  Many databases store data in relational format, with different types of
entities and information about links between the entities. The field of
statistical-relational learning (SRL) has developed a number of new statistical
models for such data. In this paper we focus on learning class-level or
first-order dependencies, which model the general database statistics over
attributes of linked objects and links (e.g., the percentage of A grades given
in computer science classes). Class-level statistical relationships are
important in themselves, and they support applications like policy making,
strategic planning, and query optimization. Most current SRL methods find
class-level dependencies, but their main task is to support instance-level
predictions about the attributes or links of specific entities. We focus only
on class-level prediction, and describe algorithms for learning class-level
models that are orders of magnitude faster for this task. Our algorithms learn
Bayes nets with relational structure, leveraging the efficiency of single-table
nonrelational Bayes net learners. An evaluation of our methods on three data
sets shows that they are computationally feasible for realistic table sizes,
and that the learned structures represent the statistical information in the
databases well. After learning compiles the database statistics into a Bayes
net, querying these statistics via Bayes net inference is faster than with SQL
queries, and does not depend on the size of the database.


  A quasiparticle description of pure glue QCD thermodynamics at T<T_c is
proposed and compared to recent lattice data. Given that a gas of glueballs
with constant mass cannot quantitatively reproduce the early stages of the
deconfinement phase transition, the problem is to identify a relevant mechanism
leading to the observed sudden increase of the pressure, trace anomaly, etc. It
is shown that the strong decrease of the gluon condensate near T_c combined
with the increasing thermal width of the lightest glueballs might be the
trigger of the phase transition.


  Reinforcement learning (RL) methods work in discrete time. In order to apply
RL to inherently continuous problems like robotic control, a specific time
discretization needs to be defined. This is a choice between sparse time
control, which may be easier to train, and finer time control, which may allow
for better ultimate performance. In this work, we propose SusACER, an
off-policy RL algorithm that combines the advantages of different time
discretization settings. Initially, it operates with sparse time discretization
and gradually switches to a fine one. We analyze the effects of the changing
time discretization in robotic control environments: Ant, HalfCheetah, Hopper,
and Walker2D. In all cases our proposed algorithm outperforms state of the art.


  Let $G$ be a permutation group on $n<\infty$ objects. Let $f(g)$ be the
number of fixed points of $g\in G$, and let $\{f(g):1\ne g\in
G\}=\{f_1,\ldots,f_r\}$. In this expository note we give a character-free proof
of a theorem of Blichfeldt which asserts that the order of $G$ divides
$(n-f_1)\ldots(n-f_r)$. We also discuss the sharpness of this bound.


  We develop a new perturbation method to study the dynamics of massive tensor
fields on extremal and near-extremal static black hole spacetimes in arbitrary
dimensions. On such backgrounds, one can classify the components of massive
tensor fields into the tensor, vector, and scalar-type components. For the
tensor-type components, which arise only in higher dimensions, the massive
tensor field equation reduces to a single master equation, whereas the vector
and scalar-type components remain coupled. We consider the near-horizon
expansion of both the geometry and the field variables with respect to the
near-horizon scaling parameter. By doing so, we reduce, at each order of the
expansion, the equations of motion for the vector and scalar-type components to
a set of five mutually decoupled wave equations with source terms consisting
only of the lower-order variables. Thus, together with the tensor-type master
equation, we obtain the set of mutually decoupled equations at each order of
the expansion that govern all dynamical degrees of freedom of the massive
tensor field on the extremal and near-extremal static black hole background.


  Recent approaches to controlled text generation (CTG) often involve
manipulating the weights or logits of base language models (LMs) at decoding
time. However, these methods are inapplicable to latest black-box LMs and
ineffective at preserving the core semantics of the base LM's original
generations. In this work, we propose Locate&Edit(L&E), an efficient and
flexible energy-based approach to CTG, which edits text outputs from a base LM
using off-the-shelf energy models. Given text outputs from the base LM, L&E
first locates spans that are most relevant to constraints (e.g., toxicity)
utilizing energy models, and then edits these spans by replacing them with more
suitable alternatives. Importantly, our method is compatible with black-box
LMs, as it requires only the text outputs. Also, since L&E doesn't mandate
specific architecture for its component models, it can work with a diverse
combination of available off-the-shelf models. Moreover, L&E preserves the base
LM's original generations, by selectively modifying constraint-related aspects
of the texts and leaving others unchanged. These targeted edits also ensure
that L&E operates efficiently. Our experiments confirm that L&E achieves
superior semantic preservation of the base LM generations and speed, while
simultaneously obtaining competitive or improved constraint satisfaction.
Furthermore, we analyze how the granularity of energy distribution impacts CTG
performance and find that fine-grained, regression-based energy models improve
constraint satisfaction, compared to conventional binary classifier energy
models.


  An inverse problem of identifying locations and certain properties of small
dielectric inhomogeneities in a homogeneous background medium from boundary
measurements on a part of the boundary is studied. Using as weights particular
background solutions constructed by solving a minimization problem, an
asymptotic (variational) method based on appropriate averaging of the partial
boundary measurements is developed.


  There have been some long-standing puzzles related to the Coulomb solutions
of the Klein-Gordon and Dirac equations, namely how to understand the physics
underlying the weakly divergent near-the-origin behavior of the $S$-wave wave
functions for the hydrogen-like atoms. Taking the Klein-Gordon wave function as
a simpler example, in this work we demonstrate that, with the aid of the
renormalization group equation, this universal short-distance behavior can be
successfully taken into account by the operator product expansion (OPE)
formulated in the nonrelativistic effective field theory (EFT), which is
tailored for Coulombic atoms. The key is to include the relativistic kinetic
correction in the EFT. Somewhat counterintuitively, these universal
near-the-origin logarithmic divergences can not be addressed by the OPE set up
in the relativistic scalar QED. We conclude that the Klein-Gordon wave function
at a length scale shorter than the electron Compton wavelength may cease to
make physical significance.


  We apply some recent developments of Baldoni-Beck-Cochet-Vergne on vector
partition function, to Kostant's and Steinberg's formulae, for classical Lie
algebras $A\_r$, $B\_r$, $C\_r$, $D\_r$. We therefore get efficient {\tt Maple}
programs that compute for these Lie algebras: the multiplicity of a weight in
an irreducible finite-dimensional representation; the decomposition
coefficients of the tensor product of two irreducible finite-dimensional
representations. These programs can also calculate associated Ehrhart
quasipolynomials.


  The kinetic energy of H and O nuclei has been studied by path integral
molecular dynamics simulations of ice Ih and water at ambient pressure. The
simulations were performed by using the q-TIP4P/F model, a point charge
empirical potential that includes molecular flexibility and anharmonicity in
the OH stretch of the water molecule. Ice Ih was studied in a temperature range
between 210-290 K, and water between 230-320 K. Simulations of an isolated
water molecule were performed in the range 210-320 K to estimate the
contribution of the intramolecular vibrational modes to the kinetic energy. Our
results for the proton kinetic energy, K_H, in water and ice Ih show both
agreement and discrepancies with different published data based on deep
inelastic neutron scattering experiments. Agreement is found for water at the
experimental melting point and in the range 290-300 K. Discrepancies arise
because data derived from the scattering experiments predict in water two
maxima of K_H around 270 K and 277 K, and that K_H is lower in ice than in
water at 269 K. As a check of the validity of the employed water potential, we
show that our simulations are consistent with other experimental thermodynamic
properties related to K_H, as the temperature dependence of the liquid density,
the heat capacity of water and ice at constant pressure, and the isotopic shift
in the melting temperature of ice upon isotopic substitution of either H or O
atoms. Moreover, the temperature dependence of K_H predicted by the q-TIP4P/F
model for ice Ih is found to be in good agreement to results of path integral
simulations using ab initio density functional theory.


  Normal estimation on 3D point clouds is a fundamental problem in 3D vision
and graphics. Current methods often show limited accuracy in predicting normals
at sharp features (e.g., edges and corners) and less robustness to noise. In
this paper, we propose a novel normal estimation method for point clouds. It
consists of two phases: (a) feature encoding which learns representations of
local patches, and (b) normal estimation that takes the learned representation
as input and regresses the normal vector. We are motivated that local patches
on isotropic and anisotropic surfaces have similar or distinct normals, and
that separable features or representations can be learned to facilitate normal
estimation. To realise this, we first construct triplets of local patches on 3D
point cloud data, and design a triplet network with a triplet loss for feature
encoding. We then design a simple network with several MLPs and a loss function
to regress the normal vector. Despite having a smaller network size compared to
most other methods, experimental results show that our method preserves sharp
features and achieves better normal estimation results on CAD-like shapes.


  We study baryon pair production in two-photon collisions, gamma gamma -> B
Bbar, within perturbative quantum chromodynamics, treating baryons as
quark-diquark systems. We extend previous work within the same approach by
treating constituent-mass effects systematically by means of an expansion in
the small parameter (mass/photon energy). Our approach enables us to give a
consistent description of the cross sections for all octet baryon channels.
Adopting the model parameters from foregoing work, we are able to reproduce the
most recent large-momentum-transfer data from LEP for the p pbar, Lambda
Lambdabar, and Sigma^0 Sigma^0bar channels in a quite satisfactory way. We also
briefly address the crossed process for the proton channel, gamma p -> gamma p.


  The prediction of cross sections for nuclei far off stability is crucial in
the field of nuclear astrophysics. We discuss the model mostly employed for
such calculations: the statistical model (Hauser-Feshbach). Special emphasis is
put on the uncertainties arising from nuclear level density descriptions and an
improved global description is presented. Furthermore, criteria for the
applicability of the statistical model are investigated and a "map" for the
applicability of the model to reactions of stable and unstable nuclei with
neutral and charged particles is given.


  We consider the problem of complementary fashion prediction. Existing
approaches focus on learning an embedding space where fashion items from
different categories that are visually compatible are closer to each other.
However, creating such labeled outfits is intensive and also not feasible to
generate all possible outfit combinations, especially with large fashion
catalogs. In this work, we propose a semi-supervised learning approach where we
leverage large unlabeled fashion corpus to create pseudo-positive and
pseudo-negative outfits on the fly during training. For each labeled outfit in
a training batch, we obtain a pseudo-outfit by matching each item in the
labeled outfit with unlabeled items. Additionally, we introduce consistency
regularization to ensure that representation of the original images and their
transformations are consistent to implicitly incorporate colour and other
important attributes through self-supervision. We conduct extensive experiments
on Polyvore, Polyvore-D and our newly created large-scale Fashion Outfits
datasets, and show that our approach with only a fraction of labeled examples
performs on-par with completely supervised methods.


