  Narrow Line Seyfert 1 galaxies represent a distinct category in the larger
family of Type 1 Active Galactic Nuclei. The occurrence of emission line
profiles not broader than 2000 km/s, combined with luminosity estimates
comparable to those of their broad line emitting analogues, suggests that some
extreme property is characterizing the fueling of their central engines. Two
hypotheses are more commonly considered: on the one hand, it was suggested that
the peculiar features of NLS1s might be interpreted as the consequence of a
nearly pole-on view over a geometrically flattened source; on the other, there
are arguments favoring the interpretation of a relatively low mass black hole,
accreting at very high rates. Both explanations provide advantages and
drawbacks, but, in spite of the different assumed physics, they agree in
identifying NLS1s as the crucial test ground for our understanding of the Broad
Line Region structure and dynamics in AGN. Here we report the results obtained
investigating asynchronous optical and X-ray spectroscopic observations,
respectively extracted from the Sloan Digital Sky Survey and the XMM-Newton
science archives, of a sample of both broad and narrow line emitting Seyfert 1
galaxies. Exploiting data collected by the different instruments carried on
board XMM, we try to identify the various components which sum up in the
observed broad band spectra of the two classes. We discuss the relation that
thermal, non-thermal, line emission and broad band absorption components of the
X-ray source show with the optical emission line profiles, as interpreted in
the framework of a composite Broad Emission Line Region structural model.


  Quantum state transfer between distant nodes is at the heart of quantum
processing and quantum networking. Stimulated by this, we propose a scheme
where one can highly achieve quantum state transfer between sites in a cavity
quantum optomechanical network. There, each individual cell site is composed of
a localized mechanical mode which interacts with a laser-driven cavity mode via
radiation pressure, and photons exchange between neighboring sites is allowed.
After the diagonalization of the Hamiltonian of each cell, we show that the
system can be reduced to an effective Hamiltonian of two decoupled bosonic
chains, and therefore we can apply the well-known results regarding quantum
state transfer in conjuction with an additional condition on the transfer
times. In fact, we show that our transfer protocol works for any arbitrary
quantum state, a result that we will illustrate within the red sideband regime.
Finally, in order to give a more realistic scenario we take into account the
effects of independent thermal reservoirs for each site. Thus, solving the
standard master equation within the Born-Markov approximation, we reassure both
the effective model as well as the feasibility of our protocol.


  We prove two partial regularity results for the scalar equation
$u_t+u_{xxxx}+\partial_{xx}u_x^2=0$, a model of surface growth arising from the
physical process of molecular epitaxy. We show that the set of space-time
singularities has (upper) box-counting dimension no larger than $7/6$ and
$1$-dimensional (parabolic) Hausdorff measure zero. These parallel the results
available for the three-dimensional Navier--Stokes equations. In fact the
mathematical theory of the surface growth model is known to share a number of
striking similarities with the Navier--Stokes equations, and the partial
regularity results are the next step towards understanding this remarkable
similarity. As far as we know the surface growth model is the only
lower-dimensional "mini-model" of the Navier--Stokes equations for which such
an analogue of the partial regularity theory has been proved. In the course of
our proof, which is inspired by the rescaling analysis of Lin (1998) and
Ladyzhenskaya & Seregin (1999), we develop certain nonlinear parabolic
Poincar\'e inequality, which is a concept of independent interest. We believe
that similar inequalities could be applicable in other parabolic equations.


  Polar diatomic molecules that have, or are expected to have a
$^2\Sigma_{1/2}$-ground state are studied systematically with respect to
simultaneous violation of parity $\mathcal{P}$ and time-reversal $\mathcal{T}$
with numerical methods and analytical models. Enhancements of
$\mathcal{P,T}$-violating effects due to an electric dipole moment of the
electron (eEDM) and $\mathcal{P,T}$-odd scalar-pseudoscalar nucleon-electron
current interactions are analyzed by comparing trends within columns and rows
of the periodic table of the elements. For this purpose electronic structure
parameters are calculated numerically within a quasi-relativistic zeroth order
regular approximation (ZORA) approach in the framework of complex generalized
Hartree-Fock (cGHF) or Kohn-Sham (cGKS). Scaling relations known from analytic
relativistic atomic structure theory are compared to these numerical results.
Based on this analysis, problems of commonly used relativistic enhancement
factors are discussed. Furthermore the ratio between both $\mathcal{P,T}$-odd
electronic structure parameters mentioned above is analyzed for various groups
of the periodic table. From this analysis an analytic measure for the
disentanglement of the two $\mathcal{P,T}$-odd electronic structure parameters
with multiple experiments in dependence of electronic structure enhancement
factors is derived.


  We compute the integral on matrix quantum (super) groups of type $A_{r|s}$
and derive from it the quantum analogue of (super) HCIZ integral.


  Semi-supervised learning, i.e. jointly learning from labeled and unlabeled
samples, is an active research topic due to its key role on relaxing human
supervision. In the context of image classification, recent advances to learn
from unlabeled samples are mainly focused on consistency regularization methods
that encourage invariant predictions for different perturbations of unlabeled
samples. We, conversely, propose to learn from unlabeled data by generating
soft pseudo-labels using the network predictions. We show that a naive
pseudo-labeling overfits to incorrect pseudo-labels due to the so-called
confirmation bias and demonstrate that mixup augmentation and setting a minimum
number of labeled samples per mini-batch are effective regularization
techniques for reducing it. The proposed approach achieves state-of-the-art
results in CIFAR-10/100, SVHN, and Mini-ImageNet despite being much simpler
than other methods. These results demonstrate that pseudo-labeling alone can
outperform consistency regularization methods, while the opposite was supposed
in previous work. Source code is available at https://git.io/fjQsC.


  We present a simple, yet accurate approximation for calculating the cosmic
microwave background anisotropy power spectrum in adiabatic models. It consists
of solving for the evolution of a two-fluid model until the epoch of
recombination and then integrating over the sources to obtain the CMB
anisotropy power spectrum. The approximation is useful both for a physical
understanding of CMB anisotropies, as well as for a quantitative analysis of
cosmological models. Comparison with exact calculations shows that the accuracy
is typically better than 20 percent over a large range of angles and
cosmological models, including those with curvature and cosmological constant.
Using this approximation we investigate the dependence of the CMB anisotropies
on the cosmological parameters. We identify six dimensionless parameters that
uniquely determine the anisotropy power spectrum within our approximation. CMB
experiments on different angular scales could in principle provide information
on all these parameters. In particular, mapping of the Doppler peaks would
allow an independent determination of baryon mass density, matter mass density
and Hubble constant.


  We experimentally studied the effect of flexibility on the flow produced by
sinusoidally pitching foil in quiescent fluid. The rigid foil produces a weak,
divergent and meandering jet. On the contrary, the foil with a flexible flap
produces an orderly, narrow, coherent jet. It has been observed that such
orderly jet is produced when the flap has appropriate flexibility. The jet
produced in quiescent fluid by the flexible foil is accompanied by a
corresponding thrust. In that sense, this is simple and different type of
hovering.


  The instabilities induced on a two-dimensional system of correlated electrons
by the anisotropies of its Fermi line are analyzed on general grounds. Simple
scaling arguments allow to predict the opening of a superconducting gap with a
well-defined symmetry prescribed by the geometry of the Fermi line. The same
arguments predict a critical dimension of 3/2 for the transition of the
two-dimensional system to non-Fermi liquid behavior. The methods are applied to
the t-t' Hubbard model in a wide range of dopings.


  We devise a polynomial-time approximation scheme for the classical geometric
problem of finding an approximate short path amid weighted regions. In this
problem, a triangulated region P comprising of n vertices, a positive weight
associated with each triangle, and two points s and t that belong to P are
given as the input. The objective is to find a path whose cost is at most
(1+epsilon)OPT where OPT is the cost of an optimal path between s and t. Our
algorithm initiates a discretized-Dijkstra wavefront from source s and
progresses the wavefront till it strikes t. This result is about a cubic factor
(in n) improvement over the Mitchell and Papadimitriou '91 result, which is the
only known polynomial time algorithm for this problem to date. Further, with
polynomial time preprocessing of P, a set of data structures are computed which
allow answering approximate weighted shortest path queries in polynomial time.


  Privacy is an increasingly important aspect of data publishing. Reasoning
about privacy, however, is fraught with pitfalls. One of the most significant
is the auxiliary information (also called external knowledge, background
knowledge, or side information) that an adversary gleans from other channels
such as the web, public records, or domain knowledge. This paper explores how
one can reason about privacy in the face of rich, realistic sources of
auxiliary information. Specifically, we investigate the effectiveness of
current anonymization schemes in preserving privacy when multiple organizations
independently release anonymized data about overlapping populations. 1. We
investigate composition attacks, in which an adversary uses independent
anonymized releases to breach privacy. We explain why recently proposed models
of limited auxiliary information fail to capture composition attacks. Our
experiments demonstrate that even a simple instance of a composition attack can
breach privacy in practice, for a large class of currently proposed techniques.
The class includes k-anonymity and several recent variants. 2. On a more
positive note, certain randomization-based notions of privacy (such as
differential privacy) provably resist composition attacks and, in fact, the use
of arbitrary side information. This resistance enables stand-alone design of
anonymization schemes, without the need for explicitly keeping track of other
releases. We provide a precise formulation of this property, and prove that an
important class of relaxations of differential privacy also satisfy the
property. This significantly enlarges the class of protocols known to enable
modular design.


  We show the problem of counting homomorphisms from the fundamental group of a
homology $3$-sphere $M$ to a finite, non-abelian simple group $G$ is
#P-complete, in the case that $G$ is fixed and $M$ is the computational input.
Similarly, deciding if there is a non-trivial homomorphism is NP-complete. In
both reductions, we can guarantee that every non-trivial homomorphism is a
surjection. As a corollary, for any fixed integer $m \ge 5$, it is NP-complete
to decide whether $M$ admits a connected $m$-sheeted covering.
  Our construction is inspired by universality results in topological quantum
computation. Given a classical reversible circuit $C$, we construct $M$ so that
evaluations of $C$ with certain initialization and finalization conditions
correspond to homomorphisms $\pi_1(M) \to G$. An intermediate state of $C$
likewise corresponds to a homomorphism $\pi_1(\Sigma_g) \to G$, where
$\Sigma_g$ is a pointed Heegaard surface of $M$ of genus $g$. We analyze the
action on these homomorphisms by the pointed mapping class group
$\text{MCG}_*(\Sigma_g)$ and its Torelli subgroup $\text{Tor}_*(\Sigma_g)$. By
results of Dunfield-Thurston, the action of $\text{MCG}_*(\Sigma_g)$ is as
large as possible when $g$ is sufficiently large; we can pass to the Torelli
group using the congruence subgroup property of $\text{Sp}(2g,\mathbb{Z})$. Our
results can be interpreted as a sharp classical universality property of an
associated combinatorial $(2+1)$-dimensional TQFT.


