  Let $R$ be a commutative Noetherian ring of prime characteristic $p$. In this
paper we give a short proof using filter regular sequences that the set of
associated prime ideals of $H^t_I(R)$ is finite for any ideal $I$ and for any
$t \ge 0$ when $R$ has finite $F$-representation type or finite singular locus.
This extends a previous result by Takagi-Takahashi and gives affirmative
answers for a problem of Huneke in many new classes of rings in positive
characteristic. We also give a criterion about the singularities of $R$ (in any
characteristic) to guarantee that the set of associated primes of $H^2_I(R)$ is
always finite.


  The jet charge is an old observable that has proven uniquely useful for
discrimination of jets initiated by different flavors of light quarks, for
example. In this Letter, we propose an approach to understanding the jet charge
by establishing simple, robust assumptions that hold to good approximation
non-perturbatively, such as isospin conservation and large particle
multiplicity in the jets, forgoing any attempt at a perturbative analysis. From
these assumptions, the jet charge distribution with fixed particle multiplicity
takes the form of a Gaussian by the central limit theorem and whose mean and
variance are related to fractional-power moments of single particle energy
distributions. These results make several concrete predictions for the scaling
of the jet charge with the multiplicity, explaining many of the results already
in the literature, and new results we validate in Monte Carlo simulation.


  We measure the angular clustering of 33 415 extremely red objects (EROs) in
the Elais-N1 field covering 5.33 deg$^{2}$, which cover the redshift range
$z=0.8$ to $2$. This sample was made by merging the UKIDSS Deep eXtragalactic
Survey (DXS) with the optical Subaru and Pan-STARRS PS1 datasets. We confirm
the existence of a clear break in the angular correlation function at $\sim
0.02^{\circ}$ corresponding to $1 h^{-1}$ Mpc at $z\sim1$. We find that redder
or brighter EROs are more clustered than bluer or fainter ones. Halo Occupation
Distribution (HOD) model fits imply that the average mass of dark matter haloes
which host EROs is over $10^{13} h^{-1} M_{\odot}$ and that EROs have a bias
ranging from 2.7 to 3.5. Compared to EROs at $z\sim1.1$, at $z\sim1.5$ EROs
have a higher bias and fewer are expected to be satellite galaxies.
Furthermore, EROs reside in similar dark matter haloes to those that host
$10^{11.0} M_{\odot}<M_{*}<10^{11.5} M_{\odot}$ galaxies. We compare our new
measurement and HOD fits with the predictions of the GALFORM semi-analytical
galaxy formation model. Overall, the clustering predicted by GALFORM gives an
encouraging match to our results. However, compared to our deductions from the
measurements, GALFORM puts EROs into lower mass haloes and predicts that a
larger fraction of EROs are satellite galaxies. This suggests that the
treatment of gas cooling may need to be revised in the model. Our analysis
illustrates the potential of clustering analyses to provide observational
constraints on theoretical models of galaxy formation.


  A system with a topological insulator slab sandwiched by two one-dimensional
photonic crystals as a defect is investigated. A giant topological
magnetoelectric effect is proposed which is characterized by two resonant peaks
with half-unit transmissions and rich polarization behaviors in the photonic
band gap. We also predict a giant optical Hall effect in our system, in which
the transverse shift of the transmitted light could be thousand times larger
than the wavelength. These effects are purely from the $\Theta$-domain walls at
the topological insulator interfaces and could be observed easily. These
effects can also be used as the sensitive detection of basic physical
constants.


  We study the structure of gauge and gravitational anomalies in 2d N=(0,2)
theories obtained by compactification of F-theory on elliptically fibered
Calabi-Yau 5-folds. Abelian gauge anomalies, induced at 1-loop in perturbation
theory, are cancelled by a generalized Green-Schwarz mechanism operating at the
level of chiral scalar fields in the 2d supergravity theory. We derive closed
expressions for the gravitational and the non-abelian and abelian gauge
anomalies including the Green-Schwarz counterterms. These expressions involve
topological invariants of the underlying elliptic fibration and the gauge
background thereon. Cancellation of anomalies in the effective theory predicts
intricate topological identities which must hold on every elliptically fibered
Calabi-Yau 5-fold. We verify these relations in a non-trivial example, but
their proof from a purely mathematical perspective remains as an interesting
open problem. Some of the identities we find on elliptic 5-folds are related in
an intriguing way to previously studied topological identities governing the
structure of anomalies in 6d N=(1,0) and 4d N=1 theories obtained from
F-theory.


  We develop and commercialize autonomous machines, such as logistic robots and
self-driving cars, around the globe. A critical challenge to our -- and any --
autonomous machine is accurate and efficient localization under resource
constraints, which has fueled specialized localization accelerators recently.
Prior acceleration efforts are point solutions in that they each specialize for
a specific localization algorithm. In real-world commercial deployments,
however, autonomous machines routinely operate under different environments and
no single localization algorithm fits all the environments. Simply stacking
together point solutions not only leads to cost and power budget overrun, but
also results in an overly complicated software stack.
  This paper demonstrates our new software-hardware co-designed framework for
autonomous machine localization, which adapts to different operating scenarios
by fusing fundamental algorithmic primitives. Through characterizing the
software framework, we identify ideal acceleration candidates that contribute
significantly to the end-to-end latency and/or latency variation. We show how
to co-design a hardware accelerator to systematically exploit the parallelisms,
locality, and common building blocks inherent in the localization framework. We
build, deploy, and evaluate an FPGA prototype on our next-generation
self-driving cars. To demonstrate the flexibility of our framework, we also
instantiate another FPGA prototype targeting drones, which represent mobile
autonomous machines. We achieve about 2x speedup and 4x energy reduction
compared to widely-deployed, optimized implementations on general-purpose
platforms.


  We have studied the chemical composition of NGC 1806, a massive,
intermediate-age globular cluster that shows a double main sequence turnoff. We
analyzed a sample of high-resolution spectra (secured with FLAMES at the Very
Large Telescope) for 8 giant stars, members of the cluster, finding an average
iron content of [Fe/H]=--0.60 +- 0.01 dex and no evidence of intrinsic
star-to-star variations in the abundances of light elements (Na, O, Mg, Al).
Also, the (m_(F814W); m_(F336W)-m_(F814W)) color-magnitude diagram obtained by
combining optical and near-UV Hubble Space Telescope photometry exhibits a
narrow red giant branch, thus ruling out intrinsic variations of C and N
abundances in the cluster. These findings demonstrate that NGC 1806 does not
harbor chemically distinct sub-populations, at variance with what was found in
old globular clusters. In turn, this indicates that the double main sequence
turnoff phenomenon cannot be explained in the context of the self-enrichment
processes usually invoked to explain the chemical anomalies observed in old
globulars. Other solutions (i.e., stellar rotation, merging between clusters or
collisions with giant molecular clouds) should be envisaged to explain this
class of globulars.


  We show that for every orthomodular poset P of finite height there can be
defined two operators forming an adjoint pair with respect to an order-like
relation defined on the power set of P. This enables us to introduce the
so-called operator residuated poset corresponding to P from which the original
orthomodular poset P can be recovered. Moreover, this correspondence is almost
one-to-one. We show that this construction of operators can be applied also to
so-called weakly orthomodular and dually weakly orthomodular posets. Examples
of such posets are included.


  The spectral distribution $f(\omega)$ of a stationary time series
$\{Y_t\}_{t\in\mathbb{Z}}$ can be used to investigate whether or not periodic
structures are present in $\{Y_t\}_{t\in\mathbb{Z}}$, but $f(\omega)$ has some
limitations due to its dependence on the autocovariances $\gamma(h)$. For
example, $f(\omega)$ can not distinguish white i.i.d. noise from GARCH-type
models (whose terms are dependent, but uncorrelated), which implies that
$f(\omega)$ can be an inadequate tool when $\{Y_t\}_{t\in\mathbb{Z}}$ contains
asymmetries and nonlinear dependencies.
  Asymmetries between the upper and lower tails of a time series can be
investigated by means of the local Gaussian autocorrelations introduced in
Tj{\o}stheim and Hufthammer (2013), and these local measures of dependence can
be used to construct the local Gaussian spectral density presented in this
paper. A key feature of the new local spectral density is that it coincides
with $f(\omega)$ for Gaussian time series, which implies that it can be used to
detect non-Gaussian traits in the time series under investigation. In
particular, if $f(\omega)$ is flat, then peaks and troughs of the new local
spectral density can indicate nonlinear traits, which potentially might
discover local periodic phenomena that remain undetected in an ordinary
spectral analysis.


  We develop an explicit model for the formation of the stellar halo from
tidally disrupted, accreted dwarf satellites in the cold dark matter (CDM)
framework, focusing on predictions testable with the Sloan Digital Sky Survey
(SDSS) and other wide-field surveys. Subhalo accretion and orbital evolution
are calculated using a semi-analytic approach within the Press-Schechter
formalism. Motivated by our previous work, we assume that low-mass subhalos (v
< 30 km/s) can form significant populations of stars only if they accreted a
substantial fraction of their mass before the epoch of reionization. With this
assumption, the model reproduces the observed velocity function of galactic
satellites in the Local Group, solving the ``dwarf satellite problem'' without
modifying the popular LCDM cosmology. The disrupted satellites yield a stellar
distribution with a total mass and radial density profile consistent with those
observed for the Milky Way stellar halo. Most significantly, the model predicts
the presence of many large-scale, coherent substructures in the outer halo.
These substructures are remnants of individual, tidally disrupted dwarf
satellite galaxies. Substructure is more pronounced at large galactocentric
radii because of the smaller number density of tidal streams and the longer
orbital times. This model provides a natural explanation for the coherent
structures in the outer stellar halo found in the SDSS commissioning data, and
it predicts that many more such structures should be found as the survey covers
more of the sky. The detection (or non-detection) and characterization of such
structures could eventually test variants of the CDM scenario, especially those
that aim to solve the dwarf satellite problem by enhancing satellite
disruption.


  We show an iterative method to solve a Dirichlet problem for a Yamabe-type
equation in small convex domains in $\mathbb{R}^3$ and small balls in
$\mathbb{R}^3$.


  Small-angle, two-particle correlation functions have been measured for 36Ar+
112,124Sn collisions at E/A = 61 MeV. Total momentum gated neutron-proton (np)
and proton-proton (pp) correlations are stronger for the 124Sn-target. Some of
the correlation functions for particle pairs involving deuterons or tritons
(nd, pt, and nt) also show a dependence on the isospin of the emitting source.


