  Measuring centrality in a social network, especially in bipartite mode, poses
several challenges such as requirement of full knowledge of the network
topology and lack of properly detection of top-k behavioral representative
users. In this paper, to overcome the aforementioned challenging issues, we
propose an accurate centrality measure, called HellRank, to identify central
nodes in bipartite social networks. HellRank is based on the Hellinger distance
between two nodes on the same side of a bipartite network. We theoretically
analyze the impact of the Hellinger distance on a bipartite network and find an
upper and lower bounds for this distance. The computation of HellRank
centrality measure can be distributed by letting each node uses only local
information on its immediate neighbors and therefore do not need a central
entity to have full knowledge of the network topological structure. We
experimentally evaluate performance of the HellRank measure in correlation with
other centrality measures on real-world networks. The results show partial
ranking similarity between the HellRank and the other conventional metrics
according to the Kendall and Spearman rank correlation coefficient.


  I present three types of applications of generalized additive models (GAMs)
to COVID-19 mortality rates in the US for the purpose of advancing methods to
document inequities with respect to which communities suffered disproportionate
COVID-19 mortality rates at specific times during the first three years of the
pandemic. First, GAMs can be used to describe the changing relationship between
COVID-19 mortality and county-level covariates (sociodemographic, economic, and
political metrics) over time. Second, GAMs can be used to perform
spatiotemporal smoothing that pools information over time and space to address
statistical instability due to small population counts or stochasticity
resulting in a smooth, dynamic latent risk surface summarizing the mortality
risk associated with geographic locations over time. Third, estimation of
COVID-19 mortality associations with county-level covariates conditional on a
smooth spatiotemporal risk surface allows for more rigorous consideration of
how socio-environmental contexts and policies may have impacted COVID-19
mortality. Each of these approaches provides a valuable perspective to
documenting inequities in COVID-19 mortality by addressing the question of
which populations have suffered the worst burden of COVID-19 mortality taking
into account the nonlinear spatial, temporal, and social patterning of disease.


  This paper studies the connection between a class of mean-field games and a
social welfare optimization problem. We consider a mean-field game in function
spaces with a large population of agents, and each agent seeks to minimize an
individual cost function. The cost functions of different agents are coupled
through a mean-field term that depends on the mean of the population states. We
show that although the mean-field game is not a potential game, under some mild
condition the $\epsilon$-Nash equilibrium of the mean-field game coincides with
the optimal solution to a social welfare optimization problem, and this is true
even when the individual cost functions are non-convex. The connection enables
us to evaluate and promote the efficiency of the mean-field equilibrium. In
addition, it also leads to several important implications on the existence,
uniqueness, and computation of the mean-field equilibrium. Numerical results
are presented to validate the solution, and examples are provided to show the
applicability of the proposed approach.


  Standard machine translation systems process sentences in isolation and hence
ignore extra-sentential information, even though extended context can both
prevent mistakes in ambiguous cases and improve translation coherence. We
introduce a context-aware neural machine translation model designed in such way
that the flow of information from the extended context to the translation model
can be controlled and analyzed. We experiment with an English-Russian subtitles
dataset, and observe that much of what is captured by our model deals with
improving pronoun translation. We measure correspondences between induced
attention distributions and coreference relations and observe that the model
implicitly captures anaphora. It is consistent with gains for sentences where
pronouns need to be gendered in translation. Beside improvements in anaphoric
cases, the model also improves in overall BLEU, both over its context-agnostic
version (+0.7) and over simple concatenation of the context and source
sentences (+0.6).


  We extend the generalised comparison principle for the Monge-Amp\`ere
equation due to Rauch & Taylor (Rocky Mountain J. Math. 7, 1977) to nonconvex
domains. From the generalised comparison principle we deduce bounds (from above
and below) on solutions of the Monge-Amp\`ere equation with sign-changing
right-hand side. As a consequence, if the right-hand side is nonpositive (and
does not vanish almost everywhere) then the equation equipped with constant
boundary condition has no solutions. In particular, due to a connection between
the two-dimensional Navier-Stokes equations and the Monge-Amp\`ere equation,
the pressure $p$ in 2D Navier-Stokes equations on a bounded domain cannot
satisfy $\Delta p \leq 0$ in $\Omega $ unless $\Delta p \equiv 0$ (at any fixed
time). As a result at any time $t>0$ there exists $z\in \Omega $ such that
$\Delta p (z,t) =0$.


  In recent years a considerable amount of attention has been devoted to the
investigation of 2D quantum field theories perturbed by certain types of
irrelevant operators. These are the composite field
$\mathrm{T}\bar{\mathrm{T}}$ - constructed out of the components of the
stress-energy tensor - and its generalisations - built from higher-spin
conserved currents. The effect of such perturbations on the infrared and
ultraviolet properties of the theory has been extensively investigated. In the
context of integrable quantum field theories, a fruitful perspective is that of
factorised scattering theory. In fact, the above perturbations were shown to
preserve integrability. The resulting deformed scattering matrices -
extensively analysed with the thermodynamic Bethe ansatz - provide the first
step in the development of a complete bootstrap program. In this letter we
present a systematic approach to computing matrix elements of operators in
generalised $\mathrm{T}\bar{\mathrm{T}}$-perturbed models, based on employing
the standard form factor program. Our approach is very general and can be
applied to all theories with diagonal scattering. We show that the deformed
form factors, just as happens for the $S$-matrix, factorise into the product of
the undeformed ones and of a perturbation- and theory-dependent term. From
these solutions, correlation functions can be obtained and their asymptotic
properties studied. Our results set the foundations of a new research program
for massive integrable quantum field theory perturbed by irrelevant operators.


  In this paper we introduce a method of characteristic sets with respect to
several term orderings for difference-differential polynomials. Using this
technique, we obtain a method of computation of multivariate dimension
polynomials of finitely generated difference-differential field extensions.
Furthermore, we find new invariants of such extensions and show how the
computation of multivariate difference-differential polynomials is applied to
the equivalence problem for systems of algebraic difference-differential
equations.


  Large-scale, big-variant, and high-quality data are crucial for developing
robust and successful deep-learning models for medical applications since they
potentially enable better generalization performance and avoid overfitting.
However, the scarcity of high-quality labeled data always presents significant
challenges. This paper proposes a novel approach to address this challenge by
developing controllable diffusion models for medical image synthesis, called
EMIT-Diff. We leverage recent diffusion probabilistic models to generate
realistic and diverse synthetic medical image data that preserve the essential
characteristics of the original medical images by incorporating edge
information of objects to guide the synthesis process. In our approach, we
ensure that the synthesized samples adhere to medically relevant constraints
and preserve the underlying structure of imaging data. Due to the random
sampling process by the diffusion model, we can generate an arbitrary number of
synthetic images with diverse appearances. To validate the effectiveness of our
proposed method, we conduct an extensive set of medical image segmentation
experiments on multiple datasets, including Ultrasound breast (+13.87%), CT
spleen (+0.38%), and MRI prostate (+7.78%), achieving significant improvements
over the baseline segmentation methods. For the first time, to our best
knowledge, the promising results demonstrate the effectiveness of our EMIT-Diff
for medical image segmentation tasks and show the feasibility of introducing a
first-ever text-guided diffusion model for general medical image segmentation
tasks. With carefully designed ablation experiments, we investigate the
influence of various data augmentation ratios, hyper-parameter settings, patch
size for generating random merging mask settings, and combined influence with
different network architectures.


  Vector representations of natural language are ubiquitous in search
applications. Recently, various methods based on contrastive learning have been
proposed to learn textual representations from unlabelled data; by maximizing
alignment between minimally-perturbed embeddings of the same text, and
encouraging a uniform distribution of embeddings across a broader corpus.
Differently, we propose maximizing alignment between texts and a composition of
their phrasal constituents. We consider several realizations of this objective
and elaborate the impact on representations in each case. Experimental results
on semantic textual similarity tasks show improvements over baselines that are
comparable with state-of-the-art approaches. Moreover, this work is the first
to do so without incurring costs in auxiliary training objectives or additional
network parameters.


  Parity-time (PT) symmetric non-Hermitian Hamiltonians bring about many novel
features and interesting applications such as quantum gates faster than those
in Hermitian systems, and topological state transfer. The performance of
evolutions under $\mathcal{PT}$-symmetric Hamiltonians is degraded by the
inevitable noise and errors due to system-environment interaction and
experimental imperfections. In contrast to Hermitian Hamiltonians, the
fluctuations in dissipative beams that are utilized to generate non-Hermitian
contributions in the PT-symmetric Hamiltonians cause additional errors. Here we
achieve the protection of PT-symmetric Hamiltonians against noise acting along
the qubit's quantization axis by combining quantum evolutions with dynamical
decoupling sequences. We demonstrate the performance of our method by numerical
simulations. Realistic noise sources and parameters are chosen including:
constant detuning error, time-varying detuning noise and dissipative-beam
noise. The fidelities of the protected evolutions are well above the
unprotected ones under all the above situations. Our work paves the way for
further studies and applications of non-Hermitian $\mathcal{PT}$-symmetric
physics in noisy quantum systems.


  We present an attempt to reconcile the solar tachocline glitch, a thin layer
immediately beneath the convection zone in which the seismically inferred sound
speed in the Sun exceeds corresponding values in standard solar models, with a
degree of partial material mixing which we presume to have resulted from a
combination of convective overshoot, wave transport and tachocline circulation.
We first summarize the effects of either modifying in the models the opacity in
the radiative interior or of incorporating either slow or fast tachocline
circulation. Neither alone is successful. We then consider, without physical
justification, incomplete material redistribution immediately beneath the
convection zone which is slow enough not to disturb radiative equilibrium. It
is modelled simply as a diffusion process. We find that, in combination with an
appropriate opacity modification, it is possible to find a density-dependent
diffusion coefficient that removes the glitch almost entirely, with a radiative
envelope that is consistent with seismology.


