  The abundances of chemical elements and their depletion factors are essential
parameters for understanding the composition of the gas and dust that are
ultimately incorporated into stars and planets. Sulfur is an abundant but
peculiar element in the sense that, despite being less volatile than other
elements (e.g., carbon), it is not a major constituent of dust grains in
diffuse interstellar clouds. Here, we determine the gas-phase carbon-to-sulfur
abundance ratio, [C]/[S], and the sulfur abundance [S] in a dense star-forming
cloud from new radio recombination lines (RRLs) detected with the Yebes 40m
telescope - at relatively high frequencies (~40 GHz ~7 mm) and angular
resolutions (down to 36'') - in the Orion Bar, a rim of the Orion Molecular
Cloud (OMC). We detect nine Cn\alpha RRLs (with n=51 to 59) as well as nine
narrow line features separated from the Cn\alpha lines by delta v=-8.4+/-0.3 km
s^-1. Based on this velocity separation, we assign these features to sulfur
RRLs, with little contribution of RRLs from the more condensable elements Mg,
Si, or Fe. Sulfur RRLs lines trace the photodissociation region (PDR) of the
OMC. In these predominantly neutral gas layers, up to A_V~4, the ions C+ and S+
lock in most of the C and S gas-phase reservoir. We determine a relative
abundance of [C]_Ori/[S]_Ori=10.4+/-0.6 and, adopting the same [C]_Ori measured
in the translucent gas toward star theta^1 Ori B, an absolute abundance of
[S]_Ori=(1.4+/-0.4)x10^-5. This value is consistent with emission models of the
observed sulfur RRLs if N(S+)~7x10^17 cm^-2 (beam-averaged). The [S]_Ori is the
''initial'' sulfur abundance in the OMC, before an undetermined fraction of the
[S]_Ori goes into molecules and ice mantles in the cloud interior. The inferred
abundance [S]_Ori matches the solar abundance, thus implying that there is
little depletion of sulfur onto rocky dust grains, with D(S)=0.0+/-0.2 dex.


  The Ising spin-glasses are investigated on three dual pairs of hierarchical
lattices, using exact renormalization-group transformation of the quenched bond
probability distribution. The goal is to investigate a recent conjecture which
relates, on such pairs of dual lattices, the locations of the multicritical
points, which occur on the Nishimori symmetry line. Towards this end we
precisely determine the global phase diagrams for these six hierarchical
spin-glasses, using up to 2.5 x 10^9 probability bins to represent the quenched
distribution subjected to an exact renormalization-group transformation. We
find in all three cases that the conjecture is realized to a very good
approximation, even when the mutually dual models belong to different spatial
dimensionalities d and have different phase diagram topologies at the
multicritical points of the conjecture and even though the contributions to the
conjecture from each lattice of the dual pair are strongly asymmetric. In all
six phase diagrams, we find reentrance near the multicritical point. In the
models with d=2 or 1.5, the spin-glass phase does not occur and the phase
boundary between the ferromagnetic and paramagnetic phases is second order with
a strong violation of universality. PACS numbers: 75.10.Nr, 64.60.Kw, 05.45.Df,
05.10.Cc


  We introduce a natural but seemingly yet unstudied generalization of the
problem of scheduling jobs on a single machine so as to minimize the number of
tardy jobs. Our generalization lies in simultaneously considering several
instances of the problem at once. In particular, we have $n$ clients over a
period of $m$ days, where each client has a single job with its own processing
time and deadline per day. Our goal is to provide a schedule for each of the
$m$ days, so that each client is guaranteed to have their job meet its deadline
in at least $k \le m$ days. This corresponds to an equitable schedule where
each client is guaranteed a minimal level of service throughout the period of
$m$ days. We provide a thorough analysis of the computational complexity of
three main variants of this problem, identifying both efficient algorithms and
worst-case intractability results.


  We study theoretically the electromagnon and its optical spectrum (OS) of the
terahertz-frequency regime in the magnetic-spiral-induced multiferroic phases
of the rare-earth (R) Mn perovskites, RMnO3, taking into account the elliptical
deformation or the higher harmonics of the spiral spin configuration, which has
been missed so far. A realistic spin Hamiltonian, which gives phase diagrams in
agreement with experiments, resolves a long standing puzzle, i.e., the
double-peak structure of the OS with a larger low-energy peak originating from
magnon modes hybridized with the zone-edge state. We also predict the magnon
branches associated with the electromagnon, which can be tested by
neutron-scattering experiment.


  With the exponential increase of the number of devices in the communication
ecosystem toward the upcoming sixth generation (6G) of wireless networks, more
enabling technologies and potential wireless architectures are necessary to
fulfill the networking requirements of high throughput, massive connectivity,
ultra reliability, and heterogeneous quality of service (QoS). In this work, we
consider an uplink network consisting of a primary user (PU) and a secondary
user (SU) and, by integrating the concept of cognitive radio and multiple
access, two protocols based on rate-splitting multiple access and
non-orthogonal multiple access with successive interference cancellation are
investigated in terms of ergodic rate. The considered protocols aim to serve
the SU in a resource block which is originally allocated solely for the PU
without negatively affecting the QoS of the PU. We extract the ergodic rate of
the SU considering a specific QoS for the PU for the two protocols. In the
numerical results, we validate the theoretical analysis and illustrate the
superiority of the considered protocols over two benchmark schemes.


  Accurate and efficient entity resolution is an open challenge of particular
relevance to intelligence organisations that collect large datasets from
disparate sources with differing levels of quality and standard. Starting from
a first-principles formulation of entity resolution, this paper presents a
novel Entity Resolution algorithm that introduces a data-driven blocking and
record-linkage technique based on the probabilistic identification of entity
signatures in data. The scalability and accuracy of the proposed algorithm are
evaluated using benchmark datasets and shown to achieve state-of-the-art
results. The proposed algorithm can be implemented simply on modern parallel
databases, which allows it to be deployed with relative ease in large
industrial applications.


  Based on Schreyer's algorithm (Schreyer, 1980, 1991; Berkesch and Schreyer,
2014), we present two refined algorithms for the computation of syzygies. The
two main ideas of the first algorithm, called LiftHybrid, are the following:
First, we may leave out certain terms of module elements during the computation
which do not contribute to the result. These terms are called "lower order
terms", see Definition 4.2. Second, we do not need to order the remaining terms
of these module elements during the computation. This significantly reduces the
number of monomial comparisons for the arithmetic operations. For the second
algorithm, called LiftTree, we additionally cache some partial results and
reuse them at the remaining steps.


  Nowadays it is widely accepted that the evolution of the universe was driven
by some scalar degrees of freedom both on its early stage and at present. The
corresponding cosmological models often involve some scalar fields introduced
ad hoc. In this paper we cultivate a different approach, which is based on a
derivation of new scalar degrees of freedom from fundamental modifications of
Einstein's gravity. In elaboration of our previous work, we here investigate
properties of the dilaton-scalar gravity obtained by dimensional reductions of
a recently proposed affine generalized gravity theory. We show that these
models possess the same symmetries as related models of GR with ordinary scalar
fields. As a result, for a rather general class of dilaton-scalar gravity
models we construct additional first integrals and formulate an integral
equation well suited for solving by iterations.


  General quantum gravity arguments predict that Lorentz symmetry might not
hold exactly in nature. This has motivated much interest in Lorentz breaking
gravity theories recently. Among such models are vector-tensor theories with
preferred direction established at every point of spacetime by a fixed-norm
vector field. The dynamical vector field defined in this way is referred to as
the \textquotedblleft aether." In this paper, we put forward the idea of a
\textit{null} aether field and introduce, for the first time, the Null Aether
Theory (NAT)--a vector-tensor theory. We first study the Newtonian limit of
this theory and then construct exact spherically symmetric black hole solutions
in the theory in four dimensions, which contain Vaidya-type non-static
solutions and static Schwarzschild-(A)dS type solutions,
Reissner-Nordstr\"{o}m-(A)dS type solutions and solutions of conformal gravity
as special cases. Afterwards, we study the cosmological solutions in NAT: We
find some exact solutions with perfect fluid distribution for spatially flat
FLRW metric and null aether propagating along the $x$ direction. We observe
that there are solutions in which the universe has big-bang singularity and
null field diminishes asymptotically. We also study exact gravitational wave
solutions--AdS-plane waves and $pp$-waves--in this theory in any dimension
$D\geq3$. Assuming the Kerr-Schild-Kundt class of metrics for such solutions,
we show that the full field equations of the theory are reduced to two, in
general coupled, differential equations when the background metric assumes the
maximally symmetric form. The main conclusion of these computations is that the
spin-0 aether field acquires a \textquotedblleft mass" determined by the
cosmological constant of the background spacetime and the Lagrange multiplier
given in the theory.


  Detection of templates (e.g., sources) embedded in low-number count Poisson
noise is a common problem in astrophysics. Examples include source detection in
X-ray images, gamma-rays, UV, neutrinos, and search for clusters of galaxies
and stellar streams. However, the solutions in the X-ray-related literature are
sub-optimal -- in some cases by considerable factors. Using the lemma of
Neyman-Pearson we derive the optimal statistics for template detection in the
presence of Poisson noise. We demonstrate that this method provides higher
completeness, for a fixed false-alarm probability value, compared with
filtering the image with the point-spread function (PSF). In turn, we find that
filtering by the PSF is better than filtering the image using the Mexican-hat
wavelet (used by wavedetect). For some background levels, our method improves
the sensitivity of source detection by more than a factor of two over the
popular Mexican-hat wavelet filtering. This filtering technique can also be
used also for fast PSF photometry and flare detection, and it is efficient, as
well as straight forward to implement. We provide an implementation in MATLAB.


  We have measured the absolute proper motion of the young globular cluster Pal
12 with respect to background galaxies, using plate material spanning a 40-year
time baseline, and measuring stars down to a magnitude V~22. The measured
absolute proper motion has an uncertainty of 0.3 mas/yr in each coordinate.
  Pal 12's young age for a globular cluster led to the hypothesis that the
cluster originated in the Large Magellanic Cloud (LMC) and was later captured
by the Milky Way (Lin and Richer 1992). Here we investigate this hypothesis
using the complete kinematical data. We present the orbital characteristics of
Pal 12 and compare them with those of the LMC and Sagittarius dwarf galaxy
(Sgr). The present kinematical data suggest that, from the two parent
candidates for Pal 12, Sgr presents a more plausible case for the host galaxy
than the LMC.
  We explore this scenario in the context of the uncertainties in the orbits
and using two different analyses: the direct comparison of the orbits of Pal 12
and Sgr as a function of time, and the analytical model of Sgr's tidal
disruption developed by Johnson (1998). We find that, within the present
uncertainties of the observables, this scenario is viable in both methods.
Moreover, both methods place this event at the same point in time. Our best
estimate of the time of Pal 12's tidal capture from Sgr is ~ 1.7 Gyr ago.


