  The influence of the relativistic covariance requirement on the optimality of
the symmetric state-dependent 1 -> 2 cloning machine is studied. Namely, given
a photonic qubit whose basis is formed from the momentum-helicity eigenstates,
the change to the optimal cloning fidelity is calculated taking into account
the Lorentz covariance unitarily represented by Wigner's little group. To
pinpoint some of the interesting results, we found states for which the optimal
fidelity of the cloning process drops to 2/3 which corresponds to the fidelity
of the optimal classical cloner. Also, an implication for the security of the
BB84 protocol is analyzed.


  A method for testing nonlinearity in time series is described based on
information-theoretic functionals -- redundancies, linear and nonlinear forms
of which allow either qualitative, or, after incorporating the surrogate data
technique, quantitative evaluation of dynamical properties of scrutinized data.
An interplay of quantitative and qualitative testing on both the linear and
nonlinear levels is analyzed and robustness of this combined approach against
spurious nonlinearity detection is demonstrated. Evaluation of redundancies and
redundancy-based statistics as functions of time lag and embedding dimension
can further enhance insight into dynamics of a system under study.


  The spectra of high-energy protons and nuclei accelerated by supernova
remnant shocks are calculated taking into account magnetic field amplification
and Alfvenic drift both upstream and downstream of the shock for different
types of supernova remnants during their evolution. The maximum energy of
accelerated particles may reach $5\cdot10^{18}$ eV for Fe ions in Type IIb
SNRs. The calculated energy spectrum of cosmic rays after propagation through
the Galaxy is in good agreement with the spectrum measured at the Earth.


  We use the multi-spacecraft capabilities of the Cluster and THEMIS missions
to show that two types of foreshock may be detected in spacecraft data. One is
the global foreshock that appears upstream of the Earth's quasi-parallel
bow-shock under steady or variable interplanetary magnetic field. Another type
is a traveling foreshock that is bounded by two rotational discontinuities in
the interplanetary magnetic field and propagates along the bow-shock. Foreshock
compressional boundaries are found at the edges of both types of foreshock. We
show that isolated foreshock cavities are a subset of the traveling foreshock
that form when two bounding rotational discontinuities are so close that the
ultra-low frequency waves do not develop in the region between them. We also
report observations of a spontaneous hot flow anomaly inside a traveling
foreshock. This means that other phenomena, such as foreshock cavitons, may
also exist inside this type of foreshock. In the second part of this work we
present statistical properties of phenomena related to the foreshock, namely
foreshock cavities, cavitons, spontaneous hot flow anomalies and foreshock
compressional boundaries. We show that spontaneous hot flow anomalies are the
most depleted transient structures in terms of the B-field and plasma density
inside them and that the foreshock compressional boundaries and foreshock
cavities are closely related structures.


  Does the quasi one-dimensional titanium pyroxene NaTiSi2O6 exhibit the novel
{\it orbital-Peierls} state? We calculate its groundstate properties by three
methods: Monte Carlo simulations, a spin-orbital decoupling scheme and a
mapping onto a classical model. The results show univocally that for the spin
and orbital ordering to occur at the same temperature --an experimental
observation-- the crystal field needs to be small and the orbitals are active.
We also find that quantum fluctuations in the spin-orbital sector drive the
transition, explaining why canonical bandstructure methods fail to find it. The
conclusion that NaTiSi2O6 shows an orbital-Peierls transition is therefore
inevitable.


  Applications of machine learning are subject to three major components that
contribute to the final performance metrics. Within the category of neural
networks, and deep learning specifically, the first two are the architecture
for the model being trained and the training approach used. This work focuses
on the third component, the data used during training. The primary questions
that arise are ``what is in the data'' and ``what within the data matters?''
Looking into the Radio Frequency Machine Learning (RFML) field of Automatic
Modulation Classification (AMC) as an example of a tool used for situational
awareness, the use of synthetic, captured, and augmented data are examined and
compared to provide insights about the quantity and quality of the available
data necessary to achieve desired performance levels. There are three questions
discussed within this work: (1) how useful a synthetically trained system is
expected to be when deployed without considering the environment within the
synthesis, (2) how can augmentation be leveraged within the RFML domain, and
lastly, (3) what impact knowledge of degradations to the signal caused by the
transmission channel contributes to the performance of a system. In general,
the examined data types each have useful contributions to a final application,
but captured data germane to the intended use case will always provide more
significant information and enable the greatest performance. Despite the
benefit of captured data, the difficulties and costs that arise from live
collection often make the quantity of data needed to achieve peak performance
impractical. This paper helps quantify the balance between real and synthetic
data, offering concrete examples where training data is parametrically varied
in size and source.


  Polarization is a powerful tool for understanding stellar atmospheres and
circumstellar environments. Mira and semi-regular variable stars have been
observed for decades and some are known to be polarimetrically variable,
however, the semi-regular variable V Canes Venatici displays an unusually
large, unexplained amount of polarization. We present ten years of optical
polarization observations obtained with the HPOL instrument, supplemented by
published observations spanning a total interval of about forty years for V
CVn. We find that V CVn shows large polarization variations ranging from 1 -
6%. We also find that for the past forty years the position angle measured for
V CVn has been virtually constant suggesting a long-term, stable, asymmetric
structure about the star. We suggest that this asymmetry is caused by the
presence of a stellar wind bow shock and tail, consistent with the star's large
space velocity.


  The momentum, electronic density, spin density, and interaction dependences
of the exponents that control the $(k,\omega)$-plane singular features of the
$\sigma =\uparrow,\downarrow$ one-electron spectral functions of the 1D Hubbard
model at finite magnetic field are studied. The usual half-filling concepts of
one-electron lower Hubbard band and upper Hubbard band are defined for all
electronic density and spin density values and the whole finite repulsion range
in terms of the rotated electrons associated with the model Bethe-ansatz
solution. Such rotated electrons are the link of the non-perturbative relation
between the electrons and the pseudofermions. Our results further clarify the
microscopic processes through which the pseudofermion dynamical theory accounts
for the $\sigma $ one-electron matrix elements between the ground state and
excited energy eigenstates.


  Generating visual layouts is an essential ingredient of graphic design. The
ability to condition layout generation on a partial subset of component
attributes is critical to real-world applications that involve user
interaction. Recently, diffusion models have demonstrated high-quality
generative performances in various domains. However, it is unclear how to apply
diffusion models to the natural representation of layouts which consists of a
mix of discrete (class) and continuous (location, size) attributes. To address
the conditioning layout generation problem, we introduce DLT, a joint
discrete-continuous diffusion model. DLT is a transformer-based model which has
a flexible conditioning mechanism that allows for conditioning on any given
subset of all the layout component classes, locations, and sizes. Our method
outperforms state-of-the-art generative models on various layout generation
datasets with respect to different metrics and conditioning settings.
Additionally, we validate the effectiveness of our proposed conditioning
mechanism and the joint continuous-diffusion process. This joint process can be
incorporated into a wide range of mixed discrete-continuous generative tasks.


  If the present dark matter in the Universe annihilates into Standard Model
particles, it must contribute to the gamma ray fluxes detected on the Earth.
The magnitude of such contribution depends on the particular dark matter
candidate, but certain features of the produced spectra may be analyzed in a
rather model-independent fashion. In this communication we briefly revise the
complete photon spectra coming from WIMP annihilation into Standard Model
particle-antiparticle pairs obtained by extensive Monte Carlo simulations and
consequent fitting functions presented by Dombriz et al. in a wide range of
WIMP masses. In order to illustrate the usefulness of these fitting functions,
we mention how these results may be applied to the so-called brane-world
theories whose fluctuations, the branons, behave as WIMPs and therefore may
spontaneously annihilate in SM particles. The subsequent $\gamma$-rays signal
in the framework of dark matter indirect searches from Milky Way dSphs and
Galactic Center may provide first evidences for this scenario.


  We exhibit an explicit full measure class of minimal interval exchange maps T
for which the cohomological equation $\Psi -\Psi\circ T=\Phi$ has a bounded
solution $\Psi$ provided that the datum $\Phi$ belongs to a finite codimension
subspace of the space of functions having on each interval a derivative of
bounded variation. The class of interval exchange maps is characterized in
terms of a diophantine condition of ``Roth type'' imposed to an acceleration of
the Rauzy--Veech--Zorich continued fraction expansion associated to T.
  CONTENTS 0. Introduction 1. The continued fraction algorithm for interval
exchange maps 1.1 Interval exchnge maps 1.2 The continued fraction algorithm
1.3 Roth type interval exchange maps 2. The cohomological equation 2.1 The
theorem of Gottschalk and Hedlund 2.2 Special Birkhoff sums 2.3 Estimates for
functions of bounded variation 2.4 Primitives of functions of bounded variation
3. Suspensions of interval exchange maps 3.1 Suspension data 3.2 Construction
of a Riemann surface 3.3 Compactification of $M_\zeta^*$ 3.4 The cohomological
equation for higher smoothness 4. Proof of full measure for Roth type 4.1 The
basic operation of the algorithm for suspensions 4.2 The Teichm\"uller flow 4.3
The absolutely continuous invariant measure 4.4 Integrability of $\log\Vert
Z_{(1)}\Vert$ 4.5 Conditions (b) and (c) have full measure 4.6 The main step
4.7 Condition (a) has full measure 4.8 Proof of the Proposition Appendix A
Roth--type conditions in a concrete family of i.e.m. Appendix B A non--uniquely
ergodic i.e.m. satsfying condition (a) References


  We investigate two sparse Sachdev-Ye-Kitaev (SYK) systems coupled by a
bilinear term as a holographic quantum mechanical description of an eternal
traversable wormhole in the low temperature limit. Each SYK system consists of
$N$ Majorana fermions coupled by random $q$-body interactions. The degree of
sparseness is captured by a regular hypergraph in such a way that the
Hamiltonian contains exactly $k\,N$ independent terms. We improve on the
theoretical understanding of the sparseness property by using known measures of
hypergraph expansion. We show that the sparse version of the two coupled SYK
model is gapped with a ground state close to a thermofield double state. Using
Krylov subspace and parallelization techniques, we simulate the system for
$q=4$ and $q=8.$ The sparsity of the model allows us to explore larger values
of $N$ than the ones existing in the literature for the all-to-all SYK. We
analyze in detail the two-point functions and the transmission amplitude of
signals between the two systems. We identify a range of parameters where
revivals obey the scaling predicted by holography and signals can be
interpreted as traversing the wormhole.


