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Within the framework of the Lee model, we analyze in detail the difference
between the energy derivative of the phase shift and the standard spectral
function of the unstable state. The fact that the model is exactly solvable
allows us to demonstrate the construction of these observables from various
exact Green functions. The connection to a formula due to Krein, Friedal, and
Lloyd is also examined. We also directly demonstrate how the derivative of the
phase shift correctly identifies the relevant interaction contributions for
consistently including an unstable state in describing the thermodynamics.
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The cluster 1ES0657-556 is an ideal astrophysical laboratory to study the
distribution and the nature of Dark Matter because this last component is
spatially separated from the intracluster gas. We show that microwave
observations can provide crucial probes of Dark Matter in this system. We
calculate the expected SZ effect from Dark Matter annihilation in the main mass
concentrations of the cluster 1ES0657-556, and we estimate the sources of
contamination, confusion and bias to asses its significance. We find that SZ
observations at a frequency of 223 GHz can resolve both spatially and
spectrally the SZ_DM signal and isolate it from the other SZ signals, and
mainly from the thermal SZ effect which is null at frequencies 220-223 GHz for
the case of 1ES0657-556. We conclude that SZ observations with sub-arcmin
resolution and micro-K sensitivity of 1ES0657-556 are crucial, and maybe
unique, to find direct astrophysical probes of the existence and of the nature
of Dark Matter, or to set strong experimental limits.
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The upper atmospheres of the planets and their satellites are more directly
exposed to sunlight and solar wind particles than the surface or the deeper
atmospheric layers. At the altitudes where the associated energy is deposited,
the atmospheres may become ionized and are referred to as ionospheres. The
details of the photon and particle interactions with the upper atmosphere
depend strongly on whether the object has anintrinsic magnetic field that may
channel the precipitating particles into the atmosphere or drive the
atmospheric gas out to space. Important implications of these interactions
include atmospheric loss over diverse timescales, photochemistry and the
formation of aerosols, which affect the evolution, composition and remote
sensing of the planets (satellites). The upper atmosphere connects the planet
(satellite) bulk composition to the near-planet (-satellite) environment.
Understanding the relevant physics and chemistry provides insight to the past
and future conditions of these objects, which is critical for understanding
their evolution. This chapter introduces the basic concepts of upper
atmospheres and ionospheres in our solar system, and discusses aspects of their
neutral and ion composition, wind dynamics and energy budget. This knowledge is
key to putting in context the observations of upper atmospheres and haze on
exoplanets, and to devise a theory that explains exoplanet demographics.
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A consensus that questions the perfunctory use of the quantum adiabatic
theorem has emerged since Marzlin and Sanders [Phys. Rev. Lett. {\bf 93},
160408 (2004)] showed the existence of an inconsistency in the applicability of
the theorem. Further analysis proved that the inconsistency may arise from the
existence of resonant terms in the Hamiltonian, but recent work indicates that
the debate about the full extent of the problem remains open. Here, we first
show that key premises required in the standard demonstration of the theorem do
not hold for a dual Hamiltonian involved in the Marzlin-Sanders inconsistency.
Also, we show that two simple conditions can identify systems for which the
adiabatic approximation fails, in spite of satisfying traditional quantitative
conditions that were believed to guarantee its validity. Finally, we prove that
the inconsistency only arises for Hamiltonians that contain resonant terms
whose amplitudes go asymptotically to zero.
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A 3D almost-Riemannian manifold is a generalized Riemannian manifold defined
locally by 3 vector fields that play the role of an orthonormal frame, but
could become collinear on some set $\Zz$ called the singular set. Under the
Hormander condition, a 3D almost-Riemannian structure still has a metric space
structure, whose topology is compatible with the original topology of the
manifold. Almost-Riemannian manifolds were deeply studied in dimension 2. In
this paper we start the study of the 3D case which appear to be reacher with
respect to the 2D case, due to the presence of abnormal extremals which define
a field of directions on the singular set. We study the type of singularities
of the metric that could appear generically, we construct local normal forms
and we study abnormal extremals. We then study the nilpotent approximation and
the structure of the corresponding small spheres. We finally give some
preliminary results about heat diffusion on such manifolds.
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We prove that the $K$-group of reciprocity functors, defined by F. Ivorra and
the first author, vanishes over a perfect field as soon as one of the
reciprocity functors is $\mathbb{G}_a$ and one is an abelian variety.
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The consequences of the constraints which de Sitter embedding of $f(R)$
theories imposes on the Lagrangian's parameters, are investigated within the
metric formalism. It is shown, in particular, that several common $f(R)$
Lagrangians do not actually admit such an embedding. Otherwise, asymptotic
matching of local solutions of the corresponding models with background
(maximally symmetric) spaces of constant curvature is either unstable or,
anti-de Sitter embedding is the only stable embedding. Additional arguments are
given in favour of a previous claim that a class of $f(R)$ models comprising
both positive and negative powers of $R$ (two different mass scales), could be
a nice scenario where to address, in a united picture, both early-time
inflation and late-time accelerated expansion of the universe. The approach
undertaken here is used, also, to check ghost-freedom of a Dirac-Born-Infeld
modification of general relativity previously studied in the bibliography.
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We analyze the accelerator constraints on the parameter space of the Minimal
Supersymmetric extension of the Standard Model, comparing those now available
from LEP II and anticipating the likely sensitivity of Tevatron Run II. The
most important limits are those from searches for charginos, neutralinos and
Higgs bosons at LEP, and searches for stop squarks, charginos and neutralinos
at the Tevatron Collider. We also incorporate the constraints derived from b
--> s + gamma decay, and discuss the relevance of charge- and colour-breaking
minima in the effective potential. We combine and compare the different
constraints on the Higgs-mixing parameter mu, the gaugino-mass parameter
m_{1/2} and the scalar-mass parameter m0, incorporating radiative corrections
to the physical particle masses. We focus on the resulting limitations on
supersymmetric dark matter, assumed to be the lightest neutralino,
incorporating coannihilation effects in the calculation of the relic abundance.
We find that m_chi > 51 GeV and tan(beta) > 2.2 if all soft
supersymmetry-breaking scalar masses are universal, including those of the
Higgs bosons, and that these limits weaken to m_chi > 46 GeV and tan(beta) >
1.9 if non-universal scalar masses are allowed. Light neutralino dark matter
cannot be primarily Higgsino in composition.
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We present a novel online learning algorithm for a class of unknown and
uncertain dynamical environments that are fully observable. First, we obtain a
novel probabilistic characterization of systems whose mean behavior is known
but which are subject to additive, unknown subGaussian disturbances. This
characterization relies on recent concentration of measure results and is given
in terms of ambiguity sets. Second, we extend the results to environments whose
mean behavior is also unknown but described by a parameterized class of
possible mean behaviors. Our algorithm adapts the ambiguity set dynamically by
learning the parametric dependence online, and retaining similar probabilistic
guarantees with respect to the additive, unknown disturbance. We illustrate the
results on a differential-drive robot subject to environmental uncertainty.
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The transmission of wave packets through tunneling barriers is studied in
detail by the method of quantum molecular dynamics. The distribution function
of the times describing the arrival of a tunneling packet in front of and
behind a barrier and the momentum distribution function of the packet are
calculated. The behavior of the average coordinate of a packet, the average
momentum, and their variances is investigated. It is found that under the
barrier a part of the packet is reflected and a Gaussian barrier increases the
average momentum of the transmitted packet and its variance in momentum space.
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We provide a measurement protocol to estimate 2- and 4-point fermionic
correlations in ultra-cold atom experiments. Our approach is based on combining
random atomic beam splitter operations, which can be realized with programmable
optical landscapes, with high-resolution imaging systems such as quantum gas
microscopes. We illustrate our results in the context of the variational
quantum eigensolver algorithm for solving quantum chemistry problems.
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For homogeneous difference equation of the second order we study the analogy
of Hartman-Wintner problem on asymptotic integration of fundamental system of
solutions as argument tends to infinity.
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The temperature dependence of AC susceptibility (ACS) has been measured for a
very high-quality plate-like slightly overdoped YBCO single crystal for
different frequencies and AC magnetic field amplitudes. Frequency dependence of
the ACS is weak irrespective of the magnetic field orientation but significant
effects of field orientation with respect to the CuO2 planes and field
magnitude on real and imaginary components of fundamental ACS were observed.
The height of the loss peak saturates as full penetration of magnetic field is
achieved. The peak temperature, Tp, in \c{hi}" shifts to lower temperatures
with increasing magnetic field amplitude for both HIIc and HIIab. The value of
Tp depends on the orientation of the magnetic field with respect to the
crystallographic axes, illustrating the anisotropy in the magnetic flux
dynamics. The superconducting transition width increases weakly with increasing
magnetic field. The Cole-Cole plot [\c{hi}"(\c{hi}')] shows qualitatively and
quantitatively identical features for HIIc and HIIab, independent of the
orientation of the magnetic field with respect to the sample geometry and
shielding current paths. The general features of \c{hi}"(\c{hi}') implies that,
there is no flux creep for the range of frequencies and AC fields employed in
this investigation. The maximum value of the loss peak and its position with
respect to \c{hi}' in the Cole-Cole plot are largely consistent with the Bean
critical state model. Slightly increased peak value in comparison to the
predicted peak value within the Bean critical state model is probably due to a
weak field dependence of Jc. The results obtained here are compared with
various theoretical models and experimental findings. Prominent differences are
noted and discussed in details in this study.
