  We study the class of state-space models and perform maximum likelihood
estimation for the model parameters. We consider a stochastic approximation
expectation-maximization (SAEM) algorithm to maximize the likelihood function
with the novelty of using approximate Bayesian computation (ABC) within SAEM.
The task is to provide each iteration of SAEM with a filtered state of the
system, and this is achieved using an ABC sampler for the hidden state, based
on sequential Monte Carlo (SMC) methodology. It is shown that the resulting
SAEM-ABC algorithm can be calibrated to return accurate inference, and in some
situations it can outperform a version of SAEM incorporating the bootstrap
filter. Two simulation studies are presented, first a nonlinear Gaussian
state-space model then a state-space model having dynamics expressed by a
stochastic differential equation. Comparisons with iterated filtering for
maximum likelihood inference, and Gibbs sampling and particle marginal methods
for Bayesian inference are presented.


  Electron transmission through molecules and molecular interfaces has been a
subject of intensive research due to recent interest in electron transfer
phenomena underlying the operation of the scanning tunneling microscope (STM)
on one hand, and in the transmission properties of molecular bridges between
conducting leads on the other. In these processes the traditional molecular
view of electron transfer between donor and acceptor species give rise to a
novel view of the molecule as a current carrying conductor, and observables
such as electron transfer rates and yields are replaced by the conductivities,
or more generally by current-voltage relationships, in molecular junctions.
  In this paper I review the current knowledge and understanding of this field,
with particular emphasis on theoretical issues. Different approaches to
computing the conduction properties of molecules and molecular assemblies are
reviewed, and the relationships between them are discussed. Following a
detailed discussion of static junctions models, a review of our current
understanding of the role played by inelastic processes, dephasing and thermal
relaxation effects, is provided. The most important molecular environment for
electron transfer and transmission is water, and our current theoretical
understanding of electron transmission through water layers is reviewed.
Finally, a brief discussion of overbarrier transmission, exemplified by
photoemission through adsorbed molecular layers or low energy electron
transmission through such layers is provided. Similarities and differences
between the different systems studied are discussed.


  A hierarchical approach to the construction of compound distributions for
process-induced faults in IC manufacture is proposed. Within this framework,
the negative binomial distribution is treated as level-1 models. The
hierarchical approach to fault distribution offers an integrated picture of how
fault density varies from region to region within a wafer, from wafer to wafer
within a batch, and so on. A theory of compound-distribution hierarchies is
developed by means of generating functions. A study of correlations, which
naturally appears in microelectronics due to the batch character of IC
manufacture, is proposed. Taking these correlations into account is of
significant importance for developing procedures for statistical quality
control in IC manufacture. With respect to applications, hierarchies of yield
means and yield probability-density functions are considered.


  The Bloom filter (BF) is a well-known space-efficient data structure that
answers set membership queries with some probability of false positives. In an
attempt to solve many of the limitations of current inter-networking
architectures, some recent proposals rely on including small BFs in packet
headers for routing, security, accountability or other purposes that move
application states into the packets themselves. In this paper, we consider the
design of such in-packet Bloom filters (iBF). Our main contributions are
exploring the design space and the evaluation of a series of extensions (1) to
increase the practicality and performance of iBFs, (2) to enable
false-negative-free element deletion, and (3) to provide security enhancements.
In addition to the theoretical estimates, extensive simulations of the multiple
design parameters and implementation alternatives validate the usefulness of
the extensions, providing for enhanced and novel iBF networking applications.


  We propose a dark energy model with a logarithmic cosmological fluid which
can result in a very small current value of the dark energy density and avoid
the coincidence problem without much fine-tuning. We construct a couple of
dynamical models that could realize this dark energy at very low energy in
terms of four scalar fields quintessence and discuss the current acceleration
of the Universe. Numerical values can be made to be consistent with the
accelerating Universe with adjustment of the two parameters of the theory. The
potential can be given only in terms of the scale factor, but the explicit form
at very low energy can be obtained in terms of the scalar field to yield of the
form V(\phi)=\exp(-2\phi)(\frac{4 A}{3}\phi+B). Some discussions and the
physical implications of this approach are given.


  We study vacuum quantum fluctuations of simple Nambu-Goldstone bosons -
derivatively coupled single scalar-field theories possessing shift-symmetry in
field space. We argue that quantum fluctuations of the interacting field can be
drastically suppressed with respect to the free-field case. Moreover, the
power-spectrum of these fluctuations can soften to become red for sufficiently
small scales. In quasiclassical approximation, we demonstrate that this
suppression can only occur for those theories that admit such classical static
backgrounds around which small perturbations propagate faster than light. Thus,
a quasiclassical softening of quantum fluctuations is only possible for
theories which classicalize instead of having a usual Lorentz invariant and
local Wilsonian UV- completion. We illustrate our analysis by estimating the
quantum fluctuations for the DBI-like theories.


  We introduce a new type of Gutzwiller variational wavefunction for correlated
electrons coupled to phonons, able to treat on equal footing electronic and
lattice degrees of freedom. We benchmark the wavefunction in the infinite-$U$
Hubbard-Holstein model away from half-filling on a Bethe lattice, where we can
directly compare with exact results by Dynamical Mean-Field Theory. For this
model, we find that variational results agree perfectly well with the exact
ones. In particular the wavefunction correctly describes the crossover to a
heavy polaron gas upon increasing the electron-phonon coupling.


  We study bound states below threshold and resonances above threshold in the
D0-K+ and Ds-eta systems, using a many-coupled-channel model for non-exotic
meson-meson scattering applied to states with the quantum numbers of c-sbar
quark-antiquark vector mesons. We fit the ground state at 2.112 GeV, whence the
lowest resonances in D0-K+ come out at 2.61, 2.72, 3.03, and 3.08 GeV. The
resonance at 2.61 GeV acquires a width of about 8 MeV, while its partial P-wave
cross section is up to six times larger in Ds-eta than in D0-K+, provided a
mechanism accounting for Okubo-Zweig-Iizuka--forbidden decays is included. The
latter finding is in agreement with the observations of the SELEX collaboration
with respect to the recently reported DsJ(2632) resonance. Therefore, we
conclude that the DsJ(2632) is most probably the first recurrence excitation of
the Ds*(2112) meson.


  Persistent currents and Drude weights are investigated for the tight-binding
approximation to one-dimensional rings threaded by a magnetic flux and with
potential given by some almost-periodic substitution sequences with different
degrees of randomness, and for various potential strengths. The Drude weight D
distinguishes correctly conductors and insulators, in accordance with the
results shown by the currents. In the case of insulators the decay of D(N) for
large ring lengths N provides an estimate for the localization length of the
system. It is shown that the more random the sequence does not imply the
smaller conducting properties. This discrepancy between the hierarchy of
disorder of the sequences and the capacity of conduction of the system is
explained by the gaps in the energy spectra.


  This paper studies the (small) quantum homology and cohomology of fibrations
$p: P\to S^2$ whose structural group is the group of Hamiltonian
symplectomorphisms of the fiber $(M,\om)$. It gives a proof that the rational
cohomology splits additively as the vector space tensor product $H^*(M)\otimes
H^*(S^2)$, and investigates conditions under which the ring structure also
splits, thus generalizing work of Lalonde-McDuff-Polterovich and Seidel. The
main tool is a study of certain operations in the quantum homology of the total
space $P$ and of the fiber $M$, whose properties reflect the relations between
the Gromov-Witten invariants of $P$ and $M$. In order to establish these
properties we further develop the language introduced in [Mc3] to describe the
virtual moduli cycle (defined by Liu-Tian, Fukaya-Ono, Li-Tian, Ruan and
Siebert).


  Difference in nucleation of Ge quantum dots during Ge deposition at low (<
600C) and high (> 600C) temperatures on the Si(001) surface is studied by high
resolution scanning tunneling microscopy. Two process resulting in appearance
of {105}-faceted clusters on the Ge wetting layer have been observed at high
temperatures: Pyramids have been observed to nucleate via the previously
described formation of strictly determined structures, resembling blossoms,
composed by 16 dimers grouped in pairs and chains of 4 dimes on tops of the
wetting layer M x N patches, each on top of a separate single patch, just like
it goes on at low temperatures; an alternative process consists in faceting of
shapeless heaps of excess Ge atoms which arise in the vicinity of strong sinks
of adatoms, such as pits or steps. The latter process has never been observed
at low temperatures; it is typical only for the high-temperature deposition
mode.


  This paper introduces scalable, sampling-based algorithms that optimize
trained neural networks with ReLU activations. We first propose an iterative
algorithm that takes advantage of the piecewise linear structure of ReLU neural
networks and reduces the initial mixed-integer optimization problem (MIP) into
multiple easy-to-solve linear optimization problems (LPs) through sampling.
Subsequently, we extend this approach by searching around the neighborhood of
the LP solution computed at each iteration. This scheme allows us to devise a
second, enhanced algorithm that reduces the initial MIP problem into smaller,
easier-to-solve MIPs. We analytically show the convergence of the methods and
we provide a sample complexity guarantee. We also validate the performance of
our algorithms by comparing them against state-of-the-art MIP-based methods.
Finally, we show computationally how the sampling algorithms can be used
effectively to warm-start MIP-based methods.


  Model checking invariant properties of designs, represented as transition
systems, with non-linear real arithmetic (NRA), is an important though very
hard problem. On the one hand NRA is a hard-to-solve theory; on the other hand
most of the powerful model checking techniques lack support for NRA. In this
paper, we present a counterexample-guided abstraction refinement (CEGAR)
approach that leverages linearization techniques from differential calculus to
enable the use of mature and efficient model checking algorithms for transition
systems on linear real arithmetic (LRA) with uninterpreted functions (EUF). The
results of an empirical evaluation confirm the validity and potential of this
approach.