  We investigate the effect of particle inertia on the merger of co-rotating
dusty vortex pairs at semi-dilute concentrations. In a particle-free flow, the
merger is triggered once the ratio of vortex core size to vortex separation
reaches a critical value. The vortex pair separation then decreases
monotonically until the two cores merge together. Using Eulerian-Lagrangian
simulations of co-rotating particle-laden vortices, we show substantial
departure from the vortex dynamics previously established in particle-free
flows. Most strikingly, we find that disperse particles with moderate inertia
cause the vortex pair to push apart to a separation nearly twice as large as
the initial separation. During this stage, the drag force exerted by particles
ejected out of the vortex cores on the fluid results in a net repulsive force
that pushes the two cores apart. Eventually, the two dusty vortices merge into
a single vortex with most particles accumulating outside the core similar to
the dusty Lamb-Oseen vortex described in Shuai & Kasbaoui (J. Fluid Mech., vol
936, 2022, A8) For weakly inertial particles, we find that the merger dynamics
follow the same mechanics as those of a single-phase flow, albeit with a
density that must be adjusted to match the mixture density. For highly inertial
particles, the feedback force exerted by the particles on the fluid may stretch
the two cores during the merger to a point where each core splits into two,
resulting in inner and outer vortex pairs. In this case, the merger occurs in
two stages where the inner vortices merge first, followed by the outer ones.


  The full one-loop supersymmetric effective potential for the Wess-Zumino
model is calculated using superfield techniques. This includes the K\"ahler
potential and the auxiliary field potential, of which the former was originally
computed in 1993 while the latter is derived for the first time. In the purely
bosonic sector our results match those of older component field calculations.
  In light of prior contradictory results found in the literature, the
calculation of the leading term in the auxiliary field potential is approached
in a variety of ways. Issues related to conditional convergence that occur
during these calculations and their possible consequences are discussed.


  Limit and Pseudotopological spaces are two generalizations of topological
spaces which are defined by indicating what filters converge under some axioms.
In this article, we introduce covering spaces and set forth some necessary
conditions for a construction for a universal covering space.


  We present a theory of a single-electron transistor exchange-coupled to a
localized spin. We show how to gain detailed quantitative knowledge about the
attached spin such as spin size, exchange coupling strength, Land\'e g-factor,
and spin decay time $T_1$ by utilizing a robust blockade phenomenon of DC
magnetotransport with accompanying noise enhancement. Our studies are of
particular relevance to spin-resolved scanning single-electron transistor
microscopy, electronic transport through nanomagnets, and the effect of
hyperfine interaction on transport electrons by surrounding nuclear spins.


  The cyclic sieving phenomenon of Reiner, Stanton, and White says that we can
often count the fixed points of elements of a cyclic group acting on a
combinatorial set by plugging roots of unity into a polynomial related to this
set. One of the most impressive instances of the cyclic sieving phenomenon is a
theorem of Rhoades asserting that the set of plane partitions in a rectangular
box under the action of promotion exhibits cyclic sieving. In Rhoades's result
the sieving polynomial is the size generating function for these plane
partitions, which has a well-known product formula due to MacMahon. We extend
Rhoades's result by also considering symmetries of plane partitions:
specifically, complementation and transposition. The relevant polynomial here
is the size generating function for symmetric plane partitions, whose product
formula was conjectured by MacMahon and proved by Andrews and Macdonald.
Finally, we explain how these symmetry results also apply to the rowmotion
operator on plane partitions, which is closely related to promotion.


  Pursuing the goal to single out the validity region of the high-energy
resummation, better known as BFKL approach, and to possibly disentangle BFKL
effects from the ones coming from a DGLAP-inspired, fixed-order description,
new predictions for the forward inclusive hadron-jet production, tailored on
the CMS and CASTOR acceptances, are given.


  The integration between the satellite network and the terrestrial network
will play a key role in the upcoming sixth-generation (6G) of mobile cellular
networks thanks to the wide coverage and bandwidth offered by satellite
networks. To leverage this integration, we propose a proactive traffic
offloading scheme in an integrated multi-satellite terrestrial network (IMSTN)
that considers the future networks' heterogeneity and predicts their
variability. Our proposed offloading scheme hinges on traffic prediction to
answer the stringent requirements of data-rate, latency and reliability imposed
by heterogeneous and coexisting services and traffic namely enhanced mobile
broadband (eMBB), massive machine-type communications (mMTC) and ultra-reliable
low latency communication (URLLC). However, the fulfilment of these
requirements during offloading in dynamic IMSTN comes at the expense of
significant energy consumption and introduces inherently supplementary latency.
Therefore, our offloading scheme aims to balance the fundamental trade-offs
first between energy consumption and the achievable data-rate and second
between energy consumption and latency while meeting the respective needs of
the present traffic. Our findings prove the importance of the cooperation
between the multi-satellite network and the terrestrial network conditioned by
traffic prediction to enhance the performance of IMTSN in terms of latency and
energy consumption.


  The pressureless Euler equations can be used as simple models of cosmology or
plasma physics. In this paper, we construct the exact solutions in non-radial
symmetry to the pressureless Euler equations in $R^{N}:$% [c]{c}%
\rho(t,\vec{x})=\frac{f(\frac{1}{a(t)^{s}}\underset{i=1}{\overset
{N}{\sum}}x_{i}^{s})}{a(t)^{N}}\text{,}\vec{u}(t,\vec{x}%
)=\frac{\overset{\cdot}{a}(t)}{a(t)}\vec{x}, a(t)=a_{1}+a_{2}t. \label{eq234}%
where the arbitrary function $f\geq0$ and $f\in C^{1};$ $s\geq1$, $a_{1}>0$ and
$a_{2}$ are constants$.$\newline In particular, for $a_{2}<0$, the solutions
blow up on the finite time $T=-a_{1}/a_{2}$.
  Moreover, the functions (\ref{eq234}) are also the solutions to the
pressureless Navier-Stokes equations.


  This paper generalizes the result of Sarnak and Ubis \cite{sarnak-ubis} about
non-concentration of primes in horocycle orbits on $PSL_2(\mathbb{Z})
\backslash PSL_2(\mathbb{R})$ to any lattice in $PSL_2(\mathbb{R})$. The proof
combines the asymptotic result of Str\"ombergsson \parencite{strombergsson} and
Venkatesh's method \parencite{venkatesh} with the approach of Sarnak and Ubis
of approximating horocycle pieces with periodic horocycles. The key step is to
establish a dichotomy between $\{\xi h(t), t \in [0, T] \}$ having good
equidistribution in $\Gamma \backslash PSL_2(\mathbb{R})$ and it being
approximable by closed horocycle pieces with small period. In a follow-up
paper, a similar approach will be used to show equidistribution of $\xi
h(n^{1+\gamma})$ for small $\gamma>0$, generalizing Venkatesh's result
\parencite{venkatesh} to non-compact $\Gamma$.


  Preliminary epidemiologic, phylogenetic and clinical findings suggest that
several novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)
variants have increased transmissibility and decreased efficacy of several
existing vaccines. Four mutations in the receptor-binding domain (RBD) of the
spike protein that are reported to contribute to increased transmission.
Understanding physical mechanism responsible for the affinity enhancement
between the SARS-CoV-2 variants and ACE2 is the "urgent challenge" for
developing blockers, vaccines and therapeutic antibodies against the
coronavirus disease 2019 (COVID-19) pandemic. Based on a
hydrophobic-interaction-based protein docking mechanism, this study reveals
that the mutation N501Y obviously increased the hydrophobic attraction and
decrease hydrophilic repulsion between the RBD and ACE2 that most likely caused
the transmissibility increment of the variants. By analyzing the
mutation-induced hydrophobic surface changes in the attraction and repulsion at
the binding site of the complexes of the SARS-CoV-2 variants and antibodies, we
found out that all the mutations of N501Y, E484K, K417N and L452R can
selectively decrease or increase their binding affinity with some antibodies.


  The Schwinger-Dyson equations of the Makeenko-Migdal type, when supplemented
with some simple equations as consequence of supersymmetry, form a closed set
of equations for Wilson loops and related quantities in the two dimensional
super-gauge theory. We solve these equations. It appears that the planar Wilson
loops are described by the Nambu string without folds. We also discuss how to
put the model on a spatial lattice, where a peculiar gauge is chosen in order
to keep one supersymmetry on the lattice. Supersymmetry is unbroken in this
theory. We comment on possible generalization of these considerations to other
models.


  Advances in artificial intelligence have facilitated the use of large
language models (LLMs) and AI-generated synthetic media in education, which may
inspire HCI researchers to develop technologies, in particular, embodied
conversational agents (ECAs) to simulate the kind of scaffolding children might
receive from a human partner. In this paper, we will propose a design prototype
of a peer-like ECA named STARie that integrates multiple AI models - GPT-3,
Speech Synthesis (Real-time Voice Cloning), VOCA (Voice Operated Character
Animation), and FLAME (Faces Learned with an Articulated Model and Expressions)
that aims to support narrative production in collaborative storytelling,
specifically for children aged 4-8. However, designing a child-centered ECA
raises concerns about age appropriateness, children privacy, gender choices of
ECAs, and the uncanny valley effect. Thus, this paper will also discuss
considerations and ethical concerns that must be taken into account when
designing such an ECA. This proposal offers insights into the potential use of
AI-generated synthetic media in child-centered AI design and how peer-like AI
embodiment may support children\textquotesingle s storytelling.


  We study the system of the Dp'-brane with Dp-brane (p<p') inside, in the case
where B_{ij} field is a nonvanishing constant. In order to understand how the
Dp-brane is viewed from the Dp'-brane worldvolume theory, we investigate the
process in which the Dp-brane is probed with p'-p' open string. We calculate
the scattering amplitudes among p-p' open strings and p'-p' open strings and
show that not only the Weyl transform of the projection operator onto the
ground state but also those onto higher excited states emerge as multiplicative
factors of the amplitudes.


  In recent years, longitudinal neuroimaging study has become increasingly
popular in neuroscience research to investigate disease-related changes in
brain functions. In current neuroscience literature, one of the most commonly
used tools to extract and characterize brain functional networks is independent
component analysis (ICA). However, existing ICA methods are not suited for
modelling repeatedly measured imaging data. In this paper, we propose a novel
longitudinal independent component model (L-ICA) which provides a formal
modeling framework for extending ICA to longitudinal studies. By incorporating
subject-specific random effects and visit-specific covariate effects, L-ICA is
able to provide more accurate estimates of changes in brain functional networks
on both the population- and individual-level, borrow information across
repeated scans within the same subject to increase statistical power in
detecting covariate effects on the networks, and allow for model-based
prediction for brain networks changes caused by disease progression, treatment
or neurodevelopment. We develop a fully traceable exact EM algorithm to obtain
maximum likelihood estimates of L-ICA. We further develop a subspace-based
approximate EM algorithm which greatly reduce the computation time while still
retaining high accuracy. Moreover, we present a statistical testing procedure
for examining covariate effects on brain network changes. Simulation results
demonstrate the advantages of our proposed methods. We apply L-ICA to ADNI2
study to investigate changes in brain functional networks in Alzheimer disease.
Results from the L-ICA provide biologically insightful findings which are not
revealed using existing methods.