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A graph is an abstract model that represents relations among entities, for
example, the interactions between characters in a novel. A background story
endows entities and relations with real-world meanings and describes the
semantics and context of the abstract model, for example, the actual story that
the novel presents. Considering practical experience and prior research, human
viewers who are familiar with the background story of a graph and those who do
not know the background story may perceive the same graph differently. However,
no previous research has adequately addressed this problem. This research paper
thus presents an evaluation that investigated the effects of background stories
on graph perception. Three hypotheses that focused on the role of visual focus
areas, graph structure identification, and mental model formation on graph
perception were formulated and guided three controlled experiments that
evaluated the hypotheses using real-world graphs with background stories. An
analysis of the resulting experimental data, which compared the performance of
participants who read and did not read the background stories, obtained a set
of instructive findings. First, having knowledge about a graph's background
story influences participants' focus areas during interactive graph
explorations. Second, such knowledge significantly affects one's ability to
identify community structures but not high degree and bridge structures. Third,
this knowledge influences graph recognition under blurred visual conditions.
These findings can bring new considerations to the design of storytelling
visualizations and interactive graph explorations.
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Stroke can have a severe impact on an individual's quality of life, leading
to consequences such as motor loss and communication problems, especially among
the elderly. Studies have shown that early and easy access to stroke
rehabilitation can improve an elderly individual's quality of life, and that
telerehabilitation is a solution that facilitates this improvement. In this
work, we visualize movement to music during rehabilitation exercises captured
by the Kinect motion sensor, using a dedicated Serious Game called `Move to the
Music'(MoMu). Our system provides a quantitative view of progress made by
patients during a motor rehabilitation regime for healthcare professionals to
track remotely (tele-rehab).
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The study of the interactions of living adherent cells with mechanically
stable (visco)elastic materials enables understanding and exploiting
physiological phenomena mediated by cell-extracellular communication. However,
insight on the interaction of cells and surrounding objects with different
stability patterns upon cell contact might unveil cell responses that may be
engineered for innovative applications. Here, it is hypothesized that the
efficiency of cell attachment, spreading and movement across a free-packed
granular bed of microparticles depend on microparticle diameter, raising the
possibility of a necessary minimum traction force for the reinforcement of
cell-particle bonds, and long-term cell adhesion. The results suggest that
microparticles with 14-20 {\mu}m are prone to cell-mediated mobility, holding
the potential of inducing early cell detachment, while objects with diameters
from 38-85 {\mu}m enable long-lasting cell adhesion and proliferation. An
in-silico hybrid particle-based model that addresses time-dependent biological
mechanisms of cell adhesion is proposed, providing inspiration for engineering
platforms to address healthcare-related challenges.
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Using the Atacama Large Millimeter/sub-millimeter Array, we have detected
CO(3-2) line and far-infrared continuum emission from a galaxy associated with
a high-metallicity ([M/H] = -0.27) damped Ly-alpha absorber (DLA) at z
=2.19289. The galaxy is located 3.5" away from the quasar sightline,
corresponding to a large impact parameter of 30 kpc at the DLA redshift. We use
archival Very Large Telescope-SINFONI data to detect Halpha emission from the
associated galaxy, and find that the object is dusty, with a dust-corrected
star formation rate of 110 +60 -30 Msun/yr. The galaxy's molecular mass is
large, Mmol = (1.4 +- 0.2) x 10^11 x (\alpha_CO/4.3) x (0.57/r_31) Msun,
supporting the hypothesis that high-metallicity DLAs arise predominantly near
massive galaxies. The excellent agreement in redshift between the CO(3-2) line
emission and low-ion metal absorption (~40 km/s) disfavors scenarios whereby
the gas probed by the DLA shows bulk motion around the galaxy. We use Giant
Metrewave Radio Telescope HI 21cm absorption spectroscopy to find that the HI
along the DLA sightline must be warm, with a stringent lower limit on the spin
temperature of T_s > 1895 x (f/0.93) K. The detection of CI absorption in the
DLA, however, also indicates the presence of cold neutral gas. To reconcile
these results requires that the cold components in the DLA contribute little to
the HI column density, yet contain roughly 50% of the metals of the absorber,
underlining the complex multi-phase nature of the gas surrounding high-z
galaxies.
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Empirical Bayes provides a powerful approach to learning and adapting to
latent structure in data. Theory and algorithms for empirical Bayes have a rich
literature for sequence models, but are less understood in settings where
latent variables and data interact through more complex designs. In this work,
we study empirical Bayes estimation of an i.i.d. prior in Bayesian linear
models, via the nonparametric maximum likelihood estimator (NPMLE). We
introduce and study a system of gradient flow equations for optimizing the
marginal log-likelihood, jointly over the prior and posterior measures in its
Gibbs variational representation using a smoothed reparametrization of the
regression coefficients. A diffusion-based implementation yields a Langevin
dynamics MCEM algorithm, where the prior law evolves continuously over time to
optimize a sequence-model log-likelihood defined by the coordinates of the
current Langevin iterate. We show consistency of the NPMLE as $n, p \rightarrow
\infty$ under mild conditions, including settings of random sub-Gaussian
designs when $n \asymp p$. In high noise, we prove a uniform log-Sobolev
inequality for the mixing of Langevin dynamics, for possibly misspecified
priors and non-log-concave posteriors. We then establish polynomial-time
convergence of the joint gradient flow to a near-NPMLE if the marginal negative
log-likelihood is convex in a sub-level set of the initialization.
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Copula-based models provide a great deal of flexibility in modelling
multivariate distributions, allowing for the specifications of models for the
marginal distributions separately from the dependence structure (copula) that
links them to form a joint distribution. Choosing a class of copula models is
not a trivial task and its misspecification can lead to wrong conclusions. We
introduce a novel class of grid-uniform copula functions, which is dense in the
space of all continuous copula functions in a Hellinger sense. We propose a
Bayesian model based on this class and develop an automatic Markov chain Monte
Carlo algorithm for exploring the corresponding posterior distribution. The
methodology is illustrated by means of simulated data and compared to the main
existing approach.
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Marketing scholars have underscored the importance of conceptual articles in
providing theoretical foundations and new perspectives to the field. This paper
supports the argument by employing two network-based measures - the number of
citations and the disruption score - and comparing them for conceptual and
empirical research. With the aid of a large language model, we classify
conceptual and empirical articles published in a substantial set of marketing
journals. The findings reveal that conceptual research is not only more
frequently cited but also has a greater disruptive impact on the field of
marketing than empirical research. Our paper contributes to the understanding
of how marketing articles advance knowledge through developmental approaches.
|
Deep learning techniques have proven high accuracy for identifying melanoma
in digitised dermoscopic images. A strength is that these methods are not
constrained by features that are pre-defined by human semantics. A down-side is
that it is difficult to understand the rationale of the model predictions and
to identify potential failure modes. This is a major barrier to adoption of
deep learning in clinical practice. In this paper we ask if two existing local
interpretability methods, Grad-CAM and Kernel SHAP, can shed light on
convolutional neural networks trained in the context of melanoma detection. Our
contributions are (i) we first explore the domain space via a reproducible,
end-to-end learning framework that creates a suite of 30 models, all trained on
a publicly available data set (HAM10000), (ii) we next explore the reliability
of GradCAM and Kernel SHAP in this context via some basic sanity check
experiments (iii) finally, we investigate a random selection of models from our
suite using GradCAM and Kernel SHAP. We show that despite high accuracy, the
models will occasionally assign importance to features that are not relevant to
the diagnostic task. We also show that models of similar accuracy will produce
different explanations as measured by these methods. This work represents first
steps in bridging the gap between model accuracy and interpretability in the
domain of skin cancer classification.
|
The results of non-local experiments in different contact configurations are
discussed in terms of a non-local behaviour of the contact arms. It is shown
that the observed reproducible fluctuations can be understood to result from
fluctuations of a non-local bulk current in the contact arms. The fluctuations
are explained by edge channel backscattering because of potential fluctuations
in the bulk region.
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We use a general relativistic approach to investigate the effects of weak
cosmological magnetic fields on linear rotational perturbations during the
radiation and dust epochs of the universe. This includes ordinary kinematic
vorticity, as well as vortex-like inhomogeneities in the density distribution
of the cosmic medium. Our study confirms that magnetic fields can source both
types of perturbations and shows that their presence also helps cosmic rotation
to survive longer. In agreement with previous Newtonian studies, we find that
during the dust era vorticity decays slower than in non-magnetised cosmologies.
Prior to equipartition the magnetic effect is more pronounced, since it helps
the aforementioned rotational distortions to maintain constant magnitude.
Overall, magnetised universes seem to provide a much better environment for the
survival of cosmic vorticity than their magnetic-free counterparts.
|
This review presents a unified view on the problem of Anderson localization
in one-dimensional weakly disordered systems with short-range and long-range
statistical correlations in random potentials. The following models are
analyzed: the models with continuous potentials, the tight-binding models of
the Anderson type, and various Kronig-Penney models with different types of
perturbations. Main attention is payed to the methods of obtaining the
localization length in dependence on the controlling parameters of the models.
Specific interest is in an emergence of effective mobility edges due to certain
long-range correlations in a disorder. The predictions of the theoretical and
numerical analysis are compared to recent experiments on microwave transmission
through randomly filled waveguides.
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Self-correcting quantum memories demonstrate robust properties that can be
exploited to improve active quantum error-correction protocols. Here we propose
a cellular automaton decoder for a variation of the color code where the bases
of the physical qubits are locally rotated, which we call the XYZ color code.
The local transformation means our decoder demonstrates key properties of a
two-dimensional fractal code if the noise acting on the system is infinitely
biased towards dephasing, namely, no string-like logical operators. As such, in
the high-bias limit, our local decoder reproduces the behavior of a partially
self-correcting memory. At low error rates, our simulations show that the
memory time diverges polynomially with system size without intervention from a
global decoder, up to some critical system size that grows as the error rate is
lowered. Furthermore, although we find that we cannot reproduce partially
self-correcting behavior at finite bias, our numerics demonstrate improved
memory times at realistic noise biases. Our results therefore motivate the
design of tailored cellular automaton decoders that help to reduce the
bandwidth demands of global decoding for realistic noise models.