  We investigate string or branelike solutions for four-dimensional vacuum
Einstein equations in the presence of cosmological constant. For the case of
negative cosmological constant, the Banados-Teitelboim-Zanelli black string is
the only warped stringlike solution. The general solutions for nonwarped
branelike configurations are found and they are characterized by the
Arnowitt-Deser-Misner mass density and two tensions. Interestingly, the sum of
these tensions is equal to the minus of the mass density. Other than the
well-known black string and soliton spacetimes, all the static solutions
possess naked singularities. The time-dependent solutions can be regarded as
the anti-de Sitter extension of the well-known Kasner solutions. The speciality
of those static regular solutions and the implication of singular solutions are
also discussed in the context of cylindrical matter collapse. For the case of
positive cosmological constant, the Kasner-de Sitter spacetime appears as
time-dependent solutions and all static solutions are found to be naked
singular.


  We show that the recently postulated non-standard definition of work
proportional to force variation rather than to displacement [A. Imparato and L.
Peliti, cond-mat arXiv:0706.1134v1] is thermodynamically inconsistent at both
microscopic and macroscopic scales and leads to non-physical results, including
free energy changes that depend on arbitrary parameters.


  In public spaces shared with humans, ensuring multi-robot systems navigate
without collisions while respecting social norms is challenging, particularly
with limited communication. Although current robot social navigation techniques
leverage advances in reinforcement learning and deep learning, they frequently
overlook robot dynamics in simulations, leading to a simulation-to-reality gap.
In this paper, we bridge this gap by presenting a new multi-robot social
navigation environment crafted using Dec-POSMDP and multi-agent reinforcement
learning. Furthermore, we introduce SAMARL: a novel benchmark for cooperative
multi-robot social navigation. SAMARL employs a unique spatial-temporal
transformer combined with multi-agent reinforcement learning. This approach
effectively captures the complex interactions between robots and humans, thus
promoting cooperative tendencies in multi-robot systems. Our extensive
experiments reveal that SAMARL outperforms existing baseline and ablation
models in our designed environment. Demo videos for this work can be found at:
https://sites.google.com/view/samarl


  An ``anomalous'' supersymmetry transformation of the gaugino axial current is
given in supersymmetric Yang-Mills theory. The contact term is computed to
one-loop order by a gauge-invariant point-splitting procedure. We reexamine the
supercurrent anomaly in this method.


  In latitude-dependent energy balance models, ice-free and ice-covered
conditions form physical boundaries of the system. With carbon dioxide treated
as a bifurcation parameter, the resulting bifurcation diagram is nonsmooth with
curves of equilibria and boundaries forming corners at points of intersection.
Over long time scales, atmospheric carbon dioxide varies dynamically and the
nonsmooth diagram becomes a set of quasi-equilibria. {However, when introducing
carbon dynamics, care must be taken with the physical boundaries and
appropriate boundary motion specified. In this article, we extend an energy
balance model to include slowly varying carbon dioxide and develop a nonsmooth
framework based on physically relevant boundary dynamics. Within this
framework, we prove existence and uniqueness of solutions, as well as
invariance of the region of phase space bounded by ice-free and ice-covered
states.


  We present a detailed study of a linear sigma model containing one chiral
nonet transforming under U(1)$_A$ as a quark-antiquark composite and another
chiral nonet transforming as a diquark-anti diquark composite (or, equivalently
from a symmetry point of view, as a two meson molecule). The model provides an
intuitive explanation of a current puzzle in low energy QCD: Recent work has
suggested the existence of a lighter than 1 GeV nonet of scalar mesons which
behave like four quark composites. On the other hand, the validity of a
spontaneously broken chiral symmetric description would suggest that these
states be chiral partners of the light pseudoscalar mesons, which are two quark
composites. The model solves the problem by starting with the two chiral nonets
mentioned and allowing them to mix with each other. The input of physical
masses in the SU(3) invariant limit for two scalar octets and an "excited" pion
octet results in a mixing pattern wherein the light scalars have a large four
quark content while the light pseudoscalars have a large two quark content. One
light isosinglet scalar is exceptionally light. In addition, the pion pion
scattering is also studied and the current algebra theorem is verified for
massless pions which contain some four quark admixture.


  The development of inductive biases has been shown to be a very effective way
to increase the accuracy and robustness of neural networks, particularly when
they are used to predict physical phenomena. These biases significantly
increase the certainty of predictions, decrease the error made and allow
considerably smaller datasets to be used.
  There are a multitude of methods in the literature to develop these biases.
One of the most effective ways, when dealing with physical phenomena, is to
introduce physical principles of recognised validity into the network
architecture.
  The problem becomes more complex without knowledge of the physical principles
governing the phenomena under study. A very interesting possibility then is to
turn to the principles of thermodynamics, which are universally valid,
regardless of the level of abstraction of the description sought for the
phenomenon under study.
  To ensure compliance with the principles of thermodynamics, there are
formulations that have a long tradition in many branches of science. In the
field of rheology, for example, two main types of formalisms are used to ensure
compliance with these principles: one-generator and two-generator formalisms.
In this paper we study the advantages and disadvantages of each, using
classical problems with known solutions and synthetic data.


  In this short Note, we establish that the constant $C_1$ in Lemma $0.4$ of
the correction (Correction to Section 19.2 of Ricci Flow and the Poincare
Conjecture, arXiv/math/DG:1512.00699 (2015)) by John Morgan and Gang Tian to
their Clay Institute Monograph (Ricci Flow and the Poincare Conjecture, vol. 3,
Clay Mathematics Monograph, AMS and Clay Institute, (2007)) can be taken to be
zero. This implies that the counter-example which we provided recently in
ArXiv/math/DG:1422760 still stands after this correction. Let us observe that
the unjustified division by $k$ in the original monograph-the only mistake
which we could find-has been addressed in the correction, so that the problem
(according to our understanding and after this Note) lies deeper. We would like
to thank John Morgan, Terry Tao and Gang Tian for a thorough mathematical
exchange of arguments. The various conclusions have now been made available to
a wider community of colleagues. Appropriate adjustments in the understanding
will hopefully follow.


  A variety of large-scale machine learning problems can be cast as instances
of constrained submodular maximization. Existing approaches for distributed
submodular maximization have a critical drawback: The capacity - number of
instances that can fit in memory - must grow with the data set size. In
practice, while one can provision many machines, the capacity of each machine
is limited by physical constraints. We propose a truly scalable approach for
distributed submodular maximization under fixed capacity. The proposed
framework applies to a broad class of algorithms and constraints and provides
theoretical guarantees on the approximation factor for any available capacity.
We empirically evaluate the proposed algorithm on a variety of data sets and
demonstrate that it achieves performance competitive with the centralized
greedy solution.


  In this paper, a transient delayed rising and fall time of
$\beta$-Ga$_2$O$_3$ NMs Schottky barrier diodes (SBDs) formed on four different
substrates (diamond, Si, sapphire, and polyimide) were measured using a
sub-micron second resolution time-resolved electrical measurement system under
a different temperature condition. The devices exhibited noticeably
less-delayed turn-on-/off- the transient time when $\beta$-Ga$_2$O$_3$ NMs SBDs
were transfer-printed on a high-k substrate. Furthermore, a relationship
between the $\beta$-Ga$_2$O$_3$ NM thicknesses and their transient
characteristics were systematically investigated and found that phonon
scattering plays an important role in heat dissipation as the thickness of
$\beta$-Ga$_2$O$_3$ NMs get thinner which is also verified by the Multiphysics
simulator. Overall, our result reveals the impact of various substrates with
different thermal properties and different \b{eta}- Ga2O3 NMs thickness with
the performance of $\beta$-Ga$_2$O$_3$ NMs based devices. Hence, these results
can guide further efforts us to optimize the performance of future
$\beta$-Ga$_2$O$_3$ devices by maximizing heat dissipation from the
$\beta$-Ga$_2$O$_3$ layer.


  We explore a knowledge sanitization approach to mitigate the privacy concerns
associated with large language models (LLMs). LLMs trained on a large corpus of
Web data can memorize and potentially reveal sensitive or confidential
information, raising critical security concerns. Our technique efficiently
fine-tunes these models using the Low-Rank Adaptation (LoRA) method, prompting
them to generate harmless responses such as ``I don't know'' when queried about
specific information. Experimental results in a closed-book question-answering
task show that our straightforward method not only minimizes particular
knowledge leakage but also preserves the overall performance of LLMs. These two
advantages strengthen the defense against extraction attacks and reduces the
emission of harmful content such as hallucinations.


  We study a system of $N$ fermions in the regime where the intensity of the
interaction scales as $1/N$ and with an effective semi-classical parameter
$\hbar=N^{-1/d}$ where $d$ is the space dimension. For a large class of
interaction potentials and of external electromagnetic fields, we prove the
convergence to the Thomas-Fermi minimizers in the limit $N\to\infty$. The limit
is expressed using many-particle coherent states and Wigner functions. The
method of proof is based on a fermionic de Finetti-Hewitt-Savage theorem in
phase space and on a careful analysis of the possible lack of compactness at
infinity.


  A novel method of electron beam cooling is considered which can be used for
linear colliders. The electron beam is cooled during collision with focused
powerful laser pulse. With reasonable laser parameters (laser flash energy
about 10 J) one can decrease transverse beam emittances by a factor about 10
per one stage. The ultimate transverse emittances are much below those
achievable by other methods. Beam depolarization during cooling is about 5--15
% for one stage. This method is especially useful for photon colliders and
opens new possibilities for e+e- colliders.


  Light charged particles emitted at about 90 deg in the frame of the
projectile-like fragment in semi-peripheral collisions of 93Nb+93Nb at 38A MeV
give evidence for the simultaneous occurrence of two different production
mechanisms. This is demonstrated by differences in the kinetic energy spectra
and in the isotopic composition of the particles. The emission with a softer
kinetic energy spectrum and a low N/Z ratio for the hydrogen isotopes is
attributed to an evaporation process. The harder emission, with a much higher
N/Z ratio, can be attributed to a ``midvelocity'' process consisting of a
non-isotropic emission, on a short time-scale, from the surface of the
projectile-like fragment.


  In paper by I.T. Habibullin and our joint paper the algorithm for
classification of integrable equations with three independent variables was
proposed. This method is based on the requirement of the existence of an
infinite set of Darboux integrable reductions and on the notion of the
characteristic Lie-Rinehart algebras. The method was applied for the
classification of integrable cases of different subclasses of equations
$u_{n,xy} = f(u_{n+1},u_n,u_{n-1}, u_{n,x},u_{n,y})$ of special forms. Under
this approach the novel integrable chain was obtained. In present paper we
construct Lax pair for the novel chain. To construct the Lax pair, we use the
scheme suggested in papers by E.V. Ferapontov. We also study the periodic
reduction of the chain.