  Understanding how humans communicate and perceive narratives is important for
media technology research and development. This is particularly important in
current times when there are tools and algorithms that are easily available for
amateur users to create high-quality content. Narrative media develops over
time a set of recognizable patterns of features across similar artifacts. Genre
is one such grouping of artifacts for narrative media with similar patterns,
tropes, and story structures. While much work has been done on genre-based
classifications in text and video, we present a novel approach to do a
multi-modal analysis of genre based on comics and manga-style visual
narratives. We present a systematic feature analysis of an annotated dataset
that includes a variety of western and eastern visual books with annotations
for high-level narrative patterns. We then present a detailed analysis of the
contributions of high-level features to genre classification for this medium.
We highlight some of the limitations and challenges of our existing
computational approaches in modeling subjective labels. Our contributions to
the community are: a dataset of annotated manga books, a multi-modal analysis
of visual panels and text in a constrained and popular medium through
high-level features, and a systematic process for incorporating subjective
narrative patterns in computational models.


  A formalisation of G\"odel's incompleteness theorems using the Isabelle proof
assistant is described. This is apparently the first mechanical verification of
the second incompleteness theorem. The work closely follows {\'S}wierczkowski
(2003), who gave a detailed proof using hereditarily finite set theory. The
adoption of this theory is generally beneficial, but it poses certain technical
issues that do not arise for Peano arithmetic. The formalisation itself should
be useful to logicians, particularly concerning the second incompleteness
theorem, where existing proofs are lacking in detail.


  The Kondo-Heinsberg chain is an interesting model of a strongly correlated
system which has a broad superconducting state with pair-density wave (PDW)
order. Some of us have recently proposed that this PDW state is a
symmetry-protected topological (SPT) state, and the gapped spin sector of the
model supports Majorana zero modes. In this work, we reexamine this problem
using a combination of numeric and analytic methods. In extensive density
matrix renormalization group calculations, we find no evidence of a topological
ground state degeneracy or the previously proposed Majorana zero modes in the
PDW phase of this model. This result motivated us to reexamine the original
arguments for the existence of the Majorana zero modes. A careful analysis of
the effective continuum field theory of the model shows that the Hilbert space
of the spin sector of the theory does not contain any single Majorana fermion
excitations. This analysis shows that the PDW state of the doped 1D
Kondo-Heisenberg model is not an SPT with Majorana zero modes.


  Recent approaches based on artificial neural networks (ANNs) have shown
promising results for short-text classification. However, many short texts
occur in sequences (e.g., sentences in a document or utterances in a dialog),
and most existing ANN-based systems do not leverage the preceding short texts
when classifying a subsequent one. In this work, we present a model based on
recurrent neural networks and convolutional neural networks that incorporates
the preceding short texts. Our model achieves state-of-the-art results on three
different datasets for dialog act prediction.


  The majority of stars have one or more stellar companions. As exoplanets
continue to be discovered, it is crucial to examine planetary systems to
identify their stellar companions. By observing a change in proper motion,
companions can be detected by the acceleration they induce on their host stars.
We selected 701 stars from the Hipparcos-Gaia Catalog of Accelerations (HGCA)
that have existing adaptive optics imaging data gathered with Gemini/NIRI. Of
these, we examined 21 stars known to host planet candidates and reduced their
archival NIRI data with Gemini's DRAGONS software. We assessed these systems
for companions using the NIRI images as well as Renormalized Unit Weight Error
values in Gaia and accelerations in the HGCA. We detected three known visible
companions and found two more systems with no visible companions but
astrometric measurements indicating likely unresolved companions.


  If the electroweak symmetry breaking is originated from a strongly coupled
sector, as for instance in composite Higgs models, the Higgs boson couplings
can deviate from their Standard Model values. In such cases, at sufficiently
high energies there could occur an onset of multiple Higgs boson and
longitudinally polarised electroweak gauge boson (V_L) production. We study the
sensitivity to anomalous Higgs couplings in inelastic processes with 3 and 4
particles (either Higgs bosons or V_L's) in the final state. We show that, due
to the more severe cancellations in the corresponding amplitudes as compared to
the usual 2 to 2 processes, large enhancements with respect to the Standard
Model can arise even for small modifications of the Higgs couplings. In
particular, we find that triple Higgs production provides the best
multiparticle channel to look for these deviations. We briefly explore the
consequences of multiparticle production at the LHC.


  For real-world mobile applications such as location-based advertising and
spatial crowdsourcing, a key to success is targeting mobile users that can
maximally cover certain locations in a future period. To find an optimal group
of users, existing methods often require information about users' mobility
history, which may cause privacy breaches. In this paper, we propose a method
to maximize mobile crowd's future location coverage under a guaranteed location
privacy protection scheme. In our approach, users only need to upload one of
their frequently visited locations, and more importantly, the uploaded location
is obfuscated using a geographic differential privacy policy. We propose both
analytic and practical solutions to this problem. Experiments on real user
mobility datasets show that our method significantly outperforms the
state-of-the-art geographic differential privacy methods by achieving a higher
coverage under the same level of privacy protection.


  We present VSA observations (~34GHz) on scales ~20 arcmin towards a complete,
X-ray-flux-limited sample of seven clusters at redshift z<0.1. Four have
significant SZ detections in the presence of CMB primordial anisotropy. We use
a bayesian MCMC method for inference from the VSA data, with X-ray priors on
cluster positions and temperatures, and radio priors on sources. We make
assumptions of beta-model gas distributions and of hydrostatic equilibrium, to
evaluate probability densities for the gas mass and total mass out to r_200.
Our combined estimate of the gas fraction is 0.08^{+0.06}_{-0.04}h^{-1} The
random errors are poor (note that the errors are higher than would have been
obtained with the usual chi-squared method) but the control of bias is good. We
have described the MCMC analysis method specifically in terms of SZ but hope
the description will be of more general use. We find that the effects of
primordial CMB contamination tend to be similar in the estimates of both the
gas mass and total mass over our narrow range of angular scales, so that there
is little effect of primordials on the gas fraction determination. Using our
total mass estimates we find a normalisation of the mass-temperature relation
based on the profiles from the VSA cluster pressure maps that is in good
agreement with recent M-T determinations from X-ray cluster measurements.


  We present evidence for the dramatically different morphology between the
rest frame UV and 7micron mid-IR emission of VV114 and Arp299, two nearby (z~0)
violently interacting infrared luminous galaxies (LIRGs). Nearly all LIRGs are
interacting systems and it is currently accepted that they dominate the IR
emission at z>1. Luminous IR galaxies located at z=1-2 could easily be detected
as unresolved sources in deep optical/near-IR ground based surveys, as well as
in upcoming 24micron surveys with the Space Infrared Telescope Facility. We
demonstrate that the spatial resolution of these surveys will result in
blending of the emission from unresolved interacting components. An increased
scatter will thus be introduced in the observed optical to mid-IR colors of
these galaxies, leading to a systematic underestimation of their dust content.


  The burgeoning field of astrophotonics explores the interface between
astronomy and photonics. Important applications include photonic OH suppression
at near-infrared wavelengths, and integrated photonic spectroscopy. These new
photonic mechanisms are not well matched to conventional multi-mode fibres and
are best fed with single or few-mode fibres. We envisage the largest gains in
astrophotonics will come from instruments that operate with single or few-mode
fibres in the diffraction limited or near diffraction limited regimes. While
astronomical instruments have largely solved the problem of coupling light into
multi-mode fibres this is largely unexplored territory for few-mode and
single-mode fibres. Here we describe a project to explore this topic in detail,
and present initial results on coupling light into single and few-mode fibres
at the diffraction limit. We find that fibres with as few as ~5 guided modes
have qualitatively different behaviour to single-mode fibres and share a number
of the beneficial characteristics of multi-mode fibres.


  Hubble Space Telescope images of high-redshift galaxies selected via color
and photometric redshifts are used to examine the size and axial-ratio
distribution of galaxies as a function of redshift at lookback times t > 8 Gyr.
These parameters are measured at rest-frame UV wavelengths (1200-2000
Angstroms) on images with a rest-frame resolution of less than 0.8 kpc. Galaxy
radii are found to scale with redshift approximately as the inverse of the
Hubble parameter H(z). This is in accord with the theoretical expectation that
the typical sizes of the luminous parts of galaxies should track the expected
evolution in the virial radius of dark-matter halos. The mean ratio of
semi-major to semi-minor axis for a bright well-resolved sample of galaxies at
z ~ 4 is b/a = 0.65, suggesting that these Lyman break galaxies are not drawn
from a spheroidal population. However the median concentration index of this
sample is C = 3.5, which is closer to the typical concentration indices, C ~ 4,
of nearby elliptical galaxies than to the values, C<2 for local disk galaxies
of type Sb and later.


  Let $D(G)$ and $D^Q(G)= Diag(Tr) + D(G)$ be the distance matrix and distance
signless Laplacian matrix of a simple strongly connected digraph $G$,
respectively, where $Diag(Tr)=\textrm{diag}(D_1,D_2,$ $\ldots,D_n)$ be the
diagonal matrix with vertex transmissions of the digraph $G$. To track the
gradual change of $D(G)$ into $D^Q(G)$, in this paper, we propose to study the
convex combinations of $D(G)$ and $Diag(Tr)$ defined by $$D_\alpha(G)=\alpha
Diag(Tr)+(1-\alpha)D(G), \ \ 0\leq \alpha\leq1.$$ This study reduces to merging
the distance spectral and distance signless Laplacian spectral theories. The
eigenvalue with the largest modulus of $D_\alpha(G)$ is called the $D_\alpha$
spectral radius of $G$, denoted by $\mu_\alpha(G)$. We determine the digraph
which attains the maximum (or minimum) $D_\alpha$ spectral radius among all
strongly connected digraphs. Moreover, we also determine the digraphs which
attain the minimum $D_\alpha$ spectral radius among all strongly connected
digraphs with given parameters such as dichromatic number, vertex connectivity
or arc connectivity.


  Irreducible representations are the building blocks of general, semisimple
Galois representations \rho, and cuspidal representations are the building
blocks of automorphic forms \pi of the general linear group. It is expected
that when an object of the former type is associated to one of the latter type,
usually in terms of an identity of L-functions, the irreducibility of the
former should imply the cuspidality of the latter, and vice-versa. It is not a
simple matter - at all - to prove this expectation in either direction, and
nothing much is known in dimensions >2. The main result of this article shows
for n < 6, in particular, that the cuspidality of a regular algebraic \pi is
implied by the irreducibility of \rho.