  We consider a time dependent, spherically outflowing wind, in Schwarzschild
space-time, consisting of electron-positron pairs and photons . Without
assuming thermal equilibrium, we account for the microphysics, including
two-body processes and their radiative three-body variants. We present a
finite-difference scheme for solving the general relativistic kinetic Boltzmann
equations for electron-positron pairs and photons. We apply this to the
concrete example of a wind from a hot, bare, strange star, predicted to be a
powerful source of hard X-ray photons and pairs created by the Coulomb barrier
at the quark surface. We study the kinetics of the wind particles and the
emerging emission in photons and pairs for stationary winds with total
luminosities in the range 10^{34}-10^{39} ergs/s, for different values of the
injected photon-to-pair ratio. The wind parameters--such as the mean optical
depth for photons, the rates of particle number and energy outflows, bulk
velocity, and number density of the pair plasma--are presented as functions of
the distance from the stellar surface, as well as characteristics of the
emergent radiation. We find that photons dominate in the emerging emission, and
the emerging photon spectrum is rather hard and differs substantially from the
thermal spectrum expected from a neutron star with the same luminosity. This
might help distinguish the putative bare strange stars from neutron stars.


  The area of Video Camouflaged Object Detection (VCOD) presents unique
challenges in the field of computer vision due to texture similarities between
target objects and their surroundings, as well as irregular motion patterns
caused by both objects and camera movement. In this paper, we introduce
TokenMotion (TMNet), which employs a transformer-based model to enhance VCOD by
extracting motion-guided features using a learnable token selection. Evaluated
on the challenging MoCA-Mask dataset, TMNet achieves state-of-the-art
performance in VCOD. It outperforms the existing state-of-the-art method by a
12.8% improvement in weighted F-measure, an 8.4% enhancement in S-measure, and
a 10.7% boost in mean IoU. The results demonstrate the benefits of utilizing
motion-guided features via learnable token selection within a transformer-based
framework to tackle the intricate task of VCOD.


  We show that for the edge ideals of a certain class of forests, the
arithmetical rank equals the projective dimension.


  This article proposes O-LoRaWAN, an adaptation of the LoRaWAN architecture
into a modular network architecture based on the Open RAN (O-RAN) principles.
In our vision, standardization of the network components and interfaces will
enable the reuse of network functions, and thus, foster an accelerated
tailoring of the network functions to the changing application demands. LoRaWAN
shares similarities to cellular networks and becomes an interesting candidate
for a transformation to the O-RAN standard. In the article we draw several
transition strategies, these include the reorganization of the LoRa gateway
functions into Radio and Distributed Units; enhancing network performance with
RAN Intelligent Controllers exploiting the network data; and the
standardization of the management and orchestration of network components. Key
for that adaptation are the O-RAN interfaces. Along the article, we analyze
them and suggest protocol extensions or adjustments for compatibility and
interoperability between network components, advocating for the design of
extensible protocols


  Flow-Aware Multi-Topology Adaptive Routing (FAMTAR) is a new approach to
multipath and adaptive routing in IP networks which enables automatic use of
alternative paths when the primary one becomes congested. It provides more
efficient network resource utilization and higher quality of transmission
compared to standard IP routing. However, thus far it has only been evaluated
through simulations. In this paper we share our experiences from building a
real-time FAMTAR router and present results of its tests in a physical network.
The results are in line with those obtained previously through simulations and
they open the way to implementation of a production grade FAMTAR router.


  We consider a long Lorentz tube with absorbing boundaries. Particles are
injected to the tube from the left end. We compute the equilibrium density
profiles in two cases: the semi-infinite tube (in which case the density is
constant) and a long finite tube (in which case the density is linear). In the
latter case, we also show that convergence to equilibrium is well described by
the heat equation. In order to prove these results, we obtain new results for
the Lorentz particle which are of independent interest. First, we show that a
particle conditioned not to hit the boundary for a long time converges to the
Brownian meander. Second, we prove several local limit theorems for particles
having a prescribed behavior in the past.


  In this paper, we consider the reducibility of the quasi-periodic linear
Hamiltonian system $$\dot{x}=(A+\varepsilon Q(t))x, $$ where $A$ is a constant
matrix with possible multiple eigenvalues, $Q(t)$ is analytic quasi-periodic
with respect to $t$, and $\varepsilon$ is a sufficiently small parameter. Under
some non-resonant conditions, it is proved that, for most sufficiently small
$\varepsilon$, the Hamiltonian system can be reduced to a constant coefficient
Hamiltonian system by means of a quasi-periodic symplectic change of variables
with the same basic frequencies as $Q(t)$. Application to quasi-periodic Hill's
equation is also given.


  We give a characterization of the two-weight inequality for a simple
vector-valued operator. Special cases of our result have been considered before
in the form of the weighted Carleson embedding theorem, the dyadic positive
operators of Nazarov, Treil, and Volberg in the square integrable case, and
Lacey, Sawyer, Uriarte-Tuero in the L^p case. The main technique of this paper
is a Sawyer-style argument and the characterization is for 1 < p < \infty. We
are unaware of instances where this operator has been given attention in the
two-weight setting before.


  Experimental and numerical studies of the magnetic field dependence of the
specific heat and magnetization of single crystals of CsNiF3 have been
performed at 2.4 K, 2.9 K, and 4.2 K in magnetic fields up to 9 T oriented
perpendicular to the easy plane. The experimental results confirm the presence
of the theoretically predicted double peak structure in the specific heat
arising from the formation of nonlinear spin modes. The demagnetizing effects
are found to be negligible, and the overall agreement between the data and
numerical predictions is better than reported for the case when the magnetic
field was oriented in the easy plane. Demagnetizing effects might play a role
in generating the difference observed between theory and experiment in previous
work analyzing the excess specific heat using the sine-Gordon model.


  The 2013 National Security Agency revelations of pervasive monitoring have
lead to an "encryption rush" across the computer and Internet industry. To push
back against massive surveillance and protect users privacy, vendors, hosting
and cloud providers have widely deployed encryption on their hardware,
communication links, and applications. As a consequence, the most of web
traffic nowadays is encrypted. However, there is still a significant part of
Internet traffic that is not encrypted. It has been argued that both costs and
complexity associated with obtaining and deploying X.509 certificates are major
barriers for widespread encryption, since these certificates are required to
established encrypted connections. To address these issues, the Electronic
Frontier Foundation, Mozilla Foundation, and the University of Michigan have
set up Let's Encrypt (LE), a certificate authority that provides both free
X.509 certificates and software that automates the deployment of these
certificates. In this paper, we investigate if LE has been successful in
democratizing encryption: we analyze certificate issuance in the first year of
LE and show from various perspectives that LE adoption has an upward trend and
it is in fact being successful in covering the lower-cost end of the hosting
market.


  Temporary fork is a fundamental phenomenon in many blockchains with proof of
work, and the analysis of temporary fork has recently drawn great attention.
Different from existing efforts that focus on the blockchain system factors
such as block size, network propagation delay or block generation speed, in
this paper we explore a new key dimension of computing power from the miners'
perspective. Specifically, we first propose a detailed mathematical model to
characterize the impact of computing power competition of the mining pools on
the temporary fork. We also derive closed-form formula of the probability of
temporary fork and the expected mining reward of a mining pool. To reveal the
long-term trends on the computing power distributions over the competing mining
pools, we then develop an evolutionary game framework based on the temporary
fork modeling and accordingly characterize the set of stable evolution
equilibriums. Both extensive numerical simulations and realistic blockchain
data based evaluation provide evidence to support our theoretical models and
discoveries.


  Up-going and Horizontal Tau Air-Showers, UpTaus and HorTaus, may trace Ultra
High Energy Neutrino Tau Earth Skimming at the edge of the horizons. Their
secondaries muon, electron pairs, and gamma bundles flashes might trace their
nature over UHECR secondaries in horizontal showers. Indeed the atmosphere act
as a perfect amplifier as well as a filter for showers: down-ward and
horizontal muon bundles may still be originated by far Ultra High Energy Cosmic
Rays skimming the terrestrial atmosphere but their rich gamma component will be
exponentially suppressed. At large zenith angles after crossing a large slant
depth X > 3 10^3 g cm^-2 the number of muons and secondary gamma (produced by
the electron pair from muon decay in flight) is comparable. On the other hand,
up-ward muon bundles from UpTaus and HorTaus may arise within a young shower
with a larger gamma-muon ratio 10^2, leaving a characteristic imprint. We
estimate the UpTaus and HorTaus rate from the Earth and we evaluate the
consequent event rate of muons, electrons pairs andgamma bundles. We show that
such events even for minimal GZK neutrino fluxes could be detected by
scintillator arrays placed on mountains at 1-5km and pointing to the horizon.
The required arrayareas are within tens-hundreds of square meters. The ideal
structure is an array of crown-like twin detectors facing the horizons. We
argue that such detectors will be able to detect both muonic bundles at a
minimal average flux of 10^-11 cm-2 s^-1 sr^-1 and electromagnetic particles
gamma and electron pairs 3 10^-9 cm^-2 s^-1 sr^-1, a few times each year for
GZK neutrino fluxes.


  Wightman function, the vacuum expectation values of the field square and the
energy-momentum tensor are evaluated for a scalar field obeying the Robin
boundary conditions on two spherical branes in (D+1)-dimensional Rindler-like
spacetime $Ri\times S^{D-1}$, with a two-dimensional Rindler spacetime $Ri$.
This spacetime approximates the near horizon geometry of (D+1)-dimensional
black hole. By using the generalized Abel-Plana formula, the vacuum expectation
values are presented as the sum of single brane and second brane induced parts.
Various limiting cases are studied. The vacuum forces acting on the branes are
decomposed into the self-action and interaction terms. The interaction forces
are investigated as functions of the brane locations and coefficients in the
boundary conditions.