  Using a navigation process with the datum $(F,V)$, in which $F$ is a Finsler
metric and the smooth tangent vector field $V$ satisfies $F(-V(x))>1$
everywhere, a Lorentz Finsler metric $\tilde{F}$ can be induced. Isoparametric
functions and isoparametric hypersurfaces with or without involving a smooth
measure can be defined for $\tilde{F}$. When the vector field $V$ in the
navigation datum is homothetic, we prove the local correspondences between
isoparametric functions and isoparametric hypersurfaces before and after this
navigation process. Using these correspondences, we provide some examples of
isoparametric functions and isoparametric hypersurfaces on a Funk space of
Lorentz Randers type.


  Recently, a class of partition functions associated with higher rank rational
and trigonometric integrable models were introduced by Foda and Manabe. We use
the dynamical $R$-matrix of the elliptic quantum group $E_{\tau,\eta}(gl_3)$ to
introduce an elliptic analogue of the partition functions associated with
$E_{\tau,\eta}(gl_3)$. We investigate the partition functions of Foda-Manabe
type by developing a nested version of the elliptic Izergin-Korepin analysis,
and present the explicit forms as symmetrization of multivariable elliptic
functions. We show that special cases are essentially the elliptic weights
functions introduced in the works by Rim\'anyi-Tarasov-Varchenko, Konno,
Felder-Rim\'anyi-Varchenko.


  We classify all the quadratic Poisson structures on $so^*(4)$ and $e^*(3)$,
which have the same foliation by symplectic leaves as the canonical Lie-Poisson
tensors. The separated variables for the some of the corresponding
bi-integrable systems are constructed.


  Synthesizing a polarizable environment surrounding a low-dimensional metal to
generate superconductivity is a simple theoretical idea that still awaits a
convincing experimental realization. The challenging requirements are satisfied
in a metallic bilayer when the ratio between the Fermi velocities is small and
both metals have a similar, low carrier density. In this case, the slower
electron gas acts as a retarded polarizable medium (a "dielectric" environment)
for the faster metal. Here we show that this concept is naturally optimized for
the case of an atomically thin bilayer consisting of a Dirac semimetal (e.g.
graphene) placed in atomic-scale proximity to a doped semiconducting transition
metal dichalcogenide (e.g. WSe$_2$). The superconducting transition temperature
that arises from the dynamically screened Coulomb repulsion is computed using
the linearized Eliashberg equation. In the case of graphene on WSe$_2$, we find
that $T_c$ can exceed 100 mK, and it increases further when the Dirac valley
degeneracy is reduced. Thus, we argue that suspended van der Waals bilayers are
in a unique position to realize experimentally this long anticipated
theoretical concept.


  The collapsar model of long gamma-ray bursts (GRBs) indicates that they may
trace the star formation history. So long GRBs may be a useful tool of
measuring the high-redshift star formation rate (SFR). The collapsar model
explains GRB formation via the collapse of a rapidly rotating massive star with
$M> 30M_\odot$ into a black hole, which may imply a decrease of SFR at high
redshift. However, we find that the \emph{Swift} GRBs during 2005-2012 are
biased tracing the SFR, including a factor about $(1+z)^{0.5}$, which is in
agreement with recent results. After taking this factor, the SFR derived from
GRBs does not show steep drop up to $z\sim 9.4$. We consider the GRBs produced
by rapidly rotating metal-poor stars with low masses to explain the
high-redshift GRB rate excess. The chemically homogeneous evolution scenario
(CHES) of rapidly rotating stars with mass larger than $12M_\odot$ is
recognized as a promising path towards collapsars in connection with long GRBs.
Our results indicate that the stars in the mass range $12M_\odot<M<30M_\odot$
for low enough metallicity $Z\leq 0.004$ with the GRB efficiency factor
$10^{-5}$ can fit the derived SFR with good accuracy. Combining these two
factors, we find that the conversion efficiency from massive stars to GRBs is
enhanced by a factor of 10, which may be able to explain the excess of the
high-redshift GRB rate. We also investigate the cosmic reionization history
using the derived SFR. The GRB-inferred SFR would be sufficient to maintain
cosmic reionization over $6<z<10$ and reproduce the observed optical depth of
Thomson scattering to the cosmic microwave background.


  The saddle-to-scission dynamics of the induced fission process is explored
using a microscopic finite-temperature model based on time-dependent nuclear
density functional theory (TDDFT), that allows to follow the evolution of local
temperature along fission trajectories. Starting from a temperature that
corresponds to the experimental excitation energy of the compound system, the
model propagates the nucleons along isentropic paths toward scission. For the
four illustrative cases of induced fission of $^{240}$Pu, $^{234}$U,
$^{244}$Cm, and $^{250}$Cf, characteristic fission trajectories are considered,
and the partition of the total energy into various kinetic and potential energy
contributions at scission is analyzed, with special emphasis on the energy
dissipated along the fission path and the prescission kinetic energy. The model
is also applied to the dynamics of neck formation and rupture, characterized by
the formation of few-nucleon clusters in the low-density region between the
nascent fragments.


  Reinforcement learning (RL) has achieved enormous progress in solving various
sequential decision-making problems, such as control tasks in robotics. Since
policies are overfitted to training environments, RL methods have often failed
to be generalized to safety-critical test scenarios. Robust adversarial RL
(RARL) was previously proposed to train an adversarial network that applies
disturbances to a system, which improves the robustness in test scenarios.
However, an issue of neural network-based adversaries is that integrating
system requirements without handcrafting sophisticated reward signals are
difficult. Safety falsification methods allow one to find a set of initial
conditions and an input sequence, such that the system violates a given
property formulated in temporal logic. In this paper, we propose
falsification-based RARL (FRARL): this is the first generic framework for
integrating temporal logic falsification in adversarial learning to improve
policy robustness. By applying our falsification method, we do not need to
construct an extra reward function for the adversary. Moreover, we evaluate our
approach on a braking assistance system and an adaptive cruise control system
of autonomous vehicles. Our experimental results demonstrate that policies
trained with a falsification-based adversary generalize better and show less
violation of the safety specification in test scenarios than those trained
without an adversary or with an adversarial network.


  We present a lightweight, decentralized algorithm for navigating multiple
nonholonomic agents through challenging environments with narrow passages. Our
key idea is to allow agents to yield to each other in large open areas instead
of narrow passages, to increase the success rate of conventional decentralized
algorithms. At pre-processing time, our method computes a medial axis for the
freespace. A reference trajectory is then computed and projected onto the
medial axis for each agent. During run time, when an agent senses other agents
moving in the opposite direction, our algorithm uses the medial axis to
estimate a Point of Impact (POI) as well as the available area around the POI.
If the area around the POI is not large enough for yielding behaviors to be
successful, we shift the POI to nearby large areas by modulating the agent's
reference trajectory and traveling speed. We evaluate our method on a row of 4
environments with up to 15 robots, and we find our method incurs a marginal
computational overhead of 10-30 ms on average, achieving real-time performance.
Afterward, our planned reference trajectories can be tracked using local
navigation algorithms to achieve up to a $100\%$ higher success rate over local
navigation algorithms alone.


  Spiking neural networks (SNNs) have ultra-low energy consumption and high
biological plausibility due to their binary and bio-driven nature compared with
artificial neural networks (ANNs). While previous research has primarily
focused on enhancing the performance of SNNs in classification tasks, the
generative potential of SNNs remains relatively unexplored. In our paper, we
put forward Spiking Denoising Diffusion Probabilistic Models (SDDPM), a new
class of SNN-based generative models that achieve high sample quality. To fully
exploit the energy efficiency of SNNs, we propose a purely Spiking U-Net
architecture, which achieves comparable performance to its ANN counterpart
using only 4 time steps, resulting in significantly reduced energy consumption.
Extensive experimental results reveal that our approach achieves
state-of-the-art on the generative tasks and substantially outperforms other
SNN-based generative models, achieving up to 12x and 6x improvement on the
CIFAR-10 and the CelebA datasets, respectively. Moreover, we propose a
threshold-guided strategy that can further improve the performances by 2.69% in
a training-free manner. The SDDPM symbolizes a significant advancement in the
field of SNN generation, injecting new perspectives and potential avenues of
exploration. Our code is available at https://github.com/AndyCao1125/SDDPM.


  Boxy/peanut bulges are considered to be part of the same stellar structure as
bars and both could be linked through the buckling instability. The Milky Way
is our closest example. The goal of this letter is determining if the mass
assembly of the different components leaves an imprint in their stellar
populations allowing to estimate the time of bar formation and its evolution.
To this aim we use integral field spectroscopy to derive the stellar age
distributions, SADs, along the bar and disc of NGC 6032. The analysis shows
clearly different SADs for the different bar areas. There is an underlying old
(>=12 Gyr) stellar population for the whole galaxy. The bulge shows star
formation happening at all times. The inner bar structure shows stars of ages
older than 6 Gyrs with a deficit of younger populations. The outer bar region
presents a SAD similar to that of the disc. To interpret our results, we use a
generic numerical simulation of a barred galaxy. Thus, we constrain, for the
first time, the epoch of bar formation, the buckling instability period and the
posterior growth from disc material. We establish that the bar of NGC 6032 is
old, formed around 10 Gyr ago while the buckling phase possibly happened around
8 Gyr ago. All these results point towards bars being long-lasting even in the
presence of gas.


  PSR J1813--1749 has peculiarities that make it a very interesting object of
study. It is one of the most energetic and the most scattered pulsar known. It
is associated with HESS J1813--178, one of the brightest and most compact TeV
sources in the sky. Recently, Ho et al. used archival X-ray Chandra
observations separated by more than 10 years and determined that the total
proper motion of PSR J1813--1749 is $\sim66$~mas~yr$^{-1}$, corresponding to a
velocity of $\sim$1900 km s$^{-1}$ for a distance of 6.2 kpc. These results
would imply that this pulsar is the fastest neutron star known in the Galaxy
and, by estimating the angular separation with respect to the center of the
associated supernova remnant, has an age of only $\sim300$ years, making it one
of the youngest pulsars known. Using archival high-angular-resolution VLA
observations taken over 12 years we have estimated the radio proper motions of
PSR~J1813--1748 to be much smaller:
($\mu_{\alpha}\cdot\cos(\delta),\,\mu_\delta$)=($-5.0\pm3.7,\,-13.2\pm6.7$)~mas~yr$^{-1}$,
or a total proper motion of $14.8\pm5.9$~mas~yr$^{-1}$. The positions
referenced against quasars make our results reliable. We conclude that PSR
J1813--1749 is not a very fast moving source. Its kinematic age using the new
total proper motion is $\sim1350$~years. This age is consistent within a factor
of a few with the characteristic age of the pulsar and with the age estimated
from the broadband spectral energy distribution of HESS J1813--178, as well as
the age of the associated SNR.