  Human social hierarchy has the unique characteristic of existing in two
forms. Firstly, as an informal hierarchy where leaders and followers are
implicitly defined by their personal characteristics, and secondly, as an
institutional hierarchy where leaders and followers are explicitly appointed by
group decision. Although both forms can reduce the time spent in organising
collective tasks, institutional hierarchy imposes additional costs. It is
therefore natural to question why it emerges at all. The key difference lies in
the fact that institutions can create hierarchy with only a single leader,
which is unlikely to occur in unregulated informal hierarchy. To investigate if
this difference can affect group decision-making and explain the evolution of
institutional hierarchy, we first build an opinion-formation model that
simulates group decision making. We show that in comparison to informal
hierarchy, a single-leader hierarchy reduces (i) the time a group spends to
reach consensus, (ii) the variation in consensus time, and (iii) the rate of
increase in consensus time as group size increases. We then use this model to
simulate the cost of organising a collective action which produces resources,
and integrate this into an evolutionary model where individuals can choose
between informal or institutional hierarchy. Our results demonstrate that
groups evolve preferences towards institutional hierarchy, despite the cost of
creating an institution, as it provides a greater organisational advantage
which is less affected by group size and inequality.


  Flows over time are a natural way to incorporate flow dynamics that arise in
various applications such as traffic networks. In this paper we introduce a
natural variant of the deterministic fluid queuing model in which users aim to
minimize their costs subject to arrival at their destination before a
pre-specified deadline. We determine the existence and the structure of Nash
flows over time and fully characterize the price of anarchy for this model. The
price of anarchy measures the ratio of the quality of the equilibrium and the
quality of the optimum flow, where we evaluate the quality using two different
natural performance measures: the throughput for a given deadline and the
makespan for a given amount of flow. While it turns out that both prices of
anarchy can be unbounded in general, we provide tight bounds for the important
subclass of parallel path networks. Surprisingly, the two performance measures
yield different results here.


  We consider the category $\mathcal S(n)$ of all pairs $X = (U,V)$, where $V$
is a finite-dimensional vector space with a nilpotent operator $T$ with $T^n =
0$, and $U$ is a subspace of $V$ such that $T(U) \subseteq U$. Our main
interest in an object $X=(U,V)$ are the three numbers $uX=\dim U$ (for the
subspace), $wX=\dim V/U$ (for the factor) and $bX=\dim {\rm Ker} T$ (for the
operator). Actually, instead of looking at the reference space $\Bbb R^3$ with
the triples $(uX,wX,bX)$, we will focus the attention to the corresponding
projective space $\Bbb T(n)$ which contains for a non-zero object $X$ the
level-colevel pair {\bf pr}$X = (uX/bX,wX/bX)$ supporting the object $X$.
  We use $\Bbb T(n)$ to visualize part of the categorical structure of
$\mathcal S(n)$: The action of the duality $D$ and the square $\tau_n^2$ of the
Auslander-Reiten translation are represented on $\Bbb T(n)$ by a reflection and
a rotation by $120^\circ$ degrees, respectively. Moreover for $n\geq 6$, each
component of the Auslander-Reiten quiver of $\mathcal S(n)$ has support either
contained in the center of $\Bbb T(n)$ or with the center as its only
accumulation point.
  We show that the only indecomposable objects $X$ in $\mathcal S(n)$ with
support having boundary distance smaller than 1 are objects with $bX=1$ which
lie on the boundary, whereas any rational vector in $\Bbb T(n)$ with boundary
distance at least 2 supports infinitely many indecomposable objects. At
present, it is not clear at all what happens for vectors with boundary distance
between 1 and 2. The use of $\Bbb T(n)$ provides even in the (quite
well-understood) case $n = 6$ some surprises: In particular, we will show that
any indecomposable object in $\mathcal S(6)$ lies on one of 12 central lines in
$\Bbb T(6)$.
  The paper is essentially self-contained, all prerequisites which are needed
are outlined in detail.


  This paper explores the seamless integration of Generative AI (GenAI) and
Evolutionary Algorithms (EAs) within the domain of large-scale multi-objective
optimization. Focusing on the transformative role of Large Language Models
(LLMs), our study investigates the potential of LLM-Assisted Inference to
automate and enhance decision-making processes. Specifically, we highlight its
effectiveness in illuminating key decision variables in evolutionarily
optimized solutions while articulating contextual trade-offs. Tailored to
address the challenges inherent in inferring complex multi-objective
optimization solutions at scale, our approach emphasizes the adaptive nature of
LLMs, allowing them to provide nuanced explanations and align their language
with diverse stakeholder expertise levels and domain preferences. Empirical
studies underscore the practical applicability and impact of LLM-Assisted
Inference in real-world decision-making scenarios.


  We develop an Eilenberg-Moore spectral sequence to compute Bredon cohomology
of spaces with an action of a group given as a pullback. Using several other
spectral sequences, and positive results on the Baum-Connes Conjecture, we are
able to compute Equivariant K-theory and K-Homology of the reduced group
C*-algebra of a 6-dimensional crystallographic group $\Gamma$ introduced by
Vafa and Witten. We also use positive results on the Farrell-Jones Conjecture
to give a vanishing result for the negative algebraic K-theory of the integral
group ring of $\Gamma$.


  Fine-tuning large language models for multilingual downstream tasks requires
a diverse set of languages to capture the nuances and structures of different
linguistic contexts effectively. While the specific number varies depending on
the desired scope and target languages, we argue that the number of languages,
language exposure, and similarity that incorporate the selection of languages
for fine-tuning are some important aspects to examine. By fine-tuning large
multilingual models on 1 to 52 languages, this paper answers one question: How
many languages are needed in instruction fine-tuning for multilingual tasks? We
investigate how multilingual instruction fine-tuned models behave on
multilingual benchmarks with an increasing number of languages and discuss our
findings from the perspective of language exposure and similarity.


  Similar to the modular vector fields in Poisson geometry, modular derivations
are defined for smooth Poisson algebras with trivial canonical bundle. By
twisting Poisson module with the modular derivation, the Poisson cochain
complex with values in any Poisson module is proved to be isomorphic to the
Poisson chain complex with values in the corresponding twisted Poisson module.
Then a version of twisted Poincar\'{e} duality is proved between the Poisson
homologies and cohomologies. Furthermore, a notion of pseudo-unimodular Poisson
structure is defined. It is proved that the Poisson cohomology as a
Gerstenhaber algebra admits a Batalin-Vilkovisky operator inherited from some
one of its Poisson cochain complex if and only if the Poisson structure is
pseudo-unimodular. This generalizes the geometric version due to P. Xu. The
modular derivation and Batalin-Vilkovisky operator are also described by using
the dual basis of the K\"{a}hler differential module.


  Electronic Coulomb correlations lead to characteristic signatures in the
spectroscopy of transition metal pnictides and chalcogenides: quasi-particle
renormalizations, lifetime effects or incoherent badly metallic behavior above
relatively low coherence temperatures are measures of many-body effects due to
local Hubbard and Hund's couplings. We review and compare the results of
angle-resolved photoemission spectroscopy experiments (ARPES) and of combined
density functional dynamical mean field theory (DFT+DMFT) calculations. We
emphasize the doping-dependence of the quasi-particle mass renormalization and
coherence properties.


  The linear coupling of a rotating heat bath to a quantum field is studied in
the framework of the Markovian master equation for the field's non-unitary time
evolution. The bath's rotation induces population inversion for the field's
low-energy modes. For bosons, this leads to superradiance, an irreversible
process in which some of the bath's kinetic energy is extracted by spontaneous
and stimulated emission. We find the energy and entropy balance for such
systems and apply our results to the theory of black hole radiation. We also
comment on how this relates to classical self-oscillations, including shear
flow instabilities in hydrodynamics.


  We present a unified geometric framework for describing both the Lagrangian
and Hamiltonian formalisms of contact autonomous mechanical systems, which is
based on the approach of the pionnering work of R. Skinner and R. Rusk. This
framework permits to skip the second order differential equation problem, which
is obtained as a part of the constraint algorithm (for singular or regular
Lagrangians), and is specially useful to describe singular Lagrangian systems.
Some examples are also discussed to illustrate the method.


  In this paper, we study fixed points of N-point gravitational lenses. We use
complex form of lens mapping to study fixed points. Complex form has an
advantage over coordinate one because we can describe N-point gravitational
lens by system of two equation in coordinate form and we can describe it by one
equation in complex form. We can easily transform the equation, which describe
N-point gravitational lens, into polynomial equation that is convenient to use
for our research. In our work, we present lens mapping as a linear combination
of two mapping: complex analytical and identity mapping. Analytical mapping is
specified by analytical function (deflection function). We studied necessary
and sufficient conditions for the existence of deflection function and proved
some theorems. Deflection function is analytical, rational, its zeroes are
fixed points of lens mapping and their number is from 1 to N-1, poles of
deflection function are coordinates of point masses, all poles are simple, the
residues at the poles are equal to the value of point masses.\\ We used
Gauss-Lucas theorem and proved that all fixed points of lens mapping are in the
convex polygon. Vertices of the polygon consist of point masses. We proved
theorem that can be used to find all fixed point of lens mapping. On the basis
of the above, we conclude that one-point gravitational lens has no fixed
points, 2-point lens has only 1 fixed point, 3-point lens has 1 or 2 fixed
points. Also we present expressions to calculate fixed points in 2-point and
3-point gravitational lenses. We present some examples of parametrization of
point masses and distribution of fixed points for this parametrization.


  Effects of the paramagnetic depairing on structural transitions between
vortex lattices of a quasi two dimensional d-wave superconductor are examined.
It is found that, in systems with Maki parameter $\alpha_{\rm M}$ of order
unity, a square lattice induced by a d-wave pairing is destabilized with {\it
increasing} fields, and that a reentrant rhombic lattice occurs in higher
fields. Further, a weak Fermi surface anisotropy competitive with the pairing
symmetry induces another structural transition near $H_{c2}$. These results are
consistent with the structure changes of the vortex lattice in CeCoIn$_5$ in
${\bf H} \parallel c$ determined from recent neutron scattering data.