  Multi-distribution learning generalizes the classic PAC learning to handle
data coming from multiple distributions. Given a set of $k$ data distributions
and a hypothesis class of VC dimension $d$, the goal is to learn a hypothesis
that minimizes the maximum population loss over $k$ distributions, up to
$\epsilon$ additive error. In this paper, we settle the sample complexity of
multi-distribution learning by giving an algorithm of sample complexity
$\widetilde{O}((d+k)\epsilon^{-2}) \cdot (k/\epsilon)^{o(1)}$. This matches the
lower bound up to sub-polynomial factor and resolves the COLT 2023 open problem
of Awasthi, Haghtalab and Zhao [AHZ23].


  We construct a measure-valued equivalent to the spatial Lambda-Fleming-Viot
process (SLFV) introduced in [Eth08]. In contrast with the construction carried
out in [Eth08], we fix the realization of the sequence of reproduction events
and obtain a quenched evolution of the local genetic diversities. To this end,
we use a particle representation which highlights the role of the genealogies
in the attribution of types (or alleles) to the individuals of the population.
This construction also enables us to clarify the state-space of the SLFV and to
derive several path properties of the measure-valued process as well as of the
labeled trees describing the genealogical relations between a sample of
individuals. We complement it with a look-down construction which provides a
particle system whose empirical distribution at time t, seen as a process in t,
has the law of the quenched SLFV. In all these results, the facts that we work
with a fixed configuration of events and that reproduction occurs only locally
in space introduce serious technical issues that are overcome by controlling
the number of events occurring and of particles present in a given area over
macroscopic time intervals.


  Technology advances give us the hope of driving without human error, reducing
vehicle emissions and simplifying an everyday task with the future of
self-driving cars. Making sure these vehicles are safe is very important to the
continuation of this field. In this paper, we formalize the
Responsibility-Sensitive Safety model (RSS) for self-driving cars and prove the
safety and optimality of this model in the longitudinal direction. We utilize
the hybrid systems theorem prover KeYmaera X to formalize RSS as a hybrid
system with its nondeterministic control choices and continuous motion model,
and prove absence of collisions. We then illustrate the practicality of RSS
through refinement proofs that turn the verified nondeterministic control
envelopes into deterministic ones and further verified compilation to Python.
The refinement and compilation are safety-preserving; as a result, safety
proofs of the formal model transfer to the compiled code, while counterexamples
discovered in testing the code of an unverified model transfer back. The
resulting Python code allows to test the behavior of cars following the motion
model of RSS in simulation, to measure agreement between the model and
simulation with monitors that are derived from the formal model, and to report
counterexamples from simulation back to the formal model.


  The Poincar\'e polynomial of the complement of an arrangements in a non
compact group is a specialization of the $G$-Tutte polynomial associated with
the arrangement. In this article we show two unimodular elliptic arrangements
(built up from two graphs) with the same Tutte polynomial, having different
Betti numbers.


  General formulations of QCD factorization for hadronic collisions extend the
notion of ordinary parton distributions to transverse-momentum dependent (TMD)
parton density and parton decay functions. We discuss the use of the recent
high-precision deep-inelastic scattering (DIS) measurements for determination
of TMD distributions. These are relevant for both low-pT and high-pT physics in
hadron collisions. We comment on applications to multi-jet final states
associated with electroweak gauge boson production at the LHC.


  Using elements from the theory of ergodic backward stochastic differential
equations (BSDE), we study the behavior of forward entropic risk measures. We
provide their general representation results (via both BSDE and convex duality)
and examine their behavior for risk positions of long maturities. We show that
forward entropic risk measures converge to some constant exponentially fast. We
also compare them with their classical counterparts and derive a parity result.


  In this paper we demonstrate that there are large classes of
Friedmann-Robertson-Walker (FRW) cosmologies that admit isotropic conformal
structures of Quiescent Cosmology. FRW models have long been known to admit
singularities such as Big Bangs and Big Crunches [1, 2] but recently it has
been shown that there are other cosmological structures that these solutions
contain. These structures are Big Rips, Sudden Singularities and Extremality
Events [1, 2]. Within the Quiescent Cosmology framework [3] there also exist
structures consistent with a cosmological singularity known as the Isotropic
Past Singularity (IPS) [4, 5]. There also exists a cosmological final state
known as a Future Isotropic Universe (FIU) [4], which strictly speaking,
doesn't fit with the fundamental ideals of Quiescent Cosmology. In this paper,
we compare the cosmological events of a large class of FRW solutions to the
conformal structures of Quiescent Cosmology [4]. In the first section of this
paper we present the relevant background information and our motivation. In the
second section of this paper we construct conformal relationships for relevant
FRW models. The third section contains a thorough discussion of a class of FRW
solutions that cannot represent any of the previously constructed isotropic
conformal structures from Quiescent Cosmology. The final section contains our
remarks and future outlook for further study of this field.


  In this article we study how the birational geometry of a normal projective
variety $X$ is influenced by a normal subvariety $A \subset X.$ One of the most
basic examples in this context is provided by the following situation. Let
$f:X\to Y$ be a surjective holomorphic map with connected fibers between
compact connected complex manifolds. It is well known that given a general
fiber $A$ of $f$ we have $$ \kappa(X)\le \kappa(A)+\dim Y. $$ This article grew
out of the realization that this result should be true with $\dim Y$ replaced
by the codimension $\cod_X A$ for a pair $(X,A)$ consisting of a normal
subvariety $A$ of a compact normal variety $X$ under weak semipositivity
conditions on the normal sheaf of $A$ and the weak singularity condition
$\cod_A (A\cap\sing X)\ge 2$. We shall now state our main results in the
special case of a submanifold $A$ in a projective manifold $X$ and we also
simplify the semipositivity notion.


  The minimal model program suggests a compactification of the moduli space of
hyperplane arrangements which is a moduli space of stable pairs. Here, a stable
pair consists of a scheme X which is a degeneration of projective space and a
divisor D=D_1+..+D_n on X which is a limit of hyperplane arrangements. For
example, in the 1-dimensional case, the stable pairs are stable curves of genus
0 with n marked points. Kapranov has defined an alternative compactification
using his Chow quotient construction, which may be described fairly explicitly.
We prove that these two compactifications coincide. We deduce a description of
all stable pairs.


  Neutron scattering is used to study
NiCl$_{2-2x}$Br$_{2x}\cdot$4SC(NH$_2$)$_2$, $x=0.06$, a bond-disordered
modification of the well-known gapped $S=1$ antiferromagnetic quantum spin
system NiCl$_{2}\cdot$4SC(NH$_2$)$_2$. The magnetic excitation spectrum
throughout Brillouin zone is mapped out at $T=60$ mK using high-resolution
time-of-flight spectroscopy. It is found that the dispersion of spin excitation
is renormalized, as compared to that in the parent compound. The lifetime of
excitations near the bottom of the band is substantially decreased. No
localized states are found below the gap energy $\Delta\simeq0.2$ meV. At the
same time, localized zero wave vector states are detected above the top of the
band. The results are consistent with a more or less continuous random
distribution of bond strengths, and a discrete, possibly bimodal, distribution
of single-ion anisotropies in the disordered material.


  This article is the author's PhD thesis. After a review of string vacua
obtained through compactification (with and wothout fluxes), it presents and
describes various aspects of the Landscape of string vacua. At first it gives
an introduction and an overview of the statistical study of the set of four
dimensional string vacua, giving the detailed study of one corner of this set
(G2-holonomy compactifications of M-theory). Then it presents the ten
dimensional approach to string vacua, concentrating on the ten dimensional
description of the Type IIA flux vacua. Finally it gives two examples of models
having some interesting and characteristic phenomenological features, and that
belong to two different corners of the Landscape: warped compactifications of
Type IIB String Theory and M-theory compactifications on G2-holonomy manifolds.


  We study dynamic matching in an infinite-horizon stochastic market. While all
agents are potentially compatible with each other, some are hard-to-match and
others are easy-to-match. Agents prefer to be matched as soon as possible and
matches are formed either bilaterally or indirectly through chains. We adopt an
asymptotic approach and compute tight bounds on the limit of waiting time of
agents under myopic policies that differ in matching technology and
prioritization.
  We find that the market composition is a key factor in the desired matching
technology and prioritization level. When hard-to-match agents arrive less
frequently than easy-to-match ones (i) bilateral matching is almost as
efficient as chains (waiting times scale similarly under both, though chains
always outperform bilateral matching by a constant factor), and (ii) assigning
priorities to hard-to-match agents improves their waiting times. When
hard-to-match agents arrive more frequently, chains are much more efficient
than bilateral matching and prioritization has no impact.
  We further conduct comparative statics on arrival rates. Somewhat
surprisingly, we find that in a heterogeneous market and under bilateral
matching, increasing arrival rate has a non-monotone effect on waiting times,
due to the fact that, under some market compositions, there is an adverse
effect of competition. Our comparative statics shed light on the impact of
merging markets and attracting altruistic agents (that initiate chains) or
easy-to-match agents.
  This work uncovers fundamental differences between heterogeneous and
homogeneous dynamic markets, and potentially helps policy makers to generate
insights on the operations of matching markets such as kidney exchange
programs.


  We investigate non-adaptive algorithms for matroid prophet inequalities.
Matroid prophet inequalities have been considered resolved since 2012 when
[KW12] introduced thresholds that guarantee a tight 2-approximation to the
prophet; however, this algorithm is adaptive. Other approaches of [CHMS10] and
[FSZ16] have used non-adaptive thresholds with a feasibility restriction;
however, this translates to adaptively changing an item's threshold to infinity
when it cannot be taken with respect to the additional feasibility constraint,
hence the algorithm is not truly non-adaptive. A major application of prophet
inequalities is in auction design, where non-adaptive prices possess a
significant advantage: they convert to order-oblivious posted pricings, and are
essential for translating a prophet inequality into a truthful mechanism for
multi-dimensional buyers. The existing matroid prophet inequalities do not
suffice for this application. We present the first non-adaptive constant-factor
prophet inequality for graphic matroids.


  This short paper proposes a simple general equilibrium approach within a
Markov-switching regime to explain how asymmetric information between lenders
and speculators may lead to currency crises. The paper concludes by providing
necessary as well as sufficient conditions for special cases.


  Automatic patch generation can significantly reduce the window of exposure
after a vulnerability is disclosed. Towards this goal, a long-standing problem
has been that of patch localization: to find a program point at which a patch
can be synthesized. We present PatchLoc, one of the first systems which
automatically identifies such a location in a vulnerable binary, given just one
exploit, with high accuracy. PatchLoc does not make any assumptions about the
availability of source code, test suites, or specialized knowledge of the
vulnerability. PatchLoc pinpoints valid patch locations in large real-world
applications with high accuracy for about 88% of 43 CVEs we study. These
results stem from a novel approach to automatically synthesizing a test-suite
which enables probabilistically ranking and effectively differentiating between
candidate program patch locations.


