  (Abridged) We present an investigation of kinematical imprints of AGN
feedback on the Warm Ionized gas Medium (WIM) of massive early-type galaxies
(ETGs). To this end, we take a two-fold approach that involves a comparative
analysis of Halpha velocity fields in 123 local ETGs from the CALIFA integral
field spectroscopy survey with 20 simulated galaxies from high-resolution
hydrodynamic cosmological SPHgal simulations. The latter were re-simulated for
two modeling setups, one with and another without AGN feedback. In order to
quantify the effects of AGN feedback on gas kinematics we measure three
parameters that probe deviations from simple regular rotation using the
kinemetry package. These indicators trace the possible presence of distinct
kinematic components in Fourier space (k3,5/k1), variations in the radial
profile of the kinematic major axis (sigma_PA), and offsets between the stellar
and gas velocity fields (Delta Phi). These quantities are monitored in the
simulations from a redshift 3 to 0.2 to assess the connection between black
hole accretion history, stellar mass growth and kinematical perturbation of the
WIM. Observed local massive galaxies show a broad range of irregularities,
indicating disturbed warm gas motions, irrespective of being classified via
diagnostic lines as AGN or not. Simulations of massive galaxies with AGN
feedback generally exhibit higher irregularity parameters than without AGN
feedback, more consistent with observations. Besides AGN feedback, other
processes like major merger events or infalling gas clouds can lead to elevated
irregularity parameters, but they are typically of shorter duration. More
specifically, k3,5/k1 is most sensitive to AGN feedback, whereas Delta Phi is
most strongly affected by gas infall.


  Accurately estimating 3D hand pose is crucial for understanding how humans
interact with the world. Despite remarkable progress, existing methods often
struggle to generate plausible hand poses when the hand is heavily occluded or
blurred. In videos, the movements of the hand allow us to observe various parts
of the hand that may be occluded or blurred in a single frame. To adaptively
leverage the visual clue before and after the occlusion or blurring for robust
hand pose estimation, we propose the Deformer: a framework that implicitly
reasons about the relationship between hand parts within the same image
(spatial dimension) and different timesteps (temporal dimension). We show that
a naive application of the transformer self-attention mechanism is not
sufficient because motion blur or occlusions in certain frames can lead to
heavily distorted hand features and generate imprecise keys and queries. To
address this challenge, we incorporate a Dynamic Fusion Module into Deformer,
which predicts the deformation of the hand and warps the hand mesh predictions
from nearby frames to explicitly support the current frame estimation.
Furthermore, we have observed that errors are unevenly distributed across
different hand parts, with vertices around fingertips having disproportionately
higher errors than those around the palm. We mitigate this issue by introducing
a new loss function called maxMSE that automatically adjusts the weight of
every vertex to focus the model on critical hand parts. Extensive experiments
show that our method significantly outperforms state-of-the-art methods by 10%,
and is more robust to occlusions (over 14%).


  We show that, up to biholomorphism, there is at most one complete
$T^n$-invariant shrinking gradient K\"ahler-Ricci soliton on a non-compact
toric manifold $M$. We also establish uniqueness without assuming
$T^n$-invariance if the Ricci curvature is bounded and if the soliton vector
field lies in the Lie algebra $\mathfrak{t}$ of $T^n$. As an application, we
show that, up to isometry, the unique complete shrinking gradient
K\"ahler-Ricci soliton with bounded scalar curvature on $\mathbb{CP}^{1} \times
\mathbb{C}$ is the standard product metric associated to the Fubini-Study
metric on $\mathbb{CP}^{1}$ and the Euclidean metric on $\mathbb{C}$.


  In this paper we establish decay estimates for Fourier transform on
Hardy-Morrey spaces and its localizable version. Our work include some aspects
to these spaces linked up with pointwise Fourier estimates, in particular a
natural approach on cancellation moment conditions. As application, we discuss
the optimality for continuity of Fourier multipliers and pseudodifferential
operators in Hardy-Morrey spaces.


  The absolute temperature of the cosmic microwave background (CMB) has been
measured at a frequency of 1280 MHz. The observation was made with a modified
version of the L-band receiver used in the Giant Metre wavelength Radio
Telescope (GMRT): the feed horn was replaced by a corrugated plate and the
receiver was placed on the ground, directed at zenith, and shielded from ground
radiation by an aluminium screen with corrugated edges. Novel techniques have
been adopted for (1) reducing and cancelling unwanted contributions to the
system temperature of the receiver and (2) calibrating the contributions from
the feed assembly and receiver. The thermodynamic temperature of the CMB is
estimated to be 3.45 +/- 0.78 K.


  Clustering using deep neural network models have been extensively studied in
recent years. Among the most popular frameworks are the VAE and GAN frameworks,
which learns latent feature representations of data through encoder / decoder
neural net structures. This is a suitable base for clustering tasks, as the
latent space often seems to effectively capture the inherent essence of data,
simplifying its manifold and reducing noise. In this article, the VAE framework
is used to investigate how probability function gradient ascent over data
points can be used to process data in order to achieve better clustering.
Improvements in classification is observed comparing with unprocessed data,
although state of the art results are not obtained. Processing data with
gradient descent however results in more distinct cluster separation, making it
simpler to investigate suitable hyper parameter settings such as the number of
clusters. We propose a simple yet effective method for investigating suitable
number of clusters for data, based on the DBSCAN clustering algorithm, and
demonstrate that cluster number determination is facilitated with gradient
processing. As an additional curiosity, we find that our baseline model used
for comparison; a GMM on a t-SNE latent space for a VAE structure with weight
one on reconstruction during training (autoencoder), yield state of the art
results on the MNIST data, to our knowledge not beaten by any other existing
model.


  We investigate the possiblity to detect Earth-like planets, in the visible
and the near infrared domains, with ground based Extremely Large Telescopes
equipped with adaptive systems capable of providing high Strehl ratios. From a
detailed analysis of the speckle noise, we derive analytical expressions of the
signal to noise ratio on the planet flux, for direct and differential imaging,
in the presence of the speckle noise and the photon noise of the residual
stellar halo. We find that a 100m telescope would detect an Earth at a distance
of 10pc, with a signal to noise ratio of 5, in an integration time of 12 hours.
This requires to control the instrumental aberrations with a precision better
than 1 nanometer rms, and to reach an image dynamics of $1.2{\rm x}10^{6}$ at
$0\farcs 1$ radius. Under the same conditions, a telescope of 30m would require
a dynamics of $1.3{\rm x}10^{7}$ for a positive detection


  We present far ultraviolet spectra of a fast (~ 300 km/s) nonradiative shock
in the Cygnus Loop supernova remnant. Our observations were performed with the
Far Ultraviolet Spectroscopic Explorer (FUSE) satellite, covering the
wavelength range 905-1187 Angstroms. The purpose of these observations was to
estimate the degree of electron-ion equilibration by (1) examining the
variation of O VI 1032, 1038 intensity with position behind the shock, and (2)
measuring the widths of the O VI lines. We find significant absorption near the
center of the O VI 1032 line, with less absorption in O VI 1038. The absorption
equivalent widths imply an O VI column density greatly exceeding that of
interstellar O VI along the Cygnus Loop line of sight. We suggest that the
absorption may be due to resonant scattering by O VI ions within the shock
itself. The widths of the O VI emission lines imply efficient ion-ion
equilibration, in agreement with predictions from Balmer-dominated spectra of
this shock.


  We suggest a nanoelectromechanical setup that generates properly entangled
ancillary ("ancilla") qubits for error correction algorithms in quantum
computing, demonstrated as an encoder for the three-qubit bit flip code. The
setup is based on mesoscopic terminal utilizing the AC Josephson effect between
voltage biased superconducting electrodes and mechanically vibrating mesoscopic
superconducting grain in the regime of the Cooper pair box, controlled by the
gate voltage. Required functionality is achieved by specifically tailored
time-protocol of operating two external parameters: bias voltage and gate
voltage. The superconducting grain is fixed on the free end of a cantilever,
performing controlled in-plane mechanical vibrations, generating the
nanomechanical coherent states organised in a pair of entangled cat-states in
two perpendicular spatial directions. Cooper pair box and nanomechanical
coherent states become three entangled qubits in a particular way: quantum
information, initially encoded in superposition of the Cooper pair box states,
is transduced into quantum superposition of two special 3-qubit entangled
states, $\vert \uparrow + \, + \rangle$ and $\vert \downarrow - \, - \rangle$.
It constitutes the basic input state for the three-qubit bit flip code, used in
quantum computation mainly for error correction, "installed" on a single
physical object in which the last two ancilla qubits are generated by the
nanoelectromechanical setup.


  Differential privacy (DP) offers a theoretical upper bound on the potential
privacy leakage of analgorithm, while empirical auditing establishes a
practical lower bound. Auditing techniques exist forDP training algorithms.
However machine learning can also be made private at inference. We propose
thefirst framework for auditing private prediction where we instantiate
adversaries with varying poisoningand query capabilities. This enables us to
study the privacy leakage of four private prediction algorithms:PATE [Papernot
et al., 2016], CaPC [Choquette-Choo et al., 2020], PromptPATE [Duan et al.,
2023],and Private-kNN [Zhu et al., 2020]. To conduct our audit, we introduce
novel techniques to empiricallyevaluate privacy leakage in terms of Renyi DP.
Our experiments show that (i) the privacy analysis ofprivate prediction can be
improved, (ii) algorithms which are easier to poison lead to much higher
privacyleakage, and (iii) the privacy leakage is significantly lower for
adversaries without query control than thosewith full control.


  Niels Bohr introduced the concept of complementarity in order to give a
general account of quantum mechanics, however he stressed that the idea of
complementarity is related to the general dificulty in the formation of human
ideas, inherent in the distinction between subject and object. Earlier, we have
introduced a development of the concept of complementarity which constitutes a
new approach to the interpretation of quantum mechanics. We argue that this
development allows a better understanding of some of the paradigmatic
interpretational problems of quantum theory.
  Within the scheme proposed by modal interpretations we analyze the relation
between holism and reductionism as well as the problems proposed by Arntzenius
and Clifton. We discuss the problem of presupposing the concept of entity
within the quantum formalism and bring into stage the concept of faculty as a
way to recover the objective character of quantum mechanics.


