  This paper studies a variant of the Pliable Index CODing (PICOD) problem,
i.e., an index coding problem where a user can be satisfied by decoding any
message that is not in its side information set, where communication is
decentralized, i.e., it occurs among users rather than by the central server,
and secure, i.e., each user is allowed to decode only one message outside its
side information set and must not be able to collect any information about any
other message that is not its decoded one. Given the difficulty of the general
version of this problem, this paper focuses on the case where the side
information sets are `$s$~circular shifts', namely, user $u$'s side information
set is the set of messages indexed by $\{u, u+1, \ldots, u+s-1\}$ for some
fixed $s$ and where the indices are intended modulo the cardinality of the
message set. This particular setting has been studied in the `decentralized
non-secure' and in the `centralized secure' settings, thus allows one to
quantify the cost of decentralized communication under security constraints on
the number of transmissions. Interestingly, the decentralized vs the
centralized secure setting incurs a multiplicative gap of approximately~three.
This is in contrast to the cases without security constraint, where the
multiplicative gap is known to be at most two.


  In this note, we propose Bernstein's problem and De Giorgi's conjecture for
spatially inhomogeneous equations, as well as De Giorgi's conjecture for system
of reaction-diffusion equations.


  Motivated by the combinatorial properties of products in Lie algebras, we
investigate the subset of permutations that naturally appears when we write the
long commutator $[x_1, x_2, ..., x_m]$ as a sum of associative monomials. We
characterize this subset and find some useful equivalences. Moreover, we
explore properties concerning the action of this subset on sequences of m
elements. In particular we describe sequences that share some special
symmetries which can be useful in the study of combinatorial properties in
graded Lie algebras.


  Branched molecules of deoxyribonucleic acid (DNA) can self-assemble into
nanostructures through complementary cohesive strand base pairing. The
production of DNA nanostructures is valuable in targeted drug delivery and
biomolecular computing. With theoretical efficiency of laboratory processes in
mind, we use a flexible tile model for DNA assembly. We aim to minimize the
number of different types of branched junction molecules necessary to assemble
certain target structures. We represent target structures as discrete graphs
and branched DNA molecules as vertices with half-edges. We present the minimum
numbers of required branched molecule and cohesive-end types under three levels
of restrictive conditions for the tadpole and lollipop graph families. These
families represent cycle and complete graphs with a path appended via a single
cut-vertex. We include three general lemmas regarding such vertex-induced path
subgraphs. Through proofs and examples, we demonstrate the challenges that can
arise in determining optimal construction strategies.


  We present further evidence that gelation is an arrested phase separation in
attractive colloid-polymer mixtures, based on a method combining confocal
microscopy experiments with numerical simulations recently established in {\bf
Nature 453, 499 (2008)}. Our results are independent of the form of the
interparticle attractive potential, and therefore should apply broadly to any
attractive particle system with short-ranged, isotropic attractions. We also
give additional characterization of the gel states in terms of their structure,
inhomogeneous character and local density.


  This paper presents an approach for autonomous underwater robots to visually
detect and identify divers. The proposed approach enables an autonomous
underwater robot to detect multiple divers in a visual scene and distinguish
between them. Such methods are useful for robots to identify a human leader,
for example, in multi-human/robot teams where only designated individuals are
allowed to command or lean a team of robots. Initial diver identification is
performed using the Faster R-CNN algorithm with a region proposal network which
produces bounding boxes around the divers' locations. Subsequently, a suite of
spatial and frequency domain descriptors are extracted from the bounding boxes
to create a feature vector. A K-Means clustering algorithm, with k set to the
number of detected bounding boxes, thereafter identifies the detected divers
based on these feature vectors. We evaluate the performance of the proposed
approach on video footage of divers swimming in front of a mobile robot and
demonstrate its accuracy.


  Motivated by the problem for the existence of K\"ahler-Einstein edge metrics,
Cheltsov and Rubinstein conjectured the K-polystability of asymptotically log
Fano varieties with small cone angles when the anti-log-canonical divisors are
not big. Cheltsov, Rubinstein and Zhang proved it affirmatively in dimension
$2$ with irreducible boundaries except for the type $(\operatorname{I.9B.}n)$
with $1\leq n\leq 6$. Unfortunately, recently, Fujita, Liu, S\"u\ss, Zhang and
Zhuang showed the non-K-polystability for some members of type
$(\operatorname{I.9B.}1)$ and for some members of type
$(\operatorname{I.9B.}2)$. In this article, we show that Cheltsov--Rubinstein's
problem is true for all of the remaining cases. More precisely, we explicitly
compute the delta-invariant for asymptotically log del Pezzo surfaces of type
$(\operatorname{I.9B.}n)$ for all $n\geq 1$ with small cone angles. As a
consequence, we finish Cheltsov--Rubinstein's problem in dimension $2$ with
irreducible boundaries.


  We introduce a general framework to construct multi-emission kernels for
parton branching algorithms at the amplitude level and across different soft
and collinear limits. We highlight the connection of kinematic
parameterizations and recoil schemes to the underlying power counting, and
discuss in detail how soft radiation can be partitioned in between different
collinear configurations beyond the single-emission picture underpinning the
traditional dipole and angular ordering approaches. Our work is a vital
cornerstone to build parton branching algorithms which include
multiply-unresolved emissions in a fully differential way, and our construction
can also be used to obtain splitting functions for probabilistic algorithms or
other cross-section level objects such as subtraction terms.


  Large Language Models (LLMs) significantly benefit from Chain-of-Thought
(CoT) prompting in performing various reasoning tasks. While CoT allows models
to produce more comprehensive reasoning processes, its emphasis on intermediate
reasoning steps can inadvertently introduce hallucinations and accumulated
errors, thereby limiting models' ability to solve complex reasoning tasks.
Inspired by how humans engage in careful and meticulous deductive logical
reasoning processes to solve tasks, we seek to enable language models to
perform explicit and rigorous deductive reasoning, and also ensure the
trustworthiness of their reasoning process through self-verification. However,
directly verifying the validity of an entire deductive reasoning process is
challenging, even with advanced models like ChatGPT. In light of this, we
propose to decompose a reasoning verification process into a series of
step-by-step subprocesses, each only receiving their necessary context and
premises. To facilitate this procedure, we propose Natural Program, a natural
language-based deductive reasoning format. Our approach enables models to
generate precise reasoning steps where subsequent steps are more rigorously
grounded on prior steps. It also empowers language models to carry out
reasoning self-verification in a step-by-step manner. By integrating this
verification process into each deductive reasoning stage, we significantly
enhance the rigor and trustfulness of generated reasoning steps. Along this
process, we also improve the answer correctness on complex reasoning tasks.
Code will be released at https://github.com/lz1oceani/verify_cot.


  In this paper, we have constrained the neutrino mass and mass hierarchy in
the $\Lambda$CDM cosmology with the neutrino mass hierarchy parameter $\Delta$,
which represents different mass orderings, by using the {\it Planck} 2015 + BAO
+ SN + $H_{0}$ data set, together with the neutrino oscillation and
neutrinoless double beta decay data. We find that the mass of the lightest
neutrinos and the total neutrino mass are no more than $0.035$eV and $0.133$ eV
at $95\%$ confidence level, respectively. Comparing the result of our joint
analysis with that obtained using cosmological data alone, we find that, by
adding the neutrino oscillation and neutrinoless double beta decay data, the
tendency for normal hierarchy has increased a lot. By means of importance
sampling, three other priors are taken into account, i.e., the flat logarithmic
prior on the absolute value of the neutrino hierarchy parameter $\Delta$, the
flat linear prior on the total neutrino mass $\Sigma m_{\nu}$, and the flat
logarithmic prior on $\Sigma m_{\nu}$. We find that the preference for the
normal hierarchy is in agreement whatever what kinds of priors we choose.
Finally, we make a Bayesian model analysis about four priors and we find that
flat-linear and the flat logarithmic priors on $\Sigma m_{\nu}$ are the most
favored priors.


  Since we are not able to replace the battery in a wireless sensor networks
(WSNs), the issues of energy and lifetime are the most important parameters. In
asymmetrical networks, different sensors with various abilities are used. Super
nodes, with higher power and wider range of communication in comparison with
common sensors, are used to cause connectivity and transmit data to base
stations in these networks. It is crucial to select the parameters of fit
function and monitoring sensors optimally in a point covering network. In this
paper, we utilized an algorithm to select monitoring sensors. The selection is
done by using a novel algorithm that used by simulated annealing. This
selection takes remained energy into consideration. This method increases
lifetime, decreases and balances energy consumption as confirmed by simulation
results.


  Well-known (non-malicious) sources of overfitting in deep neural net (DNN)
classifiers include: i) large class imbalances; ii) insufficient training-set
diversity; and iii) over-training. In recent work, it was shown that backdoor
data-poisoning also induces overfitting, with unusually large classification
margins to the attacker's target class, mediated particularly by (unbounded)
ReLU activations that allow large signals to propagate in the DNN. Thus, an
effective post-training (with no knowledge of the training set or training
process) mitigation approach against backdoors was proposed, leveraging a small
clean dataset, based on bounding neural activations. Improving upon that work,
we threshold activations specifically to limit maximum margins (MMs), which
yields performance gains in backdoor mitigation. We also provide some
analytical support for this mitigation approach. Most importantly, we show that
post-training MM-based regularization substantially mitigates non-malicious
overfitting due to class imbalances and overtraining. Thus, unlike adversarial
training, which provides some resilience against attacks but which harms clean
(attack-free) generalization, we demonstrate an approach originating from
adversarial learning that helps clean generalization accuracy. Experiments on
CIFAR-10 and CIFAR-100, in comparison with peer methods, demonstrate strong
performance of our methods.


  We propose a novel and efficient iterative two-stage variable selection
approach for multivariate sparse GLARMA models, which can be used for modelling
multivariate discrete-valued time series. Our approach consists in iteratively
combining two steps: the estimation of the autoregressive moving average (ARMA)
coefficients of multivariate GLARMA models and the variable selection in the
coefficients of the Generalized Linear Model (GLM) part of the model performed
by regularized methods. We explain how to implement our approach efficiently.
Then we assess the performance of our methodology using synthetic data and
compare it with alternative methods. Finally, we illustrate it on RNA-Seq data
resulting from polyribosome profiling to determine translational status for all
mRNAs in germinating seeds. Our approach, which is implemented in the
MultiGlarmaVarSel R package and available on the CRAN, is very attractive since
it benefits from a low computational load and is able to outperform the other
methods for recovering the null and non-null coefficients.


