  Guided by the theory of graph limits, we investigate a variant of the cut
metric for limit objects of sequences of discrete probability distributions.
Apart from establishing basic results, we introduce a natural operation called
{\em pinning} on the space of limit objects and show how this operation yields
a canonical cut metric approximation to a given probability distribution akin
to the weak regularity lemma for graphons. We also establish the cut metric
continuity of basic operations such as taking product measures.


  This paper attempts to obtain necessary and sufficient conditions to solve
the parabolic Anderson model with fractional Gaussian noises:
$\frac{\partial}{\partial t}u(t,x)=\frac{1}{2}\Delta
u(t,x)+u(t,x)\dot{W}(t,x)$, where $ {W}(t,x)$ is the fractional Brownian field
with temporal Hurst parameter $H_0\in [1/2, 1) $ and spatial Hurst parameters
$H$ $ =(H_1, \cdots, H_d)$ $ \in (0, 1)^d$, and $\dot{W}(t,x)=\frac{\partial
^{d+1}}{\partial t \partial x_1 \cdots \partial x_d}W(t,x)$. When $d=1$ and
when $(H_0,H)\in(\frac 12,1)\times(\frac 1{20},\frac 12)$ we show that the
condition $2H_0+H>5/2$ is necessary and sufficient to ensure the existence of a
unique solution for the parabolic Anderson Model. When $d\ge 2$, we find the
necessary and sufficient condition on the Hurst parameters so that each chaos
of the solution candidate is square integrable.


  An open problem in applied mathematics is to predict interesting molecules
which are realistic targets for chemical synthesis. In this paper, we use a
spin Hamiltonian-type model to predict molecular magnets (MMs) with magnetic
moments that are intrinsically robust under random shape deformations to the
molecule. Using the concept of convergence in probability, we show that for MMs
in which all spin centers lie in-plane and all spin center interactions are
ferromagnetic, the total spin of the molecule is a `weak topological invariant'
when the number of spin centers is sufficiently large. By weak topological
invariant, we mean that the total spin of the molecule only depends upon the
arrangement of spin centers in the molecule, and is unlikely to change under
shape deformations to the molecule. Our calculations show that only between 20
and 50 spin centers are necessary for the total spin of these MMs to be a weak
topological invariant. The robustness effect is particularly enhanced for 2D
ferromagnetic MMs that possess a small number of spin rings in the structure.


  In this paper, we obtain various conditions on the parameters $a,\, b,\, c\,,
d$ and $e$ for which the hypergeometric functions $z\,_3F_2(a,b,c;d,e;z)$ to be
in the class of all close-to-convex function with respect to some well known
convex functions.


  A popular Bayesian nonparametric approach to survival analysis consists in
modeling hazard rates as kernel mixtures driven by a completely random measure.
In this paper we derive asymptotic results for linear and quadratic functionals
of such random hazard rates. In particular, we prove central limit theorems for
the cumulative hazard function and for the path-second moment and path-variance
of the hazard rate. Our techniques are based on recently established criteria
for the weak convergence of single and double stochastic integrals with respect
to Poisson random measures. We illustrate our results by considering specific
models involving kernels and random measures commonly exploited in practice.


  Spectral density estimation is a core problem of system identification, which
is an important research area of system control and signal processing. There
have been numerous results on the design of spectral density estimators.
However to our best knowledge, quantitative error analyses of the spectral
density estimation have not been proposed yet. In real practice, there are two
main factors which induce errors in the spectral density estimation, including
the external additive noise and the limited number of samples. In this paper,
which is a very preliminary version, we first consider a univariate spectral
density estimator using covariance lags. The estimation task is performed by a
convex optimization scheme, and the covariance lags of the estimated spectral
density are exactly as desired, which makes it possible for quantitative error
analyses such as to derive tight error upper bounds. We analyze the errors
induced by the two factors and propose upper and lower bounds for the errors.
Then the results of the univariate spectral estimator are generalized to the
multivariate one.


  We find a family of exact solutions to the Einstein-Maxwell equations for
rotating cylindrically symmetric distributions of a perfect fluid with the
equation of state $p = w\rho$ ($|w| < 1$), carrying a circular electric current
in the angular direction. This current creates a magnetic field along the $z$
axis. Some of the solutions describe geometries resembling that of Melvin's
static magnetic universe and contain a regular symmetry axis, while some others
(in the case $w > 0$) describe traversable wormhole geometries which do not
contain a symmetry axis. Unlike Melvin's solution, those with rotation and a
magnetic field cannot be vacuum and require a current. The wormhole solutions
admit matching with flat-space regions on both sides of the throat, thus
forming a cylindrical wormhole configuration potentially visible for distant
observers residing in flat or weakly curved parts of space. The thin shells,
located at junctions between the inner (wormhole) and outer (flat) regions,
consist of matter satisfying the Weak Energy Condition under a proper choice of
the free parameters of the model, and thus we obtain new examples of
phantom-free wormhole models in general relativity. In the limit $w \to 1$, the
magnetic field tends to zero, and the wormhole model tends to the one obtained
previously, where the source of gravity is stiff matter with the equation of
state $p = \rho$.


  We consider the problem of realizing a group as the fundamental group of a
graph of groups where the vertex groups are restricted to certain classes (for
example, coming from a certain finite list of groups, or having bounded
geometric rank). We show how this places restrictions on the possible groups
that can be realized and we give a topological application of our results to
the problem of constructing manifolds from a finite set of "building blocks".


  An algorithm is given to factor an integer with $N$ digits in $\ln^m N$
steps, with $m$ approximately 4 or 5. Textbook quadratic sieve methods are
exponentially slower. An improvement with the aid of an a particular function
would provide a further exponential speedup.


  In this paper, we introduce the first large vocabulary speech recognition
system (LVSR) for the Central Kurdish language, named Jira. The Kurdish
language is an Indo-European language spoken by more than 30 million people in
several countries, but due to the lack of speech and text resources, there is
no speech recognition system for this language. To fill this gap, we introduce
the first speech corpus and pronunciation lexicon for the Kurdish language.
Regarding speech corpus, we designed a sentence collection in which the ratio
of di-phones in the collection resembles the real data of the Central Kurdish
language. The designed sentences are uttered by 576 speakers in a controlled
environment with noise-free microphones (called AsoSoft Speech-Office) and in
Telegram social network environment using mobile phones (denoted as AsoSoft
Speech-Crowdsourcing), resulted in 43.68 hours of speech. Besides, a test set
including 11 different document topics is designed and recorded in two
corresponding speech conditions (i.e., Office and Crowdsourcing). Furthermore,
a 60K pronunciation lexicon is prepared in this research in which we faced
several challenges and proposed solutions for them. The Kurdish language has
several dialects and sub-dialects that results in many lexical variations. Our
methods for script standardization of lexical variations and automatic
pronunciation of the lexicon tokens are presented in detail. To setup the
recognition engine, we used the Kaldi toolkit. A statistical tri-gram language
model that is extracted from the AsoSoft text corpus is used in the system.
Several standard recipes including HMM-based models (i.e., mono, tri1, tr2,
tri2, tri3), SGMM, and DNN methods are used to generate the acoustic model.
These methods are trained with AsoSoft Speech-Office and AsoSoft
Speech-Crowdsourcing and a combination of them. The best performance achieved
by the SGMM acoustic model which results in 13.9% of the average word error
rate (on different document topics) and 4.9% for the general topic.


  In this paper, we establish a mathematical duality between utility transforms
and probability distortions. These transforms play a central role in decision
under risk by forming the foundation for the classic theories of expected
utility, dual utility, and rank-dependent utility. Our main results establish
that probability distortions are characterized by commutation with utility
transforms, and utility transforms are characterized by commutation with
probability distortions. These results require no additional conditions, and
hence each class can be axiomatized with only one property. Moreover, under
monotonicity, rank-dependent utility transforms can be characterized by set
commutation with either utility transforms or probability distortions.


  We find a consistency between two different approaches of hard diffraction,
namely the QCD dipole model and the Soft Colour Interaction approach. A
theoretical interpretation in terms of S-Matrix and perturbative QCD properties
in the small $x_{Bj}$ regime is proposed.


  The article mainly introduces preprocessing algorithms for solving linear
equation systems. This algorithm uses three algorithms as inner iterations,
namely RPCG algorithm, ADI algorithm, and Kaczmarz algorithm. Then, it uses
BA-GMRES as an outer iteration to solve the linear equation system. These three
algorithms can indirectly generate preprocessing matrices, which are used for
solving equation systems. In addition, we provide corresponding convergence
analysis and numerical examples. Through numerical examples, we demonstrate the
effectiveness and feasibility of these preprocessing methods. Furthermore, in
the Kaczmarz algorithm, we introduce both constant step size and adaptive step
size, and extend the parameter range of the Kaczmarz algorithm to
$\alpha\in(0,\infty)$. We also study the solution rate of linear equation
systems using different step sizes. Numerical examples show that both constant
step size and adaptive step size have higher solution efficiency than the
solving algorithm without preprocessing.


  An electrical current that flows across individual atoms or molecules can
generate exotic quantum-based behavior, from memristive effects to Coulomb
blockade and the promotion of quantum excited states. These fundamental effects
typically appear one at a time in model junctions built using atomic tip or
lateral techniques. So far, however, a viable industrial pathway for such
discrete state devices has been lacking. Here, we demonstrate that a
commercialized device platform can serve as this industrial pathway for quantum
technologies. We have studied magnetic tunnel junctions with a MgO barrier
containing C atoms. The paramagnetic localized electrons due to individual C
atoms generate parallel nanotransport paths across the micronic device as
deduced from magnetotransport experiments. Coulomb blockade effects linked to
tunnelling magnetoresistance peaks can be electrically controlled, leading to a
persistent memory effect. Our results position MgO tunneling spintronics as a
promising platform to industrially implement quantum technologies.


  We present explicit, analytical heating formulas that predict the heating
rates of spherical, nonneutral plasmas stored in a Paul trap as a function of
cloud size $S$, particle number $N$, and Paul-trap control parameter $q$ in the
low-temperature regime close to the cloud $\rightarrow$ crystal phase
transition. We find excellent agreement between our analytical heating formulas
and detailed, time-dependent molecular-dynamics simulations of the trapped
plasmas. We also present the results of our numerical solutions of a
temperature-dependent mean-field equation, which are consistent with our
numerical simulations and our analytical results. This is the first time that
analytical heating formulas are presented that predict heating rates with
reasonable accuracy, uniformly for all $S$, $N$, and $q$.


