  We develop a theory of ordered *-vector spaces with an order unit. We prove
fundamental results concerning positive linear functionals and states, and we
show that the order (semi)norm on the space of self-adjoint elements admits
multiple extensions to an order (semi)norm on the entire space. We single out
three of these (semi)norms for further study and discuss their significance for
operator algebras and operator systems. In addition, we introduce a functorial
method for taking an ordered space with an order unit and forming an
Archimedean ordered space. We then use this process to describe an appropriate
notion of quotients in the category of Archimedean ordered spaces.


  We consider a class of real random polynomials, indexed by an integer d, of
large degree n and focus on the number of real roots of such random
polynomials. The probability that such polynomials have no real root in the
interval [0,1] decays as a power law n^{-\theta(d)} where \theta(d)>0 is the
exponent associated to the decay of the persistence probability for the
diffusion equation with random initial conditions in space dimension d. For n
even, the probability that such polynomials have no root on the full real axis
decays as n^{-2(\theta(d) + \theta(2))}. For d=1, this connection allows for a
physical realization of real random polynomials. We further show that the
probability that such polynomials have exactly k real roots in [0,1] has an
unusual scaling form given by n^{-\tilde \phi(k/\log n)} where \tilde \phi(x)
is a universal large deviation function.


  Relying of properties of the inductive tensor product, we construct cyclic
type homology theories for certain nuclear algebras. In this context we
establish continuity theorems. We compute the periodic cyclic homology of the
Schwartz algebra of p-adic GL(n) in terms of compactly supported de Rham
cohomology of the tempered dual of GL(n).


  Nielsen [quant-ph/0108020] introduced a model of quantum computation by
measurement-based simulation of unitary computations. In this model, a
consequence of the non-determinism of quantum measurement is the probabilistic
termination of simulations. This means that the time when simulation terminates
for a given computation is probabilistic, and this simulation may even never
end.
  We introduce (section 3) a measurement-based model with non probabilistic
termination, which permits, unlike existing models, to predict the time of
termination. This new scheme is a modification of Nielsen's. After an
introduction to Nielsen's scheme (section 1), an analysis of different temporal
organisations of elementary simulations within Nielsen's scheme (section 2)
leads to the non probabilistic model.


  In recent years, structured matrix recovery problems have gained considerable
attention for its real world applications, such as recommender systems and
computer vision. Much of the existing work has focused on matrices with
low-rank structure, and limited progress has been made matrices with other
types of structure. In this paper we present non-asymptotic analysis for
estimation of generally structured matrices via the generalized Dantzig
selector under generic sub-Gaussian measurements. We show that the estimation
error can always be succinctly expressed in terms of a few geometric measures
of suitable sets which only depend on the structure of the underlying true
matrix. In addition, we derive the general bounds on these geometric measures
for structures characterized by unitarily invariant norms, which is a large
family covering most matrix norms of practical interest. Examples are provided
to illustrate the utility of our theoretical development.


  We obtain the non-perturbative effective potential for the dual
five-dimensional N=4 strings in the context of finite-temperature regarded as a
breaking of supersymmetry into four space-time dimensions. Using the properties
of gauged N=4 supergravity we derive the universal thermal effective potential
describing all possible high-temperature instabilities of the known N=4
superstrings. These strings undergo a high-temperature transition to a new
phase in which five-branes condense. This phase is described in detail, using
both the effective supergravity and non-critical string theory in six
dimensions. In the new phase, supersymmetry is perturbatively restored but
broken at the non-perturbative level.


  We review a collection of models of random simplicial complexes together with
some of the most exciting phenomena related to them. We do not attempt to cover
all existing models, but try to focus on those for which many important results
have been recently established rigorously in mathematics, especially in the
context of algebraic topology. In application to real-world systems, the
reviewed models are typically used as null models, so that we take a
statistical stance, emphasizing, where applicable, the entropic properties of
the reviewed models. We also review a collection of phenomena and features
observed in these models, and split the presented results into two classes:
phase transitions and distributional limits. We conclude with an outline of
interesting future research directions.


  In this work, the nutation momentum acting upon the Earth from the Moon's
perigee mass that has not been taken into account in the Earth's
precession-nutation theory was revealed. This missing momentum exhibits itself
in the so-called "local latitude variation" with the Chandler's period. The
results of our work raise the question of updating the Earth's
precession-nutation theory and revising some postulates of the time service,
astronomy, geophysics, satellite navigation, etc.


  In the present note we study determinantal arrangements constructed with use
of the $3$-minors of a $3 \times 5$ generic matrix of indeterminates. In
particular, we show that certain naturally constructed hypersurface
arrangements in $\mathbb{P}^{14}_{\mathbb{C}}$ are free.


  Based on the assumption of two-quark structure for the light scalar mesons,
within the framework of perturbative QCD approach, we investigate the $B_{q}\to
D_{(s)}^{(*)} S(q=u,d,s)$ decays induced by $b\to u $ transition, where $S$
denotes a light scalar meson. Under two different scenarios, we calculate the
branching ratios of 96 decay modes totally, which are in the range of $10^{-5}$
to $10^{-8}$. The comparison between our predictions and the experimental data
will allow us to probe the inner structure of the scalar mesons. In the
standard model, since all decays can only occur through tree operators, there
are no $CP$ asymmetries. From our calculations, it has been shown that the
annihilation type diagrams, especially the nonfactorizable annihilation
diagrams, play important roles in the decay amplitudes, especially for these
color-suppressed and pure annihilation type decay modes. We also find that the
branching ratios of color-allowed type decays are sensitive to the different
scenarios, so the measurements of them will be ideal places to differentiate
the different scenarios. It can be found that the ratios between $Br(B^0\to
D^{(*)0}\sigma)$ and $Br(B^0\to D^{(*)0}f_0)$, and between $Br(B^+\to
D^{(*)+}\sigma)$ and $Br(B^{+}\to D^{(*)+}f_0)$ can be used to determine the
mixing angle of $\sigma$ and $f_0$.


  We investigate the collider phenomenology of a left-right symmetric
Randall-Sundrum model with fermions and gauge bosons in the bulk. We find that
the model is allowed by precision electroweak data as long as the ratio of the
(unwarped) Higgs vev to the curvature scale is $v/k \le 1/4$. In that region
there can be substantial modifications to the Higgs properties. In particular,
the couplings to $WW$ and $ZZ$ are reduced, the coupling to gluons is enhanced,
and the coupling to $\gamma\gamma$ can receive shifts in either direction. The
Higgs mass bound from LEP II data can potentially be relaxed to $m_H \gtrsim
80$ GeV.


  Partially motivated by the study of I. Binder, N. Makarov, and S. Smirnov
[BMS03] on dimension spectra of polynomial Cantor sets, we initiate the
investigation on some general harmonic measures, inspired by Sullivan's
dictionary, for distance-expanding dynamical systems. Let $f\colon X\to X$ be
an open distance-expanding map on a compact metric space $(X,\rho)$. A Gromov
hyperbolic tile graph $\Gamma$ associated to the dynamical system $(X,f)$ is
constructed following the ideas from M. Bonk, D. Meyer [BM17] and P.
Ha\"issinsky, K. M. Pilgrim [HP09]. We consider a class of one-sided random
walks associated with $(X,f)$ on $\Gamma$. They induce a Martin boundary of the
tile graph, which may be different from the hyperbolic boundary. We show that
the Martin boundary of such a random walk admits a surjection to $X$. We
provide a class of examples to show that the surjection may not be a
homeomorphism. Such random walks also induce measures on $X$ called harmonic
measures. When $\rho$ is a visual metric, we establish an equality between the
fractal dimension of the harmonic measure and the asymptotic quantities of the
random walk.


  With the recent discovery of transiting planetary material around WD
1145+017, a critical target has been identified that links the evolution of
planetary systems with debris disks and their accretion onto the star. We
present a series of observations, five epochs over a year, taken with Keck and
the VLT, which for the first time show variability of circumstellar absorption
in the gas disk surrounding WD 1145+017 on timescales of minutes to months.
Circumstellar absorption is measured in more than 250 lines of 14 ions among
ten different elements associated with planetary composition, e.g., O, Mg, Ca,
Ti, Cr, Mn, Fe, Ni. Broad circumstellar gas absorption with a velocity spread
of 225 km/s is detected, but over the course of a year blue shifted absorption
disappears while redshifted absorption systematically increases. A correlation
of equivalent width and oscillator strength indicates that the gas is not
highly optically thick (median tau approximately 2). We discuss simple models
of an eccentric disk coupled with magnetospheric accretion to explain the basic
observed characteristics of these high resolution and high signal-to-noise
observations. Variability is detected on timescales of minutes in the two most
recent observations, showing a loss of redshifted absorption for tens of
minutes, coincident with major transit events and consistent with gas hidden
behind opaque transiting material. This system currently presents a unique
opportunity to learn how the gas causing the spectroscopic, circumstellar
absorption is associated with the ongoing accretion evidenced by photospheric
contamination, as well as the transiting planetary material detected in
photometric observations.


  Federated learning (FL) has emerged as a promising approach to
collaboratively train machine learning models across multiple edge devices
while preserving privacy. The success of FL hinges on the efficiency of
participating models and their ability to handle the unique challenges of
distributed learning. While several variants of Vision Transformer (ViT) have
shown great potential as alternatives to modern convolutional neural networks
(CNNs) for centralized training, the unprecedented size and higher
computational demands hinder their deployment on resource-constrained edge
devices, challenging their widespread application in FL. Since client devices
in FL typically have limited computing resources and communication bandwidth,
models intended for such devices must strike a balance between model size,
computational efficiency, and the ability to adapt to the diverse and non-IID
data distributions encountered in FL. To address these challenges, we propose
OnDev-LCT: Lightweight Convolutional Transformers for On-Device vision tasks
with limited training data and resources. Our models incorporate image-specific
inductive biases through the LCT tokenizer by leveraging efficient depthwise
separable convolutions in residual linear bottleneck blocks to extract local
features, while the multi-head self-attention (MHSA) mechanism in the LCT
encoder implicitly facilitates capturing global representations of images.
Extensive experiments on benchmark image datasets indicate that our models
outperform existing lightweight vision models while having fewer parameters and
lower computational demands, making them suitable for FL scenarios with data
heterogeneity and communication bottlenecks.


