  A search for squarks and gluinos in final states containing hadronic jets,
missing transverse momentum but no electrons or muons is presented. The data
were recorded in 2015 by the ATLAS experiment in $\sqrt{s}=$ 13 TeV
proton--proton collisions at the Large Hadron Collider. No excess above the
Standard Model background expectation was observed in 3.2 fb$^{-1}$ of analyzed
data. Results are interpreted within simplified models that assume R-parity is
conserved and the neutralino is the lightest supersymmetric particle. An
exclusion limit at the 95% confidence level on the mass of the gluino is set at
1.51 TeV for a simplified model incorporating only a gluino octet and the
lightest neutralino, assuming the lightest neutralino is massless. For a
simplified model involving the strong production of mass-degenerate first- and
second-generation squarks, squark masses below 1.03 TeV are excluded for a
massless lightest neutralino. These limits substantially extend the region of
supersymmetric parameter space excluded by previous measurements with the ATLAS
detector.


  Celestial capture of dark matter provides a useful handle for constraining
its particulate properties. The capture formalism is sensitive to the phase
space distribution of dark matter in the vicinity of the celestial object. This
article aims to systematically study the impact of uncertainties and the
influence of cosmological simulations on the rate at which dark matter
particles are captured inside a variety of celestial objects. Going beyond the
framework of the Maxwell-Boltzmann distribution or the standard halo model, we
take up pragmatic dark matter velocity distributions motivated by observations
or cosmological simulations. Within the limits of the standard halo model, we
report a maximum $\sim 20\%$ change in the capture rate. This number can go up
to $\sim 200\%$ if dark matter particles within the galactic halo are favored
to have an empirical velocity distribution profile when well-resolved and
sophisticated cosmological simulations are employed to extract their parametric
values.


  Stochastic partial differential equations have been used in a variety of
contexts to model the evolution of uncertain dynamical systems. In recent
years, their applications to geophysical fluid dynamics has increased
massively. For a judicious usage in modelling fluid evolution, one needs to
calibrate the amplitude of the noise to data. In this paper we address this
requirement for the stochastic rotating shallow water (SRSW) model. This work
is a continuation of [LvLCP23], where a data assimilation methodology has been
introduced for the SRSW model. The noise used in [LvLCP23] was introduced as an
arbitrary random phase shift in the Fourier space. This is not necessarily
consistent with the uncertainty induced by a model reduction procedure. In this
paper, we introduce a new method of noise calibration of the SRSW model which
is compatible with the model reduction technique. The method is generic and can
be applied to arbitrary stochastic parametrizations. It is also agnostic as to
the source of data (real or synthetic). It is based on a principal component
analysis technique to generate the eigenvectors and the eigenvalues of the
covariance matrix of the stochastic parametrization. For SRSW model covered in
this paper, we calibrate the noise by using the elevation variable of the
model, as this is an observable easily obtainable in practical application, and
use synthetic data as input for the calibration procedure.


  Bell and Zhang have shown that if $A$ and $B$ are two connected graded
algebras finitely generated in degree one that are isomorphic as ungraded
algebras, then they are isomorphic as graded algebras. We exploit this result
to solve the isomorphism problem in the cases of quantum affine spaces, quantum
matrix algebras, and homogenized multiparameter quantized Weyl algebras. Our
result involves determining the degree one normal elements, factoring out, and
then repeating. This creates an iterative process that allows one to determine
relationships between relative parameters.


  Financial market analysis, especially the prediction of movements of stock
prices, is a challenging problem. The nature of financial time-series data,
being non-stationary and nonlinear, is the main cause of these challenges. Deep
learning models have led to significant performance improvements in many
problems coming from different domains, including prediction problems of
financial time-series data. Although the prediction performance is the main
goal of such models, dealing with ultra high-frequency data sets restrictions
in terms of the number of model parameters and its inference speed. The
Temporal Attention-Augmented Bilinear network was recently proposed as an
efficient and high-performing model for Limit Order Book time-series
forecasting. In this paper, we propose a low-rank tensor approximation of the
model to further reduce the number of trainable parameters and increase its
speed.


  We present LLaVA-OneVision, a family of open large multimodal models (LMMs)
developed by consolidating our insights into data, models, and visual
representations in the LLaVA-NeXT blog series. Our experimental results
demonstrate that LLaVA-OneVision is the first single model that can
simultaneously push the performance boundaries of open LMMs in three important
computer vision scenarios: single-image, multi-image, and video scenarios.
Importantly, the design of LLaVA-OneVision allows strong transfer learning
across different modalities/scenarios, yielding new emerging capabilities. In
particular, strong video understanding and cross-scenario capabilities are
demonstrated through task transfer from images to videos.


  We present an architecture where a feedback controller derived on an
approximate model of the environment assists the learning process to enhance
its data efficiency. This architecture, which we term as Control-Tutored
Q-learning (CTQL), is presented in two alternative flavours. The former is
based on defining the reward function so that a Boolean condition can be used
to determine when the control tutor policy is adopted, while the latter, termed
as probabilistic CTQL (pCTQL), is instead based on executing calls to the tutor
with a certain probability during learning. Both approaches are validated, and
thoroughly benchmarked against Q-Learning, by considering the stabilization of
an inverted pendulum as defined in OpenAI Gym as a representative problem.


  Observations of diffuse Galactic gamma-ray spectrum by the EGRET instrument
reveal an excess above ~ 1 GeV over the expected gamma-ray spectrum calculated
under the assumption that the locally observed cosmic-ray (CR) spectra
represent the galactic CR spectra. Assuming that Galactic CRs of energy below ~
100 TeV are accelerated by supernova remnant (SNR) shock waves and that the
shock compression ratio is SNR age dependent, the average source injection
spectra from an ensemble of SNRs is calculated both in the inner (330<l<30) and
outer (30<l<330) regions of the galaxy. The calculation considers the SNR age
distribution in the galaxy. Injecting these spectra in the galaxy and using a
3-D convection-diffusion equation, the CR electrons and protons spectra in the
two galactic regions are obtained and their spectra in the galactic disk are
found to be flatter than the observed CR spectra. The diffuse gamma-ray
spectrum produced by the interaction of these galactic CRs with the ISM and
ISRFs is compared with the experimental data in both the galactic regions.
Furthermore, the steepening of the observed local CR spectra from the galactic
disk CR spectra are discussed by propagating local CRs having a source spectrum
derived using local SNR age distribution (SNRs located within 1.5 kpc from the
Sun), for a diffusion coefficient D_0 ~ 0.3\times 10^{27} cm^2 s^{-1} in the
local region which is much less than the typical value in the galaxy D_0 ~
(1-10)\times 10^{28} cm^2 s^{-1}. The results obtained in this paper support
the SNR origin of galactic CRs.


  Holographic multiple-input multiple-output (MIMO) communications are widely
recognized as a promising candidate for the next-generation air interface. With
holographic MIMO surface, the number of the spatial degrees-of-freedom (DoFs)
considerably increases and also significantly varies as the user moves. To
fully employ the large and varying number of spatial DoFs, the number of
equipped RF chains has to be larger than or equal to the largest number of
spatial DoFs. However, this causes much waste as radio frequency (RF) chains
(especially the transmit RF chains) are costly and power-hungry. To avoid the
heavy burden, this paper investigates green holographic MIMO communications
with a few transmit RF chains under an electromagnetic-based communication
model. We not only look at the fundamental capacity limits but also propose an
effective transmission, namely non-uniform holographic pattern modulation
(NUHPM), to achieve the capacity limit in the high signal-to-noise (SNR)
regime. The analytical result sheds light on the green evaluation of MIMO
communications, which can be realized by increasing the size of the antenna
aperture without increasing the number of transmit RF chains. Numerical results
are provided to verify our analysis and to show the great performance gain by
employing the additional spatial DoFs as modulation resources.


  We present results for leading-twist azimuthal asymmetries in semi-inclusive
lepton-nucleon deep-inelastic scattering due to naively time-reversal odd
transverse-momentum dependent parton distribution functions from the light-cone
constituent quark model. We carefully discuss the range of applicability of the
model, especially with regard to positivity constraints and evolution effects.
We find good agreement with available experimental data from COMPASS and
HERMES, and present predictions to be tested in forthcoming experiments at
Jefferson Lab.


  We prove explicit upper and lower bounds for the $L^1$-moment spectra for the
Brownian motion exit time from extrinsic metric balls of submanifolds $P^m$ in
ambient Riemannian spaces $N^{n}$. We assume that $P$ and $N$ both have
controlled radial curvatures (mean curvature and sectional curvature,
respectively) as viewed from a pole in $N$. The bounds for the exit moment
spectra are given in terms of the corresponding spectra for geodesic metric
balls in suitably warped product model spaces. The bounds are sharp in the
sense that equalities are obtained in characteristic cases. As a corollary we
also obtain new intrinsic comparison results for the exit time spectra for
metric balls in the ambient manifolds $N^n$ themselves.


  Recursive Marginal Quantization (RMQ) allows fast approximation of solutions
to stochastic differential equations in one-dimension. When applied to two
factor models, RMQ is inefficient due to the fact that the optimization problem
is usually performed using stochastic methods, e.g., Lloyd's algorithm or
Competitive Learning Vector Quantization. In this paper, a new algorithm is
proposed that allows RMQ to be applied to two-factor stochastic volatility
models, which retains the efficiency of gradient-descent techniques. By
margining over potential realizations of the volatility process, a significant
decrease in computational effort is achieved when compared to current
quantization methods. Additionally, techniques for modelling the correct
zero-boundary behaviour are used to allow the new algorithm to be applied to
cases where the previous methods would fail. The proposed technique is
illustrated for European options on the Heston and Stein-Stein models, while a
more thorough application is considered in the case of the popular SABR model,
where various exotic options are also priced.


  We apply the theory of weighted bicategorical colimits to study the problem
of existence and computation of such colimits of birepresentations of finitary
bicategories. The main application of our results is the complete
classification of simple transitive birepresentations of a bicategory studied
in arXiv:1805.05724, which confirms a conjecture made therein.


