  Character-level features are currently used in different neural network-based
natural language processing algorithms. However, little is known about the
character-level patterns those models learn. Moreover, models are often
compared only quantitatively while a qualitative analysis is missing. In this
paper, we investigate which character-level patterns neural networks learn and
if those patterns coincide with manually-defined word segmentations and
annotations. To that end, we extend the contextual decomposition technique
(Murdoch et al. 2018) to convolutional neural networks which allows us to
compare convolutional neural networks and bidirectional long short-term memory
networks. We evaluate and compare these models for the task of morphological
tagging on three morphologically different languages and show that these models
implicitly discover understandable linguistic rules. Our implementation can be
found at https://github.com/FredericGodin/ContextualDecomposition-NLP .


  This paper presents Kimera-Multi, the first multi-robot system that (i) is
robust and capable of identifying and rejecting incorrect inter and intra-robot
loop closures resulting from perceptual aliasing, (ii) is fully distributed and
only relies on local (peer-to-peer) communication to achieve distributed
localization and mapping, and (iii) builds a globally consistent
metric-semantic 3D mesh model of the environment in real-time, where faces of
the mesh are annotated with semantic labels. Kimera-Multi is implemented by a
team of robots equipped with visual-inertial sensors. Each robot builds a local
trajectory estimate and a local mesh using Kimera. When communication is
available, robots initiate a distributed place recognition and robust pose
graph optimization protocol based on a novel distributed graduated
non-convexity algorithm. The proposed protocol allows the robots to improve
their local trajectory estimates by leveraging inter-robot loop closures while
being robust to outliers. Finally, each robot uses its improved trajectory
estimate to correct the local mesh using mesh deformation techniques.
  We demonstrate Kimera-Multi in photo-realistic simulations, SLAM benchmarking
datasets, and challenging outdoor datasets collected using ground robots. Both
real and simulated experiments involve long trajectories (e.g., up to 800
meters per robot). The experiments show that Kimera-Multi (i) outperforms the
state of the art in terms of robustness and accuracy, (ii) achieves estimation
errors comparable to a centralized SLAM system while being fully distributed,
(iii) is parsimonious in terms of communication bandwidth, (iv) produces
accurate metric-semantic 3D meshes, and (v) is modular and can be also used for
standard 3D reconstruction (i.e., without semantic labels) or for trajectory
estimation (i.e., without reconstructing a 3D mesh).


  Transition from a split to a forward kinetic energy cascade system is
explored in the context of rotating turbulence using direct numerical
simulations with a three-dimensional isotropic random force uncorrelated with
the velocity field. Our parametric study covers confinement effects in large
aspect ratio domains and a broad range of rotation rates. Results indicate that
for fixed geometrical dimensions the Rossby number acts as a control parameter,
whereas for a fixed Rossby number the product of the domain size along the
rotation axis and forcing wavenumber governs the amount of energy that cascades
inversely. The regime transition criterion hence depends on both control
parameters.


  We report results from a deep search for redshifted HI 21cm absorption from
eight damped Lyman-$\alpha$ absorbers (DLAs) detected in our earlier optical
survey for DLAs towards radio-loud quasars. HI 21cm absorption was detected
from the $z = 2.192$ DLA towards TXS2039+187, only the sixth case of such a
detection at $z > 2$, while upper limits on the HI 21cm optical depth were
obtained in six other DLAs at $z > 2$. Our detection of HI 21cm absorption in
the eighth system, at $z = 2.289$ towards TXS0311+430, has been reported
earlier. We also present high spatial resolution images of the background
quasars at frequencies close to the redshifted HI 21cm line frequency, allowing
us to estimate the covering factor of each DLA, and then determine its spin
temperature $T_s$. For three non-detections of HI 21cm absorption, we obtain
strong lower limits on the spin temperature, $T_s \gtrsim 790$ K, similar to
the bulk of the high-$z$ DLA population; three other DLAs yield weak lower
limits, $T_s > 140-400$ K. However, for the two DLAs with detections of HI 21cm
absorption, the derived spin temperatures are both low $T_s = (160 \pm 35)
\times (f/0.35)$ K for the $z = 2.192$ DLA towards TXS2039+187 and $T_s = (72
\pm 18) \times (f/0.52)$ K for the $z = 2.289$ DLA towards TXS0311+430. These
are the first two DLAs at $z > 1$ with $T_s$ values comparable to those
obtained in local spiral galaxies. Based on the observed correlations between
spin temperature and metallicity and velocity spread and metallicity in DLAs,
we suggest that the hosts of the two absorbers are likely to be massive,
high-metallicity galaxies.


  In this paper the relativistic quantum dynamics of a spin-1/2 neutral
particle with a magnetic moment $\mu$ in the cosmic string spacetime is
reexamined by applying the von Neumann theory of self--adjoint extensions.
Contrary to previous studies where the interaction between the spin and the
line of charge is neglected, here we consider its effects. This interaction
gives rise to a point interaction: $\boldsymbol{\nabla} \cdot \mathbf{E}=
(2\lambda/\alpha)\delta(r)/r$. Due to the presence of the Dirac delta function,
by applying an appropriated boundary condition provided by the theory of
self--adjoint extensions, irregular solutions for the Hamiltonian are allowed.
We address the scattering problem obtaining the phase shift, S-matrix and the
scattering amplitude. The scattering amplitude obtained shows a dependency with
energy which stems from the fact that the helicity is not conserved in this
system. Examining the poles of the S-matrix we obtain an expression for the
bound states. The presence of bound states for this system has not been
discussed before in the literature.


  Scoping reviews, a type of literature review, require intensive human effort
to screen large numbers of scholarly sources for their relevance to the review
objectives. This manuscript introduces GPTscreenR, a package for the R
statistical programming language that uses the GPT-4 Large Language Model (LLM)
to automatically screen sources. The package makes use of the chain-of-thought
technique with the goal of maximising performance on complex screening tasks.
In validation against consensus human reviewer decisions, GPTscreenR performed
similarly to an alternative zero-shot technique, with a sensitivity of 71%,
specificity of 89%, and overall accuracy of 84%. Neither method achieved
perfect accuracy nor human levels of intraobserver agreement. GPTscreenR
demonstrates the potential for LLMs to support scholarly work and provides a
user-friendly software framework that can be integrated into existing review
processes.


  The PADME experiment, at the Laboratori Nazionali di Frascati (LNF), in
Italy, will search for invisible decays of the hypothetical dark photon via the
process $e^+e^-\rightarrow \gamma A'$, where the $A'$ escapes detection. The
dark photon mass range sensitivity in a first phase will be 1 to 24 MeV. We
report here on measurement and simulation studies of the performance of the
Small-Angle Calorimeter, a component of PADME's detector dedicated to rejecting
2- and 3-gamma backgrounds. The crucial requirement is a timing resolution of
less than 200 ps, which is satisfied by the choice of PbF$_2$ crystals and the
newly released Hamamatsu R13478UV photomultiplier tubes (PMTs). We find a
timing resolution of 81 ps (with double-peak separation resolution of 1.8 ns)
and a single-crystal energy resolution of 5.7%/$\sqrt{E}$ with light yield of
2.07 photo-electrons per MeV, using 100 to 400 MeV electrons at the Beam Test
Facility of LNF. We also propose the investigation of a two-PMT solution
coupled to a single PbF$_2$ crystal for higher-energy applications, which has
potentially attractive features.


  We twist Zagier's function $f_{k,D}$ by a sign function and a genus
character. Assuming weight $0 < k \equiv 2 \pmod{4}$, and letting $D$ be a
positive non-square discriminant, we prove that the obstruction to modularity
caused by the sign function can be corrected obtaining a locally harmonic
Maa\ss form or a local cusp form of the same weight. In addition, we provide an
alternative representation of our new function in terms of a twisted trace of
modular cycle integrals of a Poincar\'e series due to Petersson.


  In these lectures my aim is to review enough of conformal differential
geometry in four dimensions to give an account of Penrose's conformal cyclic
geometry.


  We discuss the problem of applicability of Coordinate Systems (or Frames)
that determine (t,x,y,z) values - the initial notions for most physical
theories. Equipment that measure these values - Clocks and Meters - are based
at Reference System and are the primary measuring units. We discus when and why
physical phenomena might prevent to provide measurements of (t,x,y,z). We show
that Temperature may be the factor that can significantly influence on the
measurements of (t,x,y,z) by Reference System and that action may violate the
usage of Coordinate System. We discuss possible origin of such unmovable
Temperature and assume that it should be Gravity.


  The semi-classical limit of quantum spin systems corresponds to a dynamical
Lagrangian which contains the usual kinetic energy, the couplings and
interactions of the spins and an additional, first order kinematical term which
corresponds to the Wess-Zumino-Novikov-Witten (WZNW) term for the spin degree
of freedom \cite{og}. It was shown that in the case of the kinetic dynamics
determined only by the WZNW term, half odd integer spin systems show a lack of
tunneling phenomena whereas integer spin systems are subject to it \cite{l} in
the case of potentials with easy-plane easy-axis symmetry. Here we prove, for
the theory with a normal quadratic kinetic term of arbitrary strength or the
first order theory with azimuthal symmetry (which is equivalently the so-called
easy-axis situation), that the tunneling is in fact suppressed for all non-zero
values of spin. This model exemplifies the concept that in the presence of
complex Euclidean action, it is necessary to use the ensuing complex critical
points in order to define the quantum (perturbation) theory \cite{ampr}. In the
present example, if we do not do so, exactly the opposite, erroneous
conclusion, that the tunneling is unsuppressed for all spins, is reached.


  The frequency and temperature dependence of the dielectric constant and the
electrical conductivity of the transparent glasses in the composition
Li2O-3B2O3 (LBO) were investigated in the 100 Hz- 10 MHz frequency range. The
dielectric constant and the loss in the low frequency regime were electrode
material dependent. Dielectric and electrical relaxations were respectively
analyzed using the Cole-Cole and electric modulus formalisms. The dielectric
relaxation mechanism was discussed in the framework of electrode and charge
carrier (hopping of the ions) related polarization using generalized Cole-Cole
expression. The frequency dependent electrical conductivity was rationalized
using Jonscher's power law. The activation energy associated with the dc
conductivity was 0.80 \pm 0.02 eV, which was ascribed to the motion of Li+ ions
in the glass matrix. The activation energy associated with dielectric
relaxation was almost equal to that of the dc conductivity, indicating that the
same species took part in both the processes. Temperature dependent behavior of
the frequency exponent (n) suggested that the correlated barrier hopping model
was the most apposite to rationalize the electrical transport phenomenon in
Li2O-3B2O3 glasses. These glasses on heating at 933 K/10h resulted in the known
non-linear optical phase LiB3O5.


