic material platform to realize such loops. These
materials host a single hourglass Weyl loop circling around a high-symmetry
point. Interestingly, there is also a spin-orbit Dirac point enabled by an
additional screw axis. We show that the hourglass Weyl loop and the Dirac point
are robust under a variety of applied strains. By breaking the screw axis, the
Dirac point can be transformed into a second Weyl loop. Furthermore, by
breaking the glide mirror, the hourglass Weyl loop and the spin-orbit Dirac
point can both be transformed into a pair of spin-orbit Weyl points. Our work
offers guidance and realistic material candidates for exploring fascinating
physics of several novel 2D emergent fermions.


  The tendency for the period of the helically ordered moments in holmium to
lock into values which are commensurable with the lattice is studied
theoretically as a function of temperature and magnetic field. The
commensurable effects are derived in the mean-field approximation from
numerical calculations of the free energy of various commensurable structures,
and the results are compared with the extensive experimental evidence collected
during the last ten years on the magnetic structures in holmium. In general the
stability of the different commensurable structures is found to be in accord
with the experiments, except for the tau=5/18 structure observed a few degrees
below T_N in a b-axis field. The trigonal coupling recently detected in holmium
is found to be the interaction required to explain the increased stability of
the tau=1/5 structure around 42 K, and of the tau=1/4 structure around 96 K,
when a field is applied along the c-axis.


  Consider an urn model whose replacement matrix is triangular, has all entries
nonnegative and the row sums are all equal to one. We obtain the strong laws
for the counts of balls corresponding to each color. The scalings for these
laws depend on the diagonal elements of a rearranged replacement matrix. We use
the strong laws obtained to study further behavior of certain three color urn
models.


  The condensation of closed string tachyons localized at the fixed point of a
C^d/\Gamma orbifold can be studied in the framework of renormalization group
flow in a gauged linear sigma model. The evolution of the Higgs branch along
the flow describes a resolution of singularities via the process of tachyon
condensation. The study of the fate of D-branes in this process has lead to a
notion of a ``quantum McKay correspondence.'' This is a hypothetical
correspondence between fractional branes in an orbifold singularity in the
ultraviolet with the Coulomb and Higgs branch branes in the infrared. In this
paper we present some nontrivial evidence for this correspondence in the case
C^2/Z_n by relating the intersection form of fractional branes to that of
``Higgs branch branes,'' the latter being branes which wrap nontrivial cycles
in the resolved space.


  Many single molecule experiments for molecular motors comprise not only the
motor but also large probe particles coupled to it. The theoretical analysis of
these assays, however, often takes into account only the degrees of freedom
representing the motor. We present a coarse-graining method that maps a model
comprising two coupled degrees of freedom which represent motor and probe
particle to such an effective one-particle model by eliminating the dynamics of
the probe particle in a thermodynamically and dynamically consistent way. The
coarse-grained rates obey a local detailed balance condition and reproduce the
net currents. Moreover, the average entropy production as well as the
thermodynamic efficiency is invariant under this coarse-graining procedure. Our
analysis reveals that only by assuming unrealistically fast probe particles,
the coarse-grained transition rates coincide with the transition rates of the
traditionally used one-particle motor models. Additionally, we find that for
multicyclic motors the stall force can depend on the probe size. We apply this
coarse-graining method to specific case studies of the F1-ATPase and the
kinesin motor.


  Magnetic properties of quark matter are discussed in the light of the
observation of pulsars. Our works about spontaneous spin polarization and spin
density wave are reviewed and their implications on compact-star phenomena are
discussed. In particular, the former subject may be directly related to the
origin of strong magnetic fields. An inhomogeneous state emerges following the
chiral transition, where a kind of spin density wave develops.


  We demonstrate through numerical simulations with real data the feasibility
of using compressive sensing techniques for the acquisition of
spectro-polarimetric data. This allows us to combine the measurement and the
compression process into one consistent framework. Signals are recovered thanks
to a sparse reconstruction scheme from projections of the signal of interest
onto appropriately chosen vectors, typically noise-like vectors. The
compressibility properties of spectral lines are analyzed in detail. The
results shown in this paper demonstrate that, thanks to the compressibility
properties of spectral lines, it is feasible to reconstruct the signals using
only a small fraction of the information that is measured nowadays. We
investigate in depth the quality of the reconstruction as a function of the
amount of data measured and the influence of noise. This change of paradigm
also allows us to define new instrumental strategies and to propose
modifications to existing instruments in order to take advantage of compressive
sensing techniques.


  Renowned for its sensitivity to detect the presence of numerous substances,
graphene is an excellent chemical sensor. Unfortunately, which general features
a dopant must have in order to enter the list of substances detectable by
graphene are not exactly known. Here we demonstrate with a simple model
calculation implemented in three different ways that one of such features is
the symmetry properties of the impurity binding to graphene. In particular, we
show that electronic scattering is suppressed when dopants are bound
symmetrically to both graphene sub-lattices, giving rise to impurity
invisibility. In contrast, dopants that affect the two sublattices
asymmetrically are more strongly scattered and therefore the most likely
candidates to being chemically sensed by graphene. Furthermore, we demonstrate
that impurity invisibility is lifted with the introduction of a
symmetry-breaking perturbation such as uniaxial strain. In this case, graphene
with sublattice-symmetric dopants will function as efficient strain sensors. We
argue that by classifying dopants through their bonding symmetry leads to a
more efficient way of identifying suitable components for graphene-based
sensors.