  Through multi-agent competition, the simple objective of hide-and-seek, and
standard reinforcement learning algorithms at scale, we find that agents create
a self-supervised autocurriculum inducing multiple distinct rounds of emergent
strategy, many of which require sophisticated tool use and coordination. We
find clear evidence of six emergent phases in agent strategy in our
environment, each of which creates a new pressure for the opposing team to
adapt; for instance, agents learn to build multi-object shelters using moveable
boxes which in turn leads to agents discovering that they can overcome
obstacles using ramps. We further provide evidence that multi-agent competition
may scale better with increasing environment complexity and leads to behavior
that centers around far more human-relevant skills than other self-supervised
reinforcement learning methods such as intrinsic motivation. Finally, we
propose transfer and fine-tuning as a way to quantitatively evaluate targeted
capabilities, and we compare hide-and-seek agents to both intrinsic motivation
and random initialization baselines in a suite of domain-specific intelligence
tests.


  The Kerr-Newman metric is the unique vacuum solution of the General
Relativistic field equations, in which any singularities or spacetime
pathologies are hidden behind horizons. They are believed to describe the
spacetimes of massive astrophysical objects with no surfaces, which we call
black holes. This spacetime, which is defined entirely by the mass, spin, and
charge of the black hole, gives rise to a variety of phenomena in the motion of
particles and photons outside the horizons that have no Newtonian counterparts.
Moreover, the Kerr-Newman spacetime remains remarkably resilient to many
attempts in modifying the underlying theory of gravity. The monitoring of
stellar orbits around supermassive black holes, the detection of gravitational
waves from the coalescence of stellar-mass black holes, and the observation of
black-hole shadows in images with horizon-scale resolution, all of which have
become possible during the last decade, are offering valuable tools in testing
quantitatively the predictions of this remarkable solution to Einstein's
equations.


  The U.S. art museum sector is grappling with diversity. While previous work
has investigated the demographic diversity of museum staffs and visitors, the
diversity of artists in their collections has remained unreported. We conduct
the first large-scale study of artist diversity in museums. By scraping the
public online catalogs of 18 major U.S. museums, deploying a sample of 10,000
artist records comprising over 9,000 unique artists to crowdsourcing, and
analyzing 45,000 responses, we infer artist genders, ethnicities, geographic
origins, and birth decades. Our results are threefold. First, we provide
estimates of gender and ethnic diversity at each museum, and overall, we find
that 85% of artists are white and 87% are men. Second, we identify museums that
are outliers, having significantly higher or lower representation of certain
demographic groups than the rest of the pool. Third, we find that the
relationship between museum collection mission and artist diversity is weak,
suggesting that a museum wishing to increase diversity might do so without
changing its emphases on specific time periods and regions. Our methodology can
be used to broadly and efficiently assess diversity in other fields.


  We present MeerKAT Fornax Survey atomic hydrogen (HI) observations of the
dwarf galaxies located in the central ~2.5 x 4 deg$^2$ of the Fornax galaxy
cluster. The HI images presented in this work have a $3\sigma$ column density
sensitivity between 2.7 and 50 x 10$^{18}$ cm$^{-2}$ over 25 km s$^{-1}$ for
spatial resolution between 4 and 1 kpc. We are able to detect an impressive MHI
= 5 x 10$^{5}$ Msun 3$\sigma$ point source with a line width of 50 km s$^{-1}$
at a distance of 20 Mpc. We detect HI in 17 out of the 304 dwarfs in our field
-- 14 out of the 36 late type dwarfs (LTDs), and 3 of the 268 early type dwarfs
(ETDs). The HI-detected LTDs have likely just joined the cluster and are on
their first infall as they are located at large clustocentric radii, with
comparable MHI and mean stellar surface brightness at fixed luminosity as blue,
star-forming LTDs in the field. The HI-detected ETDs have likely been in the
cluster longer than the LTDs and acquired their HI through a recent merger or
accretion from nearby HI. Eight of the HI-detected LTDs host irregular or
asymmetric HI emission and disturbed or lopsided stellar emission. There are
two clear cases of ram-pressure shaping the HI, with the LTDs displaying
compressed HI on the side closest to the cluster centre and a one-sided,
starless tail pointing away from the cluster centre. The HI-detected dwarfs
avoid the most massive potentials, consistent with massive galaxies playing an
active role in the removal of HI. We create a simple toy model to quantify the
timescale of HI stripping in the cluster. We find that a MHI = 10$^{8}$ Msun
dwarf will be stripped in ~ 240 Myr. The model is consistent with our
observations, where low mass LTDs are directly stripped of their HI from a
single encounter and more massive LTDs can harbour a disturbed HI morphology
due to longer times or multiple encounters being required to fully strip their
HI.


  We consider the one-loop effective action due to gravitons in a FLRW
background with constant epsilon=-(dH/dt)/H^2. By expanding around epsilon=0
(corresponding to an expansion around de Sitter space), we can study how the
deviation from de Sitter space effects the quantum corrected Friedmann
equations. We find that, at zeroth order in epsilon, one-loop effects induce
only a finite shift in the coupling constants. At linear order in epsilon there
is however a divergent contribution to the equations of motion. This
contribution leads to a nontrivial term in the renormalized equations that
depends logarithmically on H and thus cannot be absorbed in local counterterms.
We find that deviations due to this term are unobservably small. Our study
shows that quantum effects in quasi de Sitter space can be fundamentally
different then in de Sitter space, albeit in the case under consideration the
effect is unobservably small.


  We define the representation ring of a saturated fusion system $\mathcal F$
as the Grothendieck ring of the semiring of $\mathcal F$-stable
representations, and study the dimension functions of $\mathcal F$-stable
representations using the transfer map induced by the characteristic idempotent
of $\mathcal F$. We find a list of conditions for an $\mathcal F$-stable super
class function to be realized as the dimension function of an $\mathcal
F$-stable virtual representation. We also give an application of our results to
constructions of finite group actions on homotopy spheres.


  We consider a class of proposed gravitational wave detectors based on
multiple atomic interferometers separated by large baselines and referenced by
common laser systems. We compute the sensitivity limits of these detectors due
to intrinsic phase noise of the light sources, non-inertial motion of the light
sources, and atomic shot noise and compare them to sensitivity limits for
traditional light interferometers. We find that atom interferometers and light
interferometers are limited in a nearly identical way by intrinsic phase noise
and that both require similar mitigation strategies (e.g. multiple arm
instruments) to reach interesting sensitivities. The sensitivity limit from
motion of the light sources is slightly different and favors the atom
interferometers in the low-frequency limit, although the limit in both cases is
severe.


  The pursuit of achieving the maximum power in microscopic thermal engines has
gained increasing attention in recent studies of stochastic thermodynamics. We
employ the optimal control theory to study the performance of Brownian heat
engines and determine the optimal heat-engine cycles in generic damped
situation, which were previously known only in the overdamped and the
underdamped limits. These optimal cycles include two isothermal processes, two
adiabatic processes, and an extra isochoric relaxation process at the upper
stiffness constraint. Our results not only interpolate the optimal cycles
between the overdamped and the underdamped limits, but also determine the
appropriate friction coefficient of the Brownian heat engine to achieve the
maximum power. These findings offer valuable insights for the development of
high-performance Brownian heat engines in experimental setups.


  For any group $G$ and set $A$, a cellular automaton over $G$ and $A$ is a
transformation $\tau : A^G \to A^G$ defined via a finite neighborhood $S
\subseteq G$ (called a memory set of $\tau$) and a local function $\mu : A^S
\to A$. In this paper, we assume that $G$ and $A$ are both finite and study
various algebraic properties of the finite monoid $\text{CA}(G,A)$ consisting
of all cellular automata over $G$ and $A$. Let $\text{ICA}(G;A)$ be the group
of invertible cellular automata over $G$ and $A$. In the first part, using
information on the conjugacy classes of subgroups of $G$, we give a detailed
description of the structure of $\text{ICA}(G;A)$ in terms of direct and wreath
products. In the second part, we study generating sets of $\text{CA}(G;A)$. In
particular, we prove that $\text{CA}(G,A)$ cannot be generated by cellular
automata with small memory set, and, when $G$ is finite abelian, we determine
the minimal size of a set $V \subseteq \text{CA}(G;A)$ such that
$\text{CA}(G;A) = \langle \text{ICA}(G;A) \cup V \rangle$.


  Depth estimation plays an important role in the robotic perception system.
Self-supervised monocular paradigm has gained significant attention since it
can free training from the reliance on depth annotations. Despite recent
advancements, existing self-supervised methods still underutilize the available
training data, limiting their generalization ability. In this paper, we take
two data augmentation techniques, namely Resizing-Cropping and
Splitting-Permuting, to fully exploit the potential of training datasets.
Specifically, the original image and the generated two augmented images are fed
into the training pipeline simultaneously and we leverage them to conduct
self-distillation. Additionally, we introduce the detail-enhanced DepthNet with
an extra full-scale branch in the encoder and a grid decoder to enhance the
restoration of fine details in depth maps. Experimental results demonstrate our
method can achieve state-of-the-art performance on the KITTI benchmark, with
both raw ground truth and improved ground truth. Moreover, our models also show
superior generalization performance when transferring to Make3D and NYUv2
datasets. Our codes are available at https://github.com/Sauf4896/BDEdepth.


  Aptly named, ice giants such as Uranus and Neptune contain significant
amounts of water. While this water cannot be present near the cloud tops, it
must be abundant in the deep interior. We investigate the likelihood of a
liquid water ocean existing in the hydrogen-rich region between the cloud tops
and deep interior. Starting from an assumed temperature at a given upper
tropospheric pressure (the photosphere), we follow a moist adiabat downward.
The mixing ratio of water to hydrogen in the gas phase is small in the
photosphere and increases with depth. The mixing ratio in the condensed phase
is near unity in the photosphere and decreases with depth; this gives two
possible outcomes. If at some pressure level the mixing ratio of water in the
gas phase is equal to that in the deep interior, then that level is the cloud
base. Alternately, if the mixing ratio of water in the condensed phase reaches
that in the deep interior, then the surface of a liquid ocean will occur. We
find that Neptune is both too warm (photospheric temperature too high) and too
dry (mixing ratio of water in the deep interior too low) for liquid oceans to
exist at present. To have a liquid ocean, Neptune's deep interior water to gas
ratio would have to be higher than current models allow, and the density at 19
kbar would have to be ~ 0.8 g/cm^3. Such a high density is inconsistent with
gravitational data obtained during the Voyager flyby. As Neptune cools, the
probability of a liquid ocean increases. Extrasolar "hot Neptunes," which
presumably migrate inward toward their parent stars, cannot harbor liquid water
oceans unless they have lost almost all of the hydrogen and helium from their
deep interiors.