  We present an overview of the LIGHTS (LBT Imaging of Galactic Halos and Tidal
Structures) survey, which currently includes 25 nearby galaxies that are on
average $\sim$ 1 mag fainter than the Milky Way, and a catalog of 54 low
central surface brightness (24 $< \mu_{0,g}$/mag arcsec$^{-2} < 28$) satellite
galaxy candidates, most of which were previously uncatalogued. The depth of the
imaging exceeds the full 10-year depth of the Rubin Observatory's Legacy Survey
of Space and Time (LSST). We find, after applying completeness corrections,
rising numbers of candidate satellites as we approach the limiting luminosity
(M$_r \sim -8$ mag) and central surface brightness ($\mu_{0,g} \sim 28$ mag
arcsec$^{-2}$). Over the parameter range we explore, each host galaxy
(excluding those that are in overdense regions, apparently groups) has nearly 4
such candidate satellites to a projected radius of $\sim$ 100 kpc. These
objects are mostly just at or beyond the reach of spectroscopy unless they are
H I rich or have ongoing star formation. We identify 3, possibly 4,
ultra-diffuse satellite galaxies (UDGs; effective radius $ > 1.5$ kpc). This
incidence rate falls within expectations of the extrapolation of the published
relationship between the number of UDGs and host halo mass. Lastly, we visually
identify 12 candidate satellites that host a nuclear star cluster (NSC). The
NSC occupation fraction for the sample (12/54) matches that published for
satellites of early-type galaxies, suggesting that the parent's morphological
type plays at most a limited role in determining the NSC occupation fraction.


  We show how static analysis for secure information flow can be expressed and
proved correct entirely within the framework of abstract interpretation. The
key idea is to define a Galois connection that directly approximates the
hyperproperty of interest. To enable use of such Galois connections, we
introduce a fixpoint characterisation of hypercollecting semantics, i.e. a "set
of set" transformer. This makes it possible to systematically derive static
analyses for hyperproperties entirely within the calculational framework of
abstract interpretation. We evaluate this technique by deriving example static
analyses. For qualitative information flow, we derive a dependence analysis
similar to the logic of Amtoft and Banerjee (SAS'04) and the type system of
Hunt and Sands (POPL'06). For quantitative information flow, we derive a novel
cardinality analysis that bounds the leakage conveyed by a program instead of
simply deciding whether it exists. This encompasses problems that are
hypersafety but not k-safety. We put the framework to use and introduce
variations that achieve precision rivalling the most recent and precise static
analyses for information flow.


  The sizes of GPU applications are rapidly growing. They are exhausting the
compute and memory resources of a single GPU, and are demanding the move to
multiple GPUs. However, the performance of these applications scales
sub-linearly with GPU count because of the overhead of data movement across
multiple GPUs. Moreover, a lack of hardware support for coherency exacerbates
the problem because a programmer must either replicate the data across GPUs or
fetch the remote data using high-overhead off-chip links. To address these
problems, we propose a multi-GPU system with truly shared memory (MGPU-TSM),
where the main memory is physically shared across all the GPUs. We eliminate
remote accesses and avoid data replication using an MGPU-TSM system, which
simplifies the memory hierarchy. Our preliminary analysis shows that MGPU-TSM
with 4 GPUs performs, on average, 3.9x? better than the current best performing
multi-GPU configuration for standard application benchmarks.


  Simulations of neutron background from rock for underground experiments are
presented. Neutron propagation through two types of rock, lead and hydrocarbon
material is discussed. The results show a reasonably good agreement between
GEANT4, MCNPX and GEANT3 in transporting low-energy neutrons.


  In 1989, Light defined communicative competence for individuals with complex
communication needs who require augmentative and alternative communication
(AAC) as a dynamic, interpersonal construct based on functionality of
communication, adequacy of communication, and sufficiency of knowledge,
judgment, and skills. Specifically, Light argued that in order to demonstrate
communicative competence, individuals who required AAC had to develop and
integrate knowledge, judgment, and skills in four interrelated domains:
linguistic, operational, social, and strategic. In 2003, Light expanded this
definition and argued that the attainment of communicative competence is
influenced not just by linguistic, operational, social, and strategic
competencies, but also by a variety of psychosocial factors (e.g., motivation,
attitude, confidence, resilience) as well as by barriers and supports in the
environment. In the 25 years since this definition of communicative competence
for individuals who use AAC was originally proposed, there have been
significant changes in the AAC field. In this paper, we review the preliminary
definition of communicative competence proposed 25 years ago, consider the
changes in the field, and then revisit the proposed definition to determine if
it is still relevant and valid for this new era of communication.


  Due to significant improvements in performance in recent years, neural
networks are currently used for an ever-increasing number of applications.
However, neural networks have the drawback that their decisions are not readily
interpretable and traceable for a human. This creates several problems, for
instance in terms of safety and IT security for high-risk applications, where
assuring these properties is crucial. One of the most striking IT security
problems aggravated by the opacity of neural networks is the possibility of
so-called poisoning attacks during the training phase, where an attacker
inserts specially crafted data to manipulate the resulting model. We propose an
approach to this problem which allows provably verifying the integrity of the
training procedure by making use of standard cryptographic mechanisms.


  We propose a number of modifications to the classical term in the dressing
phase for integrable strings in AdS3 x S3 x S3 x S1, and check these against
existing perturbative calculations, crossing symmetry, and the semiclassical
limit of the Bethe equations. The principal change is that the phase for
different masses should start with a term Q_1 Q_2, like the one-loop AdS3
dressing phase, rather than Q_2 Q_3 as for the original AdS5 AFS phase.


  Charge transport at the Dirac point in bilayer graphene exhibits two
dramatically different transport states, insulating and metallic, that occur in
apparently otherwise indistinguishable experimental samples. We demonstrate
that the existence of these two transport states has its origin in an interplay
between evanescent modes, that dominate charge transport near the Dirac point,
and disordered configurations of extended defects in the form of partial
dislocations. In a large ensemble of bilayer systems with randomly positioned
partial dislocations, the conductivity distribution $P(\sigma)$ is found to be
strongly peaked at both the insulating and metallic limits. We argue that this
distribution form, that occurs only at the Dirac point, lies at the heart of
the observation of both metallic and insulating states in bilayer graphene.


  We study the one-dimensional nonreciprocal lattices with real nearest
neighboring hopping and find that the energy spectra under open boundary
conditions can be entirely real or imaginary. We further investigate the
spectral properties and the non-Hermitian skin effect in the one-dimensional
mosaic lattices with real nonreciprocal hopping introduced at equally spaced
sites. The eigenenergies of such lattices undergo a real-complex-imaginary or
real-complex transition as the nonreciprocity varies. Moreover, the skin effect
exhibits phase transitions depending on the period of the mosaic
nonreciprocity. The bulk states are abruptly shifted from one end of the
lattice to the opposite one by crossing the critical points, accompanied by the
closing and reopening of point gaps in the spectra under periodic boundary
conditions. The phase diagrams of the transition are presented and the critical
boundaries are analytically determined. Our work unveils the intriguing
properties of the energy spectrum and skin effect in non-Hermitian systems.


  Modern wind farms comprised of horizontal-axis wind turbines (HAWTs) require
significant land resources to separate each wind turbine from the adjacent
turbine wakes. This aerodynamic constraint limits the amount of power that can
be extracted from a given wind farm footprint. The resulting inefficiency of
HAWT farms is currently compensated by using taller wind turbines to access
greater wind resources at high altitudes, but this solution comes at the
expense of higher engineering costs and greater visual, acoustic, radar and
environmental impacts. We investigated the use of counter-rotating
vertical-axis wind turbines (VAWTs) in order to achieve higher power output per
unit land area than existing wind farms consisting of HAWTs. Full-scale field
tests of 10-m tall VAWTs in various counter-rotating configurations were
conducted under natural wind conditions during summer 2010. Whereas modern wind
farms consisting of HAWTs produce 2 to 3 watts of power per square meter of
land area, these field tests indicate that power densities an order of
magnitude greater can potentially be achieved by arranging VAWTs in layouts
that enable them to extract energy from adjacent wakes and from above the wind
farm. Moreover, this improved performance does not require higher individual
wind turbine efficiency, only closer wind turbine spacing and a sufficient
vertical flux of turbulence kinetic energy from the atmospheric surface layer.
The results suggest an alternative approach to wind farming that has the
potential to concurrently reduce the cost, size, and environmental impacts of
wind farms.


  Let $\ell \geq 5$ be a prime and let $N$ be a non-squarefree integer not
divisible by $\ell$. For a rational Eisenstein prime $\mathfrak{m}$ of the
Hecke ring $\mathbb{T}(N)$ of level $N$ acting on $J_0(N)$, we precisely
compute the dimension of the kernel $J_0(N)[\mathfrak{m}]$ under a mild
assumption. In the case of level $qr^2$ which violates our mild assumption, we
propose a conjecture based on Sage computations. Assuming this conjecture, we
complete our computation in all the remaining cases.


  A common practice in microarray analysis is to transform the microarray raw
data (light intensity) by a logarithmic transformation, and the justification
for this transformation is to make the distribution more symmetric and
Gaussian-like. Since this transformation is not universally practiced in all
microarray analysis, we examined whether the discrepancy of this treatment of
raw data affect the "high level" analysis result. In particular, whether the
differentially expressed genes as obtained by $t$-test, regularized t-test, or
logistic regression have altered rank orders due to presence or absence of the
transformation. We show that as much as 20%--40% of significant genes are
"discordant" (significant only in one form of the data and not in both),
depending on the test being used and the threshold value for claiming
significance. The t-test is more likely to be affected by logarithmic
transformation than logistic regression, and regularized $t$-test more affected
than t-test. On the other hand, the very top ranking genes (e.g. up to top
20--50 genes, depending on the test) are not affected by the logarithmic
transformation.


  We characterize all groups which can occur as the topological symmetry group
or the orientation preserving topological symmetry group of some embedding of
the Petersen graph in S^3.