  We develop a general approach for designing scheduling policies for real-time
traffic over wireless channels. We extend prior work, which characterizes a
real-time flow by its traffic pattern, delay bound, timely-throughput
requirement, and channel reliability, to allow time-varying channels, allow
clients to have different deadlines, and allow for the optional employment of
rate adaptation. Thus, our model allow the treatment of more realistic fading
channels as well as scenarios with mobile nodes, and the usage of more general
transmission strategies.
  We derive a sufficient condition for a scheduling policy to be feasibility
optimal, and thereby establish a class of feasibility optimal policies. We
demonstrate the utility of the identified class by deriving a feasibility
optimal policy for the scenario with rate adaptation, time-varying channels,
and heterogeneous delay bounds. When rate adaptation is not available, we also
derive a feasibility optimal policy for time-varying channels. For the scenario
where rate adaptation is not available but clients have different delay bounds,
we describe a heuristic. Simulation results are also presented which indicate
the usefulness of the scheduling policies for more realistic and complex
scenarios.


  In this article we study a constant-roll inflationary model in the context of
the DGP brane-world cosmology caused by a quintessence scalar field. We
determine an analytical solution for the Friedman equation coupled to the
equation of motion of the scaler field. The evolution of the primordial scalar
and tensor perturbations is also studied. To check the viability of the model
we use numerical approaches and plot some figures. Our results for the scalar
spectral index and the tensor to scaler ratio show good consistency with
observations for given values of model parameters.


  The paper offers a thorough study of multiorders and their applications to
measure-preserving actions of countable amenable groups. By a~{\em multiorder}
on a~countable group we mean any probability measure $\nu$ on the collection
$\tilde{\mathcal{O}}$ of linear orders of type $\mathbb Z$ on $G$, invariant
under the natural action of $G$ on such orders. Every free measure-preserving
$G$-action $(X,\mu,G)$ has a~multiorder $(\tilde{\mathcal{O}},\nu,G)$ as a
factor and has the same orbits as the $\mathbb Z$-action $(X,\mu,S)$, where $S$
is the \emph{successor map} determined by the multiorder factor. Moreover, the
sub-sigma-algebra $\Sigma_{\tilde{\mathcal{O}}}$ associated with the multiorder
factor is invariant under $S$, which makes the corresponding $\mathbb Z$-action
$(\tilde{\mathcal{O}},\nu,\tilde S)$ a factor of $(X,\mu,S)$. We prove that the
entropy of any $G$-process generated by a finite partition of $X$, conditional
with respect to $\Sigma_{\tilde{\mathcal{O}}}$, is preserved by the orbit
equivalence with $(X,\mu,S)$. Furthermore, this entropy can be computed in
terms of the so-called random past, by a formula analogous to $
h(\mu,T,\mathcal P)=H(\mu,\mathcal P|\mathcal{P}^-)$ known for $\mathbb
Z$-actions. The above fact is then applied to prove a variant of a result by
Rudolph and Weiss. The original theorem states that orbit equivalence between
free actions of countable amenable groups preserves conditional entropy with
respect to a~sub-sigma-algebra $\Sigma$, as soon as the ``orbit change'' is
measurable with respect to $\Sigma$. In our variant, we replace the
measurability assumption by a~simpler one: $\Sigma$ should be invariant under
both actions and the actions on the resulting factor should be free. In
conclusion we provide a characterization of the Pinsker sigma-algebra of any
$G$-process in terms of an appropriately defined remote past arising from a
multiorder.


  Dendroidal sets offer a formalism for the study of $\infty$-operads akin to
the formalism of $\infty$-categories by means of simplicial sets. We present
here an account of the current state of the theory while placing it in the
context of the ideas that lead to the conception of dendroidal sets. We briefly
illustrate how the added flexibility embodied in $\infty$-operads can be used
in the study of $A_{\infty}$-spaces and weak $n$-categories in a way that
cannot be realized using strict operads.


  Direct integration technique is used to study the proper conformal vector
fields in non conformally flat Bianchi type-1 space-times. Using the above
mentioned technique we have shown that a very special class of the above
space-time admits proper conformal vector fields.


  We construct a modified Arratia flow with mass and energy conservation. We
suppose that particles have a mass obeying the conservation law, and their
diffusion is inversely proportional to the mass. Our main result asserts that
such a system exists under the assumption of the uniform mass distribution on
an interval at the starting moment. We introduce a stochastic integral with
respect to such a flow and obtain the total local time as the density of the
occupation measure for all particles.


  The Navier-Stokes-Maxwell-Stefan system describes the dynamics of an
incompressible gaseous mixture in isothermal condition. In this paper we set up
an artificial compressibility type approximation. In particular we focus on the
existence of solution for the approximated system and the convergence to the
incompressible case. The existence of the approximating system is proved by
means of semidiscretization in time and by estimating the fractional time
derivative.


  In quantizing magnetic fields, graphene superlattices exhibit a complex
fractal spectrum often referred to as the Hofstadter butterfly. It can be
viewed as a collection of Landau levels that arise from quantization of
Brown-Zak minibands recurring at rational ($p/q$) fractions of the magnetic
flux quantum per superlattice unit cell. Here we show that, in
graphene-on-boron-nitride superlattices, Brown-Zak fermions can exhibit
mobilities above 10$^6$ cm$^2$V$^{-1}$s$^{-1}$ and the mean free path exceeding
several micrometers. The exceptional quality of our devices allows us to show
that Brown-Zak minibands are $4q$ times degenerate and all the degeneracies
(spin, valley and mini-valley) can be lifted by exchange interactions below 1K.
We also found negative bend resistance at $1/q$ fractions for electrical probes
placed as far as several micrometers apart. The latter observation highlights
the fact that Brown-Zak fermions are Bloch quasiparticles propagating in high
fields along straight trajectories, just like electrons in zero field.


  We utilize lattice simulations of the dimensionally reduced effective field
theory (EQCD) to determine the quark number susceptibility of QCD at high
temperature ($T>2T_c$). We also use analytic continuation to obtain results at
finite density. The results extrapolate well from known perturbative expansion
(accurate in extremely high temperatures) to 4d lower temperature lattice data


  Recent works using deep learning to solve the Traveling Salesman Problem
(TSP) have focused on learning construction heuristics. Such approaches find
TSP solutions of good quality but require additional procedures such as beam
search and sampling to improve solutions and achieve state-of-the-art
performance. However, few studies have focused on improvement heuristics, where
a given solution is improved until reaching a near-optimal one. In this work,
we propose to learn a local search heuristic based on 2-opt operators via deep
reinforcement learning. We propose a policy gradient algorithm to learn a
stochastic policy that selects 2-opt operations given a current solution.
Moreover, we introduce a policy neural network that leverages a pointing
attention mechanism, which unlike previous works, can be easily extended to
more general k-opt moves. Our results show that the learned policies can
improve even over random initial solutions and approach near-optimal solutions
at a faster rate than previous state-of-the-art deep learning methods.


  This paper deals with the problem of output regulation for systems defined on
matrix Lie-Groups. Reference trajectories to be tracked are supposed to be
generated by an exosystem, defined on the same Lie-Group of the controlled
system, and only partial relative error measurements are supposed to be
available. These measurements are assumed to be invariant and associated to a
group action on a homogeneous space of the state space. In the spirit of the
internal model principle the proposed control structure embeds a copy of the
exosystem kinematic. This control problem is motivated by many real
applications fields in aerospace, robotics, projective geometry, to name a few,
in which systems are defined on matrix Lie-groups and references in the
associated homogenous spaces.


  The quadratic rough Heston model provides a natural way to encode Zumbach
effect in the rough volatility paradigm. We apply multi-factor approximation
and use deep learning methods to build an efficient calibration procedure for
this model. We show that the model is able to reproduce very well both SPX and
VIX implied volatilities. We typically obtain VIX option prices within the
bid-ask spread and an excellent fit of the SPX at-the-money skew. Moreover, we
also explain how to use the trained neural networks for hedging with
instantaneous computation of hedging quantities.


  A landmark result in the study of logics for formal verification is Janin &
Walukiewicz's theorem, stating that the modal $\mu$-calculus ($\mu\mathrm{ML}$)
is equivalent modulo bisimilarity to standard monadic second-order logic (here
abbreviated as $\mathrm{smso}$), over the class of labelled transition systems
(LTSs for short). Our work proves two results of the same kind, one for the
alternation-free fragment of $\mu\mathrm{ML}$ ($\mu_D\mathrm{ML}$) and one for
weak $\mathrm{mso}$ ($\mathrm{wmso}$). Whereas it was known that
$\mu_D\mathrm{ML}$ and $\mathrm{wmso}$ are equivalent modulo bisimilarity on
binary trees, our analysis shows that the picture radically changes once we
reason over arbitrary LTSs. The first theorem that we prove is that, over LTSs,
$\mu_D\mathrm{ML}$ is equivalent modulo bisimilarity to noetherian
$\mathrm{mso}$ ($\mathrm{nmso}$), a newly introduced variant of $\mathrm{smso}$
where second-order quantification ranges over "well-founded" subsets only. Our
second theorem starts from $\mathrm{wmso}$, and proves it equivalent modulo
bisimilarity to a fragment of $\mu_D\mathrm{ML}$ defined by a notion of
continuity. Analogously to Janin & Walukiewicz's result, our proofs are
automata-theoretic in nature: as another contribution, we introduce classes of
parity automata characterising the expressiveness of $\mathrm{wmso}$ and
$\mathrm{nmso}$ (on tree models) and of $\mu_C\mathrm{ML}$ and
$\mu_D\mathrm{ML}$ (for all transition systems).


