  Physics-Informed Neural Networks (PINNs) have emerged as a robust framework
for solving Partial Differential Equations (PDEs) by approximating their
solutions via neural networks and imposing physics-based constraints on the
loss function. Traditionally, Multilayer Perceptrons (MLPs) are the neural
network of choice, and significant progress has been made in optimizing their
training. Recently, Kolmogorov-Arnold Networks (KANs) were introduced as a
viable alternative, with the potential of offering better interpretability and
efficiency while requiring fewer parameters. In this paper, we present a fast
JAX-based implementation of grid-dependent Physics-Informed Kolmogorov-Arnold
Networks (PIKANs) for solving PDEs. We propose an adaptive training scheme for
PIKANs, incorporating known MLP-based PINN techniques, introducing an adaptive
state transition scheme to avoid loss function peaks between grid updates, and
proposing a methodology for designing PIKANs with alternative basis functions.
Through comparative experiments we demonstrate that these adaptive features
significantly enhance training efficiency and solution accuracy. Our results
illustrate the effectiveness of PIKANs in improving performance for PDE
solutions, highlighting their potential as a superior alternative in scientific
and engineering applications.


  This is a sequel to a previous paper, developing an intrinsic, combinatorial
homotopy theory for simplicial complexes; the latter form the cartesian closed
subcategory of 'simple presheaves' in !Smp, the topos of symmetric simplicial
sets, or presheaves on the category of finite, positive cardinals.
  We show here how this homotopy theory can be extended to the topos itself,
!Smp. As a crucial advantage, the fundamental groupoid functor !Smp --> Gpd is
left adjoint to a natural functor Gpd --> !Smp, the symmetric nerve of a
groupoid, and preserves all colimits - a strong van Kampen property. Similar
results hold in all higher dimensions. Analogously, a notion of
(non-reversible) directed homotopy can be developed in the ordinary simplicial
topos Smp, with applications to image analysis as in the previous paper. We
have now a 'homotopy n-category functor' Smp --> n-Cat, left adjoint to a nerve
functor.
  This construction can be applied to various presheaf categories; the basic
requirements seem to be: finite products of representables are finitely
presentable and there is a representable 'standard interval'.


  We study structural conditions in dense graphs that guarantee the existence
of vertex-spanning substructures such as Hamilton cycles. It is easy to see
that every Hamiltonian graph is connected, has a perfect fractional matching
and, excluding the bipartite case, contains an odd cycle. A simple consequence
of the Robust Expander Theorem of K\"uhn, Osthus and Treglown tells us that any
large enough graph that robustly satisfies these properties must already be
Hamiltonian. Our main result generalises this phenomenon to powers of cycles
and graphs of sublinear bandwidth subject to natural generalisations of
connectivity, matchings and odd cycles.
  This answers a question of Ebsen, Maesaka, Reiher, Schacht and Sch\"ulke and
solves the embedding problem that underlies multiple lines of research on
sufficient conditions for spanning structures in dense graphs. As applications,
we recover and establish Bandwidth Theorems in a variety of settings including
Ore-type degree conditions, P\'osa-type degree conditions, deficiency-type
conditions, locally dense and inseparable graphs, multipartite graphs as well
as robust expanders.


  Simulation-based software testing supports engineers in finding faults in
Simulink models. It typically relies on search algorithms that iteratively
generate test inputs used to exercise models in simulation to detect design
errors. While simulation-based software testing techniques are effective in
many practical scenarios, they are typically not fully integrated within the
Simulink environment and require additional manual effort. Many techniques
require engineers to specify requirements using logical languages that are
neither intuitive nor fully supported by Simulink, thereby limiting their
adoption in industry.
  This work presents HECATE, a testing approach for Simulink models using Test
Sequence and Test Assessment blocks from Simulink Test. Unlike existing testing
techniques, HECATE uses information from Simulink models to guide the
search-based exploration. Specifically, HECATE relies on information provided
by the Test Sequence and Test Assessment blocks to guide the search procedure.
Across a benchmark of 16 Simulink models from different domains and industries,
our comparison of HECATE with the state-of-the-art testing tool S-TALIRO
indicates that HECATE is both more effective (more failure-revealing test
cases) and efficient (less iterations and computational time) than S-TALIRO for
~94% and ~81% of benchmark models respectively. Furthermore, HECATE
successfully generated a failure-revealing test case for a representative case
study from the automotive domain demonstrating its practical usefulness.


  We provide a parametrization of a new phenomenological scaling function
obtained from a chi-square fit to a selected set of (e,e') cross section data
expanding a band centered around the quasielastic peak. We start from a
re-analysis of quasielastic electron scattering from nuclear matter within the
relativistic mean field model. The cross section depends on the relativistic
effective mass of the nucleon, $m_N^*$, and it scales with respect to a new
scaling variable, $\psi^*$. This suggests a new superscaling approach with
effective mass (SuSAM*) for predicting quasielastic cross sections within an
uncertainty band. The model reproduces previously established results on the
enhancement of the transverse response function as compared to the traditional
relativistic Fermi gas.


  This paper revisits the generation hosting capacity (HC) calculation approach
to account for grid operational flexibility--the ability to reconfigure the
system safely. In essence, the generation hosting capacity is determined
against the set of limiting factors--voltage, thermal (conductor loading),
reverse flow (at the feeder head, station transformer, or substation), and
change in the voltage (due to sudden change in generation output)). Not that
long ago, California Investor-Owned Utilities (IOUs) added a new criterion that
does not allow reverse flow at the supervisory control and data acquisition
(SCADA) points that can change the system configuration, aiming to prevent the
potential transfer of reverse flow to an adjacent feeder. This new criterion
intended to capture operational constraints as part of hosting capacity-known
as hosting capacity with operational flexibility (OpFlex). This paper explores
the shortfalls of such an approach and proposes performing actual transfer
analysis when determining hosting capacity rather than implementing the OpFlex
approach. Furthermore, we discuss the need for transition to determining
hosting capacity profile (all intervals) rather than a flat line (one, worst
performing interval) hosting capacity. A hosting capacity profile would inform
the developers of interval-by-interval limits and opportunities, creating new
opportunities to reach higher penetration of DERs at a lower cost. With
technological and computational advancements, such an approach is neither out
of implementation reach nor that computationally expensive. In return, far more
DER can be interconnected once programmed not to violate certain generation
profiles as part of the interconnection requirement, and utilities would be
better informed of their actual operational flexibility, benefiting society
overall.


  We present a simple parameterization of a running coupling constant, defined
via the static potential, that interpolates between 2-loop QCD in the UV and
the string prediction in the IR. Besides the usual $\Lam$-parameter and the
string tension, the coupling depends on one dimensionless parameter,
determining how fast the crossover from UV to IR behavior occurs (in principle
we know how to take into account any number of loops by adding more
parameters). Using a new Ansatz for the LATTICE potential in terms of the
continuum coupling, we can fit quenched and unquenched Monte Carlo results for
the potential down to ONE lattice spacing, and at the same time extract the
running coupling to high precision. We compare our Ansatz with 1-loop results
for the lattice potential, and use the coupling from our fits to quantitatively
check the accuracy of 2-loop evolution, compare with the Lepage-Mackenzie
estimate of the coupling extracted from the plaquette, and determine Sommer's
scale $r_0$ much more accurately than previously possible. For pure SU(3) we
find that the coupling scales on the percent level for $\beta\geq 6$.


  We answer a question posed by Y. Elias et al. in [8] about possible spectral
distortions of algebraic numbers. We provide a closed form for the spectral
distortion of certain classes of cyclotomic polynomials. Moreover, we present a
bound on the spectral distortion of cyclotomic polynomials.


  With the prevalence of wearable devices, inertial measurement unit (IMU) data
has been utilized in monitoring and assessment of human mobility such as human
activity recognition (HAR). Training deep neural network (DNN) models for these
tasks require a large amount of labeled data, which are hard to acquire in
uncontrolled environments. To mitigate the data scarcity problem, we design
CROMOSim, a cross-modality sensor simulator that simulates high fidelity
virtual IMU sensor data from motion capture systems or monocular RGB cameras.
It utilizes a skinned multi-person linear model (SMPL) for 3D body pose and
shape representations, to enable simulation from arbitrary on-body positions. A
DNN model is trained to learn the functional mapping from imperfect trajectory
estimations in a 3D SMPL body tri-mesh due to measurement noise, calibration
errors, occlusion and other modeling artifacts, to IMU data. We evaluate the
fidelity of CROMOSim simulated data and its utility in data augmentation on
various HAR datasets. Extensive experiment results show that the proposed model
achieves a 6.7% improvement over baseline methods in a HAR task.


  We refine the cyclic cohomological apparatus for computing the Hopf cyclic
cohomology of the Hopf algebras associated to infinite primitive Cartan-Lie
pseudogroups, and for the transfer of their characteristic classes to
foliations. The main novel feature is the precise identification as a Hopf
cyclic complex of the image of the canonical homomorphism from the Gelfand-Fuks
complex to the Bott complex for equivariant cohomology. This provides a
convenient new model for the Hopf cyclic cohomology of the geometric Hopf
algebras, which allows for an efficient transport of the Hopf cyclic classes
via characteristic homomorphisms. We illustrate the latter aspect by indicating
how to realize the universal Hopf cyclic Chern classes in terms of explicit
cocycles in the cyclic cohomology of foliation groupoids.


  Existence of a specific family of \emph{eternal solutions} in exponential
self-similar form is proved for the following porous medium equation with
strong absorption $$\partial_t u-\Delta u^m+|x|^{\sigma}u^q = 0 \;\;\text{ in
}\;\; (0,\infty)\times\mathbb{R}^N,$$ with $m>1$, $q\in(0,1)$ and
$\sigma=2(1-q)/(m-1)$. Looking for solutions of the form $$ u(t,x)=e^{-\alpha
t}f(|x|e^{\beta t}), \qquad \alpha=\frac{2}{m-1}\beta,$$ it is shown that, for
$m+q>2$, there exists a unique exponent $\beta_*\in(0,\infty)$ for which there
exists a one-parameter family of compactly supported profiles presenting a
\emph{dead core}. The precise behavior of the solutions at their interface is
also determined. Moreover, these solutions show the optimal limitations for the
finite time extinction property of genuine non-negative solutions to the Cauchy
problem, studied in previous works.