  The structure and magnetic interactions of the triplon Bose-Einstein
condensation candidates Ba$_3$Cr$_2$O$_8$ and Sr$_3$Cr$_2$O$_8$ have been
studied thoroughly in the literature, but little is known about a possible
triplon condensation in the corresponding solid solution
Ba$_{3-x}$Sr$_x$Cr$_2$O$_8$. We have prepared various members of this solid
solution and systematically examined their magnetic properties in high magnetic
fields up to 60 T and at low temperatures down to 340 mK, by means of pulsed
field and cantilever magnetometry. From these experiments for
$x\in\{3,2.9,2.8,2.7,2.6,2.5\}$, we find that the critical fields of
Ba$_{3-x}$Sr$_x$Cr$_2$O$_8$ decrease monotonically as a function of the Sr
content $x$. This change is in good agreement with the earlier reported
variation of the magnetic interactions in these compounds.


  We introduce to astrophysics the threshold probability functions S_2, C_2,
and D_2 first derived by \citet{torq+88}, which effectively samples the flux
probability distribution (PDF) of the Lya forest at different spatial scales.
These statistics are tested on mock Lya forest spectra based on various toy
models for HeII reionization, with homogeneous models with various
temperature-density relations as well as models with temperature
inhomogeneities. These mock samples have systematics and noise added to
simulate the latest Sloan Digital Sky Survey Data Release 7 (SDSS DR7) data. We
find that the flux PDF from SDSS DR7 can be used to constrain the
temperature-density relation $\gamma$ (where $T \propto (1 +
\Delta)^{\gamma-1}$) of the intergalactic medium (IGM) at z=2.5 to a precision
of $\Delta \gamma = 0.2$ at $\sim 4\sigma$ confidence. The flux PDF is
degenerate to temperature inhomogeneities in the IGM arising from HeII
reionization, but we find S_2 can detect these inhomogeneities at $\sim 3
\sigma$, with the assumption that the flux continuum of the Lya forest can be
determined to 9% accuracy, approximately the error from current fitting
methods. If the quasar continuum can be determined to 3% accuracy, then S_2 is
capable of constraining the characteristic scale of temperature
inhomogeneities, with $\sim 4 \sigma$ differentiation between toy models with
hot bubble radii of 50 Mpc/h and 25 Mpc/h, comoving.


  We present a general construction of hypersurfaces with vanishing hessian,
starting from any irreducible non-degenerate variety whose dual variety is a
hypersurface and based on the so called Dual Cayley Trick. The geometrical
properties of these hypersurfaces are different from the known series
constructed until now. In particular, their dual varieties can have arbitrary
codimension in the image of the associated polar map.


  Digital twins belong to ten of the strategic technology trends according to
the Gartner list from 2019, and have encountered a big expansion, especially
with the introduction of Industry 4.0. Sport, on the other hand, has become a
constant companion of the modern human suffering a lack of a healthy way of
life. The application of digital twins in sport has brought dramatic changes
not only in the domain of sport training, but also in managing athletes during
competitions, searching for strategical solutions before and tactical solutions
during the games by coaches. In this paper, the domain of digital twins in
sport is reviewed based on papers which have emerged in this area. At first,
the concept of a digital twin is discussed in general. Then, taxonomies of
digital twins are appointed. According to these taxonomies, the collection of
relevant papers is analyzed, and some real examples of digital twins are
exposed. The review finishes with a discussion about how the digital twins
affect changes in the modern sport disciplines, and what challenges and
opportunities await the digital twins in the future.


  In this paper, the Primal-Dual UNet for sparse view CT reconstruction is
modified to be applicable to cone beam projections and perform reconstructions
of entire volumes instead of slices. Experiments show that the PSNR of the
proposed method is increased by 10dB compared to the direct FDK reconstruction
and almost 3dB compared to the modified original Primal-Dual Network when using
only 23 projections. The presented network is not optimized wrt. memory
consumption or hyperparameters but merely serves as a proof of concept and is
limited to low resolution projections and volumes.


  Sea surface height anomalies observed by satellites in 1993--2012 are
combined with simulation and observations by surface drifters and Argo floats
to study water flow pattern in the Near Strait (NS) connected the Pacific Ocean
with the Bering Sea. Daily Lagrangian latitudinal maps, computed with the AVISO
surface velocity field, and calculation of the transport across the strait show
that the flow through the NS is highly variable and controlled by mesoscale and
submesoscale eddies in the area. On the seasonal scale, the flux through the
western part of the NR is negatively correlated with the flux through its
eastern part ($r=-0.93$). On the interannual time scale, a significant positive
correlation ($r=0.72$) is diagnosed between the NS transport and the wind
stress in winter. Increased southward component of the wind stress decreases
the northward water transport through the strait. Positive wind stress curl
over the strait area in winter--spring generates the cyclonic circulation and
thereby enhances the southward flow in the western part ($r=-0.68$) and
northward flow in the eastern part ($r=0.61$) of the NR. In fall, the water
transport in different parts of the NS is determined by the strength of the
anticyclonic mesoscale eddy located in the Alaskan Stream area.


  We establish maximal local regularity results of weak solutions or local
minimizers of \[ \operatorname{div} A(x, Du)=0 \quad\text{and}\quad \min_u
\int_\Omega F(x,Du)\,dx, \] providing new ellipticity and continuity
assumptions on $A$ or $F$ with general $(p,q)$-growth. Optimal regularity
theory for the above non-autonomous problems is a long-standing issue; the
classical approach by Giaquinta and Giusti involves assuming that the
nonlinearity $F$ satisfies a structure condition. This means that the growth
and ellipticity conditions depend on a given special function, such as $t^p$,
$\varphi(t)$, $t^{p(x)}$, $t^p+a(x)t^q$, and not only $F$ but also the given
function is assumed to satisfy suitable continuity conditions. Hence these
regularity conditions depend on given special functions.
  In this paper we study the problem without recourse to special function
structure and without assuming Uhlenbeck structure. We introduce a new
ellipticity condition using $A$ or $F$ only, which entails that the function is
quasi-isotropic, i.e.\ it may depend on the direction, but only up to a
multiplicative constant. Moreover, we formulate the continuity condition on $A$
or $F$ without specific structure and without direct restriction on the ratio
$\frac qp$ of the parameters from the $(p,q)$-growth condition. We establish
local $C^{1,\alpha}$-regularity for some $\alpha\in(0,1)$ and
$C^{\alpha}$-regularity for any $\alpha\in(0,1)$ of weak solutions and local
minimizers. Previously known, essentially optimal, regularity results are
included as special cases.


  In this paper We have investigated a homogeneous and isotropic FRW
cosmological model with perfect fluid in the framework of $f(R,Lm)$ gravity. We
have explored for the non linear case of $f(R,L_m)$ model, namely $f(R,L_m) =
R/2 + L_m$ and obtained the solution by using the condition that the
deceleration parameter is a linear function of the Hubble parameter. We employ
57 Hubble data points and 1048 Pantheon supernovae type Ia data samples to
restrict the model parameters. Additionally, we employ Markoc Chain Monte Carlo
(MCMC) simulation for our statistical analysis. Additionally, we analyse the
jerk and om diagnostic parameters for our model using the parameter values that
were obtained.


  We analyze the stationary spin-dependent transport through a single-molecule
magnet weakly coupled to external ferromagnetic leads. Using the real-time
diagrammatic technique, we calculate the sequential and cotunneling
contributions to current, tunnel magnetoresistance and Fano factor in both
linear and nonlinear response regimes. We show that the effects of cotunneling
are predominantly visible in the blockade regime and lead to enhancement of
tunnel magnetoresistance (TMR) above the Julliere value, which is accompanied
with super-Poissonian shot noise due to bunching of inelastic cotunneling
processes through different virtual spin states of the molecule. The effects of
external magnetic field and the role of type and strength of exchange
interaction between the LUMO level and the molecule's spin are also considered.
When the exchange coupling is ferromagnetic, we find an enhanced TMR, while in
the case of antiferromagnetic coupling we predict a large negative TMR effect.


  Humans demonstrate remarkable skill in transferring manipulation abilities
across objects of varying shapes, poses, and appearances, a capability rooted
in their understanding of semantic correspondences between different instances.
To equip robots with a similar high-level comprehension, we present SparseDFF,
a novel DFF for 3D scenes utilizing large 2D vision models to extract semantic
features from sparse RGBD images, a domain where research is limited despite
its relevance to many tasks with fixed-camera setups. SparseDFF generates
view-consistent 3D DFFs, enabling efficient one-shot learning of dexterous
manipulations by mapping image features to a 3D point cloud. Central to
SparseDFF is a feature refinement network, optimized with a contrastive loss
between views and a point-pruning mechanism for feature continuity. This
facilitates the minimization of feature discrepancies w.r.t. end-effector
parameters, bridging demonstrations and target manipulations. Validated in
real-world scenarios with a dexterous hand, SparseDFF proves effective in
manipulating both rigid and deformable objects, demonstrating significant
generalization capabilities across object and scene variations.


  The investigation of the electroweak symmetry breaking is one of the primary
tasks of the experiments at the CERN Large Hadron Collider (LHC). The potential
of the ATLAS experiment for the discovery of the Higgs boson(s) in Standard
Model and Minimal Supersymmetric Standard Model is presented, with emphasis on
studies which have been completed recently.


  Some popular functions used to test global optimization algorithms have
multiple local optima, all with the same value. That is all local optima are
also global optima. This paper suggests that such functions are easily
fortified by adding a localized bump at the location of one of the optima,
making the functions more difficult to optimize due to the multiple competing
local optima. This process is illustrated here for the Branin-Hoo function,
which has three global optima. We use the popular Python SciPy differential
evolution (DE) optimizer for the illustration. DE also allows the use of the
gradient-based BFGS local optimizer for final convergence. By making a large
number of replicate runs we establish the probability of reaching a global
optimum with the original and fortified Branin-Hoo. With the original function
we find 100% probability of success with a moderate number of function
evaluations. With the fortified version, the probability of getting trapped in
a non-global optimum could be made small only with a much larger number of
function evaluations. However, since the probability of ending up at the global
optimum is usually 1/3 or more, it may be beneficial to perform multiple
inexpensive optimizations rather than one expensive optimization. Then the
probability of one of them hitting the global optimum can be made high. We
found that for the most challenging global optimum, multiple runs reduced
substantially the extra cost for the fortified function compared to the
original Branin-Hoo.