  Several algorithms for RNA inverse folding have been used to design synthetic
riboswitches, ribozymes and thermoswitches, whose activity has been
experimentally validated. The RNAiFold software is unique among approaches for
inverse folding in that (exhaustive) constraint programming is used instead of
heuristic methods. For that reason, RNAiFold can generate all sequences that
fold into the target structure, or determine that there is no solution.
RNAiFold 2.0 is a complete overhaul of RNAiFold 1.0, rewritten from the now
defunct COMET language to C++. The new code properly extends the capabilities
of its predecessor by providing a user-friendly pipeline to design synthetic
constructs having the functionality of given Rfam families. In addition, the
new software supports amino acid constraints, even for proteins translated in
different reading frames from overlapping coding sequences; moreover, structure
compatibility/incompatibility constraints have been expanded. With these
features, RNAiFold 2.0 allows the user to design single RNA molecules as well
as hybridization complexes of two RNA molecules.
  The web server, source code and linux binaries are publicly accessible at
http://bioinformatics.bc.edu/clotelab/RNAiFold2.0


  We consider teleportation of an arbitrary spin-1/2 target quantum state along
the ground state of a quantum spin chain. We present a decomposition of the
Hilbert space of the many body quantum state into 4 vector spaces. Within each
of these subspaces, it is possible to take any superposition of states, and use
projective measurements to perform unit fidelity teleportation. Any such
superposition is necessarily a spin liquid state. We also show that all total
spin-0 quantum states belong in the same space, so that it is possible to
perform unit fidelity teleportation over any one-dimensional spin-0 many body
quantum state. We generalise to $n$-Bell states, and present some general
bounds on fidelity of teleportation given a general state of a quantum spin
chain.


  Spin-orbit coupling (SOC) drives interesting and non-trivial phenomena in
solid state physics, ranging from topological to magnetic to transport
properties. Thorough study of such phenomena often require effective models
where SOC term is explicitly included. However, estimation of SOC strength for
such models mostly depend on the spectroscopy experiments which can only
provide a rough estimate. In this work, we provide a simple yet effective
computational approach to estimate the on-site SOC strength using a combination
of the $ab$ $initio$ and tight-binding calculations. We demonstrate the wider
applicability and high sensitivity of our method considering materials with
varying SOC strengths and the number of SOC active ions. The estimated SOC
strengths agree well with the proposed values in literature lending support to
our methodology. This simplistic approach can readily be applied to a wide
range of materials.


  Possible deformation of odd-N nuclei with N $\approx$ 28 towards the neutron
drip line is investigated using the Nilsson diagram based on deformed
Woods-Saxon potentials. Both weakly-bound and resonant one-particle levels are
properly obtained by directly solving the Schr\"{o}dinger equation in mesh of
space coordinate with the correct boundary condition. If we use the same
diffuseness of the potential as that of $\beta$-stable nuclei, the energy
difference between the neutron 2p$_{3/2}$ and 1f$_{7/2}$ levels becomes very
small or the N=28 energy gap almost disappears, as the binding energies of
those levels approach zero. This suggests that the ground states of those
neutron drip line nuclei are likely to be deformed. In particular, the
spin-parity and the magnetic moment of the ground state of odd-N nuclei,
$^{43}_{16}$S$_{27}$ and $^{45}_{16}$S$_{29}$, are examined. Moreover, it is
suggested that in $^{39}_{12}$Mg$_{27}$ lying outside the drip line the lowest
resonant state may have 5/2$^{-}$, if the N=28 energy gap almost vanishes.


  A detailed comparison is presented of analytical and particle-in-cell (PIC)
simulation investigation of the transverse instability, in two dimensions, of
initially one-dimensional electron phase-space hole equilibria. Good
quantitative agreement is found between the shift-mode analysis and the
simulations for the magnetic field ($B$) threshold at which the instability
becomes overstable (time-oscillatory) and for the real and imaginary parts of
the frequency. The simulation $B$-threshold for full stabilization exceeds the
predictions of shift-mode analysis by 20 to 30\%, because the mode becomes
substantially narrower in spatial extent than a pure shift. This threshold
shift is qualitatively explained by the kinematic mechanism of instability.


  We study sequential prediction of real-valued, arbitrary and unknown
sequences under the squared error loss as well as the best parametric predictor
out of a large, continuous class of predictors. Inspired by recent results from
computational learning theory, we refrain from any statistical assumptions and
define the performance with respect to the class of general parametric
predictors. In particular, we present generic lower and upper bounds on this
relative performance by transforming the prediction task into a parameter
learning problem. We first introduce the lower bounds on this relative
performance in the mixture of experts framework, where we show that for any
sequential algorithm, there always exists a sequence for which the performance
of the sequential algorithm is lower bounded by zero. We then introduce a
sequential learning algorithm to predict such arbitrary and unknown sequences,
and calculate upper bounds on its total squared prediction error for every
bounded sequence. We further show that in some scenarios we achieve matching
lower and upper bounds demonstrating that our algorithms are optimal in a
strong minimax sense such that their performances cannot be improved further.
As an interesting result we also prove that for the worst case scenario, the
performance of randomized algorithms can be achieved by sequential algorithms
so that randomized algorithms does not improve the performance.


  Nanomaterials capable of confining light are desirable for enhancing
spectroscopies such as Raman scattering, infrared absorption, and nonlinear
optical processes. Plasmonic superlattices have shown the ability to host
collective resonances in the mid-infrared, but require stringent fabrication
processes to create well-ordered structures. Here, we demonstrate how
short-range-ordered Au nanoparticle multilayers on a mirror, self-assembled by
a sub-nm molecular spacer, support collective plasmon-polariton resonances in
the visible and infrared, continuously tunable beyond 11 $\mu$m by simply
varying the nanoparticle size and number of layers. The resulting
molecule-plasmon system approaches vibrational strong coupling, and displays
giant Fano dip strengths, SEIRA enhancement factors ~10$^6$, light-matter
coupling strengths g~100 cm$^{-1}$, Purcell factors ~10$^6$, and mode volume
compression factors ~10$^8$. The collective plasmon-polariton mode is highly
robust to nanoparticle vacancy disorder and is sustained by the consistent gap
size defined by the molecular spacer. Structural disorder efficiently couples
light into the gaps between the multilayers and mirror, enabling Raman and
infrared sensing of sub-picolitre sample volumes.


  Following LIGO results of intermediate mass black holes mergers, the idea
that dark matter is composed of Primordial Black Boles (PBH), made a recent
comeback. PBHs might be formed in the early Universe through a variety of
mechanisms, best known being the gravitational collapse of overdense regions
due to density fluctuations. It's widely accepted that black hole loose there
mass over time through the Hawking radiation process. Since the particle
emission rate increases with black hole temperature, PBH evaporation is a
runaway process that eventually leads to a violent explosion. It has been
argued that a class of ultra short gammay ray bursts are actually PBH
explosions. The current upper limits on the local PBH explosion rate lie in the
$10^4$--$10^5$ $\mathrm{pc}^{-3}$ $\mathrm{yr}^{-1}$ range.
  This contribution reports on the search for TeV $\gamma$-ray bursts with a
timescale of a few seconds, as expected from the final stage of PBHs
evaporation, using 2700 hours of H.E.S.S. extragalactic observations. We
present the search algorithm, statistical estimations strategies and results of
this analysis.


  Open access to research data is increasingly important for accelerating
research. Grant authorities therefore request detailed plans for how data is
managed in the projects they finance. We have recently developed such a plan
for the EU-H2020 BIG-MAP project - a cross-disciplinary project targeting
disruptive battery-material discoveries. Essential for reaching the goal is
extensive sharing of research data across scales, disciplines and stakeholders,
not limited to BIG-MAP and the European BATTERY 2030+ initiative but within the
entire battery community. The key challenges faced in developing the data
management plan for such a large and complex project were to generate an
overview of the enormous amount of data that will be produced, to build an
understanding of the data flow within the project and to agree on a roadmap for
making all data FAIR. This paper describes the process we followed and how we
structured the plan.


  Machine learning is a promising approach to visualization recommendation due
to its high scalability and representational power. Researchers can create a
neural network to predict visualizations from input data by training it over a
corpus of datasets and visualization examples. However, these machine learning
models can reflect trends in their training data that may negatively affect
their performance. Our research project aims to address training bias in
machine learning visualization recommendation systems by identifying trends in
the training data through statistical analysis.


  We present new, sensitive, near-infrared images of the Class I protostar,
Elias 29, in the Ophiuchus cloud core. To explore the relationship between the
infall envelope and the outflow, narrowband H2 1-0 S(1), Br-gamma, and
narrowband K-continuum filters were used to image the source with the
Wide-Field Infrared Camera on the Hale 5m telescope and with Persson's
Auxiliary Nasmyth Infrared Camera on the Baade 6.5 m telescope. The source
appears as a bipolar, scattered light nebula, with a wide opening angle in all
filters, as is typical for late-stage protostars. However, the pure H2
emission-line images point to the presence of a heretofore undetected
precessing jet. It is argued that high-velocity, narrow, precessing jets
provide the mechanism for creating the observed wide-angled outflow cavity in
this source.


  By computing Frobenius-Schur indicators of modules of certain weak Hopf
algebras, we give a formula for the number of involutions in symmetric groups,
which are contained in a given coset with respect to a given Young subgroup.


  In this article, we produce Grothendieck-Riemann-Roch formulas for cohomology
theories that are not oriented in the classical sense. We then specialize to
the case of cohomology theories that admit a so-called symplectic orientation
and show how to compute the relevant Todd classes in that situation. At the end
of the article, we illustrate our methods on the Borel character linking
Hermitian K-theory and rational MW-motivic cohomology.


  The observational evidence for dark matter on progressively larger cosmic
scales is reviewed in a rather pedagogical fashion. Although the emphasis is on
dark matter in galaxies and in clusters of galaxies, its cosmological evidence
as well as its physical nature are also discussed.


  For a fixed graph $F$, a graph $G$ is said to be $F$-saturated if $G$ does
not contain a subgraph isomorphic to $F$ but does contain $F$ after the
addition of any new edge.
  Let $M_k$ be a matching consisting of $k$ edges and $S_{n,k}$ be the join
graph of a complete graph $K_k$ and an empty graph $\overline{K_{n-k}}$. In
this paper, we prove that for $s \geq3$ and $k\geq 2$, $S_{n,s-2}$ contains the
minimum number of $M_k$ among all $n$-vertex $K_s$-saturated graphs for
sufficiently large $n$, and when $k \leq s-2$, it is the unique extremal graph.
In addition, we also show that $S_{n,1}$ is the unique extremal graph when
$k=2$ and $s=3$.


  This paper presents a Prolog interface to the MiniSat satisfiability solver.
Logic program- ming with satisfiability combines the strengths of the two
paradigms: logic programming for encoding search problems into satisfiability
on the one hand and efficient SAT solving on the other. This synergy between
these two exposes a programming paradigm which we propose here as a logic
programming pearl. To illustrate logic programming with SAT solving we give an
example Prolog program which solves instances of Partial MAXSAT.