  We study a special kind of local invariant sets of singular holomorphic
foliations called nodal separators. We define notions of equisingularity and
topological equivalence for nodal separators as intrinsic objects and, in
analogy with the celebrated theorem of Zariski for analytic curves, we prove
the equivalence of these notions. We give some applications in the study of
topological equivalences of holomorphic foliations. In particular, we show that
the nodal singularities and its eigenvalues in the resolution of a generalized
curve are topological invariants.


  Gluinos are expected to be one of the most massive sparticles (supersymmetric
partners of usual particles) which constitute the Minimal Supersymmetric
Standard Model (MSSM). The gluinos are the partners of the gluons and they are
color octet fermions, due this fact they can not mix with the other particles.
Therefore in several scenarios, given at SPS convention, they are the most
massive particles and their nature is a Majorana fermion. Therefore their
production is only feasible at a very energetic machine such as the Large
Hadron Collider (LHC). Being the fermion partners of the gluons, their role and
interactions are directly related with the properties of the supersymmetric QCD
(sQCD). We review the mechanisms for producing gluinos at the LHC and
investigate the total cross section and differential distributions, making an
analysis of their uncertainties, such as the gluino and squark masses, as
obtained in several scenarios, commenting on the possibilities of
discriminating among them.


  The Galactic centre Nuclear Star Cluster is one of the densest stellar
clusters in the Galaxy. The stars in its inner portions orbit the supermassive
black hole associated with compact radio source Sgr~A* at the orbital speeds of
several thousand km/s. The B-type star S2 is currently the best case to test
the general relativity as well as other theories of gravity based on its
stellar orbit. Yet its orbital period of $\sim 16\,{\rm yr}$ and the
eccentricity of $\sim 0.88$ yields the relativistic pericentre shift of $\sim
11'$, which is observationally still difficult to reliably measure due to
possible Newtonian perturbations as well as reference-frame uncertainties. A
naive way to solve this problem is to find stars with smaller pericentre
distances, $r_{\rm p}\lesssim 1529$ Schwarzschild radii ($120\,{\rm AU}$), and
thus more prominent relativistic effects. In this contribution, we show that to
detect stars on relativistic orbits is progressively less likely given the
volume shrinkage and the expected stellar density distributions. Finally, one
arrives to a sparse region, where the total number of bright stars is expected
to fall below one. One can, however, still potentially detect stars crossing
this region. In this contribution, we provide a simple formula for the
detection probability of a star crossing a sparse region. We also examine an
approximate time-scale on which the star reappears in the sparse region, i.e. a
"waiting" time-scale for observers.


  Agrivoltaics is an innovative approach in which solar photovoltaic (PV)
energy generation is collocated with agricultural production to enable
food-energy-water synergies and landscape ecological conservation. This
dual-use requirement leads to unique co-optimization challenges (e.g. shading,
soiling, spacing) that make module technology and farm topology choices
distinctly different from traditional solar farms. Here we compare the
performance of the traditional optimally-titled North/South (N/S) faced
monofacial farms with a potential alternative based on vertical East/West
(E/W)-faced bifacial farms. Remarkably, the vertical farm produces essentially
the same energy output and photosynthetically active radiation (PAR) compared
to traditional farms as long as the PV array density is reduced to half or
lower relative to that for the standard ground-mounted PV farms. Our results
explain the relative merits of the traditional mono facial vs. vertical
bifacial farms as a function of array density, acceptable PAR-deficit, and
energy production. The combined PAR/Energy yields for the vertical bifacial
farm may not always be superior, it could still be an attractive choice for
agrivoltaics due to its distinct advantages such as minimum land coverage,
least hindrance to the farm machinery and rainfall, inherent resilience to PV
soiling, easier cleaning and cost advantages due to potentially reduced
elevation.


  Given a recursive distributional equation (RDE) and a solution $\mu$ of it,
we consider the tree indexed invariant process called the recursive tree
process (RTP) with marginal $\mu$. We introduce a new type of bivariate
uniqueness property which is different from the one defined by Aldous and
Bandyopadhyay (2005), and we prove that this property is equivalent to
tail-triviality for the RTP, thus obtaining a necessary and sufficient
condition to determine tail-triviality for a RTP in general. As an application
we consider Aldous' (2000) construction of the frozen percolation process on a
infinite regular tree and show that the associated RTP has a trivial tail.


  In this article, we study the Beilinson-Bloch-Kato conjecture for motives
corresponding to the Rankin-Selberg product of conjugate self-dual automorphic
representations, within the framework of the Gan-Gross-Prasad conjecture. We
show that if the central critical value of the Rankin-Selberg $L$-function does
not vanish, then the Bloch-Kato Selmer group with coefficients in a favorable
field of the corresponding motive vanishes. We also show that if the class in
the Bloch-Kato Selmer group constructed from certain diagonal cycle does not
vanish, which is conjecturally equivalent to the nonvanishing of the central
critical first derivative of the Rankin-Selberg $L$-function, then the
Bloch-Kato Selmer group is of rank one.


  We studied resonant laser interaction with Rb atoms confined to the
interstitial cavities of a random porous glass. Due to diffusive light
propagation, the effect of atomic absorption on the light scattered by the
sample is almost entirely compensated by atomic fluorescence at low atomic
densities. For higher densities, radiation trapping increases the probability
of non-radiative decay via atom-wall collisions. A simple connection of the
fluorescence/absorption yield to the sample porosity is given.


The paper discusses some uniqueness sets for Fourier series.


  Global Climate Models are key tools for predicting the future response of the
climate system to a variety of natural and anthropogenic forcings. Here we show
how to use statistical mechanics to construct operators able to flexibly
predict climate change for a variety of climatic variables of interest. We
perform our study on a fully coupled model - MPI-ESM v.1.2 - and for the first
time we prove the effectiveness of response theory in predicting future climate
response to CO$_2$ increase on a vast range of temporal scales, from
inter-annual to centennial, and for very diverse climatic quantities. We
investigate within a unified perspective the transient climate response and the
equilibrium climate sensitivity and assess the role of fast and slow processes.
The prediction of the ocean heat uptake highlights the very slow relaxation to
a newly established steady state. The change in the Atlantic Meridional
Overturning Circulation (AMOC) and of the Antarctic Circumpolar Current (ACC)
is accurately predicted. The AMOC strength is initially reduced and then
undergoes a slow and only partial recovery. The ACC strength initially
increases as a result of changes in the wind stress, then undergoes a slowdown,
followed by a recovery leading to a overshoot with respect to the initial
value. Finally, we are able to predict accurately the temperature change in the
Northern Atlantic.


  This work examined the effect of macrostep height on the growth velocity of a
vicinal surface during reaction- (interface-) limited crystal growth under
non-equilibrium steady state conditions. The Monte Carlo method was employed,
based on a restricted solid-on-solid (RSOS) model with point-contact-type
step-step attraction (termed the p-RSOS model). Although this is a simple
lattice model, the model surface shows a variety of distinctive configurations
depending on the temperature and the driving force for crystal growth. The
results demonstrate that the surface velocity decreases as the height of the
faceted macrostep increases. In addition, the significant variation in surface
velocity recently reported by Onuma {\it et al.} in a study based on 4H-SiC was
reproduced. This work also shows that the terrace slope, elementary step
velocity and elementary step kinetic coefficient are all affected by the
faceted macrostep height.


  We investigate the behavior of sequences $(f(c_nx))$ for Lebesgue integrable
functions $f:\mathbb R^d\to\mathbb R$. In particular, we give a~description of
classes of multipliers $(c_n)$ and $(d_n)$ such that $f(c_nx)\to0$ or
$\sum_{n=1}^\infty|f(d_nx)|<\infty$ for $\lambda$ almost every $x\in\mathbb
R^d$.


  On 31 August 2019, an interstellar comet was discovered as it passed through
the Solar System (2I/Borisov). Based on initial imaging observations,
2I/Borisov appeared to be completely similar to ordinary Solar System comets -
an unexpected characteristic after the multiple peculiarities of the only
previous known interstellar visitor 1I/'Oumuamua. Spectroscopic investigations
of 2I/Borisov identified the familiar cometary emissions from CN, C2, O I, NH2,
OH, HCN, and CO, revealing a composition similar to that of carbon
monoxide-rich Solar System comets. At temperatures >700 K, comets additionally
show metallic vapors produced by the sublimation of metal-rich dust grains.
However, due to the high temperature needed, observation of gaseous metals has
been limited to bright sunskirting and sungrazing comets and giant
star-plunging exocomets. Here we report spectroscopic detection of atomic
nickel vapor in the cold coma of 2I/Borisov observed at a heliocentric distance
of 2.322 au - equivalent to an equilibrium temperature of 180 K. Nickel in
2I/Borisov seems to originate from a short-lived nickelbearing molecule with a
lifetime of $340^{+260}_{-200}$ s at 1 au and is produced at a rate of $0.9 \pm
0.3 \times 10^{22}$ atoms s$^{-1}$, or 0.002% relative to OH and 0.3% relative
to CN. The detection of gas-phase nickel in the coma of 2I/Borisov is in line
with the concurrent identification of this atom (as well as iron) in the cold
comae of Solar System comets.


  High-dimensional data sets are often analyzed and explored via the
construction of a latent low-dimensional space which enables convenient
visualization and efficient predictive modeling or clustering. For complex data
structures, linear dimensionality reduction techniques like PCA may not be
sufficiently flexible to enable low-dimensional representation. Non-linear
dimension reduction techniques, like kernel PCA and autoencoders, suffer from
loss of interpretability since each latent variable is dependent of all input
dimensions. To address this limitation, we here present path lasso penalized
autoencoders. This structured regularization enhances interpretability by
penalizing each path through the encoder from an input to a latent variable,
thus restricting how many input variables are represented in each latent
dimension. Our algorithm uses a group lasso penalty and non-negative matrix
factorization to construct a sparse, non-linear latent representation. We
compare the path lasso regularized autoencoder to PCA, sparse PCA, autoencoders
and sparse autoencoders on real and simulated data sets. We show that the
algorithm exhibits much lower reconstruction errors than sparse PCA and
parameter-wise lasso regularized autoencoders for low-dimensional
representations. Moreover, path lasso representations provide a more accurate
reconstruction match, i.e. preserved relative distance between objects in the
original and reconstructed spaces.