  It has recently been pointed out that a component of the observed gamma ray
emission in the low-latitudes of Fermi Bubble has a spectral shape that can be
explained by a 10 GeV dark matter (DM) annihilating to tau leptons with a
cross-section of 2 x 10^{-27} cm^3/s. Motivated by this possibility, we revisit
the annihilation of a 10 GeV neutralino DM in the MSSM via stau exchange. The
required stau masses and mixing, consistent with LEP direct search and
electroweak precision constraints, are correlated with a possible enhancement
of the Higgs decay rate to two photons. We also explore the implications of
such a scenario for DM relic density and the muon anomalous magnetic moment,
taking into account the recent ATLAS bounds on the chargino and the first two
generation slepton masses, as well as the constraints on the Higgsino fraction
of a 10 GeV neutralino.


  Particle acceleration and pitch-angle anisotropy resulting from magnetic
reconnection are investigated in highly magnetized ion-electron plasmas. By
means of fully kinetic particle-in-cell simulations, we demonstrate that
magnetic reconnection generates anisotropic particle distributions $f_s \left(
{|\cos \alpha|,\varepsilon} \right)$, characterized by broken power laws in the
particle energy spectrum $f_s (\varepsilon) \propto \varepsilon^{-p}$ and pitch
angle $\langle \sin^2 \alpha \rangle \propto \varepsilon^m$. Their
characteristics are determined by the ratio of the guide field to the
reconnecting field ($B_g/B_0$) and the plasma magnetization ($\sigma_0$). Below
the break energy $\varepsilon_0$, ion and electron energy spectra are extremely
hard ($p_<\lesssim 1$) for any $B_g/B_0$ and $\sigma_0 \gtrsim 1$, while above
$\varepsilon_0$, the spectral index steepens ($p_> \gtrsim 2$), displaying high
sensitivity to both $B_g/B_0$ and $\sigma_0$. The pitch angle displays
power-law ranges with negative slopes ($m_<$) below and positive slopes ($m_>$)
above $\varepsilon_{\min \alpha}$, steepening with increasing $B_g/B_0$ and
$\sigma_0$. The ratio $B_g/B_0$ regulates the redistribution of magnetic energy
between ions ($\Delta E_i$) and electrons ($\Delta E_e$), with $\Delta E_i \gg
\Delta E_e$ for $B_g/B_0 \ll 1$, $\Delta E_i \sim \Delta E_e$ for $B_g/B_0 \sim
1$, and $\Delta E_i \ll \Delta E_e$ for $B_g/B_0 \gg 1$, with $\Delta
E_i/\Delta E_e$ approaching unity when $\sigma_0 \gg 1$. The anisotropic
distribution of accelerated particles results in an optically thin synchrotron
power spectrum $F_\nu(\nu) \propto\nu^{(2-2p+m)/(4+m)}$ and a linear
polarization degree $\Pi_{\rm lin} = (p+1)/(p+7/3+m/3)$. Pitch-angle anisotropy
also induces temperature anisotropy and eases synchrotron cooling, along with
producing beamed radiation, potentially responsible for frequency-dependent
variability.


  Quantum speed limit (QSL) is the lower bound on the time required for a state
to evolve to a desired final state under a given Hamiltonian evolution. Three
well-known QSLs exist Mandelstam-Tamm (MT), Margolus-Levitin (ML), and dual ML
(ML$^*$) bounds. We consider one-dimensional systems that undergoes
delocalization-localization transition in the presence of quasiperiodic and
linear potential. By performing sudden quenches across the phase boundary, we
find that the exact dynamics get captured very well by QSLs. We show that the
MT bound is always tighter in the short time limit for any arbitrary state,
while the optimal bound for the time of orthogonalization (time required to
reach the orthogonal state) depends on the choice of the initial state.
Further, for extreme quenches, we prove that the MT bound remains tighter for
the time of orthogonalization, and it can qualitatively describe the
non-analyticity in free energy for dynamical quantum phase transition (DQPT).
Finally, we also demonstrate that the localization-delocalization transition
point can be exactly identified from QSLs, whose computation cost is much less
compared to many other diagnostic tools.


  In this paper, we investigate the problem of text-to-pedestrian synthesis,
which has many potential applications in art, design, and video surveillance.
Existing methods for text-to-bird/flower synthesis are still far from solving
this fine-grained image generation problem, due to the complex structure and
heterogeneous appearance that the pedestrians naturally take on. To this end,
we propose the Multi-Grained Discrimination enhanced Generative Adversarial
Network, that capitalizes a human-part-based Discriminator (HPD) and a
self-cross-attended (SCA) global Discriminator in order to capture the
coherence of the complex body structure. A fined-grained word-level attention
mechanism is employed in the HPD module to enforce diversified appearance and
vivid details. In addition, two pedestrian generation metrics, named Pose Score
and Pose Variance, are devised to evaluate the generation quality and
diversity, respectively. We conduct extensive experiments and ablation studies
on the caption-annotated pedestrian dataset, CUHK Person Description Dataset.
The substantial improvement over the various metrics demonstrates the efficacy
of MGD-GAN on the text-to-pedestrian synthesis scenario.


  We introduce a model for dynamic networks, where the links or the strengths
of the links change over time. We solve the model by mapping dynamic networks
to the problem of directed percolation, where the direction corresponds to the
evolution of the network in time. We show that the dynamic network undergoes a
percolation phase transition at a critical concentration $p_c$, which decreases
with the rate $r$ at which the network links are changed. The behavior near
criticality is universal and independent of $r$. We find fundamental network
laws are changed. (i) For Erd\H{o}s-R\'{e}nyi networks we find that the size of
the giant component at criticality scales with the network size $N$ for all
values of $r$, rather than as $N^{2/3}$. (ii) In the presence of a broad
distribution of disorder, the optimal path length between two nodes in a
dynamic network scales as $N^{1/2}$, compared to $N^{1/3}$ in a static network.


  We consider percolation in a multiscale Boolean model. This model is defined
as the union of scaled independent copies of a given Boolean model. The scale
factor of the $n^{\textrm{th}}$ copy is $\rho^{-n}$. We prove, under optimal
integrability assumptions, that no percolation occurs in the multiscale Boolean
model for large enough $\rho$ if the rate of the Boolean model is below some
critical value.


  Intermediate dimensions were recently introduced to provide a spectrum of
dimensions interpolating between Hausdorff and box-counting dimensions for
fractals where these differ. In particular, the self-affine Bedford-McMullen
carpets are a natural case for investigation, but until now only very rough
bounds for their intermediate dimensions have been found. In this paper, we
determine a precise formula for the intermediate dimensions $\dim_{\,
\theta}\Lambda$ of any Bedford-McMullen carpet $\Lambda$ for the whole spectrum
of $\theta \in [0,1]$, in terms of a certain large deviations rate function.
The intermediate dimensions exist and are strictly increasing in $\theta$, and
the function $\theta\mapsto \dim_{\, \theta}\Lambda$ exhibits interesting
features not witnessed on any previous example, such as having countably many
phase transitions, between which it is analytic and strictly concave.
  We make an unexpected connection to multifractal analysis by showing that two
carpets with non-uniform vertical fibres have equal intermediate dimensions if
and only if the Hausdorff multifractal spectra of the uniform Bernoulli
measures on the two carpets are equal. Since intermediate dimensions are
bi-Lipschitz invariant, this shows that the equality of these multifractal
spectra is a necessary condition for two such carpets to be Lipschitz
equivalent.


  Symmetric cones can be endowed with at least two interesting non Riemannian
metrics: the Hilbert and the Thompson metrics. It is trivial that the linear
maps preserving the cone are isometries for those two metrics. Oddly enough
those are not the only isometries in general. We give here a full description
of the isometry groups for both the Hilbert and the Thompson metrics using
essentially the theory of euclidean Jordan algebras. Those results were already
proved for the symmetric cone of complexe positive hermitian matrices by L.
Moln{\'a}r. In this paper however we do not make any assumption on the
symmetric cone under scrutiny (it could be reducible and contain exceptional
factors).


  In models with large extra dimensions all gauge singlet fields can in
principle propagate in the extra dimensional space. We have investigated
possible constraints on majoron models of neutrino masses in which the majorons
propagate in extra dimensions. It is found that astrophysical constraints from
supernovae are many orders of magnitude stronger than previous accelerator
bounds. Our findings suggest that unnatural types of the "see-saw" mechanism
for neutrino masses are unlikely to occur in nature, even in the presence of
extra dimensions.


  Network models facilitate inexpensive simulations, but require careful
handling of bifurcation conditions. We here present the graphnics library,
which combines FEniCS with NetworkX to facilitate network simulations using the
finite element method. Graphnics features (i) a FenicsGraph class built on top
of the NetworkX DiGraph class, that constructs a global mesh for a network and
provides FEniCS mesh functions describing how they relate to the graph
structure. (ii) Example models showing how the FenicsGraph class can be used to
assemble and solve different network flow models. (iii) Demos showing e.g. how
to run simulations on complex biological networks. Interestingly, the results
show that vasomotion modelled as a travelling sinusoidal wave is capable of
driving net perivascular fluid flow through an arterial tree, as has been
proposed based on experimental data.


  Both functional and structural magnetic resonance imaging (fMRI and sMRI) are
widely used for the diagnosis of mental disorder. However, combining
complementary information from these two modalities is challenging due to their
heterogeneity. Many existing methods fall short of capturing the interaction
between these modalities, frequently defaulting to a simple combination of
latent features. In this paper, we propose a novel Cross-Attentive Multi-modal
Fusion framework (CAMF), which aims to capture both intra-modal and inter-modal
relationships between fMRI and sMRI, enhancing multi-modal data representation.
Specifically, our CAMF framework employs self-attention modules to identify
interactions within each modality while cross-attention modules identify
interactions between modalities. Subsequently, our approach optimizes the
integration of latent features from both modalities. This approach
significantly improves classification accuracy, as demonstrated by our
evaluations on two extensive multi-modal brain imaging datasets, where CAMF
consistently outperforms existing methods. Furthermore, the gradient-guided
Score-CAM is applied to interpret critical functional networks and brain
regions involved in schizophrenia. The bio-markers identified by CAMF align
with established research, potentially offering new insights into the diagnosis
and pathological endophenotypes of schizophrenia.


  We examine some flavor changing processes such as rare leptonic decays of the
long-lived neutral kaon, muon-electron conversion in nuclei and radiative muon
decay which are induced by the combined effects of bilinear and trilinear
R-parity violations. These processes are used to put strong constraints on
certain products of the bilinear and trilinear couplings. We also discuss the
constraints on R-parity violation from neutrino masses and compare them with
the constraints from flavor changing decay processes. Large range of parameter
space satisfying the constraints from neutrino masses can be excluded by the
flavor changing processes considered in this paper, and also vice versa.