  A broad band X-, gamma-ray spectral study of the Seyfert 2 galaxy NGC 7172 is
presented. We use our ASCA observations from May 1995 and combine these with
the CGRO OSSE data from March 1995. The only Seyfert 2 galaxy previously to
have been modelled over such a broad spectral range is NGC 4945. We find that
the most probable model for the data is an absorbed power law, being affected
by a high energy exponential cut-off. The power law is flat with Gamma = 1.54
\pm 0.13, while N_H = (8.1 \pm 0.6) 10^{22} cm$^{-2}$. An Fe K$\alpha$ emission
line is not required by the fits. The observed flux in the 2-10 keV range is
F_{2-10} = (4.75\pm 0.09) 10^{-11} erg cm$^{-2}$ s$^{-1}$, which corresponds to
a small increase since the Ginga measurement in October 1989. The spectral
index of the underlying power law of NGC 7172 appears actually to have varied
from 1.85 to 1.5 since the Ginga observations in 1989. The e-folding energy is
relatively well constrained and lies at 140 ^{+310} _{-70} keV. We note,
however, that the CGRO OSSE spectral shape appears to be variable on a time
scale of weeks.


  We obtain a new value for the QCD coupling constant by combining lattice QCD
simulations with experimental data for hadron masses. Our lattice analysis is
the first to: 1) include vacuum polarization effects from all three light-quark
flavors (using MILC configurations); 2) include third-order terms in
perturbation theory; 3) systematically estimate fourth and higher-order terms;
4) use an unambiguous lattice spacing; and 5) use an $\order(a^2)$-accurate QCD
action. We use 28~different (but related) short-distance quantities to obtain
$\alpha_{\bar{\mathrm{MS}}}^{(5)}(M_Z) = 0.1170(12)$.


  We derive streamlined mean field variational Bayes algorithms for fitting
linear mixed models with crossed random effects. In the most general situation,
where the dimensions of the crossed groups are arbitrarily large, streamlining
is hindered by lack of sparseness in the underlying least squares system.
Because of this fact we also consider a hierarchy of relaxations of the mean
field product restriction. The least stringent product restriction delivers a
high degree of inferential accuracy. However, this accuracy must be mitigated
against its higher storage and computing demands. Faster sparse storage and
computing alternatives are also provided, but come with the price of diminished
inferential accuracy. This article provides full algorithmic details of three
variational inference strategies, presents detailed empirical results on their
pros and cons and, thus, guides the users on their choice of variational
inference approach depending on the problem size and computing resources.


  The primary tasks of a cognitive system is to survive and to maximize a
life-long utility function, like the number of offsprings. A direct
computational maximization of life-long utility is however not possible in
complex environments, especially in the context, of real-world time
constraints. The central role of emotions is to serve as an intermediate layer
in the space of policies available to agents and animals, leading to a large
dimensional reduction of complexity.
  We review our current understanding of the functional role of emotions,
stressing the role of the neuromodulators mediating emotions for the diffusive
homeostatic control system of the brain. We discuss a recent proposal, that
emotional diffusive control is characterized, in contrast to neutral diffusive
control, by interaction effects, viz by interferences between emotional arousal
and reward signaling. Several proposals for the realization of synthetic
emotions are discussed in this context, together with key open issues regarding
the interplay between emotional motivational drives and diffusive control.


  We have determined detailed radio spectra for 26 compact sources in the
starburst nucleus of M82, between 74 and 1.3 cm. Seventeen show low-frequency
turnovers. One other has a thermal emission spectrum, and we identify it as an
HII region. The low frequency turnovers are due to absorption by the
interstellar gas in M82. New information on the AGN candidate 44.01+595, shows
it to have a non-thermal falling powerlaw spectrum at the highest frequencies,
and that it is strongly absorbed below 2 GHz. We derive large magnetic fields
in the supernova remnants, of order 1-2 milliGauss, hence large pressures in
the sources suggest that the brightest ones are either expanding or are
strongly confined by a dense interstellar medium. From the largest source in
our sample, we derive a supernova rate of 0.016 SN/yr.


  Traditional algorithms of point set registration minimizing point-to-plane
distances often achieve a better estimation of rigid transformation than those
minimizing point-to-point distances. Nevertheless, recent deep-learning-based
methods minimize the point-to-point distances. In contrast to these methods,
this paper proposes the first deep-learning-based approach to point-to-plane
registration. A challenging part of this problem is that a typical solution for
point-to-plane registration requires an iterative process of accumulating small
transformations obtained by minimizing a linearized energy function. The
iteration significantly increases the size of the computation graph needed for
backpropagation and can slow down both forward and backward network
evaluations. To solve this problem, we consider the estimated rigid
transformation as a function of input point clouds and derive its analytic
gradients using the implicit function theorem. The analytic gradient that we
introduce is independent of how the error minimizing function (i.e., the rigid
transformation) is obtained, thus allowing us to calculate both the rigid
transformation and its gradient efficiently. We implement the proposed
point-to-plane registration module over several previous methods that minimize
point-to-point distances and demonstrate that the extensions outperform the
base methods even with point clouds with noise and low-quality point normals
estimated with local point distributions.


  Plasmonic resonance of a metallic nanostructure results from coherent motion
of its conduction electrons driven by incident light. At the resonance, the
induced dipole in the nanostructure is proportional to the number of the
conduction electrons, hence $10^{7}$ times larger than that in an atom. The
interaction energy between the induced dipole and fluctuating virtual field of
the incident light can reach a few tenths of an eV. Therefore, the classical
electromagnetism dominating the field becomes inadequate. We argue that quantum
electrodynamics (QED) should be used instead as the fundamental theory to
describe the virtual field and its interaction with the electrons. Based on
QED, we derive analytic expressions for the plasmonic resonant frequency, which
depends on three easily accessible material parameters. The analytic theory
reproduces very well the experimental data, and can be used for rational design
of materials.


  We demonstrate a real-time transient waveform digitizer with a record 1 TSa/s
(Tera-Sample/sec) sampling rate. This is accomplished by using a photonic time
stretch preprocessor which slows down the electrical waveform before it is
captured by an electronic digitizer.


  We present a dimensional reduction argument to derive the classification
reduction of fermionic symmetry protected topological phases in the presence of
interactions. The dimensional reduction proceeds by relating the topological
character of a $d$-dimensional system to the number of zero-energy bound states
localized at zero-dimensional topological defects present at its surface. This
correspondence leads to a general condition for symmetry preserving
interactions that render the system topologically trivial, and allows us to
explicitly write a quartic interaction to this end. Our reduction shows that
all phases with topological invariant smaller than $n$ are topologically
distinct, thereby reducing the non-interacting $\mathbb{Z}$ classification to
$\mathbb{Z}_n$.


  We study the double-copy relation between classical solutions in gauge theory
and gravity, focusing on four-dimensional vacuum metrics of algebraic type D, a
class that includes several important solutions. We present a double copy of
curvatures that applies to all spacetimes of this type -- the Weyl double copy
-- relating the curvature of the spacetime to an electromagnetic field
strength. We show that the Weyl double copy is consistent with the previously
known Kerr-Schild double copy, and in fact resolves certain ambiguities of the
latter. The most interesting new example of the classical double copy presented
here is that of the C-metric. This well-known solution, which represents a pair
of uniformly accelerated black holes, is mapped to the Lienard-Wiechert
potential for a pair of uniformly accelerated charges. We also present a new
double-copy interpretation of the Eguchi-Hanson instanton.


  The connection between granular gases and sticky gases has recently been
considered, leading to the conjecture that inelastic collapse is avoided for
space dimensions higher than 4. We report Molecular Dynamics simulations of
hard inelastic spheres in dimensions 4, 5 and 6. The evolution of the granular
medium is monitored throughout the cooling process. The behaviour is found to
be very similar to that of a two-dimensional system, with a shearing-like
instability of the velocity field and inelastic collapse when collisions are
inelastic enough, showing that the connection with sticky gases needs to be
revised.


  We study the supersymmetric structure of the spin current in four dimensional
$\mathcal{N}=1$ supersymmetric theories. By coupling the stress tensor
multiplet to a vierbein multiplet we identify a spin current with the Hodge
dual of the bottom component of the stress tensor multiplet in a wide range of
theories. This implies that in holographic theories the Hodge dual of the $R$
current may serve as a spin current, paving the way for holographic studies of
theories with background torsion.


  We introduce a dataset for evidence/rationale extraction on an extreme
multi-label classification task over long medical documents. One such task is
Computer-Assisted Coding (CAC) which has improved significantly in recent
years, thanks to advances in machine learning technologies. Yet simply
predicting a set of final codes for a patient encounter is insufficient as CAC
systems are required to provide supporting textual evidence to justify the
billing codes. A model able to produce accurate and reliable supporting
evidence for each code would be a tremendous benefit. However, a human
annotated code evidence corpus is extremely difficult to create because it
requires specialized knowledge. In this paper, we introduce MDACE, the first
publicly available code evidence dataset, which is built on a subset of the
MIMIC-III clinical records. The dataset -- annotated by professional medical
coders -- consists of 302 Inpatient charts with 3,934 evidence spans and 52
Profee charts with 5,563 evidence spans. We implemented several evidence
extraction methods based on the EffectiveCAN model (Liu et al., 2021) to
establish baseline performance on this dataset. MDACE can be used to evaluate
code evidence extraction methods for CAC systems, as well as the accuracy and
interpretability of deep learning models for multi-label classification. We
believe that the release of MDACE will greatly improve the understanding and
application of deep learning technologies for medical coding and document
classification.


  Due to the broadcast nature of wireless medium, wireless communication is
highly vulnerable to eavesdropping attack. Traditionally, secure wireless data
transmission has relied on cryptographic techniques at the network layer which
incur high computational power and complexity. As an alternative, physical
layer security (PLS) is emerging as a promising paradigm to protect wireless
systems by exploiting the physical characteristics of the wireless channels.
Among various PLS approaches, the one based on cooperative communication is
favorable and has got a lot of interest from the research community. Although
PLS schemes with half-duplex relays have been extensively discovered, the issue
of PLS in cooperative systems with full-duplex (FD) relays is far from being
comprehensively understood. In this paper, we first present the state of the
art on PLS approaches proposed for FD cooperative systems. We then provide a
case study in which a source-based jamming scheme is proposed to enhance the
secrecy performance of a cooperative system with an untrusted FD relay.
Finally, we outline several interesting yet challenging future research
problems in this topic.