  Increasing the size of embedding layers has shown to be effective in
improving the performance of recommendation models, yet gradually causing their
sizes to exceed terabytes in industrial recommender systems, and hence the
increase of computing and storage costs. To save resources while maintaining
model performances, we propose SHARK, the model compression practice we have
summarized in the recommender system of industrial scenarios. SHARK consists of
two main components. First, we use the novel first-order component of Taylor
expansion as importance scores to prune the number of embedding tables (feature
fields). Second, we introduce a new row-wise quantization method to apply
different quantization strategies to each embedding. We conduct extensive
experiments on both public and industrial datasets, demonstrating that each
component of our proposed SHARK framework outperforms previous approaches. We
conduct A/B tests in multiple models on Kuaishou, such as short video,
e-commerce, and advertising recommendation models. The results of the online
A/B test showed SHARK can effectively reduce the memory footprint of the
embedded layer. For the short-video scenarios, the compressed model without any
performance drop significantly saves 70% storage and thousands of machines,
improves 30\% queries per second (QPS), and has been deployed to serve hundreds
of millions of users and process tens of billions of requests every day.


  We consider the following nonlinear Schr\"odinger equations with critical
growth: \begin{equation} - \Delta u + V(|y|)u=u^{\frac{N+2}{N-2}},\quad u>0 \ \
\mbox{in} \ \mathbb {R}^N, \end{equation} where $V(|y|)$ is a bounded positive
radial function in $C^1$, $N\ge 5$. By using a finite reduction argument, we
show that if $r^2V(r)$ has either an isolated local maximum or an isolated
minimum at $r_0>0$ with $V(r_0)>0$, there exists infinitely many non-radial
large energy solutions which are invariant under some sub-groups of $O(3)$.


  Key advances in the generation and shaping of spatially structured photonic
fields both in the near and far field render possible the control of the
duration, the phase, and the polarization state of the field distributions. For
instance, optical vortices having a structured phase are nowadays routinely
generated and exploited for a range of applications. While the light-matter
interaction with optical vortices is meanwhile well studied, the distinctive
features of the interaction of quantum matter with vector beams, meaning fields
with spatially inhomogeneous polarization states, are still to be explored in
full detail, which is done here. We analyze the response of atomic and low
dimensional quantum structures to irradiation with radially or azimuthally
polarized cylindrical vector beams. Striking differences to vortex beams are
found: Radially polarized vector beams drive radially breathing charge-density
oscillations via electric-type quantum transitions. Azimuthally polarized
vector beams do not affect the charge at all but trigger, via a magnetic vector
potential a dynamic Aharonov-Bohm effect, meaning a vector-potential driven
oscillating magnetic moment. In contrast to vortex beams, no unidirectional
currents are generated. Atoms driven by a radially polarized vector beam
exhibit angular momentum conserving quadrupole transitions tunable by a static
magnetic field, while when excited with azimuthally polarized beam different
final-state magnetic sublevels can be accessed.


  The COVID-19 pandemic has taken the world by storm with its high infection
rate. Investigating its geographical disparities has paramount interest in
order to gauge its relationships with political decisions, economic indicators,
or mental health. This paper focuses on clustering the daily death rates
reported in several regions of Europe and the United States over eight months.
Several methods have been developed to cluster such functional data. However,
these methods are not translation-invariant and thus cannot handle different
times of arrivals of the disease, nor can they consider external covariates and
so are unable to adjust for the population risk factors of each region. We
propose a novel three-step clustering method to circumvent these issues. As a
first step, feature extraction is performed by translation-invariant wavelet
decomposition which permits to deal with the different onsets. As a second
step, single-index regression is used to neutralize disparities caused by
population risk factors. As a third step, a nonparametric mixture is fitted on
the regression residuals to achieve the region clustering. Supplementary
materials for this article, including a standardized description of the
materials available for reproducing the work, are available online.


  Three dimensional (3D) topology optimization problems always involve huge
numbers of Degrees of Freedom (DOFs) in finite element analysis (FEA) and
design variables in numerical optimization, respectively. This will inevitably
lead to large computational efforts in the solution process. In the present
paper, an efficient and explicit topology optimization approach which can
reduce not only the number of design variables but also the number of degrees
of freedom in FEA is proposed based on the Moving Morphable Voids (MMVs)
solution framework. This is achieved by introducing a set of geometry
parameters (e.g., control points of B-spline surfaces) to describe the boundary
of a structure explicitly and removing the unnecessary DOFs from the FE model
at every step of numerical optimization. Numerical examples demonstrate that
the proposed approach does can overcome the bottleneck problems associated with
a 3D topology optimization problem in a straightforward way and enhance the
solution efficiency significantly.


  In this paper we consider the weighted q-Bernoulli numbers and polynomials
which are differnt type of Carlitz's q-Bernoulli numbers and polynomials. From
these numbers and polynomials, we derive some interesting formulaes and
identities.


  Non-Abelian anyons--particles whose exchange noncommutatively transforms a
system's quantum state--are widely sought for the exotic fundamental physics
they harbor as well as for quantum computing applications. There now exist
numerous blueprints for stabilizing the simplest type of non-Abelian anyon,
defects binding Majorana modes, by judiciously interfacing widely available
materials. Following this line of attack, we introduce a device fabricated from
conventional fractional quantum Hall states and s-wave superconductors that
supports exotic non-Abelian anyons that bind `parafermions', which can be
viewed as fractionalized Majorana fermions. We show that these modes can be
experimentally identified (and distinguished from Majoranas) using Josephson
measurements. We also provide a practical recipe for braiding parafermions and
show that they give rise to non-Abelian statistics. Interestingly, braiding in
our setup produces a richer set of topologically protected qubit operations
when compared to the Majorana case. As a byproduct, we establish a new,
experimentally realistic Majorana platform in weakly spin-orbit-coupled
materials such as GaAs.


  The article gives a necessary and sufficient condition for a Frobenius
manifold to be a CDV-structure. We show that there exists a positive definite
CDV-structure on any semi-simple Frobenius manifold. We also compare three
natural connections on a CDV-structure and conclude that the underlying
Hermitian manifold of a non-trivial CDV-structure is not a Kahler manifold.
Finally, we compute the harmonic potential of a harmonic Frobenius manifolds.