  We solve the Killing spinor equations of supersymmetric IIB backgrounds which
admit one supersymmetry and the Killing spinor has stability subgroup G_2 in
Spin(9,1) x U(1). We find that such backgrounds admit a time-like Killing
vector field and the geometric structure of the spacetime reduces from
Spin(9,1) x U(1) to G_2. We determine the type of G_2 structure that the
spacetime admits by computing the covariant derivatives of the spacetime forms
associated with the Killing spinor bilinears.
  We also solve the Killing spinor equations of backgrounds with two
supersymmetries and Spin(7)\ltimes R^8-invariant spinors, and four
supersymmetries with SU(4)\ltimes R^8- and with G_2-invariant spinors. We show
that the Killing spinor equations factorize in two sets, one involving the
geometry and the five-form flux, and the other the three-form flux and the
scalars. In the Spin(7)\ltimes R^8 and SU(4)\ltimes R^8 cases, the spacetime
admits a parallel null vector field and so the spacetime metric can be locally
described in terms of Penrose coordinates adapted to the associated rotation
free, null, geodesic congruence. The transverse space of the congruence is a
Spin(7) and a SU(4) holonomy manifold, respectively. In the G_2 case, all the
fluxes vanish and the spacetime is the product of a three-dimensional Minkowski
space with a holonomy G_2 manifold.


  We present a phenomenologically motivated model which is able to give rise
both to an inflationary epoch and to the present day cosmic acceleration. We
introduce an approach where the energy density depends on the scale factor $a$
in such a way that a smooth transition from the inflation to the matter
dominated era and then to the nowadays accelerated expansion is achieved. We
use the dimensionless coordinate distance $y(z)$ to the Gold Type Ia Supernovae
dataset and to a sample comprising 20 radio galaxies, the shift parameter
${\cal{R}}$ and the acoustic peak parameter ${\cal{A}}$ to test whether the
model is in agreement with observations and to constrain its main parameters.
As an independent cross check, we also compare model predictions with the
lookback time to galaxy clusters and the age of the universe. Although
phenomenologically inspired, the model may be theoretically motivated either
resorting to a scenario with a scalar and phantom fields (eventually
interacting) or as an effective description arising from higher order gravity
theories.


  The Tomonaga-Luttinger-Liquid (TLL) has been the cornerstone of our
understanding of the properties of one dimensional systems. This universal set
of properties plays in one dimension, the same role than Fermi liquid plays for
the higher dimensional metals. I will give in these notes an overview of some
of the experimental tests that were made to probe such TLL physics. In
particular I will detail some of the recent experiments that were made in spin
systems and which provided remarkable quantitative tests of the TLL physics.


  Large graphs are sometimes studied through their degree sequences (power law
or regular graphs). We study graphs that are uniformly chosen with a given
degree sequence. Under mild conditions, it is shown that sequences of such
graphs have graph limits in the sense of Lov\'{a}sz and Szegedy with
identifiable limits. This allows simple determination of other features such as
the number of triangles. The argument proceeds by studying a natural
exponential model having the degree sequence as a sufficient statistic. The
maximum likelihood estimate (MLE) of the parameters is shown to be unique and
consistent with high probability. Thus $n$ parameters can be consistently
estimated based on a sample of size one. A fast, provably convergent, algorithm
for the MLE is derived. These ingredients combine to prove the graph limit
theorem. Along the way, a continuous version of the Erd\H{o}s--Gallai
characterization of degree sequences is derived.


  In this paper we are concerned with the recent summability notion of
I-statistically pre-Cauchy real double sequences in line of Das et. al. [6] as
a generalization of I-statistical convergence. Here we introduce the notion of
double I-natural density and present some interesting properties of
I-statistically pre-Cauchy double sequences of real numbers. Also in this paper
we investigate the notion of I-statistical cluster point of double sequences in
finite dimensional normed space.


  Quantum superconducting circuit with flexible coupler has been a powerful
platform for designing quantum thermal machines. In this letter, we employ the
tunable coupling of two superconducting resonators to realize a heat valve by
modulating magnetic flux using a superconducting quantum interference device
(SQUID). It is shown that a heat valve can be realized in a wide parameter
range. We find a consistent relation between the heat current and quantum
entanglement, which indicates the dominant role of entanglement on the heat
valve. It provides an insightful understanding of quantum features in quantum
heat machines.


  Hysteretic losses in MgB2 wound superconducting coils of a 500 kW synchronous
hybrid generator were estimated as part of the European project SUPRAPOWER led
by the Spanish company Tecnalia Research and Innovation. Particular interest
was given to the losses found in tapes in the superconducting rotor caused by
the magnetic flux ripples originating from the conventional stator during
nominal operation. To compute the losses, a 2D Finite Element Method was
applied to solve the H-formulation of Maxwell's equations considering the
nonlinear properties of both the superconducting material and its surrounding
Ni matrix. To be able to model all the different turns composing the winding of
the superconducting rotor coils, three geometrical models of single tape cross
section of decreasing complexity were studied: 1) the first model reproduced
closely the actual cross section obtained from micrographs, 2) the second model
was obtained from the computed elastoplastic deformation of a round Ni wire, 3)
the last model was based on a simplified elliptic cross section. The last
geometry allowed validating the modeling technique by comparing numerical
losses with results from well-established analytical expressions. Additionally,
the following cases of filament transpositions were studied: no, partial and
full transposition. Finally, choosing the right level of geometrical details to
predict the expected behavior of individual superconducting tapes in the rotor,
the following operational regimes were studied: Bias-DC current, ramping
current under ramping background field, and magnetic flux ripples under DC
background current and field.


  This Letter reports the first observational estimate of the heating rate in
the slowly expanding solar corona. The analysis exploits the simultaneous
remote and local observations of the same coronal plasma volume with the Solar
Orbiter/Metis and the Parker Solar Probe instruments, respectively, and relies
on the basic solar wind magnetohydrodynamic equations. As expected, energy
losses are a minor fraction of the solar wind energy flux, since most of the
energy dissipation that feeds the heating and acceleration of the coronal flow
occurs much closer to the Sun than the heights probed in the present study,
which range from 6.3 to 13.3 solar radii. The energy deposited to the
supersonic wind is then used to explain the observed slight residual wind
acceleration and to maintain the plasma in a non-adiabatic state. As derived in
the Wentzel-Kramers-Brillouin limit, the present energy transfer rate estimates
provide a lower limit, which can be very useful in refining the
turbulence-based modeling of coronal heating and subsequent solar wind
acceleration.


  We study the amplitude and spectral tilt of density perturbations in the
simplest hybrid inflation models. We give an exact expression for the amplitude
of quantum fluctuations on all scales in the limit where we can neglect the
backreaction on the metric. This is a very good approximation for values of the
inflaton field well below the Planck scale and our results remain valid far
from the usual massless limit. We confirm that the primordial density spectrum
in this model has a constant spectral index n>1 over all observable scales. For
the small values of the tilt (n<1.4) required by observations, the results
remain close to those obtained using the quasi-massless approximation.


  The large N limit of mean spectral density for the ensemble of NxN
sub-unitary matrices derived by Wei and Fyodorov (J. Phys. A: Math. Theor. 41
(2008) 50201) is calculated by a modification of the saddle point method. It is
shown that the result coincides with the one obtained within the free
probability theory by Haagerup and Larsen (J. Funct. Anal. 176 (2000) 331).


  This paper investigates the influence of the basis set on the GW self-energy
correction in the full-potential linearized augmented-plane-wave (LAPW)
approach and similar linearized all-electron methods. A systematic improvement
is achieved by including local orbitals that are defined as second and higher
energy derivatives of solutions to the radial scalar-relativistic Dirac
equation and thus constitute a natural extension of the LAPW basis set. Within
this approach linearization errors can be eliminated, and the basis set becomes
complete. While the exchange contribution to the self-energy is little affected
by the increased basis-set flexibility, the correlation contribution benefits
from the better description of the unoccupied states, as do the quasiparticle
energies. The resulting band gaps remain relatively unaffected, however; for Si
we find an increase of 0.03 eV.


  In this paper, we report improved results of the Fake News Challenge Stage 1
(FNC-1) stance detection task. This gain in performance is due to the
generalization power of large language models based on Transformer
architecture, invented, trained and publicly released over the last two years.
Specifically (1) we improved the FNC-1 best performing model adding BERT
sentence embedding of input sequences as a model feature, (2) we fine-tuned
BERT, XLNet, and RoBERTa transformers on FNC-1 extended dataset and obtained
state-of-the-art results on FNC-1 task.


  The purpose of this paper is to study the local structure of the
semi-invariant picture of a tame hereditary algebra near the null root. Using a
construction that we call co-amalgamation, we show that this local structure is
completely described by the semi-invariant pictures of a collection of
self-injective Nakayama algebras. We then describe the cones of this local
structure using cluster-like structures that we call support regular clusters.
Finally, we show that the local structure is (piecewise linearly) invariant
under cluster tilting.


  Low energy effects induced by heavy extra degrees of freedom are suppressed
by powers of the large mass scale, thus preserving, if sufficiently heavy, the
successes of the Standard Model in describing low energy phenomena. However, as
is well known, heavy right-handed neutrinos may play an important role in low
energy phenomenology as an explanation of the smallness of neutrino masses. We
consider in this paper an extension of the Standard Model by heavy right-handed
neutrinos and heavy Higgs doublets and we show, using a renormalization group
approach, that this model can simultaneously provide an explanation for the
small neutrino masses and for the mild hierarchy observed between the
atmospheric and the solar mass splittings, even when the extra degrees of
freedom are very heavy. We analyze the necessary conditions to reproduce the
oscillation parameters and we discuss possible experimental signatures of this
model.


  New neutrino interactions beyond the Standard Model (BSM) have been of much
interest in not only particle physics but also cosmology and astroparticle
physics. We numerically investigate the time delay distribution of
astrophysical neutrinos that interact with the cosmic neutrino background.
Using the Monte Carlo method, we develop a framework that enables us to
simulate the time-dependent energy spectra of high-energy neutrinos that
experience even multiple scatterings en route and to handle the sharp increase
in the cross section at the resonance energy. As an example, we focus on the
case of secret neutrino interactions with a scalar mediator. While we find the
excellent agreement between analytical and simulation results for small optical
depths, our simulations enable us to study even optically-thick cases that are
not described by the simplest analytic estimates. Our simulations are used to
understand effects of cosmological redshifts, neutrino spectra and flavors. The
developments will be useful for probing BSM neutrino interactions with not only
current neutrino detectors such as IceCube and Super-Kamiokande but also future
neutrino detectors such as IceCube-Gen2 and Hyper-Kamiokande.