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The COVID-19 Open Research Dataset (CORD-19) is a growing resource of
scientific papers on COVID-19 and related historical coronavirus research.
CORD-19 is designed to facilitate the development of text mining and
information retrieval systems over its rich collection of metadata and
structured full text papers. Since its release, CORD-19 has been downloaded
over 200K times and has served as the basis of many COVID-19 text mining and
discovery systems. In this article, we describe the mechanics of dataset
construction, highlighting challenges and key design decisions, provide an
overview of how CORD-19 has been used, and describe several shared tasks built
around the dataset. We hope this resource will continue to bring together the
computing community, biomedical experts, and policy makers in the search for
effective treatments and management policies for COVID-19.
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We obtain the static spherically symmetric solutions of a class of
gravitational models whose additions to the General Relativity (GR) action
forbid Ricci-flat, in particular, Schwarzschild geometries. These theories are
selected to maintain the (first) derivative order of the Einstein equations in
Schwarzschild gauge. Generically, the solutions exhibit both horizons and a
singularity at the origin, except for one model that forbids spherical symmetry
altogether. Extensions to arbitrary dimension with a cosmological constant,
Maxwell source and Gauss-Bonnet terms are also considered.
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A large fraction of known Jupiter like exoplanets are inflated as compared to
Jupiter. These "hot" Jupiters orbit close to their parent star and are
bombarded with intense starlight. Many theories have been proposed to explain
their radius inflation and several suggest that a small fraction of the
incident starlight is injected in to the planetary interior which helps to puff
up the planet. How will such energy injection affect the planetary dynamo? In
this Letter, we estimate the surface magnetic field strength of hot Jupiters
using scaling arguments that relate energy available in planetary interiors to
the dynamo generated magnetic fields. We find that if we take into account the
energy injected in the planetary interior that is sufficient to inflate hot
Jupiters to observed radii, then the resulting dynamo should be able generate
magnetic fields that are more than an order of magnitude stronger than the
Jovian values. Our analysis highlights the potential fundamental role of the
stellar light in setting the field strength in hot Jupiters.
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From the subsubleading chiral three-nucleon force [intermediate-range
contributions, published in Phys. Rev. C\,87, 054007 (2013)] a
density-dependent NN-interaction $V_\text{med}$ is derived in isospin-symmetric
nuclear matter. Following the division of the pertinent 3N-diagrams into
two-pion-one-pion exchange topology and ring topology, one evaluates for these
all selfclosings and concatenations of nucleon-lines to an in-medium loop. In
the case of the $2\pi 1\pi$-exchange topology, the momentum- and
$k_f$-dependent potentials associated with the isospin-operators ($1$ and
$\vec\tau_1 \!\cdot\! \vec\tau_2$) and five independent spin-structures require
at most one numerical integration. For the more challenging (concatenations of
the) ring diagrams proportional to $c_{1,2,3,4}$, one ends up with regularized
double-integrals $\int_0^\lambda dr\,r \int_0^{\pi/2} d\psi$ from which the
$\lambda^2$-divergence has been subtracted and the logarithmic piece $\sim \ln
(m_\pi/\lambda)$ is isolated. The derived semi-analytical results are most
helpful to implement the subsubleading chiral 3N-forces into nuclear many-body
calculations.
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Existing ubiquitously in the Universe with the highest luminosity, the
Lyman-$\alpha$ emission line encodes abundant physical information about the
gaseous medium it interacts with. Nevertheless, the resonant nature of
Ly$\alpha$ complicates the radiative transfer (RT) modeling of the line
profile, making the extraction of physical properties of the surrounding
gaseous medium notoriously difficult. In this paper, we revisit the problem of
deciphering the Ly$\alpha$ emission line with RT modeling. We reveal intrinsic
parameter degeneracies in the widely-used shell model in the optically thick
regime for both static and outflowing cases, which suggest the limitations of
the model. We have also explored the connection between the more physically
realistic multiphase, clumpy model and the shell model. We find that the
parameters of a ``very clumpy'' slab model and the shell model have the
following correspondences: (1) the total column density of the clumpy slab
model is equal to the HI column density of the shell model; (2) the effective
temperature of the clumpy slab model, which incorporates the clump velocity
dispersion, is equal to the effective temperature of the shell model; (3) the
average radial clump outflow velocity is equal to the shell expansion velocity;
(4) large intrinsic line widths are required in the shell model to reproduce
the wings of the clumpy slab models; (5) adding another phase of hot
inter-clump medium will increase peak separation, and the fitted shell
expansion velocity lies between the outflow velocities of two phases of gas.
Our results provide a viable solution to the major discrepancies associated
with Ly$\alpha$ fitting reported in previous literature, and emphasize the
importance of utilizing information from additional observations to break the
intrinsic degeneracies as well as interpreting the model parameters in a more
physically realistic context.
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Up-to-date poverty maps are an important tool for policy makers, but until
now, have been prohibitively expensive to produce. We propose a generalizable
prediction methodology to produce poverty maps at the village level using
geospatial data and machine learning algorithms. We tested the proposed method
for 25 Sub-Saharan African countries and validated them against survey data.
The proposed method can increase the validity of both single country and
cross-country estimations leading to higher precision in poverty maps of 44
Sub-Saharan African countries than previously available. More importantly, our
cross-country estimation enables the creation of poverty maps when it is not
practical or cost-effective to field new national household surveys, as is the
case with many low- and middle-income countries.
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Compartmentalised biochemical reactions are a ubiquitous building block of
biological systems. The interplay between chemical and compartmental dynamics
can drive rich and complex dynamical behaviors that are difficult to analyse
mathematically -- especially in the presence of stochasticity. We have recently
proposed an effective moment equation approach to study the statistical
properties of compartmentalised biochemical systems. So far, however, this
approach is limited to polynomial rate laws and moreover, it relies on suitable
moment closure approximations, which can be difficult to find in practice. In
this work we propose a systematic method to derive closed moment dynamics for
compartmentalised biochemical systems. We show that for the considered class of
systems, the moment equations involve expectations over functions that
factorize into two parts, one depending on the molecular content of the
compartments and one depending on the compartment number distribution. Our
method exploits this structure and approximates each function with suitable
polynomial expansions, leading to a closed system of moment equations. We
demonstrate the method using three systems inspired by cell populations and
organelle networks and study its accuracy across different dynamical regimes.
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Using as basic observable an angular-integrated asymmetry to be measured in
Drell-Yan lepton-pair production at the LHC, we discuss the identification
reach on the spin-2 of the lowest-lying Randall-Sundrum resonance predicted by
gravity in one warped extra dimension, against the spin-1 and spin-0
hypotheses. Numerical results indicate that, depending on the graviton coupling
strength to the standard model particles, such a spin-2 identification can
extend up to mass scales of 1.0-1.6 TeV and 2.4-3.2 TeV for LHC integrated
luminosities of 10 and 100 fb^{-1}, respectively.
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We use a locally constant field approximation (LCFA) to study the one-loop
Heisenberg-Euler effective action in a particular class of slowly varying
inhomogeneous electric fields of Lorentzian shape with $0\leq d\leq 4$
inhomogeneous directions. We show that for these fields, the LCFA of the
Heisenberg-Euler effective action can be represented in terms of a single
parameter integral, with the constant field effective Lagrangian with rescaled
argument as integration kernel. The imaginary part of the Heisenberg-Euler
effective action contains information about the instability of the quantum
vacuum towards the formation of a state with real electrons and positrons.
Here, we in particular focus on the dependence of the instantaneous vacuum
decay rate on the dimension $d$ of the field inhomogeneity. Specifically for
weak fields, we find an overall parametric suppression of the effect with
$(E_0/E_{\rm cr})^{d/2}$, where $E_0$ is the peak field strength of the
inhomogeneity and $E_{\rm cr}$ the critical electric field strength.
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A smoothing algorithm is presented for solving the soft-margin Support Vector
Machine (SVM) optimization problem with an $\ell^{1}$ penalty. This algorithm
is designed to require a modest number of passes over the data, which is an
important measure of its cost for very large datasets. The algorithm uses
smoothing for the hinge-loss function, and an active set approach for the
$\ell^{1}$ penalty. The smoothing parameter $\alpha$ is initially large, but
typically halved when the smoothed problem is solved to sufficient accuracy.
Convergence theory is presented that shows
$\mathcal{O}(1+\log(1+\log_+(1/\alpha)))$ guarded Newton steps for each value
of $\alpha$ except for asymptotic bands $\alpha=\Theta(1)$ and
$\alpha=\Theta(1/N)$, with only one Newton step provided $\eta\alpha\gg1/N$,
where $N$ is the number of data points and the stopping criterion that the
predicted reduction is less than $\eta\alpha$. The experimental results show
that our algorithm is capable of strong test accuracy without sacrificing
training speed.
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We propose a lattice statistical model to investigate the phase diagrams and
the soft responses of nematic liquid-crystal elastomers. Using suitably scaled
infinite-range interactions, we obtain exact self-consistent equations for the
tensor components of the nematic order parameter in terms of temperature, the
distortion and stress tensors, and the initial nematic order. These equations
are amenable to simple numerical calculations, which are used to characterize
the low-temperature soft regime. We find a peculiar phase diagram, in terms of
temperature and the diagonal component of the distortion tensor along the
stretching direction, with first- and second-order transitions to the soft
phase, and the prediction of tricritical points. This behavior is not
qualitatively changed if we use different values of the initial nematic order
parameter.
