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We consider a composite medium, which consists of a homogeneous matrix
containing a statistically homogeneous set of multimodal spherical inclusions.
This model is used to represent the morphology of heterogeneous solid
propellants (HSP) that are widely used in the rocket industry. The
Lubachevsky-Stillinger algorithm is used to generate morphological models of
HSP with large polydisperse packs of spherical inclusions. We modify the
algorithm by proposing a random shaking procedure that leads to the
stabilization of a statistical distribution of the simulated structure that is
homogeneous, highly mixed, and protocol independent (in sense that the
statistical parameters estimated do not depend on the basic simulation
algorithm). Increasing the number of shaking has a twofold effect. First, the
system becomes more homogeneous and well-mixed. Second, the stochastic
fluctuations of statistical parameters (such as e.g. radial distribution
function, RDF), estimated by averaging of these structures, tend to diminish.
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Near-infrared (2.5-5.0$\,\mu$m) low-resolution
($\lambda/\Delta\lambda{\sim}100$) spectra of 72 Galactic planetary nebulae
(PNe) were obtained with the Infrared Camera (IRC) in the post-helium phase.
The IRC, equipped with a $1'{\times}1'$ window for spectroscopy of a point
source, was capable of obtaining near-infrared spectra in a slit-less mode
without any flux loss due to a slit. The spectra show emission features
including hydrogen recombination lines and the 3.3-3.5$\,\mu$m hydrocarbon
features. The intensity and equivalent width of the emission features were
measured by spectral fitting. We made a catalog providing unique information on
the investigation of the near-infrared emission of PNe. In this paper, details
of the observations and characteristics of the catalog are described.
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Organizations are often faced with the challenge of providing data management
solutions for large, heterogenous datasets that may have different underlying
data and programming models. For example, a medical dataset may have
unstructured text, relational data, time series waveforms and imagery. Trying
to fit such datasets in a single data management system can have adverse
performance and efficiency effects. As a part of the Intel Science and
Technology Center on Big Data, we are developing a polystore system designed
for such problems. BigDAWG (short for the Big Data Analytics Working Group) is
a polystore system designed to work on complex problems that naturally span
across different processing or storage engines. BigDAWG provides an
architecture that supports diverse database systems working with different data
models, support for the competing notions of location transparency and semantic
completeness via islands and a middleware that provides a uniform multi--island
interface. Initial results from a prototype of the BigDAWG system applied to a
medical dataset validate polystore concepts. In this article, we will describe
polystore databases, the current BigDAWG architecture and its application on
the MIMIC II medical dataset, initial performance results and our future
development plans.
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By applying chiral-perturbation-theory methods to the QCD sector of the
Lorentz-violating Standard-Model Extension, we investigate Lorentz violation in
the strong interactions. In particular, we consider the CPT-even pure-gluon
operator of the minimal Standard-Model Extension. We construct the lowest-order
chiral effective Lagrangian for three as well as two light quark flavors. We
develop the power-counting rules and construct the heavy-baryon
chiral-perturbation-theory Lagrangian, which we use to calculate
Lorentz-violating contributions to the nucleon self energy. Using the
constructed effective operators, we derive the first stringent limits on many
of the components of the relevant Lorentz-violating parameter. We also obtain
the Lorentz-violating nucleon-nucleon potential. We suggest that this potential
may be used to obtain new limits from atomic-clock or deuteron storage-ring
experiments.
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Ground-state energies of the one- and two-electron uranium dimers are
calculated for internuclear distances in the range D=40--1000 fm and compared
with the previous calculations. The generalization of the dual-kinetic-balance
approach for axially symmetric systems is employed to solve the two-center
Dirac equation without the partial-wave expansion for the potential of two
nuclei. The one-electron one-loop QED contributions (self-energy and vacuum
polarization) to the ground-state energy are evaluated using the monopole
approximation for the two-center potential. Interelectronic interaction of the
first and second order is taken into account for the two-electron
quasimolecule. Within the QED approach one-photon-exchange contribution is
calculated in the two-center potential, while the two-photon-exchange
contribution is treated in the monopole approximation.
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In many physical systems it is important to be aware of the crossings and
avoided crossings which occur when eigenvalues of a physical observable are
varied using an external parameter. We have discovered a powerful algebraic
method of finding such crossings via a mapping to the problem of locating the
roots of a polynomial in that parameter. We demonstrate our method on atoms and
molecules in a magnetic field, where it has implications in the search for
Feshbach resonances. In the atomic case our method allows us to point out a new
class of invariants of the Breit-Rabi Hamiltonian of magnetic resonance. In the
case of molecules, it enables us to find curve crossings with practically no
knowledge of the corresponding Born-Oppenheimer potentials.
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Perturbations of the air transport network have a tremendous impact on many
sectors of activity. Therefore, a better understanding of its robustness to
targeted attacks is essential. The literature reports numerous investigations
at different levels (world, regional, airline) considering various targeted
attack strategies. However, few works consider the mesoscopic organization of
the network. To fill this gap, we rely on the component structure recently
introduced in the network literature. Indeed, the world air transportation
network possesses seven local components capturing the regional flights in
localized areas. Its global component, distributed worldwide, capture the
interregional routes. We investigate the impact of two influential attacks
(Degree, Betweenness) on the world air transportation network at the regional
and inter-regional levels. Results show that the seven regions are isolated one
after the other from the world air transportation network. Additionally,
although the Betweenness attack effectively splits the network, its impact on
regional routes is less pronounced.
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The temperature dependence of the dynamics of water inside microporous
activated carbon fibers (ACF) is investigated by means of incoherent elastic
and quasi- elastic neutron scattering techniques. The aim is to evaluate the
effect of increasing pore size on the water dynamics in these primarily
hydrophobic slit-shaped channels. Using two different micropore sizes (\sim 12
and 18 {\AA}, denoted respectively ACF-10 and ACF-20), a clear suppression of
the mobility of the water molecules is observed as the pore gap or temperature
decreases. This suppression is accompanied by a systematic dependence of the
average translational diffusion coefficient Dr and relaxation time <{\tau}_0>
of the restricted water on pore size and temperature. The observed Dr values
are tested against a proposed scaling law, in which the translational diffusion
coefficient Dr of water within a nanoporous matrix was found to depend solely
on two single parameters, a temperature independent translational diffusion
coefficient Dc associated with the water bound to the pore walls and the ratio
{\theta} of this strictly confined water to the total water inside the pore,
yielding unique characteristic parameters for water transport in these carbon
channels across the investigated temperature range.
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Pandemics and natural disasters over the years have changed the behavior of
people, which has had a tremendous impact on all life aspects. With the
technologies available in each era, governments, organizations, and companies
have used these technologies to track, control, and influence the behavior of
individuals for a benefit. Nowadays, the use of the Internet of Things (IoT),
cloud computing, and artificial intelligence (AI) have made it easier to track
and change the behavior of users through changing IoT behavior. This article
introduces and discusses the concept of the Internet of Behavior (IoB) and its
integration with Explainable AI (XAI) techniques to provide trusted and evident
experience in the process of changing IoT behavior to ultimately improving
users' behavior. Therefore, a system based on IoB and XAI has been proposed in
a use case scenario of electrical power consumption that aims to influence user
consuming behavior to reduce power consumption and cost. The scenario results
showed a decrease of 522.2 kW of active power when compared to original
consumption over a 200-hours period. It also showed a total power cost saving
of 95.04 Euro for the same period. Moreover, decreasing the global active power
will reduce the power intensity through the positive correlation.
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The jet wiping process is a cost-effective coating technique that uses
impinging gas jets to control the thickness of a liquid layer dragged along a
moving strip. This process is fundamental in various coating industries (mainly
in hot-dip galvanizing) and is characterized by an unstable interaction between
the gas jet and the liquid film that results in wavy final coating films. To
understand the dynamics of the wave formation, we extend classic laminar
boundary layer models for falling films to the jet wiping problem, including
the self-similar integral boundary layer (IBL) and the weighted integral
boundary layer (WIBL) models. Moreover, we propose a transition and turbulence
model (TTBL) to explore modelling extensions to larger Reynolds numbers and to
analyze the impact of the modelling strategy on the liquid film dynamics. The
validity of the long-wave formulation was first analyzed on a simpler problem,
consisting of a liquid film falling over an upward-moving wall, using Volume Of
Fluid (VOF) simulations. This validation proved the robustness of the integral
formulation in conditions that are well outside their theoretical limits of
validity. Finally, the three models were used to study the response of the
liquid coat to harmonic and non-harmonic oscillations and pulsations in the
impinging jet. The impact of these disturbances on the average coating
thickness and wave amplitude is analyzed, and the range of dimensionless
frequencies yielding maximum disturbance amplification is presented.
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We present a deterministic fully dynamic algorithm with subpolynomial
worst-case time per graph update such that after processing each update of the
graph, the algorithm outputs a minimum cut of the graph if the graph has a cut
of size at most $c$ for some $c = (\log n)^{o(1)}$. Previously, the best update
time was $\widetilde O(\sqrt{n})$ for any $c > 2$ and $c = O(\log n)$ [Thorup,
Combinatorica'07].
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Children's health studies support an association between maternal
environmental exposures and children's birth outcomes. A common goal is to
identify critical windows of susceptibility--periods during gestation with
increased association between maternal exposures and a future outcome. The
timing of the critical windows and magnitude of the associations are likely
heterogeneous across different levels of individual, family, and neighborhood
characteristics. Using an administrative Colorado birth cohort we estimate the
individualized relationship between weekly exposures to fine particulate matter
(PM$_{2.5}$) during gestation and birth weight. To achieve this goal, we
propose a statistical learning method combining distributed lag models and
Bayesian additive regression trees to estimate critical windows at the
individual level and identify characteristics that induce heterogeneity from a
high-dimensional set of potential modifying factors. We find evidence of
heterogeneity in the PM$_{2.5}$-birth weight relationship, with some
mother-child dyads showing a 3 times larger decrease in birth weight for an IQR
increase in exposure (5.9 to 8.5 $\mu g/m^3$ PM$_{2.5}$) compared to the
population average. Specifically, we find increased susceptibility for
non-Hispanic mothers who are either younger, have higher body mass index or
lower educational attainment. Our case study is the first precision health
study of critical windows.
