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We study the transient behavior of damage propagation in the two-dimensional
spin-$1$ Blume-Capel model using Monte Carlo simulations with Metropolis
dynamics. We find that, for a particular region in the second-order transition
regime of the crystal field--temperature phase diagram of the model, the
average Hamming distance decreases exponentially with time in the weakly
damaged system. Additionally, its rate of decay appears to depend linearly on a
number of Hamiltonian parameters, namely the crystal field, temperature,
applied magnetic field, but also on the amount of damage. Finally, a
comparative study using Metropolis and Glauber dynamics indicates a slower
decay rate of the average Hamming distance for the Glauber protocol.
|
Customization is crucial for making visualizations accessible to blind and
low-vision (BLV) people with widely-varying needs. But what makes for usable or
useful customization? We identify four design goals for how BLV people should
be able to customize screen-reader-accessible visualizations: presence, or what
content is included; verbosity, or how concisely content is presented;
ordering, or how content is sequenced; and, duration, or how long
customizations are active. To meet these goals, we model a customization as a
sequence of content tokens, each with a set of adjustable properties. We
instantiate our model by extending Olli, an open-source accessible
visualization toolkit, with a settings menu and command box for persistent and
ephemeral customization respectively. Through a study with 13 BLV participants,
we find that customization increases the ease of identifying and remembering
information. However, customization also introduces additional complexity,
making it more helpful for users familiar with similar tools.
|
The cost competitiveness of green hydrogen production via electrolysis
presents a significant challenge for its large-scale adoption. One potential
solution to make electrolyzers profitable is to diversify their products and
participate in various markets, generating additional revenue streams.
Electrolyzers can be utilized as flexible loads and participate in various
frequency-supporting ancillary service markets by adjusting their operating set
points. This paper develops a mixed-integer linear model, deriving an optimal
scheduling strategy for an electrolyzer providing Frequency Containment Reserve
(FCR) services in the Nordic synchronous region. Depending on the hydrogen
price and demand, results show that the provision of various FCR services,
particularly those for critical frequency conditions (FCR-D), could
significantly increase the profit of the electrolyzer.
|
A lot of progress has been made recently in our understanding of the
random-field Ising model thanks to large-scale numerical simulations. In
particular, it has been shown that, contrary to previous statements: the
critical exponents for different probability distributions of the random fields
and for diluted antiferromagnets in a field are the same. Therefore, critical
universality, which is a perturbative renormalization-group prediction, holds
beyond the validity regime of perturbation theory. Most notably, dimensional
reduction is restored at five dimensions, i.e., the exponents of the
random-field Ising model at five dimensions and those of the pure Ising
ferromagnet at three dimensions are the same.
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First indications of the warm/hot intergalactic medium, tracing out the large
scale structure of the universe, have been obtained in sensitive Chandra and
XMM-Newton high resolution absorption line spectroscopy of bright blazars. High
resolution X-ray spectroscopy and imaging also provides important new
constraints on the physical condition of the cooling matter in the centers of
clusters, requiring major modifications to the standard cooling flow models.
XMM-Newton and Chandra low resolution spectroscopy detected significant Fe
K_alpha absorption features in the spectrum of the ultraluminous, high redshift
lensed broad absorption line QSO APM 08279+5255, yielding new insights in the
outflow geometry indicating a supersolar Fe/O ratio. Chandra high resolution
imaging spectroscopy of the nearby ULIRG/obscured QSO NGC 6240 for the first
time gave evidence of two active supermassive black holes in the same galaxy,
likely bound to coalesce in the course of the ongoing major merger in this
galaxy. Deep X-ray surveys have shown that the cosmic X-ray background (XRB) is
largely due to the accretion onto supermassive black holes, integrated over the
cosmic time. These surveys have resolved more than 80% of the X-ray background
into discrete sources. Optical spectroscopic identifications show that the
sources producing the bulk of the X-ray background are a mixture of obscured
(type-2) and unobscured (type-1) AGNs, as predicted by the XRB population
synthesis models. A class of highly luminous type-2 AGN, so called QSO-2s, has
been detected in the deepest Chandra and XMM-Newton surveys. The new Chandra
AGN redshift distribution peaks at much lower redshifts (z~0.7) than that based
on ROSAT data, indicating that the evolution of Seyfert galaxies occurs at
significantly later cosmic time than that of QSOs.
|
We perform a canonical quantization of gravity in a second-order formulation,
taking as configuration variables those describing a 4-bein, not adapted to the
space-time splitting. We outline how, neither if we fix the Lorentz frame
before quantizing, nor if we perform no gauge fixing at all, is invariance
under boost transformations affected by the quantization.
|
Recently, a weak form of quantum steering, i.e., certification of quantum
steering in a one-sided semi-device-independent way, has been formulated
[Jebarathinam et al. Phys. Rev. A 108, 042211 (2023)]. In this work, for
two-qubit states, we study the relationships between the quantification of
one-sided semi-device-independent steerability and information-theoretic
quantification of simultaneous correlations in mutually unbiased bases [Wu et
al. Scientific Reports 4, 4036 (2014)]. For two-qubit states that belong to
Bell-diagonal states, quantifying one-sided semi-device-independent
steerability provides an operational characterization of information-theoretic
quantification of simultaneous correlations in mutually unbiased bases. For
another class of two-qubit states, we show that quantifying one-sided
semi-device-independent steerability provides operational quantification of
simultaneous correlations in mutually unbiased bases going beyond the above
information-theoretic quantification. We invoke quantum steering ellipsoid
formalism to shed intuitions on our operational characterization of
simultaneous correlations in complementary bases of two-qubit states that we
consider.
