  We prove that any non-Sasakian contact metric (\kappa,\mu)-space admits a
canonical \eta-Einstein Sasakian or \eta-Einstein paraSasakian metric. An
explicit expression for the curvature tensor fields of those metrics is given
and we find the values of \kappa and \mu for which such metrics are
Sasaki-Einstein and paraSasaki-Einstein. Conversely, we prove that, under some
natural assumptions, a K-contact or K-paracontact manifold foliated by two
mutually orthogonal, totally geodesic Legendre foliations admits a contact
metric (\kappa,\mu)-structure. Furthermore, we apply the above results to the
geometry of tangent sphere bundles and we discuss some topological and
geometrical properties of (\kappa,\mu)-spaces related to the existence of
Eistein-Weyl and Lorentzian Sasakian Einstein structures.


  Graph Neural Networks (GNNs) have shown great power in learning node
representations on graphs. However, they may inherit historical prejudices from
training data, leading to discriminatory bias in predictions. Although some
work has developed fair GNNs, most of them directly borrow fair representation
learning techniques from non-graph domains without considering the potential
problem of sensitive attribute leakage caused by feature propagation in GNNs.
However, we empirically observe that feature propagation could vary the
correlation of previously innocuous non-sensitive features to the sensitive
ones. This can be viewed as a leakage of sensitive information which could
further exacerbate discrimination in predictions. Thus, we design two feature
masking strategies according to feature correlations to highlight the
importance of considering feature propagation and correlation variation in
alleviating discrimination. Motivated by our analysis, we propose Fair View
Graph Neural Network (FairVGNN) to generate fair views of features by
automatically identifying and masking sensitive-correlated features considering
correlation variation after feature propagation. Given the learned fair views,
we adaptively clamp weights of the encoder to avoid using sensitive-related
features. Experiments on real-world datasets demonstrate that FairVGNN enjoys a
better trade-off between model utility and fairness. Our code is publicly
available at https://github.com/YuWVandy/FairVGNN.


  In this paper, a channel that is contaminated by two independent Gaussian
noises $S ~ N(0,Q)$ and $Z_0 ~ N(0,N_0)$ is considered. The capacity of this
channel is computed when independent noisy versions of $S$ are known to the
transmitter and/or receiver. It is shown that the channel capacity is greater
then the capacity when $S$ is completely unknown, but is less then the capacity
when $S$ is perfectly known at the transmitter or receiver. For example, if
there is one noisy version of $S$ known at the transmitter only, the capacity
is $0.5\log(1+\frac{P}{Q(N_1/(Q+N_1))+N_0})$, where $P$ is the input power
constraint and $N_1$ is the power of the noise corrupting $S$. Further, it is
shown that the capacity with knowledge of any independent noisy versions of $S$
at the transmitter is equal to the capacity with knowledge of the statistically
equivalent noisy versions of $S$ at the receiver.


  We present preliminary iron abundances and $\alpha$ element (Ca, Mg)
abundance ratios for a sample of 22 Red Giant Branch (RGB) Stars in the
Sagittarius dwarf spheroidal galaxy (Sgr), selected near the RGB-Tip. The
sample is representative of the Sgr dominant population. The mean iron
abundance is [Fe/H]=-0.49. The $\alpha$ element abundance ratios are slightly
subsolar, in agreement with the results recently prensented by Bonifacio et
al.(2004, A&A, 414, 503).


  We provide a very brief introduction to typical paths and the corresponding
It\^o type integration. Relying on this robust It\^o integration, we prove an
existence and uniqueness result for one-dimensional differential equations
driven by typical paths with non-Lipschitz continuous coefficients in the
spirit of Yamada--Watanabe as well as an approximation result in the spirit of
Doss--Sussmann.


  The well-known Cucker-Smale model is a macroscopic system reflecting
flocking, i.e. the alignment of velocities in a group of autonomous agents
having mutual interactions. In the present paper, we consider the mean-field
limit of that model, called the kinetic Cucker-Smale model, which is a
transport partial differential equation involving nonlocal terms. It is known
that flocking is reached asymptotically whenever the initial conditions of the
group of agents are in a favorable configuration. For other initial
configurations, it is natural to investigate whether flocking can be enforced
by means of an appropriate external force, applied to an adequate time-varying
subdomain.
  In this paper we prove that we can drive to flocking any group of agents
governed by the kinetic Cucker-Smale model, by means of a sparse centralized
control strategy, and this, for any initial configuration of the crowd. Here,
"sparse control" means that the action at each time is limited over an
arbitrary proportion of the crowd, or, as a variant, of the space of
configurations; "centralized" means that the strategy is computed by an
external agent knowing the configuration of all agents. We stress that we do
not only design a control function (in a sampled feedback form), but also a
time-varying control domain on which the action is applied. The sparsity
constraint reflects the fact that one cannot act on the whole crowd at every
instant of time.
  Our approach is based on geometric considerations on the velocity field of
the kinetic Cucker-Smale PDE, and in particular on the analysis of the particle
flow generated by this vector field. The control domain and the control
functions are designed to satisfy appropriate constraints, and such that, for
any initial configuration, the velocity part of the support of the measure
solution asymptotically shrinks to a singleton, which means flocking.


  The Cosmic Infrared Background (CIB) peaks in the Far-Infrared (FIR), and its
Spectral Energy Distribution (SED) is now well constrained. Thanks to recent
facilities and Spitzer, the populations contributing to the CIB are being
characterized: the dominant galaxy contributions to the FIR CIB are Luminous IR
galaxies (LIRGs) at 0.5<z<1.5 and, to the submm CIB, Ultra-LIRGs at z>2. These
populations of galaxies experience very high rates of evolution with redshift.
Because of confusion, the CIB is (and will remain in some domains) partially
resolved and its contributing galaxies SEDs are not well constrained. We
discuss all these aspects and show how confusion limits Spitzer observations,
and how to overcome it in order to study the unresolved part of the CIB.


  In low temperature limit, we study electron counting statistics of a
disordered conductor. We derive an expression for the distribution of charge
transmitted over a finite time interval by using a result from the random
matrix theory of quasi one dimensional disordered conductors. In the metallic
regime, we find that the peak of the distribution is Gaussian and shows
negligible sample to sample variations. We also find that the tails of the
distribution are neither Gaussian nor Poisson and exhibit strong sample to
sample variations.


  We present the general form of the operators that lift the group action on
the twisted sectors of a bosonic string on an orbifold ${\cal M}/G$, in the
presence of a Kalb-Ramond field strength $H$. These operators turn out to
generate the quasi-quantum group $D_{\omega}[G]$, introduced in the context of
orbifold conformal field theory by R. Dijkgraaf, V. Pasquier and P. Roche. The
3-cocycle $\omega$ entering in the definition of $D_{\omega}[G]$ is related to
$H$ by a series of cohomological equations in a tricomplex combining de Rham,
Cech and group coboundaries. We construct magnetic amplitudes for the twisted
sectors and show that $\omega=1$ arises as a consistency condition for the
orbifold theory. Finally, we recover discrete torsion as an ambiguity in the
lift of the group action to twisted sectors, in accordance with previous
results presented by E. Sharpe.


  We present a search for the production of neutral Higgs bosons decaying into
tautau pairs in ppbar collisions at a center-of-mass energy of 1.96 TeV. The
data, corresponding to an integrated luminosity of 5.4 fb-1, were collected by
the D0 experiment at the Fermilab Tevatron Collider. We set upper limits at the
95% C.L. on the product of production cross section and branching ratio for a
scalar resonance decaying into tautau pairs, and we then interpret these limits
as limits on the production of Higgs bosons in the minimal supersymmetric
standard model (MSSM) and as constraints in the MSSM parameter space.


  In the late nineties, Smale proposed a list of problems for the next century
and, among these, it was conjectured that for every $r\ge 1$ a $C^r$-generic
diffeomorphism has trivial centralizer. Our contribution here is to prove the
triviality of $C^r$-centralizers on hyperbolic basic sets. In particular,
$C^r$-generic transitive Anosov diffeomorphisms have a trivial
$C^1$-centralizer. These results follow from a more general criterium for
expansive homeomorphisms with the gluing orbit property. We also construct a
linear Anosov diffeomorphism on $\mathbb T^3$ with discrete, non-trivial
centralizer and with elements that are not roots. Finally, we prove that all
elements in the centralizer of an Anosov diffeomorphism preserve some of its
maximal entropy measures, and use this to characterize the centralizer of
linear Anosov diffeomorphisms on tori.


  More and more people use the Internet to work on duties of their daily work
routine. To find the right information online, Web search engines are the tools
of their choice. Apart from finding facts, people use Web search engines to
also execute rather complex and time consuming search tasks. So far search
engines follow the one-for-all approach to serve its users and little is known
about the impact of gender and age on people's Web search behavior. In this
article we present a study that examines (1) how female and male web users
carry out simple and complex search tasks and what are the differences between
the two user groups, and (2) how the age of the users impacts their search
performance. The laboratory study was done with 56 ordinary people each
carrying out 12 search tasks. Our findings confirm that age impacts behavior
and search performance significantly, while gender influences were smaller than
expected.


  We study semiclassical strings in the Klebanov-Witten and in the Non-abelian
T-dual Klebanov-Witten backgrounds. We show that both backgrounds share a
subsector of equivalent states up to conditions on the T-dual coordinates which
also impose a breaking of the R-symmetry by a discrete group. We also analyze
string configurations where the strings are stretched along the T-dual
coordinates. This semiclassical analysis predicts the existence of chiral
primary operators for the dual (strongly coupled) superconformal field theory
whose anomalous dimension depends on the T-dual coordinates. We briefly discuss
the Penrose limit of the dualised background.


  The role of transverse momentum of quarks in semi-inclusive leptoproduction
will be discussed. It involves generalized distribution and fragmentation
functions which depend on both the longitudinal lightcone momentum fraction of
the quarks and on the transverse momentum. Constraints on these functions and
relations between them arise as a consequence of the QCD equation of motion for
the quark fields, Lorentz invariance and of C, P, and T invariance of the
strong interactions. Experimentally one has access to the functions for
instance in measurements of azimuthal asymmetries in hard processes.


  There has been a surge of experimental effort recently in cooling trapped
fermionic atoms to quantum degeneracy. By varying an external magnetic field,
interactions between atoms can be made arbitrarily strong. When the S wave
scattering length becomes comparable to and larger than the interparticle
spacing, standard mean field analysis breaks down. In this case the system
exhibits a type of universality, and J-W. Chen and D. B. Kaplan recently showed
how this system can be studied from first principles using lattice field
theory. This poster presents the first results of exploratory simulations. The
existence of a continuum limit is checked and the pairing condensate is studied
as a function of the external source strength over a range of temperatures.
Preliminary results show simulations can locate the critical temperature.