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We show a spacetime positive mass theorem for asymptotically flat initial
data sets with a noncompact boundary. We develop a mass type invariant and a
boundary dominant energy condition. Our proof is based on spinors.
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It is shown that if $R$ is a ring, $p$ a prime element of an integral domain
$D\leq R$ with $\bigcap_{n=1}^\infty p^nD=0$ and $p\in U(R)$, then $R$ has a
conch maximal subring (see \cite{faith}). We prove that either a ring $R$ has a
conch maximal subring or $U(S)=S\cap U(R)$ for each subring $S$ of $R$ (i.e.,
each subring of $R$ is closed with respect to taking inverse, see
\cite{invsub}). In particular, either $R$ has a conch maximal subring or $U(R)$
is integral over the prime subring of $R$. We observe that if $R$ is an
integral domain with $|R|=2^{2^{\aleph_0}}$, then either $R$ has a maximal
subring or $|Max(R)|=2^{\aleph_0}$, and in particular if in addition
$dim(R)=1$, then $R$ has a maximal subring. If $R\subseteq T$ be an integral
ring extension, $Q\in Spec(T)$, $P:=Q\cap R$, then we prove that whenever $R$
has a conch maximal subring $S$ with $(S:R)=P$, then $T$ has a conch maximal
subring $V$ such that $(V:T)=Q$ and $V\cap R=S$. It is shown that if $K$ is an
algebraically closed field which is not algebraic over its prime subring and
$R$ is affine ring over $K$, then for each prime ideal $P$ of $R$ with
$ht(P)\geq dim(R)-1$, there exists a maximal subring $S$ of $R$ with $(S:R)=P$.
If $R$ is a normal affine integral domain over a field $K$, then we prove that
$R$ is an integrally closed maximal subring of a ring $T$ if and only if
$dim(R)=1$ and in particular in this case $(R:T)=0$.
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Abelian differentials on Riemann surfaces can be seen as translation
surfaces, which are flat surfaces with cone-type singularities. Closed
geodesics for the associated flat metrics form cylinders whose number under a
given maximal length generically has quadratic asymptotics in this length, with
a common coefficient constant for the quadratic asymptotics called a
Siegel--Veech constant which is shared by almost all surfaces in each moduli
space of translation surfaces.
Square-tiled surfaces are specific translation surfaces which have their own
quadratic asymptotics for the number of cylinders of closed geodesics. It is an
interesting question whether, as n tends to infinity, the Siegel--Veech
constants of square-tiled surfaces with n tiles tend to the generic constants
of the ambient moduli space. We prove that this is the case in the moduli space
H(2) of translation surfaces of genus two with one singularity.
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A summation formula is derived for the sum of the first m+1 terms of the
3F2(a,b,c;(a+b+1)/2,2c;1) series when c = -m is a negative integer. This
summation formula is used to derive a formula for the sum of a terminating
double hypergeometric series that arose in another project by one of us (C.D.)
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We present a computer simulation study of a disordered two-dimensional system
of localized interacting electrons at thermal equilibrium. It is shown that the
configuration of occupied sites within the Coulomb gap persistently changes at
temperatures much less than the gap width. This is accompanied by large time
dependent fluctuations of the site energies. The observed thermal equilibration
at low temperatures suggests a possible glass transition only at T=0. We
interpret the strong fluctuations in the occupation numbers and site energies
in terms of the drift of the system between multiple energy minima. The results
also imply that interacting electrons may be effectively delocalized within the
Coulomb gap. Insulating properties, such as hopping conduction, appear as a
result of long equilibration times associated with glassy dynamics. This may
shine new light on the relation between the metal-insulator transition and
glassy behavior.
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We describe an infinite-parametric class of effective metric Lagrangians that
arise from an underlying theory with two propagating degrees of freedom. The
Lagrangians start with the Einstein-Hilbert term, continue with the standard
R^2, (Ricci)^2 terms, and in the next order contain (Riemann)^3 as well as
on-shell vanishing terms. This is exactly the structure of the effective metric
Lagrangian that renormalizes quantum gravity divergences at two-loops. This
shows that the theory underlying the effective field theory of gravity may have
no more degrees of freedom than is already contained in general relativity. We
show that the reason why an effective metric theory may describe just two
propagating degrees of freedom is that there exists a (non-local) field
redefinition that maps an infinitely complicated effective metric Lagrangian to
the usual Einstein-Hilbert one. We describe this map for our class of theories
and, in particular, exhibit it explicitly for the (Riemann)^3 term.
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Many researchers have sought ways of model compression to reduce the size of
a deep neural network (DNN) with minimal performance degradation in order to
use DNNs in embedded systems. Among the model compression methods, a method
called knowledge transfer is to train a student network with a stronger teacher
network. In this paper, we propose a novel knowledge transfer method which uses
convolutional operations to paraphrase teacher's knowledge and to translate it
for the student. This is done by two convolutional modules, which are called a
paraphraser and a translator. The paraphraser is trained in an unsupervised
manner to extract the teacher factors which are defined as paraphrased
information of the teacher network. The translator located at the student
network extracts the student factors and helps to translate the teacher factors
by mimicking them. We observed that our student network trained with the
proposed factor transfer method outperforms the ones trained with conventional
knowledge transfer methods.
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We introduce small-text, an easy-to-use active learning library, which offers
pool-based active learning for single- and multi-label text classification in
Python. It features numerous pre-implemented state-of-the-art query strategies,
including some that leverage the GPU. Standardized interfaces allow the
combination of a variety of classifiers, query strategies, and stopping
criteria, facilitating a quick mix and match, and enabling a rapid and
convenient development of both active learning experiments and applications.
With the objective of making various classifiers and query strategies
accessible for active learning, small-text integrates several well-known
machine learning libraries, namely scikit-learn, PyTorch, and Hugging Face
transformers. The latter integrations are optionally installable extensions, so
GPUs can be used but are not required. Using this new library, we investigate
the performance of the recently published SetFit training paradigm, which we
compare to vanilla transformer fine-tuning, finding that it matches the latter
in classification accuracy while outperforming it in area under the curve. The
library is available under the MIT License at
https://github.com/webis-de/small-text, in version 1.3.0 at the time of
writing.
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We study the quantum fidelity (groundstate overlap) near quantum phase
transitions of the Ising universality class in one dimensional (1D) systems of
finite size L. Prominent examples occur in magnetic systems (e.g. spin-Peierls,
the anisotropic XY model), and in 1D topological insulators of any
topologically nontrivial Altland-Zirnbauer-Kitaev universality class. The
rescaled fidelity susceptibility is a function of the only dimensionless
parameter LM, where 2M is the gap in the fermionic spectrum. We present
analytic expressions for the fidelity susceptibility for periodic and open
boundaries conditions with zero, one or two edgestates. The latter are shown to
have a crucial impact and alter the susceptibility both quantitatively and
qualitatively. We support our analytical solutions with numerical data.
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The energy injection model is usually proposed to interpret the shallow-decay
phase in Swift GRB X-ray afterglows. However, very few GRBs have simultaneous
signatures of energy injection in their optical and X-ray afterglows. Here, we
report optical observations of GRB 090529A from 2000 sec to $\sim10^6$ sec
after the burst, in which an achromatic decay is seen at both wavelengths. The
optical light curve shows a decay from 0.37 to 0.99 with a break at $\sim10^5$
sec. In the same time interval, the decay indices of the X-ray light curve
changed from 0.04 to 1.2. Comparing these values with the closure relations,
the segment after 3$\times10^{4}$ sec is consistent with the prediction of the
forward shock in an ISM medium without any energy injection. The shallow-decay
phase between 2000 to 3$\times10^{4}$ sec could be due to the external shock in
a wind-type-like medium with an energy injection under the condition of $\nu_o
< \nu_c < \nu_x$. However, the constraint of the spectral region is not well
consistent with the multi-band observations. For this shallow-decay phase,
other models are also possible, such as energy injection with evolving
microphysical parameters, or a jet viewed off-axis,etc.
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Adding perforations to a continuum sheet allows new modes of deformation, and
thus modifies its elastic behavior. The failure behavior of such a perforated
sheet is explored, using a model experimental system: a material containing a
one-dimensional array of rectangular holes. In this model system, a transition
in failure mode occurs as the spacing and aspect ratio of the holes are varied:
rapid failure via a running crack is completely replaced by quasi-static
failure which proceeds via the breaking of struts at random positions in the
array of holes. I demonstrate that this transition can be connected to the loss
of stress enhancement which occurs as the material geometry is modified.
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An analytic expression is given for the growth function for linear
perturbations in a low-density universe made flat by a cosmological constant.
The result involves elliptic integrals but is otherwise short and
straight-forward.
|
We present new near-infrared (NIR) light-curve templates for fundamental (FU,
JHK) and first overtone (FO, J) Cepheids. The new templates together with PL
and PW relations provide Cepheid distances from single-epoch observations with
a precision only limited by the intrinsic accuracy of the method adopted. The
templates rely on a very large set of Galactic and Magellanic Clouds (MCs)
Cepheids (FU,~600; FO,~200) with well sampled NIR (IRSF data) and optical (V,I;
OGLE data) light curves. To properly trace the change in the shape of the light
curve as a function of period, we split the sample of calibrating Cepheids into
10 different period bins. The templates for the first time cover FO Cepheids
and the FU short-period Cepheids (P<5 days). Moreover, the zero-point phase is
anchored to the phase of the mean magnitude along the rising branch. The new
approach has several advantages in sampling the light curve of bump Cepheids
when compared with the phase of maximum light. We also provide new estimates of
the NIR-to-optical amplitude ratios for FU and FO Cepheids. We perform detailed
analytical fits using both 7th-order Fourier series and multi-Gaussian periodic
functions. The latter are characterized by a smaller number of free parameters
(9 vs 15). Mean NIR magnitudes based on the new templates are up to 80% more
accurate than single-epoch measurements and up to 50% more accurate than mean
magnitudes based on previous templates, with typical associated uncertainties
ranging from 0.015 mag (J) to 0.019 mag (K). Moreover, the errors on individual
distances of Small MC Cepheids derived from NIR PW relations, are essentially
reduced to the intrinsic scatter of the adopted relations. Thus, the new
templates are the ultimate tool to estimate precise Cepheid distances from NIR
single-epoch observations, which can be adopted to derive the 3D structure of
the MCs.