  Materials with higher operating temperatures than today's state of the art
can improve system performance in several applications and enable new
technologies. Under most scenarios, a protective oxide scale with high melting
temperatures and thermodynamic stability as well as low ionic diffusivity is
required. Thus, the design of high-temperature systems would benefit from
knowledge of these properties and related ones for all known oxides. While some
properties of interest are known for many oxides (e.g. elastic constants exist
for over 1,000 oxides), melting temperature is known for a relatively small
subset. The determination of melting temperatures is time consuming and costly,
both experimentally and computationally, thus we use data science tools to
develop predictive models from the existing data. The relatively small number
of available melting temperature values precludes the use of standard tools;
therefore, we use a multi-step approach based on sequential learning where
surrogate data from first-principles calculations is leveraged to develop
models using small datasets. We use these models to predict the desired
properties for nearly 11,000 oxides and quantify uncertainties in the space.


  We suggest a low cost, non invasive healthcare system that measures
haemoglobin levels in patients and can be used as a preliminary diagnostic test
for anaemia. A combination of image processing, machine learning and deep
learning techniques are employed to develop predictive models to measure
haemoglobin levels. This is achieved through the color analysis of the
fingernail beds, palpebral conjunctiva and tongue of the patients. This
predictive model is then encapsulated in a healthcare application. This
application expedites data collection and facilitates active learning of the
model. It also incorporates personalized calibration of the model for each
patient, assisting in the continual monitoring of the haemoglobin levels of the
patient. Upon validating this framework using data, it can serve as a highly
accurate preliminary diagnostic test for anaemia.


  Standard cosmology is constructed upon the (generally implicit) assumption of
the ``large scale'' homogeneity of our Universe. Now, structures are observed
at scales which become larger and larger as the observational distances
increase. However, the homogeneous Friedmann-Lemaitre-Robertson-Walker model
remains a cosmological paradigm, and Friedmannian relations are usually used to
work out the model, implicitly assuming that the homogeneity assumption is
valid at the studied scales. This has been the way the concordance (Lambda-CDM)
model came out from the analyses of the SNIa data. Since this model implies the
validity of the Friedmannian magnitude-redshift relation at the range of
redshifts spaned by the supernovae surveys, it has been proposed some years ago
a very simple test of this possible validity, provided the SNIa should be
confirmed as standard candles. Since we can hope that the redshifts of the
supernovae which will be observed in the years to come will allow such a test
to be performed, it would be interesting to find inside the SNIa community some
collaborators ready to perform the test.


  The paper is devoted to function theory on symplectic manifolds. We study a
natural class of functionals involving the double Poisson brackets from the
viewpoint of their robustness properties with respect to small perturbations in
the uniform norm. We observe an hierarchy of such robustness properties. The
methods involve Hofer's geometry on the symplectic side and
Landau-Hadamard-Kolmogorov inequalities on the function-theoretic side.


  Let $\mathcal{H}$ be an $r$-uniform hypergraph. The \emph{minimum positive
co-degree} of $\mathcal{H}$, denoted by $\delta_{r-1}^+(\mathcal{H})$, is the
minimum $k$ such that if $S$ is an $(r-1)$-set contained in a hyperedge of
$\mathcal{H}$, then $S$ is contained in at least $k$ hyperedges of
$\mathcal{H}$. For $r\geq k$ fixed and $n$ sufficiently large, we determine the
maximum possible size of an intersecting $r$-uniform $n$-vertex hypergraph with
minimum positive co-degree $\delta_{r-1}^+(\mathcal{H}) \geq k$ and
characterize the unique hypergraph attaining this maximum. This generalizes the
Erd\H os-Ko-Rado theorem which corresponds to the case $k=1$. Our proof is
based on the delta-system method.


  We are concerned with a stochastic mean curvature flow of graphs over a
periodic domain of any space dimension. We establish existence of martingale
solutions which are strong in the PDE sense and study their large-time
behavior. Our analysis is based on a viscous approximation and new global
bounds, namely, an $L^{\infty}_{\omega,x,t}$ estimate for the gradient and an
$L^{2}_{\omega,x,t}$ bound for the Hessian. The proof makes essential use of
the delicate interplay between the deterministic mean curvature part and the
stochastic perturbation, which permits to show that certain gradient-dependent
energies are supermartingales. Our energy bounds in particular imply that
solutions become asymptotically spatially homogeneous and approach a Brownian
motion perturbed by a random constant.


  Auxiliary field Quantum Monte Carlo simulations of interacting fermions
require sampling over a Hubbard-Stratonovich field $h$ introduced to decouple
the interactions. The weight for a given configuration involves the products of
the determinant of matrices $M_\sigma(h)$, where $\sigma$ labels the species,
and hence is typically not positive definite. Indeed, the average sign $\langle
{\cal S} \rangle$ of the determinants goes to zero exponentially with
increasing spatial size and decreasing temperature for most Hamiltonians of
interest. This statement, however, does not explicitly separate two possible
origins for the vanishing of $\langle {\cal S} \rangle$. Does $\langle {\cal S}
\rangle \rightarrow 0$ because {\it randomly} chosen field configurations have
${\rm det}\big(M(h)\big) < 0$, or does the `sign problem' arise because the
specific subset of configurations chosen by the weighting function have a
greater preponderance of negative values? In the latter case, the process of
weighting the configurations with $|{\rm det}\big(M(h)\big)|$ might steer the
simulation to a region of configuration space of $h$ where positive and
negative determinants are equally likely, even though randomly chosen $h$ would
preferentially have determinants with a single dominant sign. In this paper we
address the relative importance of these two mechanisms for the vanishing of
$\langle {\cal S} \rangle$ in quantum simulations.


  We calculate the equation of state of neutron matter with realistic two- and
three-nucleon interactions using quantum Monte Carlo techniques, and illustrate
that the short-range three-neutron interaction determines the correlation
between neutron matter energy at nuclear saturation density and higher
densities relevant to neutron stars. Our model also makes an experimentally
testable prediction for the correlation between the nuclear symmetry energy and
its density dependence -- determined solely by the strength of the short-range
terms in the three neutron force. The same force provides a significant
constraint on the maximum mass and radius of neutron stars.


  Measurements of the top quark-antiquark (t t-bar) spin correlations and the
top quark polarization are presented for t t-bar pairs produced in pp
collisions at sqrt(s) = 8 TeV. The data correspond to an integrated luminosity
of 19.5 inverse femtobarns collected with the CMS detector at the LHC. The
measurements are performed using events with two oppositely charged leptons
(electrons or muons) and two or more jets, where at least one of the jets is
identified as originating from a bottom quark. The spin correlations and
polarization are measured from the angular distributions of the two selected
leptons, both inclusively and differentially, with respect to the invariant
mass, rapidity, and transverse momentum of the t t-bar system. The measurements
are unfolded to the parton level and found to be in agreement with predictions
of the standard model. A search for new physics in the form of anomalous top
quark chromo moments is performed. No evidence of new physics is observed, and
exclusion limits on the real part of the chromo-magnetic dipole moment and the
imaginary part of the chromo-electric dipole moment are evaluated.


  Facial animation in virtual reality environments is essential for
applications that necessitate clear visibility of the user's face and the
ability to convey emotional signals. In our scenario, we animate the face of an
operator who controls a robotic Avatar system. The use of facial animation is
particularly valuable when the perception of interacting with a specific
individual, rather than just a robot, is intended. Purely keypoint-driven
animation approaches struggle with the complexity of facial movements. We
present a hybrid method that uses both keypoints and direct visual guidance
from a mouth camera. Our method generalizes to unseen operators and requires
only a quick enrolment step with capture of two short videos. Multiple source
images are selected with the intention to cover different facial expressions.
Given a mouth camera frame from the HMD, we dynamically construct the target
keypoints and apply an attention mechanism to determine the importance of each
source image. To resolve keypoint ambiguities and animate a broader range of
mouth expressions, we propose to inject visual mouth camera information into
the latent space. We enable training on large-scale speaking head datasets by
simulating the mouth camera input with its perspective differences and facial
deformations. Our method outperforms a baseline in quality, capability, and
temporal consistency. In addition, we highlight how the facial animation
contributed to our victory at the ANA Avatar XPRIZE Finals.


  A tutorial discussion of the propagation of waves in random media is
presented. In first approximation the transport of the multiple scattered waves
is given by diffusion theory, but important corrections are present. These
corrections are calculated with the radiative transfer or Schwarzschild-Milne
equation, which describes intensity transport at the ``mesoscopic'' level and
is derived from the ``microscopic'' wave equation. A precise treatment of the
diffuse intensity is derived which automatically includes the effects of
boundary layers. Effects such as the enhanced backscatter cone and imaging of
objects in opaque media are also discussed within this framework. In the second
part the approach is extended to mesoscopic correlations between multiple
scattered intensities which arise when scattering is strong. These correlations
arise from the underlying wave character. The derivation of correlation
functions and intensity distribution functions is given and experimental data
are discussed. Although the focus is on light scattering, the theory is also
applicable to micro waves, sound waves and non-interacting electrons.


  Current digital data storage systems are able to store huge amounts of data.
Even though the data density of digital information storage has increased
tremendously over the last few decades, the data longevity is limited to only a
few decades. If we want to preserve anything about the human race which can
outlast the human race itself, we require a data storage medium designed to
last for 1 million to 1 billion years. In this paper a medium is investigated
consisting of tungsten encapsulated by siliconnitride which, according to
elevated temperature tests, will last for well over the suggested time.


  This paper considers the synchronization problem for networks of coupled
nonlinear dynamical systems under switching communication topologies. Two types
of nonlinear agent dynamics are considered. The first one is non-expansive
dynamics (stable dynamics with a convex Lyapunov function $\varphi(\cdot)$) and
the second one is dynamics that satisfies a global Lipschitz condition. For the
non-expansive case, we show that various forms of joint connectivity for
communication graphs are sufficient for networks to achieve global asymptotic
$\varphi$-synchronization. We also show that $\varphi$-synchronization leads to
state synchronization provided that certain additional conditions are
satisfied. For the globally Lipschitz case, unlike the non-expansive case,
joint connectivity alone is not sufficient for achieving synchronization. A
sufficient condition for reaching global exponential synchronization is
established in terms of the relationship between the global Lipschitz constant
and the network parameters. We also extend the results to leader-follower
networks.


