  We consider what Ext(A,Z) can be when A is torsion-free and Hom(A,Z)=0. We
thereby give an answer to a question of Golasinski and Goncalves which asks for
the divisible Abelian groups which can be the type of a co-Moore space.


  The realm of algorithms with predictions has led to the development of
several new algorithms that leverage (potentially erroneous) predictions to
enhance their performance guarantees. The challenge is to devise algorithms
that achieve optimal approximation guarantees as the prediction quality varies
from perfect (consistency) to imperfect (robustness). This framework is
particularly appealing in mechanism design contexts, where predictions might
convey private information about the agents. In this paper, we design
strategyproof mechanisms that leverage predictions to achieve improved
approximation guarantees for several variants of the Generalized Assignment
Problem (GAP) in the private graph model. In this model, first introduced by
Dughmi & Ghosh (2010), the set of resources that an agent is compatible with is
private information. For the Bipartite Matching Problem (BMP), we give a
deterministic group-strategyproof (GSP) mechanism that is $(1
+1/\gamma)$-consistent and $(1 + \gamma)$-robust, where $\gamma \ge 1$ is some
confidence parameter. We also prove that this is best possible. Remarkably, our
mechanism draws inspiration from the renowned Gale-Shapley algorithm,
incorporating predictions as a crucial element. Additionally, we give a
randomized mechanism that is universally GSP and improves on the guarantees in
expectation. The other GAP variants that we consider all make use of a unified
greedy mechanism that adds edges to the assignment according to a specific
order. Our universally GSP mechanism randomizes over the greedy mechanism, our
mechanism for BMP and the predicted assignment, leading to
$(1+3/\gamma)$-consistency and $(3+\gamma)$-robustness in expectation. All our
mechanisms also provide more fine-grained approximation guarantees that
interpolate between the consistency and the robustness, depending on some
natural error measure of the prediction.


  Let $C$ be an algebraically closed field containing the finite field $F_q$
and complete with respect to an absolute value $|\;|$. We prove that under
suitable constraints on the coefficients, the series $f(z) = \sum_{n \in \Z}
a_n z^{q^n}$ converges to a surjective, open, continuous $F_q$-linear
homomorphism $C \rightarrow C$ whose kernel is locally compact. We characterize
the locally compact sub-$F_q$-vector spaces $G$ of $C$ which occur as kernels
of such series, and describe the extent to which $G$ determines the series.
  We develop a theory of Newton polygons for these series which lets us compute
the Haar measure of the set of zeros of $f$ of a given valuation, given the
valuations of the coefficients. The ``adjoint'' series $f^\ast(z) = \sum_{n \in
\Z} a_n^{1/q^n} z^{1/q^n}$ converges everywhere if and only if $f$ does, and in
this case there is a natural bilinear pairing $$ \ker f \times \ker f^\ast
\rightarrow F_q $$ which exhibits $\ker f^\ast$ as the Pontryagin dual of $\ker
f$. Many of these results extend to non-linear fractional power series. We
apply these results to construct a Drinfeld module analogue of the Weil
pairing, and to describe the topological module structure of the kernel of the
adjoint exponential of a Drinfeld module.


  There exist two groups of electron microscopy methods that are capable of
providing three-dimensional (3D) structural information of an object, i.e.,
electron tomography and depth sectioning. Electron tomography is capable of
resolving atoms in all three dimensions, but the accuracy in atomic positions
is low and the object size that can be reconstructed is limited. Depth
sectioning methods give high positional accuracy in the imaging plane, but the
spatial resolution in the third dimension is low. In this work, electron
tomography and depth sectioning are combined to form a method called
multiple-section local-orbital tomography, or nLOT in short. The nLOT method
provides high spatial resolution and high positional accuracy in all three
dimensions. The object size that can be reconstructed is extended to a million
atoms. The present method establishes a foundation for the widespread
application of atomic electron tomography.


  Employing a non-perturbative approach based on an instantaneous interaction
between a two-level Unruh-DeWitt detector and a massive scalar field, we
investigate the ability of the field to generate or destroy coherence in the
detector by deriving the cohering and decohering power of the induced quantum
evolution channel. For a field in a coherent state a previously unnoticed
effect is reported whereby the amount of coherence that the field generates
displays a revival pattern with respect to the size of the detector. It is
demonstrated that by including mass in a thermal field the set of maximally
coherent states of the detector decoheres less compared to a zero mass. In both
of the examples mentioned, by making a suitable choice of detector radius,
field energy and coupling strength it is possible to infer the mass of the
field by either measuring the coherence present in the detector in the case of
an interaction with a coherent field or the corresponding decoherence of a
maximally coherent state in the case of a thermal field. In view of recent
advances in the study of Proca metamaterials, these results suggest the
possibility of utilising the theory of massive electromagnetism for the
construction of novel applications for use in quantum technologies.


  In a recent series of works, Miller and Sheffield constructed a metric on
$\sqrt{8/3}$-Liouville quantum gravity (LQG) under which $\sqrt{8/3}$-LQG
surfaces (e.g., the LQG sphere, wedge, cone, and disk) are isometric to their
Brownian surface counterparts (e.g., the Brownian map, half-plane, plane, and
disk).
  We identify the metric gluings of certain collections of independent
$\sqrt{8/3}$-LQG surfaces with boundaries identified together according to LQG
length along their boundaries. Our results imply in particular that the metric
gluing of two independent instances of the Brownian half-plane along their
positive boundaries is isometric to a certain LQG wedge decorated by an
independent chordal SLE$_{8/3}$ curve. If one identifies the two sides of the
boundary of a single Brownian half-plane, one obtains a certain LQG cone
decorated by an independent whole-plane SLE$_{8/3}$. If one identifies the
entire boundaries of two Brownian half-planes, one obtains a different LQG cone
and the interface between them is a two-sided variant of whole-plane
SLE$_{8/3}$.
  Combined with another work of the authors, the present work identifies the
scaling limit of self-avoiding walk on random quadrangulations with SLE$_{8/3}$
on $\sqrt{8/3}$-LQG.


  Mendelian randomization (MR) is an epidemiological method that can be used to
strengthen causal inference regarding the relationship between a modifiable
environmental exposure and a medically relevant trait and to estimate the
magnitude of this relationship1. Recently, there has been considerable interest
in using MR to examine potential causal relationships between parental
phenotypes and outcomes amongst their offspring. In a recent issue of BMC
Research Notes, Woolf et al (2023) present a new method, GWAS by subtraction,
to derive genome-wide summary statistics for paternal smoking and other
paternal phenotypes with the goal that these estimates can then be used in
downstream (including two sample) MR studies. Whilst a potentially useful goal,
Woolf et al. (2023) focus on the wrong parameter of interest for useful
genome-wide association studies (GWAS) and downstream cross-generational MR
studies, and the estimator that they derive is neither efficient nor
appropriate for such use.


  Let $\Delta ^{2}$ be a ball in the complex vector space $\mathbb{C}^{2}$
centered at the origin, let $f:\Delta ^{2}\to \mathbb{C}^{2}$ be a holomorphic
mapping$,$ with $f(0)=0$, and let $M$ be a positive integer. If the origin 0 is
an isolated fixed point of the $M$ th iteration $f^{M}$ of $f,$ then one can
define the number $\mathcal{O}_{M}(f,0)$ of periodic orbits of $f$ with period
$M$ hidden at the fixed point 0, which has the meaning: any holomorphic mapping
$g:\Delta ^{2}\to \mathbb{C}^{2}$ sufficiently close to $f$ in a neighborhood
of the origin has exactly $% \mathcal{O}_{M}(f,0)$ distinct periodic orbits
with period $M$ near the origin, provided that all fixed points of $g^{M}$ near
the origin are all simple.
  It is known that $\mathcal{O}_{M}(f,0)\geq 1$ iff the linear part of $f$ at
the origin has a periodic point of period $M.$ This paper will continue to
study the number $\mathcal{O}_{M}(f,0)$. We are interested in the condition for
the linear part of $f$ at the origin such that $\mathcal{O}_{M}(f,0)\geq 2.$
  For a $2\times 2$ matrix $A$ that is arbitrarily given, the goal of this
paper is to give a necessary and sufficient condition for $A$,$ $such that $%
\mathcal{O}_{M}(f,0)\geq 2$ for all holomorphic mappings $f:\Delta ^{2}\to
\mathbb{C}^{2}$ such that $f(0)=0,$ $Df(0)=A$ and that the origin 0 is an
isolated fixed point of $f^{M}.$


  The reversible A <-> B reaction-diffusion process, when species A and B are
initially mixed and diffuse with different diffusion coefficients, is
investigated using the boundary layer function method. It is assumed that the
ratio of the characteristic time of the reaction to the characteristic time of
diffusion is taken as a small parameter of the task. It was shown that
diffusion-reaction process can be considered as a quasi-equilibrium process.
Despite this fact the contribution of the reaction in changes of the species
concentration is comparable with the diffusion contributions. Moreover the
ratios of the reaction and diffusion contributions are independent of time and
coordinate. The dependence of the reaction rate on the initial species
distribution is analyzed. It was firstly obtained that the number of the
reaction zones is determined by the initial conditions and changes with time.
The asymptotic long-time behaviour of the reaction rate also dependents on the
initial distribution.


  We discuss a new companion to Capparelli's identities. Capparelli's
identities for m=1,2 state that the number of partitions of $n$ into distinct
parts not congruent to m, -m modulo $6$ is equal to the number of partitions of
n into distinct parts not equal to m, where the difference between parts is
greater than or equal to 4, unless consecutive parts are either both
consecutive multiples of 3 or add up to to a multiple of 6. In this paper we
show that the set of partitions of n into distinct parts where the odd-indexed
parts are not congruent to m modulo 3, the even-indexed parts are not congruent
to -m modulo 3, and 3l+1 and 3l+2 do not appear together as consecutive parts
for any integer l has the same number of elements as the above mentioned
Capparelli's partitions of n. In this study we also extend the work of Alladi,
Andrews and Gordon by providing a complete set of generating functions for the
refined Capparelli partitions, and conjecture some combinatorial inequalities.