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This paper concerns the general problem of classifying the finite
deterministic automata that admit a synchronizing (or reset) word. (For our
purposes it is irrelevant if the automata has initial or final states.) Our
departure point is the study of the transition semigroup associated to the
automaton, taking advantage of the enormous and very deep progresses made
during the last decades on the theory of permutation groups, their geometry and
their combinatorial structure.
Let $X$ be a finite set. We say that a primitive group $G$ on $X$ is {\em
synchronizing} if $G$ together with any non-invertible map on $X$ generates a
constant map. It is known (by some recent results proved by P. M. Neumann) that
for some primitive groups $G$ and for some singular transformations $t$ of
uniform kernel (that is, all blocks have the same number of elements), the
semigroup $< G,t>$ does not generate a constant map. Therefore the following
concept is very natural: a primitive group $G$ on $X$ is said to be {\em almost
synchronizing} if $G$ together with any map of non-uniform kernel generates a
constant map. In this paper we use two different methods to provide several
infinite families of groups that are not synchronizing, but are almost
synchronizing. The paper ends with a number of problems on synchronization
likely to attract the attention of experts in computer science, combinatorics
and geometry, groups and semigroups, linear algebra and matrix theory.
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Coda in local earthquake exhibits resonance-like wave behaviour where the
coda emerges as long-duration small-amplitude vibration with selective
frequency, slow temporal decay, and uniform spatial energy distribution around
the earthquake source. Coda is thought to be the incoherent waves scattered
from random small-scale heterogeneity in the earth's lithosphere. Here I show
that the coda is primarily attributed to the natural resonance in strong
small-scale heterogeneity around the earthquake's hypocenter through seismic
wave field modeling for 1D heterogeneity. The natural resonance is evolved from
the low frequency resonance (LFR) in transient regime and is an emergent
phenomenon that occurs in steady state regime. Its resonance frequency
decreases with increasing heterogeneous scale, impedance contrast, or random
heterogeneous scale and velocity fluctuations; its intensity diminishes with
decreasing impedance contrast or increasing random heterogeneous scale and
velocity fluctuations.
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For a graph G, a monotone increasing graph property P and positive integer q,
we define the Client-Waiter game to be a two-player game which runs as follows.
In each turn Waiter is offering Client a subset of at least one and at most q+1
unclaimed edges of G from which Client claims one, and the rest are claimed by
Waiter. The game ends when all the edges have been claimed. If Client's graph
has property P by the end of the game, then he wins the game, otherwise Waiter
is the winner. In this paper we study several Client-Waiter games on the edge
set of the complete graph, and the H-game on the edge set of the random graph.
For the complete graph we consider games where Client tries to build a large
star, a long path and a large connected component. We obtain lower and upper
bounds on the critical bias for these games and compare them with the
corresponding Waiter-Client games and with the probabilistic intuition. For the
H-game on the random graph we show that the known results for the corresponding
Maker-Breaker game are essentially the same for the Client-Waiter game, and we
extend those results for the biased games and for trees.
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We prove the property that a function is cyclic (resp., non-cyclic) is not
preserved by norm convergence in Dirichlet-type spaces $D_\alpha$, and show how
other significant quantities for cyclicity do remain preserved under the limit
of convergent sequences in $D_\alpha$, providing a quantitative view of this
convergence issue.
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We propose a doxastic \L ukasiewicz logic \textbf{B\L} that is sound and
complete with respect to the class of Kripke-based models in which atomic
propositions and accessibility relations are both infinitely valued in the
standard MV-algebra [0,1]. We also introduce some extensions of \textbf{B\L}
corresponding to axioms \textbf{D}, \textbf{4}, and \textbf{T} of classical
epistemic logic. Furthermore, completeness of these extensions are established
corresponding to the appropriate classes of models.
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Existing neural architecture search (NAS) methods often return an
architecture with good search performance but generalizes poorly to the test
setting. To achieve better generalization, we propose a novel
neighborhood-aware NAS formulation to identify flat-minima architectures in the
search space, with the assumption that flat minima generalize better than sharp
minima. The phrase ``flat-minima architecture'' refers to architectures whose
performance is stable under small perturbations in the architecture (e.g.,
replacing a convolution with a skip connection). Our formulation takes the
``flatness'' of an architecture into account by aggregating the performance
over the neighborhood of this architecture. We demonstrate a principled way to
apply our formulation to existing search algorithms, including sampling-based
algorithms and gradient-based algorithms. To facilitate the application to
gradient-based algorithms, we also propose a differentiable representation for
the neighborhood of architectures. Based on our formulation, we propose
neighborhood-aware random search (NA-RS) and neighborhood-aware differentiable
architecture search (NA-DARTS). Notably, by simply augmenting DARTS with our
formulation, NA-DARTS outperforms DARTS and achieves state-of-the-art
performance on established benchmarks, including CIFAR-10, CIFAR-100 and
ImageNet.
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We study the query complexity of exactly reconstructing a string from
adaptive queries, such as substring, subsequence, and jumbled-index queries.
Such problems have applications, e.g., in computational biology. We provide a
number of new and improved bounds for exact string reconstruction for settings
where either the string or the queries are "mixed-up". For example, we show
that a periodic (i.e., "mixed-up") string, $S=p^kp'$, of smallest period $p$,
where $|p'|<|p|$, can be reconstructed using $O(\sigma|p|+\lg n)$ substring
queries, where $\sigma$ is the alphabet size, if $n=|S|$ is unknown. We also
show that we can reconstruct $S$ after having been corrupted by a small number
of errors $d$, measured by Hamming distance. In this case, we give an algorithm
that uses $O(d\sigma|p| + d|p|\lg \frac{n}{d+1})$ queries. In addition, we show
that a periodic string can be reconstructed using $2\sigma\lceil\lg n\rceil +
2|p|\lceil\lg \sigma\rceil$ subsequence queries, and that general strings can
be reconstructed using $2\sigma\lceil\lg n\rceil + n\lceil\lg \sigma\rceil$
subsequence queries, without knowledge of $n$ in advance. This latter result
improves the previous best, decades-old result, by Skiena and Sundaram.
Finally, we believe we are the first to study the exact-learning query
complexity for string reconstruction using jumbled-index queries, which are a
"mixed-up" typeA of query that have received much attention of late.
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We present a detailed study of second-order matter perturbations for the
general Horn- deski class of models. Being the most general scalar-tensor
theory having second-order equations of motion, it includes many known gravity
and dark energy theories and General Relativity with a cosmological constant as
a specific case. This enables us to estimate the leading order dark matter
bispectrum generated at late-times by gravitational instability. We parametrize
the evolution of the first and second-order equations of motion as proposed by
Bellini and Sawicki (2014), where the free functions of the theory are assumed
to be proportional to the dark energy density. We show that it is unnatural to
have large 10% ( 1%) deviations of the bispectrum introducing even larger ~ 30%
(~ 5%) deviations in the linear growth rate. Considering that measurements of
the linear growth rate have much higher signal-to-noise than bispectrum
measurements, this indicates that for Horndeski models which reproduce the
expansion history and the linear growth rate as predicted by GR the dark matter
bispectrum kernel can be effectively modelled as the standard GR one. On the
other hand, an observation of a large bispectrum deviation that can not be
explained in terms of bias would imply either that the evolution of
perturbations is strongly different than the evolution predicted by GR or that
the theory of gravity is exotic (e.g., breaks the weak equivalence principle)
and/or fine-tuned.
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The millimeter wave bands are being increasingly considered for wireless
communication to unmanned aerial vehicles (UAVs). Critical to this undertaking
are statistical channel models that describe the distribution of constituent
parameters in scenarios of interest. This paper presents a general modeling
methodology based on data-training a generative neural network. The proposed
generative model has a two-stage structure that first predicts the link state
(line-of-sight, non-line-of-sight, or outage), and subsequently feeds this
state into a conditional variational autoencoder (VAE) that generates the path
losses, delays, and angles of arrival and departure for all the propagation
paths. The methodology is demonstrated for 28 GHz air-to-ground channels
between UAVs and a cellular system in representative urban environments, with
training datasets produced through ray tracing. The demonstration extends to
both standard base stations (installed at street level and downtilted) as well
as dedicated base stations (mounted on rooftops and uptilted). The proposed
approach is able to capture complex statistical relations in the data and it
significantly outperforms standard 3GPP models, even after refitting the
parameters of those models to the data.
|
Existing pedestrian attribute recognition (PAR) algorithms are mainly
developed based on a static image. However, the performance is not reliable for
images with challenging factors, such as heavy occlusion, motion blur, etc. In
this work, we propose to understand human attributes using video frames that
can make full use of temporal information. Specifically, we formulate the
video-based PAR as a vision-language fusion problem and adopt pre-trained big
models CLIP to extract the feature embeddings of given video frames. To better
utilize the semantic information, we take the attribute list as another input
and transform the attribute words/phrase into the corresponding sentence via
split, expand, and prompt. Then, the text encoder of CLIP is utilized for
language embedding. The averaged visual tokens and text tokens are concatenated
and fed into a fusion Transformer for multi-modal interactive learning. The
enhanced tokens will be fed into a classification head for pedestrian attribute
prediction. Extensive experiments on a large-scale video-based PAR dataset
fully validated the effectiveness of our proposed framework.
|
We provide a novel local definition for spectrally flowed vertex operators in
the SL(2,$\mathbb{R}$)-WZW model, generalising the proposal of Maldacena and
Ooguri in [arXiv:hep-th/0111180] for the singly-flowed case to all $\omega >
1$. This allows us to establish the precise connection between the computation
of correlators using the so-called spectral flow operator, and the methods
introduced recently by Dei and Eberhardt in [arXiv:2105.12130] based on local
Ward identities. We show that the auxiliary variable $y$ used in the latter
paper arises naturally from a point-splitting procedure in the space-time
coordinate. The recursion relations satisfied by spectrally flowed correlators,
which take the form of partial differential equations in $y$-space, then
correspond to null-state conditions for generalised spectral flowed operators.