  We address the problem of testing whether a dynamic graph is temporally
connected, i.e. a temporal path ({\em journey}) exists between all pairs of
vertices. We consider a discrete version of the problem, where the topology is
given as an evolving graph $\G=\{G_1,G_2,...,G_{k}\}$ in which only the set of
(directed) edges varies. Two cases are studied, depending on whether a single
edge or an unlimited number of edges can be crossed in a same $G_i$ (strict
journeys {\it vs} non-strict journeys). For strict journeys, two existing
algorithms designed for other problems can be adapted. However, we show that a
dedicated approach achieves a better time complexity than one of these two
algorithms in all cases, and than the other one for those graphs whose density
is low at any time (though arbitrary over time). The time complexity of our
algorithm is $O(k\mu n)$, where $k=|\G|$ is the number of time steps and
$\mu=max(|E_i|)$ is the maximum {\em instant} density, to be contrasted with
$m=|\cup E_i|$, the {\em cumulated} density. Indeed, it is not uncommon for a
mobility scenario to satisfy, for instance, both $\mu=o(n)$ and
$m=\Theta(n^2)$. We characterize the key values of $k, \mu$ and $m$ for which
our algorithm should be used. For non-strict journeys, for which no algorithm
is known, we show that a similar strategy can be used to answer the question,
still in $O(k\mu n)$ time.


  We derive a systematic procedure of computing the vacuum functional and
fermion condensate of the massive Schwinger model via a perturbative expansion
in the fermion mass. We compute numerical results for the first nontrivial
order.


  We identify branched coverings (continuous open surjections p:Y->X of
Hausdorff spaces with uniformly bounded number of pre-images) with Hilbert
C*-modules C(Y) over C(X) and with faithful unital positive conditional
expectations E:C(Y)->C(X) topologically of index-finite type. The case of
non-branched coverings corresponds to projective finitely generated modules and
expectations (algebraically) of index-finite type. This allows to define
non-commutative analogues of (branched) coverings.


  We study Lie algebroids in positive characteristic and moduli spaces of their
modules. In particular, we show a Langton's type theorem for the corresponding
moduli spaces. We relate Langton's construction to Simpson's construction of
gr-semistable Griffiths transverse filtration. We use it to prove a recent
conjecture of Lan-Sheng-Zuo that semistable systems of Hodge sheaves on
liftable varieties in positive characteristic are strongly semistable.


  The most severe constraints on quark-lepton four-fermion contact interactions
come from the agreement of atomic parity violation measurements with the
Standard Model. In this letter I note that for contact interactions which arise
in theories of composite quarks and leptons, other approximate global
symmetries than parity can eliminate the contribution of contact terms to
atomic parity violation. The most stringent tests of compositeness therefore
come from the high energy collider experiments at LEP II, HERA, and the
Tevatron.


  General permutation invariant statistics in the second quantized approach are
considered. Simple interpolations between dual statistics are constructed.
Particularly, we present a new minimal interpolation between parabosons and
parafermions of any order. The connection with a simple mixing between bosons
and fermions is established. The construction is extended to anyonic-like
statistics.


  We present a new theoretical model for the luminosity functions (LFs) of
Lyman alpha (Lya) emitting galaxies in the framework of hierarchical galaxy
formation. We extend a semi-analytic model of galaxy formation that reproduces
a number of observations for local and high-z galaxies, without changing the
original model parameters but introducing a physically-motivated modelling to
describe the escape fraction of Lya photons from host galaxies (f_esc). Though
a previous study using a hierarchical clustering model simply assumed a
constant and universal value of f_esc, we incorporate two new effects on f_esc:
extinction by interstellar dust and galaxy-scale outflow induced as a star
formation feedback. It is found that the new model nicely reproduces all the
observed Lya LFs of the Lya emitters (LAEs) at different redshifts in z ~ 3-6.
Especially, the rather surprisingly small evolution of the observed LAE Lya LFs
compared with the dark halo mass function is naturally reproduced. Our model
predicts that galaxies with strong outflows and f_esc ~ 1 are dominant in the
observed LFs. This is also consistent with available observations, while the
simple universal f_esc model requires f_esc << 1 not to overproduce the
brightest LAEs. On the other hand, we found that our model significantly
overpredicts LAEs at z > 6, and absorption of Lya photons by neutral hydrogen
in intergalactic medium (IGM) is a reasonable interpretation for the
discrepancy. This indicates that the IGM neutral fraction x_HI rapidly evolves
from x_HI << 1 at z < 6 to a value of order unity at z ~ 6-7, which is broadly
consistent with other observational constraints on the reionization history.


  We study the quantum behaviour of the stadium billiard. We discuss how the
interplay between quantum localization and the rich structure of the classical
phase space influences the quantum dynamics. The analysis of this model leads
to new insight in the understanding of quantum properties of classically
chaotic systems.


  We consider a Lagrangian system $L(q,\dot q) =
  \sum_{l=1}^{N}L^{\{l\}}(q,\dot q)$, where the $q$-variable is treated by a
Generalized Additive Runge--Kutta (GARK) method. Applying the technique of
discrete variations, we show how to construct symplectic schemes. Assuming the
diagonal methods for the GARK given, we present some techinques for
constructing the transition matrices. We address the problem of the order of
the methods and discuss some semi-separable and separable problems, showing
some interesting constructions of methods with non-square coefficient matrices.


  Competition between times series often arises in sales prediction, when
similar products are on sale on a marketplace. This article provides a model of
the presence of cannibalization between times series. This model creates a
"competitiveness" function that depends on external features such as price and
margin. It also provides a theoretical guaranty on the error of the model under
some reasonable conditions, and implement this model using a neural network to
compute this competitiveness function. This implementation outperforms other
traditional time series methods and classical neural networks for market share
prediction on a real-world data set.


  The structure of human sleep changes across development as it consolidates
from the polyphasic sleep of infants to the single nighttime sleep period
typical in adults. Across this same developmental period, time scales of the
homeostatic sleep drive, the physiological drive to sleep that increases with
time spent awake, also change and presumably govern the transition from
polyphasic to monophasic sleep behavior. Using a physiologically-based,
sleep-wake regulatory network model for human sleep, we investigated the
dynamics of wake, rapid eye movement (REM) sleep, and non-REM (NREM) sleep
during this transition by varying the homeostatic sleep drive time constants.
Previously, we introduced an algorithm for constructing a one-dimensional
circle map that represents the dynamics of the full sleep-wake network model.
By tracking bifurcations in the piecewise continuous circle map as the
homeostatic sleep drive time constants are varied, we establish evidence for a
border collision bifurcation that results in period-adding-like behavior in the
number of sleep cycles per day. Interestingly, this bifurcation is preceded by
bifurcations in the number of REM bouts per sleep cycle that exhibit truncated
period-adding-like behavior. The interaction of these bifurcations in numbers
of sleep episodes and numbers of REM bouts per sleep episode generate
non-monotonic variation in sleep cycle patterns as well as quasi-periodic
patterns during the transition from polyphasic to monophasic sleep behavior.
This analysis may have implications for understanding changes in sleep in early
childhood when preschoolers transition from napping to non-napping behavior,
and the wide interindividual variation observed during this transition.


  We describe free differential algebras for non-abelian one and two form gauge
potentials in four dimensions deriving the integrability conditions for the
corresponding curvatures. We show that a realization of these algebras occurs
in M-theory compactifications on twisted tori with constant four-form flux, due
to the presence of antisymmetric tensor fields in the reduced theory.


  The group velocity of gravitational waves in a flat Friedman-Robertson-Walker
universe is investigated. For plane waves with wavelength well inside the
horizon, and a universe filled with an ideal fluid with the pressure to density
ratio less than 1/3, the group velocity is greater than the velocity of light.
As a result, a planar pulse of gravitational waves propagating through the
universe during the matter/dark energy dominated era arrives to the observer
with the peak shifted towards the forefront. For gravitational waves emitted by
inspiralling supermassive black holes at the edge of the observable universe,
the typical shift that remains after the effects of nonplanarity are suppressed
is of order of ten picoseconds.


  In this paper we describe some recent works on quantitative unique
continuation for elliptic, parabolic and dispersive equations. The elliptic
results are joint work with J.Bourgain, while the remainder of the works
discussed are joint works with L.Escauriaza, G.Ponce and L.Vega.


  Adaptive voter models (AVMs) are simple mechanistic systems that model the
emergence of mesoscopic structure from local networked processes driven by
conflict and homophily. AVMs display rich behavior, including a phase
transition from a fully-fragmented regime of "echo-chambers" to a regime of
persistent disagreement governed by low-dimensional quasistable manifolds. Many
extant methods for approximating the behavior of AVMs are either restricted in
scope, expensive in computation, or inaccurate in predicting important
statistics. In this work, we develop a novel, second-order moment closure
approximation method for binary-state rewire-to-random and rewire-to-same model
variants. We incorporate a small amount of noise via a random mutation term,
which renders the system ergodic. Using ergodicity, we then approximate the
voting process, which is non-Markovian in the second moments of the system,
with a Markovian term near the phase transition. This approximation exploits an
asymmetry between different classes of voting events. The resulting scheme
enables us to predict the location of the phase transition and the active edge
density in the regime of persistent disagreement, across the entire space of
parameters and opinion densities. Numerically, our results are nearly exact for
the rewire-to-random model, and competitive with other current approaches for
the rewire-to-same model. Moreover, our computations display constant scaling
in the mean degree, enabling approximations for denser systems than previously
possible. We conclude with suggestions for model refinements and extensions.


  The $K$-$k$-Schur functions and $k$-Schur functions appeared in the study of
$K$-theoretic and affine Schubert Calculus as polynomial representatives of
Schubert classes. In this paper, we introduce a new family of symmetric
functions $\mathcal{F}_\lambda^{(k)}$, that generalizes the constructions via
the Pieri rule of $K$-$k$-Schur functions and $ k$-Schur functions. Then we
obtain the Murnaghan-Nakayama rule for the generalized functions. The rule is
described explicitly in the cases of $K$-$k$-Schur functions and $k$-Schur
functions, with concrete descriptions and algorithms for coefficients. Our work
recovers the result of Bandlow, Schilling, and Zabrocki for $k$-Schur
functions, and explains it as a degeneration of the rule for $K$-$k$-Schur
functions. In particular, many other special cases and connections promise to
be detailed in the future.


  I start with a brief introduction to Higgs mechanism and supersymmetry. Then
I discuss the theoretical expectations, current limits and search strategies
for Higgs boson(s) at LHC --- first in the SM and then in the MSSM. Finally I
discuss the signatures and search strategies for the superparticles.