  Recently, click-through rate (CTR) prediction models have evolved from
shallow methods to deep neural networks. Most deep CTR models follow an
Embedding\&MLP paradigm, that is, first mapping discrete id features, e.g. user
visited items, into low dimensional vectors with an embedding module, then
learn a multi-layer perception (MLP) to fit the target. In this way, embedding
module performs as the representative learning and plays a key role in the
model performance. However, in many real-world applications, deep CTR model
often suffers from poor generalization performance, which is mostly due to the
learning of embedding parameters. In this paper, we model user behavior using
an interest delay model, study carefully the embedding mechanism, and obtain
two important results: (i) We theoretically prove that small aggregation radius
of embedding vectors of items which belongs to a same user interest domain will
result in good generalization performance of deep CTR model. (ii) Following our
theoretical analysis, we design a new embedding structure named res-embedding.
In res-embedding module, embedding vector of each item is the sum of two
components: (i) a central embedding vector calculated from an item-based
interest graph (ii) a residual embedding vector with its scale to be relatively
small. Empirical evaluation on several public datasets demonstrates the
effectiveness of the proposed res-embedding structure, which brings significant
improvement on the model performance.


  In this work, we propose and test a strategy for tunable, broadband wave
attenuation in electromechanical waveguides with shunted piezoelectric
inclusions. Our strategy is built upon the vast pre-existing literature on
vibration attenuation and bandgap generation in structures featuring periodic
arrays of piezo patches, but distinguishes itself for several key features.
First, we demystify the idea that periodicity is a requirement for wave
attenuation and bandgap formation. We further embrace the idea of "organized
disorder" by tuning the circuits as to resonate at distinct neighboring
frequencies. In doing so, we create a tunable "rainbow trap" [Tsakmakidis et
al. Nature 450, 397-401 (2007)] capable of attenuating waves with broadband
characteristics, by "distilling" (sequentially) seven frequencies from a
traveling wavepacket. Finally, we devote considerable attention to the
implications in terms of packet distortion of the spectral manipulation
introduced by shunting. This work is also meant to serve as a didactic tool for
those approaching the field of shunted piezoelectrics, and attempts to provide
a different perspective, with abundant details, on how to successfully design
an experimental setup involving resistive-inductive shunts.


  This article highlights interactions of diverse areas: the Heron formula for
the area of a triangle, the Descartes circle equation, and right triangles with
integer or rational sides. New and old results are synthesized. We show that
every primitive Pythagorean triple (PPT), furnishes a Descartes quadruple of
tangent circles with integral curvatures, and so generates an integral
Apollonian packing (IAP) containing a rectangle of centers. Thus Pythagorean
triples serve to generate a large number of in-equivalent integral packings.


  We report the results of exact diagonalization studies of Hubbard models on a
$4\times 4$ square lattice with periodic boundary conditions and various
degrees and patterns of inhomogeneity, which are represented by inequivalent
hopping integrals $t$ and $t^{\prime}$. We focus primarily on two patterns, the
checkerboard and the striped cases, for a large range of values of the on-site
repulsion $U$ and doped hole concentration, $x$. We present evidence that
superconductivity is strongest for $U$ of order the bandwidth, and intermediate
inhomogeneity, $0 <t^\prime< t$. The maximum value of the ``pair-binding
energy'' we have found with purely repulsive interactions is $\Delta_{pb} =
0.32t$ for the checkerboard Hubbard model with $U=8t$ and $t^\prime = 0.5t$.
Moreover, for near optimal values, our results are insensitive to changes in
boundary conditions, suggesting that the correlation length is sufficiently
short that finite size effects are already unimportant.


  We observed the northern rim of the Cygnus Loop with the \textit{Suzaku}
observatory in 5 pointings (P21-P25). From the spatially resolved analysis, all
the spectra are well fitted by the single component of the non-equilibrium
ionization plasma model. From the best-fit parameters, we found that the
abundances of the heavy elements are significantly lower than the solar values
except those at the outermost edge in P21 and P22. The origin of the depleted
metal abundances is still unclear while such deficiencies have been reported
from many other rim observations of the Loop. To explain these depletion at the
rim regions, we considered the several possibilities. The effects of the
resonance-line-scattering and the grain condensation lower the values of the
abundances. However, these are not sufficient to account for the abundance
depletion observed.
  We found that the abundances at the outermost edge in P21 and P22 are higher
than those at the other regions. From the morphological point of view, it is
reasonable to consider that this abundance inhomogeneity is derived from the
breakout or the thinness of the cavity wall of the Loop.


  Recent approaches have exploited weaknesses in monolingual question answering
(QA) models by adding adversarial statements to the passage. These attacks
caused a reduction in state-of-the-art performance by almost 50%. In this
paper, we are the first to explore and successfully attack a multilingual QA
(MLQA) system pre-trained on multilingual BERT using several attack strategies
for the adversarial statement reducing performance by as much as 85%. We show
that the model gives priority to English and the language of the question
regardless of the other languages in the QA pair. Further, we also show that
adding our attack strategies during training helps alleviate the attacks.


  The masses and radii of exoplanets are fundamental quantities needed for
their characterisation. Studying the different populations of exoplanets is
important for understanding the demographics of the different planetary types,
which can then be linked to planetary formation and evolution. We present an
updated exoplanet catalog based on reliable, robust and as much as possible
accurate mass and radius measurements of transiting planets up to 120
$M_{\oplus}$. The resulting mass-radius (M-R) diagram shows two distinct
populations, corresponding to rocky and volatile-rich exoplanets which overlap
in both mass and radius. The rocky exoplanet population shows a relatively
small density variability and ends at mass of $\sim25 M_{\oplus}$, possibly
indicating the maximum core mass that can be formed. We use the composition
line of pure-water to separate the two populations, and infer two new empirical
M-R relations based on this data: $ M = (0.9 \pm 0.06) \ R^{(3.45 \pm 0.12)}$
for the rocky population, and $ M = (1.74 \pm 0.38) \ R^{(1.58 \pm 0.10)}$ for
the volatile-rich population. While our results for the two regimes are in
agreement with previous studies, the new M-R relations better match the
population in the transition-region from rocky to volatile-rich exoplanets,
which correspond to a mass range of 5-25 $M_{\oplus}$ and a radius range of 2-3
$R_{\oplus}$.


  Continual Object Detection is essential for enabling intelligent agents to
interact proactively with humans in real-world settings. While
parameter-isolation strategies have been extensively explored in the context of
continual learning for classification, they have yet to be fully harnessed for
incremental object detection scenarios. Drawing inspiration from prior research
that focused on mining individual neuron responses and integrating insights
from recent developments in neural pruning, we proposed efficient ways to
identify which layers are the most important for a network to maintain the
performance of a detector across sequential updates. The presented findings
highlight the substantial advantages of layer-level parameter isolation in
facilitating incremental learning within object detection models, offering
promising avenues for future research and application in real-world scenarios.


  We present a comprehensive set of forecasts for the cross-correlation signal
between 21cm intensity mapping and galaxy redshift surveys. We focus on the
data sets that will be provided by the SKAO for the 21cm signal, DESI and
Euclid for galaxy clustering. We build a likelihood which takes into account
the effect of the beam for the radio observations, the Alcock-Paczynski effect,
a simple parameterization of astrophysical nuisances, and fully exploit the
tomographic power of such observations in the range $z=0.7-1.8$ at linear and
mildly non-linear scales ($k<0.25 h/$Mpc). The forecasted constraints, obtained
with Monte Carlo Markov Chains techniques in a Bayesian framework, in terms of
the six base parameters of the standard $\Lambda$CDM model, are promising. The
predicted signal-to-noise ratio for the cross-correlation can reach $\sim 50$
for $z\sim 1$ and $k\sim 0.1 h/$ Mpc. When the cross-correlation signal is
combined with current Cosmic Microwave Background (CMB) data from Planck, the
error bar on $\Omega_{\rm c}\,h^2$ and $H_0$ is reduced by a factor 3 and 6,
respectively, compared to CMB only data, due to the measurement of matter
clustering provided by the two observables. The cross-correlation signal has a
constraining power that is comparable to the auto-correlation one and combining
all the clustering measurements a sub-percent error bar of 0.33% on $H_0$ can
be achieved, which is about a factor 2 better than CMB only measurement.
Finally, as a proof-of-concept, we test the full pipeline on the real data
measured by the MeerKat collaboration (Cunnington et al. 2022) presenting some
(weak) constraints on cosmological parameters.


  In order to use quantum devices for computations, it is necessary to
understand the intricacies of the theoretical description. To this end, we
provide several novel constructions useful for the comprehension of quantum
mechanics from the perspective of mappings and designs. The unistochasticity
problem, which relates the classical and the quantum domain, is solved in
specific cases, e.g. for all matrices of dimension 4. Furthermore, we provide
an explicit formula for entangling power in the multipartite case. Most
importantly, the thesis presents and elaborates on the path that lead to the
recent construction of absolutely maximally entangled state of four subsystems
six levels each. Finally, we study cardinality as a measure of "quantumness" of
quantum Latin squares and quantum Sudoku (SudoQ). Arrays of the highest
cardinality yield families of quantum measurements of special properties. A
connection between SudoQ designs and mutually unbiased bases is demonstrated.


  Event Detection (ED) is an important task in natural language processing. In
the past few years, many datasets have been introduced for advancing ED machine
learning models. However, most of these datasets are under-explored because not
many tools are available for people to study events, trigger words, and event
mention instances systematically and efficiently. In this paper, we present an
interactive and easy-to-use tool, namely ED Explorer, for ED dataset and model
exploration. ED Explorer consists of an interactive web application, an API,
and an NLP toolkit, which can help both domain experts and non-experts to
better understand the ED task. We use ED Explorer to analyze a recent proposed
large-scale ED datasets (referred to as MAVEN), and discover several underlying
problems, including sparsity, label bias, label imbalance, and debatable
annotations, which provide us with directions to improve the MAVEN dataset. The
ED Explorer can be publicly accessed through http://edx.leafnlp.org/. The
demonstration video is available here
https://www.youtube.com/watch?v=6QPnxPwxg50.


  In this article we prove convergence of adaptive finite element methods for
second order elliptic eigenvalue problems. We consider Lagrange finite elements
of any degree and prove convergence for simple as well as multiple eigenvalues
under a minimal refinement of marked elements, for all reasonable marking
strategies, and starting from any initial triangulation.


  Recent developments in sensing technologies have enabled us to examine the
nature of human social behavior in greater detail. By applying an information
theoretic method to the spatiotemporal data of cell-phone locations, [C. Song
et al. Science 327, 1018 (2010)] found that human mobility patterns are
remarkably predictable. Inspired by their work, we address a similar
predictability question in a different kind of human social activity:
conversation events. The predictability in the sequence of one's conversation
partners is defined as the degree to which one's next conversation partner can
be predicted given the current partner. We quantify this predictability by
using the mutual information. We examine the predictability of conversation
events for each individual using the longitudinal data of face-to-face
interactions collected from two company offices in Japan. Each subject wears a
name tag equipped with an infrared sensor node, and conversation events are
marked when signals are exchanged between sensor nodes in close proximity. We
find that the conversation events are predictable to some extent; knowing the
current partner decreases the uncertainty about the next partner by 28.4% on
average. Much of the predictability is explained by long-tailed distributions
of interevent intervals. However, a predictability also exists in the data,
apart from the contribution of their long-tailed nature. In addition, an
individual's predictability is correlated with the position in the static
social network derived from the data. Individuals confined in a community - in
the sense of an abundance of surrounding triangles - tend to have low
predictability, and those bridging different communities tend to have high
predictability.