  We approximate the Riemann Zeta-Function by polynomials and Dirichlet
polynomials with restricted zeros.


  We establish the isomorphism between a nonlinear $\sigma$-model and the
abelian gauge theory on an arbitrary curved background, which allows us to
derive integrable models and the corresponding Lax representations from gauge
theoretical point of view. In our approach the spectral parameter is related to
the global degree of freedom associated with the conformal or Galileo
transformations of the spacetime. The B$\ddot{\rm a}$cklund transformations are
derived from Chern-Simons theory where the spectral parameter is defined in
terms of the extract compactified space dimension coordinate.


  We study a one-dimensional nonlinear hyperbolic-parabolic initial boundary
value problem occurring in the theory of thermoelasticity. We prove existence
and uniqueness of the local-in-time strong solution. Also, some global-in-time
weak measure valued solutions are proven to exist. To this end we introduce an
auxiliary problem with artificial viscosity and prove its global-in-time
well-posedness. Next, we show that solutions of the auxiliary problem converge,
at some short time interval to the strong solution, and to our measure valued
solution for an arbitrary time.


  This article makes the key observation that when using cylindrical algebraic
decomposition (CAD) to solve a problem with respect to a set of polynomials, it
is not always the signs of those polynomials that are of paramount importance
but rather the truth values of certain quantifier free formulae involving them.
This motivates our definition of a Truth Table Invariant CAD (TTICAD). We
generalise the theory of equational constraints to design an algorithm which
will efficiently construct a TTICAD for a wide class of problems, producing
stronger results than when using equational constraints alone. The algorithm is
implemented fully in Maple and we present promising results from
experimentation.


  The thermodynamic (TD) properties of biological membranes play a central role
for living systems. It has been suggested, for instance, that nonlinear pulses
such as action potentials (APs) can only exist if the membrane state is in
vicinity of a TD transition. Herein, two membrane properties - excitability and
AP velocity - are investigated for a broad spectrum of conditions in living
systems (temperature (T), 3D-pressure (p) and pH dependence). Based on these
data we predict parameter ranges in which a transition of the membrane is
located (15-35{\deg}C below growth temperature; 1-3 pH units below pH 7; at
~800 atm) and propose the corresponding phase diagrams. The latter explain: (i)
changes of AP velocity with T, p and pH. (ii) The existence and origin of two
qualitatively different forms of loss of nonlinear excitability ("nerve
blockage", anesthesia). (iii) The type and quantity of parameter changes that
trigger APs. Finally, a quantitative comparison between the TD behaviour of
2D-lipid model membranes with living systems is attempted. The typical shifts
in transition temperature with pH and p of model membranes agree closely with
values obtained from cell physiological measurements (excitability and
propagation velocity). Taken together, these results strongly suggest that it
is not specific molecules that control the excitability of living systems but
rather the TD properties of the quasi 2D-membrane interface. The approach as
proposed herein can be extended to other quantities (surface potential, calcium
concentration, etc.) and makes clearly falsifiable predictions, for example,
that a transition exists within the specified parameter ranges in excitable
cells.


  The creation of machine learning algorithms for intelligent agents capable of
continuous, lifelong learning is a critical objective for algorithms being
deployed on real-life systems in dynamic environments. Here we present an
algorithm inspired by neuromodulatory mechanisms in the human brain that
integrates and expands upon Stephen Grossberg\'s ground-breaking Adaptive
Resonance Theory proposals. Specifically, it builds on the concept of
uncertainty, and employs a series of neuromodulatory mechanisms to enable
continuous learning, including self-supervised and one-shot learning. Algorithm
components were evaluated in a series of benchmark experiments that demonstrate
stable learning without catastrophic forgetting. We also demonstrate the
critical role of developing these systems in a closed-loop manner where the
environment and the agent\'s behaviors constrain and guide the learning
process. To this end, we integrated the algorithm into an embodied simulated
drone agent. The experiments show that the algorithm is capable of continuous
learning of new tasks and under changed conditions with high classification
accuracy (greater than 94 percent) in a virtual environment, without
catastrophic forgetting. The algorithm accepts high dimensional inputs from any
state-of-the-art detection and feature extraction algorithms, making it a
flexible addition to existing systems. We also describe future development
efforts focused on imbuing the algorithm with mechanisms to seek out new
knowledge as well as employ a broader range of neuromodulatory processes.


  Galaxy-scale strongly lensed systems have been shown to provide a unique
technique for exploring the underlying physics of dark matter at sub-galactic
scales. In the past, much attention was given to detecting and studying
individual haloes in a strong lens system. In addition to the subhaloes,
line-of-sight haloes contribute significantly to the small perturbations in
lensed images. In prior work, we demonstrated that these line-of-sight haloes
imprint a distinctive anisotropic signature and hence give rise to a detectable
non-zero parity-even quadrupole moment in the effective convergence field's
two-point correlation function. In this study, we show that these line-of-sight
haloes also produce a non-zero curl component of the effective deflection field
with a parity-odd quadrupole moment of the two-point function. These multipole
moments have the ability to statistically separate line-of-sight haloes from
dark matter substructure. In this paper, we examine how these multipole moments
evolve in the presence of warm dark matter and self-interacting dark matter in
terms of central density evolution and dark matter halo abundance. Importantly,
we show that these different multipole moments display exquisite sensitivity to
both the amplitude and the velocity dependence of the dark matter
self-interaction cross-section. Our approach opens the door for strong lensing
observations to probe dark matter self-interaction over a broad range of
relative velocities.


  We introduce the notions of strong asymptotic uniform smoothness and
convexity. We show that the injective tensor product of strongly asymptotically
uniformly smooth spaces is asymptotically uniformly smooth. This applies in
particular to uniformly smooth spaces admitting a monotone FDD, extending a
result by Dilworth, Kutzarova, Randrianarivony, Revalski and Zhivkov. Our
techniques also provide a characterisation of Orlicz functions $M, N$ such that
the space of compact operators $\mathcal K(h_M,h_N)$ is asymptotically
uniformly smooth. Finally we show that $\mathcal K(X, Y)$ is not strictly
convex whenever $X$ and $Y$ are at least two-dimensional, which extends a
result by Dilworth and Kutzarova.


  We propose a new class of nonconvex penalty functions, based on data depth
functions, for multitask sparse penalized regression. These penalties quantify
the relative position of rows of the coefficient matrix from a fixed
distribution centered at the origin. We derive the theoretical properties of an
approximate one-step sparse estimator of the coefficient matrix using local
linear approximation of the penalty function, and provide algorithm for its
computation. For orthogonal design and independent responses, the resulting
thresholding rule enjoys near-minimax optimal risk performance, similar to the
adaptive lasso (Zou, 2006). A simulation study and real data analysis
demonstrate its effectiveness compared to some of the present methods that
provide sparse solutions in multivariate regression.


  Most of previously reported dark-bright solitons admit identical width for
the two components in both theoretical and experimental studies. We report
dark-bright solitons can admit strikingly different widths, and derive a family
of analytical solutions for them by Lagrangian variational method. The
existence regimes for these solitons become much more widespread in the space
of nonlinear parameters, than the ones for the previously known dark-bright
solitons with identical width. Our analysis indicates that the effective
quantum wells are quite different in the two components, in sharp contrast to
the ones for all previously known vector solitons. Especially, the particle
number of bright soliton can be used to control the generation of dark-bright
solitons with varied ratios of solitons' widths. Based on the current
experimental technologies, we propose an experimental scheme for observing
these novel dark-bright solitons. The results suggest that abundant vector
solitons with difference widths exist in multi-components coupled systems, and
would inspire experiments to observe them in nonlinear optical fibers,
Bose-Einstein condensates, and other nonlinear coupled systems.


  Linear systems such as room acoustics and string oscillations may be modeled
as the sum of mode responses, each characterized by a frequency, damping and
amplitude. Here, we consider finding the mode parameters from impulse response
measurements, and estimate the mode frequencies and decay rates as the
generalized eigenvalues of Hankel matrices of system response samples, similar
to ESPRIT. For greater resolution at low frequencies, such as desired in room
acoustics and musical instrument modeling, the estimation is done on a warped
frequency axis. The approach has the benefit of selecting the number of modes
to achieve a desired fidelity to the measured impulse response. An optimization
to further refine the frequency and damping parameters is presented. The method
is used to model coupled piano strings and room impulse responses, with its
performance comparing favorably to FZ-ARMA.


  In [18] we have shown that, for $p_{1},p_{2}\in(2,\infty]$, the constants of
Bennett's inequality on unimodular bilinear forms on $\ell_{p_{1}}^{n_{1}
}\times\ell_{p_{2}}^{n_{2}}$ are asymptotically bounded by $1$. In the present
paper we use a different approximation technique to investigate the remaining
cases $p_{1},p_{2}\in\lbrack1,\infty].$ This new approach also provides a
stronger asymptotic control, in the sense that the constants are "uniformly"
asymptotically bounded by $1$, with no dependence on $p_{1},p_{2}.$


  We consider the asymptotic expansion of the generalised exponential integral
involving the Mittag-Leffler function introduced recently by Mainardi and
Masina [{\it Fract. Calc. Appl. Anal.} {\bf 21} (2018) 1156--1169]. We extend
the definition of this function using the two-parameter Mittag-Leffler
function. The expansions of the similarly extended sine and cosine integrals
are also discussed. Numerical examples are presented to illustrate the accuracy
of each type of expansion obtained.


  Refined are the known descriptions of particle behavior with the help of
Hamilton function in the phase space of coordinates and their multiple
derivatives. This entails existing of circumstances when at closer distances
gravitational effects can prove considerably more strong than in case of this
situation being calculated with the help of Hamilton function in the phase
space of coordinates and their first derivatives. For example, this may be the
case if the gravitational potential is described as a power series in 1/r. At
short distances the space metrics fluctuations may also be described by a
divergent power series; henceforth, these fluctuations at smaller distances
also constitute a power series, i.e. they are functions of 1/r. For such
functions, the average of the coordinate equals zero if the frame of reference
coincides with the point of origin.


