  Spiking Neural Networks (SNNs) are distributed trainable systems whose
computing elements, or neurons, are characterized by internal analog dynamics
and by digital and sparse synaptic communications. The sparsity of the synaptic
spiking inputs and the corresponding event-driven nature of neural processing
can be leveraged by hardware implementations that have demonstrated significant
energy reductions as compared to conventional Artificial Neural Networks
(ANNs). Most existing training algorithms for SNNs have been designed either
for biological plausibility or through conversion from pre-trained ANNs via
rate encoding. This paper aims at providing an introduction to SNNs by focusing
on a probabilistic signal processing methodology that enables the direct
derivation of learning rules leveraging the unique time encoding capabilities
of SNNs. To this end, the paper adopts discrete-time probabilistic models for
networked spiking neurons, and it derives supervised and unsupervised learning
rules from first principles by using variational inference. Examples and open
research problems are also provided.


  We consider the asymptotic behavior of the fluctuations for the empirical
measures of interacting particle systems with singular kernels. We prove that
the sequence of fluctuation processes converges in distribution to a
generalized Ornstein-Uhlenbeck process. Our result considerably extends
classical results to singular kernels, including the Biot-Savart law. The
result applies to the point vortex model approximating the 2D incompressible
Navier-Stokes equation and the 2D Euler equation. We also obtain Gaussianity
and optimal regularity of the limiting Ornstein-Uhlenbeck process. The method
relies on the martingale approach and the Donsker-Varadhan variational formula,
which transfers the uniform estimate to some exponential integrals. Estimation
of those exponential integrals follows by cancellations and combinatorics
techniques and is of the type of large deviation principle.


  We investigate the use of jets to measure transverse momentum dependent
distributions (TMDs). The example we use to present our framework is the dijet
momentum decorrelation at lepton colliders. Translating this momentum
decorrelation into an angle $\theta \ll 1$, we analyze the factorization of the
cross section for the cases $\theta \gg R$, $\theta \sim R$ and $\theta \ll R$,
where $R$ is the jet radius. Critically, for the Winner-Take-All axis, the jet
TMD has the same double-scale renormalization group evolution as TMD
fragmentation functions for all radii $R$. TMD fragmentation functions in
factorization theorems may then simply be replaced by the jet TMDs we
calculate, and all ingredients to perform the resummation to
next-to-next-to-leading logarithmic accuracy are available. Our approach also
applies to semi-inclusive deep inelastic scattering (SIDIS), where a jet
instead of a hadron is measured in the final state, and we find a clean method
to probe the intrinsic transverse momentum of quarks and gluons in the proton
that is less sensitive to final-state nonperturbative effects.


  We give a proof of the non-perturbative no hair theorems for a massive 2-form
field with 3-form field strength for general stationary axisymmetric and static
(anti)-de Sitter or asymptotically flat black hole spacetimes with some
suitable geometrical properties. The generalization of this result for higher
form fields is discussed. Next, we discuss the perturbative no hair theorems
for massive spin-1/2 fields for general static backgrounds with electric or
magnetic charge. Some generalization of this result for stationary axisymmetric
spacetimes are also discussed. All calculations are done in arbitrary spacetime
dimensions.


  Speech emotion recognition (SER) systems often struggle in real-world
environments, where ambient noise severely degrades their performance. This
paper explores a novel approach that exploits prior knowledge of testing
environments to maximize SER performance under noisy conditions. To address
this task, we propose a text-guided, environment-aware training where an SER
model is trained with contaminated speech samples and their paired noise
description. We use a pre-trained text encoder to extract the text-based
environment embedding and then fuse it to a transformer-based SER model during
training and inference. We demonstrate the effectiveness of our approach
through our experiment with the MSP-Podcast corpus and real-world additive
noise samples collected from the Freesound repository. Our experiment indicates
that the text-based environment descriptions processed by a large language
model (LLM) produce representations that improve the noise-robustness of the
SER system. In addition, our proposed approach with an LLM yields better
performance than our environment-agnostic baselines, especially in low
signal-to-noise ratio (SNR) conditions. When testing at -5dB SNR level, our
proposed method shows better performance than our best baseline model by 31.8 %
(arousal), 23.5% (dominance), and 9.5% (valence).


  We consider the fully overheated single-electron transistor, where the heat
balance is determined entirely by electron transfers. We find three distinct
transport regimes corresponding to cotunneling, single-electron tunneling, and
a competition between the two. We find an anomalous sensitivity to temperature
fluctuations at the crossover between the two latter regimes that manifests in
an exceptionally large Fano factor of current noise.


  At one loop, quantum kinks are described by a sum of quantum harmonic
oscillator Hamiltonians, and so their spectra are known exactly. We find the
first correction beyond one loop to the quantum states corresponding to kinks
with an excited bound or unbound normal mode, and also the corresponding
two-loop correction to the energy cost of exciting the normal mode. In the case
of unbound normal modes, this correction is equal to sum of the corresponding
nonrelativistic kinetic energy plus the usual one-loop correction to the mass
of the corresponding plane wave in the absence of a kink. We also sketch a
diagrammatic method for such calculations.


  There is much interest in the Hierarchical Dirichlet Process Hidden Markov
Model (HDP-HMM) as a natural Bayesian nonparametric extension of the ubiquitous
Hidden Markov Model for learning from sequential and time-series data. However,
in many settings the HDP-HMM's strict Markovian constraints are undesirable,
particularly if we wish to learn or encode non-geometric state durations. We
can extend the HDP-HMM to capture such structure by drawing upon
explicit-duration semi-Markovianity, which has been developed mainly in the
parametric frequentist setting, to allow construction of highly interpretable
models that admit natural prior information on state durations.
  In this paper we introduce the explicit-duration Hierarchical Dirichlet
Process Hidden semi-Markov Model (HDP-HSMM) and develop sampling algorithms for
efficient posterior inference. The methods we introduce also provide new
methods for sampling inference in the finite Bayesian HSMM. Our modular Gibbs
sampling methods can be embedded in samplers for larger hierarchical Bayesian
models, adding semi-Markov chain modeling as another tool in the Bayesian
inference toolbox. We demonstrate the utility of the HDP-HSMM and our inference
methods on both synthetic and real experiments.


  We present a general sample reweighting scheme and its underlying theory for
the integration of an unknown function with low dimensionality. Our method
produces better results than standard weighting schemes for common sampling
strategies, while avoiding bias. Our main insight is to link the weight
derivation to the function reconstruction process during integration. The
implementation of our solution is simple and results in an improved convergence
behavior. We illustrate its benefit by applying our method to multiple Monte
Carlo rendering problems.


  Quantized circulation, absence of Galilean invariance due to a clamped normal
component, and the vortex mutual friction are the major factors that make
superfluid turbulence behave in a way different from that in classical fluids.
The model is developed for the onset of superfluid turbulence that describes
the initial avalanche-like multiplication of vortices into a turbulent vortex
tangle.


  We propose a general class of scalar-teleparallel theories, which are based
on a scalar field which is coupled to a flat connection with torsion and
nonmetricity, and study its post-Newtonian limit using the parametrized
post-Newtonian formalism. We find that among this class there are theories
whose post-Newtonian limit fully agrees with general relativity; for others
only the parameters $\beta$ and $\gamma$ deviate from their general relativity
values $\beta = \gamma = 1$, while all other parameters remain the same, thus
preserving total momentum conservation, local Lorentz invariance and local
position invariance; finally, we also find theories whose post-Newtonian limit
is pathological. Our main result is a full classification of the proposed
theories into these different cases. We apply our findings to a number of
simpler classes of theories and show that for these a subset of the
aforementioned cases can be found.


  Are microlensing searches likely to discover planets that harbor life? Given
our present state of knowledge, this is a difficult question to answer. We
therefore begin by asking a more narrowly focused question: are conditions on
planets discovered via microlensing likely to be similar to those we experience
on Earth? In this paper I link the microlensing observations to the well-known
"Goldilocks Problem" (conditions on the Earth-like planets need to be "just
right"), to find that Earth-like planets discovered via microlensing are likely
to be orbiting stars more luminous than the sun. This means that light from the
planetary system's central star may contribute a significant fraction of the
baseline flux relative to the star that is lensed. Such blending of light from
the lens with light from the lensed source can, in principle, limit our ability
to detect these events. This turns out not to be a significant problem,
however. A second consequence of blending is the opportunity to determine the
spectral type of the lensed spectral type of the lensed star. This
circumstance, plus the possibility that finite-source-size effects are
important, implies that some meaningful follow-up observations are likely to be
possible for a subset Earth-like planets discovered via microlensing. In
addition, calculations indicate that reasonable requirements on the planet's
density and surface gravity imply that the mass of Earth-like planets is likely
to be within a factor of $\sim 15$ of an Earth mass.


  A complete choice of generators of the center of the enveloping algebras of
real quasi-simple Lie algebras of orthogonal type, for arbitrary dimension, is
obtained in a unified setting. The results simultaneously include the well
known polynomial invariants of the pseudo-orthogonal algebras $so(p,q)$, as
well as the Casimirs for many non-simple algebras such as the inhomogeneous
$iso(p,q)$, the Newton-Hooke and Galilei type, etc., which are obtained by
contraction(s) starting from the simple algebras $so(p,q)$. The dimension of
the center of the enveloping algebra of a quasi-simple orthogonal algebra turns
out to be the same as for the simple $so(p,q)$ algebras from which they come by
contraction. The structure of the higher order invariants is given in a
convenient "pyramidal" manner, in terms of certain sets of "Pauli-Lubanski"
elements in the enveloping algebras. As an example showing this approach at
work, the scheme is applied to recovering the Casimirs for the (3+1)
kinematical algebras. Some prospects on the relevance of these results for the
study of expansions are also given.


  We study quasi-stationary distribution of the continuous-state branching
process with competition introduced in Berestycki, Fittipaldi and Fontbona\
(Probab. Theory Relat. Fields, 2018). This process is constructed as the unique
strong solution to a stochastic integral equation with jumps. An important
example is the logistic branching process constructed in Lambert (Ann. Appl.
Probab., 2005). We establish the strong Feller property,trajectory Feller
property, Lyapunov condition, weak Feller property and irreducibility,
respectively. These properties together allow us to prove that when the
competition term is strong enough near $+\infty$, then there is a unique
quasi-stationary distribution, which attracts all initial distributions with
exponential rates.