  We have measured the positions of water masers in Sgr B2, a massive star
forming region in the Galactic center, relative to an extragalactic radio
source with the Very Long Baseline Array. The positions measured at 12 epochs
over a time span of one year yield the trigonometric parallax of Sgr B2 and
hence a distance to the Galactic center of Ro=7.9 (+0.8/-0.7) kpc. The proper
motion of Sgr B2 relative to Sgr A* suggests that Sgr B2 is about 0.13 kpc
nearer than the Galactic center, assuming a low-eccentricity Galactic orbit.


  For any non-archimedean local field $\mathbb{K}$ and any integer $n \geq 1$,
we show that the Taibleson operator admits a bounded $H^\infty(\Sigma\_\theta)$
functional calculus for any angle $\theta \> 0$ on the Banach space
$L^p(\mathbb{K}^n)$, where $\Sigma\_\theta=\{ z \in \mathbb{C}^*: |\arg z| \<
\theta \}$ and $1 \< p \< \infty$, and even a bounded H\''ormander functional
calculus of order $\frac{3}{2}$ (with striking contrast to the Euclidean
Laplacian on $\R^n$). In our study, we explore harmonic analysis on locally
compact Spector-Vilenkin groups establishing the $R$-boundedness of a family of
convolution operators. Our results enhance the understanding of functional
calculi of operators acting on $L^p$-spaces associated to totally disconnected
spaces and have implications for the maximal regularity of the fundamental
evolution equations associated to the Taibleson operator, relevant in various
physical models.


  In this paper we clarify the role of heat flux in the hydrodynamic balance
equations, facilitating the formulation of an Onsager relation within the
framework of this theory. Previously thought to be unobtainable from the
present form of the theory [X.L. Lei, J. Cai, and L.M. Xie, Phys. Rev. B {\bf
38},1529 (1988)], our verification of the Onsager relation for linear particle
and heat flux currents driven by electric fields and temperature gradients
resolves a puzzling issue of long standing. Our results show that, for any
temperature, when electron density is sufficiently high, the linear predictions
of balance equation theory exactly satisfy the Onsager relation. The condition
of high density is consonant with the requirement of strong electron-electron
interactions for the validity of the Lei-Ting balance equations. Our results
support the validity of this theory for a weakly nonuniform system. We also
discuss a possible method of extending this theory to a system further removed
from thermal equilibrium.


  Radio giant pulses provide a unique opportunity to study the pulsar radio
emission mechanism in exquisite detail. Previous studies have revealed a wide
range of properties and phenomena, including extraordinarily high brightness
temperatures, sub-nanosecond emission features, and banded dynamic spectra. New
measurements of giant pulse characteristics can help guide and test theoretical
emission models. To this end, an extensive observation campaign has begun which
will provide more than 500 hours on the Crab with a 34-meter antenna located in
California, USA. The observations are being done as part of an educational
outreach program called the Goldstone-Apple Valley Radio Telescope (GAVRT).
This antenna has a novel wide bandwidth receiver which provides up to 8 GHz of
instantaneous bandwidth in the range of 2.5 to 14 GHz. These observations will
provide detailed information about the variability, amplitude distribution, and
detailed frequency structure of radio giant pulses. In addition, a database of
pulses from these observations and others of the Crab pulsar is being created
which will simplify multiwavelength correlation analysis.


  The microstructure, electronic structure, and chemical bonding of chromium
carbide thin films with different carbon contents have been investigated with
high-resolution transmission electron microscopy, electron energy loss
spectroscopy and soft x-ray absorption-emission spectroscopies. Most of the
films can be described as amorphous nanocomposites with non-crystalline CrCx in
an amorphous carbon matrix. At high carbon contents, graphene-like structures
are formed in the amorphous carbon matrix. At 47 at% carbon content, randomly
oriented nanocrystallites are formed creating a complex microstructure of three
components. The soft x-ray absorption-emission study shows additional peak
structures exhibiting non-octahedral coordination and bonding.


  Social inclusion is a fundamental feature of thriving societies. This paper
first investigates barriers for social inclusion in online Software Engineering
(SE) communities, by identifying a set of 11 attributes and organising them as
a taxonomy. Second, by applying the taxonomy and analysing language used in the
comments posted by members in 189 Gitter projects (with > 3 million comments),
it presents the evidence for the social exclusion problem. It employs a
keyword-based search approach for this purpose. Third, it presents a framework
for improving social inclusion in SE communities.


  This paper studies Symmetric Determinantal Representations (SDR) in
characteristic 2, that is the representation of a multivariate polynomial P by
a symmetric matrix M such that P=det(M), and where each entry of M is either a
constant or a variable.
  We first give some sufficient conditions for a polynomial to have an SDR. We
then give a non-trivial necessary condition, which implies that some
polynomials have no SDR, answering a question of Grenet et al.
  A large part of the paper is then devoted to the case of multilinear
polynomials. We prove that the existence of an SDR for a multilinear polynomial
is equivalent to the existence of a factorization of the polynomial in certain
quotient rings. We develop some algorithms to test the factorizability in these
rings and use them to find SDRs when they exist. Altogether, this gives us
polynomial-time algorithms to factorize the polynomials in the quotient rings
and to build SDRs. We conclude by describing the case of Alternating
Determinantal Representations in any characteristic.


  We study a trapped two-dimensional spin-imbalanced Fermi gas over a range of
temperatures. In the moderate temperature regime, associated with current
experiments, we find reasonable semi-quantitative agreement with the measured
density profiles as functions of varying spin imbalance and interaction
strength. Our calculations show that, in contrast to the three-dimensional
case, the phase separation which appears as a spin balanced core, can be
associated with non-condensed fermion pairs. We present predictions at lower
temperatures where a quasi-condensate will first appear, based on the pair
momentum distribution and following the protocols of Jochim and collaborators.
While these profiles also indicate phase separation, they exhibit distinctive
features which may aid in identifying the condensation regime.


  Twisted double bilayer graphene has recently emerged as an interesting
moir\'e material that exhibits strong correlation phenomena that are tunable by
an applied electric field. Here we study the atomic and electronic properties
of three different graphene double bilayers: double bilayers composed of two AB
stacked bilayers (AB/AB), double bilayers composed of two AA stacked bilayers
(AA/AA) as well as heterosystems composed of one AB and one AA bilayer (AB/AA).
The atomic structure is determined using classical force fields. We find that
the inner layers of the double bilayer exhibit significant in-plane and
out-of-plane relaxations, similar to twisted bilayer graphene. The relaxations
of the outer layers depend on the stacking: atoms in AB bilayers follow the
relaxations of the inner layers, while atoms in AA bilayers attempt to avoid
higher-energy AA stacking. For the relaxed structures, we calculate the
electronic band structures using the tight-binding method. All double bilayers
exhibit flat bands at small twist angles, but the shape of the bands depends
sensitively on the stacking of the outer layers. To gain further insight, we
study the evolution of the band structure as the outer layers are rigidly moved
away from the inner layers, while preserving their atomic relaxations. This
reveals that the hybridization with the outer layers results in an additional
flattening of the inner-layer flat band manifold. Our results establish AA/AA
and AB/AA twisted double bilayers as interesting moir\'e materials with
different flat band physics compared to the widely studied AB/AB system.


  We study the transverse propagation of photons in a magnetized vacuum
considering radiative corrections in the one-loop approximation. The dispersion
equation is modified due to the magnetized photon self-energy in the
transparency region ($0<\omega<2m_e$). The aim of our study is to explore
propagation of photons in a neutron star magnetosphere (described by magnetized
vacuum). The solution of the dispersion equation is obtained in terms of
analytic functions. The larger the magnetic field, the lower the phase velocity
and the more the dispersion curve deviates from the light-cone. For fixed
values of the frequency, we study the dependence of photon time delay with the
magnetic field strength, as well as with distance. For the latter, we adopt a
magnetic dipole configuration and obtain that -- contrary to the expectation,
according to the traditional time delay of photons in the interstellar medium
-- photons of higher energy experience a longer time delay. A discussion of
potential causes of this behaviour is presented.


  In this paper, the logics of the family ${\mathbb{I}}^n {\mathbb{P}}^k$:=$\{{
I^n P^k}\}_{(n,k) \in \omega^2}$ are formally defined by means of finite
matrices, as a simultaneous generalization of the weakly-intuitionistic logic
$I^1$ and of the paraconsistent logic $P^1$. It is proved that this family can
be naturally ordered, and it is shown an adequate axiomatics for each logic of
the form $I^n P^k$.


  We propose deep neural network algorithms to calculate efficient frontier in
some Mean-Variance and Mean-CVaR portfolio optimization problems. We show that
we are able to deal with such problems when both the dimension of the state and
the dimension of the control are high. Adding some additional constraints, we
compare different formulations and show that a new projected feedforward
network is able to deal with some global constraints on the weights of the
portfolio while outperforming classical penalization methods. All developed
formulations are compared in between. Depending on the problem and its
dimension, some formulations may be preferred.


  We investigate the contribution of cosmic string loops to the Cosmic
Microwave Background (CMB) anisotropies. This is done by extending the
Unconnected Segment Model (USM) to include the contribution of the cosmic
string loops created throughout the cosmological evolution of a cosmic string
network to the stress-energy tensor. We then implement this extended USM in the
publicly available CMBACT code and obtain the linear CDM power spectrum and the
CMB angular power spectra generated by cosmic string loops. We find that the
shape of the angular power spectra generated by loops is, in general, similar
to that of long strings. However, there is generally an enhancement of the
anisotropies on small angular scales. Vector modes produced by loops dominate
over those produced by long strings for large multipole moments $\ell$. The
contribution of loops to the CMB anisotropies generated by cosmic string
networks may reach a level of $10\%$ for large loops but decreases as the size
of loops decreases. This contribution may then be significant and, thus, this
extension provides a more accurate prediction of the CMB anisotropies generated
by cosmic string networks.


  We present a scheme of analytical calculations determining the critical
temperature and the number of condensed atoms of ideal gas Bose-Einstein
condensation in external potentials with 1D, 2D or 3D periodicity. In
particular we show that the width of the lowest energy band appears as the main
parameter determining the critical temperature of condensation. Is obtained a
very simple, proportional to 1/3 degree, regularity for this dependence. The
fundamental role of tunneling in physics of condensate establishment is
underscored.