  It is shown that different approaches towards the solution of the Einstein
equations for a static spherically symmetric perfect fluid with a gamma-law
equation of state lead to an Abel differential equation of the second kind. Its
only integrable cases at present are flat spacetime, de Sitter solution and its
Buchdahl transform, Einstein static universe and the Klein-Tolman solution.


  In conformal field theory (CFT), the four-point correlator is a fundamental
object that encodes CFT properties, constrains CFT structures, and connects to
the gravitational scattering amplitude in holography theory. However, the
four-point correlator of CFTs in dimensions higher than 2D remains largely
unexplored due to the lack of non-perturbative tools. In this paper, we
introduce a new approach for directly computing four-point correlators of 3D
CFTs. Our method employs the recently proposed fuzzy (non-commutative) sphere
regularization, and we apply it to the paradigmatic 3D Ising CFT. Specifically,
we have computed three different four-point correlators: $\langle
\sigma\sigma\sigma\sigma\rangle$, $\langle
\sigma\sigma\epsilon\epsilon\rangle$, and $\langle \sigma\sigma T_{\mu\nu}
T_{\rho\eta}\rangle$. Additionally, we verify the crossing symmetry of $\langle
\sigma\sigma\sigma\sigma\rangle$, which is a notable property arising from
conformal symmetry. Remarkably, the computed four-point correlators exhibit
continuous crossing ratios, showcasing the continuum nature of the fuzzy sphere
regularization scheme. This characteristic renders them highly suitable for
future theoretical applications, enabling further advancements and insights in
3D CFT.


  This is a pedagogical introduction to the main concepts of the sterile
neutrino - a hypothetical particle, coined to resolve some anomalies in
neutrino data and retain consistency with observed widths of the $W$ and $Z$
bosons. We briefly review existing anomalies and the oscillation parameters
that best describe these data. We discuss in more detail how sterile neutrino
can be observed, as well as the consequences of its possible existence. In
particular, we pay attention to a possible loss of coherence in a model of
neutrino oscillations with sterile neutrinos, where this effect might be of a
major importance with respect to the 3$\nu$ model. The current status of
searches for a sterile neutrino state is also briefly reviewed.


  A gambler moves between the vertices $1, \ldots, n$ of a graph using the
probability distribution $p_{1}, \ldots, p_{n}$. Multiple cops pursue the
gambler on the graph, only being able to move between adjacent vertices. We
investigate the expected capture time for the gambler against $k$ cops as a
function of $n$ and $k$ for three versions of the game: (1) known gambler: the
cops know the gambler's distribution (2) unknown gambler: the cops do not know
the gambler's distribution (3) known changing gambler: the gambler's
distribution can change every turn, but the cops know all of the gambler's
distributions from the beginning. We show for $n > k$ that if the cops are
allowed to choose their initial positions before the game starts and before
they know the gambler's distribution(s), and if both the gambler and the cops
play optimally, then the expected capture time is $\Theta(n/k)$ for the known
gambler, the unknown gambler, and the known changing gambler.


  A simple graph $G$ is \emph{overfull} if
$|E(G)|>\Delta\lfloor|V(G)|/2\rfloor$. By the pigeonhole principle, every
overfull graph $G$ has $\chi'(G)>\Delta$. The \emph{core} of a graph, denoted
$G_\Delta$, is the subgraph induced by its vertices of degree $\Delta$.
Vizing's Adjacency Lemma implies that if $\chi'(G)>\Delta$, then $G_\Delta$
contains cycles. Hilton and Zhao conjectured that if $G_\Delta$ has maximum
degree 2 and $\Delta\ge 4$, then $\chi'(G)>\Delta$ precisely when $G$ is
overfull. We prove this conjecture for the case $\Delta=4$.


  LaAlO3/SrTiO3 structures showing high mobility conduction have recently
aroused large expectations as they might represent a major step towards the
conception of all-oxide electronics devices. For the development of these
technological applications a full understanding of the dimensionality and
origin of the conducting electronic system is crucial. To shed light on this
issue, we have investigated the magnetotransport properties of a LaAlO3 layer
epitaxially grown at low oxygen pressure on a TiO2-terminated (001)-SrTiO3
substrate. In agreement with recent reports, a low-temperature mobility of
about 10^4 cm2/Vs has been found. We conclusively show that the electronic
system is three-dimensional, excluding any interfacial confinement of carriers.
We argue that the high-mobility conduction originates from the doping of SrTiO3
with oxygen vacancies and that it extends over hundreds of microns into the
SrTiO3 substrate. Such high mobility SrTiO3-based heterostructures have a
unique potential for electronic and spintronics devices.


  In the supersymmetric model with local gauged baryon and lepton
numbers(BLMSSM), the CP violating effects are considered to study the lepton
electric dipole moment(EDM). The CP violating phases in BLMSSM are more than
those in the standard model(SM) and can give large contributions. The analysis
of the EDMs for the leptons $e,\mu, \tau$ is shown in this work. It is in
favour of exploring the source of CP violation and probing the physics beyond
SM.


  Given a $k$-uniform hypergraph $G$ with vertex set $[n]$ and edge set $E(G)$,
the ABC tensor $\mathcal{ABC}(G)$ of $G$ is the $k$-order $n$-dimensional
tensor with \[
  \mathcal{ABC}(G)_{i_1, \dots, i_k}=
  \begin{cases}
  \dfrac{1}{(k-1)!}\sqrt[k]{\dfrac{\sum_{i\in e}d_{i}-k}{\prod_{i\in e}d_{i}}}
& \mbox{if $e\in E(G)$}
  0 & \mbox{otherwise} \end{cases} \] for $i_j\in [n]$ with $j\in [k]$, where
$d_i$ is the degree of vertex $i$ in $G$. The ABC spectral radius of a uniform
hypergraph is the spectral radius of its ABC tensor. We give tight lower and
upper bounds for the ABC spectra radius, and determine the maximum ABC spectral
radii of uniform hypertrees, uniform non-hyperstar hypertrees and uniform
non-power hypertrees of given size, as well as the maximum ABC spectral radii
of unicyclic uniform hypergraphs and linear unicyclic uniform hypergraphs of
given size, respectively. We also characterize those uniform hypergraphs for
which the maxima for the ABC spectral radii are actually attained in all cases.


  Recent theoretical and experimental advances have shed light on the existence
of so-called `perfectly transmitting' wavefronts with transmission coefficients
close to 1 in strongly backscattering random media. These perfectly
transmitting eigen-wavefronts can be synthesized by spatial amplitude and phase
modulation. Here, we consider the problem of transmission enhancement using
phase-only modulated wavefronts. We develop physically realizable iterative and
non-iterative algorithms for increasing the transmission through such random
media using backscatter analysis. We theoretically show that, despite the
phase-only modulation constraint, the non-iterative algorithms will achieve at
least about 25$\pi$% or about 78.5% transmission assuming there is at least one
perfectly transmitting eigen-wavefront and that the singular vectors of the
transmission matrix obey a maximum entropy principle so that they are
isotropically random.
  We numerically analyze the limits of phase-only modulated transmission in 2-D
with fully spectrally accurate simulators and provide rigorous numerical
evidence confirming our theoretical prediction in random media with periodic
boundary conditions that is composed of hundreds of thousands of non-absorbing
scatterers. We show via numerical simulations that the iterative algorithms we
have developed converge rapidly, yielding highly transmitting wavefronts using
relatively few measurements of the backscatter field. Specifically, the best
performing iterative algorithm yields approx 70% transmission using just 15-20
measurements in the regime where the non-iterative algorithms yield
approximately 78.5% transmission but require measuring the entire modal
reflection matrix.


  An important problem in quaternionic hyperbolic geometry is to classify
ordered $m$-tuples of pairwise distinct points in the closure of quaternionic
hyperbolic n-space, $\overline{{\bf H}_\bh^n}$, up to congruence in the
holomorphic isometry group ${\rm PSp}(n,1)$ of ${\bf H}_\bh^n$. In this paper
we concentrate on two cases: $m=3$ in $\overline{{\bf H}_\bh^n}$ and $m=4$ on
$\partial{\bf H}_\bh^n$ for $n\geq 2$. New geometric invariants and several
distance formulas in quaternionic hyperbolic geometry are introduced and
studied for this problem. The congruence classes are completely described by
quaternionic Cartan's angular invariants and the distances between some
geometric objects for the first case. The moduli space is constructed for the
second case.


  In this paper, we consider the initial boundary value problem of the two
dimensional multi-term time fractional mixed diffusion and diffusion-wave
equations. An alternating direction implicit (ADI) spectral method is developed
based on Legendre spectral approximation in space and finite difference
discretization in time. Numerical stability and convergence of the schemes are
proved, the optimal error is $O(N^{-r}+\tau^2)$, where $N, \tau, r$ are the
polynomial degree, time step size and the regularity of the exact solution,
respectively. We also consider the non-smooth solution case by adding some
correction terms. Numerical experiments are presented to confirm our
theoretical analysis. These techniques can be used to model diffusion and
transport of viscoelastic non-Newtonian fluids.


  Quantum state preparation is vital in quantum computing and information
processing. The ability to accurately and reliably prepare specific quantum
states is essential for various applications. One of the promising applications
of quantum computers is quantum simulation. This requires preparing a quantum
state representing the system we are trying to simulate. This research
introduces a novel simulation algorithm, the multi-Split-Steps Quantum Walk
(multi-SSQW), designed to learn and load complicated probability distributions
using parameterized quantum circuits (PQC) with a variational solver on
classical simulators. The multi-SSQW algorithm is a modified version of the
split-steps quantum walk, enhanced to incorporate a multi-agent decision-making
process, rendering it suitable for modeling financial markets. The study
provides theoretical descriptions and empirical investigations of the
multi-SSQW algorithm to demonstrate its promising capabilities in probability
distribution simulation and financial market modeling. Harnessing the
advantages of quantum computation, the multi-SSQW models complex financial
distributions and scenarios with high accuracy, providing valuable insights and
mechanisms for financial analysis and decision-making. The multi-SSQW's key
benefits include its modeling flexibility, stable convergence, and
instantaneous computation. These advantages underscore its rapid modeling and
prediction potential in dynamic financial markets.