|
Based on $14.7~\textrm{fb}^{-1}$ of $e^+e^-$ annihilation data collected with
the BESIII detector at the BEPCII collider at 17 different center-of-mass
energies between $3.7730~\textrm{GeV}$ and $4.5995~\textrm{GeV}$, Born cross
sections of the two processes $e^+e^- \to p\bar{p}\eta$ and $e^+e^- \to
p\bar{p}\omega$ are measured for the first time. No indication of resonant
production through a vector state $V$ is observed, and upper limits on the Born
cross sections of $e^+e^- \to V \to p\bar{p}\eta$ and $e^+e^- \to V \to
p\bar{p}\omega$ at the $90\%$ confidence level are calculated for a large
parameter space in resonance masses and widths. For the current world average
parameters of the $\psi(4230)$ of $m=4.2187~\textrm{GeV}/c^{2}$ and
$\Gamma=44~\textrm{MeV}$, we find upper limits on resonant production of the
$p\bar{p}\eta$ and $p\bar{p}\omega$ final states of $7.5~\textrm{pb}$ and
$10.4~\textrm{pb}$ at the $90\%$ CL, respectively.
|
The linear complexity of a sequence has been used as an important measure of
keystream strength, hence designing a sequence which possesses high linear
complexity and $k$-error linear complexity is a hot topic in cryptography and
communication. Niederreiter first noticed many periodic sequences with high
$k$-error linear complexity over GF(q). In this paper, the concept of stable
$k$-error linear complexity is presented to study sequences with high $k$-error
linear complexity. By studying linear complexity of binary sequences with
period $2^n$, the method using cube theory to construct sequences with maximum
stable $k$-error linear complexity is presented. It is proved that a binary
sequence with period $2^n$ can be decomposed into some disjoint cubes. The cube
theory is a new tool to study $k$-error linear complexity. Finally, it is
proved that the maximum $k$-error linear complexity is $2^n-(2^l-1)$ over all
$2^n$-periodic binary sequences, where $2^{l-1}\le k<2^{l}$.
|
Given a compact, three-dimensional, real-analytic Lorentzian manifold
$(M,g)$, we prove that the identity component of the conformal group preserves
a metric in the conformal class $[g]$, or $(M,g)$ is conformally flat.
|
The article deals with operations defined on convex polyhedra or polyhedral
convex functions. Given two convex polyhedra, operations like Minkowski sum,
intersection and closed convex hull of the union are considered. Basic
operations for one convex polyhedron are, for example, the polar, the conical
hull and the image under affine transformation. The concept of a
P-representation of a convex polyhedron is introduced. It is shown that many
polyhedral calculus operations can be expressed explicitly in terms of
P-representations. We point out that all the relevant computational effort for
polyhedral calculus consists in computing projections of convex polyhedra. In
order to compute projections we use a recent result saying that multiple
objective linear programming (MOLP) is equivalent to the polyhedral projection
problem. Based on the MOLP-solver bensolve a polyhedral calculus toolbox for
Matlab and GNU Octave is developed. Some numerical experiments are discussed.
|
Motivated in part by a problem in simulated tempering (a form of Markov chain
Monte Carlo) we seek to minimise, in a suitable sense, the time it takes a
(regular) diffusion with instantaneous reflection at 0 and 1 to travel to $1$
and then return to the origin (the so-called commute time from 0 to 1).
Substantially extending results in a previous paper, we consider a dynamic
version of this problem where the control mechanism is related to the
diffusion's drift via the corresponding scale function. We are only able to
choose the drift at each point at the time of first visiting that point and the
drift is constrained on a set of the form $[0,\ell)\cup(i,1]$. This leads to a
type of stochastic control problem with infinite dimensional state.
|
This work investigates the prediction performance of the kriging predictors.
We derive some error bounds for the prediction error in terms of non-asymptotic
probability under the uniform metric and $L_p$ metrics when the spectral
densities of both the true and the imposed correlation functions decay
algebraically. The Mat\'ern family is a prominent class of correlation
functions of this kind. Our analysis shows that, when the smoothness of the
imposed correlation function exceeds that of the true correlation function, the
prediction error becomes more sensitive to the space-filling property of the
design points. In particular, the kriging predictor can still reach the optimal
rate of convergence, if the experimental design scheme is quasi-uniform. Lower
bounds of the kriging prediction error are also derived under the uniform
metric and $L_p$ metrics. An accurate characterization of this error is
obtained, when an oversmoothed correlation function and a space-filling design
is used.
|
Object-centric (OC) representations, which represent the state of a visual
scene by modeling it as a composition of objects, have the potential to be used
in various downstream tasks to achieve systematic compositional generalization
and facilitate reasoning. However, these claims have not been thoroughly
analyzed yet. Recently, foundation models have demonstrated unparalleled
capabilities across diverse domains from language to computer vision, marking
them as a potential cornerstone of future research for a multitude of
computational tasks. In this paper, we conduct an extensive empirical study on
representation learning for downstream Visual Question Answering (VQA), which
requires an accurate compositional understanding of the scene. We thoroughly
investigate the benefits and trade-offs of OC models and alternative approaches
including large pre-trained foundation models on both synthetic and real-world
data, and demonstrate a viable way to achieve the best of both worlds. The
extensiveness of our study, encompassing over 800 downstream VQA models and 15
different types of upstream representations, also provides several additional
insights that we believe will be of interest to the community at large.
|
The spectra of emission-line galaxies (ELGs) from the extended Baryon
Oscillation Spectroscopic Survey (eBOSS) of the Sloan Digit Sky Survey (SDSS)
are used to study the mass-metallicity relation (MZR) at $z\sim0.8$. The
selected sample contains about 180,000 massive star-forming galaxies with $0.6
< z < 1.05$ and $9 < {\rm log}(M_{\star}/M_{\odot}) < 12$. The spectra are
stacked in bins of different parameters including redshift, stellar mass, star
formation rate (SFR), specific star formation rate (sSFR), half-light radius,
mass density, and optical color. The average MZR at $z\sim0.83$ has a downward
evolution in the MZR from local to high-redshift universe, which is consistent
with previous works. At a specified stellar mass, galaxies with higher SFR/sSFR
and larger half-light radius have systematically lower metallicity. This
behavior is reversed for galaxies with larger mass density and optical color.