  Geometrical frustration leads to novel quantum phenomena such as the
spin-liquid phase in triangular and Kagom\'e lattices. Intra-band and
inter-band Fermi surface (FS) nesting can drive unique superconducting (SC)
ground states with $d$-wave and $s^{\pm}$ pairing symmetries, respectively,
according to the criterion that the SC gap changes sign across the nesting
wavevector. For an odd number of FSs, when multiple inter-band nesting is of
comparable strength, the sign-reversal criterion between different FS sheets
can leads to frustration, which promotes novel SC order parameters. Here we
report the experimental observation of a time-reversal symmetry breaking
pairing state in Re$_2$Hf resulting from FS nesting frustration. Furthermore,
our electronic specific heat and transverse-field $\mu$SR experiments suggest a
fully gaped pairing symmetry. The first-principle electronic structure
calculation reveals multiple Fermi surface sheets with comparable inter-band
nesting strength. Implementing the {\it ab-initio} band structure, we compute
spin-fluctuation mediated SC pairing symmetry which reveals a $s+is'$-pairing
state - consistent with experimental observations. Our investigation
demonstrates a novel SC state which provides a putative setting for both
applied and fundamental study.


  A system of differential equations is proposed designed as to identify
communities in weighted networks. The input is a symmetric connectivity matrix
$A_{ij}$. A priori information on the number of communities is not needed. To
verify the dynamics, we prepared sets of separate, fully connected clusters. In
this case, the matrix $A$ has a block structure of zeros and units. A noise is
introduced as positive random numbers added to zeros and subtracted from units.
The task of the dynamics is to reproduce the initial block structure. In this
test, the system outperforms the modularity algorithm, if the number of
clusters is larger than four.


  We present the evolution of the mass-metallicity (MZ) relations at z=4-10
derived with 135 galaxies identified in the JWST/NIRSpec data taken from the
three major public spectroscopy programs of ERO, GLASS, and CEERS. Because
there are many discrepancies between flux measurements reported by early ERO
studies, we first establish our NIRSpec data reduction procedure for reliable
emission-line flux measurements and errors successfully explaining Balmer
decrements with no statistical tensions via thorough comparisons of the early
ERO studies. Applying the reduction procedure to the 135 galaxies, we obtain
emission-line fluxes for physical property measurements. We confirm that 10 out
of the 135 galaxies with [OIII]4363-lines have electron temperatures of
(1.1-2.3)*10^4K, similar to lower-z star-forming galaxies, that can be
explained by heating of young massive stars. We derive metallicities of the 10
galaxies by the direct method and the rest of the galaxies with strong lines by
the metallicity calibrations of Nakajima et al. (2022) applicable for these
low-mass metal-poor galaxies, anchoring the metallicities with the
direct-method measurements. We thus obtain MZ relations and star-formation rate
(SFR)-MZ relations over z=4-10. We find that there is a small evolution of the
MZ relation from z~2-3 to z=4-10, while interestingly that the SFR-MZ relation
shows no evolution up to z~8 but a significant decrease at z>8 beyond the
error. This SFR-MZ relation decrease at z>8 may suggest a break of the
metallicity equilibrium state via star-formation, inflow, and outflow, while
further statistical and local-baseline studies are needed for a conclusion.


  Recent nonthermal X-ray and gamma-ray observations, attributed to electron
emission processes, for the first time give an experimental confirmation that
electrons are accelerated on SNR shocks up to the energy 10^{14} eV. We have no
direct observational confirmations about proton acceleration by SNR. Different
models of gamma-emission from SNRs predict different emission mechanisms as
dominating. Only decays of neutral pion created in proton-nucleon interactions
allow us to look inside the CR nuclear component acceleration processes. A new
model for the thermal X-ray composites strongly suggest that thermal X-ray peak
inside the radio shell of SNR tells us about entering of one part of SNR shock
into a denser medium compared with other parts of the shell. This makes a TXCs
promising sites for gamma-ray generation via neutral pion decays. Detailed
consideration of SNR-cloud interaction allows to increase an expected proton
induced gamma-ray flux from SNR at least on an order of magnitude, that allows
to adjust the theoretical proton origin gamma-luminosities with observed fluxes
at least for a few SNRs even for low density (n=10-100 cm^{-3}) cloud.


  We introduce the first complete non-parametric model for the astrophysical
distribution of the binary black hole (BBH) population. Constructed from basis
splines, we use these models to conduct the most comprehensive data-driven
investigation of the BBH population to date, simultaneously fitting
non-parametric models for the BBH mass ratio, spin magnitude and misalignment,
and redshift distributions. With GWTC-3, we report the same features previously
recovered with similarly flexible models of the mass distribution, most notably
the peaks in merger rates at primary masses of ${\sim}10\,M_\odot$ and
${\sim}35\,M_\odot$. Our model reports a suppressed merger rate at low primary
masses and a mass ratio distribution consistent with a power law. We infer a
distribution for primary spin misalignments that peaks away from alignment,
supporting conclusions of recent work. We find broad agreement with the
previous inferences of the spin magnitude distribution: the majority of BBH
spins are small ($a<0.5$), the distribution peaks at $a\sim0.2$, and there is
mild support for a non-spinning subpopulation, which may be resolved with
larger catalogs. With a modulated power law describing the BBH merger rate's
evolution in redshift, we see hints of the rate evolution either flattening or
decreasing at $z\sim0.2-0.5$, but the full distribution remains entirely
consistent with a monotonically increasing power law. We conclude with a
discussion of the astrophysical context of our new findings and how
non-parametric methods in gravitational-wave population inference are uniquely
poised to complement to the parametric approach as we enter the data-rich era
of gravitational-wave astronomy.


  We demonstrate the application of recent advances in statistical mechanics to
a problem in telecommunication engineering: the assessment of the quality of a
communication channel in terms of rare and extreme events. In particular, we
discuss non-Markovian models for telecommunication traffic in continuous time
and deploy the "cloning" procedure of non-equilibrium statistical mechanics to
efficiently compute their effective bandwidths. The cloning method allows us to
evaluate the performance of a traffic protocol even in the absence of
analytical results, which are often hard to obtain when the dynamics are
non-Markovian.


  We define a new quantity called refbit, which allows one to quantify the
resource of sharing a reference frame in quantum communication protocols. By
considering both asymptotic and nonasymptotic protocols we find relations
between refbits and other communication resources. We also consider the same
resources in encoded, reference-frame independent, form. This allows one to
rephrase and unify previous work on phase references, reference frames, and
superselection rules.


  The sets used to construct other mathematical objects are pure sets, which
means that all of their elements are sets, which are themselves pure. One set
may therefore be within another, not as an element, but as an element of an
element, or even deeper, inside several layers of sets within sets. The
introduction of the term constituent to describe a set which is within a given
set, however deep, induces an apparently novel partial order on sets, and
assigns to any given set a diagram which specifies a directed graph, or
category, herein dubbed its constituent structure, indicating which sets within
it are constituents of which others. Sets with different numbers of elements
can have exactly the same constituent structure. Consequently, constituent
structure isomorphisms between sets need not preserve the number of elements,
although they are still injective, surjective, and invertible. We consider in
detail an example of an isomorphism between a one-element set and a
five-element set, which is a surjective mapping despite the mismatch in
cardinalities. The constituent structure of a set determines the mathematical
objects for which the set is a suitable representation. Different schemes for
constructing the natural numbers, such as those of von Neumann and Zermelo,
generate sets with the same constituent structures. Objects share the
constituent structures, not the elements, of the sets used to construct or
represent them. The requirement that an object's properties be faithfully
encoded within a set's constituent structure and not its non-constituent
characteristics such as its cardinality, when made explicit, dictates a
specific and novel way of representing ordered pairs and tuples of sets as
sets, providing simple formulae for addressing and extracting sets located deep
within nested tuples.


  Gaia mission offers opportunities to search for compact binaries not involved
in binary interactions (hereafter inert compact binaries), and results in the
discoveries of binaries containing one black hole (BH) or one neutron star
(NS), called "Gaia BHs" and "Gaia NSs", respectively. We have assessed if Gaia
BHs and NSs can be formed in open clusters through dynamical interactions. In
order to obtain a large number of inert compact binaries similar to Gaia BHs
and NSs, we have performed gravitational $N$-body simulations for a large
number of open clusters whose total mass is $1.2 \times 10^8 M_\odot$. These
clusters have various masses, metallicities, densities, and binary fractions.
We have found that open clusters form Gaia BHs ($10^{-6}$-$10^{-5}
M_\odot^{-1}$) much more efficiently than Gaia NSs ($\lesssim 10^{-7}
M_\odot^{-1}$) for any cluster parameters. This is quite inconsistent with
observational results, because the reported numbers of Gaia BHs and NSs are $3$
and $21$, respectively. Additionally, we have switched off NS natal kicks for
$10^4$ open clusters each weighing $10^3 M_\odot$ in order to retain a large
number of NSs in open clusters. Then, open clusters form inert NS binaries
originating from primordial binaries rather than formed through dynamical
interactions. This means that Gaia NSs are formed dominantly on isolated
fields, not in open clusters, if there is no NS natal kick. We have concluded
that Gaia BHs can be dominantly formed in open clusters, however Gaia NSs
cannot.


  For an exact chiral symmetry which is spontaneously broken at zero
temperature, we show that at nonzero temperature, generally pions travel at
{\it less} than the speed of light. This effect first appears at next to
leading order in an expansion about low temperature. When the chiral symmetry
is approximate we obtain two formulas, like that of Gell-Mann, Oakes, and
Renner, for the static and dynamic pion masses.


  Very recently, it has been shown that thermal noise and its artificial
versions (Johnson-like noises) can be utilized as an information carrier with
peculiar properties therefore it may be proper to call this topic Thermal Noise
Informatics. Zero Power (Stealth) Communication, Thermal Noise Driven
Computing, and Totally Secure Classical Communication are relevant examples. In
this paper, while we will briefly describe the first and the second subjects,
we shall focus on the third subject, the secure classical communication via
wire. This way of secure telecommunication utilizes the properties of
Johnson(-like) noise and those of a simple Kirchhoff's loop. The communicator
is unconditionally secure at the conceptual (circuit theoretical) level and
this property is (so far) unique in communication systems based on classical
physics. The communicator is superior to quantum alternatives in all known
aspects, except the need of using a wire. In the idealized system, the
eavesdropper can extract zero bit of information without getting uncovered. The
scheme is naturally protected against the man-in-the-middle attack. The
communication can take place also via currently used power lines or phone
(wire) lines and it is not only a point-to-point communication like quantum
channels but network-ready. Tests have been carried out on a model-line with
ranges beyond the ranges of any known direct quantum communication channel and
they indicate unrivalled signal fidelity and security performance. This simple
device has single-wire secure key generation/sharing rates of 0.1, 1, 10, and
100 bit/second for copper wires with diameters/ranges of 21 mm / 2000 km, 7 mm
/ 200 km, 2.3 mm / 20 km, and 0.7 mm / 2 km, respectively and it performs with
0.02% raw-bit error rate (99.98 % fidelity).