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We discuss metacognitive modelling as an enhancement to cognitive modelling
and computing. Metacognitive control mechanisms should enable AI systems to
self-reflect, reason about their actions, and to adapt to new situations. In
this respect, we propose implementation details of a knowledge taxonomy and an
augmented data mining life cycle which supports a live integration of obtained
models.
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Do object part localization methods produce bilaterally symmetric results on
mirror images? Surprisingly not, even though state of the art methods augment
the training set with mirrored images. In this paper we take a closer look into
this issue. We first introduce the concept of mirrorability as the ability of a
model to produce symmetric results in mirrored images and introduce a
corresponding measure, namely the \textit{mirror error} that is defined as the
difference between the detection result on an image and the mirror of the
detection result on its mirror image. We evaluate the mirrorability of several
state of the art algorithms in two of the most intensively studied problems,
namely human pose estimation and face alignment. Our experiments lead to
several interesting findings: 1) Surprisingly, most of state of the art methods
struggle to preserve the mirror symmetry, despite the fact that they do have
very similar overall performance on the original and mirror images; 2) the low
mirrorability is not caused by training or testing sample bias - all algorithms
are trained on both the original images and their mirrored versions; 3) the
mirror error is strongly correlated to the localization/alignment error (with
correlation coefficients around 0.7). Since the mirror error is calculated
without knowledge of the ground truth, we show two interesting applications -
in the first it is used to guide the selection of difficult samples and in the
second to give feedback in a popular Cascaded Pose Regression method for face
alignment.
|
E-communities, social groups interacting online, have recently become an
object of interdisciplinary research. As with face-to-face meetings, Internet
exchanges may not only include factual information but also emotional
information - how participants feel about the subject discussed or other group
members. Emotions are known to be important in affecting interaction partners
in offline communication in many ways. Could emotions in Internet exchanges
affect others and systematically influence quantitative and qualitative aspects
of the trajectory of e-communities? The development of automatic sentiment
analysis has made large scale emotion detection and analysis possible using
text messages collected from the web. It is not clear if emotions in
e-communities primarily derive from individual group members' personalities or
if they result from intra-group interactions, and whether they influence group
activities. We show the collective character of affective phenomena on a large
scale as observed in 4 million posts downloaded from Blogs, Digg and BBC
forums. To test whether the emotions of a community member may influence the
emotions of others, posts were grouped into clusters of messages with similar
emotional valences. The frequency of long clusters was much higher than it
would be if emotions occurred at random. Distributions for cluster lengths can
be explained by preferential processes because conditional probabilities for
consecutive messages grow as a power law with cluster length. For BBC forum
threads, average discussion lengths were higher for larger values of absolute
average emotional valence in the first ten comments and the average amount of
emotion in messages fell during discussions. Our results prove that collective
emotional states can be created and modulated via Internet communication and
that emotional expressiveness is the fuel that sustains some e-communities.
|
We derive integral representations in terms of the Macdonald functions for
the square modulus $s\mapsto | \Gamma ( a + i s ) |^2$ of the Gamma function
and its Fourier transform when $a<0$ and $a\not= -1,-2,\ldots $, generalizing
known results in the case $a>0$. This representation is based on a
renormalization argument using modified Bessel functions of the second kind,
and it applies to the representation of the solutions of the Fokker-Planck
equation.
|
In this paper we construct an explicit map from planar bicolored (plabic)
trivalent graphs representing a given irreducible positroid cell $S$ in the
totally non-negative Grassmannian $Gr^{\mbox{TNN}}(k,n)$ to the spectral data
for the relevant class of real regular Kadomtsev-Petviashvili II (KP)
solutions, thus completing search of real algebraic-geometric data for the KP
equation started in [4,6]. The spectral curve is modeled on Krichever
construction for degenerate finite-gap solutions, and is a rationally
degenerate $M$-curve, $\Gamma$, dual to the graph. The divisors are real
regular KP divisors in the ovals of $\Gamma$, i.e. they fulfill the conditions
for selecting real regular finite--gap solutions KPII solutions in [25]. Since
the soliton data are described by points in $S$, we establish a bridge between
real regular finite-gap KP solutions [25] and real regular multi-line KP
solitons which are known to be parameterized by points in
$Gr^{\mbox{TNN}}(k,n)$ [18,43].
We use the geometric characterization of spaces of relations on plabic
networks introduced in [7] to prove the invariance of this construction with
respect to the many gauge freedoms on the network. Such systems of relations
were proposed in [53] for the computation of scattering amplitudes on on--shell
diagrams $N=4$ SYM \cite{AGP1} and govern the totally non--negative
amalgamation of the little positive Grassmannians, $Gr^{\mbox{TP}}(1,3)$ and
$Gr^{\mbox{TP}}(2,3)$, into any given positroid cell $S$. In our setting they
rule the reality and regularity properties of the KP divisor.
Finally, we explain the transformation of the curve and the divisor both
under Postnikov moves and reductions and under amalgamation of positroid cells,
and apply our construction to some examples.
|
We consider a Coulomb potential plus a confinement potential $ A r^{\nu} $
and we study which of the two terms is dominant in the description of
quarkonia. We find that in general the term of confinement is dominant, which
allows us to understand why such potentials, like Martin's potential, are
successful in describing of heavy mesons.
|
We examine a simple hard disc fluid with no long range interactions on the
two dimensional space of constant negative Gaussian curvature, the hyperbolic
plane. This geometry provides a natural mechanism by which global crystalline
order is frustrated, allowing us to construct a tractable model of disordered
monodisperse hard discs. We extend free area theory and the virial expansion to
this regime, deriving the equation of state for the system, and compare its
predictions with simulation near an isostatic packing in the curved space.
Additionally, we investigate packing and dynamics on triply periodic,
negatively curved surfaces with an eye toward real biological and polymeric
systems.
|
When controlling an emerging outbreak of an infectious disease it is
essential to know the key epidemiological parameters, such as the basic
reproduction number $R_0$ and the control effort required to prevent a large
outbreak. These parameters are estimated from the observed incidence of new
cases and information about the infectious contact structures of the population
in which the disease spreads. However, the relevant infectious contact
structures for new, emerging infections are often unknown or hard to obtain.
Here we show that for many common true underlying heterogeneous contact
structures, the simplification to neglect such structures and instead assume
that all contacts are made homogeneously in the whole population, results in
conservative estimates for $R_0$ and the required control effort. This means
that robust control policies can be planned during the early stages of an
outbreak, using such conservative estimates of the required control effort.
|
We construct a unital locally matrix algebra of uncountable dimension that
(1) does not admit a primary decomposition,
(2) has an infinite locally finite Steinitz number.
It gives negative answers to questions from \cite{BezOl} and
\cite{Kurochkin}. We also show that for an arbitrary infinite Steinitz number
$s$ there exists a unital locally matrix algebra $A$ having the Steinitz number
$s$ and not isomorphic to a tensor product of finite dimensional matrix
algebras.
|
We apply homogenization theory to calculate the effective electric
conductivity and Hall coefficient tensor of passive three-dimensionally
periodic metamaterials subject to a weak external static homogeneous magnetic
field. We not only allow for variations of the conductivity and the Hall
coefficient of the constituent material(s) within the metamaterial unit cells,
but also for spatial variations of the magnetic permeability. We present four
results. First, our findings are consistent with previous numerical
calculations for finite-size structures as well as with recent experiments.
This provides a sound theoretical justification for describing such
metamaterials in terms of effective material parameters. Second, we visualize
the cofactor fields appearing in the homogenization integrals. Thereby, we
identify those parts of the metamaterial structures which are critical for the
observed effective metamaterial parameters, providing a unified view onto
various previously introduced single-constituent/multiple-constituent and
isotropic/anisotropic architectures, respectively. Third, we suggest a novel
three-dimensional non-magnetic metamaterial architecture exhibiting a sign
reversal of the effective isotropic Hall coefficient. It is conceptually
distinct from the original chainmail-like geometry, for which the sign reversal
is based on interlinked rings. Fourth, we discuss two examples for metamaterial
architectures comprising magnetic materials: Yet another possibility to reverse
the sign of the isotropic Hall coefficient and an approach to conceptually
break previous bounds for the effective mobility.
|
We propose a non-parametric, two-sample Bayesian test for checking whether or
not two data sets share a common distribution. The test makes use of data
splitting ideas and does not require priors for high-dimensional parameter
vectors as do other nonparametric Bayesian procedures. We provide evidence that
the new procedure provides more stable Bayes factors than do methods based on
P\'olya trees. Somewhat surprisingly, the behavior of the proposed Bayes
factors when the two distributions are the same is usually superior to that of
P\'olya tree Bayes factors. We showcase the effectiveness of the test by
proving its consistency, conducting a simulation study and applying the test to
Higgs boson data.
|
Measuring the average refractive index (RI) of spherical objects, such as
suspended cells, in quantitative phase imaging (QPI) requires a decoupling of
RI and size from the QPI data. This has been commonly achieved by determining
the object's radius with geometrical approaches, neglecting light-scattering.
Here, we present a novel QPI fitting algorithm that reliably uncouples the RI
using Mie theory and a semi-analytical, corrected Rytov approach. We assess the
range of validity of this algorithm in silico and experimentally investigate
various objects (oil and protein droplets, microgel beads, cells) and noise
conditions. In addition, we provide important practical cues for future studies
in cell biology.
|
We study the anisotropy theorem for Stanley-Reisner rings of simplicial
homology spheres in characteristic 2 by Papadakis and Petrotou. This theorem
implies the Hard Lefschetz theorem as well as McMullen's g-conjecture for such
spheres. Our first result is an explicit description of the quadratic form. We
use this description to prove a conjecture stated by Papadakis and Petrotou.
All anisotropy theorems for homology spheres and pseudo-manifolds in
characteristic 2 follow from this conjecture. Using a specialization argument,
we prove anisotropy for certain homology spheres over the field $\mathbb{Q}$.