  We present a general technique, based on parametric search with some twist,
for solving a variety of optimization problems on a set of semi-algebraic
geometric objects of constant complexity. The common feature of these problems
is that they involve a `growth parameter' $r$ and a semi-algebraic predicate
$\Pi(o,o';r)$ of constant complexity on pairs of input objects, which depends
on $r$ and is monotone in $r$. One then defines a graph $G(r)$ whose edges are
all the pairs $(o,o')$ for which $\Pi(o,o';r)$ is true, and seeks the smallest
value of $r$ for which some monotone property holds for $G(r)$.
  Problems that fit into this context include (i) the reverse shortest path
problem in unit-disk graphs, recently studied by Wang and Zhao, (ii) the same
problem for weighted unit-disk graphs, with a decision procedure recently
provided by Wang and Xue, (iii) extensions of these problems to three and
higher dimensions, (iv) the discrete Fr\'echet distance with one-sided
shortcuts in higher dimensions, extending the study by Ben Avraham et al., (v)
perfect matchings in intersection graphs: given, e.g., a set of fat ellipses of
roughly the same size, find the smallest value $r$ such that if we expand each
of the ellipses by $r$, the resulting intersection graph contains a perfect
matching, (vi) generalized distance selection problems: given, e.g., a set of
disjoint segments, find the $k$'th smallest distance among the pairwise
distances determined by the segments, for a given (sufficiently small but
superlinear) parameter $k$, and (vii) the maximum-height independent towers
problem, in which we want to erect vertical towers of maximum height over a
1.5-dimensional terrain so that no pair of tower tips are mutually visible.
  We obtain significantly improved solutions for problems (i), (ii) and (vi),
and new efficient solutions to the other problems.


  Research on network mechanisms and coding properties of grid cells assume
that the firing rate of a grid cell in each of its fields is the same.
Furthermore, proposed network models predict spatial regularities in the firing
of inhibitory interneurons that are inconsistent with experimental data. In
this paper, by analyzing the response of grid cells recorded from rats during
free navigation, we first show that there are strong variations in the mean
firing rate of the fields of individual grid cells and thus show that the data
is inconsistent with the theoretical models that predict similar peak
magnitudes. We then build a two population excitatory-inhibitory network model
in which sparse spatially selective input to the excitatory cells, presumed to
arise from e.g. salient external stimuli, hippocampus or a combination of both,
leads to the variability in the firing field amplitudes of grid cells. We show
that, when combined with appropriate connectivity between the excitatory and
inhibitory neurons, the variability in the firing field amplitudes of grid
cells results in inhibitory neurons that do not exhibit regular spatial firing,
consistent with experimental data. Finally, we show that even if the spatial
positions of the fields are maintained, variations in the firing rates of the
fields of grid cells are enough to cause remapping of hippocampal cells.


  Spectra of high-metallicity (12+log(O/H) > 8.2) HII regions where oxygen
auroral lines are measurable in both the O+ and O++ zones, have been extracted
from the Data Release 6 of the Sloan Digital Sky Survey (SDSS). Our final
sample consists of 181 SDSS spectra of HII regions in galaxies in the redshift
range from ~0.025 to ~0.17. The t_2,O-t_3,O diagram is examined. In the SDSS
HII regions, the electron temperature t_2,O is found to have a large scatter at
a given value of the electron temperature t_3,O. The majority of the SDSS HII
regions lie below the t_2,O-t_3,O relation derived for HII regions in nearby
galaxies, i.e. the positions of the SDSS HII regions show a systematic shift
towards lower t_2,O temperatures or/and towards higher t_3,O temperatures. The
scatter and shift of the SDSS HII regions in the t_2,O-t_3,O diagram can be
understood if they are composite nebulae excited by two or more ionizing
sources of different temperatures.


  We define the probability structure of a continuous-time time-homogeneous
Markov jump process, on a finite graph, that represents the continuous-time
counterpart of the so-called Ruelle-Bowen discrete-time random walk. It
constitutes the unique jump process having maximal entropy rate. Moreover, it
has the property that, given the number of jumps between any two specified
end-points on the graph, the probability of traversing any one of the
alternative paths that are consistent with the specified number of jumps and
end-points, is the same for all, and thereby depends only on the number of
jumps and the end-points and not the particular path being traversed.


  A condition for the presence of a "gap" between symmetric spaces sufficient
for the inclusion of one of these spaces into the other to be disjointly
strictly singular is found. This condition is stated in terms of fundamental
functions of spaces and is exact in a certain sense. In parallel, necessary and
sufficient conditions for an inclusion of Lorentz spaces to be disjointly
strictly singular are obtained.


  For any Coxeter system we introduce the concept of singular light leaves,
answering a question of Williamson raised in 2008. They provide a combinatorial
basis for Hom spaces between singular Soergel bimodules.


  We prove a large deviation principle for a greedy exploration process on an
Erd\"os-R\'enyi (ER) graph when the number of nodes goes to infinity. To prove
our main result, we use the general strategy to study large deviations of
processes proposed by Feng and Kurtz, based on the convergence of non-linear
semigroups. The rate function can be expressed in a closed-form formula, and
associated optimization problems can be solved explicitly, providing the large
deviation trajectory. Also, we derive an LDP for the size of the maximum
independent set discovered by such an algorithm and analyze the probability
that it exceeds known bounds for the maximal independent set. We also analyze
the link between these results and the landscape complexity of the independent
set and the exploration dynamic.


  In leading fault-tolerant quantum computing schemes, accurate transformation
are obtained by a two-stage process. In a first stage, a discrete, universal
set of fault-tolerant operations is obtained by error-correcting noisy
transformations and distilling resource states. In a second stage, arbitrary
transformations are synthesized to desired accuracy by combining elements of
this set into a circuit. Here, we present a scheme which merges these two
stages into a single one, directly distilling complex transformations. We find
that our scheme can reduce the total overhead to realize certain gates by up to
a few orders of magnitude. In contrast to other schemes, this efficient gate
synthesis does not require computationally intensive compilation algorithms,
and a straightforward generalization of our scheme circumvents compilation and
synthesis altogether.


  In this paper, we consider a family of Sturm-Liouville operators on the
$\omega$-periodic domain. The bifurcation with respect to the parameter region
is studied, and the elliptic regions are estimated by trace formula. At last,
these results are used to study the linear stability of the elliptic
equilibrium point along $z$-axis in Robe's restricted three-body problem.


  In complex transition metal oxides (TMO) an arrested electronic phase
separation (PS) appears by tuning the system near a Lifshitz transition in
multiband Hubbard models. The PS in La2CuO4+y near insulator to metal
transition (IMT) is made of short range Charge Density Wave (CDW) order
inhomogeneity coexisting with quenched lattice disorder. While at high doping
y=0.1 percolation gives a single superconducting phase, near the IMT at y=0.06
two coexisting superconducting phases appear: the first one with a critical
temperature Tc1=16 K and the second one with Tc2=29K. It is known that the two
superconducting phases are characterized by two different space geometry
because of two different spatial distributions of both CDW order and dopants
self-organization. Here we show that these two phases show different flux
dynamic regimes using alternating current (AC) multi-harmonic susceptibility
experiments. This is a unique technique capable to investigate multi-phase
superconductors and characterize their transport properties in a percolative
scenario. Results point out that the low critical temperature phase is well
described by a bulk-like flux pinning with a 2D geometry while the phase with
higher critical temperature shows a barrier pinning mechanism providing direct
evidence of two different superconducting vortex dynamics in different complex
geometrical spaces.


  This paper proposes to apply the
  Ultra-Relativistic Quantum Molecular Dynamic (UrQMD) approach to implement
the PANDA project (GSI).
  Modeling of $\bar{p}$A-interactions has been performed at antiproton energies
from 1 GeV to 200 GeV by using the UrQMD model. We have studied average
multiplicities, multiplicity distributions of various types of secondary
particles, correlations between the multiplicities, rapidity, and transverse
momentum distributions of the particles. The UrQMD model predictions on
inelastic $\bar{p}$A- collisions have been found to reproduce qualitatively the
experimental data. However, to reach the quantitative agreement, especially, in
fragmentation regions, it is needed to modify the UrQMD model.


  Recent advancements in large language models (LLMs) have spurred interest in
using them for generating robot programs from natural language, with promising
initial results. We investigate the use of LLMs to generate programs for
service mobile robots leveraging mobility, perception, and human interaction
skills, and where accurate sequencing and ordering of actions is crucial for
success. We contribute CodeBotler, an open-source robot-agnostic tool to
program service mobile robots from natural language, and RoboEval, a benchmark
for evaluating LLMs' capabilities of generating programs to complete service
robot tasks. CodeBotler performs program generation via few-shot prompting of
LLMs with an embedded domain-specific language (eDSL) in Python, and leverages
skill abstractions to deploy generated programs on any general-purpose mobile
robot. RoboEval evaluates the correctness of generated programs by checking
execution traces starting with multiple initial states, and checking whether
the traces satisfy temporal logic properties that encode correctness for each
task. RoboEval also includes multiple prompts per task to test for the
robustness of program generation. We evaluate several popular state-of-the-art
LLMs with the RoboEval benchmark, and perform a thorough analysis of the modes
of failures, resulting in a taxonomy that highlights common pitfalls of LLMs at
generating robot programs. We release our code and benchmark at
https://amrl.cs.utexas.edu/codebotler/.


  We present a Bayesian sampling algorithm called adaptive importance sampling
or Population Monte Carlo (PMC), whose computational workload is easily
parallelizable and thus has the potential to considerably reduce the wall-clock
time required for sampling, along with providing other benefits. To assess the
performance of the approach for cosmological problems, we use simulated and
actual data consisting of CMB anisotropies, supernovae of type Ia, and weak
cosmological lensing, and provide a comparison of results to those obtained
using state-of-the-art Markov Chain Monte Carlo (MCMC). For both types of data
sets, we find comparable parameter estimates for PMC and MCMC, with the
advantage of a significantly lower computational time for PMC. In the case of
WMAP5 data, for example, the wall-clock time reduces from several days for MCMC
to a few hours using PMC on a cluster of processors. Other benefits of the PMC
approach, along with potential difficulties in using the approach, are analysed
and discussed.


  Spectrum sensing is a fundamental component in cognitive radio. A major
challenge in this area is the requirement of a high sampling rate in the
sensing of a wideband signal. In this paper a wideband spectrum sensing model
is presented that utilizes a sub-Nyquist sampling scheme to bring substantial
savings in terms of the sampling rate. The correlation matrix of a finite
number of noisy samples is computed and used by a subspace estimator to detect
the occupied and vacant channels of the spectrum. In contrast with common
methods, the proposedmethod does not need the knowledge of signal properties
that mitigates the uncertainty problem. We evaluate the performance of this
method by computing the probability of detecting signal occupancy in terms of
the number of samples and the SNR of randomly generated signals. The results
show a reliable detection even in low SNR and small number of samples.