  We propose two models of the Boltzmann equation (BGK and Fokker-Planck
models) for rarefied flows of diatomic gases in vibrational non-equilibrium.
These models take into account the discrete repartition of vibration energy
modes, which is required for high temperature flows, like for atmospheric
re-entry problems. We prove that these models satisfy conservation and entropy
properties (H-theorem), and we derive their corresponding compressible
Navier-Stokes asymptotics.


  Enlarged lymph nodes (LNs) can provide important information for cancer
diagnosis, staging, and measuring treatment reactions, making automated
detection a highly sought goal. In this paper, we propose a new algorithm
representation of decomposing the LN detection problem into a set of 2D object
detection subtasks on sampled CT slices, largely alleviating the curse of
dimensionality issue. Our 2D detection can be effectively formulated as linear
classification on a single image feature type of Histogram of Oriented
Gradients (HOG), covering a moderate field-of-view of 45 by 45 voxels. We
exploit both simple pooling and sparse linear fusion schemes to aggregate these
2D detection scores for the final 3D LN detection. In this manner, detection is
more tractable and does not need to perform perfectly at instance level (as
weak hypotheses) since our aggregation process will robustly harness collective
information for LN detection. Two datasets (90 patients with 389 mediastinal
LNs and 86 patients with 595 abdominal LNs) are used for validation.
Cross-validation demonstrates 78.0% sensitivity at 6 false positives/volume
(FP/vol.) (86.1% at 10 FP/vol.) and 73.1% sensitivity at 6 FP/vol. (87.2% at 10
FP/vol.), for the mediastinal and abdominal datasets respectively. Our results
compare favorably to previous state-of-the-art methods.


  The experimental time-lapse images of the breakup phenomenon of a charged
droplet (diameter ~100-300 micro-m) levitated in an electrodynamic (ED) balance
is reported. During the breakup process, a levitated charged droplet undergoes
evaporation leading to a reduction in droplet size and increase in the
corresponding surface charge density. As the surface charge density reaches to
a critical value, known as the Rayleigh limit, the droplet undergoes breakup by
forming a jet which further ejects highly charged progeny droplets. All the
successive events of the droplet breakup process such as drop deformation,
breakup, and relaxation of the drop back to spherical shape after ejection of
progeny droplets have been recorded using the high-speed camera at 1.3 hundred
thousand frames per second. The droplet is observed to eject 3-5 progeny
droplets from a jet indicating end pinching mode of breakup. The jet is then
observed to relax back after ejecting 31% of the total charge and ~3\% of the
total mass. A suitable theory is provided to supplement the experimental
observations, and a reasonable agreement is observed. Additionally, the theory
is extended for the prediction of total mass loss and the entire lifetime of a
charged droplet.


  The flaring M4 dwarf GJ 1243 has become a benchmark for studying stellar
flare and starspot activity thanks to the exceptional photometric monitoring
archive from the Kepler mission. New light curves from the TESS mission for
this star allow precise stellar activity characterization over more than a
decade timescale. We have carried out the first flare and starspot analysis of
GJ 1243 from over 50 days of data from TESS Sectors 14 and 15. Using 133 flare
events detected in the 2-minute cadence TESS data, we compare the cumulative
flare frequency distributions, and find the flare activity for GJ 1243 is
unchanged between the Kepler and TESS epochs. Two distinct starspot groups are
found in the TESS data, with the primary spot having the same rotational period
and phase as seen in Kepler. The phase of the secondary spot feature is
consistent with the predicted location of the secondary starspot and
measurement of weak differential rotation, suggesting this secondary spot may
be long-lived and stable in both latitude and longitude. As expected for this
highly active star, the constant spot and flare activity reveal no sign of
solar-like activity cycles over 10 years. However, we highlight the unique
ability for Kepler and TESS to use flare rates to detect activity cycles.


  Covariant relativistic quantum theory is used to study the covariant Green's
function, which can be used to determine the proper time evolved wave functions
that are solutions to the covariant Schr\"odinger type equation for a massive
spin zero particle. The concept of covariant action is used to obtain the
Green's function for an accelerated relativistic particle.


  This paper constructs a class of complete K\"{a}hler metrics of positive
holomorphic sectional curvature on ${\bf C}^n$ and finds that the constructed
metrics satisfy the following properties: As the geodesic distance
$\rho\to\infty,$ the volume of geodesic balls grows like
$O(\rho^{\frac{2(\beta+1)n}{\beta+2}})$ and the Riemannian scalar curvature
decays like $O(\rho^{-\frac{2(\beta+1)}{\beta+2}}),$ where $\beta\geq 0.$


  The continuity properties of the convex closure of the output entropy of
infinite dimensional channels and their applications to the additivity problem
are considered.
  The main result of this paper is the statement that the superadditivity of
the convex closure of the output entropy for all finite dimensional channels
implies the superadditivity of the convex closure of the output entropy for all
infinite dimensional channels, which provides the analogous statements for the
strong superadditivity of the EoF and for the additivity of the minimal output
entropy.
  The above result also provides infinite dimensional generalization of Shor's
theorem stated equivalence of different additivity properties.
  The superadditivity of the convex closure of the output entropy (and hence
the additivity of the minimal output entropy) for two infinite dimensional
channels with one of them a direct sum of noiseless and entanglement-breaking
channels are derived from the corresponding finite dimensional results.
  In the context of the additivity problem some observations concerning
complementary infinite dimensional channels are considered.


  In various provers and deductive verification tools, logical transformations
are used extensively in order to reduce a proof task into a number of simpler
tasks. Logical transformations are often part of the trusted base of such
tools. In this paper, we develop a framework to improve confidence in their
results. We follow a modular and skeptical approach: transformations are
instrumented independently of each other and produce certificates that are
checked by a third-party tool. Logical transformations are considered in a
higher-order logic, with type polymorphism and built-in theories such as
equality and integer arithmetic. We develop a language of proof certificates
for them and use it to implement the full chain of certificate generation and
certificate verification.


  We report the measurement of the angular power spectrum of cross-correlation
between the unresolved component of the Fermi-LAT gamma-ray sky-maps and the
CMB lensing potential map reconstructed by the Planck satellite. The matter
distribution in the Universe determines the bending of light coming from the
last scattering surface. At the same time, the matter density drives the growth
history of astrophysical objects, including their capability at generating
non-thermal phenomena, which in turn give rise to gamma-ray emissions. The
Planck lensing map provides information on the integrated distribution of
matter, while the integrated history of gamma-ray emitters is imprinted in the
Fermi-LAT sky maps. We report here the first evidence of their correlation. We
find that the multipole dependence of the cross-correlation measurement is in
agreement with current models of the gamma-ray luminosity function for AGN and
star forming galaxies, with a statistical evidence of 3.0$\sigma$. Moreover,
its amplitude can in general be matched only assuming that these extra-galactic
emitters are also the bulk contribution of the measured isotopic gamma-ray
background (IGRB) intensity. This leaves little room for a big contribution
from galactic sources to the IGRB measured by Fermi-LAT, pointing toward a
direct evidence of the extragalactic origin of the IGRB.


  Topological complexity $\TC{B}$ of a space $B$ is introduced by M. Farber to
measure how much complex the space is, which is first considered on a
configuration space of a motion planning of a robot arm. We also consider a
stronger version $\TCM{B}$ of topological complexity with an additional
condition: in a robot motion planning, a motion must be stasis if the initial
and the terminal states are the same. Our main goal is to show the equalities
$\TC{B} = \catBb{\double{B}}+1$ and $\TCM{B} = \catBB{\double{B}}+1$, where
$\double{B}=B{\times}B$ is a fibrewise pointed space over $B$ whose projection
and section are given by $p_{\double{B}}=\proj_{2} : B{\times}B \to B$ the
canonical projection to the second factor and $s_{\double{B}}=\Delta_{B} : B
\to B{\times}B the diagonal. In addition, our method in studying fibrewise L-S
category is able to treat a fibrewise space with singular fibres.
  Recently, we found a problem with the proof of Theorem 1.13 which states that
for a fibrewise well-pointed space $X$ over $B$, we have $\catBB{X}$ =
\catBb{X}$ and that for a locally finite simplicial complex $B$, we have
$\TC{B} = \TCM{B}$. While we still conjecture that Theorem 1.13 is true, this
problem means that, at present, no proof is given to exist. Alternatively, we
show the difference between two invariants $\catBb{X}$ and $\catBB{X}$ is at
most 1 and the conjecture is true for some cases. We give further corrections
mainly in the proof of Theorem 1.12.


  If G is a complex semisimple algebraic group, we characterize the normality
and the smoothness of its simple linear compactifications, namely those
equivariant GxG-compactifications which possess a unique closed orbit and which
arise in a projective space of the shape P(End(V)), where V is finite
dimensional rational G-module. Both the characterizations are purely
combinatorial and are expressed in terms of the highest weights of V. In
particular, we show that Sp(2r) (with r > 0) is the unique non-adjoint simple
group which admits a simple smooth compactification.


  Using soft-graviton theorems a well-known zero-frequency limit (ZFL) for the
gravitational radiation flux $dE^{GW}/d \omega$ is re-derived and extended to
order ${{\cal O}}(\omega)$ and ${{\cal O}}(\omega^2)$ for arbitrary massless
multi-particle collisions. The (angle-integrated, unpolarized) ${{\cal
O}}(\omega)$ correction to the flux turns out to be absent in the case of
two-particle elastic collisions. The ${{\cal O}}(\omega^2)$ correction is
instead non-vanishing and takes a simple general expression which is then
applied to bremsstrahlung from two-particle elastic collisions. For a
tree-level process the outcome is finite and consistent with expectations.
Instead, if the tree-level form of the soft theorems is used at sub-sub-leading
order even when the elastic amplitude needs an all-loop (eikonal) resummation,
an unphysical infrared singularity occurs. Its origin can be traced to the
infinite Coulomb phase of gravitational scattering in four dimensions. We
briefly discuss how to get rid, in principle, of the unwanted divergences and
indicate --without carrying out-- a possible procedure to find the proper
correction to the naive soft theorems. Nevertheless, if a simple recipe
recently proposed for handling these divergences is adopted, we find
surprisingly good agreement with results obtained independently via the eikonal
approach to transplanckian-energy scattering at large (small) impact parameter
(deflection angle), where such Coulomb divergences explicitly cancel out.


