  In this paper we classify Legendrian and transverse knots in the knot types
obtained from positive torus knots by cabling. This classification allows us to
demonstrate several new phenomena. Specifically, we show there are knot types
that have non-destabilizable Legendrian representatives whose
Thurston-Bennequin invariant is arbitrarily far from maximal. We also exhibit
Legendrian knots requiring arbitrarily many stabilizations before they become
Legendrian isotopic. Similar new phenomena are observed for transverse knots.
To achieve these results we define and study "partially thickenable" tori,
which allow us to completely classify solid tori representing positive torus
knots.


  We study the spaces of rational curves on Fano threefolds with Gorenstein
terminal singularities. We generalize the results regarding Geometric Manin's
Conjecture for smooth Fano threefolds, including the classification of
subvarieties with higher a-invariants and Movable Bend-and-Break lemma. We also
show Geometric Manin's Conjecture for some singular del Pezzo threefolds.


  A nearly simultaneous X-ray/optical (Chandra and VLT) observational campaign
of RX J0806.3+1527 has been carried out during November 2001. These
observations allowed us to phase the X-ray and optical light curves for the
first time. We measured a phase-shift of about 0.5, in good agreement with the
presence of two distinct emission regions and with the X-ray irradiation
process predictions. The Chandra data allowed us also to study in details the
X-ray spectrum of RX J0806.3+1527, which is consistent with a soft (kT<70 eV)
and small (R_BB<20 km) blackbody component. We discuss the present findings on
the light of the models proposed so far to account for the X-ray emission
detected from RX J0806.3+1527, and its twin source RX J1914.4+2456.


  We quantize an inhomogeneous cosmological model using techniques that include
polymeric quantization. More explicitly, we construct well defined operators to
represent the constraints and find the physical Hilbert space formed by their
solutions, which reproduces the conventional Fock quantization for the
inhomogeneities. The initial singularity is resolved in this inhomogeneous
model in an extremely simple way and without imposing special boundary
conditions, thus ensuring the robustness and generality of this resolution.
Furthermore this quantization constitutes a well founded step towards the
extraction of physical results and consequences from loop quantum cosmology,
given the central role of the inhomogeneities in modern cosmology.


  To test the cooling flow model of early-type galaxies, we obtained a complete
magnitude-limited sample of 34 early-type galaxies, observed with the PSPC and
HRI on ROSAT. The X-ray to optical distribution of galaxies implies a lower
envelope that is consistent with the stellar emission inferred from Cen A. When
this stellar component is removed, the gaseous emission is related to the
optical luminosity by Lx proportional to L_B^m, where m = 3.0-3.5,
significantly steeper than the standard theory (m = 1.7). The dispersion about
the correlation is large, with a full range of 30-100 in Lx for a fixed L_B.
The X-ray temperature is related to the velocity dispersion temperature as Tx
proportional to Tsigma^n, where n = 1.43 +/- 0.21, although for several
galaxies, Tx is about twice Tsigma. The excessively hot galaxies are generally
the most luminous and are associated with the richest environments. We suggest
a model whereby environment influences the X-ray behavior of these galaxies:
early-type galaxies attempt to drive partial or total galactic winds, which can
be stifled by the pressure of their environment. Stifled winds should lead to
hotter and higher luminosity systems, which would occur most commonly in the
richest environments, as observed.


  The KG-BIAS 2020 workshop touches on biases and how they surface in knowledge
graphs (KGs), biases in the source data that is used to create KGs, methods for
measuring or remediating bias in KGs, but also identifying other biases such as
how and which languages are represented in automatically constructed KGs or how
personal KGs might incur inherent biases. The goal of this workshop is to
uncover how various types of biases are introduced into KGs, investigate how to
measure, and propose methods to remediate them.


  This article is the second of a three-part series that derives a
self-consistent theoretical framework of the electromechanics of arbitrarily
curved lipid membranes. Existing continuum theories commonly treat lipid
membranes as strictly two-dimensional surfaces. While this approach is
successful in many purely mechanical applications, strict surface theories fail
to capture the electric potential drop across lipid membranes, the effects of
surface charges, and electric fields within the membrane. Consequently, they do
not accurately resolve Maxwell stresses in the interior of the membrane and its
proximity. Furthermore, surface theories are generally unable to capture the
effects of distinct velocities and tractions at the interfaces between lipid
membranes and their surrounding bulk fluids. To address these shortcomings, we
apply a recently proposed dimension reduction method to the three-dimensional,
electromechanical balance laws. This approach allows us to derive an effective
surface theory without taking the limit of vanishing thickness, thus
incorporating effects arising from the finite thickness of lipid membranes. We
refer to this effective surface theory as $(2 + \delta)$-dimensional, where
$\delta$ indicates the thickness. The resulting $(2 + \delta)$-dimensional
equations of motion satisfy velocity and traction continuity conditions at the
membrane-bulk interfaces, capture the effects of Maxwell stresses, and can
directly incorporate three-dimensional constitutive models.


  PAUCam is an innovative optical narrow-band imager mounted at the William
Herschel Telescope built for the Physics of the Accelerating Universe Survey
(PAUS). Its set of 40 filters results in images that are complex to calibrate,
with specific instrumental signatures that cannot be processed with traditional
data reduction techniques. In this paper we present two pipelines developed by
the PAUS data management team with the objective of producing science-ready
catalogues from the uncalibrated raw images. The Nightly pipeline takes care of
all image processing, with bespoke algorithms for photometric calibration and
scatter-light correction. The Multi-Epoch and Multi-Band Analysis (MEMBA)
pipeline performs forced photometry over a reference catalogue to optimize the
photometric redshift performance. We verify against spectroscopic observations
that the current approach delivers an inter-band photometric calibration of
0.8% across the 40 narrow-band set. The large volume of data produced every
night and the rapid survey strategy feedback constraints require operating both
pipelines in the Port d'Informaci\'o Cientifica data centre with intense
parallelization. While alternative algorithms for further improvements in
photo-z performance are under investigation, the image calibration and
photometry presented in this work already enable state-of-the-art photometric
redshifts down to iAB=23.0.


  The chaotic properties of simple two-dimensional rotation-translation models
are explored and simulated. The models are given in difference equation forms,
while the corresponding differential equations systems are studied and the
resulting trajectories in the plane are explored and illustrated in the
computer experiments done. Characteristic patterns, egg-shaped forms and
central chaotic bulges are present when particles are introduced in the
rotating system. The resulting forms and chaotic attractors mainly depend on
the form of the nonlinear function expressing the rotation angle. Several cases
are studied corresponding to a central force rotation system.


  We present an ab initio approach to integration theory for nonunital spectral
triples. This is done without reference to local units and in the full
generality of semifinite noncommutative geometry. The main result is an
equality between the Dixmier trace and generalised residue of the zeta function
and heat kernel of suitable operators. We also examine definitions for
integrable bounded elements of a spectral triple based on zeta function, heat
kernel and Dixmier trace techniques. We show that zeta functions and heat
kernels yield equivalent notions of integrability, which imply Dixmier
traceability.


  The rupture of rubber differs from conventional fracture. It is supersonic,
and the speed is determined by strain levels ahead of the tip rather than total
strain energy as for ordinary cracks. Dissipation plays a very important role
in allowing the propagation of ruptures, and the back edges of ruptures must
toughen as they contract, or the rupture is unstable. This article presents
several levels of theoretical description of this phenomenon: first, a
numerical procedure capable of incorporating large extensions, dynamics, and
bond rupture; second, a simple continuum model that can be solved analytically,
and which reproduces several features of elementary shock physics; and third,
an analytically solvable discrete model that accurately reproduces numerical
and experimental results, and explains the scaling laws that underly this new
failure mode. Predictions for rupture speed compare well with experiment.


  Gaw\c{e}dzki and Horvai have studied a model for the motion of particles
carried in a turbulent fluid and shown that in a limiting regime with low
levels of viscosity and molecular diffusivity, pairs of particles exhibit the
phenomena of stickiness when they meet. In this paper we characterise the
motion of an arbitrary number of particles in a simplified version of their
model.


  Here we present designs for a static septum magnet with two adjacent
apertures where ideally one aperture has a uniform dipole field and the other
zero field. Two designs are considered. One is a true septum magnet with a thin
layer of coils and materials separating the dipole field region from the null
field region. During the beam switching process, the intense electron beam will
spray across this material septum leading to concerns on beam control, vacuum
quality, radiation damage, etc. due to the lost particles. Therefore, another
configuration without a material septum is also considered. With this
configuration it is more difficult to achieve high field quality near the
transition region. Shaped shims are designed to limit the degradation of beam
quality (emittance growth). This approach is closely related to a previous
septum magnet design with two oppositely oriented dipole field regions
presented by the authors [1]. Simulations are performed to obtain the magnetic
field profile in both designs. A PIC simulation is used to transport a beam
slice consisting of several thousand particles through the magnet to estimate
emittance growth in the magnet due to field non-uniformity.


  Several solid state quantum computer schemes are based on the manipulation of
electron and nuclear spins of single donor atoms in a solid matrix. The
fabrication of qubit arrays requires the placement of individual atoms with
nanometer precision and high efficieny. In this article we describe first
results from low dose, low energy implantations and our development of a low
energy (<10keV), single ion implantation scheme for 31P(q+) ions. When 31P(q+)
ions impinge on a wafer surface, their potential energy (9.3 keV for P15+) is
released, and about 20 secondary electrons are emitted. The emission of
multiple secondary electrons allows detection of each ion impact with 100%
efficiency. The beam spot on target is controlled by beam focusing and
collimation. Exactly one ion is implanted into a selected area avoiding a
Poissonian distribution of implanted ions.


  We formulate a general Kuramoto model on weighted simplicial complexes where
phases oscillators are supported on simplices of any order $k$. Crucially, we
introduce linear and non-linear frustration terms that are independent of the
orientation of the $k+1$ simplices, providing a natural generalization of the
Sakaguchi-Kuramoto model. In turn, this provides a generalized formulation of
the Kuramoto higher-order parameter as a potential function to write the
dynamics as a gradient flow. With a selection of simplicial complexes of
increasingly complex structure, we study the properties of the dynamics of the
simplicial Sakaguchi-Kuramoto model with oscillators on edges to highlight the
complexity of dynamical behaviors emerging from even simple simplicial
complexes. We place ourselves in the case where the vector of internal
frequencies of the edge oscillators lies in the kernel of the Hodge Laplacian,
or vanishing linear frustration, and, using the Hodge decomposition of the
solution, we understand how the nonlinear frustration couples the dynamics in
orthogonal subspaces. We discover various dynamical phenomena, such as the
partial loss of synchronization in subspaces aligned with the Hodge subspaces
and the emergence of simplicial phase re-locking in regimes of high
frustration.