Among the above physical parameters, the MZR has the most significant
dependency on SFR. Our galaxy sample at $0.6<z<1.05$ approximately follows the
fundamental metallicity relation (FMR) in the local universe, although the
sample inhomogeneity and incompleteness might have effect on our MZR and FMR.
|
We introduce a high resolution spatially adaptive light source, or a
projector, into a neural reflectance field that allows to both calibrate the
projector and photo realistic light editing. The projected texture is fully
differentiable with respect to all scene parameters, and can be optimized to
yield a desired appearance suitable for applications in augmented reality and
projection mapping. Our neural field consists of three neural networks,
estimating geometry, material, and transmittance. Using an analytical BRDF
model and carefully selected projection patterns, our acquisition process is
simple and intuitive, featuring a fixed uncalibrated projected and a handheld
camera with a co-located light source. As we demonstrate, the virtual projector
incorporated into the pipeline improves scene understanding and enables various
projection mapping applications, alleviating the need for time consuming
calibration steps performed in a traditional setting per view or projector
location. In addition to enabling novel viewpoint synthesis, we demonstrate
state-of-the-art performance projector compensation for novel viewpoints,
improvement over the baselines in material and scene reconstruction, and three
simply implemented scenarios where projection image optimization is performed,
including the use of a 2D generative model to consistently dictate scene
appearance from multiple viewpoints. We believe that neural projection mapping
opens up the door to novel and exciting downstream tasks, through the joint
optimization of the scene and projection images.
|
We prove multiple vector-valued and mixed-norm estimates for multilinear
operators in $\rr R^d$, more precisely for multilinear operators $T_k$
associated to a symbol singular along a $k$-dimensional space and for
multilinear variants of the Hardy-Littlewood maximal function. When the
dimension $d \geq 2$, the input functions are not necessarily in $L^p(\rr R^d)$
and can instead be elements of mixed-norm spaces $L^{p_1}_{x_1} \ldots
L^{p_d}_{x_d}$.
Such a result has interesting consequences especially when $L^\infty$ spaces
are involved. Among these, we mention mixed-norm Loomis-Whitney-type
inequalities for singular integrals, as well as the boundedness of multilinear
operators associated to certain rational symbols. We also present examples of
operators that are not susceptible to isotropic rescaling, which only satisfy
``purely mixed-norm estimates" and no classical $L^p$ estimates.
Relying on previous estimates implied by the helicoidal method, we also prove
(non-mixed-norm) estimates for generic singular Brascamp-Lieb-type
inequalities.
|
The analogies between the Moving Particle Semi-implicit method (MPS) and
Incompressible Smoothed Particle Hydrodynamics method (ISPH) are established in
this note, as an extension of the MPS consistency analysis conducted in
"Souto-Iglesias et al., Computer Physics Communications, 184(3), 2013."
|
Natural Language Counterfactual generation aims to minimally modify a given
text such that the modified text will be classified into a different class. The
generated counterfactuals provide insight into the reasoning behind a model's
predictions by highlighting which words significantly influence the outcomes.
Additionally, they can be used to detect model fairness issues or augment the
training data to enhance the model's robustness. A substantial amount of
research has been conducted to generate counterfactuals for various NLP tasks,
employing different models and methodologies. With the rapid growth of studies
in this field, a systematic review is crucial to guide future researchers and
developers. To bridge this gap, this survey comprehensively overview textual
counterfactual generation methods, particularly including those based on Large
Language Models. We propose a new taxonomy that categorizes the generation
methods into four groups and systematically summarize the metrics for
evaluating the generation quality. Finally, we discuss ongoing research
challenges and outline promising directions for future work.
|
When existing, cumulants can provide valuable information about a given
distribution and can in principle be used to either fully reconstruct or
approximate the parent distribution function. A previously reported cumulant
expansion approach for Franck-Condon profiles [Faraday Discuss., 150, 363
(2011)] is extended to describe also the profiles of vibronic transitions that
are weakly allowed or forbidden in the Franck-Condon approximation (non-Condon
profiles). In the harmonic approximation the cumulants of the vibronic spectral
profile can be evaluated analytically and numerically with a coherent
state-based generating function that accounts for the Duschinsky effect. As
illustration, the one-photon $1 ^{1}\mathrm{A_{g}}\rightarrow1
^{1}\mathrm{B_{2u}}$ UV absorption spectrum of benzene in the electric dipole
and (linear) Herzberg-Teller approximation is presented herein for zero Kelvin
and finite temperatures.
|
For an automorphism group G on an n-dimensional (n > 2) normal projective
variety or a compact K\"ahler manifold X so that G modulo its subgroup N(G) of
null entropy elements is an abelian group of maximal rank n-1, we show that
N(G) is virtually contained in Aut_0(X), the X is a quotient of a complex torus
T and G is mostly descended from the symmetries on the torus T, provided that
both X and the pair (X, G) are minimal.
|
We present PyXtal, a new package based on the Python programming language,
used to generate structures with specific symmetry and chemical compositions
for both atomic and molecular systems. This soft ware provides support for
various systems described by point, rod, layer, and space group symmetries.
With only the inputs of chemical composition and symmetry group information,
PyXtal can automatically find a suitable combination of Wyckoff positions with
a step-wise merging scheme. Further, when the molecular geometry is given,
PyXtal can generate different dimensional organic crystals with molecules
occupying both general and special Wyckoff positions. Optionally, PyXtal also
accepts user-defined parameters (e.g., cell parameters, minimum distances and
Wyckoff positions). In general, PyXtal serves three purposes: (1) to generate
custom structures, (2) to modulate the structure by symmetry relations, (3) to
interface the existing structure prediction codes that require the generation
of random symmetric structures. In addition, we provide several utilities that
facilitate the analysis of structures, including symmetry analysis, geometry
optimization, and simulations of powder X-ray diffraction (XRD). Full
documentation of PyXtal is available at \url{https://pyxtal.readthedocs.io}.
|
We present a new dynamic off-equilibrium method for the study of continuous
transitions, which represents a dynamic generalization of the usual equilibrium
cumulant method. Its main advantage is that critical parameters are derived
from numerical data obtained much before equilibrium has been attained.