  We describe the strong dual space $({\mathcal O}^s (D))^*$ for the space
${\mathcal O}^s (D) =
  H^s (D) \cap {\mathcal O} (D)$ of holomorphic functions from the Sobolev
space $H^s(D)$, $s \in \mathbb Z$, over a bounded simply connected plane domain
$D$ with infinitely differential boundary $\partial D$. We identify the dual
space with the space of holomorhic functions on ${\mathbb C}^n\setminus
\overline D$ that belong to $H^{1-s} (G\setminus \overline D)$ for any bounded
domain $G$, containing the compact $\overline D$, and vanish at the infinity.
As a corollary, we obtain a description of the strong dual space $({\mathcal
O}_F (D))^*$ for the space ${\mathcal O}_F (D)$ of holomorphic functions of
finite order of growth in $D$ (here, ${\mathcal O}_F (D)$ is endowed with the
inductive limit topology with respect to the family of spaces ${\mathcal O}^s
(D)$, $s \in \mathbb Z$).
  In this way we extend the classical Grothendieck-K{\"o}the-Sebasti\~{a}o e
Silva duality for the space of holomorphic functions.


  We consider the possible formation of the quark hadron mixed phase in
protoneutron stars. We discuss two cases: the first one, corresponding to a
vanishingly small value of the surface tension of quark matter, is the well
known mixed phase in which the global electric charge neutrality condition is
imposed. In turn, this produces a non-constant pressure mixed phase. In the
second case, corresponding to very large values of the surface tension, the
charge neutrality condition holds only locally. However, the existence in
protoneutron star matter of an additional globally conserved charge, the lepton
number, allows for a new type of non-constant pressure mixed phase. We discuss
the properties of the new mixed phase and the possible effects of its formation
during the evolution of protoneutron stars.


  The kinematics and dynamics of young stellar populations enable us to test
theories of star formation. With this aim, we continue our analysis of the
SDSS-III/APOGEE IN-SYNC survey, a high resolution near infrared spectroscopic
survey of young clusters. We focus on the Orion A star-forming region, for
which IN-SYNC obtained spectra of $\sim2700$ stars. In Paper IV we used these
data to study the young stellar population. Here we study the kinematic
properties through radial velocities ($v_r$). The young stellar population
remains kinematically associated with the molecular gas, following a
$\sim10\:{\rm{km\:s}}^{-1}$ gradient along filament. However, near the center
of the region, the $v_r$ distribution is slightly blueshifted and asymmetric;
we suggest that this population, which is older, is slightly in foreground. We
find evidence for kinematic subclustering, detecting statistically significant
groupings of co-located stars with coherent motions. These are mostly in the
lower-density regions of the cloud, while the ONC radial velocities are
smoothly distributed, consistent with it being an older, more dynamically
evolved cluster. The velocity dispersion $\sigma_v$ varies along the filament.
The ONC appears virialized, or just slightly supervirial, consistent with an
old dynamical age. Here there is also some evidence for on-going expansion,
from a $v_r$--extinction correlation. In the southern filament, $\sigma_v$ is
$\sim2$--$3$ times larger than virial in the L1641N region, where we infer a
superposition along the line of sight of stellar sub-populations, detached from
the gas. On the contrary, $\sigma_v$ decreases towards L1641S, where the
population is again in agreement with a virial state.


  The polarization and the susceptibility of a ferroelectric multilayer with a
non-ferroelectric slab are investigated within the framework of transverse
Ising model with a four-spin interaction term. The effect of the thickness and
the position of the non-ferroelectric slab are investigated in this paper. We
find that the increase of the thickness of the non-ferroelectric will decrease
the polarization and the susceptibility of the film. If the position of the
non-ferroelcetric slab shifts from the center of the film to the surface, the
number of the peaks of the susceptibility will change. And a step-like
polarization curve is found.


  We theoretically predict the occurrence of multiple hydrodynamical-like shock
phenomena in the propagation of ultrashort intense pulses in a suitably
engineered photonic crystal fiber. The shocks are due to the Raman effect,
which acts as a nonlocal term favoring their generation in the focusing regime.
It is shown that the problem is mapped to shock formation in the presence of a
slope and a gravity-like potential. The signature of multiple shocks in XFROG
signals is unveiled.


  The main aim of the paper is to present the analytical solution of the
Belavkin quantum filtering equation for damped harmonic oscillator being
initially in the squeezed coherent state for diffusion observation with complex
white noise. The comparison of the a priori and a posteriori mean value of the
optical quadrature operators and the photon number operator is given.


  Alzheimer's disease is a major cause of dementia. Its diagnosis requires
accurate biomarkers that are sensitive to disease stages. In this respect, we
regard probabilistic classification as a method of designing a probabilistic
biomarker for disease staging. Probabilistic biomarkers naturally support the
interpretation of decisions and evaluation of uncertainty associated with them.
In this paper, we obtain probabilistic biomarkers via Gaussian Processes.
Gaussian Processes enable probabilistic kernel machines that offer flexible
means to accomplish Multiple Kernel Learning. Exploiting this flexibility, we
propose a new variation of Automatic Relevance Determination and tackle the
challenges of high dimensionality through multiple kernels. Our research
results demonstrate that the Gaussian Process models are competitive with or
better than the well-known Support Vector Machine in terms of classification
performance even in the cases of single kernel learning. Extending the basic
scheme towards the Multiple Kernel Learning, we improve the efficacy of the
Gaussian Process models and their interpretability in terms of the known
anatomical correlates of the disease. For instance, the disease pathology
starts in and around the hippocampus and entorhinal cortex. Through the use of
Gaussian Processes and Multiple Kernel Learning, we have automatically and
efficiently determined those portions of neuroimaging data. In addition to
their interpretability, our Gaussian Process models are competitive with recent
deep learning solutions under similar settings.


  It is known that traversable wormhole can exist in General Relativity only if
its throat contains some exotic matter. In this paper, we obtain
$(2+1)$-dimensional (horizonless) charged magnetic brane without (curvature)
singularity. Then, we consider a nontrivial local transformation to grant a
global rotation to spacetime. After that, we generalize magnetic brane to
higher dimensional solutions and use the cut-and-paste method to construct
higher dimensional charged BTZ-like rotating wormholes such a way that they
reduce to charged magnetic BTZ solution in three dimensions, exactly. We also
show that charged BTZ-like wormhole supported by the exotic matter at its
throat $r=r_{+}$. Finally, we calculate the conserved quantities of the charged
BTZ-like wormhole such as mass, angular momentum and electric charge density,
and show that the electric charge depends on the rotation parameters,
interestingly, and the static wormhole does not have a net electric charge
density.


  We study the zero temperature Casimir energy and fermion number for Dirac
fields in a 2+1-dimensional Minkowski space-time, in the presence of a uniform
magnetic field perpendicular to the spatial manifold. Then, we go to the
finite-temperature problem with a chemical potential, introduced as a uniform
zero component of the gauge potential. By performing a Lorentz boost, we obtain
Hall's conductivity in the case of crossed electric and magnetic fields.


  The study investigates the problem of magnetohydrodynamic (MHD) free
convection over a non-isothermal axisymmetric body under the action of
transverse magnetic field. The body is embedded in a porous medium saturated
with electrically conducting non-Newtonian power law fluid. In order to obtain
similarity solution, it is assumed that the viscosity of the fluid decays
exponentially with temperature. The qualitative results are illustrated for a
vertical flat plate, horizontal cylinder and sphere.


  Although static networks have been extensively studied in machine learning,
data mining, and AI communities for many decades, the study of dynamic networks
has recently taken center stage due to the prominence of social media and its
effects on the dynamics of social networks. In this paper, we propose a
statistical model for dynamically evolving networks, together with a
variational inference approach. Our model, Neural Latent Space Model with
Variational Inference, encodes edge dependencies across different time
snapshots. It represents nodes via latent vectors and uses interaction matrices
to model the presence of edges. These matrices can be used to incorporate
multiple relations in heterogeneous networks by having a separate matrix for
each of the relations. To capture the temporal dynamics, both node vectors and
interaction matrices are allowed to evolve with time. Existing network analysis
methods use representation learning techniques for modelling networks. These
techniques are different for homogeneous and heterogeneous networks because
heterogeneous networks can have multiple types of edges and nodes as opposed to
a homogeneous network. Unlike these, we propose a unified model for homogeneous
and heterogeneous networks in a variational inference framework. Moreover, the
learned node latent vectors and interaction matrices may be interpretable and
therefore provide insights on the mechanisms behind network evolution. We
experimented with a single step and multi-step link forecasting on real-world
networks of homogeneous, bipartite, and heterogeneous nature, and demonstrated
that our model significantly outperforms existing models.


  Exploration-exploitation dilemma has long been a crucial issue in
reinforcement learning. In this paper, we propose a new approach to
automatically balance between these two. Our method is built upon the Soft
Actor-Critic (SAC) algorithm, which uses an "entropy temperature" that balances
the original task reward and the policy entropy, and hence controls the
trade-off between exploitation and exploration. It is empirically shown that
SAC is very sensitive to this hyperparameter, and the follow-up work (SAC-v2),
which uses constrained optimization for automatic adjustment, has some
limitations. The core of our method, namely Meta-SAC, is to use metagradient
along with a novel meta objective to automatically tune the entropy temperature
in SAC. We show that Meta-SAC achieves promising performances on several of the
Mujoco benchmarking tasks, and outperforms SAC-v2 over 10% in one of the most
challenging tasks, humanoid-v2.


  Electricity is an essential comfort to support our daily activities. With the
competitive increase and energy costs by the industry, new values and
opportunities for delivering electricity to customers are produced. One of
these new opportunities is electric vehicles. With the arrival of electric
vehicles, various challenges and opportunities are being presented in the
electric power system worldwide. For example, under the traditional electric
power billing scheme, electric power has to be consumed where it is needed so
that end-users could not charge their electric vehicles at different points
(e.g. a relative's house) if this the correct user is not billed (this due to
the high consumption of electrical energy that makes it expensive). To achieve
electric mobility, they must solve new challenges, such as the smart metering
of energy consumption and the cybersecurity of these measurements. The present
work shows a study of the different smart metering technologies that use
blockchain and other security mechanisms to achieve e-mobility.