  Sentiment Classification is a fundamental task in the field of Natural
Language Processing, and has very important academic and commercial
applications. It aims to automatically predict the degree of sentiment present
in a text that contains opinions and subjectivity at some level, like product
and movie reviews, or tweets. This can be really difficult to accomplish, in
part, because different domains of text contains different words and
expressions. In addition, this difficulty increases when text is written in a
non-English language due to the lack of databases and resources. As a
consequence, several cross-domain and cross-language techniques are often
applied to this task in order to improve the results. In this work we perform a
study on the ability of a classification system trained with a large database
of product reviews to generalize to different Spanish domains. Reviews were
collected from the MercadoLibre website from seven Latin American countries,
allowing the creation of a large and balanced dataset. Results suggest that
generalization across domains is feasible though very challenging when trained
with these product reviews, and can be improved by pre-training and fine-tuning
the classification model.


  Results on timing and spectral properties of the Be/X-ray binary pulsar 3A
0726-260 (4U 0728-25) are presented. The binary was observed on 2016 May 6-7
with the Large Area X-ray Proportional Counter (LAXPC) and Soft X-ray Telescope
(SXT) instruments onboard the AstroSat satellite. During this observation the
source was in non-flaring persistent state at a flux level of $\sim$ 8.6 $\pm$
0.3 $\times$10$^{-11}$ ergs cm$^{-2}$ sec$^{-1}$ in 0.4-20 keV. Strong X-ray
pulsations with a period of 103.144$\pm$0.001 seconds are detected in 0.3-7 keV
with the SXT and in 3-40 keV with the LAXPC. The pulse profile is energy
dependent, and there is an indication that the pulse shape changes from a broad
single pulse to a double pulse at higher energy. At energies above 20 keV, we
report the first time detection of pulsation period 103.145$\pm$0.001 seconds
and the double peaked pulse profile from the source. The energy spectrum of the
source is derived from the combined analysis of the SXT and LAXPC spectral data
in 0.4-20 keV. The best spectral fit is obtained by a power law model with a
photon index (1.7$\pm$0.03) with high energy spectral cut-off at 12.9 $\pm$ 0.7
keV. A broad Iron line at $\sim$ 6.3 keV is detected in the energy spectrum. We
briefly discuss the implications of these results.


  The discrete picture of geometry arising from the loop representation of
quantum gravity can be extended by a quantum deformation. The operators for
area and volume defined in the q-deformation of the theory are partly
diagonalized. The eigenstates are expressed in terms of q-deformed spin
networks. The q-deformation breaks some of the degeneracy of the volume
operator so that trivalent spin-networks have non-zero volume. These
computations are facilitated by use of a technique based on the recoupling
theory of SU(2)_q, which simplifies the construction of these and other
operators through diffeomorphism invariant regularization procedures.


  The linearized Boltzmann equation is considered to describe small spatial
perturbations of the homogeneous cooling state. The corresponding macroscopic
balance equations for the density, temperature, and flow velocity are derived
from it as the basis for a hydrodynamic description. Hydrodynamics is defined
in terms of the spectrum of the generator for the dynamics of the linearized
Boltzmann equation. The hydrodynamic eigenfunctions and eigenvalues are
calculated in the long wavelength limit. The results allow identification of
the hydrodynamic part of the solution to the linearized Boltzmann equation.
This contribution is used to calculate the fluxes in the macroscopic balance
equations, leading to the Navier-Stokes equations and associated transport
coefficients. The results agree with those obtained earlier by the
Chapman-Enskog method. The implications of this analysis for application of
methods of linear response to granular fluids and derivation of Green-Kubo
expressions for transport coefficients are discussed.


  An orthogonal Haar scattering transform is a deep network, computed with a
hierarchy of additions, subtractions and absolute values, over pairs of
coefficients. It provides a simple mathematical model for unsupervised deep
network learning. It implements non-linear contractions, which are optimized
for classification, with an unsupervised pair matching algorithm, of polynomial
complexity. A structured Haar scattering over graph data computes permutation
invariant representations of groups of connected points in the graph. If the
graph connectivity is unknown, unsupervised Haar pair learning can provide a
consistent estimation of connected dyadic groups of points. Classification
results are given on image data bases, defined on regular grids or graphs, with
a connectivity which may be known or unknown.


  We construct R-invariant grand unification models with composite Higgs
multiplets. Higgs doublets are massless due to the R symmetry, which is not
spontaneously broken at the unification scale, while Higgs triplets get large
masses from a dynamically generated superpotential, which is allowed by an R
anomaly.


  It has been conjectured, on the basis of the gauge-gravity duality, that the
ratio of the shear viscosity to the entropy density should be universally
bounded from below by 1/ 4 pi in units of the Planck constant divided by the
Boltzmann constant. Here, we prove the bound for any ghost-free extension of
Einstein gravity and the field-theory dual thereof. Our proof is based on the
fact that, for such an extension, any gravitational coupling can only increase
from its Einstein value. Therefore, since the shear viscosity is a particular
gravitational coupling, it is minimal for Einstein gravity. Meanwhile, we show
that the entropy density can always be calibrated to its Einstein value. Our
general principles are demonstrated for a pair of specific models, one with
ghosts and one without.


  The COVID-19 pandemic has influenced the lives of people globally. In the
past year many researchers have proposed different models and approaches to
explore in what ways the spread of the disease could be mitigated. One of the
models that have been used a great deal is the
Susceptible-Exposed-Infectious-Recovered (SEIR) model. Some researchers have
modified the traditional SEIR model, and proposed new versions of it. However,
to the best of our knowledge, the state-of-the-art papers have not considered
the effect of different vaccine types, meaning single shot and double shot
vaccines, in their SEIR model. In this paper, we propose a modified version of
the SEIR model which takes into account the effect of different vaccine types.
We compare how different policies for the administration of the vaccine can
influence the rate at which people are exposed to the disease, get infected,
recover, and pass away. Our results suggest that taking the double shot vaccine
such as Pfizer-BioNTech and Moderna does a better job at mitigating the spread
and fatality rate of the disease compared to the single shot vaccine, due to
its higher efficacy.


  Plato provides fast approximate analytics on time series, by precomputing and
storing compressed time series. Plato's key novelty is the delivery of tight
deterministic error guarantees for time series analytics. Plato evaluates any
time series expression composed by the linear algebra operators over vectors,
along with arithmetic operators. This large scope of possible expressions
includes common use cases such as correlation and cross-correlation
expressions. Each time series is segmented either by fixed-length segmentation
or by (a usually more effective) variable-length segmentation. Each segment is
compressed by an estimation/compression function that approximates the actual
values and is coming from a user-chosen function family, as taught by many
prior works. The novelty is that Plato associates to each segment 1 to 3
(depending on the case) precomputed error measures and, using them, Plato
computes tight deterministic error guarantees for analytics over the
compressions. Importantly, some compression families lead to much better
deterministic error guarantees. This work identifies two broad estimation
function family groups (Vector Space (VS) and Linear Scalable Family (LSF)),
which lead to theoretically and practically high-quality guarantees, even for
expressions (eg correlation) that combine multiple time series that have been
independently compressed and may, thus, use misaligned segmentations. The
theoretical aspect of "high quality" is crisply captured by the Amplitude
Independence (AI) property: An AI guarantee does not depend on the amplitude of
the involved time series, even when we combine multiple time series. The
experiments on four real-life datasets showed that when the novel AI guarantees
were applicable, the approximate query results were certified to be very close
(typically 1%) to the true results.


  We propose to use graphene-based Josephson junctions (gJjs) to detect single
photons in a wide electromagnetic spectrum from visible to radio frequencies.
Our approach takes advantage of the exceptionally low electronic heat capacity
of monolayer graphene and its constricted thermal conductance to its phonon
degrees of freedom. Such a system could provide high sensitivity photon
detection required for research areas including quantum information processing
and radio-astronomy. As an example, we present our device concepts for gJj
single photon detectors in both the microwave and infrared regimes. The dark
count rate and intrinsic quantum efficiency are computed based on parameters
from a measured gJj, demonstrating feasibility within existing technologies.


  Slime mould Physarum polycephalum is a single cell visible by unaided eye.
Let the slime mould span two electrodes with a single protoplasmic tube: if the
tube is heated to approximately 40{\deg}C, the electrical resistance of the
protoplasmic tube increases from 3 M{\Omega} to approximatively 10'000
M{\Omega}. The organism's resistance is not proportional nor correlated to the
temperature of its environment. Slime mould can therefore not be considered as
a thermistor but rather as a thermic switch. We employ the P. polycephalum
thermic switch to prototype hybrid electrical analog summator, NAND gates, and
cascade the gates into Flip-Flop latch. Computing operations performed on this
bio-hybrid computing circuitry feature high repeatability, reproducibility and
comparably low propagation delays


  The nonlocal Darboux transformation for the stationary axially symmetric
Schr\"odinger and Helmholtz equations is considered. Formulae for the nonlocal
Darboux transformation are obtained and its relation to the generalized Moutard
transformation is established. New examples of two - dimensional potencials and
exact solutions for the stationary axially symmetric Schr\"odinger and
Helmholtz equations are obtained as an application of the nonlocal Darboux
transformation.


  In this paper, we study a mixed discontinuous Galerkin (MDG) method to solve
linear elasticity problem with arbitrary order discontinuous finite element
spaces in $d$-dimension ($d=2,3$). This method uses polynomials of degree $k+1$
for the stress and of degree $k$ for the displacement ($k\geq 0$). The mixed DG
scheme is proved to be well-posed under proper norms. Specifically, we prove
that, for any $k \geq 0$, the $H({\rm div})$-like error estimate for the stress
and $L^2$ error estimate for the displacement are optimal. We further establish
the optimal $L^2$ error estimate for the stress provided that the
$\mathcal{P}_{k+2}-\mathcal{P}_{k+1}^{-1}$ Stokes pair is stable and $k \geq
d$. We also provide numerical results of MDG showing that the orders of
convergence are actually sharp.


  I review recent developments in theoretical understandings of J/psi
productions in various processes at Tevatron, B decay and J/psi photoproduction
including the color-octet mechanism.