  In-plane thermal conductivity of the thermoelectric layered cobalt oxides has
been measured using the Harman method, in which thermal conductivity is
obtained from temperature gradient induced by applied current. We have found
that the charge reservoir block (the block other than the CoO$_2$ block)
dominates the thermal conduction, where a nano-block integration concept is
effective for material design. We have further found that the thermal
conductivity shows a small but finite in-plane anisotropy between $a$ and $b$
axes, which can be ascribed to the misfit structure.


  One of the key challenges towards the reliable operation of cyber-physical
systems (CPS) is the threat of cyberattacks on system actuation signals and
measurements. In recent years, system theoretic research has focused on
effectively detecting and isolating these cyberattacks to ensure proper
restorative measures. Although both model-based and model-free approaches have
been used in this context, the latter are increasingly becoming more popular as
complexities and model uncertainties in CPS increases. Thus, in this paper we
propose a Koopman operator-based model-free cyberattack detection-isolation
scheme for CPS. The algorithm uses limited system measurements for its training
and generates real-time detection-isolation flags. Furthermore, we present a
simulation case study to detect and isolate actuation and sensor attacks in a
Lithium-ion battery system of a plug-in electric vehicle during charging.


  We evaluate exclusive semileptonic decays of ground-state spin-1/2 doubly
heavy charmed baryons. The decays are driven by a $c\to s,d$ transition at the
quark level. Our form factors are consistent with Heavy Quark Symmetry
constraints. The latter are valid in the limit of infinitely heavy quark mass
at zero recoil.


  The unit-derived method in coding theory is shown to be a unique optimal
scheme for constructing and analysing codes. In many cases efficient and
practical decoding methods are produced. Codes with efficient decoding
algorithms at maximal distances possible are derived from unit schemes. In
particular unit-derived codes from Vandermonde or Fourier matrices are
particularly commendable giving rise to mds codes of varying rates with
practical and efficient decoding algorithms. For a given rate and given error
correction capability, explicit codes with efficient error correcting
algorithms are designed to these specifications. An explicit constructive proof
with an efficient decoding algorithm is given for Shannon's theorem. For a
given finite field, codes are constructed which are `optimal' for this field.


  The observation of chiral-induced spin selectivity (CISS) in biological
molecules still awaits a full theoretical explanation. In a recent Rapid
Communication, Varela et al. [Phys. Rev. B 101, 241410(R) (2020)] presented a
model for electron transport in biological molecules by tunneling in the
presence of spin-orbit interactions. They then claimed that their model
produces a strong spin asymmetry due to the intrinsic atomic spin-orbit
strength. As their Hamiltonian is time-reversal symmetric, this result
contradicts a theorem by Bardarson [J. Phys. A: Math. Theor. 41, 405203
(2008)], which states that such a Hamiltonian cannot generate a spin asymmetry
for tunneling between two terminals (in which there are only a spin-up and a
spin-down channels). Here we solve the model proposed by Varela et al. and show
that it does not yield any spin asymmetry, and therefore cannot explain the
observed CISS effect.


  The escape rate of a Brownian particle over a potential barrier is accurately
described by the Kramers theory. A quantitative theory explicitly taking the
activity of Brownian particles into account has been lacking due to the
inherently out-of-equilibrium nature of these particles. Using an effective
equilibrium approach [Farage et al., Phys. Rev. E 91, 042310 (2015)] we study
the escape rate of active particles over a potential barrier and compare our
analytical results with data from direct numerical simulation of the colored
noise Langevin equation. The effective equilibrium approach generates an
effective potential which, when used as input to Kramers rate theory, provides
results in excellent agreement with the simulation data.


  We report on our research effort to generate large-scale multipartite
optical-mode entanglement using as few physical resources as possible. We have
previously shown that cluster- and GHZ-type N-partite continuous-variable
entanglement can be obtained in an optical resonator that contains a suitably
designed second-order nonlinear optical medium, pumped by at most O(N^2)
fields. In this paper, we show that the frequency comb of such a resonator can
be entangled into an arbitrary number of independent 2x2 and 2x3
continuous-variable cluster states by a single optical parametric oscillator
pumped by just a few optical modes.


  We discuss a number of issues arising when computing non-perturbative effects
systematically across the string theory landscape. In particular, we cast the
study of fairly generic physical properties into the language of
computability/number theory and show that this amounts to solving systems of
diophantine equations. In analogy to the negative solution to Hilbert's 10th
problem, we argue that in such systematic studies there may be no algorithm by
which one can determine all physical effects. We take large volume type IIB
compactifications as an example, with the physical property of interest being
the low-energy non-perturbative F-terms of a generic compactification. A
similar analysis is expected to hold for other kinds of string vacua, and we
discuss in particular the extension of our ideas to F-theory. While these
results imply that it may not be possible to answer systematically certain
physical questions about generic type IIB compactifications, we identify
particular Calabi-Yau manifolds in which the diophantine equations become
linear, and thus can be systematically solved. As part of the study of the
required systematics of F-terms, we develop technology for computing Z_2
equivariant line bundle cohomology on toric varieties, which determines the
presence of particular instanton zero modes via the Koszul complex. This is of
general interest for realistic IIB model building on complete intersections in
toric ambient spaces.


  We carried out detailed studies of the magnetic structure, magnetoelastic
coupling, and thermal properties of EuCrO$_3$ nano-powders from room
temperature to liquid helium temperature. Our neutron powder diffraction and
X-ray powder diffraction measurements provide precise atomic positions of all
atoms in the cell, especially for the light oxygen atoms. The low-temperature
neutron powder diffraction data revealed extra Bragg peaks of magnetic origin
which can be attributed to a $G_x$ antiferromagnetic structure with an ordered
moment of $\sim$ 2.4 $\mu_{\rm B}$ consistent with the $3d^3$ electronic
configuration of the Cr$^{3+}$ cations. Apart from previously reported
antiferromagnetic and ferromagnetic transitions in EuCrO$_3$ at low
temperatures, we also observed an anomaly at about 100 K. This anomaly was
observed in temperature dependence of sample's, lattice parameters, thermal
expansion, Raman spectroscopy, permittivity and conductance measurements. This
anomaly is attributed to the magnetoelastic distortion in the EuCrO$_3$
crystal.


  The fluid phase diagram of trimer particles composed of one central
attractive bead and two repulsive beads was determined as a function of simple
geometric parameters using flat-histogram Monte Carlo methods. A variety of
self-assembled structures were obtained including spherical micelle-like
clusters, elongated clusters and densely packed cylinders, depending on both
the state conditions and shape of the trimer. Advanced simulation techniques
were employed to determine transitions between self-assembled structures and
macro- scopic phases using thermodynamic and structural definitions. Simple
changes in particle geometry yield dramatic changes in phase behavior, ranging
from macroscopic fluid phase separation to molecular-scale self- assembly. In
special cases, both self-assembled, elongated clusters and bulk fluid phase
separation occur simultaneously. Our work suggests that tuning particle shape
and interactions can yield superstructures with controlled architecture.


  The double red clump (RC) observed in the Milky Way bulge is widely
interpreted as evidence for an X-shaped structure. We have recently suggested,
however, an alternative interpretation based on the multiple population
phenomenon, where the bright RC is from helium enhanced second-generation stars
(G2), while the faint RC is representing first-generation stars (G1) with
normal helium abundance. Here our RC models are constructed in a large
parameter space to see the effects of metallicity, age, and helium abundance on
the double RC feature. Our models show that the luminosity of RC stars is
mainly affected by helium abundance, while the RC color is primarily affected
by metallicity. The effect of age is relatively small, unless it is older than
12 Gyr or much younger than 6 Gyr. The observed double RC feature can therefore
be reproduced in a relatively large parameter space, once {\Delta}Y between G2
and G1 is assumed to be greater than $\sim$0.10. We further show that the
longitude dependence of the double RC feature at $b \approx -8.5 \deg$, which
was pointed out by Gonzalez et al. (2015) as a potential problem of our model,
is well explained in our scenario by a classical bulge embedded in a tilted
bar.


  The evolved massive binary star Eta Carinae underwent eruptive mass loss
events that formed the complex bi-polar Homunculus nebula harboring tens of
solar masses of unusually nitrogen-rich gas and dust. Despite expectations for
the presence of a significant molecular component to the gas, detections have
been observationally challenged by limited access to the far-infrared and the
intense thermal continuum. A spectral survey of the atomic and rotational
molecular transitions was carried out with the Herschel Space Observatory,
revealing a rich spectrum of broad emission lines originating in the ejecta.
Velocity profiles of selected PACS lines correlate well with known
substructures: H I in the central core; NH and weak [C II] within the
Homunculus; and [N II] emissions in fast-moving structures external to the
Homunculus. We have identified transitions from [O I], H I, and 18 separate
light C- and O-bearing molecules including CO, CH, CH+, and OH, and a wide set
of N-bearing molecules, NH, NH+, N2H+, NH2, NH3, HCN, HNC, CN, and N2H+. Half
of these are new detections unprecedented for any early-type massive star
environment. A very low ratio [12C/13C] LE 4 is estimated from five molecules
and their isotopologues. We demonstrate that non-LTE effects due to the strong
continuum are significant. Abundance patterns are consistent with line
formation in regions of carbon and oxygen depletions with nitrogen
enhancements, reflecting an evolved state of the erupting star with efficient
transport of CNO-processed material to the outer layers. The results offer many
opportunities for further observational and theoretical investigations of the
molecular chemistry under extreme physical and chemical conditions around
massive stars in their final stages of evolution.


  We propose and theoretically investigate a dispersion-engineered Si3N4
microring resonator, based on a cross-section containing a partially-etched
trench, that supports phase-locked, two-color soliton microcomb states. These
soliton states consist of a single circulating intracavity pulse with a
modulated envelope that sits on a continuous wave background. Such temporal
waveforms produce a frequency comb whose spectrum is spread over two
widely-spaced spectral windows, each exhibiting a squared hyperbolic secant
envelope, with the two windows phase-locked to each other via Cherenkov
radiation. The first spectral window is centered around the 1550 nm pump, while
the second spectral window is tailored based on straightforward geometric
control, and can be centered as short as 750 nm and as long as 3000 nm. We
numerically analyze the robustness of the design to parameter variation, and
consider its implications to self-referencing and visible wavelength comb
generation.