  Amongst the first physics results of the ATLAS detector at LHC will be an
analysis of Jpsi and Upsilon production. Even at low luminosity ATLAS will
quickly start improving on current quarkonia measurements providing world
leading results with around 10 pb-1 of data. The narrow quarkonia resonances
will also be used as tools for alignment and calibration of the trigger and
tracking systems.


  We present the latest results from the UKQCD/RBC collaborations for the
K_{l3} form factor with 2+1 flavours of dynamical domain wall quarks.
Simulations are performed on 16^3x32x16 and 24^3x64x16 lattices with three
values of the light quark mass, allowing for an extrapolation to the chiral
limit. After interpolating to zero momentum transfer, we obtain the preliminary
result f_+^{K\pi}(0)=0.9680(16), which is in excellent agreement with an
earlier N_f=2 result.


  We present results of spectral and timing analysis based on 11 RXTE PCA/HEXTE
observations of the microquasar XTE J1550-564 during its last outburst in
January 2002. The observed behaviour is comparable to most Black-Hole
Candidates in the low/hard state. This is unlike the 1998-99 outburst, when it
showed a much more complex feature, probably because of the higher luminosity.
For each of the 11 observations we extracted energy spectra and power density
spectra, finding typical features of a low/hard state.


  The HeII->HeI recombination of primordial helium plasma (z = 1500 - 3000) is
considered in terms of the standard cosmological model. This process affects
the formation of cosmic microwave background anisotropy and spectral
distortions. We investigate the effect of neutral hydrogen on the HeII->HeI
recombination kinetics with partial and complete redistributions of radiation
in frequency in the HeI resonance lines. It is shown that to properly compute
the HeII->HeI recombination kinetics, one should take into account not only the
wings in the absorption and emission profiles of the HeI resonance lines, but
also the mechanism of the redistribution of resonance photons in frequency.
Thus, for example, the relative difference in the numbers of free electrons for
the model using Doppler absorption and emission profiles and the model using a
partial redistribution in frequency is 1 - 1.3% for the epoch z = 1770 - 1920.
The relative difference in the numbers of free electrons for the model using a
partial redistribution in frequency and the model using a complete
redistribution in frequency is 1 - 3.8% for the epoch z = 1750 - 2350.


  Given a reference filtration $\mathbb{F}$, we develop in this work a generic
method for computing the semimartingale decomposition of
$\mathbb{F}$-martingales in some specific enlargements of $\mathbb{F}$. This
method is then applied to the study of progressive enlargement with multiple
non-ordered random times, for which explicit decompositions can be obtained
under the absolute continuity condition of Jacod.


  Open-sourcing research publications is a key enabler for the reproducibility
of studies and the collective scientific progress of a research community. As
all fields of science develop more advanced algorithms, we become more
dependent on complex computational toolboxes -- sharing research ideas solely
through equations and proofs is no longer sufficient to communicate scientific
developments. Over the past years, several efforts have highlighted the
importance and challenges of transparent and reproducible research; code
sharing is one of the key necessities in such efforts. In this article, we
study the impact of code release on scientific research and present statistics
from three research communities: machine learning, robotics, and control. We
found that, over a six-year period (2016-2021), the percentages of papers with
code at major machine learning, robotics, and control conferences have at least
doubled. Moreover, high-impact papers were generally supported by open-source
codes. As an example, the top 1% of most cited papers at the Conference on
Neural Information Processing Systems (NeurIPS) consistently included
open-source codes. In addition, our analysis shows that popular code
repositories generally come with high paper citations, which further highlights
the coupling between code sharing and the impact of scientific research. While
the trends are encouraging, we would like to continue to promote and increase
our efforts toward transparent, reproducible research that accelerates
innovation -- releasing code with our papers is a clear first step.


  Assuming that leading particles in high-energy hadronic and nuclear
collisions become sources of a classical pion field, we show that the direct
production of pions favors Centauro (mainly charged) events and that the
production of pions through the $ \rho$-type channel favors anti-Centauro
(mainly neutral) events. We also observe a strong negative neutral-charged
correlation in both cases.


  The magnetic-field behaviour of the off-diagonal impedance in Co-based
amorphous wires is investigated under the condition of sinusoidal (50 MHz) and
pulsed (5 ns rising time) current excitations. For comparison, the field
characteristics of the diagonal impedance are measured as well. In general,
when an alternating current is applied to a magnetic wire the voltage signal is
generated not only across the wire but also in the coil mounted on it. These
voltages are related with the diagonal and off-diagonal impedances,
respectively. It is demonstrated that these impedances have a different
behaviour as a function of axial magnetic field: the former is symmetrical and
the latter is antisymmetrical with a near linear portion within a certain field
interval. In the case of the off-diagonal response, the dc bias current
eliminating circular domains is necessary. The pulsed excitation that combines
both high and low frequency harmonics produces the off-diagonal voltage
response without additional bias current or field. This suits ideal for a
practical sensor circuit design. The principles of operation of a linear
magnetic sensor based on C-MOS transistor circuit are discussed.


  The adaptive lasso refers to a class of methods that use weighted versions of
the $L_1$-norm penalty, with weights derived from an initial estimate of the
parameter vector to be estimated. Irrespective of the method chosen to compute
this initial estimate, the performance of the adaptive lasso critically depends
on the value of a hyperparameter, which controls the magnitude of the weighted
$L_1$-norm in the penalized criterion. As for other machine learning methods,
cross-validation is very popular for the calibration of the adaptive lasso,
that this for the selection of a data-driven optimal value of this
hyperparameter. However, the most simple cross-validation scheme is not valid
in this context, and a more elaborate one has to be employed to guarantee an
optimal calibration. The discrepancy of the simple cross-validation scheme has
been well documented in other contexts, but less so when it comes to the
calibration of the adaptive lasso, and, therefore, many statistical analysts
still overlook it. In this work, we recall appropriate cross-validation schemes
for the calibration of the adaptive lasso, and illustrate the discrepancy of
the simple scheme, using both synthetic and real-world examples. Our results
clearly establish the suboptimality of the simple scheme, in terms of support
recovery and prediction error, for several versions of the adaptive lasso,
including the popular one-step lasso.


  New observations of galaxies in the direction of the Leo group, which were
classified as being candidates for M32-like dwarf galaxies by Ferguson &
Sandage (1990), show that these galaxies are normal elliptical galaxies at
redshifts between z=0.02 and z=0.06. This result adds further evidence that the
faint end of the luminosity function of elliptical galaxies falls off very
steep and that objects like M32 are extremely rare.


  We study the Hausdorff dimension of the sets on which the pointwise
convergence of the solutions to the fractional Schr\"odinger equation
$e^{it(-\Delta)^\frac m2}f$ fails when $m\in(0,1)$ in one spatial dimension.
The pointwise convergence along a non-tangential curve and a set of lines are
also considered, where we find different nature from the case when
$m\in(1,\infty)$. In particular, non-tangential curves are no longer regarded
as vertical lines.


  The electric ${\alpha}_{\pi}$ and magnetic $\beta_{\pi}$ charged pion Compton
polarizabilities are of fundamental interest in the low-energy sector of
quantum chromodynamics (QCD).They are directly linked to the phenomenon of
spontaneously broken chiral symmetry within QCD and to the dynamics of the
pion-photon interaction.The combination (${\alpha}_{\pi}-\beta_{\pi}$) was
measured by:(1) CERN COMPASS via radiative pion Primakoff scattering
(Bremsstrahlung) in the nuclear Coulomb field, ${\pi}^- Z \rightarrow {\pi}^-Z
{\gamma}$, (2) SLAC PEP Mark-II via two-photon production of pion pairs,
${\gamma}{\gamma}\rightarrow{\pi}^+{\pi}^-$, and (3) Mainz Microtron via
radiative pion photoproduction from the proton,
${\gamma}p\rightarrow{\gamma}{\pi}^+n$. COMPASS and Mark-II agree with one
another:(1) ${\alpha}_{\pi}-\beta_{\pi}=4.0\times 10^{-4}fm^3$, (2)
${\alpha}_{\pi}-\beta_{\pi}=4.4 \times 10^{-4}fm^3$. The Mainz value (3)
${\alpha}_{\pi}-\beta_{\pi}=11.6 \times 10^{-4}fm^3$ is excluded here because a
dispersion relations calculation using the Mainz value as input gives
significantly too large ${\gamma}{\gamma} \rightarrow {\pi}^0{\pi}^0$ cross
sections compared to DESY Crystal Ball data. COMPASS and Mark-II values agree
well with the two-loop chiral perturbation theory ChPT prediction
${\alpha}_{\pi}-\beta_{\pi}=5.7\times10^{-4}fm^3$, thereby strengthening the
identification of the pion with the Goldstone boson of QCD.


  Using 9.9 fb$^{-1}$ of $e^+e^-$ collision data collected by the BESIII
detector at center-of-mass energies between 4.15 and 4.30 GeV, we search for
the processes $e^+e^-\to\gamma X(3872)$ with $X(3872)\rightarrow\pi^0\chi_{c0}$
and $X(3872)\rightarrow\pi\pi\chi_{c0}$. Depending on the fitting model, the
statistical significance for $X(3872)\to\pi^0\chi_{c0}$ ranges from 1.3$\sigma$
to 2.8$\sigma$. We set upper limits (at 90\% C.L.) of
$\frac{\mathcal{B}(X(3872)\rightarrow\pi^0\chi_{c0})}{\mathcal{B}(X(3872)\to\pi^+\pi^-J/\psi)}<3.6$,
$\frac{\mathcal{B}(X(3872)\rightarrow\pi^+\pi^-\chi_{c0})}{\mathcal{B}(X(3872)\to\pi^+\pi^-J/\psi)}<0.68$,
and
$\frac{\mathcal{B}(X(3872)\rightarrow\pi^0\pi^0\chi_{c0})}{\mathcal{B}(X(3872)\to\pi^+\pi^-J/\psi)}<1.7$.
Combined with the BESIII measurement of $X(3872)\to\pi^0\chi_{c1}$, we also set
an upper limit of
$\frac{\mathcal{B}(X(3872)\rightarrow\pi^0\chi_{c0})}{\mathcal{B}(X(3872)\to\pi^0\chi_{c1})}<4.4$.