Therefore, the method is particularly useful for systems with long
equilibration times, like spin glasses. We apply it to the three-dimensional
Ising spin-glass model, obtaining accurate estimates of the critical exponents
and of the critical temperature with a limited computational effort.
|
Statistical machine translation models have made great progress in improving
the translation quality. However, the existing models predict the target
translation with only the source- and target-side local context information. In
practice, distinguishing good translations from bad ones does not only depend
on the local features, but also rely on the global sentence-level information.
In this paper, we explore the source-side global sentence-level features for
target-side local translation prediction. We propose a novel
bilingually-constrained chunk-based convolutional neural network to learn
sentence semantic representations. With the sentence-level feature
representation, we further design a feed-forward neural network to better
predict translations using both local and global information. The large-scale
experiments show that our method can obtain substantial improvements in
translation quality over the strong baseline: the hierarchical phrase-based
translation model augmented with the neural network joint model.
|
We derive from first principles equations for bosonic, non-relativistic and
self-interacting dark matter which can include both a condensed, low momentum
"fuzzy" component and one with higher momenta that may be approximated as a
collection of particles. The resulting coupled equations consist of a modified
Gross-Pitaevskii equation describing the condensate and a kinetic equation
describing the higher momentum modes, the "particles", along with the Poisson
equation for the gravitational potential sourced by the density of both
components. Our derivation utilizes the Schwinger-Keldysh path integral
formalism and applies a semi-classical approximation which can also accommodate
collisional terms amongst the particles and between the particles and the
condensate to second order in the self-coupling strength. The equations can
therefore describe both CDM and Fuzzy Dark Matter in a unified way, allowing
for the coexistence of both phases and the inclusion of quartic
self-interactions.
|
Let $G\subset GL_n(k)$ be a finite subgroup and $k[x_1,\dots, x_n]^G\subset
k[x_1,\dots, x_n]$ its ring of invariants. We show that, in many cases, the
automorphism group of $k[x_1,\dots, x_n]^G$ is $k^\times$. Version 2:
Incorporates parts of arXiv:2210.16265.
|
Free-running Fabry-Perot lasers normally operate in a single-mode regime
until the pumping current is increased beyond the single-mode instability
threshold, above which they evolve into a multimode state. As a result of this
instability, the single-mode operation of these lasers is typically constrained
to few percents of their output power range, this being an undesired limitation
in spectroscopy applications. In order to expand the span of single-mode
operation, we use an optical injection seed generated by an external-cavity
single-mode laser source to force the Fabry-Perot quantum cascade laser into a
single-mode state in the high current range, where it would otherwise operate
in a multimode regime. Utilizing this approach we achieve single-mode emission
at room temperature with a tuning range of $36 \, \mathrm{cm}^-1$ and stable
continuous-wave output power exceeding 1 W. Far-field measurements show that a
single transverse mode is emitted up to the highest optical power indicating
that the beam properties of the seeded Fabry-Perot laser remain unchanged as
compared to free-running operation.
|
Direct shooting is an efficient method to solve numerical optimal control. It
utilizes the Runge-Kutta scheme to discretize a continuous-time optimal control
problem making the problem solvable by nonlinear programming solvers. However,
conventional direct shooting raises a contradictory dynamics issue when using
an augmented state to handle {high-order} systems. This paper fills the
research gap by considering the direct shooting method for {high-order}
systems. We derive the modified Euler and Runge-Kutta-4 methods to transcribe
the system dynamics constraint directly. Additionally, we provide the global
error upper bounds of our proposed methods. A set of benchmark optimal control
problems shows that our methods provide more accurate solutions than existing
approaches.
|
A natural similarity in body dimensions of terrestrial animals noticed by
ancient philosophers remains the main key to the problem of mammalian skeletal
evolution with body mass explored in theoretical and experimental biology and
tested by comparative zoologists. We discuss the long-standing problem of
mammalian bone allometry commonly studied in terms of the so-called
''geometric'', ''elastic'', and ''static stress'' similarities by McMahon
(1973, 1975a, 1975b). We revise the fundamental assumptions underlying these
similarities and give new physical insights into geometric-shape and
elastic-force constraints imposed on spatial evolution of mammalian long bones.
|
In this paper, first we obtain some new and interesting results on projective
modules and on the upper topology of an ordinal number. Then it is shown that
the rank map of a locally of finite type projective module is continuous with
respect to the upper topology (by contract, it is well known this map is not
necessarily continuous with respect to the discrete topology). It is also
proved that a finitely generated flat module is projective if and only if its
rank map is continuous with respect to the upper topology.
|
The decay $B^0 \to K^0 \pi^0$, dominated by a $b \to s$ penguin amplitude,
holds the potential for exhibiting new physics in this amplitude. In the pure
QCD penguin limit one expects $\ckp = 0$ and $\skp = \sin 2 \beta$ for the
coefficients of $\cos \Delta m t$ and $\sin \Delta m t$ in the time-dependent
CP asymmetry. Small non-penguin contributions lead to corrections to these
expressions which are calculated in terms of isospin-related $B\to K\pi$ rates
and asymmetries, using information about strong phases from experiment. We
study the prospects for incisive tests of the Standard Model through
examination of these corrections. We update a prediction $\ckp=0.15\pm 0.04$,
pointing out the sensitivity of a prediction $\skp\approx 1$ to the measured
branching ratio for $B^0\to K^0\pi^0$ and to other observables.
|
Even in the absence of externally applied temperature gradients,
spontaneously generated temperature fluctuations arise in turbulent flows. We
experimentally study these fluctuations in a closed von Karman swirling flow of
air at Mach number of order $10^{-3}$, whose boundaries are maintained at a
constant temperature. We observe intermittent peaks of low temperature
correlated with pressure drops within the flow and show that they are caused by
vorticity filaments. The measured ratio of temperature to pressure fluctuation
agrees with the prediction based on adiabatic cooling within vortex cores. This
experimental study shows that although the Mach number of the flow is small,
there exist regions within the flow where compressible effects cannot be
discarded in the equation for temperature and locally dominate the effect of
viscous dissipation.