  The hydrodynamic equation of a spinor Bose-Einstein condensate (BEC) gives a
simple description of spin dynamics in the condensate. We introduce the
hydrodynamic equation of a ferromagnetic BEC with dissipation originating from
the energy dissipation of the condensate. The dissipative hydrodynamic equation
has the same form as an extended Landau-Lifshitz-Gilbert (LLG) equation, which
describes the magnetization dynamics of ferromagnets interacting with
spin-polarized currents. Employing the dissipative hydrodynamic equation, we
demonstrate the magnetic domain pattern dynamics of a ferromagnetic BEC in the
presence and absence of a current of particles, and discuss the effects of the
current on domain pattern formation. We also discuss the characteristic lengths
of domain patterns that have domain walls with and without finite
magnetization.


  We construct quantizations of multiplicative hypertoric varieties using an
algebra of q-difference operators on affine space, where q is a root of unity
in C. The quantization defines a matrix bundle (i.e. Azumaya algebra) over the
multiplicative hypertoric variety and admits an explicit finite \'etale
splitting. The global sections of this Azumaya algebra is a hypertoric quantum
group, and we prove a localization theorem. We introduce a general framework of
Frobenius quantum moment maps and their Hamiltonian reductions; our results
shed light on an instance of this framework.


  Fluctuations are significant in mesoscopic systems and of particular
importance in understanding quantum transport. Here, we show that fluctuations
can be considered as a resource for the operations of open quantum systems as
functional devices. We derive the statistics of the thermal transistor
amplification factor and the cooling-by-heating refrigerator efficiency under
the Gaussian fluctuation framework. Statistical properties of the stochastic
thermal transistor and the cooling-by-heating efficiency are revealed in the
linear-response regime. We clarify the unique role of inelastic processes on
thermal transport in mesoscopic systems. We further show that elastic and
inelastic processes lead to different bounds based on the linear transport
coefficients by establishing a generic theoretical framework for mesoscopic
heat transport, which treats electron and bosonic collective excitations in an
equal-footing manner. The underlying physics are illustrated concretely using a
double-quantum-dot three-terminal system, though the theory applies to more
general systems.


  Modern galaxy surveys demand extensive survey volumes and resolutions
surpassing current dark matter-only simulations' capabilities. To address this,
many methods employ effective bias models on the dark matter field to
approximate object counts on a grid. However, realistic catalogs necessitate
specific coordinates and velocities for a comprehensive understanding of the
Universe. In this research, we explore sub-grid modeling to create accurate
catalogs, beginning with coarse grid number counts at resolutions of
approximately $5.5\,h^{-1}\rm Mpc$ per side. These resolutions strike a balance
between modeling nonlinear damping of baryon acoustic oscillations and
facilitating large-volume simulations. Augmented Lagrangian Perturbation Theory
(ALPT) is utilized to model the dark matter field and motions, replicating the
clustering of a halo catalog derived from a massive simulation at $z=1.1$. Our
approach involves four key stages:
  Tracer Assignment: Allocating dark matter particles to tracers based on grid
cell counts, generating additional particles to address discrepancies.
  Attractor Identification: Defining attractors based on particle cosmic web
environments, acting as gravitational focal points.
  Tracer Collapse: Guiding tracers towards attractors, simulating structure
collapse.
  Redshift Space Distortions: Introducing redshift space distortions to
simulated catalogs using ALPT and a random dispersion term.
  Results demonstrate accurate reproduction of monopoles and quadrupoles up to
wave numbers of approximately $k=0.6\,h$ Mpc$^{-1}$. This method holds
significant promise for galaxy surveys like DESI, EUCLID, and LSST, enhancing
our understanding of the cosmos across scales.


  We propose Ray-ONet to reconstruct detailed 3D models from monocular images
efficiently. By predicting a series of occupancy probabilities along a ray that
is back-projected from a pixel in the camera coordinate, our method Ray-ONet
improves the reconstruction accuracy in comparison with Occupancy Networks
(ONet), while reducing the network inference complexity to O($N^2$). As a
result, Ray-ONet achieves state-of-the-art performance on the ShapeNet
benchmark with more than 20$\times$ speed-up at $128^3$ resolution and
maintains a similar memory footprint during inference.


  The magnetotransport properties of high mobility two dimensional electron gas
have recently attracted a significant interest due to the discovery of
microwave induced zero resistance states. Here we show experimentally that
microwave irradiation with a photon energy much smaller than the spacing
between Landau levels can induce a strong decrease in the four terminal
resistance. This effect is not predicted by the bulk transport models
introduced to explain zero resistance states, but can be naturally explained by
an edge transport model. This highlights the importance of edge channels for
zero resistance state physics that was proposed recently.


  RH rotations of the fermionic mass matrices are not observable in the
standard model, but dictate the details of the proton decay in GUTs. $P_{LR}$
symmetry in the two light families leads to a full RH mixing. We give two
versions of suitable broken $P_{LR}$ invariant SO(10) which leads to nucleon
decay modes similar to those of SUSY-GUTs with rates in the range of
observability of superKamiokande and ICARUS.


  D\'ail \'Eireann is the principal chamber of the Irish parliament. The 31st
D\'ail \'Eireann is the principal chamber of the Irish parliament. The 31st
D\'ail was in session from March 11th, 2011 to February 6th, 2016. Many of the
members of the D\'ail were active on social media and many were Twitter users
who followed other members of the D\'ail. The pattern of following amongst
these politicians provides insights into political alignment within the D\'ail.
We propose a new model, called the generalized latent space stochastic
blockmodel, which extends and generalizes both the latent space model and the
stochastic blockmodel to study social media connections between members of the
D\'ail. The probability of an edge between two nodes in a network depends on
their respective class labels as well as latent positions in an unobserved
latent space. The proposed model is capable of representing transitivity,
clustering, as well as disassortative mixing. A Bayesian method with Markov
chain Monte Carlo sampling is proposed for estimation of model parameters.
Model selection is performed using the WAIC criterion and models of different
number of classes or dimensions of latent space are compared. We use the model
to study Twitter following relationships of members of the D\'ail and interpret
structure found in these relationships. We find that the following
relationships amongst politicians is mainly driven by past and present
political party membership. We also find that the modeling outputs are
informative when studying voting within the D\'ail.


  The prescription of Kawai, Lewellen and Tye for writing the closed string
tree amplitudes as sums of products of open string tree amplitudes, is applied
to the world sheet renormalization group equation. The main point is that
regularization of the Minkowski (rather than Euclidean) world sheet theory
allows factorization into left-moving and right-moving sectors to be
maintained. Explicit calculations are done for the tachyon and the
(gauge-fixed) graviton.


  We establish a consistency result by comparing two independent notions of
generalised solutions to a large class of linear hyperbolic first order PDE
systems with constant coefficients, showing that they eventually coincide. The
first is the usual notion of weak solutions defined via duality. The second is
the new notion of $\mathcal{D}$-solutions introduced in the recent paper [K8],
which arose in connection to vectorial Calculus of Variations in $L^\infty$ and
fully nonlinear elliptic systems. This new approach is a duality-free
alternative to distributions and is based on the probabilistic representation
of limits of difference quotients.


  Modern techniques allow experiments on a single atom or system, with new
phenomena and new challenges for the theoretician. We discuss what quantum
mechanics has to say about a single system. The quantum jump approach as well
as the role of quantum trajectories are outlined and a rather sophisticated
example is given.


  As spiking neural networks receive more attention, we look toward
applications of this computing paradigm in fields other than computer vision
and signal processing. One major field, underexplored in the neuromorphic
setting, is Natural Language Processing (NLP), where most state-of-the-art
solutions still heavily rely on resource-consuming and power-hungry traditional
deep learning architectures. Therefore, it is compelling to design NLP models
for neuromorphic architectures due to their low energy requirements, with the
additional benefit of a more human-brain-like operating model for processing
information. However, one of the biggest issues with bringing NLP to the
neuromorphic setting is in properly encoding text into a spike train so that it
can be seamlessly handled by both current and future SNN architectures. In this
paper, we compare various methods of encoding text as spikes and assess each
method's performance in an associated SNN on a downstream NLP task, namely,
sentiment analysis. Furthermore, we go on to propose a new method of encoding
text as spikes that outperforms a widely-used rate-coding technique, Poisson
rate-coding, by around 13\% on our benchmark NLP tasks. Subsequently, we
demonstrate the energy efficiency of SNNs implemented in hardware for the
sentiment analysis task compared to traditional deep neural networks, observing
an energy efficiency increase of more than 32x during inference and 60x during
training while incurring the expected energy-performance tradeoff.


  Turbulence plays an important role in astrophysical phenomena, including
core-collapse supernovae (CCSN), but current simulations must rely on subgrid
models since direct numerical simulation (DNS) is too expensive. Unfortunately,
existing subgrid models are not sufficiently accurate. Recently, Machine
Learning (ML) has shown an impressive predictive capability for calculating
turbulence closure. We have developed a physics-informed convolutional neural
network (CNN) to preserve the realizability condition of Reynolds stress that
is necessary for accurate turbulent pressure prediction. The applicability of
the ML subgrid model is tested here for magnetohydrodynamic (MHD) turbulence in
both the stationary and dynamic regimes. Our future goal is to utilize this ML
methodology (available on GitHub) in the CCSN framework to investigate the
effects of accurately-modeled turbulence on the explosion of these stars.


  In this paper, we discuss the atomistic structure of two conducting bridge
computer memory materials, including Cu-doped alumina and silver-doped
GeSe$_3$. We show that the Ag is rather uniformly distributed through the
chalcogenide glass, whereas the Cu strongly clusters in the alumina material.
The copper-oxide system conducts via extended state conduction through Cu atoms
once the concentration becomes high enough to form connected Cu channels. What
is more, the addition of Cu leads to extended states throughout the large
alumina (host) optical gap. By contrast, Ag in the selenide host is not
strongly conducting even if one imposes a very narrow nanowire geometry. All of
these results are discussed using novel techniques for computing the conduction
active parts of the network.


  The dynamical structure factor of the S=1/2 bond-alternating spin chain with
a next-nearest-neighbor interaction in magnetic field is investigated using the
continued fraction method based on the Lanczos algorithm. When the plateau
exists on the magnetization curve, the longitudinal dynamical structure factor
shows a large intensity with a periodic dispersion relation, while the
transverse one shows a large intensity with an almost dispersionless mode. The
periodicity and the amplitude of the dispersion relation in the longitudinal
dynamical structure factor are sensitive to the coupling constants. The
dynamical structure factor of the S=1/2 two-leg ladder in magnetic field is
also calculated in the strong interchain-coupling regime.
  The dynamical structure factor shows gapless or gapful behavior depending on
the wave vector along the rung.