  Project GRAND, a proportional wire chamber array, is used to examine the
decreased counting rate of ground level muons during the Forbush decrease event
of September 11, 2005. Data are presented and compared to that of other cosmic
ray monitors. A directional study of the Forbush decrease was undertaken and
precursor anisotropies to this geomagnetic storm were studied utilizing GRAND's
angular resolution.


  Video Corpus Moment Retrieval (VCMR) is a new video retrieval task aimed at
retrieving a relevant moment from a large corpus of untrimmed videos using a
text query. The relevance between the video and query is partial, mainly
evident in two aspects:~(1)~Scope: The untrimmed video contains many frames,
but not all are relevant to the query. Strong relevance is typically observed
only within the relevant moment.~(2)~Modality: The relevance of the query
varies with different modalities. Action descriptions align more with visual
elements, while character conversations are more related to textual
information.Existing methods often treat all video contents equally, leading to
sub-optimal moment retrieval. We argue that effectively capturing the partial
relevance between the query and video is essential for the VCMR task. To this
end, we propose a Partial Relevance Enhanced Model~(PREM) to improve VCMR. VCMR
involves two sub-tasks: video retrieval and moment localization. To align with
their distinct objectives, we implement specialized partial relevance
enhancement strategies. For video retrieval, we introduce a multi-modal
collaborative video retriever, generating different query representations for
the two modalities by modality-specific pooling, ensuring a more effective
match. For moment localization, we propose the focus-then-fuse moment
localizer, utilizing modality-specific gates to capture essential content. We
also introduce relevant content-enhanced training methods for both retriever
and localizer to enhance the ability of model to capture relevant content.
Experimental results on TVR and DiDeMo datasets show that the proposed model
outperforms the baselines, achieving a new state-of-the-art of VCMR. The code
is available at \url{https://github.com/hdy007007/PREM}.


  The process $\psi(3686) \to \pi^0 h_c, h_c \to \gamma \eta_c$ has been
studied with a data sample of $106 \pm 4$ million $\psi(3686)$ events collected
with the BESIII detector at the BEPCII storage ring. The mass and width of the
$P$-wave charmonium spin-singlet state $h_c(^1P_1)$ are determined by
simultaneously fitting distributions of the $\pi^0$ recoil mass for 16
exclusive $\eta_c$ decay modes. The results, $M(\hc) = 3525.31 \pm 0.11 {\rm
(stat.)} \pm 0.14 {\rm (syst.)}$\,MeV/$c^2$ and $\Gamma(\hc) = 0.70 \pm 0.28
\pm 0.22$\,MeV, are consistent with and more precise than previous
measurements. We also determine the branching ratios for the 16 exclusive
$\eta_c$ decay modes, five of which have not been measured previously. New
measurements of the $\eta_c$ line-shape parameters in the $E1$ transition
$h_c\to\gamma\eta_c$ are made by selecting candidates in the $h_c$ signal
sample and simultaneously fitting the hadronic mass spectra for the 16 $\eta_c$
decay channels. The resulting $\eta_c$ mass and width values are $M(\eta_c) =
2984.49 \pm 1.16 \pm 0.52$\,MeV/$c^2$ and $\Gamma(\eta_c) = 36.4 \pm 3.2 \pm
1.7$\,MeV.


  Recently an N=1 supersymmetric model of BCS superconductivity was proposed
realizing spontaneous symmetry breaking of a U(1)_R symmetry. Due to scalar
contributions the superconducting phase transition turned out to be first order
rather than second order as in standard BCS theory. Here we consider the
effects of an external magnetic field and spatial fluctuations of the gap in
that model. This allows us to compute the magnetic penetration length and the
coherence length, and also to distinguish between type I and type II
superconductors. We compare the supersymmetric and standard relativistic BCS
results, where the main differences come from the different orders of the phase
transition.


  Cosmological gamma-ray bursts are potentially associated with systems
harboring a black rotating black hole. Calorimetry on yet "unseen" emissions in
gravitational waves from a surrounding torus may provide a measure for its
rotational energy. We introduce a compactness parameter $\alpha=2\pi\int fdE$
for the fluence $E$ and frequency $f$ in gravitational waves. For black
hole-torus systems, $\alpha\simeq 2\pi Ef\simeq 0.005-0.05$ may exceed the
upper bound $\alpha^*\simeq 0.005$ for rapidly rotating neutron stars. A
duration in gravitational radiation consistent with the redshift corrected
durations of the BATSE catalogue defines an association with long GRBs. This
promises a new test for Kerr black holes as objects in Nature.


  An experiment for the speckle reconstruction of solar features was developed
for observing the partial eclipse of the sun as viewed from Bangalore on
October 24, 1995. No data could be obtained because of cloudy sky but the
experimental details are described.


  Disordered hyperuniformity is a description of hidden correlations in point
distributions revealed by an anomalous suppression in fluctuations of local
density at various coarse-graining length scales. In the absorbing phase of
models exhibiting an active-absorbing state transition, this suppression
extends up to a hyperuniform length scale that diverges at the critical point.
Here, we demonstrate the existence of additional many-body correlations beyond
hyperuniformity. These correlations are hidden in the higher moments of the
probability distribution of the local density, and extend up to a longer length
scale with a faster divergence than the hyperuniform length on approaching the
critical point. Our results suggest that a hidden order beyond hyperuniformity
may generically be present in complex disordered systems.


  We present CURL: Contrastive Unsupervised Representations for Reinforcement
Learning. CURL extracts high-level features from raw pixels using contrastive
learning and performs off-policy control on top of the extracted features. CURL
outperforms prior pixel-based methods, both model-based and model-free, on
complex tasks in the DeepMind Control Suite and Atari Games showing 1.9x and
1.2x performance gains at the 100K environment and interaction steps benchmarks
respectively. On the DeepMind Control Suite, CURL is the first image-based
algorithm to nearly match the sample-efficiency of methods that use state-based
features. Our code is open-sourced and available at
https://github.com/MishaLaskin/curl.


  We develop an axiomatic theory of information acquisition that captures the
idea of constant marginal costs in information production: the cost of
generating two independent signals is the sum of their costs, and generating a
signal with probability half costs half its original cost. Together with
Blackwell monotonicity and a continuity condition, these axioms determine the
cost of a signal up to a vector of parameters. These parameters have a clear
economic interpretation and determine the difficulty of distinguishing states.


  The decay of $^{56}Ni^*$, formed in $^{32}S+^{24}Mg$ reaction at the incident
energies $E_{cm}$=51.6 and 60.5 MeV, is calculated as a cluster decay process
within the Preformed Cluster-decay Model (PCM) of Gupta et al. re-formulated
for hot compound systems. The observed deformed shapes of the exit channel
fragments are simulated by introducing the neck-length parameter at the
scission configuration, which nearly coincides the $^{56}Ni$ saddle
configuration. This is the only parameter of the model, which though is also
defined in terms of the binding energy of the hot compound system and the
ground-state binding energies of the various emitted fragments. The calculated
s-wave cross sections for nuclear shapes with outgoing fragments separated
within nuclear proximity limit (here $\sim$0.3 fm) can be compared with the
experimental data, and the TKEs are found to be in reasonably good agreement
with experiments for the angular momentum effects added in the sticking limit
for the moment of inertia. Also, some light particle production (other than the
statistical evaporation residue, not treated here) is predicted at these
energies and, interestingly, $^4He$, which belongs to evaporation residue, is
found missing as a dynamical cluster-decay fragment.


  We investigate and solve the weak noise theory for the semi-discrete
O'Connell-Yor directed polymer. In the large deviation regime, the most
probable evolution of the partition function obeys a classical non-linear
system which is a non-standard discretisation of the nonlinear Schrodinger
equation with mixed initial-final conditions. We show that this system is
integrable and find its general solution through an inverse scattering method
and a novel Fredholm determinant framework that we develop. This allows to
obtain the large deviation rate function of the free energy of the polymer
model from its conserved quantities and to study its convergence to the large
deviations of the Kardar-Parisi-Zhang equation. Our model also degenerates to
the classical Toda chain, which further substantiates the applicability of our
Fredholm framework.


  A textile structure is a periodic arrangement of threads in the thickened
plane. A topological classification of textile structures is harder than for
classical knots and links that are non-periodic and restricted to a bounded
region. The first important problem is to encode all textile structures in a
simple combinatorial way. This paper extends the notion of the Gauss code in
classical knot theory, providing a tool for topological computation on these
structures. As a first application, we present a linear time algorithm for
determining whether a code represents a textile in the physical sense. This
algorithm, along with invariants of textile structures, allowed us for the
first time to classify all oriented textile structures woven from a single
component up to complexity five.


  The Fermi-LAT collaboration recently confirmed EGRET finding of a discrepancy
between the observed longitudinal profile of gamma-ray diffuse emission from
the Galaxy and that computed with GALPROP assuming that cosmic rays are
produced by Galactic supernova remnants. The accurate Fermi-LAT measurements
make this anomaly hardly explainable in terms of conventional diffusion
schemes. Here we use DRAGON numerical diffusion code to implement a physically
motivated scenario in which the diffusion coefficient is spatially correlated
to the source density. We show that under those conditions we are able to
reproduce the observed flat emissivity profile in the outer Galaxy with no need
to change the source term, the diffusion halo height, or the CO-H2 conversion
factor (XCO) with respect to their preferred values/distributions. We also show
that our models are compatible with gamma-ray longitudinal profiles measured by
Fermi-LAT, and still provide a satisfactory fit of all observed
secondary-to-primary ratios, such as B/C and antiprotons/protons.