  New scaling behavior has been both predicted and observed in the spontaneous
production of fluxons in quenched $Nb-Al/Al_{ox}/Nb$ annular Josephson tunnel
junctions as a function of the quench time, $\tau_{Q}$. The probability $f_{1}$
to trap a single defect during the N-S phase transition clearly follows an
allometric dependence on $\tau_{Q}$ with a scaling exponent $\sigma = 0.5$, as
predicted from the Zurek-Kibble mechanism for {\it realistic} JTJs formed by
strongly coupled superconductors. This definitive experiment replaces one
reported by us earlier, in which an idealised model was used that predicted
$\sigma = 0.25$, commensurate with the then much poorer data. Our experiment
remains the only condensed matter experiment to date to have measured a scaling
exponent with any reliability.


  The Bitcoin system is an anonymous, decentralized crypto-currency. There are
some deanonymizating techniques to cluster Bitcoin addresses and to map them to
users' identifications in the two research directions of Analysis of
Transaction Chain (ATC) and Analysis of Bitcoin Protocol and Network (ABPN).
Nowadays, there are also some anonymization methods such as coin-mixing and
transaction remote release (TRR) to cover the relationship between Bitcoin
address and the user. This paper studies anonymization and de-anonymization
technologies and proposes some directions for further research.


  Information scrambling and the butterfly effect in chaotic quantum systems
can be diagnosed by out-of-time-ordered (OTO) commutators through an
exponential growth and large late time value. We show that the latter feature
shows up in a strongly correlated many-body system, a Luttinger liquid, whose
density fluctuations we study at long and short wavelengths, both in
equilibrium and after a quantum quench. We find rich behaviour combining
robustly universal and non-universal features. The OTO commutators display
temperature and initial state independent behaviour, and grow as $t^2$ for
short times. For the short wavelength density operator, they reach a sizeable
value after the light cone only in an interacting Luttinger liquid, where the
bare excitations break up into collective modes. We benchmark our findings
numerically on an interacting spinless fermion model in 1D, and find
persistence of central features even in the non-integrable case. As a
non-universal feature, the short time growth exhibits a distance dependent
power.


  The problem of random motion of 1D quantum reactive harmonic oscillator
(QRHO) is formulated in terms of a wave functional regarded as a complex
probability process in an extended space. In the complex stochastic
differential equation (SDE) for this process the variables are separated with
the help of the Langevin-type model SDE introduced in the functional space. The
complete positive Fokker-Plank measure of the functional space is obtained. The
average wave function of roaming QRHO is obtained by means of functional
integration over the process with the complete Fokker-Plank measure in the
functional space. The local and averaged transition matrices of roaming QRHO
were constructed. The thermodynamics of nonrelativistic vacuum is investigated
in detail and expressions for the internal energy, Helmholtzian energy and
entropy are obtained. The oscillator's ground state energy, its shift and
broadening are calculated.


  The lacunar spinel GaV$_{4}$S$_{8}$ was recently suggested to be a prototype
multiferroic material hosting skyrmion lattice states with a sizeable
polarization $\boldsymbol{P}$ coupled to magnetic order. We explain this
phenomenon on the microscopic level. On the basis of density functional theory,
we construct an effective model describing the behavior of magnetically active
electrons in a weakly coupled lattice formed by molecular orbitals of the
(V$_{4}$S$_{4}$)$^{5+}$ clusters. By applying superexchange theory combined
with the Berry-phase theory for $\boldsymbol{P}$, we derive a compass model
relating the energy and polarization change with the directions of spins
$\boldsymbol{e}_{i}$ in magnetic bonds. We argue that, although each skyrmion
layer is mainly formed by superexchange interactions in the same plane, the
spin-dependence of $\boldsymbol{P}$ arises from the stacking misalignment of
such planes in the perpendicular direction, which is inherent to the lacunar
spinel structure. We predict a strong competition of isotropic, $\sim
\boldsymbol{e}_{i}\boldsymbol{e}_{j}$, and antisymmetric, $\sim
\boldsymbol{e}_{i} \times \boldsymbol{e}_{j}$, contributions to
$\boldsymbol{P}$ that explains the experimentally observed effect.


  We develop a Hodge theory for relative simple normal crossing varieties over
an Artinian base scheme. We introduce the notion of a mixed Hodge structure
over an Artin ring, which axiomatizes the structure that is found on the
cohomology of such a variety. As an application we prove that the maps between
the graded pieces of the Hodge bundles have constant rank.


  The measurement of the trilinear and quartic Higgs self-couplings is
necessary for the reconstruction of the Higgs potential. This way the Higgs
mechanism as the origin of electroweak symmetry breaking can be tested. The
couplings are accessible in multi-Higgs production processes at the LHC. In
this paper we investigate the prospects of measuring the trilinear Higgs
coupling in composite Higgs models. In these models, the Higgs boson emerges as
a pseudo-Goldstone boson of a strongly interacting sector, and the Higgs
potential is generated by loops of the Standard Model (SM) gauge bosons and
fermions. The Higgs self-couplings are modified compared to the SM and
controlled by the compositeness parameter $\xi$ in addition to the Higgs boson
mass. We construct areas of sensitivity to the trilinear Higgs coupling in the
relevant parameter space for various final states.


  Context: We investigate the possible theoretical properties of the putative
pulsar associated with the pulsar wind nebula IGR J18135-1751/HESS J1813-178
based upon recent gamma-ray observations and archival multi-wavelength
observations. Aims: We show that when using the standard equations for magnetic
dipole radiation with recent soft gamma-ray observations leads to deriving an
extreme set of parameters (magnetic field, period and spin down rate) for the
putative pulsar. Alternative scenarios that generate more typical parameter
values are explored. Methods: The properties of the putative pulsar are
calculated assuming that the 20-100 keV luminosity corresponds to 1% of Edot,
that the source is 4.5 kpc away, and that the pulsar age is 300 yrs. This gives
P = 0.55 s, Pdot = 3E-11 s/s, and B = 1.28E14 G. This is a very extreme set
compared to the population of known pulsars in PWN systems. Using the equations
for magnetic dipole losses makes it possible to adjust the initial assumptions
to see what is required for a more reasonable set of pulsar parameters.
Results: The current measured properties for IGR J18135-1751/HESS J1813-178
(i.e. luminosity, distance, and age) result in extreme properties of the unseen
pulsar within the PWN. The simplest method for achieving more reasonable
properties for the pulsar is to decouple the spin-down age of the pulsar from
the actual age for the system.


  We develop a family of reformulations of an arbitrary consistent linear
system into a stochastic problem. The reformulations are governed by two
user-defined parameters: a positive definite matrix defining a norm, and an
arbitrary discrete or continuous distribution over random matrices. Our
reformulation has several equivalent interpretations, allowing for researchers
from various communities to leverage their domain specific insights. In
particular, our reformulation can be equivalently seen as a stochastic
optimization problem, stochastic linear system, stochastic fixed point problem
and a probabilistic intersection problem. We prove sufficient, and necessary
and sufficient conditions for the reformulation to be exact. Further, we
propose and analyze three stochastic algorithms for solving the reformulated
problem---basic, parallel and accelerated methods---with global linear
convergence rates. The rates can be interpreted as condition numbers of a
matrix which depends on the system matrix and on the reformulation parameters.
This gives rise to a new phenomenon which we call stochastic preconditioning,
and which refers to the problem of finding parameters (matrix and distribution)
leading to a sufficiently small condition number. Our basic method can be
equivalently interpreted as stochastic gradient descent, stochastic Newton
method, stochastic proximal point method, stochastic fixed point method, and
stochastic projection method, with fixed stepsize (relaxation parameter),
applied to the reformulations.


  A new approach to disintegration of measures is presented, allowing one to
drop the usually taken separability assumption. The main tool is a result on
fibers in the spectrum of algebra of essentially bounded functions established
recently by the first-named author.


  The structure of Pais-Uhlenbeck oscillator in the equal-frequency limit has
been recently studied by Mannheim and Davidson [Phys.Rev. A71 (2005), 042110].
It appears that taking this limit, as presented in the above paper, is quite
subtle and the resulting structure of space of states - involved. In order to
clarify the situation we present here the proper way of taking the
equal-frequency limit, first under the assumption that the scalar product in
the space of states is positive defined. We discuss also the case of indefinite
metric space of states. We show that, irrespective of the way the limit is
defined, the limiting theory can be hardly viewed as satisfactory.


  We study the approximation of the spectrum of least-squares operators arising
from linear elasticity. We consider a two-field (stress/displacement) and a
three-field (stress/displacement/vorticity) formulation; other formulations
might be analyzed with similar techniques. We prove a priori estimates and we
confirm the theoretical results with simple two-dimensional numerical
experiments.


  One of the enticing features common to most of the two-dimensional electronic
systems that are currently at the forefront of materials science research is
the ability to easily introduce a combination of planar deformations and
bending in the system. Since the electronic properties are ultimately
determined by the details of atomic orbital overlap, such mechanical
manipulations translate into modified electronic properties. Here, we present a
general-purpose optimization framework for tailoring physical properties of
two-dimensional electronic systems by manipulating the state of local strain,
allowing a one-step route from their design to experimental implementation. A
definite example, chosen for its relevance in light of current experiments in
graphene nanostructures, is the optimization of the experimental parameters
that generate a prescribed spatial profile of pseudomagnetic fields in
graphene. But the method is general enough to accommodate a multitude of
possible experimental parameters and conditions whereby deformations can be
imparted to the graphene lattice, and complies, by design, with graphene's
elastic equilibrium and elastic compatibility constraints. As a result, it
efficiently answers the inverse problem of determining the optimal values of a
set of external or control parameters that result in a graphene deformation
whose associated pseudomagnetic field profile best matches a prescribed target.
The ability to address this inverse problem in an expedited way is one key step
for practical implementations of the concept of two-dimensional systems with
electronic properties strain-engineered to order. The general-purpose nature of
this calculation strategy means that it can be easily applied to the
optimization of other relevant physical quantities which directly depend on the
local strain field, not just in graphene but in other two-dimensional
electronic membranes.