  Experimental 21 cm cosmology aims to detect the formation of the first stars
during the cosmic dawn and the subsequent epoch of reionization by utilizing
the 21 cm hydrogen line transition. While several experiments have published
results that begin to constrain the shape of this signal, a definitive
detection has yet to be achieved. In this paper, we investigate the influence
of uncertain antenna-sky interactions on the possibility of detecting the
signal. This paper aims to define the level of accuracy to which a simulated
antenna beam pattern is required to agree with the actual observing beam
pattern of the antenna to allow for a confident detection of the global 21 cm
signal. By utilising singular value decomposition, we construct a set of
antenna power patterns that incorporate minor, physically motivated variations.
We take the absolute mean averaged difference between the original beam and the
perturbed beam averaged over frequency ($\Delta D$) to quantifying this
difference, identifying the correlation between $\Delta D$ and antenna
temperature. To analyse the impact of $\Delta D$ on making a confident
detection, we utilize the REACH Bayesian analysis pipeline and compare the
Bayesian evidence $\log \mathcal{Z}$ and root-mean-square error for antenna
beams of different $\Delta D$ values. Our calculations suggest that achieving
an agreement between the original and perturbed antenna power pattern with
$\Delta D$ better than -35 dB is necessary for confident detection of the
global 21 cm signal. Furthermore, we discuss potential methods to achieve the
required high level of accuracy within a global 21~cm experiment.


  The spectral theory of the Fourier operator (non-truncated) is expounded. The
known construction of basis of eigenvectors consisting of the Hermite functions
is presented. The detail description of the eigenspaces in the spirit of a work
by Hardy and Titchmarsh is done.


  Any 4d theory possessing $\mathcal{N}=1$ supersymmetry admits a so called
$\mathcal{S}$-multiplet, containing the conserved energy-momentum tensor and
supercurrent. When a defect is introduced into such a theory, the
$\mathcal{S}$-multiplet receives contributions localised on the defect, which
indicate the breaking of some translation symmetry and consequently also some
supersymmetries. We call this the defect multiplet. We classify such terms
corresponding to half-BPS defects which can be either three-dimensional,
preserving 3d $\mathcal{N}=1$, or two-dimensional, preserving
$\mathcal{N}=(0,2)$. The new terms localised on the defect furnish multiplets
of the reduced symmetry and give rise to the displacement operator.


  The transmitter optimization (i.e., steering vectors and power allocation)
for a MISO Broadcast Channel (MISO-BC) subject to general linear constraints is
considered. Such constraints include, as special cases, the sum power, the
per-antenna or per-group-of-antennas power, and "forbidden interference
direction" constraints. We consider both the optimal dirty-paper coding and the
simple suboptimal linear zero-forcing beamforming strategies, and provide
numerically efficient algorithms that solve the problem in its most general
form. As an application, we consider a multi-cell scenario with partial cell
cooperation, where each cell optimizes its precoder by taking into account
interference constraints on specific users in adjacent cells. The effectiveness
of the proposed methods is evaluated in a simple system scenario including two
adjacent cells, under different fairness criteria that emphasize the bottleneck
role of users near the cell "boundary". Our results show that "active"
Inter-Cell Interference (ICI) mitigation outperforms the conventional "static"
ICI mitigation based on fractional frequency reuse.


  If gamma ray bursts produce a total energy of 10^54 ergs and this energy is
concentrated on the high energy tail of the spectrum E> 1 TeV, then they may
account for the observed diffuse extragalactic gamma ray emission for energies
> 100 MeV. Such an energy could be released if the GRB's are produced by the
burning of the total mass of a neutron star in a phase transition which
violates baryon number.


  We define lifting properties for universal algebras, which we study in this
general context and then particularize to various such properties in certain
classes of algebras. Next we focus on residuated lattices, in which we
investigate lifting properties for Boolean and idempotent elements modulo
arbitrary, as well as specific kinds of filters. We give topological
characterizations to the lifting property for Boolean elements and several
properties related to it, many of which we obtain by means of the reticulation.


  In his recent Comments E. Shuryak reiterates old, unfortunately misleading
arguments in favor of deconfined Quark-Gluon Plasma (QGP) immediately above the
chiral restoration pseudocritical temperature. In a Comment devoted to our view
of QCD at high temperatures he does not address and even mention the essence of
our arguments. In recent years a new "hidden" symmetry in QCD was discovered.
It is a symmetry of the electric sector of QCD, that is higher than the chiral
symmetry of the QCD Lagrangian as the whole. This symmetry was clearly observed
above T_c in spatial correlators and very recently also in time correlators.
The latter correlators are directly related to observable spectral density.
Then in a model-independent way we conclude that degrees of freedom in QCD
above T_c, but below roughly 3T_c, are chirally symmetric quarks bound by the
chromoelectric field into color-singlet compounds without the chromomagnetic
effects. This regime of QCD has been referred to as a Stringy Fluid since such
objects are very reminiscent of strings.At higher temperatures there is a very
smooth transition to the partonic degrees of freedom, i.e. to the QGP regime.
Here we will address some of the points made by Shuryak.


  Hereditarily non uniformly perfect (HNUP) sets were introduced by Stankewitz,
Sugawa, and Sumi in \cite{SSS} who gave several examples of such sets based on
Cantor set-like constructions using nested intervals. We exhibit a class of
examples in non-autonomous iteration where one considers compositions of
polynomials from a sequence which is in general allowed to vary. In particular,
we give a sharp criterion for when Julia sets from our class will be HNUP and
we show that the maximum possible Hausdorff dimension of $1$ for these Julia
sets can be attained. The proof of the latter considers the Julia set as the
limit set of a non-autonomous conformal iterated function system and we
calculate the Hausdorff dimension using a version of Bowen's formula given in
the paper by Rempe-Gillen and Urb\'{a}nski \cite{RU}.


  How much information do we need about a process' past to faithfully simulate
its future? The statistical complexity is a prominent quantifier of structure
for stochastic processes. Quantum machines, however, can simulate classical
stochastic processes while storing significantly less information than their
optimal classical counterparts. This implies qualitative divergences between
classical and quantum statistical complexity. Here, we develop error-tolerant
techniques to witness such divergences, enabling us to account for the
inevitable imperfections in realising quantum stochastic simulators with
present-day quantum technology. We apply these tools to experimentally verify
the quantum memory advantage in simulating an Ising spin chain, even when
accounting for experimental distortion. This then leads us to observe a
recently conjectured effect, the ambiguity of simplicity$\unicode{x2013}$the
notion that the relative complexity of two different processes can depend on
whether we model the process using classical or quantum means of information
processing.


  In this paper, the SIR dynamics is extended by considering another
compartmental which represents hospitalization of the critical cases. So a
system of differential equations with four blocks is considered when there is
intensive care unit (ICU) to cure critical cases. Outgoing rate of survived
infected individuals is divided into $nI$ and $\frac{bI}{I+b}$. The second term
represents the rate of critical cases who enter ICUs. It is proved that there
are forward, backward and Hopf bifurcations in different regimes of parameters.


  Progress in the development of techniques for the construction of multiuser
quantum communications networks is reviewed in light of the plans for an EU
quantum communications infrastructure (EU QCI). Quantum key distribution
networks may be classified as trusted node; quantum
repeater-entanglement-swapping based; point-to-multipoint based on passive beam
splitters, active optical switchers or WDM; high dimensional-multipartite
entanglement and flexible reconfigurable multipartite networks. Both satellite
and terrestrial implementations are possible and ore both planned for EU QCI;
their relative merits are discussed. Current technology falls short in several
respects of what is required to address use cases well. Bit rates as a function
of distance are currently limited by the characteristics of available devices
and are an order of magnitude or more below the theoretical bounds. Non-ideal
device behaviour can open loopholes for side-channel attacks. Limited range
constrains network geometry. New techniques are being developed to overcome
these problems. The more sophisticated schemes depend on ongoing advances in
the generation and distribution of entanglement. Particularly promising are the
measurement device independent protocol, which eliminates photon-detector
related security weaknesses, and the twin-field protocol, which uses similar
techniques to extend range, in principle even beyond previously accepted
theoretical bounds. Agreement of keys between more than two users can be
accomplished classically after pairwise quantum key exchange but direct quantum
multipartite agreement using may offer advantages. The same applies to secret
sharing. Practical quantum repeaters, to eliminate the need for trusted nodes,
are closer to being realised due to recent progress in optical memories.


  Various samples of sodium cobalt oxyhydrate with relatively large amounts of
Na$^{+}$ ions were synthesized by a modified soft-chemical process in which a
NaOH aqueous solution was added in the final step of the procedure. From these
samples, a superconducting phase diagram was determined for a section of a
cobalt valence of $\sim$+3.48, which was compared with a previously obtained
one of $\sim$+3.40. The superconductivity was significantly affected by the
isovalent exchanger of Na$^{+}$ and H$_{3}$O$^{+}$, rather than by variation of
Co valence, suggesting the presence of multiple kinds of Fermi surface.
Furthermore, the high-field magnetic susceptibility measurements for one sample
up to 30 T indicated an upper critical field much higher than the Pauli limit
supporting the validity of the spin-triplet pairing mechanism.


  In this sequel to [arXiv:1412.4114], we prove an $L^{d/2}$ energy gap result
for Yang-Mills connections on principal $G$-bundles, $P$, over arbitrary,
closed, Riemannian, smooth manifolds of dimension $d\geq 2$. We apply our
version of the Lojasiewicz-Simon gradient inequality [arXiv:1409.1525,
arXiv:1510.03815] to remove a positivity constraint on a combination of the
Ricci and Riemannian curvatures in a previous $L^{d/2}$-energy gap result due
to Gerhardt (2010) and a previous $L^\infty$-energy gap result due to
Bourguignon, Lawson, and Simons (1981, 1979), as well as an $L^2$-energy gap
result due to Nakajima (1987) for a Yang-Mills connection over the sphere,
$S^d$, but with an arbitrary Riemannian metric. The main correction in this
version involves replacement of the role of Corollary 4.3 due to Uhlenbeck
(1985) and Theorem 5.1 due to the author in the published version of this
article at http://dx.doi.org/10.1016/j.aim.2017.03.023 by that of Theorems 1
and 9 due to the author in arXiv:1906.03954.