  We construct a quantum Ginsburg-Landau theory to study the quantum phases and
transitions in electron hole bilayer system. We propose that in the dilute
limit as distance is increased, there is a first order transition from the
excitonic superfluid (ESF) to the excitonic supersolid (ESS) driven by the
collapsing of a roton minimum, then a 2nd order transition from the ESS to
excitonic normal solid. We show the latter transition is in the same
universality class of superfluid to Mott transition in a rigid lattice. We then
study novel elementary low energy excitations inside the ESS. We find that
there are two "supersolidon" longitudinal modes (one upper branch and one lower
branch) inside the ESS, while the transverse mode in the ESS stays the same as
that inside a ENS. We also work out various experimental signatures of these
novel elementary excitations by evaluating the Debye-Waller factor,
density-density correlation, specific heat and vortex -vertex interactions. For
the meta-stable supersolid generated by photon pumping, we show that the angle
resolved spectrum is dominated by the macroscopic super-radiance from its
superfluid component, even it is just a very small percentage of the the whole
system. This fact can be used to detect the metastable ESS state generated by
photon pumping by a power spectrum experiment easily and without any ambiguity.


  In this paper, we define an intuitionistic version of Computation Tree Logic.
After explaining the semantic features of intuitionistic logic, we examine how
these characteristics can be interesting for formal verification purposes.
Subsequently, we define the syntax and semantics of our intuitionistic version
of CTL and study some simple properties of the so obtained logic. We conclude
by demonstrating that some fixed-point axioms of CTL are not valid in the
intuitionistic version of CTL we have defined.


  Currently, there are mainly three kinds of Transformer encoder based
streaming End to End (E2E) Automatic Speech Recognition (ASR) approaches,
namely time-restricted methods, chunk-wise methods, and memory-based methods.
Generally, all of them have limitations in aspects of linear computational
complexity, global context modeling, and parallel training. In this work, we
aim to build a model to take all these three advantages for streaming
Transformer ASR. Particularly, we propose a shifted chunk mechanism for the
chunk-wise Transformer which provides cross-chunk connections between chunks.
Therefore, the global context modeling ability of chunk-wise models can be
significantly enhanced while all the original merits inherited. We integrate
this scheme with the chunk-wise Transformer and Conformer, and identify them as
SChunk-Transformer and SChunk-Conformer, respectively. Experiments on AISHELL-1
show that the SChunk-Transformer and SChunk-Conformer can respectively achieve
CER 6.43% and 5.77%. And the linear complexity makes them possible to train
with large batches and infer more efficiently. Our models can significantly
outperform their conventional chunk-wise counterparts, while being competitive,
with only 0.22 absolute CER drop, when compared with U2 which has quadratic
complexity. A better CER can be achieved if compared with existing chunk-wise
or memory-based methods, such as HS-DACS and MMA. Code is released.


  Analyzing the tunneling probability of a Schwarzschild black hole with a
negative log-area correction to Bekenstein-Hawking entropy, I argue that this
correction may be closely related to a black hole remnant. The value for the
minimal black hole mass is also discussed.


  We describe basic diffeological structures related to splittings and
Grassmannians for infinite dimensional vector spaces. We analyze and expand the
notion of non-commutative cross-ratio and prove its smoothness. Then we
illustrate this theory by examples, with some of them extracted from the
existing literature related to infinite dimensional (Banach) Grassmannians, and
others where the diffeological setting is a key primary step for rigorous
definitions.


  Society is characterized by the presence of a variety of social norms:
collective patterns of sanctioning that can prevent miscoordination and
free-riding. Inspired by this, we aim to construct learning dynamics where
potentially beneficial social norms can emerge. Since social norms are
underpinned by sanctioning, we introduce a training regime where agents can
access all sanctioning events but learning is otherwise decentralized. This
setting is technologically interesting because sanctioning events may be the
only available public signal in decentralized multi-agent systems where reward
or policy-sharing is infeasible or undesirable. To achieve collective action in
this setting we construct an agent architecture containing a classifier module
that categorizes observed behaviors as approved or disapproved, and a
motivation to punish in accord with the group. We show that social norms emerge
in multi-agent systems containing this agent and investigate the conditions
under which this helps them achieve socially beneficial outcomes.


  We examine the effect of walking technicolor dynamics on the electroweak $S$
parameter and contrast it with the effect of QCD-like technicolor dynamics. Our
main tools are the operator product expansion for the high-momentum behavior of
the electroweak gauge boson vacuum polarizations and the analyticity of these
polarizations which relate their low and high momentum behaviors. We show that
whereas in large QCD-like technicolor models $S$ is large and positive, in
walking technicolor models a negative contribution is emphasized, related to
the large anomalous dimension of the technifermion condensate. Thus in walking
technicolor $S$ is determined by a large cancellation of two competing effects.
This may result in much smaller values of $S$ than in QCD-like technicolor,
although considerable uncertainties are involved. We conclude that it is
impossible to rule out walking technicolor based on the present experimental
limits on $S$ and the present theoretical technology.


  Using Gross-Pitaevskii equation, we study the time reversibility of
Bose-Einstein condensates (BEC) in kicked optical lattices, showing that inside
the regime of quantum chaos the dynamics can be inverted from explosion to
collapse. The accuracy of time reversal decreases with the increase of atom
interactions inside BEC, until it is completely lost. Surprisingly, quantum
chaos helps to restore time reversibility. These predictions can be tested with
existing experimental setups.


  We discuss the form of the string-loop-corrected effective action obtained by
compactification of the heterotic string theory on the manifold $K3\times T^2$
or on its orbifold limit and the loop-corrected magnetic black hole solutions
of the equations of motion. Effective 4D theory has N=2 local supersymmetry.
Using the string-loop-corrected prepotential of the N=2 supersymmetric theory,
which receives corrections only from the string world sheets of torus topology,
we calculate the loop corrections to the tree-level gauge couplings and solve
the loop-corrected equations of motion. At the string-tree level, the effective
gauge couplings decrease at small distances from the origin, and in this region
string-loop corrections to the gauge couplings become important. A possibility
of smearing the singularity of the tree-level supersymmetric solution with
partially broken supersymmetry by quantum corrections is discussed.