  We prove that a uniformly chosen proper $3$-coloring of the $d$-dimensional
discrete torus has a very rigid structure when the dimension $d$ is
sufficiently high. We show that with high probability the coloring takes just
one color on almost all of either the even or the odd sub-torus. In particular,
one color appears on nearly half of the torus sites. This model is the zero
temperature case of the $3$-state anti-ferromagnetic Potts model from
statistical physics.
  Our work extends previously obtained results for the discrete torus with
specific boundary conditions. The main challenge in this extension is to
overcome certain topological obstructions which appear when no boundary
conditions are imposed on the model. Locally, a proper $3$-coloring defines the
discrete gradient of an integer-valued height function which changes by exactly
one between adjacent sites. However, these locally-defined functions do not
always yield a height function on the entire torus, as the gradients may
accumulate to a non-zero quantity when winding around the torus. Our main
result is that in high dimensions, a global height function is well defined
with high probability, allowing to deduce the rigid structure of the coloring
from previously known results. Moreover, the probability that the gradients
accumulate to a vector $m$, corresponding to the winding in each of the $d$
directions, is at most exponentially small in the product of $\|m\|_\infty$ and
the area of a cross-section of the torus.
  In the course of the proof we develop discrete analogues of notions from
algebraic topology. This theory is developed in some generality and may be of
use in the study of other models.


  When robots retrieve specific objects from cluttered scenes, such as home and
warehouse environments, the target objects are often partially occluded or
completely hidden. Robots are thus required to search, identify a target
object, and successfully grasp it. Preceding works have relied on pre-trained
object recognition or segmentation models to find the target object. However,
such methods require laborious manual annotations to train the models and even
fail to find novel target objects. In this paper, we propose an Image-driven
Object Searching and Grasping (IOSG) approach where a robot is provided with
the reference image of a novel target object and tasked to find and retrieve
it. We design a Target Similarity Network that generates a probability map to
infer the location of the novel target. IOSG learns a hierarchical policy; the
high-level policy predicts the subtask type, whereas the low-level policies,
explorer and coordinator, generate effective push and grasp actions. The
explorer is responsible for searching the target object when it is hidden or
occluded by other objects. Once the target object is found, the coordinator
conducts target-oriented pushing and grasping to retrieve the target from the
clutter. The proposed pipeline is trained with full self-supervision in
simulation and applied to a real environment. Our model achieves a 96.0% and
94.5% task success rate on coordination and exploration tasks in simulation
respectively, and 85.0% success rate on a real robot for the search-and-grasp
task.


  We use a functional approach to study various aspects of the quantum
effective dynamics of moving, planar, dispersive mirrors, coupled to scalar or
Dirac fields, in different numbers of dimensions. We first compute the
Euclidean effective action, and use it to derive the imaginary part of the
`in-out' effective action. We also obtain, for the case of the real scalar
field in 1+1 dimensions, the Schwinger-Keldysh effective action and a
semiclassical Langevin equation that describes the motion of the mirror
including noise and dissipative effects due to its coupling to the quantum
fields.


  We introduce the mean topological dimension for random bundle
transformations, and show that continuous bundle random dynamical systems with
finite topological entropy, or the small boundary property have zero mean
topological dimensions.


  In this paper, we propose an optimization-based sparse learning approach to
identify the set of most influential reactions in a chemical reaction network.
This reduced set of reactions is then employed to construct a reduced chemical
reaction mechanism, which is relevant to chemical interaction network modeling.
The problem of identifying influential reactions is first formulated as a
mixed-integer quadratic program, and then a relaxation method is leveraged to
reduce the computational complexity of our approach. Qualitative and
quantitative validation of the sparse encoding approach demonstrates that the
model captures important network structural properties with moderate
computational load.


  Image segmentation is the task of associating pixels in an image with their
respective object class labels. It has a wide range of applications in many
industries including healthcare, transportation, robotics, fashion, home
improvement, and tourism. Many deep learning-based approaches have been
developed for image-level object recognition and pixel-level scene
understanding-with the latter requiring a much denser annotation of scenes with
a large set of objects. Extensions of image segmentation tasks include 3D and
video segmentation, where units of voxels, point clouds, and video frames are
classified into different objects. We use "Object Segmentation" to refer to the
union of these segmentation tasks. In this monograph, we investigate both
traditional and modern object segmentation approaches, comparing their
strengths, weaknesses, and utilities. We examine in detail the wide range of
deep learning-based segmentation techniques developed in recent years, provide
a review of the widely used datasets and evaluation metrics, and discuss
potential future research directions.


  We consider Laplacians on periodic equilateral metric graphs. The spectrum of
the Laplacian consists of an absolutely continuous part (which is a union of an
infinite number of non-degenerated spectral bands) plus an infinite number of
flat bands, i.e., eigenvalues of infinite multiplicity. We estimate the
Lebesgue measure of the bands on a finite interval in terms of geometric
parameters of the graph. The proof is based on spectral properties of discrete
Laplacians.


  We study the diffusion of Brownian particles on the surface of a sphere and
compute the distribution of solid angles enclosed by the diffusing particles.
This function describes the distribution of geometric phases in two state
quantum systems (or polarised light) undergoing random evolution. Our results
are also relevant to recent experiments which observe the Brownian motion of
molecules on curved surfaces like micelles and biological membranes. Our
theoretical analysis agrees well with the results of computer experiments.


  There is growing interest in visual data management systems that support
queries with specialized operations ranging from resizing an image to running
complex machine learning models. With a plethora of such operations, the basic
need to receive query responses in minimal time takes a hit, especially when
the client desires to run multiple such operations in a single query. Existing
systems provide an ad-hoc approach where different solutions are clubbed
together to provide an end-to-end visual data management system. Unlike such
solutions, the Visual Data Management System (VDMS) natively executes queries
with multiple operations, thus providing an end-to-end solution. However, a
fixed subset of native operations and a synchronous threading architecture
limit its generality and scalability.
  In this paper, we develop VDMS-Async that adds the capability to run
user-defined operations with VDMS and execute operations within a query on a
remote server. VDMS-Async utilizes an event-driven architecture to create an
efficient pipeline for executing operations within a query. Our experiments
have shown that VDMS-Async reduces the query execution time by 2-3X compared to
existing state-of-the-art systems. Further, remote operations coupled with an
event-driven architecture enables VDMS-Async to scale query execution time
linearly with the addition of every new remote server. We demonstrate a 64X
reduction in query execution time when adding 64 remote servers.


  This work aims to develop an end-to-end solution for seizure onset detection.
We design the SeizNet, a Convolutional Neural Network for seizure detection. To
compare SeizNet with traditional machine learning approach, a baseline
classifier is implemented using spectrum band power features with Support
Vector Machines (BPsvm). We explore the possibility to use the least number of
channels for accurate seizure detection by evaluating SeizNet and BPsvm
approaches using all channels and two channels settings respectively. EEG Data
is acquired from 29 pediatric patients admitted to KK Woman's and Children's
Hospital who were diagnosed as typical absence seizures. We conduct
leave-one-out cross validation for all subjects. Using full channel data, BPsvm
yields a sensitivity of 86.6\% and 0.84 false alarm (per hour) while SeizNet
yields overall sensitivity of 95.8 \% with 0.17 false alarm. More
interestingly, two channels seizNet outperforms full channel BPsvm with a
sensitivity of 93.3\% and 0.58 false alarm. We further investigate
interpretability of SeizNet by decoding the filters learned along convolutional
layers. Seizure-like characteristics can be clearly observed in the filters
from third and forth convolutional layers.


  Consideration is given to the influence of an underwater landslide on waves
at the surface of a shallow body of fluid. The equations of motion which govern
the evolution of the barycenter of the landslide mass include various
dissipative effects due to bottom friction, internal energy dissipation, and
viscous drag. The surface waves are studied in the Boussinesq scaling, with
time-dependent bathymetry. A numerical model for the Boussinesq equations is
introduced which is able to handle time-dependent bottom topography, and the
equations of motion for the landslide and surface waves are solved
simultaneously. The numerical solver for the Boussinesq equations can also be
restricted to implement a shallow-water solver, and the shallow-water and
Boussinesq configurations are compared. A particular bathymetry is chosen to
illustrate the general method, and it is found that the Boussinesq system
predicts larger wave run-up than the shallow-water theory in the example
treated in this paper. It is also found that the finite fluid domain has a
significant impact on the behavior of the wave run-up.


  With decreasing temperature Sr$_2$VO$_4$ undergoes two structural phase
transitions, tetragonal-to-orthorhombic-to-tetragonal, without long-range
magnetic order. Recent experiments suggest, that only at very low temperature
Sr$_{2}$VO$_{4}$ might enter some, yet unknown, phase with long-range magnetic
order, but without orthorhombic distortion. By combining relativistic density
functional theory with an extended spin-1/2 compass-Heisenberg model we find an
antiferromagnetic single-stripe ground state with highly competing exchange
interactions, involving a non negligible inter-layer coupling, which places the
system at the crossover between between the XY and Heisenberg picture. Most
strikingly, we find a strong two-site "spin-compass" exchange anisotropy which
is relieved by the orthorhombic distortion induced by the spin stripe order.
Based on these results we discuss the origin of the hidden order phase and the
possible formation of a spin-liquid at low temperatures.


  Anticipating the motion of neighboring vehicles is crucial for autonomous
driving, especially on congested highways where even slight motion variations
can result in catastrophic collisions. An accurate prediction of a future
trajectory does not just rely on the previous trajectory, but also, more
importantly, a simulation of the complex interactions between other vehicles
nearby. Most state-of-the-art networks built to tackle the problem assume
readily available past trajectory points, hence lacking a full end-to-end
pipeline with direct video-to-output mechanism. In this article, we thus
propose a novel end-to-end architecture that takes raw video inputs and outputs
future trajectory predictions. It first extracts and tracks the 3D location of
the nearby vehicles via multi-head attention-based regression networks as well
as non-linear optimization. This provides the past trajectory points which then
feeds into the trajectory prediction algorithm consisting of an attention-based
LSTM encoder-decoder architecture, which allows it to model the complicated
interdependence between the vehicles and make an accurate prediction of the
future trajectory points of the surrounding vehicles. The proposed model is
evaluated on the large-scale BLVD dataset, and has also been implemented on
CARLA. The experimental results demonstrate that our approach outperforms
various state-of-the-art models.


  In fermion mixing phenomenology, the matrix of moduli squared, P=(|U|^2), is
well-known to carry essentially the same information as the complex mixing
matrix U itself, but with the advantage of being phase-convention independent.
The matrix K (analogous to the Jarlskog CP-invariant J) formed from the real
parts of the mixing matrix "plaquette" products is similarly invariant. In this
paper, the P and K matrices are shown to be entirely equivalent, both being
directly related (in the leptonic case) to the observable, locally L/E-averaged
transition probabilities in neutrino oscillations. We study an (over-)complete
set of flavour-symmetric Jarlskog-invariant functions of mass-matrix
commutators, rewriting them simply as moment-transforms of such (real)
invariant matrices.