  We have measured a quantum ratchet effect for vortices moving in a
quasi-one-dimensional Josephson junction array. In this solid-state device the
shape of the vortex potential energy, and consequently the band structure, can
be accurately designed. This band structure determines the presence or absence
of the quantum ratchet effect, as observed in the presented experiments. In
particular, asymmetric structures possessing only one band below the barrier do
not exhibit current rectification at low temperatures and bias currents. The
quantum nature of transport is also revealed in a universal/non-universal
power-law dependence of the measured voltage-current characteristics for
samples without/with rectification.


  The topology and dynamics of the solar chromosphere are greatly affected by
the presence of magnetic fields. The magnetic field can be inferred by
analyzing polarimetric observations of spectral lines. Polarimetric signals
induced by chromospheric magnetic fields are, however, particularly weak, and
in most cases very close to the detection limit of current instrumentation.
Because of this, there are only few observational studies that have
successfully reconstructed the three components of the magnetic field vector in
the chromosphere. Traditionally, the signal-to-noise ratio of observations has
been improved by performing time-averages or spatial averages, but in both
cases, some information is lost. More advanced techniques, like
principal-component-analysis, have also been employed to take advantage of the
sparsity of the observations in the spectral direction. In the present study,
we propose to use the spatial coherence of the observations to reduce the noise
using deep-learning techniques. We design a neural network that is capable of
recovering weak signals under a complex noise corruption (including
instrumental artifacts and non-linear post-processing). The training of the
network is carried out without a priori knowledge of the clean signals, or an
explicit statistical characterization of the noise or other corruption. We only
use the same observations as our generative model. The performance of this
method is demonstrated on both, synthetic experiments and real data. We show
examples of the improvement in typical signals obtained in current telescopes
such as the Swedish 1-meter Solar Telescope. The presented method can recover
weak signals equally well no matter on what spectral line or spectral sampling
is used. It is especially suitable for cases when the wavelength sampling is
scarce.


  It is known in \cite{beccari} that the standard explicit Euler-type scheme
(such as the exponential Euler and the linear-implicit Euler schemes) with a
uniform timestep, though computationally efficient, may diverge for the
stochastic Allen--Cahn equation. To overcome the divergence, this paper
proposes and analyzes adaptive time-stepping schemes, which adapt the timestep
at each iteration to control numerical solutions from instability. The
\textit{a priori} estimates in $\mathcal {C}(\mathcal {O})$-norm and
$\dot{H}^{\beta}(\mathcal{O})$-norm of numerical solutions are established
provided the adaptive timestep function is suitably bounded, which plays a key
role in the convergence analysis. We show that the adaptive time-stepping
schemes converge strongly with order $\frac{\beta}{2}$ in time and
$\frac{\beta}{d}$ in space with $d$ ($d=1,2,3$) being the dimension and
$\beta\in(0,2]$. Numerical experiments show that the adaptive time-stepping
schemes are simple to implement and at a lower computational cost than a scheme
with the uniform timestep.


  The particular case of the integrable two component (2+1)-dimensional
hydrodynamical type systems, which generalises the so-called Hamiltonian
subcase, is considered. The associated system in involution is integrated in a
parametric form. A dispersionless Lax formulation is found.


  Exploration in environments which differ across episodes has received
increasing attention in recent years. Current methods use some combination of
global novelty bonuses, computed using the agent's entire training experience,
and \textit{episodic novelty bonuses}, computed using only experience from the
current episode. However, the use of these two types of bonuses has been ad-hoc
and poorly understood. In this work, we shed light on the behavior of these two
types of bonuses through controlled experiments on easily interpretable tasks
as well as challenging pixel-based settings. We find that the two types of
bonuses succeed in different settings, with episodic bonuses being most
effective when there is little shared structure across episodes and global
bonuses being effective when more structure is shared. We develop a conceptual
framework which makes this notion of shared structure precise by considering
the variance of the value function across contexts, and which provides a
unifying explanation of our empirical results. We furthermore find that
combining the two bonuses can lead to more robust performance across different
degrees of shared structure, and investigate different algorithmic choices for
defining and combining global and episodic bonuses based on function
approximation. This results in an algorithm which sets a new state of the art
across 16 tasks from the MiniHack suite used in prior work, and also performs
robustly on Habitat and Montezuma's Revenge.


  Difficult it is to formulate achievable sensitivity bounds for quantum
multiparameter estimation. Consider a special case, one parameter from many:
many parameters of a process are unknown; estimate a specific linear
combination of these parameters without having the ability to control any of
the parameters. Superficially similar to single-parameter estimation, the
problem retains genuinely multiparameter aspects. Geometric reasoning
demonstrates the conditions, necessary and sufficient, for saturating the
fundamental and attainable quantum-process bound in this context.


  Recurrent neural networks (RNN) are powerful tools to explain how attractors
may emerge from noisy, high-dimensional dynamics. We study here how to learn
the ~N^(2) pairwise interactions in a RNN with N neurons to embed L manifolds
of dimension D << N. We show that the capacity, i.e. the maximal ratio L/N,
decreases as |log(epsilon)|^(-D), where epsilon is the error on the position
encoded by the neural activity along each manifold. Hence, RNN are flexible
memory devices capable of storing a large number of manifolds at high spatial
resolution. Our results rely on a combination of analytical tools from
statistical mechanics and random matrix theory, extending Gardner's classical
theory of learning to the case of patterns with strong spatial correlations.


  We analytically and numerically analyze the one-dimensional "thin-torus"
limit of Fractional Topological Insulators in a series of simple models
exhibiting exactly flat bands with local hopping. These models are the
one-dimensional limit of two dimensional Chern Insulators, and the Hubbard-type
interactions projected into their lowest band take particularly simple forms.
By exactly solving the many-body interacting spectrum of these models, we show
that, just like in the Fractional Quantum Hall effect, the zero modes of the
thin-torus limit are CDW states of occupation numbers satisfying generalized
Pauli principles. As opposed to the FQH where the thin-torus CDW appear in
orbital space, in the thin-torus FCI states, the CDW states are in real-space.
We show the counting of the quasihole excitations in the energy spectrum cannot
distinguish between a CDW state and a FQH state. However, by exactly computing
the entanglement spectrum for the thin-torus states, we show that it can
qualitatively and quantitatively distinguish between a CDW and a fractional
topological state such as the FCI. We then discover a previously unknown
separation of energy scales of the full FQH energy spectrum in the thin torus
limit and find that Chern insulator models exhibiting strong isotropic FCI
states have a similar structure in their thin-torus limit spectrum. We close by
numerically computing the evolution of energy and entanglement spectra from the
thin-torus to the isotropic limit. Our results can also be interpreted as an
analysis of one-body, 1-dimensional topological insulators stabilized by
inversion symmetry in the presence of interactions.


  The quantum Rabi model (QRM) is a fundamental model for light-matter
interactions. A fascinating feature of the QRM is that it manifests a quantum
phase transition which is applicable for critical quantum metrology (CQM).
Effective application for CQM needs the exact location of the transition point,
however the conventional expression for the transition coupling is only valid
in the extreme limit of low frequency, while apart from zero frequency an
accurate location is still lacking. In the present work we conversely use the
quantum Fisher information (QFI) in the CQM to identify the transition
coupling, which finds out that transition coupling indeed much deviates from
the conventional one once a finite frequency is turned on. Polaron picture is
applied to analytically reproduce the numeric QFI. An accurate expression for
the transition coupling is obtained by the inspiration from the
fractional-power-law effect of polaron frequency renormalization. From the QFI
in the polaron picture we find that the transition occurs around a point where
the effective velocity and the susceptibility of the single-photon absorption
rate reach maximum. Our result provides an accurate reference of transition
couplings for quantum metrology at non-zero frequencies. The formulation of the
QFI in the polaron picture also prepares an analytic method with an accurate
compensation for the parameter regime difficult to access for the numerics.
Besides the integer/fractional power law analysis to extract the underlying
physics of transition, the QFI/velocity relation may also add some insight in
bridging the QFI and transition observables.


  Let $N$ be a connected nonorientable surface with or without boundary and
punctures, and $j\colon S\rightarrow N$ be the orientation double covering. It
has previously been proved that the orientation double covering $j$ induces an
embedding $\iota\colon\mathrm{Mod}(N)$ $\hookrightarrow$ $\mathrm{Mod}(S)$ with
one exception. In this paper, we prove that this injective homomorphism $\iota$
is a quasi-isometric embedding. The proof is based on the semihyperbolicity of
$\mathrm{Mod}(S)$, which has already been established. We also prove that the
embedding $\mathrm{Mod}(F') \hookrightarrow \mathrm{Mod}(F)$ induced by an
inclusion of a pair of possibly nonorientable surfaces $F' \subset F$ is a
quasi-isometric embedding.


  Randomized vaccine trials are used to assess vaccine efficacy and to
characterize the durability of vaccine induced protection. If efficacy is
demonstrated, the treatment of placebo volunteers becomes an issue. For
COVID-19 vaccine trials, there is broad consensus that placebo volunteers
should be offered a vaccine once efficacy has been established. This will
likely lead to most placebo volunteers crossing over to the vaccine arm, thus
complicating the assessment of long term durability. We show how to analyze
durability following placebo crossover and demonstrate that the vaccine
efficacy profile that would be observed in a placebo controlled trial is
recoverable in a trial with placebo crossover. This result holds no matter when
the crossover occurs and with no assumptions about the form of the efficacy
profile. We only require that the vaccine efficacy profile applies to the newly
vaccinated irrespective of the timing of vaccination. We develop different
methods to estimate efficacy within the context of a proportional hazards
regression model and explore via simulation the implications of placebo
crossover for estimation of vaccine efficacy under different efficacy dynamics
and study designs. We apply our methods to simulated COVID-19 vaccine trials
with durable and waning vaccine efficacy and a total follow-up of two years.


  A $b$-ghost was constructed for the $D=11$ non-minimal pure spinor
superparticle by requiring that $\{Q , b\} = T$ where $Q =
\Lambda^{\alpha}D_{\alpha} + R^{\alpha}\bar{W}_{\alpha}$ is the usual
non-minimal pure spinor BRST operator. As was done for the $D=10$ $b$-ghost, we
will show that the $D=11$ $b$-ghost can be simplified by introducing an
$SO(10,1)$ fermionic vector $\bar{\Sigma}^{i}$ constructed out of the fermionic
spinor $D_{\alpha}$ and pure spinor variables. This simplified version will be
shown to satisfy $\{Q, b\} = T$ and $\{b , b\} =$ BRST - trivial.