  We provide a primal-dual framework for randomized approximation algorithms
utilizing semidefinite programming (SDP) relaxations. Our framework pairs a
continuum of APX-complete problems including MaxCut, Max2Sat, MaxDicut, and
more generally, Max-Boolean Constraint Satisfaction and MaxQ (maximization of a
positive semidefinite quadratic form over the hypercube) with new APX-complete
problems which are stated as convex optimization problems with exponentially
many variables. These new dual counterparts, based on what we call Grothendieck
covers, range from fractional cut covering problems (for MaxCut) to tensor sign
covering problems (for MaxQ). For each of these problem pairs, our framework
transforms the randomized approximation algorithms with the best known
approximation factors for the primal problems to randomized approximation
algorithms for their dual counterparts with reciprocal approximation factors
which are tight with respect to the Unique Games Conjecture. For each
APX-complete pair, our algorithms solve a single SDP relaxation and generate
feasible solutions for both problems which also provide approximate optimality
certificates for each other. Our work utilizes techniques from areas of
randomized approximation algorithms, convex optimization, spectral
sparsification, as well as Chernoff-type concentration results for random
matrices.


  Radial mass-to-light ratio gradients cause the half-mass and half-light radii
of galaxies to differ, potentially biasing studies that use half-light radii.
Here we present the largest catalog to date of galaxy half-mass radii at z > 1:
7,006 galaxies in the CANDELS fields at 1.0 < z < 2.5. The sample includes both
star-forming and quiescent galaxies with stellar masses 9.0 < log(M_* /
M_\odot) < 11.5. We test three methods for calculating half-mass radii from
multi-band PSF-matched HST imaging: two based on spatially-resolved SED
modeling, and one that uses a rest-frame color profile. All three methods
agree, with scatter <~0.3 dex. In agreement with previous studies, most
galaxies in our sample have negative color gradients (the centers are redder
than the outskirts, and r_e,mass < r_e,light). We find that color gradient
strength has significant trends with increasing stellar mass, half-light
radius, U-V color, and stellar mass surface density. These trends have not been
seen before at z>1. Furthermore, color gradients of star-forming and quiescent
galaxies show a similar redshift evolution: they are flat at z>~2, then steeply
decrease as redshift decreases. This affects the galaxy mass-size relation. The
normalizations of the star-forming and quiescent r_mass-M_* relations are
10-40% smaller than the corresponding r_light-M_* relations; the slopes are
~0.1-0.3 dex shallower. Finally, the half-mass radii of star-forming and
quiescent galaxies at M_* = 10^{10.5}M_\odot only grow by ~1%$ and ~8% between
z~2.25 and z~1.25. This is significantly less than the ~37% and ~47% size
increases found when using the half-light radius.


  Transmission through a potential barrier, and the related issue of particle
production from a parametric resonance, are topics of considerable general
interest in quantum physics. The authors have developed a rather general bound
on quantum transmission probabilities, and recently applied it to bounding the
greybody factors of a Schwarzschild black hole. In the current article we take
a different tack -- we use the Miller-Good transformation (which maps an
initial Schrodinger equation to a final Schrodinger equation for a different
potential) to significantly generalize the previous bound.


  We develop a theory for the magnon Kerr effect in a cavity magnonics system,
consisting of magnons in a small yttrium iron garnet (YIG) sphere strongly
coupled to cavity photons, and use it to study the bistability in this hybrid
system. To have a complete picture of the bistability phenomenon, we analyze
two different cases in driving the cavity magnonics system, i.e., directly
pumping the YIG sphere and the cavity, respectively. In both cases, the magnon
frequency shifts due to the Kerr effect exhibit a similar bistable behavior but
the corresponding critical powers are different. Moreover, we show how the
bistability of the system can be demonstrated using the transmission spectrum
of the cavity. Our results are valid in a wide parameter regime and generalize
the theory of bistability in a cavity magnonics system.


  Phase retrieval problems occur in a width range of applications in physics
and engineering such as crystallography, astronomy, and laser optics. Common to
all of them is the recovery of an unknown signal from the intensity of its
Fourier transform. Because of the well-known ambiguousness of these problems,
the determination of the original signal is generally challenging. Although
there are many approaches in the literature to incorporate the assumption of
non-negativity of the solution into numerical algorithms, theoretical
considerations about the solvability with this constraint occur rarely. In this
paper, we consider the one-dimensional discrete-time setting and investigate
whether the usually applied a priori non-negativity can overcame the
ambiguousness of the phase retrieval problem or not. We show that the assumed
non-negativity of the solution is usually not a sufficient a priori condition
to ensure uniqueness in one-dimensional phase retrieval. More precisely, using
an appropriate characterization of the occurring ambiguities, we show that
neither the uniqueness nor the ambiguousness are rare exceptions.


  If $E=\{e_i\}$ and $F=\{f_i\}$ are two 1-unconditional basic sequences in
$L_1$ with $E$ $r$-concave and $F$ $p$-convex, for some $1\le r<p\le 2$, then
the space of matrices $\{a_{i,j}\}$ with norm
  $\|\{a_{i,j}\}\|_{E(F)}=\big\|\sum_k \|\sum_l a_{k,l}f_l\|e_k\big\|$ embeds
into $L_1$. This generalizes a recent result of Prochno and Sch\"utt.


  It is well known that, by the Reeb stability theorem, the leaf space of a
Riemannian foliation with compact leaves is an orbifold. We prove that, under
mild completeness conditions, the leaf space of a Killing Riemannian foliation
is a diffeological quasifold: as a diffeological space, it is locally modelled
by quotients of Cartesian space by countable groups acting affinely.
Furthermore, we prove that the holonomy groupoid of the foliation is, locally,
Morita equivalent to the action groupoid of a countable group acting affinely
on Cartesian space.


  In this paper we address the problem of establishing correspondences between
different instances of the same object. The problem is posed as finding the
geometric transformation that aligns a given image pair. We use a convolutional
neural network (CNN) to directly regress the parameters of the transformation
model. The alignment problem is defined in the setting where an unordered set
of semantic key-points per image are available, but, without the correspondence
information. To this end we propose a novel loss function based on cyclic
consistency that solves this 2D point set registration problem by inferring the
optimal geometric transformation model parameters. We train and test our
approach on a standard benchmark dataset Proposal-Flow
(PF-PASCAL)\cite{proposal_flow}. The proposed approach achieves
state-of-the-art results demonstrating the effectiveness of the method. In
addition, we show our approach further benefits from additional training
samples in PF-PASCAL generated by using category level information.


  The band structure of a strongly correlated semiconductor as NiO has been the
object of much debate [PRL 103, 036404 (2009); PRL 102, 226401 (2009)]. Most
authors, using computational techniques well beyond the simple density
functional theory and the approximations GGA or LDA, claim that the band gap is
about 4.0 eV and that the conduction band is of Ni-3d nature. Thus they seem to
forget the results of electron energy-loss spectroscopy and inelastic x-ray
scattering, both able to determine electronic transitions of only about 1.0 eV
to an optically forbidden Ni-3d band. Further, a simple atomic calculation of
the Ni++ spin flip energy demonstrates that a Ni-3d band at 4.0 eV is
impossible. To set the issue straight, we calculated NiO with the very
successful technique of PRB 78, 125116 (2008). It turns out that a band at 4.0
eV is optically accessible and made of excited atomic states, not Ni-3d. Aside
from that, we also found a narrow Ni-3d band at about 1.0 eV. To confirm our
procedures once again, we also calculated MnO and obtained the standard results
of the good calculations as those cited above, and of experiment.


  Dynamic response of sandwich beams with resonators embedded in the cores
subjected to impact loads is studied. Using finite element models the
effectiveness of various local resonator frequencies under a given impact load
is compared to the behavior of an equivalent mass beam. It is shown that
addition of appropriately chosen local resonators into the sandwich beam is an
effective method of improving its flexural bending behavior under impact loads.
The effect of a given local resonance frequency under different impact load
durations is also studied. It is demonstrated that the choice of appropriate
local resonance frequency depends on the impact duration. Further, by
performing transverse impact experiments, the finite element models are
verified and the advantage of using internal resonators under impact loading
conditions is demonstrated.


  The advent of large language models (LLMs) has facilitated the development of
natural language text generation. It also poses unprecedented challenges, with
content hallucination emerging as a significant concern. Existing solutions
often involve expensive and complex interventions during the training process.
Moreover, some approaches emphasize problem disassembly while neglecting the
crucial validation process, leading to performance degradation or limited
applications. To overcome these limitations, we propose a Markov Chain-based
multi-agent debate verification framework to enhance hallucination detection
accuracy in concise claims. Our method integrates the fact-checking process,
including claim detection, evidence retrieval, and multi-agent verification. In
the verification stage, we deploy multiple agents through flexible Markov
Chain-based debates to validate individual claims, ensuring meticulous
verification outcomes. Experimental results across three generative tasks
demonstrate that our approach achieves significant improvements over baselines.


  Optical surveys have become increasingly adept at identifying candidate Tidal
Disruption Events (TDEs) in large numbers, but classifying these generally
requires extensive spectroscopic resources. Here we present
$\texttt{tdescore}$, a simple binary photometric classifier that is trained
using a systematic census of $\sim$3000 nuclear transients from the Zwicky
Transient Facility (ZTF). The sample is highly imbalanced, with TDEs
representing $\sim$2% of the total. $\texttt{tdescore}$ is nonetheless able to
reject non-TDEs with 99.6% accuracy, yielding a sample of probable TDEs with
recall of 77.5% for a precision of 80.2%. $\texttt{tdescore}$ is thus
substantially better than any available TDE photometric classifier scheme in
the literature, with performance not far from spectroscopy as a method for
classifying ZTF nuclear transients, despite relying solely on ZTF data and
multi-wavelength catalogue cross-matching. In a novel extension, we use
`SHapley Additive exPlanations' ($\texttt{SHAP}$) to provide a human-readable
justification for each individual $\texttt{tdescore}$ classification, enabling
users to understand and form opinions about the underlying classifier
reasoning. $\texttt{tdescore}$ can serve as a model for photometric
identification of TDEs with time-domain surveys, such as the upcoming Rubin
observatory.


  The connection between the Dirac field as the field of matter and the
spacetime metric is discussed within the framework of classical field theory.
Polarization structure of the Dirac field is shown to be rich enough to
determine the spacetime metric locally and to explain the emergence of observed
matter as localized waveforms. The localization of the waveforms is explained
as the result of the local time slowdown and the Lorentz contraction as a
dynamic re-shaping of the waveforms in the course of their acceleration. A
definition of mass as a limiting curvature of the spinor-induced metric is
proposed. A view of the vacuum as a uniformly distributed unit invariant
density of the Dirac field with an explicitly preserved invariance of the light
cone is brought forward. Qualitative explanation of the observed charge
asymmetry as the consequence of the dynamics of localization is given. The
origin of the CP-violation is associated with the loss of the Poincare
invariance due to localization. Neutrinos are identified with the signals
emitted in the abrupt processes of creation or decay of localized objects and
the concept of the Majorana neutrino is revisited. The wave equation for the
classical pion field is derived from the Dirac equation. Its connection with
stresses, mass and charge fluxes in localized waveforms of the Dirac field is
traced. Some implications of the finite size of colliding objects for
high-energy processes are discussed. A possible difference between the
lifetimes and gyromagnetic ratios for positive and negative charges is
predicted. A hypothesis that known internal degrees of freedom are the local
spacetime (angular) coordinates that have no precise counterparts in Riemannian
geometry is proposed.