  We prove a combination theorem for trees of (strongly) relatively hyperbolic
spaces and finite graphs of (strongly) relatively hyperbolic groups. This gives
a geometric extension of Bestvina and Feighn's Combination Theorem for
hyperbolic groups and answers a question of Swarup. We also prove a converse to
the main Combination Theorem.


  Recent studies show that pre-trained language models (LMs) are vulnerable to
textual adversarial attacks. However, existing attack methods either suffer
from low attack success rates or fail to search efficiently in the
exponentially large perturbation space. We propose an efficient and effective
framework SemAttack to generate natural adversarial text by constructing
different semantic perturbation functions. In particular, SemAttack optimizes
the generated perturbations constrained on generic semantic spaces, including
typo space, knowledge space (e.g., WordNet), contextualized semantic space
(e.g., the embedding space of BERT clusterings), or the combination of these
spaces. Thus, the generated adversarial texts are more semantically close to
the original inputs. Extensive experiments reveal that state-of-the-art (SOTA)
large-scale LMs (e.g., DeBERTa-v2) and defense strategies (e.g., FreeLB) are
still vulnerable to SemAttack. We further demonstrate that SemAttack is general
and able to generate natural adversarial texts for different languages (e.g.,
English and Chinese) with high attack success rates. Human evaluations also
confirm that our generated adversarial texts are natural and barely affect
human performance. Our code is publicly available at
https://github.com/AI-secure/SemAttack.


  Stellar spectra with a high resolution of 115000 obtained with the HARPS
spectrograph provide an opportunity to examine turbulence velocities and their
depth distributions in the photosphere of stars. Fourier analysis was performed
for 17 iron lines in the spectra of 13 stars with an effective temperature of
4900--6200 K and a logarithm of surface gravity of 3.9--5.0 as well as in the
spectrum of the Sun as a star. Models of stellar atmospheres were taken from
the MARCS database. The standard concept of isotropic Gaussian microturbulence
was assumed in this study. A satisfactory fit between the synthesized profiles
of spectral lines and observational data verified the reliability of the
Fourier method. The most likely estimates of turbulence velocities, the
rotation velocity, and the iron abundance and their photospheric depth
distribution profiles were obtained as a result. Microturbulence does not vary
to any significant degree with depth, while macroturbulence has a marked depth
dependence. The macroturbulence velocity increases with depth in the stellar
atmosphere. The higher the effective temperature of a star and the stronger the
surface gravity, the steeper the expected macroturbulence gradient. The mean
macroturbulence velocity increases for stars with higher temperatures, weaker
gravity, and faster rotation. The mean macro- and microturbulence velocities
are correlated with each other and with the rotation velocity in the examined
stars. The ratio between the macroturbulence velocity and the rotation velocity
in solar-type stars varies from 1 (the hottest stars) to 1.7 (the coolest
stars). The age dependence of the rotation velocity is more pronounced than
that of the velocity of macroturbulent motions.


  In this paper, we investigate the impact of network coding at the relay node
on the stable throughput rate in multicasting cooperative wireless networks.
The proposed protocol adopts Network-level cooperation in contrast to the
traditional physical layer cooperative protocols and in addition uses random
linear network coding at the relay node. The traffic is assumed to be bursty
and the relay node forwards its packets during the periods of source silence
which allows better utilization for channel resources. Our results show that
cooperation will lead to higher stable throughput rates than conventional
retransmission policies and that the use of random linear network coding at the
relay can further increase the stable throughput with increasing Network Coding
field size or number of packets over which encoding is performed.


  We discuss two solvable grokking (generalisation beyond overfitting) models
in a rule learning scenario. We show that grokking is a phase transition and
find exact analytic expressions for the critical exponents, grokking
probability, and grokking time distribution. Further, we introduce a
tensor-network map that connects the proposed grokking setup with the standard
(perceptron) statistical learning theory and show that grokking is a
consequence of the locality of the teacher model. As an example, we analyse the
cellular automata learning task, numerically determine the critical exponent
and the grokking time distributions and compare them with the prediction of the
proposed grokking model. Finally, we numerically analyse the connection between
structure formation and grokking.


  For multiscale gas flows, kinetic-continuum hybrid method is usually used to
balance the computational accuracy and efficiency. However, the
kinetic-continuum coupling is not straightforward since the coupled methods are
based on different theoretical frameworks. In particular, it is not easy to
recover the non-equilibrium information required by the kinetic method which is
lost by the continuum model at the coupling interface. Therefore, we present a
multiscale lattice Boltzmann (LB) method which deploys high-order LB models in
highly rarefied flow regions and low-order ones in less rarefied regions. Since
this multiscale approach is based on the same theoretical framework, the
coupling precess becomes simple. The non-equilibrium information will not be
lost at the interface as low-order LB models can also retain this information.
The simulation results confirm that the present method can achieve model
accuracy with reduced computational cost.


  We study linear scaling relations in electron-phonon superconductors. By
combining numerical and analytical techniques, we find linear Homes scaling
relations between the zero-temperature superfluid density and the normal-state
DC conductivity. This is due to Galilean invariance being broken, either via a
large impurity scattering rate or inelastic scattering of electrons and
Einstein phonons at large electron-phonon coupling. Our work thus shows that
Homes scaling is more universal than either cuprate or BCS-like physics, and is
instead a fundamental result in a wide class of superconductors.


  For a convex domain $D$ bounded by the hypersurface $\partial D$ in a space
of constant curvature we give sharp bounds on the width $R-r$ of a spherical
shell with radii $R$ and $r$ that can enclose $\partial D$, provided that
normal curvatures of $\partial D$ are pinched by two positive constants.
Furthermore, in the Euclidean case we also present sharp estimates for the
quotient $R/r$. From the obtained estimates we derive stability results for
almost umbilical hypersurfaces in the constant curvature spaces.


  We study the algebraic properties of plethystic vertex operators, introduced
in J. Phys. A: Math. Theor. 43 405202 (2010), underlying the structure of
symmetric functions associated with certain generalized universal character
rings of subgroups of the general linear group, defined to stabilize tensors of
Young symmetry type characterized by a partition of arbitrary shape \pi. Here
we establish an extension of the well-known boson-fermion correspondence
involving Schur functions and their associated (Bernstein) vertex operators:
for each \pi, the modes generated by the plethystic vertex operators and their
suitably constructed duals, satisfy the anticommutation relations of a complex
Clifford algebra. The combinatorial manipulations underlying the results
involve exchange identities exploiting the Hopf-algebraic structure of certain
symmetric function series and their plethysms.


  Let $X$ be a smooth scheme over an algebraically closed field. When $X$ is
proper, it was proved in \cite{me1} that the moduli of $\ell$-adic continuous
representations of $\pi_1^\et(X)$, $\LocSys(X)$, is representable by a
(derived) $\Ql$-analytic space. However, in the non-proper case one cannot
expect that the results of \cite{me1} hold mutatis mutandis. Instead, assuming
$\ell$ is invertible in $X$, one has to bound the ramification at infinity of
those considered continuous representations. The main goal of the current text
is to give a proof of such representability statements in the open case. We
also extend the representability results of \cite{me1}. More specifically,
assuming $X$ is assumed to be proper, we show that $\LocSys(X)$ admits a
canonical shifted symplectic form and we give some applications of such
existence result.


  We present a method of computing elements of spin groups in the case of
arbitrary dimension. This method generalizes Hestenes method for the case of
dimension 4. We use the method of averaging in Clifford's geometric algebra
previously proposed by the author. We present explicit formulas for elements of
spin group that correspond to the elements of orthogonal groups as two-sheeted
covering. These formulas allow us to compute rotors, which connect two
different frames related by a rotation in geometric algebra of arbitrary
dimension.


  Quantum decoherence, the evolution of pure states into mixed states, may be a
feature of quantum-gravity models. In most cases, such models lead to fewer
neutrinos of all active flavours being detected in a long baseline experiment
as compared to three-flavour standard neutrino oscillations. We discuss the
potential of the CNGS and J-PARC beams in constraining models of
quantum-gravity induced decoherence using neutrino oscillations as a probe. We
use as much as possible model-independent parameterizations, even though they
are motivated by specific microscopic models, for fits to the expected
experimental data which yield bounds on quantum-gravity decoherence parameters.


  A new noise, based on vortex structures in 2D (point vortices) and 3D (vortex
filaments), is introduced. It is defined as the scaling limit of a jump process
which explores vortex structures and it can be defined in any domain, also with
boundary. The link with Fractional Gaussian Fields and Kraichnan noise is
discussed. The vortex noise is finally shown to be suitable for the
investigation of the eddy dissipation produced by small scale turbulence.


  The human brain is capable of learning, memorizing, and regenerating a
panoply of temporal patterns. A neuro-dynamical mechanism called conceptors
offers a method for controlling the dynamics of a recurrent neural network by
which a variety of temporal patterns can be learned and recalled. However,
conceptors are matrices whose size scales quadratically with the number of
neurons in the recurrent neural network, hence they quickly become impractical.
In the work reported in this thesis, a variation of conceptors is introduced,
called diagonal conceptors, which are diagonal matrices, thus reducing the
computational cost drastically. It will be shown that diagonal conceptors
achieve the same accuracy as conceptors, but are slightly more unstable. This
instability can be improved, but requires further research. Nevertheless,
diagonal conceptors show to be a promising practical alternative to the
standard full matrix conceptors.


  We present late-time HST images of the site of supernova (SN) 2009ip taken
almost 3 yr after its bright 2012 luminosity peak. SN 2009ip is now slightly
fainter in broad filters than the progenitor candidate detected by HST in 1999.
The current source continues to be dominated by ongoing late-time CSM
interaction that produces strong H-alpha emission and a weak pseudo-continuum,
as found previously for 1-2 yr after explosion. The intent of these
observations was to search for evidence of recent star formation in the local
(1kpc; 10 arcsec) environment around SN 2009ip, in the remote outskirts of its
host spiral galaxy NGC 7259. We can rule out the presence of any massive
star-forming complexes like 30 Dor or the Carina Nebula at the SN site or
within a few kpc. If the progenitor of SN 2009ip was really a 50-80 Msun star
as archival HST images suggested, then it is strange that there is no sign of
this type of massive star formation anywhere in the vicinity. A possible
explanation is that the progenitor was the product of a merger or binary mass
transfer, rejuvenated after a lifetime that was much longer than 4-5 Myr,
allowing its natal H II region to have faded. A smaller region like the Orion
Nebula would be an unresolved but easily detected point source. This is ruled
out within 1.5 kpc around SN 2009ip, but a small H II region could be hiding in
the glare of SN 2009ip itself. Later images after a few more years have passed
are needed to confirm that the progenitor candidate is truly gone and to test
for the presence of a small H II region or cluster at the SN position.