  We describe the conditions for extra supersymmetry in N=(2,2) supersymmetric
nonlinear sigma models written in terms of semichiral superfields. We find that
some of these models have additional off-shell supersymmetry. The (4,4)
supersymmetry introduces geometrical structures on the target-space which are
conveniently described in terms of Yano f-structures and Magri-Morosi
concomitants. On-shell, we relate the new structures to the known
bi-hypercomplex structures.


  I give some claims on primorial prime numbers for interested readers in
number theory.


  Bayesian reward learning from demonstrations enables rigorous safety and
uncertainty analysis when performing imitation learning. However, Bayesian
reward learning methods are typically computationally intractable for complex
control problems. We propose Bayesian Reward Extrapolation (Bayesian REX), a
highly efficient Bayesian reward learning algorithm that scales to
high-dimensional imitation learning problems by pre-training a low-dimensional
feature encoding via self-supervised tasks and then leveraging preferences over
demonstrations to perform fast Bayesian inference. Bayesian REX can learn to
play Atari games from demonstrations, without access to the game score and can
generate 100,000 samples from the posterior over reward functions in only 5
minutes on a personal laptop. Bayesian REX also results in imitation learning
performance that is competitive with or better than state-of-the-art methods
that only learn point estimates of the reward function. Finally, Bayesian REX
enables efficient high-confidence policy evaluation without having access to
samples of the reward function. These high-confidence performance bounds can be
used to rank the performance and risk of a variety of evaluation policies and
provide a way to detect reward hacking behaviors.


  We extend the impulse theory for unsteady aerodynamics, from its classic
global form to finite-domain formulation then to minimum-domain form, and from
incompressible to compressible flows. For incompressible flow, the
minimum-domain impulse theory raises the finding of Li and Lu (J. Fluid Mech.,
712: 598-613, 2012) to a theorem: The entire force with discrete wake is
completely determined by only the time rate of impulse of those vortical
structures still connecting to the body, along with the Lamb-vector integral
thereof that captures the contribution of all the rest disconnected vortical
structures. For compressible flow, we find that the global form in terms of the
curl of momentum, obtained by Huang (Unsteady Vortical Aerodynamics. Shanghai
Jiaotong Univ. Press, 1994), can be generalized to having arbitrary finite
domain, but the formula is cumbersome and in general the curl of momentum no
longer has discrete structure and hence no minimum-domain theory exists.
Nevertheless, as the measure of transverse process only, the unsteady field of
vorticity may still have discrete wake. This leads to a minimum-domain
compressible vorticity-moment theory in terms of density-weighted vorticity
(but it is beyond the classic concept of impulse). These new findings and
applications have been confirmed by our numerical experiments. The results not
only open an avenue to combine the theory with computation-experiment in wide
applications, but also reveals a physical truth that it is no longer necessary
to account for all wake vortical structures in computing the force and moment.


  In a social network, influence diffusion is the process of spreading
innovations from user to user. An activation state identifies who are the
active users who have adopted the target innovation. Given an activation state
of a certain diffusion, effector detection aims to reveal the active users who
are able to best explain the observed state. In this paper, we tackle the
effector detection problem from two perspectives. The first approach is based
on the influence distance that measures the chance that an active user can
activate its neighbors. For a certain pair of users, the shorter the influence
distance, the higher probability that one can activate the other. Given an
activation state, the effectors are expected to have short influence distance
to active users while long to inactive users. By this idea, we propose the
influence-distance-based effector detection problem and provide a
3-approximation. Second, we address the effector detection problem by the
maximum likelihood estimation (MLE) approach. We prove that the optimal MLE can
be obtained in polynomial time for connected directed acyclic graphs. For
general graphs, we first extract a directed acyclic subgraph that can well
preserve the information in the original graph and then apply the MLE approach
to the extracted subgraph to obtain the effectors. The effectiveness of our
algorithms is experimentally verified via simulations on the real-world social
network.


  Renewable energy sources such as solar and wind are critical to combatting
global warming. Nevertheless, their intermittent energy generation requires the
development of large-scale grid energy storage, in contrast to the on-demand
generation of coal-based power plants. Sodium-ion batteries offer a promising
potential technology, yet because sodium ions are larger than lithium ions,
sodium-ion intercalation results in more drastic structural rearrangements. An
improved understanding of structural dynamics and ionic diffusion pathways is
crucial to developing more durable sodium-ion batteries. Here we synthesize
epitaxial NaxCoO2 by using molecular-beam epitaxy and topotactic
transformation. In the synthesized epitaxial films, the CoO2 layers are canted
with respect to the film surface, allowing electrochemical extraction of sodium
ions, which we confirm via ex-situ x-ray diffraction. We anticipate the
epitaxial thin films reported here to enable future operando studies of
interfaces, subtle lattice distortions, and microstructure during
electrochemical cycling.


  We have performed high-resolution hydrodynamic simulations of the Lyman-alpha
forest in a variety of popular cold dark matter dominated cosmologies,
including a low density and a vacuum-dominated model. The fluctuation amplitude
of these models is chosen to match the observed abundance of galaxy clusters at
low redshift. We assume that the intergalactic medium is photoionized and
photoheated by a uniform UV-background with the required amplitude to give the
observed mean hydrogen absorption. We produce simulated spectra, analyze them
by fitting Voigt profiles and compare line statistics with those obtained from
high resolution observations. All models give column density distributions in
good agreement with observations. However, the distribution of line widths (the
b-parameter distribution) reflects differences in the temperature of the
intergalactic medium between the models, with colder models producing more
narrow lines. All the models with a low baryon density, Omega_b h^2=0.0125, are
too cold to produce a b-parameter distribution in agreement with observations.
Models with a higher baryon density, Omega_b h^2=0.025, are hotter and provide
better fits. Peculiar velocities contribute significantly to the line widths in
models with low matter density, and this improves the agreement with
observations further. We briefly discuss alternative mechanisms for reconciling
the simulations with the observed b-parameter distributions.


  The increasing maturity of big data applications has led to a proliferation
of models targeting the same objectives within the same scenarios and datasets.
However, selecting the most suitable model that considers model's features
while taking specific requirements and constraints into account still poses a
significant challenge. Existing methods have focused on worker-task assignments
based on crowdsourcing, they neglect the scenario-dataset-model assignment
problem. To address this challenge, a new problem named the Scenario-based
Optimal Model Assignment (SOMA) problem is introduced and a novel framework
entitled Scenario and Model Associative percepts (SMAP) is developed. SMAP is a
heterogeneous information framework that can integrate various types of
information to intelligently select a suitable dataset and allocate the optimal
model for a specific scenario. To comprehensively evaluate models, a new score
function that utilizes multi-head attention mechanisms is proposed. Moreover, a
novel memory mechanism named the mnemonic center is developed to store the
matched heterogeneous information and prevent duplicate matching. Six popular
traffic scenarios are selected as study cases and extensive experiments are
conducted on a dataset to verify the effectiveness and efficiency of SMAP and
the score function.


  The coframe (teleparallel) description of gravity is known as a viable
alternative to GR. One of advantages of this model is the existence of a
conserved energy-momentum current witch is covariant under all symmetries of
the three-parameter Lagrangian. In this paper we study the relation between the
covector valued current and the energy-momentum tensor. Algebraic properties of
the conserved current for different values of parameters are derived. It is
shown that the tensor corresponding to the coframe current is traceless and, in
contrast to the electromagnetic field, has in general a non vanishing
antisymmetric part. The symmetric part is also non zero for all values of the
parameters. Consequently, the conserved current involves the energy-momentum as
well as the rotational (spin) properties of the field.


  We propose a new class of models for variable clustering called Asymptotic
Independent block (AI-block) models, which defines population-level clusters
based on the independence of the maxima of a multivariate stationary mixing
random process among clusters. This class of models is identifiable, meaning
that there exists a maximal element with a partial order between partitions,
allowing for statistical inference. We also present an algorithm depending on a
tuning parameter that recovers the clusters of variables without specifying the
number of clusters \emph{a priori}. Our work provides some theoretical insights
into the consistency of our algorithm, demonstrating that under certain
conditions it can effectively identify clusters in the data with a
computational complexity that is polynomial in the dimension. A data-driven
selection method for the tuning parameter is also proposed. To further
illustrate the significance of our work, we applied our method to neuroscience
and environmental real-datasets. These applications highlight the potential and
versatility of the proposed approach.


  The isobaric yield ratios of the fragments produced in the neutron-rich 48Ca
and 64Ni projectile fragmentation are analyzed in the framework of a modified
Fisher model. The correlations between the isobaric yield ratios (R) and the
energy coefficients in the Weisz\"acker-Beth semiclassical mass formula (the
symmetry-energy term asym, the Coulomb-energy term ac, and the pairing-energy
term ap) and the difference between the chemical potentials of the neutron and
proton ({\mu}n-{\mu}p) are investigated. Simple correlations between
({\mu}n-{\mu}p)/T, ac/T, asym/T, and ap/T (where T is the temperature), and lnR
are obtained. It is suggested that ({\mu}n-{\mu}p)/T, ac/T, asym/T, and ap/T of
neutron-rich nuclei can be extracted using isobaric yield ratios for heavy-ion
collisions at intermediate energies.


  We study the problem of $k$-center clustering with outliers in arbitrary
metrics and Euclidean space. Though a number of methods have been developed in
the past decades, it is still quite challenging to design quality guaranteed
algorithm with low complexity for this problem. Our idea is inspired by the
greedy method, Gonzalez's algorithm, for solving the problem of ordinary
$k$-center clustering. Based on some novel observations, we show that this
greedy strategy actually can handle $k$-center clustering with outliers
efficiently, in terms of clustering quality and time complexity. We further
show that the greedy approach yields small coreset for the problem in doubling
metrics, so as to reduce the time complexity significantly. Our algorithms are
easy to implement in practice. We test our method on both synthetic and real
datasets. The experimental results suggest that our algorithms can achieve near
optimal solutions and yield lower running times comparing with existing
methods.