  A subset of a Carnot group is said to be precisely monotone if the
restriction of its characteristic function to each integral curve of every
left-invariant horizontal vector field is monotone. Equivalently, a precisely
monotone set is a h-convex set with h-convex complement. Such sets have been
introduced and classified in the Heisenberg setting by Cheeger and Kleiner in
the 2010's. In the present paper, we study precisely monotone sets in the wider
setting of step-2 Carnot groups, equivalently step-2 Carnot algebras. In
addition to general properties, we prove a classification in step-2 rank-3
Carnot algebras that generalizes the classification already known in the
Heisenberg setting using sublevel sets of h-affine functions. A significant
novelty is that such sublevel sets can be different from half-spaces.


  Detailed study of the energy and momentum carried by the electromagnetic
field can be a source of clues to possible new physics underlying the Maxwell
Equations. But such study has been impeded by expressions for the parameters of
the electromagnetic energy flow that are inconsistent with the transformation
rules of special relativity.
  This paper begins by correcting a basic parameter, the local velocity of
electromagnetic energy flow. This correction is derived by the direct
application of the transformation rules of special relativity.
  After this correction, the electromagnetic energy-momentum tensor can then be
expressed in a reference system comoving with the energy flow. This tensor can
be made diagonal in the comoving system, and brought into a canonical form
depending only on the energy density and one other parameter.
  The corrected energy flow and its energy-momentum tensor are illustrated by a
simple example using static electric and magnetic fields
  The proposal that electromagnetic momentum results from the motion of a
relativistic mass contained in the fields is examined in the context of the
corrected flow velocity. It is found that electromagnetic field momentum,
though real, cannot be explained as due only to the motion of relativistic
mass.
  The paper concludes that introducing the requirement of consistency with
special relativity opens the study of electromagnetic energy and momentum to
new possibilities.


  The ability to now make measurements of Be and B as well as put constraints
on \lisix\ abundances in metal-poor stars has led to a detailed reexamination
of Big Bang Nucleosynthesis in the $A\groughly6$ regime. The nuclear reaction
network has been significantly expanded with many new rates added. It is
demonstrated that although a number of $A>7$ reaction rates are poorly
determined, even with extreme values chosen, the standard homogeneous model is
unable to produce significant yields (Be/H and B/H $<10^{-17}$ when $A\le7$
abundances fit) above $A=7$ and the \liseven/\lisix\ ratio always exceeds 500.
We also preliminarily explore inhomogeneous models, such as those inspired by a
first order quark-hadron phase transition, where regions with high
neutron/proton ratios can allow some leakage up to $A>7$. However models that
fit the $A\le7$ abundances still seem to have difficulty in obtaining
significant $A>7$ yields.


  This article is concerned with the reconstruction of obstacle $\O$ immersed
in a fluid flowing in a bounded domain $\Omega$ in the two dimensional case. We
assume that the fluid motion is governed by the Stokes-Brinkmann equations. We
make an internal measurement and then have a least-square approach to locate
the obstacle. The idea is to rewrite the reconstruction problem as a topology
optimization problem. The existence and the stability of the optimization
problem are demonstrated. We use here the concept of the topological gradient
in order to determine the obstacle and it's rough location. The topological
gradient is computed using a straightforward way based on a penalization
technique without the truncation method used in the literature. The unknown
obstacle is reconstructed using a level-set curve of the topological gradient.
Finally, we make some numerical examples exploring the efficiency of the
method.


  The unexpectedly hard very-high-energy (VHE; $E > 100$ GeV) $\gamma$-ray
spectra of a few distant blazars have been interpreted as evidence for a
reduction of the $\gamma\gamma$ opacity of the Universe due to the interaction
of VHE $\gamma$-rays with the extragalactic background light (EBL) compared to
the expectation from our current knowledge of the density and cosmological
evolution of the EBL. One of the suggested solutions to this problem consisted
of the inhomogeneity of the EBL. In this paper, we study the effects of such
inhomogeneities on the energy density of the EBL (which then also becomes
anisotropic) and the resulting $\gamma\gamma$ opacity. Specifically, we
investigate the effects of cosmic voids along the line of sight to a distant
blazar. We find that the effect of such voids on the $\gamma\gamma$ opacity,
for any realistic void size, is only of the order of $\lesssim 1$ % and much
smaller than expected from a simple linear scaling of the $\gamma\gamma$
opacity with the line-of-sight galaxy under-density due to a cosmic void.


  We argue that the effective theory describing the long-wavelength dynamics of
black branes is the same effective theory that describes the dynamics of
biophysical membranes. We improve the phase structure of higher-dimensional
black rings by considering finite thickness corrections in this effective
theory, showing a striking agreement between our analytical results and recent
numerical constructions while simultaneously drawing a parallel between gravity
and the effective theory of biophysical membranes.


  We study arithmetical and combinatorial properties of $\beta$-integers for
$\beta$ being the root of the equation $x^2=mx-n, m,n \in \mathbb N, m \geq
n+2\geq 3$. We determine with the accuracy of $\pm 1$ the maximal number of
$\beta$-fractional positions, which may arise as a result of addition of two
$\beta$-integers. For the infinite word $u_\beta$ coding distances between
consecutive $\beta$-integers, we determine precisely also the balance. The word
$u_\beta$ is the fixed point of the morphism $A \to A^{m-1}B$ and $B\to
A^{m-n-1}B$. In the case $n=1$ the corresponding infinite word $u_\beta$ is
sturmian and therefore 1-balanced. On the simplest non-sturmian example with
$n\geq 2$, we illustrate how closely the balance and arithmetical properties of
$\beta$-integers are related.