  We utilize a 3D hybrid hydro+micro model for a comprehensive and consistent
description of soft and hard particle production in ultra-relativistic
heavy-ion collisions at RHIC. In the soft sector we focus on the dynamics of
(multi-)strange baryons, where a clear strangeness dependence of their
collision rates and freeze-out is observed. In the hard sector we study the
radiative energy loss of hard partons in a soft medium in the multiple soft
scattering approximation. While the nuclear suppression factor $R_{AA}$ does
not reflect the high quality of the medium description (except in a reduced
systematic uncertainty in extracting the quenching power of the medium), the
hydrodynamical model also allows to study different centralities and in
particular the angular variation of $R_{AA}$ with respect to the reaction
plane, allowing for a controlled variation of the in-medium path-length.


  Mixed surfactant systems with strongly bound counterions show many
interesting phases such as the random mesh phase consisting of a disordered
array of defects (water-filled nano-pores in the bilayers). The present study
addresses the non-equilibrium phase transition of the random mesh phase under
shear to an ordered mesh phase with a high degree of coherence between
nano-pores in three-dimension. In-situ small-angle synchrotron X-ray study
under different shear stress conditions shows sharp Bragg peaks in the X-ray
diffraction, successfully indexed to the rhombohedral lattice with R$\bar{3}$m
space group symmetry. The ordered mesh phase shows isomorphic twinning and
buckling at higher shear stress. Our experimental studies bring out rich
non-equilibrium phase transitions in concentrated cationic surfactant systems
with strongly bound counterions hitherto not well-explored and provide
motivation for a quantitative understanding.


  To test the theoretical understanding that finding bright CO emission depends
primarily on dust shielding, we investigate the relationship between CO
emission ($I_{\rm CO}$) and the amount of dust (estimated from IR emission and
expressed as "$A_V$") across the Large Magellanic Cloud, the Small Magellanic
Cloud, and the Milky Way. We show that at our common resolution of 10 pc
scales, $I_{\rm CO}$ given a fixed line-of-sight $A_V$ is similar across all
three systems despite the difference in metallicity. We find some evidence for
a secondary dependence of $I_{\rm CO}$ on radiation field; in the LMC, $I_{\rm
CO}$ at a given $A_V$ is smaller in regions of high $T_{\rm dust}$, perhaps
because of an increased photodissociating radiation field. We suggest a simple
but useful picture in which the CO-to-H$_2$ conversion factor (\xco) depends on
two separable factors: (1) the distribution of gas column densities, which maps
to an extinction distribution via a dust-to-gas ratio; and (2) the dependence
of $I_{\rm CO}$ on $A_V$. Assuming that the probability distribution function
(PDF) of local Milky Way clouds is universal, this approach predicts a
dependence of \xco\ on $Z$ between $Z^{-1}$ and $Z^{-2}$ above about a third
solar metallicity. Below this metallicity, CO emerges from only the high column
density parts of the cloud and so depends very sensitively on the adopted PDF
and the H$_2$/{\sc Hi} prescription. The PDF of low metallicity clouds is thus
of considerable interest and the uncertainty associated with even an ideal
prescription for \xco\ at very low metallicity will be large.


  A stack of disks with numerous holes composed of a non-interacting charged
Bose gas is modeled as a low dimensional disk. The Bose condensation of the
net-like disk system in a uniform magnetic field is studied. Calculation of the
condensate fraction of the net-like disk system showed that there still exists
a non-zero condensate fraction at low temperature and in weak field.


  Image-guided drawing can compensate for the lack of skills but often requires
a significant number of repetitive strokes to create textures. Existing
automatic stroke synthesis methods are usually limited to predefined styles or
require indirect manipulation that may break the spontaneous flow of drawing.
We present a method to autocomplete repetitive short strokes during users'
normal drawing process. Users can draw over a reference image as usual. At the
same time, our system silently analyzes the input strokes and the reference to
infer strokes that follow users' input style when certain repetition is
detected. Users can accept, modify, or ignore the system predictions and
continue drawing, thus maintaining the fluid control of drawing. Our key idea
is to jointly analyze image regions and operation history for detecting and
predicting repetitions. The proposed system can effectively reduce users'
workload in drawing repetitive short strokes and facilitates users in creating
results with rich patterns.


  This presentation explains why models with a dynamical symmetry often work
extraordinarily well even in the presence of large symmetry breaking
interactions. A model may be a caricature of a more realistic system with a
"quasi-dynamical" symmetry. The existence of quasi-dynamical symmetry in
physical systems and its significance for understanding collective dynamics in
complex nuclei is explained in terms of the precise mathematical concept of an
"embedded representation". Examples are given which exhibit quasi-dynamical
symmetry to a remarkably high degree. Understanding this unusual symmetry and
why it occurs, is important for recognizing why dynamical symmetries appear to
be much moreprevalent than they would otherwise have any right to be and for
interpreting the implications of a model's successes. We indicate when
quasi-dynamical symmetry is expected to apply and present a challenge as to how
best to make use of this potentially powerful algebraic structure.


  We obtain polynomial decay rates for $C_{0}$-semigroups, assuming that the
resolvent grows polynomially at infinity in the complex right half-plane. Our
results do not require the semigroup to be uniformly bounded, and for unbounded
semigroups we improve upon previous results by, for example, removing a
logarithmic loss on non-Hilbertian Banach spaces.


  We give some evidences which imply that W(1+infinity) algebra describes the
symmetry behind AGT(-W) conjecture: a correspondence between the partition
function of N=2 supersymmetric quiver gauge theories and the correlators of
Liouville (Toda) field theory.


  In this paper we consider the problem of the existence of higher derivatives
of the function $t\mapsto\f(A+tK)$, where $\f$ is a function on the real line,
$A$ is a self-adjoint operator, and $K$ is a bounded self-adjoint operator. We
improve earlier results by Sten'kin. In order to do this, we give a new
approach to multiple operator integrals. This approach improves the earlier
approach given by Sten'kin. We also consider a similar problem for unitary
operators.


  Within medical imaging, manual curation of sufficient well-labeled samples is
cost, time and scale-prohibitive. To improve the representativeness of the
training dataset, for the first time, we present an approach to utilize large
amounts of freely available web data through web-crawling. To handle noise and
weak nature of web annotations, we propose a two-step transfer learning based
training process with a robust loss function, termed as Webly Supervised
Learning (WSL) to train deep models for the task. We also leverage search by
image to improve the search specificity of our web-crawling and reduce
cross-domain noise. Within WSL, we explicitly model the noise structure between
classes and incorporate it to selectively distill knowledge from the web data
during model training. To demonstrate improved performance due to WSL, we
benchmarked on a publicly available 10-class fine-grained skin lesion
classification dataset and report a significant improvement of top-1
classification accuracy from 71.25 % to 80.53 % due to the incorporation of
web-supervision.


  In this paper, we investigate the geometry of Einstein-type equation on a
Riemannian manifold, unifying various particular geometric structures recently
studied in the literature, such as critical point equation and vacuum static
equation. We show various rigidity results of Einstein-type manifolds under
assumptions of several curvature conditions.


  At finite temperature, conserved charges undergo thermal fluctuations in a
quantum many-body system in the grand canonical ensemble. The full structure of
the fluctuations of the total U(1) charge $Q$ can be succinctly captured by the
generating function $G(\theta)=\left\langle e^{i \theta Q}\right\rangle$. For a
1D translation-invariant spin chain, in the thermodynamic limit the magnitude
$|G(\theta)|$ scales with the system size $L$ as $\ln
|G(\theta)|=-\alpha(\theta)L+\gamma(\theta)$, where $\gamma(\theta)$ is the
scale-invariant contribution and may encode universal information about the
underlying system. In this work we investigate the behavior and physical
meaning of $\gamma(\theta)$ when the system is periodic. We find that
$\gamma(\theta)$ only takes non-zero values at isolated points of $\theta$,
which is $\theta=\pi$ for all our examples. In two exemplary lattice systems we
show that $\gamma(\pi)$ takes quantized values when the U(1) symmetry exhibits
a specific type of 't Hooft anomaly with other symmetries. In other cases, we
investigate how $\gamma(\theta)$ depends on microscopic conditions (such as the
filling factor) in field theory and exactly solvable lattice models.


  In Northern Italy, between 1796 and 1814, Napoleon Bonaparte formed a
Republic, and then a Kingdom, controlled by France. Milan was the capital of
the State, and the Brera Palace was the main cultural centre, as regards both
the arts and the sciences. Bonaparte probably intended to strengthen this
characteristic of Brera, aiming at increasing its Italian and European
relevance. We will discuss in detail in which way he interacted with the
astronomers of Brera Observatory, and in particular with Barnaba Oriani, that
was considered the local main representative of the 'republique des lettres',
that is, the world of literature, arts and sciences. We propose a possible
reconstruction of the effects of those complicated historical events on the
Italian astronomy and on its relations with the European one.


  Related to the electronic structure of cuprate high-Tc superconductors there
are two prevailing views: In one view, Pines and collaborators argue that
cuprates consist of two electronic subsystems: one with localized spins and the
other having itinerant character. Contrary to that, Phil Anderson has argued
for one-component or one-band model for cuprates. Thus, a very natural question
arrises: What is the actual electronic system in cuprates? Are these
two-component or one-component systems? After a careful consideration of both
the views, we argue in favor of one-component or Andersonian view. The key lies
in the dual character of electrons in narrow d bands, and we put forward a
semiclassical model using which we could quantitatively account for oxygen NMR
shift data in $La_{2-x}Sr_xCuO_4$ within the single component view.


  The electrical conductivity behavior of highly crystallized undoped
hydrogenated microcrystalline silicon films having different microstructures
was studied. The dark conductivity is seen to follow Meyer Neldel rule (MNR) in
some films and anti MNR in others, depending on the details of microstructural
attributes and corresponding changes in the effective density of states
distributions. A band tail transport and statistical shift of Fermi level are
used to explain the origin of MNR as well as anti-MNR in our samples. We
present the evidence of anti-MNR in the various experimental transport data of
microcrystalline silicon materials reported in literature and analyze these
data together with ours to show the consistency and physical plausibility of
statistical shift model. The calculated MNR parameters and other significant
material parameters derived therefrom are tenable for a wide microstructural
range of the microcrystalline silicon system.