  Astrophysical jets are often observed as bent or curved structures. We also
know that the different jet sources may be binary in nature, which may lead to
a regular, periodic motion of the jet nozzle, an orbital motion or precession.
Here, we present the results of 2D (M)HD simulations in order to investigate
how a precessing or orbiting jet nozzle affects the propagation of a high-speed
jet. We have performed a parameter study of systems with different precession
angles, orbital periods or separations, and different magnetic field strengths.
We find that these kinds of nozzles lead to curved jet propagation which is
determined by the main parameters that define the jet nozzle. We find C-shaped
jets from orbiting nozzles and S-shaped jets from precessing nozzles. Over long
time and long distances, the initially curved jet motion bores a broad channel
into the ambient gas that is filled with high-speed jet material which lateral
motion is damped, however. A strong (longitudinal) magnetic field can damp the
jet curvature that is enforced by either precession of orbital motion of the
jet sources. We have investigated the force balance across the jet and ambient
medium and found that the lateral magnetic pressure and gas pressure gradients
are almost balanced, but that a lack of gas pressure on the concave side of the
curvature is leading to the lateral motion. Magnetic tension does not play a
significant role. Our results are obtained in code units, but we provide
scaling relations such that our results may be applied to young stars,
micro-quasars, symbiotic stars or AGN.


  Within the framework of a Modified Poisson-Boltzmann theory accounting for
steric effects of microions, we prove analytically that the effective pair
interactions between like-charge colloids immersed in a confined electrolyte
are repulsive. Our approach encompasses and extends previously known results to
the case of complete confinement, and further incorporates the finite size of
the microions which is absent in the standard Poisson-Boltzmann theory.


  A generalized bridge is the law of a stochastic process that is conditioned
on N linear functionals of its path. We consider two types of representations
of such bridges: orthogonal and canonical.
  The orthogonal representation is constructed from the entire path of the
underlying process. Thus, future knowledge of the path is needed. The
orthogonal representation is provided for any continuous Gaussian process.
  In the canonical representation the filtrations and the linear spaces
generated by the bridge process and the underlying process coincide. Thus, no
future information of the underlying process is needed. Also, in the
semimartingale case the canonical bridge representation is related to the
enlargement of filtration and semimartingale decompositions. The canonical
representation is provided for the so-called prediction-invertible Gaussian
processes. All martingales are trivially prediction-invertible. A typical
non-semimartingale example of a prediction-invertible Gaussian process is the
fractional Brownian motion.
  We apply the canonical bridges to insider trading.


  We present the discovery of Kepler-88 d ($P_d = 1403\pm14$ days,
$M\mathrm{sin}i_d = 965\pm44\,M_\oplus = 3.04\pm0.14\,M_J$, $e_d =
0.41\pm0.03$) based on six years of radial velocity (RV) follow-up from the W.
M. Keck Observatory HIRES spectrograph. Kepler-88 has two previously identified
planets. Kepler-88 b (KOI-142.01) transits in the NASA \Kepler\ photometry and
has very large transit timing variations. \citet{Nesvorny2013} perfomed a
dynamical analysis of the TTVs to uniquely identify the orbital period and mass
of the perturbing planet (Kepler-88 c), which was later was confirmed with RVs
from the Observatoire de Haute-Provence (OHP, Barros et al. 2014). To fully
explore the architecture of this system, we performed photodynamical modeling
on the \Kepler\ photometry combined with the RVs from Keck and OHP and stellar
parameters from spectroscopy and Gaia. Planet d is not detectable in the
photometry, and long-baseline RVs are needed to ascertain its presence. A
photodynamical model simultaneously optimized to fit the RVs and \Kepler\
photometry yields the most precise planet masses and orbital properties yet for
b and c: $P_b = 10.91647\pm0.00014\,\mathrm{days}$, $M_b=9.5\pm1.2\,M_\oplus$,
$P_c=22.2649\pm0.0007\,\mathrm{days}$, and $M_c=214.1\pm5.3\,M_\oplus$. The
photodynamical solution also finds that planets b and c have low eccentricites
and low mutual inclination, are apsidally anti-aligned, and have conjunctions
on the same hemisphere of the star. Continued RV follow-up of systems with
small planets will improve our understanding of the link between inner
planetary system architectures and giant planets.


  At near-grounded glacier termini, calving can lead to the capsize of
kilometer-scale unstable icebergs. The transient contact force applied by the
capsizing iceberg on the glacier front generates seismic waves that propagate
over teleseismic distances. The inversion of this seismic signal is of great
interest to get insight into actual and past capsize dynamics. However, the
iceberg size, which is of interest for geophysical and climatic studies, cannot
be recovered from the seismic amplitude alone. This is because the capsize is a
complex process involving interactions between the iceberg, the glacier and the
surrounding water. This paper presents a first step towards the construction of
a complete model, and is focused on the capsize in the open ocean without
glacier front nor ice-m\'elange. The capsize dynamics of an iceberg in the open
ocean is captured by computational fluid dynamics (CFD) simulations, which
allows assessing the complexity of the fluid motion around a capsizing iceberg
and how far the ocean is affected by iceberg rotation. Expressing the results
in terms of appropriate dimensionless variables, we show that laboratory scale
and field scale capsizes can be directly compared. The capsize dynamics is
found to be highly sensitive to the iceberg aspect ratio and to the water and
ice densities. However, dealing at the same time with the fluid dynamics and
the contact between the iceberg and the deformable glacier front requires
highly complex coupling that often goes beyond actual capabilities of
fluid-structure interaction softwares. Therefore, we developed a
semi-analytical simplified fluid-structure model (SAFIM) that can be
implemented in solid mechanics computations dealing with contact dynamics of
deformable solids. This model accounts for hydrodynamic forces through
calibrated drag and added-mass effects, and is calibrated against the reference
CFD simulations...


  We report a study on spin conductance in ultra-thin films of Yttrium Iron
Garnet (YIG), where spin transport is provided by propagating spin waves, that
are generated and detected by direct and inverse spin Hall effects in two Pt
wires deposited on top. While at low current the spin conductance is dominated
by transport of thermal magnons, at high current, the spin conductance is
dominated by low-damping non-equilibrium magnons thermalized near the spectral
bottom by magnon-magnon interaction, with consequent a sensitivity to the
applied magnetic field and a longer decay length. This picture is supported by
microfocus Brillouin Light Scattering spectroscopy.


  The results of the microwave observations of the Sun made with the RATAN-600
have shown the existence of many types of spectral peculiarities in polarized
emission of active regions, which produce powerful flares. These phenomena
happen at microwaves and reflect inhomogeneous structure of magnetic field in
magnetospheres of flaring active regions in wide range of heights above the
photosphere. In this presentation we demonstrate an analysis of the AR 9415
during all the period of its passage across the solar disk. Results of the
study point out to existence of different scenarios of circular polarization
variations in the radio wave band. Here, we separated the phenomenon of the
cyclotron emission passage through the quasi-transverse magnetic field
(QT-region) and several effects connected with flare activity of active region.
New observational data are presented and compared with the data of several
observatories: SSRT, NoRH, MDI SOHO, GOES and MEES. The preliminary
interpretation of the phenomena are given.


  In this work, we propose a new method to track extended targets of different
shapes such as ellipses, rectangles and rhombi. We provide an analytical
framework to express these shapes as superelliptical contours and propose a
Bayesian filtering scheme that can handle measurements from the contour of the
object. The method utilizes the Rao-Blackwellized particle filtering algorithm
with novel sensor-object geometry constraints. The success of the algorithm is
demonstrated using both simulations and real-data experiments, and the
algorithm has been demonstrated to be of high performance in various
challenging scenarios.


  Shannon's secrecy system is studied in a setting, where both the legitimate
decoder and the wiretapper have access to side information sequences correlated
to the source, but the wiretapper receives both the coded information and the
side information via channels that are more noisy than the respective channels
of the legitmate decoder, which in turn, also shares a secret key with the
encoder. A single--letter characterization is provided for the achievable
region in the space of five figures of merit: the equivocation at the
wiretapper, the key rate, the distortion of the source reconstruction at the
legitimate receiver, the bandwidth expansion factor of the coded channels, and
the average transmission cost (generalized power). Beyond the fact that this is
an extension of earlier studies, it also provides a framework for studying
fundamental performance limits of systematic codes in the presence of a wiretap
channel. The best achievable performance of systematic codes is then compared
to that of a general code in several respects, and a few examples are given.


  In 2014, Braverman, Kazhdan, Patnaik and Bardy-Panse, Gaussent and Rousseau
associated Iwahori-Hecke algebras to Kac-Moody groups over non-Archimedean
local fields. In a previous paper, we defined and studied their principal
series representations. In 1982, Kato provided an irreducibility criterion for
these representations, in the reductive case. We had obtained partially this
criterion in the Kac-Moody case. In this paper, we prove this criterion in the
Kac-Moody case.


  Interferometric gravitational wave antennas are based on Michelson
interferometers whose sensitivity to small differential length changes has been
enhanced by adding multiple coupled optical resonators. The use of optical
cavities is essential for reaching the required sensitivity, but sets
challenges for the control system which must maintain the cavities near
resonance. The goal for the strain sensitivity of the Laser Interferometer
Gravitational-wave Observatory (LIGO) is 10^-21 rms, integrated over a 100 Hz
bandwidth centered at 150 Hz. We present the major design features of the LIGO
length and frequency sensing and control system which will hold the
differential length to within 5 10^-14 m of the operating point. We also
highlight the restrictions imposed by couplings of noise into the gravitational
wave readout signal and the required immunity against them.


  We investigate the microwave spectra of ultracold alkali metal dimers in
magnetic, electric and combined fields, taking account of the hyperfine
structure due to the nuclear spins. We consider the molecules 41K87Rb and
7Li133Cs, which are the targets of current experiments and demonstrate two
extremes of large and small nuclear quadrupole coupling. We calculate the
frequencies and intensities of transitions that may be used to transfer
ultracold molecules between hyperfine states in a magnetic field, employing
different polarizations of microwave radiation. In an electric field, the
hyperfine levels display narrow avoided crossings at specific fields that we
explain in terms of molecular alignment. The hyperfine splittings that arise in
electric fields may hinder individual addressing in schemes to use ultracold
molecules in quantum computation, but the structure of the spectra is
suppressed in combined fields.


  In this paper a novel tool BioDiVinEfor parallel analysis of biological
models is presented. The tool allows analysis of biological models specified in
terms of a set of chemical reactions. Chemical reactions are transformed into a
system of multi-affine differential equations. BioDiVinE employs techniques for
finite discrete abstraction of the continuous state space. At that level,
parallel analysis algorithms based on model checking are provided. In the
paper, the key tool features are described and their application is
demonstrated by means of a case study.