  We present Sandwich Batch Normalization (SaBN), a frustratingly easy
improvement of Batch Normalization (BN) with only a few lines of code changes.
SaBN is motivated by addressing the inherent feature distribution heterogeneity
that one can be identified in many tasks, which can arise from data
heterogeneity (multiple input domains) or model heterogeneity (dynamic
architectures, model conditioning, etc.). Our SaBN factorizes the BN affine
layer into one shared sandwich affine layer, cascaded by several parallel
independent affine layers. Concrete analysis reveals that, during optimization,
SaBN promotes balanced gradient norms while still preserving diverse gradient
directions -- a property that many application tasks seem to favor. We
demonstrate the prevailing effectiveness of SaBN as a drop-in replacement in
four tasks: conditional image generation, neural architecture search (NAS),
adversarial training, and arbitrary style transfer. Leveraging SaBN immediately
achieves better Inception Score and FID on CIFAR-10 and ImageNet conditional
image generation with three state-of-the-art GANs; boosts the performance of a
state-of-the-art weight-sharing NAS algorithm significantly on NAS-Bench-201;
substantially improves the robust and standard accuracies for adversarial
defense; and produces superior arbitrary stylized results. We also provide
visualizations and analysis to help understand why SaBN works. Codes are
available at: https://github.com/VITA-Group/Sandwich-Batch-Normalization.


  A recently introduced method for determining the critical indices of the
deconfinement transition in gauge theories, already tested for the case of 3D
SU(3) pure gauge theory, is applied here to 4D SU(2) pure gauge theory. The
method is inspired by universality and based on the finite size scaling
behavior of the expectation value of simple lattice operators, such as the
plaquette. We obtain an accurate determination of the critical index $\nu$, in
agreement with the prediction of the Svetitsky-Yaffe conjecture.


  We propose a theoretical scheme for secure quantum key distribution network
following the ideas in quantum dense coding. In this scheme, the server of the
network provides the service for preparing and measuring the Bell states, and
the users encodes the states with local unitary operations. For preventing the
server from eavesdropping, we design a decoy when the particle is transmitted
between the users. It has high capacity as one particle carries two bits of
information and its efficiency for qubits approaches 100%. Moreover, it is not
necessary for the users to store the quantum states, which makes this scheme
more convenient for application than others.


  Since the industrial revolution, accelerated urban growth has overflown
administrative divisions, merged cities into large built extensions, and
blurred the boundaries between urban and rural land-uses. These traits, present
in most of contemporary metropolis, complicate the definition of cities, a
crucial issue considering that objective and comparable metrics are the basic
inputs needed for the planning and design of sustainable urban environments. In
this context, city definitions that respond to administrative or political
criteria usually overlook human dynamics, a key factor that could help to make
cities comparable across the urban fabric of diverse social, cultural and
economic realities. Using a technique based on the spectral analysis of complex
networks, we rank places in 11 of the major Chilean urban regions from a
high-resolution human mobility dataset: Official origin-destination (OD)
surveys. We propose a method for further distinguishing urban and rural
land-uses within these regions, by means of a network centrality measure from
which we construct a spectre of geographic places. This spectre, constructed
from the ranking of locations as measured by their approximate number of
embedded human flows, allows us to probe several urban boundaries. From the
analysis of the urban scaling exponent of trips in relation to the population
across these city delineations, we identify two clearly distinct scaling
regimes occurring in urban and rural areas. The comparison of our results with
land cover derived from remote sensing suggests that, for the case of trips,
the scaling exponent in urban areas is close to linear. We conclude with
estimations for well-formed cities in the Chilean urban system, which according
to our analysis could emerge from clusters composed by places that capture at
least ~138 trips (over the expectation) of the underlying mobility network.


  We present an approach that improves the sample complexity for a variety of
curve fitting problems, including active learning for linear regression,
polynomial regression, and continuous sparse Fourier transforms. In the active
linear regression problem, one would like to estimate the least squares
solution $\beta^*$ minimizing $\|X\beta - y\|_2$ given the entire unlabeled
dataset $X \in \mathbb{R}^{n \times d}$ but only observing a small number of
labels $y_i$. We show that $O(d)$ labels suffice to find a constant factor
approximation $\tilde{\beta}$:
  \[
  \mathbb{E}[\|X\tilde{\beta} - y\|_2^2] \leq 2 \mathbb{E}[\|X \beta^* -
y\|_2^2].
  \] This improves on the best previous result of $O(d \log d)$ from leverage
score sampling. We also present results for the \emph{inductive} setting,
showing when $\tilde{\beta}$ will generalize to fresh samples; these apply to
continuous settings such as polynomial regression. Finally, we show how the
techniques yield improved results for the non-linear sparse Fourier transform
setting.


  We propose a scheme to squeeze mechanical motion and to entangle optical
field with mechanical motion in an optomechanical system containing a
parametric amplification. The scheme is based on optical bistability which
emerges in the system for a strong enough driving field. By considering the
steady state's lower branch of the bistability, the system shows weak
entanglement and almost no mechanical squeezing. When the steady state is on
the upper branch of the bistable shape, both squeezing and entanglement are
greatly enhanced. Specifically, the entanglement shows three degrees of
magnitude enhancement. However, this giant entanglement is fragile against
decoherence and thermal fluctuation. Regarding the mechanical squeezing, it
reaches the standard quantum limit (SQL) in the upper branch of the
bistability. Our proposal provides a way to improve quantum effects in
optomechanical systems by taking advantage of nonlinearities. This scheme can
be realized in similar systems such as superconducting microwave, and hybrid
optomechanical systems.