|
A non-perturbative formalism is developed that simplifies the understanding
of self-forces and self-torques acting on extended scalar charges in curved
spacetimes. Laws of motion are locally derived using momenta generated by a set
of generalized Killing fields. Self-interactions that may be interpreted as
arising from the details of a body's internal structure are shown to have very
simple geometric and physical interpretations. Certain modifications to the
usual definition for a center-of-mass are identified that significantly
simplify the motions of charges with strong self-fields. A derivation is also
provided for a generalized form of the Detweiler-Whiting axiom that pointlike
charges should react only to the so-called regular component of their
self-field. Standard results are shown to be recovered for sufficiently small
charge distributions.
|
We describe a first attempt to apply adaptive optics to the study of resolved
stellar populations in galaxies. Advantages over traditional approaches are (i)
improved spatial resolution and point-source sensitivity through adaptive
optics, and (ii) use of the near-infrared region, where the peak of the
spectral energy distribution for old populations is found. Disadvantages are
the small area covered and the need for excellent seeing. We made observations
with the ADONIS system at the European Southern Observatory of the peculiar
elliptical galaxy NGC 5128; the irregular galaxy IC 5152 (a possible outer
member of the Local Group); the Sc galaxy NGC 300 (a member of the Sculptor
group); and the Sgr window in the bulge of the Milky Way. These different
fields give excellent test cases for the potential of adaptive optics. In the
first two cases, we failed to obtain photometry of individual stars, which
would have required excellent seeing. For NGC 300 we measured magnitudes for
nine individual supergiants (H = 18.3 to 20.2), but did not go deep enough to
detect the tip of the RGB of an old population. For the Sgr field we produced a
infrared luminosity function and colour-magnitude diagram for 70 stars down to
about K = 19.5. These are the deepest yet measured for the Galactic bulge,
reaching beyond the turn-off.
|
The dielectric permittivity of salt water decreases on dissolving more salt.
For nearly a century, this phenomenon has been explained by invoking saturation
in the dielectric response of the solvent water molecules. Herein, we employ an
advanced deep neural network (DNN), built using data from density functional
theory, to study the dielectric permittivity of sodium chloride solutions.
Notably, the decrease in the dielectric permittivity as a function of
concentration, computed using the DNN approach, agrees well with experiments.
Detailed analysis of the computations reveals that the dominant effect, caused
by the intrusion of ionic hydration shells into the solvent hydrogen-bond
network, is the disruption of dipolar correlations among water molecules.
Accordingly, the observed decrease in the dielectric permittivity is mostly due
to increasing suppression of the collective response of solvent waters.
|
The Minkowski functionals are a mathematical tool to quantify morphological
features of patterns. Some applications to the matter distribution in galaxy
catalogues and N-body simulations are reviewed, with an emphasis on the effects
of cosmic variance. The conclusions are that (i) the observed large-scale
morphology is sensitive to cosmic variance on scales much larger than the
nonlinear length (approx. 8 Mpc/h), and (ii) the large-scale morphology
predicted by simulations is thus affected by finite-size effects, but
nonetheless a Lambda-CDM model is favored.
|
Image segmentation is about grouping pixels with different semantics, e.g.,
category or instance membership, where each choice of semantics defines a task.
While only the semantics of each task differ, current research focuses on
designing specialized architectures for each task. We present Masked-attention
Mask Transformer (Mask2Former), a new architecture capable of addressing any
image segmentation task (panoptic, instance or semantic). Its key components
include masked attention, which extracts localized features by constraining
cross-attention within predicted mask regions. In addition to reducing the
research effort by at least three times, it outperforms the best specialized
architectures by a significant margin on four popular datasets. Most notably,
Mask2Former sets a new state-of-the-art for panoptic segmentation (57.8 PQ on
COCO), instance segmentation (50.1 AP on COCO) and semantic segmentation (57.7
mIoU on ADE20K).
|
The HFB self-consistent method has been applied to study the properties of
several neutron deficient superheavy nuclei with Z=120-124, N=160-168. Their
distinctive feature is the existence of minima of the total HFB energy for
strongly deformed, oblate shapes. The self-consistent results agree quite
remarkably with those currently obtained by using microscopic-macroscopic
method.
|
I present a brief review of the history of the Instituto Argentino de
Radioastronom\'ia, a description of its current facilities and projects, and a
view of his prospects for the future.
|
This paper enriches the list of properties of the congruence sequences
starting from the universal relation and successively performing the operations
of lower $t$ and lower $k$. Three classes of completely regular semigroups,
namely semigroups for which $\ker{\sigma}$ is a cryptogroup, semigroups for
which $\ker{\nu}$ is a cryptogroup and semigroups for which $\kappa$ is over
rectangular bands, are studied. $((\omega_t)_k)_t$, $((\mathcal{D}_t)_k)_t$ and
$((\omega_k)_t)_k$ are found to be the least congruences on $S$ such that the
quotient semigroups are semigroups for which $\ker{\sigma}$ is a cryptogroup,
$\ker{\nu}$ is a cryptogroup and $\kappa$ is over rectangular bands,
respectively. The results obtained present a response to three problems in
Petrich and Reilly's textbook \textquoteleft\textquoteleft Completely Regular
Semigroups\textquoteright\textquoteright.
|
The first systematic experimental study of the neutron-rich Br isotopes with
two complementary state-of-the-art techniques is presented. These isotopes have
been populated in the fission process at two different facilities, GANIL and
ILL. New spectroscopic information has been obtained for odd-even $^{87-93}$Br
isotopes and the experimental results have been compared with state-of-the-art
Large-Scale Shell-Model and DNO Shell-Model calculations. As a result of such
theoretical approaches, a transition from prolate ($^{87,89}$Br) to oblate
($^{91,93}$Br) shapes is obtained from the subtle balance between proton and
neutron quadrupole deformations, as a clear signature of pseudo-SU3 quadrupole
regime.
|
Using matrix-model methods we study three different N=2 models: U(N) x U(N)
with matter in the bifundamental representation, U(N) with matter in the
symmetric representation, and U(N) with matter in the antisymmetric
representation. We find that the (singular) cubic Seiberg-Witten curves (and
associated Seiberg-Witten differentials) implied by the matrix models, although
of a different form from the ones previously proposed using M-theory, can be
transformed into the latter and are thus physically equivalent. We also
calculate the one-instanton corrections to the gauge-coupling matrix using the
perturbative expansion of the matrix model. For the U(N) theories with
symmetric or antisymmetric matter we use the modified matrix-model prescription
for the gauge-coupling matrix discussed in ref. [hep-th/0303268]. Moreover, in
the matrix model for the U(N) theory with antisymmetric matter, one is required
to expand around a different vacuum than one would naively have anticipated.