  In a recent paper Ozdogan (Z. Naturforsch, 59a(2004)743) published formulas
for evaluating the two-center overlap and nuclear attraction integrals over
integer and noninteger Slater type orbitals. The purpose of this article is to
point out that the same formulas have previously been established by Guseinov
et al. (J.Mol.Model.,8(2002)272) by using the same method. As we demonstrated
in our Comment (Int.J.Quantum Chem., 91(2003)62), the expansion formula for the
product of two normalized associated Legendre functions in elliptical
coordinates and the expansion coefficients presented by Ozdogan are obtained
from the use of given in our papers general formulas (I.I.Guseinov,
J.Phys.,B,3(1970)1399; Phys.Rev.,A,32(1985)1864; J.Mol.Struct
(Theochem),336(1995)17) by changing the summation indices. It should be noted
that the published by Ozdogan results are on the use of formulas for the
evaluation of multicenter integrals presented in his other papers, which are
also obtained from the literature (see, e.g., C.C.J. Roothaan, J.Chem.Phys., 19
(1951) 1445; A.Lofthus, Mol. Phys., 5 (1962) 105) and our articles by changing
the summation indices (see Comments: I.I.Guseinov, Commun.Theor.Phys., 38
(2002) 256; Int.J.Quantum Chem., 91 (2003) 62; J.Math.Chem., 36 (2004) 123;
J.Chin.Chem.Soc., 51 (2004) 877; J. Chin. Chem. Soc., 51 (2004) 1077;
I.I.Guseinov, B.A.Mamedov, Can.J.Phys., 82(2004) 205, p.206).


  Given a reaction (network) we are looking for minimal sets of species
starting from which all the species will have positive concentrations for all
positive times in the domain of existence of the solution of the induced
kinetic differential equation. We present three algorithms to solve the
problem. The first one essentially checks all the possible subsets of the sets
of species. This can obviously work for only a few dozen species because of
combinatorial explosion. The second one is based on an integer programming
reformulation of the problem. The third one walks around the state space of the
problem in a systematic way and produces all the minimal sets of the
advantageous initial species, and works also for large systems. All the
algorithms rely heavily on the concept of Volpert indices, used earlier for the
decomposition of overall reactions [Kov\'acs \textit{et al., Physical Chemistry
Chemical Physics} 2004, 6, 1236]. Relations to the permanence hypothesis,
possible economic or medical uses of the solution of the problem are analyzed,
and open problems are formulated at the end.


  The complexity of the simple and the Kac modules over the general linear Lie
superalgebra $\mathfrak{gl}(m|n)$ of type $A$ was computed by Boe, Kujawa, and
Nakano in 2012. A natural continuation to their work is computing the
complexity of the same family of modules over the ortho-symplectic Lie
superalgebra $\mathfrak{osp}(2|2n)$ of type $C$. The two Lie superalgebras are
both of Type I which will result in similar computations. In fact, our
geometric interpretation of the complexity agrees with theirs. We also compute
a categorical invariant, z-complexity, introduced in Boe et al., and we
interpret this invariant geometrically in terms of a specific detecting
subsuperalgebra. In addition, we compute the complexity and the z-complexity of
the simple modules over the Type II Lie superalgebras $\mathfrak{osp}(3|2)$,
$D(2,1;\alpha)$, $G(3)$, and $F(4)$.


  The performance of tau-lepton reconstruction and identification algorithms is
studied using a data sample of proton-proton collisions at sqrt(s)=7 TeV,
corresponding to an integrated luminosity of 36 inverse picobarns collected
with the CMS detector at the LHC. The tau leptons that decay into one or three
charged hadrons, zero or more short-lived neutral hadrons, and a neutrino are
identified using final-state particles reconstructed in the CMS tracker and
electromagnetic calorimeter. The reconstruction efficiency of the algorithms is
measured using tau leptons produced in Z-boson decays. The tau-lepton
misidentification rates for jets and electrons are determined.


  We study the monotonic behaviour of the zeros of the multiple
Jacobi-Angelesco orthogonal polynomials, in the diagonal case, with respect to
the parameters $\alpha,\beta$ and $\gamma$. We prove that the zeros are
monotonic functions of $\alpha$ and $\gamma$ and consider some special cases of
how the zeros depend on $\beta$, especially in the presence of symmetry. As a
consequence we obtain results about monotonicity of zeros of Jacobi-Laguerre
and Laguerre-Hermite multiple orthogonal polynomials too.


  We introduce and study a one parameter deformation of the polynuclear growth
(PNG) in $(1+1)$-dimensions, which we call the $t$-PNG model. It is defined by
requiring that, when two expanding islands merge, with probability $t$ they
sprout another island on top of the merging location. At $t=0$, this becomes
the standard (non-deformed) PNG model that, in the droplet geometry, can be
reformulated through longest increasing subsequences of uniformly random
permutations or through an algorithm known as patience sorting. In terms of the
latter, the $t$-PNG model allows errors to occur in the sorting algorithm with
probability $t$.
  We prove that the $t$-PNG model exhibits one-point Tracy-Widom GUE
asymptotics at large times for any fixed $t\in [0,1)$, and one-point
convergence to the narrow wedge solution of the Kardar-Parisi-Zhang (KPZ)
equation as $t$ tends to $1$. We further construct distributions for an
external source that are likely to induce Baik-Ben Arous-Peche type phase
transitions. The proofs are based on solvable stochastic vertex models and
their connection to the determinantal point processes arising from Schur
measures on partitions.


  We present kinematically forbidden dark matter annihilations into Standard
Model leptons. This mechanism precisely selects the dark matter mass that gives
the observed relic abundance. This is qualitatively different from existing
models of thermal dark matter, where fixing the relic density typically leaves
open orders of magnitude of viable dark matter masses. Forbidden annihilations
require the dark matter to be close in mass to the particles that dominate its
annihilation rate. We show examples where the dark matter mass is close to the
muon mass, the tau mass, or the average of the tau and muon masses. We find
that most of the relevant parameter space can be covered by the next generation
of proposed beam-dump experiments and future high-luminosity electron positron
colliders. Forbidden dark matter predicts large couplings to the Standard Model
that can explain the observed value of $(g-2)_\mu$.


  In this work, we extend the quantum optimal control theory of molecules
subject to ultrashort laser pulses to the case of solvated systems, explicitly
including the solvent dielectric properties in the system Hamiltonian. A
reliable description of the solvent polarization is accounted for within the
Polarizable Continuum Model (PCM). The electronic dynamics for the molecule in
solution is coupled with the dynamics of the surrounding polarizable
environment, that affects the features of the optimized light pulse. Examples
on test molecules are presented and discussed to illustrate such effects.


  Energy dependence of $\gamma^*p$ total cross section is considered. It is
known from the HERA data that the cross section grows with energy, and the rate
of growth is an increasing function of the virtuality $Q^2$ of the photon
$\gamma^*$. This dependence can be explained in a simple and generic way by the
Froissart bound. To implement this mechanism quantitatively a theory satisfying
$s$-channel unitarity is required. This is achieved by computing the total
cross section from the optical theorem, and the forward elastic amplitude from
the phase shifts in the impact-parameter representation. A recipe to do so in
perturbative QCD is discussed, together with an expose of the advantage to
calculate the elastic amplitude via phase shift, rather than direct sum of all
Feynman diagrams. A two-loop computation of phase shift and total cross section
is presented, and compared with the HERA data with good agreements.


  In a recent paper (J.R. Morris, Quant. Stud. Math. Found. 2 (2015) 359), an
inhomogeneous compactification of the extra dimension of a five-dimensional
Kaluza-Klein metric has been shown to generate a position-dependent mass (PDM)
in the corresponding four-dimensional system. As an application of this
dimensional reduction mechanism, a specific static dilatonic scalar field has
been connected with a PDM Lagrangian describing a well-known nonlinear PDM
oscillator. Here we present more instances of this construction that lead to
PDM systems with radial symmetry, and the properties of their corresponding
inhomogeneous extra dimensions are compared with the ones in the nonlinear
oscillator model. Moreover, it is also shown how the compactification
introduced in this type of models can alternatively be interpreted as a novel
mechanism for the dynamical generation of curvature.


  Recent research has demonstrated the importance of flexibly controlling for
covariates in instrumental variables estimation. In this paper we study the
finite sample and asymptotic properties of various weighting estimators of the
local average treatment effect (LATE), motivated by Abadie's (2003) kappa
theorem and offering the requisite flexibility relative to standard practice.
We argue that two of the estimators under consideration, which are weight
normalized, are generally preferable. Several other estimators, which are
unnormalized, do not satisfy the properties of scale invariance with respect to
the natural logarithm and translation invariance, thereby exhibiting
sensitivity to the units of measurement when estimating the LATE in logs and
the centering of the outcome variable more generally. We also demonstrate that,
when noncompliance is one sided, certain weighting estimators have the
advantage of being based on a denominator that is strictly greater than zero by
construction. This is the case for only one of the two normalized estimators,
and we recommend this estimator for wider use. We illustrate our findings with
a simulation study and three empirical applications, which clearly document the
sensitivity of unnormalized estimators to how the outcome variable is coded. We
implement the proposed estimators in the Stata package kappalate.


  The high energy blazar, Markarian 501 was observed as a part of
multi-instrument and multiwavelength campaign spanning the whole
electromagnetic spectrum for 4.5 months during March 15 to August 1, 2009. On
May 1, Whipple 10m telescope observed a very strong $\gamma$-ray flare in a
time interval of about 0.5 h. Apart from this flare, high state and low state
emissions were also observed by Whipple, VERITAS and MAGIC telescopes. Using
the photohadronic model and accounting for the absorption of the extragalactic
background light (EBL) to these very high energy $\gamma$-rays, excellent fits
are obtained for the observed spectra. We have shown that the intrinsic
spectrum for low state emission is flat, however, for high and very high states
this is a power-law with slowly increasing exponent.


  The quantum algorithms of Deutsch, Simon and Shor are described in a way
which highlights their dependence on the Fourier transform. The general
construction of the Fourier transform on an Abelian group is outlined and this
provides a unified way of understanding the efficacy of these algorithms.
Finally we describe an efficient quantum factoring algorithm based on a general
formalism of Kitaev and contrast its structure to the ingredients of Shor's
algorithm.