  It is well known that a $2$-dimensional cyclic quotient singularity
$\overline{W}$ has the same singularity category as a finite dimensional
associative algebra $\overline{R}$ introduced by Kalck and Karmazyn. We study
the deformations of the algebra $\overline{R}$ induced by the deformations of
the surface $\overline{W}$ to a smooth surface. We show that they are
Morita--equivalent to path algebras $\hat{R}$ of acyclic quivers for general
smoothings within each irreducible component of the versal deformation space of
$\overline{W}$ (as described by Koll\'ar and Shepherd-Barron). Furthermore,
$\hat{R}$ is semi-simple if and only if the smoothing is
$\mathbb{Q}$-Gorenstein (one direction is due to Kawamata). We provide many
applications. For example, we describe strong exceptional collections of length
$10$ on all Dolgachev surfaces and classify admissible embeddings of derived
categories of quivers into derived categories of rational surfaces.


  Ridgeless regression has garnered attention among researchers, particularly
in light of the ``Benign Overfitting'' phenomenon, where models interpolating
noisy samples demonstrate robust generalization. However, kernel ridgeless
regression does not always perform well due to the lack of flexibility. This
paper enhances kernel ridgeless regression with Locally-Adaptive-Bandwidths
(LAB) RBF kernels, incorporating kernel learning techniques to improve
performance in both experiments and theory. For the first time, we demonstrate
that functions learned from LAB RBF kernels belong to an integral space of
Reproducible Kernel Hilbert Spaces (RKHSs). Despite the absence of explicit
regularization in the proposed model, its optimization is equivalent to solving
an $\ell_0$-regularized problem in the integral space of RKHSs, elucidating the
origin of its generalization ability. Taking an approximation analysis
viewpoint, we introduce an $l_q$-norm analysis technique (with $0<q<1$) to
derive the learning rate for the proposed model under mild conditions. This
result deepens our theoretical understanding, explaining that our algorithm's
robust approximation ability arises from the large capacity of the integral
space of RKHSs, while its generalization ability is ensured by sparsity,
controlled by the number of support vectors. Experimental results on both
synthetic and real datasets validate our theoretical conclusions.


  We consider the problem of controlling a possibly unknown linear dynamical
system with adversarial perturbations, adversarially chosen convex loss
functions, and partially observed states, known as non-stochastic control. We
introduce a controller parametrization based on the denoised observations, and
prove that applying online gradient descent to this parametrization yields a
new controller which attains sublinear regret vs. a large class of closed-loop
policies. In the fully-adversarial setting, our controller attains an optimal
regret bound of $\sqrt{T}$-when the system is known, and, when combined with an
initial stage of least-squares estimation, $T^{2/3}$ when the system is
unknown; both yield the first sublinear regret for the partially observed
setting.
  Our bounds are the first in the non-stochastic control setting that compete
with \emph{all} stabilizing linear dynamical controllers, not just state
feedback. Moreover, in the presence of semi-adversarial noise containing both
stochastic and adversarial components, our controller attains the optimal
regret bounds of $\mathrm{poly}(\log T)$ when the system is known, and
$\sqrt{T}$ when unknown. To our knowledge, this gives the first end-to-end
$\sqrt{T}$ regret for online Linear Quadratic Gaussian controller, and applies
in a more general setting with adversarial losses and semi-adversarial noise.


  A wide class of boundary problems in quantum mechanics is discussed by using
path integrals. This includes motion in half-spaces, radial boxes, rings, and
moving boundaries. As a preparation the formalism for the incorporation of
$\delta$-function perturbations is outlined, which includes the discussion of
multiple $\delta$-function perturbations, $\delta$-function perturbations along
perpendicular lines and planes, and moving $\delta$-function perturbations. The
limiting process, where the strength of the $\delta$-function perturbations
gets infinite repulsive, has the effect of producing impenetrable walls at the
locations of the $\delta$-function perturbations, i.e.\ a consistent
description for boundary problems with Dirichlet boundary-condition emerges.
Several examples illustrate the formalism.


  In X-ray CT scan with metallic objects, it is known that direct application
of the filtered back-projection (FBP) formula leads to streaking artifacts in
the reconstruction. These are characterized mathematically in terms of wave
front sets in [13]. In this work, we give a quantitative microlocal analysis of
such artifacts. We consider metal regions with strictly convex smooth
boundaries and show that the streaking artifacts are conormal distributions to
straight lines tangential to at least two boundary curves. For metal regions
with piecewise smooth boundaries, we analyze the streaking artifacts especially
due to the corner points. Finally, we study the reduction of the artifacts
using appropriate filters.


  Empirical Mode Decomposition is an adaptive and local tool that extracts
underlying analytical components of a non-linear and non-stationary process, in
turn, is the basis of Hilbert Huang transform, however, there are problems such
as interfering modes or ensuring the orthogonality of decomposition. Three
variants of the algorithm are evaluated, with different experimental parameters
and on a set of 10 time series obtained from surface electromyography.
Experimental results show that obtaining low error in reconstruction with the
analytical signals obtained from a process is not a valid characteristic to
ensure that the purpose of decomposition has been fulfilled (physical
significance and no interference between modes), in addition, freedom must be
generated in the iterative processes of decomposition so that it has
consistency and does not generate biased information. This project was
developed within the framework of the research group DIGITI of the Universidad
Distrital Francisco Jos\'e de Caldas.


  We make some considerations and remarks on D=11 supergravity and its integral
form. We start from the geometrical formulation of supergravity and by means of
the integral form technique we provide a superspace action that reproduces (at
the quadratic level) the recent formulation of supergravity in pure spinor
framework. We also make some remarks on Chevalley-Eilenberg cocycles and their
Hodge duals.


  In this paper we discuss on the phenomenological footprints of gauge
invariant theories of gravity where the gravitational effects are due not only
to spacetime curvature, but also to vectorial nonmetricity. We explore the
possibility that vectorial nonmetricity and gauge symmetry may survive after
$SU(2)\times U(1)$ (electroweak) symmetry breaking, so that these may have
impact on the explanation of certain cosmological puzzles, such as the nature
of the dark matter and of the dark energy. We show that this is possible only
for theories with gradient nonmetricity, i. e., when the vectorial nonmetricity
amounts to a gradient of a scalar. The possibility that vectorial nonmetricity
may have played a role in the quantum epoch is not ruled out. We also present
an alternative interpretation of gauge invariance of theories with vectorial
nonmetricity which we call as ``many-worlds'' interpretation due to its overall
similitude with the known interpretation of quantum physics.


  We consider the analysis of sets of categorical sequences consisting of
piecewise homogeneous Markov segments. The sequences are assumed to be governed
by a common underlying process with segments occurring in the same order for
each sequence. Segments are defined by a set of unobserved changepoints where
the positions and number of changepoints can vary from sequence to sequence. We
propose a Bayesian framework for analyzing such data, placing priors on the
locations of the changepoints and on the transition matrices and using Markov
chain Monte Carlo (MCMC) techniques to obtain posterior samples given the data.
Experimental results using simulated data illustrates how the methodology can
be used for inference of posterior distributions for parameters and
changepoints, as well as the ability to handle considerable variability in the
locations of the changepoints across different sequences. We also investigate
the application of the approach to sequential data from two applications
involving monsoonal rainfall patterns and branching patterns in trees.


  We present a mathematical framework for mapping second-order logic relations
onto a simple state vector algebra. Using this algebra, basic theorems of set
theory can be proven in an algorithmic way, hence by an expert system. We
illustrate the use of the algebra with simple examples and show that, in
principle, all theorems of basic set theory can be recovered in an elementary
way. The developed technique can be used for an automated theorem proving in
the 1st and 2nd order logic.


  The estimation of parameters in the frequency spectrum of a seasonally
persistent stationary stochastic process is addressed. For seasonal persistence
associated with a pole in the spectrum located away from frequency zero, a new
Whittle-type likelihood is developed that explicitly acknowledges the location
of the pole. This Whittle likelihood is a large sample approximation to the
distribution of the periodogram over a chosen grid of frequencies, and
constitutes an approximation to the time-domain likelihood of the data, via the
linear transformation of an inverse discrete Fourier transform combined with a
demodulation. The new likelihood is straightforward to compute, and as will be
demonstrated has good, yet non-standard, properties. The asymptotic behaviour
of the proposed likelihood estimators is studied; in particular,
$N$-consistency of the estimator of the spectral pole location is established.
Large finite sample and asymptotic distributions of the score and observed
Fisher information are given, and the corresponding distributions of the
maximum likelihood estimators are deduced. A study of the small sample
properties of the likelihood approximation is provided, and its superior
performance to previously suggested methods is shown, as well as agreement with
the developed distributional approximations.


  We give a complete classification of Q_l-cohomology projective planes with
isolated ADE-singularities and numerically trivial canonical bundle in odd
characteristic. This leads to a beautiful relation with certain Enriques
surfaces which parallels the situation in characteristic zero, yet displays
intriguing subtleties.


  In this short note, we show that the higher-order derivatives of the adjugate
matrix $\mbox{Adj}(z-A)$, are related to the nilpotent matrices and projections
in the Jordan decomposition of the matrix $A$. These relations appear as a
factorization of the derivative of the adjugate matrix as a product of factors
related to the eigenvalues, nilpotent matrices and projectors. The novel
relations are obtained using the Riesz projector and functional calculus. The
results presented here can be considered to be a generalization of Thompson and
McEnteggert's theorem relating the adjugate matrix to the orthogonal projection
on the eigenspace of simple eigenvalues for symmetric matrices. They can also
be seen as a complement to some earlier results by B. Parisse, M. Vaughan that
relate derivatives of the adjugate matrix to the invariant subspaces associated
with an eigenvalue. Our results can also be interpreted as a general
eigenvector-eigenvalue identity. Many previous works have dealt with relations
between the projectors on the eigenspaces and the derivatives of the adjugate
matrix with the characteristic spaces but it seems that there is no explicit
mention in the literature of the factorization of the higher-order derivatives
of the adjugate matrix as a matrix multiplication involving nilpotent and
projector matrices, which appear in the Jordan decomposition theorem.


  We describe measurements of the X-ray reflectance in the range 2 to 10 keV of
samples representative of coated silicon wafers that are proposed for the
fabrication of the XEUS (X-ray Evolving Universe Spectrometer) mission. We
compare the reflectance of silicon samples coated with bare Pt, with that for
samples with an additional 10nm thick carbon over-coating. We demonstrate a
significant improvement in reflectance in the energy range ~1 to 4 keV, and at
a grazing incidence angle of 10 mrad (0.57 degrees). We consider the resulting
effective area that could be attained with an optimized design of the XEUS
telescope. Typically an improvement of 10 to 60 % in effective area, depending
on photon energy, can be achieved using the carbon overcoat.