  In the Randall-Sundrum model there can be a rich new phenomenology associated
with Higgs-radion mixing. A photon-photon collider would provide a crucial
complement to the LHC and a future ILC collider for fully determining the
parameters of the model and definitively testing it.


  We present simulation data for the motion of a polymer chain through a
regular lattice of impenetrable obstacles (Evans-Edwards model). Chain lengths
range from N=20 to N=640, and time up to $10^{7}$ Monte Carlo steps. For $N
\geq 160$ we for the central segment find clear $t^{1/4}$-behavior as an
intermediate asymptote. The also expected $t^{1/2}$-range is not yet developed.
For the end segment also the $t^{1/4}$-behavior is not reached. All these data
compare well to our recent analytical evaluation of the reptation model, which
shows that for shorter times $(t \alt 10^{4})$ the discreteness of the
elementary motion cannot be neglected, whereas for longer times and short
chains $(N \alt 100)$ tube renewal plays an essential role also for the central
segment. Due to the very broad crossover behavior both the diffusion
coefficient and the reptation time within the range of our simulation do not
reach the asymptotic power laws predicted by reptation theory. We present
results for the center-of-mass motion, showing the expected intermediate
$t^{1/2}$-behavior, but again only for very long chains. In addition we show
results for the motion of the central segment relative to the center of mass,
where in some intermediate range we see the expected increase of the effective
power beyond the $t^{1/4}$-law, before saturation sets in. Analysis and
simulations agree on defining a new set of criteria as characteristic for
reptation of finite chains.


  Galaxy clusters identified from the Sunyaev Zel'dovich (SZ) effect are a key
ingredient in multi-wavelength cluster-based cosmology. We present a comparison
between two methods of cluster identification: the standard Matched Filter (MF)
method in SZ cluster finding and a method using Convolutional Neural Networks
(CNN). We further implement and show results for a `combined' identifier. We
apply the methods to simulated millimeter maps for several observing
frequencies for an SPT-3G-like survey. There are some key differences between
the methods. The MF method requires image pre-processing to remove point
sources and a model for the noise, while the CNN method requires very little
pre-processing of images. Additionally, the CNN requires tuning of
hyperparameters in the model and takes as input, cutout images of the sky.
Specifically, we use the CNN to classify whether or not an 8 arcmin $\times$ 8
arcmin cutout of the sky contains a cluster. We compare differences in purity
and completeness. The MF signal-to-noise ratio depends on both mass and
redshift. Our CNN, trained for a given mass threshold, captures a different set
of clusters than the MF, some of which have SNR below the MF detection
threshold. However, the CNN tends to mis-classify cutouts whose clusters are
located near the edge of the cutout, which can be mitigated with staggered
cutouts. We leverage the complementarity of the two methods, combining the
scores from each method for identification. The purity and completeness of the
MF alone are both 0.61, assuming a standard detection threshold. The purity and
completeness of the CNN alone are 0.59 and 0.61. The combined classification
method yields 0.60 and 0.77, a significant increase for completeness with a
modest decrease in purity. We advocate for combined methods that increase the
confidence of many lower signal-to-noise clusters.


  We propose a scenario that explains the apparent nitrogen deficiency in
comets in a way consistent with the fact that the surfaces of Pluto and Triton
are dominated by nitrogen-rich ice. We use a statistical thermodynamic model to
investigate the composition of the successive multiple guest clathrates that
may have formed during the cooling of the primordial nebula from the most
abundant volatiles present in the gas phase. These clathrates agglomerated with
the other ices (pure condensates or stoichiometric hydrates) and formed the
building blocks of comets. We report that molecular nitrogen is a poor
clathrate former, when we consider a plausible gas phase composition of the
primordial nebula. This implies that its trapping into cometesimals requires a
low disk temperature ($\sim$20 K) in order to allow the formation of its pure
condensate. We find that it is possible to explain the lack of molecular
nitrogen in comets as a consequence of their postformation internal heating
engendered by the decay of short-lived radiogenic nuclides. This scenario is
found consistent with the presence of nitrogen-rich ice covers on Pluto and
Triton. Our model predicts that comets should present xenon-to-water and
krypton-to-water ratios close to solar xenon-to-oxygen and krypton-to-oxygen
ratios, respectively. In contrast, the argon-to-water ratio is predicted to be
depleted by a factor of $\sim$300 in comets compared to solar argon-to-oxygen,
as a consequence of poor trapping efficiency and radiogenic heating.


  In this paper, vertex representations of the 2-toroidal Lie superalgebras of
type $D(m, n)$ are constructed using both bosonic fields and vertex operators
based on their loop algebraic presentation.


  Through Variational Monte Carlo simulation we show the d-wave RVB pairing in
the Heisenberg model on triangular lattice can be better described in terms of
a two component order parameter. The fully gapped chiral d-wave RVB state,
which is predicted by the mean field theory to be the unique minimum of
variational energy in the two dimensional representation space of d-wave
pairing, is found to be actually a local maximum and the true minimum of energy
is reached by the non-chiral $d_{xy}$ state with line nodes. We also find that
the usual Gutzwiller approximation, which enjoys great success for the square
lattice system, fails badly on the triangular lattice as a result of the
geometric frustration inherent of the system. An improved version of the
Gutzwiiler approximation is proposed and is found to give a much better results
than the usual one.


  We describe the structure of the vacuum states of quiver gauge theories
obtained via dimensional reduction over homogeneous spaces, in the explicit
example of SU(3)-equivariant dimensional reduction of Yang-Mills-Dirac theory
on manifolds of the form M x CP(2). We pay particular attention to the role of
topology of background gauge fields on the internal coset spaces, in this case
U(1) magnetic monopoles and SU(2) instantons on CP(2). The reduction of
Yang-Mills theory induces a quiver gauge theory involving coupled
Yang-Mills-Higgs systems on M with a Higgs potential leading to dynamical
symmetry breaking. The criterion for a ground state of the Higgs potential can
be written as the vanishing of a non-abelian Yang-Mills flux on the quiver
diagram, regarded as a lattice with group elements attached to the links. The
reduction of SU(3)-symmetric fermions yields Dirac fermions on M transforming
under the low-energy gauge group with Yukawa couplings. The fermionic zero
modes on CP(2) yield exactly massless chiral fermions on M, though there is a
unique choice of spin(c) structure on CP(2) for which some of the zero modes
can acquire masses through Yukawa interactions. We work out the spontaneous
symmetry breaking patterns and determine the complete physical particle
spectrum in a number of explicit examples, some of which possess quantum number
assignments qualitatively analogous to the manner in which vector bosons,
quarks and leptons acquire masses in the standard model.


  In evolutionary robotics an encoding of the control software, which maps
sensor data (input) to motor control values (output), is shaped by stochastic
optimization methods to complete a predefined task. This approach is assumed to
be beneficial compared to standard methods of controller design in those cases
where no a-priori model is available that could help to optimize performance.
Also for robots that have to operate in unpredictable environments, an
evolutionary robotics approach is favorable. We demonstrate here that such a
model-free approach is not a free lunch, as already simple tasks can represent
unsolvable barriers for fully open-ended uninformed evolutionary computation
techniques. We propose here the 'Wankelmut' task as an objective for an
evolutionary approach that starts from scratch without pre-shaped controller
software or any other informed approach that would force the behavior to be
evolved in a desired way. Our focal claim is that 'Wankelmut' represents the
simplest set of problems that makes plain-vanilla evolutionary computation
fail. We demonstrate this by a series of simple standard evolutionary
approaches using different fitness functions and standard artificial neural
networks as well as continuous-time recurrent neural networks. All our tested
approaches failed. We claim that any other evolutionary approach will also fail
that does per-se not favor or enforce modularity and does not freeze or protect
already evolved functionalities. Thus we propose a hard-to-pass benchmark and
make a strong statement for self-complexifying and generative approaches in
evolutionary computation. We anticipate that defining such a 'simplest task to
fail' is a valuable benchmark for promoting future development in the field of
artificial intelligence, evolutionary robotics and artificial life.


  Coadjoint orbits of the Virasoro and Kac-Moody algebras provide geometric
actions for matter coupled to gravity and gauge fields in two dimensions.
However, the Gauss' law constraints that arise from these actions are not
necessarily endemic to two-dimensional topologies. Indeed the constraints
associated with Yang-Mills naturally arise from the coadjoint orbit
construction of the WZW model. One may in fact use a Yang-Mills theory to
provide dynamics to the otherwise fixed coadjoint vectors that define the
orbits. In this letter we would like to exhibit an analogue of the Yang-Mills
classical action for the diffeomorphism sector. With this analogue one may
postulate a 4D theory of gravitation that is related to an underlying two
dimensional theory. Instead of quadratic differentials, a (1,3) pseudo tensor
becomes the dynamical variable. We briefly discuss how this tensor may be
classically coupled to matter.


  We present a detailed study of the static spherically symmetric solutions in
de Rham-Gabadadze-Tolley (dRGT) theory. Since the diffeomorphism invariance can
be restored by introducing the St\"{u}ckelberg fields $\phi^a$, there is new
invariant $I^{ab}=g^{\mu\nu}\partial_{\mu}\phi^a\partial_\nu\phi^b$ in the
massive gravity, which adds to the ones usually encountered in general
relativity (GR). In the unitary gauge $\phi^a=x^\mu\delta_\mu^a$, any inverse
metric $g^{\mu\nu}$ that has divergence including the coordinate singularity in
GR would exhibit a singularity in the invariant $I^{ab}$. Therefore, there is
no conventional Schwarzschild metric if we choose unitary gauge. In this paper,
we obtain a self-consistent static spherically symmetric ansatz in the
nonunitary gauge. Under this ansatz, we find that there are seven solutions
including the Schwarzschild solution, Reissner-Nordstr\"{o}m solution and five
other solutions. These solutions may possess an event horizon depending upon
the physical parameters (Schwarzschild radius $r_s$, scalar charge $S$ and/or
electric charge $Q$). If these solutions possess an event horizon, we show that
the singularity of $I^{ab}$ is absent at the horizon. Therefore, these
solutions may become candidates for black holes in dRGT.