  A class of dynamical models of turbulence living on a one-dimensional
dyadic-tree structure is introduced and studied. The models are obtained as a
natural generalization of the popular GOY shell model of turbulence. These
models are found to be chaotic and intermittent. They represent the first
example of (1+1)-dimensional dynamical systems possessing non trivial
multifractal properties. The dyadic structure allows to study spatial and
temporal fluctuations. Energy dissipation statistics and its scaling properties
are studied. Refined Kolmogorov Hypothesis is found to hold.


  Not only a review of Weintraub's Differential Forms: Theory and Practice but
also a discussion of why differential forms should be taught to undergraduates
and an overview of some of the other possible texts that could be used.


  In this work, the Dirac-type integro di{\S}erential system with one classical
boundary condition and another nonlocal integral boundary condition is
considered. We obtain the asymptotic formulae for the solutions, eigenvalues
and nodal points. We also investigate the inverse nodal problem and prove that
given a dense subset of nodal points uniquely determines the boundary condition
parameter and the potential function of the considered di{\S}erential system.
We also provide an e{\S}ective procedure for solving the inverse nodal problem.


  An excitonic method proper to study conjugated oligomers and polymers is
described and its applicability tested on the ground state and first excited
states of trans-polyacetylene, taken as a model. From the Pariser-Parr-Pople
Hamiltonian, we derive an effective Hamiltonian based on a local description of
the polymer in term of monomers; the relevant electronic configurations are
build on a small number of pertinent local excitations. The intuitive and
simple microscopic physical picture given by our model supplement recent
results, such as the Rice and Garstein ones. Depending of the parameters, the
linear absorption appears dominated by an intense excitonic peak.


  In this work we study the viable parameter space of the scalar sector in the
type-II seesaw model. In identifying the allowed parameter space, we employ
constraints from low energy precision measurements, theoretical considerations
and the 125-GeV Higgs data. These tools prove effective in constraining the
model parameter space. Moreover, the triplet also offers a rich collider
phenomenology from having additional scalars that have unique collider
signatures. We find that direct collider searches for these scalars can further
probe various parts of the viable parameter space. These parts can be
parametrized by the electroweak scalar triplet vacuum expectation value, the
mass splitting of the singly- and doubly-charged scalars, and the
doubly-charged Higgs mass. We find that different regions of the viable
parameter space give rise to different collider signatures, such as the
same-sign dilepton, the same-sign $W$ and the multilepton signatures. By
investigating various LEP and LHC measurements, we derive the most updated
constraints over the whole range of parameter space of the type-II seesaw
model.


  Prompt-based interfaces for Large Language Models (LLMs) have made
prototyping and building AI-powered applications easier than ever before.
However, identifying potential harms that may arise from AI applications
remains a challenge, particularly during prompt-based prototyping. To address
this, we present Farsight, a novel in situ interactive tool that helps people
identify potential harms from the AI applications they are prototyping. Based
on a user's prompt, Farsight highlights news articles about relevant AI
incidents and allows users to explore and edit LLM-generated use cases,
stakeholders, and harms. We report design insights from a co-design study with
10 AI prototypers and findings from a user study with 42 AI prototypers. After
using Farsight, AI prototypers in our user study are better able to
independently identify potential harms associated with a prompt and find our
tool more useful and usable than existing resources. Their qualitative feedback
also highlights that Farsight encourages them to focus on end-users and think
beyond immediate harms. We discuss these findings and reflect on their
implications for designing AI prototyping experiences that meaningfully engage
with AI harms. Farsight is publicly accessible at:
https://PAIR-code.github.io/farsight.


  The $\mathcal{F}$-statistic is a detection statistic used widely in searches
for continuous gravitational waves with terrestrial, long-baseline
interferometers. A new implementation of the $\mathcal{F}$-statistic is
presented which accelerates the existing "resampling" algorithm using graphics
processing units (GPUs). The new implementation runs between 10 and 100 times
faster than the existing implementation on central processing units without
sacrificing numerical accuracy. The utility of the GPU implementation is
demonstrated on a pilot narrowband search for four newly discovered millisecond
pulsars in the globular cluster Omega Centauri using data from the second Laser
Interferometer Gravitational-Wave Observatory observing run. The computational
cost is $17.2$ GPU-hours using the new implementation, compared to 1092
core-hours with the existing implementation.


  Highly relativistic jets are most probably driven by strong magnetic fields
and launched from the accretion disk surrounding a central black hole. Applying
the jet flow parameters (velocity, density, temperature) calculated from the
magnetohydrodynamic (MHD) equations, we derive the thermal X-ray luminosity
along the inner jet flow in the energy range 0.2-10.1 keV. Here, we concentrate
on the case of Galactic microquasars emitting highly relativistic jets. For a 5
solar masses central object and a jet mass flow rate of 10^{-8} solar
masses/year we obtain a jet X-ray luminosity L_x ~ 10^{33} erg\sec. Emission
lines of Fe XXV and Fe XXVI are clearly visible. Relativistic effects such as
Doppler shift and Doppler boosting were considered for different inclinations
of the jet axis. Due to the chosen geometry of the MHD jet the inner X-ray
emitting part is not yet collimated. Therefore, depending on the viewing angle,
the Doppler boosting does not play a major role in the total spectra.


  The reasoning segmentation task, which demands a nuanced comprehension of
intricate queries to accurately pinpoint object regions, is attracting
increasing attention. However, Multi-modal Large Language Models (MLLM) often
find it difficult to accurately localize the objects described in complex
reasoning contexts. We believe that the act of reasoning segmentation should
mirror the cognitive stages of human visual search, where each step is a
progressive refinement of thought toward the final object. Thus we introduce
the Chains of Reasoning and Segmenting (CoReS) and find this top-down visual
hierarchy indeed enhances the visual search process. Specifically, we propose a
dual-chain structure that generates multi-modal, chain-like outputs to aid the
segmentation process. Furthermore, to steer the MLLM's outputs into this
intended hierarchy, we incorporate in-context inputs as guidance. Extensive
experiments demonstrate the superior performance of our CoReS, which surpasses
the state-of-the-art method by 6.5\% on the ReasonSeg dataset. Project:
https://chain-of-reasoning-and-segmentation.github.io/.


  The main purpose of this paper is to develop new algorithms for computing
invariant rings in a general setting. This includes invariants of nonreductive
groups but also of groups acting on algebras over certain rings. In particular,
we present an algorithm for computing invariants of a finite group acting on a
finitely generated algebra over a Euclidean ring. This may be viewed as a first
step in "computational arithmetic invariant theory." As a special case, the
algorithm can compute multiplicative invariant rings. Other algorithms are
applicable to nonreductive groups and are, when applied to reductive groups,
often faster than the algorithms known to date.
  The main tool is a generalized and modified version of an ideal that was
already used by Derksen in his algorithm for computing invariants of linearly
reductive groups. As a further application, these so-called extended Derksen
ideals give rise to invariantization maps, which turn an arbitrary ring element
into an invariant.
  For the most part, the algorithms of this paper have been implemented.


  We review new constraints on the Yukawa-type corrections to Newtonian gravity
obtained recently from gravitational experiments and from the measurements of
the Casimir force. Special attention is paid to the constraints following from
the most precise dynamic determination of the Casimir pressure between the two
parallel plates by means of a micromechanical torsional oscillator. The
possibility of setting limits on the predictions of chameleon field theories
using the results of gravitational experiments and Casimir force measurements
is discussed.


  The X-Shooter Spectral Library (XSL) contains more than 800 spectra of stars
across the color-magnitude diagram, that extend from near-UV to near-IR
wavelengths (320-2450 nm). We summarize properties of the spectra of O-rich
Long Period Variables in XSL, such as phase-related features, and we confront
the data with synthetic spectra based on static and dynamical stellar
atmosphere models. We discuss successes and remaining discrepancies, keeping in
mind the applications to population synthesis modeling that XSL is designed
for.


  Highly polarized, multi-kiloampere-current electron bunches from compact
laser-plasma accelerators are desired for numerous applications. Current
proposals to produce these beams suffer from intrinsic limitations to the
reproducibility, charge, beam shape and final polarization degree. In this
Letter, we propose colliding pulse injection as a technique for the generation
of highly polarized electron bunches from pre-polarized plasma sources. Using
particle-in-cell simulations, we show that colliding pulse injection enables
trapping and precise control over electron spin evolution, resulting in the
generation of high-current (multi-kA) electron bunches with high degrees of
polarization (up to 95 % for > 2 kA). Bayesian optimization is employed to
optimize the multidimensional parameter space associated with colliding pulse
injection to obtain percent-level energy spread, sub-micron normalized
emittance electron bunches with 90 % polarization using 100-TW class laser
systems.


  The properties of matrix valued polynomials generated by the scalar-type
Rodrigues' formulas are analyzed. A general representation of these polynomials
is found in terms of products of simple differential operators. The recurrence
relations, leading coefficients, completeness are established, as well as, in
the commutative case, the second order equations for which these polynomials
are eigenfunctions and the corresponding eigenvalues, and ladder operators.
  The conjecture of Duran and Grunbaum that if the weights are self-adjoint and
positive semidefinite then they are necessarily of scalar type is proved for
Q(x)=x and Q(x)=x^2-1 in dimension two, and for any dimension under genericity
assumptions.
  Commutative classes of quasi-orthogonal polynomials are found, which satisfy
all the properties usually associated to orthogonal polynomials.


  This is an English translation of the monograph "Die Klassenk\"orper der
komplexen Multiplikation" by Max Deuring, published in 1958 as Enzyklop\"adie
der Mathematischen Wissenschaften, Band I-2, Heft 10, Teil II by B.G. Teuber
Verlagsgesellschaft, Stuttgart. It gives a systematic exposition of the
analytic method in the theory of complex multiplication -- the interrelations
between elliptic functions, modular functions and algebraic numbers.
  This translation was done as an exercise for learning the German language.
The mathematical notation and terminology are kept as closely as possible to
those given in the German original work. No attempt has been made to modernize
the exposition, other than rectifying a (very) few obviously-correctable
typographical errors.