These results provide another self-contained proof of the g-conjecture for
homology spheres in characteristic 2.
|
We prove that on overtwisted contact manifolds there can be no positive loops
of contactomorphisms that are generated by a $C^0$-small Hamiltonian function.
|
A mathematical procedure is suggested to obtain deformed entropy formulas of
type K(S_K) = sum_i P_i K(-ln P_i), by requiring zero mutual K(S_K)-information
between a finite subsystem and a finite reservoir. The use of this method is
first demonstrated on the ideal gas equation of state with finite constant heat
capacity, C, where it delivers the Renyi and Tsallis formulas. A novel
interpretation of the qstar = 2-q duality arises from the comparison of
canonical subsystem and total microcanonical partition approaches. Finally a
new, generalized deformed entropy formula is constructed for the linear
relation C(S) = C_0 + C_1 S.
|
We provide an easy characterization for the locus of indeterminacy of the
Prym map in terms of the dual graphs of stable curves. As a corollary, we show
that the closure of the Fridman-Smith locus coincides with the locus of
indeterminacy of the Prym map.
|
We present Ordinary Differential Equation Variational Auto-Encoder
(ODE$^2$VAE), a latent second order ODE model for high-dimensional sequential
data. Leveraging the advances in deep generative models, ODE$^2$VAE can
simultaneously learn the embedding of high dimensional trajectories and infer
arbitrarily complex continuous-time latent dynamics. Our model explicitly
decomposes the latent space into momentum and position components and solves a
second order ODE system, which is in contrast to recurrent neural network (RNN)
based time series models and recently proposed black-box ODE techniques. In
order to account for uncertainty, we propose probabilistic latent ODE dynamics
parameterized by deep Bayesian neural networks. We demonstrate our approach on
motion capture, image rotation and bouncing balls datasets. We achieve
state-of-the-art performance in long term motion prediction and imputation
tasks.
|
Structural, thermal, resistive and magnetic properties of melt quenched Bi
0.88 Sb 0.12 alloys are reported. The samples are heated at three different
temperatures, followed by rapid quenching in liquid nitrogen. Large temperature
difference between liquidus and solidus lines, led to microscopic
in-homogeneity in the alloy. The effect of quenching from different
temperatures in polycrystalline Bi 0.88 Sb 0.12 alloy has been studied. The
parameters such as strain, unit cell volume, and resistivity are found to
increase with temperature. Thermal variation of resistivity depicts non
monotonic temperature dependence. The total negative susceptibility increases
and band gap of semiconducting Bi 0.88 Sb 0.12 samples decreases with
increasing temperature.
|
As the demand of, requesting the Internet without any disturbance by the
mobile users of any network is increasing the IETF started working on Network
Mobility (NEMO). Maintaining the session of all the nodes in mobile network
with its home network and external nodes can be provided by the basic Network
Mobility support protocol. It provides mobility at IP level to complete
networks, allowing a Mobile Network to change its point of attachment to the
Internet, while maintaining the ongoing sessions of the nodes of the network.
The Mobile Router (MR) manages the mobility even though the nodes don't know
the status of mobility. This article discusses few basic concepts and
limitations of NEMO protocol and proposes two ways to optimize the NEMO routing
technique for registered and unregistered Correspondent Nodes (CN) of the
Mobile Network Node (MNN).
|
We present the abundances of N in a sample of 62 stars on the red giant
branch (RGB) in the peculiar globular cluster NGC 1851. The values of [N/Fe]
ratio were obtained by comparing the flux measured in the observed spectra with
that from synthetic spectra for up to about 15 features of CN. This is the
first time that N abundances are obtained for such a large sample of RGB stars
from medium-resolution spectroscopy in this cluster. With these abundances we
provide a chemical tagging of the split red giant branch found from several
studies in NGC 1851. The secondary, reddest sequence on the RGB is populated
almost exclusively by N-rich stars, confirming our previous suggestion based on
Stromgren magnitudes and colours. These giants are also, on average, enriched
in s-process elements such as Ba, and are likely the results of pollution from
low mass stars that experienced episodes of third dredge-up in the asymptotic
giant branch phase.
|
An unexpected experimental finding is reported where the primary morphology
developed during polymerization-induced phase separation in a rubber-modified
thermoplastic disappears at high conversions. This process was evidenced by
light scattering (LS) and scanning electron microscopy (SEM) for a particular
composition of solutions of polyisobutylene oligomers (PIB) in
isobornylmethacrylate (IBoMA), during the free-radical polymerization of the
monomer. The primary phase separation produced a dispersion of domains rich in
PIB containing significant amounts of the monomer (IBoMA). Polymerization of
the monomer in these domains occurred at high overall conversions producing the
filling of dispersed domains with a PIBoMA-PIB blend. Under these conditions
the final material had the appearance of a homogeneous blend. The process might
be adapted to produce new types of rubber-modified thermoplastics where rubber
particles are replaced by rubber-rich domains that do not exhibit definite
boundaries. Keywords:
|
A Web browser utilizes a device's CPU to parse HTML, build a Document Object
Model, a Cascading Style Sheets Object Model, and render trees, and parse,
compile, and execute computationally-heavy JavaScript. A powerful CPU is
required to perform these tasks as quickly as possible and provide the user
with a great experience. However, increased CPU performance comes with
increased power consumption and reduced battery life on mobile devices. As an
option to extend battery life, Android offers a battery-saver mode that when
activated, turns off the power-hungry and faster processor cores and turns on
the battery-conserving and slower processor cores on the device. The transition
from using faster processor cores to using slower processor cores throttles the
CPU clock speed on the device, and therefore impacts the webpage load process.
We utilize a large-scale data-set collected by a real user monitoring system of
a major content delivery network to investigate the impact of Android's
battery-saver mode on various mobile Web performance metrics. Our analysis
suggests that users of select smartphones of Huawei and Sony experience a
sudden or gradual degradation in Web performance when battery-saver mode is
active. Battery-saver mode on newer flagship smartphones, however, does not
impact the mobile Web performance. Finally, we encourage for new website design
goals that treat slow (and throttled-CPU) devices kindly in favor of improving
end-user experience and suggest that Web performance measurements should be
aware of user device battery charge levels to correctly associate Web
performance.
|
We prove that the Random-Edge simplex algorithm requires an expected number
of at most 13n/sqrt(d) pivot steps on any simple d-polytope with n vertices.
This is the first nontrivial upper bound for general polytopes. We also
describe a refined analysis that potentially yields much better bounds for
specific classes of polytopes. As one application, we show that for
combinatorial d-cubes, the trivial upper bound of 2^d on the performance of
Random-Edge can asymptotically be improved by any desired polynomial factor in
d.
|
In this paper, we study the problem of opening centers to cluster a set of
clients in a metric space so as to minimize the sum of the costs of the centers
and of the cluster radii, in a dynamic environment where clients arrive and
depart, and the solution must be updated efficiently while remaining
competitive with respect to the current optimal solution. We call this dynamic
sum-of-radii clustering problem.
We present a data structure that maintains a solution whose cost is within a
constant factor of the cost of an optimal solution in metric spaces with
bounded doubling dimension and whose worst-case update time is logarithmic in
the parameters of the problem.
|
The ROSEBUD experiment for Direct Dark Matter detection settled in 1999 in
the Canfranc Underground Laboratory. The first phase of the experiment was
dedicated to the understanding and reduction of the radioactive background
following successive removals of the radioimpure materials. Sapphire (25g, 50g)
and germanium (67g) absorbers were used. Thresholds respectively lower than
1keV and 450 eV were achieved on these detectors. The second phase of the
experiment plans to use scintillating bolometers to discriminate between
recoiling nuclei and electrons. Prototypes using commercial CaWO4 (54g) and BGO
(46g) were designed for this purpose. While internal contamination was found
and identified in both targets, neutron calibrations revealed their high
discrimination power. A 6 keV threshold on the heat channel of the BGO
bolometer points out the interest of such a novel material, for Dark Matter
research on neutralinos having spin-dependent or spin-independent interactions.
|
Littlewood polynomials are polynomials with each of their coefficients in
{-1,1}. A sequence of Littlewood polynomials that satisfies a remarkable
flatness property on the unit circle of the complex plane is given by the
Rudin-Shapiro polynomials. It is shown in this paper that the Mahler measure
and the maximum modulus of the Rudin-Shapiro polynomials on the unit circle of
the complex plane have the same size. It is also shown that the Mahler measure
and the maximum norm of the Rudin-Shapiro polynomials have the same size even
on not too small subarcs of the unit circle of the complex plane. Not even
nontrivial lower bounds for the Mahler measure of the Rudin Shapiro polynomials
have been known before.
|
We apply the linear response theory developed in \cite{Ruelle} to analyze how
a periodic signal of weak amplitude, superimposed upon a chaotic background, is
transmitted in a network of non linearly interacting units. We numerically
compute the complex susceptibility and show the existence of specific poles
(stable resonances) corresponding to the response to perturbations transverse
to the attractor. Contrary to the poles of correlation functions they depend on
the pair emitting/receiving units. This dynamic differentiation, induced by non
linearities, exhibits the different ability that units have to transmit a
signal in this network.
|
The results of a single-crystal X-ray-diffraction study of the evolution of
crystal structures of VI3 with temperature with emphasis on phase transitions
are presented. Some related specific-heat and magnetization data are included.