  We numerically investigate the long time dynamics of spatially periodic
breather solutions of the 1-D nonlinear Schr\"odinger equation under parametric
forcing of the form $f(x)=f_0 \exp(iKx)$ along with dissipation. In the absence
of dissipation, robust soliton-like excitations are observed that travel with
constant amplitude and velocity. With dissipation, these solitons lose energy
(and amplitude) yet gain speed - a characteristic not observed in an ordinary
soliton. Moreover, these novel solitons are found to be stable against random
perturbations.


  Scar theory is one of the fundamental pillars in the field of quantum chaos,
and scarred functions a superb tool to carry out studies in it. Several
methods, usually semiclassical, have been described to cope with these two
phenomena. In this paper, we present an alternative method, based on the novel
machine learning algorithm known as Reservoir Computing, to calculate such
scarred wavefunctions together with the associated eigenstates of the system.
The resulting methodology achieves outstanding accuracy while reducing
execution times by a factor of ten. As an illustration of the effectiveness of
this method, we apply it to the widespread chaotic two-dimensional coupled
quartic oscillator.


  This paper presents Chinese Poker Self-Playing Robot, an integrated system
enabling a TM5-900 robotic arm to independently play the four-person card game
Chinese poker. The robot uses a custom sucker mechanism to pick up and play
cards. An object detection model based on YOLOv5 is utilized to recognize the
suit and number of 13 cards dealt to the robot. A greedy algorithm is developed
to divide the 13 cards into optimal hands of 3, 5, and 5 cards to play.
Experiments demonstrate that the robot can successfully obtain the cards,
identify them using computer vision, strategically select hands to play using
the algorithm, and physically play the selected cards in the game. The system
showcases effective integration of mechanical design, computer vision,
algorithm design, and robotic control to accomplish the complex task of
independently playing cards.


  The Stabbing Planes proof system was introduced to model the reasoning
carried out in practical mixed integer programming solvers. As a proof system,
it is powerful enough to simulate Cutting Planes and to refute the Tseitin
formulas -- certain unsatisfiable systems of linear equations mod 2 -- which
are canonical hard examples for many algebraic proof systems. In a recent (and
surprising) result, Dadush and Tiwari showed that these short refutations of
the Tseitin formulas could be translated into quasi-polynomial size and depth
Cutting Planes proofs, refuting a long-standing conjecture. This translation
raises several interesting questions. First, whether all Stabbing Planes proofs
can be efficiently simulated by Cutting Planes. This would allow for the
substantial analysis done on the Cutting Planes system to be lifted to
practical mixed integer programming solvers. Second, whether the
quasi-polynomial depth of these proofs is inherent to Cutting Planes.
  In this paper we make progress towards answering both of these questions.
First, we show that any Stabbing Planes proof with bounded coefficients SP* can
be translated into Cutting Planes. As a consequence of the known lower bounds
for Cutting Planes, this establishes the first exponential lower bounds on SP*.
Using this translation, we extend the result of Dadush and Tiwari to show that
Cutting Planes has short refutations of any unsatisfiable system of linear
equations over a finite field. Like the Cutting Planes proofs of Dadush and
Tiwari, our refutations also incur a quasi-polynomial blow-up in depth, and we
conjecture that this is inherent. As a step towards this conjecture, we develop
a new geometric technique for proving lower bounds on the depth of Cutting
Planes proofs. This allows us to establish the first lower bounds on the depth
of Semantic Cutting Planes proofs of the Tseitin formulas.


  Learning big data by matrix decomposition always suffers from expensive
computation, mixing of complicated structures and noise. In this paper, we
study more adaptive models and efficient algorithms that decompose a data
matrix as the sum of semantic components with incoherent structures. We firstly
introduce "GO decomposition (GoDec)", an alternating projection method
estimating the low-rank part $L$ and the sparse part $S$ from data matrix
$X=L+S+G$ corrupted by noise $G$. Two acceleration strategies are proposed to
obtain scalable unmixing algorithm on big data: 1) Bilateral random projection
(BRP) is developed to speed up the update of $L$ in GoDec by a closed-form
built from left and right random projections of $X-S$ in lower dimensions; 2)
Greedy bilateral (GreB) paradigm updates the left and right factors of $L$ in a
mutually adaptive and greedy incremental manner, and achieve significant
improvement in both time and sample complexities. Then we proposes three
nontrivial variants of GoDec that generalizes GoDec to more general data type
and whose fast algorithms can be derived from the two strategies......


  In this work, we focus on an infinite horizon mean-field linear-quadratic
stochastic control problem with jumps. Firstly, the infinite horizon linear
mean-field stochastic differential equations and backward stochastic
differential equations with jumps are studied to support the research of the
control problem. The global integrability properties of their solution
processes are studied by introducing a kind of so-called dissipation conditions
suitable for the systems involving the mean-field terms and jumps. For the
control problem, we conclude a sufficient and necessary condition of open-loop
optimal control by the variational approach. Besides, a kind of infinite
horizon fully coupled linear mean-field forward-backward stochastic
differential equations with jumps is studied by using the method of
continuation. Such a research makes the characterization of the open-loop
optimal controls more straightforward and complete.


  We introduce and develop fine shape, which has a very simple definition and
aims to supersede all previously known shape theories for metrizable spaces.
  The problem with known shape theories of metrizable spaces is illustrated by
the following bizarre situation. \v{C}ech cohomology is an invariant of shape,
and a fortiori of strong shape. But Steenrod-Sitnikov homology is not shape
invariant (already for compacta) and has not been proved to be strong shape
invariant (in more than 40 years). Worse yet, there is an ordinary homology
theory that is strong shape invariant by design, but it cannot be computed in
ZFC for simplest non-compact non-ANRs (such as the disjoint union of countably
many copies of the one-point compactification of the countable discrete space).
On the other hand, Steenrod-Sitnikov homology is an invariant of antishape
(=compactly generated strong shape), and a fortiori of strong antishape.
However, \v{C}ech cohomology is not antishape invariant (already for ANRs) and
has not been proved to be strong antishape invariant. And there is an ordinary
cohomology theory that is strong antishape invariant by design, but it cannot
be computed in ZFC for simplest non-compact non-ANRs.
  Even though strong shape and strong antishape differ from each other by
exchanging direct and inverse limits, we show that their natural "corrections"
(taking into account a topology on the indexing sets) coincide for all
metrizable spaces. This common "correction", called fine shape, is much simpler
than the original theories and has both \v{C}ech cohomology and
Steenrod-Sitnikov homology as its invariants. For ANRs fine shape coincides
with homotopy, for compacta with strong shape, and for locally compact
separable metrizable spaces - with strong antishape.
  We prove that a (co)homology theory is fine shape invariant if and only if it
satisfies the map excision axiom.


  While autonomous navigation of mobile robots on rigid terrain is a
well-explored problem, navigating on deformable terrain such as tall grass or
bushes remains a challenge. To address it, we introduce an explainable,
physics-aware and end-to-end differentiable model which predicts the outcome of
robot-terrain interaction from camera images, both on rigid and non-rigid
terrain. The proposed MonoForce model consists of a black-box module which
predicts robot-terrain interaction forces from onboard cameras, followed by a
white-box module, which transforms these forces and a control signals into
predicted trajectories, using only the laws of classical mechanics. The
differentiable white-box module allows backpropagating the predicted trajectory
errors into the black-box module, serving as a self-supervised loss that
measures consistency between the predicted forces and ground-truth trajectories
of the robot. Experimental evaluation on a public dataset and our data has
shown that while the prediction capabilities are comparable to state-of-the-art
algorithms on rigid terrain, MonoForce shows superior accuracy on non-rigid
terrain such as tall grass or bushes. To facilitate the reproducibility of our
results, we release both the code and datasets.


  The symmetric logarithmic derivative Cram\'er-Rao bound (SLDCRB) provides a
fundamental limit to the minimum variance with which a set of unknown
parameters can be estimated in an unbiased manner. It is known that the SLDCRB
can be saturated provided the optimal measurements for the individual
parameters commute with one another. However, when this is not the case the
SLDCRB cannot be attained in general. In the experimentally relevant setting,
where quantum states are measured individually, necessary and sufficient
conditions for when the SLDCRB can be saturated are not known. In this setting
the SLDCRB is attainable provided the SLD operators can be chosen to commute on
an extended Hilbert space. However, beyond this relatively little is known
about when the SLD operators can be chosen in this manner. In this paper we
present explicit examples which demonstrate novel aspects of this condition.
Our examples demonstrate that the SLD operators commuting on any two of the
following three spaces: support space, support-kernel space and kernel space,
is neither a necessary nor sufficient condition for commutativity on the
extended space. We present a simple analytic example showing that the
Nagaoka-Hayashi Cram\'er-Rao bound is not always attainable. Finally, we
provide necessary and sufficient conditions for the attainability of the SLDCRB
in the case when the kernel space is one-dimensional. These results provide new
information on the necessary and sufficient conditions for the attainability of
the SLDCRB.


  We study the asymptotic profile, as $\hbar\rightarrow 0$, of positive
solutions to $$-\hbar^2\Delta u+V(x)u-\hbar^{2+\gamma}u\Delta
u^2=K(x)|u|^{p-2}u,\ \ x\in \mathbb{R}^N $$ where $\gamma\geq 0$ is a parameter
with relevant physical interpretations, $V$ and $K$ are given potentials and
$N\geq 5$. We investigate the concentrating behavior of solutions when
$\gamma>0$ and, differently form the case $\gamma=0$ where the leading
potential is $V$, the concentration is here localized by the source potential
$K$. Moreover, surprisingly for $\gamma>0$ we find a different concentration
behavior of solutions in the case $p=\frac{2N}{N-2}$ and when
$\frac{2N}{N-2}<p<\frac{4N}{N-2}$. This phenomenon does not occur when
$\gamma=0$.


  We have analyzed the size distribution of voids in 2D slices of the Las
Campanas Redshift Survey (LCRS). The characteristic sizes show a scaling $D =
D_0 + \nu\lambda$ with the mean galaxy separation $\lambda$. Comparison with
mock samples of the LCRS in 2D and 3D, using various simulations, cosmologies
and galaxy identification schemes, gives a similar scaling, but with steeper
slope and a lack of large voids. Best results are obtained for dark matter
halos in a $\Lambda$CDM model.