  We have used Simple Denoising Algorithm using Wavelet Transform on the
monthly solar neutrino flux data from (1) SAGE detector during the period from
1st January 1990 to 31st December 2000; (2) SAGE detector during the period
from April 1998 to December 2001; (3) GALLEX detector during the period from
May 1991 to January 1997; (4) GNO detector during the period from May 1998 to
December 2001; (5) GALLEX-GNO detector (combined data) from May 1991 to
December 2001 and (6) average of the data from GNO and SAGE detectors during
the period from May 1998 to December 2001. (1) exhibits periodicity around 20,
27, 36, 70, 90 and 114 months. (2) shows periodicity around 21, 28, 31 and 33
months. For (3) we observe periodicity around 24, 40, 54, 57, 59, 62 and 64
months. For (4) periodicity is seen around 23, 30 and 34 months. (5) gives
periodicity around 49, 57, 64, 74, 79, 88, 95 and 99 months while (6) shows
periodicity around 24, 32, 35 and 38 months. We have found almost similar
periods in the solar flares, sunspot data, solar proton data which indicates
that the solar activity cycle may be due to the variable character of nuclear
energy generation inside the sun.


  PKS 0558-504 is the brightest radio-loud Narrow-Line Seyfert 1 galaxy at
X-ray energies. Here we present results from the radio, optical, UV, and X-ray
bands obtained with Swift, XMM, and ATCA during a 10-day monitoring campaign in
September 2008. The simultaneous coverage at several wavelengths makes it
possible to investigate in detail the broadband spectral energy distribution
(SED) and the energetic of this source. The main results can be summarized as
follows. The ATCA reveals the presence of an extended radio emission in PKS
0558-504 with two lobe-like structures at ~7" from the bright central source.
The extended radio structure and the low value of the radio-loudness similar to
radio-quiet Seyfert galaxies coupled with constraints from higher energy bands
argue against a jet-dominated emission. The study of the SED, which is
dominated by a nearly constant optical-UV emission, supports the conclusion
that PKS 0558-504 is accreting at super-Eddington rate. This conclusion was
reached assuming M_BH=2.5e8 M_sun, which was obtained with a new scaling method
based on X-ray spectral variability results. A comparison between the accretion
luminosity and the kinetic power associated with the jet suggests that in this
source the accretion power dominates in agreement with the results obtained
from Radiation-MHD simulations of Galactic black holes (GBHs) accreting at the
Eddington rate. The combined findings from this panchromatic investigation
strongly suggest that PKS 0558-504 is a large-scale analog of GBHs in their
highly accreting intermediate state. Importantly, PKS 0558-504 may also be the
prototype of the parent population of the very radio-loud NLS1s recently
detected at gamma-ray energies.


  Several time dependent backgrounds, with perfect fluid matter, can be used to
construct solutions of Einstein equations in the presence of a negative
cosmological constant along with some matter sources. In this work we focus on
the non-vacuum Kasner-AdS geometry and its solitonic generalization. To
characterize these space-times, we provide ways to embed them in higher
dimensional flat space-times. General space-like geodesics are then studied and
used to compute the two point boundary correlators within the geodesic
approximation.


  A growing body of work uses Natural Language Processing (NLP) methods to
automatically generate medical notes from audio recordings of doctor-patient
consultations. However, there are very few studies on how such systems could be
used in clinical practice, how clinicians would adjust to using them, or how
system design should be influenced by such considerations. In this paper, we
present three rounds of user studies, carried out in the context of developing
a medical note generation system. We present, analyse and discuss the
participating clinicians' impressions and views of how the system ought to be
adapted to be of value to them. Next, we describe a three-week test run of the
system in a live telehealth clinical practice. Major findings include (i) the
emergence of five different note-taking behaviours; (ii) the importance of the
system generating notes in real time during the consultation; and (iii) the
identification of a number of clinical use cases that could prove challenging
for automatic note generation systems.


  I present a more refined analysis of the mass-splittings between the
different heavy quarkonia states, using {\it new double ratios} of exponential
moments of different two-point functions. Then, I test the validity of the
$1/m$-expansion, extract $\alpha_s(M_Z)=0.127\pm 0.011$ from $M_{\chi_c(P^1_1)}
- M_{\chi_c(P^3_1)}$, and provide a new estimate of the gluon condensate from
$M_\psi -M_{\eta_c}$ and $M_{\chi_b}-M_\Upsilon$, which combined with the
recent estimate from the $\tau$-like decay sum rules in $e^+e^-\rar I=1$
hadrons data, leads to the {\it update average value} $\la\alpha_s G^2\ra =
(7.1\pm 0.9)\times 10^{-2}$ GeV$^4$ from the light and heavy quark systems. I
also find $M_{\Upsilon}-M_{\eta_b}\approx 63^{-29}_{+51}$ MeV implying the
possible observation of the $\eta_b$ in the $\Upsilon$-radiative decay.


  Recent E-commerce applications benefit from the growth of deep learning
techniques. However, we notice that many works attempt to maximize business
objectives by closely matching offline labels which follow the supervised
learning paradigm. This results in models obtain high offline performance in
terms of Area Under Curve (AUC) and Normalized Discounted Cumulative Gain
(NDCG), but cannot consistently increase the revenue metrics such as purchases
amount of users. Towards the issues, we build a simulated search engine AESim
that can properly give feedback by a well-trained discriminator for generated
pages, as a dynamic dataset. Different from previous simulation platforms which
lose connection with the real world, ours depends on the real data in
AliExpress Search: we use adversarial learning to generate virtual users and
use Generative Adversarial Imitation Learning (GAIL) to capture behavior
patterns of users. Our experiments also show AESim can better reflect the
online performance of ranking models than classic ranking metrics, implying
AESim can play a surrogate of AliExpress Search and evaluate models without
going online.


  The last decade has witnessed the development of several alternative neutron
detector technologies, as a consequence of upcoming neutron sources and
upgrades, as well the world-wide shortage of $^3$He. One branch of development
is the family of $^{10}$B-based gaseous detectors. This work focuses on the
boron coated straws (BCS) by Proportional Technologies Inc., a commercial
solution designed for use in homeland security and neutron science. A detailed
Geant4 simulation study of the BCS is presented, which investigates various
aspects of the detector performance, e.g. efficiency, activation, absorption
and the impact of scattering on the measured signal. The suitability of the BCS
detector for Small Angle Neutron Scattering (SANS), direct chopper spectrometry
and imaging is discussed.


  We consider frequency-weighted damping optimization for vibrating systems
described by a second-order differential equation. The goal is to determine
viscosity values such that eigenvalues are kept away from certain undesirable
areas on the imaginary axis. To this end, we present two complementary
techniques. First, we propose new frameworks using nonsmooth constrained
optimization problems, whose solutions both damp undesirable frequency bands
and maintain stability of the system. These frameworks also allow us to weight
which frequency bands are the most important to damp. Second, we also propose a
fast new eigensolver for the structured quadratic eigenvalue problems that
appear in such vibrating systems. In order to be efficient, our new eigensolver
exploits special properties of diagonal-plus-rank-one complex symmetric
matrices, which we leverage by showing how each quadratic eigenvalue problem
can be transformed into a short sequence of such linear eigenvalue problems.
The result is an eigensolver that is substantially faster than standard
techniques. By combining this new solver with our new optimization frameworks,
we obtain our overall algorithm for fast computation of optimal viscosities.
The efficiency and performance of our new methods are verified and illustrated
on several numerical examples.


  We investigate the competition between electron-solid and quantum-liquid
phases in graphene, which arise in partially filled Landau levels. The
differences in the wave function describing the electrons in the presence of a
perpendicular magnetic field in graphene with respect to the conventional
semiconductors, such as GaAs, can be captured in a form factor which carries
the Landau level index. This leads to a quantitative difference in the
electron-solid and -liquid energies. For the lowest Landau level, there is no
difference in the wave function of relativistic and non-relativistic systems.
We compute the cohesive energy of the solid phase analytically using a
Hartree-Fock Hamiltonian. The liquid energies are computed analytically as well
as numerically, using exact diagonalization. We find that the liquid phase
dominates in the n=1 Landau level, whereas the Wigner crystal and
electron-bubble phases become more prominent in the n=2 and n=3 Landau level.


  In this paper, we consider the Strichartz inequality for a fourth-order
Schr\"odinger equation on $\mathbb{R}^3$. We show that extremizers exist using
a linear profile decomposition. Based on the existence of extremizers, we use
the associated Euler-Lagrange equation to show that the extremizers have
exponential decay and consequently must be analytic. Furthermore, we also prove
that extremizers must have the even property
$|\widehat{f}(\xi)|=|\widehat{f}(-\xi)|$ almost everywhere.


  Quantum systems driven by a time-periodic field are a platform of condensed
matter physics where effective (quasi)stationary states, termed "Floquet
states", can emerge with external-field-dressed quasiparticles during driving.
They appear, for example, as a prethermal intermediate state in isolated driven
quantum systems or as a nonequilibrium steady state in driven open quantum
systems coupled to environment. Floquet states may have various intriguing
physical properties, some of which can be drastically different from those of
the original undriven systems in equilibrium. In this article, we review
fundamental aspects of Floquet states, and discuss recent topics and
applications of Floquet states in condensed matter physics.


  We prove the irreducibility of the space parametrizing branched covers of a
fixed Riemann surface $B$ of degree $d$, with at least 2d branch points, and
with monodromy group equal to $S_d$. The result is classical for $g(B)=0$. The
result is well-known for $g(B) > 0$, but we could find no reference.


  With the example of Proxima Centauri we discuss the feasibility of detecting
terrestrial planets (1 to a few M_Earth) using the high precision radial
velocity (RV) technique. If a very high RV precision for M stars is achieved
even planets with these extremely low masses become detectable. For Proxima Cen
(M5V), one of the prime targets of our M-stars planet search program using the
UVES spectrograph & iodine cell at the ESO VLT UT2, we obtain a long term RV
precision of 2.5 m/s. Based on numerical simulations we determine that this
level of precision would have already allowed us to detect planets with m sin i
= 4 to 6 M_Earth inside the habitable zone of Proxima Cen.


  We investigate the long-time evolution of magnetic fields generated by the
two-stream instability at ultra- and sub-relativistic astrophysical
collisionless shocks. Based on 3D PIC simulation results, we introduce a 2D toy
model of interacting current filaments. Within the framework of this model, we
demonstrate that the field correlation scale in the region far downstream the
shock grows nearly as the light crossing time, lambda(t) ~ ct, thus making the
diffusive field dissipation inefficient. The obtained theoretical scaling is
tested using numerical PIC simulations. This result extends our understanding
of the structure of collisionless shocks in gamma-ray bursts and other
astrophysical objects.