  This paper presents a portable phenotyping system that is capable of
integrating both rule-based and statistical machine learning based approaches.
Our system utilizes UMLS to extract clinically relevant features from the
unstructured text and then facilitates portability across different
institutions and data systems by incorporating OHDSI's OMOP Common Data Model
(CDM) to standardize necessary data elements. Our system can also store the key
components of rule-based systems (e.g., regular expression matches) in the
format of OMOP CDM, thus enabling the reuse, adaptation and extension of many
existing rule-based clinical NLP systems. We experimented with our system on
the corpus from i2b2's Obesity Challenge as a pilot study. Our system
facilitates portable phenotyping of obesity and its 15 comorbidities based on
the unstructured patient discharge summaries, while achieving a performance
that often ranked among the top 10 of the challenge participants. This
standardization enables a consistent application of numerous rule-based and
machine learning based classification techniques downstream.


  We find spin charge recombination is a generic feature of projected wave
functions. We find this effect is responsible for a series of differences
between mean field theory prediction and the result from projected wave
functions. We also find spin charge recombination plays an important role in
determining the dissipation of supercurrent, the quasiparticle properties and
the hole - hole correlation.


  In this paper we present a finite element method for the direct transcription
of constrained non-linear optimal control problems.
  We prove that our method converges of high order under mild assumptions. Our
analysis uses a regularized penalty-barrier functional. The convergence result
is obtained from local strict convexity and Lipschitz-continuity of this
functional in the finite-element space.
  The method is very flexible. Each component of the numerical solution can be
discretized with a different mesh. General differential-algebraic constraints
of arbitrary index can be treated easily with this new method.
  From the discretization results an unconstrained non-linear programming
problem (NLP) with penalty- and barrier-terms. The derivatives of the NLP
functions have a sparsity pattern that can be analysed and tailored in terms of
the chosen finite-element bases in an easy way. We discuss how to treat the
resulting NLP in a practical way with general-purpose software for constrained
non-linear programming.


  As digital games continue to be explored as solutions to educational and
behavioural challenges, the need for evaluation methodologies which support
both the unique nature of the format and the need for comparison with other
approaches continues to increase. In this workshop paper, a range of challenges
are described related specifically to the case of cultural learning using
digital games, in terms of how it may best be assessed, understood, and
sustained through an iterative process supported by research. An evaluation
framework is proposed, identifying metrics for reach and impact and their
associated challenges, as well as presenting ethical considerations and the
means to utilize evaluation outcomes within an iterative cycle, and to provide
feedback to learners. Presenting as a case study a serious game from the Mobile
Assistance for Social Inclusion and Empowerment of Immigrants with Persuasive
Learning Technologies and Social Networks (MASELTOV) project, the use of the
framework in the context of an integrative project is discussed, with emphasis
on the need to view game-based learning as a blended component of the cultural
learning process, rather than a standalone solution. The particular case of
mobile gaming is also considered within this case study, providing a platform
by which to deliver and update content in response to evaluation outcomes.
Discussion reflects upon the general challenges related to the assessment of
cultural learning, and behavioural change in more general terms, suggesting
future work should address the need to provide sustainable, research-driven
platforms for game-based learning content.


  Existing studies of training state-of-the-art Contrastive Language-Image
Pretraining (CLIP) models on large-scale data involve hundreds of or even
thousands of GPUs due to the requirement of a large batch size. However, such a
large amount of resources is not accessible to most people. While advanced
compositional optimization techniques for optimizing global contrastive losses
have been demonstrated effective for removing the requirement of large batch
size, their performance on large-scale data remains underexplored and not
optimized. To bridge the gap, this paper explores several aspects of CLIP
training with limited resources (e.g., up to tens of GPUs). First, we introduce
FastCLIP, a general CLIP training framework built on advanced compositional
optimization techniques while designed and optimized for the distributed
setting. Our framework is equipped with an efficient gradient reduction
strategy to reduce communication overhead. Second, to further boost training
efficiency, we investigate three components of the framework from an
optimization perspective: the schedule of the inner learning rate, the update
rules of the temperature parameter and the model parameters, respectively.
Experiments on different strategies for each component shed light on how to
conduct CLIP training more efficiently. Finally, we benchmark the performance
of FastCLIP and the state-of-the-art training baseline (OpenCLIP) on different
compute scales up to 32 GPUs on 8 nodes, and three data scales ranging from 2.7
million, 9.1 million to 315 million image-text pairs to demonstrate the
significant improvement of FastCLIP in the resource-limited setting. We release
the code of FastCLIP at https://github.com/Optimization-AI/fast_clip .


  We examine the phenomenological consequences of quadratically divergent
contributions to the scalar potential in supergravity effective Lagrangians. We
focus specifically on the effect of these corrections on the vacuum
configuration of scalar fields in softly-broken supersymmetric theories and the
role these corrections play in generating non-diagonal soft scalar masses. Both
effects can only be properly studied when the divergences are regulated in a
manifestly supersymmetric manner -- something which has thus far been neglected
in past treatments. We show how a supersymmetric regularization can impact past
conclusions about both types of phenomena and discuss what types of high-energy
theories are likely to be safe from unwanted flavor-changing neutral current
interactions in the context of supergravity theories derived from heterotic
string compactifications.


  This paper relates uniform alpha-Hoelder continuity, or alpha-dimensionality,
of spectral measures in an arbitrary interval to the Fourier transform of the
measure. This is used to show that scaling exponents of exponential sums
obtained from time series give local upper bounds on the degree of Hoelder
continuity of the power spectrum of the series. The results have applications
to generalized random walk, numerical detection of singular continuous spectra
and to the energy growth in driven oscillators.


  A sixth order quadrupole boson Hamiltonian is treated through a time
dependent variational principle approach choosing as trial function a coherent
state with respect to zeroth $b^{\dagger}_0$ and second
$b^{\dagger}_2+b^{\dagger}_{-2}$ components of the quadrupole bosons. The
coefficients involved in the model Hamiltonian are chosen so that the classical
effective potential energy term has two distinct minima. The equation of motion
for the radial coordinate is analytically solved and the resulting trajectories
are extensively studied. One distinguishes three energy regions exhibiting
different types of trajectories. When one passes from the region characterized
by two wells to the region of energies higher than the maximum value of the
effective potential the trajectories period exhibits a singularity which
reflects a phase transition. The classical trajectories are quantized by a
constraint similar to the Bohr-Sommerfeld quantization condition. The
semiclassical spectra corresponding to the two potential wells have specific
properties. The tunneling process through the potential barrier is also
studied. The transmission coefficients exhibit jumps in magnitude when the
angular momentum acquires certain values.


  A $^{13}$C NMR study of the normal and superconducting states of the
all-organic charge-transfer salt
$\beta"$-(BEDT-TTF)$_2$SF$_5$CH$_2$CF$_2$SO$_3$ is presented. We find that the
normal state is a charge-ordered metal configured as vertical stripes, produced
by a combination of 1/4-filling, correlations, and a polar counterion
sublattice. The NMR properties associated with the superconducting state are
consistent with gap nodes and singlet pairing, and therefore similar to other
organic superconductors. Quite distinct, however, is the absence of evidence
for low-energy antiferromagnetic spin fluctuations for $T>T_c=4.5$ K. Both
aspects are discussed in the context of a proposal that the pairing in this
compound is driven by charge fluctuations.


  We study the problem of constructing synthetic graphs that resemble
real-world directed graphs in terms of their degree correlations. We define the
problem of directed 2K construction (D2K) that takes as input the directed
degree sequence (DDS) and a joint degree and attribute matrix (JDAM) so as to
capture degree correlation specifically in directed graphs. We provide
necessary and sufficient conditions to decide whether a target D2K is
realizable, and we design an efficient algorithm that creates realizations with
that target D2K. We evaluate our algorithm in creating synthetic graphs that
target real-world directed graphs (such as Twitter) and we show that it brings
significant benefits compared to state-of-the-art approaches.


  Several authors have explained that the likelihood ratio measures the
strength of the evidence represented by observations in statistical problems.
This idea works fine when the goal is to evaluate the strength of the available
evidence for a simple hypothesis versus another simple hypothesis. However, the
applicability of this idea is limited to simple hypotheses because the
likelihood function is primarily defined on points (simple hypotheses) of the
parameter space. In this paper we define a general weight of evidence that is
applicable to both simple and composite hypotheses. It is based on the
Dempster-Shafer concept of plausibility and is shown to be a generalization of
the likelihood ratio. Functional models are of a fundamental importance for the
general weight of evidence proposed in this paper. The relevant concepts and
ideas are explained by means of a familiar urn problem and the general analysis
of a real-world medical problem is presented.


  Conditional ceteris paribus preference networks (CP-nets) are commonly used
to capture qualitative conditional preferences. In many use cases, when the
preferential structure of an agent is incomplete, information from other
preferential structures (e.g. that of other users) preferences can be used to
fill in the gaps. Earlier works proposed methods to symmetrically merge
multiple incomplete CP-nets by means of voting semantics. However, the merged
CP-net can contain preference relations that do not fit to a given user's
original preference profile. This paper proposes an asymmetric merging (or
enriching) method to obtain and fill-in preference relations of a user's CP-net
from another CP-net in a way that preserves the original preference relations.


  In this paper, we study the distribution of the number of internal equilibria
of a multi-player two-strategy random evolutionary game. Using techniques from
the random polynomial theory, we obtain a closed formula for the probability
that the game has a certain number of internal equilibria. In addition, by
employing Descartes' rule of signs and combinatorial methods, we provide useful
estimates for this probability. Finally, we also compare our analytical results
with those obtained from samplings.