  We report time-resolved measurements of Landau-Zener tunneling of
Bose-Einstein condensates in accelerated optical lattices, clearly resolving
the step-like time dependence of the band populations. Using different
experimental protocols we were able to measure the tunneling probability both
in the adiabatic and in the diabatic bases of the system. We also
experimentally determine the contribution of the momentum width of the Bose
condensates to the width of the tunneling steps and discuss the implications
for measuring the jump time in the Landau-Zener problem.


  Present theoretical investigations aim to explore the fusion characteristics
of various isotopes of Z=120 within the relativistic mean-field (RMF)
formalism. We predict the most suitable projectile-target combination for the
synthesis of element Z=120. The microscopic nucleon-nucleon R3Y interaction and
the RMF density distributions for targets and projectiles are used to calculate
the nuclear interaction potential using the double folding approach. 17
different projectile-target combinations that allow a high $N$/$Z$ ratio are
considered in the present analysis to calculate the capture and/or fusion
cross-section of various isotopes of Z=120 within the $\ell-$summed Wong
formula. Further, the equivalent surface diffusion parameter is estimated to
correlate the surface properties interacting nuclei with the fusion
cross-section. The four Ti-based reactions with the heaviest available target
$^{x}$Cf, namely, $^{46}$Ti+$^{248}$Cf, $^{46}$Ti+$^{249}$Cf,
$^{50}$Ti+$^{249}$Cf, and $^{50}$Ti+$^{252}$Cf, and also $^{54}$Cr+$^{250}$Cm
are found to have the most suitable target-projectile combinations for the
synthesis of various isotopes Z=120. We also notice that $^{48}$Ca beams merely
provide the required number of protons to synthesize the element with Z=120. We
established a correlation among the surface properties of interacting nuclei
with the fusion characteristics in terms of the equivalent surface diffusion
parameter.


  In the merging-compression method of plasma start-up, two flux-ropes with
parallel toroidal current are formed around in-vessel poloidal field coils,
before merging to form a spherical tokamak plasma. This start-up method, used
in the Mega-Ampere Spherical Tokamak (MAST), is studied as a high Lundquist
number and low plasma-beta magnetic reconnection experiment.
  In this paper, 2D fluid simulations are presented of this merging process in
order to understand the underlying physics, and better interpret the
experimental data. These simulations examine the individual and combined
effects of tight-aspect ratio geometry and two-fluid physics on the merging.
The ideal self-driven flux-rope dynamics are coupled to the diffusion layer
physics, resulting in a large range of phenomena. For resistive MHD
simulations, the flux-ropes enter the sloshing regime for normalised
resistivity eta < 1E-5. In Hall-MHD three regimes are found for the qualitative
behaviour of the current sheet, depending on the ratio of the current sheet
width to the ion-sound radius. These are a stable collisional regime, an open
X-point regime, and an intermediate regime that is highly unstable to
tearing-type instabilities.
  In toroidal axisymmetric geometry, the final state after merging is a
MAST-like spherical tokamak with nested flux-surfaces. It is also shown that
the evolution of simulated 1D radial density profiles closely resembles the
Thomson scattering electron density measurements in MAST. An intuitive
explanation for the origin of the measured density structures is proposed,
based upon the results of the toroidal Hall-MHD simulations.


  In this work, we follow Kim and Yamada (JHEP1107 (2011) 120) and utilize AdS
in light-cone frame to derive thermodynamic and transport properties of two
kinds of Schr\"{o}dinger black holes with hyperscaling violation. In that case,
we show entropy and temperature are depend on $\theta$. In $\theta=0$ we see
our results are agree with the work of Kim and Yamada. We also construct
R-charged black hole with hyperscaling violation and obtain thermodynamics and
transport properties.


  A search for Theta^+(1540) and Xi^{--}_{3/2}(1862) pentaquark candidates has
been performed in proton-induced reactions on C, Ti and W targets at sqrt(s) =
41.6 GeV studying the pK_s resp. Xi^-pi^- and Xi^-pi^+ (and charge conjugated)
decay channels at mid-rapidity. With sensitivities of (Br)x(dsigma/dx_F) < 5 to
25 microbarn/nucleon, we find no evidence for narrow pentaquark peaks in any of
the studied final states. Preliminary values for the upper limit of relative
yield ratios at mid-rapidity are (Theta^+(1540)) / (Lambda(1520)) < 0.02,
(Br)x(Xi^{--}_{3/2}(1862)) / (Xi(1530)^0) < 0.077, and
(Br)x(Xi_bar^{++}_{3/2}(1862)) / (Xi_bar(1530)^0) < 0.058 at 95% CL.


  Universal relations and constants have important applications in
understanding a physical theory. In this article, we explore this issue for
Hawking-Page phase transitions in Schwarzschild anti-de Sitter black holes. We
find a novel exact dual relation between the minimum temperature of the
($d$+1)-dimensional black hole and the Hawking-Page phase transition
temperature in $d$ dimensions, reminiscent of the holographic principle.
Furthermore, we find that the normalized Ruppeiner scalar curvature is a
universal constant at the Hawking-Page transition point. Since the Ruppeiner
curvature can be treated as an indicator of the intensity of the interactions
amongst black hole microstructures, we conjecture that this universal constant
denotes an interaction threshold, beyond which a virtual black hole becomes a
real one. This new dual relation and universal constant are fundamental in
understanding Hawking-Page phase transitions, and might have new important
applications in the black hole physics in the near future.


  We combine deep, wide-field near-IR and optical imaging to demonstrate a
reddening-independent quasar selection technique based on identifying outliers
in the (g-z) / (z-H) colour diagram. In three fields covering a total of ~0.7
deg^2 to a depth of m_H~18, we identified 68 quasar candidates. Follow-up
spectroscopy for 32 objects from this candidate list confirmed 22 quasars
(0.86<z<2.66), five with significant IR excesses. 2 of 8 quasars from a
subsample with U band observations do not exhibit UVX colours. From these
preliminary results, we suggest that this combined optical and near-IR
selection technique has a high selection efficiency (> 65% success rate), a
high surface density of candidates, and is relatively independent of reddening.
We discuss the implications for star/galaxy separation for IR based surveys for
quasars. We provide the coordinate list and follow-up spectroscopy for the
sample of 22 confirmed quasars.


  We report on the strengths of three spectral indicators - Mg_2, Hbeta, and
Hn/Fe - in the integrated light of a sample of 100 field and cluster E/S0
galaxies. The measured indices are sensitive to age and/or and metallicity
variations within the galaxy sample. Using linear regression analysis for data
with non-uniform errors, we determine the intrinsic scatter present among the
spectral indices of our galaxy sample as a function of internal velocity
dispersion. Our analysis indicates that there is significantly more intrinsic
scatter in the two Balmer line indices than in the Mg_2 index, indicating that
the Balmer indices provide more dynamic range in determining the age of a
stellar population than does the Mg_2 index. Furthermore, the scatter is much
larger for the low velocity dispersion galaxies, indicating that star formation
has occurred more recently in the lower mass galaxies.


  This paper is motivated by the panel surveys, called Statistics on Income and
Living Conditions (SILC), conducted annually on (randomly selected)
country-representative households to monitor EU 2020 aims on poverty reduction.
We particularly consider the surveys conducted in Turkey, within the scope of
integration to the EU, between 2010 and 2013. Our main interests are on health
aspects of economic and living conditions. The outcome is {\it self-reported
health} that is clustered longitudinal ordinal, since repeated measures of it
are nested within individuals and individuals are nested within families.
Economic and living conditions were measured through a number of individual-
and family-level explanatory variables. The questions of interest are on the
marginal relationships between the outcome and covariates that are addressed
using a polytomous logistic regression with Bridge distributed random-effects.
This choice of distribution allows one to {\it directly} obtain marginal
inferences in the presence of random-effects. Widely used Normal distribution
is also considered as the random-effects distribution. Samples from the joint
posterior density of parameters and random-effects are drawn using Markov Chain
Monte Carlo. Interesting findings from public health point of view are that
differences were found between sub-groups of employment status, income level
and panel year in terms of odds of reporting better health.


  This paper focuses on performance analyzing and dynamic modeling of the
current grid-tied fixed array 6.84kW solar photovoltaic system located at
Florida Atlantic University (FAU). A battery energy storage system is designed
and applied to improve the systems stability and reliability. An overview of
the entire system and its PV module are presented. In sequel, the corresponding
I-V and P-V curves are obtained using MATLAB-Simulink package. Actual data was
collected and utilized for the modeling and simulation of the system. In
addition, a grid- connected PV/Battery system with Maximum Power Point Tracking
(MPPT) controller is modeled to analyze the system performance that has been
evaluated under two different test conditions: (1) PV power production is
higher than the load demand (2) PV generated power is less than required load.
A battery system has also been sized to provide smoothing services to this
array. The simulation results show the effective of the proposed method. This
system can be implemented in developing countries with similar weather
conditions to Florida.


  Non-orthogonal multiple access (NOMA) allows multiple users to share a
time-frequency resource block by using different power levels. An important
challenge associated with NOMA is the selection of users that share a resource
block. This is referred to as clustering, which generally exploits the channel
disparity (i.e. distinctness) among the users. We discuss clustering and the
related resource allocation challenges (e.g. power allocation) associated with
NOMA and highlight open problems that require further investigation. We review
the related literature on exploiting channel disparity for clustering and
resource allocation. There have been several misconceptions regarding NOMA
clustering including: 1) clustering users with low channel disparity is
detrimental, 2) similar power allocation is disastrous for NOMA. We clarify
such misunderstandings with numerical examples.