  A pulsed technique for electrons in 2D systems, in some ways analogous to
spin echo in nuclear magnetic resonance, is discussed. We show that a sequence
of optical below-band gap pulses can be used to suppress the electron spin
relaxation due to the D'yakonov-Perel' spin relaxation mechanism. The spin
relaxation time is calculated for several pulse sequences within a Monte Carlo
simulation scheme. The maximum of spin relaxation time as a function of
magnitude/width of the pulses corresponds to $\pi$-pulse. It is important that
even relatively distant pulses efficiently suppress spin relaxation.


  In this research, we introduce magnetically charged stars in the framework of
non-singular metric which is explained with nonlinear electrodynamics(NED).
This model allows us to have an upper limit for the maximum limit for the mass
of stars in the presence of NED. We explain our model for magnetized compact
object by considering the polytropic equation of states(EoS)


  We introduce the digital projective product spaces based on Davis' projective
product spaces. We determine an upper bound for the digital LS-category of the
digital projective product spaces. In addition, we obtain an upper bound for
the digital topological complexity of these spaces. We prove the relation
between the digital topological complexity of the digital projective product
spaces and sum of the digital topological complexity of the digital projective
space by associating with the first digital sphere and the digital topological
complexity of the remaining digital spheres through an explicit motion planning
construction, which shows digital perspective validity of the results given by
S. Fi\c{s}ekci and L. Vandembroucq. We apply our outcomes on specific spaces in
order to be more clear.


  Tremendous progress has been made in sequential processing with the recent
advances in recurrent neural networks. However, recurrent architectures face
the challenge of exploding/vanishing gradients during training, and require
significant computational resources to execute back-propagation through time.
Moreover, large models are typically needed for executing complex sequential
tasks. To address these challenges, we propose a novel neuron model that has
cosine activation with a time varying component for sequential processing. The
proposed neuron provides an efficient building block for projecting sequential
inputs into spectral domain, which helps to retain long-term dependencies with
minimal extra model parameters and computation. A new type of recurrent network
architecture, named Oscillatory Fourier Neural Network, based on the proposed
neuron is presented and applied to various types of sequential tasks. We
demonstrate that recurrent neural network with the proposed neuron model is
mathematically equivalent to a simplified form of discrete Fourier transform
applied onto periodical activation. In particular, the computationally
intensive back-propagation through time in training is eliminated, leading to
faster training while achieving the state of the art inference accuracy in a
diverse group of sequential tasks. For instance, applying the proposed model to
sentiment analysis on IMDB review dataset reaches 89.4% test accuracy within 5
epochs, accompanied by over 35x reduction in the model size compared to LSTM.
The proposed novel RNN architecture is well poised for intelligent sequential
processing in resource constrained hardware.


  Effective, robust, and automatic tools for brain tumor segmentation are
needed for the extraction of information useful in treatment planning from
magnetic resonance (MR) images. Context-aware artificial intelligence is an
emerging concept for the development of deep learning applications for
computer-aided medical image analysis. In this work, it is investigated whether
the addition of contextual information from the brain anatomy in the form of
white matter, gray matter, and cerebrospinal fluid masks and probability maps
improves U-Net-based brain tumor segmentation. The BraTS2020 dataset was used
to train and test two standard 3D U-Net models that, in addition to the
conventional MR image modalities, used the anatomical contextual information as
extra channels in the form of binary masks (CIM) or probability maps (CIP). A
baseline model (BLM) that only used the conventional MR image modalities was
also trained. The impact of adding contextual information was investigated in
terms of overall segmentation accuracy, model training time, domain
generalization, and compensation for fewer MR modalities available for each
subject. Results show that there is no statistically significant difference
when comparing Dice scores between the baseline model and the contextual
information models, even when comparing performances for high- and low-grade
tumors independently. Only in the case of compensation for fewer MR modalities
available for each subject did the addition of anatomical contextual
information significantly improve the segmentation of the whole tumor. Overall,
there is no overall significant improvement in segmentation performance when
using anatomical contextual information in the form of either binary masks or
probability maps as extra channels.


  In this work, we study the time-dependent behaviour of quantum correlations
of a system of an inverted oscillator governed by out-of-equilibrium dynamics
using the well-known Schwinger-Keldysh formalism in presence of quantum
mechanical quench. Considering a generalized structure of a time-dependent
Hamiltonian for an inverted oscillator system, we use the invariant operator
method to obtain its eigenstates and continuous energy eigenvalues. Using the
expression for the eigenstates, we further derive the most general expression
for the generating function as well as the out-of-time-ordered correlators
(OTOC) for the given system using this formalism. Further, considering the
time-dependent coupling and frequency of the quantum inverted oscillator
characterized by quench parameters, we comment on the dynamical behaviour,
specifically the early, intermediate and late time-dependent features of the
OTOC for the quenched quantum inverted oscillator. Next, we study a specific
case, where the system of inverted oscillator exhibits chaotic behaviour by
computing the quantum Lyapunov exponent from the time-dependent behaviour of
OTOC in presence of the given quench profile.


  We propose a new Integral Probability Metric (IPM) between distributions: the
Sobolev IPM. The Sobolev IPM compares the mean discrepancy of two distributions
for functions (critic) restricted to a Sobolev ball defined with respect to a
dominant measure $\mu$. We show that the Sobolev IPM compares two distributions
in high dimensions based on weighted conditional Cumulative Distribution
Functions (CDF) of each coordinate on a leave one out basis. The Dominant
measure $\mu$ plays a crucial role as it defines the support on which
conditional CDFs are compared. Sobolev IPM can be seen as an extension of the
one dimensional Von-Mises Cram\'er statistics to high dimensional
distributions. We show how Sobolev IPM can be used to train Generative
Adversarial Networks (GANs). We then exploit the intrinsic conditioning implied
by Sobolev IPM in text generation. Finally we show that a variant of Sobolev
GAN achieves competitive results in semi-supervised learning on CIFAR-10,
thanks to the smoothness enforced on the critic by Sobolev GAN which relates to
Laplacian regularization.


  We consider smooth electrovac spacetimes which represent either (A) an
asymptotically flat, stationary black hole or (B) a cosmological spacetime with
a compact Cauchy horizon ruled by closed null geodesics. The black hole event
horizon or, respectively, the compact Cauchy horizon of these spacetimes is
assumed to be a smooth null hypersurface which is non-degenerate in the sense
that its null geodesic generators are geodesically incomplete in one direction.
In both cases, it is shown that there exists a Killing vector field in a
one-sided neighborhood of the horizon which is normal to the horizon. We
thereby generalize theorems of Hawking (for case (A)) and Isenberg and Moncrief
(for case (B)) to the non-analytic case.


  We obtain dimension free estimates for noncommutative Riesz transforms
associated to conditionally negative length functions on group von Neumann
algebras. This includes Poisson semigroups, beyond Bakry's results in the
commutative setting. Our proof is inspired by Pisier's method and a new
Khintchine inequality for crossed products. New estimates include Riesz
transforms associated to fractional laplacians in $\mathbb{R}^n$ (where Meyer's
conjecture fails) or to the word length of free groups. Lust-Piquard's work for
discrete laplacians on LCA groups is also generalized in several ways. In the
context of Fourier multipliers, we will prove that H\"ormander-Mihlin
multipliers are Littlewood-Paley averages of our Riesz transforms. This is
highly surprising in the Euclidean and (most notably) noncommutative settings.
As application we provide new Sobolev/Besov type smoothness conditions. The
Sobolev type condition we give refines the classical one and yields dimension
free constants. Our results hold for arbitrary unimodular groups.


  Assuming a minimal seesaw model with two heavy neutrinos (N), we examine
effects of leptonic CP violation induced by approximate mu-tau symmetric
interactions. As long as N is subject to the mu-tau symmetry, we can choose CP
phases of Dirac mass terms without loss of generality in such a way that these
phases arise from mu-tau symmetry breaking interactions. In the case that no
phase is present in heavy neutrino mass terms, leptonic CP phases are
controlled by two phases alpha and beta. The similar consideration is extended
to N blind to the mu-tau symmetry. It is argued that N subject (blind) to the
mu-tau symmetry necessarily describes the normal (inverted) mass hierarchy. We
restrict ourselves to mu-tau symmetric textures giving the tri-bimaximal mixing
and calculate flavor neutrino masses to estimate CP-violating Dirac and
Majorana phases as well as neutrino mixing angles as functions of alpha and
beta. Since alpha and beta are generated by mu-tau symmetry breaking
interactions, CP-violating Majorana phase tends to be suppressed and is found
to be at most O(0.1) radian. On the other hand, CP-violating Dirac phase tends
to show a proportionality to alpha or to beta.


  The first detailed comparison of the low-momentum interaction V_{low k} with
G matrices is presented. We use overlaps to measure quantitatively the
similarity of shell-model matrix elements for different cutoffs and oscillator
frequencies. Over a wide range, all sets of V_{low k} matrix elements can be
approximately obtained from a universal set by a simple scaling. In an
oscillator mean-field approach, V_{low k} reproduces satisfactorily many
features of the single-particle and single-hole spectra on closed-shell nuclei,
in particular through remarkably good splittings between spin-orbit partners on
top of harmonic oscillator closures. The main deficiencies of pure two-nucleon
interactions are associated with binding energies and with the failure to
ensure magicity for the extruder-intruder closures. Here, calculations
including three-nucleon interactions are most needed. V_{low k} makes it
possible to define directly a meaningful unperturbed monopole Hamiltonian, for
which the inclusion of three-nucleon forces is tractable.


  A mesh-free numerical method for solving linear elliptic PDE's using the
local kernel theory that was developed for manifold learning is proposed. In
particular, this novel approach exploits the local kernel theory which allows
one to approximate the Kolmogorov operator associated with It\^o processes on
compact Riemannian manifolds without boundary or with Neumann boundary
conditions using an integral operator. Theoretical justification for the
convergence of this numerical technique is provided under the standard
conditions for the existence of the weak solutions of the PDEs. Numerical
results on various instructive examples, ranging from PDE's defined on flat and
non-flat manifolds with known and unknown embedding functions show accurate
approximation with error on the order of the kernel bandwidth parameter.