  We consider a nano-patterned planar wall consisting of a periodic array of
stripes of width $L$, which are completely wet by liquid (contact angle
$\theta=0$), separated by regions of width $D$ which are completely dry
(contact angle $\theta=\pi)$. Using microscopic Density Functional Theory we
show that in the presence of long-ranged dispersion forces, the wall-gas
interface undergoes a first-order wetting transition, at bulk coexistence, as
the separation $D$ is reduced to a value $D_w\propto\ln L$, induced by the
bridging between neighboring liquid droplets. Associated with this is a line of
pre-wetting transitions occurring off coexistence. By varying the stripe width
$L$ we show that the pre-wetting line shows universal scaling behaviour and
data collapse. This verifies predictions based on mesoscopic models for the
scaling properties associated with finite-size effects at complete wetting
including the logarithmic singular contribution to the surface free-energy.


  We find multi-scalar effective field theories (EFTs) that can achieve a slow
inflationary roll despite having a scalar potential that does not satisfy the
usual slow-roll condition (d V)^2 << V^2/Mp^2. They evade the usual slow-roll
conditions on $V$ because their kinetic energies are dominated by
single-derivative terms rather than the usual two-derivative terms. Single
derivatives dominate during slow roll and so do not require a breakdown of the
usual derivative expansion that underpins calculational control in much of
cosmology. The presence of such terms requires some sort of UV Lorentz-symmetry
breaking during inflation (besides the usual cosmological breaking).
Chromo-natural inflation provides an example of a UV theory that can generate
the multi-field single-derivative terms we consider, and we argue that the EFT
we find indeed captures the slow-roll conditions for the background evolution
for Chromo-natural inflation. We also show that our EFT can be understood as a
multi-field generalization of the single-field Cuscuton models. The multi-field
case introduces a new feature, however: the scalar kinetic terms define a
target-space 2-form, F_{ab}, whose antisymmetry gives new ways for slow roll to
be achieved.


  The deterministic generation of multiexcitation subradiant states proves to
be challenging. Here, we present a viable path towards their transient
generation in finite-sized ordered arrays of dipole-dipole coupled quantum
emitters, based on incoherent driving of the atomic ensemble. In particular, we
show that a maximal coupling to long-lived subradiant states is achieved if
only half of the atoms are initially excited. We characterize the nature of the
resulting states by calculating the dynamic fluorescence spectrum of the
emitted light. Finally, we elucidate the role of coherent interactions during
the decay process of sufficiently dense atomic arrays, which result in a
coherently driven radiation burst that leads to a subsequent reduction of the
chances to prepare multiexcitation subradiant states.


  We investigate analytically and numerically the classical ground states of
frustrated Heisenberg models on pyrochlore and kagome lattices in zero and
finite magnetic fields. Each model has a wide region in the microscopic
parameter space, where the propagation vector is turned to a commensurate
position equal to a half of the reciprocal lattice vector with a nontrivial
star. Within these regions the zero-field ground states for both models
correspond to noncoplanar triple-k spin configurations. A universal appearance
of the 3-k states can be related to the spin-space dimensionality. A strong
magnetic field freezes the longitudinal spin component reducing the spin-space
dimensionality. Accordingly, we find transitions into the double-k magnetic
structures induced by applied field for both spin models. The predicted
transition between 3-k and 2-k states may explain the hitherto unexplained
transitions observed experimentally in cubic spinels GeNi2O4 and GeCo2O4 under
magnetic field.


  We prove that the scalar curvature of a homogeneous Ricci flow solution blows
up at a forward or backward finite-time singularity.


  We expand the notion of characteristic formula to infinite finitely
presentable subdirectly irreducible algebras. We prove that there is a
continuum of varieties of Heyting algebras containing infinite finitely
presentable subdirectly irreducible algebras. Moreover, we prove that there is
a continuum of intermediate logics that can be axiomatized by characteristic
formulas of infinite algebras while they are not axiomatizable by standard
Jankov formulas. We give the examples of intermediate logics that are not
axiomatizable by characteristic formulas of infinite algebras. Also, using the
Goedel-McKinsey-Tarski translation we extend these results to the varieties of
interior algebras and normal extensions of S4


  We study the reciprocal of the mean quantum Fisher information (RMQFI),
$\chi^2$ for general three qubit states, having graph and hypergraph states as
special cases, for identifying genuine multi party entanglement characterized
by $\chi^2 <1$. We demonstrate that the most symmetric graph state and the GHZ
state have the lowest RMQFI values leading to the highest statistical speed
showing that both these states attain the Heisenberg limit in phase
sensitivity. Unlike the GHZ state, graph states have the same RMQFI values for
measurement through different parameters, a property shared by the hypergraph
states. Three qubit graph and hypergraph states can violate Bell's inequality
as $F_Q > N$. Both the GHZ state and the most symmetric graph state have the
highest concurrence equalling 3 and the maximum QFI values.


  Among the models addressing the Hubble tension, those introducing a dynamical
dark component around recombination have been the most promising thus far.
Their study has highlighted that, in fact, cosmic microwave background (CMB)
and baryon acoustic oscillation (BAO) observations can allow for such
components before and near recombination.
  The new dynamical degree of freedom can be early dark energy (EDE) or early
modified gravity depending on its coupling to gravity. We study a new model,
$\mathcal{G}$EDE, featuring the cubic Galileon operator $X\Box\phi$ and test it
against the most recent Planck PR4 CMB and Cepheid calibrated Pantheon+ type Ia
Supernovae data. Thanks to the kinetic braiding effects, $\mathcal{G}$EDE gives
a better fit to the data, with a higher $H_0$, and is preferred over the
canonical EDE with a Bayes factor $\ln B=0.9$, despite introducing one more
parameter. This calls for further explorations of modified gravity near and
before last scattering. To facilitate these, we introduce a substantial
extension of the cosmological code \texttt{EFTCAMB} that allows to fully evolve
the background and linear dynamics of any covariant theory, oscillatory or not,
belonging to the Horndeski class.


  Robust and efficient interpretation of QSAR methods is quite useful to
validate AI prediction rationales with subjective opinion (chemist or biologist
expertise), understand sophisticated chemical or biological process mechanisms,
and provide heuristic ideas for structure optimization in pharmaceutical
industry. For this purpose, we construct a multi-layer self-attention based
Graph Neural Network framework, namely Ligandformer, for predicting compound
property with interpretation. Ligandformer integrates attention maps on
compound structure from different network blocks. The integrated attention map
reflects the machine's local interest on compound structure, and indicates the
relationship between predicted compound property and its structure. This work
mainly contributes to three aspects: 1. Ligandformer directly opens the
black-box of deep learning methods, providing local prediction rationales on
chemical structures. 2. Ligandformer gives robust prediction in different
experimental rounds, overcoming the ubiquitous prediction instability of deep
learning methods. 3. Ligandformer can be generalized to predict different
chemical or biological properties with high performance. Furthermore,
Ligandformer can simultaneously output specific property score and visible
attention map on structure, which can support researchers to investigate
chemical or biological property and optimize structure efficiently. Our
framework outperforms over counterparts in terms of accuracy, robustness and
generalization, and can be applied in complex system study.


  The Fermilab crystal-extraction experiment E853 at Tevatron was simulated by
Monte Carlo code CATCH [1] tested earlier in the CERN-SPS experiment [2-4].
Predictions for the extraction efficiency, angular scans and extracted beam
profiles are presented. Several ideas are proposed and tested by the
simulation, how to get in E853 the key information of the extraction
experiment: the "septum width" of a crystal and dependence of extraction
efficiency on it, the impact parameters of protons at crystal, and the
contribution of the first and multi passes to the extraction. The ways to
optimize E853 are analyzed.


  We investigate the occurrence of multicritical points under pressure and
magnetic field in a model that describes two 5f bands (of either $\alpha$ or
$\beta$ characters) which hybridize with a single itinerant conduction band.
The 5f-electrons interact through Coulomb and exchange terms. The AF order
parameter is a N\'eel vector, which is assumed to be fixed by an Ising
anisotropy. The applied magnetic field is transverse to the anisotropy axis.
Without field, our results for the temperature - pressure phase diagram show
that, at low temperatures, a first-order phase transition occurs between two
distinct antiferromagnetic phases, AF$_1$ and AF$_2$, as the pressure is
increased. The two phases are characterized by the gaps of bands $\alpha$ and
$\beta$ given by $\Delta_{\alpha}$ and $\Delta_{\beta}$, respectively. The
AF$_1$ phase occurs when $\Delta_{\beta}>\Delta_{\alpha}>0$, while in the
AF$_2$ phase, the gaps satisfy $\Delta_{\alpha}>\Delta_{\beta}>0$. The
application of a magnetic field produces a drastic change in the phase diagram.
The AF1 and AF2 phases separate with the latter acquiring a dome shape which is
eventually suppressed for large values of the applied field. The evolution of
the phase diagram under pressure, without and with magnetic field, shows the
presence of multicritical points. Our results show that the evolution of these
multicritical points by the simultaneous application of pressure and field is
also drastic with the suppression of some multicritical points and the
emergence of others ones. We believe that these results may have relevance for
the growing field of multicritical points (classical and quantum) in the
physics of Uranium compounds.


  We examine regular and irregular repeat-accumulate (RA) codes with repetition
degrees which are all even. For these codes and with a particular choice of an
interleaver, we give an upper bound on the decoding error probability of a
linear-programming based decoder which is an inverse polynomial in the block
length. Our bound is valid for any memoryless, binary-input, output-symmetric
(MBIOS) channel. This result generalizes the bound derived by Feldman et al.,
which was for regular RA(2) codes.


  Recently it has become clear that the resonant amplification of quantum field
fluctuations at preheating must be accompanied by resonant amplification of
scalar metric perturbations, since the two are united by Einstein's equations.
Furthermore, this "metric preheating" enhances particle production and leads to
gravitational rescattering effects even at linear order. In multi-field models
with strong preheating (q \gg 1), metric perturbations are driven nonlinear,
with the strongest amplification typically on super-Hubble scales (k \to 0).
This amplification is causal, being due to the super- Hubble coherence of the
inflaton condensate, and is accompanied by resonant growth of entropy
perturbations. The amplification invalidates the use of the linearized Einstein
field equations, irrespective of the amount of fine-tuning of the initial
conditions. This has serious implications at all scales - from the large-angle
cosmic microwave background (CMB) anisotropies to primordial black holes. We
investigate the (q,k) parameter space in a two-field model, and introduce the
time to nonlinearity, t_{nl}, as the timescale for the breakdown of the
linearized Einstein equations. Backreaction effects are expected to shut down
the linear resonances, but cannot remove the existing amplification, which
threatens the viability of strong preheating when confronted with the CMB. We
discuss ways to escape the above conclusions, including secondary phases of
inflation and preheating solely to fermions. Finally we rank known classes of
inflation from strongest (chaotic and strongly coupled hybrid inflation) to
weakest (hidden sector, warm inflation) in terms of the distortion of the
primordial spectrum due to these resonances in preheating.