  In this paper, we construct, investigate and, in some cases, classify several
new classes of (simple) modules over the Takiff $\mathfrak{sl}_{2}$. More
precisely, we first explicitly construct and classify, up to isomorphism, all
modules over the Takiff $\mathfrak{sl}_{2}$ that are
$U\left(\overline{\mathfrak{h}}\right)$-free of rank one. These split into
three general families of modules. The sufficient and necessary conditions for
simplicity of these modules are presented, and their isomorphism classes are
determined. Using the vector space duality and Mathieu's twisting functors,
these three classes of modules are used to construct new families of weight
modules over the Takiff $\mathfrak{sl}_{2}$. We give necessary and sufficient
conditions for these weight modules to be simple and, in some cases, completely
determine their submodule structure.


  In this letter, we discuss the Wheeler-DeWitt equation with an ordering
parameter in the Friedmann-Robertson-Walker universe. The solutions when the
universe was very small and at the end of the expansion are obtained in terms
of Bessel and Heun functions, respectively. We also obtain a boundary condition
which should be satisfied by the ordering parameter, namely, $0 \leq p \leq 2$.
We investigate the minimum value of the scale factor with respect to the
maximum value of the probability density.


  Attention based neural TTS is elegant speech synthesis pipeline and has shown
a powerful ability to generate natural speech. However, it is still not robust
enough to meet the stability requirements for industrial products. Besides, it
suffers from slow inference speed owning to the autoregressive generation
process. In this work, we propose FeatherTTS, a robust and efficient
attention-based neural TTS system. Firstly, we propose a novel Gaussian
attention which utilizes interpretability of Gaussian attention and the strict
monotonic property in TTS. By this method, we replace the commonly used stop
token prediction architecture with attentive stop prediction. Secondly, we
apply block sparsity on the autoregressive decoder to speed up speech
synthesis. The experimental results show that our proposed FeatherTTS not only
nearly eliminates the problem of word skipping, repeating in particularly hard
texts and keep the naturalness of generated speech, but also speeds up acoustic
feature generation by 3.5 times over Tacotron. Overall, the proposed FeatherTTS
can be $35$x faster than real-time on a single CPU.


  The asymmetries of both light-flavor antiquark $\bar{d}(x)-\bar{u}(x)$ and
strange-antistrange $s(x)-\bar{s}(x)$ distributions of the nucleon sea are
considered with more details in the effective chiral quark model. We find that
the asymmetric distribution of light-flavor antiquarks $\bar{d}(x)-\bar{u}(x)$
matches the experiment data well and that the asymmetry of strange and
antistrange distributions can bring about 60-100% correction to the NuTeV
anomaly of $\sin^{2}\theta_{w}$, which are three standard deviations from the
world average value measured in other electroweak processes. The results on the
correction to the NuTeV anomaly are insensitive to the inputs of the
constituent quark distributions and the cut-off parameters. The ratios of
$\bar{d}(x)/\bar{u}(x)$ and $s(x)/\bar{s}(x)$ are also discussed, and it is
found that the ratio $s(x)/\bar{s}(x)$ is compatible with the available
experiments with an additional symmetric sea contribution being considered
effectively.


  In the $J/\psi$ radiative decay channels $J/\psi\to \gamma V\bar{V}$, the
result of partial wave analysis indicates that the $V\bar{V}$ systems are
predominately pseudoscalar component, and most of these channels have
relatively large branching ratios at an order of $10^{-3}$. Meanwhile, vector
mesons, such as $\rho$, $\omega$ and $K^*$, have strong couplings with nucleons
and/or hyperons. This suggests a dynamical mechanism describing the $\eta
p\bar{p}$ form factors for higher $\eta$ mesons, such as $\eta(1405/1475)$ and
$\eta(1760)$. It is thus natural to expect that rescatterings of these vector
meson pairs into $p\bar{p}$ of $0^-$ partial wave could be an important source
contributing to $J/\psi\to\gamma p\bar{p}$ of which the branching ratio is at
the order of $10^{-4}$. Our calculation justifies this point. In particular, we
find that interferences between different rescattering amplitudes can produce a
significant threshold enhancement in the invariant mass spectrum of $p\bar{p}$.
Without introducing dramatic ingredients, our model provides a natural
explanation for the peculiar threshold enhancement observed by BES-II in
$J/\psi\to \gamma p\bar{p}$. Additional experimental constraints on the
$V\bar{V}\to p\bar{p}$ transitions are examined. This mechanism in $J/\psi\to
\omega p\bar{p}$ is also discussed.


  In data sequences measured over space or time, an important problem is
accurate detection of abrupt changes. In partially labeled data, it is
important to correctly predict presence/absence of changes in positive/negative
labeled regions, in both the train and test sets. One existing dynamic
programming algorithm is designed for prediction in unlabeled test regions (and
ignores the labels in the train set); another is for accurate fitting of train
labels (but does not predict changepoints in unlabeled test regions). We
resolve these issues by proposing a new optimal changepoint detection model
that is guaranteed to fit the labels in the train data, and can also provide
predictions of unlabeled changepoints in test data. We propose a new dynamic
programming algorithm, Labeled Optimal Partitioning (LOPART), and we provide a
formal proof that it solves the resulting non-convex optimization problem. We
provide theoretical and empirical analysis of the time complexity of our
algorithm, in terms of the number of labels and the size of the data sequence
to segment. Finally, we provide empirical evidence that our algorithm is more
accurate than the existing baselines, in terms of train and test label error.


  Linear complementary dual codes (or codes with complementary duals) are codes
whose intersections with their dual codes are trivial. We study binary linear
complementary dual $[n,k]$ codes with the largest minimum weight among all
binary linear complementary dual $[n,k]$ codes. We characterize binary linear
complementary dual codes with the largest minimum weight for small dimensions.
A complete classification of binary linear complementary dual $[n,k]$ codes
with the largest minimum weight is also given for $1 \le k \le n \le 16$.


  When analyzing temporal networks, a fundamental task is the identification of
dense structures (i.e., groups of vertices that exhibit a large number of
links), together with their temporal span (i.e., the period of time for which
the high density holds). In this paper we tackle this task by introducing a
notion of temporal core decomposition where each core is associated with two
quantities, its coreness, which quantifies how densely it is connected, and its
span, which is a temporal interval: we call such cores \emph{span-cores}.
  For a temporal network defined on a discrete temporal domain $T$, the total
number of time intervals included in $T$ is quadratic in $|T|$, so that the
total number of span-cores is potentially quadratic in $|T|$ as well. Our first
main contribution is an algorithm that, by exploiting containment properties
among span-cores, computes all the span-cores efficiently. Then, we focus on
the problem of finding only the \emph{maximal span-cores}, i.e., span-cores
that are not dominated by any other span-core by both their coreness property
and their span. We devise a very efficient algorithm that exploits theoretical
findings on the maximality condition to directly extract the maximal ones
without computing all span-cores.
  Finally, as a third contribution, we introduce the problem of \emph{temporal
community search}, where a set of query vertices is given as input, and the
goal is to find a set of densely-connected subgraphs containing the query
vertices and covering the whole underlying temporal domain $T$. We derive a
connection between this problem and the problem of finding (maximal)
span-cores. Based on this connection, we show how temporal community search can
be solved in polynomial-time via dynamic programming, and how the maximal
span-cores can be profitably exploited to significantly speed-up the basic
algorithm.


  J.J. Schaeffer proved that for $any$ induced matrix norm and $any$ invertible
$T=T(n)$ the inequality \[\left|\det T\right|\left\Vert T^{-1}\right\Vert
\leq\mathcal{S}\left\Vert T\right\Vert ^{n-1}\] holds with
$\mathcal{S}=\mathcal{S}(n)\leq\sqrt{en}$. He conjectured that the best
$\mathcal{S}$ was actually bounded. This was rebutted by Gluskin-Meyer-Pajor
and subsequent contributions by J. Bourgain and H. Queffelec that successively
improved lower estimates on $\mathcal{S}$. These articles rely on a link to the
theory of power sums of complex numbers. A probabilistic or number theoretic
analysis of such inequalities is employed to prove the existence of $T$ with
growing $\mathcal{S}$ but the explicit construction of such $T$ remains an open
task. In this article we propose a constructive approach to Schaeffer's
conjecture that is not related to power sum theory. As a consequence we present
an explicit sequence of Toeplitz matrices with singleton spectrum
$\{\lambda\}\subset\mathbb{D}-\{0\}$ such that $\mathcal{S}\geq
c(\lambda)\sqrt{n}$. Our framework naturally extends to provide lower estimates
on the resolvent $\left\Vert (\zeta-T)^{-1}\right\Vert$ when $\zeta\neq0$. We
also obtain new upper estimates on the resolvent when the spectrum is given.
This yields new upper bounds on $\left\Vert T^{-1}\right\Vert$ in terms of the
eigenvalues of $T$ which slightly refine Schaeffer's original estimate.


  Depth map estimation is a crucial task in computer vision, and new approaches
have recently emerged taking advantage of light fields, as this new imaging
modality captures much more information about the angular direction of light
rays compared to common approaches based on stereoscopic images or multi-view.
In this paper, we propose a novel depth estimation method from light fields
based on existing optical flow estimation methods. The optical flow estimator
is applied on a sequence of images taken along an angular dimension of the
light field, which produces several disparity map estimates. Considering both
accuracy and efficiency, we choose the feature flow method as our optical flow
estimator. Thanks to its spatio-temporal edge-aware filtering properties, the
different disparity map estimates that we obtain are very consistent, which
allows a fast and simple aggregation step to create a single disparity map,
which can then converted into a depth map. Since the disparity map estimates
are consistent, we can also create a depth map from each disparity estimate,
and then aggregate the different depth maps in the 3D space to create a single
dense depth map.