  We study the characteristics of the QCD phase transitions in dense hadronic
matter using the Skyrme model constructed on S^3. We find numerically the
localized solutions on $S^3$ using the extended Skyrme model which implements
correctly the scale symmetry of QCD. The transition from the localized phase to
the delocalized phase is found to be of first order at the critical radius of
the hypersphere, $L_c$. The chiral restoration and the gluon decondensation
also take place at the same critical size.


  Milgrom's modified Newtonian dynamics (MOND) has done a great job on
accounting for the rotation curves of a variety of galaxies by assuming that
Newtonian dynamics breaks down for extremely low acceleration typically found
in the galactic contexts. This breakdown of Newtonian dynamics may be a result
of modified gravity or a manifest of modified inertia. The MOND phenomena are
derived here based on three general assumptions: 1) Gravitational mass is
conserved; 2) Inverse-square law is applicable at large distance; 3) Inertial
mass depends on external gravitational fields. These assumptions not only
recover the deep-MOND behaviour, the accelerating expansion of the universe is
also a result of these assumptions. Then Lagrangian formulae are developed and
it is found that the assumed universal acceleration constant a0 is actually
slowly varying by a factor no more than 4. This varying 'constant' is just
enough to account for the mass-discrepancy presented in bright clusters.


  Recently, neural networks have improved MinSum message-passing decoders for
low-density parity-check (LDPC) codes by multiplying or adding weights to the
messages, where the weights are determined by a neural network. The neural
network complexity to determine distinct weights for each edge is high, often
limiting the application to relatively short LDPC codes. Furthermore, storing
separate weights for every edge and every iteration can be a burden for
hardware implementations. To reduce neural network complexity and storage
requirements, this paper proposes a family of weight-sharing schemes that use
the same weight for edges that have the same check node degree and/or variable
node degree. Our simulation results show that node-degree-based weight-sharing
can deliver the same performance requiring distinct weights for each node.
  This paper also combines these degree-specific neural weights with a
reconstruction-computation-quantization (RCQ) decoder to produce a weighted RCQ
(W-RCQ) decoder. The W-RCQ decoder with node-degree-based weight sharing has a
reduced hardware requirement compared with the original RCQ decoder. As an
additional contribution, this paper identifies and resolves a gradient
explosion issue that can arise when training neural LDPC decoders.


  A number of companies recently worked together to release the new Open
Compute Project MX standard for low-precision computation, aimed at efficient
neural network implementation. In this paper, we describe and evaluate the
first open-source FPGA implementation of the arithmetic defined in the
standard. Our designs fully support all the standard's concrete formats for
conversion into and out of MX formats and for the standard-defined arithmetic
operations, as well as arbitrary fixed-point and floating-point formats.
Certain elements of the standard are left as implementation-defined, and we
present the first concrete FPGA-inspired choices for these elements, which we
outline in the paper. Our library of optimized hardware components is available
open source, and can be used to build larger systems. For this purpose, we also
describe and release an open-source Pytorch library for quantization into the
new standard, integrated with the Brevitas library so that the community can
develop novel neural network designs quantized with MX formats in mind. We
demonstrate the usability and efficacy of our libraries via the implementation
of example neural networks such as ResNet-18 on the ImageNet ILSVRC12 dataset.
Our testing shows that MX is very effective for formats such as INT5 or FP6
which are not natively supported on GPUs. This gives FPGAs an advantage as they
have the flexibility to implement a custom datapath and take advantage of the
smaller area footprints offered by these formats.


  The NGC 1333 IRAS 4B region was observed in the 6.9 mm and 1.3 cm continuum
with an angular resolution of about 0.4 arcseconds. IRAS 4BI was detected in
both bands, and BII was detected in the 6.9 mm continuum only. The 1.3 cm
source of BI seems to be a disk-like flattened structure with a size of about
50 AU. IRAS 4BI does not show any sign of multiplicity. Examinations of
archival infrared images show that the dominating emission feature in this
region is a bright peak in the southern outflow driven by BI, corresponding to
the molecular hydrogen emission source HL 9a. Both BI and BII are undetectable
in the mid-IR bands. The upper limit on the far-IR flux of IRAS 4BII suggests
that it may be a very low luminosity young stellar object.


  We calculate the resolved photon contribution to leptoquark production at
$e\gamma$ colliders for the center of mass energies $\sqrt s=500$~GeV and
1~TeV. We also calculate the resolved photon contribution to leptoquark
production at $e^+ e^-$ colliders for the center of mass energies $\sqrt{s} =
1$~and~2~TeV. In both cases we find that these contributions are considerably
larger than the standard contributions considered in the literature.


  General expressions for the R\'enyi entropies and central charges for higher
derivative free spinors and scalars on even spheres are obtained using a direct
spectral method on a compact lune division of the sphere. Formulae and numbers
are rapidly obtained for any dimension and order of derivative.
  The relation between the conformal anomaly and the hyperbolic free energy is
briefly explored using standard expansions.
  A field theoretic derivation of the central charge formula for higher
derivative scalars in any (even) dimension, given by Osborn and Stergiou and by
Gliozzi {\it et al}, is thereby provided. The corresponding extension to
spinors is made.
  Generalised Bernoulli polynomials play an important technical role.


  Open charm spectra at mid-rapidity from direct reconstruction of $D^{0}\to
K\pi$ and indirect electron/positron measurements via charm semileptonic decay
in p+p and d+Au collisions at $\sqrt{s_{_{\rm NN}}}$ = 200 GeV are reported.
The combined spectra cover open charm transverse momentum range
$0.1{}^{<}_{\sim}p_{T}{}^{<}_{\sim}6$ GeV/$c$. The electron spectra show
approximate binary scaling between p+p and d+Au collisions. From these two
independent analyses, the differential cross section per nucleon-nucleon
interaction at mid-rapidity for open charm production at RHIC is
$d\sigma^{NN}_{c\bar{c}}/dy$=0.31$\pm$0.04(stat.)$\pm$0.08(syst.) mb. The
next-to-leading-order pQCD calculation underpredicts the charm yields.


  In this paper we study an SU(5) x A5 flavour model which exhibits a neutrino
mass sum rule and golden ratio mixing in the neutrino sector which is corrected
from the charged lepton Yukawa couplings. We give the full renormalizable
superpotential for the model which breaks SU(5) and A5 after integrating out
heavy messenger fields and minimising the scalar potential. The mass sum rule
allows for both mass orderings but we will show that inverted ordering is not
valid in this setup. For normal ordering we find the lightest neutrino to have
a mass of about 10-50 meV, and all leptonic mixing angles in agreement with
experiment.


  Central regions of the early-type disk galaxies NGC 524 and NGC 6340 have
been investigated with the Multi-Pupil Field Spectrograph at the 6m telescope
of the Special Astrophysical Observatory of the Russian Academy of Sciences. I
confirm the existence of chemically distinct stellar nuclei in these galaxies
which have been claimed earlier. The metallicity differences which are found
between the nuclei and the bulges, 0.5 - 1.0 kpc from the centers, reach 0.5 -
0.6 dex. Both nuclei are magnesium overabundant, but the bulges have different
magnesium-to-iron ratios: it is solar in NGC 6340 and the same as the nuclear
one in NGC 524. The kinematical and morphological analyses reveal the existence
of inclined central disks in these galaxies. In NGC 524 the central disk
consists of stars, dust, and ionized gas; its extension may be as large as up
to R=3 kpc, and it is inclined by more than 20 deg to the global galactic
plane. In NGC 6340 only a gaseous polar disk with the radius less than 500 pc
is detected.


  We show how sign problems in simulations of many-body systems can manifest
themselves in the form of heavy-tailed correlator distributions, similar to
what is seen in electron propagation through disordered media. We propose an
alternative statistical approach for extracting ground state energies in such
systems, illustrating the method with a toy model and with lattice data for
unitary fermions and for baryons in QCD.


  We suggest to combine the Anthropic Principle with the Many-Worlds
Interpretation of Quantum Theory. Realizing the multiplicity of worlds it
provides an opportunity of explanation of some important events which are
assumed to be extremely improbable. The Mesoscopic Anthropic Principle
suggested here is aimed to explain appearance of such events which are
necessary for emergence of Life and Mind. It is complementary to the
Cosmological Anthropic Principle explaining the fine tuning of fundamental
constants. We briefly discuss various possible applications of the Mesoscopic
Anthropic Principle including the Solar Eclipses and assembling of complex
molecules. Besides, we address the problem of Time's Arrow in the framework of
the Many-Worlds Interpretation. We suggest the recipe for disentangling of
quantities defined by fundamental physical laws and by an anthropic selection.
The main emphasis is made on the problem of the biological evolution.


  We suggest that there are time-varying quanta of mass (gomidia) and of length
(somia), thus pointing to a quantization of geometry and gravitation. The
present numerical value of the gomidium and somium, are, 10 to the power minus
65 grams, and 10 to the power minus 91 centimeters. Gomidia may be responsible
for dark matter in the Universe; Heisenberg's principle, confirms the numerical
estimates for gomidia and somia, either for the present Universe, or for
Planck's time.


  We search for candidate island regions in FRW cosmologies supported by
radiation, cosmological constant $\Lambda$, and non-zero spatial curvature. The
radiation is assumed to be in a thermal state. We apply the necessary
conditions introduced in [arXiv:2008.01022]. Both for the open and closed
universes with $\Lambda<0$, the Friedmann equation admits recollapsing
solutions with a time-symmetric slice. In the case of closed universes, there
is always an island that is the whole Cauchy slice. However, for $\Lambda<0$,
we also find another finite-sized candidate island region, in the middle of the
spacetime, at the turnaround time. In the case of the open universes, we only
find a candidate island region for $\Lambda<0$, that appears at the turnaround
time. It starts from a finite value of the radial coordinate and extends to
infinity. Looking at both open and closed universes, we conclude that the key
ingredient that allows the existence of islands is the negative cosmological
constant. We provide analytic results along the time-symmetric slices and
support our results with numerics in the whole spacetime.