  A time-reversal-violating spin-correlation coefficient in the total cross
section for polarized neutrons incident on a tensor rank-2 polarized target is
calculated by assuming a time-reversal-noninvariant, parity-conserving
``five-fold" interaction in the neutron-nucleus optical potential. Results are
presented for the system $n + {^{165}{\rm Ho}}$ for neutron incident energies
covering the range 1--20 MeV. From existing experimental bounds, a strength of
$2 \pm 10$ keV is deduced for the real and imaginary parts of the five-fold
term, which implies an upper bound of order $10^{-4}$ on the relative $T$-odd
strength when compared to the central real optical potential.


  We perform a theoretical analysis of atomic four-wave mixing via a collision
of two Bose-Einstein condensates of metastable helium atoms, and compare the
results to a recent experiment. We calculate atom-atom pair correlations within
the scattering halo produced spontaneously during the collision. We also
examine the expected relative number squeezing of atoms on the sphere. The
analysis includes first-principles quantum simulations using the positive
P-representation method. We develop a unified description of the experimental
and simulation results.


  We consider the scalar conservation law with stochastic forcing $$ \partial_t
u +\mathrm{div}_g {\mathfrak f}(\mx,u)= \Phi(\mx,u) dW, \ \ {\bf x} \in M, \ \
t\geq 0 $$ on a smooth compact Riemannian manifold $(M,g)$ where $W$ is the
Wiener process and ${\bf x}\mapsto {\mathfrak f}(\mx,\xi)$ is a vector field on
$M$ for each $\xi\in {\bf R}$. We introduce admissibility conditions, derive
the kinetic formulation and use it to prove well posedness.


  We present a study of the radio emission from rotating, charged dust grains
immersed in the ionized gas constituting the thick, H$\alpha$-emitting disk of
many spiral galaxies. Using up-to-date optical constants, the charge on the
grains exposed to the diffuse galactic UV flux has been calculated. An
analytical approximation for the grain charge has been derived, which is then
used to obtain the grain rotation frequency. Grains are found to have
substantial radio emission peaked at a cutoff frequency in the range
10-100~GHz, depending on the grain size distribution and on the efficiency of
the radiative damping of the grain rotation. The dust radio emission is
compared to the free-free emission from the ionized gas component; some
constraints on the magnetic field strength in the observed dusty filaments are
also discussed. The model can be used to test the disk-halo interface
environment in spiral galaxies, to determine the amount and size distribution
of dust in their ionized component, and to investigate the rotation mechanisms
for the dust. Numerical estimates are given for experimental purposes.


  Growth dynamic of real networks because of emerging complexities is an open
and interesting question. Indeed it is not realistic to ignore history impact
on the current events. The mystery behind that complexity could be in the role
of history in some how. To regard this point, the average effect of history has
been included by a kernel function in differential equation of Barabasi Albert
(BA) model . This approach leads to a fractional order BA differential equation
as a generalization of BA model. As opposed to unlimited growth for degree of
nodes, our results show that over time the memory impact will cause a decay for
degrees. This gives a higher chance to younger members for turning to a hub. In
fact in a real network, there are two competitive processes. On one hand, based
on preferential attachment mechanism nodes with higher degree are more likely
to absorb links. On the other hand, node history through aging process prevents
new connections. Our findings from simulating a network grown by considering
these effects also from studying a real network of collaboration between
Hollywood movie actors conforms the results and significant effects of history
and time on dynamic.


  We introduce a novel meshless method called the Constrained Least-Squares
Ghost Sample Points (CLS-GSP) method for solving partial differential equations
on irregular domains or manifolds represented by randomly generated sample
points. Our approach involves two key innovations. Firstly, we locally
reconstruct the underlying function using a linear combination of radial basis
functions centered at a set of carefully chosen \textit{ghost sample points}
that are independent of the point cloud samples. Secondly, unlike conventional
least-squares methods, which minimize the sum of squared differences from all
sample points, we regularize the local reconstruction by imposing a hard
constraint to ensure that the least-squares approximation precisely passes
through the center. This simple yet effective constraint significantly enhances
the diagonal dominance and conditioning of the resulting differential matrix.
We provide analytical proofs demonstrating that our method consistently
estimates the exact Laplacian. Additionally, we present various numerical
examples showcasing the effectiveness of our proposed approach in solving the
Laplace/Poisson equation and related eigenvalue problems.


  The term `preheating' has been introduced recently to denote the process in
which energy is transferred from a classical inflaton field into fluctuating
field (particle) degrees of freedom without generating yet a real thermal
ensemble. The models considered up to now include, besides the inflaton field,
scalar or fermionic fluctuations. On the other hand the typical ingredient of
an inflationary scenario is a nonabelian spontaneously broken gauge theory. So
the formalism should also be developed to include gauge field fluctuations
excited by the inflaton or Higgs field. We have chosen here, as the simplest
nonabelian example, the SU(2) Higgs model. We consider the model at temperature
zero. From the technical point of view we generalize an analytical and
numerical renormalized formalism developed by us recently to coupled channnel
systems. We use the 't Hooft-Feynman gauge and dimensional regularization. We
present some numerical results but reserve a more exhaustive discussion of
solutions within the paramter space of two couplings and the initial value of
the Higgs field to a future publication.


  Understanding the emergence of biodiversity patterns in nature is a central
problem in biology. Theoretical models of speciation have addressed this
question in the macroecological scale, but little has been investigated in the
macroevolutionary context. Knowledge of the evolutionary history allows the
study of patterns underlying the processes considered in these models,
revealing their signatures and the role of speciation and extinction in shaping
macroevolutionary patterns. In this paper we introduce two algorithms to record
the evolutionary history of populations in individual-based models of
speciation, from which genealogies and phylogenies can be constructed. The
first algorithm relies on saving ancestral-descendant relationships, generating
a matrix that contains the times to the most recent common ancestor between all
pairs of individuals at every generation (the Most Recent Common Ancestor Time
matrix, MRCAT). The second algorithm directly records all speciation and
extinction events throughout the evolutionary process, generating a matrix with
the true phylogeny of species (the Sequential Speciation and Extinction Events,
SSEE). We illustrate the use of these algorithms in a spatially explicit
individual-based model of speciation. We compare the trees generated via MRCAT
and SSEE algorithms with trees inferred by methods that use only genetic
distance among extant species, commonly used in empirical studies and applied
here to simulated genetic data. Comparisons between tress are performed with
metrics describing the overall topology, branch length distribution and
imbalance of trees. We observe that both MRCAT and distance-based trees differ
from the true phylogeny, with the first being closer to the true tree than the
second.


  We present a simple yet effective self-supervised framework for audio-visual
representation learning, to localize the sound source in videos. To understand
what enables to learn useful representations, we systematically investigate the
effects of data augmentations, and reveal that (1) composition of data
augmentations plays a critical role, i.e. explicitly encouraging the
audio-visual representations to be invariant to various transformations~({\em
transformation invariance}); (2) enforcing geometric consistency substantially
improves the quality of learned representations, i.e. the detected sound source
should follow the same transformation applied on input video frames~({\em
transformation equivariance}). Extensive experiments demonstrate that our model
significantly outperforms previous methods on two sound localization
benchmarks, namely, Flickr-SoundNet and VGG-Sound. Additionally, we also
evaluate audio retrieval and cross-modal retrieval tasks. In both cases, our
self-supervised models demonstrate superior retrieval performances, even
competitive with the supervised approach in audio retrieval. This reveals the
proposed framework learns strong multi-modal representations that are
beneficial to sound localisation and generalization to further applications.
\textit{All codes will be available}.


  This paper classifies all the Dirac series (that is, irreducible unitary
representations having non-zero Dirac cohomology) of $E_{7(7)}$. Enhancing the
Helgason-Johnson bound in 1969 for the group $E_{7(7)}$ is one key ingredient.
Our calculation partially supports Vogan's fundamental parallelepiped (FPP)
conjecture. As applications, when passing to Dirac index, we continue to find
cancellation between the even part and the odd part of Dirac cohomology.
Moreover, for the first time, we find Dirac series whose spin lowest $K$-types
have multiplicities.


  Terzan 5 is a stellar system located in the inner Bulge of the Galaxy and has
been historically catalogued as a globular cluster. However, recent photometric
(Ferraro et al. 2009) and spectroscopic (Origlia et al. 2011; Origlia et al.
2013) investigations have shown that it hosts at least three stellar
populations with different iron abundances (with a total spread of
Delta[Fe/H]>1 dex) thus demonstrating that Terzan 5 is not a genuine globular
cluster. In addition, the striking similarity between the chemical patterns of
this system and those of its surrounding environment, the Galactic Bulge, from
the point of view of both the metallicity distribution and the alpha-element
enrichment, suggests that Terzan 5 could be a pristine fragment of the Bulge
itself.


  This paper has been withdrawn by the author due to serious flaws in certain
proofs. For instance, the method used to construct certain automorphic
representations is flawed.


  Indications of a discrepancy between simulations and data on the number of
muons in cosmic ray showers exist over a large span of energies. We focus on
the excess of multi-muon bundles observed by the DELPHI detector at LEP and on
the excess in the muon number in general reported by the Pierre Auger
Observatory. Even though the primary CR energies relevant for these experiments
differ by orders of magnitude, we can find a single mechanism which can
simultaneously increase predicted muon counts for both, while not violating
constraints from accelerators or from the longitudinal shower development as
observed by the Pierre Auger Observatory. We present a brief motivation and
describe a practical implementation of such a model, based on the addition of
soft particles to interactions above a chosen energy threshold. Results of an
extensive set of simulations show the behavior of this model in various parts
of a simplified parameter space.


  Bayesian optimization is a powerful tool to optimize a black-box function,
the evaluation of which is time-consuming or costly. In this paper, we propose
a new approach to Bayesian optimization called GP-MGC, which maximizes
multiscale graph correlation with respect to the global maximum to determine
the next query point. We present our evaluation of GP-MGC in applications
involving both synthetic benchmark functions and real-world datasets and
demonstrate that GP-MGC performs as well as or even better than
state-of-the-art methods such as max-value entropy search and GP-UCB.


  Invariant complex structures on the homogeneous manifold $U(n+1)/U(n)\times
U(p+1)/U(p)$ are reseached. The critical point of the functional of the scalar
curvature is found.