  We formulate conditions under which the asymptotically expanded spectral
action on an almost commutative manifold is renormalizable as a
higher-derivative gauge theory. These conditions are of graph theoretical
nature, involving the Krajewski diagrams that classify such manifolds. This
generalizes our previous result on (super)renormalizability of the
asymptotically expanded Yang-Mills spectral action to a more general class of
particle physics models that can be described geometrically in terms of a
noncommutative space. In particular, it shows that the asymptotically expanded
spectral action which at lowest order gives the Standard Model of elementary
particles is renormalizable.


  We have observed a common problem of solving for the marginal covariance of
parameters introduced in new observations. This problem arises in several
situations, including augmenting parameters to a Kalman filter, and computing
weight for relative pose constraints. To handle this problem, we derive a
solution in a least squares sense. The solution is applied to the above two
instance situations and verified by independently reported results.


  This study presents a basin wide assessment about the spatio-temporal
variability of streamflows in Ecuador for the period 1979-2015. The influence
of the tropical Pacific sea surface temperature (SST) on stremaflow
variariability from February to April (FMA) period, as the months showing
maximum stramflow for the wet season in Ecuador, and from the June to August
(JJA), correspondign to the dry season, was analysed. First, a long-term trend
analysis was carried out by applying the Sen's slope estimator and the
Mann-Kendall test to monthly streamflow data from 45 gaging stations located in
different basins across Ecuador. While the coastal region showed the highest
generalized positive trends from July to January, the results for the Pacific
Andean area suggested a strengthening of the seasonality, presenting an overall
increase in the streamflow for all months except August, September and October,
which showed negative trends. Second, a singular-value decomposition (SVD) was
applied in order to find the main coupled variability patterns between the FMA
streamflow and the quasi-coetaneous SST (December-February, DJF) and between
the JJA streamflow and the coetaneous SST. The results revealed two main
coupled modes for DJF SST/FMA streamflow, the first associated with the
canonical El Ni\~no and the second with El Ni\~no Modoki. The latter exerted a
major influence on FMA streamflow over most of Ecuador. For JJA streamflow,
however, the pattern associated with the traditional El Ni\~no was even more
relevant. These results establish the foundations for streamflow modelling in
Ecuador based on the Pacific SST, showing the strong response of the
streamflows to different types of El Ni\~no events


  We report the first demonstration of a phonon-mediated silicon detector
technology that provides a primary phonon measurement in a low-voltage region,
and a simultaneous indirect measurement of the ionization signal through
Neganov-Trofimov-Luke amplification in a high voltage region, both in a
monolithic crystal. We present characterization of charge and phonon transport
between the two stages of the detector and the resulting background
discrimination capability at low energies. This new detector technology has the
potential to significantly enhance the sensitivity of dark matter and coherent
neutrino scattering experiments beyond the capabilities of current technologies
that have limited discrimination at low energies.


  CrCl3 is a layered insulator that undergoes a crystallographic phase
transition below room temperature and orders antiferromagnetically at low
temperature. Weak van der Waals bonding between the layers and ferromagnetic
in-plane magnetic order make it a promising material for obtaining atomically
thin magnets and creating van der Waals heterostructures. In this work we have
grown crystals of CrCl3, revisited the structural and thermodynamic properties
of the bulk material, and explored mechanical exfoliation of the crystals. We
find two distinct anomalies in the heat capacity at 14 and 17 K confirming that
the magnetic order develops in two stages on cooling, with ferromagnetic
correlations forming before long range antiferromagnetic order develops between
them. This scenario is supported by magnetization data. A magnetic phase
diagram is constructed from the heat capacity and magnetization results. We
also find an anomaly in the magnetic susceptibility at the crystallographic
phase transition, indicating some coupling between the magnetism and the
lattice. First principles calculations accounting for van der Waals
interactions also indicate spin-lattice coupling, and find multiple nearly
degenerate crystallographic and magnetic structures consistent with the
experimental observations. Finally, we demonstrate that monolayer and few-layer
CrCl3 specimens can be produced from the bulk crystals by exfoliation,
providing a path for the study of heterostructures and magnetism in ultrathin
crystals down to the monolayer limit.


  If one introduces causality into quantum cosmology, then the prescription for
the no-boundary universe should be revised. We show that the thermodymanic
arrow of time associated with the perturbation modes should be reversed at the
maximum expansion for the oscillating Hawking model. To an observer equipped
with the time arrow, the universe will terminate its evolution after an half
cycle.


  The total mass, the Witten type gauge conditions and the spectral properties
of the Sen-Witten and the 3-surface twistor operators in closed universes are
investigated. It has been proven that a recently suggested expression ${\tt M}$
for the total mass density of closed universes is vanishing if and only if the
spacetime is flat with toroidal spatial topology; it coincides with the first
eigenvalue of the Sen-Witten operator; and it is vanishing if and only if
Witten's gauge condition admits a non-trivial solution.
  Here we generalize slightly the result above on the zero-mass configurations:
${\tt M}=0$ if and only if the spacetime is holonomically trivial with toroidal
spatial topology. Also, we show that the multiplicity of the eigenvalues of the
(square of the) Sen-Witten operator is at least two, and a potentially viable
gauge condition is suggested. The monotonicity properties of ${\tt M}$ through
the examples of closed Bianchi I and IX cosmological spacetimes are also
discussed. A potential spectral characterization of these cosmological
spacetimes, in terms of the spectrum of the Riemannian Dirac operator and the
Sen-Witten and the 3-surface twistor operators, is also indicated.


  We study the stability of a vector field associated to a nearly-integrable
Hamiltonian dynamical system to which a dissipation is added. Such a system is
governed by two parameters, named the perturbing and dissipative parameters,
and it depends on a drift function. Assuming that the frequency of motion
satisfies some resonance assumption, we investigate the stability of the
dynamics, and precisely the variation of the action variables associated to the
conservative model. According to the structure of the vector field, one can
find linear and exponential stability times, which are established under
smallness con- ditions on the parameters. We also provide some applications to
concrete examples, which exhibit a linear or exponential stability behavior.


  Tripartite mutual information (TMI) is an efficient observable to quantify
the ability of scrambler for unitary time-evolution operator with quenched
many-body Hamiltonian. In this paper, we give numerical demonstrations of the
TMI in disorder-free (translational invariant) spin models with 3-body and
4-body multiple-spin interactions. The dynamical behavior of the TMI of these
models does {\it not} exhibit linear light-cone for sufficiently strong
interactions. In early-time evolution, the TMI displays distinct negative
increase behavior fitted by a logarithmic-like function. This is in contrast to
the conventional linear light-cone behavior present in the XXZ model and its
near integrable vicinity. The late-time evolution of the TMI in finite-size
systems is also numerically investigated. The multiple-spin interactions make
the system nearly integrable and weakly suppress the spread of information and
scrambling. The observation of the late-time value of the TMI indicates that
the scrambling nature of the system changes by interactions and this change can
be characterized by a phase-transition-like behavior of the TMI, reflecting the
system's integrability and breaking of eigenstate thermalization hypothesis.


  When a population exhibits heterogeneity, we often model it via a finite
mixture: decompose it into several different but homogeneous subpopulations.
Contemporary practice favors learning the mixtures by maximizing the likelihood
for statistical efficiency and the convenient EM-algorithm for numerical
computation. Yet the maximum likelihood estimate (MLE) is not well defined for
the most widely used finite normal mixture in particular and for finite
location-scale mixture in general. We hence investigate feasible alternatives
to MLE such as minimum distance estimators. Recently, the Wasserstein distance
has drawn increased attention in the machine learning community. It has
intuitive geometric interpretation and is successfully employed in many new
applications. Do we gain anything by learning finite location-scale mixtures
via a minimum Wasserstein distance estimator (MWDE)? This paper investigates
this possibility in several respects. We find that the MWDE is consistent and
derive a numerical solution under finite location-scale mixtures. We study its
robustness against outliers and mild model mis-specifications. Our moderate
scaled simulation study shows the MWDE suffers some efficiency loss against a
penalized version of MLE in general without noticeable gain in robustness. We
reaffirm the general superiority of the likelihood based learning strategies
even for the non-regular finite location-scale mixtures.


  The ultrafast response of metals to light is governed by intriguing
non-equilibrium dynamics involving the interplay of excited electrons and
phonons. The coupling between them gives rise to nonlinear diffusion behavior
on ultrashort timescales. Here, we use scanning ultrafast thermo-modulation
microscopy to image the spatio-temporal hot-electron diffusion in a thin gold
film. By tracking local transient reflectivity with 20 nm and 0.25 ps
resolution, we reveal two distinct diffusion regimes, consisting of an initial
rapid diffusion during the first few picoseconds after optical excitation,
followed by about 100-fold slower diffusion at longer times. We simulate the
thermo-optical response of the gold film with a comprehensive three-dimensional
model, and identify the two regimes as hot-electron and phonon-limited thermal
diffusion, respectively.


  Also recently, exciting strides forward have been made in the area of image
restoration, particularly for image denoising and single image
super-resolution. Deep learning techniques contributed to this significantly.
The top methods differ in their formulations and assumptions, so even if their
average performance may be similar, some work better on certain image types and
image regions than others. This complementarity motivated us to propose a novel
3D convolutional fusion (3DCF) method. Unlike other methods adapted to
different tasks, our method uses the exact same convolutional network
architecture to address both image denois- ing and single image
super-resolution. As a result, our 3DCF method achieves substantial
improvements (0.1dB-0.4dB PSNR) over the state-of-the-art methods that it
fuses, and this on standard benchmarks for both tasks. At the same time, the
method still is computationally efficient.