  Cosmological weak lensing has been a highly successful and rapidly developing
research field since the first detection of cosmic shear in 2000. However, it
has recently been pointed out in Yoo et al. that the standard weak lensing
formalism yields gauge-dependent results and, hence, does not meet the level of
accuracy demanded by the next generation of weak lensing surveys. Here, we show
that the Jacobi mapping formalism provides a solid alternative to the standard
formalism, as it accurately describes all the relativistic effects contributing
to the weak lensing observables. We calculate gauge-invariant expressions for
the distortion in the luminosity distance, the cosmic shear components and the
lensing rotation to linear order including scalar, vector and tensor
perturbations. In particular, the Jacobi mapping formalism proves that the
rotation is fully vanishing to linear order. Furthermore, the cosmic shear
components contain an additional term in tensor modes which is absent in the
results obtained with the standard formalism. Our work provides further support
and confirmation of the gauge-invariant lensing formalism needed in the era of
precision cosmology.


  The cover time of a finite connected graph is the expected number of steps
needed for a simple random walk on the graph to visit all the vertices. It is
known that the cover time on any n-vertex, connected graph is at least (1+o(1))
n log(n) and at most (1+o(1))(4/27)n^3. This paper proves that for
bounded-degree planar graphs the cover time is at least c n(log n)^2, and at
most 6n^2, where c is a positive constant depending only on the maximal degree
of the graph. The lower bound is established via use of circle packings.


  I review the properties of the interstellar medium in the Magellanic Clouds
and Local Group dwarf galaxies. The more massive, star-forming galaxies show a
complex, multi-phase ISM full of shells and holes ranging from very cold phases
(a few 10 K) to extremely hot gas (> 10^6 K). In environments with high UV
radiation fields the formation of molecular gas is suppressed, while in dwarfs
with low UV fields molecular gas can form at lower than typical Galactic column
densities. There is evidence of ongoing interactions, gas accretion, and
stripping of gas in the Local Group dwarfs. Some dwarf galaxies appear to be in
various stages of transition from gas-rich to gas-poor systems. No ISM was
found in the least massive dwarfs.


  e study the properties of the mean-type mappings ${\bf M}\colon I^p \to I^p$
of the form $${\bf
M}(x_1,\dots,x_p):=\big(M_1(x_{\alpha_{1,1}},\dots,x_{\alpha_{1,d_1}}),\dots,M_p(x_{\alpha_{p,1}},\dots,x_{\alpha_{p,d_p}})\big),$$
where $p$ and $d_i$-s are positive integers, each $M_i$ is a $d_i$-variable
mean on an interval $I \subset \mathbb{R}$, and $\alpha_{i,j}$-s are elements
from $\{1,\dots,p\}$.
  We show that, under some natural assumption on $M_i$-s, the problem of
existing the unique $\bf M$-invariant mean can be reduced to the ergodicity of
the directed graph with vertexes $\{1,\dots,p\}$ and edges $\{(\alpha_{i,j},i)
\colon i,j \text{ admissible}\}$.


  In this work, we develop a wavelet-inspired, $L^3$-based convex integration
framework for constructing weak solutions to the three-dimensional
incompressible Euler equations. The main innovations include a new multi-scale
building block, which we call an intermittent Mikado bundle; a wavelet-inspired
inductive set-up which includes assumptions on spatial and temporal support, in
addition to $L^p$ and pointwise estimates for Eulerian and Lagrangian
derivatives; and sharp decoupling lemmas, inverse divergence estimates, and
space-frequency localization technology which is well-adapted to functions
satisfying $L^p$ estimates for $p$ other than $1$, $2$, or $\infty$. We develop
these tools in the context of the Euler-Reynolds system, enabling us to give
both a new proof of the intermittent Onsager theorem (An Intermittent Onsager
Theorem, Inventiones Mathematicae, (2023), 233) in this paper, and a proof of
the $L^3$-based strong Onsager conjecture in a companion paper
(arXiv:2305.18509).


  Besides an indicator of the GDP, the Central Bank of Venezuela generates the
so called Monthly Economic Activity General Indicator. The a priori knowledge
of this indicator, which represents and sometimes even anticipates the
economy's fluctuations, could be helpful in developing public policies and in
investment decision making. The purpose of this study is forecasting the IGAEM
through non parametric methods, an approach that has proven effective in a wide
variety of problems in economics and finance.


  In this letter, we study the self-force in the Parikh-Wilczek tunneling model
of Hawking radiation for Reissner-Nordstroem black holes. We conclude that the
repulsive self-force speeds up the emission and the radiation becomes an
irreversible process. We also find an upper bound of charge-mass ratio for
emitted particles.


  We extend the three dimensional stringy black hole of Horne and Horowitz to
four dimensions. After a brief discussion of the global properties of the
metric, we discuss the stability of the background with respect to small
perturbations, following the methods of Gilbert and of Chandrasekhar. The
potential for axial perturbations is found to be positive definite.


  Recently, increasing efforts have been focused on Weakly Supervised Scene
Graph Generation (WSSGG). The mainstream solution for WSSGG typically follows
the same pipeline: they first align text entities in the weak image-level
supervisions (e.g., unlocalized relation triplets or captions) with image
regions, and then train SGG models in a fully-supervised manner with aligned
instance-level "pseudo" labels. However, we argue that most existing WSSGG
works only focus on object-consistency, which means the grounded regions should
have the same object category label as text entities. While they neglect
another basic requirement for an ideal alignment: interaction-consistency,
which means the grounded region pairs should have the same interactions (i.e.,
visual relations) as text entity pairs. Hence, in this paper, we propose to
enhance a simple grounding module with both object-aware and interaction-aware
knowledge to acquire more reliable pseudo labels. To better leverage these two
types of knowledge, we regard them as two teachers and fuse their generated
targets to guide the training process of our grounding module. Specifically, we
design two different strategies to adaptively assign weights to different
teachers by assessing their reliability on each training sample. Extensive
experiments have demonstrated that our method consistently improves WSSGG
performance on various kinds of weak supervision.


  Technological advances have enabled multiple countries to consider
implementing Smart City Infrastructure to provide in-depth insights into
different data points and enhance the lives of citizens. Unfortunately, these
new technological implementations also entice adversaries and cybercriminals to
execute cyber-attacks and commit criminal acts on these modern infrastructures.
Given the borderless nature of cyber attacks, varying levels of understanding
of smart city infrastructure and ongoing investigation workloads, law
enforcement agencies and investigators would be hard-pressed to respond to
these kinds of cybercrime. Without an investigative capability by
investigators, these smart infrastructures could become new targets favored by
cybercriminals.
  To address the challenges faced by investigators, we propose a common
definition of smart city infrastructure. Based on the definition, we utilize
the STRIDE threat modeling methodology and the Microsoft Threat Modeling Tool
to identify threats present in the infrastructure and create a threat model
which can be further customized or extended by interested parties. Next, we map
offences, possible evidence sources and types of threats identified to help
investigators understand what crimes could have been committed and what
evidence would be required in their investigation work. Finally, noting that
Smart City Infrastructure investigations would be a global multi-faceted
challenge, we discuss technical and legal opportunities in digital forensics on
Smart City Infrastructure.


  A degeneration of compact Kaehler manifolds gives rise to a monodromy action
on Betti moduli space H^1(X, G) = Hom(\pi_1(X),G)/G over smooth fibres with a
complex algebraic structure group G being either abelian or reductive. Assume
that the singularities of the central fibre is of normal crossing. When G = C,
the invariant cohomology classes arise from the global classes. This is no
longer true in general. In this paper, we produce large families of locally
invariant classes that do not arise from global ones for reductive G. These
examples exist even when G is abelian, as long as G contains multiple torsion
points. Finally, for general G, we make a new conjecture on local invariant
classes and produce some suggestive examples.


  In this contribution I briefly review the dynamics of strange mesons and
baryons with dense nuclear matter, paying a special attention to their presence
in the inner core of neutron stars and the consequences for the structure of
these compact stars.


  We have realized a quantum optics like Hanbury Brown and Twiss (HBT)
experiment by partitioning, on an electronic beam-splitter, single elementary
electronic excitations produced one by one by an on-demand emitter. We show
that the measurement of the output currents correlations in the HBT geometry
provides a direct counting, at the single charge level, of the elementary
excitations (electron/hole pairs) generated by the emitter at each cycle. We
observe the antibunching of low energy excitations emitted by the source with
thermal excitations of the Fermi sea already present in the input leads of the
splitter, which suppresses their contribution to the partition noise. This
effect is used to probe the energy distribution of the emitted wave-packets.


  It has been shown that the thin brane model in a five-dimensional Weyl
gravity can deal with the wrong-signed Friedmann-like equation in the
Randall--Sundrum-1 (RS1) model. In the Weyl brane model, there are also two
branes with opposite brane tensions, but the four-dimensional graviton (the
gravity zero mode) is localized near the negative tension brane, while our
four-dimensional universe is localized on the positive tension brane. In this
paper, we consider the mass spectra of various bulk matter fields (i.e.,
scalar, vector, and fermion fields) on the Weyl brane. It is shown that the
zero modes of those matter fields can be localized on the positive tension
brane under some conditions. The mass spectra of the bulk matter fields are
equidistant for the higher excited states, and relatively sparse for the lower
excited states. The size of the extra dimension determines the gap of the mass
spectra. We also consider the correction to the Newtonian potential in this
model and it is proportional to $1/r^{3}$.


  We report observations of 240 Cepheid variables obtained with the Near
Infrared Camera (NICMOS) through the F160W filter on the Hubble Space Telescope
(HST). The Cepheids are distributed across six recent hosts of Type Ia
supernovae (SNe Ia) and the "maser galaxy" NGC 4258, allowing us to directly
calibrate the peak luminosities of the SNe Ia from the precise, geometric
distance measurements provided by the masers. New features of our measurement
include the use of the same instrument for all Cepheid measurements across the
distance ladder and homogeneity of the Cepheid periods and metallicities thus
necessitating only a differential measurement of Cepheid fluxes and reducing
the largest systematic uncertainties in the determination of the fiducial SN Ia
luminosity. The NICMOS measurements reduce differential extinction in the host
galaxies by a factor of 5 over past optical data. Combined with an expanded of
240 SNe Ia at z<0.1 which define their magnitude-redshift relation, we find
H_0=74.2 +/-3.6, a 4.8% uncertainty including both statistical and systematic
errors. We show that the factor of 2.2 improvement in the precision of H_0 is a
significant aid to the determination of the equation-of-state of dark energy, w
= P/(rho c^2). Combined with the WMAP 5-year measurement of Omega_M h^2, we
find w= -1.12 +/- 0.12 independent of high-redshift SNe Ia or baryon acoustic
oscillations (BAO). This result is also consistent with analyses based on the
combination of high-z SNe Ia and BAO. The constraints on w(z) now with high-z
SNe Ia and BAO are consistent with a cosmological constant and improved by a
factor of 3 from the refinement in H_0 alone. We show future improvements in
H_0 are likely and will further contribute to multi-technique studies of dark
energy.