  It is shown that the Dzialoshinskii-Moriya interaction leads to asymmetrical
deformation of the transverse domain wall profile in one-dimensional biaxial
magnet. Amplitude of the deformation is linear with respect to the
Dzialoshinskii constant $D$. Corrections caused by the Dzialoshinskii-Moriya
interaction are obtained for the number of the domain wall parameters: energy
density, Doering mass, Walker field. The modified $q$-$\Phi$ model with an
additional pair of conjugated collective variables is proposed for studying the
dynamical properties of the wall with taking into account the internal degrees
of freedom.


  A cyclic urn is an urn model for balls of types $0,\ldots,m-1$. The urn
starts at time zero with an initial configuration. Then, in each time step,
first a ball is drawn from the urn uniformly and independently from the past.
If its type is $j$, it is then returned to the urn together with a new ball of
type $j+1 \mod m$. The case $m=2$ is the well-known Friedman urn. The
composition vector, i.e., the vector of the numbers of balls of each type after
$n$ steps is, after normalization, known to be asymptotically normal for $2\le
m\le 6$. For $m\ge 7$ the normalized composition vector is known not to
converge. However, there is an almost sure approximation by a periodic random
vector.
  In the present paper the asymptotic fluctuations around this periodic random
vector are identified. We show that these fluctuations are asymptotically
normal for all $7\le m\le 12$. For $m\ge 13$ we also find asymptotically normal
fluctuations when normalizing in a more refined way. These fluctuations are of
maximal dimension $m-1$ only when $6$ does not divide $m$. For $m$ being a
multiple of $6$ the fluctuations are supported by a two-dimensional subspace.


  We briefly present the history of technical solutions aimed at improving the
efficiency of spectroscopy on small- and moderate-diameter telescopes. We
assess the current state of spectroscopy techniques and some of the
perspectives.


  High-precision electroweak experiments such as parity-violating Moller
scattering can provide indirect access to physics at multi-TeV scales and play
an important complementary role to the LHC research program. However, before
physics of interest can be extracted from experimental data, electroweak
radiative corrections, which can significantly reduce the cross-section
asymmetry, must be calculated with an unprecedented completeness and accuracy.
Although the two-loop corrections are strongly suppressed relative to the
one-loop corrections, they can no longer be dismissed for the upcoming
precision experiments. We evaluate a full gauge-invariant set of one-loop and
several types of two-loop radiative corrections for the parity-violating
electron-electron scattering asymmetry by combining two distinct but
mutually-reinforcing techniques: semiautomatic, precise, with FeynArts and
FormCalc as base languages, and by hand, with some approximations. For 11 GeV
relevant for the ultra-precise MOLLER experiment planned at JLab, the results
obtained by two approaches are in excellent agreement, which gives us assurance
that our calculations are error-free.


  Video captioning is a popular task that challenges models to describe events
in videos using natural language. In this work, we investigate the ability of
various visual feature representations derived from state-of-the-art
convolutional neural networks to capture high-level semantic context. We
introduce the Weighted Additive Fusion Transformer with Memory Augmented
Encoders (WAFTM), a captioning model that incorporates memory in a transformer
encoder and uses a novel method, to fuse features, that ensures due importance
is given to more significant representations. We illustrate a gain in
performance realized by applying Word-Piece Tokenization and a popular
REINFORCE algorithm. Finally, we benchmark our model on two datasets and obtain
a CIDEr of 92.4 on MSVD and a METEOR of 0.091 on the ActivityNet Captions
Dataset.


  Although Physics is the same worldwide, students belonging to different
learning systems as well as different cultural environments may develop
different styles of approaching and reasoning out Physics problems. In a first
experiment we compare student physics problem-solving styles between two
different student populations: a group of typical American students (from an
OSU calculus-based introductory course) and a group of Romanian students (from
a second-year class at Bucharest University). We discuss one of the problems
given in a short E&M survey, in which students from both populations were
presented with a point charge in a region containing a uniform magnetic field.
We asked students to determine the force on the charge for different initial
conditions. In a second experiment, three American physics students and three
Romanian physics students were given the same problem and were asked to explain
loudly their answer to each question. Their answers were tape-recorded.
Students' answers depend on an understanding of the Lorentz force and their
general knowledge from classical mechanics. Observed similarities and
differences in approach between these student groups are discussed, and our
study's results described.


  We study the spatial structure of a granular material, N particles subject to
inelastic mutual collisions, when it is stirred by a bidimensional smooth
chaotic flow. A simple dynamical model is introduced where four different time
scales are explicitly considered: i) the Stokes time, accounting for the
inertia of the particles, ii) the mean collision time among the grains, iii)
the typical time scale of the flow, and iv) the inverse of the Lyapunov
exponent of the chaotic flow, which gives a typical time for the separation of
two initially close parcels of fluid. Depending on the relative values of these
different times a complex scenario appears for the long-time steady spatial
distribution of particles, where clusters of particles may or not appear.


  Highlighting while reading is a natural behavior for people to track salient
content of a document. It would be desirable to teach an extractive summarizer
to do the same. However, a major obstacle to the development of a supervised
summarizer is the lack of ground-truth. Manual annotation of extraction units
is cost-prohibitive, whereas acquiring labels by automatically aligning human
abstracts and source documents can yield inferior results. In this paper we
describe a novel framework to guide a supervised, extractive summarization
system with question-answering rewards. We argue that quality summaries should
serve as a document surrogate to answer important questions, and such
question-answer pairs can be conveniently obtained from human abstracts. The
system learns to promote summaries that are informative, fluent, and perform
competitively on question-answering. Our results compare favorably with those
reported by strong summarization baselines as evaluated by automatic metrics
and human assessors.


  The array is a data structure used in a wide range of programs. Its compact
storage and constant time random access makes it highly efficient, but
arbitrary indexing complicates the analysis of code containing array accesses.
Such analyses are important for compiler optimisations such as bounds check
elimination. The aim of this work is to gain a better understanding of how
arrays are used in real-world programs. While previous work has applied static
analyses to understand how arrays are accessed and used, we take a dynamic
approach. We empirically examine various characteristics of array usage by
instrumenting programs to log all array accesses, allowing for analysis of
array sizes, element types, from where arrays are accessed and to which extent
sequences of array accesses form recognizable patterns. The programs in the
study were collected from the Renaissance benchmark suite, all running on the
Java Virtual Machine.
  We account for characteristics displayed by the arrays investigated, finding
that most arrays have a small size, are accessed by only one or two classes and
by a single thread. On average over the benchmarks, 69.8% of the access
patterns consist of uncomplicated traversals. Most of the instrumented classes
(over 95%) do not use arrays directly at all. These results come from tracing
data covering 3,803,043,390 array accesses made across 168,686 classes. While
our analysis has only been applied to the Renaissance benchmark suite, the
methodology can be applied to any program running on the Java Virtual Machine.
This study, and the methodology in general, can inform future runtime
implementations and compiler optimisations.


  The properties of H-rich, type II-plateau supernova (SN II-P) progenitors
remain uncertain, and this is primarily due to the complexities associated with
red supergiant (RSG) wind-mass loss. Recent studies have suggested that the
interaction of the ejecta with a standard RSG wind should produce unambiguous
signatures in the optical (e.g., a broad, boxy H${\alpha}$ profile) and in the
UV (especially Ly ${\alpha}$ and Mg ii ${\lambda}{\lambda}$ 2795, 2802) a few
years following the explosion. Such features are expected to be generic in all
SNe II-P and can be utilized to constrain RSG winds. Here, we investigate the
possibility of detecting late-time (0.3-10 years since explosion) SNe II-P in
the NUV with the China Space Station Telescope (CSST). Convolving the existing
model spectra of ejecta-wind interactions in SNe II-P with the transmission
functions of the CSST, we calculated the associated multiband light curves, in
particular, the NUV (255 nm${\sim}$317 nm) band, as well as the $NUV-r$ color.
We find that the CSST will be able to detect the NUV radiation associated with
ejecta-wind interaction for hundreds SNe II-P out to a few hundred Mpc over its
ten-year main sky survey. The CSST will therefore provide a sizable sample of
SNe II-P with the NUV signatures of ejecta-wind interaction. This will be
helpful for understanding the mass loss history of SN II-P progenitors and
their origins.


  This work considers the multiple-access multicast error-correction scenario
over a packetized network with $z$ malicious edge adversaries. The network has
min-cut $m$ and packets of length $\ell$, and each sink demands all information
from the set of sources $\sources$. The capacity region is characterized for
both a "side-channel" model (where sources and sinks share some random bits
that are secret from the adversary) and an "omniscient" adversarial model
(where no limitations on the adversary's knowledge are assumed). In the
"side-channel" adversarial model, the use of a secret channel allows higher
rates to be achieved compared to the "omniscient" adversarial model, and a
polynomial-complexity capacity-achieving code is provided. For the "omniscient"
adversarial model, two capacity-achieving constructions are given: the first is
based on random subspace code design and has complexity exponential in $\ell
m$, while the second uses a novel multiple-field-extension technique and has
$O(\ell m^{|\sources|})$ complexity, which is polynomial in the network size.
Our code constructions are "end-to-end" in that all nodes except the sources
and sinks are oblivious to the adversaries and may simply implement predesigned
linear network codes (random or otherwise). Also, the sources act independently
without knowledge of the data from other sources.


  Video captioning has shown impressive progress in recent years. One key
reason of the performance improvements made by existing methods lie in massive
paired video-sentence data, but collecting such strong annotation, i.e.,
high-quality sentences, is time-consuming and laborious. It is the fact that
there now exist an amazing number of videos with weak annotation that only
contains semantic concepts such as actions and objects. In this paper, we
investigate using weak annotation instead of strong annotation to train a video
captioning model. To this end, we propose a progressive visual reasoning method
that progressively generates fine sentences from weak annotations by inferring
more semantic concepts and their dependency relationships for video captioning.
To model concept relationships, we use dependency trees that are spanned by
exploiting external knowledge from large sentence corpora. Through traversing
the dependency trees, the sentences are generated to train the captioning
model. Accordingly, we develop an iterative refinement algorithm that refines
sentences via spanning dependency trees and fine-tunes the captioning model
using the refined sentences in an alternative training manner. Experimental
results demonstrate that our method using weak annotation is very competitive
to the state-of-the-art methods using strong annotation.