  A potential function is presented for describing a system of flexible H$_2$O
molecules based on the single center multipole expansion (SCME) of the
electrostatic interaction. The model, referred to as SCME/f, includes the
variation of the molecular quadrupole moment as well as the dipole moment with
changes in bond length and angle so as to reproduce results of high level
electronic structure calculations. The multipole expansion also includes fixed
octupole and hexadecapole moments, as well as anisotropic dipole-dipole,
dipole-quadrupole and quadrupole-quadrupole polarizability tensors. The model
contains five adjustable parameters related to the repulsive interaction and
damping functions in the electrostatic and dispersion interactions. Their
values are adjusted to reproduce the lowest energy isomers of small clusters,
(H$_2$O)$_n$ with $n=2-6$, as well as measured properties of the ice Ih
crystal. Subsequent calculations of the energy difference between the various
isomer configurations of the clusters show that SCME/f gives good agreement
with results of electronic structure calculations and represents a significant
improvement over the previously presented rigid SCME potential function.
Analysis of the vibrational frequencies of the clusters and structural
properties of ice Ih crystal show the importance of accurately describing the
variation of the quadrupole moment with molecular structure.


  Introducing an extended Lie derivative along the dual of A, the three-form
field of d=11 supergravity, the full diffeomorphism algebra of d=11
supergravity is presented. This algebra suggests a new formulation of the
theory, where the three-form field A is replaced by bivector B^{ab}, bispinor
B^{\alpha\beta}, and spinor-vector \eta^{a\beta} one-forms. Only the bivector
one-form B^{ab} is propagating, and carries the same degrees of freedom of the
three-form in the usual formulation, its curl \Dcal_{[\mu} B^{ab}_{\nu]} being
related to the F_{\mu \nu a b} curl of the three-form. The other one-forms are
auxiliary, and the transformation rules on all the fields close on the
equations of motion of d=11 supergravity.


  The primary contribution of this paper is to give a formal, categorical
treatment to Penrose's abstract tensor notation, in the context of traced
symmetric monoidal categories. To do so, we introduce a typed, sum-free version
of an abstract tensor system and demonstrate the construction of its associated
category. We then show that the associated category of the free abstract tensor
system is in fact the free traced symmetric monoidal category on a monoidal
signature. A notable consequence of this result is a simple proof for the
soundness and completeness of the diagrammatic language for traced symmetric
monoidal categories.


  We present a model of optimal training of a rational, sluggish agent. A
trainer commits to a discrete-time, finite-state Markov process that governs
the evolution of training intensity. Subsequently, the agent monitors the state
and adjusts his capacity at every period. Adjustments are incremental: the
agent's capacity can only change by one unit at a time. The trainer's objective
is to maximize the agent's capacity - evaluated according to its lowest value
under the invariant distribution - subject to an upper bound on average
training intensity. We characterize the trainer's optimal policy, and show how
stochastic, time-varying training intensity can dramatically increase the
long-run capacity of a rational, sluggish agent. We relate our theoretical
findings to "periodization" training techniques in exercise physiology.


  In this paper we review the asymptotic matching conjectures for $r$-regular
bipartite graphs, and their connections in estimating the monomer-dimer
entropies in $d$-dimensional integer lattice and Bethe lattices. We prove new
rigorous upper and lower bounds for the monomer-dimer entropies, which support
these conjectures. We describe a general construction of infinite families of
$r$-regular tori graphs and give algorithms for computing the monomer-dimer
entropy of density $p$, for any $p\in [0,1]$, for these graphs. Finally we use
tori graphs to test the asymptotic matching conjectures for certain infinite
$r$-regular bipartite graphs.


  We start by presenting the current status of a complex flavour conserving
two-Higgs doublet model. We will focus on some very interesting scenarios where
unexpectedly the light Higgs couplings to leptons and to b-quarks can have a
large pseudoscalar component with a vanishing scalar component. Predictions for
the allowed parameter space at end of the next run with a total collected
luminosity of $300 \, fb^{-1}$ and $3000 \, fb^{-1}$ are also discussed. These
scenarios are not excluded by present data and most probably will survive the
next LHC run. However, a measurement of the mixing angle $\phi_\tau$, between
the scalar and pseudoscalar component of the 125 GeV Higgs, in the decay $h \to
\tau^+ \tau^-$ will be able to probe many of these scenarios, even with low
luminosity. Similarly, a measurement of $\phi_t$ in the vertex $\bar t t h$
could help to constrain the low $\tan \beta$ region in the Type I model.


  We adopt the Chiellini integrability method to find the solutions of various
generalizations of the damped Milne-Pinney equations. In particular, we find
the solution of the damped Ermakov-Painlev\'e II equation and generalized
dissipative Milne-Pinney equation.


  In this work, we introduce a stochastic maximum principle (SMP) approach for
solving the reinforcement learning problem with the assumption that the
unknowns in the environment can be parameterized based on physics knowledge.
For the development of numerical algorithms, we shall apply an effective online
parameter estimation method as our exploration technique to estimate the
environment parameter during the training procedure, and the exploitation for
the optimal policy will be achieved by an efficient backward action learning
method for policy improvement under the SMP framework. Numerical experiments
will be presented to demonstrate that our SMP approach for reinforcement
learning can produce reliable control policy, and the gradient descent type
optimization in the SMP solver requires less training episodes compared with
the standard dynamic programming principle based methods.


  If the Galaxy contains ~10^{11}M_sol in cold gas clouds of ~Jovian mass and
\~AU size, these clouds will act as converging lenses for optical light,
magnifying background stars at a detectable rate. The resulting light curves
can resemble those due to gravitational lensing by a point mass, raising the
possibility that some of the events attributed to gravitational microlensing
might in fact be due to ``gaseous lensing''. During a lensing event, the lens
would impose narrow infrared and far-red H_2 absorption lines on the stellar
spectrum. Existing programs to observe gravitational microlensing, supplemented
by spectroscopy, can therefore be used to either detect such events or place
limits on the number of such gas clouds present in the Galaxy.


  In this paper we present generic properties of quantum transport in
mono-layer graphene. In the scheme of the Kubo-Geenwood formula, we compute the
square spreading of wave packets of a given energy with is directly related to
conductivity. As a first result, we compute analytically the time dependent
diffusion for pure graphene. In addition to the semi-classical term a second
term exists that is due to matrix elements of the velocity operator between
electron and hole bands. This term is related to velocity fluctuations i.e.
Zitterbewegung effect. Secondly, we study numerically the quantum diffusion in
graphene with simple vacancies and pair of neighboring vacancies (divacancies),
that simulate schematically oxidation, hydrogenation and other
functionalisations of graphene. We analyze in particular the time dependence of
the diffusion and its dependence on energy in relation with the electronic
structure. We compute also the mean free path and the semi-classical value of
the conductivity as a function of energy in the limit of small concentration of
defects.


  Super-luminous supernovae (SLSNe) are rare events defined as being
significantly more luminous than normal terminal stellar explosions. The source
of the extra powering needed to achieve such luminosities is still unclear.
Discoveries in the local Universe (i.e. $z<0.1$) are scarce, but afford dense
multi-wavelength observations. Additional low-redshift objects are therefore
extremely valuable. We present early-time observations of the type I SLSN
ASASSN-18km/SN~2018bsz. These data are used to characterise the event and
compare to literature SLSNe and spectral models. Host galaxy properties are
also analysed. Optical and near-IR photometry and spectroscopy were analysed.
Early-time ATLAS photometry was used to constrain the rising light curve. We
identified a number of spectral features in optical-wavelength spectra and
tracked their time evolution. Finally, we used archival host galaxy photometry
together with HII region spectra to constrain the host environment.
ASASSN-18km/SN~2018bsz is found to be a type I SLSN in a galaxy at a redshift
of 0.0267 (111 Mpc), making it the lowest-redshift event discovered to date.
Strong CII lines are identified in the spectra. Spectral models produced by
exploding a Wolf-Rayet progenitor and injecting a magnetar power source are
shown to be qualitatively similar to ASASSN-18km/SN~2018bsz, contrary to most
SLSNe-I that display weak/non-existent CII lines. ASASSN-18km/SN~2018bsz
displays a long, slowly rising, red 'plateau' of $>$26 days, before a steeper,
faster rise to maximum. The host has an absolute magnitude of --19.8 mag ($r$),
a mass of M$_{*}$ = 1.5$^{+0.08}_{-0.33}$ $\times$10$^{9}$ M$_{\odot}$ , and a
star formation rate of = 0.50$^{+2.22}_{-0.19}$ M$_{\odot}$ yr$^{-1}$. A nearby
HII region has an oxygen abundance (O3N2) of 8.31$\pm$0.01 dex.


  Stochastic sampling based trackers have shown good performance for abrupt
motion tracking so that they have gained popularity in recent years. However,
conventional methods tend to use a two-stage sampling paradigm, in which the
search space needs to be uniformly explored with an inefficient preliminary
sampling phase. In this paper, we propose a novel sampling-based method in the
Bayesian filtering framework to address the problem. Within the framework,
nearest neighbor field estimation is utilized to compute the importance
proposal probabilities, which guide the Markov chain search towards promising
regions and thus enhance the sampling efficiency; given the motion priors, a
smoothing stochastic sampling Monte Carlo algorithm is proposed to approximate
the posterior distribution through a smoothing weight-updating scheme.
Moreover, to track the abrupt and the smooth motions simultaneously, we develop
an abrupt-motion detection scheme which can discover the presence of abrupt
motions during online tracking. Extensive experiments on challenging image
sequences demonstrate the effectiveness and the robustness of our algorithm in
handling the abrupt motions.


  We propose a data-driven technique to automatically learn the uncertainty
sets in robust optimization. Our method reshapes the uncertainty sets by
minimizing the expected performance across a family of problems subject to
guaranteeing constraint satisfaction. Our approach is very flexible and can
learn a wide variety of uncertainty sets while preserving tractability. We
solve the constrained learning problem using a stochastic augmented Lagrangian
method that relies on differentiating the solutions of the robust optimization
problems with respect to the parameters of the uncertainty set. Due to the
nonsmooth and nonconvex nature of the augmented Lagrangian function, we apply
the nonsmooth conservative implicit function theorem to establish convergence
to a critical point, which is a feasible solution of the constrained problem
under mild assumptions. Using empirical process theory, we show finite-sample
probabilistic guarantees of constraint satisfaction for the resulting
solutions. Numerical experiments show that our method outperforms traditional
approaches in robust and distributionally robust optimization in terms of
out-of-sample performance and constraint satisfaction guarantees.