  A central problem in extremal graph theory is to estimate, for a given graph
$H$, the number of $H$-free graphs on a given set of $n$ vertices. In the case
when $H$ is not bipartite, fairly precise estimates on this number are known.
In particular, thirty years ago, Erd\H{o}s, Frankl, and R\"odl proved that
there are $2^{(1+o(1))\text{ex}(n,H)}$ such graphs. In the bipartite case,
however, nontrivial bounds have been proven only for relatively few special
graphs $H$.
  We make a first attempt at addressing this enumeration problem for a general
bipartite graph $H$. We show that an upper bound of $2^{O(\text{ex}(n,H))}$ on
the number of $H$-free graphs with $n$ vertices follows merely from a rather
natural assumption on the growth rate of $n \mapsto \text{ex}(n,H)$; an
analogous statement remains true when $H$ is a uniform hypergraph.
Subsequently, we derive several new results, along with most previously known
estimates, as simple corollaries of our theorem. At the heart of our proof lies
a general supersaturation statement that extends the seminal work of Erd\H{o}s
and Simonovits. The bounds on the number of $H$-free hypergraphs are derived
from it using the method of hypergraph containers.


  Deep Neural Networks (DNNs) are a revolutionary force in the ongoing
information revolution, and yet their intrinsic properties remain a mystery. In
particular, it is widely known that DNNs are highly sensitive to noise, whether
adversarial or random. This poses a fundamental challenge for hardware
implementations of DNNs, and for their deployment in critical applications such
as autonomous driving. In this paper we construct robust DNNs via error
correcting codes. By our approach, either the data or internal layers of the
DNN are coded with error correcting codes, and successful computation under
noise is guaranteed. Since DNNs can be seen as a layered concatenation of
classification tasks, our research begins with the core task of classifying
noisy coded inputs, and progresses towards robust DNNs. We focus on binary data
and linear codes. Our main result is that the prevalent parity code can
guarantee robustness for a large family of DNNs, which includes the recently
popularized binarized neural networks. Further, we show that the coded
classification problem has a deep connection to Fourier analysis of Boolean
functions. In contrast to existing solutions in the literature, our results do
not rely on altering the training process of the DNN, and provide
mathematically rigorous guarantees rather than experimental evidence.


  During the third observing run (O3) of the Advanced LIGO and Advanced Virgo
detectors, dozens of candidate gravitational-wave (GW) events have been
catalogued. A challenge of this observing run has been the rapid identification
and public dissemination of compact binary coalescence (CBC) signals, a task
carried out by low-latency searches such as PyCBC Live. During the later part
of O3, we developed a method of classifying CBC sources, via their
probabilities of containing neutron star or black hole components, within PyCBC
Live, in order to facilitate immediate follow-up observations by
electromagnetic and neutrino observatories. This fast classification uses the
chirp mass recovered by the search as input, given the difficulty of measuring
the mass ratio with high accuracy for lower-mass binaries. We also use a
distance estimate derived from the search output to correct for the bias in
chirp mass due to the cosmological redshift. We present results for simulated
signals, and for confirmed candidate events identified in low latency over O3.


  We study the arithmetic geometry of the reduction modulo $p$ of the Siegel
modular variety with parahoric level structure. We realize the
EKOR-stratification on this variety as the fibers of a smooth morphism into an
algebraic stack parametrizing homogeneously polarized chains of certain
truncated displays.


  An algorithm for calculating three gauge-invariant helicities (self-, mutual-
and Berger relative helicity) for a magnetic field specified in a rectangular
box is described. The algorithm is tested on a well-known force-free model (Low
and Lou, 1990) presented in vector-potential form.


  We work out a specific class of three-loop diagrams (of order $\alpha_s^2$)
contributing to the decay amplitude for $b \to s \gamma$ associated with the
current-current operators $O_1$ and $O_2$ at the physical value of the
charm-quark mass $m_c$. For many of the considered diagrams we were able to
solve the master integrals using differential equations in the canonical form.
For some diagrams we did not find a transformation to canonical form and
therefore calculated the corresponding master integral directly as an expansion
around $z=m_c^2/m_b^2=0$, retaining power terms up to $z^{10}$ and keeping the
accompanying $\log(z)$ terms to all powers. The results for the sum of all
considered diagrams are given in tabular form, while contributions of
individual diagrams (or combinations thereof) are given in electronic form.


  Numerical simulation results of basic exactly solvable fluid flows using the
previously proposed Lattice Boltzmann Method (LBM) formulated on a general
curvilinear coordinate system are presented. As was noted in the theoretical
work of H. Chen, such curvilinear Lattice Boltzmann Method preserves a
fundamental one-to-one exact advection feature in producing minimal numerical
diffusion, as the Cartesian lattice Boltzmann model. As we numerically show,
the new model converges to exact solutions of basic fluid flows with the
increase of grid resolution in the presence of both natural curvilinear
geometry and/or grid non-uniform contraction, both for near equilibrium and
non-equilibrium LBM parameter choices.


  The transverse energies and the charged particle multiplicities at
midrapidity as well as their ratio, $dE_{T}/d\eta\mid_{mid} /
dN_{ch}/d\eta|_{mid}$, are evaluated in a statistical model with expansion for
the wide range of heavy-ion collisions, from AGS to RHIC at $\sqrt{s_{NN}}=200$
GeV. Full description of decays of hadron resonances is applied in calculations
of both $dE_{T}/d\eta|_{mid}$ and $dN_{ch}/d\eta|_{mid}$. The predictions of
the model at the freeze-out parameters, established independently from observed
particle yields and $p_{T}$ spectra, agree well with the experimental data.


  The supertree problem asking for a tree displaying a set of consistent input
trees has been largely considered for the reconstruction of species trees.
Here, we rather explore this framework for the sake of reconstructing a gene
tree from a set of input gene trees on partial data. In this perspective, the
phylogenetic tree for the species containing the genes of interest can be used
to choose among the many possible compatible "supergenetrees", the most natural
criteria being to minimize a reconciliation cost. We develop a variety of
algorithmic solutions for the construction and correction of gene trees using
the supertree framework. A dynamic programming supertree algorithm for
constructing or correcting gene trees, exponential in the number of input
trees, is first developed for the less constrained version of the problem. It
is then adapted to gene trees with nodes labeled as duplication or speciation,
the additional constraint being to preserve the orthology and paralogy
relations between genes. Then, a quadratic time algorithm is developed for
efficiently correcting an initial gene tree while preserving a set of "trusted"
subtrees, as well as the relative phylogenetic distance between them, in both
cases of labeled or unlabeled input trees. By applying these algorithms to the
set of Ensembl gene trees, we show that this new correction framework is
particularly useful to correct weaklysupported duplication nodes. The C++
source code for the algorithms and simulations described in the paper are
available at https://github.com/UdeM-LBIT/SuGeT.


  Let $\ag$ be an affine Lie algebra, and let $\Ua$ be the quantum affine
algebra introduced by Drinfeld and Jimbo. In [Kas94] Kashiwara introduced a
$\Ua$-module $V(\lambda)$, having a global crystal base for an integrable
weight $\lambda$ of level 0. We call it an {\it extremal weight module}.
  In [\S13]{Kas00} Kashiwara gave a conjecture on the structure of extremal
weight modules. We prove his conjecture when $\ag$ is an untwisted affine Lie
algebra of a simple Lie algebra $\g$ of type $ADE$, using a result of
Beck-Chari-Pressley [BCP].


  We review lattice results related to pion, kaon, D- and B-meson physics with
the aim of making them easily accessible to the particle physics community.
More specifically, we report on the determination of the light-quark masses,
the form factor f+(0), arising in semileptonic K -> pi transition at zero
momentum transfer, as well as the decay constant ratio fK/fpi of decay
constants and its consequences for the CKM matrix elements Vus and Vud.
Furthermore, we describe the results obtained on the lattice for some of the
low-energy constants of SU(2)LxSU(2)R and SU(3)LxSU(3)R Chiral Perturbation
Theory and review the determination of the BK parameter of neutral kaon mixing.
The inclusion of heavy-quark quantities significantly expands the FLAG scope
with respect to the previous review. Therefore, for this review, we focus on D-
and B-meson decay constants, form factors, and mixing parameters, since these
are most relevant for the determination of CKM matrix elements and the global
CKM unitarity-triangle fit. In addition we review the status of lattice
determinations of the strong coupling constant alpha_s.


  We obtain a general formula for the transition probabilities between any
state of the algebra of the canonical commutation relations (CCR-algebra) and a
squeezed quasifree state. Applications of this formula are made for the case of
multimode thermal squeezed states of quantum optics using a general canonical
decomposition of the correlation matrix valid for any quasifree state. In the
particular case of a one mode CCR-algebra we show that the transition
probability between two quasifree squeezed states is a decreasing function of
the geodesic distance between the points of the upper half plane representing
these states. In the special case of the purification map it is shown that the
transition probability between the state of the enlarged system and the product
state of real and fictitious subsystems can be a measure for the entanglement.


  A chiral constituent quark model approach, embodying s- and u-channel
exchanges,complemented with a Reggeized treatment for t-channel is presented. A
model is obtained allowing data for $\pi^- p \to \eta n$ and $\gamma p \to \eta
p$ to be describe satisfactorily. For the latter reaction, recently released
data by CLAS and CBELSA/TAPS Collaborations in the system total energy range
$1.6 \lesssim W \lesssim 2.8$ GeV are well reproduced due to the inclusion of
Reggeized trajectories instead of simple $\rho$ and $\omega$ poles.
Contribution from "missing" resonances is found to be negligible in the
considered processes.