  We study the existence of solutions to the cubic Schr\"odinger system $$
-\Delta u_i = \sum_{j =1}^m \beta_{ij} u_j^2u_i + \lambda_i u_i\ \hbox{in}\
\Omega,\ u_i=0\ \hbox{on}\ \partial\Omega,\ i =1,\dots,m, $$ when $\Omega$ is a
bounded domain in $\mathbb R^4, $ $\lambda_i$ are positive small numbers,
$\beta_{ij}$ are real numbers so that $\beta_{ii}>0$ and
$\beta_{ij}=\beta_{ji}$, $i\neq j$. We assemble the components $u_i$ in groups
so that all the interaction forces $\beta_{ij}$ among components of the same
group are attractive, i.e. $\beta_{ij}>0$, while forces among components of
different groups are repulsive or weakly attractive, i.e.
$\beta_{ij}<\overline\beta$ for some $\overline\beta$ small. We find solutions
such that each component within a given group blows-up around the same point
and the different groups blow-up around different points, as all the parameters
$\lambda_i$'s approach zero.


  The main goal is to find the Homfly polynomial of a link formed by decorating
each component of the Hopf link with the closure of a directly oriented tangle.
Such decorations are spanned in the Homfly skein of the annulus by elements
Q_\lambda, depending on partitions \lambda. We show how to find the 2-variable
Homfly invariant <\lambda,\mu> of the Hopf link arising from decorations
Q_\lambda and Q_\mu in terms of the Schur symmetric function s_\mu of an
explicit power series depending on \lambda. We show also that the quantum
invariant of the Hopf link coloured by irreducible sl(N)_q modules V_\lambda
and V_\mu, which is a 1-variable specialisation of <\lambda,\mu>, can be
expressed in terms of an N x N minor of the Vandermonde matrix (q^{ij}).


  Due to particle conservation, Canonical Molecular Dynamics (MD) simulations
fail in the description of surface phase transitions involving coverage or
lateral density changes. However, a step on the surface can act effectively as
a source or a sink of atoms, in the simulation as well as in real life. A
single surface step can be introduced by suitably modifying planar Periodic
Boundary Conditions (PBC), to accommodate the generally inequivalent stacking
of two adjacent layers. We discuss here how, through the introduction of two
orthogonal surface steps, particle number conservation may no longer represent
a fatal constraint for the study of these surface transitions. As an example,
we apply the method for estimating temperature-induced lateral density increase
of the reconstructed
  Au (001) surface; the resulting anisotropic cell change is consistent with
experimental observations. Moreover, we implement this kind of scheme in
conjunction with the variable curvature MD method, recently introduced by our
group.


  This study investigates the dynamics of non-spatial specializations in
hippocampal place cells during exposure to novel environments. Hippocampal
place cells, known for their role in spatial mapping, exhibit multi-modal
responses to sensory cues. The research focuses on understanding how these
cells adapt their specialization in response to novel stimuli, specifically
examining non-spatial determinants such as odors and social interactions. Using
a social-driven food odor recognition model in mice, the study records CA1
hippocampal neuron activity through miniscope imaging. The experimental design
involves demonstrations of novel odors to mice, followed by observation
sessions with food options. The analysis employs deep neural network tools for
behavior tracking and the custom-developed INTENS software package for
identifying neural specializations. Results indicate multiple specializations,
particularly those related to odor, with differences observed between training
and testing sessions. The findings suggest a temporal aspect to the formation
of these specializations in novel conditions, necessitating further
investigation for precise tracking.


  We propose a new evolutionary process of protoplanetary disks "co-evolution
of dust grains and protoplanetary disks", revealed by dust-gas two-fluid
non-ideal magnetohydrodynamics simulations considering the growth of dust and
associated changes in magnetic resistivity. We found that the dust growth
significantly affects disk evolution by changing the coupling between the gas
and magnetic field. Moreover, once the dust grains sufficiently grow and the
adsorption of charged particles on dust grains becomes negligible, the physical
quantities (e.g., density and magnetic field) of the disk are well described by
characteristic power laws. In this disk structure, the radial profile of
density is steeper and the disk mass is smaller than those of the model
ignoring dust growth. We analytically derive these power laws from the basic
equations of non-ideal magnetohydrodynamics. The analytical power laws are
determined only by observable physical quantities, e.g., central stellar mass
and mass accretion rate, and do not include difficult-to-determine parameters
e.g., viscous parameter $\alpha$. Therefore, our model is observationally
testable and this disk structure is expected to provide a new perspective for
future studies on protostar and disk evolution.


  Recently, nonlinear ICA has surfaced as a popular alternative to the many
heuristic models used in deep representation learning and disentanglement. An
advantage of nonlinear ICA is that a sophisticated identifiability theory has
been developed; in particular, it has been proven that the original components
can be recovered under sufficiently strong latent dependencies. Despite this
general theory, practical nonlinear ICA algorithms have so far been mainly
limited to data with one-dimensional latent dependencies, especially
time-series data. In this paper, we introduce a new nonlinear ICA framework
that employs $t$-process (TP) latent components which apply naturally to data
with higher-dimensional dependency structures, such as spatial and
spatio-temporal data. In particular, we develop a new learning and inference
algorithm that extends variational inference methods to handle the combination
of a deep neural network mixing function with the TP prior, and employs the
method of inducing points for computational efficacy. On the theoretical side,
we show that such TP independent components are identifiable under very general
conditions. Further, Gaussian Process (GP) nonlinear ICA is established as a
limit of the TP Nonlinear ICA model, and we prove that the identifiability of
the latent components at this GP limit is more restricted. Namely, those
components are identifiable if and only if they have distinctly different
covariance kernels. Our algorithm and identifiability theorems are explored on
simulated spatial data and real world spatio-temporal data.


  We present an experimental study of the high-energy excitation spectra of
unitary Fermi gases. Using focussed beam Bragg spectroscopy, we locally probe
atoms in the central region of a harmonically trapped cloud where the density
is nearly uniform, enabling measurements of the dynamic structure factor for a
range of temperatures both below and above the superfluid transition. Applying
sum-rules to the measured Bragg spectra, we resolve the characteristic
behaviour of the universal contact parameter, ${\cal C}$, across the superfluid
transition. We also employ a recent theoretical result for the kinetic
(second-moment) sum-rule to obtain the internal energy of gases at unitarity.


  We study how quantum fluctuations of the metric in covariant Horava-Lifshitz
gravity influence the propagation of classical fields (complex scalar and
photon). The effective Lorentz-symmetry violation induced by the breaking of
4-dimensional diffeomorphism is then evaluated, by comparing the dressed
dispersion relations for both external fields. The constraint of vanishing
3-dimensional Ricci scalar is imposed in the path integral, which therefore
explicitly depends on two propagating gravitational degrees of freedom only.
Because the matter fields are classical, the present model contains only
logarithmic divergences. Furthermore, it imposes the characteristic
Horava-Lifshitz scale to be smaller than $10^{10}$ GeV, if one wishes not to
violate the current bounds on Lorentz symmetry violation.


  Study of the ground-state electronic spin-polarization can permit discovery
and identification of novel correlated phases in the quantum Hall (QH) system.
It can thus determine the potential usefulness of QH states for quantum
computing. However, prior measurements involving optical and NMR techniques may
perturb the system away from delicate ground-states. Here, we present
spin-resolved pulsed tunneling (SRPT) that precisely determines the complete
phase diagram of the ground-state spin-polarization as a function of magnetic
field (B) and filling factor ({\nu}). We observe fully-polarized {\nu} = 5/2
and 8/3 states at very small B, suggesting strong deviation from the
weakly-interacting composite-fermion model that largely successfully describes
our phase diagram for the lowest Landau level. The results establish SRPT as a
powerful technique for investigating correlated electron phenomena.


  We propose a way to simulate Cherenkov detector response using a generative
adversarial neural network to bypass low-level details. This network is trained
to reproduce high level features of the simulated detector events based on
input observables of incident particles. This allows the dramatic increase of
simulation speed. We demonstrate that this approach provides simulation
precision which is consistent with the baseline and discuss possible
implications of these results.


  In this paper, we propose state- and static output-feedback generalized
guaranteed cost control (GCC) approaches for discrete-time linear systems
subject to norm-bounded structured parametric uncertainties. This method
enables the convex synthesis for a more general class of systems, where
uncertainties are uncorrelated block diagonal, and no feed-through uncertainty
is multiplicative with control input ones. It also provides necessary and
sufficient conditions for state-feedback and sufficient conditions for static
output-feedback. We also present a comparative study among the proposed
controllers, standard Linear Quadratic Regulator, and Guaranteed Cost
Controller found in the literature.


  We calculate the tree-level oblique corrections to electroweak precision
observables generated in higgless models of electroweak symmetry breaking with
a 5D SU(2)_L x SU(2)_R x U(1)_{B-L} gauge group on a warped background. In the
absence of brane induced kinetic terms (and equal left and right gauge
couplings) we find the S parameter to be ~1.15, while T,U~0, as in technicolor
theories. Planck brane induced kinetic terms and unequal left-right couplings
can lower S, however for sufficiently low values of S tree-level unitarity will
be lost. A kinetic term localized on the TeV brane for SU(2)_D will generically
increase S, however an induced kinetic term for U(1)_{B-L} on the TeV brane
will lower S. With an appropriate choice of the value of this induced kinetic
term S~0 can be achieved. In this case the mass of the lowest Z' mode will be
lowered to about ~300 GeV.


  The nuclear magnetic resonance (NMR) spectrum of spin-3/2 nuclei in a static
magnetic field aligned with one of the electric field gradient (EFG) principal
axes is developed analytically, based on fictitious spin-1/2 formalism. Compact
closed-form expressions for the eigenstates and transitions frequencies, as
well as the expectation value of the magnetic moment after resonant excitation,
are derived. Emphasis is placed on defining and interpreting the associated
Rabi frequencies, as a function of excitation direction and ellipticity. It is
found transitions inherently fall into two subsets, depending on their
sensitivity to excitation direction, with the Rabi frequency of one subset
directly depending on the asymmetry of the EFG. A natural application is the
study of Fe-based superconductors, whose antiferromagnetic ordering at low
temperatures leads to a strong intrinsic magnetic field aligned with the EFG
principal axes. Zero external-field NMR spectra, from powder samples of two
such Fe-based superconductors, BaFe$_2$As$_2$ and CaFe$_2$As$_2$, are analyzed
and exemplify the simplicity in extracting the internal magnetic field, the
quadrupole coupling constant, and the EFG asymmetry parameter, which are
important for studying magnetic ordering, structural properties, phase
transitions, and NMR dynamics. Results compare favorably to conventional
high-field NMR experiments done with the rotation of single crystals. Overall,
the physical insights, afforded by the exact and concise expressions, will lead
to ready interpretation of spin-3/2 spectra as well as precipitate new
experimental directions.