  Our study is motivated by the prospect of several metastable states in the
Sb$ ^{+} $, Au$ ^{+} $, and Hg$ ^{2+} $ ions being used as possible candidates
for optical clocks. We calculate several atomic properties relevant to the
development of optical clocks for those clock transitions using two different
approaches of relativistic many-body calculations, configuration interaction
with single-double coupled-cluster (CI+SD) method, and configuration
interaction with perturbation theory (CIPT) method. Our results demonstrate
that the relative black body radiation shifts for these transitions are small,
$ \sim 10 ^{-16} $. It is also found that there is considerable sensitivity to
new physics, as evidenced by a significant enhancement of the effect of the
time variation of the fine structure constant $\alpha$ on the frequencies of
the clock transitions. The corresponding factor ranges from -5.56 to 2.20. Our
results are compared with available previous data.


  The details of the physical process through which high-mass stars form
remains nearly as much of a mystery now as it was when the Parkes radio
telescope commenced operation. The energy output from high-mass stars
influence, or directly drive many important processes in the evolution of
galaxies and so understanding in detail when and how they form is important for
a broad range of fields of astrophysics. Interstellar masers are one of the
most readily observed signposts of regions where young high-mass stars have
formed. We have recently made great progress towards using the different maser
species and transitions to construct a maser-based evolutionary timeline for
high-mass star formation. Here we give an overview of this work, highlighting
the particular contribution that past and on-going observations with the Parkes
64m radio telescope have made to this area.


  The detection of the first electromagnetic counterpart to a
gravitational-wave signal in August 2017 marked the start of a new era of
multi-messenger astrophysics. An unprecedented number of telescopes around the
world were involved in hunting for the source of the signal, and although more
gravitational-wave signals have been since detected, no further electromagnetic
counterparts have been found.
  In this thesis, I present my work to help build a telescope dedicated to the
hunt for these elusive sources: the Gravitational-wave Optical Transient
Observer (GOTO). I detail the creation of the GOTO Telescope Control System,
G-TeCS, which includes the software required to control multiple wide-field
telescopes on a single robotic mount. G-TeCS also includes software that
enables the telescope to complete a sky survey and transient alert follow-up
observations completely autonomously, whilst monitoring the weather conditions
and automatically fixing any hardware issues that arise. I go on to describe
the routines used to determine target priorities, as well as how the all-sky
survey grid is defined, how gravitational-wave and other transient alerts are
received and processed, and how the optimum follow-up strategies for these
events were determined.
  The GOTO prototype, situated on La Palma, saw first light in June 2017. I
detail the work I carried out on the site to help commission the prototype, and
how the control software was developed during the commissioning phase. I also
analyse the GOTO CCD cameras and optics, building a complete theoretical model
of the system to confirm the performance of the prototype. Finally, I describe
the results of simulations I carried out predicting the future of the GOTO
project, with multiple robotic telescopes on La Palma and in Australia, and how
G-TeCS might be modified to operate these telescopes as a single, global
observatory.


  3D-aware Generative Adversarial Networks (GANs) have shown remarkable
progress in learning to generate multi-view-consistent images and 3D geometries
of scenes from collections of 2D images via neural volume rendering. Yet, the
significant memory and computational costs of dense sampling in volume
rendering have forced 3D GANs to adopt patch-based training or employ
low-resolution rendering with post-processing 2D super resolution, which
sacrifices multiview consistency and the quality of resolved geometry.
Consequently, 3D GANs have not yet been able to fully resolve the rich 3D
geometry present in 2D images. In this work, we propose techniques to scale
neural volume rendering to the much higher resolution of native 2D images,
thereby resolving fine-grained 3D geometry with unprecedented detail. Our
approach employs learning-based samplers for accelerating neural rendering for
3D GAN training using up to 5 times fewer depth samples. This enables us to
explicitly "render every pixel" of the full-resolution image during training
and inference without post-processing superresolution in 2D. Together with our
strategy to learn high-quality surface geometry, our method synthesizes
high-resolution 3D geometry and strictly view-consistent images while
maintaining image quality on par with baselines relying on post-processing
super resolution. We demonstrate state-of-the-art 3D gemetric quality on FFHQ
and AFHQ, setting a new standard for unsupervised learning of 3D shapes in 3D
GANs.


  A series of dual-phase high-entropy ultrahigh temperature ceramics
(DPHE-UHTCs) are fabricated starting from N binary borides and (5-N) binary
carbides powders. >~99% relative densities have been achieved with virtually no
native oxides. These DPHE-UHTCs consist of a hexagonal high-entropy boride
(HEB) phase and a cubic high-entropy carbide (HEC) phase. A thermodynamic
relation that governs the compositions of the HEB and HEC phases in equilibrium
is discovered and a thermodynamic model is proposed. These DPHE-UHTCs exhibit
tunable grain size, Vickers microhardness, Young' and shear moduli, and thermal
conductivity. The DPHE-UHTCs have higher hardness than the weighted linear
average of the two single-phase HEB and HEC, which are already harder than the
rule-of-mixture averages of individual binary borides and carbides. This study
extends the state of the art by introducing dual-phase high-entropy ceramics
(DPHECs), which provide a new platform to tailor various properties via
changing the phase fraction and microstructure.


  We calculate numerically the eigenvalue distribution of the overlap Dirac
operator in the quenched Schwinger model on a lattice. The distribution does
not fit any of the three universality classes of spontaneous chiral symmetry
breaking, and its strong volume dependence indicates that the chiral condensate
in the quenched theory is an ill-defined and divergent quantity. When we
reweight configurations with the Dirac determinant to study the theory with
N_f=1, we obtain a distribution of eigenvalues that is well-behaved and
consistent with the theory of explicit symmetry breaking due to the anomaly.


  In the past two decades, the complex nature of sunspots has been disclosed
with high-resolution observations. One of the most important findings is the
"uncombed" penumbral structure, where a more horizontal magnetic component
carrying most of Evershed Flows is embedded in a more vertical magnetic
background (Solanki & Montavon 1993). The penumbral bright grains are locations
of hot upflows and dark fibrils are locations of horizontal flows that are
guided by nearly horizontal magnetic field. On the other hand, it was found
that flares may change the topology of sunspots in $\delta$ configuration: the
structure at the flaring polarity inversion line becomes darkened while
sections of peripheral penumbrae may disappear quickly and permanently
associated with flares (Liu et al. 2005). The high spatial and temporal
resolution observations obtained with Hinode/ SOT provide an excellent
opportunity to study the evolution of penumbral fine structure associated with
major flares. Taking advantage of two near-limb events, we found that in
sections of peripheral penumbrae swept by flare ribbons, the dark fibrils
completely disappear, while the bright grains evolve into faculae that are
signatures of vertical magnetic flux tubes. The corresponding magnetic fluxes
measured in the decaying penumbrae show stepwise changes temporally correlated
with the flares. These observations suggest that the horizontal magnetic field
component of the penumbra could be straightened upward (i.e., turning from
horizontal to vertical) due to magnetic field restructuring associated with
flares, which results in the transition of penumbrae to faculae.


  Continuous-variable cluster states (CVCSs) can be supplemented with
Gottesman-Kitaev-Preskill (GKP) states to form a hybrid cluster state with the
power to execute universal, fault-tolerant quantum computing in a
measurement-based fashion. As the resource states that comprise a hybrid
cluster state are of a very different nature, a natural question arises: Why do
GKP states interface so well with CVCSs? To answer this question, we apply the
recently introduced subsystem decomposition of a bosonic mode, which divides a
mode into logical and gauge-mode subsystems, to three types of cluster state:
CVCSs, GKP cluster states, and hybrid CV-GKP cluster states. We find that each
of these contains a "hidden" qubit cluster state across their logical
subsystems, which lies at the heart of their utility for measurement-based
quantum computing. To complement the analytical approach, we introduce a simple
graphical description of these CV-mode cluster states that depicts precisely
how the hidden qubit cluster states are entangled with the gauge modes, and we
outline how these results would extend to the case of finitely squeezed states.
This work provides important insight that is both conceptually satisfying and
helps to address important practical issues like when a simpler resource (such
as a Gaussian state) can stand in for a more complex one (like a GKP state),
leading to more efficient use of the resources available for CV quantum
computing.


  Axion models with generation-dependent Peccei-Quinn charges can lead to
flavor-changing neutral currents, thus motivating QCD axion searches at
precision flavor experiments. We rigorously derive limits on the most general
effective flavor-violating couplings from current measurements and assess their
discovery potential. For two-body decays we use available experimental data to
derive limits on $q\to q' a$ decay rates for all flavor transitions. Axion
contributions to neutral-meson mixing are calculated in a systematic way using
chiral perturbation theory and operator product expansion. We also discuss in
detail baryonic decays and three-body meson decays, which can lead to the best
search strategies for some of the couplings. For instance, a strong limit on
the $\Lambda\to n a$ transition can be derived from the supernova SN 1987A. In
the near future, dedicated searches for $q\to q' a$ decays at ongoing
experiments could potentially test Peccei-Quinn breaking scales up to $10^{12}$
GeV at NA62 or KOTO, and up to $10^{9}$ GeV at Belle II or BES III.


  We review and discuss recent work exploring the implications of the Higgs
field for early universe cosmology, and vice versa. Depending on the model
under consideration the Higgs may be one of a few scalar fields determining the
evolution and fate of the Universe, or the Higgs field may be connected to a
rich sector of scalar moduli with complicated dynamics. In particular we look
at the potential consequences of the Higgs field for inflation and its
predictions, for the (meta)stability of the Standard Model vacuum, and for the
existence of dynamical selection mechanisms in the landscape.


  A promising technique of discovering disease biomarkers is to measure the
relative protein abundance in multiple biofluid samples through liquid
chromatography with tandem mass spectrometry (LC-MS/MS) based quantitative
proteomics. The key step involves peptide feature detection in LC-MS map, along
with its charge and intensity. Existing heuristic algorithms suffer from
inaccurate parameters since different settings of the parameters result in
significantly different outcomes. Therefore, we propose PointIso, to serve the
necessity of an automated system for peptide feature detection that is able to
find out the proper parameters itself, and is easily adaptable to different
types of datasets. It consists of an attention based scanning step for
segmenting the multi-isotopic pattern of peptide features along with charge and
a sequence classification step for grouping those isotopes into potential
peptide features. PointIso is the first point cloud based, arbitrary-precision
deep learning network to address the problem and achieves 98% detection of high
quality MS/MS identifications in a benchmark dataset, which is higher than
several other widely used algorithms. Besides contributing to the proteomics
study, we believe our novel segmentation technique should serve the general
image processing domain as well.