  Can the entire plane be paved with a single tile that forces aperiodicity?
This is known as the ein Stein problem (in German, ein Stein means one tile).
This paper presents a monotile that delivers aperiodic tiling by design. It is
based on the monotile developed by Taylor and Socolar (whose aperiodicity is
forced by means of a non-connected tile that is mainly hexagonal) and
motif-based hexagonal tilings that followed this major discovery. Here instead,
a single substitution rule makes its shape, and when applying it, forces the
tiling to be aperiodic. The proposed monotile, called HexSeed, is self-ruling.
It consists of 16 identical hexagons, called subtiles, all with edgy borders
representing the same binary marking. No motif is needed on the subtiles to
make it work. Additional motifs can be added to the monotile to provide some
insights. The proof of aperiodicity is presented with the use of such motifs.


  We present new mock catalogues for two of the largest stage-IV
next-generation surveys in the optical and infrared: LSST and Euclid, based on
an N-body simulation+semi-analytical cone with a posterior modification with
\texttt{PhotReal}. This technique modifies the original photometry by using an
empirical library of spectral templates to make it more realistic. The
reliability of the catalogues is confirmed by comparing the obtained
color-magnitude relation, the luminosity and mass function and the angular
correlation function with those of real data.
  Consistent comparisons between the expected photometric redshifts for
different surveys are also provided. Very deep near infrared surveys such as
Euclid will provide very good performance ($\Delta z/(1+z) \sim 0.025-0.053$)
down to $H\sim24$ AB mag and up to $z\sim3$ depending on the optical
observations available from the ground whereas extremely deep optical surveys
such as LSST will obtain an overall lower photometric redshift resolution
($\Delta z/(1+z) \sim 0.045$) down to $i\sim27.5$ AB mag, being considerably
improved ($\Delta z/(1+z) \sim 0.035$) if we restrict the sample down to
i$\sim$24 AB mag. Those numbers can be substantially upgraded by selecting a
subsample of galaxies with the best quality photometric redshifts. We finally
discuss the impact that these surveys will have for the community in terms of
photometric redshift legacy.
  This is the first of a series of papers where we set a framework for
comparability between mock catalogues and observations with a particular focus
on cluster surveys. The Euclid and LSST mocks are made publicly available in
the following link: http://photmocks.obspm.fr/.


  The recently-introduced concept of "synthetic dimensions" allows for the
realization of higher-dimensional topological phenomena in lower-dimensional
systems. In this work we study the complementary aspect that synthetic
dimensions provide a natural route to topological states in mesoscopic hybrid
devices. We demonstrate this for the current induced into a closed
one-dimensional Aharonov-Bohm ring by the interaction with a dynamic mesoscopic
magnet. The quantization of the magnetic moment provides a synthetic dimension
that complements the charge motion around the ring. We present a direct mapping
that places the combined ring-magnet system into the class of quantum Hall
models, and demonstrate that topological features, combined with the magnet's
anisotropy, can lead to clear signatures in the persistent current of the
single-particle ground state.


  This is a preliminary study for bifurcation in fractional order dynamical
systems. Stability, persistence and hopf bifurcation are studied. Some studies
are also done for functional equations.


  Improved limits as well as tentative claims for dark matter annihilation into
gamma-ray lines have been presented recently. We study the direct detection
cross section induced from dark matter annihilation into two photons in a
model-independent fashion, assuming no additional couplings between dark matter
and nuclei. We find a striking non-standard recoil spectrum due to different
destructively interfering contributions to the dark matter nucleus scattering
cross section. While in the case of s-wave annihilation the current sensitivity
of direct detection experiments is insufficient to compete with indirect
detection searches, for p-wave annihilation the constraints from direct
searches are comparable. This will allow to test dark matter scenarios with
p-wave annihilation that predict a large di-photon annihilation cross section
in the next generation of experiments.


  Next generation virtual assistants are envisioned to handle multimodal inputs
(e.g., vision, memories of previous interactions, in addition to the user's
utterances), and perform multimodal actions (e.g., displaying a route in
addition to generating the system's utterance). We introduce Situated
Interactive MultiModal Conversations (SIMMC) as a new direction aimed at
training agents that take multimodal actions grounded in a co-evolving
multimodal input context in addition to the dialog history. We provide two
SIMMC datasets totalling ~13K human-human dialogs (~169K utterances) using a
multimodal Wizard-of-Oz (WoZ) setup, on two shopping domains: (a) furniture
(grounded in a shared virtual environment) and, (b) fashion (grounded in an
evolving set of images). We also provide logs of the items appearing in each
scene, and contextual NLU and coreference annotations, using a novel and
unified framework of SIMMC conversational acts for both user and assistant
utterances. Finally, we present several tasks within SIMMC as objective
evaluation protocols, such as Structural API Prediction and Response
Generation. We benchmark a collection of existing models on these SIMMC tasks
as strong baselines, and demonstrate rich multimodal conversational
interactions. Our data, annotations, code, and models are publicly available.


  Most advanced visual grounding methods rely on Transformers for
visual-linguistic feature fusion. However, these Transformer-based approaches
encounter a significant drawback: the computational costs escalate
quadratically due to the self-attention mechanism in the Transformer Encoder,
particularly when dealing with high-resolution images or long context
sentences. This quadratic increase in computational burden restricts the
applicability of visual grounding to more intricate scenes, such as
conversation-based reasoning segmentation, which involves lengthy language
expressions. In this paper, we propose an efficient and effective multi-task
visual grounding (EEVG) framework based on Transformer Decoder to address this
issue, which reduces the cost in both language and visual aspects. In the
language aspect, we employ the Transformer Decoder to fuse visual and
linguistic features, where linguistic features are input as memory and visual
features as queries. This allows fusion to scale linearly with language
expression length. In the visual aspect, we introduce a parameter-free approach
to reduce computation by eliminating background visual tokens based on
attention scores. We then design a light mask head to directly predict
segmentation masks from the remaining sparse feature maps. Extensive results
and ablation studies on benchmarks demonstrate the efficiency and effectiveness
of our approach. Code is available in https://github.com/chenwei746/EEVG.


  We describe a bottom-up framework, based on the identification of appropriate
order parameters and determination of phase diagrams, for understanding
progressively refined agent-based models and simulations of financial markets.
We illustrate this framework by starting with a deterministic toy model,
whereby $N$ independent traders buy and sell $M$ stocks through an order book
that acts as a clearing house. The price of a stock increases whenever it is
bought and decreases whenever it is sold. Price changes are updated by the
order book before the next transaction takes place. In this deterministic
model, all traders based their buy decisions on a call utility function, and
all their sell decisions on a put utility function. We then make the
agent-based model more realistic, by either having a fraction $f_b$ of traders
buy a random stock on offer, or a fraction $f_s$ of traders sell a random stock
in their portfolio. Based on our simulations, we find that it is possible to
identify useful order parameters from the steady-state price distributions of
all three models. Using these order parameters as a guide, we find three
phases: (i) the dead market; (ii) the boom market; and (iii) the jammed market
in the the phase diagram of the deterministic model. Comparing the phase
diagrams of the stochastic models against that of the deterministic model, we
realize that the primary effect of stochasticity is to eliminate the dead
market phase.


  The role of the effective momentum approximation to disentangle Coulomb
distortion effects in quasielastic $(e,e')$ reactions is investigated. The
separation of the cross section in longitudinal and transverse components is
discussed including higher order DWBA corrections due to the focusing of the
electron waves.The experimental studies performed, in the last few years,
making use of different approximate treatments are shown to be sometime
inconsistent. As a consequence some of the longitudinal and transverse
responses, extracted from the inclusive cross sections cannot be considered
reliable. A separation procedure based on the effective momentum approximation
is discussed in connection with the recent experimental data on
electron/positron quasielastic scattering on $^{12}$C and $^{208}$Pb.


  In this paper we show that a substantial Riemannian submersion of S(15) with
7- dimensional fibres is congruent to the standard Hopf fibration. As a
consequence we prove a slightly weak form of of the Diameter Rigidity theorem
for the Cayley plane which is considerably stronger than the very recent Radius
Rigidity Theorem of Wilhelm.


  Evolutionary game theory has been an important tool for describing economic
and social behaviour for decades. Approximate mean value equations describing
the time evolution of strategy concentrations can be derived from the players'
microscopic update rules. We show that they can be generalized to a learning
process. As an example, we compare a restricted imitation process, in which
unused parts of the role model's meta-strategy are hidden from the imitator,
with the widely used imitation rule that allows the imitator to adopt the
entire meta-strategy of the role model. This change in imitation behaviour
greatly affects dynamics and stationary states in the iterated prisoner
dilemma. Particularly we find Grim Trigger to be a more successful strategy
than Tit-For-Tat especially in the weak selection regime.


  In the years between 2000 and 2002 several pre-series and series modules of
the ATLAS EM barrel and end-cap calorimeter were exposed to electron, photon
and pion beams. The performance of the calorimeter with respect to its finely
segmented first sampling has been studied. The polar angle resolution has been
found to be in the range 50-60 mrad/sqrt(E (GeV)). The neutral pion rejection
has been measured to be about 3.5 for 90% photon selection efficiency at pT=50
GeV/c. Electron-pion separation studies have indicated that a pion fake rate of
(0.07-0.5)% can be achieved while maintaining 90% electron identification
efficiency for energies up to 40 GeV.


  Casimir friction between a polarizable particle and a semi-infinite space is
a delicate physical phenomenon, as it concerns the interaction between a
microscopic quantum particle and a semi-infinite reservoir. Not unexpectedly,
results obtained in the past about the friction force obtained via different
routes are sometimes, at least apparently, wildly different from each other.
  Recently, we considered the Casimir friction force for two dielectric
semi-infinite plates moving parallel to each other [J. S. H{\o}ye and I.
Brevik, Eur. Phys. J. D {\bf 68}, 61 (2014)], and managed to get essential
agreement with results obtained by Pendry (1997), Volokitin and Persson (2007),
and Barton (2011). Our method was based upon use of the Kubo formalism. In the
present paper we focus on the interaction between a polarizable particle and a
dielectric half-space again, and calculate the friction force using the same
basic method as before. The new ingredient in the present analysis is that we
take into account radiative damping, and derive the modifications thereof. Some
comparisons are also made with works from others. Essential agreement with the
results of Intravaia, Behunin, and Dalvit can also be achieved using the
modification of the atomic polarizability by the metallic plate.