  We consider a network of identical piecewise smooth systems that synchronizes
on the manifold given by a periodic orbit of a single agent. We explicitly
characterize the fundamental matrix solution of the network along the
synchronous solution and extend the Master Stability Function tool to the
present case of non-smooth dynamics.


  The recently proposed Minimal Complexity Machine (MCM) finds a hyperplane
classifier by minimizing an exact bound on the Vapnik-Chervonenkis (VC)
dimension. The VC dimension measures the capacity of a learning machine, and a
smaller VC dimension leads to improved generalization. On many benchmark
datasets, the MCM generalizes better than SVMs and uses far fewer support
vectors than the number used by SVMs. In this paper, we describe a neural
network based on a linear dynamical system, that converges to the MCM solution.
The proposed MCM dynamical system is conducive to an analogue circuit
implementation on a chip or simulation using Ordinary Differential Equation
(ODE) solvers. Numerical experiments on benchmark datasets from the UCI
repository show that the proposed approach is scalable and accurate, as we
obtain improved accuracies and fewer number of support vectors (upto 74.3%
reduction) with the MCM dynamical system.


  We discuss the process of opinion formation in a completely homogeneous,
democratic population using a class of probabilistic cellular automata models
with two absorbing states. Each individual can have one of two opinions that
can change according to that of his neighbors. It is dominated by an
overwhelming majority and can disagree against a marginal one. We present the
phase diagram in the mean field approximation and from numerical experiments
for the simplest nontrivial case. For arbitrarily large neighborhoods we
discuss the mean field results for a non-conformist society, where each
individual adheres to the overwhelming majority of its neighbors and choses an
opposite opinion in other cases. Mean field results and preliminary lattice
simulations with long-range connections among individuals show the presence of
coherent temporal oscillations of the population.


  We establish a new sufficient condition under which a monoid is non-finitely
based and apply this condition to show that the 9-element monoid $L_4^1$ is
non-finitely based. The monoid $L_4^1$ was the only unsolved case in the finite
basis problem for Lee monoids $L_\ell^1$, obtained by adjoining an identity
element to the semigroup generated by two idempotents $a$ and $b$ subjected to
the relation $0=abab \cdots$ (length $\ell$). We also prove a syntactic
sufficient condition which is equivalent to the sufficient condition of Lee
under which a semigroup is non-finitely based. This gives a new proof to the
results of Zhang-Luo and Lee that the semigroup $L_\ell$ is non-finitely based
each $\ell \ge 3$.


  We investigated the non-thermal hard X-ray emission in the Ophiuchus cluster
of galaxies. Our aim was to characterise the physical properties of the
non-thermal component and its interaction with the cosmic microwave background.
We performed spatially resolved spectroscopy and imaging using XMM-Newton data
to model the thermal emission. Combining this with INTEGRAL ISGRI data, we
modeled the 0.6-140 keV band total emission in the central 7 arcmin region. The
models that best describe both PN and ISGRI data contain a power-law component
with a photon index in a range 2.2-2.5. This component produces ~10% of the
total flux in the 1-10 keV band. The pressure of the non-thermal electrons is
~1% of that of the thermal electrons. Our results support the scenario whereby
a relativistic electron population, which produces the recently detected radio
mini-halo in Ophiuchus, also produces the hard X-rays via inverse compton
scattering of the CMB photons. The best-fit models imply a differential
momentum spectrum of the relativistic electrons with a slope of 3.4-4.0 and a
magnetic field strength B=0.05-0.15 microG. The lack of evidence for a recent
major merger in the Ophiuchus center allows the possibility that the
relativistic electrons are produced by turbulence or hadronic collisions.


  We present a data-driven nonintrusive model order reduction method for
dynamical systems with moving boundaries. The proposed method draws on the
proper orthogonal decomposition, Gaussian process regression, and moving least
squares interpolation. It combines several attributes that are not
simultaneously satisfied in the existing model order reduction methods for
dynamical systems with moving boundaries. Specifically, the method requires
only snapshot data of state variables at discrete time instances and the
parameters that characterize the boundaries, but not further knowledge of the
full-order model and the underlying governing equations. The dynamical systems
can be generally nonlinear. The movements of boundaries are not limited to
prescribed or periodic motions but can be free motions. In addition, we
numerically investigate the ability of the reduced order model constructed by
the proposed method to forecast the full-order solutions for future times
beyond the range of snapshot data. The error analysis for the proposed reduced
order modeling and the criteria to determine the furthest forecast time are
also provided. Through numerical experiments, we assess the accuracy and
efficiency of the proposed method in several benchmark problems. The snapshot
data used to construct and validate the reduced order model are from
analytical/numerical solutions and experimental measurements.


  The concept of Nature-Based Solutions (NBS) has emerged to foster sustainable
development by transversally addressing social, economic, and environmental
urban challenges. However, there is still a considerable lack of agreement on
the conceptualization of NBS, especially concerning typologies, nomenclature,
and performance assessments in terms of ecosystem services (ES) and urban
challenges (UC). Therefore, this article consolidates the knowledge from 4
European projects to set a path for a common understanding of NBS and thus,
facilitate their mainstreaming.


  We study the entropy of chiral 2+1-dimensional topological phases, where
there are both gapped bulk excitations and gapless edge modes. We show how the
entanglement entropy of both types of excitations can be encoded in a single
partition function. This partition function is holographic because it can be
expressed entirely in terms of the conformal field theory describing the edge
modes. We give a general expression for the holographic partition function, and
discuss several examples in depth, including abelian and non-abelian fractional
quantum Hall states, and p+ip superconductors. We extend these results to
include a point contact allowing tunneling between two points on the edge,
which causes thermodynamic entropy associated with the point contact to be lost
with decreasing temperature. Such a perturbation effectively breaks the system
in two, and we can identify the thermodynamic entropy loss with the loss of the
edge entanglement entropy. From these results, we obtain a simple
interpretation of the non-integer `ground state degeneracy' which is obtained
in 1+1-dimensional quantum impurity problems: its logarithm is a
2+1-dimensional topological entanglement entropy.


  With the evolution of quantum computing, researchers now-a-days tend to
incline to find solutions to NP-complete problems by using quantum algorithms
in order to gain asymptotic advantage. In this paper, we solve $k$-coloring
problem (NP-complete problem) using Grover's algorithm in any dimensional
quantum system or any $d$-ary quantum system for the first time to the best of
our knowledge, where $d \ge 2$. A newly proposed comparator-based approach
helps to generalize the implementation of the $k$-coloring problem in any
dimensional quantum system. Till date, $k$-coloring problem has been
implemented only in binary and ternary quantum system, hence, we abide to $d=2$
or $d=3$, that is for binary and ternary quantum system for comparing our
proposed work with the state-of-the-art techniques. This proposed approach
makes the reduction of the qubit cost possible, compared to the
state-of-the-art binary quantum systems. Further, with the help of newly
proposed ternary comparator, a substantial reduction in quantum gate count for
the ternary oracle circuit of the $k$-coloring problem than the previous
approaches has been obtained. An end-to-end automated framework has been put
forward for implementing the $k$-coloring problem for any undirected and
unweighted graph on any available Near-term quantum devices or Noisy
Intermediate-Scale Quantum (NISQ) devices or multi-valued quantum simulator,
which helps in generalizing our approach.


  We find that thin peptide films and coatings doped with metallic
nanoparticles are more stable due to the role of electromagnetic fluctuations.
It is shown that for the doped freestanding in vacuum peptide film the Casimir
attraction becomes larger in magnitude. For dielectric substrates coated with
peptide films, the nanoparticle doping leads to a wider range of film
thicknesses where the Casimir pressure is attractive and to larger pressure
magnitudes at the points of extremum. The doping of peptide coatings with
magnetic nanoparticles preserves all the advantages of nonmagnetic ones and
simultaneously imparts superparamagnetic properties to the coating which could
extend significantly the application areas of bioelectronics.


  This paper presents Whisper, a fast and reliable protocol to flood small
amounts of data into a multi-hop network. Whisper makes use of synchronous
transmissions, a technique first introduced by the Glossy flooding protocol. In
contrast to Glossy, Whisper does not let the radio switch from receive to
transmit mode between messages. Instead, it makes nodes continuously transmit
identical copies of the message and eliminates the gaps between subsequent
transmissions. To this end, Whisper embeds the message to be flooded into a
signaling packet that is composed of multiple packlets -- where a packlet is a
portion of the message payload that mimics the structure of an actual packet. A
node must intercept only one of the packlets to detect that there is an ongoing
transmission and that it should start forwarding the message. This allows
Whisper to speed up the propagation of the flood, and thus, to reduce the
overall radio-on time of the nodes. Our evaluation on the FlockLab testbed
shows that Whisper achieves comparable reliability but 2x lower radio-on time
than Glossy. We further show that by embedding Whisper in an existing data
collection application, we can more than double the lifetime of the network.


  We propose a multigrid extension of convolutional neural networks (CNNs).
Rather than manipulating representations living on a single spatial grid, our
network layers operate across scale space, on a pyramid of grids. They consume
multigrid inputs and produce multigrid outputs; convolutional filters
themselves have both within-scale and cross-scale extent. This aspect is
distinct from simple multiscale designs, which only process the input at
different scales. Viewed in terms of information flow, a multigrid network
passes messages across a spatial pyramid. As a consequence, receptive field
size grows exponentially with depth, facilitating rapid integration of context.
Most critically, multigrid structure enables networks to learn internal
attention and dynamic routing mechanisms, and use them to accomplish tasks on
which modern CNNs fail.
  Experiments demonstrate wide-ranging performance advantages of multigrid. On
CIFAR and ImageNet classification tasks, flipping from a single grid to
multigrid within the standard CNN paradigm improves accuracy, while being
compute and parameter efficient. Multigrid is independent of other
architectural choices; we show synergy in combination with residual
connections. Multigrid yields dramatic improvement on a synthetic semantic
segmentation dataset. Most strikingly, relatively shallow multigrid networks
can learn to directly perform spatial transformation tasks, where, in contrast,
current CNNs fail. Together, our results suggest that continuous evolution of
features on a multigrid pyramid is a more powerful alternative to existing CNN
designs on a flat grid.


  We discuss the high-temperature superconductivity in copper oxide ceramics.
We propose an effective Hamiltonian to describe the dynamics of electrons or
holes injected into the copper oxide layers. We show that our approach is able
to account for both the pseudogap and the superconductivity gap. For the
hole-doped cuprates we discuss in details the underdoped, optimal doped, and
overdoped regions of the phase diagram. In the underdoped region we determine
the doping dependence of the upper critical magnetic field, the vortex region,
and the discrete states bounded to the core of isolated vortices. We explain
the origin of the Fermi arcs and Fermi pockets. Moreover, we discuss the
recently reported peculiar dependence of the specific heat on the applied
magnetic field. We determine the critical doping where the pseudogap vanishes.
We find that in the overdoped region the superconducting transition is
described by the conventional d-wave BCS theory. We discuss the optimal doping
region and the crossover between the underdoped region and the overdoped
region. We also discuss briefly the electron-doped cuprate superconductors.