  The pepper-pot method is a popular emittance measurement technique for high
intensity beams at low energy such as those generated by photo-injectors. In
this paper, the beam dynamics in the space charge dominated regime and
analytical design criteria for a mask-based emittance measurement (pepper-pot
method) are revisited. A tracking code developed to test the performance of a
pepper-pot setup is introduced. Examples of such testing are presented with
particle distributions that were generated using PARMELA under different
focusing conditions. These distributions were numerically tested against a
series of mask geometries suggested by analytical criteria. The resulting
fine-tuned geometries and beam dynamics features observed are presented.


  We give a formula for the values of automorphic Green functions on the
special rational 0-cycles (big CM points) attached to certain maximal tori in
the Shimura varieties associated to rational quadratic spaces of signature
(2d,2). Our approach depends on the fact that the Green functions in question
are constructed as regularized theta lifts of harmonic weak Mass forms, and it
involves the Siegel-Weil formula and the central derivatives of incoherent
Eisenstein series for totally real fields. In the case of a weakly holomorphic
form, the formula is an explicit combination of quantities obtained from the
Fourier coefficients of the central derivative of the incoherent Eisenstein
series. In the case of a general harmonic weak Maass form, there is an
additional term given by the central derivative of a Rankin-Selberg type
convolution.


  We propose a model for the propagation of a heavy-quark in a hot plasma, to
be viewed as a first step towards a full description of the dynamics of heavy
quark systems in a quark-gluon plasma, including bound state formation. The
heavy quark is treated as a non relativistic particle interacting with a
fluctuating field, whose correlator is determined by a hard thermal loop
approximation. This approximation, which concerns only the medium in which the
heavy quark propagates, is the only one that is made, and it can be improved.
The dynamics of the heavy quark is given exactly by a quantum mechanical path
integral that is calculated in this paper in the Euclidean space-time using
numerical Monte Carlo techniques. The spectral function of the heavy quark in
the medium is then reconstructed using a Maximum Entropy Method. The path
integral is also evaluated exactly in the case where the mass of the heavy
quark is infinite; one then recovers known results concerning the complex
optical potential that controls the long time behavior of the heavy quark. The
heavy quark correlator and its spectral function is also calculated
semi-analytically at the one-loop order, which allows for a detailed
description of the coupling between the heavy quark and the plasma collective
modes.


  We study the features of the additional Higgs bosons in the Next-to-Minimal
Supersymmetric Standard Model where the lightest beyond Standard Model Higgs
boson does not dominantly couple to up-type quarks. The new state is dominantly
singlet-like while it can also accommodate a small down-type Higgs component.
The gluon-gluon fusion cannot be adequate enough for such a Higgs production.
We show that the vector-boson fusion may become the leading production
mechanism to probe this new scalar at the LHC. Using the existing 13 TeV LHC
data for an integrated luminosity $36.1~fb^{-1}$, we show the LHC constraints
on the parameter space. Finally, we also study the reach of the planned high
luminosity LHC (${\mathcal L}=3~{\rm ab}^{-1}$ at $\sqrt s=$~14 TeV) and the
proposed high energy upgrade of the LHC (${\mathcal L}=15~{\rm ab}^{-1}$ at
$\sqrt s=$~27 TeV) to probe this singlet-like Higgs scalar.


  Different scenarios for the creation of constituent mass in the hadron
formation process are discussed. Effects of these may be observable in hadron
momentum spectra.


  We describe a novel algorithm that recovers the Hamiltonian and temperature
of a quantum state in thermal equilibrium using a restricted set of
measurements. The algorithm works by imposing a semidefinite constraint based
on free energy minimization, which we interpret in terms of thermodynamic
stability. We benchmark the algorithm on the problem of learning a
nearest-neighbour Hamiltonian on a 100-qubit spin chain.


  An expansion is developed for the Weil-Petersson Riemann curvature tensor in
the thin region of the Teichm\"{u}ller and moduli spaces. The tensor is
evaluated on the gradients of geodesic-lengths for disjoint geodesics. A
precise lower bound for sectional curvature in terms of the surface systole is
presented. The curvature tensor expansion is applied to establish continuity
properties at the frontier strata of the augmented Teichm\"{u}ller space. The
curvature tensor has the asymptotic product structure already observed for the
metric and covariant derivative. The product structure is combined with the
earlier negative sectional curvature results to establish a classification of
asymptotic flats. Furthermore, tangent subspaces of more than half the
dimension of Teichm\"{u}ller space contain sections with a definite amount of
negative curvature. Proofs combine estimates for uniformization group
exponential-distance sums and potential theory bounds.


  Up to present, the largest data set of SEP events in the inner heliosphere
are the observations by the two Helios spacecraft. We re-visit a sample of 15
solar relativistic electron events measured by the Helios mission with the goal
of better characterising the injection histories of solar energetic particles
and their interplanetary transport conditions at heliocentric distances <1 AU.
The measurements provided by the E6 instrument on board Helios provide us with
the electron directional distributions in eight different sectors that we use
to infer the detailed evolution of the electron pitch-angle distributions. The
results of a Monte Carlo interplanetary transport model, combined with a full
inversion procedure, were used to fit the observed directional intensities in
the 300-800 keV nominal energy channel. Unlike previous studies, we have
considered both the energy and angular responses of the detector. This method
allowed us to infer the electron release time profile at the source and
determine the electron interplanetary transport conditions. We discuss the
duration of the release time profiles and the values of the radial mean free
path, and compare them with the values reported previously in the literature
using earlier approaches. Five of the events show short injection histories
(<30 min) at the Sun and ten events show long-lasting (>30 min) injections. The
values of mean free path range from 0.02 AU to 0.27 AU. The inferred injection
histories match with the radio and soft x-ray emissions found in literature. We
find no dependence of the radial mean free path on the radial distance. In
addition, we find no apparent relation between the strength of interplanetary
scattering and the size of the solar particle release.


  It has been recently shown that general policies for many classical planning
domains can be expressed and learned in terms of a pool of features defined
from the domain predicates using a description logic grammar. At the same time,
most description logics correspond to a fragment of $k$-variable counting logic
($C_k$) for $k=2$, that has been shown to provide a tight characterization of
the expressive power of graph neural networks. In this work, we make use of
these results to understand the power and limits of using graph neural networks
(GNNs) for learning optimal general policies over a number of tractable
planning domains where such policies are known to exist. For this, we train a
simple GNN in a supervised manner to approximate the optimal value function
$V^{*}(s)$ of a number of sample states $s$. As predicted by the theory, it is
observed that general optimal policies are obtained in domains where general
optimal value functions can be defined with $C_2$ features but not in those
requiring more expressive $C_3$ features. In addition, it is observed that the
features learned are in close correspondence with the features needed to
express $V^{*}$ in closed form. The theory and the analysis of the domains let
us understand the features that are actually learned as well as those that
cannot be learned in this way, and let us move in a principled manner from a
combinatorial optimization approach to learning general policies to a
potentially, more robust and scalable approach based on deep learning.


  The increasing interest in Large Language Models (LLMs) within the
telecommunications sector underscores their potential to revolutionize
operational efficiency. However, the deployment of these sophisticated models
is often hampered by their substantial size and computational demands, raising
concerns about their viability in resource-constrained environments. Addressing
this challenge, recent advancements have seen the emergence of small language
models that surprisingly exhibit performance comparable to their larger
counterparts in many tasks, such as coding and common-sense reasoning. Phi-2, a
compact yet powerful model, exemplifies this new wave of efficient small
language models. This paper conducts a comprehensive evaluation of Phi-2's
intrinsic understanding of the telecommunications domain. Recognizing the
scale-related limitations, we enhance Phi-2's capabilities through a
Retrieval-Augmented Generation approach, meticulously integrating an extensive
knowledge base specifically curated with telecom standard specifications. The
enhanced Phi-2 model demonstrates a profound improvement in accuracy, answering
questions about telecom standards with a precision that closely rivals the more
resource-intensive GPT-3.5. The paper further explores the refined capabilities
of Phi-2 in addressing problem-solving scenarios within the telecom sector,
highlighting its potential and limitations.


  We study the current density and transport coefficients in the fully ionized
plasma with the q-distributions in nonextensive statistics and in strong
magnetic field. By using the generalized Boltzmann transport equation in
nonextensive statistics, we derive the current density and the expressions of
the transport coefficients, including the conductivity, the thermoelectric
coefficient, the Hall coefficient, and the Nernst coefficient. It is shown that
these new transport coefficients has been generalized to the nonequilibrium
complex plasmas with q-distributions in nonextensive statistics, which depend
strongly on the q-parameters and when we take the limit q to 1, they perfectly
return to those for the plasma based on a Maxwellian distribution.


  We develop an inertial coupling method for modeling the dynamics of
point-like 'blob' particles immersed in an incompressible fluid, generalizing
previous work for compressible fluids. The coupling consistently includes
excess (positive or negative) inertia of the particles relative to the
displaced fluid, and accounts for thermal fluctuations in the fluid momentum
equation. The coupling between the fluid and the blob is based on a no-slip
constraint equating the particle velocity with the local average of the fluid
velocity, and conserves momentum and energy. We demonstrate that the
formulation obeys a fluctuation-dissipation balance, owing to the
non-dissipative nature of the no-slip coupling. We develop a spatio-temporal
discretization that preserves, as best as possible, these properties of the
continuum formulation. In the spatial discretization, the local averaging and
spreading operations are accomplished using compact kernels commonly used in
immersed boundary methods. We find that the special properties of these kernels
make the discrete blob a particle with surprisingly physically-consistent
volume, mass, and hydrodynamic properties. We develop a second-order
semi-implicit temporal integrator that maintains discrete
fluctuation-dissipation balance, and is not limited in stability by viscosity.
Furthermore, the temporal scheme requires only constant-coefficient Poisson and
Helmholtz linear solvers, enabling a very efficient and simple FFT-based
implementation on GPUs. We numerically investigate the performance of the
method on several standard test problems...


  In this paper, we establish the existence and uniqueness theorem for entire
solutions of Hessian equations with prescribed asymptotic behavior at infinity.
This extends the previous results on Monge-Amp\`{e}re equations. Our approach
also makes the prescribed asymptotic order optimal within the range preset in
exterior Dirichlet problems. In addition, we show a Liouville type result for
$k$-convex solutions. This partly removes the $(k+1)$- or $n$-convexity
restriction imposed in existing work.