  We present results for the quark mass function in Minkowski space calculated
from an interaction kernel that consists of an effective one-gluon-exchange and
a constant interaction. We analyze the gauge dependence of our results and
compare them in the spacelike region to the available lattice QCD data.


  If a light gluino, with a mass of the order of GeV, exists in the minimal
supersymmetric extension of the Standard Model, then it can contribute to the
production rate of the top quark pairs at hadron colliders via the process
gluino + gluino --> t + tbar. Because the top quark is heavy, the masses of the
superpartners of the left-handed and right-handed top quarks can be very
different such that a parity-violating observable can be induced at the tree
level. We discuss the phenomenology of this parity violating asymmetry at the
CERN Large Hadron Collider.


  Masked image modeling (MIM) has become a leading self-supervised learning
strategy. MIMs such as Masked Autoencoder (MAE) learn strong representations by
randomly masking input tokens for the encoder to process, with the decoder
reconstructing the masked tokens to the input. However, MIM pre-trained
encoders often exhibit a limited attention span, attributed to MIM's sole focus
on regressing masked tokens only, which may impede the encoder's broader
context learning. To tackle the limitation, we improve MIM by explicitly
incorporating unmasked tokens into the training process. Specifically, our
method enables the encoder to learn from broader context supervision, allowing
unmasked tokens to experience broader contexts while the decoder reconstructs
masked tokens. Thus, the encoded unmasked tokens are equipped with extensive
contextual information, empowering masked tokens to leverage the enhanced
unmasked tokens for MIM. As a result, our simple remedy trains more
discriminative representations revealed by achieving 84.2% top-1 accuracy with
ViT-B on ImageNet-1K with 0.6%p gain. We attribute the success to the enhanced
pre-training method, as evidenced by the singular value spectrum and attention
analyses. Finally, our models achieve significant performance gains at the
downstream semantic segmentation and fine-grained visual classification tasks;
and on diverse robust evaluation metrics. Code is available at
https://github.com/naver-ai/lut


  We consider random sub-graphs of a fixed graph $G=(V,E)$ with large minimum
degree. We fix a positive integer $k$ and let $G_k$ be the random sub-graph
where each $v\in V$ independently chooses $k$ random neighbors, making $kn$
edges in all. When the minimum degree $\delta(G)\geq
(\frac12+\epsilon)n,\,n=|V|$ then $G_k$ is $k$-connected w.h.p. for $k=O(1)$;
Hamiltonian for $k$ sufficiently large. When $\delta(G) \geq m$, then $G_k$ has
a cycle of length $(1-\epsilon)m$ for $k\geq k_\epsilon$. By w.h.p. we mean
that the probability of non-occurrence can be bounded by a function $\phi(n)$
(or $\phi(m)$) where $\lim_{n\to\infty}\phi(n)=0$.


  General relativity (GR) has been well tested up to solar system scales, but
it is much less certain that standard gravity remains an accurate description
on the largest, that is, cosmological, scales. Many extensions to GR have been
studied that are not yet ruled out by the data, including by that of the recent
direct gravitational wave detections. Degeneracies among the standard model
($\Lambda$CDM) and modified gravity (MG) models, as well as among different MG
parameters, must be addressed in order to best exploit information from current
and future surveys and to unveil the nature of dark energy. We propose various
higher-order statistics in the weak-lensing signal as a new set of observables
able to break degeneracies between massive neutrinos and MG parameters. We have
tested our methodology on so-called $f(R)$ models, which constitute a class of
viable models that can explain the accelerated universal expansion by a
modification of the fundamental gravitational interaction. We have explored a
range of these models that still fit current observations at the background and
linear level, and we show using numerical simulations that certain models which
include massive neutrinos are able to mimic $\Lambda$CDM in terms of the 3D
power spectrum of matter density fluctuations. We find that depending on the
redshift and angular scale of observation, non-Gaussian information accessed by
higher-order weak-lensing statistics can be used to break the degeneracy
between $f(R)$ models and $\Lambda$CDM. In particular, peak counts computed in
aperture mass maps outperform third- and fourth-order moments.


  Recent experimental results on two hcp phases of barium under high pressure
show interesting variation of the lattice parameters. They are here interpreted
in terms of electronic structure calculation by using the LMTO method and
generalized pseudopotential theory (GPT) with a NFE-TBB approach. In phase II
the dramatic drop in c/a is an instability analogous to that in the group II
metals but with the transfer of s to d electrons playing a crucial role in Ba.
Meanwhile in phase V, the instability decrease a lot due to the core repulsion
at very high pressure. PACS numbers: 62.50+p, 61.66Bi, 71.15.Ap, 71.15Hx,
71.15La


  We present a class of reductions of M\"obius type for the lattice equations
known as Q1, Q2, and Q3 from the ABS list. The deautonomised form of one
particular reduction of Q3 is shown to exist on the $A_1^{(1)}$ surface which
belongs to the multiplicative type of rational surfaces in Sakai's
classification of Painlev\'e systems. Using the growth of degrees of iterates,
all other mappings that result from the class of reductions considered here are
shown to be linearisable. Any possible linearisations are calculated explicitly
by constructing a birational transformation defined by invariant curves in the
blown up space of initial values for each reduction.


  Recent experiments on Ce$_2$Zr$_2$O$_7$ suggest that this material may host a
novel form of quantum spin ice, a three-dimensional quantum spin liquid with an
emergent photon. The Ce$^{3+}$ local moments on the pyrochlore lattice are
described by pseudospin 1/2 degrees of freedom, whose components transform as
dipolar and octupolar moments under symmetry operations. In principle, there
exist four possible quantum spin ice regimes, depending on whether the Ising
component is in the dipolar/octupolar channel, and two possible flux
configurations of the emergent gauge field. In this work, using exact
diagonalization and molecular dynamics, we investigate the equal-time and
dynamical spin structure factors in all four quantum spin ice regimes using
quantum and classical computations. Contrasting the distinct signatures of
quantum and classical results for the four possible quantum spin ice regimes
and elucidating the role of quantum fluctuations, we show that the quantum
structure factor computed for the $\pi$-flux octupolar quantum spin ice regime
is most compatible with the neutron scattering results on Ce$_2$Zr$_2$O$_7$.


  Generative AI systems (ChatGPT, DALL-E, etc) are expanding into multiple
areas of our lives, from art Rombach et al. [2021] to mental health Rob Morris
and Kareem Kouddous [2022]; their rapidly growing societal impact opens new
opportunities, but also raises ethical concerns. The emerging field of AI
alignment aims to make AI systems reflect human values. This paper focuses on
evaluating the ethics of multimodal AI systems involving both text and images -
a relatively under-explored area, as most alignment work is currently focused
on language models. We first create a multimodal ethical database from human
feedback on ethicality. Then, using this database, we develop algorithms,
including a RoBERTa-large classifier and a multilayer perceptron, to
automatically assess the ethicality of system responses.


  Multi-agent reinforcement learning (MARL) has become a significant research
topic due to its ability to facilitate learning in complex environments. In
multi-agent tasks, the state-action value, commonly referred to as the Q-value,
can vary among agents because of their individual rewards, resulting in a
Q-vector. Determining an optimal policy is challenging, as it involves more
than just maximizing a single Q-value. Various optimal policies, such as a Nash
equilibrium, have been studied in this context. Algorithms like Nash Q-learning
and Nash Actor-Critic have shown effectiveness in these scenarios. This paper
extends this research by proposing a deep Q-networks (DQN) algorithm capable of
learning various Q-vectors using Max, Nash, and Maximin strategies. The
effectiveness of this approach is demonstrated in an environment where dual
robotic arms collaborate to lift a pot.


  We prove autoduality for curves of compact type and, more generally, treelike
curves with planar singularities. More precisely, we produce an isomorphism
between the generalized Jacobian of such a curve and the connected component of
the identity of the Picard scheme of the compactified Jacobian of the curve.


  A potential flux of high-energy neutrinos from the annihilation of dark
matter particles trapped within the Sun has been exploited to place indirect
limits on particle dark matter. In most models, the dark matter interacts
weakly, but the possibility of a dark matter particle with a large cross
section for elastic scattering with itself has been proposed in several
contexts. I study the consequences of such dark matter self-interactions for
the high-energy neutrino flux from annihilation within the Sun. The
self-interaction may allow dark matter in the halo to be captured within the
Sun by scattering off of previously-captured dark matter within the Sun. This
effect is not negligible in acceptable and accessible regions of parameter
space. Enhancements in the predicted high-energy neutrino flux from the Sun of
tens to hundreds of percent can be realized in broad regions of parameter
space. Enhancements as large as factors of several hundred may be realized in
extreme regions of the viable parameter space. Large enhancements require the
dark matter annihilation cross section to be relatively small, sigma*v <~
10^-27 cm^3/s. This phenomenology is interesting. First, self-capture is
negligible for the Earth, so dark matter self-interactions break the
correspondence between the solar and terrestrial neutrino signals. Likewise,
the correspondence between indirect and direct detection limits on scattering
cross sections on nuclei is broken by the self-interaction. These broken
correspondences may evince strong dark matter self-interactions. In some cases,
self-capture can lead to observable indirect signals in regions of parameter
space where limits on dark matter-nucleon cross sections from direct detection
would indicate that no such signal should be observable.


  This work analyzes the minimum tollbooth problem in atomic network congestion
games with unsplittable flows. The goal is to place tolls on edges, such that
there exists a pure Nash equilibrium in the tolled game that is a social
optimum in the untolled one. Additionally, we require the number of tolled
edges to be the minimum. This problem has been extensively studied in
non-atomic games, however, to the best of our knowledge, it as not been
considered for atomic games before. By a reduction from the weighted CNF SAT
problem, we show both the NP-hardness of the problem and the W[2]-hardness when
parameterizing the problem with the number of tolled edges. On the positive
side, we present a polynomial time algorithm for networks on series-parallel
graphs that turns any given state of the untolled game into a pure Nash
equilibrium of the tolled game with the minimum number of tolled edges.