  The original formulation of the Bohr-van Leeuwen (BvL) theorem states that,
in a uniform magnetic field and in thermal equilibrium, the magnetization of an
electron gas in the classical Drude-Lorentz model vanishes identically. This
stems from classical statistics which assign the canonical momenta all values
ranging from $-\infty$ to $\infty$ what makes the free energy density
magnetic-field-independent. When considering a classical (Maxwell-Boltzmann)
interacting electron gas, it is usually admitted that the BvL theorem holds
upon condition that the potentials modeling the interactions are
particle-velocities-independent and do not cause the system to rotate after
turning on the magnetic field. From a rigorous viewpoint, when treating large
macroscopic systems one expects the BvL theorem to hold provided the
thermodynamiclimit of the free energy density exists (and the equivalence of
ensemble holds). This requires suitable assumptions on the many-body
interactions potential and on the possible external potentials to prevent the
system from collapsing or flying apart. Starting from quantum statistical
mechanics, the purpose of this article is to give, within the linear-response
theory, a proof of the BvL theorem in the semiclassical limit when considering
a dilute electron gas in the canonical conditions subjected to a class of
translational invariant external potentials.


  Suppose that $A$ is a semi-simple and commutative Banach algebra. In this
paper we try to characterize the character space of the Banach algebra
$C_{\rm{BSE}}(\Delta(A))$ consisting of all BSE-functions on $\Delta(A)$ where
$\Delta(A)$ denotes the character space of $A$. Indeed, in the case that
$A=C_0(X)$ where $X$ is a non-empty locally compact Hausdroff space, we give a
complete characterization of $\Delta(C_{\rm{BSE}}(\Delta(A)))$ and in the
general case we give a partial answer. Also, using the Fourier algebra, we show
that $C_{\rm{BSE}}(\Delta(A))$ is not a $C^*$-algebra in general. Finally for
some subsets $E$ of $A^*$, we define the subspace of BSE-like functions on
$\Delta(A)\cup E$ and give a nice application of this space related to
Goldstine's theorem.


  Current time-series forecasting problems use short-term weather attributes as
exogenous inputs. However, in specific time-series forecasting solutions (e.g.,
demand prediction in the supply chain), seasonal climate predictions are
crucial to improve its resilience. Representing mid to long-term seasonal
climate forecasts is challenging as seasonal climate predictions are uncertain,
and encoding spatio-temporal relationship of climate forecasts with demand is
complex.
  We propose a novel modeling framework that efficiently encodes seasonal
climate predictions to provide robust and reliable time-series forecasting for
supply chain functions. The encoding framework enables effective learning of
latent representations -- be it uncertain seasonal climate prediction or other
time-series data (e.g., buyer patterns) -- via a modular neural network
architecture. Our extensive experiments indicate that learning such
representations to model seasonal climate forecast results in an error
reduction of approximately 13\% to 17\% across multiple real-world data sets
compared to existing demand forecasting methods.


  A multi-shot target assembly and automatic alignment procedure for
laser-plasma proton acceleration at high-repetition-rate are introduced. The
assembly is based on a multi-target rotating wheel capable of hosting $>$5000
targets, mounted on a three-dimensional motorised stage to allow rapid
replenishment and alignment of the target material between laser irradiations.
The automatic alignment procedure consists of a detailed mapping of the impact
positions at the target surface prior to the irradiation that ensures stable
operation of the target, which alongside the purpose-built design of the target
wheel, enable the operation at rates up to 10 Hz. Stable and continuous
laser-driven proton acceleration is demonstrated, with observed cut-off energy
stability about 15%.


  Various massive gravity theories in three dimensions are conjecturally dual
to logarithmic conformal field theories (LCFTs). We summarise the status of
these conjectures. LCFTs are characterised by the values of the central charges
and the so-called "new anomalies". We employ a short-cut to calculate these new
anomalies in generalised massive gravity and in the recently proposed
higher-derivative gravity theories with holographic c-theorem. Both cases
permit LCFTs exhibiting intriguing features, like rank three Jordan cells or
non-zero central charges. Finally, as an example we discuss in some detail the
partially massless version of new massive gravity, a theory with several
special properties that we call "partially massless gravity".


  The shape of light cures of fundamental-mode and of first-overtone pulsators,
as observed in RR~Lyrae variables and Cepheids, differ characteristically. The
stellar physical origin of the morphological differences is not well documented
and the topic seems not to be part of the elementary curriculum of students of
stellar variability. To ameliorate the situation, this exposition analyzes
hydrodynamical simulations of radial pulsations computed with the newly
available numerical instrument RSP in MESA. The stellar physical processes that
affect the light curves are identified and contrasted to the explanation based
on experiments with one-zone models. The encounter of first-overtone pulsators
sporting light curves that mimic those of fundamental-mode variables serves as
a warning that light-curve morphology alone is not a reliable path to correctly
classify pulsating variables; the exposition closes with a short discussion of
constraints these modes might impose on understanding the origin of anomalous
Cepheids.


  We introduce the notion of Bohr chaoticity, which is a topological invariant
for topological dynamical systems, and which is opposite to the property
required by Sarnak's conjecture. We prove the Bohr chaoticity for all systems
which have a horseshoe and for all toral affine dynamical systems of positive
entropy, some of which don't have a horseshoe. But uniquely ergodic dynamical
systems are not Bohr chaotic.


  For nearly every major stock market there exist equity and implied volatility
indices. These play important roles within finance: be it as a benchmark, a
measure of general uncertainty or a way of investing or hedging. It is well
known in the academic literature, that correlations and higher moments between
different indices tend to vary in time. However, to the best of our knowledge,
no one has yet considered a global setup including both, equity and implied
volatility indices of various continents, and allowing for a changing
dependence structure. We aim to close this gap by applying Markov-switching
$R$-vine models to investigate the existence of different, global dependence
regimes. In particular, we identify times of "normal" and "abnormal" states
within a data set consisting of North-American, European and Asian indices. Our
results confirm the existence of joint points in time at which global regime
switching takes place.


  We study collections of additive categories $\mathcal{M}(G)$, indexed by
finite groups $G$ and related by induction and restriction in a way that
categorifies usual Mackey functors. We call them `Mackey 2-functors'. We
provide a large collection of examples in particular thanks to additive
derivators. We prove the first properties of Mackey 2-functors, including
separable monadicity of restriction to subgroups. We then isolate the initial
such structure, leading to what we call `Mackey 2-motives'. We also exhibit a
convenient calculus of morphisms in Mackey 2-motives, by means of string
diagrams. Finally, we show that the 2-endomorphism ring of the identity of $G$
in this 2-category of Mackey 2-motives is isomorphic to the so-called crossed
Burnside ring of $G$.


  We show that the $C^*$-algebraic approach to T-duality of Mathai and
Rosenberg is equivalent to the topological approach of Bunke and Schick.


  A novel solution for the content-based 3D shape retrieval problem using an
unsupervised clustering approach, which does not need any label information of
3D shapes, is presented in this work. The proposed shape retrieval system
consists of two modules in cascade: the irrelevance filtering (IF) module and
the similarity ranking (SR) module. The IF module attempts to cluster gallery
shapes that are similar to each other by examining global and local features
simultaneously. However, shapes that are close in the local feature space can
be distant in the global feature space, and vice versa. To resolve this issue,
we propose a joint cost function that strikes a balance between two distances.
Irrelevant samples that are close in the local feature space but distant in the
global feature space can be removed in this stage. The remaining gallery
samples are ranked in the SR module using the local feature. The superior
performance of the proposed IF/SR method is demonstrated by extensive
experiments conducted on the popular SHREC12 dataset.


  We describe how quartic ($\lambda \phi^4$) inflation with non-minimal
coupling to gravity is realized in realistic supersymmetric $SO(10)$ models. In
a well-motivated example the $16-\overline{16}$ Higgs multiplets, which break
$SO(10)$ to $SU(5)$ and yield masses for the right-handed neutrinos, provide
the inflaton field $\phi$. Thus, leptogenesis is a natural outcome in this
class of $SO(10)$ models. Moreover, the adjoint (45-plet) Higgs also acquires a
GUT scale value during inflation so that the monopole problem is evaded. The
scalar spectral index $n_s$ is in good agreement with the observations and $r$,
the tensor to scalar ratio, is predicted for realistic values of GUT parameters
to be of order $10^{-3}-10^{-2}$.


  We present an empirical method for estimating the underlying redshift
distribution N(z) of galaxy photometric samples from photometric observables.
The method does not rely on photometric redshift (photo-z) estimates for
individual galaxies, which typically suffer from biases. Instead, it assigns
weights to galaxies in a spectroscopic subsample such that the weighted
distributions of photometric observables (e.g., multi-band magnitudes) match
the corresponding distributions for the photometric sample. The weights are
estimated using a nearest-neighbor technique that ensures stability in sparsely
populated regions of color-magnitude space. The derived weights are then summed
in redshift bins to create the redshift distribution. We apply this weighting
technique to data from the Sloan Digital Sky Survey as well as to mock catalogs
for the Dark Energy Survey, and compare the results to those from the
estimation of photo-z's derived by a neural network algorithm. We find that the
weighting method accurately recovers the underlying redshift distribution,
typically better than the photo-z reconstruction, provided the spectroscopic
subsample spans the range of photometric observables covered by the photometric
sample.


  We have investigated the X-ray spectral properties of a sample of 138 X-ray
sources detected serendipitously in $XMM-Newton$ observations of the Galactic
plane, at an intermediate to faint flux level. We divide our sample into 5
subgroups according to the spectral hardness of the sources, and stack (i.e.
co-add) the individual source spectra within each subgroup. As expected these
stacked spectra show a softening trend from the hardest to the softest
subgroups, which is reflected in the inferred line-of-sight column density. The
spectra of the three hardest subgroups are characterized by a hard continuum
plus superimpose Fe-line emission in the 6--7 keV bandpass. The average
equivalent width (EW) of the 6.7-keV He-like Fe-K$\alpha$ line is
170$^{+35}_{-32}$ eV, whereas the 6.4-keV Fe-K fluorescence line from neutral
iron and the 6.9-keV H-like Fe-Ly$\alpha$ line have EWs of 89$^{+26}_{-25}$ eV
and 81$^{+30}_{-29}$ eV respectively, i.e. roughly half that of the 6.7-keV
line. The remaining subgroups exhibit soft thermal spectra. Virtually all of
the spectrally-soft X-ray sources can be associated with relatively nearby
coronally-active late-type stars, which are evident as bright near-infrared
(NIR) objects within the X-ray error circles. On a similar basis only a
minority of the spectrally-hard X-ray sources have likely NIR identifications.
The average continuum and Fe-line properties of the spectrally-hard sources are
consistent with those of magnetic cataclysmic variables but the direct
identification of large numbers of such systems in Galactic X-ray surveys,
probing intermediate to faint flux levels, remains challenging.