  The local spectral statistics of random matrices forms distinct universality
classes, strongly depending on the position in the spectrum. Surprisingly, the
spacing between consecutive eigenvalues at the spectral edges has received
little attention, where the density diverges or vanishes, respectively. This
different behaviour is called hard or soft edge. We show that the spacings at
the edges are almost indistinguishable from the spacing in the bulk of the
spectrum. We present analytical results for consecutive spacings between the
$k$th and $(k+1)$st smallest eigenvalues in the chiral Gaussian unitary
ensemble, both for finite- and large-$n$. The result depends on the number of
the generic zero modes $\nu$ and the number of flavours $N_{\rm f}$, which are
given in terms of characteristic polynomials, as motivated by Quantum
Chromodynamics (QCD). We find that the convergence in $n$ is very rapid. The
same can be said separately about the limit $k\to\infty$ (limit to the bulk)
and $\nu\to\infty$ (limit to the soft edge). Interestingly, the Wigner surmise
is a very good approximation for all these cases and, apart from $k=1$, shows a
deviation below one percent. These findings are corroborated with Monte-Carlo
simulations. We finally compare for $k=1$ with data from QCD on the lattice,
being in this symmetry class.


  Based on a continuum theory, we investigate the manipulation of the
non-equilibrium behavior of a sheared liquid crystal via closed-loop feedback
control. Our goal is to stabilize a specific dynamical state, that is, the
stationary "flow-alignment", under conditions where the uncontrolled system
displays oscillatory director dynamics with in-plane symmetry. To this end we
employ time-delayed feedback control (TDFC), where the equation of motion for
the ith component, q_i(t), of the order parameter tensor is supplemented by a
control term involving the difference q_i(t)-q_i(t-\tau). In this diagonal
scheme, \tau is the delay time. We demonstrate that the TDFC method
successfully stabilizes flow alignment for suitable values of the control
strength, K, and \tau; these values are determined by solving an exact
eigenvalue equation. Moreover, our results show that only small values of K are
needed when the system is sheared from an isotropic equilibrium state, contrary
to the case where the equilibrium state is nematic.


  Recent text generation research has increasingly focused on open-ended
domains such as story and poetry generation. Because models built for such
tasks are difficult to evaluate automatically, most researchers in the space
justify their modeling choices by collecting crowdsourced human judgments of
text quality (e.g., Likert scores of coherence or grammaticality) from Amazon
Mechanical Turk (AMT). In this paper, we first conduct a survey of 45
open-ended text generation papers and find that the vast majority of them fail
to report crucial details about their AMT tasks, hindering reproducibility. We
then run a series of story evaluation experiments with both AMT workers and
English teachers and discover that even with strict qualification filters, AMT
workers (unlike teachers) fail to distinguish between model-generated text and
human-generated references. We show that AMT worker judgments improve when they
are shown model-generated output alongside human-generated references, which
enables the workers to better calibrate their ratings. Finally, interviews with
the English teachers provide deeper insights into the challenges of the
evaluation process, particularly when rating model-generated text.


  We study the effect of the stochastic gradient noise on the training of
generative adversarial networks (GANs) and show that it can prevent the
convergence of standard game optimization methods, while the batch version
converges. We address this issue with a novel stochastic variance-reduced
extragradient (SVRE) optimization algorithm, which for a large class of games
improves upon the previous convergence rates proposed in the literature. We
observe empirically that SVRE performs similarly to a batch method on MNIST
while being computationally cheaper, and that SVRE yields more stable GAN
training on standard datasets.


  Studying the antiferromagnetic phase of the Hubbard model by dynamical mean
field theory, we observe striking differences with static (Hartree-Fock) mean
field: The Slater band is strongly renormalized and spectral weight is
transferred to spin-polaron side bands. Already for intermediate values of the
interaction $U$ the overall bandwidth is larger than in Hartree-Fock, and the
gap is considerably smaller. Such differences survive any renormalization of
$U$. Our photoemission experiments for Cr-doped V$_2$O$_3$ show spectra
qualitatively well described by dynamical mean field theory.


  This dissertation concerns the classification of groupoid and higher-rank
graph C*-algebras and has two main components. Firstly, for a groupoid it is
shown that the notions of strength of convergence in the orbit space and
measure-theoretic accumulation along the orbits are equivalent ways of
realising multiplicity numbers associated to a sequence of induced
representations of the groupoid C*-algebra. Examples of directed graphs are
given, showing how to determine the multiplicity numbers associated to various
sequences of induced representations of the directed graph C*-algebras.
  The second component of this dissertation uses path groupoids to develop
various characterisations of the C*-algebras of higher-rank graphs. Necessary
and sufficient conditions are developed for the Cuntz-Krieger C*-algebras of
row-finite higher-rank graphs to be liminal and to be postliminal. When Kumjian
and Pask's path groupoid is principal, it is shown precisely when these
C*-algebras have bounded trace, are Fell, and have continuous trace. Necessary
and sufficient conditions are provided for the path groupoids of row-finite
higher-rank graphs without sources to have closed orbits and to have locally
closed orbits. When these path groupoids are principal, necessary and
sufficient conditions are provided for them to be integrable, to be Cartan and
to be proper.


  In order to study the influence of quenched disorder on second-order phase
transitions, high-temperature series expansions of the \sus and the free energy
are obtained for the quenched bond-diluted Ising model in $d = 3$--5
dimensions. They are analysed using different extrapolation methods tailored to
the expected singularity behaviours. In $d = 4$ and 5 dimensions we confirm
that the critical behaviour is governed by the pure fixed point up to dilutions
near the geometric bond percolation threshold. The existence and form of
logarithmic corrections for the pure Ising model in $d = 4$ is confirmed and
our results for the critical behaviour of the diluted system are in agreement
with the type of singularity predicted by renormalization group considerations.
In three dimensions we find large crossover effects between the pure Ising,
percolation and random fixed point. We estimate the critical exponent of the
\sus to be $\gamma =1.305(5)$ at the random fixed point.