  In connection with his counter-example to the fourteenth problem of Hilbert,
Nagata formulated a conjecture concerning the postulation of r fat points of
the same multiplicity in the projective plane and proved it when r is a square.
Iarrobino formulated a similar conjecture in any projective space P^d. We prove
Iarrobino's conjecture when r is a d-th power. As a corollary, we obtain new
counter-examples modeled on those by Nagata.


  Ensuring the reliability of cloud systems is critical for both cloud vendors
and customers. Cloud systems often rely on virtualization techniques to create
instances of hardware resources, such as virtual machines. However,
virtualization hinders the observability of cloud systems, making it
challenging to diagnose platform-level issues. To improve system observability,
we propose to infer functional clusters of instances, i.e., groups of instances
having similar functionalities. We first conduct a pilot study on a large-scale
cloud system, i.e., Huawei Cloud, demonstrating that instances having similar
functionalities share similar communication and resource usage patterns.
Motivated by these findings, we formulate the identification of functional
clusters as a clustering problem and propose a non-intrusive solution called
Prism. Prism adopts a coarse-to-fine clustering strategy. It first partitions
instances into coarse-grained chunks based on communication patterns. Within
each chunk, Prism further groups instances with similar resource usage patterns
to produce fine-grained functional clusters. Such a design reduces noises in
the data and allows Prism to process massive instances efficiently. We evaluate
Prism on two datasets collected from the real-world production environment of
Huawei Cloud. Our experiments show that Prism achieves a v-measure of ~0.95,
surpassing existing state-of-the-art solutions. Additionally, we illustrate the
integration of Prism within monitoring systems for enhanced cloud reliability
through two real-world use cases.


  Mathematical mean-field approaches play an important role in different fields
of Physics and Chemistry, but have found in recent works also their application
in Economics, Finance and Game Theory. The objective of our paper is to
investigate a special mean-field problem in a purely stochastic approach: for
the solution $(Y,Z)$ of a mean-field backward stochastic differential equation
driven by a forward stochastic differential of McKean--Vlasov type with
solution $X$ we study a special approximation by the solution $(X^N,Y^N,Z^N)$
of some decoupled forward--backward equation which coefficients are governed by
$N$ independent copies of $(X^N,Y^N,Z^N)$. We show that the convergence speed
of this approximation is of order $1/\sqrt{N}$. Moreover, our special choice of
the approximation allows to characterize the limit behavior of
$\sqrt{N}(X^N-X,Y^N-Y,Z^N-Z)$. We prove that this triplet converges in law to
the solution of some forward--backward stochastic differential equation of
mean-field type, which is not only governed by a Brownian motion but also by an
independent Gaussian field.


  We present a synthesis of a number of developments which have been made
around the celebrated Tsirelson's equation (1975), conveniently modified in the
framework of a Markov chain taking values in a compact group $ G $, and indexed
by negative time. To illustrate, we discuss in detail the case of the
one-dimensional torus $ G=\bT $.


  We consider a volume preserving curvature evolution of surfaces in an
asymptotically Euclidean initial data set with positive ADM-energy. The speed
is given by a nonlinear function of the mean curvature which generalizes the
spacetime mean curvature recently considered by Cederbaum-Sakovich. Following a
classical approach by Huisken-Yau, we show that the flow starting from suitably
round initial surfaces exists for all times and converges to a constant
(spacetime) curvature limit. This provides an alternative construction of the
ST-CMC foliation by Cederbaum-Sakovich and has applications in the definition
of center of mass of an isolated system in General Relativity.


  Let $G$ be a $p$-group for some prime $p$. Let $n$ be the positive integer so
that $|G:Z(G)| = p^n$. Suppose $A$ is a maximal abelian subgroup of $G$. Let
$$p^l = {\rm max} \{|Z(C_G (g)):Z(G)| : g \in G \setminus Z(G)\},$$ $$p^b =
{\rm max} \{|cl(g)| : g \in G \setminus Z(G) \},$$ and $p^a = |A:Z(G)|$. Then
we show that $a \ge n/(b+l)$.


  We propose a protocol for the preparation of high-fidelity entangled cat
states with composite pulses. The physical model contains two Kerr-nonlinear
resonators and a cavity. By properly designing the parameters, each
Kerr-nonlinear resonator is confined in the cat-state subspace and the
entangled cat states can be generated efficiently. We introduce composite
two-photon drives with multiple amplitudes and frequencies to improve the
fidelity of the entangled cat states in the presence of parameter errors. The
performance of the protocol is estimated by taking into account the parametric
errors and decoherence. Numerical simulation results show that the protocol is
insensitive to timing error and detuning error, and has strong robustness to
decoherence. We hope the protocol may provide a method for preparing stable
entangled cat states.


  The deployment of large language models (LLMs) in healthcare has demonstrated
substantial potential for enhancing clinical decision-making, administrative
efficiency, and patient outcomes. However, the underrepresentation of diverse
groups in the development and application of these models can perpetuate
biases, leading to inequitable healthcare delivery. This paper presents a
comprehensive scientometric analysis of LLM research for healthcare, including
data from January 1, 2021, to June 16, 2024. By analyzing metadata from PubMed
and Dimensions, including author affiliations, countries, and funding sources,
we assess the diversity of contributors to LLM research. Our findings highlight
significant gender and geographic disparities, with a predominance of male
authors and contributions primarily from high-income countries (HICs). We
introduce a novel journal diversity index based on Gini impurity to measure the
inclusiveness of scientific publications. Our results underscore the necessity
for greater representation in order to ensure the equitable application of LLMs
in healthcare. We propose actionable strategies to enhance diversity and
inclusivity in artificial intelligence research, with the ultimate goal of
fostering a more inclusive and equitable future in healthcare innovation.


  We compute primordial light-element abundances for cases with fine structure
constant alpha different from the present value, including many sources of
alpha dependence neglected in previous calculations. Specifically, we consider
contributions arising from Coulomb barrier penetration, photon coupling to
nuclear currents, and the electromagnetic components of nuclear masses. We find
the primordial abundances to depend more weakly on alpha than previously
estimated, by up to a factor of 2 in the case of ^7Li. We discuss the
constraints on variations in alpha from the individual abundance measurements
and the uncertainties affecting these constraints. While the present best
measurements of primordial D/H, ^4He/H, and ^7Li/H may be reconciled pairwise
by adjusting alpha and the universal baryon density, no value of alpha allows
all three to be accommodated simultaneously without consideration of systematic
error. The combination of measured abundances with observations of acoustic
peaks in the cosmic microwave background favors no change in alpha within the
uncertainties.


  The conventional detectors tend to make imbalanced classification and suffer
performance drop, when the distribution of the training data is severely
skewed. In this paper, we propose to use the mean classification score to
indicate the classification accuracy for each category during training. Based
on this indicator, we balance the classification via an Equilibrium Loss (EBL)
and a Memory-augmented Feature Sampling (MFS) method. Specifically, EBL
increases the intensity of the adjustment of the decision boundary for the weak
classes by a designed score-guided loss margin between any two classes. On the
other hand, MFS improves the frequency and accuracy of the adjustment of the
decision boundary for the weak classes through over-sampling the instance
features of those classes. Therefore, EBL and MFS work collaboratively for
finding the classification equilibrium in long-tailed detection, and
dramatically improve the performance of tail classes while maintaining or even
improving the performance of head classes. We conduct experiments on LVIS using
Mask R-CNN with various backbones including ResNet-50-FPN and ResNet-101-FPN to
show the superiority of the proposed method. It improves the detection
performance of tail classes by 15.6 AP, and outperforms the most recent
long-tailed object detectors by more than 1 AP. Code is available at
https://github.com/fcjian/LOCE.


  Four-dimensional simplicial quantum gravity is modified either by coupling it
to U(1) gauge fields or by introducing a measure weighted by the orders of the
triangles. Strong coupling expansion and Monte Carlo simulations are used.
Although the two modifications of the standard pure-gravity model are
apparently very distinct, they produce strikingly similar results, as far as
the geometry of random manifolds is concerned. In particular, for an
appropriate choice of couplings, the branched polymer phase is replaced by a
crinkled phase, characterized by the susceptibility exponent $\gamma < 0$ and
the fractal dimension $d_H > 2$. The quasi-equivalence between the two models
is exploited to get further insight into the extended phase diagram of the
theory.


  (abbreviated) We show that there is a limit relation between the black hole
mass and the width at the half maximum of H$\beta$ for active galactic nuclei
(AGNs) with super-Eddington accretion rates. When a black hole has a
super-Eddington accretion rate, the empirical relation of reverberation mapping
has two possible ways. First, it reduces to a relation between the black hole
mass and the size of the broad line region due to the photon trapping effects
inside the accretion disk. For the Kaspi et al.'s empirical reverberation
relation, we get the limit relation as $M_{\rm BH}=(2.9 - 12.6)\times
10^6M_{\odot} (\upsilon_{\rm FWHM}/10^3{\rm km s^{-1}})^{6.67}$, called as the
Eddington limit. Second, the Eddington limit luminosity will be relaxed if the
trapped photons can escape from the magnetized super-Eddington accretion disk
via the photon bubble instability, and the size of the broad line region will
be enlarged according to the empirical reverberation relation, leading to a
relatively narrow width of H$\beta$. We call this the Begelman limit.
  Super-Eddington accretions in a sample composed of 164 AGNs have been
searched by this limit relation. We find there are a handful of objects locate
between the Eddington and Begelman limit lines, they may be candidates of
super-Eddington accretors in a hybrid structure of photon trapping and photon
bubble instability. The maximum width of H$\beta$ is in the reange of $(3.0 -
3.8)\times 10^3$ km s$^{-1}$ for the maximum mass black holes with
super-Eddington accretion rates among AGNs. We suggest that this limit relation
is more reliable and convenient to test whether a source is super-Eddington and
useful to probe the structure of the super-Eddington accretion process.


  The $\mathcal{O}(\partial^2)$ background independent flow equations for
conformally reduced gravity are shown to be equivalent to flow equations
naturally adapted to scalar field theory with a wrong sign kinetic term. This
sign change is shown to have a profound effect on the renormalization group
properties, broadly resulting in a continuum of fixed points supporting both a
discrete and a continuous eigenoperator spectrum, the latter always including
relevant directions. The properties at the Gaussian fixed point are understood
in particular depth, but also detailed studies of the local potential
approximation, and the full $\mathcal{O}(\partial^2)$ approximation are given.
These results are related to evidence for asymptotic safety found by other
authors.