We highlight the role of the SL(2,$\mathbb{R}$) series identifications in this
context, and prove the validity of the conjecture put forward in
[arXiv:2105.12130] for $y$-space structure constants of three-point functions
with arbitrary spectral flow charges.
|
We show obstructions to the existence of a coclosed $G_2$-structure on a Lie
algebra $\mathfrak g$ of dimension seven with non-trivial center. In
particular, we prove that if there exist a Lie algebra epimorphism from
$\mathfrak g$ to a six-dimensional Lie algebra $\mathfrak h$, with kernel
contained in the center of $\mathfrak g$, then any coclosed $G_2$-structure on
$\mathfrak g$ induces a closed and stable three form on $\mathfrak h$ that
defines an almost complex structure on $\mathfrak h$. As a consequence, we
obtain a classification of the 2-step nilpotent Lie algebras which carry
coclosed $G_2$-structures. We also prove that each one of these Lie algebras
has a coclosed $G_2$-structure inducing a nilsoliton metric, but this is not
true for 3-step nilpotent Lie algebras with coclosed $G_2$-structures. The
existence of contact metric structures is also studied.
|
The isospin mass splittings of the pseudoscalar and vector D and B
light-heavy quark system have been calculated using the method of QCD sum
rules. Nonperturbative QCD effects are shown to be very small, so that mass
splittings arise almost completely from current quark mass splitting and
electromagnetic effects, for which a new gauge invariant QED treatment is used.
The results are consistent with experiment. A measurement of the isospin
splitting of the vector B mesons would give valuable information about quark
mass splittings.
|
In this work, we develop a posteriori error control for a generalized
Boussinesq model in which thermal conductivity and viscosity are
temperature-dependent. Therein, the stationary Navier-Stokes equations are
coupled with a stationary heat equation. The coupled problem is modeled and
solved in a monolithic fashion. The focus is on multigoal-oriented error
estimation with the dual-weighted residual method in which an adjoint problem
is utilized to obtain sensitivity measures with respect to several goal
functionals. The error localization is achieved with the help of a
partition-of-unity in a weak formulation, which is specifically convenient for
coupled problems as we have at hand. The error indicators are used to employ
adaptive algorithms, which are substantiated with several numerical tests such
as one benchmark and two further experiments that are motivated from laser
material processing. Therein, error reductions and effectivity indices are
consulted to establish the robustness and efficiency of our framework.
|
We describe a new method for adding a prescribed amount of kinetic energy to
simulated gas modeled on a cartesian grid by directly altering grid cells' mass
and velocity in a distributed fashion. The method is explored in the context of
supernova feedback in high-resolution ($\sim 10$ pc) hydrodynamic simulations
of galaxy formation. Resolution-dependence is a primary consideration in our
application of the method and simulations of isolated explosions (performed at
different resolutions) motivate a resolution-dependent scaling for the injected
fraction of kinetic energy that we apply in cosmological simulations of a
$10^9$ Msun dwarf halo. We find that in high density media ($\gtrsim$ 50
cm$^{-3}$) with coarse resolution ($\gtrsim 4$ pc per cell), results are
sensitive to the initial kinetic energy fraction due to early and rapid
cooling. In our galaxy simulations, the deposition of small amounts of
supernova energy in kinetic form (as little as 1%) has a dramatic impact on the
evolution of the system, resulting in an order of magnitude suppression of
stellar mass. The overall behavior of the galaxy in the two highest resolution
simulations we perform appears to converge. We discuss the resulting
distribution of stellar metallicities, an observable sensitive to galactic wind
properties, and find that while the new method demonstrates increased agreement
with observed systems, significant discrepancies remain, likely due to
simplistic assumptions that neglect contributions from Type Ia supernovae and
stellar winds.
|
We consider the formulation and quantization of the N=3 superparticle model,
both with and without central charge. Without the central charge the action
possesses U(3) invariance and therefore is naturally quantized in the N=3
harmonic superspace. The quantization reproduces the N=3 supergauge strength
multiplets, described by analytic N=3 superfields and a gravitino multiplet as
a constrained N=3 chiral superfield. When the central charge is present, it
breaks the U(3) R-symmetry of N=3 superalgebra down to SU(2)xU(1), and the
corresponding superparticle model is formulated in the N=2 harmonic superspace
extended by a pair of extra Grassmann variables. The quantization of such a
model leads to the massive BPS N=3 vector multiplet. It is shown that upon
additional superfield constraints such multiplet reduces to the massive N=2
vector multiplet.
|
We point out the dominant importance of plasma injection effects for
relativistic winds from pulsars and black holes. We demonstrate that outside
the light cylinder the magnetically dominated outflows while sliding along the
helical magnetic field move in fact nearly radially with very large Lorentz
factors $\gamma_0 \gg 1 $, imprinted into the flow during pair production
within the gaps. Only at larger distances, $r \geq \gamma_0 (c/\Omega)$, the
MHD acceleration $\Gamma \propto r$ takes over. As a result, Blandford-Znajek
(BZ) driven outflows would produce spine-brightened images. The best-resolved
case of the jet in M87 shows both bright edge-brightened features, as well as
weaker spine-brightened feature. Only the spine-brightened component can be
BZ-driven/originate from the BH's magnetosphere.
|
We provide a significant extension of the Hyperboloidal Foliation Method
introduced by the authors in 2014 in order to establish global existence
results for systems of quasilinear wave equations posed on a curved space, when
wave equations and Klein-Gordon equations are coupled. This method is based on
a (3+1) foliation (of the interior of a future light cone in Minkowski
spacetime) by spacelike and asymptotically hyperboloidal hypersurfaces. In the
new formulation of the method, we succeed to cover wave-Klein-Gordon systems
containing "strong interaction" terms at the level of the metric, and then
generalize our method in order to establish a new existence theory for the
Einstein equations of general relativity. Following pioneering work by Lindblad
and Rodnianski on the Einstein equations in wave coordinates, we establish the
nonlinear stability of Minkowski spacetime for self-gravitating massive scalar
fields.
|
We report the discovery of two transiting extrasolar planets from the
HATSouth survey. HATS-11, a V=14.1 G0-star shows a periodic 12.9 mmag dip in
its light curve every 3.6192 days and a radial velocity variation consistent
with a Keplerian orbit. HATS-11 has a mass of 1.000 $\pm$ 0.060 M$_{\odot}$, a
radius of 1.444 $\pm$ 0.057 M$_{\odot}$ and an effective temperature of 6060
$\pm$ 150 K, while its companion is a 0.85 $\pm$ 0.12 M$_J$, 1.510 $\pm$ 0.078
R$_J$ planet in a circular orbit. HATS-12 shows a periodic 5.1 mmag flux
decrease every 3.1428 days and Keplerian RV variations around a V=12.8 F-star.
HATS-12 has a mass of 1.489 $\pm$ 0.071 M$_{\odot}$, a radius of 2.21 $\pm$
0.21 R$_{\odot}$, and an effective temperature of 6408 $\pm$ 75 K. For HATS-12,
our measurements indicate that this is a 2.38 $\pm$ 0.11 M$_J$, 1.35 $\pm$ 0.17
R$_J$ planet in a circular orbit. Both host stars show sub-solar metallicity of
-0.390 $\pm$ 0.060 dex and -0.100 $\pm$ 0.040 dex, respectively and are
(slightly) evolved stars. In fact, HATS-11 is amongst the most metal-poor and,
HATS-12 is amongst the most evolved stars hosting a hot Jupiter planet.
Importantly, HATS-11 and HATS-12 have been observed in long cadence by Kepler
as part of K2 campaign 7 (EPIC216414930 and EPIC218131080 respectively).
|
We study Topological Defects (TD) in hidden (mirror) matter as possible
sources of ultra-high energy neutrinos. The hidden/mirror and ordinary matter
are assumed to interact very weakly through gravity or superheavy particles. An
inflationary scenario is outlined in which superheavy defects are formed in
hidden/mirror matter (and not in ordinary matter), and at the same time the
density of mirror matter produced at the end of inflation is much smaller than
that of ordinary matter. Superheavy particles produced by hidden-sector TD and
the products of their decays are all sterile in our world. Only mirror
neutrinos oscillate into ordinary neutrinos. We show that oscillations with
maximal mixing of neutrinos from both worlds are possible and that values of
$\Delta m^2$, needed for for solution of solar-neutrino and
atmospheric-neutrino problems, allow the oscillation of ultra-high energy
neutrinos on a timescale of the age of the Universe. A model of mass-degenerate
visible and mirror neutrinos with maximal mixing is constructed. Constraints on
UHE neutrino fluxes are obtained. The estimated fluxes can be 3 orders of
magnitude higher than those from ordinary matter. Detection of these fluxes is
briefly discussed.
|
The Hall coefficient (R_H) of high-Tc cuprates in the normal state shows the
striking non-Fermi liquid behavior: R_H follows a Curie-Weiss type temperature
dependence, and |R_H|>>1/|ne| at low temperatures in the under-doped compounds.