  We present a method for synthesizing naturally looking images of multiple
people interacting in a specific scenario. These images benefit from the
advantages of synthetic data: being fully controllable and fully annotated with
any type of standard or custom-defined ground truth. To reduce the
synthetic-to-real domain gap, we introduce a pipeline consisting of the
following steps: 1) we render scenes in a context modeled after the real world,
2) we train a human parsing model on the synthetic images, 3) we use the model
to estimate segmentation maps for real images, 4) we train a conditional
generative adversarial network (cGAN) to learn the inverse mapping -- from a
segmentation map to a real image, and 5) given new synthetic segmentation maps,
we use the cGAN to generate realistic images. An illustration of our pipeline
is presented in Figure 2. We use the generated data to train a multi-task model
on the challenging tasks of UV mapping and dense depth estimation. We
demonstrate the value of the data generation and the trained model, both
quantitatively and qualitatively on the CMU Panoptic Dataset.


  We investigate the effect of the Coulomb interaction on the applicability of
quantum gates on a system of two Coulomb-coupled quantum dots. We calculate the
fidelity for a single- and a two-qubit gate and the creation of Bell states in
the system. The influence of radiative damping is also studied. We find that
the application of quantum gates based on the Coulomb interaction leads to
significant input state-dependent errors which strongly depend on the Coulomb
coupling strength. By optimizing the Coulomb matrix elements via the material
and the external field parameters, error rates in the range of $10^{-3}$ can be
reached. Radiative dephasing is a more serious problem and typically leads to
larger errors on the order of $10^{-2}$ for the considered gates. In the
specific case of the generation of a maximally entangled Bell state, error
rates in the range of $10^{-3}$ can be achieved even in the presence of
radiative dephasing.


  We study mass and population imbalance effect on density (in-phase) and spin
(out-of-phase) collective modes in a two-component normal Fermi gas. By
calculating eigenmodes of the linearized Boltzmann equation as well as the
density/spin dynamic structure factor, we show that mass and population
imbalance effects offer a variety of collective mode crossover behaviors from
collisionless to hydrodynamic regimes. The mass imbalance effect shifts the
crossover regime to the higher-temperature, and a significant peak of the spin
dynamic structure factor emerges only in the collisionless regime. This is in
contrast to the case of mass and population balanced normal Fermi gases, where
the spin dynamic response is always absent. Although the population imbalance
effect does not shift the crossover regime, the spin dynamic structure factor
survives both in the collisionless and hydrodynamic regimes.


  The main topic of the paper is the construction of various explicit flat
families of border bases. To begin with, we cover the punctual Hilbert scheme
Hilb^\mu(A^n) by border basis schemes and work out the base changes. This
enables us to control flat families obtained by linear changes of coordinates.
Next we provide an explicit construction of the principal component of the
border basis scheme, and we use it to find flat families of maximal dimension
at each radical point. Finally, we connect radical points to each other and to
the monomial point via explicit flat families on the principal component.


  Exciton pulses transport excitation and entanglement adiabatically through
Rydberg aggregates, assemblies of highly excited light atoms, which are set
into directed motion by resonant dipole-dipole interaction. Here, we
demonstrate the coherent splitting of such pulses as well as the spatial
segregation of electronic excitation and atomic motion. Both mechanisms exploit
local nonadiabatic effects at a conical intersection, turning them from a
decoherence source into an asset. The intersection provides a sensitive knob
controlling the propagation direction and coherence properties of exciton
pulses. The fundamental ideas discussed here have general implications for
excitons on a dynamic network.


  We have studied the dark matter (DM) distribution in a approx 10^12 h^-1
M_sun mass halo extracted from a simulation consistent with the concordance
cosmology, where the physics regulating the transformation of gas into stars
was allowed to change producing galaxies with different morphologies. The
presence of baryons produces the concentration of the DM halo with respect to
its corresponding dissipationless run, but we found that this response does not
only depend on the amount of baryons gathered in the central region but also on
the way they have been assembled. DM and baryons affect each other in a complex
way so the formation history of a galaxy plays an important role on its final
total mass distribution. Supernova (SN) feedback regulates the star formation
and triggers galactic outflows not only in the central galaxy but also in its
satellites. Our results suggest that, as the effects of SN feedback get
stronger, satellites get less massive and can even be more easily disrupted by
dynamical friction, transferring less angular momentum. We found indications
that this angular momentum could be acquired not only by the outer part of the
DM halo but also by the inner ones and by the stellar component in the central
galaxy. The latter effect produces stellar migration which contributes to
change the inner potential well, probably working against further DM
contraction. As a consequence of the action of these processes, when the halo
hosts a galaxy with an important disc structure formed by smooth gas accretion,
it is more concentrated than when it hosts a spheroidal system which
experienced more massive mergers and interactions. (abridged)


  The possibility of meson condensation in stars and in heavy-ion collisions
has been discussed in the past. Here, we study whether rho meson condensation
($\rho^{-}$) can occur in very dense matter and determine the effect of strong
magnetic fields on this condensation. We find that rho meson condensates can
appear in the core of the neutron star assuming a rho mass which is reduced due
to in-medium effects. We find that the magnetic field has a non-negligible
effect in triggering condensation.


  In classical two-party computation, a trusted initializer who prepares
certain initial correlations, known as one-time tables, can help make the
inputs of both parties information-theoretically secure. We propose some
bipartite quantum protocols with possible aborts for approximately generating
such bipartite classical correlations with varying degrees of privacy, without
introducing a third party. Under some weak requirements for the parties, the
security level is nontrivial for use in bipartite computation. We show that the
security is sometimes dependent on the noise level, but we propose a method for
dealing with noise. The security is "forced security", which implies that the
probability that some useful one-time tables are generated can approach $1$ in
the noiseless case under quite weak assumptions about the parties, although the
protocols allow aborts. We show how to use the generated one-time tables to
achieve nontrivial information-theoretic security in generic two-party
classical or quantum computation tasks, including (interactive) quantum
homomorphic encryption. Our methods provide check-based implementations of some
no-signaling correlations, including the PR-box type, with the help of
communication which carry no information about the inputs in the generated
correlations.


  This paper addresses the air traffic flow management research problem of
determining reroute, ground delay and air delay for flights using stochastic
weather forecast information. The overall goal is to minimize system-wide
reroute and delay costs. This problem is a primary concern in United States and
especially in its northeastern region, and is also the key in enhancing the
performance of the new FAA Traffic Management Initiative called Collaborative
Trajectory Options Program (CTOP). In this work we present six stochastic
integer programming models, including two two-stage models and four multistage
models, which are based on a notable strong deterministic flight-by-flight
level traffic flow formulation and an aggregate Eulerian traffic flow
formulation. Our preliminary numerical results show that completely integer
solutions can be achieved from linear relaxation, for all proposed models and
for both no-route and reroute cases.


  Grand unified theory defined on higher-dimensional orbifolds provides a new
way to solve the hierarchy problem. In gauge theory on an orbifold many
different sets of boundary conditions imposed at orbifold fixed points (branes)
are related by large gauge transformations, forming an equivalent class of
boundary conditions. Thanks to the Hosotani mechanism the physics remains the
same in all theories in a given equivalent class, though the symmetry of
boundary conditions differs from each other. Quantum dynamics of Wilson line
phases rearranges the gauge symmetry. In the nonsupersymmetric SU(5) model the
presence of bulk fermions leads to the spontaneous breaking of color SU(3). In
the supersymmetric model with Scherk-Schwarz SUSY breaking, color SU(3) is
spontaneously broken even in the absence of bulk fermions if there are Higgs
multiplets.


  Let g be a semi-simple Lie algebra, and let g^ be the corresponding affine
Kac-Moody algebra. Consider the category of g^-modules at the critical level,
on which the action of the Iwahori subalgebra integrates to algebraic action of
the Iwahori subgroup I. We study the action on this category of the convolution
functors with the "central" sheaves on the affine flag scheme G((t))/I. We show
that each object of our category is an "eigen-module" with respect to these
functors. In order to prove this, we use the fusion product of modules over the
affine Kac-Moody algebra.


  After a brief historical survey, the paper introduces the notion of entropic
model sets (cut and project sets), and, more generally, the notion of
diffractive point sets with entropy. Such sets may be thought of as
generalizations of lattice gases. We show that taking the site occupation of a
model set stochastically results, with probabilistic certainty, in well-defined
diffractive properties augmented by a constant diffuse background. We discuss
both the case of independent, but identically distributed (i.i.d.) random
variables and that of independent, but different (i.e., site dependent) random
variables. Several examples are shown.


  Following ideas of Bloch, Esnault, and Kerz, the deformational part of
Grothendieck's variational Hodge conjecture is established for proper, smooth
schemes over $K[[t]]$, where $K$ is an algebraic extension of the rational
numbers. The main tool is a pro Hochschild-Kostant-Rosenberg theorem for
Hochschild homology.


  The effects of error propagation in the reproduction of diploid organisms are
studied within the populational genetics framework of the quasispecies model.
The dependence of the error threshold on the dominance parameter is fully
investigated. In particular, it is shown that dominance can protect the
wild-type alleles from the error catastrophe. The analysis is restricted to a
diploid analogue of the single-peaked landscape.


  Arbitrary representations of a commutative unital ($\ast$-)
$\mathbb{F}$-algebra $A$ as a subalgeba of $\mathbb{F}^X$ are considered, where
$\mathbb{F}=\mathbb{C}$ or $\mathbb{R}$ and $X\neq\emptyset$. The Gelfand
spectrum of $A$ is explained as a topological extension of $X$ where a seminorm
on the image of $A$ in $\mathbb{F}^X$ is present. It is shown that among all
seminormes, the $\sup$-norm is of special importance which reduces
$\mathbb{F}^X$ to $\ell^{\infty}(X)$. The Banach subalgebra of
$\ell^{\infty}(X)$ of all $\Sigma$-measurable bounded functions on $X$, is
studied for which $\Sigma$ is a $\sigma$-algebra of subsets of $X$. In
particular, we study lifting of positive measures from $(X, \Sigma)$ to the
Gelfand spectrum of this algebra and observe an unexpected shift in the support
of measures. In the case that $\Sigma$ is the Borel algebra of a topology, we
study the relation of the underlying topology of $X$ and the one of the Gelfand
spectrum.