  The generic Hidden Local Symmetry (HLS) model has given rise to the BHLS$_2$
variant which introduces symmetry breaking in the vector meson sector; the
central mechanism is a modification of the covariant derivative at the root of
the HLS approach. However, the description of the Belle $\tau$ dipion spectra
is not satisfactory whereas the dealing with its annihilation sector ($e^+ e^-
\rightarrow \pi^+ \pi^-/\pi^+ \pi^-\pi^0/ \pi^0 \gamma/\eta \gamma/K^+ K^-/K_L
K_S$) is optimum. This issue is solved by an additional breaking term allowing
to include the $[\pi^0,\eta,\eta^\prime]$ system. This extension of the usual
't~Hooft determinant term only affects the BHLS$_2$ kinetic energy term. One
obtains a fair account for the $\tau$ dipion spectra as well as for the
annihilation channels.
  The Belle dipion spectrum provides evidence for a violation of CVC in the
$\tau$ lepton decay; this evidence is strengthened by imposing the conditions
$<0|J_\mu^q |[q^\prime \overline{q^\prime}](p)>=ip_\mu f_q \delta_{q q^\prime
},
  \{ [q \overline{q}], q=u,d,s\}$ on BHLS$_2$ axial current matrix elements.
BHLS$_2$ is found to recover the usual (completed) formulae for the
[$\pi^0,~\eta,~\eta^\prime$] mixing parameters and the global fits return
mixing parameter values in agreement with expectations and better
uncertainties. Updating the muon HVP, one argues that the strong tension
between the KLOE and BaBar pion form factors imposes to provide two solutions :
$a_\mu^{HVP-LO}({\rm KLOE})=687.31 \pm 2.93$ and $a_\mu^{HVP-LO}({\rm
BaBar})=692.36 \pm 2.95$, in units of $10^{-10}$, rather than some combination
of these. Taking into account common systematics, their differences with the
experimental BNL-FNAL average value exhibit significances $> 5.4\sigma$ (KLOE)
and $> 4.1\sigma$ (BaBar) with fit probabilities favoring the former.


  This paper goes beyond Katz-Sarnak theory on the distribution of curves over
finite fields according to their number of rational points, theoretically,
experimentally and conjecturally. In particular, we give a formula for the
limits of the moments measuring the asymmetry of this distribution for
(non-hyperelliptic) curves of genus $g \geq 3$. The experiments point to a
stronger notion of convergence than the one provided by the Katz-Sarnak
framework for all curves of genus $\geq 3$. However, for elliptic curves and
for hyperelliptic curves of every genus we prove that this stronger convergence
cannot occur.


  In this study we provide the first numerical demonstration of the effects of
turbulence on the mean Lorentz force and the resulting formation of large-scale
magnetic structures. Using three-dimensional direct numerical simulations (DNS)
of forced turbulence we show that an imposed mean magnetic field leads to a
decrease of the turbulent hydromagnetic pressure and tension. This phenomenon
is quantified by determining the relevant functions that relate the sum of the
turbulent Reynolds and Maxwell stresses with the Maxwell stress of the mean
magnetic field. Using such a parameterization, we show by means of
two-dimensional and three-dimensional mean-field numerical modelling that an
isentropic density stratified layer becomes unstable in the presence of a
uniform imposed magnetic field. This large-scale instability results in the
formation of loop-like magnetic structures which are concentrated at the top of
the stratified layer. In three dimensions these structures resemble the
appearance of bipolar magnetic regions in the Sun. The results of DNS and
mean-field numerical modelling are in good agreement with theoretical
predictions. We discuss our model in the context of a distributed solar dynamo
where active regions and sunspots might be rather shallow phenomena.


  We study the 4-dimensional pressureless Navier--Stokes-Poisson equations with
density-dependent viscosity. The analytical solutions with arbitrary time
blowup, in radial symmetry, are constructed in this paper.


  Traditional recommender systems are typically passive in that they try to
adapt their recommendations to the user's historical interests. However, it is
highly desirable for commercial applications, such as e-commerce, advertisement
placement, and news portals, to be able to expand the users' interests so that
they would accept items that they were not originally aware of or interested in
to increase customer interactions. In this paper, we present Influential
Recommender System (IRS), a new recommendation paradigm that aims to
proactively lead a user to like a given objective item by progressively
recommending to the user a sequence of carefully selected items (called an
influence path). We propose the Influential Recommender Network (IRN), which is
a Transformer-based sequential model to encode the items' sequential
dependencies. Since different people react to external influences differently,
we introduce the Personalized Impressionability Mask (PIM) to model how
receptive a user is to external influence to generate the most effective
influence path for the user. To evaluate IRN, we design several performance
metrics to measure whether or not the influence path can smoothly expand the
user interest to include the objective item while maintaining the user's
satisfaction with the recommendation. Experimental results show that IRN
significantly outperforms the baseline recommenders and demonstrates its
capability of influencing users' interests.


  In this paper we discuss the analysis of a cross-diffusion PDE system for a
mixture of hard spheres, which was derived by Bruna and Chapman from a
stochastic system of interacting Brownian particles using the method of matched
asymptotic expansions. The resulting cross-diffusion system is valid in the
limit of small volume fraction of particles. While the system has a gradient
flow structure in the symmetric case of all particles having the same size and
diffusivity, this is not valid in general. We discuss local stability and
global existence for the symmetric case using the gradient flow structure and
entropy variable techniques. For the general case, we introduce the concept of
an asymptotic gradient flow structure and show how it can be used to study the
behavior close to equilibrium. Finally we illustrate the behavior of the model
with various numerical simulations.


  This paper is concerned with an overlapping information linear-quadratic (LQ)
Stackelberg stochastic differential game with two leaders and two followers,
where the diffusion terms of the state equation contain both the control and
state variables. A distinct feature lies in that, the noisy information
available to the leaders and the followers may be asymmetric and have
overlapping part. Using a coupled system of Riccati equations, the followers
first solve an LQ nonzero-sum stochastic differential Nash game with partial
information, and then the leaders solve a partial information LQ nonzero-sum
stochastic differential Nash game driven by a conditional mean-field type
forward-backward stochastic differential equation (CMF-FBSDE). By maximum
principle, completion of squares and decoupling methods, the state-estimate
feedback representation of the Stackelberg-Nash equilibrium is obtained.


  Given two jointly distributed random variables $(X,Y)$, a functional
representation of $X$ is a random variable $Z$ independent of $Y$, and a
deterministic function $g(\cdot, \cdot)$ such that $X=g(Y,Z)$. The problem of
finding a minimum entropy functional representation is known to be equivalent
to the problem of finding a minimum entropy coupling where, given a collection
of probability distributions $P_1, \dots, P_m$, the goal is to find a coupling
$X_1, \dots, X_m$ ($X_i \sim P_i)$ with the smallest entropy $H_\alpha(X_1,
\dots, X_m)$. This paper presents a new information spectrum converse, and
applies it to obtain direct lower bounds on minimum entropy in both problems.
The new results improve on all known lower bounds, including previous lower
bounds based on the concept of majorization. In particular, the presented
proofs leverage both - the information spectrum and the majorization -
perspectives on minimum entropy couplings and functional representations.


  Cabling tasks (pulling, clipping, and plug insertion) are today mostly manual
work, limiting the cost-effectiveness of electrification. Feasibility for the
robotic grasping and insertion of plugs, as well as the manipulation of cables,
have been shown in research settings. However, in many industrial tasks the
complete process from picking, insertion, routing, and validation must be
solved with one system. This often means the cable must be directly manipulated
for routing, and the plug must be manipulated for insertion, often in cluttered
environments with tight space constraints.
  Here we introduce an analysis of the complete industrial cabling tasks and
demonstrate a solution from grasp, plug insertion, clipping, and final plug
insertion. Industrial requirements are summarized, considering the space
limitations, tolerances, and possible ways that the cabling process can be
integrated into the production process.
  This paper proposes gripper designs and general robotic assembly methods for
the widely used FASTON and a cubical industrial connector. The proposed methods
cover the cable gripping, handling, routing, and inserting processes of the
connector. Customized grippers are designed to ensure the reliable gripping of
the plugs and the pulling and manipulation of the cable segments. A passive
component to correct the cable orientation is proposed, allowing the robot to
re-grip the plug before insertion. In general, the proposed method can perform
cable assembly with mere position control, foregoing complex control
approaches.
  This solution is demonstrated with an industrial product with realistic space
requirements and tolerances, identifying difficult aspects of current cabling
scenarios and potential to improve the automation-friendliness in the product
design.


  The ability to rapidly detect hydrogen gas upon occurrence of a leak is
critical for the safe large-scale implementation of hydrogen (energy)
technologies. However, to date, no technically viable sensor solution exists
that meets the corresponding response time targets set by stakeholders at
technically relevant conditions. Here, we demonstrate how a tailored Long
Short-term Transformer Ensemble Model for Accelerated Sensing (LEMAS)
accelerates the response of a state-of-the-art optical plasmonic hydrogen
sensor by up to a factor of 40 in an oxygen-free inert gas environment, by
accurately predicting its response value to a hydrogen concentration change
before it is physically reached by the sensor hardware. Furthermore, it
eliminates the pressure dependence of the response intrinsic to metal
hydride-based sensors, while leveraging their ability to operate in
oxygen-starved environments that are proposed to be used for inert gas
encapsulation systems of hydrogen installations. Moreover LEMAS provides a
measure for the uncertainty of the predictions that is pivotal for
safety-critical sensor applications. Our results thus advertise the use of deep
learning for the acceleration of sensor response, also beyond the realm of
plasmonic hydrogen detection.


  Motivated by recent observations of "electron-only" magnetic reconnection,
without an ion-scale sheet or ion outflows, in both the Earth's magnetosheath
and in numerical simulations, we study the formation and reconnection of
electron-scale current sheets at low plasma beta. We first show that ideal
sheets collapse to thicknesses much smaller than the ion scales, by deriving an
appropriate analogue of the Chapman-Kendall collapse solution. Second, we show
that, in practice, reconnection onset happens in these collapsing sheets once
they reach a critical aspect ratio, because the tearing instability then
becomes faster than their collapse timescale. We show that this can happen for
sheet thicknesses larger than the ion scale or at only a few times the electron
scale, depending on plasma parameters and the aspect ratio of the collapsing
structure, thereby unifying the usual picture of ion-coupled reconnection and
the new regime of electron-only reconnection. %and thus the usual picture of
ion-coupled reconnection and the new regime of electron-only reconnection can
be unified. We derive relationships between plasma beta, ion-to-electron
temperature ratio, the aspect ratio, electron outflow velocity, and the final
thickness of the sheets, and thus determine under what circumstances
electron-scale sheets form and reconnect.


  We present a theory of the anomalous Hall effect in ferromagnetic (Mn,III)V
semiconductors. Our theory relates the anomalous Hall conductance of a
homogeneous ferromagnet to the Berry phase acquired by a quasiparticle
wavefunction upon traversing closed paths on the spin-split Fermi surface of a
ferromagnetic state. It can be applied equally well to any itinerant electron
ferromagnet. The quantitative agreement between our theory and experimental
data in both (In,Mn)As and (Ga,Mn)As systems suggests that this disorder
independent contribution to the anomalous Hall conductivity dominates in
diluted magnetic semiconductors.