  In this paper, we follow in the footsteps of Onsager and Machlup (OM) and
consider diffusion-like paths that are explored by a particle moving via a
conservative force while being in thermal equilibrium with its surroundings.
Instead of considering diffusion (Brownian dynamics), we use a Metropolis
algorithm to derive an OM-like functional. Through the lens of the Metropolis
algorithm, we are able to elucidate the errors made when using a nonzero time
increment.
  Of particular interest are transition paths that transverse an energy barrier
that is large (but not too large) compared to the typical thermal energy. These
transitions have probabilities that are only small and yet not so small as to
be considered a violation of thermodynamics. As such, we turn our attention to
the "double-ended" problem, where the OM functional can be interpreted as a
"thermodynamic" action and employed to sample paths that start and end at
predetermined points. We find that sampling the continuous-time limit of the OM
functional, i.e., the Ito-Girsanov form, produces unphysical paths due to
thermodynamic inconsistency arising from the singular nature of the limit.
These unphysical effects are due to the correlation between the particles
position and the random fluctuating noise that is introduced in the limiting
process. Such a correlation is a direct consequence of the form of the
Ito-Girsanov functional, does not originate from numerical inaccuracies, and is
a violation of thermodynamics as embodied by Seifert's Integral Fluctuation
Theorem.


  We define a notion of isotropy for discrete set distributions. If $\mu$ is a
distribution over subsets $S$ of a ground set $[n]$, we say that $\mu$ is in
isotropic position if $P[e \in S]$ is the same for all $e\in [n]$. We design a
new approximate sampling algorithm that leverages isotropy for the class of
distributions $\mu$ that have a log-concave generating polynomial; this class
includes determinantal point processes, strongly Rayleigh distributions, and
uniform distributions over matroid bases. We show that when $\mu$ is in
approximately isotropic position, the running time of our algorithm depends
polynomially on the size of the set $S$, and only logarithmically on $n$. When
$n$ is much larger than the size of $S$, this is significantly faster than
prior algorithms, and can even be sublinear in $n$. We then show how to
transform a non-isotropic $\mu$ into an equivalent approximately isotropic form
with a polynomial-time preprocessing step, accelerating subsequent sampling
times. The main new ingredient enabling our algorithms is a class of negative
dependence inequalities that may be of independent interest.
  As an application of our results, we show how to approximately count bases of
a matroid of rank $k$ over a ground set of $n$ elements to within a factor of
$1+\epsilon$ in time $ O((n+1/\epsilon^2)\cdot poly(k, \log n))$. This is the
first algorithm that runs in nearly linear time for fixed rank $k$, and
achieves an inverse polynomially low approximation error.


  For arbitrary values of a parameter $\lambda\in R$, finite-time blow-up of
solutions to the generalized, inviscid Proudman-Johnson equation is studied via
a direct approach which involves the derivation of representation formulae for
solutions to the problem.


  We report on the determination of high-pressure elasticity from thermal
diffuse x-ray scattering of magnesium oxide at pressures up to 28 GPa. We find
that the full elasticity tensor as a function of pressure can be extracted from
x-ray scattering of single crystals. This enables the simultaneous measurement
of elasticity and crystal structure from a single experiment and thus marks a
decisive step towards establishing reliable calibration for extreme pressures.
Elastic constants can be extracted with this method from small crystals of
arbitrary symmetry, shape and optical properties and will allow for significant
progress in our understanding of the elastic behaviour of planets interior at
geophysically relevant conditions, structural phase transitions and fundamental
interactions of phonons with other quasi-particles.


  When we are fortunate enough to view an exoplanetary system nearly edge-on,
the star and planet periodically eclipse each other. Observations of eclipses
(transits and occultations) provide a bonanza of information that cannot be
obtained from radial-velocity data alone, such as the relative dimensions of
the planet and its host star, as well as the orientation of the planet's orbit
relative to the sky plane and relative to the stellar rotation axis. The
wavelength-dependence of the eclipse signal gives clues about the the
temperature and composition of the planetary atmosphere. Anomalies in the
timing or other properties of the eclipses may betray the presence of
additional planets or moons. Searching for eclipses is also a productive means
of discovering new planets. This chapter reviews the basic geometry and physics
of eclipses, and summarizes the knowledge that has been gained through eclipse
observations, as well as the information that might be gained in the future.


  This paper gives a tableau formula for expanding the product of a Lascoux
polynomial and a stable Grothendieck polynomial into Lascoux polynomials.
Lascoux and stable Grothendieck polynomials are inhomogeneous analogues of key
polynomials and Stanley symmetric functions, respectively. Our formula refines
the K-theoretic Littlewood-Richardson rule of Buch and extends the key
expansion of key times Schur established by Haglund, Luoto, Mason, and van
Willigenburg. Our proof is combinatorial, relying heavily on a novel row
insertion algorithm of Huang, Shimozono and Yu.


  The \textit{domination number} $\gamma(\mathcal{H})$ of a hypergraph
$\mathcal{H}=(V(\mathcal{H}),E(\mathcal{H})$ is the minimum size of a subset
$D\subset V(\mathcal{H}$ of the vertices such that for every $v\in
V(\mathcal{H})\setminus D$ there exist a vertex $d \in D$ and an edge $H\in
E(\mathcal{H})$ with $v,d\in H$. We address the problem of finding the minimum
number $n(k,\gamma)$ of vertices that a $k$-uniform hypergraph $\mathcal{H}$
can have if $\gamma(\mathcal{H})\ge \gamma$ and $\mathcal{H}$ does not contain
isolated vertices. We prove that $$n(k,\gamma)=k+\Theta(k^{1-1/\gamma})$$ and
also consider the $s$-wise dominating and the distance-$l$ dominating version
of the problem. In particular, we show that the minimum number
$n_{dc}(k,\gamma, l)$ of vertices that a connected $k$-uniform hypergraph with
distance-$l$ domination number $\gamma$ can have is roughly $\frac{k\gamma
l}{2}$


  Flavor structure of soft supersymmetry breaking parameters is studied in a
certain type of effective supergravity theory derived from moduli/dilaton
dominated supersymmetry breaking. Some interesting sum rules for soft scalar
masses are presented. They constrain their flavor structure and predict some
interesting patterns appeared in soft scalar masses in the non-universal case.
We also study the alignment phenomena in the flavor space of soft breaking
parameters due to Yukawa couplings and discuss their phenomenological
consequences.


  We have studied the wave properties of the cold and isothermal plasma in the
vicinity of the Schwarzschild black hole event horizon. The Fourier analyzed
perturbed 3+1 GRMHD equations are taken on the basis of which the complex
dispersion relations are obtained for non-rotating, rotating non-magnetized and
rotating magnetized backgrounds. The propagation and attenuation vectors along
with the refractive index are obtained (shown in graphs) to study the
dispersive properties of the medium near the event horizon. The results show
that no information can be obtained from the Schwarzschild magnetosphere.
Further, the pressure ceases the existence of normal dispersion of waves.


  We investigate bifurcations in feedforward coupled cell networks. Feedforward
structure (the absence of feedback) can be defined by a partial order on the
cells. We use this property to study generic one-parameter steady state
bifurcations for such networks. Branching solutions and their asymptotics are
described in terms of Taylor coefficients of the internal dynamics. They can be
determined via an algorithm that only exploits the network structure. Similar
to previous results on feedforward chains, we observe amplifications of the
growth rates of steady state branches induced by the feedforward structure.
However, contrary to these earlier results, as the interaction scenarios can be
more complicated in general feedforward networks, different branching patterns
and different amplifications can occur for different regions in the space of
Taylor coefficients.


  We study, in the framework of the Landauer theory, the thermal emission in
far-field regime, of arbitrary indefinite planar media and finite size systems.
We prove that the flux radiated by the former is bounded by the blackbody
emission while, for the second, there is in principle, no upper limit
demonstrating so the possibility for a super-Planckian thermal emission with
finite size systems.


  We revisit sheaves on locales by placing them in the context of the theory of
quantale modules. The local homeomorphisms $p:X\to B$ are identified with the
Hilbert $B$-modules that are equipped with a natural notion of basis. The
homomorphisms of these modules are necessarily adjointable, and the resulting
self-dual category yields a description of the equivalence between local
homeomorphisms and sheaves whereby morphisms of sheaves arise as the ``operator
adjoints'' of the maps of local homeomorphisms.


  The PHOBOS experiment at RHIC has measured the total multiplicity of primary
charged particles as a function of collision centrality in Au+Au collisions at
sqrt(s_NN) = 19.6, 130 and 200 GeV. Above sqrt(s_NN) ~ 20 GeV, the total
multiplicity per participating nucleon pair (<N_ch>/<N_part/2>) in central
events scales with sqrt(s) in the same way as <N_ch> in e+e- data. This is
suggestive of a universal mechanism of particle production in
strongly-interacting systems, controlled mainly by the amount of energy
available for particle production (per participant pair for heavy ion
collisions). The same effect has been observed in pp/pbar-p data after
correcting for the energy taken away by leading particles. An approximate
independence of <N_ch>/<N_part/2> on the number of participating nucleons is
also observed, reminiscent of ``wounded nucleon'' scaling (<N_ch> proportional
to <N_part>), but with the constant of proportionality set by the multiplicity
measured in e+e- data rather than by pp/pbar-p data.


  Network traffic classification is a crucial research area aiming to enhance
service quality, streamline network management, and bolster cybersecurity. To
address the growing complexity of transmission encryption techniques, various
machine learning and deep learning methods have been proposed. However,
existing approaches face two main challenges. Firstly, they struggle with model
inefficiency due to the quadratic complexity of the widely used Transformer
architecture. Secondly, they suffer from inadequate traffic representation
because of discarding important byte information while retaining unwanted
biases. To address these challenges, we propose NetMamba, an efficient
linear-time state space model equipped with a comprehensive traffic
representation scheme. We adopt a specially selected and improved
unidirectional Mamba architecture for the networking field, instead of the
Transformer, to address efficiency issues. In addition, we design a traffic
representation scheme to extract valid information from massive traffic data
while removing biased information. Evaluation experiments on six public
datasets encompassing three main classification tasks showcase NetMamba's
superior classification performance compared to state-of-the-art baselines. It
achieves an accuracy rate of nearly 99% (some over 99%) in all tasks.
Additionally, NetMamba demonstrates excellent efficiency, improving inference
speed by up to 60 times while maintaining comparably low memory usage.
Furthermore, NetMamba exhibits superior few-shot learning abilities, achieving
better classification performance with fewer labeled data. To the best of our
knowledge, NetMamba is the first model to tailor the Mamba architecture for
networking.