  The unprecedented volume and rate of transient events that will be discovered
by the Large Synoptic Survey Telescope (LSST) demands that the astronomical
community update its followup paradigm. Alert-brokers -- automated software
system to sift through, characterize, annotate and prioritize events for
followup -- will be critical tools for managing alert streams in the LSST era.
The Arizona-NOAO Temporal Analysis and Response to Events System (ANTARES) is
one such broker. In this work, we develop a machine learning pipeline to
characterize and classify variable and transient sources only using the
available multiband optical photometry. We describe three illustrative stages
of the pipeline, serving the three goals of early, intermediate and
retrospective classification of alerts. The first takes the form of variable vs
transient categorization, the second, a multi-class typing of the combined
variable and transient dataset, and the third, a purity-driven subtyping of a
transient class. While several similar algorithms have proven themselves in
simulations, we validate their performance on real observations for the first
time. We quantitatively evaluate our pipeline on sparse, unevenly sampled,
heteroskedastic data from various existing observational campaigns, and
demonstrate very competitive classification performance. We describe our
progress towards adapting the pipeline developed in this work into a real-time
broker working on live alert streams from time-domain surveys.


  We present simulations which predict significantly higher laser to X-ray
efficiencies than those previously found in high intensity (1e20-1e22 W/cm2)
laser-solid simulations. The bremsstrahlung emission is shown to last for
10-100 ps, which is difficult to model with conventional particle-in-cell (PIC)
codes. The importance of collective effects is also demonstrated, showing the
limitations of Monte Carlo modelling in these systems. A new, open-source
hybrid-PIC code with bremsstrahlung routines has been developed to model this
X-ray production in 3D. Special boundary conditions are used to emulate complex
electron refluxing behaviour, which has been characterised in 2D full-PIC
simulations. The peak X-ray efficiency was recorded in thick gold targets, with
7.4% conversion of laser energy into X-rays of energy 1 MeV or higher. The
target size is shown to play a role in the conversion efficiency and angular
distribution of emitted X-rays, and a simple analytic model is presented for
estimating these efficiencies.


  Building on an insight due to Avramidi, we provide a system of transport
equations for determining key fundamental bi-tensors, including derivatives of
the world-function, \sigma(x,x'), the square root of the Van Vleck determinant,
\Delta^{1/2}(x,x'), and the tail-term, V(x,x'), appearing in the Hadamard form
of the Green function. These bi-tensors are central to a broad range of
problems from radiation reaction to quantum field theory in curved spacetime
and quantum gravity. Their transport equations may be used either in a
semi-recursive approach to determining their covariant Taylor series
expansions, or as the basis of numerical calculations. To illustrate the power
of the semi-recursive approach, we present an implementation in
\textsl{Mathematica} which computes very high order covariant series expansions
of these objects. Using this code, a moderate laptop can, for example,
calculate the coincidence limit a_7(x,x) and V(x,x') to order (\sigma^a)^{20}
in a matter of minutes. Results may be output in either a compact notation or
in xTensor form. In a second application of the approach, we present a scheme
for numerically integrating the transport equations as a system of coupled
ordinary differential equations. As an example application of the scheme, we
integrate along null geodesics to solve for V(x,x') in Nariai and Schwarzschild
spacetimes.


  Ortega-Cerd\`a -- Seip demonstrated that there are bounded multiplicative
Hankel forms which do not arise from bounded symbols. On the other hand, when
such a form is in the Hilbert-Schmidt class $\mathcal{S}_2$, Helson showed that
it has a bounded symbol. The present work investigates forms belonging to the
Schatten classes between these two cases. It is shown that for every
$p>(1-\log{\pi}/\log{4})^{-1}$ there exist multiplicative Hankel forms in the
Schatten class $\mathcal{S}_p$ which lack bounded symbols. The lower bound on
$p$ is in a certain sense optimal when the symbol of the multiplicative Hankel
form is a product of homogeneous linear polynomials.


  In this paper, a metric on $S_b$-metric space analogous to the Hausdorff
metric has been introduced and some basic properties are obtained on
multi-valued $S_b$-metric space. Further, the fundamental multi-valued
contraction of Nadler(1962) has been extended to the $S_b$-metric space
setting, and two results have been established. The entire study is supported
by suitable examples.


  The final merger of a pair of massive black holes in a galactic nucleus is
compelled by gravitational radiation. Gravitational waves from the mergers of
black holes of masses (10^5-10^7)(1+z)^{-1} Msun at redshifts of 1-20 will be
readily detectable by the Laser Interferometer Space Antenna (LISA), but an
electromagnetic afterglow would be helpful in pinpointing the source and its
redshift. Long before the merger, the binary "hollows out" any surrounding gas
and shrinks slowly compared to the viscous timescale of a circumbinary disk.
The inner gas disk is truncated at the radius where gravitational torque from
the binary balances the viscous torque, and accretion onto the black holes is
diminished. Initially, the inner truncation radius is able to follow the
shrinking binary inward. But eventually the gravitational radiation timescale
becomes shorter than the viscous timescale in the disk, leading to a merged
black hole surrounded by a hollow disk of gas. We show that the subsequent
viscous evolution of the hollow, radiation-pressure dominated disk will create
a ~10^{43.5}(M/10^6Msun) ergs s^{-1} X-ray source on a timescale
\~7(1+z)(M/10^6Msun)^{1.32} yr. This justifies follow-up monitoring of
gravitational wave events with next-generation X-ray observatories. Analysis of
the detailed light curve of these afterglows will yield new insights into the
subtle physics of accretion onto massive black holes.


  Airborne Wind Energy is a lightweight technology that allows power extraction
from the wind using airborne devices such as kites and gliders, where the
airfoil orientation can be dynamically controlled in order to maximize
performance. The dynamical complexity of turbulent aerodynamics makes this
optimization problem unapproachable by conventional methods such as classical
control theory, which rely on accurate and tractable analytical models of the
dynamical system at hand. Here we propose to attack this problem through
Reinforcement Learning, a technique that -- by repeated trial-and-error
interactions with the environment -- learns to associate observations with
profitable actions without requiring prior knowledge of the system. We show
that in a simulated environment Reinforcement Learning finds an efficient way
to control a kite so that it can tow a vehicle for long distances. The
algorithm we use is based on a small set of intuitive observations and its
physically transparent interpretation allows to describe the approximately
optimal strategy as a simple list of manoeuvring instructions.


  For a finite smooth algebraic group $F$ over a field $k$ and a smooth
algebraic group $\bar G$ over the separable closure of $k$, we define the
notion of $F$-kernel in $\bar G$ and we associate to it a set of nonabelian
2-cohomology. We use this to study extensions of $F$ by an arbitrary smooth
$k$-group $G$. We show in particular that any such extension comes from an
extension of finite $k$-groups when $k$ is perfect and we give explicit bounds
on the order of these finite groups when $G$ is linear. We prove moreover some
finiteness results on these sets.


  The appearance of topological effects in systems exhibiting a non-trivial
topological band structure strongly relies on the coherent wave nature of the
equations of motion. Here, we reveal topological dynamics in a classical
stochastic random walk version of the Su-Schrieffer-Heeger model with no
relation to coherent wave dynamics. We explain that the commonly used
topological invariant in the momentum space translates into an invariant in a
counting-field space. This invariant gives rise to clear signatures of the
topological phase in an associated escape time distribution.


  In a recent paper the authors make a study on the determination of the
S-matrix elements for scattering of particles in the infinite volume from the
energy levels in the finite box for the case of multiple channels. The study is
done with a toy model in 1+1 dimension and the authors find that there is some
ambiguity in the sign of nondiagonal matrix elements, casting doubts on whether
the needed observables in the infinite volume can be obtained from the energy
levels of the box. In this paper I present an easy derivation, confirming the
ambiguity of the sign and argue that this, however, does not put restrictions
in the determination of observables.


  The nature of the ground states for a system composed of two coupled cavities
with each containing a pair of dipole-coupled two-level atoms are studied over
a wide range of detunings and dipole coupling strengths. The cases for three
limits of exact resonance, large positive and negative detunings are discussed,
and four types of the ground states are revealed. Then the phase diagrams of
the ground state are plotted by choosing three different "order parameters". We
find that the phase space, determined by the combinative action of detuning and
the dipole coupling strength, is divided into four regions. This is different
from the general Bose-Hubbard model and more richer physics are presented in
the two-site coupled cavities system. That is, the insulator region may be
polaritonic or atomic and the superfluid region may be polaritonic or photonic
in nature.


  Explicit solutions for extended objects of a Q-ball type were found
analytically in a model describing complex scalar field with piecewise
parabolic potential in (3+1)- and (1+1)-dimensional space-times. Such a
potential provides a variety of solutions which were thoroughly examined. It
was shown that, depending on the values of the parameters of the model and
according to the known stability criteria, there exist stable and unstable
solutions. The classical stability of solutions in (1+1)-dimensional space-time
was examined in the linear approximation and it was shown explicitly that the
spectrum of linear perturbations around some solutions contains exponentially
growing modes while it is not so for other solutions.


  Self-supervised vision-and-language pretraining (VLP) aims to learn
transferable multi-modal representations from large-scale image-text data and
to achieve strong performances on a broad scope of vision-language tasks after
finetuning. Previous mainstream VLP approaches typically adopt a two-step
strategy relying on external object detectors to encode images in a multi-modal
Transformer framework, which suffer from restrictive object concept space,
limited image context and inefficient computation. In this paper, we propose an
object-aware end-to-end VLP framework, which directly feeds image grid features
from CNNs into the Transformer and learns the multi-modal representations
jointly. More importantly, we propose to perform object knowledge distillation
to facilitate learning cross-modal alignment at different semantic levels. To
achieve that, we design two novel pretext tasks by taking object features and
their semantic labels from external detectors as supervision: 1.) Object-guided
masked vision modeling task focuses on enforcing object-aware representation
learning in the multi-modal Transformer; 2.) Phrase-region alignment task aims
to improve cross-modal alignment by utilizing the similarities between noun
phrases and object labels in the linguistic space. Extensive experiments on a
wide range of vision-language tasks demonstrate the efficacy of our proposed
framework, and we achieve competitive or superior performances over the
existing pretraining strategies.