  Physics-informed neural networks (PINNs) have emerged as promising surrogate
modes for solving partial differential equations (PDEs). Their effectiveness
lies in the ability to capture solution-related features through neural
networks. However, original PINNs often suffer from bottlenecks, such as low
accuracy and non-convergence, limiting their applicability in complex physical
contexts. To alleviate these issues, we proposed auxiliary-task learning-based
physics-informed neural networks (ATL-PINNs), which provide four different
auxiliary-task learning modes and investigate their performance compared with
original PINNs. We also employ the gradient cosine similarity algorithm to
integrate auxiliary problem loss with the primary problem loss in ATL-PINNs,
which aims to enhance the effectiveness of the auxiliary-task learning modes.
To the best of our knowledge, this is the first study to introduce
auxiliary-task learning modes in the context of physics-informed learning. We
conduct experiments on three PDE problems across different fields and
scenarios. Our findings demonstrate that the proposed auxiliary-task learning
modes can significantly improve solution accuracy, achieving a maximum
performance boost of 96.62% (averaging 28.23%) compared to the original
single-task PINNs. The code and dataset are open source at
https://github.com/junjun-yan/ATL-PINN.


  The search for the production of three massive vector bosons in
proton$-$proton collisions, performed using data at $\sqrt{s}$ = 13 TeV
recorded with the ATLAS detector at the Large Hadron Collider in the years
2015$-$2017, corresponding to an integrated luminosity of $79.8$ fb$^{-1}$, is
presented. Events with two same-sign leptons $\ell$ (electrons or muons) and at
least two reconstructed jets are selected to search for $WWW \to \ell \nu \ell
\nu qq$. Events with three leptons without any same-flavour opposite-sign
lepton pairs are used to search for $WWW \to \ell \nu \ell\nu \ell \nu$, while
events with three leptons and at least one same-flavour opposite-sign lepton
pair and one or more reconstructed jets are used to search for $WWZ \to \ell
\nu qq \ell \ell$. Finally, events with four leptons are analysed to search for
$WWZ \to \ell \nu \ell \nu \ell \ell$ and $WZZ \to qq \ell \ell \ell \ell$.
Evidence for the joint production of three massive vector bosons is observed
with a significance of 4.1 standard deviations, where the expectation is 3.1
standard deviations.


  Code-switching occurs when more than one language is mixed in a given
sentence or a conversation. This phenomenon is more prominent on social media
platforms and its adoption is increasing over time. Therefore code-mixed NLP
has been extensively studied in the literature. As pre-trained
transformer-based architectures are gaining popularity, we observe that real
code-mixing data are scarce to pre-train large language models. We present
L3Cube-HingCorpus, the first large-scale real Hindi-English code mixed data in
a Roman script. It consists of 52.93M sentences and 1.04B tokens, scraped from
Twitter. We further present HingBERT, HingMBERT, HingRoBERTa, and HingGPT. The
BERT models have been pre-trained on codemixed HingCorpus using masked language
modelling objectives. We show the effectiveness of these BERT models on the
subsequent downstream tasks like code-mixed sentiment analysis, POS tagging,
NER, and LID from the GLUECoS benchmark. The HingGPT is a GPT2 based generative
transformer model capable of generating full tweets. We also release
L3Cube-HingLID Corpus, the largest code-mixed Hindi-English language
identification(LID) dataset and HingBERT-LID, a production-quality LID model to
facilitate capturing of more code-mixed data using the process outlined in this
work. The dataset and models are available at
https://github.com/l3cube-pune/code-mixed-nlp .


  We investigate the possibility of detecting dark matter at TeV scale linear
colliders in the scenario where the dark matter interacts with standard model
particles only via the Higgs boson. In this scenario, the dark matter would be
difficult to be tested at the LHC especially when the decay of the Higgs boson
into a dark matter pair is not kinematically allowed. In this talk, we discuss
whether even such a case can be explored or not at the ILC and CLIC via the Z
boson fusion process. This talk is mainly based on Phys. Rev. D 82, 055026
(2010) and Phys. Lett. B 701, 591 (2011).


  This paper improves a previously established test involving only coefficients
to decide a priori whether or not non-trivial symmetries of a large class of
space-time dependent diffusion processes on the real line exist. When the
existence of these symmetries are ensured, the transformation to canonical
forms admitting either four- or six-dimensional symmetry groups and the full
list of their infinitesimal generators are then immediately at our disposal
without any cumbersome calculations that happen when at least one of the
coefficients is arbitrarily chosen. We study in depth symmetry and reducibility
properties and physically important solutions of six models arising in
applications.


  Federated learning (FL) is a distributed machine learning technique that
enables collaborative model training while avoiding explicit data sharing. The
inherent privacy-preserving property of FL algorithms makes them especially
attractive to the medical field. However, in case of heterogeneous client data
distributions, standard FL methods are unstable and require intensive
hyperparameter tuning to achieve optimal performance. Conventional
hyperparameter optimization algorithms are impractical in real-world FL
applications as they involve numerous training trials, which are often not
affordable with limited compute budgets. In this work, we propose an efficient
reinforcement learning (RL)-based federated hyperparameter optimization
algorithm, termed Auto-FedRL, in which an online RL agent can dynamically
adjust hyperparameters of each client based on the current training progress.
Extensive experiments are conducted to investigate different search strategies
and RL agents. The effectiveness of the proposed method is validated on a
heterogeneous data split of the CIFAR-10 dataset as well as two real-world
medical image segmentation datasets for COVID-19 lesion segmentation in chest
CT and pancreas segmentation in abdominal CT.


  We consider Z-actions (single automorphisms) on a unital simple AH algebra
with real rank zero and slow dimension growth and show that the uniform
outerness implies the Rohlin property under some technical assumptions.
Moreover, two Z-actions with the Rohlin property on such a C^*-algebra are
shown to be cocycle conjugate if they are asymptotically unitarily equivalent.
We also prove that locally approximately inner and uniformly outer Z^2-actions
on a unital simple AF algebra with a unique trace have the Rohlin property and
classify them up to cocycle conjugacy employing the OrderExt group as
classification invariants.


  We construct halo occupation distribution (HOD) models of high redshift ($z
\gtrsim 7.5$) galaxies with $M_{*}>10^8~M_{\odot}/h$ using the BlueTides
hydrodynamic simulation suite, with a particular emphasis on modelling the
small scale / 1-halo clustering ($0.01\lesssim r \lesssim 1~ h^{-1}\rm{Mpc}$).
Similar to low redshift studies, we find that the central and satellite mean
HODs ($\left<N_{\mathrm{cen}}\right>$ and $\left<N_{\mathrm{sat}}\right>$) can
be modeled by a smoothed step function and a power law respectively. The number
density of satellite galaxies is however significantly suppressed compared to
low redshift (satellite fractions drop from $\sim 50 \%$ at $z=0$ to $\lesssim
10 \%$ at $z=7.5$). The mean number of satellites,
$\left<N_{\mathrm{sat}}\right> < 1$ for halo masses below $3 \times 10^{11}
M_{\odot}/h$ (a rare halo at these redshifts). For the radial number density
profiles, satellites with $10^8 \lesssim M^* \lesssim 10^{9} M_{\odot}/h$ in
halos with $M_H \gtrsim 3 \times10^{11} M_{\odot}/h$ are consistent with NFW
(with concentrations $c_{\mathrm{sat}} \sim 10-40$). Within halos of mass
$M_H\lesssim 3 \times 10^{11} M_{\odot}/h$ satellites exhibit a power law
profile with slope -3. Because these halos dominate the small scale clustering,
the resulting 1-halo term is steeper than predicted using standard NFW
profiles. Using this power-law profile for satellites, we can successfully
reproduce the small-scale clustering exhibited by BlueTides galaxies using HOD
modelling. We predict the highest probability of detecting satellites at
$z>7.5$ is around centrals of $M^*\sim 3 \times 10^{10} M_{\odot}/h$ (with
$M^{*}\gtrsim$ a few $10^{7} M_{\odot}/h$ ). This should be achievable with the
James Webb Space Telescope (JWST).


  Meet-distributive lattices form an intriguing class of lattices, because they
are precisely the lattices obtainable from a closure operator with the
so-called anti-exchange property. Moreover, meet-distributive lattices are join
semidistributive. Therefore, they admit two natural, secondary structures: the
core label order is an alternative order on the lattice elements and the
canonical join complex is the flag-simplicial complex on canonical join
representations. In this article we present a characterization of finite
meet-distributive lattices in terms of the core label order and the canonical
join complex, and we show that the core label order of a finite
meet-distributive lattice is always a meet-semilattice.


  We go beyond the Standard Model guided by presymmetry, the discrete
electroweak quark-lepton symmetry hidden by topological effects which explain
quark fractional charges as in condense matter physics. Partners of the
particles of the Standard Model and the discrete symmetry associated with this
partnership appear as manifestations of a residual presymmetry and its
extension from matter to forces. This duplication of the spectrum of the
Standard Model keeps spin and comes nondegenerated about the TeV scale.


  In this article we study the asymptotic behavior of solutions, in sense of
global pullback attractors, of the evolution system $$ \begin{cases} u_{tt}
+\eta\Delta^2 u+a(t)\Delta\theta=f(t,u), & t>\tau,\ x\in\Omega,\\
\theta_t-\kappa\Delta \theta-a(t)\Delta u_t=0, & t>\tau,\ x\in\Omega,
\end{cases} $$ subject to boundary conditions $$ u=\Delta u=\theta=0,\ t>\tau,\
x\in\partial\Omega, $$ where $\Omega$ is a bounded domain in $\mathbb{R}^N$
with $N\geqslant 2$, which boundary $\partial\Omega$ is assumed to be a
$\mathcal{C}^4$-hypersurface, $\eta>0$ and $\kappa>0$ are constants, $a$ is an
H\"older continuous function, $f$ is a dissipative nonlinearity locally
Lipschitz in the second variable.