  In this paper, we propose a deep learning framework based on randomized
neural network. In particular, inspired by the principles of Random Vector
Functional Link (RVFL) network, we present a deep RVFL network (dRVFL) with
stacked layers. The parameters of the hidden layers of the dRVFL are randomly
generated within a suitable range and kept fixed while the output weights are
computed using the closed form solution as in a standard RVFL network. We also
propose an ensemble deep network (edRVFL) that can be regarded as a marriage of
ensemble learning with deep learning. Unlike traditional ensembling approaches
that require training several models independently from scratch, edRVFL is
obtained by training a single dRVFL network once. Both dRVFL and edRVFL
frameworks are generic and can be used with any RVFL variant. To illustrate
this, we integrate the deep learning networks with a recently proposed
sparse-pretrained RVFL (SP-RVFL). Extensive experiments on benchmark datasets
from diverse domains show the superior performance of our proposed deep RVFL
networks.


  Recent asteroseismic analyses have revealed the presence of strong (B
$\gtrsim 10^5$ G) magnetic fields in the cores of many red giant stars. Here,
we examine the implications of these results for the evolution of stellar
magnetic fields, and we make predictions for future observations. Those stars
with suppressed dipole modes indicative of strong core fields should exhibit
moderate but detectable quadrupole mode suppression. The long magnetic
diffusion times within stellar cores ensure that dynamo-generated fields are
confined to mass coordinates within the main sequence convective core, and the
observed sharp increase in dipole mode suppression rates above $1.5 \, M_\odot$
may be explained by the larger convective core masses and faster rotation of
these more massive stars. In clump stars, core fields of $\sim10^5 \, {\rm G}$
can suppress dipole modes, whose visibility should be equal to or less than the
visibility of suppressed modes in ascending red giants. High dipole mode
suppression rates in low-mass ($M \lesssim 2 \, M_\odot$) clump stars would
indicate that magnetic fields generated during the main sequence can withstand
subsequent convective phases and survive into the compact remnant phase.
Finally, we discuss implications for observed magnetic fields in white dwarfs
and neutron stars, as well as the effects of magnetic fields in various types
of pulsating stars.


  We consider the problem of estimating the incidence of residential burglaries
that occur over a well-defined period of time within the 10 most populous
cities in North Carolina. Our analysis typifies some of the general issues that
arise in estimating and comparing local crime rates over time and for different
cities. Typically, the only information we have about crime incidence within
any particular city is what that city's police department tells us, and the
police can only count and describe the crimes that come to their attention. To
address this, our study combines information from police-based residential
burglary counts and the National Crime Victimization Survey to obtain interval
estimates of residential burglary incidence at the local level. We use those
estimates as a basis for commenting on the fragility of between-city and
over-time comparisons that often appear in both public discourse about crime
patterns.


  We have reviewed the characteristics of the extended red emission (ERE) as
observed in many dusty astronomical environments, in particular, the diffuse
interstellar medium of the Galaxy. The spectral nature and the photon
conversion efficiency of the ERE identify the underlying process as highly
efficient photoluminescence by an abundant component of interstellar dust. We
have compared the photoluminescence properties of a variety of carbon- and
silicon-based materials proposed as sources for the ERE with the
observationally established constraints. We found that silicon nanoparticles
provide the best match to the spectrum and the efficiency requirement of the
ERE. If present in interstellar space with an abundance sufficient to explain
the intensity of the ERE, silicon nanoparticles will also contribute to the
interstellar 9.7 micron Si-O stretch feature in absorption, to the near- and
mid-IR nonequilibrium thermal background radiation, and to the continuum
extinction in the near- and far-UV. About 36% of the interstellar silicon
depleted into the dust phase would be needed in the form of silicon
nanoparticles, amounting to less than 5% of the interstellar dust mass. We
propose that silicon nanoparticles form through the nucleation of SiO in
oxygen-rich stellar mass outflows and that they represent an important
small-grain component of the interstellar dust spectrum.


  We investigate the properties of the spanning trees of various real-world and
model networks. The spanning tree representing the communication kernel of the
original network is determined by maximizing total weight of edges, whose
weights are given by the edge betweenness centralities. We find that a
scale-free tree and shortcuts organize a complex network. The spanning tree
shows robust betweenness centrality distribution that was observed in
scale-free tree models. It turns out that the shortcut distribution
characterizes the properties of original network, such as the clustering
coefficient and the classification of networks by the betweenness centrality
distribution.


  We estimate the sensitivity of future galaxy surveys to cosmological
parameters, using the redshift dependent angular power spectra of galaxy number
counts, $C_\ell(z_1,z_2)$, calculated with all relativistic corrections at
first order in perturbation theory. We pay special attention to the redshift
dependence of the non-linearity scale and present Fisher matrix forecasts for
Euclid-like and DES-like galaxy surveys. We compare the standard $P(k)$
analysis with the new $C_\ell(z_1,z_2)$ method. We show that for surveys with
photometric redshifts the new analysis performs significantly better than the
$P(k)$ analysis. For spectroscopic redshifts, however, the large number of
redshift bins which would be needed to fully profit from the redshift
information, is severely limited by shot noise. We also identify surveys which
can measure the lensing contribution and we study the monopole, $C_0(z_1,z_2)$.


  We devise a new and highly accurate quantization procedure for the inner
product representation, both in configuration and momentum space. Utilizing the
representation $\Psi(\xi) = \sum_{i}a_i[E]\xi^i R_{\beta}(\xi)$, for an
appropriate reference function, $R_{\beta}(\xi)$, we demonstrate that the
(convergent) zeroes of the coefficient functions, $a_i[E] = 0$, approximate the
exact bound/resonance state energies with increasing accuracy as $i \to
\infty$. The validity of the approach is shown to be based on an extension of
the Hill determinant quantization procedure. Our method has been applied, with
remarkable success, to various quantum mechanical problems.


  Technical trading rules have been widely used by practitioners in financial
markets for a long time. The profitability remains controversial and few
consider the stationarity of technical indicators used in trading rules. We
convert MA, KDJ and Bollinger bands into stationary processes and investigate
the profitability of these trading rules by using 3 high-frequency data(15s,30s
and 60s) of CSI300 Stock Index Futures from January 4th 2012 to December 31st
2016. Several performance and risk measures are adopted to assess the practical
value of all trading rules directly while ADF-test is used to verify the
stationarity and SPA test to check whether trading rules perform well due to
intrinsic superiority or pure luck. The results show that there are several
significant combinations of parameters for each indicator when transaction
costs are not taken into consideration. Once transaction costs are included,
trading profits will be eliminated completely. We also propose a method to
reduce the risk of technical trading rules.


  We demonstrate observational evidence for the occurrence of convectively
driven internal gravity waves (IGW) in young massive O-type stars observed with
high-precision CoRoT space photometry. This evidence results from a comparison
between velocity spectra based on 2D hydrodynamical simulations of IGW in a
differentially-rotating massive star and the observed spectra.We also show that
the velocity spectra caused by IGW may lead to detectable line-profile
variability and explain the occurrence of macroturbulence in the observed line
profiles of OB stars. Our findings provide predictions that can readily be
tested by including a sample of bright slowly and rapidly rotating OB-type
stars in the scientific programme of the K2 mission accompanied by
high-precision spectroscopy and their confrontation with multi-dimensional
hydrodynamic simulations of IGW for various masses and ages.


  Given a sequence of integers, we want to find a longest increasing
subsequence of the sequence. It is known that this problem can be solved in
$O(n \log n)$ time and space. Our goal in this paper is to reduce the space
consumption while keeping the time complexity small. For $\sqrt{n} \le s \le
n$, we present algorithms that use $O(s \log n)$ bits and $O(\frac{1}{s} \cdot
n^{2} \cdot \log n)$ time for computing the length of a longest increasing
subsequence, and $O(\frac{1}{s} \cdot n^{2} \cdot \log^{2} n)$ time for finding
an actual subsequence. We also show that the time complexity of our algorithms
is optimal up to polylogarithmic factors in the framework of sequential access
algorithms with the prescribed amount of space.


  It has long been realized that the natural orbit space for non-abelian
Yang-Mills dynamics is a positively curved (infinite dimensional) Riemannian
manifold. Expanding on this result I.M. Singer proposed that strict positivity
of the corresponding Ricci tensor (computable through zeta function
regularization) could play a fundamental role in establishing that the
associated Schroedinger operator admits a spectral gap. His argument was based
on representing the (regularized) kinetic term in the Schroedinger operator as
a Laplace-Beltrami operator on this positively curved orbit space. We revisit
Singer's proposal and show how, when the contribution of the Yang-Mills
potential energy is taken into account, the role of the original orbit space
Ricci tensor is instead played by a Bakry-Emery Ricci tensor computable from
the ground state wave functional of the quantum theory. We next review our
ongoing Euclidean-signature-semi-classical program for deriving asymptotic
expansions for such wave functionals and discuss how, by keeping the dynamical
nonlinearities and non-abelian gauge invariances intact at each level of the
analysis, our approach surpasses that of conventional perturbation theory for
the generation of approximate wave functionals. Though our main focus is on
Yang-Mills theory we derive the orbit space curvature for scalar
electrodynamics and prove that, whereas the Maxwell factor remains flat, the
interaction naturally induces positive curvature in the (charged) scalar factor
of the resulting orbit space. This has led us to the conjecture that such orbit
space curvature effects could furnish a source of mass for ordinary
Klein-Gordon type fields provided the latter are (minimally) coupled to gauge
fields, even in the abelian case. Finally we discuss the potential
applicability of our Euclidean-signature program to the Wheeler-DeWitt equation
of canonical quantum gravity.


  Let $\{G_i :i\in\N\}$ be a family of finite Abelian groups. We say that a
subgroup $G\leq \prod\limits_{i\in \N}G_i$ is \emph{order controllable} if for
every $i\in \mathbb{N}$ there is $n_i\in \mathbb{N}$ such that for each $c\in
G$, there exists $c_1\in G$ satisfying that $c_{1|[1,i]}=c_{|[1,i]}$, $supp
(c_1)\subseteq [1,n_i]$, and order$(c_1)$ divides order$(c_{|[1,n_i]})$. In
this paper we investigate the structure of order controllable subgroups. It is
proved that every order controllable, profinite, abelian group contains a
subset $\{g_n : n\in\N\}$ that topologically generates the group and whose
elements $g_n$ all have finite support. As a consequence, sufficient conditions
are obtained that allow us to encode, by means of a topological group
isomorphism, order controllable profinite abelian groups. Some applications of
these results to group codes will appear subsequently \cite{FH:2021}.