  By blowing up the ambient space along the curve wrapped by B-branes, we study
the brane superpotentials and Ooguri-Vafa invariants on complete intersections
Calabi-Yau threefolds. On the topological B-model side, B-brane superpotentials
are expressed in terms of the period integral of the blow-up manifolds. By
mirror maps, the superpotentials are generating functions of Ooguri-Vafa
invariants counting holomorphic disks on the topological A-model side.


  We discuss the asymptotic dynamical evolution of spatially homogeneous
brane-world cosmological models close to the initial singularity. We find that
generically the cosmological singularity is isotropic in Bianchi type IX
brane-world models and consequently these models do not exhibit Mixmaster or
chaotic-like behaviour close to the initial singularity. We argue that this is
typical of more general cosmological models in the brane-world scenario. In
particular, we show that an isotropic singularity is a past-attractor in all
orthogonal Bianchi models and is a local past-attractor in a class of
inhomogeneous brane-world models.


  In view of the realistic possibility for operating high-energy polarized
proton beams in future collider machines, it is highly desirable to propose for
such beams, an absolute calibration allowing to measure accurately their degree
of polarization. We consider more specifically one practical method based on pp
elastic scattering near the forward direction and we discuss its limitations.


  Gaussian wavepackets are a popular tool for semiclassical analyses of
classically chaotic systems. We demonstrate that they are extremely powerful in
the semiquantal analysis of such systems, too, where their dynamics can be
recast in an extended potential formulation. We develop Gaussian semiquantal
dynamics to provide a phase space formalism and construct a propagator with
desirable qualities. We qualitatively evaluate the behaviour of these
semiquantal equations, and show that they reproduce the quantal behavior better
than the standard Gaussian semiclassical dynamics. We also show that these
semiclassical equations arise as truncations to semiquantal dynamics
non-self-consistent in $\hbar$. This enables us to introduce an extended
semiclassical dynamics that retains the power of the Hamiltonian phase space
formulation. Finally, we show how to obtain approximate eigenvalues and
eigenfunctions in this formalism, and demonstrate with an example that this
works well even for a classically strongly chaotic Hamiltonian.


  We prove that for every smooth projective integral curve $X$ of genus at
least $2$ over $\mathbb C$, there exists $x \in X(\mathbb C)$ such that no
connected finite \'etale cover of $X-\{x\}$ admits a nonconstant morphism to
$\mathbb G_m$. This has implications for the applicability of Baker's method to
determining integral points on curves.


  Using an experimental work on "stopped light" as an example, we show how a
classical phenomenon of linear optics - interference of polarized light - can
imitate the effect of electromagnetically induced transparency.


  In this paper, a methodology to calculate the sensitivity of the least stable
modes of fluid-structure interaction systems with respect to local forces is
presented. We make use of the adjoint equations of the flow-structure coupled
system to calculate the gradients, and the algorithms were implemented using
the spectral/\emph{hp} element method for the spatial discretization. The
methodology was applied to two-dimensional incompressible laminar steady flows
around an elastically-mounted circular cylinder, and we obtained the gradients
of the real and imaginary parts of the least stable eigenvalues with respect to
forces located at arbitrary points in the flow domain. Selected values of mass
ratio and reduced velocity were considered in the simulations, and the results
were compared to those obtained for a fixed cylinder at the same Reynolds
number. We noticed that the sensitivity fields of the fluid-structure
interaction system can be very different from its fixed structure counterpart,
and amongst the cases, with an elastic structure, the fields vary greatly
according to the reduced velocity. Finally, the sensitivity results were
verified against linear and nonlinear simulations of flows with small control
cylinders placed at locations selected according to the sensitivity fields. The
agreement between the predictions made with the sensitivity analyses and the
linear and nonlinear results of the forced flows was excellent. In some cases,
it was possible to completely suppress the cylinder vibration.


  We review a result obtained with Andrew Ledoan and Marco Merkli. Consider a
random analytic function $f(z) = \sum_{n=0}^{\infty} a_n X_n z^n$, where the
$X_n$'s are i.i.d., complex valued random variables with mean zero and unit
variance, and the coefficients $a_n$ are non-random and chosen so that the
variance transforms covariantly under conformal transformations of the domain.
If the $X_n$'s are Gaussian, this is called a Gaussian analytic function (GAF).
We prove that, even if the coefficients are not Gaussian, the zero set
converges in distribution to that of a GAF near the boundary of the domain.


  Luo, Tian and Wu [Discrete Math. 345 (4) (2022) 112788] conjectured that for
any tree $T$ with bipartition $(X,Y)$, every $k$-connected bipartite graph $G$
with minimum degree at least $k+w$, where $w=\max\{|X|,|Y|\}$, contains a tree
$T'\cong T$ such that $\kappa(G-V(T'))\geq k$. In the paper, we confirm the
conjecture for the spider by a new method, where a spider is a tree with at
most one vertex of degree at least three.


  The grid-forming converter is an important unit in the future power system
with more inverter-interfaced generators. However, improving its performance is
still a key challenge. This paper proposes a generalized architecture of the
grid-forming converter from the view of multivariable feedback control. As a
result, many of the existing popular control strategies, i.e., droop control,
power synchronization control, virtual synchronous generator control, matching
control, dispatchable virtual oscillator control, and their improved forms are
unified into a multivariable feedback control transfer matrix working on
several linear and nonlinear error signals. Meanwhile, unlike the traditional
assumptions of decoupling between AC and DC control, active power and reactive
power control, the proposed configuration simultaneously takes all of them into
consideration, which therefore can provide better performance. As an example, a
new multi-input-multi-output-based grid-forming (MIMO-GFM) control is proposed
based on the generalized configuration. To cope with the multivariable
feedback, an optimal and structured $H_{\infty}$ synthesis is used to design
the control parameters. At last, simulation and experimental results show
superior performance and robustness of the proposed configuration and control.


  I review current efforts to measure the mean density of dark matter near the
Sun. This encodes valuable dynamical information about our Galaxy and is also
of great importance for 'direct detection' dark matter experiments. I discuss
theoretical expectations in our current cosmology; the theory behind mass
modelling of the Galaxy; and I show how combining local and global measures
probes the shape of the Milky Way dark matter halo and the possible presence of
a 'dark disc'. I stress the strengths and weaknesses of different methodologies
and highlight the continuing need for detailed tests on mock data -
particularly in the light of recently discovered evidence for disequilibria in
the Milky Way disc. I highlight several recent measurements in order of
increasing data complexity and prior, and, correspondingly, decreasing formal
error bars. Comparing these measurements with spherical extrapolations from the
Milky Way's rotation curve, I show that the Milky Way is consistent with having
a spherical dark matter halo at the Solar position R0. The very latest measures
based on ~10,000 stars from the Sloan Digital Sky Survey appear to favour
little halo flattening at R0, suggesting that the Galaxy has a rather weak dark
matter disc, with a correspondingly quiescent merger history [Abridged].


  In the domain of scientific imaging, interpreting visual data often demands
an intricate combination of human expertise and deep comprehension of the
subject materials. This study presents a novel methodology to linguistically
emulate and subsequently evaluate human-like interactions with Scanning
Electron Microscopy (SEM) images, specifically of glass materials. Leveraging a
multimodal deep learning framework, our approach distills insights from both
textual and visual data harvested from peer-reviewed articles, further
augmented by the capabilities of GPT-4 for refined data synthesis and
evaluation. Despite inherent challenges--such as nuanced interpretations and
the limited availability of specialized datasets--our model (GlassLLaVA) excels
in crafting accurate interpretations, identifying key features, and detecting
defects in previously unseen SEM images. Moreover, we introduce versatile
evaluation metrics, suitable for an array of scientific imaging applications,
which allows for benchmarking against research-grounded answers. Benefiting
from the robustness of contemporary Large Language Models, our model adeptly
aligns with insights from research papers. This advancement not only
underscores considerable progress in bridging the gap between human and machine
interpretation in scientific imaging, but also hints at expansive avenues for
future research and broader application.


  We present a detailed analysis of Magellanic Bridge Cepheid sample
constructed using the OGLE Collection of Variable Stars. Our updated Bridge
sample contains 10 classical and 13 anomalous Cepheids. We calculate their
individual distances using optical period--Wesenheit relations and construct
three-dimensional maps. Classical Cepheids on-sky locations match very well
neutral hydrogen and young stars distributions, thus they add to the overall
Bridge young population. In three dimensions, eight out of ten classical
Cepheids form a bridge-like connection between the Magellanic Clouds. The other
two are located slightly farther and may constitute the Counter Bridge. We
estimate ages of our Cepheids to be less than 300 Myr for five up to eight out
of ten, depending on whether the rotation is included. This is in agreement
with a scenario where these stars were formed in-situ after the last encounter
of the Magellanic Clouds. Cepheids' proper motions reveal that they are moving
away from both Large and Small Magellanic Cloud. Anomalous Cepheids are more
spread than classical Cepheids in both two and three dimensions. Even though,
they form a rather smooth connection between the Clouds. However, this
connection does not seem to be bridge-like, as there are many outliers around
both Magellanic Clouds.


  Starting from the product of a $3$-torus and a compact K\"ahler
(respectively, hyperK\"ahler) manifold we construct via mapping tori
generalized K\"ahler manifolds of split (respectively, non-split) type. In this
way we obtain new non-K\"ahler examples and we recover the known examples of
generalized K\"ahler solvmanifolds. Moreover, we investigate the formality and
the Dolbeault cohomology of the generalized K\"ahler mapping tori.


  We report on the status of the Fermilab-MILC calculation of the form factor
f_+^{K pi}(0), needed to extract the CKM matrix element |V_{us}| from
experimental data on K semileptonic decays. The HISQ formulation is used in the
simulations for the valence quarks, while the sea quarks are simulated with the
asqtad action (MILC N_f=2+1 configurations). We discuss the general methodology
of the calculation, including the use of twisted boundary conditions to get
values of the momentum transfer close to zero and the different techniques
applied for the correlators fits. We present initial results for lattice
spacings a=0.12fm and a=0.09fm, and several choices of the light quark masses.