  Consider an eigenvector of the adjacency matrix of a G(n, p) graph. A nodal
domain is a connected component of the set of vertices where this eigenvector
has a constant sign. It is known that with high probability, there are exactly
two nodal domains for each eigenvector corresponding to a non-leading
eigenvalue. We prove that with high probability, the sizes of these nodal
domains are approximately equal to each other.


  We present our recent results on the Prandtl-Meyer reflection for supersonic
potential flow past a solid ramp. When a steady supersonic flow passes a solid
ramp, there are two possible configurations: the weak shock solution and the
strong shock solution. Elling-Liu's theorem (2008) indicates that the steady
supersonic weak shock solution can be regarded as a long-time asymptotics of an
unsteady flow for a class of physical parameters determined by certain
assumptions for potential flow. In this paper we discuss our recent progress in
removing these assumptions and establishing the stability theorem for steady
supersonic weak shock solutions as the long-time asymptotics of unsteady flows
for all the physical parameters for potential flow. We apply new mathematical
techniques developed in our recent work to obtain monotonicity properties and
uniform apriori estimates for weak solutions, which allow us to employ the
Leray-Schauder degree argument to complete the theory for the general case.


  Let $X$ be a two-dimensional smooth manifold with boundary $S^{1}$ and
$Y=[1,\infty)\times S^{1}$. We consider a family of complete surfaces arising
by endowing $X\cup_{S^{1}}Y$ with a parameter dependent Riemannian metric, such
that the restriction of the metric to $Y$ converges to the hyperbolic metric as
a limit with respect to the parameter. We describe the associated spectral and
scattering theory of the Laplacian for such a surface. We further show that on
$Y$ the zero $S^{1}$-Fourier coefficient of the generalized eigenfunction of
this Laplacian, as a family with respect to the parameter, approximates in a
certain sense, for large values of the spectral parameter, the zero
$S^{1}$-Fourier coefficient of the generalized eigenfunction of the Laplacian
for the case of a surface with hyperbolic cusp.


  Decentralization, which has backed the hyper growth of many blockchains,
comes at the cost of scalability. To understand this fundamental limitation,
this paper proposes a quantitative measure of blockchain decentralization, and
discusses its implications to various trust models and consensus algorithms.
Further, we identify the major challenges in blockchain decentralization. Our
key findings are that true decentralization is hard to achieve due to the
skewed mining power and that a fully decentralized blockchain inherently limits
scalability as it incurs a throughput upper bound and prevents scaling smart
contract execution. To address these challenges, we outline three research
directions to explore the trade-offs between decentralization and scalability.


  This report presents some studies of the gauge/string theory correspondence,
a deep relation that is possible to establish between quantum field theories
with local gauge symmetry and superstring theories including gravity. In its
original version, known as AdS/CFT duality, the correspondence involves N=4
Super Yang-Mills theory in four space-time dimensions, which is a
superconformal theory with a high degree of supersymmetry, thus very far from
describing the physical world.
  We explore extensions of the correspondence towards less supersymmetric and
non-conformal gauge theories. Specifically, we study gauge theories in three
and four dimensions, with eight or four preserved supersymmetries and
exhibiting a scale anomaly, by means of supergravity solutions describing
D-brane configurations of type II string theory. We show how relevant
information on these gauge theories can be extracted from the dual classical
solutions, both at the perturbative (e.g. running coupling constant, chiral
anomaly) and non-perturbative level (e.g. effective superpotential).


  We present a bound for the weak Lindel\"of number of the
$G_\delta$-modification of a Hausdorff space which implies various known
cardinal inequalities, including the following two fundamental results in the
theory of cardinal invariants in topology: $|X|\le 2^{L(X)\chi(X)}$
(Arhangel'skii) and $|X|\le 2^{c(X)\chi (X)}$ (Hajnal-Juhasz). This solves a
question that goes back to Bell, Ginsburg and Woods and is mentioned in Hodel's
survey on Arhangel'skii's Theorem. In contrast to previous attempts we do not
need any separation axiom beyond $T_2$.


  Quantum technologies present new opportunities for fundamental tests of
nature. One potential application is to probe the interplay between quantum
physics and general relativity - a field of physics with no empirical evidence
yet. Here we show that quantum networks open a new window to test this
interface. We demonstrate how photon mediated entanglement between atomic or
atom-like systems can be used to probe time-dilation induced entanglement and
interference modulation. Key are non-local measurements between clocks in a
gravitational field, which can be achieved either through direct photon
interference or by using auxiliary entanglement. The resulting observable
depends on the interference between different proper times, and can only be
explained if both quantum theory and general relativity are taken into account.
The proposed protocol enables clock interferometry on km-scale separations and
beyond. Our work thus shows a realistic experimental route for a first test of
quantum theory on curved space-time, opening up new scientific opportunities
for quantum networks.


  Estimating 3D rotations is a common procedure for 3D computer vision. The
accuracy depends heavily on the rotation representation. One form of
representation -- rotation matrices -- is popular due to its continuity,
especially for pose estimation tasks. The learning process usually incorporates
orthogonalization to ensure orthonormal matrices. Our work reveals, through
gradient analysis, that common orthogonalization procedures based on the
Gram-Schmidt process and singular value decomposition will slow down training
efficiency. To this end, we advocate removing orthogonalization from the
learning process and learning unorthogonalized `Pseudo' Rotation Matrices
(PRoM). An optimization analysis shows that PRoM converges faster and to a
better solution. By replacing the orthogonalization incorporated representation
with our proposed PRoM in various rotation-related tasks, we achieve
state-of-the-art results on large-scale benchmarks for human pose estimation.


  We study strong and radiative decays of excited singly heavy baryons (SHBs)
using an effective chiral Lagrangian based on the diquark picture proposed in
Ref. [1]. The effective Lagrangian contains a $U_A (1)$ anomaly term, which
induces an inverse mass ordering between strange and non-strange SHBs with
spin-parity $1/2^-$. We find that the effect of the $U_A (1)$ anomaly combined
with flavor-symmetry breaking modifies the Goldberger-Treiman relation for the
mass difference between the ground state $\Lambda_Q (1/2^+)$ and its chiral
partner $\Lambda_Q (1/2^-)$, and $\Lambda_Q (1/2^-) \Lambda_Q (1/2^+) \eta$
coupling, which results in suppression of the decay width of $\Lambda_Q (1/2^-)
\to \Lambda_Q (1/2^+) \eta$. We also investigate the other various decays such
as $\Lambda_Q (1/2^-) \to \Sigma_Q (1/2^+, \, 3/2^+) \pi \pi$, $\Lambda_Q
(1/2^-) \to \Sigma_Q (1/2^+) \pi$, $\Lambda_Q (1/2^-) \to \Sigma_Q (1/2^+, \,
3/2^+) \gamma$, and $\Lambda_Q (1/2^-) \to \Lambda_Q (1/2^+) \pi^0$ for wide
range of mass of $\Lambda_Q (1/2^-)$.


  We investigate perfect codes in $\mathbb{Z}^n$ under the $\ell_p$ metric.
Upper bounds for the packing radius $r$ of a linear perfect code, in terms of
the metric parameter $p$ and the dimension $n$ are derived. For $p = 2$ and $n
= 2, 3$, we determine all radii for which there are linear perfect codes. The
non-existence results for codes in $\mathbb{Z}^n$ presented here imply
non-existence results for codes over finite alphabets $\mathbb{Z}_q$, when the
alphabet size is large enough, and has implications on some recent
constructions of spherical codes.


  Domestic violence, which is often perceived as a gendered issue among female
victims, has gained increasing attention in recent years. Despite this focus,
male victims of domestic abuse remain primarily overlooked, particularly in
Bangladesh. Our study represents a pioneering exploration of the underexplored
realm of male domestic violence (MDV) within the Bangladeshi context, shedding
light on its prevalence, patterns, and underlying factors. Existing literature
predominantly emphasizes female victimization in domestic violence scenarios,
leading to an absence of research on male victims. We collected data from the
major cities of Bangladesh and conducted exploratory data analysis to
understand the underlying dynamics. We implemented 11 traditional machine
learning models with default and optimized hyperparameters, 2 deep learning,
and 4 ensemble models. Despite various approaches, CatBoost has emerged as the
top performer due to its native support for categorical features, efficient
handling of missing values, and robust regularization techniques, achieving 76%
accuracy. In contrast, other models achieved accuracy rates in the range of
58-75%. The eXplainable AI techniques, SHAP and LIME, were employed to gain
insights into the decision-making of black-box machine learning models. By
shedding light on this topic and identifying factors associated with domestic
abuse, the study contributes to identifying groups of people vulnerable to MDV,
raising awareness, and informing policies and interventions aimed at reducing
MDV. Our findings challenge the prevailing notion that domestic abuse primarily
affects women, thus emphasizing the need for tailored interventions and support
systems for male victims. ML techniques enhance the analysis and understanding
of the data, providing valuable insights for developing effective strategies to
combat this pressing social issue.


  We study the light scattered from randomly rough, one-dimensional self-affine
fractal silver surfaces with nanoscale lower cutoff, illuminated by s- or
p-polarized Gaussian beams a few microns wide. By means of rigorous numerical
calculations based on the Green theorem integral equation formulation, we
obtain both the far- and near-field scattered intensities. The influence of
diminishing the fractal lower scale cutoff (from below a hundred, down to a few
nanometers) is analyzed in the case of both single realizations and ensemble
average magnitudes. For s polarization, variations are small in the far field,
being only significant in the higher spatial frequency components of evanescent
character in the near field. In the case of p polarization, however, the
nanoscale cutoff has remarkable effects stemming from the roughness-induced
excitation of surface-plasmon polaritons. In the far field, the effect is
noticed both in the speckle pattern variation and in the decrease of the total
reflected energy upon ensemble averaging, due to increased absorption. In the
near field, more efficient excitation of localized optical modes is achieved
with smaller cutoff, which in turn leads to huge surface electric field
enhancements.