The existence of the room-temperature trigonal crystal structure R-3 (148) has
been confirmed. Upon cooling, VI3 undergoes a structural phase transition to a
monoclinic phase at Ts ~ 79 K. Ts is reduced in magnetic fields applied along
the trigonal c-axis. When VI3 becomes ferromagnetic at TFM1 ~ 50 K,
magnetostriction-induced changes of the monoclinic-structure parameters are
observed. Upon further cooling, the monoclinic structure transforms into a
triclinic variant at 32 K which is most likely occurring in conjunction with
the previously reported transformation of the ferromagnetic structure. The
observed phenomena are preliminarily attributed to strong magnetoelastic
interactions.
|
We develop a prescription for characterizing the strengths of metal lines
associated with Lyman-alpha forest absorbers (LYFAs) of a given neutral
hydrogen column density N_HI and metallicity [Fe/H]. This Line Observability
Index (LOX) is line-specific and translates, for weak lines, into a measure of
the equivalent width. It can be evaluated quickly for thousands of transitions
within the framework of a given model of the Lyman-alpha forest, providing a
ranking of the lines in terms of their strengths and enabling model builders to
select the lines that should be detectable in observed spectra of a given
resolution and signal-to-noise ratio. We compute the LOX for a large number of
elements and transitions in two cosmological models of the Lyman-alpha forest
at z=3 derived from a hydrodynamic simulation of structure formation, and we
discuss how the LOX depends on redshift and on model parameters such as the
mean baryonic density and radiation field. We find that the OVI (1032,1038)
doublet is the best probe of the metallicity in low column density LYFAs N_{HI}
\approx 10^{14.5} cm^{-2}). Metallicities down to [O/H] \sim -3 ([Fe/H] \sim
-3.5 with the assumed [O/Fe] ratio) yield OVI absorption features that should
be detectable in current high-quality spectra, provided that the expected
position of the OVI feature is not contaminated by HI absorption. The strongest
transitions in lower ionisation states of oxygen are OV(630), OIV(788), and
OIII(833), and are likely to be detected with next generation UV instruments.
Of the lines with rest wavelengths \lambda_r > 1216, which can potentially be
observed redwards of the \lya forest, the CIV(1548,1551) doublet is expected to
dominate in all LYFAs, regardless of the value of N_HI.
|
We show the equivalence of the Number Partition Problem and the two processor
scheduling problem. We establish a priori bounds on the completion times for
the scheduling problem which are tighter than Graham's but almost on par with a
posteriori bounds of Coffman and Sethi. We conclude the paper with a
characterization of the asymptotic behavior of the scheduling problem which
relates to the spread of the processing times and the number of jobs.
|
We present simulation results for long ($N\leq 4000$) self-avoiding walks in
four dimensions. We find definite indications of logarithmic corrections, but
the data are poorly described by the asymptotically leading terms. Detailed
comparisons are presented with renormalization group flow equations derived in
direct renormalization and with results of a field theoretic calculation.
|
The Trojan Y Chromosome Strategy (TYC) is an extremely well investigated
biological control method for controlling invasive populations with an XX-XY
sex determinism. In \cite{GP12, WP14} various dynamical properties of the
system are analyzed, including well posedness, boundedness of solutions, and
conditions for extinction or recovery. These results are derived under the
assumption of positive solutions. In the current manuscript, we show that if
the introduction rate of trojan fish is zero, under certain large data
assumptions, negative solutions are possible for the male population, which in
turn can lead to finite time blow-up in the female and male populations. A
comparable result is established for \emph{any} positive initial condition if
the introduction rate of trojan fish is large enough. Similar finite time
blow-up results are obtained in a spatial temporal TYC model that includes
diffusion. Lastly, we investigate improvements to the TYC modeling construct
that may dampen the mechanisms to the blow-up phenomenon or remove the
negativity of solutions. The results draw into suspect the reliability of
current TYC models under certain situations.
|
The $\overline{B_s^0} \rightarrow \chi_{c2} K^+ K^- $ decay mode is observed
and its branching fraction relative to the corresponding $\chi_{c1}$ decay
mode, in a $\pm 15 \textrm{MeV}/c^2$ window around the $\phi$ mass, is found to
be $\frac{\mathcal{B}(\overline{B_s^0} \rightarrow \chi_{c2} K^+ K^-) }{
\mathcal{B}(\overline{B_s^0} \rightarrow \chi_{c1} K^+ K^-)} = (17.1 \pm 3.1
\pm 0.4 \pm 0.9)\%,$ where the first uncertainty is statistical, the second
systematic and the third due to the knowledge of the branching fractions of
radiative $\chi_c$ decays. The decay mode $\overline{B_s^0} \rightarrow
\chi_{c1} K^+ K^- $ allows the $ B_s^0$ mass to be measured as $m(B_s^0) =
5366.83 \pm 0.25 \pm 0.27 \, \textrm{MeV}/c^2,$ where the first uncertainty is
statistical and the second systematic. A combination of this result with other
LHCb determinations of the $B_s^0$ mass is made.
|
In this work, we study discrete-time Markov decision processes (MDPs) under
constraints with Borel state and action spaces and where all the performance
functions have the same form of the expected total reward (ETR) criterion over
the infinite time horizon. One of our objective is to propose a convex
programming formulation for this type of MDPs. It will be shown that the values
of the constrained control problem and the associated convex program coincide
and that if there exists an optimal solution to the convex program then there
exists a stationary randomized policy which is optimal for the MDP. It will be
also shown that in the framework of constrained control problems, the supremum
of the expected total rewards over the set of randomized policies is equal to
the supremum of the expected total rewards over the set of stationary
randomized policies. We consider standard hypotheses such as the so-called
continuity-compactness conditions and a Slater-type condition. Our assumptions
are quite weak to deal with cases that have not yet been addressed in the
literature. An example is presented to illustrate our results with respect to
those of the literature.
|
We report the discovery of a novel skyrmion phase in the multiferroic
insulator Cu2OSeO3 for magnetic fields below the equilibrium skyrmion pocket.
This phase can be accessed by exciting the sample out of equilibrium with
near-infrared (NIR) femtosecond laser pulses but can not be reached by any
conventional field cooling protocol. From the strong wavelength dependence of
the photocreation process and via spin dynamics simulations, we identify the
magnetoelastic effect as the most likely photocreation mechanism. This effect
results in a transient modification of the magnetic interaction extending the
equilibrium skyrmion pocket to lower magnetic fields. Once created, the
skyrmions rearrange and remain stable over a long time, reaching minutes. The
presented results are relevant for designing high-efficiency non-volatile data
storage based on magnetic skyrmions.
|
Fat tails in financial time series and increase of stocks cross-correlations
in high volatility periods are puzzling facts that ask for new paradigms. Both
points are of key importance in fundamental research as well as in Risk
Management (where extreme losses play a key role). In this paper we present a
new model for an ensemble of stocks that aims to encompass in a unitary picture
both these features. Equities are modelled as quasi random walk variables,
where the non-Brownian components of stocks movements are leaded by the market
trend, according to typical trader strategies. Our model suggests that
collective effects may play a very important role in the characterization of
some significantly statistical properties of financial time series.
|
Measure the Sloan g' magnitudes of the Starlink's STARLINK-1130 (Darksat) and
1113 LEO communication satellites and determine the effectiveness of the
Darksat darkening treatment at 475.4\,nm. Two observations of the Starlink's
Darksat LEO communication satellite were conducted on 2020/02/08 and 2020/03/06
using a Sloan r' and g' filter respectively. While a second satellite,
STARLINK-1113 was observed on 2020/03/06 using a Sloan g' filter. The initial
observation on 2020/02/08 was a test observation when Darksat was still
manoeuvring to its nominal orbit and orientation. Based on the successful test
observation, the first main observation was conducted on 2020/03/06 along with
an observation of the second Starlink satellite. The calibration, image
processing and analysis of the Darksat Sloan g' image gives an estimated Sloan
g' magnitude of $7.46\pm0.04$ at a range of 976.50\,km. For STARLINK-1113 an
estimated Sloan g' magnitude of $6.59\pm0.05$ at a range of 941.62\,km was
found. When scaled to a range of 550\,km and corrected for the solar and
observer phase angles, a reduction by a factor of two is seen in the reflected
solar flux between Darksat and STARLINK-1113. The data and results presented in
this work, show that the special darkening coating used by Starlink for Darksat
has darkened the Sloan g' magnitude by $0.77\pm0.05$\,mag, when the range is
equal to a nominal orbital height (550\,km). This result will serve members of
the astronomical community modelling the satellite mega-constellations, to
ascertain their true impact on both the amateur and professional astronomical
communities. Concurrent and further observations are planned to cover the full
optical and NIR spectrum, from an ensemble of instruments, telescopes and
observatories.
|
Studies of large-scale structures in the Universe, such as superstructures or
cosmic voids, have been widely used to characterize the properties of the
cosmic web through statistical analyses. On the other hand, the 2-point
correlation function of large-scale tracers such as galaxies or halos provides
a reliable statistical measure. However, this function applies to the spatial
distribution of point-like objects, and therefore it is not appropriate for
extended large structures which strongly depart from spherical symmetry. Here
we present an analysis based on the standard correlation function formalism
that can be applied to extended objects exhibiting arbitrary shapes. Following
this approach, we compute the probability excess $\Xi$ of having spheres
sharing parts of cosmic structures with respect to a realization corresponding
to a distribution of the same structures in random positions. For this aim, we
identify superstructures defined as Future Virialized Structures (FVSs) in
semi-anaytic galaxies on the MPDL2 MultiDark simulation. We have also
identified cosmic voids to provide a joint study of their relative distribution
with respect to the superstructures. Our analysis suggests that $\Xi$ provides
useful characterizations of the large scale distribution, as suggested from an
analysis of sub-sets of the simulation. Even when superstructure properties may
exhibit negligible variations across the sub-sets, $\Xi$ has the sensitivity to
statistically distinguish sub-boxes that departs from the mean at larger
scales. Thus, our methods can be applied in analysis of future surveys to
provide characterizations of large-scale structure suitable to distinguish
different theoretical scenarios.
|
The collision of convex bodies is considered for small impact velocity, when
plastic deformation and fragmentation may be disregarded. In this regime the
contact is governed by forces according to viscoelastic deformation and by
adhesion. The viscoelastic interaction is described by a modified Hertz law,
while for the adhesive interactions, the model by Johnson, Kendall and Roberts
(JKR) is adopted. We solve the general contact problem of convex viscoelastic
bodies in quasi-static approximation, which implies that the impact velocity is
much smaller than the speed of sound in the material and that the viscosity
relaxation time is much smaller than the duration of a collision. We estimate
the threshold impact velocity which discriminates restitutive and sticking
collisions. If the impact velocity is not large as compared with the threshold
velocity, adhesive interaction becomes important, thus limiting the validity of
the pure viscoelastic collision model.