  In this article, we prove that the Chow group of algebraic cycles of a smooth
cubic hypersurface $X$ over an arbitrary field $k$ is generated, via the
natural cylinder homomorphism, by the algebraic cycles of its Fano variety of
lines $F(X)$, under an assumption on the $1$-cycles of $X/k$. As an
application, if $X/\mathbb{C}$ is a smooth complex cubic fourfold, using the
result, we provide a proof of the integral Hodge conjecture for curve classes
on the polarized hyper-K\"ahler variety $F(X)$. In addition, when $X/k$ is a
smooth cubic fourfold over a finitely generated field $k$ with
$\text{char}(k)\neq 2, 3$, our result enable us to prove the integral analog of
the Tate conjecture for $1$-cycles on $F(X)$.


  Using data from e+e- annihilation into hadrons, taken with the OPAL detector
at LEP at the Z pole between 1991 and 1995, we performed a simultaneous
measurement of the colour factors of the underlying gauge group of the strong
interaction, CF and CA, and the strong coupling, alpha(s). The measurement was
carried out by fitting next-to-leading order perturbative predictions to
measured angular correlations of 4-jet events together with multi-jet related
variables. Our results,
  CA = 3.02 +/- 0.25 (stat.) +/- 0.49 (syst.),
  CF = 1.34 +/- 0.13 (stat.) +/- 0.22 (syst.), alpha(s)(M_Z) = 0.120 +/- 0.011
(stat.) +/- 0.020 (syst.), provide a test of perturbative QCD in which the only
assumptions are non-abelian gauge symmetry and standard hadronization models.
The measurements are in agreement with SU(3) expectations for CF and CA and the
world average of alpha(s)(M_Z).


  Second-pass rescoring is an important component in automatic speech
recognition (ASR) systems that is used to improve the outputs from a first-pass
decoder by implementing a lattice rescoring or $n$-best re-ranking. While
pretraining with a masked language model (MLM) objective has received great
success in various natural language understanding (NLU) tasks, it has not
gained traction as a rescoring model for ASR. Specifically, training a
bidirectional model like BERT on a discriminative objective such as minimum WER
(MWER) has not been explored. Here we show how to train a BERT-based rescoring
model with MWER loss, to incorporate the improvements of a discriminative loss
into fine-tuning of deep bidirectional pretrained models for ASR. Specifically,
we propose a fusion strategy that incorporates the MLM into the discriminative
training process to effectively distill knowledge from a pretrained model. We
further propose an alternative discriminative loss. This approach, which we
call RescoreBERT, reduces WER by 6.6%/3.4% relative on the LibriSpeech
clean/other test sets over a BERT baseline without discriminative objective. We
also evaluate our method on an internal dataset from a conversational agent and
find that it reduces both latency and WER (by 3 to 8% relative) over an LSTM
rescoring model.


  We study a class of stochastic processes of the type $\frac{d^n x}{dt^n}=
v_0\, \sigma(t)$ where $n>0$ is a positive integer and $\sigma(t)=\pm 1$
represents an `active' telegraphic noise that flips from one state to the other
with a constant rate $\gamma$. For $n=1$, it reduces to the standard run and
tumble process for active particles in one dimension. This process can be
analytically continued to any $n>0$ including non-integer values. We compute
exactly the mean squared displacement at time $t$ for all $n>0$ and show that
at late times while it grows as $\sim t^{2n-1}$ for $n>1/2$, it approaches a
constant for $n<1/2$. In the marginal case $n=1/2$, it grows very slowly with
time as $\sim \ln t$. Thus the process undergoes a {\em localisation}
transition at $n=1/2$. We also show that the position distribution $p_n(x,t)$
remains time-dependent even at late times for $n\ge 1/2$, but approaches a
stationary time-independent form for $n<1/2$. The tails of the position
distribution at late times exhibit a large deviation form, $p_n(x,t)\sim
\exp\left[-\gamma\, t\, \Phi_n\left(\frac{x}{x^*(t)}\right)\right]$, where
$x^*(t)= v_0\, t^n/\Gamma(n+1)$. We compute the rate function $\Phi_n(z)$
analytically for all $n>0$ and also numerically using importance sampling
methods, finding excellent agreement between them. For three special values
$n=1$, $n=2$ and $n=1/2$ we compute the exact cumulant generating function of
the position distribution at all times $t$.


  We consider the following Cauchy problem for the four-dimensional energy
critical heat equation \begin{equation*} \begin{cases} u_t=\Delta u+u^{3}
~&\mbox{ in }~ {\mathbb R}^4 \times (0,\infty),\\ u(x,0)=u_0(x) ~&\mbox{ in }~
{\mathbb R}^4. \end{cases} \end{equation*}
  We construct a positive infinite time blow-up solution $u(x,t)$ with the
blow-up rate $ \| u(\cdot,t)\|_{L^\infty({\mathbb R}^4)} \sim \ln t$ as $t\to
\infty$ and show the stability of the infinite time blow-up. This gives a
rigorous proof of a conjecture by Fila and King \cite[Conjecture
1.1]{filaking12}.


  This article presents an original method for Text-to-Sign Translation. It
compensates data scarcity using a domain-specific parallel corpus of alignments
between text and hierarchical formal descriptions of Sign Language videos in
AZee. Based on the detection of similarities present in the source text, the
proposed algorithm recursively exploits matches and substitutions of aligned
segments to build multiple candidate translations for a novel statement. This
helps preserving Sign Language structures as much as possible before falling
back on literal translations too quickly, in a generative way. The resulting
translations are in the form of AZee expressions, designed to be used as input
to avatar synthesis systems. We present a test set tailored to showcase its
potential for expressiveness and generation of idiomatic target language, and
observed limitations. This work finally opens prospects on how to evaluate
translation and linguistic aspects, such as accuracy and grammatical fluency.


  Let R be a hyperbolic Riemann surface with boundary $\partial R$ and suppose
that $\gamma:[0,T]\to R\cup\partial R$ is a simple curve growing from the
boundary of R. By lifting $R_{t}=R\setminus \gamma(0,t]$ to the universal
covering space of R (which we assume is the upper half-plane
$\mathbb{H}=\{z\in\mathbb{C}:Im[z]>0\}$) via the covering map
$\pi:\mathbb{H}\to R$, we can define a family of simply-connected domains
$D_{t}=\pi^{-1}(R_{t})$. For each $t\in[0,T]$, suppose that f_{t} is a
conformal map of \mathbb{H} onto D_{t} such that f(z,t)=f_{t}(z) is
differentiable almost everywhere in (0,T) with respect to t. In this paper, we
will derive a differential equation that describes how f(z,t) evolves in time
t. This should be viewed as an extension of the Loewner differential equation
to curves on Riemann surfaces with boundary.
  The motivation of this paper is the desire to extend Schramm's stochastic
Loewner evolution (SLE) to multiply-connected domains and Riemann surfaces.


  We present a quasi-linear algorithm to compute isogenies between Jacobians of
curves of genus 2 and 3 starting from the equation of the curve and a maximal
isotropic subgroup of the l-torsion, for l an odd prime number, generalizing
the V\'elu's formula of genus 1. This work is based from the paper "Computing
functions on Jacobians and their quotients" of Jean-Marc Couveignes and Tony
Ezome. We improve their genus 2 case algorithm, generalize it for genus 3
hyperelliptic curves and introduce a way to deal with the genus 3
non-hyperelliptic case, using algebraic theta functions.


  We review on and give some further details about the thermodynamical
properties of the \mu-Bose gas model (arXiv:1309.1363) introduced by us
recently. This model was elaborated in connection with \mu-deformed
oscillators. Here, we present the necessary concepts and tools from the
so-called \mu-calculus. For the high temperatures, we obtain the virial
expansion of the equation of state, as well as five virial coefficients. In the
regime of low temperatures, the critical temperature of condensation is
inferred. We also obtain the specific heat, internal energy, and entropy for a
\mu-Bose gas for both low and high temperatures. All thermodynamical functions
depend on the deformation parameter \mu. The dependences of the entropy and the
specific heat on the deformation parameter are visualized.


  Let $\FP(X)$ be the free paratopological group on a topological space $X$.
For $n\in \N$, denote by $\FP_n(X)$ the subset of $\FP(X)$ consisting of all
words of reduced length at most $n$, and by $i_n$ the natural mapping from
$(X\oplus X^{-1}\oplus \{e\})^n$ to $\FP_n(X)$. In this paper a neighbourhood
base at the identity $e$ in $\FP_2(X)$ is found. A number of characterisations
are then given of the circumstances under which $i_2\colon (X\oplus
X^{-1}_d\oplus \{e\})^2\to \FP_2(X)$ is a quotient map, where $X$ is a $T_1$
space and $X^{-1}_d$ denotes the set $X^{-1}$ equipped with the discrete
topology. Further characterisations are given in the case where $X$ is a
transitive $T_1$ space. Several specific spaces and classes of spaces are also
examined. For example, $i_2$ is a quotient for every countable subspace of
$\R$, $i_2$ is not a quotient for any uncountable compact subspace of $\R$, and
it is undecidable in ZFC whether an uncountable subspace of $\R$ exists for
which $i_2$ is a quotient.


  TC++ is a free/libre open-source software of the transcorrelated (TC) method
for first-principles calculation of solids. Here, the TC method is one of the
promising wave-function theories that can be applied to periodic systems with
reasonable computational cost and satisfactory accuracy. We present our
implementation of TC++ including a detailed description of the divergence
correction technique applied to the TC effective interactions. We also present
the way to use TC++ and some results of application to simple periodic systems:
bulk silicon and homogeneous electron gas.


  The phase transitions between the various polymorphs of FAPbI$_{3}$ (FAPI, FA
= formamidinium CH(NH$_{2}$)$_{2}^+$) are studied by anelastic, dielectric and
X--ray diffraction measurements on samples pressed from $\delta -$FAPI (2H
phase) yellow powder. The samples become orange after application of as little
as 0.2~GPa, which has been explained in terms of partial transformations to the
other hexagonal polymorphs 4H and 6H. The phenomenon is discussed in the light
of what is known about the stability of the various polymorphs of hybrid and
inorganic perovskites ABX$_{3}$ with large A cations and hence large tolerance
factor $t$. Remarkably, FAPI at room and higher temperature behaves like a
perovskite with large $t$, while just below room temperature it behaves like a
perovskite with small $t$. The kinetics of the transformations between the
polymorphs is enhanced by small amounts of intercalated water. It seems
therefore worthy to try improving the atomic diffusion and crystallization
during synthesis, and hence the final photovoltaic performance, through
controlled small amounts of water that should be thoroughly removed after a
sufficiently homogeneous and smooth microstructure is achieved.