  The metal-poor stars in the bulge are important relics of the Milky Way's
formation history, as simulations predict that they are some of the oldest
stars in the Galaxy. In order to determine if they are truly ancient stars, we
must understand the origins of this population. Currently, it is unclear if the
metal-poor stars in the bulge ([Fe/H] < -1 dex) are merely halo interlopers, a
unique accreted population, part of the boxy/peanut-shaped (B/P) bulge or a
classical bulge population. In this work, we use spectra from the VLT/FLAMES
spectrograph to obtain metallicity estimates using the Ca-II triplet (CaT) of
473 bulge stars (187 of which have [Fe/H]<-1 dex), targeted using SkyMapper
photometry. We also use Gaia DR2 parallaxes and proper motions to infer the
Galactic positions and velocities along with orbital properties for 523 bulge
stars. We employ a probabilistic orbit analysis and find that about half of our
sample has a > 50\% probability of being bound to the bulge, and half are halo
interlopers. We also see that the occurrence rate of halo interlopers increases
steadily with decreasing metallicity across the full range of our sample (-3 <
[Fe/H] < 0.5). Our examination of the kinematics of the confined compared to
the unbound stars indicates the metal-poor bulge ([Fe/H] < -1 dex) comprises at
least two populations; those confined to the boxy/peanut bulge and halo stars
passing through the inner galaxy. We conclude that an orbital analysis
approach, as we have employed, is important to uncover and understand the
composite nature of the metal-poor stars in the inner region.


  We obtain bounds for the number of variables required to establish Hasse
principles, both for existence of solutions and for asymptotic formulae, for
systems of additive equations containing forms of differing degree but also
multiple forms of like degree. Apart from the very general estimates of Schmidt
and Browning--Heath-Brown, which give weak results when specialized to the
diagonal situation, this is the first result on such "hybrid" systems.


  We consider energy (heat) transport in quantum systems, and establish a
relationship between energy spread and energy current-current correlation
function. The energy current-current correlation is related to thermal
conductivity by the Green-Kubo formula, and thus this relationship allows us to
study conductivity directly from the energy spread process. As an example, we
investigate a spinless fermion model; the numerical results confirm the
relationship.


  In this paper we investigate computational properties of the Diophantine
problem for spherical equations in some classes of finite groups. We classify
the complexity of different variations of the problem, e.g., when $G$ is fixed
and when $G$ is a part of the input.
  When the group $G$ is constant or given as multiplication table, we show that
the problem always can be solved in polynomial time. On the other hand, for the
permutation groups $S_n$ (with $n$ part of the input), the problem is
NP-complete. The situation for matrix groups is quite involved: while we
exhibit sequences of 2-by-2 matrices where the problem is NP-complete, in the
full group $GL(2,p)$ ($p$ prime and part of the input) it can be solved in
polynomial time. We also find a similar behaviour with subgroups of matrices of
arbitrary dimension over a constant ring.


  We investigated the stability of the spherically symmetric non-abelian
(Bartnik-McKinnon) black hole solution of the SU(2) Einstein-Yang-Mills system
using the multiple-scale analysis. It is found, in contrast with the vacuum
situation, that a spherically symmetric oscillatory perturbation to second
order cannot be constructed. The singular behavior of gravitational waves is
induced by the coupling of the gravitational waves to the Yang-Mills waves.


  This paper investigates the assumption of homogeneous effects of federal tax
changes across the U.S. states and identifies where and why that assumption may
not be valid. More specifically, what determines the transmission mechanism of
tax shocks at the state level? How vital are states' fiscal structures,
financial conditions, labor market rigidities, and industry mix? Do these
economic and structural characteristics drive the transmission mechanism of the
tax changes at the state level at different horizons? This study employs a
panel factor-augmented vector autoregression (FAVAR) technique to answer these
issues. The findings show that state economies respond homogeneously in terms
of employment and price levels; however, they react heterogeneously in real GDP
and personal income growth. In most states, these reactions are statistically
significant, and the heterogeneity in the effects of tax cuts is significantly
related to the state's fiscal structure, manufacturing and financial
composition, and the labor market's rigidity. A cross-state regression analysis
shows that states with higher tax elasticity, higher personal income tax,
strict labor market regulation, and economic policy uncertainties are
relatively less responsive to federal tax changes. In contrast, the magnitude
of the response in real GDP, personal income, and employment to tax cuts is
relatively higher in states with a larger share of finance, manufacturing,
lower tax burdens, and flexible credit markets.


  A random geometric irrigation graph $\Gamma_n(r_n,\xi)$ has $n$ vertices
identified by $n$ independent uniformly distributed points $X_1,\ldots,X_n$ in
the unit square $[0,1]^2$. Each point $X_i$ selects $\xi_i$ neighbors at
random, without replacement, among those points $X_j$ ($j\neq i$) for which
$\|X_i-X_j\| < r_n$, and the selected vertices are connected to $X_i$ by an
edge. The number $\xi_i$ of the neighbors is an integer-valued random variable,
chosen independently with identical distribution for each $X_i$ such that
$\xi_i$ satisfies $1\le \xi_i \le \kappa$ for a constant $\kappa>1$. We prove
that when $r_n = \gamma_n \sqrt{\log n/n}$ for $\gamma_n \to \infty$ with
$\gamma_n =o(n^{1/6}/\log^{5/6}n)$, then the random geometric irrigation graph
experiences explosive percolation in the sense that when $\mathbf E \xi_i=1$,
then the largest connected component has size $o(n)$ but if $\mathbf E \xi_i
>1$, then the size of the largest connected component is with high probability
$n-o(n)$. This offers a natural non-centralized sparsification of a random
geometric graph that is mostly connected.


  Reasoning has been a central topic in artificial intelligence from the
beginning. The recent progress made on distributed representation and neural
networks continues to improve the state-of-the-art performance of natural
language inference. However, it remains an open question whether the models
perform real reasoning to reach their conclusions or rely on spurious
correlations. Adversarial attacks have proven to be an important tool to help
evaluate the Achilles' heel of the victim models. In this study, we explore the
fundamental problem of developing attack models based on logic formalism. We
propose NatLogAttack to perform systematic attacks centring around natural
logic, a classical logic formalism that is traceable back to Aristotle's
syllogism and has been closely developed for natural language inference. The
proposed framework renders both label-preserving and label-flipping attacks. We
show that compared to the existing attack models, NatLogAttack generates better
adversarial examples with fewer visits to the victim models. The victim models
are found to be more vulnerable under the label-flipping setting. NatLogAttack
provides a tool to probe the existing and future NLI models' capacity from a
key viewpoint and we hope more logic-based attacks will be further explored for
understanding the desired property of reasoning.


  A possible data source for the estimation of asset correlations is default
time series. This study investigates the systematic error that is made if the
exposure pool underlying a default time series is assumed to be homogeneous
when in reality it is not. We find that the asset correlation will always be
underestimated if homogeneity with respect to the probability of default (PD)
is wrongly assumed, and the error is the larger the more spread out the PD is
within the exposure pool. If the exposure pool is inhomogeneous with respect to
the asset correlation itself then the error may be going in both directions,
but for most PD- and asset correlation ranges relevant in practice the asset
correlation is systematically underestimated. Both effects stack up and the
error tends to become even larger if in addition a negative correlation between
asset correlation and PD is assumed, which is plausible in many circumstances
and consistent with the Basel RWA formula. It is argued that the generic
inhomogeneity effect described is one of the reasons why asset correlations
measured from default data tend to be lower than asset correlations derived
from asset value data.


  With SKA precursor and pathfinder operations in full swing, radio and
(sub-)mm astronomy is entering the era of super big data. The big questions is
how to make (sub-)mm and radio data available to the astronomical community,
preferably using FAIR (findable, accessible, interoperable and re-useable;
Wilkinson et al. 2016) principles. There are already a lot of efforts going on
around the globe: facilities such as ALMA, LOFAR, MWA, NRAO and ASKAP are
already publishing much of their imaging data in the form of "science ready"
products, SKA regional centres are being formed and a radio astronomy interest
group has been initiated within the IVOA. In addition, also non-imaging data,
like timing, pulsar or beam forming data, needs to be available to the
community as well. This BoF intended to bring everyone interested in this topic
around one virtual table to hear about and discuss the following questions:
What is the status of efforts to expose both visibility and science ready data?
What is already there, maybe has been used for decades by traditional
observatories? What is still missing? Where do we want to go next?


  We study the combinatorial analogues of the classical invariants of
measurable equivalence relations. We introduce the notion of cost and
$\beta$-invariants (the analogue of the first $L^2$-Betti number introduced by
Gaboriau) for sequences of finite graphs with uniformly bounded vertex degrees
and examine the relation of these invariants and the rank gradient resp. mod
$p$ homology gradient invariants introduced by Lackenby for residually finite
groups.


  We study how lepton flavor violation (LFV) is related to the reactor angle
$\theta_{13}$, LHC/dark matter (DM) signal with a successful leptogenesis in a
radiative seesaw model through $A_4$ flavor symmetry breaking, in the light of
the deviation of tri-bimaximal mixing (TBM) angles and the recent precision
oscillation data. To do this, we consider the normal mass spectrum of light
neutrino giving a successful leptogenesis at electroweak (EW) scale or more
with a relatively large $\sin\theta_{13}\simeq{\cal O}(0.1)$, where a
successful leptogenesis requires LHC/DM signal $m_{-}\lesssim$ a few keV in our
scenario, and we show that the measurement of $\tau\rightarrow\mu\gamma$ is
strongly dependent on $m_{-}$ and the leptogenesis scale. Especially, we show
that $\mu\rightarrow e\gamma$ and $\mu-e$ conversion are proportional to the
value of $\theta_{13}$, and the measurements of both $\mu\rightarrow e\gamma$
(and/or $\mu-e$ conversion) and $\theta_{13}$ can give a prediction of
$\tau\rightarrow\mu\gamma$ with a successful leptogenesis.