  We propose two graph neural network layers for graphs with features in a
Riemannian manifold. First, based on a manifold-valued graph diffusion
equation, we construct a diffusion layer that can be applied to an arbitrary
number of nodes and graph connectivity patterns. Second, we model a tangent
multilayer perceptron by transferring ideas from the vector neuron framework to
our general setting. Both layers are equivariant with respect to node
permutations and isometries of the feature manifold. These properties have been
shown to lead to a beneficial inductive bias in many deep learning tasks.
Numerical examples on synthetic data as well as on triangle meshes of the right
hippocampus to classify Alzheimer's disease demonstrate the very good
performance of our layers.


  Investigations into the magnetic properties of sputtered Mn$_{x}$CoGe films
in the range $0.8 \leq x \leq 2.5$ uncovered ferrimagnetic order, unlike the
ferromagnetic order reported in bulk samples. These films formed hexagonal
Ni$_{2}$In-type structures when annealed at temperatures below 600$^{\circ}$C.
While the Curie temperatures of the films are comparable to those of hexagonal
bulk MnCoGe, there is a reduction in the magnetization of the Mn$_{x}$CoGe
films relative to bulk MnCoGe, and a magnetization compensation point is
observed in the $x<1$ samples. To understand the behavior, we calculated the
magnetic moments of Mn-antisite defects in MnCoGe with density-function theory
(DFT) calculations. Models constructed from the calculation suggest that films
become ferrimagnetic due to the presence of Mn on the Co and Ge sites. In the
$x<1$ samples, these defects arose from the disorder in the films, whereas for
$x>1$, the excess Mn was driven onto the antisites. Mean field modeling of the
temperature dependence of the magnetization provides additional evidence for
ferrimagnetism. Our mean field and DFT models provide a description of how the
variation in film defects with composition will transition the magnetic
behavior from a compensated (V-type) to an uncompensated (Q-type) ferrimagnet.


  This paper presents a novel approach for the Vision-and-Language Navigation
(VLN) task in continuous 3D environments, which requires an autonomous agent to
follow natural language instructions in unseen environments. Existing
end-to-end learning-based VLN methods struggle at this task as they focus
mostly on utilizing raw visual observations and lack the semantic
spatio-temporal reasoning capabilities which is crucial in generalizing to new
environments. In this regard, we present a hybrid transformer-recurrence model
which focuses on combining classical semantic mapping techniques with a
learning-based method. Our method creates a temporal semantic memory by
building a top-down local ego-centric semantic map and performs cross-modal
grounding to align map and language modalities to enable effective learning of
VLN policy. Empirical results in a photo-realistic long-horizon simulation
environment show that the proposed approach outperforms a variety of
state-of-the-art methods and baselines with over 22% relative improvement in
SPL in prior unseen environments.


  Deep Reinforcement Learning (DRL) has achieved impressive success in many
applications. A key component of many DRL models is a neural network
representing a Q function, to estimate the expected cumulative reward following
a state-action pair. The Q function neural network contains a lot of implicit
knowledge about the RL problems, but often remains unexamined and
uninterpreted. To our knowledge, this work develops the first mimic learning
framework for Q functions in DRL. We introduce Linear Model U-trees (LMUTs) to
approximate neural network predictions. An LMUT is learned using a novel
on-line algorithm that is well-suited for an active play setting, where the
mimic learner observes an ongoing interaction between the neural net and the
environment. Empirical evaluation shows that an LMUT mimics a Q function
substantially better than five baseline methods. The transparent tree structure
of an LMUT facilitates understanding the network's learned knowledge by
analyzing feature influence, extracting rules, and highlighting the
super-pixels in image inputs.


  We report results of a high-resolution numerical-relativity simulation for
the merger of black hole-magnetized neutron star binaries on Japanese
supercomputer "K". We focus on a binary that is subject to tidal disruption and
subsequent formation of a massive accretion torus. We find the launch of
thermally driven torus wind, subsequent formation of a funnel wall above the
torus and a magnetosphere with collimated poloidal magnetic field, and high
Blandford-Znajek luminosity. We show for the first time this picture in a
self-consistent simulation. The turbulence-like motion induced by the
non-axisymmetric magnetorotational instability as well as the Kelvin-Helmholtz
instability inside the accretion torus works as an agent to drive the mass
accretion and converts the accretion energy to thermal energy, which results in
the generation of a strong wind. By an in-depth resolution study, we reveal
that high resolution is essential to draw such a picture. We also discuss the
implication for the r-process nucleosynthesis, the radioactively-powered
transient emission, and short gamma-ray bursts.


  In [K--S 1] it was shown that
  $$ \underset {\pi} \to {\text{Ave}} (\sum_{i=1}^{n}|x_i a_{\pi(i)}|^2)^{\frac
{1}{2}} $$
  is equivalent to an Orlicz norm whose Orlicz function is 2-concave. Here we
give a formula for the sequence $a_1, a_2,....,a_n$ so that the above
expression is equivalent to a given Orlicz norm.


  The main idea of our research is to estimate the physical coalescence time of
the double supermassive black hole (SMBH) system in the centre of NGC 6240
based on the X-ray observations from the Chandra space observatory. The spectra
of the Northern and Southern nuclei were fitted by spectral models from Sherpa
and both presented the narrow component of the Fe K$\alpha$ emission line. It
enabled us to apply the spectral model to these lines and to find relative
offset $\approx0.02$ keV. The enclosed dynamical mass of the central region of
NGC 6240 with radius 1 kpc was estimated $\approx 2.04\times 10^{11} \rm\;
M_{\odot}$. These data allowed us to carry on the high resolution direct N-body
simulations with Newtonian and post-Newtonian (up to $2.5\mathcal{PN}$
correction) dynamics for this particular double SMBH system. As a result, from
our numerical models we approximated the central SMBH binary merging time for
the different binary eccentricities. In our numerical parameters range the
upper limit for the merging time, even for the very small eccentricities, is
still below $\approx70$ Myr. Gravitational waveforms and amplitude-frequency
pictures from such events can be detected using Pulsar Timing Array (PTA)
projects at the last merging phase.


  Following the Nambu mechanics framework we demonstrate that the
non-dissipative part of the Lorenz system can be generated by the intersection
of two quadratic surfaces that form a doublet under the group SL(2,R). All
manifolds are classified into four dinstict classes; parabolic, elliptical,
cylindrical and hyperbolic. The Lorenz attractor is localized by a specific
infinite set of one parameter family of these surfaces. The different classes
correspond to different physical systems. The Lorenz system is identified as a
charged rigid body in a uniform magnetic field with external torque and this
system is generalized to give new strange attractors.


  A first measurement is presented of exclusive photoproduction of $\rho^0$
mesons associated with leading neutrons at HERA. The data were taken with the
H1 detector in the years $2006$ and $2007$ at a centre-of-mass energy of
$\sqrt{s}=319$ GeV and correspond to an integrated luminosity of $1.16$
pb$^{-1}$. The $\rho^0$ mesons with transverse momenta $p_T<1$ GeV are
reconstructed from their decays to charged pions, while leading neutrons
carrying a large fraction of the incoming proton momentum, $x_L>0.35$, are
detected in the Forward Neutron Calorimeter. The phase space of the measurement
is defined by the photon virtuality $Q^2 < 2$ GeV$^2$, the total energy of the
photon-proton system $20 < W_{\gamma p} < 100$ GeV and the polar angle of the
leading neutron $\theta_n < 0.75$ mrad. The cross section of the reaction
$\gamma p \to \rho^0 n \pi^+$ is measured as a function of several variables.
The data are interpreted in terms of a double peripheral process, involving
pion exchange at the proton vertex followed by elastic photoproduction of a
$\rho^0$ meson on the virtual pion. In the framework of one-pion-exchange
dominance the elastic cross section of photon-pion scattering, $\sigma^{\rm
el}(\gamma\pi^+ \to \rho^0\pi^+)$, is extracted. The value of this cross
section indicates significant absorptive corrections for the exclusive reaction
$\gamma p\to\rho^0 n \pi^+$.


  The measurement of $K^*(892)^0$ resonance production via its $K^+ \pi^-$
decay mode in inelastic p+p collisions at beam momenta 40--158 GeV/c
($\sqrt{s_{NN}}$=8.8--17.3 GeV) is presented. The data were recorded by the
NA61/SHINE hadron spectrometer at the CERN Super Proton Synchrotron. The
analysis of $K^*(892)^0$ was done with the template method. The results include
the double differential spectra $d^2 n/(dydp_T)$, $d^2 n/(m_T dm_T dy)$ as well
as dn/dy spectra.


  We present a dynamic decomposition analysis of the wake flow in
fluid-structure interaction (FSI) systems under both laminar and turbulent flow
conditions. Of particular interest is to provide the significance of
low-dimensional wake flow features and their interaction dynamics to sustain
the free vibration of a square cylinder at a relatively low mass ratio. To
obtain the high-dimensional data, we employ a body-conforming variational
fluid-structure interaction solver based on the recently developed partitioned
iterative scheme and the dynamic subgrid-scale turbulence model for a moderate
Reynolds number. The snapshot data from high-dimensional FSI simulations are
projected to a low-dimensional subspace using the proper orthogonal
decomposition (POD). We utilize each corresponding POD mode for detecting
features: the vortex street, the shear layer and the near-wake bubble. We find
that the vortex shedding modes contribute solely to the lift force, while the
near-wake and shear layer modes play a dominating role to the drag force. We
further examine the fundamental mechanism of this dynamical behavior and
propose a force decomposition technique via low-dimensional approximation. We
ascertain quantitatively that the shear layer feeds the vorticity flux to the
wake vortices and the near-wake bubble during the wake-body synchronization.
Based on the decomposition of wake dynamics, we suggest an interaction cycle
for the frequency lock-in during the wake-body interaction, which provides the
inter-relationship between the high amplitude motion and the dominating wake
features. Through our investigation of wake-body synchronization below critical
Re range, we discover that the bluff body can undergo a synchronized
high-amplitude vibration due to flexibility-induced unsteadiness. The
interaction cycle for the wake-synchronization is found to be valid for the
turbulent wake flow.