  We present the results of ab initio calculations describing the adsorption of
certain small organic molecules on clean and oxidized Al(111) surfaces as well
as on the alpha-Al2O3(0001) surface. Our results show that adsorption of
benzene on the clean and oxidized Al(111) surfaces is generally weak, the
adsorption energy being at most around -0.5 eV per benzene molecule, and the
molecule adsorbed at a considerable distance from the surfaces. The adsorption
energy varies weakly at the different adsorption sites and as a function of the
oxygen coverage. For the alumina surface, we find no benzene adsorption at all.
We have also calculated a phenol molecule on the aluminium and alumina
surfaces, since it is similar to the benzene molecule. The results show a weak
adsorption for phenol on the alumina surface and no adsorption on the aluminium
or oxidized aluminium surfaces at all. For the propane molecule there is no
adsorption on either the oxidized aluminium or the alumina surface, whereas the
carbonic acid molecule binds strongly to the alumina but not to the aluminium
surface.


  There is an increased emphasis on visualizing neuroimaging results in more
intuitive ways. Common statistical tools for dissemination, such as bar charts,
lack the spatial dimension that is inherent in neuroimaging data. Here we
present two packages for the statistical software R, ggseg and ggseg3d, that
integrate this spatial component. The ggseg and ggseg3d packages visualize
pre-defined brain segmentations as both 2D polygons and 3D meshes,
respectively. Both packages are integrated with other well-established
R-packages, allowing great flexibility. In this tutorial, we present the main
data and functions in the ggseg and ggseg3d packages for brain atlas
visualization. The main highlighted functions are able to display brain
segmentation plots in R. Further, the accompanying ggsegExtra-package includes
a wider collection of atlases, and is intended for community-based efforts to
develop more compatible atlases to ggseg and ggseg3d. Overall, the
ggseg-packages facilitate parcellation-based visualizations in R, improve and
ease the dissemination of the results, and increase the efficiency of the
workflows.


  The subject of optomechanics involves interactions between optical and
mechanical degrees of freedom, and is currently of great interest as an enabler
of fundamental investigations in quantum mechanics, as well as a platform for
ultrasensitive measurement devices. The majority of optomechanical
configurations rely on the exchange of linear momentum between light and
matter. We will begin this tutorial with a brief description of such systems.
Subsequently, we will introduce optomechanical systems based on angular
momentum exchange. In this context, optical fields carrying polarization and
orbital angular momentum will be considered, while for the mechanics, torsional
and free rotational motion will be of relevance. Our overall aims will be to
supply basic analyses of some of the existing theoretical proposals, to provide
functional descriptions of some of the experiments conducted thus far, and to
consider some directions for future research. We hope this tutorial will be
useful to both theorists and experimentalists interested in the subject.


  Event-scale analysis techniques using correlation and fluctuation measures
are applied to heavy-ion collision data with the goal of discovering,
characterizing, and understanding deconfined quark matter. In service of these
goals development of a scale-local thermodynamics is discussed and applied to a
broad range of toy models, simulations, and data. Scale-local partitioning is
discussed at length and an ideal theoretical reference is derived for
comparison to data. The dimension of the chaotic attractor of the Henon map is
calculated as a function of scale, and the implications of scale-local
dimension are explored. Event spaces with discriminatory power are developed
and applied to the face recognition problem, detector triggering, and STAR and
NA49 data. Event-wise mean transverse momentum fluctuations in STAR data are
analyzed with a minimally biased central-limit based measure using numerical
and graphical methods. Cut efficiencies, corrections, and systematic error
sources are all addressed. A connection between non-statistical fluctuations
and two-particle correlations is found and exploited. Two-particle correlation
space formation is discussed and methods for minimizing error from event mixing
are discovered. Central data from STAR and NA49 are analyzed, confirming the
results of the fluctuation analysis and providing additional insight into the
physics sources contributing to correlations in heavy-ion collisions.


  Building an infinite square-free word by appending one letter at a time while
simultaneously avoiding the creation of squares is most likely to fail. When
the alphabet has two letters this approach is impossible. When the alphabet has
three or more letters, one will most probably create a word in which the
addition of any letter invariably creates a square. When one restricts the set
of undesired squares to a finite one, this can be possible. We study the
constraints on the alphabet and the set of squares which permit this approach
to work.


  Recently a simple solution of the vacuum Einstein-Maxwell field equations was
given describing a plane electromagnetic shock wave sharing its wave front with
a plane gravitational impulse wave. We present here an exact solution of the
vacuum Einstein-Maxwell field equations describing the head-on collision of
such a wave with a plane gravitational impulse wave. The solution has the
Penrose-Khan solution and a solution obtained by Griffiths as separate limiting
cases.


  In this paper, we present new results regarding the orbital stability of
solitary standing waves for the general fourth-order Schr\"odinger equation
with mixed dispersion. The existence of solitary waves can be determined both
as minimizers of a constrained complex functional and by using a numerical
approach. In addition, for specific values of the frequency associated with the
standing wave, one obtains explicit solutions with a hyperbolic secant profile.
Despite these explicit solutions being minimizers of the constrained
functional, they cannot be seen as a smooth curve of solitary waves, and this
fact prevents their determination of stability using classical approaches in
the current literature. To overcome this difficulty, we employ a numerical
approach to construct a smooth curve of solitary waves. The existence of a
smooth curve is useful for showing the existence of a threshold power
$\alpha_0\approx 4.8$ of the nonlinear term such that if $\alpha\in
(0,\alpha_0),$ the explicit solitary wave is stable, and if $\alpha>\alpha_0$,
the wave is unstable. An important feature of our work, caused by the presence
of the mixed dispersion term, concerns the fact that the threshold value
$\alpha_0 \approx 4.8$ is not the same as that established for proving the
existence of global solutions in the energy space, as is well known for the
classical nonlinear Schr\"odinger equation.


  The meaning of time asymmetry in quantum physics is discussed. On the basis
of a mathematical theorem, the Stone--von Neumann theorem, the solutions of the
dynamical equations, the Schr\"odinger equation (1) for states or the
Heisenberg equation (6a) for observables are given by a unitary group. Dirac
kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions;
for this kind of RHS a mathematical theorem also leads to time symmetric group
evolution. Scattering theory suggests to distinguish mathematically between
states (defined by a preparation apparatus) and observables (defined by a
registration apparatus (detector)). If one requires that scattering resonances
of width $\Gamma$ and exponentially decaying states of lifetime
$\tau=\frac{\hbar}{\Gamma}$ should be the same physical entities (for which
there is sufficient evidence) one is led to a pair of RHS's of Hardy functions
and connected with it, to a semigroup time evolution $t_{0}\leq t<\infty$, with
the puzzling result that there is a quantum mechanical beginning of time, just
like the big bang time for the universe, when it was a quantum system. The
decay of quasi-stable particles is used to illustrate this quantum mechanical
time asymmetry. From the analysis of these processes, we show that the
properties of rigged Hilbert spaces of Hardy functions are suitable for a
formulation of time asymmetry in quantum mechanics.


  Let $C$ be a nodal curve and $L$ be an invertible sheaf on $C$. Let
$\alpha_{L}:C\dashrightarrow J_{C}$ be the degree-$1$ rational Abel map, which
takes a smooth point $Q\in C$ to $\left[ m_{Q}\otimes L\right] $ in the
Jacobian of $C$. In this work we extend $\alpha_{L}$ to a morphism
$\overline{\alpha}_{L}:C\rightarrow\overline{J}_{E}^{P}$ taking values on
Esteves' compactified Jacobian for any given polarization $E$. The maps
$\overline{\alpha}_{L}$ are limits of Abel maps of smooth curves of the type
$\alpha_{L}$.


  Randomized controlled trials are often run in settings with many
subpopulations that may have differential benefits from the treatment being
evaluated. We consider the problem of sample selection, i.e., whom to enroll in
a randomized trial, such as to optimize welfare in a heterogeneous population.
We formalize this problem within the minimax-regret framework, and derive
optimal sample-selection schemes under a variety of conditions. Using data from
a COVID-19 vaccine trial, we also highlight how different objectives and
decision rules can lead to meaningfully different guidance regarding optimal
sample allocation.


  The antiferromagnetic (AFM) to ferromagnetic (FM) first order phase
transition of an epitaxial FeRh thin-film has been studied with x-ray magnetic
circular dichroism using photoemission electron microscopy. The FM phase is
magnetized in-plane due to shape anisotropy, but the magnetocrystalline
anisotropy is negligible and there is no preferred in-plane magnetization
direction. When heating through the AFM to FM phase transition the nucleation
of the FM phase occurs at many independent nucleation sites with random domain
orientation. The domains subsequently align to form the final FM domain
structure. We observe no pinning of the FM domain structure.


  We study an interacting Majorana chain with an open boundary condition. In
the case without interactions, the system shows a prototypical Majorana edge
zero mode in the sector of the ground state with a spectral gap above the
sector. We prove that both of the Majorana edge zero mode and the non-vanishing
spectral gap are stable against generic weak interactions whose fermion parity
is even. We also deal with the corresponding ladder systems, and discuss the
$\mathbb{Z}_2$ index for the Majorana edge zero modes.


  The power law $1/f^{\alpha}$ in the power spectrum characterizes the
fluctuating observables of many complex natural systems. Considering the energy
levels of a quantum system as a discrete time series where the energy plays the
role of time, the level fluctuations can be characterized by the power
spectrum. Using a family of quantum billiards, we analyze the order to chaos
transition in terms of this power spectrum. A power law $1/f^{\alpha}$ is found
at all the transition stages, and it is shown that the exponent $\alpha$ is
related to the chaotic component of the classical phase space of the quantum
system.


  We present a first order system least squares (FOSLS) method for the
Helmholtz equation at high wave number k, which always deduces Hermitian
positive definite algebraic system. By utilizing a non-trivial solution
decomposition to the dual FOSLS problem which is quite different from that of
standard finite element method, we give error analysis to the hp-version of the
FOSLS method where the dependence on the mesh size h, the approximation order
p, and the wave number k is given explicitly. In particular, under some
assumption of the boundary of the domain, the L2 norm error estimate of the
scalar solution from the FOSLS method is shown to be quasi optimal under the
condition that kh/p is sufficiently small and the polynomial degree p is at
least O(\log k). Numerical experiments are given to verify the theoretical
results.