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Because conical segments of quasispherical ultrarelativistic blastwaves are
causally disconnected on angular scales larger than the blastwave inverse
Lorentz factor, astrophysical blastwaves can sustain initial anisotropy,
imprinted by the process that drives the explosion, while they remain
relativistic. We show that initial angular energy fluctuations in
ultrarelativistic blastwaves imply a production of vorticity in the blastwave,
and calculate the vortical energy production rate. In gamma-ray burst (GRB)
afterglows, the number of vortical eddy turnovers as the shocked fluid crosses
the blastwave shell is about unity for marginally nonlinear anisotropy. Thus
the anisotropy must be nonlinear to explain the magnetic energy density
inferred in measured GRB spectra.
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The architectures of biological hard materials reveal finely tailored complex
assemblies of mineral crystals. Numerous recent studies associate the design of
these local assemblies with impressive macroscopic response. Reproducing such
exquisite control in technical ceramics conflicts with commonly used processing
methods. Here, we circumvent this issue by combining the recently developed
Magnetically-Assisted Slip Casting (MASC) technique with the well-established
process of Templated Grain Growth (TGG). MASC enables the local control over
the orientation of platelets dispersed among smaller isotropic particles. After
a high temperature pressure-less treatment, the grains of the final ceramic
follow the same orientation of the initial platelets. This combination allows
us to produce 95 % dense alumina part with a grain orientation following any
deliberate orientation. We successfully fabricated microstructures inspired
from biological materials with ceramics that present periodically varying
patterns with a programmable pitch of a few tens of microns. We confirmed the
capacity of the process to tailor local mechanical properties through local
grains orientation using micro-indentation. This micrometer scale control over
the local mechanical properties could be applied to adapt ceramic structures to
complex loads using this inexpensive and scalable process. In systems where
functional properties also depend on anisotropic grain orientation, the
principle presented here could enable the creation of new multifunctional
ceramics.
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Observations of dense molecular gas towards the supernova remnants CTB 37A
(G348.5+0.1) and G348.5-0.0 were carried out using the Mopra and Nanten2 radio
telescopes. We present CO(2-1) and CS(1-0) emission maps of a region
encompassing the CTB 37A TeV gamma-ray emission, HESS J1714-385, revealing
regions of dense gas within associated molecular clouds. Some gas displays good
overlap with gamma-ray emission, consistent with hadronic gamma-ray emission
scenarios. Masses of gas towards the HESS J1714-385 TeV gamma-ray emission
region were estimated, and were of the order of 10^3-10^4 solar masses. In the
case of a purely hadronic origin for the gamma-ray emission, the cosmic ray
flux enhancement is ~80-1100 times the local solar value. This enhancement
factor and other considerations allow a discussion of the age of CTB 37A, which
is consistent with ~10^4 yr.
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We analyze four-dimensional symplectic manifolds of type $X=S^1 \times M^3$
where $M^3$ is an open $3$-manifold admitting inequivalent fibrations leading
to inequivalent symplectic structures on $X$. For the case where $M^3 \subset
S^3$ is the complement of a $4$-component link constructed by McMullen-Taubes,
we provide a general algorithm for computing the monodromy of the fibrations
explicitly. We use this algorithm to show that certain inequivalent symplectic
structures are distinguished by the dimensions of the primitive cohomologies of
differential forms on $X$. We also calculate the primitive cohomologies on $X$
for a class of open $3$-manifolds that are complements of a family of fibered
graph links in $S^3$. In this case, we show that there exist pairs of
symplectic forms on $X$, arising from either equivalent or inequivalent pairs
of fibrations on the link complement, that have different dimensions of the
primitive cohomologies.
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Team collaboration among individuals with diverse sets of expertise and
skills is essential for solving complex problems. As part of an
interdisciplinary effort, we studied the effects of Capture the Flag (CTF)
game, a popular and engaging education/training tool in cybersecurity and
engineering, in enhancing team construction and collaboration. We developed a
framework to incorporate CTF as part of a computer-human process for expertise
recognition and role assignment and evaluated and tested its effectiveness
through a study with cybersecurity students enrolled in a Virtual Teams course.
In our computer-human process framework, the post-CTF algorithm using the CTF
outcomes assembles the team (assigning individuals to teams) and provides the
initial role assignments, which then gets updated by human-based team
discussions. This paper shares our insights, design choices/rationales, and
analyses of our CTF-incorporated computer-human process framework. The
students' evaluations revealed that the computer-human process framework was
helpful in learning about their team members' backgrounds and expertise and
assigning roles accordingly made a positive impact on the learning outcomes for
the team collaboration skills in the course. This experience report showcases
the utility of CTF as a tool for expertise recognition and role assignments in
teams and highlights the complementary roles of CTF-based and discussion-based
processes for an effective team collaboration among engineering students.
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Recently it has been shown how a topologically twisted version of ${\cal
N}=4$ super Yang-Mills may be discretized in such a way as to preserve one
scalar supersymmetry at nonzero lattice spacing. The remaining fifteen
supersymmetries are broken by terms of ${\cal O}(a)$ where $a$ is the lattice
spacing. One would like to know whether these remaining supersymmetries are
regained in the continuum limit $a \to 0$ and, if not, how much tuning of the
couplings in the lattice action is required. In this paper we derive the form
of these additional twisted supersymmetries by combining a set of discrete
R-symmetries of the continuum theory with the action of the scalar
supersymmetry. We then argue that restoration of rotational symmetry in the
continuum limit of the lattice theory likely implies restoration of R-symmetry
and hence should lead to an automatic enhancement to the full ${\cal N}=4$
supersymmetry without further fine-tuning.
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With rising technologies, the protection of privacy-sensitive information is
becoming increasingly important. In industry and production facilities, image
or video recordings are beneficial for documentation, tracing production errors
or coordinating workflows. Individuals in images or videos need to be
anonymized. However, the anonymized data should be reusable for further
applications. In this work, we apply the Deep Learning-based full-body
anonymization framework DeepPrivacy2, which generates artificial identities, to
industrial image and video data. We compare its performance with conventional
anonymization techniques. Therefore, we consider the quality of identity
generation, temporal consistency, and the applicability of pose estimation and
action recognition.
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Recently, it has been pointed out that the twisting of bilayer WSe$_2$ would
generate topologically non-trivial flat bands near the Fermi energy. In this
work, we show that twisted bilayer WSe$_2$ (tWSe$_2$) with uniaxial strain
exhibits a large nonlinear Hall (NLH) response due to the non-trivial Berry
curvatures of the flat bands. Moreover, the NLH effect is greatly enhanced near
the topological phase transition point which can be tuned by a vertical
displacement field. Importantly, the nonlinear Hall signal changes sign across
the topological phase transition point and provides a way to identify the
topological phase transition and probe the topological properties of the flat
bands. The strong enhancement and high tunability of the NLH effect near the
topological phase transition point renders tWSe$_2$ and related moire materials
new platforms for rectification and second harmonic generations.
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The initial value problem for Hookean incompressible viscoelastictic motion
in three space dimensions has global strong solutions with small displacements.
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Dark matter in variations of constrained minimal supersymmetric standard
models will be discussed. Particular attention will be given to the comparison
between accelerator and direct detection constraints.
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Complex structural effects in the nuclide production from the projectile
fragmentation of 1 A GeV 238U nuclei in a titanium target are reported. The
structure seems to be insensitive to the excitation energy induced in the
reaction. This is in contrast to the prominent structural features found in
nuclear fission and in transfer reactions, which gradually disappear with
increasing excitation energy. Using the statistical model of nuclear reactions,
relations to structural effects in nuclear binding and in the nuclear level
density are demonstrated.
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We present new results on the star formation history of the dwarf irregular
galaxy NGC 1569. The data were obtained with Hubble Space Telescope's
NICMOS/NIC2 in the F110W (J) and F160W (H) near-infrared (NIR) filters and
interpreted with the synthetic color-magnitude diagram method. The galaxy
experienced a complex star formation (SF) activity. The best fit to the data is
found by assuming three episodes of activity in the last 1-2 Gyr. The most
recent and strong episode constrained by these NIR data started ~37 Myr ago and
ended ~13 Myr ago, although we cannot exclude the possibility that up to three
SF episodes occurred in this time interval. The average star-formation rate
(SFR) of the episode is 3.2 Msun yr-1 kpc-2, in agreement with literature data.
A previous episode produced stars between 150 Myr and 40 Myr ago, with a mean
SFR about 2/3 lower than the mean SFR of the youngest episode. An older SF
episode occurred about 1 Gyr ago. All these SFRs are 2-3 orders of magnitude
higher than those derived for late-type dwarfs of the Local Group. In all cases
an initial mass function similar to Salpeter's allows for a good reproduction
of the data, but we cannot exclude flatter mass functions. These results have
been obtained adopting a distance of 2.2 Mpc and a reddening E(B-V)=0.56. A
larger distance would require younger episodes and higher SFRs. We have
explored some possible scenarios using the astrated mass in the best fit model,
in order to constrain the past star formation history. We cannot rule out a low
rate in the past SF but we can safely conclude that the last 1-2 Gyr have been
peculiar.