  Knowledge of fundamental traffic flow characteristics of traffic simulation
models is an essential requirement when using these models for the planning,
design, and operation of transportation systems. In this paper we discuss the
following: a description of how features relevant to traffic flow are currently
under implementation in the TRANSIMS microsimulation, a proposition for
standardized traffic flow tests for traffic simulation models, and the results
of these tests for two different versions of the TRANSIMS microsimulation.


  We present an investigation of MgII absorbers characterized as single-cloud
weak systems at z~1. We measured column densities and Doppler parameters for
MgII and FeII in 15 systems found in HIRES/Keck spectra at 6.6 km/s. Using
these quantities and CIV, Lyman alpha and Lyman limit absorption observed with
FOS/HST (resolution ~230 km/s) we applied photoionization models to each system
to constrain metallicities, densities, ionization conditions, and sizes.
  We find that: (1) Single-cloud weak systems are optically thin in neutral
hydrogen and may have their origins in a population of objects distinct from
the optically thick strong MgII absorbers, which are associated with bright
galaxies. (2) Weak systems account for somewhere between 25% to 100% of the z <
1 Lyman alpha forest clouds in the range 15.8<log N(HI)<16.8 cm^-2. (3) At
least seven of 15 systems have two or more ionization phases of gas (multiphase
medium). (4) We identify a subset of weak MgII absorber that we term
``iron-rich''. These clouds are not alpha-group enhanced and are constrained to
have sizes of ~10 pc. At that size, to produce the observed redshift path
density, they would need to outnumber L* galaxies by approximately six orders
of magnitude.
  We discuss these results and the implications that the iron-rich systems
require enrichment from Type Ia supernovae. Further, we address how star
clusters or supernova remnants in dwarf galaxies might give rise to absorbers
with the inferred properties. This would imply far larger numbers of such
objects than are presently known, even locally. We compare the weak systems to
the weak kinematic subsystems in strong MgII absorbers and to Galactic high
velocity clouds. (abridged)


  Previous methods for dynamic facial expression in the wild are mainly based
on Convolutional Neural Networks (CNNs), whose local operations ignore the
long-range dependencies in videos. To solve this problem, we propose the
spatio-temporal Transformer (STT) to capture discriminative features within
each frame and model contextual relationships among frames. Spatio-temporal
dependencies are captured and integrated by our unified Transformer.
Specifically, given an image sequence consisting of multiple frames as input,
we utilize the CNN backbone to translate each frame into a visual feature
sequence. Subsequently, the spatial attention and the temporal attention within
each block are jointly applied for learning spatio-temporal representations at
the sequence level. In addition, we propose the compact softmax cross entropy
loss to further encourage the learned features have the minimum intra-class
distance and the maximum inter-class distance. Experiments on two in-the-wild
dynamic facial expression datasets (i.e., DFEW and AFEW) indicate that our
method provides an effective way to make use of the spatial and temporal
dependencies for dynamic facial expression recognition. The source code and the
training logs will be made publicly available.


  We present results of the VLA radio continuum total power and polarised
intensity observations of Stephan's Quintet at 1.43 and 4.86 GHz along with
complementary 4.85 and 8.35 GHz Effelsberg observations. Our study shows a
large envelope of radio emission encompassing all the member galaxies and hence
a large volume of intergalac- tic matter. Infall of the galaxy NGC 7318B
produces a ridge of intergalactic, polarised emission, for which the magnetic
field strength was estimated as 11.0 \pm 2.2 {\mu}G, with an ordered component
of 2.6 \pm 0.8 {\mu}G. The energy density of the field within the ridge area is
of the same order as estimates of the thermal component, implying a significant
role of the magnetic field in the dynamics of the intergalactic matter. We also
report that the tidal dwarf galaxy candidate SQ-B possesses a strong and highly
anisotropic magnetic field with the total strength being equal to 6.5 \pm 1.9
{\mu}G and an ordered component reaching 3.5 \pm 1.2 {\mu}G, which is
comparable to that found in normal-sized galaxies.


  Animals must constantly make decisions on the move, such as when choosing
among multiple options, or "targets", in space. Recent evidence suggests that
this results from a recursive feedback between the (vectorial) neural
representation of the targets and the resulting motion defined by this
consensus, which then changes the egocentric neural representation of the the
options, and so on. Here we employ a simple model of this process to both
explore how its dynamics account for the experimentally-observed
abruptly-branching trajectories exhibited by animals during spatial
decision-making, and to provide new insights into spatiotemporal computation.
Essential neural dynamics, notably local excitation and long-range inhibition,
are captured in our model via spin-system dynamics, with groups of Ising-spins
representing neural "activity bumps" corresponding to target directions.
Analysis, employing a novel "mean-field trajectory" approach, reveals the
nature of the spontaneous symmetry breaking - bifurcations in the model that
result in literal bifurcations in trajectory space and how it results in new
geometric principles for spatiotemporal decision-making. We find that all
bifurcation points, beyond the very first, fall on a small number of
"bifurcation curves". It is the spatial organization of these curves that is
shown to be key to determining the shape of the trajectories, such as
self-similar or space filling, exhibited during decision-making, irrespective
of the trajectory's starting point. Furthermore, we find that a non-Euclidean
representation of space considerably reduces the number of bifurcation points
in many geometrical configurations, preventing endless indecision and promoting
effective spatial decision-making. This suggests that a non-Euclidean neural
representation of space may be expected to have evolved across species in order
to facilitate spatial decision-making.


  Prosody modeling is an essential component in modern text-to-speech (TTS)
frameworks. By explicitly providing prosody features to the TTS model, the
style of synthesized utterances can thus be controlled. However, predicting
natural and reasonable prosody at inference time is challenging. In this work,
we analyzed the behavior of non-autoregressive TTS models under different
prosody-modeling settings and proposed a hierarchical architecture, in which
the prediction of phoneme-level prosody features are conditioned on the
word-level prosody features. The proposed method outperforms other competitors
in terms of audio quality and prosody naturalness in our objective and
subjective evaluation.


  We consider an infinite system of quasilinear first-order partial
differential equations, generalized to contain spacial integration, which
describes an incompressible fluid mixture of infinite components in a line
segment whose motion is driven by unbounded and space-time dependent
evaporation rates. We prove unique existence of the solution to the
initial-boundary value problem, with conservation-of-fluid condition at the
boundary. The proof uses a map on the space of collection of characteristics,
and a representation based on a non-Markovian point process with
last-arrival-time dependent intensity.


  Neutron stars are rich laboratories of multiple branches of modern physics.
These include gravitational physics, nuclear and particle physics, (quantum)
electrodynamics, and plasma astrophysics. In this chapter, we present the
pioneering theoretical studies and the pivotal historical observations on which
our understanding of neutron stars is based on. Then, we discuss the usage of
neutron stars as probes of fundamental theories of physics.


  Next-generation weak lensing (WL) surveys, such as by the Vera Rubin
Observatory's LSST, the $\textit{Roman}$ Space Telescope, and the
$\textit{Euclid}$ space mission, will supply vast amounts of data probing
small, highly nonlinear scales. Extracting information from these scales
requires higher-order statistics and the controlling of related systematics
such as baryonic effects. To account for baryonic effects in cosmological
analyses at reduced computational cost, semi-analytic baryonic correction
models (BCMs) have been proposed. Here, we study the accuracy of BCMs for WL
peak counts, a well studied, simple, and effective higher-order statistic. We
compare WL peak counts generated from the full hydrodynamical simulation
IllustrisTNG and a baryon-corrected version of the corresponding dark
matter-only simulation IllustrisTNG-Dark. We apply galaxy shape noise expected
at the depths reached by DES, KiDS, HSC, LSST, $\textit{Roman}$, and
$\textit{Euclid}$. We find that peak counts in BCMs are (i) accurate at the
percent level for peaks with $\mathrm{S/N}<4$, (ii) statistically
indistinguishable from IllustrisTNG in most current and ongoing surveys, but
(iii) insufficient for deep future surveys covering the largest solid angles,
such as LSST and $\textit{Euclid}$. We find that BCMs match individual peaks
accurately, but underpredict the amplitude of the highest peaks. We conclude
that existing BCMs are a viable substitute for full hydrodynamical simulations
in cosmological parameter estimation from beyond-Gaussian statistics for
ongoing and future surveys with modest solid angles. For the largest surveys,
BCMs need to be refined to provide a more accurate match, especially to the
highest peaks.


  Fusion frames enable signal decompositions into weighted linear subspace
components. For positive integers p, we introduce p-fusion frames, a sharpening
of the notion of fusion frames. Tight p-fusion frames are closely related to
the classical notions of designs and cubature formulas in Grassmann spaces and
are analyzed with methods from harmonic analysis in the Grassmannians. We
define the p-fusion frame potential, derive bounds for its value, and discuss
the connections to tight p-fusion frames.


  In this paper we present algorithms for a number of problems in geometric
pattern matching where the input consist of a collections of segments in the
plane. Our work consists of two main parts. In the first, we address problems
and measures that relate to collections of orthogonal line segments in the
plane. Such collections arise naturally from problems in mapping buildings and
robot exploration.
  We propose a new measure of segment similarity called a \emph{coverage
measure}, and present efficient algorithms for maximising this measure between
sets of axis-parallel segments under translations. Our algorithms run in time
$O(n^3\polylog n)$ in the general case, and run in time $O(n^2\polylog n)$ for
the case when all segments are horizontal. In addition, we show that when
restricted to translations that are only vertical, the Hausdorff distance
between two sets of horizontal segments can be computed in time roughly
$O(n^{3/2}{\sl polylog}n)$. These algorithms form significant improvements over
the general algorithm of Chew et al. that takes time $O(n^4 \log^2 n)$. In the
second part of this paper we address the problem of matching polygonal chains.
We study the well known \Frd, and present the first algorithm for computing the
\Frd under general translations. Our methods also yield algorithms for
computing a generalization of the \Fr distance, and we also present a simple
approximation algorithm for the \Frd that runs in time $O(n^2\polylog n)$.