  Deep matrix factorizations (deep MFs) are recent unsupervised data mining
techniques inspired by constrained low-rank approximations. They aim to extract
complex hierarchies of features within high-dimensional datasets. Most of the
loss functions proposed in the literature to evaluate the quality of deep MF
models and the underlying optimization frameworks are not consistent because
different losses are used at different layers. In this paper, we introduce two
meaningful loss functions for deep MF and present a generic framework to solve
the corresponding optimization problems. We illustrate the effectiveness of
this approach through the integration of various constraints and
regularizations, such as sparsity, nonnegativity and minimum-volume. The models
are successfully applied on both synthetic and real data, namely for
hyperspectral unmixing and extraction of facial features.


  It is shown, that Bose-Einstein condensation can occur not only in spatially
extended equilibrium systems, but also in the systems far from thermal
equilibrium, which show order-disorder phase transition. The investigation is
performed by solving the Complex Ginzburg-Landau equation, a universal model
for nonequilibrium order-disorder phase transitions.


  We discuss in detail potential NRQED (pNRQED), a previously proposed
effective field theory for ultrasoft photons. The pNRQED lagrangian for the
equal mass case is presented and it is shown that it correctly reproduces the
positronium spectrum at order $m\alpha^5$. The pNRQED lagrangian for the
unequal mass case is also presented at the same order. Dimensional
regularization is used throughout.


  An overview and synthesis of results and criteria for open-loop
controllability of Hamiltonian quantum systems obtained using Lie group and Lie
algebra techniques is presented. Negative results for open-loop controllability
of dissipative systems are discussed, and the superiority of closed-loop
(feedback) control for quantum systems is established.


  In the past decades, the finite difference methods for space fractional
operators develop rapidly; to the best of our knowledge, all the existing
finite difference schemes, including the first and high order ones, just work
on uniform meshes. The nonlocal property of space fractional operator makes it
difficult to design the finite difference scheme on non-uniform meshes. This
paper provides a basic strategy to derive the first and high order
discretization schemes on non-uniform meshes for fractional operators. And the
obtained first and second schemes on non-uniform meshes are used to solve space
fractional diffusion equations. The error estimates and stability analysis are
detailedly performed; and extensive numerical experiments confirm the
theoretical analysis or verify the convergence orders.


  Sign languages, often categorised as low-resource languages, face significant
challenges in achieving accurate translation due to the scarcity of parallel
annotated datasets. This paper introduces Select and Reorder (S&R), a novel
approach that addresses data scarcity by breaking down the translation process
into two distinct steps: Gloss Selection (GS) and Gloss Reordering (GR). Our
method leverages large spoken language models and the substantial lexical
overlap between source spoken languages and target sign languages to establish
an initial alignment. Both steps make use of Non-AutoRegressive (NAR) decoding
for reduced computation and faster inference speeds. Through this
disentanglement of tasks, we achieve state-of-the-art BLEU and Rouge scores on
the Meine DGS Annotated (mDGS) dataset, demonstrating a substantial BLUE-1
improvement of 37.88% in Text to Gloss (T2G) Translation. This innovative
approach paves the way for more effective translation models for sign
languages, even in resource-constrained settings.


  In this paper, we prove that in bounded planar domains with $C^{2,\alpha}$
boundary, for almost every initial condition in the sense of the Lebesgue
measure, the point vortex system has a global solution, meaning that there is
no collision between two point-vortices or with the boundary. This extends the
work previously done in [13] for the unit disk. The proof requires the
construction of a regularized dynamics that approximates the real dynamics and
some strong inequalities for the Green's function of the domain. In this paper,
we make extensive use of the estimates given in [7]. We establish our relevant
inequalities first in simply connected domains using conformal maps, then in
multiply connected domains.


  We investigate achievable degrees of freedom (DoF) for a multiple-input
multiple-output (MIMO) multiway relay channel (mRC) with $L$ clusters and $K$
users per cluster. Each user is equipped with $M$ antennas and the relay with
$N$ antennas. We assume a new data exchange model, termed \emph{clustered full
data exchange}, i.e., each user in a cluster wants to learn the messages of all
the other users in the same cluster. Novel signal alignment techniques are
developed to systematically construct the beamforming matrices at the users and
the relay for efficient physical-layer network coding. Based on that, we derive
an achievable DoF of the MIMO mRC with an arbitrary network configuration of
$L$ and $K$, as well as with an arbitrary antenna configuration of $M$ and $N$.
We show that our proposed scheme achieves the DoF capacity when $\frac{M}{N}
\leq \frac{1}{LK-1}$ and $\frac{M}{N} \geq \frac{(K-1)L+1}{KL}$.


  The advances in cold atom experiments have allowed construction of confining
traps in the form of curved surfaces. This opens up the possibility of studying
quantum gases in curved manifolds. On closed surfaces, many fundamental
processes are affected by the local and global properties, i.e. the curvature
and the topology of the surface. In this paper, we study the problem of
potential scattering on a spherical surface and discuss its difference with
that on a 2D plane. For bound states with angular momentum $m$, their energies
($E_{m}$) on a sphere are related to those on a 2D plane ($-|E_{m,o}|$) as
$E_{m}= - |E_{m, o}| + E_{R}^{} \left[ \frac{m^2-1}{3} + O\left(
\frac{r_o^2}{R^2} \right) \right] $, where $E_{R}^{} = \hbar^2/(2M R^2)$, and
$R$ is the radius of the sphere. Due to the finite extent of the manifold, the
phase shifts on a sphere at energies $E\sim E_{R}^{}$ differ significantly from
those on a 2D plane. As energy $E$ approaches zero, the phase shift in the
planar case approaches $0$, whereas in the spherical case it reaches a constant
that connects the microscopic length scale to the largest length scale $R$.


  An accelerated particle sees the Minkowski vacuum as thermally excited, and
the particle moves stochastically due to an interaction with the thermal bath.
This interaction fluctuates the particle's transverse momenta like the Brownian
motion in a heat bath. Because of this fluctuating motion, it has been
discussed that the accelerated charged particle emits extra radiation (the
Unruh radiation) in addition to the classical Larmor radiation, and experiments
are under planning to detect such radiation by using ultrahigh intensity lasers
constructed in near future. There are, however, counterarguments that the
radiation is canceled by an interference effect between the vacuum fluctuation
and the fluctuating motion. In fact, in the case of an internal detector where
the Heisenberg equation of motion can be solved exactly, there is no additional
radiation after the thermalization is completed. In this paper, we revisit the
issue in the case of an accelerated charged particle in the scalar-field analog
of QED. We prove the equipartition theorem of transverse momenta by
investigating a stochastic motion of the particle, and show that the Unruh
radiation is partially canceled by an interference effect.


  We present a new approach to formulating open superstring field theory based
on the covering of the supermoduli space of super-Riemann surfaces and
explicitly construct a gauge-invariant action in the Neveu-Schwarz sector up to
quartic interactions. The cubic interaction takes a form of an integral over an
odd modulus of disks with three punctures and the associated ghost is inserted.
The quartic interaction takes a form of an integral over one even modulus and
two odd moduli, and it can be interpreted as the integral over the region of
the supermoduli space of disks with four punctures which is not covered by
Feynman diagrams with two cubic vertices and one propagator. As our approach is
based on the covering of the supermoduli space, the resulting theory naturally
realizes an $A_\infty$ structure, and the two-string product and the
three-string product used in defining the cubic and quartic interactions are
constructed to satisfy the $A_\infty$ relations to this order.


  Liquid xenon detectors such as XENON10 and XENON100 obtain a significant
fraction of their sensitivity to light (<10 GeV) particle dark matter by
looking for nuclear recoils of only a few keV, just above the detector
threshold. Yet in this energy regime a correct treatment of the detector
threshold and resolution remains unclear. The energy dependence of the
scintillation yield of liquid xenon for nuclear recoils also bears heavily on
detector sensitivity, yet numerous measurements have not succeeded in obtaining
concordant results. In this article we show that the ratio of detected
ionization to scintillation can be leveraged to constrain the scintillation
yield. We also present a rigorous treatment of liquid xenon detector threshold
and energy resolution. Notably, the effective energy resolution differs
significantly from a simple Poisson distribution. We conclude with a
calculation of dark matter exclusion limits, and show that existing data from
liquid xenon detectors strongly constrain recent interpretations of light dark
matter.


  The emergence of neural networks has revolutionized the field of motion
synthesis. Yet, learning to unconditionally synthesize motions from a given
distribution remains challenging, especially when the motions are highly
diverse. In this work, we present MoDi -- a generative model trained in an
unsupervised setting from an extremely diverse, unstructured and unlabeled
dataset. During inference, MoDi can synthesize high-quality, diverse motions.
Despite the lack of any structure in the dataset, our model yields a
well-behaved and highly structured latent space, which can be semantically
clustered, constituting a strong motion prior that facilitates various
applications including semantic editing and crowd simulation. In addition, we
present an encoder that inverts real motions into MoDi's natural motion
manifold, issuing solutions to various ill-posed challenges such as completion
from prefix and spatial editing. Our qualitative and quantitative experiments
achieve state-of-the-art results that outperform recent SOTA techniques. Code
and trained models are available at https://sigal-raab.github.io/MoDi.


  We attempt to reconcile Gabaix and Koijen's (GK) recent Inelastic Market
Hypothesis (IMH) with the order-driven view of markets that emerged within the
microstructure literature in the past 20 years. We review the most salient
empirical facts and arguments that give credence to the idea that market price
fluctuations are mostly due to order flow, whether informed or non-informed. We
show that the Latent Liquidity Theory of price impact makes a precise
prediction for GK's multiplier $M$, which measures by how many dollars, on
average, the market value of a company goes up if one buys one dollar worth of
its stocks. Our central result is that $M$ is of order unity, as found by GK,
and increases with the volatility of the stock and decreases with the fraction
of the market cap. traded daily. We discuss several empirical results
suggesting that the lion's share of volatility is due to trading activity. We
argue that the IMH holds for all asset classes, beyond the case of stock
markets considered by GK.


  In this article we consider the linear elasticity problem in an axisymmetric
three dimensional domain, with data which are axisymmetric and have zero
angular component. The weak formulation of the the three dimensional problem
reduces to a two dimensional problem on the meridian domain, involving weighted
integrals. The problem is formulated in a mixed method framework with both the
stress and displacement treated as unknowns. The symmetry condition for the
stress tensor is weakly imposed. Well posedness of the continuous weak
formulation and its discretization are shown. Two approximation spaces are
discussed and corresponding numerical computations presented.