  We first investigate the attractor solution associated with Assisted
Inflation in Heterotic M-Theory to see if it is stable. By perturbing the
solutions we find a solitary stable fixed point with the general path through
phase space dependent upon the Calabi-Yau data and the number of five-branes.
We then go on to examine the effect of including non-perturbative corrections
to the inflaton potential arising from boundary-brane instantons as well as
higher order brane interaction terms. The result is that Assisted Inflation is
only possible if we allow fine tuning of the superpotential, and that generic
non-perturbative superpotentials will prevent this kind of inflation from
occurring.


  We prove the following local version of Kakutani's characterization of
ellipsoids: Let $V$ be a finite-dimensional real vector space, $B\subset V$ a
convex body with 0 in its interior, and ${2\le k<\dim V}$ an integer. Suppose
that the body $B$ is contained in a cylinder based on the cross-section $B \cap
X$ for any $k$-plane $X$ from a connected open set of linear $k$-planes in $V$.
Then in the region of $V$ swept by these $k$-planes $B$ coincides with either
an ellipsoid, or a cylinder over an ellipsoid, or a cylinder over a
$k$-dimensional base.
  For $k=2$ and $k=3$ we obtain as a corollary a local solution to Banach's
isometric subspace problem: If all cross-sections of $B$ by $k$-planes from a
connected open set are linearly equivalent, then the same conclusion as above
holds.


  Several lifetimes in 23Mg have been determined for the first time using the
Doppler-shift attenuation method. A Monte Carlo simulation code has been
written to model the gamma-ray line shape. An upper limit of 12 fs at the 95%
C.L. has been obtained for the astrophysically important 7787 keV state.


  We elaborate on the distinction between geometric and dynamical phase in
quantum theory and show that the former is intrinsically linked to the quantum
mechanical probabilistic structure. In particular, we examine the appearance of
the Berry phase in the consistent histories scheme and establish that it is the
basic building block of the decoherence functional.
  These results are consequences of the novel temporal structure of
histories-based theories.


  We analyzed the convergence properties of likelihood- weighting algorithms on
a two-level, multiply connected, belief-network representation of the QMR
knowledge base of internal medicine. Specifically, on two difficult diagnostic
cases, we examined the effects of Markov blanket scoring, importance sampling,
demonstrating that the Markov blanket scoring and self-importance sampling
significantly improve the convergence of the simulation on our model.


  Between September 2006 and February 2007, the galactic binary LS I +61 303
was monitored in the TeV band with the VERITAS array of imaging Cherenkov
telescopes. These observations confirm LS I +61 303 as a variable TeV gamma-ray
source, with emission peaking between orbital phase 0.6 and 0.7. During this
observational period, monitoring in the X-ray regime was also carried out using
both the RXTE and Swift detectors, which offered complementary coverage of the
source. Outbursts in the 0.2-10 keV band were observed by both satellites at
close to the same orbital phase as the TeV peak during the 2 orbital cycles
covered simultaneously in both bands. While this source has been extensively
studied in the X-ray band in the past, this is the first observational campaign
to utilize contemporaneous X-ray and TeV data on LS I +61 303.


  In this paper, we study the regularity of the value function associated with
a stochastic control problem where two controls act simultaneously on a
modulated multidimensional diffusion process. The first is a switching control
modelling a random clock. Every time the random clock rings, the generator
matrix is replaced by another, resulting in a different dynamic for the finite
state Markov chain of the modulated diffusion process. The second is a singular
stochastic control that is executed on the process within each regime.


  We develop a framework for simulating measure-preserving, ergodic dynamical
systems on a quantum computer. Our approach provides a new operator-theoretic
representation of classical dynamics by combining ergodic theory with quantum
information science. The resulting quantum embedding of classical dynamics
(QECD) enables efficient simulation of spaces of classical observables with
exponentially large dimension using a quadratic number of quantum gates. The
QECD framework is based on a quantum feature map for representing classical
states by density operators on a reproducing kernel Hilbert space, $\mathcal H
$, and an embedding of classical observables into self-adjoint operators on
$\mathcal H$. In this scheme, quantum states and observables evolve unitarily
under the lifted action of Koopman evolution operators of the classical system.
Moreover, by virtue of the reproducing property of $\mathcal H$, the quantum
system is pointwise-consistent with the underlying classical dynamics. To
achieve an exponential quantum computational advantage, we project the state of
the quantum system to a density matrix on a $2^n$-dimensional tensor product
Hilbert space associated with $n$ qubits. By employing discrete Fourier-Walsh
transforms, the evolution operator of the finite-dimensional quantum system is
factorized into tensor product form, enabling implementation through a quantum
circuit of size $O(n)$. Furthermore, the circuit features a state preparation
stage, also of size $O(n)$, and a quantum Fourier transform stage of size
$O(n^2)$, which makes predictions of observables possible by measurement in the
standard computational basis. We prove theoretical convergence results for
these predictions as $n\to\infty$. We present simulated quantum circuit
experiments in Qiskit Aer, as well as actual experiments on the IBM Quantum
System One.


  The collection of all topologies on the set of three points is studied
treating the topology as quantum-like observable. It turns out to be possible
under the assumption of the asymmetry between the spaces of bra- and
ket-vectors. The analogies between the introduced topologimeter and the
Stern-Gerlach experiments are outlined.


  The behaviour of a static thin shell embedded in dS space is investigated. To
satisfy the junction conditions at the boundary, one rescales the time
variable. The surface energy $\sigma$ on the shell is positive but its surface
tension $\tau$ is negative when $r << a$, where $a$ is the horizon radius. The
repulsive character of the radial acceleration of a static inner observer is
fortified by the process of sinking in the Sitter universe. An upper limit for
$\sigma$ has to be imposed for the shell mass to remain positive.


  We present the concept of Simultaneous Lightwave Information and Power
Transfer (SLIPT) for indoor Internet-of-Things (IoT) applications.
Specifically, we propose novel and fundamental SLIPT strategies, which can be
implemented through Visible Light or Infrared communication systems, equipped
with a simple solar panel-based receiver. These strategies are performed at the
transmitter or at the receiver, or at both sides, named Adjusting transmission,
Adjusting reception and Coordinated adjustment of transmission and reception,
correspondingly. Furthermore, we deal with the fundamental trade-off between
harvested energy and quality-of-service (QoS), by maximizing the harvested
energy, while achieving the required user's QoS. To this end, two optimization
problems are formulated and optimally solved. Computer simulations validate the
optimum solutions and reveal that the proposed strategies considerably increase
the harvested energy, compared to SLIPT with fixed policies.


  Federated Learning (FL) is an intriguing distributed machine learning
approach due to its privacy-preserving characteristics. To balance the
trade-off between energy and execution latency, and thus accommodate different
demands and application scenarios, we formulate an optimization problem to
minimize a weighted sum of total energy consumption and completion time through
two weight parameters. The optimization variables include bandwidth,
transmission power and CPU frequency of each device in the FL system, where all
devices are linked to a base station and train a global model collaboratively.
Through decomposing the non-convex optimization problem into two subproblems,
we devise a resource allocation algorithm to determine the bandwidth
allocation, transmission power, and CPU frequency for each participating
device. We further present the convergence analysis and computational
complexity of the proposed algorithm. Numerical results show that our proposed
algorithm not only has better performance at different weight parameters (i.e.,
different demands) but also outperforms the state of the art.


  Low power deep learning accelerators on the speech processing enable
real-time applications on edge devices. However, most of the existing
accelerators suffer from high power consumption and focus on image applications
only. This paper presents a low power accelerator for speech separation through
algorithm and hardware optimizations. At the algorithm level, the model is
compressed with structured sensitivity as well as unstructured pruning, and
further quantized to the shifted 8-bit floating-point format instead of the
32-bit floating-point format. The computations with the zero kernel and zero
activation values are skipped by decomposition of the dilated and transposed
convolutions. At the hardware level, the compressed model is then supported by
an architecture with eight independent multipliers and accumulators (MACs) with
a simple zero-skipping hardware to take advantage of the activation sparsity
and low power processing. The proposed approach reduces the model size by
95.44\% and computation complexity by 93.88\%. The final implementation with
the TSMC 40 $nm$ process can achieve real-time speech separation and consumes
1.6 mW power when operated at 150 MHz. The normalized energy efficiency and
area efficiency are 2.344 TOPS/W and 14.42 GOPS/mm$^2$, respectively.


  The phase diagram of nuclear matter is quite rich - it shows such phenomena
as phase-transitions, formation of condensates, clustering, etc. From the
analysis of the spinodal instability, one can learn about the region of
liquid-gas coexistence in nuclear matter at low densities and finite isospin
asymmetries. In a recent paper, we have shown that asymmetric nuclear matter at
sub-nuclear densities should undergo only one type of instability. The
associated order parameter is dominated by the isoscalar density and so the
transition is of liquid-gas type. The instability goes in the direction of a
restoration of the isospin symmetry leading to a fractionation phenomenon.


  To enhance therapeutic outcomes from a pharmacological perspective, we
propose MiranDa, designed for medication recommendation, which is the first
actionable model capable of providing the estimated length of stay in hospitals
(ELOS) as counterfactual outcomes that guide clinical practice and model
training. In detail, MiranDa emulates the educational trajectory of doctors
through two gradient-scaling phases shifted by ELOS: an Evidence-based Training
Phase that utilizes supervised learning and a Therapeutic Optimization Phase
grounds in reinforcement learning within the gradient space, explores optimal
medications by perturbations from ELOS. Evaluation of the Medical Information
Mart for Intensive Care III dataset and IV dataset, showcased the superior
results of our model across five metrics, particularly in reducing the ELOS.
Surprisingly, our model provides structural attributes of medication
combinations proved in hyperbolic space and advocated "procedure-specific"
medication combinations. These findings posit that MiranDa enhanced medication
efficacy. Notably, our paradigm can be applied to nearly all medical tasks and
those with information to evaluate predicted outcomes. The source code of the
MiranDa model is available at https://github.com/azusakou/MiranDa.


  Recollements of triangulated categories may be seen as exact sequences of
such categories. Iterated recollements of triangulated categories are analogues
of geometric or topological stratifications and of composition series of
algebraic objects. We discuss the question of uniqueness of such a
stratification, up to ordering and derived equivalence, for derived module
categories. The main result is a positive answer in the form of a Jordan
H\"older theorem for derived module categories of hereditary artin algebras. We
also provide examples of derived simple rings.


  Data from the HERA collider experiments, H1 and ZEUS, have been fundamental
to the rapid recent development of our understanding of the partonic
composition of the proton and of QCD. This report focuses on inclusive
measurements of neutral and charged current cross sections at HERA, using the
full available data taken to date. The present precision on the proton parton
densities and the further requirements for future measurements at the Tevatron
and LHC are explored. Emphasis is also placed on the region of very low
Bjorken-x and Q^2. In this region, the `confinement' transition takes place
from partons to hadrons as the relevant degrees of freedom and novel or exotic
QCD effects associated with large parton densities are most likely to be
observed. Finally, prospects for the second phase of HERA running are
discussed.