With these modifications of the matrix-model prescription, the results of this
paper are in complete agreement with those of Seiberg-Witten theory obtained
using M-theory methods.
|
We propose a novel way of investigating the universal properties of spin
systems by coupling them to an ensemble of causal dynamically triangulated
lattices, instead of studying them on a fixed regular or random lattice.
Somewhat surprisingly, graph-counting methods to extract high- or
low-temperature series expansions can be adapted to this case. For the
two-dimensional Ising model, we present evidence that this ameliorates the
singularity structure of thermodynamic functions in the complex plane, and
improves the convergence of the power series.
|
Alloy is a lightweight formal specification language, supported by an IDE,
which has proven well-suited for reasoning about software design in early
development stages. The IDE provides a visualizer that produces graphical
representations of analysis results, which is essential for the proper
validation of the model. Alloy is a rich language but inherently static, so
behavior needs to be explicitly encoded and reasoned about. Even though this is
a common scenario, the visualizer presents limitations when dealing with such
models. The main contribution of this paper is a principled approach to
generate instance visualizations, which improves the current Alloy Visualizer,
focusing on the representation of behavior.
|
We study various probabilistic and analytical properties of a class of
degenerate diffusion operators arising in Population Genetics, the so-called
generalized Kimura diffusion operators. Our main results is a stochastic
representation of weak solutions to a degenerate parabolic equation with
singular lower-order coefficients, and the proof of the scale-invariant Harnack
inequality for nonnegative solutions to the Kimura parabolic equation. The
stochastic representation of solutions that we establish is a considerable
generalization of the classical results on Feynman-Kac formulas concerning the
assumptions on the degeneracy of the diffusion matrix, the boundedness of the
drift coefficients, and on the a priori regularity of the weak solutions.
|
The Gaussian-filtered Navier-Stokes equations are examined theoretically and
a generalized theory of their numerical stability is proposed. Using the exact
expansion series of subfilter-scale stresses or integration by parts, the terms
describing the interaction between the mean and fluctuation portions in a
statistically steady state are theoretically rewritten into a closed form in
terms of the known filtered quantities. This process involves high-order
derivatives with time-independent coefficients. Detailed stability analyses of
the closed formulas are presented for determining whether a filtered system is
numerically stable when finite difference schemes or others are used to solve
it. It is shown that by the Gaussian filtering operation, second and higher
even-order derivatives are derived that always exhibit numerical instability in
a fixed range of directions; hence, if the filter widths are unsuitably large,
the filtered Navier-Stokes equations can in certain cases be unconditionally
unstable even though there is no error in modeling the subfilter-scale stress
terms. As is proved by a simple example, the essence of the present discussion
can be applied to any other smooth filters; that is, such a numerical
instability problem can arise whenever the dependent variables are smoothed out
by a filter.
|
Molecular species in planetary atmospheres provide key insights into their
atmospheric processes and formation conditions. In recent years,
high-resolution Doppler spectroscopy in the near-infrared has allowed
detections of H$_2$O and CO in the atmospheres of several hot Jupiters. This
method involves monitoring the spectral lines of the planetary thermal emission
Doppler-shifted due to the radial velocity of the planet over its orbit.
However, aside from CO and H$_2$O, which are the primary oxygen- and
carbon-bearing species in hot H$_2$-rich atmospheres, little else is known
about molecular compositions of hot Jupiters. Several recent studies have
suggested the importance and detectability of nitrogen-bearing species in such
atmospheres. In this Letter, we confirm potential detections of CO and H$_2$O
in the hot Jupiter HD 209458b using high-resolution spectroscopy. We also
report a cross-correlation peak with a signal-to-noise ratio of $4.7$ from a
search for HCN. The results are obtained using high-resolution phase-resolved
spectroscopy with the Very Large telescope CRyogenic high-resolution InfraRed
Echelle Spectrograph (VLT CRIRES) and standard analysis methods reported in the
literature. A more robust treatment of telluric contamination and other
residuals would improve confidence and enable unambiguous molecular detections.
The presence of HCN could provide constraints on the C/O ratio of HD~209458b
and its potential origins.
|
The gas phase structure and excited state lifetime of the
p-aminophenol...p-cresol heterodimer have been investigated by REMPI and LIF
spectroscopy with nanosecond laser pulses and pump-probe experiments with
picosecond laser pulses as a model system to study the competition between p-p
and H-bonding interactions in aromatic dimers. The excitation is a broad and
unstructured band. The excitedstate of the heterodimer is long lived (2.5 +/-
0.5) ns with a very broad fluorescence spectrum red-shifted by 4000 cm^{-1}
with respect to the excitation spectrum. Calculations at the MP2/RI-CC2 and
DFT-oB97X-D levels indicate that hydrogen-bonded (HB) and p-stacked isomers are
almost isoenergetic in the ground state while in the excited state only the
p-stacked isomer exists. This suggests that the HB isomer cannot be excited due
to negligible Franck-Condon factors and therefore the excitation spectrum is
associated with the p-stacked isomer that reaches vibrationally excited states
in the S1 state upon vertical excitation. The excited state structure is an
exciplex responsible for the fluorescence of the complex. Finally,a comparison
was performed between the p-stacked structure observed for the
p-aminophenol...p-cresol heterodimer and the HB structure reported for the
(p-cresol)2 homodimer indicating that the differences are due to different
optical properties (oscillator strengths and Franck-Condon factors) of the
isomers of both dimers and not to the interactions involved in the ground state
|
We show how to compute the edit distance between two strings of length n up
to a factor of 2^{\~O(sqrt(log n))} in n^(1+o(1)) time. This is the first
sub-polynomial approximation algorithm for this problem that runs in
near-linear time, improving on the state-of-the-art n^(1/3+o(1)) approximation.