  Typed Clojure is an optional type system for Clojure, a dynamic language in
the Lisp family that targets the JVM. Typed Clojure enables Clojure programmers
to gain greater confidence in the correctness of their code via static type
checking while remaining in the Clojure world, and has acquired significant
adoption in the Clojure community. Typed Clojure repurposes Typed Racket's
occurrence typing, an approach to statically reasoning about predicate tests,
and also includes several new type system features to handle existing Clojure
idioms. In this paper, we describe Typed Clojure and present these type system
extensions, focusing on three features widely used in Clojure. First,
multimethods provide extensible operations, and their Clojure semantics turns
out to have a surprising synergy with the underlying occurrence typing
framework. Second, Java interoperability is central to Clojure's mission but
introduces challenges such as ubiquitous null; Typed Clojure handles Java
interoperability while ensuring the absence of null-pointer exceptions in typed
programs. Third, Clojure programmers idiomatically use immutable dictionaries
for data structures; Typed Clojure handles this with multiple forms of
heterogeneous dictionary types. We provide a formal model of the Typed Clojure
type system incorporating these and other features, with a proof of soundness.
Additionally, Typed Clojure is now in use by numerous corporations and
developers working with Clojure, and we present a quantitative analysis on the
use of type system features in two substantial code bases.


  We revisit the dyon-anti-dyon liquid model for the Yang-Mills confining
vacuum discussed by Diakonov and Petrov, by retaining the effects of the
classical interactions mediated by the streamline between the dyons and
anti-dyons. In the SU(2) case the model describes a 4-component strongly
interacting Coulomb liquid in the center symmetric phase. We show that in the
linearized screening approximation the streamline interactions yield
Debye-Huckel type corrections to the bulk parameters such as the pressure and
densities, but do not alter significantly the large distance behavior of the
correlation functions in leading order. The static scalar and charged structure
factors are consistent with a plasma of a dyon-anti-dyon liquid with a Coulomb
parameter $\Gamma_{D\bar D}\approx 1$ in the dyon-anti-dyon channel. Heavy
quarks are still linearly confined and the large spatial Wilson loops still
exhibit area laws in leading order. The t$^\prime$ Hooft loop is shown to be 1
modulo Coulomb corrections.


  DensePose estimation task is a significant step forward for enhancing user
experience computer vision applications ranging from augmented reality to cloth
fitting. Existing neural network models capable of solving this task are
heavily parameterized and a long way from being transferred to an embedded or
mobile device. To enable Dense Pose inference on the end device with current
models, one needs to support an expensive server-side infrastructure and have a
stable internet connection. To make things worse, mobile and embedded devices
do not always have a powerful GPU inside. In this work, we target the problem
of redesigning the DensePose R-CNN model's architecture so that the final
network retains most of its accuracy but becomes more light-weight and fast. To
achieve that, we tested and incorporated many deep learning innovations from
recent years, specifically performing an ablation study on 23 efficient
backbone architectures, multiple two-stage detection pipeline modifications,
and custom model quantization methods. As a result, we achieved $17\times$
model size reduction and $2\times$ latency improvement compared to the baseline
model.


  This study is motivated by a series of recent papers that show that, if a
given deterministic sequence in the unit interval has a Poisson pair
correlation function, then the sequence is uniformly distributed. Analogous
results have been proved for point sequences on higher-dimensional tori. The
purpose of this paper is to describe a simple statistical argument that
explains this observation and furthermore permits a generalisation to bounded
Euclidean domains as well as compact Riemannian manifolds.


  Let S(g,N,p) be the Siegel modular variety of principally polarized abelian
varieties of dimension g with a \Gamma_0(p)-level structure and a full N-level
structure (where p is a prime not dividing N \geq 3 and \Gamma_0(p) is the
inverse image of a Borel subgroup of Sp(2g,F_p) in Sp(2g,Z)). This variety has
a natural integral model over Z[1/N] which is not semi-stable over the prime p
if g>1.
  Using the theory of local models of Rapoport-Zink, we construct a semi-stable
model of S(g,N,p) over Z[1/N] for g=2 and g=3.
  For g=2, our construction differs from de Jong's one though the resulting
model is the same.


  With exploiting contextual information over large image regions in an
efficient way, the deep convolutional neural network has shown an impressive
performance for single image super-resolution (SR). In this paper, we propose a
deep convolutional network by cascading the well-designed inception-residual
blocks within the deep Laplacian pyramid framework to progressively restore the
missing high-frequency details of high-resolution (HR) images. By optimizing
our network structure, the trainable depth of the proposed network gains a
significant improvement, which in turn improves super-resolving accuracy. With
our network depth increasing, however, the saturation and degradation of
training accuracy continues to be a critical problem. As regard to this, we
propose an effective two-stage training strategy, in which we firstly use
images downsampled from the ground-truth HR images as the optimal objective to
train the inception-residual blocks in each pyramid level with an extremely
high learning rate enabled by gradient clipping, and then the ground-truth HR
images are used to fine-tune all the pre-trained inception-residual blocks for
obtaining the final SR model. Furthermore, we present a new loss function
operating in both image space and local rank space to optimize our network for
exploiting the contextual information among different output components.
Extensive experiments on benchmark datasets validate that the proposed method
outperforms existing state-of-the-art SR methods in terms of the objective
evaluation as well as the visual quality.


  New and surprisingly simple representation is found for the heterotic string
bosonic effective action in three dimensions in terms of complex potentials.
The system is presented as a K\"ahler $\sigma$--model using complex symmetric
$2\times 2$ matrix (matrix dilaton--axion) which depends linearly on three
Ernst--type potentials and transforms under $U$--duality via matrix valued
$SL(2,R)$. Two discrete automorphisms relating ten isometries of the target
space (U--duality transformations) are found and used to generate the
non--trivial Ehlers--Harrison sector by a map from the trivial gauge sector.
Finite transformations are obtained in a simple form in terms of complex
potentials. New solution generating technique is used to construct EMDA
double--Kerr solution.


  An approximate approach to quantum vibrational dynamics, "Brownian Chain
Molecular Dynamics (BCMD)", is proposed to alleviate the chain resonance and
curvature problems in the imaginary time-based path integral (PI) simulation.
Here the non-centroid velocity is randomized at each step when solving the
equation of motion of path integral molecular dynamics. This leads to a
combination of the Newton equation and the overdamped Langevin equation for the
centroid and non-centroid variables, respectively. BCMD shares the basic
properties of other PI approaches such as centroid and ring polymer molecular
dynamics: It gives the correct Kubo-transformed correlation function at short
times, conserves the time symmetry, has the correct high-temperature/classical
limits, gives exactly the position and velocity autocorrelations of harmonic
oscillator systems, and does not have the zero-point leakage problem. Numerical
tests were done on simple molecular models and liquid water. On-the-fly ab
initio BCMD simulations were performed for the protonated water cluster,
H$_5$O$_2^+$, and its isotopologue, D$_5^{}$O$_2^+$.


  In quantum field theory, the vacuum is widely considered to be a complex
medium populated with virtual particle + antiparticle pairs. To an observer
experiencing uniform acceleration, it is generally held that these virtual
particles become real, appearing as a gas at a temperature which grows with the
acceleration. This is the Unruh effect. However, it can be shown that vacuum
complexity is an artifact, produced by treating quantum field theory in a
manner that does not manifestly enforce causality. Choosing a quantization
approach that patently enforces causality, the quantum field theory vacuum is
barren, bereft even of virtual particles. We show that acceleration has no
effect on a trivial vacuum; hence, there is no Unruh effect in such a treatment
of quantum field theory. Since the standard calculations suggesting an Unruh
effect are formally consistent, insofar as they have been completed, there must
be a cancelling contribution that is omitted in the usual analyses. We argue
that it is the dynamical action of conventional Lorentz transformations on the
structure of an Unruh detector. Given the equivalence principle, an Unruh
effect would correspond to black hole radiation. Thus, our perspective has
significant consequences for quantum gravity and black hole physics: no Unruh
effect entails the absence of black hole radiation evaporation.


  We propose a model-based procedure for automatically preventing security
threats using formal models. We encode system models and potential threats as
satisfiability modulo theory (SMT) formulas. This model allows us to ask
security questions as satisfiability queries. We formulate threat prevention as
an optimization problem over the same formulas. The outcome of our threat
prevention procedure is a suggestion of model attribute repair that eliminates
threats. Whenever threat prevention fails, we automatically explain why the
threat happens. We implement our approach using the state-of-the-art Z3 SMT
solver and interface it with the threat analysis tool THREATGET. We demonstrate
the value of our procedure in two case studies from automotive and smart home
domains, including an industrial-strength example.


  In supersymmetric models, there are new CP violating phases which, if
unsuppressed, would give a too large neutron electric dipole moment. We examine
the possibility of small SUSY phases in string-inspired supergravity models in
which supersymmetry is broken by the auxiliary components of the dilaton and
moduli superfields. It is found that the SUSY phases can be suppressed by a
small factor governing the breakdown of the approximate Peccei Quinn symmetries
nonlinearly realized for the moduli superfields that participate in
supersymmetry breaking. In many cases, the symmetry breaking factors are
exponentially small for moderately large values of the moduli, leading to small
phase values in a natural way.


  In the present paper, as a generalization of the classical periodic rings, we
explore those rings whose elements are additively generated by two (or more)
periodic elements by calling them additively periodic. We prove that, in some
major cases, additively periodic rings remain periodic too; this includes, for
instance, algebraic algebras, group rings, and matrix rings over commutative
rings. Moreover, we also obtain some independent results for the new class of
rings; for example, the triangular matrix rings retain that property.


  Transportation safety, one of the main driving forces of the development of
vehicular communication (VC) systems, relies on high-rate safety messaging
(beaconing). At the same time, there is consensus among authorities, industry,
and academia on the need to secure VC systems. With specific proposals in the
literature, a critical question must be answered: can secure VC systems be
practical and satisfy the requirements of safety applications, in spite of the
significant communication and processing overhead and other restrictions
security and privacy-enhancing mechanisms impose? To answer this question, we
investigate in this paper the following three dimensions for secure and
privacy-enhancing VC schemes: the reliability of communication, the processing
overhead at each node, and the impact on a safety application. The results
indicate that with the appropriate system design, including sufficiently high
processing power, applications enabled by secure VC can be in practice as
effective as those enabled by unsecured VC.