  It is commonly accepted that the study of 2+1 dimensional quantum gravity
could teach us something about the 3+1 dimensional case. The non-perturbative
methods developed in this case share, as basic ingredient, a reformulation of
gravity as a gauge field theory. However, these methods suffer many problems.
Firstly, this perspective abandon the non-degeneracy of the metric and
causality as fundamental principles, hoping to recover them in a certain
low-energy limit. Then, it is not clear how these combinatorial techniques
could be used in the case where matter fields are added, which are however the
essential ingredients in order to produce non trivial observables in a
generally covariant approach. Endly, considering the status of the observer in
these approaches, it is not clear at all if they really could produce a
completely covariant description of quantum gravity. We propose to re-analyse
carefully these points. This study leads us to a really covariant description
of a set of self-gravitating point masses in a closed universe. This approach
is based on a set of observables associated to the measurements accessible to a
participant-observer, they manage to capture the whole dynamic in Chern-Simons
gravity as well as in true gravity. The Dirac algebra of these observables can
be explicitely computed, and exhibits interesting algebraic features related to
Poisson-Lie groupoids theory.


  In this work, we explore whether modeling recurrence into the Transformer
architecture can both be beneficial and efficient, by building an extremely
simple recurrent module into the Transformer. We compare our model to baselines
following the training and evaluation recipe of BERT. Our results confirm that
recurrence can indeed improve Transformer models by a consistent margin,
without requiring low-level performance optimizations, and while keeping the
number of parameters constant. For example, our base model achieves an absolute
improvement of 2.1 points averaged across 10 tasks and also demonstrates
increased stability in fine-tuning over a range of learning rates.


  This article, produced as a result of the Symposium on Statistical Inference,
is an introduction to the literature on the function of expertise, judgment,
and choice in the practice of statistics and scientific research. In
particular, expert judgment plays a critical role in conducting Frequentist
hypothesis tests and Bayesian models, especially in selection of appropriate
prior distributions for model parameters. The subtlety of interpreting results
is also discussed. Finally, external recommendations are collected for how to
more effectively encourage proper use of judgment in statistics. The paper
synthesizes the literature for the purpose of creating a single reference and
inciting more productive discussions on how to improve the future of statistics
and science.


  New research has highlighted a shortfall in the Standard Model (SM) because
it predicts neutrinos to have zero mass. However, recent experiments on
neutrino oscillation have revealed that the majority of neutrino parameters
indeed indicate their significant mass. In response, scientists are
increasingly incorporating discrete symmetries alongside continuous ones for
better justification of observed patterns of neutrino mixing. In this study, we
have examined a model within $A_4\times Z_3\times Z_{10}$ symmetry to estimate
the neutrino masses using particle swarm optimization technique for both mass
hierarchy of neutrino. This model employed a hybrid seesaw mechanism, a
combination of seesaw mechanism of type-I and type-II, to establish the
effective Majorana neutrino mass matrix. After calculating the mass eigenvalues
and lepton mixing matrix upto second order perturbation theory in this
framework, this study seeks to investigate the scalar potential for vacuum
expectation values (VEVs), optimize the parameters, $U_{PMNS}$ matrix, neutrino
masses: $|{m_{1}^{\prime}}^N|=0.0292794-0.0435082\ eV$,
$|{m_{2}^{\prime}}^N|=1.78893\times 10^{-18}-0.0293509\ eV$,
$|{m_{3}^{\prime}}^N|=0.0307414-0.0471467\ eV$,
$|{m_{1}^{\prime}}^I|=0.00982013-0.0453623\ eV$,
$|{m_{2}^{\prime}}^I_|=0.0379702-0.0471197\ eV$, and
$|{m_{3}^{\prime}}^I|=0.0122063-0.027544\ eV$, effective neutrino mass
parameters: $\langle {m_{ee}} \rangle^N=(0.170-3.93)\times10^{-2}\ eV$,
$\langle {m_{\beta}} \rangle^N=(0.471-1.39)\times10^{-2}\ eV$, $\langle
{m_{ee}} \rangle^I=(1.85-4.55)\times10^{-2}\ eV$ and $\langle {m_{\beta}}
\rangle^I=(2.26-4.56)\times10^{-2}\ eV$, are predicted for both mass hierarchy
through particle swarm optimization (PSO), showing strong agreement with recent
experimental findings.


  Causality lays the foundation for the trajectory of our world. Causal
inference (CI), which aims to infer intrinsic causal relations among variables
of interest, has emerged as a crucial research topic. Nevertheless, the lack of
observation of important variables (e.g., confounders, mediators, exogenous
variables, etc.) severely compromises the reliability of CI methods. The issue
may arise from the inherent difficulty in measuring the variables.
Additionally, in observational studies where variables are passively recorded,
certain covariates might be inadvertently omitted by the experimenter.
Depending on the type of unobserved variables and the specific CI task, various
consequences can be incurred if these latent variables are carelessly handled,
such as biased estimation of causal effects, incomplete understanding of causal
mechanisms, lack of individual-level causal consideration, etc. In this survey,
we provide a comprehensive review of recent developments in CI with latent
variables. We start by discussing traditional CI techniques when variables of
interest are assumed to be fully observed. Afterward, under the taxonomy of
circumvention and inference-based methods, we provide an in-depth discussion of
various CI strategies to handle latent variables, covering the tasks of causal
effect estimation, mediation analysis, counterfactual reasoning, and causal
discovery. Furthermore, we generalize the discussion to graph data where
interference among units may exist. Finally, we offer fresh aspects for further
advancement of CI with latent variables, especially new opportunities in the
era of large language models (LLMs).


  The most general form for symmetric modes of nonlinear discrete-symmetry
systems with nonlinearity depending on the modulus of the field is presented.
Vortex solutions are demonstrated to behave as Bloch modes characterized by an
angular Bloch momentum associated to a periodic variable, periodicity being
fixed by the order of discrete point-symmetry of the system. The concept of
angular Bloch momentum is thus introduced to generalize the usual definition of
angular momentum to cases where O(2) -symmetry no longer holds. The
conservation of angular Bloch momentum during propagation is demonstrated.


  Despite decades of anti-caste efforts, sociocultural practices that
marginalize lower-caste groups in India remain resilient and have even
proliferated with the use of social media. This paper examines how groups
engaged in caste-based discrimination leverage platform affordances of the
social media site X (formerly Twitter) to circulate and reinforce caste
ideologies. Our analysis builds upon previous HCI conceptualizations of online
harms and safety to inform how to address caste-based othering. We offer
theoretical and methodological suggestions for critical HCI research focused on
studying the mechanisms of power along other social categories.