  We survey some important results concerning the finite--dimensional
representations of the loop algebra of a simple complex Lie algebra, and their
twisted loop subalgebras. In particular, we review the parametrization and
description of the Weyl modules and of the irreducible finite--dimensional
representations of such algebras, describe a block decomposition of the
(non--semisimple) category of their finite--dimensional representations, and
conclude with recent developments in the representation theory of multiloop
algebras.


  We study the photometric parameters of the bulges of galaxies of different
Hubble types including ellipticals, lenticulars, early and late type spirals
and early type dwarf galaxies. Analyzing the distributions of various
photometric parameters, and two- and three-dimensional correlations between
them, we find that there is a difference in the correlations exhibited by
bright (M_K < -22) and faint bulges, irrespective of their Hubble type.
Importantly, the bright bulges, which include typically E/S0 galaxies and
bulges of early type spirals, are tightly distributed around a common
photometric plane (PP), while their fainter counter parts, mainly bulges of
late type spirals and dwarf galaxies show significant deviation from the planar
distribution. We show that the specific entropy, determined from the bulge
structural parameters, systematically increases as we move from late to early
Hubble types. We interpret this as evidence for hierarchical merging and
passive evolution scenarios for bright and faint bulges respectively.


  Recent results from HERA are presented on a range of topics: charged
multiplicities, production of non-strange mesons and strange particles, charm
fragmentation, baryons decaying to strange particles, antideuteron production,
Bose-Einstein correlations, and new interpretations of results on prompt photon
production in DIS.


  Neutral models, in which individual agents with equal fitness undergo a
birth-death-mutation process, are very popular in population genetics and
community ecology. Usually these models are applied to populations and
communities with spatial structure, but the analytic results presented so far
are limited to well-mixed or mainland-island scenarios. Here we present a new
technique, based on interface dynamics analysis, and apply it to the neutral
dynamics in one, two and three spatial dimensions. New results are derived for
the correlation length and for the main characteristics of the community, like
total biodiversity and the species abundance distribution above the correlation
length. Our results are supported by extensive numerical simulations, and
provide qualitative and quantitative insights that allow for a rigorous
comparison between model predictions and empirical data.


  Data rate selection algorithms for Wi-Fi devices are an important area of
research because they directly impact performance. Most of the proposals are
based on measuring the transmission success probability for a given data rate.
In dense scenarios, however, this probing approach will fail because frame
collisions are misinterpreted as erroneous data rate selection. We propose
FTMRate which uses the fine timing measurement (FTM) feature, recently
introduced in IEEE 802.11. FTM allows stations to measure their distance from
the AP. We argue that knowledge of the distance from the receiver can be useful
in determining which data rate to use. We apply statistical learning (a form of
machine learning) to estimate the distance based on measurements, estimate
channel quality from the distance, and select data rates based on channel
quality. We evaluate three distinct estimation approaches: exponential
smoothing, Kalman filter, and particle filter. We present a performance
evaluation of the three variants of FTMRate and show, in several dense and
mobile (though line-of-sight only) scenarios, that it can outperform two
benchmarks and provide close to optimal results in IEEE 802.11ax networks.


  Given a graph $G$ with maximum degree $\Delta\ge 3$, we prove that the
acyclic edge chromatic number $a'(G)$ of $G$ is such that $a'(G)\le\lceil 9.62
(\Delta-1)\rceil$. Moreover we prove that:
  $a'(G)\le \lceil 6.42(\Delta-1)\rceil$ if $G$ has girth $g\ge 5\,$; $a'(G)\le
\lceil5.77 (\Delta-1)\rc$ if
  $G$ has girth $g\ge 7$; $a'(G)\le \lc4.52(\D-1)\rc$ if $g\ge 53$;
  $a'(G)\le \D+2\,$ if $g\ge \lceil25.84\D\log\D(1+ 4.1/\log\D)\rceil$.
  We further prove that the acyclic (vertex) chromatic number $a(G)$ of $G$ is
such that
  $a(G)\le \lc 6.59 \Delta^{4/3}+3.3\D\rc$. We also prove that the
star-chromatic number $\chi_s(G)$ of $G$ is such that $\chi_s(G)\le
\lc4.34\Delta^{3/2}+ 1.5\D\rc$. We finally prove that the $\b$-frugal chromatic
number $\chi^\b(G)$ of $G$ is such that $\chi^\b(G)\le \lc\max\{k_1(\b)\D,\;
k_2(\b){\D^{1+1/\b}/ (\b!)^{1/\b}}\}\rc$, where $k_1(\b)$ and $k_2(\b)$ are
decreasing functions of $\b$ such that $k_1(\b)\in[4, 6]$ and
$k_2(\b)\in[2,5]$.
  To obtain these results we use an improved version of the Lov\'asz Local
Lemma due to Bissacot, Fern\'andez, Procacci and Scoppola \cite{BFPS}.


  Understanding the topological characteristics of complex networks and how
they affect navigability is one of the most important goals in science today,
as it plays a central role in various economic, biological, ecological and
social systems. Here, we apply First Passage analysis tools to investigate the
properties and characteristics of random walkers in networks with different
topology. Starting with the simplest two-dimensional square lattice, we modify
its topology incrementally by randomly reconnecting links between sites. We
characterize these networks by First Passage Time from a significant number of
random walkers without interaction, varying the departure and arrival
locations. We also apply the concept of First Passage Simultaneity, which
measures the likelihood of two walkers reaching their destination together.
These measures, together with the site occupancy statistics during the
processes, allowed to differentiate the studied networks, especially the random
networks from the scale-free networks, by their navigability. We also show that
small world features can also be highlighted with the proposed technique.


  We briefly sketch the methods for a numerically stable evaluation of tensor
one-loop integrals that have been used in the calculation of the complete
electroweak one-loop corrections to $\Pep\Pem\to4 $fermions. In particular, the
improvement of the new methods over the conventional Passarino--Veltman
reduction is illustrated for some 4-point integrals in the delicate limits of
small Gram (and other kinematical) determinants.


  We extend the approach of Casini, Huerta and Myers to a new calculation of
the Renyi entropy of a general CFT in d dimensions with a spherical entangling
surface, in terms of certain thermal partition functions. We apply this
approach to calculate the Renyi entropy in various holographic models. Our
results indicate that in general, the Renyi entropy will be a complicated
nonlinear function of the central charges and other parameters which
characterize the CFT. We also exhibit the relation between this new thermal
calculation and a conventional calculation of the Renyi entropy where a twist
operator is inserted on the spherical entangling surface. The latter insight
also allows us to calculate the scaling dimension of the twist operators in the
holographic models.


  We give an algebraic proof for the result of Eilenberg and Mac Lane that the
second cohomology group of a simplicial group G can be computed as a quotient
of a fibre product involving the first two homotopy groups and the first
Postnikov invariant of G. Our main tool is the theory of crossed module
extensions of groups.


  We present a numerical approximation method for linear diffusion-reaction
problems with possibly discontinuous Dirichlet boundary conditions. The
solution of such problems can be represented as a linear combination of
explicitly known singular functions as well as of an $H^2$-regular part. The
latter part is expressed in terms of an elliptic problem with regularized
Dirichlet boundary conditions, and can be approximated by means of a Nitsche
finite element approach. The discrete solution of the original problem is then
defined by adding the singular part of the exact solution to the Nitsche
approximation. In this way, the discrete solution can be shown to converge of
second order with respect to the mesh size.


  We construct of the main object of the Partite Lemma as the colimit over a
certain diagram. This gives a purely category theoretic take on the Partite
Lemma and establishes the canonicity of the object. Additionally, the
categorical point of view allows us to unify the direct Partite Lemma in the
Ne\v{s}et\v{r}il--R\"odl Theorem with the dual Paritite Lemma by Solecki.


  In recent times, an increasing number of researchers have been devoted to
utilizing deep neural networks for end-to-end flight navigation. This approach
has gained traction due to its ability to bridge the gap between perception and
planning that exists in traditional methods, thereby eliminating delays between
modules. However, the practice of replacing original modules with neural
networks in a black-box manner diminishes the overall system's robustness and
stability. It lacks principled explanations and often fails to consistently
generate high-quality motion trajectories. Furthermore, such methods often
struggle to rigorously account for the robot's kinematic constraints, resulting
in the generation of trajectories that cannot be executed satisfactorily. In
this work, we combine the advantages of traditional methods and neural networks
by proposing an optimization-embedded neural network. This network can learn
high-quality trajectories directly from visual inputs without the need of
mapping, while ensuring dynamic feasibility. Here, the deep neural network is
employed to directly extract environment safety regions from depth images.
Subsequently, we employ a model-based approach to represent these regions as
safety constraints in trajectory optimization. Leveraging the availability of
highly efficient optimization algorithms, our method robustly converges to
feasible and optimal solutions that satisfy various user-defined constraints.
Moreover, we differentiate the optimization process, allowing it to be trained
as a layer within the neural network. This approach facilitates the direct
interaction between perception and planning, enabling the network to focus more
on the spatial regions where optimal solutions exist. As a result, it further
enhances the quality and stability of the generated trajectories.


  The low density interstellar medium (ISM) close to the Sun and inside of the
heliosphere provides a unique laboratory for studying interstellar dust grains.
Grain characteristics in the nearby ISM are obtained from observations of
interstellar gas and dust inside of the heliosphere and the interstellar gas
towards nearby stars. Comparison between the gas composition and solar
abundances suggests that grains are dominated by olivines and possibly some
form of iron oxide. Measurements of the interstellar Ne/O ratio by the
Interstellar Boundary Explorer spacecraft indicate that a high fraction of
interstellar oxygen in the ISM must be depleted onto dust grains. Local
interstellar abundances are consistent with grain destruction in ~150 km/s
interstellar shocks, provided that the carbonaceous component is hydrogenated
amorphous carbon and carbon abundances are correct. Variations in relative
abundances of refractories in gas suggest variations in the history of grain
destruction in nearby ISM. The large observed grains, > 1 micron, may indicate
a nearby reservoir of denser ISM. Theoretical three-dimensional models of the
interaction between interstellar dust grains and the solar wind predict that
plumes of about 0.18 micron dust grains form around the heliosphere.