  The cytoskeleton, consisting of biopolymer filaments, molecular motors, and
passive crosslinking proteins, provides the internal structure of cells that
facilitate movement, growth, and cell division. Understanding the microscopic
motor-filament kinetics and dynamics is essential for comprehending macroscopic
behaviors of reconstituted cytoskeletal assemblies, such as self-organized flow
and active stress. In this study, we employ an adaptive fast Chebyshev
approximator based on tree search and parallel computing to accurately recover
the equilibrium distribution of crosslinking proteins. Therefore, it satisfies
detailed balance in binding through kinetic Monte Carlo sampling while
maintaining cost-effectiveness. Additionally, we offer expandable features,
including segregating the simulation process via pre-building and allowing the
free-loading of different closed-form formulations of the motor's potential
energy. Overall, this research contributes to computational advancement in
function approximation and has the potential to better describe the evolution
of cytoskeletal active matter.


  Prior research on exposure fairness in the context of recommender systems has
focused mostly on disparities in the exposure of individual or groups of items
to individual users of the system. The problem of how individual or groups of
items may be systemically under or over exposed to groups of users, or even all
users, has received relatively less attention. However, such systemic
disparities in information exposure can result in observable social harms, such
as withholding economic opportunities from historically marginalized groups
(allocative harm) or amplifying gendered and racialized stereotypes
(representational harm). Previously, Diaz et al. developed the expected
exposure metric -- that incorporates existing user browsing models that have
previously been developed for information retrieval -- to study fairness of
content exposure to individual users. We extend their proposed framework to
formalize a family of exposure fairness metrics that model the problem jointly
from the perspective of both the consumers and producers. Specifically, we
consider group attributes for both types of stakeholders to identify and
mitigate fairness concerns that go beyond individual users and items towards
more systemic biases in recommendation. Furthermore, we study and discuss the
relationships between the different exposure fairness dimensions proposed in
this paper, as well as demonstrate how stochastic ranking policies can be
optimized towards said fairness goals.


  Graphene/hexagonal boron nitride (hBN) moir\'e superlattices have attracted
interest for use in the study of many-body effects and fractal physics in Dirac
fermion systems. Many exotic transport properties have been intensively
examined in such superlattices, but previous studies have not focused on
single-carrier transport. The investigation of the single-carrier behavior in
these superlattices would lead to an understanding of the transition of
single-particle/correlated phenomena. Here, we show the single-carrier
transport in a high-quality bilayer graphene/hBN superlattice-based quantum dot
device. We demonstrate remarkable device controllability in the energy range
near the charge neutrality point (CNP) and the hole-side satellite point. Under
a perpendicular magnetic field, Coulomb oscillations disappear near the CNP,
which could be a signature of the crossover between Coulomb blockade and
quantum Hall regimes. Our results pave the way for exploring the relationship
of single-electron transport and fractal quantum Hall effects with correlated
phenomena in two-dimensional quantum materials.


  In this paper we study the $L^2$-gradient flow of the penalized elastic
energy on networks of $q$-curves in $\R^{n}$ for $q \geq 3$. Each curve is
fixed at one end-point and at the other is joint to the other curves at a
movable $q$-junction. For this geometric evolution problem with natural
boundary condition we show the existence of smooth solutions for a (possibly)
short interval of time. Since the geometric problem is not well-posed, due to
the freedom in reparametrization of curves, we consider a fourth-order
non-degenerate parabolic quasilinear system, called the analytic problem, and
show first a short-time existence result for this parabolic system. The proof
relies on applying Solonnikov's theory on linear parabolic systems and Banach
fixed point theorem in proper H\"{o}lder spaces. Then the original geometric
problem is solved by establishing the relation between the analytical solutions
and the solutions to the geometrical problem.


  We observe that the ratio of the on-shell scattering amplitude to the
Bethe-Salpeter (BS) wave function outside the interaction range is almost
independent of time in our quenched calculation of the $I=2$ two-pion
scattering with almost zero momentum. In order to discuss the time
independence, we present a relation between the two-pion scattering amplitude
and the surface term of the BS wave function at the boundary. Using the
relation under some assumptions, we show that the ratio is independent of time
if the two-pion four-point function in early time is dominated by scattering
states with almost zero momentum in addition to the ground state of the
two-pion scattering.


  We explore an interior solution of a physically symmetric vierbein with two
unknown functions in conformal teleparallel gravity. The field equations can be
described in a closed system for a particular form of the metric potentials and
an appropriate anisotropic function. As a result, we find a new set of
configurations consistent with observed pulsars. In particular, the boundary
conditions for the interior spacetime are used for the Schwarzschild spacetime
to constrain the conformal field that with a unit value through the surface of
a compact object. Furthermore, we apply the present model to the pulsar
$4U1608-52$ with approximated radius $R= 9.52 \pm 0.15$ km and mass $M= 1.74
\pm 0.14\, M_{\circledcirc}$. To analyze the stability, we also study the
causality conditions and the adiabatic index by assuming the
Tolman-Oppenheimer-Volkov equation, adiabatic index and the static state.
Moreover, the consistency of the model under consideration with other pulsars
is investigated.


  The rich and fascinating physics of topological spin textures in van der
Waals two-dimensional magnets has motivated recent growing interests, though a
comprehensive understanding remains elusive. Here, in atomistic simulations on
monolayer CrSBr, we find two magnetic phases emerging under non-equilibrium
conditions at distinct temperatures, a standard ferromagnetic transition Tc and
a lower temperature T*. Moreover, the real-space analysis of the spin texture
reveals the emergence of metastable topological bimeron defects below T*,
showing an algebraic-like decaying spin-spin correlation function. The
Dzyaloshinskii-Moriya interaction, induced by the local site asymmetry in the
centrosymmetric CrSBr monolayer, is proved to be the origin of the bimerons
formation. Furthermore, the increasing bimerons density upon increasing the
cooling rate follows a Kibble-Zurek behavior, suggesting a handle to drive and
control topological bimerons below T*. Our results put forward CrSBr as an
important candidate for the investigation of the dynamical behavior of bimerons
in vdW magnets.


  Let E be an elliptic curve defined over Q and let G = E(Q)_tors be the
associated torsion subgroup. We study, for a given G, which possible groups G
<= H could appear such that H=E(K)_tors, for [K:Q]=4 and H is one of the
possible torsion structures that occur infinitely often as torsion structures
of elliptic curves defined over quartic number fields.


  The purpose of this paper is point out connections between scattering theory,
double operator integrals, Kreins spectral shift function, integration theory,
bimeasures, Feynman path integrals, harmonic and functional analysis and many
other applications to quantum physics made since the last 50 years or so. The
starting point is Kluvaneks Integration Structures which he hoped to apply to
quantum physics and is now bearing fruit from the contributions of many
authors, especially former Soviet mathematical physicists in the intervening
years. Soon, a practical quantum field theory in four space-time dimensions
satisfying the Wightman axioms may be proved to exist. This is the aim of one
of the Clay Prizes. At the moment, only toy models exist in fewer than four
space-time dimensions.


  We study the time evolution of a system of $N$ spinless fermions in
$\mathbb{R}^3$ which interact through a pair potential, e.g., the Coulomb
potential. We compare the dynamics given by the solution to Schr{\"o}dinger's
equation with the time-dependent Hartree-Fock approximation, and we give an
estimate for the accuracy of this approximation in terms of the kinetic energy
of the system. This leads, in turn, to bounds in terms of the initial total
energy of the system.


  The singleton defect of an $[n,k,d]$ linear code ${\cal C}$ is defined as
$s({\cal C})=n-k+1-d$. Codes with $S({\cal C})=0$ are called maximum distance
separable (MDS) codes, and codes with $S(\cal C)=S(\cal C ^{\bot})=1$ are
called near maximum distance separable (NMDS) codes. Both MDS codes and NMDS
codes have good representations in finite projective geometry.
  MDS codes over $F_q$ with length $n$ and $n$-arcs in PG$(k-1,q)$ are
equivalent objects. When $k=3$, NMDS codes of length $n$ are equivalent to
$(n,3)$-arcs in PG$(2,q)$. In this paper, we deal with the NMDS codes with
dimension 3. By adding some suitable projective points in maximal arcs of
PG$(2,q)$, we can obtain two classes of $(q+5,3)$-arcs (or equivalently
$[q+5,3,q+2]$ NMDS codes) for any prime power $q$.
  We also determine the exact weight distribution
  and the locality of such NMDS codes and their duals. It turns out that the
resultant NMDS codes and their duals are both distance-optimal and
dimension-optimal locally recoverable codes.


  Normalising flows (NFs) for discrete data are challenging because
parameterising bijective transformations of discrete variables requires
predicting discrete/integer parameters. Having a neural network architecture
predict discrete parameters takes a non-differentiable activation function (eg,
the step function) which precludes gradient-based learning. To circumvent this
non-differentiability, previous work has employed biased proxy gradients, such
as the straight-through estimator. We present an unbiased alternative where
rather than deterministically parameterising one transformation, we predict a
distribution over latent transformations. With stochastic transformations, the
marginal likelihood of the data is differentiable and gradient-based learning
is possible via score function estimation. To test the viability of
discrete-data NFs we investigate performance on binary MNIST. We observe great
challenges with both deterministic proxy gradients and unbiased score function
estimation. Whereas the former often fails to learn even a shallow
transformation, the variance of the latter could not be sufficiently controlled
to admit deeper NFs.


  This article introduce a new data storage method called DWDD(Domain Wall
Displacement Detection) and tell you why it succeed.