  In vitro fertilization (IVF) comprises a sequence of interventions concerned
with the creation and culture of embryos which are then transferred to the
patient's uterus. While the clinically important endpoint is birth, the
responses to each stage of treatment contain additional information about the
reasons for success or failure. As such, the ability to predict not only the
overall outcome of the cycle, but also the stage-specific responses, can be
useful. This could be done by developing separate models for each response
variable, but recent work has suggested that it may be advantageous to use a
multivariate approach to model all outcomes simultaneously. Here, joint
analysis of the sequential responses is complicated by mixed outcome types
defined at two levels (patient and embryo). A further consideration is whether
and how to incorporate information about the response at each stage in models
for subsequent stages. We develop a case study using routinely collected data
from a large reproductive medicine unit in order to investigate the feasibility
and potential utility of multivariate prediction in IVF. We consider two
possible scenarios. In the first, stage-specific responses are to be predicted
prior to treatment commencement. In the second, responses are predicted
dynamically, using the outcomes of previous stages as predictors. In both
scenarios, we fail to observe benefits of joint modelling approaches compared
to fitting separate regression models for each response variable.


  Generative semantic hashing is a promising technique for large-scale
information retrieval thanks to its fast retrieval speed and small memory
footprint. For the tractability of training, existing generative-hashing
methods mostly assume a factorized form for the posterior distribution,
enforcing independence among the bits of hash codes. From the perspectives of
both model representation and code space size, independence is always not the
best assumption. In this paper, to introduce correlations among the bits of
hash codes, we propose to employ the distribution of Boltzmann machine as the
variational posterior. To address the intractability issue of training, we
first develop an approximate method to reparameterize the distribution of a
Boltzmann machine by augmenting it as a hierarchical concatenation of a
Gaussian-like distribution and a Bernoulli distribution. Based on that, an
asymptotically-exact lower bound is further derived for the evidence lower
bound (ELBO). With these novel techniques, the entire model can be optimized
efficiently. Extensive experimental results demonstrate that by effectively
modeling correlations among different bits within a hash code, our model can
achieve significant performance gains.


  We derive the model of homogenized von K\'arm\'an shell theory, starting from
three dimensional nonlinear elasticity. The original three dimensional model
contains two small parameters: the oscillations of the material $\e$ and the
thickness of the shell $h$. Depending on the asymptotic ratio of these two
parameters, we obtain different asymptotic theories. In the case $h\ll\e$ we
identify two different asymptotic theories, depending on the ratio of $h$ and
$\e^2$. In the case of convex shells we obtain a complete picture in the whole
regime $h\ll\e$.


  In this paper we show that the leading coefficient $\mu(y,w)$ of certain
Kazhdan-Lusztig polynomials $P_{y,w}$ of the permutation group $\mathfrak S_n$
of 1,2,...,n are not greater than 1. More precisely, we show that the leading
coefficients $\mu(y,w)$ are not greater than 1 whenever $a(y)< a(w)$, where $a:
\mathfrak S_n\to\mathbf N$ is the function defined by Lusztig.


  An efficient quantum modular exponentiation method is indispensible for
Shor's factoring algorithm. But we find that all descriptions presented by
Shor, Nielsen and Chuang, Markov and Saeedi, et al., are flawed. We also remark
that some experimental demonstrations of Shor's algorithm are misleading,
because they violate the necessary condition that the selected number $q=2^s$,
where $s$ is the number of qubits used in the first register, must satisfy $n^2
\leq q < 2n^2$, where $n$ is the large number to be factored.


  We present a new, tractable method for solving and analyzing risk-aware
control problems over finite and infinite, discounted time-horizons where the
dynamics of the controlled process are described as a martingale problem.
Supposing general Polish state and action spaces, and using generalized,
relaxed controls, we state a risk-aware dynamic optimal control problem of
minimizing risk of costs described by a generic risk function. We then
construct an alternative formulation that takes the form of a nonlinear
programming problem, constrained by the dynamic, {i.e.} time-dependent, and
linear Kolmogorov forward equation describing the distribution of the state and
accumulated costs. We show that the formulations are equivalent, and that the
optimal control process can be taken to be Markov in the controlled process
state, running costs, and time. We further prove that under additional
conditions, the optimal value is attained. An example numeric problem is
presented and solved.


  We present the K-band Hubble diagrams (K-z relations) of sub-mm-selected
galaxies and hyperluminous galaxies (HLIRGs). We report the discovery of a
remarkably tight K-z relation of HLIRGs, indistinguishable from that of the
most luminous radiogalaxies. Like radiogalaxies, the HLIRG K-z relation at z<~3
is consistent with a passively evolving ~3L* instantaneous starburst starting
from a redshift of z~10. In contrast, many sub-mm selected galaxies are >~2
magnitudes fainter, and the population has a much larger dispersion. We argue
that dust obscuration and/or a larger mass range may be responsible for this
scatter. The galaxies so far proved to be hyperluminous may have been biased
towards higher AGN bolometric contributions than sub-mm-selected galaxies due
to the 60 micron selection of some, so the location on the K-z relation may be
related to the presence of the most massive AGN. Alternatively, a particular
host galaxy mass range may be responsible for both extreme star formation and
the most massive active nuclei.


  Can large language models (LLMs) express their uncertainty in situations
where they lack sufficient parametric knowledge to generate reasonable
responses? This work aims to systematically investigate LLMs' behaviors in such
situations, emphasizing the trade-off between honesty and helpfulness. To
tackle the challenge of precisely determining LLMs' knowledge gaps, we
diagnostically create unanswerable questions containing non-existent concepts
or false premises, ensuring that they are outside the LLMs' vast training data.
By compiling a benchmark, UnknownBench, which consists of both unanswerable and
answerable questions, we quantitatively evaluate the LLMs' performance in
maintaining honesty while being helpful. Using a model-agnostic unified
confidence elicitation approach, we observe that most LLMs fail to consistently
refuse or express uncertainty towards questions outside their parametric
knowledge, although instruction fine-tuning and alignment techniques can
provide marginal enhancements. Moreover, LLMs' uncertainty expression does not
always stay consistent with the perceived confidence of their textual outputs.


  Source-free domain adaptation (SFDA) alleviates the domain discrepancy among
data obtained from domains without accessing the data for the awareness of data
privacy. However, existing conventional SFDA methods face inherent limitations
in medical contexts, where medical data are typically collected from multiple
institutions using various equipment. To address this problem, we propose a
simple yet effective method, named Uncertainty-aware Adaptive Distillation
(UAD) for the multi-source-free unsupervised domain adaptation (MSFDA) setting.
UAD aims to perform well-calibrated knowledge distillation from (i) model level
to deliver coordinated and reliable base model initialisation and (ii) instance
level via model adaptation guided by high-quality pseudo-labels, thereby
obtaining a high-performance target domain model. To verify its general
applicability, we evaluate UAD on two image-based diagnosis benchmarks among
two multi-centre datasets, where our method shows a significant performance
gain compared with existing works. The code will be available soon.


  It has been proposed that the energy evolution of QCD amplitudes in the
high-energy regime falls in the universality class of reaction-diffusion
processes. We review the arguments for this correspondence, and we explain how
it enables one to compute analytically asymptotic features of QCD amplitudes.


  We propose an approach for constructing spatial slices of (3+1) spacetimes
with cosmological constant but without a matter content, which yields (2+1)
vacuum with $\Lambda$ solutions. The reduction mechanism from (3+1) to (2+1)
gravity is supported on a criterion in which the Weyl tensor components are
required to vanish together with a dimensional reduction via an appropriate
foliation. By using an adequate reduction mechanism from the
Pleba\'nski-Carter[A] solution in (3+1) gravity, the (2+1) BTZ solution can be
obtained.


  Following earlier findings, we argue that the low-$|t|$ structure in the
elastic diffractive cone, recently reported by the TOTEM Collaboration at $8$
TeV, is a consequence of the threshold singularity required by $t-$channel
unitarity, such as revealed earlier at the ISR. By using simple Regge-pole
models, we analyze the available data on the $pp$ elastic differential cross
section in a wide range of c.m. energies, namely those from ISR to LHC8,
obtaining good fits of all datasets. This study hints at the fact that the
non-exponential behaviour observed at LHC8 is a recurrence of the low-$|t|$
"break" phenomenon, observed in the seventies at ISR, being induced by the
presence of a two-pion loop singularity in the Pomeron trajectory.


  Ensuring the safety of Reinforcement Learning (RL) is crucial for its
deployment in real-world applications. Nevertheless, managing the trade-off
between reward and safety during exploration presents a significant challenge.
Improving reward performance through policy adjustments may adversely affect
safety performance. In this study, we aim to address this conflicting relation
by leveraging the theory of gradient manipulation. Initially, we analyze the
conflict between reward and safety gradients. Subsequently, we tackle the
balance between reward and safety optimization by proposing a soft switching
policy optimization method, for which we provide convergence analysis. Based on
our theoretical examination, we provide a safe RL framework to overcome the
aforementioned challenge, and we develop a Safety-MuJoCo Benchmark to assess
the performance of safe RL algorithms. Finally, we evaluate the effectiveness
of our method on the Safety-MuJoCo Benchmark and a popular safe RL benchmark,
Omnisafe. Experimental results demonstrate that our algorithms outperform
several state-of-the-art baselines in terms of balancing reward and safety
optimization.


  We have synthesized two Nb@C composites with an order of magnitude difference
in the density of single-atom niobium substituted into graphitic layers. The
concentration and sites of single-atom Nb are identified using
aberration-corrected scanning transmission electron microscopy and density
functional theory. Comparing the complex permittivity spectra show that the
representative dielectric resonance at ~16 GHz originates from the intrinsic
polarization of single-atom Nb sites, confirmed by theoretical simulations. The
single-atom dielectric resonance represents the physical limit of the
electromagnetic response of condensed matter, and thus might open up a new
avenue for designing electromagnetic wave absorption materials. Single-atom
resonance also has important implications in understanding the correlation
between the macroscopic dielectric behaviors and the atomic-scale structural
origin.