  SmB6 is one of the candidate compounds for topological Kondo insulators, a
class of materials which combines a non-trivial topological band structure with
strong electronic correlations. Here we employ a multiband tight-binding
description, supplemented by a slave-particle approach to account for strong
interactions, to theoretically study the surface-state signatures in scanning
tunneling spectroscopy (STS) and quasiparticle interference (QPI). We discuss
the spin structure of the three surface Dirac cones of SmB6 and provide
concrete predictions for the energy and momentum dependence of the resulting
QPI signal. Our results also apply to PuB6, a strongly correlated topological
insulator with a very similar electronic structure.


  We obtain a new symplectic Lagrangian density and deduce Faddeev-Jackiw (FJ)
generalized brackets of the gauge invariant self-dual fields interacting with
gauge fields. We further give FJ quantization of this system. Furthermore, the
FJ method is compared with Dirac method, the results show the two methods are
equivalent in the quantization of this system. And by the practical research in
this letter, it can be found that the FJ method is really simpler than the
Dirac method, namely, the FJ method obviates the need to distinguish primary
and secondary constraints and first- and second-class constraints. Therefore,
the FJ method is a more economical and effective method of quantization.


  This paper provides global formulations of Lagrangian and Hamiltonian
variational dynamics evolving on the product of an arbitrary number of
two-spheres. Four types of Euler-Lagrange equations and Hamilton's equations
are developed in a coordinate-free fashion on two-spheres, without relying on
local parameterizations that may lead to singularities and cumbersome equations
of motion. The proposed intrinsic formulations of Lagrangian and Hamiltonian
dynamics are novel in that they incorporate the geometry of two-spheres,
resulting in equations of motion that are expressed compactly, and they are
useful in analysis and computation of the global dynamics.


  For any $p>2$ we give an example of big action $(X,G)$ with non abelian
derived subgroup. It is obtained as a covering of a curve related to the Ree
curve.


  We study which von Neumann algebras can be embedded into uniform Roe algebras
and quasi-local algebras associated to a uniformly locally finite metric space
$X$. Under weak assumptions, these $\mathrm{C}^*$-algebras contain embedded
copies of $\prod_{k}\mathrm{M}_{n_k}(\mathbb C)$ for any \emph{bounded}
countable (possibly finite) collection $(n_k)_k$ of natural numbers; we aim to
show that they cannot contain any other von Neumann algebras.
  One of our main results shows that $L_\infty[0,1]$ does not embed into any of
those algebras, even by a not-necessarily-normal $*$-homomorphism. In
particular, it follows from the structure theory of von Neumann algebras that
any von Neumann algebra which embeds into such algebra must be of the form
$\prod_{k}\mathrm{M}_{n_k}(\mathbb C)$ for some countable (possibly finite)
collection $(n_k)_k$ of natural numbers. Under additional assumptions, we also
show that the sequence $(n_k)_k$ has to be bounded: in other words, the only
embedded von Neumann algebras are the ``obvious'' ones.


  This paper presents a method for analysis of the vote space created from the
local features extraction process in a multi-detection system. The method is
opposed to the classic clustering approach and gives a high level of control
over the clusters composition for further verification steps. Proposed method
comprises of the graphical vote space presentation, the proposition generation,
the two-pass iterative vote aggregation and the cascade filters for
verification of the propositions. Cascade filters contain all of the minor
algorithms needed for effective object detection verification. The new approach
does not have the drawbacks of the classic clustering approaches and gives a
substantial control over process of detection. Method exhibits an exceptionally
high detection rate in conjunction with a low false detection chance in
comparison to alternative methods.


  Deuterium-to-hydrogen (D/H) enrichments in molecular species provide clues
about their original formation environment. The organic materials in primitive
solar system bodies have generally higher D/H ratios and show greater D/H
variation when compared to D/H in solar system water. We propose this
difference arises at least in part due to 1) the availability of additional
chemical fractionation pathways for organics beyond that for water, and 2) the
higher volatility of key carbon reservoirs compared to oxygen. We test this
hypothesis using detailed disk models, including a sophisticated, new disk
ionization treatment with a low cosmic ray ionization rate, and find that disk
chemistry leads to higher deuterium enrichment in organics compared to water,
helped especially by fractionation via the precursors CH$_2$D$^+$/CH$_3^+$. We
also find that the D/H ratio in individual species varies significantly
depending on their particular formation pathways. For example, from $\sim20-40$
AU, CH$_4$ can reach $\rm{D/H\sim2\times10^{-3}}$, while D/H in CH$_3$OH
remains locally unaltered. Finally, while the global organic D/H in our models
can reproduce intermediately elevated D/H in the bulk hydrocarbon reservoir,
our models are unable to reproduce the most deuterium-enriched organic
materials in the solar system, and thus our model requires some inheritance
from the cold interstellar medium from which the Sun formed.


  This paper investigates contextual word representation models from the lens
of similarity analysis. Given a collection of trained models, we measure the
similarity of their internal representations and attention. Critically, these
models come from vastly different architectures. We use existing and novel
similarity measures that aim to gauge the level of localization of information
in the deep models, and facilitate the investigation of which design factors
affect model similarity, without requiring any external linguistic annotation.
The analysis reveals that models within the same family are more similar to one
another, as may be expected. Surprisingly, different architectures have rather
similar representations, but different individual neurons. We also observed
differences in information localization in lower and higher layers and found
that higher layers are more affected by fine-tuning on downstream tasks.


  We demonstrate that for every two-qubit state there is a X-counterpart, i.e.,
a corresponding two-qubit X-state of same spectrum and entanglement, as
measured by concurrence, negativity or relative entropy of entanglement. By
parametrizing the set of two-qubit X-states and a family of unitary
transformations that preserve the sparse structure of a two-qubit X-state
density matrix, we obtain the parametric form of a unitary transformation that
converts arbitrary two-qubit states into their X-counterparts. Moreover, we
provide a semi-analytic prescription on how to set the parameters of this
unitary transformation in order to preserve concurrence or negativity. We also
explicitly construct a set of X-state density matrices, parametrized by their
purity and concurrence, whose elements are in one-to-one correspondence with
the points of the concurrence versus purity (CP) diagram for generic two-qubit
states.


  A two-dimensional inviscid and diffusive Oldroyd-B model was investigated by
[T. M. Elgindi, F. Rousset, Commun. Pure Appl. Math. 68 (2015), 2005--2021]
where the global existence and uniqueness of the strong solution were
established for arbitrarily large initial data. As pointed out by [A. V. Bhave,
R. C. Armstrong, R. A. Brown, J. Chem. Phys. 95(1991), 2988--3000], the
diffusion coefficient is significantly smaller than other effects, it is
interesting to study the non-diffusive model. In the present work, we obtain
the global-in-time existence and uniqueness of the strong solution to the
non-diffusive model with small initial data via deriving some uniform
regularity estimates and taking vanishing diffusion limits. In addition, the
large time behavior of the solution is studied and the optimal time-decay rates
for each order of spatial derivatives are obtained. The main challenges focus
on the lack of dissipation and regularity effects of the system and on the
slower decay in the two-dimensional settings. A combination of the spectral
analysis and the Fourier splitting method is adopted.


  Modeling, understanding, and reconstructing the real world are crucial in
XR/VR. Recently, 3D Gaussian Splatting (3D-GS) methods have shown remarkable
success in modeling and understanding 3D scenes. Similarly, various 4D
representations have demonstrated the ability to capture the dynamics of the 4D
world. However, there is a dearth of research focusing on segmentation within
4D representations. In this paper, we propose Segment Any 4D Gaussians (SA4D),
one of the first frameworks to segment anything in the 4D digital world based
on 4D Gaussians. In SA4D, an efficient temporal identity feature field is
introduced to handle Gaussian drifting, with the potential to learn precise
identity features from noisy and sparse input. Additionally, a 4D segmentation
refinement process is proposed to remove artifacts. Our SA4D achieves precise,
high-quality segmentation within seconds in 4D Gaussians and shows the ability
to remove, recolor, compose, and render high-quality anything masks. More demos
are available at: https://jsxzs.github.io/sa4d/.


  Deep learning (DL) has been a revolutionary technique in various domains. To
facilitate the model development and deployment, many deep learning frameworks
are proposed, among which PyTorch is one of the most popular solutions. The
performance of ecosystem around PyTorch is critically important, which saves
the costs of training models and reduces the response time of model inferences.
In this paper, we propose TorchBench, a novel benchmark suite to study the
performance of PyTorch software stack. Unlike existing benchmark suites,
TorchBench encloses many representative models, covering a large PyTorch API
surface. TorchBench is able to comprehensively characterize the performance of
the PyTorch software stack, guiding the performance optimization across models,
PyTorch framework, and GPU libraries. We show two practical use cases of
TorchBench. (1) We profile TorchBench to identify GPU performance
inefficiencies in PyTorch. We are able to optimize many performance bugs and
upstream patches to the official PyTorch repository. (2) We integrate
TorchBench into PyTorch continuous integration system. We are able to identify
performance regression in multiple daily code checkins to prevent PyTorch
repository from introducing performance bugs. TorchBench is open source and
keeps evolving.


  We prove that for q>=1, there exists r(q)<1 such that for p>r(q), the number
of points in large boxes which belongs to the infinite cluster has a normal
central limit behaviour under the random cluster measure phi_{p,q} on Z^d,
d>=2. Particularly, we can take r(q)=p_g^* for d=2, which is commonly
conjectured to be equal to p_c. These results are used to prove a q-dimensional
central limit theorems relative to the fluctuation of the empirical measures
for the ground Gibbs measures of the q-state Potts model at very low
temperature and the Gibbs measures which reside in the convex hull of them. A
similar central limit theorem is also given in the high temperature regime.
Some particular properties of the Ising model are also discussed.


  The battery management system plays a vital role in ensuring the safety and
dependability of electric and hybrid vehicles. It is responsible for various
functions, including state evaluation, monitoring, charge control, and cell
balancing, all integrated within the BMS. Nonetheless, due to the uncertainties
surrounding battery performance, implementing these functionalities poses
significant challenges. In this study, we explore the latest approaches for
assessing battery states, highlight notable advancements in battery management
systems (BMS), address existing issues with current BMS technology, and put
forth possible solutions for predicting battery charging voltage.