  Beside simplices, $n$-cubes form an important class of simple polyhedra.
Unlike hyperbolic Coxeter simplices, hyperbolic Coxeter $n$-cubes are not
classified. We show that there is no hyperbolic Coxeter $n$-cube for $n\geq~6$,
and provide a full classification for $n\leq 5$. Our methods, which are
essentially of combinatorial and algebraic nature, can be (and have been
successfully) implemented in a symbolic computation software such as
Mathematica$^\circledR$.


  In the context of the littlest Higgs$(LH)$ model, we study the process $
e^{+}e^{-}\to t\bar{t}$. We find that the new gauge bosons $Z_{H}$ and $B_{H}$
can produce significant correction effects on this process, which can be
further enhanced by the suitably polarized beams. In most of the parameter
space preferred by the electroweak precision data, the absolute value of the
relative correction parameter $R_{B_{H}}$ is larger than 5%. As long as
$1TeV\leq M_{Z_{H}}\leq 1.5TeV$ and $0.3\leq c\leq 0.5,$ the absolute value of
the relative correction parameter $R_{Z_{H}}$ is larger than 5%. With
reasonable values of the parameters of the $LH$ model, the possible signals of
the new gauge bosons $B_{H}$ and $Z_{H}$ can be detected via the process $
e^{+}e^{-} \to t\bar{t}$ in the future $LC$ experiments with the c.m. energy
$\sqrt{S}=800GeV$. $B_{H}$ exchange and $Z_{H}$ exchange can generate
significantly corrections to the forward-backward asymmetry $A_{FB}(t\bar{t})$
only in small part of the parameter space.


  There have been many recent investigations into prompt-based training of
transformer language models for new text genres in low-resource settings. The
prompt-based training approach has been found to be effective in generalizing
pre-trained or fine-tuned models for transfer to resource-scarce settings. This
work, for the first time, reports results on adopting prompt-based training of
transformers for \textit{scholarly knowledge graph object prediction}. The work
is unique in the following two main aspects. 1) It deviates from the other
works proposing entity and relation extraction pipelines for predicting objects
of a scholarly knowledge graph. 2) While other works have tested the method on
text genera relatively close to the general knowledge domain, we test the
method for a significantly different domain, i.e. scholarly knowledge, in turn
testing the linguistic, probabilistic, and factual generalizability of these
large-scale transformer models. We find that (i) per expectations, transformer
models when tested out-of-the-box underperform on a new domain of data, (ii)
prompt-based training of the models achieve performance boosts of up to 40\% in
a relaxed evaluation setting, and (iii) testing the models on a starkly
different domain even with a clever training objective in a low resource
setting makes evident the domain knowledge capture gap offering an
empirically-verified incentive for investing more attention and resources to
the scholarly domain in the context of transformer models.


  We develop a geometric approach to stable homotopy groups of spheres in the
spirit of the work of Pontrjagin and Rokhlin. A new proof of the Hopf Invariant
One Theorem by J.F.Adams is obtained in all dimensions except 15 and 31.
  To prove that the stable Hopf invariant H: \Pi_n \to Z/2 vanishes for n>31,
we apply methods of geometric topology. The Pontrjagin-Thom construction along
with Hirsch's compression lemma identify every \alpha \in \Pi_n with the framed
bordism class of a framed immersion of a closed n-manifold into R^{n+k}, for
any given k>0. Its self-intersection M projects to an immersion f: M \to R^n
which is framed by k copies of a line bundle \kappa. It is well-known that
H(\alpha) = <w_1(\kappa)^{n-k}, [M]>. The self-intersection N of f is framed by
k copies of a plane bundle with structure group D_4. We observe that H(\alpha)
= <w_1(i^*\kappa)^{n-2k}, [\bar N]>, where i immerses the double cover \bar N
of N into M. The hardest part of the proof is to show that, after modifying f
in its skew-framed bordism class, the classifying map g: N \to K(D_4,1) factors
through K(Z/4,1), provided that n=2^l-1, l>5 and n-2k=15. This is achieved by
analyzing immersions in the regular homotopy class of f that approximate the
composition of the classifying map M \to RP^{n-k}, the projection of RP^{n-k}
onto the join of copies of S^1/(Z/4) (the standard sphere), and an embedding of
this join in R^n. The last step is proved with the quaternions.


  User Simulators are one of the major tools that enable offline training of
task-oriented dialogue systems. For this task the Agenda-Based User Simulator
(ABUS) is often used. The ABUS is based on hand-crafted rules and its output is
in semantic form. Issues arise from both properties such as limited diversity
and the inability to interface a text-level belief tracker. This paper
introduces the Neural User Simulator (NUS) whose behaviour is learned from a
corpus and which generates natural language, hence needing a less labelled
dataset than simulators generating a semantic output. In comparison to much of
the past work on this topic, which evaluates user simulators on corpus-based
metrics, we use the NUS to train the policy of a reinforcement learning based
Spoken Dialogue System. The NUS is compared to the ABUS by evaluating the
policies that were trained using the simulators. Cross-model evaluation is
performed i.e. training on one simulator and testing on the other. Furthermore,
the trained policies are tested on real users. In both evaluation tasks the NUS
outperformed the ABUS.


  Correlated electrons often crystalize to the Mott insulator usually with some
magnetic orders, whereas the "quantum spin liquid" has been a long-sought
issue. We report numerical evidences that a nonmagnetic insulating (NMI) phase
gets stabilized near the Mott transition with remarkable properties:
  The 2D Mott insulators on geometrically frustrated lattices contain a phase
with gapless spin excitations and degeneracy of the ground state in the whole
Brillouin zone of the total momentum. It has an interpretation for an
unexplored type of a quantum liquid. The present concept is useful in analyzing
a variety of experimental results in frustrated magnets including organic
BEDT-TTF compounds.


  We have investigated the magnetic and dielectric properties of
$A_2$CoSi$_2$O$_7$ ($A$=Ca, Sr, and Ba) crystals with a two-dimensional network
of CoO$_4$ and SiO$_4$ tetrahedra connected with each other through the
corners. In Ca$_2$CoSi$_2$O$_7$, a weak ferromagnetic transition occurs at 5.7
K, where the dielectric constant parallel to the c axis shows a concomitant
anomaly. The large magnetocapacitance effect is observed below 5.7 K; $\Delta
\varepsilon (H)/\varepsilon (0) \equiv [\varepsilon (H)-\varepsilon
(0)]/\varepsilon (0)$ reaches 13 % at 5.1<EMAIL_ADDRESS>These results indicate a strong
coupling between the magnetism and dielectricity in Ca$_2$CoSi$_2$O$_7$.
Sr$_2$CoSi$_2$O$_7$ shows a similar magnetoelectric behavior to that of
Ca$_2$CoSi$_2$O$_7$. In contrast, in Ba$_2$CoSi$_2$O$_7$, which has the
different arrangement of SiO$_4$ and CoO$_4$ tetrahedra from that of
Ca$_2$CoSi$_2$O$_7$, the magnetocapacitance is hardly observed. The key for the
magnetocapacitance effect of $A_2$CoSi$_2$O$_7$ lies in the
quasi-two-dimensional crystal structure.


  Feature engineering is a crucial step in the process of predictive modeling.
It involves the transformation of given feature space, typically using
mathematical functions, with the objective of reducing the modeling error for a
given target. However, there is no well-defined basis for performing effective
feature engineering. It involves domain knowledge, intuition, and most of all,
a lengthy process of trial and error. The human attention involved in
overseeing this process significantly influences the cost of model generation.
We present a new framework to automate feature engineering. It is based on
performance driven exploration of a transformation graph, which systematically
and compactly enumerates the space of given options. A highly efficient
exploration strategy is derived through reinforcement learning on past
examples.


  Cu-exchanged zeolites rely on mobile solvated Cu+ cations for their catalytic
activity, but the role of framework composition on transport is not fully
understood. Ab initio molecular dynamics simulations can provide quantitative
atomistic insight but are too computationally expensive to explore large
length- and time-scales or diverse compositions. We report a machine-learning
interatomic potential that accurately reproduces ab initio results and
effectively generalizes to allow multi-nanosecond simulations of large
supercells and diverse chemical compositions. Biased and unbiased simulations
of [Cu(NH3)2]+ mobility show that aluminum pairing in eight-membered rings
accelerates local hopping, and demonstrate that increased NH3 concentration
enhances long-range diffusion. The probability of finding two [Cu(NH3)2]+
complexes in the same cage - key for SCR-NOx reaction - increases with Cu
content and Al content, but does not correlate with the long-range mobility of
Cu+. Supporting experimental evidence was obtained from reactivity tests of
Cu-CHA catalysts with controlled chemical composition.


  Cloud computing customers often submit repeating jobs and computation
pipelines on \emph{approximately} regular schedules, with arrival and running
times that exhibit variance. This pattern, typical of training tasks in machine
learning, allows customers to partially predict future job requirements. We
develop a model of cloud computing platforms that receive statements of work
(SoWs) in an online fashion. The SoWs describe future jobs whose arrival times
and durations are probabilistic, and whose utility to the submitting agents
declines with completion time. The arrival and duration distributions, as well
as the utility functions, are considered private customer information and are
reported by strategic agents to a scheduler that is optimizing for social
welfare.
  We design pricing, scheduling, and eviction mechanisms that incentivize
truthful reporting of SoWs. An important challenge is maintaining incentives
despite the possibility of the platform becoming saturated. We introduce a
framework to reduce scheduling under uncertainty to a relaxed scheduling
problem without uncertainty. Using this framework, we tackle both adversarial
and stochastic submissions of statements of work, and obtain logarithmic and
constant competitive mechanisms, respectively.


  Transient reflectivity measurements of thin films, ranging from 6 to 40 nm in
thickness, of the topological insulator Bi2Se3 revealed a strong dependence of
the carrier relaxation time on the film thickness. For thicker films the
relaxation dynamics are similar to those of bulk Bi2Se3, where the contribution
of the bulk insulating phase dominates over that of the surface metallic phase.
The carrier relaxation time shortens with decreasing film thickness, reaching
values comparable to those of noble metals. This effect may result from the
hybridization of Dirac cone states at the opposite surfaces for the thinnest
films.