  Score based learning (SBL) is a promising approach for learning Bayesian
networks in the discrete domain. However, when employing SBL in the continuous
domain, one is either forced to move the problem to the discrete domain or use
metrics such as BIC/AIC, and these approaches are often lacking. Discretization
can have an undesired impact on the accuracy of the results, and BIC/AIC can
fall short of achieving the desired accuracy. In this paper, we introduce two
new scoring metrics for scoring Bayesian networks in the continuous domain: the
three-part minimum description length and the renormalized normalized maximum
likelihood metric. We rely on the minimum description length principle in
formulating these metrics. The metrics proposed are free of hyperparameters,
decomposable, and are asymptotically consistent. We evaluate our solution by
studying the convergence rate of the learned graph to the generating network
and, also, the structural hamming distance of the learned graph to the
generating network. Our evaluations show that the proposed metrics outperform
their competitors, the BIC/AIC metrics. Furthermore, using the proposed RNML
metric, SBL will have the fastest rate of convergence with the smallest
structural hamming distance to the generating network.


  In this work we prove the existence of a classical positive solution for an
elliptic equation with a sublinear term. We use Galerkin approximations to show
existence of such solution on bounded domains in RN.


  Impulse formulations of the Euler (and Navier-Stokes) equations were
considered by Kuz'min [1] and Oseledets [2] and different impulse formulations
are produced by various gauge transformations (Russo and Smereka[3]). The
extension of the Kuz'min-Oseledets formulation to the compressible, barotropic
case was considered by Tur and Yanovsky [4] and Shivamoggi [5]. Here, we
construct exact solutions for the fluid impulse density for incompressible and
compressible barotropic flows and discuss their physical signifcance.


  Motivated by a recent experiment by L.-H. Reydellet et al., Phys. Rev. Lett.
90, 176803 (2003), we discuss an interpretation of photon-assisted shot noise
in mesoscopic multiprobe conductors in terms of electron-hole pair excitations.
AC-voltages are applied to the contacts of the sample. Of interest are
correlations resulting from the fact that electrons and holes are generated in
pairs. We show that with two out-of-phase ac-potentials of equal magnitude and
frequency, applied to different contacts, it is possible to trace out the
Hanbury Brown Twiss exchange interference correlations in a four probe
conductor. We calculate the distribution of Hanbury Brown Twiss phases for a
four-probe single channel chaotic dot.


  Item response theory (IRT) can be applied to the analysis of the evaluation
of results from AI benchmarks. The two-parameter IRT model provides two
indicators (difficulty and discrimination) on the side of the item (or AI
problem) while only one indicator (ability) on the side of the respondent (or
AI agent). In this paper we analyse how to make this set of indicators dual, by
adding a fourth indicator, generality, on the side of the respondent.
Generality is meant to be dual to discrimination, and it is based on
difficulty. Namely, generality is defined as a new metric that evaluates
whether an agent is consistently good at easy problems and bad at difficult
ones. With the addition of generality, we see that this set of four key
indicators can give us more insight on the results of AI benchmarks. In
particular, we explore two popular benchmarks in AI, the Arcade Learning
Environment (Atari 2600 games) and the General Video Game AI competition. We
provide some guidelines to estimate and interpret these indicators for other AI
benchmarks and competitions.


  Monocular dense 3D reconstruction of deformable objects is a hard ill-posed
problem in computer vision. Current techniques either require dense
correspondences and rely on motion and deformation cues, or assume a highly
accurate reconstruction (referred to as a template) of at least a single frame
given in advance and operate in the manner of non-rigid tracking. Accurate
computation of dense point tracks often requires multiple frames and might be
computationally expensive. Availability of a template is a very strong prior
which restricts system operation to a pre-defined environment and scenarios. In
this work, we propose a new hybrid approach for monocular non-rigid
reconstruction which we call Hybrid Deformation Model Network (HDM-Net). In our
approach, deformation model is learned by a deep neural network, with a
combination of domain-specific loss functions. We train the network with
multiple states of a non-rigidly deforming structure with a known shape at
rest. HDM-Net learns different reconstruction cues including texture-dependent
surface deformations, shading and contours. We show generalisability of HDM-Net
to states not presented in the training dataset, with unseen textures and under
new illumination conditions. Experiments with noisy data and a comparison with
other methods demonstrate robustness and accuracy of the proposed approach and
suggest possible application scenarios of the new technique in interventional
diagnostics and augmented reality.


  IT industries in current scenario have to struggle effectively in terms of
cost, quality, service or innovation for their subsistence in the global
market. Due to the swift transformation of technology, software industries owe
to manage a large set of data having precious information hidden. Data mining
technique enables one to effectively cope with this hidden information where it
can be applied to code optimization, fault prediction and other domains which
modulates the success nature of software projects. Additionally, the efficiency
of the product developed further depends upon the quality of the project
personnel. The position of the paper therefore is to explore potentials of
project personnel in terms of their competency and skill set and its influence
on quality of project. The above mentioned objective is accomplished using a
Bayesian classifier in order to capture the pattern of human performance. By
this means, the hidden and valuable knowledge discovered in the related
databases will be summarized in the statistical structure. This mode of
predictive study enables the project managers to reduce the failure ratio to a
significant level and improve the performance of the project using the right
choice of project personnel.


  We show that the functor of $p$-typical co-Witt vectors on commutative
algebras over a perfect field $k$ of characteristic $p$ is defined on, and in
fact only depends on, a weaker structure than that of a $k$-algebra. We call
this structure a $p$-polar $k$-algebra. By extension, the functors of points
for any $p$-adic affine commutative group scheme and for any formal group are
defined on, and only depend on, $p$-polar structures. In terms of abelian Hopf
algebras, we show that a cofree cocommutative Hopf algebra can be defined on
any $p$-polar $k$-algebra $P$, and it agrees with the cofree commutative Hopf
algebra on a commutative $k$-algebra $A$ if $P$ is the $p$-polar algebra
underlying $A$; a dual result holds for free commutative Hopf algebras on
finite $k$-coalgebras.


  We calculate the graviton's $\beta$-function in $AdS$ string-theoretic
sigma-model, perturbed by vertex operators for Vasiliev's higher spin gauge
fields in $AdS_5$. The result is given by $\beta_{mn}=R_{mn}+4T_{mn}(g,u)$
(with the AdS radius set to 1 and the graviton polarized along the $AdS_5$
boundary), with the matter stress-energy tensor given by that of conformal
holographic fluid in $d=4$, evaluated at the temperature given by
$T={1\over{\pi}}$. The stress-energy tensor is given by
$T_{mn}={g_{mn}}+4u_mu_n+\sum_{N}T^{(N)}_{mn}$ where $u$ is the vector
excitation satisfying $u^2=-1$ and $N$ is the order of the gradient expansion
in the dissipative part of the tensor. We calculate the contributions up to
N=2. The higher spin excitations contribute to the $\beta$-function, ensuring
the overall Weyl covariance of the matter stress tensor. We conjecture that the
structure of gradient expansion in $d=4$ conformal hydrodynamics at higher
orders is controlled by the higher spin operator algebra in $AdS_5$.


  Holoraumy is a tool being developed for dimensional enhancement
(supersymmetry holography) where the goal is to build higher dimensional
supersymmetric multiplets from lower dimensional supersymmetric multiplets. In
this paper, for the first time we investigate holoraumy for on-shell
supersymmetry. Specifically, the holoraumy tensors for a number of familiar 4D,
$\mathcal{N}=1$ multiplets are calculated. It is shown in all of these cases of
on-shell theories, the holoraumy is of the form of an electromagnetic duality
charge multiplying a composite transformation involving an electromagnetic
duality rotation through an angle of $\pi/2$ times a space time translation.
The details of our calculations can be found at the HEPTHools Data Repository
at https://hepthools.github.io/Data/.


  The coupling of an unparticle operator O_U to Standard Model particles opens
up the possibility of unparticle decays into standard model fields. We study
this issue by analyzing the pole structure (and spectral function) of the
unparticle propagator, corrected to account for one-loop polarization effects
from virtual SM particles. We find that the propagator of a scalar unparticle
(of scaling dimension 1 < d_U < 2) with a mass gap m_g develops an isolated
pole, m_p^2-i m_p Gamma_p, with m_p^2 < m_g^2 below the unparticle continuum
that extends above m_g (showing that the theory would be unstable without a
mass gap). If that pole lies below the threshold for decay into two standard
model particles the pole corresponds to a stable unparticle state (and its
width Gamma_p is zero). For m_p^2 above threshold the width is non zero and
related to the unparticle decay rate into Standard Model particles. This
picture is valid for any value of d_U in the considered range.


  In this paper, we show that the Jacobiator $J$ of a pre-Courant algebroid is
closed naturally. The corresponding equivalence class $[J^\flat]$ is defined as
the Pontryagin class, which is the obstruction of a pre-Courant algebroid to be
deformed into a Courant algebroid. We construct a Leibniz 2-algebra and a Lie
2-algebra associated to a pre-Courant algebroid and prove that these algebraic
structures are isomorphic under deformations. Finally, we introduce the twisted
action of a Lie algebra on a manifold to give more examples of pre-Courant
algebroids, which include the Cartan geometry.


  The PageRank is a popularity measure designed by Google to rank Web pages.
Experiments confirm that the PageRank obeys a `power law' with the same
exponent as the In-Degree. This paper presents a novel mathematical model that
explains this phenomenon. The relation between the PageRank and In-Degree is
modelled through a stochastic equation, which is inspired by the original
definition of the PageRank, and is analogous to the well-known distributional
identity for the busy period in the M/G/1 queue. Further, we employ the theory
of regular variation and Tauberian theorems to analytically prove that the tail
behavior of the PageRank and the In-Degree differ only by a multiplicative
factor, for which we derive a closed-form expression. Our analytical results
are in good agreement with experimental data.


  Resonance assignment is a critical first step in the investigation of protein
structures using NMR spectroscopy. The development of assignment methods that
require less experimental data is possible with prior knowledge of the
macromolecular structure. Automated methods of performing the task of resonance
assignment can significantly reduce the financial cost and time requirement for
protein structure determination. Such methods can also be beneficial in
validating a protein's solution state structure. Here we present a new approach
to the assignment problem. Our approach uses only RDC data to assign backbone
resonances. It provides simultaneous order tensor estimation and assignment.
Our approach compares independent order tensor estimates to determine when the
correct order tensor has been found. We demonstrate the algorithm's viability
using simulated data from the protein domain 1A1Z.