Moreover, R_H is positive for hole-doped compounds and is negative for
electron-doped ones, although each of them has a similar hole-like Fermi
surface. In this paper, we give the explanation of this long-standing problem
from the standpoint of the nearly antiferromagnetic (AF) Fermi liquid. We
consider seriously the vertex corrections for the current which are
indispensable to satisfy the conservation laws, which are violated within the
conventional Boltzmann transport approximation. The obtained total current J_k
takes an enhanced value and is no more perpendicular to the Fermi surface due
to the strong AF fluctuations. By virtue of this mechanism, the anomalous
behavior of R_H in high-Tc cuprates is neutrally explained. We find that both
the temperature and the (electron, or hole) doping dependences of R_H in
high-T_c cuprates are reproduced well by numerical calculations based on the
fluctuation-exchange (FLEX) approximation, applied to the single-band Hubbard
model. We also discuss the temperature dependence of R_H in other nearly AF
metals, e.g., V_2O_3, kappa-BEDT-TTF organic superconductors, and heavy fermion
systems close to the AF phase boundary.
|
In this paper, we introduce HoughToRadon Transform layer, a novel layer
designed to improve the speed of neural networks incorporated with Hough
Transform to solve semantic image segmentation problems. By placing it after a
Hough Transform layer, "inner" convolutions receive modified feature maps with
new beneficial properties, such as a smaller area of processed images and
parameter space linearity by angle and shift. These properties were not
presented in Hough Transform alone. Furthermore, HoughToRadon Transform layer
allows us to adjust the size of intermediate feature maps using two new
parameters, thus allowing us to balance the speed and quality of the resulting
neural network. Our experiments on the open MIDV-500 dataset show that this new
approach leads to time savings in document segmentation tasks and achieves
state-of-the-art 97.7% accuracy, outperforming HoughEncoder with larger
computational complexity.
|
Online advertising is progressively moving towards a programmatic model in
which ads are matched to actual interests of individuals collected as they
browse the web. Letting the huge debate around privacy aside, a very important
question in this area, for which little is known, is: How much do advertisers
pay to reach an individual? In this study, we develop a first of its kind
methodology for computing exactly that -- the price paid for a web user by the
ad ecosystem -- and we do that in real time. Our approach is based on tapping
on the Real Time Bidding (RTB) protocol to collect cleartext and encrypted
prices for winning bids paid by advertisers in order to place targeted ads. Our
main technical contribution is a method for tallying winning bids even when
they are encrypted. We achieve this by training a model using as ground truth
prices obtained by running our own "probe" ad-campaigns. We design our
methodology through a browser extension and a back-end server that provides it
with fresh models for encrypted bids. We validate our methodology using a one
year long trace of 1600 mobile users and demonstrate that it can estimate a
user's advertising worth with more than 82% accuracy.
|
In this paper, we introduce a general numerical method to approximate the
reproduction numbers of a large class of multi-group, age-structured,
population models with a finite age span. To provide complete flexibility in
the definition of the birth and transition processes, we propose an equivalent
formulation for the age-integrated state within the extended space framework.
Then, we discretize the birth and transition operators via pseudospectral
collocation. We discuss applications to epidemic models with continuous and
piecewise continuous rates, with different interpretations of the age variable
(e.g., demographic age, infection age and disease age) and the transmission
terms (e.g., horizontal and vertical transmission). The tests illustrate that
the method can compute different reproduction numbers, including the basic and
type reproduction numbers as special cases.
|
We introduce a new methodology based on the multirevolution idea for
constructing integrators for stochastic differential equations in the situation
where the fast oscillations themselves are driven by a Stratonovich noise.
Applications include in particular highly-oscillatory Kubo oscillators and
spatial discretizations of the nonlinear Schr\"odinger equation with fast white
noise dispersion. We construct a method of weak order two with computational
cost and accuracy both independent of the stiffness of the oscillations. A
geometric modification that conserves exactly quadratic invariants is also
presented.
|
We develop a framework for displaying the stable homotopy theory of the
sphere, at least after localization at the second Morava K-theory K(2). At the
prime 3, we write the spectrum L_{K(2)S^0 as the inverse limit of a tower of
fibrations with four layers. The successive fibers are of the form E_2^hF where
F is a finite subgroup of the Morava stabilizer group and E_2 is the second
Morava or Lubin-Tate homology theory. We give explicit calculation of the
homotopy groups of these fibers. The case n=2 at p=3 represents the edge of our
current knowledge: n=1 is classical and at n=2, the prime 3 is the largest
prime where the Morava stabilizer group has a p-torsion subgroup, so that the
homotopy theory is not entirely algebraic.
|
We present a multiwavelength study of the black hole X-ray binary V404 Cyg in
quiescence, focusing upon the spectral energy distribution (SED). Radio,
optical, UV, and X-ray coverage is simultaneous. We supplement the SED with
additional non-simultaneous data in the optical through infrared where
necessary. The compiled SED is the most complete available for this, the X-ray
and radio brightest quiescent black hole system. We find no need for a
substantial contribution from accretion light from the near-UV to the near-IR,
and in particular the weak UV emission constrains published spectral models for
V404 Cyg. We confirm that no plausible companion spectrum and interstellar
extinction can fully explain the mid-IR, however, and an IR excess from a jet
or cool disc appears to be required. The X-ray spectrum is consistent with a
Gamma~2 power-law as found by all other studies to date. There is no evidence
for any variation in the hardness over a range of a factor of 10 in luminosity.
The radio flux is consistent with a flat spectrum (in f(nu)). The break
frequency between a flat and optically thin spectrum most likely occurs in the
mid or far-IR, but is not strongly constrained by these data. We find the radio
to be substantially variable but with no clear correlation with X-ray
variability.
|
The conventional thermoelectric figure of merit and the power factor are not
sufficient as a measure of thin film quality of thermoelectric materials, where
the power conversion efficiency depends on the film dimensions. By considering
the film size, the effective thermoelectric figure of merit and effective
Seebeck coefficient are introduced to guarantee that the maximum energy
conversion efficiency increases as the effective thermoelectric figure of merit
increases. Similarly, the effective power factor is defined. By introducing
typical material properties for Bi$_2$Te$_3$ and PEDOT, we study the thickness
dependence of the effective figure of merit and the effective power factor.
|
The complex elastic compliance and dielectric susceptibility of
(Na_{0.5}Bi_{0.5})_{1-x}Ba_{x}TiO_{3} (NBT-BT) have been measured in the
composition range between pure NBT and the morphotropic phase boundary
included, 0 <= x <= 0.08. The compliance of NBT presents sharp peaks at the
rhombohedral/tetragonal and tetragonal/cubic transitions, allowing the
determination of the tetragonal region of the phase diagram, up to now
impossible due to the strong lattice disorder and small distortions and
polarizations involved. In spite of ample evidence of disorder and structural
heterogeneity, the R-T transition remains sharp up to x = 0.06, whereas the T-C
transition merges into the diffuse and relaxor-like transition associated with
broad maxima of the dielectric and elastic susceptibilities. An attempt is made
at relating the different features in the anelastic and dielectric curves to
different modes of octahedral rotations and polar cation shifts. The
possibility is also considered that the cation displacements locally have
monoclinic symmetry, as for PZT near the morphotropic phase boundary.
|
We consider here a nonlocal phase transition energy in a periodic medium and
we construct solutions whose interfaces lie at a bounded distance from any
given hyperplane.
These solutions are either periodic or quasiperiodic, depending on the
rational dependency of the normal direction to the reference hyperplane.
Remarkably, the oscillations of the interfaces with respect to the reference
hyperplane are bounded by a universal constant times the periodicity scale of
the medium.
This geometric property allows us to establish, in the limit, the existence
of planelike nonlocal minimal surfaces in a periodic structure.
The proofs rely on new optimal density and energy estimates. In particular,
roughly speaking, the energy of phase transition minimizers is controlled, both
from above and below, by the energy of one-dimensional transition layers.
|
Let $(x_\alpha)$ be a net in a vector lattice normed by locally solid lattice
$(X,p,E_\tau)$. We say that $(x_\alpha)$ is unbounded $p_\tau$-convergent to
$x\in X$ if $p(\lvert x_\alpha-x\rvert\wedge u)\xrightarrow{\tau} 0$ for every
$u\in X_+$. This convergence has been studied recently for lattice-normed
vector lattices as the $up$-convergence in \cite{AGG,AEEM,AEEM2}, the
$uo$-convergence in \cite{GTX}, and, as the $un$-convergence in
\cite{DOT,GX,GTX,KMT,Tr2}. In this paper, we study the general properties of
the unbounded $p_\tau$-convergence.
|
Let T^* be a standard Young tableau of k cells. We show that the probability
that a Young tableau of n cells contains T^* as a subtableau is, in the limit n
-> \infty, equal to \nu(\pi(T^*))/k!, where \pi(T^*) is the shape (= Ferrers
diagram) of T^* and \nu(\pi) is the number of all tableaux of shape \pi. In
other words, the probability that a large tableau contains T^* is equal to the
number of tableaux whose shape is that of T^*, divided by k!.
We give several applications, to the probabilities that a set of prescribed
entries will appear in a set of prescribed cells of a tableau, and to the
probabilities that subtableaux of given shapes will occur.
Our argument rests on a notion of quasirandomness of families of
permutations, and we give sufficient conditions for this to hold. We then
extend these results by finding an explicit formula for the limiting
probability that a Young tableau has a given set of entries in a given set of
positions. The result is that the limiting probability that a Young tableau has
a prescribed set of entries k_1,k_2,..., k_m in a prescribed set of m cells is
equal to the sum of the measures of all tableaux on K cells (K=\max{\{k_i\}})
that have the given entries in the given positions, where the measure of a
tableau of K cells is the number of tableaux of its shape divided by K!.