  Here we present a sample of sources with convex radio spectra peaking at
frequencies above a few GHz. We call these radio sources High Frequency Peakers
(HFPs). This sample extends to higher turnover frequencies than the samples of
Compact Steep Spectrum (CSS) and GHz Peaked Spectrum (GPS) radio sources. HFPs
are rare due to the strong bias against them caused by their turnover occurring
at frequencies about one order of magnitude higher than in CSS-GPS samples. The
sample has been selected by a comparison between the Green Bank survey (87GB)
at 4.9 GHz and the NRAO VLA Sky Survey (NVSS) at 1.4 GHz. Then the candidates
have been observed with the VLA at 1.365, 1.665, 4.535, 4.985, 8.085, 8.485,
14.96 and 22.46 GHz in order to derive a simultaneous radio spectrum, and
remove variable sources from the sample. The final list of genuine HFP sources
consists of 55 objects with flux density exceeding 300 mJy at 4.9 GHz at the
time of the 87GB observation. Optical identifications are available for 29 of
them; 24 are high redshift quasars, 3 are galaxies (one of them has indeed
broad lines in the optical spectrum) and 2 are BL Lac objects. The remaining
sources are mostly empty fields (17) on the digitised POSS or have uncertain
classification (9).


  Heavy ion collisions are rich and complex systems that involve different
aspects of QCD and electromagnetic phenomena. From head-on collisions to the
case in which the nuclei miss each other, many of QCD and photo-induced probes
are being actively investigated. In this contribution we briefly discuss both
of these different topics and some of the CMS results on top quark production
and vector meson photo-production, as well as the physics motivation to study
these processes are presented.


  In particle accelerator components, parasitic resonances must be reduced
because they heat up the equipment and cause beam instabilities. In this paper,
a method for designing and characterizing Higher Order Mode (HOM) couplers for
reducing such resonances in a broad bandwidth is proposed. A case study is
considered for a specific component, called QuattroTank, showing geometrical
discontinuities and thus causing significant electro-magnetic resonances.
Results of numerical simulation and experimental emulation prove the capability
of the proposed method to reduce the peaks and the $Q-factor of the resonances.


  This paper discusses the stability assessment of low-inertia power systems
through a real-world large-scale low-inertia system, namely, the All-Island
power system (AIPS) of Ireland and Northern Ireland. This system currently
accommodates world-record levels of system non-synchronous penetration namely
75% (planning to increase to 80% next year). The paper discusses one-month
results obtained with the state-of-the-art stability tool called look-ahead
security assessment (LSAT). This tool carries out rotor-angle, frequency and
voltage stability analyses and is implemented in the control centres of the
transmission system operators (TSOs). The paper shows that, at the time of
writing, the main binding stability constraint of the AIPS is related to the
limits on the rate of change of frequency (RoCoF).


  In this article, we study certain type of boundary behaviour of positive
solutions of the heat equation on the upper half-space of $\R^{n+1}$. We prove
that the existence of the parabolic limit of a positive solution of the heat
equation at a point in the boundary is equivalent to the existence of the
strong derivative of the boundary measure of the solution at that point.
Moreover, the parabolic limit and the strong derivative are equal.


  The attractor mechanism in five dimensional Einstein-Maxwell Chern-Simons
theory is studied. The expression of the five dimensional rotating black object
potential depending on Taub-NUT, electric and magnetic charges as well as on
all the scalar and gauge fields, is investigated. The first order formalism in
d=5 is constructed and analyzed. We derive a general expression defining the
fake superpotential which is valid for all charge configurations. An explicit
expression for the fake superpotential is constructed, for all very special
geometries, in the case of vanishing Taub-NUT charge. We carry out an analogous
construction in the very special geometries corresponding to $t^3$ and $stu$
models, for the most general charge configurations. The attractor flows and
horizon values of all fields are given.


  We describe QGLAB, a new MATLAB package for analyzing partial differential
equations on quantum graphs. The software is built on the existing,
object-oriented MATLAB directed-graph class, inheriting its structure and
adding additional easy-to-use features. The package allows one to construct a
quantum graph and accurately compute the spectrum of elliptic operators,
solutions to Poisson problems, the linear and nonlinear time evolution of a
variety of PDEs, the continuation of branches of steady states (including
locating and switching branches at bifurcations) and more. It uses a unified
framework to implement finite-difference and Chebyshev discretizations of
differential operators on a quantum graph. For simplicity, the package
overloads many built-in MATLAB functions to work on the class.


  We demonstrate focusing and imaging through a scattering medium noninvasively
by using wavefront shaping. Our concept is based on utilizing the spatial
fluorescence contrast which naturally exists in the hidden target object. By
scanning the angle of incidence of the illuminating laser beam and maximizing
the variation of the detected fluorescence signal from the object, as measured
by a bucket detector at the front of the scattering medium, we are able to
generate a tightly focused excitation spot. Thereafter, an image is obtained by
scanning the focus over the object. The requirements for applicability of the
method are discussed.


  By exploiting the underlying symmetries of the relative phases of the
pseudoscalar meson photoproduction amplitude, we determine all the possible
sets of four double-spin observables that resolve the phase ambiguity of the
amplitude in transversity basis up to an overall phase. The present results
corroborate the original findings by Chiang and Tabakin [Phys. Rev. C 55, 2054
(1997)]. However, it is found that the completeness condition of four
double-spin observables to resolve the phase ambiguity holds only when the
relative phases do not meet the condition of equal magnitudes. In situations
where this condition occurs, it is shown that one needs extra chosen
observables, resulting in the minimum number of observables required to resolve
the phase ambiguity to reach up to eight, depending on the particular set of
four double-spin observables considered. Furthermore, a way of gauging when the
condition of equal magnitudes occurs is provided.