  Objective: Survival rate of oral squamous cell carcinoma (OSCC) patients is
very poor and can be improved using highly sensitive, specific and accurate
techniques. Autofluorescence and fluorescence techniques are very sensitive and
useful in cancer screening. Furthermore, fluorescence spectroscopy is directly
linked with molecular levels of human tissue and can be used as quantitative
tool for cancer detection. Materials and Methods: Here, we report development
of multi-modal autofluorescence and fluorescence imaging and spectroscopic
(MAF-IS) smartphone-based systems for fast and real time oral cancer screening.
Fluorescence-autofluorescence images and spectroscopic datasets shows
significant change in oral cancer and normal tissue in terms of
fluorescence-intensity, spectral-shape, and red-shift respectively. Results: In
this study, total 68 samples (33 cancerous and 35 normal) of 18 OSCC patients
and 13 patients of precancerous tissues (dysplasia and fibrosis) are screened.
Main remarkable finding of the study is presence of three peaks viz ~636 nm,
~680 nm and ~705 nm with decrease in intensity around 450 nm ~ 520 nm in OSCC
in case of autofluorescence. Another finding is red shift in fluorescence
spectroscopy of OSCC, dysplasia and fibrosis from normal which is 6.59+-4.54
nm, 3+-4.78 nm and 1.5+-0.5 nm respectively and can be used as cancer marker in
real-time screening. Finally, support vector machine (SVM) based classifier is
applied for classification of OSCC tissue from normal tissue. The average
sensitivity, specificity and accuracy are found as 88.89% ,100 %, and 95%,
respectively. Conclusion: Autofluorescence and fluorescence-based imaging and
spectroscopy is used for pre-clinical screening of different oral lesions.


  In order to protect the intellectual property (IP) of deep neural networks
(DNNs), many existing DNN watermarking techniques either embed watermarks
directly into the DNN parameters or insert backdoor watermarks by fine-tuning
the DNN parameters, which, however, cannot resist against various attack
methods that remove watermarks by altering DNN parameters. In this paper, we
bypass such attacks by introducing a structural watermarking scheme that
utilizes channel pruning to embed the watermark into the host DNN architecture
instead of crafting the DNN parameters. To be specific, during watermark
embedding, we prune the internal channels of the host DNN with the channel
pruning rates controlled by the watermark. During watermark extraction, the
watermark is retrieved by identifying the channel pruning rates from the
architecture of the target DNN model. Due to the superiority of pruning
mechanism, the performance of the DNN model on its original task is reserved
during watermark embedding. Experimental results have shown that, the proposed
work enables the embedded watermark to be reliably recovered and provides a
sufficient payload, without sacrificing the usability of the DNN model. It is
also demonstrated that the proposed work is robust against common transforms
and attacks designed for conventional watermarking approaches.


  We report anisotropic magnetodielectric (MD) coupling in layered van der
Waals (vdW) antiferromagnetic (AFM) FePS$_3$ (N\'eel temperature
$T_{\mathrm{N}}$ $\sim$ 120K) with perpendicular anisotropy. Above $T_N$, while
dielectric response function along \textit{c}-axis shows frequency dependent
relaxations, in-plane data is frequency independent and reveals a deviation
from phonon-anharmonicity in the ordered state, thereby implying a connection
to spin-phonon coupling known to be indicative of onset of magnetic ordering.
At low temperature (below 40 K), atypical anomaly in the dielectric constant is
corroborated with temperature dependent DC and AC susceptibility. The
magnetodielectric response across this anomaly differs significantly for both,
in-plane and out-of-plane cases. We have explained this in terms of
preferential orientation of magnetic AFM-z alignment, implied by the in-plane
structural anisotropy as confirmed by \textit{ab-initio} calculations.
Controlling relative strength of magnetodielectric coupling with magnetic
anisotropy opens up a strategy for tracking subtle modifications of structure,
such as in-plane anisotropy, with potential application to spintronic
technologies.


  The assumption of free will - the ability of an experimentalist to make
random choices - is central to proving the indeterminism of quantum resources,
the primary tool in quantum cryptography. Relaxing the assumption in a Bell
test allows violation of the usual classical threshold by correlating the
random number generators used to select measurements with the devices that
perform them. In this paper, we examine not only these correlations, but those
across multiple runs of the experiment. This enables an explicit exposition of
the optimal cheating strategy and how the correlations manifest themselves
within this strategy. Similar to other recent results, we prove that there
remain Bell violations for a sufficiently high, yet non-maximal degree of free
will which cannot be simulated by a classical attack, regardless of how many
runs of the experiment those choices are correlated over.


  The finite-temperature Hartree-Fock-Bogoliubov (HFB) approximation often
breaks symmetries of the underlying many-body Hamiltonian. Restricting the
calculation of the HFB partition function to a subspace with good quantum
numbers through projection after variation restores some of the correlations
lost in breaking these symmetries, although effects of the broken symmetries
such as sharp kinks at phase transitions remain. However, the most general
projection after variation formula in the finite-temperature HFB approximation
is limited by a sign ambiguity. Here, we extend the Pfaffian formula for the
many-body traces of HFB density operators introduced by L. M. Robledo in Ref.
[1] to eliminate this sign ambiguity and evaluate the more complicated
many-body traces required in projection after variation in the most general HFB
case. We validate our method through a proof-of-principle calculation of the
particle-number-projected HFB thermal energy in a simple model.


  This paper introduces novel method of simulation of lipid biomembranes based
on Metropolis Hastings algorithm and Graphic Processing Unit computational
power. Method gives up to 55 times computational boost in comparison to
classical computations. Extensive study of algorithm correctness is provided.
Analysis of simulation results and results obtained with classical simulation
methodologies are presented.


  The Anthropocene is characterized by close interdependencies between the
natural Earth system and the human society, posing novel challenges to model
development. Here we present a conceptual model describing the long-term
coevolution of natural and socioeconomic subsystems of Earth. While the climate
is represented via a global carbon cycle, we use economic concepts to model
socio-metabolic flows of biomass and fossil fuels between nature and society. A
wellbeing-dependent parametrization of fertility and mortality governs human
population dynamics. Our analysis focuses on assessing possible asymptotic
states of the Earth system for a qualitative understanding of its complex
dynamics rather than quantitative predictions. Low dimension and simple
equations enable a parameter-space analysis allowing us to identify
preconditions of several asymptotic states and hence fates of humanity and
planet. These include a sustainable co-evolution of nature and society, a
global collapse and everlasting oscillations. We consider scenarios
corresponding to different socio-cultural stages of human history. The
necessity of accounting for the "human factor" in Earth system models is
highlighted by the fact that carbon stocks during the past centuries evolved
opposing to what would "naturally" be expected on a planet without humans. The
intensity of biomass use and the contribution of ecosystem services to human
well-being are found to be crucial determinants of the asymptotic state in a
biomass-only scenario. The capitalistic, fossil-based scenario reveals that
trajectories with fundamentally different asymptotic states might still be
almost indistinguishable during a very long transient phase. Given current
population levels, our study also supports the claim that besides reducing the
global demand for energy, only the extensive use of renewable energies may pave
the way into a sustainable future.


  We prove that a connected locally compact median space of finite rank which
admits a transitive action is isometric to $\mathbb{R}^n$ endowed with the
$\ell^1$-metric. In the other side, replacing the transitivity assumption on
the group of isometries by a certain regularity of the action on the
compactification of the space, we show that all orbits are discrete. In our way
to prove these results, we give a characterization of the compactness in
complete median spaces of finite rank by the combinatorics of their halfspaces.


  Pipe dreams and bumpless pipe dreams for vexillary permutations are each
known to be in bijection with certain semistandard tableaux via maps due to
Lenart and Weigandt, respectively. Recently, Gao and Huang have defined a
bijection between the former two sets. In this note we show for vexillary
permutations that the Gao-Huang bijection preserves the associated tableaux,
giving a new proof of Lenart's result. Our methods extend to give a recording
tableau for any bumpless pipe dream.


  Injective resolutions of modules are key objects of homological algebra,
which are used for the computation of derived functors. Semiinjective
resolutions of chain complexes are more general objects, which are used for the
computation of $\operatorname{Hom}$ spaces in the derived category
$\mathscr{D}( A )$ of a ring $A$. Minimal semiinjective resolutions have the
additional property of being unique.
  The $Q$-shaped derived category $\mathscr{D}_Q( A )$ consists of $Q$-shaped
diagrams for a suitable preadditive category $Q$, and it generalises
$\mathscr{D}( A )$. Some special cases of $\mathscr{D}_Q( A )$ are the derived
categories of differential modules, $m$-periodic chain complexes, and
$N$-complexes, and there are many other possibilities. The category
$\mathscr{D}_Q( A )$ shares some key properties of $\mathscr{D}( A )$; for
instance, it is triangulated and compactly generated.
  This paper establishes a theory of minimal semiinjective resolutions in
$\mathscr{D}_Q( A )$. As a sample application, it generalises a theorem by
Ringel--Zhang on differential modules.


  We consider nonnegative r-potent matrices with finite dimensions and study
their decomposability. We derive the precise conditions under which an r-potent
matrix is decomposable. We further determine a general structure for the
r-potent matrices based on their decomposability. Finally, we establish that
semigroups of r-potent matrices are also decomposable.


  We evaluate the correlation function of the spectral staircase and use it to
evaluate the mesoscopic particle number fluctuations in integrable systems.


  This is a continuation of [15, 16]. We shall show that for type D_n the
realization of crystal bases obtained from the decorated geometric crystals in
[2] coincides with the polyhedral realizations of crystal bases.


  The $O(3)$ non-linear sigma model (NLSM) is a prototypical field theory for
QCD and ferromagnetism, and provides a simple system in which to study
topological effects. In lattice QCD, the gradient flow has been demonstrated to
remove ultraviolet singularities from the topological susceptibility. In
contrast, lattice simulations of the NLSM find that the topological
susceptibility diverges in the continuum limit, even in the presence of the
gradient flow. We introduce a $\theta$-term and analyze the topological charge
as a function of $\theta$ under the gradient flow. Our results show that
divergence persists in the presence of the flow, even at non-zero $\theta$.