In the proof we also develop conditions that ensure the quasirandomness of
certain families of permutations.
|
The key role that dust plays in the interstellar medium has motivated the
development of numerical codes designed to study the coupled evolution of dust
and gas in systems such as turbulent molecular clouds and protoplanetary discs.
Drift between dust and gas has proven to be important as well as numerically
challenging. We provide simple benchmarking problems for dusty gas codes by
numerically solving the two-fluid dust-gas equations for steady, plane-parallel
shock waves. The two distinct shock solutions to these equations allow a
numerical code to test different forms of drag between the two fluids, the
strength of that drag and the dust to gas ratio. We also provide an
astrophysical application of J-type dust-gas shocks to studying the structure
of accretion shocks onto protoplanetary discs. We find that two-fluid effects
are most important for grains larger than 1 um, and that the peak dust
temperature within an accretion shock provides a signature of the dust-to-gas
ratio of the infalling material.
|
We consider complete Riemannian $3$-manifolds whose Ricci tensors have
constant eigenvalues $(\lambda, \lambda, 0)$. When $\pi_1$ is finitely
generated, we classify the topology of such manifolds by showing that they have
a free fundamental group if non-trivial and that every free group is obtained.
We give a description up to isometry, when the metric is locally irreducible or
when it is analytic.
|
C. Thomassen (Proc. London Math. Soc. (3) 42 (1981), 231-251) gave a
characterization of strongly connected non-Hamiltonian digraphs of order $p\geq
3$ with minimum degree $p-1$. In this paper we give an analogous
characterization of strongly connected non-Hamiltonian digraphs with
Meyniel-type condition (the sum of degrees of every pair of non-adjacent
vertices $x$ and $y$ at least $2p-2$). Moreover, we prove that such digraphs
$D$ contain cycles of all lengths $k$, for $2\leq k\leq m$, where $m$ is the
length of a longest cycle in $D$.
|
We discuss actions of free groups on the circle with "ping-pong" dynamics;
these are dynamics determined by a finite amount of combinatorial data,
analogous to Schottky domains or Markov partitions. Using this, we show that
the free group $F_n$ admits an isolated circular order if and only if n is
even, in stark contrast with the case for linear orders. This answers a
question from (Mann, Rivas, 2016). Inspired by work of Alvarez, Barrientos,
Filimonov, Kleptsyn, Malicet, Menino and Triestino, we also exhibit examples of
"exotic" isolated points in the space of all circular orders on $F_2$.
Analogous results are obtained for linear orders on the groups $F_n \times
\mathbb{Z}$.
|
This note is concerned with the scaling limit as N approaches infinity of
n-point correlations between zeros of random holomorphic polynomials of degree
N in m variables. More generally we study correlations between zeros of
holomorphic sections of powers L^N of any positive holomorphic line bundle L
over a compact Kahler manifold. Distances are rescaled so that the average
density of zeros is independent of N. Our main result is that the scaling
limits of the correlation functions and, more generally, of the "correlation
forms" are universal, i.e. independent of the bundle L, manifold M or point on
M.
|
This paper presents a framework that allows online
dynamic-stability-constrained optimal trajectory planning of a mobile
manipulator robot working on rough terrain. First, the kinematics model of a
mobile manipulator robot, and the Zero Moment Point (ZMP) stability measure are
presented as theoretical background. Then, a sampling-based quasi-static
planning algorithm modified for stability guarantee and traction optimization
in continuous dynamic motion is presented along with a mathematical proof. The
robot's quasi-static path is then used as an initial guess to warm-start a
nonlinear optimal control solver which may otherwise have difficulties finding
a solution to the stability-constrained formulation efficiently. The
performance and computational efficiency of the framework are demonstrated
through an application to a simulated timber harvesting mobile manipulator
machine working on varying terrain. The results demonstrate feasibility of
online trajectory planning on varying terrain while satisfying the dynamic
stability constraint.
|
We show how the Wess-Zumino terms of the different branes in string theory
can be embedded within double field theory. Crucial ingredients in our
construction are the identification of the correct brane charge tensors and the
use of the double field theory potentials that arise from dualizing the
standard double field theory fields. This leads to a picture where under
T-duality the brane does not change its worldvolume directions but where,
instead, it shows different faces depending on whether some of the worldvolume
and/or transverse directions invade the winding space. As a non-trivial
by-product we show how the different Wess-Zumino terms are modified when the
brane propagates in a background with a non-zero Romans mass parameter.
Furthermore, we show that for non-zero mass parameter the brane creation
process, when one brane passes through another brane, gets generalized to brane
configurations that involve exotic branes as well.
|
We refine the intersection product in homology to an equivariant setting,
which unifies several known constructions. As an application, we give a common
generalisation of the Chas-Sullivan string product on a manifold and the
Chataur-Menichi string product on the classifying space by defining a string
product on the Borel construction of a manifold. We prove a vanishing result
which enables us to define a secondary product. The secondary product is then
used to construct secondary versions of the Chataur-Menichi string product, and
the equivariant intersection product in the Borel equivariant homology of a
manifold with an action of a compact Lie group. The latter reduces to the
product in homology of the classifying space defined by Kreck, which coincides
with the cup product in negative Tate cohomology if the group is finite.
|
We mainly study Pogorelov type $C^2$ estimates for solutions to the Dirichlet
problem of Sum Hessian equations. We establish respectively Pogorelov type
$C^2$ estimates for $k$-convex solutions and admissible solutions under some
conditions. Furthermore, we apply such estimates to obtain a rigidity theorem
for $k$-convex solutions of Sum Hessian equations in Euclidean space.
|
In this note it is shown that two key results on transcendental singularities
for meromorphic functions of finite lower order have refinements which hold
under the weaker hypothesis that the logarithmic derivative has finite lower
order.
|
By applying Miyamoto's $\mathbb{Z}_{3}$-orbifold construction to the lattice
vertex operator algebras associated to Niemeier lattices and their
automorphisms of order 3, we construct holomorphic vertex operator algebras of
central charge 24 whose Lie algebras of the weight one spaces are of types
$A_{2,3}^6$, $E_{6,3}G_{2,1}^{3}$, and $A_{5,3}D_{4,3}A_{1,1}^{3}$, which
correspond to No.6, No.17, and No.32 on Schellekens' list, respectively.
|
Drowsiness, which is the state when drivers do not have scheduled breaks
while traveling long distances, is the main reason behind serious motorway
accidents. Accordingly, experts claim that drowsy state is hard to be
recognized early enough to prevent serious accidents that may lead even to road
deaths. In this work, we propose a new drowsiness state detection system based
on physiological signals and eye blinking. An experiment has been directed to
justify the utility of the proposed approach. This system uses a smart video
camera that takes drivers faces images and supervises the eye blink (open and
close); also, it uses the Emotiv EPOC headset to acquire the
electroencephalogram (EEG) signals. Eye detection is done by Viola and Jones
technique, EEG. Finally, we have chosen the fuzzy logic techniques to classify
the EEG signals and eye blinking detection to analyze the results.
|
We consider Bell tests in which the distant observers can perform local
filtering before testing a Bell inequality. Notably, in this setup, certain
entangled states admitting a local hidden variable model in the standard Bell
scenario can nevertheless violate a Bell inequality after filtering, displaying
so-called hidden nonlocality. Here we ask whether all entangled states can
violate a Bell inequality after well-chosen local filtering. We answer this
question in the negative by showing that there exist entangled states without
hidden nonlocality. Specifically, we prove that some two-qubit Werner states
still admit a local hidden variable model after any possible local filtering on
a single copy of the state.
|
Determining the preferred spatial location of the energy input to solar
coronal loops would be an important step forward towards a more complete
understanding of the coronal heating problem. Following on from Sarkar & Walsh
(2008) this paper presents a short 10e9 cm "global loop" as 125 individual
strands, where each strand is modelled independently by a one-dimensional
hydrodynamic simulation. The strands undergo small-scale episodic heating and
are coupled together through the frequency distribution of the total energy
input to the loop which follows a power law distribution with index ~ 2.29. The
spatial preference of the swarm of heating events from apex to footpoint is
investigated. From a theoretical perspective, the resulting emission measure
weighted temperature profiles along these two extreme cases does demonstrate a
possible observable difference. Subsequently, the simulated output is folded
through the TRACE instrument response functions and a re-derivation of the
temperature using different filter-ratio techniques is performed. Given the
multi-thermal scenario created by this many strand loop model, a broad
differential emission measure results; the subsequent double and triple filter
ratios are very similar to those obtained from observations. However, any
potential observational signature to differentiate between apex and footpoint
dominant heating is possibly below instrumental thresholds. The consequences of
using a broadband instrument like TRACE and Hinode-XRT in this way are
discussed.
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We construct real numbers $\alpha$ for which the pair correlation function
\[N^{-1}#\{m<n\le N:||\alpha m^2-\alpha n^2||\le XN^{-1}\}\] tends to $X$ as
$N$ grows. Moreover we show for any "Diophantine" $\alpha$ that the pair
correlation function is $X+O(X^{7/8})+O((\log N)^{-1}$ for $1\le X\le\log N$.
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Software verification of evolving systems is challenging mainstream
methodologies and tools. Formal verification techniques often conflict with the
time constraints imposed by change management practices for evolving systems.
Since changes in these systems are often local to restricted parts, an
incremental verification approach could be beneficial.
This paper introduces SiDECAR, a general framework for the definition of
verification procedures, which are made incremental by the framework itself.
Verification procedures are driven by the syntactic structure (defined by a
grammar) of the system and encoded as semantic attributes associated with the
grammar. Incrementality is achieved by coupling the evaluation of semantic
attributes with an incremental parsing technique.
We show the application of SiDECAR to the definition of two verification
procedures: probabilistic verification of reliability requirements and
verification of safety properties.
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Cleavage crack propagation has been investigated in a low-carbon
lath-martensitic steel using electron back-scattered diffraction technique. The
ability of different martensitic boundaries within prior-austenite grain, such
as sub-block, block and packet boundaries to resist cleavage crack propagation
has been estimated in terms of Kurdjumov-Sachs crystallographic variants.