  The broadcast nature of the wireless medium allows unintended users to
eavesdrop the confidential information transmission. In this regard, we
investigate the problem of secure communication between a source and a
destination via a wireless energy harvesting untrusted node which acts as a
helper to relay the information; however, the source and destination nodes wish
to keep the information confidential from the relay node. To realize the
positive secrecy rate, we use destination-assisted jamming. Being an
energy-starved node, the untrusted relay harvests energy from the received
radio frequency signals, which include the source's information signal and the
destination's jamming signal. Thus, we utilize the jamming signal efficiently
by leveraging it as a useful energy source. At the relay, to enable energy
harvesting and information processing, we adopt power splitting (PS) and time
switching (TS) policies. To evaluate the secrecy performance of this proposed
scenario, we derive analytical expressions for two important metrics, viz., the
secrecy outage probability and the ergodic secrecy rate. The numerical analysis
reveals the design insights into the effects of different system parameters
like power splitting ratio, energy harvesting time, target secrecy rate,
transmit signal-to-noise ratio (SNR), relay location, and energy conversion
efficiency factor, on the secrecy performance. Specifically, the PS policy
achieves better optimal secrecy outage probability and optimal ergodic secrecy
rate than that of the TS policy at higher target secrecy rate and transmit SNR,
respectively.


  Min-cut clustering, based on minimizing one of two heuristic cost-functions
proposed by Shi and Malik, has spawned tremendous research, both analytic and
algorithmic, in the graph partitioning and image segmentation communities over
the last decade. It is however unclear if these heuristics can be derived from
a more general principle facilitating generalization to new problem settings.
Motivated by an existing graph partitioning framework, we derive relationships
between optimizing relevance information, as defined in the Information
Bottleneck method, and the regularized cut in a K-partitioned graph. For fast
mixing graphs, we show that the cost functions introduced by Shi and Malik can
be well approximated as the rate of loss of predictive information about the
location of random walkers on the graph. For graphs generated from a stochastic
algorithm designed to model community structure, the optimal information
theoretic partition and the optimal min-cut partition are shown to be the same
with high probability.


  This work proposes a model-reduction methodology that preserves Lagrangian
structure (equivalently Hamiltonian structure) and achieves computational
efficiency in the presence of high-order nonlinearities and arbitrary parameter
dependence. As such, the resulting reduced-order model retains key properties
such as energy conservation and symplectic time-evolution maps. We focus on
parameterized simple mechanical systems subjected to Rayleigh damping and
external forces, and consider an application to nonlinear structural dynamics.
To preserve structure, the method first approximates the system's `Lagrangian
ingredients'---the Riemannian metric, the potential-energy function, the
dissipation function, and the external force---and subsequently derives
reduced-order equations of motion by applying the (forced) Euler--Lagrange
equation with these quantities. From the algebraic perspective, key
contributions include two efficient techniques for approximating parameterized
reduced matrices while preserving symmetry and positive definiteness: matrix
gappy POD and reduced-basis sparsification (RBS). Results for a parameterized
truss-structure problem demonstrate the importance of preserving Lagrangian
structure and illustrate the proposed method's merits: it reduces computation
time while maintaining high accuracy and stability, in contrast to existing
nonlinear model-reduction techniques that do not preserve structure.


  The nanoscale distribution of magnetic anisotropies was measured in
core@shell MnFe$_2$O$_4$@CoFe$_2$O$_4$ 7.0 nm particles using a combination of
element selective magnetic spectroscopies with different probing depths. As
this picture is not accessible by any other technique, emergent magnetic
properties were revealed. The coercive field is not constant in a whole
nanospinel. The very thin (0.5 nm) CoFe$_2$O$_4$ hard shell imposes a strong
magnetic anisotropy to the otherwise very soft MnFe$_2$O$_4$ core: a large
gradient in coercivity was measured inside the MnFe$_2$O$_4$ core with lower
values close to the interface region, while the inner core presents a
substantial coercive field (0.54 T) and a very high remnant magnetization (90%
of the magnetization at saturation).


  We study closed photon orbits in spherically-symmetric static solutions of
supergravity theories, a Horndeski theory, and a theory of quintessence. These
orbits lie in what we shall call a photon sphere (anti-photon sphere) if the
orbit is unstable (stable). We show that in all the asymptotically flat
solutions we examine that admit a regular event horizon, and whose
energy-momentum tensor satisfies the strong energy condition, there is one and
only one photon sphere outside the event horizon. We give an example of a
Horndeski theory black hole (whose energy-momentum tensor violates the strong
energy condition) whose metric admits both a photon sphere and an anti-photon
sphere. The uniqueness and non-existence also holds for asymptotically anti-de
Sitter solutions in gauged supergravity. The latter also exhibit the projective
symmetry that was first discovered for the Schwarzschild-de Sitter metrics: the
unparameterised null geodesics are the same as when the cosmological or gauge
coupling constant vanishes. We also study the closely related problem of
accretion flows by perfect fluids in these metrics. For a radiation fluid,
Bondi's sonic horizon coincides with the photon sphere. For a general
polytropic equation of state this is not the case. Finally we exhibit
counterexamples to a conjecture of Hod's.


  We study the transport through side-coupled double quantum dots, connected to
normal and superconducting (SC) leads with a T-shape configuration. We find,
using the numerical renormalization group, that the Coulomb interaction
suppresses SC interference in the side dot, and enhances the conductance
substantially in the Kondo regime. This behavior stands in total contrast to a
wide Kondo valley seen in the normal transport. The SC proximity penetrating
into the interfacial dot pushes the Kondo clouds, which screens the local
moment in the side dot, towards the normal lead to make the singlet bond long.
The conductance shows a peak of unitary limit as the cloud expands.
Furthermore, two separate Fano structures appear in the gate-voltage dependence
of the Andreev transport, where a single reduced plateau appears in the normal
transport.


  Scene text is an important feature to be extracted, especially in
vision-based mobile robot navigation as many potential landmarks such as
nameplates and information signs contain text. In this paper, a novel two-step
text localization method for Indoor Mobile Robot Navigation is introduced. This
method is based on morphological operators and machine learning techniques and
can be used in real time environments. The proposed method has two steps. At
First, a new set of morphological operators is applied with a particular
sequence to extract high contrast areas that have high probability of text
existence. Using of morphological operators has many advantages such as: high
computation speed, being invariant to several geometrical transformations like
translation, rotations, and scaling, and being able to extract all areas
containing text. After extracting text candidate regions, a set of nine
features are extracted for accurate detection and deletion of the regions that
don't have text. These features are descriptors for texture properties and are
computed in real time. Then, we use a SVM classifier to detect the existence of
text in the region. Performance of the proposed algorithm is compared against a
number of widely used text localization algorithms and the results show that
this method can quickly and effectively localize and extract text regions from
real scenes and can be used in mobile robot navigation under an indoor
environment to detect text based landmarks.


  Superconductivity of YBa$_2$Cu$_3$O$_{7-\delta}$ single crystals was
investigated in small magnetic fields. In magnetic measurements the
superconducting transition for $\textbf{H} \| c$ appears 0.4 K higher than for
$\textbf{H} \bot c$. In this temperature range superconductivity is
two-dimensional and the total thickness of superconducting layers is about 0.83
of the sample thickness, which is a consequence of the occurrence of the
quasi-insulating plane in the unit cell of the crystal structure. Resistivity
in the \textit{ab}-plane and along the \textit{c}-axis was measured
simultaneously. In these measurements two-dimensional superconductivity was
observed in a temperature range of 0.6-0.8 K with the clear signs of the
Berezinskii-Kosterlitz-Touless (BKT) transition which occurs approximately 0.15
K below $T_c$, the mean-field transition temperature.


  One model of real-life spreading processes is First Passage Percolation (also
called SI model) on random graphs. Social interactions often follow bursty
patterns, which are usually modelled with i.i.d.~heavy-tailed passage times on
edges. On the other hand, random graphs are often locally tree-like, and
spreading on trees with leaves might be very slow, because of bottleneck edges
with huge passage times. Here we consider the SI model with passage times
following a power law distribution $\mathbb{P}(\xi>t)\sim t^{-\alpha}$, with
infinite mean. For any finite connected graph $G$ with a root $s$, we find the
largest number of vertices $\kappa(G,s)$ that are infected in finite expected
time, and prove that for every $k \leq \kappa(G,s)$, the expected time to
infect $k$ vertices is at most $O(k^{1/\alpha})$. Then, we show that adding a
single edge from $s$ to a random vertex in a random tree $\mathcal{T}$
typically increases $\kappa(\mathcal{T},s)$ from a bounded variable to a
fraction of the size of $\mathcal{T}$, thus severely accelerating the process.
We examine this acceleration effect on some natural models of random graphs:
critical Galton-Watson trees conditioned to be large, uniform spanning trees of
the complete graph, and on the largest cluster of near-critical
Erd\H{o}s-R\'enyi graphs. In particular, at the upper end of the critical
window, the process is already much faster than exactly at criticality.


  Restrictions imposed by gauge invariance in noncommutative spaces together
with the effects of ultraviolet/infrared mixing lead to strong constraints on
possible candidates for a noncommutative extension of the Standard Model. We
study a general class of noncommutative models consistent with these
restrictions. Specifically we consider models based upon a gauge theory with
the gauge group U(N_1)\times U(N_2)\times ...\times U(N_m) coupled to matter
fields transforming in the (anti)-fundamental, bi-fundamental and adjoint
representations. We pay particular attention to overall trace-U(1) factors of
the gauge group which are affected by the ultraviolet/infrared mixing.
Typically, these trace-U(1) gauge fields do not decouple sufficiently fast in
the infrared, and lead to sizable Lorentz symmetry violating effects in the
low-energy effective theory. In a 4-dimensional theory on a continuous
space-time making these effects unobservable would require making the effects
of noncommutativity tiny, M_NC>>M_P. This severely limits the phenomenological
prospects of such models. However, adding additional universal extra dimensions
the trace-U(1) factors decouple with a power law and the constraint on the
noncommutativity scale is weakened considerably. Finally, we briefly mention
some interesting properties of the photon that could arise if the
noncommutative theory is modified at a high energy scale.


  This article presents a novel application of the t-distributed Stochastic
Neighbor Embedding (t-SNE) clustering algorithm to the telecommunication field.
t-SNE is a dimensionality reduction (DR) algorithm that allows the
visualization of large dataset into a 2D plot. We present the applicability of
this algorithm in a communication channel dataset formed by several scenarios
(anechoic, reverberation, indoor and outdoor), and by using six channel
features. Applying this artificial intelligence (AI) technique, we are able to
separate different environments into several clusters allowing a clear
visualization of the scenarios. Throughout the article, it is proved that t-SNE
has the ability to cluster into several subclasses, obtaining internal
classifications within the scenarios themselves. t-SNE comparison with
different dimensionality reduction techniques (PCA, Isomap) is also provided
throughout the paper. Furthermore, post-processing techniques are used to
modify communication scenarios, recreating a real communication scenario from
measurements acquired in an anechoic chamber. The dimensionality reduction and
classification by using t-SNE and Variational AutoEncoders (VAE) show good
performance distinguishing between the recreation and the real communication
scenario. The combination of these two techniques opens up the possibility for
new scenario recreations for future mobile communications. This work shows the
potential of AI as a powerful tool for clustering, classification and
generation of new 5G propagation scenarios.