  Intuitively there is a drastic distinction between the pure decentralized
block-chain systems like Defis and those that only utilize block-chain as an
enhancing technology but remain centralized with real-world business model and
conventional technologies like database, application server, etc. Our study
explores extensively this distinction from a methodological point of view,
classifies them into blockchain-complete and blockchain-partial, analyzes key
features of the two types, and reveals the root cause of this distinction. We
analyze the function or, in more strong words, the "ultimate purpose" of
blockchain in the blockchain-partial systems, and present a conceptual model we
named proof-chain that quite satisfactorily represented the general paradigm of
blockchain in blockchain-partial systems. A universal tension between strength
of proof-chain and privacy is then revealed and the zero-knowledge based
proof-chain takes shape. Several case studies demonstrate the explaining power
of our proof-chain methodology. We then apply proof-chain methodology to the
analysis of the ecosystem of a collaborating group of blockchain-partial
systems, representing the paradigm of public and private data domain whose
border the proof-chain crosses. Finally, some derived guidelines from this
methodology speak usefulness of our methodology.


  Generative adversarial networks (GANs) are successful deep generative models.
GANs are based on a two-player minimax game. However, the objective function
derived in the original motivation is changed to obtain stronger gradients when
learning the generator. We propose a novel algorithm that repeats the density
ratio estimation and f-divergence minimization. Our algorithm offers a new
perspective toward the understanding of GANs and is able to make use of
multiple viewpoints obtained in the research of density ratio estimation, e.g.
what divergence is stable and relative density ratio is useful.


  Replicator equations (RE) are among the basic tools in mathematical theory of
selection and evolution. We develop a method for reducing a wide class of the
RE, which in general are systems of differential equations in Banach space to
escort systems of ODEs that in many cases can be explored analytically. The
method has potential for different applications; some examples are given.


  Exemplar-based colorization approaches rely on reference image to provide
plausible colors for target gray-scale image. The key and difficulty of
exemplar-based colorization is to establish an accurate correspondence between
these two images. Previous approaches have attempted to construct such a
correspondence but are faced with two obstacles. First, using luminance
channels for the calculation of correspondence is inaccurate. Second, the dense
correspondence they built introduces wrong matching results and increases the
computation burden. To address these two problems, we propose Semantic-Sparse
Colorization Network (SSCN) to transfer both the global image style and
detailed semantic-related colors to the gray-scale image in a coarse-to-fine
manner. Our network can perfectly balance the global and local colors while
alleviating the ambiguous matching problem. Experiments show that our method
outperforms existing methods in both quantitative and qualitative evaluation
and achieves state-of-the-art performance.


  We derive new integrals for $\mathrm{Sp}_{2n}\times\mathrm{GL}_k$ from the
generalized doubling method of Cai, Friedberg, Ginzburg and Kaplan for any
positive even integer $n$ and any positive integer $k$, following a strategy
and extending a previous result of Ginzburg and Soudry. We show that these new
integrals unfold to non-unique models on $\mathrm{Sp}_{2n}$. When $k$ divides
$n$, we carry out the unramified computation and show that these integrals
represent the tensor product $L$-function for
$\mathrm{Sp}_{2n}\times\mathrm{GL}_k$ via the New Way method, generalizing a
previous result of the second-named author on
$\mathrm{Sp}_{4}\times\mathrm{GL}_2$.


  We review a recent proposal to describe dark matter and dark energy based on
an Eddington-Born-Infeld action. The theory is successful in describing the
evolution of the expansion factor as well as galactic flat rotation curves.
Fluctuations and the CMB spectra are currently under study. This paper in
written in honor of Claudio Bunster on the occasion of his sixtieth birthday.


  In this comment we discuss some serious inconsistencies presented by Gomes,
Malacarne and da Silva in their paper, Phys.Rev. D60 (1999) 125016
(hep-th/9908181).


  Video podcast teasers are short videos that can be shared on social media
platforms to capture interest in the full episodes of a video podcast. These
teasers enable long-form podcasters to reach new audiences and gain new
followers. However, creating a compelling teaser from an hour-long episode is
challenging. Selecting interesting clips requires significant mental effort;
editing the chosen clips into a cohesive, well-produced teaser is
time-consuming. To support the creation of video podcast teasers, we first
investigate what makes a good teaser. We combine insights from both audience
comments and creator interviews to determine a set of essential ingredients. We
also identify a common workflow shared by creators during the process. Based on
these findings, we introduce a human-AI co-creative tool called PodReels to
assist video podcasters in creating teasers. Our user study shows that PodReels
significantly reduces creators' mental demand and improves their efficiency in
producing video podcast teasers.


  We investigate a scaling limit of gradient stochastic dynamics associated to
Gibbs states in classical continuous systems on ${\mathbb R}^d, d \ge 1$. The
aim is to derive macroscopic quantities from a given micro- or mesoscopic
system. The scaling we consider has been investigated in \cite{Br80},
\cite{Ro81}, \cite{Sp86}, and \cite{GP86}, under the assumption that the
underlying potential is in $C^3_0$ and positive. We prove that the Dirichlet
forms of the scaled stochastic dynamics converge on a core of functions to the
Dirichlet form of a generalized Ornstein--Uhlenbeck process. The proof is based
on the analysis and geometry on the configuration space which was developed in
\cite{AKR98a}, \cite{AKR98b}, and works for general Gibbs measures of Ruelle
type. Hence, the underlying potential may have a singularity at the origin,
only has to be bounded from below, and may not be compactly supported.
Therefore, singular interactions of physical interest are covered, as e.g. the
one given by the Lennard--Jones potential, which is studied in the theory of
fluids. Furthermore, using the Lyons--Zheng decomposition we give a simple
proof for the tightness of the scaled processes. We also prove that the
corresponding generators, however, do not converge in the $L^2$-sense. This
settles a conjecture formulated in \cite{Br80}, \cite{Ro81}, \cite{Sp86}.


  Aerial robot solutions are becoming ubiquitous for an increasing number of
tasks. Among the various types of aerial robots, blimps are very well suited to
perform long-duration tasks while being energy efficient, relatively silent and
safe. To address the blimp navigation and control task, in our recent work, we
have developed a software-in-the-loop simulation and a PID-based controller for
large blimps in the presence of wind disturbance. However, blimps have a
deformable structure and their dynamics are inherently non-linear and
time-delayed, often resulting in large trajectory tracking errors. Moreover,
the buoyancy of a blimp is constantly changing due to changes in the ambient
temperature and pressure. In the present paper, we explore a deep reinforcement
learning (DRL) approach to address these issues. We train only in simulation,
while keeping conditions as close as possible to the real-world scenario. We
derive a compact state representation to reduce the training time and a
discrete action space to enforce control smoothness. Our initial results in
simulation show a significant potential of DRL in solving the blimp control
task and robustness against moderate wind and parameter uncertainty. Extensive
experiments are presented to study the robustness of our approach. We also
openly provide the source code of our approach.


  Let $(X_t)$ be a reflected diffusion process in a bounded convex domain in
$\mathbb R^d$, solving the stochastic differential equation $$dX_t = \nabla
f(X_t) dt + \sqrt{2f (X_t)} dW_t, ~t \ge 0,$$ with $W_t$ a $d$-dimensional
Brownian motion. The data $X_0, X_D, \dots, X_{ND}$ consist of discrete
measurements and the time interval $D$ between consecutive observations is
fixed so that one cannot `zoom' into the observed path of the process. The goal
is to infer the diffusivity $f$ and the associated transition operator
$P_{t,f}$. We prove injectivity theorems and stability inequalities for the
maps $f \mapsto P_{t,f} \mapsto P_{D,f}, t<D$. Using these estimates we
establish the statistical consistency of a class of Bayesian algorithms based
on Gaussian process priors for the infinite-dimensional parameter $f$, and show
optimality of some of the convergence rates obtained. We discuss an underlying
relationship between the degree of ill-posedness of this inverse problem and
the `hot spots' conjecture from spectral geometry.


  We introduce a twisted cohomology cocycle over the Teichmueller flow and
prove a "spectral gap" for its Lyapunov spectrum with respect to the
Masur-Veech measures. We then derive Hoelder estimates on spectral measures and
bounds on the speed of weak mixing for almost all translation flows in every
stratum of Abelian differentials on Riemann surfaces, as well as bounds on the
deviation of ergodic averages for product translation flows on the product of a
translation surface with a circle.


  We have numerically computed planar central configurations of $n=1000$ bodies
of equal masses. A classification of central configurations is proposed based
on the numerical value of the complexity, $\mathcal{C}$. The main result of our
work is the discovery of filaments and voids in planar central configurations
with random complexity values. Suggestions are given for future work in the
context of central configurations with random complexity values.


  Particulates and dust can limit accelerator performance in various ways. In
this paper the basic properties and mechanisms of contaminations due to
particulates are described. With this knowledge countermeasures can be
implemented to minimize degradation due to particulates inside the accelerator
vacuum systems.


  We use the matching method to investigate the first-order phase transition in
holographic superconductor and superfluid. We first use the simple holographic
superconductor model to describe the matching method and mention how to see the
first-order phase transition. Next, we study the holographic superconductor
with St\"uckelberg term and see that the analytic results indicate the
existence of first-order phase transition. Finally, we study the holographic
superfluid and show that the first-order phase transition can be found for some
values of parameters. We determine the critical value analytically and compare
it with the previous numerical result.


  Alternating direction multiplication is a powerful technique for solving
convex optimisation problems. When challenging subproblems are encountered in
the real world, it is useful to solve them by introducing neighbourhood terms.
When the neighbourhood matrix is positive definite, the algorithm converges but
at the same time makes the iteration step small. Recent studies have revealed
the potential non-positive definiteness of the neighbourhood matrix. In this
paper, we present an adaptive linearized alternating direction multiplier
method with a relaxation step, combining the relaxation step with an adaptive
technique. The novelty of the method is to use the information of the current
iteration point to dynamically select the neighbourhood matrix, increase the
iteration step size, and speed up the convergence of the algorithm.We prove the
global convergence of the algorithm theoretically and illustrate the
effectiveness of the algorithm using numerical experiments.