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Quantum field theory, which is generally used to describe the origin of
large-scale gravitational perturbations during cosmic inflation, has been shown
to omit an important physical effect in curved space-time, the nonlocal
entanglement among quantized modes from their gravitational effect on causal
structure. It is argued here that in a different model of quantum gravity that
coherently preserves nonlocal directional and causal relationships, primordial
perturbations originate instead from coherent quantum distortions of emergent
inflationary horizons; and moreover, that causal constraints account for
approximate symmetries of cosmic microwave background correlations measured at
large angular separations, which are highly anomalous in the standard picture.
Thus, symmetries already apparent in the large-angle CMB pattern may be unique
signatures of the emergence of locality and causal structure from quantum
gravity.
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General ideas of gauge/gravity duality allow for the possibility of time
dependent solutions that interpolate between a perturbative gauge theory phase
and a weakly curved string/gravity phase. Such a scenario applied to cosmology
would exhibit a non-geometric phase before the big bang. We investigate a toy
model for such a cosmology, whose endpoint is the classical limit of the
two-dimensional non-critical string. We discuss the basic dynamics of this
model, in particular how it evolves toward the double scaling limit required
for stringy dynamics. We further comment on the physics that will determine the
fluctuation spectrum of the scalar tachyon. Finally, we discuss various
features of this model, and what relevance they might have for a more
realistic, higher dimensional scenario.
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The combination of established nanofabrication with attractive material
properties makes silicon a promising material for quantum technologies, where
implanted dopants serve as qubits with high density and excellent coherence
even at elevated temperatures. In order to connect and control these qubits,
interfacing them with light in nanophotonic waveguides offers unique promise.
Here, we present resonant spectroscopy of implanted erbium dopants in such
waveguides. We overcome the requirement of high doping and above-bandgap
excitation that limited earlier studies. We thus observe erbium incorporation
at well-defined lattice sites with a thousandfold reduced inhomogeneous
broadening of about 1 GHz and a spectral diffusion linewidth down to 45 MHz.
Our study thus introduces a novel materials platform for the implementation of
on-chip quantum memories, microwave-to-optical conversion, and distributed
quantum information processing, with the unique feature of operation in the
main wavelength band of fiber-optic communication.
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Using nanoprobe X-ray diffraction microscopy, we investigate the relationship
between residual strains from crystal growth in CsPbBr$_3$ thin film crystals,
their stability, and local bandgap. We find that out-of-plane compressive
strain that arises from cooldown from crystallization is detrimental to
material stability under X-ray irradiation. We also find that the optical
photoluminescence red shifts as a result of the out-of-plane compressive
strain. The sensitivity of bandgap to strain suggests possible applications
such as stress-sensitive sensors. Mosaicity, the formation of small
misorientations in neighboring crystalline domains we observe in some
CsPbBr$_3$ single crystals, indicates the significant variations in crystal
quality that can occur even in single-crystal halide perovskites. The
nano-diffraction results suggest that reducing local strains is a necessary
path to enhance the stability of perovskite optoelectronic materials and
devices from light-emitting diodes to high-energy detectors.
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Recent years have seen a dramatic expansion of tasks and datasets posed as
question answering, from reading comprehension, semantic role labeling, and
even machine translation, to image and video understanding. With this
expansion, there are many differing views on the utility and definition of
"question answering" itself. Some argue that its scope should be narrow, or
broad, or that it is overused in datasets today. In this opinion piece, we
argue that question answering should be considered a format which is sometimes
useful for studying particular phenomena, not a phenomenon or task in itself.
We discuss when a task is correctly described as question answering, and when a
task is usefully posed as question answering, instead of using some other
format.
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Neural abstractive summarization models have led to promising results in
summarizing relatively short documents. We propose the first model for
abstractive summarization of single, longer-form documents (e.g., research
papers). Our approach consists of a new hierarchical encoder that models the
discourse structure of a document, and an attentive discourse-aware decoder to
generate the summary. Empirical results on two large-scale datasets of
scientific papers show that our model significantly outperforms
state-of-the-art models.
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This paper summarizes the results from measurements aiming to characterize
ultracold neutron detection with 6Li-doped glass scintillators. Single GS10 or
GS20 scintillators, with a thickness of 100-200 micrometer, fulfill the
ultracold neutron detection requirements with an acceptable neutron-gamma
discrimination. This discrimination is clearly improved with a stack of two
scintillators: a 6Li-depleted glass bonded to a 6Li-enriched glass. The optical
contact bonding is used between the scintillators in order to obtain a perfect
optical contact. The scintillator's detection efficiency is similar to that of
a 3He Strelkov gas detector. Coupled to a digital data acquisition system,
counting rates up to a few 10^5 counts/s can be handled. A detector based on
such a scintillator stack arrangement was built and has been used in the
neutron electric dipole moment experiment at the Paul Scherrer Institute since
2010. Its response for the regular runs of the neutron electric dipole moment
experiment is presented.
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We show that combining vibrational spectroscopy with signal processing can
result in a scheme for ultrasensitive detection of molecules. We consider the
vibrational spectrum as a signal on the energy axis and apply a matched filter
on that axis. On the example of a nerve agent molecule, we show that this
allows detecting a molecule by its vibrational spectrum even when the recorded
spectrum is completely buried in noise, when conventional spectroscopic
detection is impossible. Detection is predicted to be possible with
signal-to-noise ratios in recorded spectra as low as 0.1. We study the
importance of spectral range used for detection as well as of the quality of
the computed spectrum used to program the filter, specifically, the role of
anharmonicity, of the exchange correlation functional, and of the basis set.
The use of the full spectral range rather than of a narrow spectral window with
key vibrations is shown to be advantageous, as well as accounting for
anharmonicity.
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We discuss matters related to the point that topological quantization in the
strong interaction is a consequence of an infinite spacetime volume. Because of
the ensuing order of limits, i.e. infinite volume prior to summing over
topological sectors, CP is conserved. Here, we show that this reasoning is
consistent with the construction of the path integral from steepest-descent
contours. We reply to some objections that aim to support the case for CP
violation in the strong interactions that are based on the role of the CP-odd
theta-parameter in three-form effective theories, the correct sampling of all
configurations in the dilute instanton gas approximation and the volume
dependence of the partition function. We also show that the chiral effective
field theory derived from taking the volume to infinity first is in no
contradiction with analyses based on partially conserved axial currents.
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In recent years modelling crowd and evacuation dynamics has become very
important, with increasing huge numbers of people gathering around the world
for many reasons and events. The fact that our global population grows
dramatically every year and the current public transport systems are able to
transport large amounts of people, heightens the risk of crowd panic or crush.
Pedestrian models are based on macroscopic or microscopic behaviour. In this
paper, we are interested in developing models that can be used for evacuation
control strategies. This model will be based on microscopic pedestrian
simulation models, and its evolution and design requires a lot of information
and data. The people stream will be simulated, based on mathematical models
derived from empirical data about pedestrian flows. This model is developed
from image data bases, so called empirical data, taken from a video camera or
data obtained using human detectors. We consider the individuals as autonomous
particles interacting through social and physical forces, which is one approach
that has been used to simulate crowd behaviour.
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The continuous-time model of Nesterov's momentum provides a thought-provoking
perspective for understanding the nature of the acceleration phenomenon in
convex optimization. One of the main ideas in this line of research comes from
the field of classical mechanics and proposes to link Nesterov's trajectory to
the solution of a set of Euler-Lagrange equations relative to the so-called
Bregman Lagrangian. In the last years, this approach led to the discovery of
many new (stochastic) accelerated algorithms and provided a solid theoretical
foundation for the design of structure-preserving accelerated methods. In this
work, we revisit this idea and provide an in-depth analysis of the action
relative to the Bregman Lagrangian from the point of view of calculus of
variations. Our main finding is that, while Nesterov's method is a stationary
point for the action, it is often not a minimizer but instead a saddle point
for this functional in the space of differentiable curves. This finding
challenges the main intuition behind the variational interpretation of
Nesterov's method and provides additional insights into the intriguing geometry
of accelerated paths.
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I briefly review the current state of the modelling of photospheric activity
based on the high-precision optical light curves obtained with MOST, CoRoT, and
Kepler. These models can be used to search for active longitudes where activity
is preferentially concentrated, estimate the amplitude of stellar differential
rotation, and look for short-term activity cycles as, e.g., in the case of
CoRoT-2. In the case of a late-type star accompanied by a transiting hot
Jupiter, the small light modulations observed during transits when a dark spot
is occulted by the disc of the planet are also briefly considered. They can be
used to derive information on individual active regions as well as on stellar
rotation and the spin-orbit alignment of the system.
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Popular investment structured products in Puerto Rico are stock market tied
Individual Retirement Accounts (IRA), which offer some stock market growth
while protecting the principal. The performance of these retirement strategies
has not been studied. This work examines the expected return and risk of Puerto
Rico stock market IRA (PRIRAs) and compares their statistical properties with
other investment instruments before and after tax. We propose a parametric
modeling approach for structured products and apply it to PRIRAs. Our method
first estimates the conditional expected return (and variance) of PRIRA assets
from which we extract marginal moments through the Law of Iterated Expectation.
Our results indicate that PRIRAs underperform against investing directly in the
stock market while still carrying substantial risk. The expected return of the
stock market IRA from Popular Bank (PRIRA1) after tax is slightly greater than
that of investing in U.S. bonds, while PRIRA1 has almost two times the risk.
The stock market IRA from Universal (PRIRA2) performs similarly to PRIRA1,
while PRIRA2 has a lower risk than PRIRA1. PRIRAs may be reasonable for some
risk-averse investors due to their principal protection and tax deferral.
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