  We analyze the renormalization-group (RG) flows of two effective Lagrangians,
one for measurement induced transitions of monitored quantum systems and one
for entanglement transitions in random tensor networks. These Lagrangians,
previously proposed on grounds of replica symmetry, are derived in a controlled
regime for an illustrative family of tensor networks. They have different forms
in the two cases, and involve distinct replica limits. The perturbative RG is
controlled by working close to a critical dimensionality, ${d_c=6}$ for
measurements and ${d_c=10}$ for random tensors, where interactions become
marginal. The resulting RG flows are surprising in several ways. They indicate
that in high dimensions $d>d_c$ there are at least two (stable) universality
classes for each kind of transition, separated by a nontrivial tricritical
point. In each case one of the two stable fixed points is Gaussian, while the
other is nonperturbative. In lower dimensions, $d<d_c$, the flow always runs to
the nonperturbative regime. This picture clarifies the "mean-field theory" of
these problems, including the phase diagram of all-to-all quantum circuits. It
suggests a way of reconciling exact results on tree tensor networks with field
theory. Most surprisingly, the perturbation theory for the random tensor
network (which also applies to a version of the measurement transition with
"forced" measurements) formally possesses a dimensional reduction property
analogous to that of the random-field Ising model. When only the leading
interactions are retained, perturbative calculations in $d$ dimensions reduce
to those in a simple scalar field theory in ${d-4}$ dimensions. We show that
this holds to all orders by writing the action in a superspace formulation.


  We introduce the notion of a ``projective hull'' for subsets of complex
projective varieties, parallel to the idea of the polynomial hull in affine
varieties. With this concept, a generalization of J. Wermer's classical theorem
on the hull of a curve in $C^n$ is established in the projective setting. The
projective hull is shown to have interesting properties and is related to
various extremal functions and capacities in pluripotential theory. A main
analytic result asserts that for any point x in the projective hull K^ of a
compact set K in $P^n$, there exists a positive current T of bidimension (1,1)
with support in the closure of K^, and a probability measure $\mu$ on K with $d
d^cT=\mu- [x]$. This result generalizes to any Kahler manifold and has strong
consequences for the structure of K^. We also introduce the notion of a
projective spectrum for Banach graded algebras, parallel to the Gelfand
spectrum of a Banach algebra. This projective spectrum has universal properties
exactly like those in the Gelfand case. Moreover, the projective hull is shown
to play a role (for graded algebras) completely analogous to that played by the
polynomial hull in the study of finitely generated Banach algebras. This paper
gives foundations for generalizing many of the results on boundaries of
varieties in $C^n$ to general algebraic manifolds.


  Although deep-learning-based methods have markedly improved the performance
of speech separation over the past few years, it remains an open question how
to integrate multi-channel signals for speech separation. We propose two
methods, namely, early-fusion and late-fusion methods, to integrate
multi-channel information based on the time-domain audio separation network,
which has been proven effective in single-channel speech separation. We also
propose channel-sequential-transfer learning, which is a transfer learning
framework that applies the parameters trained for a lower-channel network as
the initial values of a higher-channel network. For fair comparison, we
evaluated our proposed methods using a spatialized version of the wsj0-2mix
dataset, which is open-sourced. It was found that our proposed methods can
outperform multi-channel deep clustering and improve the performance
proportionally to the number of microphones. It was also proven that the
performance of the late-fusion method is consistently higher than that of the
single-channel method regardless of the angle difference between speakers.


  We analyse three years of nearly-continuous Kepler spacecraft short cadence
observations of the pulsating subdwarf B star KIC 3527751. We detect a total of
251 periodicities, most in the g-mode domain, but some where p-modes occur,
confirming that KIC 3527751 is a hybrid pulsator. We apply seismic tools to the
periodicities to characterize the properties of KIC 3527751. Techniques to
identify modes include asymptotic period spacing relationships, frequency
multiplets, and the separation of multiplet splittings. These techniques allow
for 189 (75%) of the 251 periods to be associated with pulsation modes.
Included in these are three sets of ell=4 multiplets and possibly an ell=9
multiplet. Period spacing sequences indicate ell=1 and 2 overtone spacings of
266.4 +/-0.2 and 153.2 +/-0.2 seconds, respectively. We also calculate reduced
periods, from which we find evidence of trapped pulsations. Such mode trappings
can be used to constrain the core/atmosphere transition layers. Interestingly,
frequency multiplets in the g-mode region, which sample deep into the star,
indicate a rotation period of 42.6 +/-3.4 days while p-mode multiplets, which
sample the outer envelope, indicate a rotation period of 15.3 +/-0.7 days. We
interpret this as differential rotation in the radial direction with the core
rotating more slowly. This is the first example of differential rotation for a
subdwarf B star.


  In a recent paper, Phys. Rev. Lett. 87, 167010/1-4 (2001), Moukouri and
Jarrell presented evidence that in the two-dimensional (d=2) Hubbard model at
half-filling there is a metal-insulator transition (MIT) at finite temperature
even in weak coupling. While we agree with the numerical results of that paper,
we arrive at different conclusions: The apparent gap at finite-temperature can
be understood, at weak-coupling, as a crossover phenomenon involving large (but
not infinite) antiferromagnetic (AFM) correlation length. Phase-space effects
on the self-energy in d=2 are crucial, as are the ratio between AFM correlation
length and single-particle thermal de Broglie wavelength. In weak coupling,
d=2, there is in general no finite-temperature MIT transition in the
thermodynamic sense.


  Two tunnel-coupled few-electron quantum dots were fabricated in a GaAs/AlGaAs
quantum well. The absolute number of electrons in each dot could be determined
from finite bias Coulomb blockade measurements and gate voltage scans of the
dots, and allows the number of electrons to be controlled down to zero. The
Zeeman energy of several electronic states in one of the dots was measured with
an in-plane magnetic field, and the g-factor of the states was found to be no
different than that of electrons in bulk GaAs. Tunnel-coupling between dots is
demonstrated, and the tunneling strength was estimated from the peak splitting
of the Coulomb blockade peaks of the double dot.


  We present a kinetic stability analysis of the solar wind electron
distribution function consisting of the Maxwellian core and the magnetic-field
aligned strahl, a superthermal electron beam propagating away from the sun. We
use an electron strahl distribution function obtained as a solution of a weakly
collisional drift-kinetic equation, representative of a strahl affected by
Coulomb collisions but unadulterated by possible broadening from turbulence.
This distribution function is essentially non-Maxwellian and varies with the
heliospheric distance. The stability analysis is performed with the
Vlasov-Maxwell linear solver LEOPARD. We find that depending on the
heliospheric distance, the core-strahl electron distribution becomes unstable
with respect to sunward-propagating kinetic-Alfv\'en, magnetosonic, and
whistler modes, in a broad range of propagation angles. The wavenumbers of the
unstable modes are close to the ion inertial scales, and the radial distances
at which the instabilities first appear are on the order of 1 AU. However, we
have not detected any instabilities driven by resonant wave interactions with
the superthermal strahl electrons. Instead, the observed instabilities are
triggered by a relative drift between the electron and ion cores necessary to
maintain zero electric current in the solar wind frame (ion frame). Contrary to
strahl distributions modeled by shifted Maxwellians, the electron strahl
obtained as a solution of the kinetic equation is stable. Our results are
consistent with the previous studies based on a more restricted solution for
the electron strahl.


  We report high-resolution inelastic x-ray scattering measurements of the
acoustic phonons in the single-layer cuprate
$Bi_{2}Sr_{2-x)La_{x}CuO_{6+\delta}$. These measurements reveal anomalous
broadening of the longitudinal acoustic phonon near the (1/4,1/4,0) wavevector.
The observed wavevector and its doping dependence indicate the coupling of the
phonons to an underlying electronic density wave state. In addition, a
comparison of the scattered intensities for x-ray energy-gain and x-ray
energy-loss indicates that both time-reversal and inversion symmetries are
broken in the material. Upon cooling, the effects of symmetry breaking are
enhanced in the pseudogap state.


  We investigate morphological properties of 61 Lyman-alpha emitters (LAEs) at
z = 4.86 identified in the COSMOS field, based on Hubble Space Telescope
Advanced Camera for Surveys (ACS) imaging data in the F814W-band. Out of the 61
LAEs, we find the ACS counterparts for the 54 LAEs. Eight LAEs show
double-component structures with a mean projected separation of 0."63 (~ 4.0
kpc at z = 4.86). Considering the faintness of these ACS sources, we carefully
evaluate their morphological properties, that is, size and ellipticity. While
some of them are compact and indistinguishable from the PSF half-light radius
of 0."07 (~ 0.45 kpc), the others are clearly larger than the PSF size and
spatially extended up to 0."3 (~ 1.9 kpc). We find that the ACS sources show a
positive correlation between ellipticity and size and that the ACS sources with
large size and round shape are absent. Our Monte Carlo simulation suggests that
the correlation can be explained by (1) the deformation effects via PSF
broadening and shot noise or (2) the source blending in which two or more
sources with small separation are blended in our ACS image and detected as a
single elongated source. Therefore, the 46 single-component LAEs could contain
the sources which consist of double (or multiple) components with small spatial
separation (i.e., < 0."3 or 1.9 kpc). Further observation with high angular
resolution at longer wavelengths (e.g., rest-frame wavelengths of > 4000 A) is
inevitable to decipher which interpretation is adequate for our LAE sample.


  We prove a unique continuation property for the fractional Laplacian
$(-\Delta)^s$ when $s \in (-n/2,\infty)\setminus \mathbb{Z}$. In addition, we
study Poincar\'e-type inequalities for the operator $(-\Delta)^s$ when $s\geq
0$. We apply the results to show that one can uniquely recover, up to a gauge,
electric and magnetic potentials from the Dirichlet-to-Neumann map associated
to the higher order fractional magnetic Schr\"odinger equation. We also study
the higher order fractional Schr\"odinger equation with singular electric
potential. In both cases, we obtain a Runge approximation property for the
equation. Furthermore, we prove a uniqueness result for a partial data problem
of the $d$-plane Radon transform in low regularity. Our work extends some
recent results in inverse problems for more general operators.