  We report an efficient technique to treat density functionals of the
meta-generalized gradient approximation (mGGA) class in conjunction with
density fitting of Coulomb terms (DF-J) and exchange-correlation terms (DF-X).
While the kinetic energy density $\tau$ cannot be computed in the context of a
DF-JX calculation, we show that the Laplacian of the density $\upsilon$ can be
computed with almost no extra cost. With this technique, $\upsilon$-form mGGAs
become only slightly more expensive (10%--20%) than GGAs in DF-JX
treatment---and several times faster than regular $\tau$-based mGGA
calculations with DF-J and regular treatment of the density functional. We
investigate the translation of $\upsilon$-form mGGAs into $\tau$-form mGGAs by
employing a kinetic energy functional, but find this insufficiently reliable at
this moment. However, $\upsilon$ and $\tau$ are believed to carry essentially
equivalent information beyond $\rho$ and $\Vert\vec\nabla\rho\Vert$ [Phys. Rev.
B 2007, 75, 155109], so a reparametrization of accurate mGGAs from the
$\tau$-form into the $\upsilon$-form should be possible. Once such functionals
become available, we expect the presented technique to become a powerful tool
in the computation of reaction paths, intermediates, and transition states of
medium sized molecules.


  Updating an abstract Voronoi diagram after deletion of one site in linear
time has been a well-known open problem; similarly, for concrete Voronoi
diagrams of non-point sites. In this paper, we present an expected linear-time
algorithm to update an abstract Voronoi diagram after deletion of one site. We
introduce the concept of a Voronoi-like diagram, a relaxed version of an
abstract Voronoi construct that has a structure similar to an ordinary Voronoi
diagram, without, however, being one. We formalize the concept, and prove that
it is robust under insertion, therefore, enabling its use in incremental
constructions. The time-complexity analysis of the resulting simple randomized
incremental construction is non-standard, and interesting in its own right,
because the intermediate Voronoi-like structures are order-dependent. We
further extend the approach to compute the following structures in expected
linear time: the order-(k+1) subdivision within an order-k Voronoi region, and
the farthest abstract Voronoi diagram after the order of its regions at
infinity is known.


  Classical light fields are considered physical examples of nonquantum
entanglement\cite{Eberly2011}. We apply concurrence and Schmidt approach to
evaluate the degree of entanglement for a generalized polarization state that
Qian and Eberly suggested, and we obtained an analytic form of the general
entanglement state for planar polarization states of classical light.


  Motivated by questions from quantum group and field theories, we review
structures on manifolds that are weaker versions of Poisson structures, and
variants of the notion of Lie algebroid. We give a simple definition of the
Courant algebroids and introduce the notion of a deriving operator for the
Courant bracket of the double of a proto-bialgebroid. We then describe and
relate the various quasi-Poisson structures, which have appeared in the
literature since 1991, and the twisted Poisson structures studied by Severa and
Weinstein.


  Although extreme learning machine (ELM) has been successfully applied to a
number of pattern recognition problems, it fails to pro-vide sufficient good
results in hyperspectral image (HSI) classification due to two main drawbacks.
The first is due to the random weights and bias of ELM, which may lead to
ill-posed problems. The second is the lack of spatial information for
classification. To tackle these two problems, in this paper, we propose a new
framework for ELM based spectral-spatial classification of HSI, where
probabilistic modelling with sparse representation and weighted composite
features (WCF) are employed respectively to derive the op-timized output
weights and extract spatial features. First, the ELM is represented as a
concave logarithmic likelihood function under statistical modelling using the
maximum a posteriori (MAP). Second, the sparse representation is applied to the
Laplacian prior to effi-ciently determine a logarithmic posterior with a unique
maximum in order to solve the ill-posed problem of ELM. The variable splitting
and the augmented Lagrangian are subsequently used to further reduce the
computation complexity of the proposed algorithm and it has been proven a more
efficient method for speed improvement. Third, the spatial information is
extracted using the weighted compo-site features (WCFs) to construct the
spectral-spatial classification framework. In addition, the lower bound of the
proposed method is derived by a rigorous mathematical proof. Experimental
results on two publicly available HSI data sets demonstrate that the proposed
methodology outperforms ELM and a number of state-of-the-art approaches.


  The goal of this study is to develop focal, accurate and robust finite
element method (FEM) based approaches which can predict the electric potential
on the surface of the computational domain given its structure and internal
primary source current distribution. While conducting an EEG evaluation, the
placement of source currents to the geometrically complex grey matter
compartment is a challenging but necessary task to avoid forward errors
attributable to tissue conductivity jumps. Here, this task is approached via a
mathematically rigorous formulation, in which the current field is modeled via
divergence conforming H(div) basis functions. Both linear and quadratic
functions are used while the potential field is discretized via the standard
linear Lagrangian (nodal) basis. The resulting model includes dipolar sources
which are interpolated into a random set of positions and orientations
utilizing two alternative approaches: the position based optimization (PBO) and
the mean position/orientation (MPO) method. These results demonstrate that the
present dipolar approach can reach or even surpass, at least in some respects,
the accuracy of two classical reference methods, the partial integration (PI)
and St. Venant (SV) approach which utilize monopolar loads instead of dipolar
currents.


  A toy model for glioma treatment by a radio frequency electric field is
suggested. This low-intensity, intermediate-frequency alternating electric
field is known as the tumor-treating-field (TTF). In the framework of this
model the efficiency of this TTF is estimated, and the interplay between the
TTF and the migration-proliferation dichotomy of cancer cells is considered.
The model is based on a modification of a comb model for cancer cells, where
the migration-proliferation dichotomy becomes naturally apparent. Considering
glioma cancer as a fractal dielectric composite of cancer cells and normal
tissue cells, a new effective mechanism of glioma treatment is suggested in the
form of a giant enhancement of the TTF. This leads to the irreversible
electroporation that may be an effective non-invasive method of treating brain
cancer.


  The success of applications for sharing GPS trajectories raises serious
privacy concerns, in particular about users' home addresses. In this paper we
show that a Bayesian approach is natural and effective for a rigorous analysis
of home-identification attacks and their countermeasures, in terms of privacy.
We focus on a family of countermeasures named "privacy-region strategies",
consisting in publishing each trajectory from the first exit to the last
entrance from/into a privacy region. Their performance is studied through
simulations on Brownian motions.


  One of the phenomena that causes high decoding failure rates is trapping
sets. Characterization of $(a,b)$ elementary trapping sets (ETSs), their
graphical properties and the lower bounds on their size in variable regular
LDPC codes with column weights 3, 4, 5 and 6, where $a$ is the size of the ETS
and $b$ is the number of degree-one check nodes, have been an interesting
subject among researchers. Although progressive-edge-growth method (PEG) to
construct LDPC codes free of an specific ETS has been proposed in the
literature, it is mostly applied to LDPC codes with column weight 3. In this
paper, we focus on constructing QC-LDPC codes with column weight 4 whose Tanner
graphs are free of small ETSs. Using coloring the edges of the variable node
(VN) graph corresponding to an ETS, we provide the sufficient conditions to
obtain QC-LDPC codes with column weight 4, girth 6 and free of $(5,b)$ ETSs,
where $b\leq4$, and $(6,b)$ ETs, where $b\leq2$. Moreover, for $(4,n)$-regular
QC-LDPC codes with girth 8, we present a method to remove $(7,4)$ ETSs from
Tanner graphs.


  Intermediate-mass black holes (IMBHs, $10^{3-6} \, \rm{M_\odot}$), are
typically found at the center of dwarf galaxies and might be wandering, thus
far undetected, in the Milky Way (MW). We use model spectra for
advection-dominated accretion flows to compute the typical fluxes, in a range
of frequencies spanning from radio to X-rays, emitted by a putative population
of $10^5 \, \rm{M_\odot}$ IMBHs wandering in five realistic, volume-weighted,
MW environments. We predict that $\sim 27\%$ of the wandering IMBHs can be
detected in the X-ray with Chandra, $\sim 37\%$ in the near-infrared with the
Roman Space Telescope, $\sim 49\%$ in the sub-mm with CMB-S4 and $\sim 57\%$ in
the radio with ngVLA. We find that the brightest fluxes are emitted by IMBHs
passing through molecular clouds or cold neutral medium, where they are always
detectable. We propose criteria to facilitate the selection of candidates in
multi-wavelength surveys. Specifically, we compute the X-ray to optical ratio
($\alpha_{\rm ox}$) and the optical to sub-mm ratio, as a function of the
accretion rate of the IMBH. We show that at low rates the sub-mm emission of
IMBHs is significantly higher than the optical, UV and X-ray emission. Finally,
we place upper limits on the number $N_\bullet$ of these objects in the MW:
$N_\bullet<2000$ and $N_\bullet<100$, based on our detectability expectations
and current lack of detections in molecular clouds and cold neutral medium,
respectively. These predictions will guide future searches of IMBHs in the MW,
which will be instrumental to understanding their demographics and evolution.


  In this note, we prove that if G is a countable group that contains a
nonabelian free subgroup then every pair of nontrivial Bernoulli shifts over G
are weakly isomorphic.


  A variational technique is used to derive analytical expressions for the
sensitivity of recirculation length to steady forcing in separated flows.
Linear sensitivity analysis is applied to the two-dimensional steady flow past
a circular cylinder for Reynolds numbers $40 \leq Re \leq 120$, both in the
subcritical and supercritical regimes. Regions which are the most sensitive to
volume forcing and wall blowing/suction are identified. Control configurations
which reduce the recirculation length are designed based on the sensitivity
information, in particular small cylinders used as control devices in the wake
of the main cylinder, and fluid suction at the cylinder wall. Validation
against full non-linear Navier-Stokes calculations shows excellent agreement
for small-amplitude control. The linear stability properties of the controlled
flow are systematically investigated. At moderate Reynolds numbers, we observe
that regions where control reduces the recirculation length correspond to
regions where it has a stabilising effect on the most unstable global mode
associated to vortex shedding, while this property does not hold any more at
larger Reynolds numbers.