  We introduce a novel integrated hybrid plasmonic-photonic device for
all-optical switching and reading of nanoscale ferrimagnet bits. The racetrack
memory made of synthetic ferrimagnetic material with a perpendicular magnetic
anisotropy is coupled on to a photonic waveguide onto the indium phosphide
membrane on silicon platform. The device which is composed of a double V-shaped
gold plasmonic nanoantenna coupled with a photonic crystal cavity can enable
switching and reading of the magnetization state in nanoscale magnetic bits by
enhancing the absorbed energy density and polar magneto-optical Kerr effect
(PMOKE) locally beyond the diffraction limit. Using a three-dimensional
finite-difference time-domain method, we numerically show that our device can
switch and read the magnetization state in targeted bits down to ~100 nm in the
presence of oppositely magnetized background regions in the racetrack with
widths of 30 to 120 nm, clearly outperforming a bare photonic waveguide. Our
hybrid device tackles the challenges of nonlinear absorption in the waveguide,
weak PMOKE, and size mismatch between spintronics and integrated photonics.
Thus, it provides missing link between the integrated photonics and nanoscale
spintronics, expediting the development of ultrafast and energy efficient
advanced on-chip applications.


  The Uhlmann-Jozsa fidelity (or, equivalently, the Bures distance) is a basic
concept of quantum communication and quantum information, which however is very
difficult to measure efficiently without recourse to quantum tomography. Here
we propose a direct experimental method to estimate the fidelity between two
unknown two-qubit mixed states via the measurement of the upper and lower
bounds of the fidelity, which are referred to as the superfidelity and
subfidelity, respectively. Our method enables a direct measurement of the
first- and second-order overlaps between two arbitrary two-qubit states. In
particular, the method can be applied to measure the purity (or linear entropy)
of a single two-qubit mixed state in a direct experiment. We also propose and
critically compare several experimental strategies for measuring the sub- and
superfidelities of polarization states of photons in various linear-optical
setups.


  Application telemetry refers to measurements taken from software systems to
assess their performance, availability, correctness, efficiency, and other
aspects useful to operators, as well as to troubleshoot them when they behave
abnormally. Many modern observability platforms support dimensional models of
telemetry signals where the measurements are accompanied by additional
dimensions used to identify either the resources described by the telemetry or
the business-specific attributes of the activities (e.g., a customer
identifier). However, most of these platforms lack any semantic understanding
of the data, by not capturing any metadata about telemetry, from simple aspects
such as units of measure or data types (treating all dimensions as strings) to
more complex concepts such as purpose policies. This limits the ability of the
platforms to provide a rich user experience, especially when dealing with
different telemetry assets, for example, linking an anomaly in a time series
with the corresponding subset of logs or traces, which requires semantic
understanding of the dimensions in the respective data sets.
  In this paper, we describe a schema-first approach to application telemetry
that is being implemented at Meta. It allows the observability platforms to
capture metadata about telemetry from the start and enables a wide range of
functionalities, including compile-time input validation, multi-signal
correlations and cross-filtering, and even privacy rules enforcement. We
present a collection of design goals and demonstrate how schema-first approach
provides better trade-offs than many of the existing solutions in the industry.


  We review statistical theories and numerical methods employed to consider the
sample size dependence of the failure strength distribution of disordered
materials. We first overview the analytical predictions of extreme value
statistics and fiber bundle models and discuss their limitations. Next, we
review energetic and geometric approaches to fracture size effects for
specimens with a flaw. Finally, we overview the numerical simulations of
lattice models and compare with theoretical models.


  The concept of chirality is of great relevance in nature, from chiral
molecules such as sugar to parity transformations in particle physics. In
condensed matter physics, recent studies have demonstrated chiral fermions and
their relevance in emergent phenomena closely related to topology. The
experimental verification of chiral phonons (bosons) remains challenging,
however, despite their expected strong impact on fundamental physical
properties. Here we show experimental proof of chiral phonons using resonant
inelastic X-ray scattering with circularly polarized X rays. Using the
prototypical chiral material, quartz, we demonstrate that circularly polarized
X rays, which are intrinsically chiral, couple to chiral phonons at specific
positions in reciprocal space, allowing us to determine the chiral dispersion
of the lattice modes. Our experimental proof of chiral phonons demonstrates a
new degree of freedom in condensed matter that is both of fundamental
importance and opens the door to exploration of novel emergent phenomena based
on chiral bosons


  Recent advances in the description of electromagnetic two-nucleon knockout
reactions are reviewed. The sensitivity to different types of correlations and
to their treatment in the nuclear wave functions, the effects of final-state
interactions and the role of center-of-mass effects in connection with the
problem of the lack of orthogonality between initial bound states and final
scattering states obtained by the use of an energy-dependent optical-model
potential are discussed. Results are presented for proton-proton and
proton-neutron knockout off 16O also in comparison with the available data.


  Semi-Markov models are widely used for survival analysis and reliability
analysis. In general, there are two competing parameterizations and each
entails its own interpretation and inference properties. On the one hand, a
semi-Markov process can be defined based on the distribution of sojourn times,
often via hazard rates, together with transition probabilities of an embedded
Markov chain. On the other hand, intensity transition functions may be used,
often referred to as the hazard rates of the semi-Markov process. We summarize
and contrast these two parameterizations both from a probabilistic and an
inference perspective, and we highlight relationships between the two
approaches. In general, the intensity transition based approach allows the
likelihood to be split into likelihoods of two-state models having fewer
parameters, allowing efficient computation and usage of many survival analysis
tools. {Nevertheless, in certain cases the sojourn time based approach is
natural and has been exploited extensively in applications.} In contrasting the
two approaches and contemporary relevant R packages used for inference, we use
two real datasets highlighting the probabilistic and inference properties of
each approach. This analysis is accompanied by an R vignette.


  We have performed resistivity and inelastic neutron scattering measurements
on three samples of Fe0.98-zCuzTe0.5Se0.5 with z = 0, 0.02, and 0.1. It is
found that with increasing Cu doping the sample's resistivity deviates
progressively from that of a metal. However, in contrast to expectations that
replacing Fe with Cu would suppress the magnetic correlations, the low-energy
(no larger than 12 meV) magnetic scattering is enhanced in strength, with
greater spectral weight and longer dynamical spin-spin correlation lengths.
Such enhancements can be a consequence of either enlarged local moments or a
slowing down of the spin fluctuations. In either case, the localization of the
conduction states induced by the Cu doping should play a critical role. Our
results are not applicable to models that treat 3d transition metal dopants
simply as effective electron donors.


  Typical constraints on embedded systems include code size limits, upper
bounds on energy consumption and hard or soft deadlines. To meet these
requirements, it may be necessary to improve the software by applying various
kinds of transformations like compiler optimizations, specific mapping of code
and data in the available memories, code compression, etc. However, a
transformation that aims at improving the software with respect to a given
criterion might engender side effects on other criteria and these effects must
be carefully analyzed. For this purpose, we have developed a common framework
that makes it possible to experiment various code transfor-mations and to
evaluate their impact of various criteria. This work has been carried out
within the French ANR MORE project.


  Collider searches for long-lived particles yield a promising avenue to probe
the freeze-in production of Dark Matter via the decay of a parent particle. We
analyze the prospects of probing the parameter space of Dark Matter freeze-in
from the decay of neutral parent particles at the LHC and beyond, taking as a
case study a freeze-in Dark Matter scenario via the Standard Model Higgs. We
obtain the projected sensitivity of the proposed MATHUSLA surface detector (for
MATHUSLA100 and MATHUSLA200 configurations) for long-lived particle searches to
the freeze-in Dark Matter parameter space, and study its complementarity to
searches by ATLAS and CMS at HL-LHC, as well as the interplay with constraints
from Cosmology: Big-Bang Nucleosynthesis and Lyman-$\alpha$ forest
observations. We then analyze the improvement in sensitivity that would come
from a forward detector within a future 100 TeV $pp$-collider. In addition, we
discuss several technical aspects of the present Dark Matter freeze-in
scenario: the role of the electroweak phase transition; the inclusion of
thermal masses, which have been previously disregarded in freeze-in from decay
studies; the impact of $2\to 2$ scattering processes on the Dark Matter relic
abundance; and the interplay between freeze-in and super-WIMP Dark Matter
production mechanisms.


  The Weyl$-$Yang gravitational gauge theory is investigated in the structure
of a pure higher-dimensional non-Abelian Kaluza$-$Klein background. We
construct the dimensionally reduced field equations and stress-energy-momentum
tensors as well as the four dimensional modified Weyl$-$Yang$+$Yang$-$Mills
theory from an arbitrary curved $internal$ space in the anholonomic frame which
are the extensions of our previous model for the non-Abelian case. In
particular, the coset space reduction is considered to explicitly obtain the
interactions between the gravitational and the gauge fields. The resulting
equations not only appear to be generalization of the well-established
equations of non-Abelian theory but also contain intrinsically the generalized
gravitational source term which does not exist in the literature so far and the
Yang$-$Mills force density which is exactly equivalent to the negative gradient
of a Yang$-$Mills quadratic invariant.


  $V$ is a complete intersection scheme in a multiprojective space if it can be
defined by an ideal $I$ with as many generators as $\textrm{codim}(V)$. We
investigate the multigraded regularity of complete intersections scheme in
$\mathbb{P}^n\times \mathbb{P}^m$. We explicitly compute many values of the
Hilbert functions of $0$-dimensional complete intersections. We show that these
values only depend upon $n,m$, and the bidegrees of the generators of $I$. As a
result, we provide a sharp upper bound for the multigraded regularity of
$0$-dimensional complete intersections.