  Encrypted traffic classification is the task of identifying the application
or service associated with encrypted network traffic. One effective approach
for this task is to use deep learning methods to encode the raw traffic bytes
directly and automatically extract features for classification (byte-based
models). However, current byte-based models input raw traffic bytes, whether
plaintext or encrypted text, for automated feature extraction, neglecting the
distinct impacts of plaintext and encrypted text on downstream tasks.
Additionally, these models primarily focus on improving classification
accuracy, with little emphasis on the efficiency of models. In this paper, for
the first time, we analyze the impact of plaintext and encrypted text on the
model's effectiveness and efficiency. Based on our observations and findings,
we propose a two-phase approach to balance the trade-off between plaintext and
encrypted text in traffic classification. Specifically, Stage one is to
Determine whether the Plain text is enough to be accurately Classified (DPC)
using the proposed DPC Selector. This stage quickly identifies samples that can
be classified using plaintext, leveraging explicit byte features in plaintext
to enhance model's efficiency. Stage two aims to adaptively make a
classification with the result from stage one. This stage incorporates
encrypted text information for samples that cannot be classified using
plaintext alone, ensuring the model's effectiveness on traffic classification
tasks. Experiments on two datasets demonstrate that our proposed model achieves
state-of-the-art results in both effectiveness and efficiency.


  $Aims$: We revisit with new augmented accuracy the theoretical dynamics of
basic isotope exchange reactions involved in the $^{12}$C/$^{13}$C,
$^{16}$O/$^{18}$O, and $^{14}$N/$^{15}$N balance because these reactions have
already been studied experimentally in great detail. $Methods$: Electronic
structure methods were employed to explore potential energy surfaces,
full-dimensional rovibrational calculations to compute rovibrational energy
levels that are numerically exact, and chemical network models to estimate the
abundance ratios under interstellar conditions. $Results$: New exothermicities,
derived for HCO$^+$ reacting with CO, provide rate coefficients markedly
different from previous theoretical values in particular at low temperatures,
resulting in new abundance ratios relevant for carbon chemistry networks. In
concrete terms, we obtain a reduction in the abundance of H$^{12}$C$^{18}$O$^+$
and an increase in the abundance of H$^{13}$C$^{16}$O$^+$ and
D$^{13}$C$^{16}$O$^+$. In all studied cases, the reaction of the ion with a
neutral polarizable molecule proceeds through the intermediate proton-bound
complex found to be very stable. For the complexes OCH$^+$...CO, OCH$^+$...OC,
COHOC$^+$, N$_2$...HCO$^+$, N$_2$H$^+$...OC, and N$_2$HN$_2^+$, we also
calculated vibrational frequencies and dissociation energies. $Conclusions$:
The linear proton-bound complexes possess sizeable dipole moments, which may
facilitate their detection.


  We construct an explicit algebraic example of a subshift of finite type over
a group $\Gamma$ with an invariant Markov measure which has completely positive
sofic entropy (with respect to `most' sofic approximations) and yet does not
have a direct Bernoulli factor, because its model spaces shatter into
exponentially many clusters of sub-exponential size. The example and its
analysis are related to random low-density parity-check (LDPC) codes.


  Stochastic motion of particles in a highly unstable potential generates a
number of diverging trajectories leading to undefined statistical moments of
the particle position. This makes experiments challenging and breaks down a
standard statistical analysis of unstable mechanical processes and their
applications. A newly proposed approach takes advantage of the local
characteristics of the most probable particle motion instead of the divergent
averages. We experimentally verify its theoretical predictions for a Brownian
particle moving near an inflection in a highly unstable cubic optical
potential. The most-likely position of the particle atypically shifts against
the force despite the trajectories diverge in the opposite direction. The local
uncertainty around the most-likely position saturates even for strong diffusion
and enables well-resolved position detection. Remarkably, the measured particle
distribution quickly converges to the quasi-stationary one with the same
atypical shift for different initial particle positions. The demonstrated
experimental confirmation of the theoretical predictions approves the utility
of local characteristics for highly unstable systems which can be exploited in
thermodynamic processes to uncover energetics of unstable systems.


  First of all, we prove that open mappings in Orlicz-Sobolev classes
$W^{1,\phi}_{\rm loc}$ under the Calderon type condition on $\phi$ have the
total differential a.e. that is a generalization of the well-known theorems of
Gehring-Lehto-Menchoff in the plane and of V\"ais\"al\"a in ${\Bbb R}^n$,
$n\geqslant3$. Under the same condition on $\phi$, we show that continuous
mappings $f$ in $W^{1,\phi}_{\rm loc}$, in particular, $f\in W^{1,p}_{\rm loc}$
for $p>n-1$ have the $(N)$-property by Lusin on a.e. hyperplane. Our examples
demonstrate that the Calderon type condition is not only sufficient but also
necessary for this and, in particular, there exist homeomorphisms in
$W^{1,n-1}_{\rm loc}$ which have not the $(N)$-property with respect to the
$(n-1)$-dimensional Hausdorff measure on a.e. hyperplane. It is proved on this
base that under this condition on $\phi$ the homeomorphisms $f$ with finite
distortion in $W^{1,\phi}_{\rm loc}$ and, in particular, $f\in W^{1,p}_{\rm
loc}$ for $p>n-1$ are the so-called lower $Q$-homeomorphisms where $Q(x)$ is
equal to its outer dilatation $K_f(x)$ as well as the so-called ring
$Q_*$-homeomorphisms with $Q_*(x)=[K_{f}(x)]^{n-1}$. This makes possible to
apply our theory of the local and boundary behavior of the lower and ring
$Q$-homeomorphisms to homeomorphisms with finite distortion in the
Orlicz-Sobolev classes.


  We introduce PHFL, a probabilistic extension of higher-order fixpoint logic,
which can also be regarded as a higher-order extension of probabilistic
temporal logics such as PCTL and the $\mu^p$-calculus. We show that PHFL is
strictly more expressive than the $\mu^p$-calculus, and that the PHFL
model-checking problem for finite Markov chains is undecidable even for the
$\mu$-only, order-1 fragment of PHFL. Furthermore the full PHFL is far more
expressive: we give a translation from Lubarsky's $\mu$-arithmetic to PHFL,
which implies that PHFL model checking is $\Pi^1_1$-hard and $\Sigma^1_1$-hard.
As a positive result, we characterize a decidable fragment of the PHFL
model-checking problems using a novel type system.


  The standard paired-sample testing approach in the multidimensional setting
applies multiple univariate tests on the individual features, followed by
p-value adjustments. Such an approach suffers when the data carry numerous
features. A number of studies have shown that classification accuracy can be
seen as a proxy for two-sample testing. However, neither theoretical
foundations nor practical recipes have been proposed so far on how this
strategy could be extended to multidimensional paired-sample testing. In this
work, we put forward the idea that scoring functions can be produced by the
decision rules defined by the perpendicular bisecting hyperplanes of the line
segments connecting each pair of instances. Then, the optimal scoring function
can be obtained by the pseudomedian of those rules, which we estimate by
extending naturally the Hodges-Lehmann estimator. We accordingly propose a
framework of a two-step testing procedure. First, we estimate the bisecting
hyperplanes for each pair of instances and an aggregated rule derived through
the Hodges-Lehmann estimator. The paired samples are scored by this aggregated
rule to produce a unidimensional representation. Second, we perform a Wilcoxon
signed-rank test on the obtained representation. Our experiments indicate that
our approach has substantial performance gains in testing accuracy compared to
the traditional multivariate and multiple testing, while at the same time
estimates each feature's contribution to the final result.


  In this talk I review the connections between Feynman integrals and multiple
polylogarithms. After an introductory section on loop integrals I discuss the
Mellin-Barnes transformation and shuffle algebras. In a subsequent section
multiple polylogarithms are introduced. Finally, I discuss how certain Feynman
integrals evaluate to multiple polylogarithms.


  We discuss the extension of the matrix element method (MEM) to
Next-to-Leading Order (NLO) in perturbation theory. In particular we focus on
the production of a Standard Model Higgs boson which decays into four leptons.


  Charged lepton flavor violation (cLFV) processes, potentially important for
various Beyond the Standard Model Physics scenarios are analyzed in the
Standard Model Effective Field Theory (SMEFT) framework. We consider the most
relevant 2 quark-2 lepton $(2q2\ell)$ operators for the leptonic and
semi-leptonic LFV B-decay (LFVBD) processes $B_s\to \mu^+e^- , B^+\to
K^+\mu^+e^-, B^0\to K^{*0}\mu^+ e^-, {\rm and}~ B_s\to \phi\mu^-e^+$. We
analyse the interplay among the Wilson coefficients responsible for these
LFVBDs and other cLFV processes like $\rm CR (\mu\to e)$, $\ell_i \to \ell_j
\gamma$, $\ell_i \to\ell_j\ell_k\ell_m$ and $Z \to \ell_i \ell_j$, to find the
maximal possible LFV effects in $B$-meson decays. We probe the scale of new
physics in relation to the constraints imposed by both classes of the LFV
decays while considering both the present bounds and future expectations. In
view of proposed experiments at LHCb-II and Belle II to study charged LFV
processes, we have also provided the upper limits on the indirect constraints
on such LFVBDs. For the processes where $B$ meson is decaying to $\mu^{\pm}$
and $e^{\mp}$, we show that new physics can be constrained by an enhancement of
2-4 orders of magnitude on the current sensitivities of the BRs of $B^+\to
K^+\mu^+e^-, B^0\to K^{*0}\mu^+ e^- {\rm and}~ B_s\to\phi\mu^{\pm}e^{\mp}$.


  Experimental evaluation is a major research methodology for investigating
clustering algorithms and many other machine learning algorithms. For this
purpose, a number of benchmark datasets have been widely used in the literature
and their quality plays a key role on the value of the research work. However,
in most of the existing studies, little attention has been paid to the
properties of the datasets and they are often regarded as black-box problems.
For example, it is common to use datasets intended for classification in
clustering research and assume class la-bels as the ground truth for judging
the quality of cluster-ing. In our work, with the help of advanced
visualization and dimension reduction techniques, we show that this practice
may seriously compromise the research quality and produce misleading results.
We suggest that the applicability of existing benchmark datasets should be
carefully revisited and significant efforts need to be devoted to improving the
current practice of experimental evaluation of clustering algorithms to ensure
an essential match between algorithms and problems.


  The microscopic transport model UrQMD and a micro+macro hybrid model are used
to calculate direct photon spectra from U+U-collisions at Elab = 35 AGeV as
will be measured by the CBM-collaboration at FAIR. In the hybrid model, the
intermediate high-density part of the nuclear interaction is described with
ideal 3+1-dimensional hydrodynamics. Different equations of state of the matter
created in the heavy-ion collisions are investigated and the resulting spectra
of direct photons are predicted. The emission patterns of direct photons in
space and time are discussed.