  In this outline of a program, based on rigorous renormalization group theory,
we introduce new definitions which allow one to formulate precise mathematical
conjectures related to conformal invariance as studied by physicists in the
area known as higher-dimensional conformal bootstrap which has developed at a
breathtaking pace over the last few years. We also explore a second theme,
intimately tied to conformal invariance for random distributions, which can be
construed as a search for very general first and second-quantized
Kolmogorov-Chentsov Theorems. First-quantized refers to regularity of sample
paths. Second-quantized refers to regularity of generalized functionals or Hida
distributions and relates to the operator product expansion. We formulate this
program in both the Archimedean and $p$-adic situations. Indeed, the study of
conformal field theory and its connections with probability provides a golden
opportunity where $p$-adic analysis can lead the way towards a better
understanding of open problems in the Archimedean setting. Finally, we present
a summary of progress made on a $p$-adic hierarchical model and point out
possible connections to number theory. Parts of this article were presented in
author's talk at the 6th International Conference on $p$-adic Mathematical
Physics and its Applications, Mexico 2017.


  We present a study of the impact of a bright quasar on the redshifted 21cm
signal during the Epoch of Reionization (EoR). Using three different
cosmological radiative transfer simulations, we investigate if quasars are
capable of substantially changing the size and morphology of the H II regions
they are born in. We choose stellar and quasar luminosities in a way that is
favourable to seeing such an effect. We find that even the most luminous of our
quasar models is not able to increase the size of its native H II region
substantially beyond those of large H II regions produced by clustered stellar
sources alone. However, the quasar H II region is found to be more spherical.
We next investigate the prospects of detecting such H II regions in the
redshifted 21cm data from the Low Frequency Array (LOFAR) by means of a matched
filter technique. We find that H II regions with radii ~ 25 comoving Mpc or
larger should have a sufficiently high detection probability for 1200 hours of
integration time. Although the matched filter can in principle distinguish
between more and less spherical regions, we find that when including realistic
system noise this distinction can no longer be made. The strong foregrounds are
found not to pose a problem for the matched filter technique. We also
demonstrate that when the quasar position is known, the redshifted 21cm data
can still be used to set upper limits on the ionizing photon rate of the
quasar. If both the quasar position and its luminosity are known, the
redshifted 21 cm data can set new constrains on quasar lifetimes.


  We show a sufficient criterion to determine if a planar set $\Omega$ is a
minimizer of the prescribed curvature functional among all of its subsets. As a
special case, we derive a sufficient criterion to determine if $\Omega$ is a
self-Cheeger set, i.e. if it minimizes the ratio $P(E)/|E|$ among all of its
subsets. Specifically, if a Jordan domain $\Omega$ possesses the interior disk
property of radius $|\Omega|/P(\Omega)$, then it is a self-Cheeger set; if it
possesses the strict interior disk property then it is a minimal Cheeger set,
i.e. the unique minimizer. As a side effect we provide a way to build
self-Cheeger sets.


  Building blocks and tiles are an excellent way of learning about geometry and
mathematics in general. There are several versions of tiles that are either
snapped together or connected with magnets that can be used to introduce topics
like volume, tessellations, and Platonic solids. However, since these tiles are
made of hard plastic, they are not very suitable for creating hyperbolic
surfaces or shapes where the tiles need to bend. Curvagons are flexible regular
polygon building blocks that allow you to quickly build anything from
hyperbolic surfaces and tori to dinosaurs and shoes. They can be used to
introduce mathematical concepts from Archimedean solids to Gauss-Bonnet
theorem. You can also let your imagination run free and build whatever comes to
mind.


  This is a brief review of various families of coherent and squeezed states
(and their generalizations) for a charged particle in a magnetic field, that
have been constructed for the past 50 years. Although the main attention is
paid to the Gaussian states, various families of non-Gaussian states are also
discussed, and the list of relevant references is provided.


  Let X be a set of smooth points in P^2, and I = \oplus_{t >= d} I_t the
defining ideal of X. In this paper, we give a set of defining equations for the
Rees algebra R(I_{d+1}) of the ideal generated by I_{d+1}. This study give
information to completely answer questions on the defining ideals of projective
embeddings of the blowup of P^2 along the points in X, which has been studied
by many authors. In this paper, we also study the asymptotic behaviour of the
Rees algebras R(I_t) of the ideal generated by I_t, as t gets large.


  We consider a new partial differential equation, of a similar form to the
Camassa-Holm shallow water wave equation, which was recently obtained by
Degasperis and Procesi using the method of asymptotic integrability. We prove
the exact integrability of the new equation by constructing its Lax pair, and
we explain its connection with a negative flow in the Kaup-Kupershmidt
hierarchy via a reciprocal transformation. The infinite sequence of conserved
quantities is derived together with a proposed bi-Hamiltonian structure. The
equation admits exact solutions in the form of a superposition of
multi-peakons, and we describe the integrable finite-dimensional peakon
dynamics and compare it with the analogous results for Camassa-Holm peakons.


  Recently neural response generation models have leveraged large pre-trained
transformer models and knowledge snippets to generate relevant and informative
responses. However, this does not guarantee that generated responses are
factually correct. In this paper, we examine factual correctness in
knowledge-grounded neural response generation models. We present a human
annotation setup to identify three different response types: responses that are
factually consistent with respect to the input knowledge, responses that
contain hallucinated knowledge, and non-verifiable chitchat style responses. We
use this setup to annotate responses generated using different stateof-the-art
models, knowledge snippets, and decoding strategies. In addition, to facilitate
the development of a factual consistency detector, we automatically create a
new corpus called Conv-FEVER that is adapted from the Wizard of Wikipedia
dataset and includes factually consistent and inconsistent responses. We
demonstrate the benefit of our Conv-FEVER dataset by showing that the models
trained on this data perform reasonably well to detect factually inconsistent
responses with respect to the provided knowledge through evaluation on our
human annotated data. We will release the Conv-FEVER dataset and the human
annotated responses.


  In this work we introduce a fully-connected graph structure in the Deep
Gaussian Conditional Random Field (G-CRF) model. For this we express the
pairwise interactions between pixels as the inner-products of low-dimensional
embeddings, delivered by a new subnetwork of a deep architecture. We
efficiently minimize the resulting energy by solving the resulting low-rank
linear system with conjugate gradients, and derive an analytic expression for
the gradient of our embeddings which allows us to train them end-to-end with
backpropagation.
  We demonstrate the merit of our approach by achieving state of the art
results on three challenging Computer Vision benchmarks, namely semantic
segmentation, human parts segmentation, and saliency estimation. Our
implementation is fully GPU based, built on top of the Caffe library, and will
be made publicly available.


  The high-energy phonons in La1.5Sr0.5NiO4, in which the checkerboard charge
ordering is formed, was investigated by the inelastic neutron scattering. We
found that the longitudinal modes show strong anomalies compared with La2NiO4.
We argue the similarity and difference in the phonon anomalies between the
present sample and the preceding works of different compositions.


  This paper discusses dynamical systems for disk-covering and sphere-packing
problems. We present facility location functions from geometric optimization
and characterize their differentiable properties. We design and analyze a
collection of distributed control laws that are related to nonsmooth gradient
systems. The resulting dynamical systems promise to be of use in coordination
problems for networked robots; in this setting the distributed control laws
correspond to local interactions between the robots. The technical approach
relies on concepts from computational geometry, nonsmooth analysis, and the
dynamical system approach to algorithms.


  Malaria is a disease of global concern according to the World Health
Organization. Billions of people in the world are at risk of Malaria today.
Microscopy is considered the gold standard for Malaria diagnosis. Microscopic
assessment of blood samples requires the need of trained professionals who at
times are not available in rural areas where Malaria is a problem. Full
automation of Malaria diagnosis is a challenging task. In this work, we put
forward a framework for diagnosis of malaria. We adopt a two layer approach,
where we detect infected cells using a Faster-RCNN in the first layer, crop
them out, and feed the cropped cells to a seperate neural network for
classification. The proposed methodology was tested on an openly available
dataset, this will serve as a baseline for the future methods as currently
there is no common dataset on which results are reported for Malaria Diagnosis.


  Following the gaze of people inside videos is an important signal for
understanding people and their actions. In this paper, we present an approach
for following gaze across views by predicting where a particular person is
looking throughout a scene. We collect VideoGaze, a new dataset which we use as
a benchmark to both train and evaluate models. Given one view with a person in
it and a second view of the scene, our model estimates a density for gaze
location in the second view. A key aspect of our approach is an end-to-end
model that solves the following sub-problems: saliency, gaze pose, and
geometric relationships between views. Although our model is supervised only
with gaze, we show that the model learns to solve these subproblems
automatically without supervision. Experiments suggest that our approach
follows gaze better than standard baselines and produces plausible results for
everyday situations.


  Graphs are a popular data type found in many domains. Numerous techniques
have been proposed to find interesting patterns in graphs to help understand
the data and support decision-making. However, there are generally two
limitations that hinder their practical use: (1) they have multiple parameters
that are hard to set but greatly influence results, (2) and they generally
focus on identifying complex subgraphs while ignoring relationships between
attributes of nodes.Graphs are a popular data type found in many domains.
Numerous techniques have been proposed to find interesting patterns in graphs
to help understand the data and support decision-making. However, there are
generally two limitations that hinder their practical use: (1) they have
multiple parameters that are hard to set but greatly influence results, (2) and
they generally focus on identifying complex subgraphs while ignoring
relationships between attributes of nodes. To address these problems, we
propose a parameter-free algorithm named CSPM (Compressing Star Pattern Miner)
which identifies star-shaped patterns that indicate strong correlations among
attributes via the concept of conditional entropy and the minimum description
length principle. Experiments performed on several benchmark datasets show that
CSPM reveals insightful and interpretable patterns and is efficient in runtime.
Moreover, quantitative evaluations on two real-world applications show that
CSPM has broad applications as it successfully boosts the accuracy of graph
attribute completion models by up to 30.68\% and uncovers important patterns in
telecommunication alarm data.