  Using a functional renormalization group approach we show that at low
temperatures and in a certain range of magnetic fields the longitudinal dynamic
structure factor of quantum Heisenberg ferromagnets in dimensions $D\leq 2$
exhibits a well-defined quasi-particle peak with linear dispersion that we
identify as zero-magnon sound. In $D>2$ the larger phase space available for
the decay into transverse spin waves leads only to a broad hump centered at
zero frequency whose width scales linearly in momentum.


  Consider a message processing system whose objective is to produce the most
current information as measured by the quantity known as "age of information".
We have argued in previous papers that if we are allowed to design the message
processing policy ad libitum, we should keep a small buffer and operate
according to a LIFO policy. In this small note we provide an analysis for the
AoI of the P_m system which uses a buffer of size m, a single server, operating
without service preemption and in a LIFO manner for stored messages. Analytical
expressions for the mean (or even distribution) of the AoI in steady-state are
possible but with the aid computer algebra. We explain the the analysis for
m=3.


  Facial analysis technologies have recently measured up to the capabilities of
expert clinicians in syndrome identification. To date, these technologies could
only identify phenotypes of a few diseases, limiting their role in clinical
settings where hundreds of diagnoses must be considered.
  We developed a facial analysis framework, DeepGestalt, using computer vision
and deep learning algorithms, that quantifies similarities to hundreds of
genetic syndromes based on unconstrained 2D images. DeepGestalt is currently
trained with over 26,000 patient cases from a rapidly growing
phenotype-genotype database, consisting of tens of thousands of validated
clinical cases, curated through a community-driven platform. DeepGestalt
currently achieves 91% top-10-accuracy in identifying over 215 different
genetic syndromes and has outperformed clinical experts in three separate
experiments.
  We suggest that this form of artificial intelligence is ready to support
medical genetics in clinical and laboratory practices and will play a key role
in the future of precision medicine.


  We present here a technique for developing a high-throughput algorithm to fit
a combination of template pulse shapes while simultaneously subtracting
parameterized background noise. By convolving the psuedoinverse of the
least-squares fit design matrix along a regularly sampled waveform trace, the
time evolution of the fit parameters for each basis function can be determined
in real-time. We approximate these sliding linear fit response functions using
piecewise polynomials, and develop an FPGA-friendly algorithm to be implemented
in high sample-rate data acquisition systems. This is a robust universal filter
that compares well to common filters optimized for energy
calibration/resolution, as well as filters optimized for timing performance,
even when significant noise components are present.


  Experiments on disordered superconducting thin films have revealed a
magnetoresistance peak of several orders of magnitude. Starting from the
disordered negative-U Hubbard model, we employ an ab initio approach that
includes thermal fluctuations to calculate the resistance, and fully reproduces
the experimental phenomenology. Maps of the microscopic current flow and local
potential allow us to pinpoint the source of the magnetoresistance peak -- the
conducting weak links change from normal on the low-field side of the peak to
superconducting on the high-field side. Finally, we formulate a simple
one-dimensional model to demonstrate how small superconducting regions will act
as weak links in such a disordered thin film.


  Halide perovskites have emerged as a promising class of materials for
photovoltaic applications. A challenge in these applications is how to prevent
the crystal structure from degradation to photovoltaically inactive phases,
which requires an understanding of the free energy landscape of these
materials. Here, we uncover the free energy landscape of two prototypical
halide perovskites, CsPbBr$_3$ and MAPbI$_3$ via atomic scale simulations using
umbrella sampling and machine-learned potentials. For CsPbBr$_3$ we find very
small free energy differences and barriers close to the transition temperatures
for both the tetragonal-to-cubic and the orthorhombic-to-tetragonal transition.
For MAPbI$_3$, however, the situation is more intricate. In particular the
orthorhombic-to-tetragonal transition exhibits a large free energy barrier and
there are several competing tetragonal phases. Using large-scale molecular
dynamics simulations we explore the character of these transition and observe
latent heat and a discrete change in structural parameters for the
tetragonal-to-cubic phase transition in both CsPbBr$_3$ and MAPbI$_3$
indicating first-order transitions. We find that in MAPbI$_3$ the orthorhombic
phase has an extended metastability range and furthermore identify a second
metastable tetragonal phase. Finally, we compile a phase diagram for MAPbI$_3$
that includes potential metastable phases.


  We use the theory of differential tensor algebras and their modules to
produce explicit representations of extended Dynkin quivers.


  For any prime $p>3$ and $j\in\mathbb{N}$ we construct examples of
non-$FSZ_{p^j}$ groups of order $p^{p^j+2j-1}$. In the special case of $j=1$
this yields groups of order $p^{p+1}$, which is the minimum possible order for
a non-$FSZ$ $p$-group.


  In this paper, we discussed an infinitely distributed delayed viral infection
model with nonlinear immune response and general incidence rate. We proved the
existence and uniqueness of the equilibria. By using the Lyapunov functional
and LaSalle invariance principle, we obtained the conditions of global
stabilities of the infection-free equilibrium, the immune-exhausted equilibrium
and the endemic equilibrium. Numerical simulations are given to verify the
analytical results.


  The detection method of gravitational waves (GW) using electromagnetic (EM)
cavities has garnered significant attention in recent years. This paper
thoroughly examines the analysis for the perturbation of the EM field and
raises some issues in the existing literature. Our work demonstrates that the
rigid condition imposed on the material, as provided in the literature, is
inappropriate due to its reliance on a gauge-dependent quantity that cannot be
controlled experimentally. Instead, we incorporate elasticity into the material
and revise the governing equations for the electric field induced by GWs,
expressing them solely in terms of gauge-invariant quantities. Applying these
equations to a cylindrical cavity with the TM010 mode, we present the GW
antenna pattern for the detector.


  The CYGNO project has the goal to use a gaseous TPC with optical readout to
detect dark matter and solar neutrinos with low energy threshold and
directionality. The CYGNO demonstrator will consist of 1 m 3 volume filled with
He:CF 4 gas mixture at atmospheric pressure. Optical readout with high
granularity CMOS sensors, combined with fast light detectors, will provide a
detailed reconstruction of the event topology. This will allow to discriminate
the nuclear recoil signal from the background, mainly represented by low energy
electron recoils induced by radioactivity. Thanks to the high reconstruction
efficiency, CYGNO will be sensitive to low mass dark matter, and will have the
potential to overcome the neutrino floor, that ultimately limits
non-directional dark matter searches.


  Traffic congestion is one of the major challenges faced by the transportation
industry. While this problem carries a high economical and environmental cost,
the need for an efficient design of optimal paths for passengers in multilayer
network infrastructures is imperative. We consider an approach based on optimal
transport theory to route passengers preferably along layers that are more
carbon efficient than the road, e.g. rails. By analyzing the impact of this
choice on performance, we find that this approach reduces carbon emissions
considerably, compared to shortest-path minimization. Similarly, we find that
this approach distributes traffic more homogeneously thus alleviating the risk
of traffic congestions. Our results shed light on the impact of distributing
traffic flexibly across layers guided by optimal transport theory.


  Neuroimage analysis usually involves learning thousands or even millions of
variables using only a limited number of samples. In this regard, sparse
models, e.g. the lasso, are applied to select the optimal features and achieve
high diagnosis accuracy. The lasso, however, usually results in independent
unstable features. Stability, a manifest of reproducibility of statistical
results subject to reasonable perturbations to data and the model, is an
important focus in statistics, especially in the analysis of high dimensional
data. In this paper, we explore a nonnegative generalized fused lasso model for
stable feature selection in the diagnosis of Alzheimer's disease. In addition
to sparsity, our model incorporates two important pathological priors: the
spatial cohesion of lesion voxels and the positive correlation between the
features and the disease labels. To optimize the model, we propose an efficient
algorithm by proving a novel link between total variation and fast network flow
algorithms via conic duality. Experiments show that the proposed nonnegative
model performs much better in exploring the intrinsic structure of data via
selecting stable features compared with other state-of-the-arts.


  As programmers turn to software-defined hardware (SDH) to maintain a high
level of productivity while programming hardware to run complex algorithms,
heavy-lifting must be done by the compiler to automatically partition on-chip
arrays. In this paper, we introduce an automatic memory partitioning system
that can quickly compute more efficient partitioning schemes than prior
systems. Our system employs a variety of resource-saving optimizations and an
ML cost model to select the best partitioning scheme from an array of
candidates. We compared our system against various state-of-the-art SDH
compilers and FPGAs on a variety of benchmarks and found that our system
generates solutions that, on average, consume 40.3% fewer logic resources,
78.3% fewer FFs, 54.9% fewer Block RAMs (BRAMs), and 100% fewer DSPs.


  Reinforcement learning is an emerging approach to control dynamical systems
for which classical approaches are difficult to apply. However, trained agents
may not generalize against the variations of system parameters. This paper
presents the concept of dual-scale homogeneity, an important property in
understating the scaling behavior of nonlinear systems. Furthermore, it also
presents an effective yet simple approach to designing a parameter-dependent
control law that homogenizes a nonlinear system. The presented approach is
applied to two systems, demonstrating its ability to provide a consistent
performance irrespective of parameters variations. To demonstrate the
practicality of the proposed approach, the control policy is generated by a
deep deterministic policy gradient to control the load position of a quadrotor
with a slung load. The proposed synergy between the homogeneity transformations
and reinforcement learning yields superior performance compared to other recent
learning-based control techniques. It achieves a success rate of 96% in
bringing the load to its designated target with a 3D RMSE of 0.0253 m. The
video that shows the experimental results along with a summary of the paper is
available at this link.


  One of the most challenging problems in evolutionary computation is to select
from its family of diverse solvers one that performs well on a given problem.
This algorithm selection problem is complicated by the fact that different
phases of the optimization process require different search behavior. While
this can partly be controlled by the algorithm itself, there exist large
differences between algorithm performance. It can therefore be beneficial to
swap the configuration or even the entire algorithm during the run. Long deemed
impractical, recent advances in Machine Learning and in exploratory landscape
analysis give hope that this dynamic algorithm configuration~(dynAC) can
eventually be solved by automatically trained configuration schedules. With
this work we aim at promoting research on dynAC, by introducing a simpler
variant that focuses only on switching between different algorithms, not
configurations. Using the rich data from the Black Box Optimization
Benchmark~(BBOB) platform, we show that even single-switch dynamic Algorithm
selection (dynAS) can potentially result in significant performance gains. We
also discuss key challenges in dynAS, and argue that the BBOB-framework can
become a useful tool in overcoming these.