  5G has expanded the traditional focus of wireless systems to embrace two new
connectivity types: ultra-reliable low latency and massive communication. The
technology context at the dawn of 6G is different from the past one for 5G,
primarily due to the growing intelligence at the communicating nodes. This has
driven the set of relevant communication problems beyond reliable transmission
towards semantic and pragmatic communication. This paper puts the evolution of
low-latency and massive communication towards 6G in the perspective of these
new developments. At first, semantic/pragmatic communication problems are
presented by drawing parallels to linguistics. We elaborate upon the relation
of semantic communication to the information-theoretic problems of
source/channel coding, while generalized real-time communication is put in the
context of cyber-physical systems and real-time inference. The evolution of
massive access towards massive closed-loop communication is elaborated upon,
enabling interactive communication, learning, and cooperation among wireless
sensors and actuators.


  We calculate bottom-hadron mass splittings with respect to $B_d$ and
$\Lambda_b$ using full QCD with 2+1 flavors of dynamical Kogut-Susskind sea
quarks and domain-wall valence quarks along with a static heavy quark. Our
lattices have spatial volume of $(2.5{fm})^3$ with lattice spacing about 0.124
fm and a range of pion masses as low as 291 MeV. Our results are in agreement
with experimental observations and other lattice calculations within our
statistical and systematic errors. In particular, we find the mass of the
$\Omega_b$ to be consistent with the recent CDF measurement. We also predict
the mass for the as yet unobserved $\Xi^\prime_b$ to be 5955(27) MeV.


  Visual question answering (VQA) task not only bridges the gap between images
and language, but also requires that specific contents within the image are
understood as indicated by linguistic context of the question, in order to
generate the accurate answers. Thus, it is critical to build an efficient
embedding of images and texts. We implement DualNet, which fully takes
advantage of discriminative power of both image and textual features by
separately performing two operations. Building an ensemble of DualNet further
boosts the performance. Contrary to common belief, our method proved effective
in both real images and abstract scenes, in spite of significantly different
properties of respective domain. Our method was able to outperform previous
state-of-the-art methods in real images category even without explicitly
employing attention mechanism, and also outperformed our own state-of-the-art
method in abstract scenes category, which recently won the first place in VQA
Challenge 2016.


  We give the exact contributions of Harish-Chandra transform,
$(\mathcal{H}f)(\lambda),$ of Schwartz functions $f$ to the harmonic analysis
of spherical convolutions and the corresponding $L^{p}-$ Schwartz algebras on a
connected semisimple Lie group $G$ (with finite center). One of our major
results gives the proof of how the Trombi-Varadarajan Theorem enters into the
spherical convolution transform of $L^{p}-$ Schwartz functions.


  A model is presented that explains the `torsional oscillation' pattern of
deviations in the solar rotation rate as a geostrophic flow. The flow is driven
by temperature variations near the surface due to the enhanced emission of
radiation by the small scale magnetic field. The model explains the sign of the
flow, its amplitude and the fact that the maxima occur near the boundaries of
the main activity belts. The amplitude of the flow decreases with depth from
its maximum at the surface but penetrates over much of the depth of the
convection zone, in agreement with the data from helioseismology. It predicts
that the flow is axisymmetric only on average, and in reality consists of a
superposition of circulations around areas of enhanced magnetic activity. It
must be accompanied by a meridional flow component, which declines more rapidly
with depth.


  We develop a method to compute thermally-mediated transition rates between
the ground state and long-lived isomers in nuclei. We also establish criteria
delimiting a thermalization temperature above which a nucleus may be considered
a single species and below which it must be treated as two separate species: a
ground state species, and an astrophysical isomer ("astromer") species. Below
the thermalization temperature, the destruction rates dominate the internal
transition rates between the ground state and the isomer. If the destruction
rates also differ greatly from one another, the nuclear levels fall out of or
fail to reach thermal equilibrium. Without thermal equilibrium, there may not
be a safe assumption about the distribution of occupation probability among the
nuclear levels when computing nuclear reaction rates. In these conditions, the
isomer has astrophysical consequences and should be treated a separate astromer
species which evolves separately from the ground state in a nucleosynthesis
network. We apply our transition rate methods and perform sensitivity studies
on a few well-known astromers. We also study transitions in several other
isomers of likely astrophysical interest.


  We report on the status of ongoing investigations aiming at locating the
deconfinement critical point with standard Wilson fermions and $N_f=2$ flavors
towards the continuum limit (standard Columbia plot); locating the tricritical
masses at imaginary chemical potential with unimproved staggered fermions at
$N_f=2$ (extended Columbia plot); identifying the order of the chiral phase
transition at $\mu=0$ for $N_f=2$ via extrapolation from non integer $N_f$
(alternative Columbia plot).


  In software engineering processes, systems are first specified using a
modeling language such as UML. These initial designs are often collaboratively
created, many times in meetings where different domain experts use whiteboards,
paper or other types of quick supports to create drawings and blueprints that
then will need to be formalized. These proper, machine-readable, models are key
to ensure models can be part of automated processes (e.g. input of a low-code
generation pipeline, a model-based testing system, ...). But going from
hand-drawn diagrams to actual models is a time-consuming process that sometimes
ends up with such drawings just added as informal images to the software
documentation, reducing their value a lot. To avoid this tedious task, we
explore the usage of Large Language Models (LLM) to generate the formal
representation of (UML) models from a given drawing. More specifically, we have
evaluated the capabilities of different LLMs to convert images of UML class
diagrams into the actual models represented in the images. While the results
are good enough to use such an approach as part of a model-driven engineering
pipeline we also highlight some of their current limitations and the need to
keep the human in the loop to overcome those limitations.


  Certain reductions of the rank 2, genera 2 and 3 Hitchin systems are
considered, which are shown to give an integrable system of 2, resp. 3,
interacting points on the line. It is shown that the reduced systems are
particular cases of a certain universal integrable system related to the
Lagrange interpolation polynomial. Admissibility of the reduction is proved
using computer technique. The corresponding codes are given in the text.


  As a cool star evolves, it loses mass and angular momentum due to magnetized
stellar winds which affect its rotational evolution. This change has
consequences that range from the alteration of its activity to influences over
the atmosphere of any orbiting planet. Despite their importance, observations
constraining the properties of stellar winds in cool stars are extremely
limited. Therefore, numerical simulations provide a valuable way to understand
the structure and properties of these winds. In this work, we simulate the
magnetized winds of 21 cool main-sequence stars (F-type to M-dwarfs), using a
state-of-the-art 3D MHD code driven by observed large-scale magnetic field
distributions. We perform a qualitative and quantitative characterization of
our solutions, analyzing the dependencies between the driving conditions (e.g.,
spectral type, rotation, magnetic field strength) and the resulting stellar
wind parameters (e.g., Alfv\'en surface size, mass loss rate, angular momentum
loss rate, stellar wind speeds). We compare our models with the current
observational knowledge on stellar winds in cool stars and explore the
behaviour of the mass loss rate as a function of the Rossby number.
Furthermore, our 3D models encompass the entire classical Habitable Zones (HZ)
of all the stars in our sample. This allows us to provide the stellar wind
dynamic pressure at both edges of the HZ and analyze the variations of this
parameter across spectral type and orbital inclination. The results here
presented could serve to inform future studies of stellar wind-magnetosphere
interactions and stellar wind erosion of planetary atmospheres via ion escape
processe.


  Numerical integration on spheres, including the computation of the areas of
spherical triangles, is a core computation in geomathematics. The commonly used
techniques sometimes suffer from instabilities and significant loss of
accuracy. We describe a new algorithm, called ARPIST, for accurate and stable
integration of functions on spherical triangles. ARPIST is based on an
easy-to-implement transformation to the spherical triangle from its
corresponding linear triangle via radial projection to achieve high accuracy
and efficiency. More importantly, ARPIST overcomes potential instabilities in
computing the Jacobian of the transformation, even for poorly shaped triangles
that may occur at poles in regular longitude-latitude meshes, by avoiding
potential catastrophic rounding errors. We compare our proposed technique with
L'Huilier's Theorem for computing the area of spherical triangles, and also
compare it with the recently developed LSQST method (J. Beckmann, H.N. Mhaskar,
and J. Prestin, GEM - Int. J. Geomath., 5:143-162, 2014) and a
radial-basis-function-based technique (J. A. Reeger and B. Fornberg, Stud.
Appl. Math., 137:174-188, 2015) for integration of smooth functions on
spherical triangulations. Our results show that ARPIST enables superior
accuracy and stability over previous methods while being orders of magnitude
faster and significantly easier to implement.


  Many vehicles spend a significant amount of time in urban traffic congestion.
Due to the evolution of autonomous cars, driver assistance systems, and
in-vehicle entertainment, many vehicles have plentiful computational and
communication capacity. How can we deploy data collection and processing tasks
on these (slowly) moving vehicles to productively use any spare resources? To
answer this question, we study the efficient placement of distributed services
on a moving vehicle cluster. We present a macroscopic flow model for an
intersection in Dublin, Ireland, using real vehicle density data. We show that
such aggregate flows are highly predictable (even though the paths of
individual vehicles are not known in advance), making it viable to deploy
services harnessing vehicles' sensing capabilities. Our main contribution is a
detailed mathematical specification for a task-based, distributed service
placement model that scales according to the resource requirements and is
robust to the changes caused by the mobility of the cluster. We formulate this
as a constrained optimization problem, with the objective of minimizing overall
processing and communication costs. Our results show that jointly scaling tasks
and finding a mobility-aware, optimal placement results in reduced processing
and communication costs compared to an autonomous vehicular edge
computing-based na\"{i}ve solution.


  We consider magnetic geodesic flows of the normal metrics on a class of
homogeneous spaces, in particular (co)adjoint orbits of compact Lie groups. We
give the proof of the non-commutative integrability of flows and show, in
addition, for the case of (co)adjoint orbits, the usual Liouville integrability
by means of analytic integrals. We also consider the potential systems on
adjoint orbits, which are generalizations of the magnetic spherical pendulum.
The complete integrability of such system is proved for an arbitrary adjoint
orbit of a compact semisimple Lie group.