  We study the single particle velocity distribution for a granular fluid of
inelastic hard spheres or disks, using the Enskog-Boltzmann equation, both for
the homogeneous cooling of a freely evolving system and for the stationary
state of a uniformly heated system, and explicitly calculate the fourth
cumulant of the distribution. For the undriven case, our result agrees well
with computer simulations of Brey et al. \cite{brey}. Corrections due to
non-Gaussian behavior on cooling rate and stationary temperature are found to
be small at all inelasticities. The velocity distribution in the uniformly
heated steady state exhibits a high energy tail $\sim \exp(-A c^{3/2})$, where
$c$ is the velocity scaled by the thermal velocity and $A\sim 1/\sqrt{\eps}$
with $\eps$ the inelasticity.


  Given a planar pentagon, construct two new pentagons: the vertices of the
first one are the intersection points of the diagonals of the original
pentagon, and the vertices of the second one are the tangency points of the
conic inscribed in the original pentagon. E. Kasner theorem, published in 1928,
asserts that these two operations on pentagons commute. We extend Kasner's
result to Poncelet polygons, that is, the polygons inscribed into a conic and
circumscribed about a conic.


  It is believed that the first star-forming galaxies are the main drivers of
cosmic reionization. It is usually assumed that there is a one-to-one
relationship between the star formation rate (SFR) inside a galaxy and the host
halo mass in semi-analytical/numerical modeling of large-scale reionization.
However, more accurate simulations and observations suggest that the SFR and
ionizing luminosity in galaxies may vary considerably even if the host halo
mass is the same. This astrophysical scatter can introduce an additional
non-Gaussianity in the HI 21-cm signal, which the power spectrum might not
capture adequately. In this work, we have studied the impact of the scatter on
the HI 21-cm bispectrum using semi-numerical simulations. Although the
fractional change in the HI 21-cm bispectra due to the scatter is found to be
more than a factor of $10$ at large scales ($k_1 \lesssim 1\, {\rm Mpc}^{-1}$)
for $z=7.4$, it is found to be statistically insignificant. However, at small
scales ($k_1\sim2.55$~Mpc$^{-1}$), we have found the impact due to the scatter
to be high in magnitude ($|\langle \Delta B \rangle/B_{\text{no-scatter}}| \sim
1$) and statistically significant ($|\langle\Delta B\rangle/\sigma_{\Delta B}|
\gtrsim 5$) at neutral fraction, $\overline{x}_{\rm HI}\sim 0.8$ for $z=7.4$.
The impact due to scatter is found to be even more prominent ($|\langle \Delta
B \rangle/B_{\text{no-scatter}}| \gtrsim 10$) at small scales for $z=10$ and
$\overline{x}_{\rm HI}\sim 0.8$, but with reduced statistical significance
($|\langle\Delta B\rangle/\sigma_{\Delta B}| \sim 3$), compared to $z=7.4$ at
the same neutral fraction. In the most optimistic scenario, SKA1-Low might be
able to detect these signatures of astrophysical scatter, at $\sim 3\sigma$ and
$\sim 5\sigma$ detection significance for $\overline{x}_{\rm HI} \sim$ 0.8 and
0.9 respectively, for the equilateral HI 21-cm bispectrum at $z=7.4$.


  The main result of this paper is a formula for the scalar product of
semiclassical eigenvectors of two integrable systems on the same symplectic
manifold. An important application of this formula is the Ponzano-Regge type of
asymptotic of Racah-Wigner coefficients.


  For a flat universe presently dominated by smooth energy, either cosmological
constant (LCDM) or quintessence (QCDM), we calculate the asymptotic collapsed
mass fraction as function of the present ratio of smooth energy to matter
energy $\mathcal R_0$. Identifying the normalized collapsed fraction as a
conditional probability for habitable galaxies, we observe that the observed
present ratio $\mathcal R_0 \sim 2$ is likely in LCDM, but more likely in QCDM.
Inverse application of Bayes' Theorem makes the Anthropic Principle a
predictive scientific principle: the data implies that the prior probability
for $\mathcal R_0$ must be essentially flat over the anthropically allowed
range. Interpreting this prior as a distribution over {\em theories} lets us
predict that any future theory of initial conditions must be indifferent to
$\mathcal R_0$. This application of the Anthropic Principle does not demand the
existence of other universes.


  We show that polaritons in an array of interacting micro-cavities with strong
atom-photon coupling can form a two-component Bose-Hubbard model. Both
polariton species are thereby protected against spontaneous emission as their
atomic part is stored in two ground states of the atoms. The parameters of the
effective model can be tuned via the driving strength of external lasers. We
also describe a method to measure the number statistics in one cavity for each
polariton species independently.


  The center of the Milkyway is a host to energetic phenomena across many
electromagnetic wave-bands and now possibly of high-energy neutrinos. We show
that 5 out of 21 IceCube shower-like events, including a PeV event, likely
originated from the Galactic Center region. Hard spectrum and flux inferred
from these events are inconsistent with atmospheric neutrinos. The flux of
these neutrinos is consistent with an extrapolation of the gamma-ray flux
measured by Fermi-LAT from the inner Galactic region. This indicates a common
hadronic origin of both, powered by supernovae. Three other shower-like events
are spatially correlated with the Fermi bubbles, originating from the Galactic
Center activity, within the uncertainty of reconstructing their arrival
directions. Origin of the other neutrino events, including 7 track-like events,
is still elusive.


  The dipole strength of the nuclide $^{76}$Ge was studied in photon-scattering
experiments using bremsstrahlung produced with electron beams of energies of
7.8 and 12.3 MeV at the $\gamma$ELBE facility. We identified 210 levels up to
an excitation energy of 9.4 MeV and assigned spin $J$ = 1 to most of them. The
quasicontinuum of unresolved transitions was included in the analysis of the
spectra and the intensities of branching transitions were estimated on the
basis of simulations of statistical $\gamma$-ray cascades. The photoabsorption
cross section up to the neutron-separation energy was determined and is
compared with predictions of the statistical reaction model. The derived photon
strength function is compared with results of experiments using other
reactions.


  We study the type of solutions to which stochastic gradient descent converges
when used to train a single hidden-layer multivariate ReLU network with the
quadratic loss. Our results are based on a dynamical stability analysis. In the
univariate case, it was shown that linearly stable minima correspond to network
functions (predictors), whose second derivative has a bounded weighted $L^1$
norm. Notably, the bound gets smaller as the step size increases, implying that
training with a large step size leads to `smoother' predictors. Here we
generalize this result to the multivariate case, showing that a similar result
applies to the Laplacian of the predictor. We demonstrate the tightness of our
bound on the MNIST dataset, and show that it accurately captures the behavior
of the solutions as a function of the step size. Additionally, we prove a depth
separation result on the approximation power of ReLU networks corresponding to
stable minima of the loss. Specifically, although shallow ReLU networks are
universal approximators, we prove that stable shallow networks are not. Namely,
there is a function that cannot be well-approximated by stable single
hidden-layer ReLU networks trained with a non-vanishing step size. This is
while the same function can be realized as a stable two hidden-layer ReLU
network. Finally, we prove that if a function is sufficiently smooth (in a
Sobolev sense) then it can be approximated arbitrarily well using shallow ReLU
networks that correspond to stable solutions of gradient descent.


  In recent years, ridesharing platforms have become a prominent mode of
transportation for the residents of urban areas. As a fundamental problem,
route recommendation for these platforms is vital for their sustenance. The
works done in this direction have recommended routes with higher passenger
demand. Despite the existing works, statistics have suggested that these
services cause increased greenhouse emissions compared to private vehicles as
they roam around in search of riders. This analysis provides finer details
regarding the functionality of ridesharing systems and it reveals that in the
face of their boom, they have not utilized the vehicle capacity efficiently. We
propose to overcome the above limitations and recommend routes that will fetch
multiple passengers simultaneously which will result in increased vehicle
utilization and thereby decrease the effect of these systems on the
environment. As route recommendation is NP-hard, we propose a k-hop-based
sliding window approximation algorithm that reduces the search space from
entire road network to a window. We further demonstrate that maximizing
expected demand is submodular and greedy algorithms can be used to optimize our
objective function within a window. We evaluate our proposed model on
real-world datasets and experimental results demonstrate superior performance
by our proposed model.


  We prove a topological rigidity theorem for closed hypersurfaces of the
Euclidean sphere and of an elliptic space form. It asserts that, under a lower
bound hypothesis on the absolute value of the principal curvatures, the
hypersurface is diffeomorphic to a sphere or to a quotient of a sphere by a
group action. We also prove another topological rigidity result for
hypersurfaces of the sphere that involves the spherical image of its usual
Gauss map.


  We observed nine primary transits of the hot Jupiter TrES-3b in several
optical and near-UV photometric bands from 2009 June to 2012 April in an
attempt to detect its magnetic field. Vidotto, Jardine and Helling suggest that
the magnetic field of TrES-3b can be constrained if its near-UV light curve
shows an early ingress compared to its optical light curve, while its egress
remains unaffected. Predicted magnetic field strengths of Jupiter-like planets
should range between 8 G and 30 G. Using these magnetic field values and an
assumed B_star of 100 G, the Vidotto et al. method predicts a timing difference
of 5-11 min. We did not detect an early ingress in our three nights of near-UV
observations, despite an average cadence of 68 s and an average photometric
precision of 3.7 mmag. However, we determined an upper limit of TrES-3b's
magnetic field strength to range between 0.013 and 1.3 G (for a 1-100 G
magnetic field strength range for the host star, TrES-3) using a timing
difference of 138 s derived from the Nyquist-Shannon sampling theorem. To
verify our results of an abnormally small magnetic field strength for TrES-3b
and to further constrain the techniques of Vidotto et al., we propose future
observations of TrES-3b with other platforms capable of achieving a shorter
near-UV cadence. We also present a refinement of the physical parameters of
TrES-3b, an updated ephemeris and its first published near-UV light curve. We
find that the near-UV planetary radius of Rp = 1.386+0.248-0.144 RJup is
consistent with the planet's optical radius.


  In this comment, we want to emphasize that when the state of the two qubit is
$|0>_{B}|1>_{A}$ or $|1>_{A}|0>_{B}$, Bob's Bell basis measurement outcome can
not be $|\phi ^{\pm}>$. Also, when the product state is $|0> |0>$ or $|1> |1>$,
Bob's measurement outcome can not be $|\psi ^{\pm}>$.