  We investigate a model for a Mott insulator in presence of a time-periodic
modulated interaction and a coupling to a thermal reservoir. The combination of
drive and dissipation leads to non-equilibrium steady states with a large
number of doublon excitations, well above the maximum thermal-equilibrium
value. We interpret this effect as an enhancement of local pairing
correlations, providing analytical arguments based on a Floquet Hamiltonian.
Remarkably, this Hamiltonian shows a tendency to develop long-range staggered
superconducting correlations. This suggests the possibility of realizing the
elusive eta-pairing phase in driven-dissipative Mott Insulators.


  We consider a conservative coupled oscillators systems which arises as a
simplified model of the interaction of flexural and torsional modes of
vibration along the deck of the so-called fish-bone model of suspension
bridges. The elastic response of the cables is supposed to be asymptotically
linear under traction, and asymptotically constant when compressed (a
generalization of the slackening regime). We show that for vibrations of
sufficiently large amplitude, transfer of energy from flexural modes to
torsional modes may occur provided a certain condition on the parameters is
satisfied. The main result is a non-trivial extension of a theorem in an our
previous article to the case when the frequencies of the normal modes are no
more supposed to be the same. Several numerical computations of instability
diagrams for various slackening models respecting our assumptions are
presented.


  The aim of this work is to present theoretical tools to study wave
propagation in elastic waveguides and perform multi-frequency scattering
inversion to reconstruct small shape defects in a 2D and 3D elastic plate.
Given surface multi-frequency wavefield measurements, we use a Born
approximation to reconstruct localized defect in the geometry of the plate. To
justify this approximation, we introduce a rigorous framework to study the
propagation of elastic wavefield generated by arbitrary sources. By studying
the decreasing rate of the series of inhomogeneous Lamb mode, we prove the
well-posedness of the PDE that model elastic wave propagation in 2D and 3D
planar waveguides. We also characterize the critical frequencies for which the
Lamb decomposition is not valid. Using these results, we generalize the shape
reconstruction method already developed for acoustic waveguide to 2D elastic
waveguides and provide a stable reconstruction method based on a mode-by-mode
spacial Fourier inversion given by the scattered field.


  This paper describes the solution of Bazinga Team for Tmall Recommendation
Prize 2014. With real-world user action data provided by Tmall, one of the
largest B2C online retail platforms in China, this competition requires to
predict future user purchases on Tmall website. Predictions are judged on
F1Score, which considers both precision and recall for fair evaluation. The
data set provided by Tmall contains more than half billion action records from
over ten million distinct users. Such massive data volume poses a big
challenge, and drives competitors to write every single program in MapReduce
fashion and run it on distributed cluster. We model the purchase prediction
problem as standard machine learning problem, and mainly employ regression and
classification methods as single models. Individual models are then aggregated
in a two-stage approach, using linear regression for blending, and finally a
linear ensemble of blended models. The competition is approaching the end but
still in running during writing this paper. In the end, our team achieves
F1Score 6.11 and ranks 7th (out of 7,276 teams in total).


  This paper investigates how certain relationship between observed and
counterfactual distributions serves as an identifying condition for treatment
effects when the treatment is endogenous, and shows that this condition holds
in a range of nonparametric models for treatment effects. To this end, we first
provide a novel characterization of the prevalent assumption restricting
treatment heterogeneity in the literature, namely rank similarity. Our
characterization demonstrates the stringency of this assumption and allows us
to relax it in an economically meaningful way, resulting in our identifying
condition. It also justifies the quest of richer exogenous variations in the
data (e.g., multi-valued or multiple instrumental variables) in exchange for
weaker identifying conditions. The primary goal of this investigation is to
provide empirical researchers with tools that are robust and easy to implement
but still yield tight policy evaluations.


  In this paper, we are concerned with the three dimensional Euler equations
driven by an additive stochastic forcing. First, we construct global H\"{o}lder
continuous (stationary) solutions in $C(\mathbb{R};C^{\vartheta})$ space for
some $\vartheta>0$ via a different method from \cite{LZ24}. Our approach is
based on applying stochastic convex integration to the construction of Euler
flows in \cite{DelSze13} to derive uniform moment estimates independent of
time. Second, for any divergence-free H\"{o}lder continuous initial condition,
we show the existence of infinitely many global-in-time probabilistically
strong and analytically weak solutions in
$L^p_{\rm{loc}}([0,\infty);C^{\vartheta'}) \cap
C_{\rm{loc}}([0,\infty);H^{-1})$ for all $p\in [1,\infty)$ and some
$\vartheta'>0$.


  Very light pseudoscalars can arise from the symmetry-breaking sector in many
extensions of the Standard Model. If their mass is below 200 MeV, they can be
long-lived and have interesting phenomenology. We discuss the experimental
constraints on several models with light pseudoscalars, including one in which
the pseudoscalar is naturally fermiophobic. Taking into account the stringent
bounds from rare K and B decays, we find allowed parameter space in each model
that may be accessible in direct production experiments. In particular, we
study the photoproduction of light pseudoscalars at Jefferson Lab and conclude
that a beam dump experiment could explore some of the allowed parameter space
of these models.


  A hypergraph can be obtained from a simplicial complex by deleting some
non-maximal simplices. In this paper, we study the embedded homology as well as
the homology of the (lower-)associated simplicial complexes for hypergraphs. We
generalize the discrete Morse functions on simplicial complexes. We study the
discrete Morse functions on hypergraphs as well as the discrete Morse functions
on the (lower-)associated simplicial complexes of the hypergraphs.


  Face Super-Resolution (SR) is a domain-specific super-resolution problem. The
specific facial prior knowledge could be leveraged for better super-resolving
face images. We present a novel deep end-to-end trainable Face Super-Resolution
Network (FSRNet), which makes full use of the geometry prior, i.e., facial
landmark heatmaps and parsing maps, to super-resolve very low-resolution (LR)
face images without well-aligned requirement. Specifically, we first construct
a coarse SR network to recover a coarse high-resolution (HR) image. Then, the
coarse HR image is sent to two branches: a fine SR encoder and a prior
information estimation network, which extracts the image features, and
estimates landmark heatmaps/parsing maps respectively. Both image features and
prior information are sent to a fine SR decoder to recover the HR image. To
further generate realistic faces, we propose the Face Super-Resolution
Generative Adversarial Network (FSRGAN) to incorporate the adversarial loss
into FSRNet. Moreover, we introduce two related tasks, face alignment and
parsing, as the new evaluation metrics for face SR, which address the
inconsistency of classic metrics w.r.t. visual perception. Extensive benchmark
experiments show that FSRNet and FSRGAN significantly outperforms state of the
arts for very LR face SR, both quantitatively and qualitatively. Code will be
made available upon publication.


  Majorana zero-energy bound states (ZEBSs) have been proposed to exist at the
ends of one-dimensional Rashba nanowires proximity-coupled to an s-wave
superconductor in an external magnetic field induced Zeeman field. Such hybrid
structures have been a central platform in the search for non-Abelian Majorana
zero modes (MZMs) toward fault-tolerant topological quantum computing. Here we
report the discovery of ZEBSs simultaneously appearing at each end of a
one-dimensional atomic line defect in monolayer iron-based high-temperature
superconductor FeTe0.5Se0.5 films grown on SrTiO3(001) substrates. The
spectroscopic properties of the ZEBSs, including the temperature and tunneling
barrier dependences, as well as their fusion induced by coupling on line
defects of different lengths are found to be robust and consistent with those
of the MZMs. These observations suggest a realization of topological Shockley
defects at the ends of an atomic line defect in a two-dimensional s-wave
superconductor that can host a Kramers pair of MZMs protected by time-reversal
symmetry along the chain. Our findings reveal an unprecedented class of
topological line defect excitations in two-dimensional superconductor
FeTe0.5Se0.5 monolayer films and offer an advantageous platform for generating
topological zero-energy excitations at higher operating temperatures, in a
single material, and under zero external magnetic field.


  We propose a transition-based bubble parser to perform coordination structure
identification and dependency-based syntactic analysis simultaneously. Bubble
representations were proposed in the formal linguistics literature decades ago;
they enhance dependency trees by encoding coordination boundaries and internal
relationships within coordination structures explicitly. In this paper, we
introduce a transition system and neural models for parsing these
bubble-enhanced structures. Experimental results on the English Penn Treebank
and the English GENIA corpus show that our parsers beat previous
state-of-the-art approaches on the task of coordination structure prediction,
especially for the subset of sentences with complex coordination structures.


  We consider the following general model of a sorting procedure: we fix a
hereditary permutation class $\mathcal{C}$, which corresponds to the operations
that the procedure is allowed to perform in a single step. The input of sorting
is a permutation $\pi$ of the set $[n]=\{1,2,\dotsc,n\}$, i.e., a sequence
where each element of $[n]$ appears once. In every step, the sorting procedure
picks a permutation $\sigma$ of length $n$ from $\mathcal{C}$, and rearranges
the current permutation of numbers by composing it with $\sigma$. The goal is
to transform the input $\pi$ into the sorted sequence $1,2,\dotsc,n$ in as few
steps as possible.
  This model of sorting captures not only classical sorting algorithms, like
insertion sort or bubble sort, but also sorting by series of devices, like
stacks or parallel queues, as well as sorting by block operations commonly
considered, e.g., in the context of genome rearrangement.
  Our goal is to describe the possible asymptotic behavior of the worst-case
number of steps needed when sorting with a hereditary permutation class. As the
main result, we show that any hereditary permutation class $\mathcal{C}$ falls
into one of five distinct categories. Disregarding the classes that cannot sort
all permutations, the number of steps needed to sort any permutation of $[n]$
with $\mathcal{C}$ is either $\Theta(n^2)$, a function between $O(n)$ and
$\Omega(\sqrt{n})$, a function betwee $O(\log^2 n)$ and $\Omega(\log n), or
$1$, and for each of these cases we provide a structural characterization of
the corresponding hereditary classes.