  In this work we study the occurrence of finite-time cosmological
singularities in a cosmological system comprising from three fluids.
Particularly, the system contains two dark fluids, namely that of dark energy
and dark matter, which are interacting, and of a non-interacting baryonic
fluid. For the study we adopt the phase space approach by constructing the
cosmological dynamical system in such a way so that it rendered to be an
autonomous polynomial dynamical system, and in order to achieve this, we
appropriately choose the variables of the dynamical system. By employing a
rigid mathematical framework, that of dominant balances analysis, we
demonstrate that there exist non-singular solutions of the dynamical system,
which correspond to a general set of initial conditions, which proves that no
Big Rip or Type III finite-time singularities occur in this LQC multifluid
dynamical system. Thus the new feature of this work is that we are able to do
this using an analytic technique instead of adopting a numerical approach. In
addition, we perform a fixed point analysis of the cosmological dynamical
system, and we examine the behavior of the total effective equation of state
parameter, at the fixed points, as a function of the free parameters of the
system. Finally, we investigate the phenomenological implications of the dark
energy equation of state which we assumed that it governs the dark energy
fluid.


  In the 1990s, Joshua Angrist and Guido Imbens studied the causal
interpretation of Instrumental Variable estimates (a widespread methodology in
economics) through the lens of potential outcomes (a classical framework to
formalize causality in statistics). Bridging a gap between those two strands of
literature, they stress the importance of treatment effect heterogeneity and
show that, under defendable assumptions in various applications, this method
recovers an average causal effect for a specific subpopulation of individuals
whose treatment is affected by the instrument. They were awarded the Nobel
Prize primarily for this Local Average Treatment Effect (LATE). The first part
of this article presents that methodological contribution in-depth: the
origination in earlier applied articles, the different identification results
and extensions, and related debates on the relevance of LATEs for public policy
decisions. The second part reviews the main contributions of the authors beyond
the LATE. J. Angrist has pursued the search for informative and varied
empirical research designs in several fields, particularly in education. G.
Imbens has complemented the toolbox for treatment effect estimation in many
ways, notably through propensity score reweighting, matching, and, more
recently, adapting machine learning procedures.


  Many speech enhancement methods try to learn the relationship between noisy
and clean speech, obtained using an acoustic room simulator. We point out
several limitations of enhancement methods relying on clean speech targets; the
goal of this work is proposing an alternative learning algorithm, called
acoustic and adversarial supervision (AAS). AAS makes the enhanced output both
maximizing the likelihood of transcription on the pre-trained acoustic model
and having general characteristics of clean speech, which improve
generalization on unseen noisy speeches. We employ the connectionist temporal
classification and the unpaired conditional boundary equilibrium generative
adversarial network as the loss function of AAS. AAS is tested on two datasets
including additive noise without and with reverberation, Librispeech + DEMAND
and CHiME-4. By visualizing the enhanced speech with different loss
combinations, we demonstrate the role of each supervision. AAS achieves a lower
word error rate than other state-of-the-art methods using the clean speech
target in both datasets.


  We consider a real-time streaming system where messages are created
sequentially at the source, and are encoded for transmission to the receiver
over a packet erasure link. Each message must subsequently be decoded at the
receiver within a given delay from its creation time. The goal is to construct
an erasure correction code that achieves the maximum message size when all
messages must be decoded by their respective deadlines under a specified set of
erasure patterns (erasure model). We present an explicit intrasession code
construction that is asymptotically optimal under erasure models containing a
limited number of erasures per coding window, per sliding window, and
containing erasure bursts of a limited length.


  In the Korean culture the family members are recorded in special family
books. This makes it possible to follow the distribution of Korean family names
far back in history. It is here shown that these name distributions are well
described by a simple null model, the random group formation (RGF) model. This
model makes it possible to predict how the name distributions change and these
predictions are shown to be borne out. In particular, the RGF model predicts
that, for married women entering a collection of family books in a certain
year, the occurrence of the most common family name "Kim" should be directly
proportional the total number of married women with the same proportionality
constant for all the years. This prediction is also borne out to high degree.
We speculate that it reflects some inherent social stability in the Korean
culture. In addition, we obtain an estimate of the total population of the
Korean culture down to year 500 AD, based on the RGF model and find about ten
thousand Kims.


  We examine the possibility of probing superconductivity effects in metal
nanoclusters via diamond magnetometry. Metal nanoclusters have been proposed as
constitutive elements of high T$_c$ superconducting nanostructured materials.
Magnetometry based on the detection of spin-selective fluorescence of
nitrogen-vacancy (NV) centers in diamond is capable of nanoscale spatial
resolution and could be used as a tool for investigating the properties of
single or multiple clusters interacting among each other or with a surface. We
have carried out sensitivity estimates and experiments to understand how these
magnetometers could be used in such a situation. We studied the behavior of the
sensor as a function of temperature and detected the flux exclusion effect in a
superconductor by monitoring the [111]-orientation fine structure spectrum in
high-NV density diamond. Our results show that phase transitions can be
ascertained in a bulk superconductor with this technique while the principal
zero field splitting parameter ($D$) demonstrates a temperature dependence that
may require compensation schemes.


  In this paper we use the model of extragalactic background light to
investigate the factors that have influence on the confusion noise. It was
shown that (1) Large-Scale Structure of the Universe is an important factor;
(2) gravitational lensing does not have a significant effect on the confusion
noise; (3) lower redshift limit of objects that contribute to the confusion
noise does not depend on the wavelength and is about $z_{min}\sim 0.5-0.6$,
while upper redshift limit gradually changes from $\sim4$ to $\sim3$ with the
increase of wavelength from 70$\mu m$ up to 2000$\mu m$; (4) at rather short
wavelengths ($\simeq70\mu m$) galaxies with luminosities in the range
$10^7L_\odot$ -- $10^9L_\odot$ give the most contribution to the confusion
noise, while at larger wavelengths (650-2000$\mu m$) their luminosities are
greater than $L\geq10^{10}L_\odot$; (5) contribution from objects with
different color characteristics is considered; (6) the variability of the
extragalactic background on the timescale from 1 day to 1 year is noticeable at
short wavelengths (70--350$\mu m$) and manifests at fluxes ${}^<_\sim$ 1~mJy.


  Dark Matter experiments searching for Weakly interacting massive particles
(WIMPs) primarily use nuclear recoils (NRs) in their attempt to detect WIMPs.
Migdal-induced electronic recoils (ERs) provide additional sensitivity to light
Dark Matter with $\mathcal{O}(\text{GeV}/c^2)$ masses. In this work, we use
Bayesian inference to find the parameter space where future detectors like
XENONnT and SuperCDMS SNOLAB will be able to detect WIMP Dark Matter through
NRs, Migdal-induced ERs or a combination thereof. We identify regions where
each detector is best at constraining the Dark Matter mass and spin independent
cross-section and infer where two or more detection configurations are
complementary to constraining these Dark Matter parameters through a combined
analysis.


  In-memory computing (IMC) has gained significant attention recently as it
attempts to reduce the impact of memory bottlenecks. Numerous schemes for
digital IMC are presented in the literature, focusing on logic operations.
Often, an application's description has data dependencies that must be
resolved. Contemporary IMC architectures perform read followed by write
operations for this purpose, which results in performance and energy penalties.
To solve this fundamental problem, this paper presents in-memory mirroring
(IMM). IMM eliminates the need for read and write-back steps, thus avoiding
energy and performance penalties. Instead, we perform data movement within
memory, involving row-wise and column-wise data transfers. Additionally, the
IMM scheme enables parallel cloning of entire row (word) with a complexity of
$\mathcal{O}(1)$. Moreover, our analysis of the energy consumption of the
proposed technique using resistive random-access memory crossbar and
experimentally validated JART VCM v1b model. The IMM increases energy
efficiency and shows 2$\times$ performance improvement compared to conventional
data movement methods.


  Small volume, finite conductivity and high frequencies are major imperatives
in the design of communications infrastructure. The radiation efficiency
$\eta_r$ impacts on the optimal gain, quality factor, and bandwidth. The
current efficiency limit applies to structures confined to a radian sphere $ka$
($k$ is the wave number, $a$ is the radius). Here we present new absolute
limits to $\eta_r$ for arbitrary antenna shapes based on $k^2S$ where $S$ is
the conductor surface area. For a dipole with an electrical length of $10^{-5}$
our result is four orders of magnitude closer to the analytical solution when
compared with previous bounds on the efficiency. The improved bound on $\eta_r$
is more accurate, more general, and easier to calculate than other limits. The
efficiency of an antenna cannot be larger than the case where the surface of
the antenna is 'peeled' off and assembled into a planar sheet with area $S$,
and a uniform current is excited along the surface of this sheet.


  Convex algebras, also called (semi)convex sets, are at the heart of modelling
probabilistic systems including probabilistic automata. Abstractly, they are
the Eilenberg-Moore algebras of the finitely supported distribution monad.
Concretely, they have been studied for decades within algebra and convex
geometry.
  In this paper we study the problem of extending a convex algebra by a single
point. Such extensions enable the modelling of termination in probabilistic
systems. We provide a full description of all possible extensions for a
particular class of convex algebras: For a fixed convex subset $D$ of a vector
space satisfying additional technical condition, we consider the algebra of
convex subsets of $D$. This class contains the convex algebras of convex
subsets of distributions, modelling (nondeterministic) probabilistic automata.
We also provide a full description of all possible extensions for the class of
free convex algebras, modelling fully probabilistic systems. Finally, we show
that there is a unique functorial extension, the so-called black-hole
extension.


  The statistical measurement of agreement is important in a number of fields,
e.g., content analysis, education, computational linguistics, biomedical
imaging. We propose Sklar's Omega, a Gaussian copula-based framework for
measuring intra-coder, inter-coder, and inter-method agreement as well as
agreement relative to a gold standard. We demonstrate the efficacy and
advantages of our approach by applying it to both simulated and experimentally
observed datasets, including data from two medical imaging studies. Application
of our proposed methodology is supported by our open-source R package,
sklarsomega, which is available for download from the Comprehensive R Archive
Network.


  In a typical mid-air haptics system, focused airborne ultrasound provides
vibrotactile sensations to localized areas on a bare skin. Herein, a method for
displaying thermal sensations to hands where mesh fabric gloves are worn is
proposed. The gloves employed in this study are commercially available mesh
fabric gloves with sound absorption characteristics, such as cotton work gloves
without any additional devices such as Peltier elements. The method proposed in
this study can also provide vibrotactile sensations by changing the ultrasonic
irradiation pattern. In this paper, we report basic experimental investigations
on the proposed method. By performing thermal measurements, we evaluate the
local heat generation on the surfaces of both the glove and the skin by focused
airborne ultrasound irradiation. In addition, we performed perceptual
experiments, thereby confirming that the proposed method produced both thermal
and vibrotactile sensations. Furthermore, these sensations were selectively
provided to a certain extent by changing the ultrasonic irradiation pattern.
These results validate the effectiveness of our method and its feasibility in
mid-air haptics applications.