  Sparsity-based approaches have been popular in many applications in image
processing and imaging. Compressed sensing exploits the sparsity of images in a
transform domain or dictionary to improve image recovery from undersampled
measurements. In the context of inverse problems in dynamic imaging, recent
research has demonstrated the promise of sparsity and low-rank techniques. For
example, the patches of the underlying data are modeled as sparse in an
adaptive dictionary domain, and the resulting image and dictionary estimation
from undersampled measurements is called dictionary-blind compressed sensing,
or the dynamic image sequence is modeled as a sum of low-rank and sparse (in
some transform domain) components (L+S model) that are estimated from limited
measurements. In this work, we investigate a data-adaptive extension of the L+S
model, dubbed LASSI, where the temporal image sequence is decomposed into a
low-rank component and a component whose spatiotemporal (3D) patches are sparse
in some adaptive dictionary domain. We investigate various formulations and
efficient methods for jointly estimating the underlying dynamic signal
components and the spatiotemporal dictionary from limited measurements. We also
obtain efficient sparsity penalized dictionary-blind compressed sensing methods
as special cases of our LASSI approaches. Our numerical experiments demonstrate
the promising performance of LASSI schemes for dynamic magnetic resonance image
reconstruction from limited k-t space data compared to recent methods such as
k-t SLR and L+S, and compared to the proposed dictionary-blind compressed
sensing method.


  The axisymmetric flow in an aspect-ratio-one cylinder whose upper and lower
bounding disks are maintained at different temperatures and rotate at equal and
opposite velocities is investigated. In this combined Rayleigh-Benard/von
Karman problem, the imposed temperature gradient is measured by the Rayleigh
number Ra and the angular velocity by the Reynolds number Re. Although fluid
motion is present as soon as Re is non-zero, a symmetry-breaking transition
analogous to the onset of convection takes place at a finite Rayleigh number
higher than that for Re=0. For Re<95, the transition is a pitchfork bifurcation
to a pair of steady states, while for Re>95, it is a Hopf bifurcation to a
limit cycle. The steady states and limit cycle are connected via a pair of
SNIPER bifurcations except very near the Takens-Bogdanov codimension-two point,
where the scenario includes global bifurcations. Detailed phase portraits and
bifurcation diagrams are presented, as well as the evolution of the leading
part of the spectrum, over the parameter ranges 0<Re<120 and 0<Ra<30,000.


  Placing D3-branes at conical Calabi-Yau threefold singularities produces many
AdS$_5$/CFT$_4$ duals. Recent progress in differential geometry has produced a
technique (called K-stability) to recognize which singularities admit conical
Calabi-Yau metrics. On the other hand, the algebraic technique of
non-commutative crepant resolutions, involving matrix factorizations, has been
developed to associate a quiver to a singularity. In this paper, we put
together these ideas to produce new AdS$_5$/CFT$_4$ duals, with special
emphasis on non-toric singularities.


  An integer sequence a(n) is called a jump sequence if a(1)=1 and 1<=a(n)<n
for n>=2. Such a sequence has the property that a^k(n)=a(a(...(a(n))...)) goes
to 1 in finitely many steps and we call the pattern
(n,a(n),a^2(n),...,a^k(n)=1) a jumping pattern from n down to 1. In this paper
we look at jumping sequences which are weight minimizing with respect to
various weight functions (where a weight w(i,j) is given to each jump from j
down to i).
  Our main result is to show that if w(i,j)=(i+j)/i^2 then the cost minimizing
jump sequence has the property that the number m satisfies m=a^q(p) for
arbitrary q and some p (depending on q) if and only if m is a Pell number.


  Realistic reconstruction of 3D clothing from an image has wide applications,
such as avatar creation and virtual try-on. This paper presents a novel
framework that reconstructs the texture map for 3D garments from a single image
with pose. Assuming that 3D garments are modeled by stitching 2D garment sewing
patterns, our specific goal is to generate a texture image for the sewing
patterns. A key component of our framework, the Texture Unwarper, infers the
original texture image from the input clothing image, which exhibits warping
and occlusion of texture due to the user's body shape and pose. The Texture
Unwarper effectively transforms between the input and output images by mapping
the latent spaces of the two images. By inferring the unwarped original texture
of the input garment, our method helps reconstruct 3D garment models that can
show high-quality texture images realistically deformed for new poses. We
validate the effectiveness of our approach through a comparison with other
methods and ablation studies.


  Generalizing an old result proved by P. Rao [see MR 83i:14025] for
arithmetically Cohen-Macaulay, self-linked subschemes of codimension 2 in the
projective n-space P, we give a characterization of self-linked pure subschemes
of codimension 2 in P satisfying a necessary parity condition, in
characteristic different from 2. We make use of the theory of quadratic sheaves
described in a previous paper of the authors [see MR 99h:14044].


  We consider a chain of Abelian Klebanov-Tarnopolsky fermionic tensor models
coupled through quartic nearest-neighbor interactions. We characterize the
gauge-singlet spectrum for small chains ($L=2,3,4,5$) and observe that the
spectral statistics exhibits strong evidences in favor of quasi-many body
localization.


  Motivated by problems in categorical database theory, we introduce and
compare two notions of presentation for profunctors, uncurried and curried,
which arise intuitively from thinking of profunctors either as functors
$\mathcal{C}^\text{op} \times \mathcal{D} \to \textbf{Set}$ or
$\mathcal{C}^\text{op} \to \textbf{Set}^{\mathcal{D}}$. Although the Cartesian
closure of $\textbf{Cat}$ means these two perspectives can be used
interchangeably at the semantic level, a surprising amount of subtlety is
revealed when looking through the lens of syntax. Indeed, we prove that finite
uncurried presentations are strictly more expressive than finite curried
presentations, hence the two notions do not induce the same class of finitely
presentable profunctors. Moreover, an explicit construction for the composite
of two curried presentations shows that the class of finitely curried
presentable profunctors is closed under composition, in contrast with the
larger class of finitely uncurried presentable profunctors, which is not. This
shows that curried profunctor presentations are more appropriate for
computational tasks that use profunctor composition. We package our results on
curried profunctor presentations into a double equivalence from a syntactic
double category into the double category of profunctors. Finally, we study the
relationship between curried and uncurried presentations, leading to the
introduction of curryable presentations. These constitute a subcategory of
uncurried presentations which is equivalent to the category of curried
presentations, therefore acting as a bridge between the two syntactic choices.


  We measure the UV-continuum slope beta for over 4000 high-redshift galaxies
over a wide range of redshifts z~4-8 and luminosities from the HST HUDF/XDF,
HUDF09-1, HUDF09-2, ERS, CANDELS-N, and CANDELS-S data sets. Our new beta
results reach very faint levels at z~4 (-15.5 mag: 0.006 L*(z=3)), z~5 (-16.5
mag: 0.014L*(z=3)), and z~6 and z~7 (-17 mag: 0.025 L*(z=3)). Inconsistencies
between previous studies led us to conduct a comprehensive review of systematic
errors and develop a new technique for measuring beta that is robust against
biases that arise from the impact of noise. We demonstrate, by object-by-object
comparisons, that all previous studies, including our own and those done on the
latest HUDF12 dataset, suffer from small systematic errors in beta. We find
that after correcting for the systematic errors (typically d(beta) ~0.1-0.2)
all beta results at z~7 from different groups are in excellent agreement. The
mean beta we measure for faint (-18 mag: 0.1L*(z=3)) z~4, z~5, z~6, and z~7
galaxies is -2.03+/-0.03+/-0.06 (random and systematic errors),
-2.14+/-0.06+/-0.06, -2.24+/-0.11+/-0.08, and -2.30+/-0.18+/-0.13,
respectively. Our new beta values are redder than we have reported in the past,
but bluer than other recent results. Our previously reported trend of bluer
beta's at lower luminosities is confirmed, as is the evolution to bluer beta's
at high redshifts. beta appears to show only a mild luminosity dependence
faintward of M(UV,AB) ~ -19 mag, suggesting that the mean beta asymptotes to ~
-2.2 to -2.4 for faint z>~4 galaxies. At z~7, the observed beta's suggest
non-zero, but low dust extinction, and they agree well with values predicted in
cosmological hydrodynamical simulations.


  This paper presents ESCAPE, an informed moving target defense mechanism for
cloud containers. ESCAPE models the interaction between attackers and their
target containers as a "predator searching for a prey" search game. Live
migration of Linux-containers (prey) is used to avoid attacks (predator) and
failures. The entire process is guided by a novel host-based
behavior-monitoring system that seamlessly monitors containers for indications
of intrusions and attacks. To evaluate ESCAPE effectiveness, we simulated the
attack avoidance process based on a mathematical model mimicking the
prey-vs-predator search game. Simulation results show high container survival
probabilities with minimal added overhead.


  We update the hadronic tau determination of |V_{us}|, showing that current
strange branching fractions produce results 2-3 sigma lower than 3-family
unitarity expectations. Issues related to the size of theoretical uncertainties
and results from an alternate, mixed tau-electroproduction sum rule
determination (which, by construction, produces a much smaller theoretical
uncertainty), are also considered.


  Inpatient falls are a serious safety issue in hospitals and healthcare
facilities. Recent advances in video analytics for patient monitoring provide a
non-intrusive avenue to reduce this risk through continuous activity
monitoring. However, in-bed fall risk assessment systems have received less
attention in the literature. The majority of prior studies have focused on fall
event detection, and do not consider the circumstances that may indicate an
imminent inpatient fall. Here, we propose a video-based system that can monitor
the risk of a patient falling, and alert staff of unsafe behaviour to help
prevent falls before they occur. We propose an approach that leverages recent
advances in human localisation and skeleton pose estimation to extract spatial
features from video frames recorded in a simulated environment. We demonstrate
that body positions can be effectively recognised and provide useful evidence
for fall risk assessment. This work highlights the benefits of video-based
models for analysing behaviours of interest, and demonstrates how such a system
could enable sufficient lead time for healthcare professionals to respond and
address patient needs, which is necessary for the development of fall
intervention programs.


  We study the effect of a non-Abelian SU(2) gauge potential on the topological
semimetal induced by a magnetic field having {\pi}-flux per plaquette and
acting on fermions in a cubic lattice. The Abelian {\pi}-flux term gives rise
to a spectrum characterized by Weyl points. When the non-Abelian part is turned
on, due to the presence of a C4 rotation symmetry, the Weyl points assume a
quadratic dispersion along two directions and constitute double monopoles for
the Berry curvature. We examine both analytically and numerically the main
features of this system, focusing on its gapless surface modes, the so-called
Fermi arcs. We discuss the stability of the system under confining hard-wall
and harmonic potentials, relevant for the implementation in ultracold atom
settings, and the effect of rotation symmetry breaking.