  We present Residual Policy Learning (RPL): a simple method for improving
nondifferentiable policies using model-free deep reinforcement learning. RPL
thrives in complex robotic manipulation tasks where good but imperfect
controllers are available. In these tasks, reinforcement learning from scratch
remains data-inefficient or intractable, but learning a residual on top of the
initial controller can yield substantial improvements. We study RPL in six
challenging MuJoCo tasks involving partial observability, sensor noise, model
misspecification, and controller miscalibration. For initial controllers, we
consider both hand-designed policies and model-predictive controllers with
known or learned transition models. By combining learning with control
algorithms, RPL can perform long-horizon, sparse-reward tasks for which
reinforcement learning alone fails. Moreover, we find that RPL consistently and
substantially improves on the initial controllers. We argue that RPL is a
promising approach for combining the complementary strengths of deep
reinforcement learning and robotic control, pushing the boundaries of what
either can achieve independently. Video and code at
https://k-r-allen.github.io/residual-policy-learning/.


  We study the interaction of non-Abelian topological $BF$ theories defined on
two dimensional manifolds with point sources carrying non-Abelian charges. We
identify the most general solution for the field equations on simply and
multiply connected two-manifolds. Taking the particular choice of the so-called
extended Poincar\'e group as the gauge group we discuss how recent discussions
of two dimensional gravity models do fit in this formalism.


  A brief review of the motivation and the present status of Fractional
Superstring is presented. Talk at ``Strings 93'', Berkeley, May 1993.


  We propose pixelNeRF, a learning framework that predicts a continuous neural
scene representation conditioned on one or few input images. The existing
approach for constructing neural radiance fields involves optimizing the
representation to every scene independently, requiring many calibrated views
and significant compute time. We take a step towards resolving these
shortcomings by introducing an architecture that conditions a NeRF on image
inputs in a fully convolutional manner. This allows the network to be trained
across multiple scenes to learn a scene prior, enabling it to perform novel
view synthesis in a feed-forward manner from a sparse set of views (as few as
one). Leveraging the volume rendering approach of NeRF, our model can be
trained directly from images with no explicit 3D supervision. We conduct
extensive experiments on ShapeNet benchmarks for single image novel view
synthesis tasks with held-out objects as well as entire unseen categories. We
further demonstrate the flexibility of pixelNeRF by demonstrating it on
multi-object ShapeNet scenes and real scenes from the DTU dataset. In all
cases, pixelNeRF outperforms current state-of-the-art baselines for novel view
synthesis and single image 3D reconstruction. For the video and code, please
visit the project website: https://alexyu.net/pixelnerf


  The $\alpha+d\rightarrow\, ^6{\rm Li}+\gamma$ radiative capture is studied in
order to predict the $^6$Li primordial abundance. Within a two-body framework,
the $\alpha$ particle and the deuteron are considered the structureless
constituents of $^6$Li. Five $\alpha+d$ potentials are used to solve the
two-body problem: four of them are taken from the literature, only one having
also a tensor component. A fifth model is here constructed in order to
reproduce, besides the $^6$Li static properties as binding energy, magnetic
dipole and electric quadrupole moments, also the $S$-state asymptotic
normalization coefficient (ANC). The two-body bound and scattering problem is
solved with different techniques, in order to minimize the numerical
uncertainty of the present results. The long-wavelength approximation is used,
and therefore only the electric dipole and quadrupole operators are retained.
The astrophysical $S$-factor is found to be significantly sensitive to the ANC,
but in all the cases in good agreement with the available experimental data.
The theoretical uncertainty has been estimated of the order of few % when the
potentials which reproduce the ANC are considered, but increases up to $\simeq
20$ % when all the five potential models are retained. The effect of this
$S$-factor prediction on the $^6$Li primordial abundance is studied, using the
public code PArthENoPE. For the five models considered here we find $^6{\rm
Li}/$H$ = (0.9 - 1.8) \times 10^{-14}$, with the baryon density parameter in
the 3-$\sigma$ range of Planck 2015 analysis, $\Omega_b h^2= 0.02226 \pm
0.00023$.


  As contemporary software-intensive systems reach increasingly large scale, it
is imperative that failure detection schemes be developed to help prevent
costly system downtimes. A promising direction towards the construction of such
schemes is the exploitation of easily available measurements of system
performance characteristics such as average number of processed requests and
queue size per unit of time. In this work, we investigate a holistic
methodology for detection of abrupt changes in time series data in the presence
of quasi-seasonal trends and long-range dependence with a focus on failure
detection in computer systems. We propose a trend estimation method enjoying
optimality properties in the presence of long-range dependent noise to estimate
what is considered "normal" system behaviour. To detect change-points and
anomalies, we develop an approach based on the ensembles of "weak" detectors.
We demonstrate the performance of the proposed change-point detection scheme
using an artificial dataset, the publicly available Abilene dataset as well as
the proprietary geoinformation system dataset.


  The angular momentum of the Earth-Moon system was initially dominated by
Earth's rotation with a short solar day of around 5 hours duration. Since then,
Earth gradually transferred angular momentum through tidal friction to the
orbit of the Moon, resulting in an increasing orbital radius and a deceleration
of Earth's rotation. Geologic observations of tidal deposits can be used to
verify and constrain models of lunar orbital evolution. In this work we
reexamine the oldest tidal record suitable for analysis from the Moodies Group,
South Africa, with an age of 3.22 billion years. Time frequency analysis of the
series of thicknesses of the sandstone-shale layers yields a periodicity of
15.0 layers, taking into account the possibility of missing laminae. Assuming a
mixed tidal system, the duration of two neap-spring-neap cycles was 30.0 lunar
days for dominant semidiurnal or 30.0 sidereal days for dominant diurnal tides.
We derive the relationship between this observation and the past Earth-Moon
distance and re-visit related published work. We find that the Earth-Moon
distance 3.2 billion years ago was about 70% of today's value. The Archean
solar day was around 13 hours long. The ratio of solar to lunar tide-raising
torque controls the leakage of angular momentum from the Earth-Moon system, but
deviation from the assumed ratio of 0.211 results in only moderate changes. A
duration of a postulated 21-hour atmospheric resonance shorter than 200 million
years would be consistent with our observation; it would significantly alter
Earth-Moon distance.


  We present systematic constructions of tensor-network wavefunctions for
bosonic symmetry protected topological (SPT) phases respecting both onsite and
spatial symmetries. From the classification point of view, our results show
that in spatial dimensions $d=1,2,3$, the cohomological bosonic SPT phases
protected by a general symmetry group $SG$ involving onsite and spatial
symmetries are classified by the cohomology group $H^{d+1}(SG,U(1))$, in which
both the time-reversal symmetry and mirror reflection symmetries should be
treated as anti-unitary operations. In addition, for every SPT phase protected
by a discrete symmetry group and some SPT phases protected by continous
symmetry groups, generic tensor-network wavefunctions can be constructed which
would be useful for the purpose of variational numerical simulations. As a
by-product, our results demonstrate a generic connection between rather
conventional symmetry enriched topological phases and SPT phases via an anyon
condensation mechanism.


  SU(3) symmetry relations between the octet baryons are introduced in order to
connect both the unpolarized and polarized quark distributions of the octet
baryons with those of the nucleon. Two different parametrizations of the
nucleon quark distributions are used. A new scenario of quark flavor and spin
structure of the $\Lambda$ is found and compared with two other models: a
perturbative QCD based analysis and a quark diquark model. The $u$ and $d$
quarks inside the $\Lambda$ are predicted to be positively polarized at large
Bjorken variable $x$ in the new scenario. By using an approximate relation
connecting the quark fragmentation functions with the quark distributions, the
hadron polarizations of the octet baryons in $e^+e^-$-annihilation, polarized
charged lepton deep inelastic scattering (DIS) processes, and neutrino
(antineutrino) DIS processes are predicted. The predictions for $\Lambda$
polarizations in several processes are compatible with the available data at
large fragmentation momentum fraction $z$, and support the prediction of
positively polarized $u$ and $d$ quarks inside the $\Lambda$ at large $x$.
Predictions for Drell-Yan processes from $\Sigma^{\pm}$ and $\Xi^-$ beams on an
isoscalar target are also given and discussed.


  We study theoretically the spontaneous edge current in a small chiral
superconductor with surface roughness. We obtained self-consistent solutions of
the pair potential and the vector potential by solving the quasiclassical
Eilenberger equation and the Maxwell equation simultaneously. We then employed
them to calculate numerically the spatial distribution of the chiral edge
current in a small superconductor. The characteristic behavior of the
spontaneous edge current depends strongly on the symmetries of the order
parameters such as chiral $p$-, chiral $d$- and chiral $f$-wave pairing. The
edge current is robust under the surface roughness in the chiral $p$- and
chiral $d$-wave superconductors. In the chiral $d$-wave case, the surface
roughness tends to flip the direction of the chiral current. On the other hand,
the edge current in a chiral $f$-wave superconductor is fragile when there is
surface roughness. We also discuss the temperature dependence of a spontaneous
magnetization, which is a measurable value in standard experiments.


  We demonstrate five-dimensional anti-de Sitter black hole emerges as dual
geometry holographic to weakly interacting N=4 superconformal Yang-Mills
theory. We first note that an ideal probe of the dual geometry is the
Yang-Mills instanton, probing point by point in spacetime. We then study
instanton moduli space at finite temperature by adopting Hitchin's proposal
that geometry of the moduli space is definable by Fisher-Rao "information
geometry". In Yang-Mills theory, the information metric is measured by a novel
class of gauge-invariant, nonlocal operators in the instanton sector. We show
that the moduli space metric exhibits (1) asymptotically anti-de Sitter, (2)
horizon at radial distance set by the Yang-Mills temperature, and (3) after
Wick rotation of the moduli space to the Lorentzian signature, a singularity at
the origin. We argue that the dual geometry emerges even for rank of gauge
groups of order unity and for weak `t Hooft coupling.


  We consider an Electroweak string in the background of a uniform distribution
of cold fermionic matter. As a consequence of the fermion number
non-conservation in the Weinberg-Salam model, the string produces a long-range
magnetic field.


  We present an analysis of enhanced wave transmission through random media
with mirror symmetry about a reflecting barrier. The mathematical model is the
acoustic wave equation and we consider two setups, where the wave propagation
is along a preferred direction: in a randomly layered medium and in a randomly
perturbed waveguide. We use the asymptotic stochastic theory of wave
propagation in random media to characterize the statistical moments of the
frequency dependent random transmission and reflection coefficients, which are
scalar valued in layered media and matrix valued in waveguides. With these
moments, we can quantify explicitly the enhancement of the net mean transmitted
intensity, induced by wave interference near the barrier.