  In this paper, we study upper bounds on the minimum length of frameproof
codes introduced by Boneh and Shaw to protect copyrighted materials. A $q$-ary
$(k,n)$-frameproof code of length $t$ is a $t \times n$ matrix having entries
in $\{0,1,\ldots, q-1\}$ and with the property that for any column $\mathbf{c}$
and any other $k$ columns, there exists a row where the symbols of the $k$
columns are all different from the corresponding symbol (in the same row) of
the column $\mathbf{c}$. In this paper, we show the existence of $q$-ary
$(k,n)$-frameproof codes of length $t = O(\frac{k^2}{q} \log n)$ for $q \leq
k$, using the Lov\'asz Local Lemma, and of length $t =
O(\frac{k}{\log(q/k)}\log(n/k))$ for $q > k$ using the expurgation method.
Remarkably, for the practical case of $q \leq k$ our findings give codes whose
length almost matches the lower bound $\Omega(\frac{k^2}{q\log k} \log n)$ on
the length of any $q$-ary $(k,n)$-frameproof code and, more importantly, allow
us to derive an algorithm of complexity $O(t n^2)$ for the construction of such
codes.


  Let $\Omega \subset \mathbb{R}^N$ be an open set. In this work we consider
solutions of the following gradient elliptic system \[ -\text{div}(A(x)\nabla
u_{i,\beta}) = f_i(x,u_{i,\beta}) + a(x)\beta |u_{i, \beta}|^{\gamma -1}u_{i,
\beta}
  \mathop{\sum_{j=1}^l}_{j\neq i} |u_{j, \beta}|^{\gamma + 1}, \] for
$i=1,\ldots, l$. We work in the competitive case, namely $\beta<0$. Under
suitable assumptions on $A$, $a$, $f_i$ and on the exponent $\gamma$, we prove
that uniform $L^\infty$-bounds on families of positive solutions
$\{u_\beta\}_{\beta<0}=\{(u_{1,\beta},\ldots, u_{l,\beta})\}_{\beta<0}$ imply
uniform Lipschitz bounds (which are optimal).
  One of the main points in the proof are suitable generalizations of Almgren's
and Alt-Caffarelli-Friedman's monotonicity formulas for solutions of such
systems. Our work generalizes previous results, where the case $A(x)=Id$ (i.e.
the operator is the Laplacian) was treated.


  New results on strong-consistency, in the Hilbert-Schmidt and trace operator
norms, are obtained, in the parameter estimation of an autoregressive
Hilbertian process of order one (ARH(1) process). In particular, a
strongly-consistent diagonal componentwise estimator of the autocorrelation
operator is derived, based on its empirical singular value decomposition.


  We consider the new game of Cops and Attacking Robbers, which is identical to
the usual Cops and Robbers game except that if the robber moves to a vertex
containing a single cop, then that cop is removed from the game. We study the
minimum number of cops needed to capture a robber on a graph $G$, written
$cc(G)$. We give bounds on $cc(G)$ in terms of the cop number of $G$ in the
classes of bipartite graphs and diameter two, $K_{1,m}$-free graphs.


  Large language models (LLMs) for automatic code generation have achieved
breakthroughs in several programming tasks. Their advances in competition-level
programming problems have made them an essential pillar of AI-assisted pair
programming, and tools such as GitHub Copilot have emerged as part of the daily
programming workflow used by millions of developers. The training data for
these models is usually collected from the Internet (e.g., from open-source
repositories) and is likely to contain faults and security vulnerabilities.
This unsanitized training data can cause the language models to learn these
vulnerabilities and propagate them during the code generation procedure. While
these models have been extensively assessed for their ability to produce
functionally correct programs, there remains a lack of comprehensive
investigations and benchmarks addressing the security aspects of these models.
  In this work, we propose a method to systematically study the security issues
of code language models to assess their susceptibility to generating vulnerable
code. To this end, we introduce the first approach to automatically find
generated code that contains vulnerabilities in black-box code generation
models. To achieve this, we present an approach to approximate inversion of the
black-box code generation models based on few-shot prompting. We evaluate the
effectiveness of our approach by examining code language models in generating
high-risk security weaknesses. Furthermore, we establish a collection of
diverse non-secure prompts for various vulnerability scenarios using our
method. This dataset forms a benchmark for evaluating and comparing the
security weaknesses in code language models.


  The Effective Field Theory of Large-Scale Structure (EFTofLSS) provides a
novel formalism that is able to accurately predict the clustering of
large-scale structure (LSS) in the mildly non-linear regime. Here we provide
the first computation of the power spectrum of biased tracers in redshift space
at one loop order, and we make the associated code publicly available. We
compare the multipoles $\ell=0,2$ of the redshift-space halo power spectrum,
together with the real-space matter and halo power spectra, with data from
numerical simulations at $z=0.67$. For the samples we compare to, which have a
number density of $\bar n=3.8 \cdot 10^{-2}(h \ {\rm Mpc}^{-1})^3$ and $\bar
n=3.9 \cdot 10^{-4}(h \ {\rm Mpc}^{-1})^3$, we find that the calculation at
one-loop order matches numerical measurements to within a few percent up to
$k\simeq 0.43 \ h \ {\rm Mpc}^{-1}$, a significant improvement with respect to
former techniques. By performing the so-called IR-resummation, we find that the
Baryon Acoustic Oscillation peak is accurately reproduced. Based on the results
presented here, long-wavelength statistics that are routinely observed in LSS
surveys can be finally computed in the EFTofLSS. This formalism thus is ready
to start to be compared directly to observational data.


  Percolation on complex networks is used both as a model for dynamics on
networks, such as network robustness or epidemic spreading, and as a benchmark
for our models of networks, where our ability to predict percolation measures
our ability to describe the networks themselves. In many applications,
correctly identifying the phase transition of percolation on real-world
networks is of critical importance. Unfortunately, this phase transition is
obfuscated by the finite size of real systems, making it hard to distinguish
finite size effects from the inaccuracy of a given approach that fails to
capture important structural features. Here, we borrow the perspective of
smeared phase transitions and argue that many observed discrepancies are due to
the complex structure of real networks rather than to finite size effects only.
In fact, several real networks often used as benchmarks feature a smeared phase
transition where inhomogeneities in the topological distribution of the order
parameter do not vanish in the thermodynamic limit. We find that these smeared
transitions are sometimes better described as sequential phase transitions
within correlated subsystems. Our results shed light not only on the nature of
the percolation transition in complex systems, but also provide two important
insights on the numerical and analytical tools we use to study them. First, we
propose a measure of local susceptibility to better detect both clean and
smeared phase transitions by looking at the topological variability of the
order parameter. Second, we highlight a shortcoming in state-of-the-art
analytical approaches such as message passing, which can detect smeared
transitions but not characterize their nature.


  Quasars are the most luminous of active galactic nuclei (AGN), and are
perhaps responsible for quenching star formation in their hosts. The Stripe 82X
catalog covers 31.3 deg$^2$ of the Stripe 82 field, of which the 15.6 deg$^2$
covered with XMM-Newton is also covered by Herschel/SPIRE. We have 2500 X-ray
detected sources with multi-wavelength counterparts, and 30% of these are
unobscured quasars, with $L_X > 10^{44}\,$erg/s and $M_B < -23$. We define a
new population of quasars which are unobscured, have X-ray luminosities in
excess of $10^{44}\,$erg/s, have broad emission lines, and yet are also bright
in the far-infrared, with a 250$\mu$m flux density of $S_{\rm 250}>30$mJy. We
refer to these Herschel-detected, unobscured quasars as "Cold Quasars". A mere
4% (21) of the X-ray- and optically-selected unobscured quasars in Stripe 82X
are detected at 250$\mu$m. These Cold Quasars lie at $z\sim1-3$, have $L_{\rm
IR}>10^{12}\,L_\odot$, and have star formation rates of
$\sim200-1400\,M_\odot$/yr. Cold Quasars are bluer in the mid-IR than the full
quasar population, and 72% of our Cold Quasars have WISE W3 $<$ 11.5 [Vega],
while only 19% of the full quasar sample meets this criteria. Crucially, Cold
Quasars have on average $\sim9\times$ as much star formation as the main
sequence of star forming galaxies at similar redshifts. Although dust-rich,
unobscured quasars have occasionally been noted in the literature before, we
argue that they should be considered as a separate class of quasars due to
their high star formation rates. This phase is likely short-lived, as the
central engine and immense star formation consume the gas reservoir. Cold
Quasars are type-1 blue quasars that reside in starburst galaxies.


  Pretrained transformers achieve the state of the art across tasks in natural
language processing, motivating researchers to investigate their inner
mechanisms. One common direction is to understand what features are important
for prediction. In this paper, we apply information bottlenecks to analyze the
attribution of each feature for prediction on a black-box model. We use BERT as
the example and evaluate our approach both quantitatively and qualitatively. We
show the effectiveness of our method in terms of attribution and the ability to
provide insight into how information flows through layers. We demonstrate that
our technique outperforms two competitive methods in degradation tests on four
datasets. Code is available at https://github.com/bazingagin/IBA.


  We present a separable expansion approximation method for Coulomb-like
potentials which is based on Schwinger variational principle and uses
Coulomb-Sturmian functions as basis states. The new scheme provides faster
convergence with respect to our formerly used non-variational approach.


  An important problem in the particle physics is interaction of the Higgs
boson with the fermions. It is in the processes, which involve $h f f $
interaction, the manifestations of $CP$ violation are possible. This in turn
can be helpful in solving the problem of the dominance of matter over
antimatter in the Universe. In this connection, in the present paper, the
effect of longitudinal polarization of leptons and quarks produced in the decay
of the Higgs boson is investigated and calculated. We consider the case in
which the Higgs boson interacts with fermions via a mixture of scalar and
pseudoscalar couplings. Under this assumption, the longitudinal polarization
can acquire non-zero values due to imaginary part of loop corrections to
tree-level amplitudes. This polarization is a direct signature of the $CP$
violation in the Higgs sector. Effects of the longitudinal polarization of
$\tau$ leptons on the energy distribution of the pions in the two-step
Higgs-boson decay $h \to \tau^- \tau^+ \to \pi^- \nu_\tau \pi^+ \bar{\nu}_\tau$
are also studied, and the energy asymmetry with corresponding moments are
calculated.


  Existing research on fairness evaluation of document classification models
mainly uses synthetic monolingual data without ground truth for author
demographic attributes. In this work, we assemble and publish a multilingual
Twitter corpus for the task of hate speech detection with inferred four author
demographic factors: age, country, gender and race/ethnicity. The corpus covers
five languages: English, Italian, Polish, Portuguese and Spanish. We evaluate
the inferred demographic labels with a crowdsourcing platform, Figure Eight. To
examine factors that can cause biases, we take an empirical analysis of
demographic predictability on the English corpus. We measure the performance of
four popular document classifiers and evaluate the fairness and bias of the
baseline classifiers on the author-level demographic attributes.