  We consider the one-dimensional nonlinear Schr\"odinger equation with
focusing, power nonlinearity, and a repulsive delta potential. We show that if
the potential is not too strong, the construction by Nguy\~{\^e}n (2019) of
solutions converging strongly at time infinity to a pair of logarithmically
separating solitons can be adapted to accommodate the effect of the potential.
On the other hand, we show that if the potential is stronger, no such solutions
exist.


  The paper contains two results pointing to the lack of symmetry between
measure and category.
  Assume CH. There exists a strongly meager subset of the Cantor set that can
be mapped onto the Cantor set by a uniformly continuous function. (It is well
known that uniformly continuous image of a strongly null set is strongly null).
  A ZFC version of this result is also given.


  Hybrid beamforming is known to be a cost-effective and wide-spread solution
for a system with large-scale antenna arrays. This work studies the
optimization of the analog and digital components of the hybrid beamforming
solution for remote radio heads (RRHs) in a downlink cloud radio access network
(C-RAN) architecture. Digital processing is carried out at a baseband
processing unit (BBU) in the "cloud" and the precoded baseband signals are
quantized prior to transmission to the RRHs via finite-capacity fronthaul
links. In this system, we consider two different channel state information
(CSI) scenarios: 1) ideal CSI at the BBU 2) imperfect effective CSI.
Optimization of digital beamforming and fronthaul quantization strategies at
the BBU as well as analog radio frequency (RF) beamforming at the RRHs is a
coupled problem, since the effect of the quantization noise at the receiver
depends on the precoding matrices. The resulting joint optimization problem is
examined with the goal of maximizing the weighted downlink sum-rate and the
network energy efficiency. Fronthaul capacity and per-RRH power constraints are
enforced along with constant modulus constraint on the RF beamforming matrices.
For the case of perfect CSI, a block coordinate descent scheme is proposed
based on the weighted minimum-mean-square-error approach by relaxing the
constant modulus constraint of the analog beamformer. Also, we present the
impact of imperfect CSI on the weighted sum-rate and network energy efficiency
performance, and the algorithm is extended by applying the sample average
approximation. Numerical results confirm the effectiveness of the proposed
scheme and show that the proposed algorithm is robust to estimation errors.


  In the past few years, neural architecture search (NAS) has become an
increasingly important tool within the deep learning community. Despite the
many recent successes of NAS, however, most existing approaches operate within
highly structured design spaces, and hence explore only a small fraction of the
full search space of neural architectures while also requiring significant
manual effort from domain experts. In this work, we develop techniques that
enable efficient NAS in a significantly larger design space. To accomplish
this, we propose to perform NAS in an abstract search space of program
properties. Our key insights are as follows: (1) the abstract search space is
significantly smaller than the original search space, and (2) architectures
with similar program properties also have similar performance; thus, we can
search more efficiently in the abstract search space. To enable this approach,
we also propose a novel efficient synthesis procedure, which accepts a set of
promising program properties, and returns a satisfying neural architecture. We
implement our approach, $\alpha$NAS, within an evolutionary framework, where
the mutations are guided by the program properties. Starting with a ResNet-34
model, $\alpha$NAS produces a model with slightly improved accuracy on CIFAR-10
but 96% fewer parameters. On ImageNet, $\alpha$NAS is able to improve over
Vision Transformer (30% fewer FLOPS and parameters), ResNet-50 (23% fewer
FLOPS, 14% fewer parameters), and EfficientNet (7% fewer FLOPS and parameters)
without any degradation in accuracy.


  Emergency navigation algorithms direct evacuees to exits when disastrous
events such as fire take place. Due to the spread of hazards, latency in
information updating and unstable flows of civilians, emergency evacuation is
absolutely a complex transshipment problem involving numerous sources and
multiple destinations. Previous algorithms which commonly need either a full
graph search or a convergence process suffer from high computational and
communication overheads. This research report surveys the current emergency
navigation algorithms and adapts the concept of Cognitive Packet Network (CPN)
to the context of emergency evacuation. By using random neural networks, the
CPN based algorithm can explore optimal routes rapidly and adaptively in a
highly dynamic emergency environment with low expense. Simultaneously, in
emergency situations there are typically different categories of evacuees such
as people of different age groups. However, current algorithms only consider
"normal" evacuees and do not meet the specific requirements of diverse
evacuees. Our algorithms make use of the flexibility of CPN which can operate
with different user-defined goals to customize appropriate paths for each
category. The CPN algorithm is simulated in a graph based discrete-event
simulator and Dijkstra's shortest path algorithm is taken as reference. The
results show that the CPN algorithm reaches the performance of ideal
path-finding algorithm and quality of service is improved by using specific
goal functions for diverse categories of evacuees. Finally, we present a future
plan for further research.


  We prove a Smith-type inequality for regular covering spaces in monopole
Floer homology. Using the monopole Floer / Heegaard Floer correspondence, we
deduce that if a 3-manifold Y admits a p^n-sheeted regular cover that is a
Z/pZ-L-space (for p prime), then Y is a Z/pZ-L-space. Further, we obtain
constraints on surgeries on a knot being regular covers over other surgeries on
the same knot, and over surgeries on other knots.


  Galaxy clusters are the most massive virialized structures in the Universe
and are formed through the gravitational accretion of matter over cosmic time.
The discovery of an evolved galaxy cluster at redshift z=2, corresponding to a
look-back time of 10.4 billion years, provides an opportunity to study its
properties. The galaxy cluster XLSSC 122 was originally detected as a faint,
extended X-ray source in the XMM Large Scale Structure survey and was revealed
to be coincident with a compact over-density of galaxies with photometric
redshifts of 1.9 +/- 0.2. Subsequent observations at millimetre wavelengths
detected a Sunyaev-Zel'dovich decrement along the line of sight to XLSSC 122,
thus confirming the existence of hot intracluster gas, while deep imaging
spectroscopy from the European Space Agency's X-ray Multi-Mirror Mission
(XMM-Newton) revealed an extended, X-ray bright gaseous atmosphere with a
virial temperature of 60 million Kelvin, enriched with metals to the same
extent as are local clusters. Here we report rest frame optical spectroscopic
observations of XLSSC 122 and identify 37 member galaxies at a mean redshift of
1.98, corresponding to a look-back time of 10.4 billion years. We use
photometry to determine a mean, dust-free stellar age of 2.98 billion years,
indicating that star formation commenced in these galaxies at a mean redshift
of 12, when the Universe was only 370 million years old. The full range of
inferred formation redshifts, including the effects of dust, covers the
interval from 7 to 13. These observations confirm that XLSSC 122 is a
remarkably mature galaxy cluster with both evolved stellar populations in the
member galaxies and a hot, metal-rich gas composing the intracluster medium.


  Traceability, security and freshness monitoring are crucial to the food and
pharmaceutical industries. Currently, barcodes and sensors are almost
exclusively located on product packaging. Making them edible and introducing
them into edible products could significantly enhance their functions. Here,
several types of microlasers made entirely out of edible substances were
developed. It is striking that olive oil already contains enough chlorophyll to
be used as a laser when dispersed in water as droplets. The edible lasers can
be embedded directly into edible products and serve as barcodes and sensors.
Due to their much narrower spectral lines compared to fluorescent or
color-changing sensors, they are significantly more sensitive to various
environmental factors. The edible lasers were employed to sense sugar
concentration, pH, the presence of bacteria, and exposure to too-high
temperatures. They can also encode tens of data bits, such as manufacturer's
information and expiration date. The microlasers are entirely safe for
consumption, do not change the appearance and taste of food considerably, and
are environmentally friendly. The developed barcodes and sensors could also be
applied to non-edible items, such as cosmetic and agricultural products, for
environmental monitoring and biomedical applications.


  In this paper we propose a method to construct logarithmic signatures which
are not amalgamated transversal and further do not even have a periodic block.
The latter property was crucial for the successful attack on the system MST3 by
Blackburn et al. [1]. The idea for our construction is based on the theory in
Szab\'o's book about group factorizations [12].


  Analysis of the observations of the SOL2001-12-26 event related to
ground-level-event GLE63, including microwave spectra and images from NoRH at
17 and 34 GHz, SSRT at 5.7 GHz, and TRACE in 1600 \AA\ has led to the following
results. A flare ribbon overlapped with the sunspot umbra, which is typical of
large particle events. Atypical were: i) long duration of the flare of more
than one hour; ii) moderate intensity of a microwave burst, about $10^4$ sfu;
iii) low peak frequency of the gyrosynchrotron spectrum, around 6 GHz; and its
insensitivity to the flux increase by more than one order of magnitude. This
was accompanied by a nearly constant ratio of the flux emitted by the volume in
the high-frequency part of the spectrum to its elevated low-frequency part
determined by the area of the source. With the self-similarity of the spectrum,
a similarity was observed between the moving microwave sources and the
brightest parts of the flare ribbons in 1600 \AA. Comparison of the 17 GHz and
1600 \AA\ images has confirmed that the microwave sources were associated with
multiple flare loops, whose footpoints appeared in ultraviolet as intermittent
bright kernels. To understand the properties of the event, we simulated its
microwave emission using a system of several homogeneous gyrosynchrotron
sources above the ribbons. The scatter between the spectra and sizes of the
individual sources is determined by the inhomogeneity of the magnetic field
within the ribbons. The microwave flux is mainly governed by the magnetic flux
passing through the ribbons and the sources. An apparent simplicity of
microwave structures is caused by a poorer spatial resolution and dynamic range
of the microwave imaging. The results indicate that microwave manifestations of
accelerated electrons correspond to the structures observed in thermal
emissions, as well-known models predict.


  We solve the Symmetrized Principal Minor Assignment Problem, that is we show
how to determine if for a given vector $v\in \mathbb{C}^{n}$ there is an
$n\times n$ matrix that has all $i\times i$ principal minors equal to $v_{i}$.
We use a special isomorphism (a non-linear change of coordinates to cycle-sums)
that simplifies computation and reveals hidden structure. We use the symmetries
that preserve symmetrized principal minors and cycle-sums to treat 3 cases:
symmetric, skew-symmetric and general square matrices. We describe the matrices
that have such symmetrized principal minors as well as the ideal of relations
among symmetrized principal minors / cycle-sums. We also connect the resulting
algebraic varieties of symmetrized principal minors to tangential and secant
varieties, and Eulerian polynomials.