  Synthetic aperture radar (SAR) data is becoming increasingly available to a
wide range of users through commercial service providers with resolutions
reaching 0.5m/px. Segmenting SAR data still requires skilled personnel,
limiting the potential for large-scale use. We show that it is possible to
automatically and reliably perform urban scene segmentation from next-gen
resolution SAR data (0.15m/px) using deep neural networks (DNNs), achieving a
pixel accuracy of 95.19% and a mean IoU of 74.67% with data collected over a
region of merely 2.2km${}^2$. The presented DNN is not only effective, but is
very small with only 63k parameters and computationally simple enough to
achieve a throughput of around 500Mpx/s using a single GPU. We further identify
that additional SAR receive antennas and data from multiple flights massively
improve the segmentation accuracy. We describe a procedure for generating a
high-quality segmentation ground truth from multiple inaccurate building and
road annotations, which has been crucial to achieving these segmentation
results.


  We consider the Navier-Stokes equations in vorticity form in $\mathbb{R}^2$
with a white noise forcing term of multiplicative type, whose spatial
covariance is not regular enough to apply the It\^o calculus in $L^q$ spaces,
$1<q<\infty$. We prove the existence of a unique strong (in the probability
sense) solution.


  Motivated by the ongoing study of dispersive shock waves in non integrable
systems, we propose and analyze a set of wave parameters for periodic waves of
a large class of Hamiltonian partial differential systems -- including the
generalized Korteweg de Vries equations and the Euler-Korteweg systems -- that
are well-behaved in both the small amplitude and small wavelength limits. We
use this parametrization to determine fine asymptotic properties of the
associated modulation systems, including detailed descriptions of eigenmodes.
As a consequence, in the solitary wave limit we prove that modulational
instability is decided by the sign of the second derivative -- with respect to
speed, fixing the endstate -- of the Boussinesq moment of instability; and, in
the harmonic limit, we identify an explicit modulational instability index, of
Benjamin--Feir type.


  The RPA long range correlations are known to play a significant role in
understanding the depletion of single particle-hole states observed in (e, e')
and (e, e'p) measurements. Here the Random Phase Approximation (RPA) theory,
implemented using the D1S force is considered for the specific purpose of
building correlated ground states and related one-body density matrix elements.
These may be implemented and tested in a fully microscopic optical model for NA
scattering off doubly-closed-shell nuclei. A method is presented to correct for
the correlations overcounting inherent to the RPA formalism. One-body density
matrix elements in the uncorrelated (i.e. Hartree-Fock) and correlated (i.e.
RPA) ground states are then challenged in proton scattering studies based on
the Melbourne microscopic optical model to highlight the role played by the RPA
correlations. Effects of such correlations which deplete the nuclear matter at
small radial distance (r $<$ 2 fm) and enhance its surface region, are getting
more and more sizeable as the incident energy increases. Illustrations are
given for proton scattering observables measured up to 201 MeV for the
$^{16}$O, $^{40}$Ca, $^{48}$Ca and $^{208}$Pb target nuclei. Handling the RPA
correlations systematically improves the agreement between scattering
predictions and data for energies higher than 150 MeV.


  Unfortunately, many people die in car accidents. To reduce these accidents,
cars are equipped with driving safety systems. With autonomous vehicles, the
driver's behavior becomes irrelevant as the car drives autonomously. All
autonomous driving algorithms must undergo extensive testing and validation,
especially for safety-critical scenarios. Therefore, the detection of
safety-critical driving scenarios is essential for autonomous vehicles. This
publication describes safety indicator metrics based on time series covering
longitudinal driving data to detect safety-critical driving scenarios.


  We tackle the problem of finding good architectures for multimodal
classification problems. We propose a novel and generic search space that spans
a large number of possible fusion architectures. In order to find an optimal
architecture for a given dataset in the proposed search space, we leverage an
efficient sequential model-based exploration approach that is tailored for the
problem. We demonstrate the value of posing multimodal fusion as a neural
architecture search problem by extensive experimentation on a toy dataset and
two other real multimodal datasets. We discover fusion architectures that
exhibit state-of-the-art performance for problems with different domain and
dataset size, including the NTU RGB+D dataset, the largest multi-modal action
recognition dataset available.


  We investigate the recent suggestions by Barausse et al. (astro-ph/0501152)
and Kolb et al. (hep-th/0503117) that the acceleration of the universe could be
explained by large superhorizon fluctuations generated by inflation. We show
that no acceleration can be produced by this mechanism. We begin by showing how
the application of Raychaudhuri equation to inhomogeneous cosmologies results
in several ``no go'' theorems for accelerated expansion. Next we derive an
exact solution for a specific case of initial perturbations, for which
application of the Kolb et al. expressions leads to an acceleration, while the
exact solution reveals that no acceleration is present. We show that the
discrepancy can be traced to higher order terms that were dropped in the Kolb
et al. analysis. We proceed with the analysis of initial value formulation of
general relativity to argue that causality severely limits what observable
effects can be derived from superhorizon perturbations. By constructing a
Riemann normal coordinate system on initial slice we show that no infrared
divergence terms arise in this coordinate system. Thus any divergences found
previously can be eliminated by a local rescaling of coordinates and are
unobservable. We perform an explicit analysis of the variance of the
deceleration parameter for the case of single field inflation using usual
coordinates and show that the infrared divergent terms found by Barausse et al.
and Kolb et al. cancel against several additional terms not considered in their
analysis. Finally, we argue that introducing isocurvature perturbations does
not alter our conclusion that the accelerating expansion of the universe cannot
be explained by superhorizon modes.


  The thermal and magnetic histories of planetesimals provide unique insights
into the formation and evolution of Earth's building blocks. These histories
can be gleaned from meteorites by using numerical models to translate measured
properties into planetesimal behaviour. In this paper, we present a new 1D
planetesimal thermal evolution and dynamo generation model. This magnetic field
generation model is the first of a differentiated, mantled planetesimal that
includes both mantle convection and non-eutectic core solidification. We have
improved fundamental aspects of mantle heat transport by including a more
detailed viscosity model and stagnant lid convection parametrisations
consistent with internal heating. We have also added radiogenic heating from
$^{60}Fe$ in the metallic Fe-FeS core. Additionally, we implement a combined
thermal and compositional buoyancy flux, as well as the latest magnetic field
scaling laws to predict magnetic field strengths during the planetesimal's
thermal evolution until core solidification is complete. We illustrate the
consequences of our model changes with an example run for a 500 km radius
planetesimal. These effects include more rapid erosion of core thermal
stratification and longer duration of mantle convection compared to previous
studies. The additional buoyancy from core solidification has a marginal effect
on dynamo strength, but for some initial core sulfur contents it can prevent
cessation of the dynamo when mantle convection ends. Our model can be used to
investigate the effects of individual parameters on dynamo generation and
constrain properties of specific meteorite parent bodies. Combined, these
updates mean this model can predict the most reliable and complete magnetic
field history for a planetesimal to date, so is a valuable tool for deciphering
planetesimal behaviour from meteorite properties.


  In patchy particle systems where there is competition between the
self-assembly of finite clusters and liquid-vapour phase separation, reentrant
phase behaviour is observed, with the system passing from a monomeric vapour
phase to a region of liquid-vapour phase coexistence and then to a vapour phase
of clusters as the temperature is decreased at constant density. Here, we
present a classical statistical mechanical approach to the determination of the
complete phase diagram of such a system. We model the system as a van der Waals
fluid, but one where the monomers can assemble into monodisperse clusters that
have no attractive interactions with any of the other species. The resulting
phase diagrams show a clear region of reentrance. However, for the most
physically reasonable parameter values of the model, this behaviour is
restricted to a certain range of density, with phase separation still
persisting at high densities.


  Hybrid and mixed strategy EAs have become rather popular for tackling various
complex and NP-hard optimization problems. While empirical evidence suggests
that such algorithms are successful in practice, rather little theoretical
support for their success is available, not mentioning a solid mathematical
foundation that would provide guidance towards an efficient design of this type
of EAs. In the current paper we develop a rigorous mathematical framework that
suggests such designs based on generalized schema theory, fitness levels and
drift analysis. An example-application for tackling one of the classical
NP-hard problems, the "single-machine scheduling problem" is presented.


  We offer a novel approach to image composition, which integrates multiple
input images into a single, coherent image. Rather than concentrating on
specific use cases such as appearance editing (image harmonization) or semantic
editing (semantic image composition), we showcase the potential of utilizing
the powerful generative prior inherent in large-scale pre-trained diffusion
models to accomplish generic image composition applicable to both scenarios. We
observe that the pre-trained diffusion models automatically identify simple
copy-paste boundary areas as low-density regions during denoising. Building on
this insight, we propose to optimize the composed image towards high-density
regions guided by the diffusion prior. In addition, we introduce a novel
maskguided loss to further enable flexible semantic image composition.
Extensive experiments validate the superiority of our approach in achieving
generic zero-shot image composition. Additionally, our approach shows promising
potential in various tasks, such as object removal and multiconcept
customization.


  We report electrical resistivity measurements on a high-quality
Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ thin film ($x=0.4$) under pressure. The
superconducting transition temperature (=39.95 K) of the optimally-doped thin
film shows a dome shape with pressure, reaching a maximal value 40.8 K at 11.8
kbar. The unusually high superconducting transition temperature and its
anomalous pressure dependence are ascribed to a lattice mismatch between the
LaAlO$_3$ substrate and the thin film. The local temperature exponent of the
resistivity ($n=d\text{ln}\Delta\rho/d\text{ln}T$) shows a funnel shape around
the optimal pressure, suggesting that fluctuations associated with the
anomalous normal state are responsible for high-temperature superconductivity.


  We present optical and near-infrared finding charts taken from the DSS and
2MASS surveys of 94 IRAS sources selected from the GLMP catalogue
(Garc\'{\i}a-Lario 1992), and accurate astrometry (~0.2") for most of them.
Selection criteria were very red IRAS colours representative for OH/IR stars
with optically thick circumstellar shells and the presence of variability
according to the IRAS variability index (VAR>50). The main photometric
properties of the stars in this `GLMP sample' are presented, discussed and
compared with the correspondent properties of the `Arecibo sample' of OH/IR
stars studied in Jim\'enez-Esteban et al. (2005a). We find that 37% of the
sample (N=34) have no counterpart in the 2MASS, implying extremely high optical
depths of their shells. Most of the sources identified in the 2MASS are faint
(K>~8) and of very red colour in the near-infrared, as expected. The brightest
2MASS counterpart (K=5.3mag) was found for IRAS 18299--1705. Its blue colour
H--K=1.3 suggests that IRAS 8299--1705 is a post-AGB star. A couple of GLMP
sources have faint but relatively blue counterparts. They might be misidentifed
field stars or stars hich experienced recently a drop of their mass loss rates.
The `GLMP sample' in general is made of oxygen-rich AGB stars, which are highly
obscured by their circumstellar shells. They belong to the same population as
the reddest OH/IR stars in the `Arecibo sample'.