  We prove an extension theorem of "Ohsawa-Takegoshi type" for Dolbeault
q$-classes of cohomology ($q\geq 1$) on smooth compact hypersurfaces in a
weakly pseudoconvex K\"ahler manifold


  We study the stability of the hydrogen molecule interacting with the
environment according to the balanced gain and loss energy scheme. We
determined the properties of the molecule taking into account all electronic
interactions, where the parameters of the Hamiltonian have been computed by
using the variational method. The interaction of the hydrogen molecule with the
environment was modeled parametrically ($\gamma$) with the help of the
non-hermitian operator. We have shown that the hydrogen molecule is dynamically
unstable. The dissociation time ($T_{D}$) decreases, if the $\gamma$ parameter
increases (for $\gamma\rightarrow 0$, we get $T_{D}\rightarrow +\infty$). At
the dynamic instability of the hydrogen molecule overlaps its static
instability as the coupling constant $\gamma$ increases. We observed the
decrease in the dissociation energy and the existence of the metastable state
of the molecule ($\gamma_{MS}=0.659374$~Ry). The hydrogen molecule is
statically unstable for $\gamma >\gamma_{D}=1.024638$~Ry. One can also observed
the $\mathcal{PT}$ symmetry breaking effect for the electronic Hamiltonian
($\gamma_{\mathcal {PT}}=0.520873$~Ry). However, it does not affect the
properties of the hydrogen molecule, such as: the electronic Hamiltonian
parameters, the phonon and rotational energy, and the values of the
electron-phonon coupling constants.


  A long-standing problem of strong lensing by galaxy clusters regards the
observed high rate of giant gravitational arcs as compared to the predictions
in the framework of the "standard" cosmological model. Recently, few other
inconsistencies between theoretical expectations and observations have been
claimed which regard the large size of the Einstein rings and the high
concentrations of few clusters with strong lensing features. All of these
problems consistently indicate that observed galaxy clusters may be
gravitational lenses stronger than expected. We use clusters extracted from the
MareNostrum Universe to build up mock catalogs of galaxy clusters selected
through their X-ray flux. We use these objects to estimate the probability
distributions of lensing cross sections, Einstein rings, and concentrations for
the sample of 12 MACS clusters at $z>0.5$ presented in Ebeling et al. (2007)
and discussed in Zitrin et al. (2010). We find that simulated clusters produce
$\sim 50%$ less arcs than observed clusters do. The medians of the
distributions of the Einstein ring sizes differ by $\sim 25%$ between
simulations and observations. We estimate that, due to cluster triaxiality and
orientation biases affecting the lenses with the largest cross sections, the
concentrations of the individual MACS clusters inferred from the lensing
analysis should be up to a factor of $\sim 2$ larger than expected from the
$\Lambda$CDM model. The arc statistics, the Einstein ring, and the
concentration problems in strong lensing clusters are mitigated but not solved
on the basis of our analysis. Nevertheless, due to the lack of redshifts for
most of the multiple image systems used for modeling the MACS clusters, the
results of this work will need to be verified with additional data. The
upcoming CLASH program will provide an ideal sample for extending our
comparison (abridged).


  We derive the general form of the anomaly for chiral spinors and self-dual
antisymmetric tensors living on D-brane and O-plane interesections, using both
path-integral and index theorem methods. We then show that the anomalous
couplings to RR forms of D-branes and O-planes in a general background are
precisely those required to cancel these anomalies through the inflow
mechanism. This allows, for instance, for local anomaly cancellation in generic
orientifold models, the relevant Green-Schwarz term being given by the sum of
the anomalous couplings of all the D-branes and O-planes in the model.


  Fully analytical dynamical models usually have an infinite extent, while real
star clusters, galaxies, and dark matter haloes have a finite extent. The
standard method for generating dynamical models with a finite extent consists
of taking a model with an infinite extent and applying a truncation in binding
energy. This method, however, cannot be used to generate models with a pre-set
analytical mass density profile. We investigate the self-consistency and
dynamical properties of a family of power-law spheres with a general tangential
Cuddeford (TC) orbital structure. By varying the density power-law slope
$\gamma$ and the central anisotropy $\beta_0$, these models cover a wide
parameter space in density and anisotropy profiles. We explicitly calculate the
phase-space distribution function for various parameter combinations, and
interpret our results in terms of the energy distribution of bound orbits. We
find that truncated power-law spheres can be supported by a TC orbital
structure if and only if $\gamma \geqslant 2\beta_0$, which means that the
central density slope-anisotropy inequality is both a sufficient and a
necessary condition for this family. We provide closed expressions for
structural and dynamical properties such as the radial and tangential velocity
dispersion profiles, which can be compared against more complex numerical
modelling results. This work significantly adds to the available suite of
self-consistent dynamical models with a finite extent and an analytical
description.


  Let $PU_n$ denote the projective unitary group of rank $n$ and $BPU_n$ be its
classifying space, for $n>1$. By using the Serre spectral sequence induced by
the fibration $BU_n\to BPU_n\to K(\mathbb{Z},3)$, we compute the integral
cohomology of $BPU_n$ in dimensions less than $15$ except for $4\mid n$ in
dimension $14$.


  We propose a definition by generators and relations of the rank $n-2$
Askey-Wilson algebra $\mathfrak{aw}(n)$ for any integer $n$, generalising the
known presentation for the usual case $n=3$. The generators are indexed by
connected subsets of $\{1,\dots,n\}$ and the simple and rather small set of
defining relations is directly inspired from the known case of $n=3$. Our first
main result is to prove the existence of automorphisms of $\mathfrak{aw}(n)$
satisfying the relations of the braid group on $n+1$ strands. We also show the
existence of coproduct maps relating the algebras for different values of $n$.
An immediate consequence of our approach is that the Askey-Wilson algebra
defined here surjects onto the algebra generated by the intermediate Casimir
elements in the $n$-fold tensor product of the quantum group ${\rm
U}_q(\mathfrak{sl}_2)$ or, equivalently, onto the Kauffman bracket skein
algebra of the $(n+1)$-punctured sphere. We also obtain a family of central
elements of the Askey-Wilson algebras which are shown, as a direct by-product
of our construction, to be sent to $0$ in the realisation in the $n$-fold
tensor product of ${\rm U}_q(\mathfrak{sl}_2)$, thereby producing a large
number of relations for the algebra generated by the intermediate Casimir
elements.


  In this letter, instead of investigating the compaction of granular materials
under tapping or cyclic shearing, we focused more on the gyratory shearing
compaction, where particles are subjected to constant pressure and shear rate
continuously. Such a phenomenon is crucial to the compaction of asphalt
mixtures or soil in civil engineering and can be extended to other areas, such
as powder processing and pharmaceutical engineering. In this study, we found
that the gyratory speed or interstitial fluid viscosity has almost no impact on
the compaction behavior, while the pressure plays a more important role.
Additionally, it is the inertial time scale which dictates the compaction
behavior under gyratory shearing in most cases, whereas the viscous time scale
can also have influence in some conditions.


  Kautz and de Bruijn graphs have a high degree of connectivity which makes
them ideal candidates for massively parallel computer network topologies. In
order to realize a practical computer architecture based on these graphs, it is
useful to have a means of constructing a large-scale system from smaller,
simpler modules. In this paper we consider the mathematical problem of
uniformly tiling a de Bruijn or Kautz graph. This can be viewed as a
generalization of the graph bisection problem. We focus on the problem of graph
tilings by a set of identical subgraphs. Tiles should contain a maximal number
of internal edges so as to minimize the number of edges connecting distinct
tiles. We find necessary and sufficient conditions for the construction of
tilings. We derive a simple lower bound on the number of edges which must leave
each tile, and construct a class of tilings whose number of edges leaving each
tile agrees asymptotically in form with the lower bound to within a constant
factor. These tilings make possible the construction of large-scale computing
systems based on de Bruijn and Kautz graph topologies.


  This article proposes a dynamical system modeling approach for the analysis
of longitudinal data of self-regulated systems experiencing multiple
excitations. The aim of such an approach is to focus on the evolution of a
signal (e.g., heart rate) before, during, and after excitations taking the
system out of its equilibrium (e.g., physical effort during cardiac stress
testing). Dynamical modeling can be applied to a broad range of outcomes such
as physiological processes in medicine and psychosocial processes in social
sciences, and it allows to extract simple characteristics of the signal
studied. The model we propose is based on a first order linear differential
equation defined by three main parameters corresponding to the initial
equilibrium value, the dynamic characteristic time, and the reaction to the
excitation. In this paper, several estimation procedures for this model are
considered and tested in a simulation study, that clarifies under which
conditions accurate estimates are provided. Finally, applications of this model
are illustrated using cardiology data recorded during effort tests.


  We study the fundamental limitations of cooling to absolute zero for a qubit,
interacting with a single mode of the electromagnetic field. Our results show
that the dynamical Casimir effect, which is unavoidable in any finite-time
thermodynamic cycle, forbids the attainability of the absolute zero of
temperature, even in the limit of an infinite number of cycles.


  We find that the energy-momentum tensor of electromagnetic waves in media is
very similar to that of ordinary fluids, and concepts such as density,
pressure, and energy transfer rate can be similarly defined. On this basis, we
conducted a detailed theoretical analysis on the mean momentum and equivalent
mass of photons in the medium, the relationship between pressure and
polarization of beams, the influence of polarization energy and magnetization
energy of the medium, the Bernoulli effect of beams and the energy-momentum
tensor of beams in moving media. We also obtain a conservation new
energy-momentum tensor based on the interaction term between the
electromagnetic field and the medium. From this energy-momentum tensor, we can
derive both the Minkowski momentum and the Abraham momentum simultaneously. We
find that Minkowski momentum is actually a canonical momentum that considers
the influence of the interaction between electromagnetic waves and media, while
Abraham momentum is actually a mechanical momentum that does not consider the
influence of the interaction between electromagnetic waves and media. Based on
the theory obtained in this paper, we have provided theoretical explanations
for Jones'experiment of light pressure in a medium, Ashkin's free liquid
surface deformation experiment, Weilong's optical fiber deformation experiment,
and frequency shift measurement experiment. The theory obtained in this paper
can self-consistently explain the above experiments simultaneously. Unlike the
Minkowski and Abraham tensors, according to the energy-momentum tensor proposed
in this paper, a beam in a medium also generates a pressure on its side, and
the direction of this pressure is related to the polarization of the beam. The
findings of this paper may shed new light on the application of light.