  The intrinsically rectifying-resistive switching (IR-RS) has been regarded as
an effective way to address the crosstalk issue, due to the Schottky diodes
formed at the metal/oxide interfaces in the ON states to suppress the sneak
current at reverse biases. In this letter, we report for the first time another
type of IR-RS that is related to the built-in homojunction. The IR-RS study was
usually limited to macroscopic samples with micron-order pad-type electrodes,
while this work is on NiO nanodots fabricated with ultrathin
anodic-aluminum-oxide templates and acting as nanoscaled analogs of real
devices. The NiO nanodots show high storage density and high uniformity, and
the IR-RS behaviors are of good device performances in terms of retention,
endurance, switching ratio and rectification ratio. The feasibility of the
IR-RS for selection device-free memory application has been demonstrated, by
calculating the maximum crossbar array size under the worst-case scenario to be
3 Mbit.


  Dialogue state tracking (DST) aims at estimating the current dialogue state
given all the preceding conversation. For multi-domain DST, the data sparsity
problem is a major obstacle due to increased numbers of state candidates and
dialogue lengths. To encode the dialogue context efficiently, we utilize the
previous dialogue state (predicted) and the current dialogue utterance as the
input for DST. To consider relations among different domain-slots, the schema
graph involving prior knowledge is exploited. In this paper, a novel context
and schema fusion network is proposed to encode the dialogue context and schema
graph by using internal and external attention mechanisms. Experiment results
show that our approach can obtain new state-of-the-art performance of the
open-vocabulary DST on both MultiWOZ 2.0 and MultiWOZ 2.1 benchmarks.


  We present the photometric observations of blazars S5 0716+714 and 3C 273
with high temporal resolution (30--60s) in the $I$ or $R$ bands. The
observations were performed with a 1.02 m optical telescope from 2007 March 07
to 2012 May 16. The $F$-test, one-way analysis of variance (ANOVA) test, and
$z$-transformed discrete correlation function (ZDCF) cross-correlation zero lag
test are used to search for intra-day variability (IDV). Four and five reliable
IDVs survive three tests for S5 0716+714 and 3C 273, respectively. IDVs are
found for S5 0716+714 and 3C 273. A flare on 2008 May 08 has $\Delta I \approx$
0.06$\pm$0.01 mag in a duration of 0.54 hr for S5 0716+714. A flare on 2011 May
10 shows $\Delta R \approx$ 0.05$\pm$0.01 mag in a duration of 0.40 hr for 3C
273. Sharp dips appear on 2011 May 9 for 3C 273, and show $\Delta R \approx$
0.05$\pm$0.01 mag. Under the assumptions that the IDV is tightly connected to
black hole mass, $M_{\bullet}$, and that the flare durations are representative
of the minimum characteristic timescales, we can estimate upper bounds to
$M_{\bullet}$. In the case of the Kerr black holes, $M_{\bullet} \la 10^{8.91}
M_{\odot}$ and $M_{\bullet} \la 10^{9.02} M_{\odot}$ are given for S5 0716+714
and 3C 273, respectively. These mass measurements are consistent with those
measurements reported in the literatures. Also, we discuss the origins of
optical variations found in this work.


  Precise neutrino--nucleus interaction measurements in the sub-multi GeV
region are important to reduce the systematic uncertainty in future neutrino
oscillation experiments. Furthermore, the excess of ${\nu_e}$ interactions, as
a possible interpretation of the existence of a sterile neutrino has been
observed in such an energy region. The nuclear emulsion technique can measure
all the final state particles with low energy threshold for a variety of
targets (Fe, C, H${_2}$O, and so on). Its sub-$\mu$m position resolution allows
measurements of the ${\nu_e}$ cross-section with good electron/gamma separation
capability. We started a new experiment at J-PARC to study sub-multi GeV
neutrino interactions by introducing the nuclear emulsion technique. The J-PARC
T60 experiment has been implemented as a first step of such a project.
Systematic neutrino event analysis with full scanning data in the nuclear
emulsion detector was performed for the first time. The first neutrino event
detection and its analysis is described in this paper.


  Written language is a useful tool for non-visual creative activities like
writing essays and planning searches. This paper investigates the integration
of written language in to the visualization design process. We create the idea
of a 'writing rudder,' which acts as a guiding force or strategy for the
design. Via an interview study of 24 working visualization designers, we first
established that only a minority of participants systematically use writing to
aid in design. A second study with 15 visualization designers examined four
different variants of written rudders: asking questions, stating conclusions,
composing a narrative, and writing titles. Overall, participants had a positive
reaction; designers recognized the benefits of explicitly writing down
components of the design and indicated that they would use this approach in
future design work. More specifically, two approaches - writing questions and
writing conclusions/takeaways - were seen as beneficial across the design
process, while writing narratives showed promise mainly for the creation stage.
Although concerns around potential bias during data exploration were raised,
participants also discussed strategies to mitigate such concerns. This paper
contributes to a deeper understanding of the interplay between language and
visualization, and proposes a straightforward, lightweight addition to the
visualization design process.


  In an optical trap, the ground state of spin-1 Bosons such as $^{23}$Na,
$^{39}$K, and $^{87}$Rb can be either a ferromagnetic or a "polar" state,
depending on the scattering lengths in different angular momentum channel. The
collective modes of these states have very different spin character and spatial
distributions. While ordinary vortices are stable in the polar state, only
those with unit circulation are stable in the ferromagnetic state. The
ferromagnetic state also has coreless (or Skyrmion) vortices like those of
superfluid $^{3}$He-A. Current estimates of scattering lengths suggest that the
ground states of $^{23}$Na and $^{87}$Rb condensate are a polar state and a
ferromagnetic state respectively.


  Mayall II = G1 is one of the most luminous globular clusters (GCs) in M31.
Here, we determine its age and mass by comparing multicolor photometry with
theoretical stellar population synthesis models. Based on far- and
near-ultraviolet GALEX photometry, broad-band UBVRI, and infrared JHK_s 2MASS
data, we construct the most extensive spectral energy distribution of G1 to
date, spanning the wavelength range from 1538 to 20,000 A. A quantitative
comparison with a variety of simple stellar population (SSP) models yields a
mean age that is consistent with G1 being among the oldest building blocks of
M31 and having formed within ~1.7 Gyr after the Big Bang. Irrespective of the
SSP model or stellar initial mass function adopted, the resulting mass
estimates (of order $10^7 M_\odot$) indicate that G1 is one of the most massive
GCs in the Local Group. However, we speculate that the cluster's exceptionally
high mass suggests that it may not be a genuine GC. We also derive that G1 may
contain, on average, $(1.65\pm0.63)\times10^2 L_\odot$ far-ultraviolet-bright,
hot, extreme horizontal-branch stars, depending on the SSP model adopted. On a
generic level, we demonstrate that extensive multi-passband photometry coupled
with SSP analysis enables one to obtain age estimates for old SSPs to a similar
accuracy as from integrated spectroscopy or resolved stellar photometry,
provided that some of the free parameters can be constrained independently.


  The general system of images for regularized Stokeslets (GSIRS) developed by
Cortez and Varela (2015) is used extensively to model Stokes flow phenomena
such as microorganisms swimming near a boundary. Our collaborative team uses
dynamically similar scaled macroscopic experiments to test theories for forces
and torques on spheres moving near a boundary and use these data and the method
of regularized Stokeslets (MRS) created by Cortez et al. (2015) to calibrate
the GSIRS. We find excellent agreement between theory and experiments, which
provides the first experimental validation of such series solutions for spheres
moving near an infinite plane boundary. We test two surface discretization
methods commonly used in the literature: the six-patch method and the spherical
centroidal Voronoi tessellation (SCVT) method. Our data show that the SCVT
method provides the most accurate results when the motional symmetry is broken
by the presence of a boundary. We use theory and the MRS to find optimal values
for the regularization parameter in free space and show that the optimal
regularization parameter values can be fit with simple formulae when using the
SCVT method, so that other researchers have an easy reference. We also present
a regularization function with higher order accuracy when compared with the
regularization function previously introduced by Cortez et al. (2005). The
simulated force and torque values compare very well with experiments and theory
for a wide range of boundary distances. But, we find the simulations lose
accuracy when the gap between the edge of the sphere and the wall is smaller
than the average distance between grid points using the SCVT method. Our
computational parameters and MATLAB and PYTHON implementations of the Lee and
Leal (1980) theory provide researchers with important resources to optimize the
numerical simulations of spheres moving near boundaries.


  We propose a method to probe the local density of states (LDOS) of atomic
systems that provides both spatial and energy resolution. The method combines
atomic and tunneling techniques to supply a simple, yet quantitative and
operational, definition of the LDOS for both interacting and non-interacting
systems: It is the rate at which particles can be siphoned from the system of
interest by a narrow energy band of non-interacting states contacted locally to
the many-body system of interest. Ultracold atoms in optical lattices are a
natural platform for implementing this broad concept to visualize the energy
and spatial dependence of the atom density in interacting, inhomogeneous
lattices. This includes models of strongly correlated condensed matter systems,
as well as ones with non-trivial topologies.


  These lecture notes from a first course in algebraic topology use the
fundamental group and orbit categories to classify covering spaces.


  This paper presents a complete analysis of the observability property of heat
equations with time-dependent real analytic memory kernels. More precisely, we
characterize the geometry of the space-time measurable observation sets
ensuring sharp observability inequalities, which are relevant both for control
and inverse problems purposes.
  Despite the abundant literature on the observation of heat-like equations,
existing methods do not apply to models involving memory terms.
  We present a new methodology and observation strategy, relying on the
decomposition of the flow, the time-analyticity of solutions and the
propagation of singularities. This allows us to obtain a sufficient and
necessary geometric condition on the measurable observation sets for sharp
two-sided observability inequalities. In addition, some applications to control
and relevant open problems are presented.