Previously, approximation of 2^{\~O(sqrt(log n))} was known only for embedding
edit distance into l_1, and it is not known if that embedding can be computed
in less than quadratic time.
|
Recent neutrino data have been favourable to a nearly bimaximal mixing, which
suggests a simple form of the neutrino mass matrix. Stimulated by this matrix
form, a possibility that all the mass matrices of quarks and leptons have the
same form as in the neutrinos is investigated. The mass matrix form is
constrained by a discrete symmetry Z_3 and a permutation symmetry S_2. The
model, of course, leads to a nearly bimaximal mixing for the lepton sectors,
while, for the quark sectors, it can lead to reasonable values of the CKM
mixing matrix and masses.
|
Modeling of the shock cone formed around a static, hairy Horndeski black hole
with Bondi-Hoyle-Lyttleton (BHL) accretion has been conducted. We model the
dynamical changes of the shock cone resulting from the interaction of matter
with the Horndeski black hole. The effects of the scalar hair, the black hole
rotation parameter, and the impacts of the asymptotic speed have been examined.
As the absolute value of the hair parameter increases, the matter in the region
of the shock cone is observed to move away from the black hole horizon. After
h/M<-0.6, a visible change in the physical structure of the shock cone occurs.
On the other hand, it has been revealed that the asymptotic speed significantly
affects the formation of the shock cone. As h/M increases in the negative
direction and the asymptotic speed increases, the stagnation point moves closer
to the black hole horizon. When the value of the hair parameter changes, the
rest-mass density of the matter inside the cone decreases, whereas the opposite
is observed with the asymptotic speed. Additionally, the formed shock cone has
excited QPO modes. The deformation of the cone due to the hair parameter has
led to a change or complete disappearance of the QPOs. Meanwhile, at asymptotic
speeds of V_{\infty}/c< 0.4, all fundamental frequency modes are formed, while
at V_{\infty}/c=0.4, only the azimuthal mode is excited, and 1:2:3:4:...
resonance conditions occur. No QPOs have formed at V_{\infty}/c = 0.6. The
results obtained from numerical calculations have been compared with
theoretical studies for M87*, and it has been observed that the possible values
of h/M found in the numerical simulations are consistent with the theory.
Additionally, the results have been compared with those for the GRS 1915+105
black hole, and the hair parameters corresponding to the observed frequencies
have been determined.
|
Self-similarity induced by critical gravitational collapse is used as a
paradigm to probe the mass distribution of subsolar objects. At large mass
(solar mass and above) there is widespread agreement as to both the form and
parameter values arising in the mass distribution of stellar objects. At
subsolar mass there is still considerable disagreement as to the qualitative
form of the mass distribution, let alone the specific parameter values
characterizing that distribution.
For the first time, the paradigm of critical gravitational collapse is
applied to several concrete astrophysical scenarios to derive robust
qualitative features of the subsolar mass distribution. We further contrast
these theoretically derived ideas with the observational situation. In
particular, we demonstrate that at very low mass the distribution is given by a
power law, with an exponent opposite in sign to that observed in the high-mass
regime. The value of this low-mass exponent is in principle calculable via
dynamical systems theory applied to gravitational collapse. Qualitative
agreement between theory, numerical experiments, and observational data is
good, though quantitative issues remain troublesome.
|
An alternate set of equations to describe the electrodynamics of
superconductors at a macroscopic level is proposed. These equations resemble
equations originally proposed by the London brothers but later discarded by
them. Unlike the conventional London equations the alternate equations are
relativistically covariant, and they can be understood as arising from the
'rigidity' of the superfluid wave function in a relativistically covariant
microscopic theory. They predict that an internal 'spontaneous' electric field
exists in superconductors, and that externally applied electric fields, both
longitudinal and transverse, are screened over a London penetration length, as
magnetic fields are. The associated longitudinal dielectric function predicts a
much steeper plasmon dispersion relation than the conventional theory, and a
blue shift of the minimum plasmon frequency for small samples. It is argued
that the conventional London equations lead to difficulties that are removed in
the present theory, and that the proposed equations do not contradict any known
experimental facts. Experimental tests are discussed.
|
We derive a recursive formula for certain relative Gromov-Witten invariants
with maximal tangency condition via the Witten-Dijkgraaf-Verlinde-Verlinde
equation. For certain relative pairs, we get explicit formulae of invariants
using the recursive formula.
|
We give an identification of the triple reduced product of three coadjoint
orbits in SU(3) with a space of Hitchin pairs over a genus 0 curve with three
punctures, where the residues of the Higgs field at the punctures are
constrained to lie in fixed coadjoint orbits. Using spectral curves for the
corresponding Hitchin system, we identify the moment map for a Hamiltonian
circle action on the reduced product. Finally, we make use of results of Adams,
Harnad, and Hurtubise to find Darboux coordinates and a differential equation
for the Hamiltonian.
|
There has been a growing interest in developing multimodal machine
translation (MMT) systems that enhance neural machine translation (NMT) with
visual knowledge. This problem setup involves using images as auxiliary
information during training, and more recently, eliminating their use during
inference. Towards this end, previous works face a challenge in training
powerful MMT models from scratch due to the scarcity of annotated multilingual
vision-language data, especially for low-resource languages. Simultaneously,
there has been an influx of multilingual pre-trained models for NMT and
multimodal pre-trained models for vision-language tasks, primarily in English,
which have shown exceptional generalisation ability. However, these are not
directly applicable to MMT since they do not provide aligned multimodal
multilingual features for generative tasks. To alleviate this issue, instead of
designing complex modules for MMT, we propose CLIPTrans, which simply adapts
the independently pre-trained multimodal M-CLIP and the multilingual mBART. In
order to align their embedding spaces, mBART is conditioned on the M-CLIP
features by a prefix sequence generated through a lightweight mapping network.