  4U 1820-30 is a low-mass X-ray binary near the center of the globular cluster
NGC 6624 consisting of, at least, one neutron star and one helium white dwarf.
Analyzing 16 years of data from the Rossi X-ray Timing Explorer (RXTE) allows
us to measure its orbital period and its time derivative with unprecedented
accuracy to be P = 685.01197 +- 0.00003 s and dP/dt /P = -5.3 +- 0.3x10^-8
yr^-1. Hence, we confirm that the period derivative is significantly negative
at the >17 sigma level, contrary to theoretical expectations for an isolated
X-ray binary. We discuss possible scenarios that could explain this
discrepancy, and conclude that the center of NGC 6624 most likely contains
large amounts of non-luminous matter such as dark remnants. We also discuss the
possibility of an IMBH inside NGC 6624, or that a dark remnant close to 4U
1820-30 causes the observed shift.


  The electrical transport properties of graphene are greatly influenced by its
environment. Owing to its high dielectric constant, strontium titanate (STO) is
expected to suppress the long-range charged impurity scattering and
consequently to enhance the mobility. However, the absence of such enhancement
has caused some controversies regarding the scattering mechanism. In graphene
devices transferred from SiO2 to STO using a newly developed technique, we
observe a moderate mobility enhancement near the Dirac point, which is the
point of charge neutrality achieved by adjusting the Fermi level. While bulk
STO is not known as a ferroelectric material, its surface was previously
reported to exhibit an outward displacement of oxygen atoms and
ferroelectric-like dipole moment. When placed on STO, graphene shows strong and
asymmetric hysteresis in resistivity, which is consistent with the dipole
picture associated with the oxygen displacement. The hysteretic response of the
surface dipole moment diminishes the polarizability, therefore weakens the
ability of STO to screen the Coulomb potential of the impurities.


  We investigate the decidability and computational complexity of conservative
extensions and the related notions of inseparability and entailment in Horn
description logics (DLs) with inverse roles. We consider both query
conservative extensions, defined by requiring that the answers to all
conjunctive queries are left unchanged, and deductive conservative extensions,
which require that the entailed concept inclusions, role inclusions, and
functionality assertions do not change. Upper bounds for query conservative
extensions are particularly challenging because characterizations in terms of
unbounded homomorphisms between universal models, which are the foundation of
the standard approach to establishing decidability, fail in the presence of
inverse roles. We resort to a characterization that carefully mixes unbounded
and bounded homomorphisms and enables a decision procedure that combines tree
automata and a mosaic technique. Our main results are that query conservative
extensions are 2ExpTime-complete in all DLs between ELI and Horn-ALCHIF and
between Horn-ALC and Horn-ALCHIF, and that deductive conservative extensions
are 2ExpTime-complete in all DLs between ELI and ELHIF_\bot. The same results
hold for inseparability and entailment.


  Memory-assisted quantum key distribution (MA-QKD) has recently been proposed
as a technique to improve the rate-versus-distance behavior of QKD systems by
using existing, or nearly-achievable, quantum technologies. The promise is that
MA-QKD would require less demanding quantum memories than the ones needed for
probabilistic quantum repeaters. Nevertheless, early investigations suggest
that, in order to beat the conventional no-memory QKD schemes, the quantum
memories used in the MA-QKD protocols must have high bandwidth-storage products
and short interaction times. Among different types of quantum memories,
ensemble-based memories offer some of the required specifications, but they
typically suffer from multiple excitation effects. To avoid the latter issue,
in this paper, we propose two new variants of MA-QKD both relying on
single-photon sources (SPSs) for entangling purposes. One is based on known
techniques for entanglement distribution in quantum repeaters. This scheme
turns out to offer no advantage even if one uses ideal SPSs. By finding the
root cause of the problem, we then propose another setup, which can outperform
single no-QM setups even if we allow for some imperfections in our SPSs. For
such a scheme, we compare the key rate for different types of ensemble-based
memories and show that certain classes of atomic ensembles can improve the
rate-versus-distance behavior.


  In this paper we review recent results by the author on the problem of
quantization of measures. More precisely, we propose a dynamical approach, and
we investigate it in dimensions 1 and 2. Moreover, we discuss a recent general
result on the static problem on arbitrary Riemannian manifolds.


  Zipf's law of city-size distributions can be expressed by three types of
mathematical models: one-parameter form, two-parameter form, and
three-parameter form. The one-parameter and one of the two-parameter models are
familiar to urban scientists. However, the three-parameter model and another
type of two-parameter model have not attracted attention. This paper is devoted
to exploring the conditions and scopes of application of this Zipf models. By
mathematical reasoning and empirical analysis, new discoveries are made as
follows. First, if the size distribution of cities in a geographical region
cannot be described with the one- or two-parameter model, maybe it can be
characterized by the three-parameter model with a scaling factor and a
scale-translational factor. Second, all these Zipf models can be unified by
hierarchical scaling laws based on cascade structure. Third, the patterns of
city-size distributions seems to evolve from three-parameter mode to
two-parameter mode, and then to one-parameter mode. Four-year census data of
China's cities are employed to verify the three-parameter Zipf's law and the
corresponding hierarchical structure of rank-size distributions. This study is
revealing for people to understand the scientific laws of social systems and
the property of urban development.


  In the paper, we develop a composite version of Mirror Prox algorithm for
solving convex-concave saddle point problems and monotone variational
inequalities of special structure, allowing to cover saddle point/variational
analogies of what is usually called "composite minimization" (minimizing a sum
of an easy-to-handle nonsmooth and a general-type smooth convex functions "as
if" there were no nonsmooth component at all). We demonstrate that the
composite Mirror Prox inherits the favourable (and unimprovable already in the
large-scale bilinear saddle point case) $O(1/\epsilon)$ efficiency estimate of
its prototype. We demonstrate that the proposed approach can be naturally
applied to Lasso-type problems with several penalizing terms (e.g. acting
together $\ell_1$ and nuclear norm regularization) and to problems of the
structure considered in the alternating directions methods, implying in both
cases methods with the $O(\epsilon^{-1})$ complexity bounds.


  We explore the coherent dynamics of a three-level V-system interacting with a
thermal bath in the regime where thermal excitation occurs much faster than
spontaneous decay. We present analytic solutions of the Bloch-Redfield quantum
master equations, which show that strong incoherent pumping can generate
long-lived quantum coherences among the excited states of the V-system in the
overdamped regime defined by the condition $\Delta/(\bar{n}\gamma)<f(p)$, where
$\Delta$ is the excited-state level splitting, $\gamma$ is the spontaneous
decay rate, $\bar{n}\gg 1$ is the effective photon occupation number
proportional to the pumping intensity, and $f(p)$ is a universal function of
the transition dipole alignment parameter $p$. In the limit of nearly parallel
transition dipoles ($p\to 1$) the coherence lifetime $\tau_c = 1.34
(\bar{n}/\gamma) (\Delta/\gamma)^{-2}$ scales linearly with $\bar{n}$ and is
enhanced by the factor $0.67 \bar{n}$ with respect to the weak-pumping limit
[Phys. Rev. Lett. 113, 113601 (2014); J. Chem. Phys. 144, 244108 (2016)]. We
also establish the existence of long-lived quasistationary states, which occur
in the overdamped regime and affect the process of thermalization of the
V-system with the bath, slowing down the approach to thermal equilibrium. In
the case of nonparallel transition dipole moments ($p<1$), no quasistationary
states are formed and the coherence lifetime decreases sharply. Our results
reveal new regimes of long-lived quantum coherent dynamics, which could be
observed in thermally driven atomic and molecular systems.


  Selleri's paradox, based on an analysis of rotating frames, appears to show
that the speed of light in an inertial system is not normally isotropic. This
in turn seems at odds with the second postulate of special relativity requiring
a universal light speed in inertial systems. First, it is demonstrated how to
circumvent Selleri's argument using Einstein synchronization in rotating
frames. Then the nature of Selleri's result is exposed: it simply corresponds
to the adoption of a synchronization procedure different from Einstein's. In
this scheme, anisotropic one-way speeds of light by no means contradict special
relativity.


  We introduce the PBS-calculus to represent and reason on quantum computations
involving coherent control of quantum operations. Coherent control, and in
particular indefinite causal order, is known to enable multiple computational
and communication advantages over classically ordered models like quantum
circuits. The PBS-calculus is inspired by quantum optics, in particular the
polarising beam splitter (PBS for short). We formalise the syntax and the
semantics of the PBS-diagrams, and we equip the language with an equational
theory, which is proved to be sound and complete: two diagrams are representing
the same quantum evolution if and only if one can be transformed into the other
using the rules of the PBS-calculus. Moreover, we show that the equational
theory is minimal. Finally, we consider applications like the implementation of
controlled permutations and the unrolling of loops.


  The optimal operation of electrical energy systems by solving a security
constrained optimal power flow (SCOPF) problem is still a challenging research
aspect. Especially, for conventional optimization methods like sequential
quadratic constrained quadratic programming (SQCQP) the formulation of the
incremental control variables like in-phase and quadrature voltage controlled
transformers in a solver suitable way is complex. Compared to this, the
implementation of these control variables within heuristic approaches like the
particle swarm optimization (PSO) is simple but problem specific adaptations of
the classic PSO algorithm are necessary to avoid an unfortunate swarm behavior
and local convergence in bad results. The objective of this paper is to
introduce a SQCQP and a modified PSO approach in detail to solve the SCOPF
problem adequately under consideration of flexible incremental in-phase and
quadrature transformers tap sets and to compare and benchmark the results of
both approaches for an adapted IEEE 118-bus system. The casestudy shows that
both approaches lead to suitable results of the SCOPF with individual
advantages of the SQCQP concerning the quality and the reproducibility of the
results while the PSO lead to faster solutions when the complexity of the
investigation scenario increases.


  Nucleation is generally viewed as a structural fluctuation that passes a
critical size to eventually become a stable emerging new phase. However, this
concept leaves out many details, such as changes in cluster composition and
competing pathways to the new phase. In this work, both experimental and
computer modeling studies are used to understand the cluster composition and
pathways. Monte Carlo and molecular dynamics approaches are used to analyze the
thermodynamic and kinetic contributions to the nucleation landscape in barium
silicate glasses. Experimental techniques examine the resulting polycrystals
that form. Both the modeling and experimental data indicate that a silica rich
core plays a dominant role in the nucleation process.