  The ratio of branching fractions ${\cal{R}}(D^{*-})\equiv {\cal{B}}(B^0 \to
D^{*-} \tau^+ \nu_{\tau})/{\cal{B}}(B^0 \to D^{*-} \mu^+\nu_{\mu})$ is measured
using a data sample of proton-proton collisions collected with the LHCb
detector at center-of-mass energies of 7 and 8 TeV, corresponding to an
integrated luminosity of 3$~$fb$^{-1}$. The $\tau$ lepton is reconstructed with
three charged pions in the final state. A novel method is used that exploits
the different vertex topologies of signal and backgrounds to isolate samples of
semitauonic decays of $b$ hadrons with high purity. Using the $B^0 \to
D^{*-}\pi^+\pi^-\pi^+$ decay as the normalization channel, the ratio
${\cal{B}}(B^0 \to D^{*-} \tau^+ \nu_{\tau})/{\cal{B}}(B^0 \to
D^{*-}\pi^+\pi^-\pi^+)$ is measured to be $1.97 \pm 0.13 \pm 0.18$, where the
first uncertainty is statistical and the second systematic. An average of
branching fraction measurements for the normalization channel is used to derive
${\cal{B}}(B^0 \to D^{*-} \tau^+ \nu_{\tau}) = (1.42 \pm 0.094 \pm 0.129 \pm
0.054) \%$, where the third uncertainty is due to the limited knowledge of
${\cal{B}}(B^0\to D^{*-}\pi^+\pi^-\pi^+)$. A test of lepton flavor universality
is performed using the well-measured branching fraction ${\cal{B}}(B^0 \to
D^{*-} \mu^+\nu_{\mu})$ to compute ${\cal{R}}(D^{*-}) = 0.291 \pm 0.019 \pm
0.026 \pm 0.013$, where the third uncertainty originates from the uncertainties
on ${\cal{B}}(B^0 \to D^{*-}\pi^+\pi^-\pi^+)$ and ${\cal{B}}(B^0 \to D^{*-}
\mu^+\nu_{\mu})$. This measurement is in agreement with the Standard Model
prediction and with previous measurements.


  In recent years, significant progress has been made in image recognition
technology based on deep neural networks. However, improving recognition
performance under low-light conditions remains a significant challenge. This
study addresses the enhancement of recognition model performance in low-light
conditions. We propose an image-adaptive learnable module which apply
appropriate image processing on input images and a hyperparameter predictor to
forecast optimal parameters used in the module. Our proposed approach allows
for the enhancement of recognition performance under low-light conditions by
easily integrating as a front-end filter without the need to retrain existing
recognition models designed for low-light conditions. Through experiments, our
proposed method demonstrates its contribution to enhancing image recognition
performance under low-light conditions.


  We present a simple analytical formula for the geometric concentration ratio
of a circular trough optical concentrator coupled to a flat (planar) receiver.
The receiver is sized to achieve full collection (no spillage) for any
combination of acceptance and rim angle. The development reveals the existence
of two concentration ratio regimes, one controlled by the edge ray caustics,
and the other controlled by the intersection of the edge rays from the rim
alone. Notably, we show that in the latter rim ray regime, the circular trough
achieves the exact same geometric concentration ratio as a parabolic trough.
The provided formula fills a gap towards the development of a complete
catalogue of concentration ratio formulas for different concentrator/receiver
geometries.


  We study the supersymmetric Wilson loop as introduced by Caron-Huot, which
attaches to lightlike polygons certain edge and vertex operators, whose shape
is determined by supersymmetry constraints. We state explicit formulas for the
vertex operators to all orders in the Gra{\ss}mann expansion, thus filling a
gap in the literature. This is achieved by deriving a recursion formula out of
the supersymmetry constraints.


  We present an original approach to quantization based on operator-valued
measure that generalizes the so-called Berezin-Klauder-Toeplitz quantization,
and more generally coherent state quantization approches.


  The combined effect of the magnetic field background in the form of a
singular vortex and the Dirichlet boundary condition at the location of the
vortex on the vacuum of quantized scalar field is studied. We find the induced
vacuum energy density and current to be periodic functions of the vortex flux
and holomorphic functions of the space dimension.


  An active learner is given a class of models, a large set of unlabeled
examples, and the ability to interactively query labels of a subset of these
examples; the goal of the learner is to learn a model in the class that fits
the data well.
  Previous theoretical work has rigorously characterized label complexity of
active learning, but most of this work has focused on the PAC or the agnostic
PAC model. In this paper, we shift our attention to a more general setting --
maximum likelihood estimation. Provided certain conditions hold on the model
class, we provide a two-stage active learning algorithm for this problem. The
conditions we require are fairly general, and cover the widely popular class of
Generalized Linear Models, which in turn, include models for binary and
multi-class classification, regression, and conditional random fields.
  We provide an upper bound on the label requirement of our algorithm, and a
lower bound that matches it up to lower order terms. Our analysis shows that
unlike binary classification in the realizable case, just a single extra round
of interaction is sufficient to achieve near-optimal performance in maximum
likelihood estimation. On the empirical side, the recent work in
~\cite{Zhang12} and~\cite{Zhang14} (on active linear and logistic regression)
shows the promise of this approach.


  The multifaceted nature of human perception and comprehension indicates that,
when we think, our body can naturally take any combination of senses, a.k.a.,
modalities and form a beautiful picture in our brain. For example, when we see
a cattery and simultaneously perceive the cat's purring sound, our brain can
construct a picture of a cat in the cattery. Intuitively, generative AI models
should hold the versatility of humans and be capable of generating images from
any combination of modalities efficiently and collaboratively. This paper
presents ImgAny, a novel end-to-end multi-modal generative model that can mimic
human reasoning and generate high-quality images. Our method serves as the
first attempt in its capacity of efficiently and flexibly taking any
combination of seven modalities, ranging from language, audio to vision
modalities, including image, point cloud, thermal, depth, and event data. Our
key idea is inspired by human-level cognitive processes and involves the
integration and harmonization of multiple input modalities at both the entity
and attribute levels without specific tuning across modalities. Accordingly,
our method brings two novel training-free technical branches: 1) Entity Fusion
Branch ensures the coherence between inputs and outputs. It extracts entity
features from the multi-modal representations powered by our specially
constructed entity knowledge graph; 2) Attribute Fusion Branch adeptly
preserves and processes the attributes. It efficiently amalgamates distinct
attributes from diverse input modalities via our proposed attribute knowledge
graph. Lastly, the entity and attribute features are adaptively fused as the
conditional inputs to the pre-trained Stable Diffusion model for image
generation. Extensive experiments under diverse modality combinations
demonstrate its exceptional capability for visual content creation.


  This is the reply to a comment by Andreas Aste [hep-th/0302103] on a previous
article of mine in Can.J.Phys. The counter-arguments used by Aste utilize a
mathematical limit without physical meaning. We still contend that in QCD, the
particles ``gluons'' and ``quarks'' are merely artifacts of an approximation
method (the perturbative expansion) and are simply absent in the exact theory.


  The temperature dependence of the magnetic field distribution in the mixed
superconducting phase of randomly oriented MgB$_2$ powder was probed by $%
^{11}$B NMR spectroscopy. Below the temperature of the second critical ($B_{%
{c2}}$) field, $T_{{c2}}\approx 27$K, our spectra reveal two NMR signal
components, one mapping the magnetic field distribution in the mixed
superconducting state and the other one arising from the normal state. The
complementary use of bulk magnetization and NMR measurements reveals that
MgB$_2$ is an anisotropic superconductor with a $B_{c2}^c<2.35$ Tesla
anisotropy parameter $\gamma\approx 6$.


  We study the problem of experiment design to learn causal structures from
interventional data. We consider an active learning setting in which the
experimenter decides to intervene on one of the variables in the system in each
step and uses the results of the intervention to recover further causal
relationships among the variables. The goal is to fully identify the causal
structures with minimum number of interventions. We present the first deep
reinforcement learning based solution for the problem of experiment design. In
the proposed method, we embed input graphs to vectors using a graph neural
network and feed them to another neural network which outputs a variable for
performing intervention in each step. Both networks are trained jointly via a
Q-iteration algorithm. Experimental results show that the proposed method
achieves competitive performance in recovering causal structures with respect
to previous works, while significantly reducing execution time in dense graphs.


  We address recent experiments shedding light on the energy spectrum of under-
and optimally doped cuprates at temperatures above superconducting transition.
Angle resolved photoemission reveals coherent excitation only near nodal points
on parts of the "bare" Fermi surface known as the Fermi arcs. The question
debated in the literature is whether the small normal pocket, seen via quantum
oscillations exists at higher temperatures or forms below a charge order
transition in strong magnetic fields. Assuming the former case as possibility,
expressions derived for the resistivity and the Hall coefficient (in weak and
strong magnetic fields) with both types of carriers participating in transport.
There are two regimes. At higher temperatures (at a fixed field) electrons are
dragged by the Fermi arcs' holes. The pocket being small its contribution into
conductivity and the Hall coefficient is negligible. At lower temperatures
electrons decouple from holes behaving as a Fermi gas in the magnetic field.
Mobility of holes on the arcs decreasing in strong fields with decrease of
temperature, below a crossover point the pocket electrons prevail changing sign
of the Hall coefficient in the low temperature limit. Such behavior finds its
confirmation in recent high-field experiments.


  In this paper, we present a general framework to construct recurrent fractal
interpolation surfaces (RFISs) on rectangular grids. Then we introduce bilinear
RFISs, which are easy to be generated while there are no restrictions on
interpolation points and vertical scaling factors. We also obtain the box
dimension of bilinear RFISs under certain constraints, where the main
assumption is that vertical scaling factors have uniform sums under a
compatible partition.


  It was experimentally confirmed that if steel cyclic stress reduces to less
than tensile yield stress values, i.e. in case of high-cycle fatigue, the
mechanism of fracture changes from dislocation to vacancy one. This conclusion
was based on the fact that steel density determined by the method of liquid
displacement is less than that of steel in both initial condition and after
fracture under the cyclic loads exceeding tensile yield stress values. In the
latter case steel hardness increases, whereas the steels fractured under the
cyclic stresses less than their tensile yield stress values show no change in
hardness. It means that in such a case metal fractures without strain
hardening, i.e. undergoes brittle fracturing developing by vacancy mechanism
rather than by dislocation one. As a result such steel obtains the structure
and properties similar to those appearing after its exposure to radiation, i.e.
friability and brittleness. The results obtained allow us to explain the
presence of a horizontal section in the W\"ohler fatigue failure diagram


  Cluster synchronization is a phenomenon in which oscillators in a given
network are partitioned into synchronous clusters. As recently shown, diverse
cluster synchronization patterns can be found using network symmetry when the
oscillators are identical. For such symmetry-induced cluster synchronization
patterns, subsets called intertwined clusters can exist, in which every cluster
in the same subset should synchronize or desynchronize concurrently. In this
work, to reflect the existence of noise in real systems, we consider networks
composed of nearly identical oscillators. We show that every cluster in the
same intertwined cluster set is nearly synchronized concurrently when the
nearly synchronous state of the set is stable. We also consider an extreme case
where only one cluster of an intertwined cluster set is composed of nearly
identical oscillators while every other cluster in the set is composed of
identical oscillators. In this case, deviation from the synchronous state of
every cluster in the same set increases linearly with the magnitude of
parameter mismatch within the cluster of nearly identical oscillators. We
confirm these results by numerical simulation.