  Robotic surgery has been proven to offer clear advantages during surgical
procedures, however, one of the major limitations is obtaining haptic feedback.
Since it is often challenging to devise a hardware solution with accurate force
feedback, we propose the use of "visual cues" to infer forces from tissue
deformation. Endoscopic video is a passive sensor that is freely available, in
the sense that any minimally-invasive procedure already utilizes it. To this
end, we employ deep learning to infer forces from video as an attractive
low-cost and accurate alternative to typically complex and expensive hardware
solutions. First, we demonstrate our approach in a phantom setting using the da
Vinci Surgical System affixed with an OptoForce sensor. Second, we then
validate our method on an ex vivo liver organ. Our method results in a mean
absolute error of 0.814 N in the ex vivo study, suggesting that it may be a
promising alternative to hardware based surgical force feedback in endoscopic
procedures.


  We study the limitations to the relative number squeezing between photons and
atoms coupled out from a homogeneous Bose-Einstein-Condensate. We consider the
coupling between the translational atomic states by two photon Bragg processes,
with one of the photon modes involved in the Bragg process in a coherent state,
and the other initially unpopulated. We start with an interacting Bose-
condensate at zero temperature and compute the time evolution for the system.
We study the squeezing, i.e. the variance of the occupation number difference
between the second photon and the atomic c.m. mode. We discuss how collisions
between the atoms and photon rescattering affect the degree of squeezing which
may be reached in such experiments.


  As the fourth stage of the project multi-indexed orthogonal polynomials, we
present the multi-indexed Meixner and little $q$-Jacobi (Laguerre) polynomials
in the framework of `discrete quantum mechanics' with real shifts defined on
the semi-infinite lattice in one dimension. They are obtained, in a similar way
to the multi-indexed Laguerre and Jacobi polynomials reported earlier, from the
quantum mechanical systems corresponding to the original orthogonal polynomials
by multiple application of the discrete analogue of the Darboux transformations
or the Crum-Krein-Adler deletion of virtual state vectors. The virtual state
vectors are the solutions of the matrix Schr\"odinger equation on all the
lattice points having negative energies and infinite norm. This is in good
contrast to the ($q$-)Racah systems defined on a finite lattice, in which the
`virtual state' vectors satisfy the matrix Schr\"odinger equation except for
one of the two boundary points.


  We explore the build-up of stellar mass in galaxies over a wide redshift
range 0.4 < z < 5.0 by studying the evolution of the specific star formation
rate (SSFR), defined as the star formation rate per unit stellar mass, as a
function of stellar mass and age. Our work is based on a combined sample of ~
9000 galaxies from the FORS Deep Field and the GOODS-S field, providing high
statistical accuracy and relative insensitivity against cosmic variance. As at
lower redshifts, we find that lower-mass galaxies show higher SSFRs than higher
mass galaxies, although highly obscured galaxies remain undetected in our
sample. Furthermore, the highest mass galaxies contain the oldest stellar
populations at all redshifts, in principle agreement with the existence of
evolved, massive galaxies at 1 < z < 3. It is remarkable, however, that this
trend continues to very high redshifts of z ~ 4. We also show that with
increasing redshift the SSFR for massive galaxies increases by a factor of ~
10, reaching the era of their formation at z ~ 2 and beyond. These findings can
be interpreted as evidence for an early epoch of star formation in the most
massive galaxies, and ongoing star-formation activity in lower mass galaxies.


  In estimation of a normal mean matrix under the matrix quadratic loss, we
develop a general formula for the matrix quadratic risk of orthogonally
invariant estimators. The derivation is based on several formulas for matrix
derivatives of orthogonally invariant functions of matrices. As an application,
we calculate the matrix quadratic risk of a singular value shrinkage estimator
motivated by Stein's proposal for improving on the Efron--Morris estimator 50
years ago.


  In this work, we study the impact of a relay node to a network with a finite
number of users-sources and a destination node. We assume that the users have
saturated queues and the relay node does not have packets of its own; we have
random access of the medium and the time is slotted. The relay node stores a
source packet that it receives successfully in its queue when the transmission
to the destination node has failed. The relay and the destination nodes have
multi-packet reception capabilities. We obtain analytical equations for the
characteristics of the relay's queue such as average queue length, stability
conditions etc. We also study the throughput per user and the aggregate
throughput for the network.


  Consider a family of Boolean models, indexed by integers $n \ge 1$, where the
$n$-th model features a Poisson point process in ${\mathbb{R}}^n$ of intensity
$e^{n \rho_n}$ with $\rho_n \to \rho$ as $n \to \infty$, and balls of
independent and identically distributed radii distributed like $\bar X_n
\sqrt{n}$, with $\bar X_n$ satisfying a large deviations principle. It is shown
that there exist three deterministic thresholds: $\tau_d$ the degree threshold;
$\tau_p$ the percolation threshold; and $\tau_v$ the volume fraction threshold;
such that asymptotically as $n$ tends to infinity, in a sense made precise in
the paper: (i) for $\rho < \tau_d$, almost every point is isolated, namely its
ball intersects no other ball; (ii) for $\tau_d< \rho< \tau_p$, almost every
ball intersects an infinite number of balls and nevertheless there is no
percolation; (iii) for $\tau_p< \rho< \tau_v$, the volume fraction is 0 and
nevertheless percolation occurs; (iv) for $\tau_d< \rho< \tau_v$, almost every
ball intersects an infinite number of balls and nevertheless the volume
fraction is 0; (v) for $\rho > \tau_v$, the whole space covered. The analysis
of this asymptotic regime is motivated by related problems in information
theory, and may be of interest in other applications of stochastic geometry.


  Sparse coding provides a versatile framework for efficiently capturing and
representing crucial data (information) concisely, which plays an essential
role in various computer science fields, including data compression, feature
extraction, and general signal processing. In this study, we propose a
symmetric quantum neural network for realizing sparse coding and decoding
algorithms. Our networks consist of multi-layer, two-level unitary
transformations that are naturally suited for optical circuits. Each gate is
described by two real parameters, corresponding to reflectivity and phase
shift. Specifically, the two networks can be efficiently trained together or
separately using a quantum natural gradient descent algorithm, either
simultaneously or independently. Utilizing the trained model, we achieve sparse
coding and decoding of binary and grayscale images in classical problems, as
well as that of complex quantum states in quantum problems separately. The
results demonstrate an accuracy of 98.77\% for image reconstruction and a
fidelity of 97.68\% for quantum state revivification. Our quantum sparse coding
and decoding model offers improved generalization and robustness compared to
the classical model, laying the groundwork for widespread practical
applications in the emerging quantum era.


  We describe limits of line bundles on nodal curves in terms of toric
arrangements associated to Voronoi tilings of Euclidean spaces. These tilings
encode information on the relationship between the possibly infinitely many
limits, and ultimately give rise to a new definition of limit linear series.
This paper and its second and third companion parts are the first in a series
aimed to explore this new approach.
  In the present article, we set up the combinatorial framework and show how
graphs with integer lengths associated to the edges provide tilings of
Euclidean spaces by certain polytopes associated to the graph itself and to
certain of its subgraphs. We further provide a description of the combinatorial
structure of these polytopes and the way they are glued together in the tiling.
  In the second part of the series, we describe the arrangements of toric
varieties associated to these tilings. These results will be of use in the
third part to achieve our goal of describing all stable limits of a family of
line bundles along a degenerating family of curves.


  This paper aims to learn a domain-generalizable (DG) person re-identification
(ReID) representation from large-scale videos \textbf{without any annotation}.
Prior DG ReID methods employ limited labeled data for training due to the high
cost of annotation, which restricts further advances. To overcome the barriers
of data and annotation, we propose to utilize large-scale unsupervised data for
training. The key issue lies in how to mine identity information. To this end,
we propose an Identity-seeking Self-supervised Representation learning (ISR)
method. ISR constructs positive pairs from inter-frame images by modeling the
instance association as a maximum-weight bipartite matching problem. A
reliability-guided contrastive loss is further presented to suppress the
adverse impact of noisy positive pairs, ensuring that reliable positive pairs
dominate the learning process. The training cost of ISR scales approximately
linearly with the data size, making it feasible to utilize large-scale data for
training. The learned representation exhibits superior generalization ability.
\textbf{Without human annotation and fine-tuning, ISR achieves 87.0\% Rank-1 on
Market-1501 and 56.4\% Rank-1 on MSMT17}, outperforming the best supervised
domain-generalizable method by 5.0\% and 19.5\%, respectively. In the
pre-training$\rightarrow$fine-tuning scenario, ISR achieves state-of-the-art
performance, with 88.4\% Rank-1 on MSMT17. The code is at
\url{https://github.com/dcp15/ISR_ICCV2023_Oral}.


  The use of deep neural networks to make high risk decisions creates a need
for global and local explanations so that users and experts have confidence in
the modeling algorithms. We introduce a novel technique to find global and
local explanations for time series data used in binary classification machine
learning systems. We identify the most salient of the original features used by
a black box model to distinguish between classes. The explanation can be made
on categorical, continuous, and time series data and can be generalized to any
binary classification model. The analysis is conducted on time series data to
train a long short-term memory deep neural network and uses the time dependent
structure of the underlying features in the explanation. The proposed technique
attributes weights to features to explain an observations risk of belonging to
a class as a multiplicative factor of a base hazard rate. We use a variation of
the Cox Proportional Hazards regression, a Generalized Additive Model, to
explain the effect of variables upon the probability of an in-class response
for a score output from the black box model. The covariates incorporate time
dependence structure in the features so the explanation is inclusive of the
underlying time series data structure.


  We propose a Lagrangian for the low-energy theory that resides at the
(1+1)-dimensional intersection of N semi-infinite M2-branes ending orthogonally
on M M5-branes in ${\mathbb R}^{1,2} \times {\mathbb C}^4/{\mathbb Z}_k$ (for
arbitrary positive integers N,M,k). We formulate this theory as a 2d boundary
theory with explicit ${\cal N}=(1,1)$ supersymmetry that contains two
superfields in the bi-fundamental representation of $U(N)\times U(M)$
interacting with the (2+1)-dimensional $U(N)_k\times U(N)_{-k}$ ABJM
Chern-Simons-matter theory in the bulk. We postulate that the boundary theory
exhibits in the deep infrared supersymmetry enhancement to ${\cal N}=(4,2)$, or
${\cal N}=(4,4)$ depending on the value of k. Arguments in favor of the
proposal follow from the study of the open string theory of a U-dual type IIB
Hanany-Witten setup. To formulate the bulk-boundary interactions special care
is taken to incorporate all the expected boundary effects on gauge symmetry,
supersymmetry, and other global symmetries.