  The impact forces during switching operations of short-stroke actuators may
cause bouncing, audible noise and mechanical wear. The application of
soft-landing control strategies to these devices aims at minimizing the impact
velocities of their moving components to ultimately improve their lifetime and
performance. In this paper, a novel approach for soft-landing trajectory
planning, including probability functions, is proposed for optimal control of
the actuators. The main contribution of the proposal is that it considers
uncertainty in the contact position and hence the obtained trajectories are
more robust against system uncertainties. The problem is formulated as an
optimal control problem and transformed into a two-point boundary value problem
for its numerical resolution. Simulated and experimental tests have been
performed using a dynamic model and a commercial short-stroke solenoid valve.
The results show a significant improvement in the expected velocities and
accelerations at contact with respect to past solutions in which the contact
position is assumed to be perfectly known.


  In this paper, the performance of different structural models based on global
approach in evaluating the static response of curvilinear fibre composite
laminates is analyzed. A Co shear flexible Quad-8 element developed based on
higher-order structural theory is employed for the present study. The
structural theory accounting for the realistic variation of displacements
through the thickness and the possible discontinuity in the slope at the
interface is considered. Four alternate discrete structural models, deduced
from the generic structural model by retaining various terms in the
displacement functions are examined for their applicability. The accuracy of
the present formulation is demonstrated considering the problems for which
analytical solutions are available. A systematic numerical study, assuming
different ply-angle and lay-up, is conducted in bringing out the influence of
various structural models on the static response of composite laminates with
curvilinear fibres.


  In this paper we consider the " exterior approach " to solve the inverse
obstacle problem for the heat equation. This iterated approach is based on a
quasi-reversibility method to compute the solution from the Cauchy data while a
simple level set method is used to characterize the obstacle. We present
several mixed formulations of quasi-reversibility that enable us to use some
classical conforming finite elements. Among these, an iterated formulation that
takes the noisy Cauchy data into account in a weak way is selected to serve in
some numerical experiments and show the feasibility of our strategy of
identification.


  Planetary population synthesis is a tool to understand the physics of
planetary system formation. It builds on a model that includes a multitude of
physical processes. The outcome can be statistically compared with exoplanet
observations. Here, we review the population synthesis method and then use one
population to explore how different planetary system architectures emerge and
which conditions lead to their formation. The systems can be classified into
four main architectures: Class I of near-in situ compositionally ordered
terrestrial and ice planets, Class II of migrated sub-Neptunes, Class III of
mixed low-mass and giant planets, broadly similar to the Solar System, and
Class IV of dynamically active giants without inner low-mass planets. These
four classes exhibit distinct typical formation pathways and are characterised
by certain mass scales. Class I systems form from the local accretion of
planetesimals followed by a giant impact phase, and the final planet masses
correspond to the `Goldreich mass'. Class II systems form when planets reach
the `equality mass' (equal accretion and migration timescales) before the
dispersal of the gas disc, but not large enough to allow for rapid gas
accretion. Giant planets form when the `equality mass' allows for rapid gas
accretion while the planet are migrating, i.e. when the critical core mass is
reached. The main discriminant of the four classes is the initial mass of
solids in the disc, with contributions from the lifetime and mass of the gas
disc. The breakdown into classes allows to better understand which physical
processes are dominant. Comparison with observations reveals certain
differences to the actual population, pointing at limitation of theoretical
understanding. For example, the overrepresentation of synthetic super Earths
and sub-Neptunes in Class I causes these planets to be found at lower
metallicities than in observations.


  Model-based reinforcement learning (RL) has demonstrated remarkable successes
on a range of continuous control tasks due to its high sample efficiency. To
save the computation cost of conducting planning online, recent practices tend
to distill optimized action sequences into an RL policy during the training
phase. Although the distillation can incorporate both the foresight of planning
and the exploration ability of RL policies, the theoretical understanding of
these methods is yet unclear. In this paper, we extend the policy improvement
step of Soft Actor-Critic (SAC) by developing an approach to distill from
model-based planning to the policy. We then demonstrate that such an approach
of policy improvement has a theoretical guarantee of monotonic improvement and
convergence to the maximum value defined in SAC. We discuss effective design
choices and implement our theory as a practical algorithm -- Model-based
Planning Distilled to Policy (MPDP) -- that updates the policy jointly over
multiple future time steps. Extensive experiments show that MPDP achieves
better sample efficiency and asymptotic performance than both model-free and
model-based planning algorithms on six continuous control benchmark tasks in
MuJoCo.


  The physical non-existence of gravitational waves (GW's) as a consequence of
the non-existence in general relativity (GR) of physically privileged reference
frames, and of the ``plasticity'' of relativistic notion of a coordinate
system.


  The main purpose of this paper is to revisit the well known potentials,
called stress functions, needed in order to study the parametrizations of the
stress equations, respectively provided by G.B. Airy (1863) for 2-dimensional
elasticity, then by E. Beltrami (1892), J.C. Maxwell (1870) and G. Morera
(1892) for 3-dimensional elasticity, finally by A. Einstein (1915) for
4-dimensional elasticity, both with a variational procedure introduced by C.
Lanczos (1949,1962) in order to relate potentials to Lagrange multipliers.
Using the methods of Algebraic Analysis, namely mixing differential geometry
with homological algebra and combining the double duality test involved with
the Spencer cohomology, we shall be able to extend these results to an
arbitrary situation with an arbitrary dimension n. We shall also explain why
double duality is perfectly adapted to variational calculus with differential
constraints as a way to eliminate the corresponding Lagrange multipliers. For
example, the canonical parametrization of the stress equations is just
described by the formal adjoint of the n2(n2 -- 1)/12 components of the
linearized Riemann tensor considered as a linear second order differential
operator but the minimum number of potentials needed in elasticity theory is
equal to n(n -- 1)/2 for any minimal parametrization. Meanwhile, we can provide
all the above results without even using indices for writing down explicit
formulas in the way it is done in any textbook today. The example of
relativistic continuum mechanics with n = 4 is provided in order to prove that
it could be strictly impossible to obtain such results without using the above
methods. We also revisit the possibility (Maxwell equations of electromag-
netism) or the impossibility (Einstein equations of gravitation) to obtain
canonical or minimal parametrizations for various other equations of physics.
It is nevertheless important to notice that, when n and the algorithms
presented are known, most of the calculations can be achieved by using
computers for the corresponding symbolic computations. Finally, though the
paper is mathematically oriented as it aims providing new insights towards the
mathematical foundations of elasticity theory and mathematical physics, it is
written in a rather self-contained way.


  Let (G,w) be a weighted graph. The necessary and sufficient conditions under
which a weight w : E(G)-->R^+ can be extended to a pseudoultrametric on V(G)
are found. A criterion of the uniqueness of this extension is also obtained. It
is proved that G is complete k-partite with k >= 2 if and only if, for every
pseudoultrametrizable weight w, there exists the smallest pseudoultrametric
agreed with w. We characterize the structure of graphs for which the
subdominant pseudoultrametric is an ultrametric for every strictly positive
pseudoultrametrizable weight.


  Given a polarized manifold there are obstructions for asymptotic Chow
semistability described as integral invariants. One of them is an obstruction
to the existence for the first Chern class of the polarization to admit a
constant scalar curvature K\"ahler (cscK) metric. A natural question is whether
or not the other obstructions are linearly dependent on the obstruction to the
existence of a cscK metric. The purpose of this paper is to see that this is
not the case by exhibiting toric Fano threefolds in which these obstructions
span at least two dimension. To see this we show that on toric Fano manifolds
these obstructions are obtained as derivatives of the Hilbert series. This last
observation should be regarded as an extension of the volume minimization of
Martelli, Sparks and Yau.


  The determination of the specific angular momentum radial profile, $j(r)$, in
the early stages of star formation is crucial to constrain star and
circumstellar disk formation theories. The specific angular momentum is
directly related to the largest Keplerian disk possible, and it could constrain
the angular momentum removal mechanism. We determine $j(r)$ towards two Class 0
objects and a first hydrostatic core candidate in the Perseus cloud, which is
consistent across all three sources and well fit with a single power-law
relation between 800 and 10,000\,au:
$j_{fit}(r)=10^{-3.60\pm0.15}\left(r/\textrm{1,000au}\right)^{1.80\pm0.04}$ km
s$^{-1}$ pc. This power-law relation is in between solid body rotation
($\propto r^2$) and pure turbulence ($\propto r^{1.5}$). This strongly suggests
that even at 1,000\,au, the influence of the dense core's initial level of
turbulence or the connection between core and the molecular cloud is still
present. The specific angular momentum at 10,000\,au is $\approx3\times$ higher
than previously estimated, while at 1,000\,au it is lower by $2\times$. We do
not find a region of conserved specific angular momentum, although it could
still be present at a smaller radius. We estimate an upper limit to the largest
Keplerian disk radius of 60\,au, which is small but consistent with published
upper limits. Finally, these results suggest that more realistic initial
conditions for numerical simulations of disk formation are needed. Some
possible solutions include: a) use a larger simulation box to include some
level of driven turbulence or connection to the parental cloud, or b)
incorporate the observed $j(r)$ to setup the dense core kinematics initial
conditions.


  The aim of this paper is to prove the two-variable anticyclotomic Iwasawa
main conjecture for Hida families and a definite version of the horizontal
non-vanishing conjecture, which are formulated in Longo-Vigni. Our approach is
based on the two-variable anticyclotomic control theorem for Selmer groups for
Hida families and the relation between the two-variable anticyclotomic
$L$-function for Hida families built out of $p$-adic families of Gross points
on definite Shimura curves studied in Castella-Longo and Castella-Kim-Longo and
the self-dual twist of the specialisation to the anticyclotomic line of the
three-variable $p$-adic $L$-function of Skinner-Urban.


  When a robot executes a task, it is necessary to model the relationship among
its body, target objects, tools, and environment, and to control its body to
realize the target state. However, it is difficult to model them using
classical methods if the relationship is complex. In addition, when the
relationship changes with time, it is necessary to deal with the temporal
changes of the model. In this study, we have developed Deep Predictive Model
with Parametric Bias (DPMPB) as a more human-like adaptive intelligence to deal
with these modeling difficulties and temporal model changes. We categorize and
summarize the theory of DPMPB and various task experiments on the actual
robots, and discuss the effectiveness of DPMPB.