Crystallographic study of crack path indicated that block boundaries are more
effective in cleavage crack deviation as compared to packet boundaries, whilst
sub-block boundaries are ineffective in that respect. Moreover, characterizing
the boundaries in terms of misorientation angle (angle-axis pair) may be
misleading if their effectiveness in retarding cleavage crack propagation is
considered.
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We propose in this work the first symmetric hyperbolic system of conservation
laws to describe viscoelastic flows of Maxwell fluids, i.e. fluidswith memory
that are characterized by one relaxation-time parameter. Precisely, the system
of quasilinear PDEs is detailed for the shallow-water regime, i.e. for
hydrostatic incompressible 2D flows with free surface under gravity. It
generalizes Saint-Venant system to viscoelastic flows of Maxwell fluids, and
encompasses previous works with F. Bouchut. It also generalizes the
(thin-layer) elastodynamics of hyperelastic materials to viscous fluids, and to
various rheologies between solid and liquid states that can be formulated using
our new variable as material parameter.The new viscoelastic flow model has many
potential applications, additionally to falling into the theoretical framework
of (symmetric hyper-bolic) systems of conservation laws. In computational
rheology, it offers a new approach to the High-Weissenberg Number Problem
(HWNP). Fortransient geophysical flows, it offers perspectives of
thermodynamically-compatible numerical simulations, with a Finite-Volume (FV)
discretization say. Besides, one FV discretization of the new continuum model
is proposed herein to precise our ideas incl. the physical meaning of the
solutions. Perspectives are finally listed after some numerical simulations.
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We study the possibility of the generation of the photo-induced image
currents at a distance from the surface of nano-sized metal clusters by using
time-dependent perturbation theory. We reveal that the wave function of an
electron excited to the image state is localized outside the surface and
current flows in a spherical shell whose radius is a few times the radius of
the sphere. Spin polarized light has been applied to a perfect icosahedral
metal cluster Li$_{13}$ whose optimization is achieved by molecular dynamic
simulation and band structure is obtained by DFT method and by solution of
radial Schr\"odinger equation. Up to our knowledge, despite the great effort on
their characteristics, image electrons have not been the subject of the studies
on photo-induced current.
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Examining the effect of different encoding techniques on entity and context
embeddings, the goal of this work is to challenge commonly used Ordinal
encoding for tabular learning. Applying different preprocessing methods and
network architectures over several datasets resulted in a benchmark on how the
encoders influence the learning outcome of the networks. By keeping the test,
validation and training data consistent, results have shown that ordinal
encoding is not the most suited encoder for categorical data in terms of
preprocessing the data and thereafter, classifying the target variable
correctly. A better outcome was achieved, encoding the features based on string
similarities by computing a similarity matrix as input for the network. This is
the case for both, entity and context embeddings, where the transformer
architecture showed improved performance for Ordinal and Similarity encoding
with regard to multi-label classification tasks.
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We have searched for prompt production of $\chi_{c1}$, $\chi_{c2}$ and
X(3872) in continuum e^+e^- annihilations using a 386 fb^{-1} data sample
collected around $\sqrt{s} = 10.6$ GeV with the BABAR detector using the
$\gamma J/\psi$ decay mode. After accounting for the feed-down from
$\psi(2S)\to\gamma\chi_{c1,2}$, no significant signal for prompt $\chi_{c1,2}$
production is observed. We present improved upper limits on the cross-section,
with the rest of the event consisting of more than two charged tracks, to be 77
fb for $\chi_{c1}$ and 79 fb for $\chi_{c2}$ with $e^+e^-$ center-of-mass frame
$\chi_c$ momentum greater than 2.0 GeV at 90% confidence level. These limits
are consistent with NRQCD predictions. We also set an upper limit on the prompt
production of X(3872) through the decay $X(3872)\to \gamma J/\psi$.
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This paper has been withdrawn by the author as it has already been submitted
under the title "Twisted character of a small Representation of GL(4)".
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We study experimentally and theoretically structural defects which are formed
during the transition from a laser cooled cloud to a Coulomb crystal,
consisting of tens of ions in a linear radio frequency trap. We demonstrate the
creation of predicted topological defects (`kinks') in purely two-dimensional
crystals, and also find kinks which show novel dynamical features in a regime
of parameters not considered before. The kinks are always observed at the
centre of the trap, showing a large nonlinear localized excitation, and the
probability of their occurrence surprisingly saturates at ~0.5. Simulations
reveal a strong anharmonicity of the kink's internal mode of vibration, due to
the kink's extension into three dimensions. As a consequence, the periodic
Peierls-Nabarro potential experienced by a discrete kink becomes a globally
confining potential, capable of trapping one cooled defect at the center of the
crystal.
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Driven or self-propelling particles moving in viscoelastic fluids recently
emerge as novel class of active systems showing a complex yet rich set of
phenomena due to the non-Newtonian nature of the dispersing medium. Here we
investigate the one-dimensional growth of clusters made of active colloidal
shakers, which are realized by oscillating magnetic rotors dispersed within a
viscoelastic fluid and at different concentration of the dissolved polymer.
These magnetic particles when actuated by an oscillating field display a flow
profile similar to that of a shaker force dipole, i.e. without any net
propulsion. We design a protocol to assemble clusters of colloidal shakers and
induce their controlled expansion into elongated zigzag structures. We observe
a power law growth of the mean chain length and use theoretical arguments to
explain the measured $1/3$ exponent. These arguments agree well with both
experiments and particle based numerical simulations.
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The factor graph of an instance of a symmetric constraint satisfaction
problem on n Boolean variables and m constraints (CSPs such as k-SAT, k-AND,
k-LIN) is a bipartite graph describing which variables appear in which
constraints. The factor graph describes the instance up to the polarity of the
variables, and hence there are up to 2km instances of the CSP that share the
same factor graph. It is well known that factor graphs with certain structural
properties make the underlying CSP easier to either solve exactly (e.g., for
tree structures) or approximately (e.g., for planar structures). We are
interested in the following question: is there a factor graph for which if one
can solve every instance of the CSP with this particular factor graph, then one
can solve every instance of the CSP regardless of the factor graph (and
similarly, for approximation)? We call such a factor graph universal. As one
needs different factor graphs for different values of n and m, this gives rise
to the notion of a family of universal factor graphs. We initiate a systematic
study of universal factor graphs, and present some results for max-kSAT. Our
work has connections with the notion of preprocessing as previously studied for
closest codeword and closest lattice-vector problems, with proofs for the PCP
theorem, and with tests for the long code. Many questions remain open.
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Recommendation systems have become an important solution to information
search problems. This article proposes a neural matrix factorization
recommendation system model based on the multimodal large language model called
BoNMF. This model combines BoBERTa's powerful capabilities in natural language
processing, ViT in computer in vision, and neural matrix decomposition
technology. By capturing the potential characteristics of users and items, and
after interacting with a low-dimensional matrix composed of user and item IDs,
the neural network outputs the results. recommend. Cold start and ablation
experimental results show that the BoNMF model exhibits excellent performance
on large public data sets and significantly improves the accuracy of
recommendations.
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Non-reciprocal interactions fueled by local energy consumption can be found
in biological and synthetic active matter at scales where viscoelastic forces
are important. Such systems can be described by "odd" viscoelasticity, which
assumes fewer material symmetries than traditional theories. Here we study odd
viscoelasticity analytically and using lattice Boltzmann simulations. We
identify a pattern-forming instability which produces an oscillating array of
fluid vortices, and we elucidate which features govern the growth rate,
wavelength, and saturation of the vortices. Our observation of pattern
formation through odd mechanical response can inform models of biological
patterning and guide engineering of odd dynamics in soft active matter systems.
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We interpret the 750~GeV diphoton excess recently found in the 13~TeV LHC
data as a singlet scalar in an extra dimensional model, where one extra
dimension is introduced. In the model, the scalar couples to multiple
vector-like fermions, which are just the KK modes of SM fermions. Mediated by
the loops of these vector-like fermions, the $\phi$ effective couplings to
gluons and photons can be significantly large. Therefore, it is quite easy to
obtain an observed cross section for the diphoton excess. We also calculate the
cross sections for other decay channels of $\phi$, and find that this
interpretation can evade the bounds from the 8~TeV LHC data.
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We present a new technique of VLSI chip-level thermal analysis. We extend a
newly developed method of solving two dimensional Laplace equations to thermal
analysis of four adjacent materials on a mother board. We implement our
technique in C and compare its performance to that of a commercial CAD tool.
Our experimental results show that our program runs 5.8 and 8.9 times faster
while keeping smaller residuals by 5 and 1 order of magnitude, respectively.
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The fcc-based structure of Yb2.75C60 is unique among metal-doped fullerene
compounds, exhibiting long-range-ordered vacancies, significantly off-centered
divalent Yb cations, and distorted, crystallographically inequivalent,
orientationally ordered C60 anions. A simple electrostatic-energy analysis,
which models the constituents using point charges, is shown to provide insight
into how each of these features stabilizes this unusual crystal structure. The
results have general implications for a variety of other intercalated metal
fullerides.
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We show how to extend classical work-stealing to deal also with data parallel
tasks that can require any number of threads r >= 1 for their execution. We
explain in detail the so introduced idea of work-stealing with deterministic
team-building which in a natural way generalizes classical work-stealing. A
prototype C++ implementation of the generalized work-stealing algorithm has
been given and is briefly described. Building on this, a serious, well-known
contender for a best parallel Quicksort algorithm has been implemented, which
naturally relies on both task and data parallelism. For instance, sorting
2^27-1 randomly generated integers we could improve the speed-up from 5.1 to
8.7 on a 32-core Intel Nehalem EX system, being consistently better than the
tuned, task-parallel Cilk++ system.