  This paper deals with bathymetry-oriented optimization in the case of long
waves with small amplitude. Under these two assumptions, the free-surface
incompressible Navier-Stokes system can be written as a wave equation where the
bathymetry appears as a parameter in the spatial operator. Looking then for
time-harmonic fields and writing the bottom topography as a perturbation of a
flat bottom, we end up with a heterogeneous Helmholtz equation with impedance
boundary condition. In this way, we study some PDE-constrained optimization
problem for a Helmholtz equation in heterogeneous media whose coefficients are
only bounded with bounded variation. We provide necessary condition for a
general cost function to have at least one optimal solution. We also prove the
convergence of a finite element approximation of the solution to the considered
Helmholtz equation as well as the convergence of discrete optimum toward the
continuous ones. We end this paper with some numerical experiments to
illustrate the theoretical results and show that some of their assumptions
could actually be removed.


  Enabled by recent advances in symmetry and electronic structure, researchers
have observed signatures of unconventional threefold degeneracies in tungsten
carbide, challenging a longstanding paradigm in nodal semimetals.


  In the setting of a general Borel measure $\mu$ on $R^d$ with the natural
ball size condition $$\mu[B(x,r)]\leq Cr^s,$$ we establish the
$L^p(\mu)$-$L^q(\mu)$-estimate for the generalized Radon transform
$$(Af)(x):=\int_{\Phi(x,y)=0}(f\mu)(y)\psi(x,y)d\sigma_x(y),$$ where $\Phi$ is
a smooth function away from the diagonal.
  Among other reasonable assumptions, an $L^2$-Sobolev bound on $A$ on $R^d$ is
imposed. This bound is satisfied in many natural situations. The main result
is, in general, sharp up to endpoints.


  We compute for all orientable irreducible geometric 3-manifolds certain
complexity functions that approximate from above Matveev's natural complexity,
known to be equal to the minimal number of tetrahedra in a triangulation. We
can show that the upper bounds on Matveev's complexity implied by our
computations are sharp for thousands of manifolds, and we conjecture they are
for infinitely many, including all Seifert manifolds. Our computations and
estimates apply to all the Dehn fillings of M6_1^3 (the complement of the
three-component chain-link, conjectured to be the smallest triply cusped
hyperbolic manifold), whence to infinitely many among the smallest closed
hyperbolic manifolds. Our computations are based on the machinery of the
decomposition into `bricks' of irreducible manifolds, developed in a previous
paper. As an application of our results we completely describe the geometry of
all 3-manifolds of complexity up to 9.


  We present a simple and predictive model of radiative neutrino masses. It is
a special case of the Zee model which introduces two Higgs doublets and a
charged singlet. We impose a family-dependent Z_4 symmetry acting on the
leptons, which reduces the number of parameters describing neutrino
oscillations to four. A variety of predictions follow: The hierarchy of
neutrino masses must be inverted; the lightest neutrino mass is extremely small
and calculable; one of the neutrino mixing angles is determined in terms of the
other two; the phase parameters take CP-conserving values with \delta_{CP} =
\pi; and the effective mass in neutrinoless double beta decay lies in a narrow
range, m_{\beta \beta} = (17.6 - 18.5) meV. The ratio of vacuum expectation
values of the two Higgs doublets, tan\beta, is determined to be either 1.9 or
0.19 from neutrino oscillation data. Flavor-conserving and flavor-changing
couplings of the Higgs doublets are also determined from neutrino data. The
non-standard neutral Higgs bosons, if they are moderately heavy, decay
dominantly into \mu and \tau with prescribed branching ratios. Observable rates
for the decays \mu \to e \gamma and \tau \to 3\mu are predicted if these
scalars have masses in the range of 150-500 GeV.


  Using first-principles calculations, we found the topological phase
transition induced by electric fields in one-bilayer Bi(111). The bandgap
decreased with increasing electric field strength, and it is closed at 2.1
V/{\AA}. For fields exceeding 2.1 V/{\AA}, the bandgap increased with
increasing electric field strength, reaching 0.34 eV at 4.0 V/{\AA}. We
computed the $Z_{2}$ invariant that characterizes topological insulator phases.
As results, one-bilayer Bi(111) showed a topological phase transition induced
by the electric field, from the topological insulator phase to the trivial
insulator phase through a Dirac semimetal. This topological phase transition
could be applied to novel devices.


  We provide a class of necessary and sufficient conditions for the
discreteness of spectrum of Schr\"odinger operators with scalar potentials
which are semibounded below. The classical discreteness of spectrum criterion
by A.M.Molchanov (1953) uses a notion of negligible set in a cube as a set
whose Wiener's capacity is less than a small constant times the capacity of the
cube. We prove that this constant can be taken arbitrarily between 0 and 1.
This solves a problem formulated by I.M.Gelfand in 1953. Moreover, we extend
the notion of negligibility by allowing the constant to depend on the size of
the cube. We give a complete description of all negligibility conditions of
this kind. The a priori equivalence of our conditions involving different
negligibility classes is a non-trivial property of the capacity. We also
establish similar strict positivity criteria for the Schr\"odinger operators
with non-negative potentials.


  Using Landau-Ginzburg-Devonshire approach we calculated the equilibrium
distributions of electric field, polarization and space charge in the
ferroelectric-semiconductor heterostructures containing proper or incipient
ferroelectric thin films. The role of the polarization gradient and intrinsic
surface energy, interface dipoles and free charges on polarization dynamics are
specifically explored. The intrinsic field effects, which originated at the
ferroelectric-semiconductor interface, lead to the surface band bending and
result into the formation of depletion space-charge layer near the
semiconductor surface. During the local polarization reversal (caused by the
inhomogeneous electric field induced by the nanosized tip of the Scanning Probe
Microscope (SPM) probe) the thickness and charge of the interface layer
drastically changes, it particular the sign of the screening carriers is
determined by the polarization direction. Obtained analytical solutions could
be extended to analyze polarization-mediated electronic transport.


  A totally asymmetric exclusion process on a ring with $\nu$ non-conserved
internal degrees of freedom, where particles hop forward with a rate that
depends on their internal state, has been studied. We show, using a mapping of
the model to a zero range process with $\nu$ different kinds of boxes, that
steady state weights can be written in a matrix product form and calculate the
spatial correlations exactly. A comparison of the model with an equivalent
conserved system reveals that unequal hopping rates of particles belonging to
different internal states is responsible for the non-trivial correlations.


  In this paper we show that conifold transitions between Calabi-Yau 3-folds
can be used for the construction of mirror manifolds and for the computation of
the instanton numbers of rational curves on complete intersection Calabi-Yau
3-folds in Grassmannians. Using a natural degeneration of Grassmannians
$G(k,n)$ to some Gorenstein toric Fano varieties $P(k,n)$ with conifolds
singularities which was recently described by Sturmfels, we suggest an explicit
mirror construction for Calabi-Yau complete intersections $X \subset G(k,n)$ of
arbitrary dimension. Our mirror construction is consistent with the formula for
the Lax operator conjectured by Eguchi, Hori and Xiong for gravitational
quantum cohomology of Grassmannians.


  The SM unitarity triangle (UT) is completely determined by the parameters
$\gamma$ and $|V_{ub}|$ which can be extracted from tree-level processes and
are assumed to be free of new physics. By comparison with other determinations
of UT parameters one can impose constraints on new physics in loop processes,
in particular $B$ mixing.


  The Kepler Mission was designed to identify and characterize transiting
planets in the Kepler Field of View and to determine their occurrence rates.
Emphasis was placed on identification of Earth-size planets orbiting in the
Habitable Zone of their host stars. Science data were acquired for a period of
four years. Long-cadence data with 29.4 min sampling were obtained for ~200,000
individual stellar targets in at least one observing quarter in the primary
Kepler Mission. Light curves for target stars are extracted in the Kepler
Science Data Processing Pipeline, and are searched for transiting planet
signatures. A Threshold Crossing Event is generated in the transit search for
targets where the transit detection threshold is exceeded and transit
consistency checks are satisfied. These targets are subjected to further
scrutiny in the Data Validation (DV) component of the Pipeline. Transiting
planet candidates are characterized in DV, and light curves are searched for
additional planets after transit signatures are modeled and removed. A suite of
diagnostic tests is performed on all candidates to aid in discrimination
between genuine transiting planets and instrumental or astrophysical false
positives. Data products are generated per target and planet candidate to
document and display transiting planet model fit and diagnostic test results.
These products are exported to the Exoplanet Archive at the NASA Exoplanet
Science Institute, and are available to the community. We describe the DV
architecture and diagnostic tests, and provide a brief overview of the data
products. Transiting planet modeling and the search for multiple planets on
individual targets are described in a companion paper. The final revision of
the Kepler Pipeline code base is available to the general public through
GitHub. The Kepler Pipeline has also been modified to support the TESS Mission
which will commence in 2018.


  Population attributable risk (PAR) is used in epidemiology to predict the
impact of removing a risk factor from the population. Until recently, no
standard approach for calculating confidence intervals or the variance for PAR
was available in the literature. Pirikahu et al. (2016) outlined a fully
Bayesian approach to provide credible intervals for the PAR from a
cross-sectional study, where the data was presented in the form of a 2 x 2
table. However, extensions to cater for other frequently used study designs
were not provided. In this paper we provide methodology to calculate credible
intervals for the PAR for case-control and cohort studies. Additionally, we
extend the cross-sectional example to allow for the incorporation of
uncertainty that arises when an imperfect diagnostic test is used. In all these
situations the model becomes over-parameterised, or non-identifiable, which can
result in standard "off-the-shelf" Markov chain Monte Carlo updaters taking a
long time to converge or even failing altogether. We adapt an importance
sampling methodology to overcome this problem, and propose some novel MCMC
samplers that take into consideration the shape of the posterior ridge to aid
in the convergence of the Markov chain.