  Higher shares of fluctuating generation from renewable energy sources in the
power system lead to an increase in grid balancing demand. One approach for
avoiding curtailment of renewable energies is to use excess electricity feed-in
for heating applications. To assess in which regions power-to-heat technologies
can contribute to renewable energy integration, detailed data on the spatial
distribution of the heat demand are needed. We determine the overall heat load
in the residential building sector and the share covered by electric heating
technologies for each administrative district in Germany, with a temporal
resolution of 15 minutes. Using a special evaluation of German census data, we
defined 729 building categories and assigned individual heat demand values.
Furthermore, heating types and different classes of installed heating capacity
were defined. Our analysis showed that the share of small-scale single-storey
heating and large-scale central heating is higher in cities, whereas there is
more medium-scale central heating in rural areas. This results from the
different shares of single and multi-family houses in the respective regions.
To determine the electrically-covered heat demand, we took into account heat
pumps and resistive heating technologies. All results, as well as the developed
code, are published under open source licenses and can thus also be used by
other researchers for the assessment of power-to-heat for renewable energy
integration.


  We discuss Wiseman, Cavalcanti and Rieffel's "thoughtful" local friendliness
no-go theorem and the experimental programme they propose to test local
friendliness inequalities. We argue that, to prove the theorem, the assumptions
need to be strengthened to exclude the possibility of variable numbers of
thoughtful agents existing in different phases of the experiment. We argue
further that this possibility may arise naturally, even in one-world versions
of quantum theory. We also query whether the motivations they give for their
assumptions hold up well under their definition of "thoughtfulness" as
displaying human-level cognitive ability, and suggest that their justification
requires replacing "thoughtfulness" by "consciousness" or "conscious
thoughtfulness".


  Lung cancer has been one of the major threats to human life for decades.
Computer-aided diagnosis can help with early lung nodul detection and
facilitate subsequent nodule characterization. Large Visual Language models
(VLMs) have been found effective for multiple downstream medical tasks that
rely on both imaging and text data. However, lesion level detection and
subsequent diagnosis using VLMs have not been explored yet. We propose CADe,
for segmenting lung nodules in a zero-shot manner using a variant of the
Segment Anything Model called MedSAM. CADe trains on a prompt suite on input
computed tomography (CT) scans by using the CLIP text encoder through prefix
tuning. We also propose, CADx, a method for the nodule characterization as
benign/malignant by making a gallery of radiomic features and aligning
image-feature pairs through contrastive learning. Training and validation of
CADe and CADx have been done using one of the largest publicly available
datasets, called LIDC. To check the generalization ability of the model, it is
also evaluated on a challenging dataset, LUNGx. Our experimental results show
that the proposed methods achieve a sensitivity of 0.86 compared to 0.76 that
of other fully supervised methods.The source code, datasets and pre-processed
data can be accessed using the link:


  We show that the recent magnetoresistance data on thin-film
La$_{2-x}$Sr$_{x}$CuO$_4$ (LSCO) in strong magnetic fields ($B$) obeys a
single-parameter scaling of the form MR$(B,T)=f(\mu_H(T)B)$, where
$\mu_H^{-1}(T)\sim T^{\alpha}$ ($1\le\alpha\le2$), from $T=180$K until
$T\sim20$K, at which point the single-parameter scaling breaks down. The
functional form of the MR is distinct from the simple quadratic-to-linear
quadrature combination of temperature and magnetic field found in the optimally
doped iron superconductor BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$. Further,
low-temperature departure of the MR in LSCO from its high-temperature scaling
law leads us to conclude that the MR curve collapse is not the result of
quantum critical scaling. We examine the classical effective medium theory
(EMT) previously used to obtain the quadrature resistivity dependence on field
and temperature for metals with a $T$-linear zero-field resistivity. It appears
that this scaling form results only for a binary, random distribution of
metallic components. More generally, we find a low-temperature, high-field
region where the resistivity is simultaneously $T$ and $B$ linear when multiple
metallic components are present. Our findings indicate that if mesoscopic
disorder is relevant to the magnetoresistance in strange metal materials, the
binary-distribution model which seems to be relevant to the iron pnictides is
distinct from the more broad-continuous distributions relevant to the cuprates.
Using the latter, we examine the applicability of classical effective medium
theory to the MR in LSCO and compare calculated MR curves with the experimental
data.


  Motivated by indoor localization by tripwire lasers, we study the problem of
cutting a polygon into small-size pieces, using the chords of the polygon.
Several versions are considered, depending on the definition of the "size" of a
piece. In particular, we consider the area, the diameter, and the radius of the
largest inscribed circle as a measure of the size of a piece. We also consider
different objectives, either minimizing the maximum size of a piece for a given
number of chords, or minimizing the number of chords that achieve a given size
threshold for the pieces. We give hardness results for polygons with holes and
approximation algorithms for multiple variants of the problem.


  The first measurements of Delta- xF3 are higher than current theoretical
predictions. We investigate the sensitivity of these theoretical predictions
upon a variety of factors including: renormalization scheme and scale, quark
mass effects, higher twist, isospin violation, and PDF uncertainties.


  Segmentation is the assigning of a semantic class to every pixel in an image
and is a prerequisite for various statistical analysis tasks in materials
science, like phase quantification, physics simulations or morphological
characterization. The wide range of length scales, imaging techniques and
materials studied in materials science means any segmentation algorithm must
generalise to unseen data and support abstract, user-defined semantic classes.
Trainable segmentation is a popular interactive segmentation paradigm where a
classifier is trained to map from image features to user drawn labels. SAMBA is
a trainable segmentation tool that uses Meta's Segment Anything Model (SAM) for
fast, high-quality label suggestions and a random forest classifier for robust,
generalizable segmentations. It is accessible in the browser
(https://www.sambasegment.com/) without the need to download any external
dependencies. The segmentation backend is run in the cloud, so does not require
the user to have powerful hardware.


  Thermoelectric (TE) materials achieve localised conversion between thermal
and electric energies, and the conversion efficiency is determined by a figure
of merit zT. Up to date, two-dimensional electron gas (2DEG) related TE
materials hold the records for zT near room-temperature. A sharp increase in zT
up to ~2.0 was observed previously for superlattice materials such as PbSeTe,
Bi2Te3/Sb2Te3 and SrNb0.2Ti0.8O3/SrTiO3, when the thicknesses of these TE
materials were spatially confine within sub-nanometre scale. The
two-dimensional confinement of carriers enlarges the density of states near the
Fermi energy3-6 and triggers electron phonon coupling. This overcomes the
conventional {\sigma}-S trade-off to more independently improve S, and thereby
further increases thermoelectric power factors (PF=S2{\sigma}). Nevertheless,
practical applications of the present 2DEG materials for high power energy
conversions are impeded by the prerequisite of spatial confinement, as the
amount of TE material is insufficient. Here, we report similar TE properties to
2DEGs but achieved in SrNb0.2Ti0.8O3 films with thickness within sub-micrometer
scale by regulating interfacial and lattice polarizations. High power factor
(up to 103 {\mu}Wcm-1K-2) and zT value (up to 1.6) were observed for the film
materials near room-temperature and below. Even reckon in the thickness of the
substrate, an integrated power factor of both film and substrate approaching to
be 102 {\mu}Wcm-1K-2 was achieved in a 2 {\mu}m-thick SrNb0.2Ti0.8O3 film grown
on a 100 {\mu}m-thick SrTiO3 substrate. The dependence of high TE performances
on size-confinement is reduced by ~103 compared to the conventional
2DEG-related TE materials. As-grown oxide films are less toxic and not
dependent on large amounts of heavy elements, potentially paving the way
towards applications in localised refrigeration and electric power generations.


  In the present comment we discuss the qualitative and the quantitative
differences between the neutron stars models in $f(R)$ gravity presented in the
recent paper \cite{Capozziello2015} (Capozziello et al. (2015)) and in our
paper \cite{Yazadjiev2014} (Yazadjiev et al. (2014)). The authors of
\cite{Capozziello2015} claim that these differences come from the fact that
they are using the physical Jordan frame while we are working in the Einstein
frame. The results in \cite{Yazadjiev2014} are very well tested by two
numerical codes using different formulations of the field equations that give
us the confidence that they are correct. Thus we decided to perform an
additional test. Namely, we derive the relevant set of field equations in the
Jordan frame and solve them numerically in order to disprove the claim in
\cite{Capozziello2015} that the difference comes from the use of different
frame. The obtained results are in perfect agreement with our previous work
\cite{Yazadjiev2014} and therefore the numerical results in
\cite{Capozziello2015} seem to be incorrect. At the end we point out several
possible sources of error in \cite{Capozziello2015} that can lead to the
observed large deviations.


  Using the self-consistent Hartree-Fock approximation, we study the
compressibility instability of the interacting electrons in bilayer graphene.
The chemical potential and the compressibility of the electrons can be
significantly altered by an energy gap (tunable by external gate voltages)
between the valence and conduction bands. For zero gap case, we show that the
homogeneous system is stable. When the gap is finite, the compressibility of
the electron system becomes negative at low carrier doping concentrations and
low temperature. The phase diagram distinguishing the stable and unstable
regions of a typically gapped system in terms of temperature and doping is also
presented.


  A principal motivation to develop graphene for future devices has been its
promise for quantum spintronics. Hyperfine and spin-orbit interactions are
expected to be negligible in single-layer graphene. Spin transport experiments,
on the other hand, show that graphene's spin relaxation is orders of magnitude
faster than predicted. We present a quantum interference measurement that
disentangles sources of magnetic and non-magnetic decoherence in graphene.
Magnetic defects are shown to be the primary cause of spin relaxation, while
spin-orbit interaction is undetectably small.


  Despite decades of extensive research, the large-scale analysis of membrane
proteins remains a difficult task. This is due to the fact that membrane
proteins require a carefully balanced hydrophilic and lipophilic environment,
which optimum varies with different proteins, while most protein chemistry
methods work mainly, if not only, in water-based media. Taking this review
[Santoni, Molloy and Rabilloud, Membrane proteins and proteomics: un amour
impossible? Electrophoresis 2000, 21, 1054-1070] as a pivotal paper, the
current paper analyzes how the field of membrane proteomics exacerbated the
trend in proteomics, i.e. developing alternate methods to the historical
two-dimensional electrophoresis, and thus putting more and more pressure on the
mass spectrometry side. However, in the case of membrane proteins, the
incentive in doing so is due to the poor solubility of membrane proteins. This
review also shows that in some situations, where this solubility problem is
less acute, two-dimensional electrophoresis remains a method of choice. Last
but not least, this review also critically examines the alternate approaches
that have been used for the proteomic analysis of membrane proteins.