  Online feature selection has been an active research area in recent years. We
propose a novel diverse online feature selection method based on Determinantal
Point Processes (DPP). Our model aims to provide diverse features which can be
composed in either a supervised or unsupervised framework. The framework aims
to promote diversity based on the kernel produced on a feature level, through
at most three stages: feature sampling, local criteria and global criteria for
feature selection. In the feature sampling, we sample incoming stream of
features using conditional DPP. The local criteria is used to assess and select
streamed features (i.e. only when they arrive), we use unsupervised scale
invariant methods to remove redundant features and optionally supervised
methods to introduce label information to assess relevant features. Lastly, the
global criteria uses regularization methods to select a global optimal subset
of features. This three stage procedure continues until there are no more
features arriving or some predefined stopping condition is met. We demonstrate
based on experiments conducted on that this approach yields better compactness,
is comparable and in some instances outperforms other state-of-the-art online
feature selection methods.


  In this paper we present new, short and elementary proofs of the famous
projection and section theorems that are used in Stochastic Calculus.


  Disentanglement aims to recover meaningful latent ground-truth factors from
the observed distribution solely, and is formalized through the theory of
identifiability. The identifiability of independent latent factors is proven to
be impossible in the unsupervised i.i.d. setting under a general nonlinear map
from factors to observations. In this work, however, we demonstrate that it is
possible to recover quantized latent factors under a generic nonlinear
diffeomorphism. We only assume that the latent factors have independent
discontinuities in their density, without requiring the factors to be
statistically independent. We introduce this novel form of identifiability,
termed quantized factor identifiability, and provide a comprehensive proof of
the recovery of the quantized factors.


  We show that if two of four generations of the bi-spinor Standard Model are
mass-degenerate or sufficiently close in mass only three generations can be
observed. We argue that the Standard Model and its bi-spinor analog are
indistinguishable on the level of the electroweak precision variables S, T, U.
As a result the bi-spinor Standard Model, which describes experimental observed
textures of flavor mixing matrices is a better fit to the data then the
Standard Model, where the textures are arbitrary.


  The rings of linear continuous operators on the topological spaces of
$\mathfrak{G}$-zero maps were described, where $\mathfrak{G}$ is a filter on a
set with an involution. This applies to modules of formal series with well
ordered support over left ordered groups.


  The carbon-silicate cycle regulates the atmospheric $CO_2$ content of
terrestrial planets on geological timescales through a balance between the
rates of $CO_2$ volcanic outgassing and planetary intake from rock weathering.
It is thought to act as an efficient climatic thermostat on Earth and, by
extension, on other habitable planets. If, however, the weathering rate
increases with the atmospheric $CO_2$ content, as expected on planets lacking
land vascular plants, the carbon-silicate cycle feedback can become severely
limited. Here we show that Earth-like planets receiving less sunlight than
current Earth may no longer possess a stable warm climate but instead
repeatedly cycle between unstable glaciated and deglaciated climatic states.
This has implications for the search for life on exoplanets in the habitable
zone of nearby stars.


  We derive an exact expression for the probability density of work done on a
particle that diffuses in a parabolic potential with a stiffness varying by an
arbitrary piecewise constant protocol. Based on this result, the work
distribution for time-continuous protocols of the stiffness can be determined
up to any degree of accuracy. This is achieved by replacing the continuous
driving by a piecewise constant one with a number $n$ of positive or negative
steps of increasing or decreasing stiffness. With increasing $n$, the work
distributions for the piecewise protocols approach that for the continuous
protocol. The moment generating function of the work is given by the inverse
square root of a polynomial of degree $n$, whose coefficients are efficiently
calculated from a recurrence relation. The roots of the polynomials are real
and positive (negative) steps of the protocol are associated with negative
(positive) roots. Using these properties the inverse Laplace transform of the
moment generating function is carried out explicitly. Fluctuation theorems are
used to derive further properties of the polynomials and their roots.


  We prove a probabilistic Fourier extension theorem that says Fourier
extension holds when averaged over certain smooth Alpert multipliers. The
proofs use smooth Alpert wavelets with the classical techniques of stationary
phase and interpolation of L^2 and L^4 estimates. The correct L^4 bounds for
resonant forms require an expectation over Alpert multipliers.


  We propose the use of modulated spectra of astronomical sources due to
gravitational lensing to probe Ellis wormholes. The modulation factor due to
gravitational lensing by the Ellis wormhole is calculated. Within the
geometrical optics approximation, the normal point mass lens and the Ellis
wormhole are indistinguishable unless we know the source's unlensed luminosity.
This degeneracy is resolved with the significant wave effect in the low
frequency domain if we take the deviation from the geometrical optics into
account. We can roughly estimate the upper bound for the number density of
Ellis wormholes as $n\lesssim 10^{-9}\{AU}^{-3}$ with throat radius $a\sim1\cm$
from the existing femto-lensing analysis for compact objects.


  We analyse with the algebraic, regularisation independant, cohomological
B.R.S. methods, the renormalisability of torsionless N=2 and N= 4
supersymmetric non-linear $\si$ models built on K\"ahler spaces. Surprisingly
enough with respect to the common wisdom, in the case of N=2 supersymmetry, we
obtain an anomaly candidate, at least in the compact K\"ahler Ricci-flat case.
If its coefficient does differ from zero, such anomaly would imply the breaking
of global N=2 supersymmetry and get into trouble some schemes of superstring
compactification as such non-linear $\si$ models offer candidates for the
superstring vacuum state. In the compact homogeneous K\"ahler case, as
expected, the anomaly candidate disappears. The same phenomena occurs when one
enforces N=4 supersymmetry : in that case, we obtain the first rigorous proof
of the expected all-orders renormalisability -`` in the space of metrics"- of
the corresponding non-linear $\si$ models. PAR/LPTHE/94-11


  Test-driven development (TDD) is a widely-employed software development
practice that mandates writing test cases based on requirements before writing
the actual code. While writing test cases is the centerpiece of TDD, it is
time-consuming, expensive, and often shunned by developers. To address these
issues associated with TDD, automated test case generation approaches have
recently been investigated. Such approaches take source code as input, but not
the requirements. Therefore, existing work does not fully support true TDD, as
actual code is required to generate test cases. In addition, current deep
learning-based test case generation approaches are trained with one learning
objective, i.e., to generate test cases that are exactly matched with the
ground-truth test cases. However, such approaches may limit the model's ability
to generate different yet correct test cases. In this paper, we introduce
PyTester, a Text-to-Testcase generation approach that can automatically
generate syntactically correct, executable, complete, and effective test cases
while being aligned with a given natural language requirement. We evaluate
PyTester on the public APPS benchmark dataset, and the results show that our
Deep RL approach enables PyTester, a small language model, to outperform much
larger language models like GPT3.5, StarCoder, and InCoder. Our findings
suggest that future research could consider improving small over large LMs for
better resource efficiency by integrating the SE domain knowledge into the
design of reinforcement learning architecture.


  In the synthesis model signals are represented as a sparse combinations of
atoms from a dictionary. Dictionary learning describes the acquisition process
of the underlying dictionary for a given set of training samples. While ideally
this would be achieved by optimizing the expectation of the factors over the
underlying distribution of the training data, in practice the necessary
information about the distribution is not available. Therefore, in real world
applications it is achieved by minimizing an empirical average over the
available samples. The main goal of this paper is to provide a sample
complexity estimate that controls to what extent the empirical average deviates
from the cost function. This estimate then provides a suitable estimate to the
accuracy of the representation of the learned dictionary. The presented
approach exemplifies the general results proposed by the authors in Sample
Complexity of Dictionary Learning and other Matrix Factorizations, Gribonval et
al. and gives more concrete bounds of the sample complexity of dictionary
learning. We cover a variety of sparsity measures employed in the learning
procedure.


  Our aim is to extract information about literary characters in unstructured
texts. We employ natural language processing and reasoning on domain
ontologies. The first task is to identify the main characters and the parts of
the story where these characters are described or act. We illustrate the system
in a scenario in the folktale domain. The system relies on a folktale ontology
that we have developed based on Propp's model for folktales morphology.


  Classical ways of cooling require some of these elements: phase transition,
compressor, non-linearity, valve, and/or switch. A recent example is the 2018
patent of Linear Technology Corporation; they utilize the shot noise of a diode
to produce a standalone nonlinear resistor that has T/2 noise temperature
(about 150 Kelvin). While such "resistor" can cool its environment when it is
AC coupled to a resistor, the thermally cooling effect is only academically
interesting. The importance of the invention is of another nature: In low-noise
electronics, it is essential to have resistors with low noise temperature to
improve the signal-to-noise ratio. A natural question is raised: can we use a
linear system with feedback to cool and, most importantly, to show reduced
noise temperature? Exploring this problem, were able to produce standalone
linear resistors showing strongly reduced thermal noise. Our must successful
test shows T/100 (about 3 Kelvin) noise temperature, as if the resistor would
have been immersed in liquid helium. We also found that there is an old
solution offering similar results utilizing the virtual ground of an inverting
amplifier at negative feedback. There the "cold" resistor is generated at the
input of an amplifier. On the other hand, our system generates the "cold"
resistance at the output, which can have practical advantages.


  Human actions often involve complex interactions across several inter-related
objects in the scene. However, existing approaches to fine-grained video
understanding or visual relationship detection often rely on single object
representation or pairwise object relationships. Furthermore, learning
interactions across multiple objects in hundreds of frames for video is
computationally infeasible and performance may suffer since a large
combinatorial space has to be modeled. In this paper, we propose to efficiently
learn higher-order interactions between arbitrary subgroups of objects for
fine-grained video understanding. We demonstrate that modeling object
interactions significantly improves accuracy for both action recognition and
video captioning, while saving more than 3-times the computation over
traditional pairwise relationships. The proposed method is validated on two
large-scale datasets: Kinetics and ActivityNet Captions. Our SINet and
SINet-Caption achieve state-of-the-art performances on both datasets even
though the videos are sampled at a maximum of 1 FPS. To the best of our
knowledge, this is the first work modeling object interactions on open domain
large-scale video datasets, and we additionally model higher-order object
interactions which improves the performance with low computational costs.