  This paper considers single-sensor estimation of vortex shedding in cylinder
wakes at $Re=100$ in simulations and at $Re=1036$ in experiments. A model based
on harmonic decomposition is developed to capture the periodic dynamics of
vortex shedding. Two model-based methods are proposed to estimate time-resolved
flow fields. First, Linear Estimation (LE) which implements a Kalman Filter to
estimate the flow. Second, Linear-Trigonometric Estimation (LTE), which
utilizes the same Kalman Filter together with a nonlinear relationship between
harmonics of the vortex shedding frequency. LTE shows good performance and
outperforms LE regarding the reconstruction of vortex shedding. Physically this
suggests that, at the Reynolds numbers considered, the higher harmonic motions
in the cylinder wake are slave to the fundamental frequency.


  In the article, we prove the large data scattering for two problems, i.e. the
defocusing quintic nonlinear Schr{\"o}dinger equation on $\mathbb{R}^2$
$\times$ $\mathbb{T}$ and the defocusing cubic nonlinear Schr{\"o}dinger
equation on $\mathbb{R}^3$ $\times$ $\mathbb{T}$. Both of the two equations are
mass supercritical and energy critical. The main ingredients of the proofs
contain global Stricharz estimate, profile decomposition and energy induction
method. This paper is the second project of our series work (two papers,
together with [36]) on large data scattering for the defocusing critical NLS
with integer index nonlinearity on low dimensional waveguides. At this point,
that type of problems are almost solved except for two remaining resonant
system conjectures and the quintic NLS problem on $\mathbb{R}\times
\mathbb{T}$.


  We consider collective motion and damping of dipolar Fermi gases in the
hydrodynamic regime. We investigate the trajectories of collective oscillations
-- here dubbed ``weltering'' motions -- in cross-dimensional rethermalization
experiments via Monte Carlo simulations, where we find stark differences from
the dilute regime. These observations are interpreted within a semi-empirical
theory of viscous hydrodynamics for gases confined to anisotropic harmonic
potentials. The derived equations of motion provide a simple effective theory
that show favorable agreement with full numerical solutions. To do so, the
theory must carefully account for the size and shape of the effective volume
within which the gas' behavior is hydrodynamic. Although formulated for dipolar
molecules, our theoretical framework retains a flexibility to accommodate
arbitrary elastic cross sections.


  A new approach to describing correlation properties of complex dynamic
systems with long-range memory based on a concept of additive Markov chains
(Phys. Rev. E 68, 061107 (2003)) is developed. An equation connecting a memory
function of the chain and its correlation function is presented. This equation
allows reconstructing the memory function using the correlation function of the
system. Thus, we have elaborated a novel method to generate a sequence with
prescribed correlation function. Effectiveness and robustness of the proposed
method is demonstrated by simple model examples. Memory functions of concrete
coarse-grained literary texts are found and their universal power-law behavior
at long distances is revealed.


  We have conducted the first systematic search for interday variability in a
large sample of extragalactic radio sources at 15 GHz. From the sample of 1158
radio-selected blazars monitored over a $\sim$10 year span by the Owens Valley
Radio Observatory 40-m telescope, we identified 20 sources exhibiting
significant flux density variations on 4-day timescales. The sky distribution
of the variable sources is strongly dependent on the line-of-sight Galactic
H$\alpha$ intensities from the Wisconsin H$\alpha$ Mapper Survey, demonstrating
the contribution of interstellar scintillation (ISS) to their interday
variability. 21% of sources observed through sight-lines with H$\alpha$
intensities larger than 10 rayleighs exhibit significant ISS persistent over
the $\sim$10 year period. The fraction of scintillators is potentially larger
when considering less significant variables missed by our selection criteria,
due to ISS intermittency. This study demonstrates that ISS is still important
at 15 GHz, particularly through strongly scattered sight-lines of the Galaxy.
Of the 20 most significant variables, 11 are observed through the
Orion-Eridanus superbubble, photoionized by hot stars of the Orion OB1
association. The high-energy neutrino source TXS0506$+$056 is observed through
this region, so ISS must be considered in any interpretation of its short-term
radio variability. J0616$-$1041 appears to exhibit large $\sim$20% interday
flux density variations, comparable in magnitude to that of the very rare class
of extreme, intrahour scintillators that includes PKS0405$-$385, J1819$+$3845
and PKS1257$-$326; this needs to be confirmed by higher cadence follow-up
observations.


  We have obtained echelle spectroscopy of 14 Population II objects selected
from those previously observed by Bonifacio & Molaro (1997). For one object, HD
140283, we obtained exquisite data with the High Dispersion Spectrograph on the
Subaru Telescope, with S/N exceeding 1000 per 0.018A pixel. Li abundances have
been determined by spectral synthesis from both the 6708A resonance line and
also from 6104A subordinate feature. Firm detections of the weak line have been
made in seven objects, and upper limits are reported for the remainder. Our
6708A abundances agree with those reported by Bonifacio & Molaro at the
99%-confidence level. Abundances from the 6104A line hint at a higher Li
abundance than that determined from the resonance feature, but this evidence is
mixed; the weakness of the 6104A line and the large number of upper limits make
it difficult to draw firm conclusions. NLTE-corrections increase (rather than
eliminate) the size of the (potential) discrepancy, and binarity appears
unlikely to affect any abundance difference. The effect of multi-dimensional
atmospheres on the line abundances was also considered, although it appears
that use of 3-D (LTE) models could again act to increase the discrepancy, if
one is indeed present.


  Over the last decades, the world has been witnessing growing threats to the
security in urban spaces, which has augmented the relevance given to visual
surveillance solutions able to detect, track and identify persons of interest
in crowds. In particular, unmanned aerial vehicles (UAVs) are a potential tool
for this kind of analysis, as they provide a cheap way for data collection,
cover large and difficult-to-reach areas, while reducing human staff demands.
In this context, all the available datasets are exclusively suitable for the
pedestrian re-identification problem, in which the multi-camera views per ID
are taken on a single day, and allows the use of clothing appearance features
for identification purposes. Accordingly, the main contributions of this paper
are two-fold: 1) we announce the UAV-based P-DESTRE dataset, which is the first
of its kind to provide consistent ID annotations across multiple days, making
it suitable for the extremely challenging problem of person search, i.e., where
no clothing information can be reliably used. Apart this feature, the P-DESTRE
annotations enable the research on UAV-based pedestrian detection, tracking,
re-identification and soft biometric solutions; and 2) we compare the results
attained by state-of-the-art pedestrian detection, tracking, reidentification
and search techniques in well-known surveillance datasets, to the effectiveness
obtained by the same techniques in the P-DESTRE data. Such comparison enables
to identify the most problematic data degradation factors of UAV-based data for
each task, and can be used as baselines for subsequent advances in this kind of
technology. The dataset and the full details of the empirical evaluation
carried out are freely available at http://p-destre.di.ubi.pt/.


  Shock heating by radio jets is potentially an important process in a range of
environments, as it will increase the entropy of the heated gas. Although this
process is expected to occur in the most powerful radio-loud AGN, strong shocks
have so far only been detected in nearby low-power radio galaxies. Here we
discuss X-ray detections of strong shocks in nearby galaxies, including a new
detection of shocked gas around both lobes of the nearby radio galaxy NGC 3801
with inferred Mach numbers of 3 - 6 and a total injected energy comparable to
the thermal energy of the ISM within 11 kpc. We discuss possible links between
shock heating, AGN fuelling and galaxy mergers and the role of this type of
system in feedback models.


  We study the decay of a pseudovector glueball with quantum numbers
$J^{PC}=1^{+-}$, the lightest glueball with spin different from zero or two, in
the top-down holographic Witten-Sakai-Sugimoto model. This glueball is dual to
the string-theoretic Kalb-Ramond tensor field, which completely fixes all its
couplings by gauge invariance and $D$-brane anomaly inflow. The dominant decay
channels are determined by a Chern-Simons-like action for the flavor branes;
couplings from the Dirac-Born-Infeld action turn out to be subdominant. While
the resulting width is parametrically of order $N_c^{-2}\lambda^{-1}$ for $N_c$
colors and 't Hooft coupling $\lambda$, when extrapolated to $N_c=3$ and with
$\lambda$ matched to experimental data, the prediction is that the pseudovector
glueball is an extremely broad resonance.


  In the past 20 years, the enumeration of plane lattice walks confined to a
convex cone -- normalized into the first quadrant -- has received a lot of
attention, stimulated the development of several original approaches, and led
to a rich collection of results. Most of them deal with the nature of the
associated generating function: for which models is it algebraic, D-finite,
D-algebraic? By model, what we mean is a finite collection of allowed steps.
  More recently, similar questions have been raised for non-convex cones,
typically the three-quadrant cone $C = \{ (i,j) : i \geq 0 \text{ or } j \geq 0
\}$. They turn out to be more difficult than their quadrant counterparts. In
this paper, we investigate a collection of eight models in $C$. This collection
consists of diagonally symmetric models in $\{-1, 0,1\}^2\setminus\{(-1,1),
(1,-1)\}$. Three of them are known not to be D-algebraic. We show that the
remaining five can be solved in a uniform fashion using Tutte's notion of
\emph{invariants}, which has already proved useful for some quadrant models.
Three models are found to be algebraic, one is (only) D-finite, and the last
one is (only) D-algebraic. We also solve in the same fashion the diagonal model
$\{ \nearrow, \nwarrow, \swarrow, \searrow\}$, which is D-finite. The three
algebraic models are those of the Kreweras trilogy, $S=\{\nearrow, \leftarrow,
\downarrow\}$, $S'=\{\rightarrow, \uparrow, \swarrow\}$, and $S\cup S'$.
  Our solutions take similar forms for all six models. Roughly speaking, the
square of the generating function of three-quadrant walks with steps in $S$ is
an explicit rational function in the quadrant generating function with steps in
$\{(j-i,j): (i,j) \in S\}$. We derive various corollaries, including an
explicit algebraic description of the positive harmonic function in $C$ for the
five models that are at least D-finite.