  By using the Gold map, we construct a partition of the hypercube into cosets
of Hamming codes such that for every two cosets the corresponding Hamming codes
are maximally nonparallel, that is, their intersection cardinality is as small
as possible to admit nonintersecting cosets.


  The efficiency of energy conversion during magnetic reconnection is related
to the reconnection rate. While the stable reconnection rate has been studied
extensively, its growth between the time of reconnection onset and the peak
reconnection rate has not been thoroughly discussed. We use a 2D
particle-in-cell (PIC) simulation to examine how the non-ideal reconnection
electric field evolves during the growth process and how it relates to changes
near the x-line. We identify three phases of growth: 1) slow quasi-linear
growth, 2) rapid exponential growth, and 3) tapered growth followed by negative
growth after the reconnection rate peaks. Through analysis of the structural
changes of the EDR, we associate the early phases with the breaking of x-line
symmetry through the erosion of the pre-onset bipolar Ez and the emergence of a
diverging Ex pattern at the neutral line in phase 1 followed by the expansion
of the inflow region and the enhancement of inflow Poynting flux Sz associated
with the out-of-plane electric field Ey in phase 2. We show how the Hall fields
facilitate rapid growth in phase 2 by opening up the exhaust, relieving the
electron-scale bottleneck and allowing large Poynting flux across the
separatrices. We find that the rapid inflow of electromagnetic energy
accumulates until the downstream electromagnetic energy density in phase 3
approaches the initial upstream asymptotic value. Finally, we examine how the
electron outflow and the downstream ion populations interact in phase 3 and how
each species exchanges energy with the local field structures in the exhaust.


  In this paper, we investigate the preservability of the curvature-adaptedness
along the mean curvature flow starting from a compact curvature-adapted
hypersurface in locally symmetric spaces, where the curvature-adaptedness means
that the shape operator and the normal Jacobi operator of the hypersurface
commute.


  Plumitifs (dockets) were initially a tool for law clerks. Nowadays, they are
used as summaries presenting all the steps of a judicial case. Information
concerning parties' identity, jurisdiction in charge of administering the case,
and some information relating to the nature and the course of the preceding are
available through plumitifs. They are publicly accessible but barely
understandable; they are written using abbreviations and referring to
provisions from the Criminal Code of Canada, which makes them hard to reason
about. In this paper, we propose a simple yet efficient multi-source language
generation architecture that leverages both the plumitif and the Criminal
Code's content to generate intelligible plumitifs descriptions. It goes without
saying that ethical considerations rise with these sensitive documents made
readable and available at scale, legitimate concerns that we address in this
paper.


  We determine an $\mathfrak{sl}_2$ module structure on the equivariant
Khovanov-Rozanksy homology of T(2,k)-torus links following the framework
defined in arXiv:2306.10729.


  New generation of neutron decay experiments, which can be done with high
accuracy at new Spallation Neutron Sources, are very important for solution of
current problems of fundamental physics and for tests of the Standard Model.
The open problems of theory related to these experiments and possible
approaches to their solutions are discussed.


  As one key enabler of Intelligent Transportation System (ITS), Vehicular Ad
Hoc Network (VANET) has received remarkable interest from academia and
industry. The emerging vehicular applications and the exponential growing data
have naturally led to the increased needs of communication, computation and
storage resources, and also to strict performance requirements on response time
and network bandwidth. In order to deal with these challenges, Mobile Edge
Computing (MEC) is regarded as a promising solution. MEC pushes powerful
computational and storage capacities from the remote cloud to the edge of
networks in close proximity of vehicular users, which enables low latency and
reduced bandwidth consumption. Driven by the benefits of MEC, many efforts have
been devoted to integrating vehicular networks into MEC, thereby forming a
novel paradigm named as Vehicular Edge Computing (VEC). In this paper, we
provide a comprehensive survey of state-of-art research on VEC. First of all,
we provide an overview of VEC, including the introduction, architecture, key
enablers, advantages, challenges as well as several attractive application
scenarios. Then, we describe several typical research topics where VEC is
applied. After that, we present a careful literature review on existing
research work in VEC by classification. Finally, we identify open research
issues and discuss future research directions.


  We study nonclassical correlations beyond entanglement in a family of
two-mode non-Gaussian states which represent the continuous-variable
counterpart of two-qubit Werner states. We evaluate quantum discord and other
quantumness measures obtaining exact analytical results in special instances,
and upper and lower bounds in the general case. Non-Gaussian measurements such
as photon counting are in general necessary to solve the optimization in the
definition of quantum discord, whereas Gaussian measurements are strictly
suboptimal for the considered states. The gap between Gaussian and optimal
non-Gaussian conditional entropy is found to be proportional to a measure of
non-Gaussianity in the regime of low squeezing, for a subclass of
continuous-variable Werner states. We further study an example of a
non-Gaussian state which is positive under partial transposition, and whose
nonclassical correlations stay finite and small even for infinite squeezing.
Our results pave the way to a systematic exploration of the interplay between
nonclassicality and non-Gaussianity in continuous-variable systems, in order to
gain a deeper understanding of -and to draw a bigger advantage from- these two
important resources for quantum technology.


  This article presents a whisper speech detector in the far-field domain. The
proposed system consists of a long-short term memory (LSTM) neural network
trained on log-filterbank energy (LFBE) acoustic features. This model is
trained and evaluated on recordings of human interactions with
voice-controlled, far-field devices in whisper and normal phonation modes. We
compare multiple inference approaches for utterance-level classification by
examining trajectories of the LSTM posteriors. In addition, we engineer a set
of features based on the signal characteristics inherent to whisper speech, and
evaluate their effectiveness in further separating whisper from normal speech.
A benchmarking of these features using multilayer perceptrons (MLP) and LSTMs
suggests that the proposed features, in combination with LFBE features, can
help us further improve our classifiers. We prove that, with enough data, the
LSTM model is indeed as capable of learning whisper characteristics from LFBE
features alone compared to a simpler MLP model that uses both LFBE and features
engineered for separating whisper and normal speech. In addition, we prove that
the LSTM classifiers accuracy can be further improved with the incorporation of
the proposed engineered features.


  Hydrogen is central to the global energy transition when produced at low
emissions. This paper introduces a renewable hydrogen production system model
(HPSM) that optimizes a hybrid hydrogen production system (HPS) on a worldwide
50x50 km grid, considering country-specific interest rates. Besides the
renewable energy's impact on the HPS design, we analyze the effect of
country-specific interest rates on the levelized cost of hydrogen (LCOH)
production. LCOH production ranges between 2.7 Euro/kg and 28.4 Euro/kg, with
an average of 9.1 Euro/kg. Over one third (40.0%) of all cells have an
installed PV capacity share between 50% and 70%, and 76.4% have a hybrid
configuration. Hybrid HPSs can significantly reduce the LCOH production
compared to non-hybrid designs, whereas country-specific interest rates lead to
significant increases in the LCOH production. Hydrogen storage is deployed
rather than battery storage to balance production and demand.


  We introduce the isoclinism of crossed modules. We also give GAP
implementations for constructing the isoclinism families of finite crossed
modules and consequently give an enumeration about isoclinic crossed modules
existing in the GAP library.


  A model of a mixed helium-hydrogenic atmosphere of the isolated neutron star
1E1207.4-5209 is proposed. It is based on the assumption that the main
components in the atmosphere are the exotic molecular ions $He_2^{3+}$ and
$H_3^{2+}$ with the presence of $He^{+}, (HeH)^{2+}, H_2^{+}$ under a surface
magnetic field $\approx 4.4 \times 10^{13}$ G. In addition to two absorption
features observed by {\it Chandra} observatory (Sanwal et al, 2002) the model
predicts one more narrow absorption feature at $\approx 400$ eV.


  We propose a detail theoretical approach modeling molecular librations in
liquid investigated by ultrafast optically heterodyne detected optical Kerr
effect (OHD-OKE). The approach has been applied for fluoroform molecular liquid
and new information about spectrum, relaxation time and time domain librations
has been obtained.


  In this paper we consider a single-server, cyclic polling system with
switch-over times. A distinguishing feature of the model is that the rates of
the Poisson arrival processes at the various queues depend on the server
location. For this model we study the joint queue length distribution at
polling epochs and at server's departure epochs. We also study the marginal
queue length distribution at arrival epochs, as well as at arbitrary epochs
(which is not the same in general, since we cannot use the PASTA property). A
generalised version of the distributional form of Little's law is applied to
the joint queue length distribution at customer's departure epochs in order to
find the waiting time distribution for each customer type. We also provide an
alternative, more efficient way to determine the mean queue lengths and mean
waiting times, using Mean Value Analysis. Furthermore, we show that under
certain conditions a Pseudo-Conservation Law for the total amount of work in
the system holds. Finally, typical features of the model under consideration
are demonstrated in several numerical examples.


  We present a characterization of operator log-convex functions by using
positive linear mappings. Moreover, we study the non-commutative f-divergence
functional of operator log-convex functions. In particular, we prove that f is
operator log-convex if and only if the non-commutative f-divergence functional
is operator log-convex in its first variable and operator convex in its second
variable.


  This paper addresses the scalar regression problem through a novel solution
to exactly optimize the Huber loss in a general semi-supervised setting, which
combines multi-view learning and manifold regularization. We propose a
principled algorithm to 1) avoid computationally expensive iterative schemes
while 2) adapting the Huber loss threshold in a data-driven fashion and 3)
actively balancing the use of labelled data to remove noisy or inconsistent
annotations at the training stage. In a wide experimental evaluation, dealing
with diverse applications, we assess the superiority of our paradigm which is
able to combine robustness towards noise with both strong performance and low
computational cost.


  This thesis concerns the research on a Lorentzian generalization of Alain
Connes' noncommutative geometry. In the first chapter, we present an
introduction to noncommutative geometry within the context of unification
theories. The second chapter is dedicated to the basic elements of
noncommutative geometry as the noncommutative integral, the Riemannian distance
function and spectral triples. In the last chapter, we investigate the problem
of the generalization to Lorentzian manifolds. We present a first step of
generalization of the distance function with the use of a global timelike
eikonal condition. Then we set the first axioms of a temporal Lorentzian
spectral triple as a generalization of a pseudo-Riemannian spectral triple
together with a notion of global time in noncommutative geometry.


  We generalize the classical sharp bounds for the largest eigenvalue of the
normalized Laplace operator, $\frac{N}{N-1}\leq \lambda_N\leq 2$, to the case
of chemical hypergraphs.