  The best upper bounds on the masses of stable and unstable light neutrinos
derive from the upper bound on the total mass density, as inferred from the
lower limit $t_0> 13$ Gyr on the dynamical age of the Universe: If the Universe
is matter-dominated, $m_\nu<35(23)\times$ max$ [1, (t_0/\tau_\nu)^{1/2}]$ eV,
according as a cosmological constant is (is not) allowed. The best constraints
on the radiative decay of light neutrinos derive from the failure to observe
prompt gamma rays accompanying the neutrinos from Supernova 1987A: For any
$m_{\nu} > 630$ eV, this provides a stronger bound on the neutrino transition
moment than that obtained from red giants or white dwarfs. For $m_\nu > 250$ eV
or $\tau_\nu < t_{rec}\sim 7\times 10^{12}$ sec, the upper limit on the
radiative branching ratio is even smaller than that obtained from the limits on
$\mu$-distortion of the cosmic background radiation. Our results improve on
earlier cosmological and radiative decay constraints by an overall factor
twenty, and allow neutrinos more massive than 35 eV, only if they decay
overwhelmingly into singlet majorons or other new particles.


  Microbial colonization of surfaces represents the first step towards biofilm
formation, which is a recurring phenomenon in nature with beneficial and
detrimental implications in technological and medical settings. Consequently,
there is a current interest in elucidating the fundamental aspects of the
initial stages of biofilm formation of microorganisms on solid surfaces. While
most of the research is oriented to understand bacterial surface colonization,
such observations at a fundamental level using photosynthetic microalgae are
thus far elusive. Recent single-cell studies showed that the flagellar adhesion
of Chlamydomonas is switched on in blue light and switched off under red light
[Kreis et al., Nature Physics, 2018, 14, 45-49]. Here, we study this
light-switchable surface association of C. reinhardtii on the population level
and measure the kinetics of adsorption and desorption of suspensions of motile
cells on glass surfaces using bright field optical microscopy. We observe that
both processes exhibit a response lag relative to the time at which the blue-
and red-light conditions are set and model this feature using time-delayed
Langmuir-type kinetics. We find that cell adsorption occurs significantly
faster than desorption, which we attribute to the protein-mediated molecular
adhesion mechanism of the cells. Adsorption experiments using phototactically
blind Chlamydomonas mutants demonstrate that phototaxis does not affect the
cell adsorption kinetics. Hence, this method can be used as an assay for
characterizing the dynamics of the surface colonization of microbial species
exhibiting light-regulated surface adhesion.


  We demonstrate the complete reconstruction of the electric field of
visible-infrared pulses with energy as low as a few tens of nanojoules. The
technique allows for the reconstruction of the instantaneous electric field
vector direction and magnitude, thus giving access to the characterisation of
pulses with an arbitrary time-dependent polarisation state. The technique
combines extreme ultraviolet interferometry with the generation of isolated
attosecond pulses.


  Given a ring $A$ and an $A$-coring $\cC$ we study when the forgetful functor
from the category of right $\cC$-comodules to the category of right $A$-modules
and its right adjoint $-\otimes_A\cC$ are separable. We then proceed to study
when the induction functor $-\otimes_A\cC$ is also the left adjoint of the
forgetful functor. This question is closely related to the problem when $A\to
{}_A{\rm Hom}(\cC,A)$ is a Frobenius extension.
  We introduce the notion of a Galois coring and analyse when the tensor
functor over the subring of $A$ fixed under the coaction of $\cC$ is an
equivalence. We also comment on possible dualisation of the notion of a coring.


  Halide perovskites consist a class of materials under intense investigation
due to their potential technological applications like solar cells,
optoelectronic devices and catalysis. Recently we have studied using electronic
band structure calculations from first principles, the cubic MABX$_3$ compounds
[A. Koliogiorgos et al., Comput. Mater. Sci. \textbf{138}, 92 (2017)], where MA
stands for the methylammonium cation, B is a divalent cation and X a halogen.
We expand our study in the case where Cs stands in place of the MA cation. Our
results suggest that the Cs-based compounds exhibit also a variety of lattice
constants and energy band gaps. The calculated equilibrium lattice constants
differ substantially from the experimental ones. The calculated energy gaps
also show large deviations for these lattice constants. Moreover, the use of
more sophisticated functionals leads to conflicting changes in the energy gap
values and its effect is materials dependent. Our results suggest that contrary
to the MA halide perovskites, the Cs halide perovskites consist a more delicate
case and there is still a long way for \textit{ab-initio} calculations to
accurate describe their structural and electronic properties.


  We report for the first time the pattern dynamics in the vicinity of an
inverse homoclinic bifurcation in an extended dissipative system. We observe,
in direct numerical simulations of three dimensional Rayleigh-B\'{e}nard
convection, a spontaneous breaking of a competition of two mutually
perpendicular sets of oscillating cross rolls to one of two possible sets of
oscillating cross rolls as the Rayleigh number is raised above a critical
value. The time period of the cross-roll patterns diverges, and shows scaling
behavior near the bifurcation point. This is an example of a transition from
nonlocal to local pattern dynamics near an inverse homoclinic bifurcation. We
also present a simple four-mode model that captures the pattern dynamics quite
well.


  We construct a four-parameter family of Markov processes on infinite
Gelfand-Tsetlin schemes that preserve the class of central (Gibbs) measures.
Any process in the family induces a Feller Markov process on the
infinite-dimensional boundary of the Gelfand-Tsetlin graph or, equivalently,
the space of extreme characters of the infinite-dimensional unitary group
U(infinity). The process has a unique invariant distribution which arises as
the decomposing measure in a natural problem of harmonic analysis on
U(infinity) posed in arXiv:math/0109193. As was shown in arXiv:math/0109194,
this measure can also be described as a determinantal point process with a
correlation kernel expressed through the Gauss hypergeometric function.


  A nonlinear optimization method is proposed for the solution of inverse
medium problems with spatially varying properties. To avoid the prohibitively
large number of unknown control variables resulting from standard grid-based
representations, the misfit is instead minimized in a small subspace spanned by
the first few eigenfunctions of a judicious elliptic operator, which itself
depends on the previous iteration. By repeatedly adapting both the dimension
and the basis of the search space, regularization is inherently incorporated at
each iteration without the need for extra Tikhonov penalization. Convergence is
proved under an angle condition, which is included into the resulting
\emph{Adaptive Spectral Inversion} (ASI) algorithm. The ASI approach compares
favorably to standard grid-based inversion using $L^2$-Tikhonov regularization
when applied to an elliptic inverse problem. The improved accuracy resulting
from the newly included angle condition is further demonstrated via numerical
experiments from time-dependent inverse scattering problems.


  The main purpose of this paper is to demonstrate and illustrate, once again,
the potency of the variational technique as an approximation procedure for the
quantization of quantum mechanical systems. By choosing particle-in-a-box
wavefunctions as trial wavefunctions, with the size of the box as the variation
parameter, approximate eigenenergies and the corresponding eigenfunctions are
obtained for the one dimensional free harmonic oscillator.


  I present recent CLEO measurements of inclusive semileptonic B decay spectra
and the branching fraction. I also report preliminary results from a combined
fit to spectral moments, which are compared to expectations in the Heavy Quark
Expansion and used to precisely determine |V_cb|.


  Let N be a symmetric space of dimension n > 5 whose de Rham decomposition
contains no factors of constant curvature and let W be the Weyl tensor of N at
some point. We prove that a Riemannian manifold whose Weyl tensor at every
point is a positive multiple of W is conformally equivalent to N (the case N =
R^n is the Weyl-Schouten Theorem).


  Solving zero-dimensional polynomial systems using Gr\"obner bases is usually
done by, first, computing a Gr\"obner basis for the degree reverse
lexicographic order, and next computing the lexicographic Gr\"obner basis with
a change of order algorithm. Currently, the change of order now takes a
significant part of the whole solving time for many generic instances.
  Like the fastest known change of order algorithms, this work focuses on the
situation where the ideal defined by the system satisfies natural properties
which can be recovered in generic coordinates. First, the ideal has a
\emph{shape} lexicographic Gr\"obner basis. Second, the set of leading terms
with respect to the degree reverse lexicographic order has a \emph{stability}
property; in particular, the multiplication matrix can be read on the input
Gr\"obner basis.
  The current fastest algorithms rely on the sparsity of this matrix. Actually,
this sparsity is a consequence of an algebraic structure, which can be
exploited to represent the matrix concisely as a univariate polynomial matrix.
We show that the Hermite normal form of that matrix yields the sought
lexicographic Gr\"obner basis, under assumptions which cover the shape position
case. Under some mild assumption implying $n \le t$, the arithmetic complexity
of our algorithm is $O\tilde{~}(t^{\omega-1}D)$, where $n$ is the number of
variables, $t$ is a sparsity indicator of the aforementioned matrix, $D$ is the
degree of the zero-dimensional ideal under consideration, and $\omega$ is the
exponent of matrix multiplication. This improves upon both state-of-the-art
complexity bounds $O\tilde{~}(tD^2)$ and $O\tilde{~}(D^\omega)$, since $\omega
< 3$ and $t\le D$. Practical experiments, based on the libraries msolve and
PML, confirm the high practical benefit.


  As artificial intelligence continues its unprecedented global expansion,
accompanied by a proliferation of benefits, an increasing apprehension about
the privacy and security implications of AI-enabled systems emerges. The
pivotal question of effectively controlling AI development at both
jurisdictional and organizational levels has become a prominent theme in
contemporary discourse. While the European Parliament and Council have taken a
decisive step by reaching a political agreement on the EU AI Act, the first
comprehensive AI law, organizations still find it challenging to adapt to the
fast-evolving AI landscape, lacking a universal tool for evaluating the privacy
and security dimensions of their AI models and systems. In response to this
critical challenge, this study conducts a systematic literature review spanning
the years 2020 to 2023, with a primary focus on establishing a unified
definition of key concepts in AI Ethics, particularly emphasizing the domains
of privacy and security. Through the synthesis of knowledge extracted from the
SLR, this study presents a conceptual framework tailored for privacy- and
security-aware AI systems. This framework is designed to assist diverse
stakeholders, including organizations, academic institutions, and governmental
bodies, in both the development and critical assessment of AI systems.
Essentially, the proposed framework serves as a guide for ethical
decision-making, fostering an environment wherein AI is developed and utilized
with a strong commitment to ethical principles. In addition, the study unravels
the key issues and challenges surrounding the privacy and security dimensions,
delineating promising avenues for future research, thereby contributing to the
ongoing dialogue on the globalization and democratization of AI ethics.