  We investigate the variability properties of blazars in the GeV band using
the data of the Fermi/LAT telescope. We find that blazars exhibit variability
on the scales down to the minimal timescale resolvable by Fermi, which is a
function of the peak photon count rate in the LAT. This implies that the real
minimal variability timescales for the majority of blazars are typically
shorter than those resolvable by the LAT. We find that for several blazars
these minimal variability timescales reach those associated to the blazar
central engine, the supermassive black hole. At the same time, none of the
blazars exhibits variability on the timescale shorter than the black hole
horizon light crossing time and/or the period of rotation around the last
stable circular orbit. Based on this fact, we argue that the timing properties
of the gamma-ray signal could be determined by the processes in the direct
vicinity of the supermassive black hole.


  Submillimeter (and in some cases millimeter) wavelength continuum
measurements are presented for a sample of 40 active galactic nuclei (probably
all quasars) lensed by foreground galaxies. The object of this study is to use
the lensing boost, anywhere from ~3- 20 times, to detect dust emission from
more typical AGNs than the extremely luminous ones currently accessible without
lensing. The sources are a mix of radio loud and radio quiet quasars, and,
after correction for synchrotron radation (in the few cases where necessary),
23 of the 40 (58%) are detected in dust emission at 850um; 11 are also detected
at 450um. Dust luminosities and masses are derived after correction for lensing
magnification, and luminosities are plotted against redshift from z = 1 to z =
4.4, the redshift range of the sample. The main conclusions are (1)
Monochromatic submillimeter luminosities of quasars are, on average, only a few
times greater than those of local IRAS galaxies; (2) Radio quiet and radio loud
quasars do not differ significantly in their dust lumimosity; (3) Mean dust
luminosities of quasars and radio galaxies over the same redshift range are
comparable; (4) Quasars and radio galaxies alike show evidence for more
luminous and massive dust sources toward higher redshift, consistent with an
early epoch of formation and possibly indicating that the percentage of
obscured AGNs increases with redshift.


  In the current manuscript, an attempt has been made to understand the
dynamics of a time-delayed predator-prey system with modified Leslie-Gower and
Beddington-DeAngelis type functional responses for large initial data. In
\cite{RK15}, we have seen that the model does possess globally bounded
solutions, for small initial conditions, under certain parametric restrictions.
Here, we show that actually solutions to this model system can blow-up in
finite time, for large initial condition, \emph{even} under the parametric
restrictions derived in \cite{RK15}. We prove blow-up in the delayed model, as
well as the non delayed model, providing sufficient conditions on the largeness
of data, required for finite time blow-up. Numerical simulations show, that
actually the initial data does not have to be very large, to induce blow-up.
The spatially explicit system is seen to possess Turing instability. We have
also studied Hopf-bifurcation direction in the spatial system, as well as
stability of the spatial Hopf-bifurcation using the central manifold theorem
and normal form theory.


  A systematic procedure to synthesize interval observers for nonlinear
discrete-time systems is proposed. The feedback gains and other matrices are
found from the solutions to semidefinite feasibility programs. Two cases are
considered: (1) the interval observer is in the same coordinate frame as the
given system, and (2) the interval observer uses a coordinate transformation.
The conditions where coordinate transformations are necessary are detailed.
Numerical examples are provided to showcase the effectiveness of the interval
observers and demonstrate their application to sampled-data systems.


  This paper studies random cubical sets in $\mathbb{R}^d$. Given a cubical set
$X\subset \mathbb{R}^d$, a random variable $\omega_Q\in[0,1]$ is assigned for
each elementary cube $Q$ in $X$, and a random cubical set $X(t)$ is defined by
the sublevel set of $X$ consisting of elementary cubes with $\omega_Q\leq t$
for each $t\in[0,1]$. Under this setting, the main results of this paper show
the limit theorems (law of large numbers and central limit theorem) for Betti
numbers and lifetime sums of random cubical sets and filtrations. In addition
to the limit theorems, the positivity of the limiting Betti numbers is also
shown.


  BACKGROUND: In 1967, Frederick Lord posed a conundrum that has confused
scientists for over 50-years. Subsequently named Lord's 'paradox', the puzzle
centres on the observation that two common approach to analyses of 'change'
between two time-points can produce radically different results. Approach 1
involves analysing the follow-up minus baseline (i.e., 'change score') and
Approach 2 involves analysing the follow-up conditional on baseline. METHODS:
At the heart of Lord's 'paradox' lies another puzzle concerning the use of
'change scores' in observational data. Using directed acyclic graphs and data
simulations, we introduce, explore, and explain the 'paradox', consider the
philosophy of change, and discuss the warnings and lessons of this 50-year
puzzle. RESULTS: Understanding Lord's 'paradox' starts with recognising that a
variable may change for three reasons: (A) 'endogenous change', which
represents simple changes in scale, (B) 'random change', which represents
change due to random processes, and (C) 'exogenous change', which represents
all non-endogenous, non-random change. Unfortunately, in observational data,
neither Approach 1 nor Approach 2 are able to reliably estimate the causes of
'exogenous change'. Approach 1 evaluates obscure estimands with little, if any,
real-world interpretation. Approach 2 is susceptible to mediator-outcome
confounding and cannot distinguish exogenous change from random change. Valid
and precise estimates of a useful causal estimand instead require appropriate
multivariate methods (such as g-methods) and more than two measures of the
outcome. CONCLUSION: Lord's 'paradox' reiterates the dangers of analysing
change scores in observational data and highlights the importance of
considering causal questions within a causal framework.


  This paper focuses on a class of important two-hop relay mobile ad hoc
networks (MANETs) with limited-buffer constraint and any mobility model that
leads to the uniform distribution of the locations of nodes in steady state,
and develops a general theoretical framework for the end-to-end (E2E) delay
modeling there. We first combine the theories of Fixed-Point,
Quasi-Birth-and-Death process and embedded Markov chain to model the limiting
distribution of the occupancy states of a relay buffer, and then apply the
absorbing Markov chain theory to characterize the packet delivery process, such
that a complete theoretical framework is developed for the E2E delay analysis.
With the help of this framework, we derive a general and exact expression for
the E2E delay based on the modeling of both packet queuing delay and delivery
delay. To demonstrate the application of our framework, case studies are
further provided under two network scenarios with different MAC protocols to
show how the E2E delay can be analytically determined for a given network
scenario. Finally, we present extensive simulation and numerical results to
illustrate the efficiency of our delay analysis as well as the impacts of
network parameters on delay performance.


  Possibility of a quartet superfluidity in fermionic systems is studied as a
new aspect of atomic gas at ultra low temperatures. The four-fold degeneracy of
hyperfine state and moderate coupling is indispensable for the quartet
superfluidity to occur. Possible superconductivity with quartet condensation in
electron systems is discussed.


  This talk gives an overview of the recently-formulated Fluid/Gravity
correspondence, which was developed in the context of gauge/gravity duality.
Mathematically, it posits that Einstein's equations (with negative cosmological
constant) in d+1 dimensions capture the (generalized) Navier-Stokes equations
in d dimensions. Given an arbitrary fluid dynamical solution, we can
systematically construct a corresponding asymptotically AdS black hole
spacetime with a regular horizon whose properties mimic that of the fluid flow.
Apart from an overview of this construction, we describe some of its
applications. The presentation is intended for a broad audience of relativists,
and does not assume prior knowledge of string theory or gauge/gravity duality.


  This is an introduction to the study of abstract homotopy theory by means of
model categories and $(\infty,1)$-categories. The only prerequisites are very
basic general topology and abstract algebra. None categorical background is
needed. The final objective is to show that classical homotopy theory for
topological spaces can be more naturally understood in terms of categorical
language.


  A convenient framework for dealing with hadron structure and hadronic physics
in the few-GeV energy range is relativistic quantum mechanics. Unlike
relativistic quantum field theory, one deals with a fixed, or at least
restricted number of degrees of freedom while maintaining relativistic
invariance. For systems of interacting particles this is achieved by means of
the, so called, "Bakamjian-Thomas construction", which is a systematic
procedure for implementing interaction terms in the generators of the Poincare
group such that their algebra is preserved. Doing relativistic quantum
mechanics in this way one, however, faces a problem connected with the physical
requirement of cluster separability as soon as one has more than two
interacting particles. Cluster separability, or sometimes also termed
"macroscopic causality", is the property that if a system is subdivided into
subsystems which are then separated by a sufficiently large spacelike distance,
these subsystems should behave independently. In the present contribution we
discuss the problem of cluster separability and sketch the procedure to resolve
it.


  We present a simplified model for the colossal magnetoresistance in doped
manganites by exactly solving a double-exchange model (with Ising-like local
spins) and quenched binary disorder within dynamical mean field theory. We
examine the magnetic properties and the electrical and thermal transport. Our
solution illustrates three different physical regimes: (i) a weak-disorder
regime, where the system acts like a renormalized double-exchange system (which
is insufficient to describe the behavior in the manganites); (ii) a
strong-disorder regime, where the system is described by strong-coupling
physics about an insulating phase (which is the most favorable for large
magnetoresistance); and (iii) a transition region of moderate disorder, where
both double-exchange and strong-coupling effects are important. We use the
thermopower as a stringent test for the applicability of this model to the
manganites and find that the model is unable to properly account for the sign
change of the thermopower seen in experiment.


  The complete electroweak O(alpha) radiative corrections to the Higgs-boson
production processes e+ e- -> nu_l anti-nu_l H (l=e,mu,tau) are calculated in
the electroweak Standard Model. For e+ e- -> nu_e anti-nu_e H, where ZH
production and W-boson fusion contribute, both production channels are added
coherently. The calculation of the corrections is described in some detail
including, in particular, the treatment of the Z-boson resonance in the
ZH-production channel. The discussion of numerical results focusses on the
total cross section as well as on angular and energy distributions of the Higgs
boson. In the Gmu-scheme, the bulk of the corrections is due to initial-state
radiation. The corrections turn out to reduce the total cross section by \sim
10% for high energies, where the W-boson fusion dominates. In this region, the
corrections depend only weakly on the energy and the production angle of the
Higgs boson. Based on an analysis of the leading universal corrections, a
simple improved Born approximation is introduced. This approximation describes
the corrected cross section within about 3%.


  We present a coherently combined laser amplifier with 16 channels from a
multicore fiber in a proof-of-principle demonstration. Filled aperture beam
splitting and combination together with temporal phasing is realized in a
compact and low-component-count setup. Combined average power of up to 70 W
with 40 ps pulses are achieved with combination efficiencies around 80%.