  Let $V$ be a smooth, projective, convex variety. We define tautological
$\psi$ and $\kappa$ classes on the moduli space of stable maps $\M_{0,n}(V)$,
give a (graphical) presentation for these classes in terms of boundary strata,
derive differential equations for the generating functions of the Gromov-Witten
invariants of $V$ twisted by these tautological classes, and prove that these
intersection numbers are completely determined by the Gromov-Witten invariants
of $V$. This results in families of Frobenius manifold structures on the
cohomology ring of $V$ which includes the quantum cohomology as a special case.


  With the widespread use of toxic language online, platforms are increasingly
using automated systems that leverage advances in natural language processing
to automatically flag and remove toxic comments. However, most automated
systems -- when detecting and moderating toxic language -- do not provide
feedback to their users, let alone provide an avenue of recourse for these
users to make actionable changes. We present our work, RECAST, an interactive,
open-sourced web tool for visualizing these models' toxic predictions, while
providing alternative suggestions for flagged toxic language. Our work also
provides users with a new path of recourse when using these automated
moderation tools. RECAST highlights text responsible for classifying toxicity,
and allows users to interactively substitute potentially toxic phrases with
neutral alternatives. We examined the effect of RECAST via two large-scale user
evaluations, and found that RECAST was highly effective at helping users reduce
toxicity as detected through the model. Users also gained a stronger
understanding of the underlying toxicity criterion used by black-box models,
enabling transparency and recourse. In addition, we found that when users focus
on optimizing language for these models instead of their own judgement (which
is the implied incentive and goal of deploying automated models), these models
cease to be effective classifiers of toxicity compared to human annotations.
This opens a discussion for how toxicity detection models work and should work,
and their effect on the future of online discourse.


  Efficient transport algorithms are essential to the numerical resolution of
incompressible fluid flow problems. Semi-Lagrangian methods are widely used in
grid based methods to achieve this aim. The accuracy of the interpolation
strategy then determines the properties of the scheme. We introduce a simple
multi-stage procedure which can easily be used to increase the order of
accuracy of a code based on multi-linear interpolations. This approach is an
extension of a corrective algorithm introduced by Dupont \& Liu (2003, 2007).
This multi-stage procedure can be easily implemented in existing parallel codes
using a domain decomposition strategy, as the communications pattern is
identical to that of the multi-linear scheme. We show how a combination of a
forward and backward error correction can provide a third-order accurate
scheme, thus significantly reducing diffusive effects while retaining a
non-dispersive leading error term.


  Let $ \{T_n\}_{n\geq 0} $ be the sequence of Tribonacci numbers. In this
paper, we study the exponential Diophantine equation $T_n-2^x3^y=c$, for
$n,x,y\in \mathbb{Z}_{\ge0}$. In particular, we show that there is no integer
$c$ with at least six representations of the form $T_n-2^x3^y$.


  We report on the strong coupling between a metallic ferromagnetic Fe75Co25
thin film patterned element and a range of superconducting Nb half-wavelength
co-planar waveguide (CPW) resonators. By varying the volume of the ferromagnet
we demonstrate that the coupling rate scales linearly with the square root of
the number of spins and achieve a coupling rate over 700 MHz, approaching the
ultrastrong coupling regime. Experiments varying the center conductor width
while maintaining constant magnetic volume verify that decreasing the center
conductor width increases coupling and cooperativity. Our results show that the
frequency dependence of the coupling rate is linear with the fundamental and
higher order odd harmonics of the CPW, but with differing efficiencies. The
results show promise for scaling planar superconducting resonator/magnetic
hybrid systems to smaller dimensions.


  In this short note, we reformulate the task of calculating the pair
correlation statistics of a Kronecker sequence as a lattice point counting
problem. This can be done analogously to the lattice based approach which was
used to (re-)prove the famous three gap property for Kronecker sequences. We
show that recently developed lattice point counting techniques can then be
applied to derive that a certain class of Kronecker sequences have $\beta$-pair
correlations for all $0 < \beta < 1$.


  Increasing evidence suggests that, similar to face-to-face communications,
human emotions also spread in online social media. However, the mechanisms
underlying this emotional contagion, for example, whether different feelings
spread in unlikely ways or how the spread of emotions relates to the social
network, is rarely investigated. Indeed, because of high costs and
spatio-temporal limitations, explorations of this topic are challenging using
conventional questionnaires or controlled experiments. Because they are
collection points for natural affective responses of massive individuals,
online social media sites offer an ideal proxy for tackling this issue from the
perspective of computational social science. In this paper, based on the
analysis of millions of tweets in Weibo, surprisingly, we find that anger is
more contagious than joy, indicating that it can spark more angry follow-up
tweets. Moreover, regarding dissemination in social networks, anger travels
easily along weaker ties than joy, meaning that it can infiltrate different
communities and break free of local traps because strangers share such content
more often. Through a simple diffusion model, we reveal that greater contagion
and weaker ties function cooperatively to speed up anger's spread. The
diffusion of real-world events with different dominant emotions provides
further testimony to the findings. To the best of our knowledge, this is the
first time that quantitative long-term evidence has been presented that reveals
a difference in the mechanism by which joy and anger are disseminated. Our
findings shed light on both personal anger management in human communications
and on controlling collective outrage in cyberspace.


  In this paper we present a new approach for the generation of
multi-instrument symbolic music driven by musical emotion. The principal
novelty of our approach centres on conditioning a state-of-the-art transformer
based on continuous-valued valence and arousal labels. In addition, we provide
a new large-scale dataset of symbolic music paired with emotion labels in terms
of valence and arousal. We evaluate our approach in a quantitative manner in
two ways, first by measuring its note prediction accuracy, and second via a
regression task in the valence-arousal plane. Our results demonstrate that our
proposed approaches outperform conditioning using control tokens which is
representative of the current state of the art.


  ZnAs2 nanoclusters were fabricated by incorporation into pores of zeolite
Na-X and by laser ablation. Absorption and photoluminescence spectra of ZnAs2
nanoclusters in zeolite were measured at the temperatures of 4.2, 77 and 293 K.
Both absorption and PL spectra consist of two bands which demonstrate the blue
shift from the line of free exciton in bulk crystal. We performed the
calculations aimed to find the most stable clusters in the size region up to
size of the zeolite Na-X supercage. The most stable clusters are (ZnAs2)6 and
(ZnAs2)8 with binding energies of 7.181 eV and 8.012 eV per (ZnAs2)1 formula
unit respectively. Therefore, we attributed two bands observed in absorption
and PL spectra to these stable clusters. The measured Raman spectrum of ZnAs2
clusters in zeolite was explained to be originated from (ZnAs2)6 and (ZnAs2)8
clusters as well. The PL spectrum of ZnAs2 clusters produced by laser ablation
consists of a single band which has been attributed to emission of (ZnAs2)8
cluster.


  I give a pedagogical summary of the methods of light-cone variables, rapidity
and pseudo-rapidity. Then I show how these methods are useful in analyzing
diffractive high-energy collisions.


  In this paper, a new speech feature fusion method is proposed for speaker
recognition on the basis of the cross gate parallel convolutional neural
network (CG-PCNN). The Mel filter bank features (MFBFs) of different frequency
resolutions can be extracted from each speech frame of a speaker's speech by
several Mel filter banks, where the numbers of the triangular filters in the
Mel filter banks are different. Due to the frequency resolutions of these MFBFs
are different, there are some complementaries for these MFBFs. The CG-PCNN is
utilized to extract the deep features from these MFBFs, which applies a cross
gate mechanism to capture the complementaries for improving the performance of
the speaker recognition system. Then, the fusion feature can be obtained by
concatenating these deep features for speaker recognition. The experimental
results show that the speaker recognition system with the proposed speech
feature fusion method is effective, and marginally outperforms the existing
state-of-the-art systems.


  Multi-sensor fusion stands as a pivotal technique in addressing numerous
safety-critical tasks and applications, e.g., self-driving cars and automated
robotic arms. With the continuous advancement in data-driven artificial
intelligence (AI), MSF's potential for sensing and understanding intricate
external environments has been further amplified, bringing a profound impact on
intelligent systems and specifically on their perception systems. Similar to
traditional software, adequate testing is also required for AI-enabled MSF
systems. Yet, existing testing methods primarily concentrate on single-sensor
perception systems (e.g., image-/point cloud-based object detection systems).
There remains a lack of emphasis on generating multi-modal test cases for MSF
systems. To address these limitations, we design and implement MultiTest, a
fitness-guided metamorphic testing method for complex MSF perception systems.
MultiTest employs a physical-aware approach to synthesize realistic multi-modal
object instances and insert them into critical positions of background images
and point clouds. A fitness metric is designed to guide and boost the test
generation process. We conduct extensive experiments with five SOTA perception
systems to evaluate MultiTest from the perspectives of: (1) generated test
cases' realism, (2) fault detection capabilities, and (3) performance
improvement. The results show that MultiTest can generate realistic and
modality-consistent test data and effectively detect hundreds of diverse faults
of an MSF system under test. Moreover, retraining an MSF system on the test
cases generated by MultiTest can improve the system's robustness.


  We report finding kiloparsec-scale radio emissions aligned with parsec-scale
jet structures in the narrow-line Seyfert 1 (NLS1) galaxy Mrk 1239 using the
Very Large Array and the Very Long Baseline Array. Thus, this radio-quiet NLS1
has a jet-producing central engine driven by essentially the same mechanism as
that of other radio-loud active galactic nuclei (AGNs). Most of the radio
luminosity is concentrated within 100 parsecs and overall radio morphology
looks edge-darkened; the estimated jet kinetic power is comparable to
Fanaroff--Riley Type I radio galaxies. The conversion from accretion to jet
power appears to be highly inefficient in this highly accreting low-mass black
hole system compared with that in a low-luminosity AGN with similar radio power
driven by a sub-Eddington, high-mass black hole. Thus, Mrk 1239 is a crucial
probe to the unexplored parameter spaces of central engines for a jet
formation.


  We solve, using localization, for the large-N master field of N=2*
super-Yang-Mills theory. From that we calculate expectation values of large
Wilson loops and the free energy on the four-sphere. At weak coupling, these
observables only receive non-perturbative contributions. The analytic solution
holds for a finite range of the 't Hooft coupling and terminates at the point
of a large-N phase transition. We find evidence that as the coupling is further
increased the theory undergoes an infinite sequence of similar transitions that
accumulate at infinity.