  We use replicator dynamics to study an iterated prisoners' dilemma game with
memory. In this study, we investigate the characteristics of all 32 possible
strategies with a single-step memory by observing the results when each
strategy encounters another one. Based on these results, we define similarity
measures between the 32 strategies and perform a network analysis of the
relationship between the strategies by constructing a strategies network.
Interestingly, we find that a win-lose circulation, like rock-paper-scissors,
exists between strategies and that the circulation results from one unusual
strategy.


  We present a mitigation strategy to reduce the impact of non-linear galaxy
bias on the joint `$3 \times 2 $pt' cosmological analysis of weak lensing and
galaxy surveys. The $\Psi$-statistics that we adopt are based on Complete
Orthogonal Sets of E/B Integrals (COSEBIs). As such they are designed to
minimise the contributions to the observable from the smallest physical scales
where models are highly uncertain. We demonstrate that $\Psi$-statistics carry
the same constraining power as the standard two-point galaxy clustering and
galaxy-galaxy lensing statistics, but are significantly less sensitive to
scale-dependent galaxy bias. Using two galaxy bias models, motivated by
halo-model fits to data and simulations, we quantify the error in a standard $3
\times 2$pt analysis where constant galaxy bias is assumed. Even when adopting
conservative angular scale cuts, that degrade the overall cosmological
parameter constraints, we find of order $1 \sigma$ biases for Stage III surveys
on the cosmological parameter $S_8 = \sigma_8(\Omega_{\rm m}/0.3)^{\alpha}$.
This arises from a leakage of the smallest physical scales to all angular
scales in the standard two-point correlation functions. In contrast, when
analysing $\Psi$-statistics under the same approximation of constant galaxy
bias, we show that the bias on the recovered value for $S_8$ can be decreased
by a factor of $\sim 2$, with less conservative scale cuts. Given the
challenges in determining accurate galaxy bias models in the highly non-linear
regime, we argue that $3 \times 2$pt analyses should move towards new
statistics that are less sensitive to the smallest physical scales.


  In finite-size scaling analyses of Monte Carlo simulations of second-order
phase transitions one often needs an extended temperature range around the
critical point. By combining the parallel tempering algorithm with cluster
updates and an adaptive routine to find the temperature window of interest, we
introduce a flexible and powerful method for systematic investigations of
critical phenomena. As a result, we gain one to two orders of magnitude in the
performance for 2D and 3D Ising models in comparison with the recently proposed
Wang-Landau recursion for cluster algorithms based on the multibondic
algorithm, which is already a great improvement over the standard
multicanonical variant.


  Using light spectra is an essential element in many applications, for
example, in material classification. Often this information is acquired by
using a hyperspectral camera. Unfortunately, these cameras have some major
disadvantages like not being able to record videos. Therefore, multispectral
cameras with wide-band filters are used, which are much cheaper and are often
able to capture videos. However, using multispectral cameras requires an
additional reconstruction step to yield spectral information. Usually, this
reconstruction step has to be done in the presence of imaging noise, which
degrades the reconstructed spectra severely. Typically, same or similar pixels
are found across the image with the advantage of having independent noise. In
contrast to state-of-the-art spectral reconstruction methods which only exploit
neighboring pixels by block-based processing, this paper introduces non-local
filtering in spectral reconstruction. First, a block-matching procedure finds
similar non-local multispectral blocks. Thereafter, the hyperspectral pixels
are reconstructed by filtering the matched multispectral pixels collaboratively
using a reconstruction Wiener filter. The proposed novel procedure even works
under very strong noise. The method is able to lower the spectral angle up to
18% and increase the peak signal-to-noise-ratio up to 1.1dB in noisy scenarios
compared to state-of-the-art methods. Moreover, the visual results are much
more appealing.


  We present a quantum field theoretic description on the t$-$J model on a
square lattice with dilute holes (i.e. near half-filling), based on the compact
mutual Chern-Simons gauge theory. We show that, due to the presence of
non-perturbative monopole plasma configuration from the antiferromagnetic
background, holons (carrying electric charge) are linearly confined and
strongly localized even without extrinsic disorder taken into account.
Accordingly, the translation symmetry is spontaneously broken at ground state.
Such an exotic localization is distinct from Anderson localization and
essentially rooted in intrinsic Mott physics of the t$-$J model. Finally, a
finite-temperature phase diagram is proposed. The metal-insulator transition
observed in in-plane resistivity measurement is identified to a
confinement-deconfinement transition from the perspective of gauge theory. The
transition is characterized by the order parameter "Polyakov-line".


  Nowadays, deep neural networks (DNNs) have become the main instrument for
machine learning tasks within a wide range of domains, including vision, NLP,
and speech. Meanwhile, in an important case of heterogenous tabular data, the
advantage of DNNs over shallow counterparts remains questionable. In
particular, there is no sufficient evidence that deep learning machinery allows
constructing methods that outperform gradient boosting decision trees (GBDT),
which are often the top choice for tabular problems. In this paper, we
introduce Neural Oblivious Decision Ensembles (NODE), a new deep learning
architecture, designed to work with any tabular data. In a nutshell, the
proposed NODE architecture generalizes ensembles of oblivious decision trees,
but benefits from both end-to-end gradient-based optimization and the power of
multi-layer hierarchical representation learning. With an extensive
experimental comparison to the leading GBDT packages on a large number of
tabular datasets, we demonstrate the advantage of the proposed NODE
architecture, which outperforms the competitors on most of the tasks. We
open-source the PyTorch implementation of NODE and believe that it will become
a universal framework for machine learning on tabular data.


  Chaotic orbits of mushroom billiards display intermittent behaviors. We
investigate statistical properties of this system by constructing an infinite
partition on the chaotic part of a Poincar\'e surface which illustrates details
of chaotic dynamics. Each piece of the infinite partition has an unique escape
time from the half disk region, and from this result it is shown that, for
fixed values of the system parameters, the escape time distribution obeys power
law $1/t_{\rm esc}^3$.


  We consider the twin problems of estimating the effective rank and the
Schatten norms $\|{\bf A}\|_{s}$ of a rectangular $p\times q$ matrix ${\bf A}$
from noisy observations. When $s$ is an even integer, we introduce a
polynomial-time estimator of $\|{\bf A}\|_s$ that achieves the minimax rate
$(pq)^{1/4}$. Interestingly, this optimal rate does not depend on the
underlying rank of the matrix. When $s$ is not an even integer, the optimal
rate is much slower. A simple thresholding estimator of the singular values
achieves the rate $(q\wedge p)(pq)^{1/4}$, which turns out to be optimal up to
a logarithmic multiplicative term. The tight minimax rate is achieved by a more
involved polynomial approximation method. This allows us to build estimators
for a class of effective rank indices. As a byproduct, we also characterize the
minimax rate for estimating the sequence of singular values of a matrix.


  Calder\'on-Zygmund decompositions of functions have been used to prove
weak-type (1,1) boundedness of singular integral operators. In many examples,
the decomposition is done with respect to a family of balls that corresponds to
some family of dilations. We study singular integral operators $T$ that require
more particular families of balls, providing new spaces of homogeneous type.
Rotations play a decisive role in the construction of these balls. Boundedness
of $T$ can then be shown via Calder\'on-Zygmund decompositions with respect to
this space of homogeneous type. We prove weak-type (1,1) and $\LP^p$ estimates
for operators $T$ acting on $\LP^p(G)$, where $G$ is a homogeneous Lie group.
Our results apply to the setting where the underlying group is the Heisenberg
group and the rotations are symplectic automorphisms. They also apply to
operators that arise from some hydrodynamical problem involving rotations.


  This paper shows how the application of stochastic geometry to the analysis
of wireless networks is greatly facilitated by (i) a clear separation of time
scales, (ii) the abstraction of small-scale effects via ergodicity, and (iii)
an interference model that reflects the receiver's lack of knowledge of how
each individual interference term is faded. These procedures render the
analysis both more manageable and more precise, as well as more amenable to the
incorporation of subsequent features. In particular, the paper presents
analytical characterizations of the ergodic spectral efficiency of cellular
networks with single-user multiple-input multiple-output (MIMO) and
sectorization. These characterizations, in the form of easy-to-evaluate
expressions, encompass the coverage, the distribution of spectral efficiency
over the network locations, and the average thereof.


  The gravitationally induced entanglement is a type of quantum entanglement
that can be generated between two mesoscopic particles using their Newtonian
gravitational interaction. It has attracted a great deal of attention as a new
platform for studying quantum aspects of gravity. The present paper analyzes
the gravitationally induced entanglement as a pure interference effect and
shows that the entanglement is induced solely by a sign change associated with
the destructive quantum interference. It is also shown that when the
entanglement is non-maximal, the preparation for destructive interference for
one of the particles can recover a maximum visibility interference pattern for
the other particle. Therefore, the non-maximally entangled state can be
extremely effective for experimental testing since it can help in reducing
requirements (on masses of the particles and their interaction duration,
separation distances and sources) and preserve the information about
entanglement at the same time. As a result, the improvement in the
signal-to-noise ratio is demonstrated and a parameter that determines minimal
requirements for experimental testing is defined.


  State-of-the-art offline Optical Character Recognition (OCR) frameworks
perform poorly on semi-structured handwritten domain-specific documents due to
their inability to localize and label form fields with domain-specific
semantics. Existing techniques for semi-structured document analysis have
primarily used datasets comprising invoices, purchase orders, receipts, and
identity-card documents for benchmarking. In this work, we build the first
semi-structured document analysis dataset in the legal domain by collecting a
large number of First Information Report (FIR) documents from several police
stations in India. This dataset, which we call the FIR dataset, is more
challenging than most existing document analysis datasets, since it combines a
wide variety of handwritten text with printed text. We also propose an
end-to-end framework for offline processing of handwritten semi-structured
documents, and benchmark it on our novel FIR dataset. Our framework used
Encoder-Decoder architecture for localizing and labelling the form fields and
for recognizing the handwritten content. The encoder consists of Faster-RCNN
and Vision Transformers. Further the Transformer-based decoder architecture is
trained with a domain-specific tokenizer. We also propose a post-correction
method to handle recognition errors pertaining to the domain-specific terms.
Our proposed framework achieves state-of-the-art results on the FIR dataset
outperforming several existing models