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We develop a sharp boundary trace theory in arbitrary bounded Lipschitz
domains which, in contrast to classical results, allows "forbidden" endpoints
and permits the consideration of functions exhibiting very limited regularity.
This is done at the (necessary) expense of stipulating an additional regularity
condition involving the action of the Laplacian on the functions in question
which, nonetheless, works perfectly with the Dirichlet and Neumann realizations
of the Schr\"odinger differential expression $-\Delta+V$. In turn, this
boundary trace theory serves as a platform for developing a spectral theory for
Schr\"odinger operators on bounded Lipschitz domains, along with their
associated Weyl-Titchmarsh operators. Overall, this pushes the present state of
knowledge a significant step further. For example, we succeed in extending the
Dirichlet and Neumann trace operators in such a way that all self-adjoint
extensions of a Schr\"odinger operator on a bounded Lipschitz domain may be
described with explicit boundary conditions, thus providing a final answer to a
problem that has been investigated for more than 60 years in the mathematical
literature. Along the way, a number of other open problems are solved. The most
general geometric and analytic setting in which the theory developed here
yields satisfactory results is that of Lipschitz subdomains of Riemannian
manifolds and for the corresponding Laplace-Beltrami operator (in place of the
standard flat-space Laplacian). In particular, such an extension yields results
for variable coefficient Schr\"odinger operators on bounded Lipschitz domains.
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A popular universal gate set for quantum computing with qubits is Clifford+T,
as this can be readily implemented on many fault-tolerant architectures. For
qutrits, there is an equivalent T gate, that, like its qubit analogue, makes
Clifford+T approximately universal, is injectable by a magic state, and
supports magic state distillation. However, it was claimed that a better gate
set for qutrits might be Clifford+R, where R=diag(1,1,-1) is the metaplectic
gate, as certain protocols and gates could more easily be implemented using the
R gate than the T gate. In this paper we show that when we have at least two
qutrits, the qutrit Clifford+R unitaries form a strict subset of the Clifford+T
unitaries, by finding a direct decomposition of $R \otimes \mathbb{I}$ as a
Clifford+T circuit and proving that the T gate cannot be exactly synthesized in
Clifford+R. This shows that in fact the T gate is at least as powerful as the R
gate, up to a constant factor. Moreover, we additionally show that it is
impossible to find a single-qutrit Clifford+T decomposition of the R gate,
making our result tight.
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We examine the different element abundances exhibited by the closed loop
solar corona and the slow speed solar wind. Both are subject to the First
Ionization Potential (FIP) Effect, the enhancement in coronal abundance of
elements with FIP below 10 eV (e.g. Mg, Si, Fe) with respect to high FIP
elements (e.g. O, Ne, Ar), but with subtle differences. Intermediate elements,
S, P, and C, with FIP just above 10 eV, behave as high FIP elements in closed
loops, but are fractionated more like low FIP elements in the solar wind. On
the basis of FIP fractionation by the ponderomotive force in the chromosphere,
we discuss fractionation scenarios where this difference might originate.
Fractionation low in the chromosphere where hydrogen is neutral enhances the S,
P and C abundances. This arises with nonresonant waves, which are ubiquitous in
open field regions, and is also stronger with torsional Alfven waves, as
opposed to shear (i.e. planar) waves. We discuss the bearing these findings
have on models of interchange reconnection as the source of the slow speed
solar wind. The outflowing solar wind must ultimately be a mixture of the
plasma in the originally open and closed fields, and the proportions and degree
of mixing should depend on details of the reconnection process. We also
describe novel diagnostics in ultraviolet and extreme ultraviolet spectroscopy
now available with these new insights, with the prospect of investigating slow
speed solar wind origins and the contribution of interchange reconnection by
remote sensing.
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In this paper, we study the Poisson equation and heat equation in a model
matrix geometry $M_n$. Our main results are about the Poisson equation and
global behavior of the heat equation on $M_n$. We can show that if $c_0$ is the
initial positive definite matrix in $M_n$, then $c(t)$ exists for all time and
is positive definite too. We can also show the entropy stability of the
solutions to the heat equation.
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The localization spectra of Lyapunov vectors in many-particle systems at low
density exhibit a characteristic bending behavior. It is shown that this
behavior is due to a restriction on the maximum number of the most localized
Lyapunov vectors determined by the system configuration and mutual
orthogonality. For a quasi-one-dimensional system this leads to a predicted
bending point at n_c \approx 0.432 N for an N particle system. Numerical
evidence is presented that confirms this predicted bending point as a function
of the number of particles N.
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The Superstripes 2016 conference, held on June 23-29, 2016 in the island of
Ischia in Italy celebrated the 20th anniversary of this series of conferences.
For 20 years structural, electronic, and magnetic phase inhomogeneities in
quantum matter have been the scientific focus for a growing physics community
interested in complexity in quantum matter. It has been the meeting point for
different scientific communities facing the challenging project to unveil the
complex space and time landscapes in quantum matter. The interesting spatial
inhomogeneity length scale of multiple coexisting phase ranges from atomic to
mesoscopic and the time fluctuations are spread over multiple time scales. The
response of these materials changes using different experimental techniques
with different spatial and time resolution probing different aspects of the
quantum complexity.
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This work sought to find out the effectiveness of Anambra Broadcasting
Service (ABS) Radio news on teaching and learning. The study focused mainly on
listeners of ABS radio news broadcast in Awka, the capital of Anambra State,
Nigeria. Its objectives were to find out; if Awka based students are exposed to
ABS radio; to discover the ABS radio program students favorite; the need
gratification that drives students to listen to ABS radio news; the
contributions of radio news to students teaching and learning; and
effectiveness of ABS radio news on teaching and learning in Awka. The
population of Awka students is 198,868. This is also the population of the
study. But a sample size of 400 was chosen and administered with
questionnaires. The study was hinged on the uses and gratification theory. It
adopted a survey research design. The data gathered was analyzed using simple
percentages and frequency of tables. The study revealed that news is very
effective in teaching and learning. It was concluded that news is the best
instructional media to be employed in teaching and learning. Among other
things, it was recommended that teachers and students should listen to and make
judicious use of news for academic purposes.
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Quantum imaging with undetected photons relies on the principle of induced
coherence without induced emission and uses two sources of photon-pairs with a
signal- and an idler photon. Each pair shares strong quantum correlations in
both position and momentum, which allows to image an object illuminated with
idler photons by just measuring signal photons that never interact with the
object. In this work, we theoretically investigate the transverse resolution of
this non-local imaging scheme through a general formalism that treats
propagating photons beyond the commonly used paraxial approximation. We hereby
prove that the resolution of quantum imaging with undetected photons is
fundamentally diffraction limited to the longer wavelength of the signal and
idler pairs. Moreover, we conclude that this result is also valid for other
non-local two-photon imaging schemes.
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In this paper, we have investigated the late time cosmic acceleration issue
in the context of $f(R,T)$ gravity. The matter field is considered to be that
of viscous fluid. The model has been framed as a mathematical formalism and the
effect of viscous fluid on the cosmic expansion has been shown. The equation of
state parameter indicates the quintessence behaviour of the Universe at late
time. The theoretical results obtained here shows its alignment with the
cosmological observations result.
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Although superconducting systems provide a promising platform for quantum
computing, their networking poses a challenge as they cannot be interfaced to
light---the medium used to send quantum signals through channels at room
temperature. We show that mechanical oscillators can mediated such coupling and
light can be used to measure the joint state of two distant qubits. The
measurement provides information on the total spin of the two qubits such that
entangled qubit states can be postselected. Entanglement generation is possible
without ground-state cooling of the mechanical oscillators for systems with
optomechanical cooperativity moderately larger than unity; in addition, our
setup tolerates a substantial transmission loss. The approach is scalable to
generation of multipartite entanglement and represents a crucial step towards
quantum networks with superconducting circuits.
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In this paper, we obtain $C^{1,\alpha}$ estimates for weak solutions of
certain quasilinear parabolic equations satisfying nonstandard growth
conditions, the prototype examples being $$u_t - \text{div} (|\nabla u|^{p-2}
\nabla u + a(t)|\nabla u|^{q-2} \nabla u) = 0,$$ $$u_t - \text{div} (|\nabla
u|^{p(t)-2} \nabla u) = 0.$$ under the assumption that the solutions a priori
have bounded gradient. We build on the recently developed scaling and covering
argument which allows us to consider the singular and degenerate cases in a
uniform manner and with minimal regularity requirements on the phase switching
factor $a(t)$ and the variable exponent $p(t)$. Moreover, we are able to take
any $p \leq q < \infty$ to obtain the desired regularity.
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We present a comprehensive study of the dust and gas properties in the
after-head-on-collision UGC12914/15 galaxy system using multi-transition CO
data and SCUBA sub-mm continuum images at both 450 and 850$\mu$m. CO(3-2) line
emission was detected in the disks of UGC 12914 and UGC 12915 as well as in a
bridge connecting the two galaxies. Dust emission at 450$\mu$m was detected for
the first time in the two galactic disks and in the connecting bridge. Using an
LVG excitation analysis model we have obtained good estimates of the physical
parameters in different regions of this system and the amount of molecular gas
was found to be 3-4 times lower than that estimated by other investigators
using the standard Galactic CO-to-H2 conversion factor. Comparing with the dust
mass derived from the SCUBA data, we found that the gas-to-dust ratio was
comparable to the Galactic value in the two galaxy disks but a factor of ~3
higher in the bridge. The physical condition of the molecular gas in the bridge
is comparable to that in the diffuse clouds in our Galaxy. Our result is
consistent with the scenario that the bridge molecular gas originated from the
disk molecular clouds and has been drawn out of the galactic disks due to
direct cloud-cloud collision.
Our data indicate that the global star formation efficiency (SFE) in UGC
12915 is comparable to that of normal spiral galaxies, and the SFE is 40% lower
in UGC 12914 than in UGC 12915. Little star formation activity was found in the
bridge except in an HII region adjacent to the disk of UGC 12915.
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