  We consider a system of two coupled KdV equations (one for left-movers, the
other for right-movers) and investigate its ultra-relativistic and
non-relativistic limits in the sense of BMS$_3$/GCA$_2$ symmetry. We show that
there is no local ultra-relativistic limit of the system with positive energy,
regardless of the coupling constants in the original relativistic Hamiltonian.
By contrast, local non-relativistic limits with positive energy exist, provided
there is a non-zero coupling between left- and right-movers. In these limits,
the wave equations reduce to Hirota-Satsuma dynamics (of type IV) and become
integrable. This is thus a situation where input from high-energy physics
contributes to nonlinear science - in this case, uncovering the limiting
relation between integrable structures of KdV and Hirota-Satsuma.


  We contruct here the Hopf algebra structure underlying the process of
renormalization of non-commutative quantum field theory.


  The design process of photovoltaic (PV) modules can be greatly enhanced by
using advanced and accurate models in order to predict accurately their
electrical output behavior. The main aim of this paper is to investigate the
application of an advanced neural network based model of a module to improve
the accuracy of the predicted output I--V and P--V curves and to keep in
account the change of all the parameters at different operating conditions.
Radial basis function neural networks (RBFNN) are here utilized to predict the
output characteristic of a commercial PV module, by reading only the data of
solar irradiation and temperature. A lot of available experimental data were
used for the training of the RBFNN, and a backpropagation algorithm was
employed. Simulation and experimental validation is reported.


  The nuclear $(n;t)-$reaction of the three-electron ${}^{6}$Li atom with
thermal/slow neutrons is considered. An effective method has been developed for
determining the probabilities of formation of various atoms and ions in
different bound states. We discuss a number of fundamental questions directly
related to numerical computations of the final state atomic probabilities. A
few appropriate variational expansions for atomic wave functions of the
incident lithium atom and final helium atom and/or tritium negatively charged
ion are discussed. It appears that the final ${}^4$He atom arising during the
nuclear $(n,{}^{6}$Li; ${}^4$He$,t)$-reaction in the three-electron Li atom can
also be created in its triplet states. The formation of the quasi-stable
three-electron $e^{-}_3$ during the nuclear $(n; t)-$reaction at the Li atom is
briefly discussed. Bremsstrahlung emitted by atomic electrons accelerated by
the rapidly moving nuclear fragments from this reaction is analyzed. The
frequency spectrum of the emitted radiation is investigated.


  We propose a new, self-consistent and dynamical scenario which gives rise to
well-defined initial conditions for five-dimensional brane-world cosmologies
with radion stabilization. At high energies, the five-dimensional effective
theory is assumed to have a scale invariance so that it admits an expanding
scaling solution as a future attractor. The system automatically approaches the
scaling solution and, hence, the initial condition for the subsequent
low-energy brane cosmology is set by the scaling solution. At low energies, the
scale invariance is broken and a radion stabilization mechanism drives the
dynamics of the brane-world system. We present an exact, analytic scaling
solution for a class of scale-invariant effective theories of five-dimensional
brane-world models which includes the five-dimensional reduction of the
Horava-Witten theory, and provide convincing evidence that the scaling solution
is a future attractor.


  In this paper, we design an association scheme to maximize the sum energy
efficiency for massive multiple-input and multiple-output (MIMO) enabled
heterogeneous cellular networks (HCNs). Considering that the final formulated
problem is in a sum-of-ratio form, we first need to transform it into a
parametric nonfractional form, by which we can achieve its solution through a
two-layer iterative algorithm. The outer layer searches the energy efficiency
parameters and multipliers associated with signal-interference-plus-noise-ratio
(SINR) constraints using Newton-like method, and the inner layer optimizes the
association indices using Lagrange multiplier method. In fact, the inner layer
doesn't need iterative steps when the SINR constraints are not involved in the
original problem, and then the whole algorithm should be a one-layer iterative
one. As for the two-layer iterative algorithm, we also give the corresponding
convergence proof. Numerical results show that the proposed scheme
significantly outperforms the existing one in system throughput and network
energy efficiency. In addition, we also investigate the impacts of the number
of massive antennas and the transmit power of each pico base station on these
association performances.


  A family of simple and minimal extensions of the standard cosmological
$\Lambda$CDM model in which dark matter experiences an additional long-range
scalar interaction is demonstrated to alleviate the long lasting Hubble-tension
while letting primordial nucleosynthesis predictions unaffected and passing by
construction all current local tests of general relativity. This article
describes their theoretical formulation and their implications for dark matter.
Then, it investigates their cosmological signatures, both at the background and
perturbation levels. A detailed comparison to astrophysical data is performed
to discuss their ability to fit existing data. A thorough discussion of the
complementarity of the low- and high-redshift data and on their constraining
power highlights how these models improve the predictions of the $\Lambda$CDM
model whatever the combination of datasets used and why they can potentially
resolve the Hubble tension. Being fully predictive in any environment, they
pave the way to a better understanding of gravity in the dark matter sector.


  Three coarse-grained models of the double-stranded DNA are proposed and
compared in the context of mechanical manipulation such as twisting and various
schemes of stretching. The models differ in the number of effective beads
(between two and five) representing each nucleotide. They all show similar
behavior and, in particular, lead to a torque-force phase diagrams
qualitatively consistent with experiments and all-atom simulations.


  We study those Banach spaces $X$ for which $S_X$ does not admit a finite
$\eps$-net consisting of elements of $S_X$ for any $\eps < 2$. We give
characterisations of this class of spaces in terms of $\ell_1$-type sequences
and in terms of the almost Daugavet property. The main result of the paper is:
a separable Banach space $X$ is isomorphic to a space from this class if and
only if $X$ contains an isomorphic copy of $\ell_1$.


  We present a method of obtaining the entire unitarity triangle from
measurements of B -> pi K decay rates alone. Electroweak penguin amplitudes are
included, and are related to tree operators. Discrete ambiguities are removed
by comparing solutions with independent experimental data. The theoretical
uncertainty in this method is rather small, in the range 5--10%.


  The discovery of superconductivity at 203K in SH$_3$ is an important step
toward higher values of $T_c$. Predictions based on state-of-the-art DFT for
the electronic structure, including one preceding experimental confirmation,
showed the mechanism to be the electron-phonon interaction. This was confirmed
in optical spectroscopy measurements. For photon energies between $\sim 450$
and 600 meV in SH$_3$, the reflectance in the superconducting state is below
that in its normal state. This difference decreases as $T$ approaches $T_c$.
Decreasing absorption with increasing $T$ is opposite to what is expected in
ordinary metals. Such an anomalous behavior can be traced back to the energy
dependence of the superconducting density of states which is highly peaked at
the energy gap value $\Delta$ but decays back to the constant normal state
value as energy is increased, on a scale of a few $\Delta$, or by increasing
$T$ towards $T=T_c$. The process of phonon-assisted optical absorption is
encoded with a knowledge of the $T$-dependence of $\Delta$, the order parameter
of the superconducting state. Should the energy of the phonon involved be very
large, of order 200 meV or more, this process offers the possibility of
observing the closing of the superconducting order parameter with $T$ at
correspondingly very large energies. The very recent experimental observation
of a $T_c\simeq 250$ K in LaH$_{10}$ has further heightened interest in the
hydrides. We compare the relevant phonon structure seen in optics with related
features in the real and imaginary part of the frequency dependent gap,
quasiparticle density of states, reflectance, absorption, and optical
scattering rate. The phonon structures all carry information on the $T_c$ value
and the $T$-dependence of the order parameter, and can be used to confirm that
the mechanism involved in superconductivity is the electron-phonon interaction.


  Optimizing an industrial-scale supercritical water gasification process
requires detailed knowledge of chemical reaction pathways, rates, and product
yields. Laboratory-scale reactors are employed to develop this knowledge base.
The rationale behind designs and component selection of continuous flow,
laboratory-scale supercritical water gasification reactors is analyzed. Some
design challenges have standard solutions, such as pressurization and
preheating, but issues with solid precipitation and feedstock pretreatment
still present open questions. Strategies for reactant mixing must be evaluated
on a system-by-system basis, depending on feedstock and experimental goals, as
mixing can affect product yields, char formation, and reaction pathways.
In-situ Raman spectroscopic monitoring of reaction chemistry promises to
further fundamental knowledge of gasification and decrease experimentation
time. High-temperature, high-pressure spectroscopy in supercritical water
conditions is performed, however, long-term operation flow cell operation is
challenging. Comparison of Raman spectra for decomposition of formic acid in
the supercritical region and cold section of the reactor demonstrates the
difficulty in performing quantitative spectroscopy in the hot zone. Future
designs and optimization of SCWG reactors should consider well-established
solutions for pressurization, heating, and process monitoring, and effective
strategies for mixing and solids handling for long-term reactor operation and
data collection.


  We consider the problem of reconstructing graphs or labeled graphs from
neighborhoods of a given radius r. Special instances of this problem include
the well known: DNA shotgun assembly; the lesser-known: neural network
reconstruction; and a new problem: assembling random jigsaw puzzles. We provide
some necessary and some sufficient conditions for correct recovery both in
combinatorial terms and for some generative models including random labelings
of lattices, Erdos-Renyi random graphs, and the random jigsaw puzzle model.
Many open problems and conjectures are provided.


  Decoding of seen visual contents with non-invasive brain recordings has
important scientific and practical values. Efforts have been made to recover
the seen images from brain signals. However, most existing approaches cannot
faithfully reflect the visual contents due to insufficient image quality or
semantic mismatches. Compared with reconstructing pixel-level visual images,
speaking is a more efficient and effective way to explain visual information.
Here we introduce a non-invasive neural decoder, termed as MindGPT, which
interprets perceived visual stimuli into natural languages from fMRI signals.
Specifically, our model builds upon a visually guided neural encoder with a
cross-attention mechanism, which permits us to guide latent neural
representations towards a desired language semantic direction in an end-to-end
manner by the collaborative use of the large language model GPT. By doing so,
we found that the neural representations of the MindGPT are explainable, which
can be used to evaluate the contributions of visual properties to language
semantics. Our experiments show that the generated word sequences truthfully
represented the visual information (with essential details) conveyed in the
seen stimuli. The results also suggested that with respect to language decoding
tasks, the higher visual cortex (HVC) is more semantically informative than the
lower visual cortex (LVC), and using only the HVC can recover most of the
semantic information. The code of the MindGPT model will be publicly available
at https://github.com/JxuanC/MindGPT.