  In this paper, we propose a green beamforming design for the integrated
sensing and communication (ISAC) system, using beam-matching error to assess
radar performance. The beam-matching error metric, which considers the mean
square error between the desired and designed beam patterns, provides a more
practical evaluation approach. To tackle the non-convex challenge inherent in
beamforming design, we apply semidefinite relaxation (SDR) to address the
rank-one relaxation issue, followed by the iterative rank minimization
algorithm (IRM) for rank-one recovery. The simulation results showcase the
effectiveness of our proposed optimal beamforming design, emphasizing the
exceptional performance of the radar component in sensing tasks.


  We consider some local entropy properties of dynamical systems under the
assumption of shadowing. In the first part, we give necessary and sufficient
conditions for shadowable points to be certain entropy points. In the second
part, we give some necessary and sufficient conditions for (non)
h-expansiveness under the assumption of shadowing and chain transitivity; and
use the result to present a counter-example for a question raised by Artigue et
al. [Proc. Amer. Math. Soc. 150 (2022), 3369-3378].


  A novel way of defining limits in classical statistics is proposed. This is a
natural extension of the original Neyman's method, and has the desirable
property that only information relevant to the problem is used in making
statistical inferences. The result is a strong restriction on the allowed
confidence bands, excluding in full generality pathologies as empty confidence
regions or unstable solutions. The method is completely general and directly
applicable to all problems of limits.


  Although shape correspondence is a central problem in geometry processing,
most methods for this task apply only to two-dimensional surfaces. The
neglected task of volumetric correspondence--a natural extension relevant to
shapes extracted from simulation, medical imaging, and volume
rendering--presents unique challenges that do not appear in the two-dimensional
case. In this work, we propose a method for mapping between volumes represented
as tetrahedral meshes. Our formulation minimizes a distortion energy designed
to extract maps symmetrically, i.e., without dependence on the ordering of the
source and target domains. We accompany our method with theoretical discussion
describing the consequences of this symmetry assumption, leading us to select a
symmetrized ARAP energy that favors isometric correspondences. Our final
formulation optimizes for near-isometry while matching the boundary. We
demonstrate our method on a diverse geometric dataset, producing low-distortion
matchings that align closely to the boundary.


  Harmonic potentials provide globally convergent potential fields that are
provably free of local minima. Due to its analytical format, it is particularly
suitable for generating safe and reliable robot navigation policies. However,
for complex environments that consist of a large number of overlapping
non-sphere obstacles, the computation of associated transformation functions
can be tedious. This becomes more apparent when: (i) the workspace is initially
unknown and the underlying potential fields are updated constantly as the robot
explores it; (ii) the high-level mission consists of sequential navigation
tasks among numerous regions, requiring the robot to switch between different
potentials. Thus, this work proposes an efficient and automated scheme to
construct harmonic potentials incrementally online as guided by the task
automaton. A novel two-layer harmonic tree (HT) structure is introduced that
facilitates the hybrid combination of oriented search algorithms for task
planning and harmonic-based navigation controllers for non-holonomic robots.
Both layers are adapted efficiently and jointly during online execution to
reflect the actual feasibility and cost of navigation within the updated
workspace. Global safety and convergence are ensured both for the high-level
task plan and the low-level robot trajectory. Known issues such as oscillation
or long-detours for purely potential-based methods and sharp-turns or high
computation complexity for purely search-based methods are prevented. Extensive
numerical simulation and hardware experiments are conducted against several
strong baselines.


  This paper aims at obtaining, by means of integral transforms, analytical
approximations in short times of solutions to boundary value problems for the
one-dimensional reaction-diffusion equation with constant coefficients. The
general form of the equation is considered on a bounded generic interval and
the three classical types of boundary conditions, i.e., Dirichlet as well as
Neumann and mixed boundary conditions are considered in a unified way. The
Fourier and Laplace integral transforms are successively applied and an exact
solution is obtained in the Laplace domain. This operational solution is proven
to be the accurate Laplace transform of the infinite series obtained by the
Fourier decomposition method and presented in the literature as solutions to
this type of problem. On the basis of this unified operational solution, four
cases are distinguished where innovative formulas expressing consistent
analytical approximations in short time limits are derived with respect to the
behavior of the solution at the boundaries. Compared to the infinite series
solutions, the analytical approximations may open new perspectives and
applications, among which can be noted the improvement of numerical efficiency
in simulations of one-dimensional moving boundary problems, such as in Stefan
models.


  We present an end-to-end framework to learn partial differential equations
that brings together initial data production, selection of boundary conditions,
and the use of physics-informed neural operators to solve partial differential
equations that are ubiquitous in the study and modeling of physics phenomena.
We first demonstrate that our methods reproduce the accuracy and performance of
other neural operators published elsewhere in the literature to learn the 1D
wave equation and the 1D Burgers equation. Thereafter, we apply our
physics-informed neural operators to learn new types of equations, including
the 2D Burgers equation in the scalar, inviscid and vector types. Finally, we
show that our approach is also applicable to learn the physics of the 2D linear
and nonlinear shallow water equations, which involve three coupled partial
differential equations. We release our artificial intelligence surrogates and
scientific software to produce initial data and boundary conditions to study a
broad range of physically motivated scenarios. We provide the source code, an
interactive website to visualize the predictions of our physics informed neural
operators, and a tutorial for their use at the Data and Learning Hub for
Science.


  We study Picard groups in profinite perfectoid limits of rigid spaces in the
case of good reduction. Our main result is that for sufficiently large covers,
these can be described in terms of the special fibre: For example, our
description implies that for a supersingular variety $X$ of good reduction
$\bar{X}$ over a perfectoid field of characteristic $p$,
  \[\mathrm{Pic}(X^{perf})=\mathrm{Pic}(\bar{X})[1/p].\] Via Raynaud
uniformisation, it moreover allows us to describe Picard groups of pro-\'etale
covers of abeloid varieties, which has applications to pro-\'etale
uniformisation.
  We use our results to answer some general questions about Picard groups and
Picard functors of perfectoid spaces, e.g. we show that these are not always
$p$-divisible. Along the way we construct a "multiplicative Hodge--Tate
spectral sequence" for $\mathcal{O}^\times$.
  This is part III of a series on line bundles on diamonds.


  In the framework of the Regge-eikonal model of hadron interaction, based on
the analyticity of the scattering amplitude with taking into account the hadron
structure, the simultaneous analysis is carried out of the 90 sets of data.
These sets include the data obtained at low energies ($\sqrt{s} > 3.6 $ GeV and
at high energies at FNAL, ISR, $S\bar{p}pS$, TEVATRON and LHC with 4326
experimental points, including the polarization data of analysing power. The
energy and momentum transfer dependence of separate sets of data is analyzed on
the basis of the eikonalized Born amplitude with taking into account two
additional anomalous terms. Different origins of the nonlinear behavior of the
slope of the scattering amplitude are compared. No contribution of hard-Pomeron
in the elastic hadron scattering is shown. However, the importance of Odderon's
contribution is presented. The form and energy dependence of different terms of
the cross-even and cross-odd parts of the elastic nucleon-nucleon scattering
amplitude is determined in the framework of the High Energy Generalize
Structure (HEGS) model. In the framework of the HEGS model, using the
electromagnetic and gravitomagnetic form factors, the differential cross
sections in the Coulomb Nuclear Interference (CNI) region and at large momentum
transfer are described well in a wide energy region simultaneously. It is shown
that the cross-even part includes the soft pomeron growing like $\ln^{2}(s)$
and an additional term with a large slope and with and with energy dependence
$\ln^2(s)$. The cross-odd part includes the maximal odderon term and an
additional oscillation term with $\ln(s)$. It is shown that both additional
terms are proportional to charge distributions but the maximal odderon term is
proportional to matter distributions.


  We address the question of how to improve the agreement between theoretical
nuclear single-particle energies (SPEs) and experiment. Empirically, in doubly
magic nuclei, the SPEs can be deduced from spectroscopic properties of odd
nuclei that have one more, or one less neutron or proton. Theoretically, bare
SPEs, before being confronted with experiment, must be corrected for the
effects of the particle-vibration-coupling (PVC). In the present work, we
determine the PVC corrections in a fully self-consistent way. Then, we adjust
the SPEs, with PVC corrections included, to empirical data. In this way, the
agreement with experiment, on average, improves; nevertheless, large
discrepancies still remain. We conclude that the main source of disagreement is
still in the underlying mean fields, and not in including or neglecting the PVC
corrections.


  In the rapidly evolving fields of Artificial Intelligence (AI) and Machine
Learning (ML), the reproducibility crisis underscores the urgent need for clear
validation methodologies to maintain scientific integrity and encourage
advancement. The crisis is compounded by the prevalent confusion over
validation terminology. Responding to this challenge, we introduce a validation
framework that clarifies the roles and definitions of key validation efforts:
repeatability, dependent and independent reproducibility, and direct and
conceptual replicability. This structured framework aims to provide AI/ML
researchers with the necessary clarity on these essential concepts,
facilitating the appropriate design, conduct, and interpretation of validation
studies. By articulating the nuances and specific roles of each type of
validation study, we hope to contribute to a more informed and methodical
approach to addressing the challenges of reproducibility, thereby supporting
the community's efforts to enhance the reliability and trustworthiness of its
research findings.


  We prove that any closed connected exact Lagrangian manifold L in a connected
cotangent bundle T*N is up to a finite covering space lift a homology
equivalence. We prove this by constructing a fibrant parametrized family of
ring spectra FL parametrized by the manifold N. The homology of FL will be
(twisted) symplectic cohomology of T*L. The fibrancy property will imply that
there is a Serre spectral sequence converging to the homology of FL and the
product combined with intersection product on N induces a product on this
spectral sequence. This product structure and its relation to the intersection
product on L is then used to obtain the result. Combining this result with work
of Abouzaid we arrive at the conclusion that L -> N is always a homotopy
equivalence.


  Information Synchronization of semi-structured data across languages is
challenging. For instance, Wikipedia tables in one language should be
synchronized across languages. To address this problem, we introduce a new
dataset InfoSyncC and a two-step method for tabular synchronization. InfoSync
contains 100K entity-centric tables (Wikipedia Infoboxes) across 14 languages,
of which a subset (3.5K pairs) are manually annotated. The proposed method
includes 1) Information Alignment to map rows and 2) Information Update for
updating missing/outdated information for aligned tables across multilingual
tables. When evaluated on InfoSync, information alignment achieves an F1 score
of 87.91 (en <-> non-en). To evaluate information updation, we perform
human-assisted Wikipedia edits on Infoboxes for 603 table pairs. Our approach
obtains an acceptance rate of 77.28% on Wikipedia, showing the effectiveness of
the proposed method.