  We perform a resolvent analysis of a compressible turbulent jet, where the
optimisation domain of the response modes is located in the acoustic field,
excluding the hydrodynamic region, in order to promote acoustically efficient
modes. We examine the properties of the acoustic resolvent and assess its
potential for jet-noise modelling, focusing on the subsonic regime. Resolvent
forcing modes, consistent with previous studies, are found to contain
supersonic waves associated with Mach wave radiation in the response modes.
This differs from the standard resolvent in which hydrodynamic instabilities
dominate. We compare resolvent modes with SPOD modes educed from LES data.
Acoustic resolvent response modes generally have better alignment with acoustic
SPOD modes than standard resolvent response modes. For the optimal mode, the
angle of the acoustic beam is close to that found in SPOD modes for moderate
frequencies. However, there is no significant separation between the singular
values of the leading and sub-optimal modes. Some suboptimal modes are
furthermore shown to contain irrelevant structure for jet noise. Thus, even
though it contains essential acoustic features absent from the standard
resolvent approach, the SVD of the acoustic resolvent alone is insufficient to
educe a low-rank model for jet noise. But because it identifies the prevailing
mechanisms of jet noise, it provides valuable guidelines in the search of a
forcing model (Karban \textit{et al.} An empirical model of noise sources in
subsonic jets. \textit{Journal of Fluid Mechanics} (2023): A18).


  The planned LBL experiments will be able to prove the hypothesis of flavor
oscillation between muon and tau neutrinos. We explore the possibility of a
second generation long baseline experiment at very long baseline, i.e. L in the
range 5000-7000 km. This distance requires intense neutrino beams that could be
available from very intense muon beams as those needed for $\mu$ colliders.
Such baselines allow the study of neutrino oscillations with $E/L \approx
2\times 10^{-3} eV^2$ with neutrinos of energy $E_\nu \approx 10 GeV$, i.e.
above tau threshold. Moreover, matter effects inside the Earth could lead to
observable effects in $\nu_e \to \nu_\mu$ oscillations. These effects are
interchanged between neutrinos and antineutrinos, and therefore they can be
tested by comparing the oscillated spectra obtained running the storage ring
with positive and negative muons.


  The automorphism group of the vertex operator algebra $V_L^+$ is studied by
using its action on isomorphism classes of irreducible $V_L^+$-modules. In
particular, the shape of the automorphism group of $V_L^+$ is determined when
$L$ is isomorphic to an even unimodular lattice without roots, $\sqrt2R$ for an
irreducible root lattice $R$ of type $ADE$ and the Barnes-Wall lattice of rank
16.


  Building on Talagrand's proof of the Hoffmann-J{\o}rgensen inequality for
$L_p$ spaces and its version for the exponential Orlicz spaces we provide a
full characterization of Orlicz functions $\Psi$ for which an analogous
inequality holds in the Orlicz space $L_\Psi(F)$, where $F$ is an arbitrary
Banach space.
  As an application we present a characterization of Talagrand-type
concentration inequality for suprema of empirical processes with envelope in
$L_\Psi$ (equivalently for sums of independent $F$-valued random variables in
$L_\Psi(F)$). This result generalizes in particular an inequality by the
first-named author concerning exponentially integrable summands and a recent
inequality due to Chamakh-Gobet-Liu on summands with $\beta$-heavy tails.
Another corollary concerns concentration for convex functions of independent,
unbounded random variables, generalizing recent results due to
Klochkov-Zhivotovskiy and Sambale.
  We also obtain a corollary concerning boundedness in $L_\Psi(F)$ of partial
sums of a series of independent random variables, generalizing the original
result by Hoffmann-J{\o}rgensen.


  In this paper we consider an obstacle problem for a generalization of the
p-elastic energy among graphical curves with fixed ends. Taking into account
that the Euler--Lagrange equation has a degeneracy, we address the question
whether solutions have a flat part, i.e. an open interval where the curvature
vanishes. We also investigate which is the main cause of the loss of
regularity, the obstacle or the degeneracy. Moreover, we give several
conditions on the obstacle that assure existence and nonexistence of solutions.
The analysis can be refined in the special case of the p-elastica functional,
where we obtain sharp existence results and uniqueness for symmetric
minimizers.


  Functional Connectivity between brain regions is known to be altered in
Alzheimer's disease, and promises to be a biomarker for early diagnosis of the
disease. While several approaches for functional connectivity obtain an
un-directed network representing stochastic associations (correlations) between
brain regions, association does not necessarily imply causation. In contrast,
Causal Functional Connectivity is more informative, providing a directed
network representing causal relationships between brain regions. In this paper,
we obtained the causal functional connectome for the whole brain from
recordings of resting-state functional magnetic resonance imaging (rs-fMRI) for
subjects from three clinical groups: cognitively normal, mild cognitive
impairment, and Alzheimer's disease. We applied the recently developed
Time-aware PC (TPC) algorithm to infer the causal functional connectome for the
whole brain. TPC supports model-free estimation of whole brain causal
functional connectivity based on directed graphical modeling in a time series
setting. We then perform an exploratory analysis to identify the causal brain
connections between brain regions which have altered strengths between pairs of
subject groups, and over the three subject groups, based on edge-wise p-values
from statistical tests. We used the altered causal brain connections thus
obtained to compile a comprehensive list of brain regions impacted by
Alzheimer's disease according to the current data set. The brain regions thus
identified are found to be in agreement with literature on brain regions
impacted by Alzheimer's disease, published by researchers from clinical/medical
institutions.


  In this paper, we illustrated one scenario to modify the
Ivanenko-Landau-K\"ahler equation. Since Ivanenko and Landau introduced the
equation in 1928, the equation has been regarded as having a certain role as a
fermion in particular in the discrete Lattice. Also, although it correctly is
formulated as an alternative classical field equation by the Ideal projection
for the Dirac equation in the Minkowski space-time, so does it only in that
flat geometry. I. M. Benn and R. W. Tucker in 1985 and Yu. N. Obukhov and S. N.
Solodukhin in 1994 suggested two resolutions respectively. They modified the
equation in order for it to make senses as an alternative for the Dirac
equation in the general space-time. This paper advances a still another
approach, however in the Minkowski space yet, as the first stage toward the
generalization. Two ingredients for the modifications are essential. One is the
restriction of the space of anti-symmetric tensor field to only its
subalgebras, not to its Ideals. The other is the modification on the mass term
for the equation to mean the eigenvalue problem generating physical states. The
Vector U(1) and the Axial U(1) symmetries built in the modified equation are
described.


  If neutrinos are Dirac particles, their right-handed partners must be present
in the theory. Once introduced in the Standard Model (SM), the difference
between the baryon number $B$ and the lepton number $L$ can be promoted to a
local $U(1)_{B-L}$ symmetry since the corresponding gauge anomalies can be
canceled by the right-handed neutrinos. Furthermore, the extremely small
neutrino mass can be explained naturally if it is originated from the quantum
correction. In this work, we propose simplest models of radiative Dirac
neutrino mass using only $U(1)_{B-L}$ symmetry, and without introducing
additional fermions and without imposing ad hoc symmetries. In this simple
framework, we provide minimal models where Dirac neutrino mass appears at the
(i) one-loop, (ii) two-loop and (iii) three-loop. By performing systematic
analysis, we show that the minimal one-loop model requires three beyond SM
scalar multiplets, whereas minimal two-loop and three-loop models require five.
The presented two-loop and three-loop Dirac mass models have not appeared in
the literature before.


  The 1998 September outburst of the black-hole X-ray binary XTE J1550-564 was
monitored at X-ray, optical and radio wavelengths. We divide the outburst
sequence into five phases and discuss their multiwavelength properties. The
outburst starts with a hard X-ray spike, while the soft X-ray flux rises with a
longer timescale. We suggest that the onset of the outburst is determined by an
increased mass transfer rate from the companion star, but the outburst
morphology is determined by the distribution of specific angular momentum in
the accreting matter. The companion in XTE J1550-564 is likely to be an active
magnetic star, with a surface field strong enough to influence the dynamics of
mass transfer. We suggest that its magnetic field can create a magnetic bag
capable of confining gas inside the Roche lobe of the primary. The impulsive
rise in the hard X-rays is explained by the inflow of material with low angular
momentum onto the black hole, on a free-fall timescale, when the magnetic
confinement breaks down. At the same time, high angular momentum matter,
transferred via ordinary Roche-lobe overflow, is responsible for the formation
of a disk.


  Phase space dynamics in classical mechanics is described by transport along
trajectories. Anharmonic quantum mechanical systems do not allow for a
trajectory-based description of their phase space dynamics. This invalidates
some approaches to quantum phase space studies. We first demonstrate the
absenceof trajectories in general terms. We then give an explicit proof for all
quantum phase space distributions with negative values: we show that the
generation of coherences in anharmonic quantum mechanical systems is
responsible for the occurrence of singularities in their phase space velocity
fields, and vice versa. This explains numerical problems repeatedly reported in
the literature, and provides deeper insight into the nature of quantum phase
space dynamics.


  In this paper we introduce a rule-based, compositional, and hierarchical
modeling of action using Therbligs as our atoms. Introducing these atoms
provides us with a consistent, expressive, contact-centered representation of
action. Over the atoms we introduce a differentiable method of rule-based
reasoning to regularize for logical consistency. Our approach is complementary
to other approaches in that the Therblig-based representations produced by our
architecture augment rather than replace existing architectures'
representations. We release the first Therblig-centered annotations over two
popular video datasets - EPIC Kitchens 100 and 50-Salads. We also broadly
demonstrate benefits to adopting Therblig representations through evaluation on
the following tasks: action segmentation, action anticipation, and action
recognition - observing an average 10.5\%/7.53\%/6.5\% relative improvement,
respectively, over EPIC Kitchens and an average 8.9\%/6.63\%/4.8\% relative
improvement, respectively, over 50 Salads. Code and data will be made publicly
available.


  We consider the entropy associated to the phonons generated via the Hawking
mechanism in a sonic hole in a Bose-Einsten condensate. In a previous paper, we
looked at the (1+1)-dimensional case both in the hydrodynamic limit and in the
case when high-frequency dispersion is taken in account. Here, we extend the
analysis, based on the 't Hooft brick wall model, by including transverse
excitations. We show that they can cure the infrared divergence that appears in
the (1+1)-dimensional case, by acting as an effective mass for the phonons. In
the hydrodynamic limit, where high-frequency dispersion is neglected, the
ultraviolet divergence remains. On the contrary, in the dispersive case the
entropy not only is finite, but it is completely fixed by the geometric
parameters of the system.


  We experimentally demonstrate an all-optical programmable thresholder on a
silicon photonic circuit. By exploiting the nonlinearities in a
resonator-enhanced Mach-Zehnder interferometer (MZI), the proposed optical
thresholder can discriminate two optical signals with very similar amplitudes.
We experimentally achieve a signal contrast enhancement of 40, which leads to a
bit error rate (BER) improvement by 5 orders of magnitude and a receiver
sensitivity improvement of 11 dB. We present the thresholding function of our
device and validate the function with experimental data. Furthermore, we
investigate potential device speed improvement by reducing the carrier
lifetime.