  Let $\mathbf G$ be a graphing, that is a Borel graph defined by $d$ measure
preserving involutions. We prove that if $\mathbf G$ is {\em treeable} then it
arises as the local limit of some sequence $(G_n)_{n\in\mathbb{N}}$ of graphs
with maximum degree at most $d$. This extends a result by Elek [G. Elek, Note
on limits of finite graphs, Combinatorica 27 (2007)] (for $\mathbf G$ a
treeing) and consequently extends the domain of the graphings for which
Aldous-Lyons conjecture is known to be true.


  In this paper we develop a new family of Ordered Weighted Averaging (OWA)
operators. Weight vector is obtained from a desired orness of the operator.
Using Faulhaber's formulas we obtain direct and simple expressions for the
weight vector without any iteration loop. With the exception of one weight, the
remaining follow a straight line relation. As a result, a fast and robust
algorithm is developed. The resulting weight vector is suboptimal according
with the Maximum Entropy criterion, but it is very close to the optimal.
Comparisons are done with other procedures.


  For a compact oriented smooth $n$-manifold $M$ and a codimension-$1$ homology
class $\phi \in \operatorname{H}_{n-1}(M, \partial M)$, we investigate a
simplicial complex $\mathcal{S}^\dagger(M, \phi)$ relating the properly
embedded hypersurfaces in $M$ representing $\phi$. Its definition is akin to
that of other classical complexes, such as the curve complex of a surface or
the Kakimizu complex of a knot, with the difference that hypersurfaces are not
taken up to isotopy.
  We prove that $\mathcal{S}^\dagger(M, \phi)$ is connected and simply
connected in every dimension $n$. We also show connectedness of a similar
complex $\mathcal{T}^\dagger(M, \phi)$ adapted to the $3$-dimensional case,
where only Thurston norm-realizing surfaces are considered. The connectedness
results are transported to the complexes $\mathcal{S}(M, \phi), \mathcal{T}(M,
\phi)$ where hypersurfaces are taken up to isotopy, and for $n=2$ the simple
connectedness result carries over as well. We also briefly discuss extensions
to a context studied by Turaev, where regular graphs in $2$-complexes are used
to represent $1$-dimensional cohomology classes.
  We finish with two applications: we give an alternative proof of the fact
that all Seifert surfaces for a fixed knot in a rational homology sphere are
tube-equivalent, and we use connectedness of $\mathcal{T}^\dagger(M, \phi)$ to
define a new $\ell^2$-invariant of $2$-dimensional homology classes in
irreducible and boundary-irreducible oriented compact connected $3$-manifolds
with empty or toroidal boundary.


  Due to the drastic gap in complexity between sequential and batch statistical
learning, recent work has studied a smoothed sequential learning setting, where
Nature is constrained to select contexts with density bounded by 1/{\sigma}
with respect to a known measure {\mu}. Unfortunately, for some function
classes, there is an exponential gap between the statistically optimal regret
and that which can be achieved efficiently. In this paper, we give a
computationally efficient algorithm that is the first to enjoy the
statistically optimal log(T/{\sigma}) regret for realizable K-wise linear
classification. We extend our results to settings where the true classifier is
linear in an over-parameterized polynomial featurization of the contexts, as
well as to a realizable piecewise-regression setting assuming access to an
appropriate ERM oracle. Somewhat surprisingly, standard disagreement-based
analyses are insufficient to achieve regret logarithmic in 1/{\sigma}. Instead,
we develop a novel characterization of the geometry of the disagreement region
induced by generalized linear classifiers. Along the way, we develop numerous
technical tools of independent interest, including a general anti-concentration
bound for the determinant of certain matrix averages.


  In turbulent fragmentation, star formation occurs in condensations created by
converging flows. The condensations must be sufficiently massive, dense and
cool to be gravitationally unstable, so that they start to contract; {\it and}
they must then radiate away thermal energy fast enough for self-gravity to
remain dominant, so that they continue to contract. For the metallicities and
temperatures in local star forming clouds, this second requirement is only met
robustly when the gas couples thermally to the dust, because this delivers the
capacity to radiate across the full bandwidth of the continuum, rather than
just in a few discrete spectral lines. This translates into a threshold for
vigorous star formation, which can be written as a minimum ram-pressure Pcrit ~
4 10^-11 dyne. Pcrit is independent of temperature, and corresponds to flows
with molecular hydrogen number-density nH2 and velocity v satisfying nH2 v^2 >
800 cm^-3 (km/s)^2. This in turn corresponds to a minimum molecular hydrogen
column-density for vigorous star formation, NH2crit ~ 4 10^21 cm^-2 (SIGMAcrit
~ 100 MSun pc^-2), and a minimum visual extinction AVcrit ~ 9. The
characteristic diameter and line-density for a star-forming filament when this
threshold is just exceeded -- a sweet spot for local star formation regions --
are 2Rfil ~ 0.1 pc and mufil ~ 13 MSun pc^-2. The characteristic diameter and
mass for a prestellar core condensing out of such a filament are 2Rcore ~ 0.1
pc, and Mcore ~ MSun. We also show that fragmentation of a shock-compressed
layer is likely to commence while the convergent flows creating the layer are
still ongoing, and we stress that, under this circumstance, the phenomenology
and characteristic scales for fragmentation of the layer are fundamentally
different from those derived traditionally for pre-existing layers.


  We investigate a special variant of chip-firing, in which we consider an
infinite set of rooms on a number line, some of which are occupied by
violinists. In a move, we take two violinists in adjacent rooms, and send one
of them to the closest unoccupied room to the left and the other to the closest
unoccupied room to the right. We classify the different possible final states
from repeatedly performing this operation. We introduce numbers $R(N,\ell,x)$
that count labeled recursive rooted trees with $N$ vertices, $\ell$ leaves, and
the smallest rooted path ending in $x$. We describe the properties of these
numbers and connect them to permutations. We conjecture that these numbers
describe the probabilities ending with different final states when the moves
are chosen uniformly.


  We study via RG, numerics, exact bounds and qualitative arguments the
equilibrium Gibbs measure of a particle in a $d$-dimensional gaussian random
potential with {\it translationally invariant logarithmic} spatial
correlations. We show that for any $d \ge 1$ it exhibits a transition at
$T=T_c>0$. The low temperature glass phase has a non trivial structure, being
dominated by {\it a few} distant states (with replica symmetry breaking
phenomenology). In finite dimension this transition exists only in this
``marginal glass'' case (energy fluctuation exponent $\theta=0$) and disappears
if correlations grow faster (single ground state dominance $\theta>0$) or
slower (high temperature phase). The associated extremal statistics problem for
correlated energy landscapes exhibits universal features which we describe
using a non linear (KPP) RG equation. These include the tails of the
distribution of the minimal energy (or free energy) and the finite size
corrections which are universal. The glass transition is closely related to
Derrida's random energy models. In $d=2$ the glass transition of the particle
exhibits interesting similarities with the weak to strong coupling transition
in Liouville ($c=1$ barrier) and with a transition that we conjecture for the
sinh-Gordon model. Glassy freezing of the particle is associated with the
generation under RG of new local operators and of non-smooth configurations in
Liouville. Applications to Dirac fermions in random magnetic fields at
criticality reveals a peculiar ``quasi-localized'' regime (the glass phase for
the particle) where eigenfunctions are concentrated over {\it a finite number}
of distant regions, and allows to recover the multifractal spectrum.


  We report a model for hyperthermia therapies based on heat diffusion in a
biological tissue containing a topological defect. Biological tissues behave
like active liquid crystals with the presence of topological defects which are
likely to anchor tumors during the metastatic phase of cancer evolution and the
therapy challenge is to destroy the cancer cells without damaging surrounding
healthy tissues. The defect creates an effective non-Euclidean geometry for
low-energy excitations, modifying the bio-heat equation. Applications to
protocols of thermal ablation for various biological tissues (liver, prostate,
and skin) is analyzed and discussed.


  Incomplete neutralization refers to phonetic traces of underlying contrasts
in phonologically neutralizing contexts. The present study examines one such
context: Russian assimilatory palatalization in C+j sequences. Russian
contrasts plain and palatalized consonants, with the plain consonants having a
secondary articulation involving retraction of the tongue dorsum
(velarization/uvularization). However, Russian also has stop-glide sequences
that form near-minimal pairs with palatalized stops. In the environment
preceding palatal glides, the contrast between palatalized and plain consonants
is neutralized, due to the palatalization of the plain stop (assimilatory
palatalization). The purpose of the study is to explore whether the
neutralization is complete. To do so, we conducted an electromagnetic
articulography (EMA) experiment examining temporal coordination and the spatial
position of the tongue body in underlyingly palatalized consonants and those
derived from assimilatory palatalization. Articulatory results from four native
speakers of Russian revealed that gestures in both conditions are coordinated
as complex segments, i.e., they are palatalized consonants. However, there are
differences across conditions consistent with the residual presence of a tongue
dorsum retraction gesture in the plain obstruents. We conclude that
neutralization of the plain-palatal contrast in Russian is incomplete;
consonants in the assimilatory palatalization condition exhibit inter-gestural
coordination characteristic of palatalized consonants along with residual
evidence of an underlying tongue dorsum retraction (velarization/uvularization)
gesture.


  A Non-Orthogonal Unicast and Multicast (NOUM) transmission system allows a
multicast stream intended to all receivers to be jointly transmitted with
unicast streams in the same time-frequency resource blocks. While the capacity
of the two-user multi-antenna NOUM with perfect Channel State Information at
the Transmitter (CSIT) is known and achieved by Dirty Paper Coding
(DPC)-assisted NOUM with Superposition Coding (SC), the capacity and the
capacity-achieving strategy of the multi-antenna NOUM with partial CSIT remain
unknown. In this work, we focus on the partial CSIT setting and make two major
contributions. First, we show that linearly precoded Rate-Splitting (RS),
relying on splitting unicast messages into common and private parts, encoding
the common parts together with the multicast message and linearly precoding at
the transmitter, can achieve larger rate regions than DPC-assisted NOUM with
partial CSIT. Second, we study Dirty Paper Coded Rate-Splitting (DPCRS), that
marries RS and DPC. We show that the rate region of DPCRS-assisted NOUM is
enlarged beyond that of conventional DPC-assisted NOUM and that of linearly
precoded RS-assisted NOUM with partial CSIT.