  Emergence of generalized synchronization patterns in a ring of identical and
locally coupled Kuramoto-type rotators are investigated by different methods.
These approaches offer a useful visual picture for understanding the complexity
of the dynamics in the high dimensional state-space of this system. Beside the
known stable stationary points novel unstable states are revealed. We find that
the prediction of the final stationary state is limited by the presence of such
saddle points. This is illustrated by considering and comparing two different
attempts for forecasting the final stationary state


  We propose a purity correction to subtract effects of combinatorial
backgrounds from cumulants of hyperon number distributions. We argue that
cumulants and mix-cumulants of sidebands, whose yield is comparable with that
of background particles in the signal region, can be used for the correction.
The method is demonstrated in a simple toy model by introducing effects of
reconstruction efficiencies and backgrounds. We show that topological cut
parameters for hyperon reconstructions can be optimized to achieve the best
statistical significance after purity and efficiency corrections. The method
will enable us to measure cumulants of net-baryon, net-strangenss, and their
correlations with better figure of merit than the conventional approach.


  We specialize Olver's and Rosenau's side condition heuristics for the
determination of particular invariant sets of ordinary differential equations.
It turns out that side conditions of so-called LaSalle type are of special
interest. Moreover we put side condition properties of symmetric and partially
symmetric equations in a wider context. In the final section we present an
application to parameter-dependent systems, in particular to quasi-steady state
for chemical reactions.


  Let $G = N \rtimes A$, where $N$ is a stratified group and $A = \mathbb{R}$
acts on $N$ via automorphic dilations. Homogeneous sub-Laplacians on $N$ and
$A$ can be lifted to left-invariant operators on $G$ and their sum is a
sub-Laplacian $\Delta$ on $G$. Here we prove weak type $(1,1)$,
$L^p$-boundedness for $p \in (1,2]$ and $H^1 \to L^1$ boundedness of the Riesz
transforms $Y \Delta^{-1/2}$ and $Y \Delta^{-1} Z$, where $Y$ and $Z$ are any
horizontal left-invariant vector fields on $G$, as well as the corresponding
dual boundedness results. At the crux of the argument are large-time bounds for
spatial derivatives of the heat kernel, which are new when $\Delta$ is not
elliptic.


  Robust qubit-qubit interactions mediated by bosonic modes are central to many
quantum technologies. Existing proposals combining fast oscillator-mediated
gates with dynamical decoupling require strong pulses or fast control over the
qubit-boson coupling. Here, we present a method based on dynamical decoupling
techniques that leads to faster-than-dispersive entanglement gates with
low-intensity pulses. Our method is general, i.e., it is applicable to any
quantum platform that has qubits interacting with bosonic mediators via
longitudinal coupling. Moreover, the protocol provides robustness to
fluctuations in qubit frequencies and control fields, while also being
resistant to common errors such as frequency shifts and heating in the mediator
as well as crosstalk effects. We illustrate our method with an implementation
for trapped ions coupled via magnetic field gradients. With detailed numerical
simulations, we show that entanglement gates with infidelities of $10^{-3}$ or
$10^{-4}$ are possible with current or near-future experimental setups,
respectively.


  Digital arts have gained an unprecedented level of popularity with the
emergence of non-fungible tokens (NFTs). NFTs are cryptographic assets that are
stored on blockchain networks and represent a digital certificate of ownership
that cannot be forged. NFTs can be incorporated into a smart contract which
allows the owner to benefit from a future sale percentage. While digital art
producers can benefit immensely with NFTs, their production is time consuming.
Therefore, this paper explores the possibility of using generative adversarial
networks (GANs) for automatic generation of digital arts. GANs are deep
learning architectures that are widely and effectively used for synthesis of
audio, images, and video contents. However, their application to NFT arts have
been limited. In this paper, a GAN-based architecture is implemented and
evaluated for novel NFT-style digital arts generation. Results from the
qualitative case study indicate that the generated artworks are comparable to
the real samples in terms of being interesting and inspiring and they were
judged to be more innovative than real samples.


  We construct a densely defined torus action on the symplectic quotient of the
product of three complete flag varieties. The closure of the image of the
corresponding moment map is a convex polytope. The dimension of the geometric
quantization of this space gives the structure constants of the representation
ring of $SU(n)$, which we show is given by counting lattice points in the image
of the moment map. Such lattice point formulas for the structure constants were
given by Berenstein-Zelevinsky; our results show how such formulas arise
geometrically as an example of `invariance of polarization', analogous to the
description of the Gelfand-Cetlin polytopes by Guillemin-Sternberg. We outline
applications to loop groups and to moduli spaces of vector bundles.


  We investigate collective dissipative properties of vibrated granular
materials by means of molecular dynamics simulations. Rates of energy losses
indicate three different regimes or "phases"in the amplitude-frequency plane of
the external forcing, namely, solid, convective, and gas-like regimes. The
behavior of effective damping decrement in the solid regime is glassy.
Practical applications are dicussed.


  Polynomial regression is widely used and can help to express nonlinear
patterns. However, considering very high polynomial orders may lead to
overfitting and poor extrapolation ability for unseen data. The paper presents
a method for constructing a high-order polynomial regression based on the
Taylor map factorization. This method naturally implements multi-target
regression and can capture internal relationships between targets.
Additionally, we introduce an approach for model interpretation in the form of
systems of differential equations. By benchmarking on UCI open access datasets,
Feynman symbolic regression datasets, and Friedman-1 datasets, we demonstrate
that the proposed method performs comparable to the state-of-the-art regression
methods and outperforms them on specific tasks.


  Aligning AI systems to users' interests requires understanding and
incorporating humans' complex values and preferences. Recently, language models
(LMs) have been used to gather information about the preferences of human
users. This preference data can be used to fine-tune or guide other LMs and/or
AI systems. However, LMs have been shown to struggle with crucial aspects of
preference learning: quantifying uncertainty, modeling human mental states, and
asking informative questions. These challenges have been addressed in other
areas of machine learning, such as Bayesian Optimal Experimental Design (BOED),
which focus on designing informative queries within a well-defined feature
space. But these methods, in turn, are difficult to scale and apply to
real-world problems where simply identifying the relevant features can be
difficult. We introduce OPEN (Optimal Preference Elicitation with Natural
language) a framework that uses BOED to guide the choice of informative
questions and an LM to extract features and translate abstract BOED queries
into natural language questions. By combining the flexibility of LMs with the
rigor of BOED, OPEN can optimize the informativity of queries while remaining
adaptable to real-world domains. In user studies, we find that OPEN outperforms
existing LM- and BOED-based methods for preference elicitation.


  We explore the flavor-changing parameters mediated by a Higgs boson within
the THDM-III context. In particular, the $h\to t^* c$ processes, and check the
high suppression for the FC in the THDM-III context for the low $t_\beta$
parameters. Our exploration in the $\chi_{ij}^{u}-\chi_{ij}^{d}-$parameter
space shows the allowed regions for different $t_\beta^{}$ values. We explored
different modes for Higgs decays, considered the experimental constraints to
get scattering plots for the FC parameters and some relevant decay modes. We
expect future results to figure out the FC and its implications in the scalar
sector.


  A numerical solution to the Fokker-Planck equation using a two-level scheme
is presented. The Fokker-Planck (FP) equation is of parabolic type equation
govern the time evolution of probability density function of the stochastic
processes. The FP equation also preserves the positivity and conservative of
the total probability. A Chang-Cooper discretization scheme is used to ensure
the positiveness and conservation of the total probability with second-order
accuracy. We investigate a two-level scheme with factor-three-coarsening
strategy and have a significant reduction in computations and CPU time.
Numerical experiments are performed to validate the efficiency and second-order
accuracy of the proposed two-level algorithm with backward time-difference
schemes.


  Multiple-input multiple-output (MIMO) broadcast channels (BCs) (MIMO-BCs)
with perfect channel state information (CSI) at the transmitter are considered.
As joint user selection (US) and vector precoding (VP) (US-VP) with
zero-forcing transmit beamforming (ZF-BF), US and continuous VP (CVP) (US-CVP)
and data-dependent US (DD-US) are investigated. The replica method, developed
in statistical physics, is used to analyze the energy penalties for the two
US-VP schemes in the large-system limit, where the number of users, the number
of selected users, and the number of transmit antennas tend to infinity with
their ratios kept constant. Four observations are obtained in the large-system
limit: First, the assumptions of replica symmetry (RS) and 1-step replica
symmetry breaking (1RSB) for DD-US can provide acceptable approximations for
low and moderate system loads, respectively. Secondly, DD-US outperforms CVP
with random US in terms of the energy penalty for low-to-moderate system loads.
Thirdly, the asymptotic energy penalty of DD-US is indistinguishable from that
of US-CVP for low system loads. Finally, a greedy algorithm of DD-US proposed
in authors' previous work can achieve nearly optimal performance for
low-to-moderate system loads.


  AI has been proposed as an important tool to support several efforts related
to nature-based climate solutions such as the detection of wildfires that
affect forests and vegetation-based offsets. While this and other use-cases
provide important demonstrative value of the power of AI in climate change
mitigation, such efforts have typically been undertaken in silos, without
awareness of the integrative nature of real-world climate policy-making. In
this paper, we propose a novel overarching framework for AI-aided integrated
and comprehensive decision support for various aspects of nature-based climate
decision-making. Focusing on vegetation-based solutions such as forests, we
demonstrate how different AI-aided decision support models such as AI-aided
wildfire detection, AI-aided vegetation carbon stock assessment, reversal risk
mitigation, and disaster response planning can be integrated into a
comprehensive framework. Rather than being disparate elements, we posit that
the exchange of data and analytical results across elements of the framework,
and careful mitigation of uncertainty propagation will provide tremendous value
relative to the status-quo for real-world climate policy-making.


  The threshold, or saturation phenomenon of spatially coupled systems is
revisited in the light of Lyapunov's theory of dynamical systems. It is shown
that an application of Lyapunov's direct method can be used to quantitatively
describe the threshold phenomenon, prove convergence, and compute threshold
values. This provides a general proof methodology for the various systems
recently studied. Examples of spatially coupled systems are given and their
thresholds are computed.