We train this in a two-stage pipeline which warms up the model with image
captioning before the actual translation task. Through experiments, we
demonstrate the merits of this framework and consequently push forward the
state-of-the-art across standard benchmarks by an average of +2.67 BLEU. The
code can be found at www.github.com/devaansh100/CLIPTrans.
|
Temporal feature extraction is an important issue in video-based action
recognition. Optical flow is a popular method to extract temporal feature,
which produces excellent performance thanks to its capacity of capturing
pixel-level correlation information between consecutive frames. However, such a
pixel-level correlation is extracted at the cost of high computational
complexity and large storage resource. In this paper, we propose a novel
temporal feature extraction method, named Attentive Correlated Temporal Feature
(ACTF), by exploring inter-frame correlation within a certain region. The
proposed ACTF exploits both bilinear and linear correlation between successive
frames on the regional level. Our method has the advantage of achieving
performance comparable to or better than optical flow-based methods while
avoiding the introduction of optical flow. Experimental results demonstrate our
proposed method achieves the state-of-the-art performances of 96.3% on UCF101
and 76.3% on HMDB51 benchmark datasets.
|
We present a version of the domino shuffling algorithm (due to Elkies,
Kuperberg, Larsen and Propp) which works on a different lattice: the hexagonal
lattice superimposed on its dual graph. We use our algorithm to count perfect
matchings on a family of finite subgraphs of this lattice whose boundary
conditions are compatible with our algorithm. In particular, we re-prove an
enumerative theorem of Ciucu, as well as finding a related family of subgraphs
which have 2^{(n+1)^2} perfect matchings. We also give three-variable
generating functions for perfect matchings on both families of graphs, which
encode certain statistics on the height functions of these graphs.
|
An important challenge in quantum science is to fully understand the
efficiency of energy flow in networks. Here we present a simple and intuitive
explanation for the intriguing observation that optimally efficient networks
are not purely quantum, but are assisted by some interaction with a `noisy'
classical environment. By considering the system's dynamics in both the
site-basis and the momentum-basis, we show that the effect of classical noise
is to sustain a broad momentum distribution, countering the depletion of high
mobility terms which occurs as energy exits from the network. This picture
predicts that the optimal level of classical noise is reciprocally related to
the linear dimension of the lattice; our numerical simulations verify this
prediction to high accuracy for regular 1D and 2D networks over a range of
sizes up to thousands of sites. This insight leads to the discovery that
dramatic further improvements in performance occur when a driving field targets
noise at the low mobility components.
|
Inspired by the exact solution of the Majumdar-Ghosh model, a family of
one-dimensional, translationally invariant spin hamiltonians is constructed.
The exchange coupling in these models is antiferromagnetic, and decreases
linearly with the separation between the spins. The coupling becomes
identically zero beyond a certain distance. It is rigorously proved that the
dimer configuration is an exact, superstable ground state configuration of all
the members of the family on a periodic chain. The ground state is two-fold
degenerate, and there exists an energy gap above the ground state. The
Majumdar-Ghosh hamiltonian with two-fold degenerate dimer ground state is just
the first member of the family.
The scheme of construction is generalized to two and three dimensions, and
illustrated with the help of some concrete examples. The first member in two
dimensions is the Shastry-Sutherland model. Many of these models have
exponentially degenerate, exact dimer ground states.
|
This paper presents a novel mathematical framework for understanding
pixel-driven approaches for the parallel beam Radon transform as well as for
the fanbeam transform, showing that with the correct discretization strategy,
convergence - including rates - in the $L^2$ operator norm can be obtained.
These rates inform about suitable strategies for discretization of the
occurring domains/variables, and are first established for the Radon transform.
In particular, discretizing the detector in the same magnitude as the image
pixels (which is standard practice) might not be ideal and in fact,
asymptotically smaller pixels than detectors lead to convergence. Possible
adjustments to limited-angle and sparse-angle Radon transforms are discussed,
and similar convergence results are shown. In the same vein, convergence
results are readily extended to a novel pixel-driven approach to the fanbeam
transform. Numerical aspects of the discretization scheme are discussed, and it
is shown in particular that with the correct discretization strategy, the
typical high-frequency artifacts can be avoided.
|
We investigate the effect of ergodic inclusions in putative many-body
localized systems. To this end, we consider the random field Heisenberg chain,
which is many-body localized at strong disorder and we couple it to an ergodic
bubble, modeled by a random matrix Hamiltonian. Recent theoretical work
suggests that the ergodic bubble destabilizes the apparent localized phase at
intermediate disorder strength and finite sizes. We tentatively confirm this by
numerically analyzing the response of the local thermality, quantified by
one-site purities, to the insertion of the bubble. For a range of intermediate
disorder strengths, this response decays very slowly, or not at all, with
increasing distance to the bubble. This suggests that at those disorder
strengths, the system is delocalized in the thermodynamic limit. However, the
numerics is unfortunately not unambiguous and we cannot definitely rule out
artefacts.
|
A dual-phase xenon time-projection chamber was built at Nikhef in Amsterdam
as a direct dark matter detection R&D facility. In this paper, the setup is
presented and the first results from a calibration with a $^{22}$Na gamma-ray
source are presented. The results show an average light yield of (5.6 $\pm$
0.3) photoelectrons/keV (calculated to 122 keV and zero field) and an electron
lifetime of (429 $\pm$ 26) $\mu$s. The best energy resolution $\sigma_E/E$ is
(5.8 $\pm$ 0.2)% at an energy of 511 keV. This was achieved using a combination
of the scintillation and the ionization signals. A photomultiplier tube gain
calibration technique, based on the electroluminescence signals occurring from
isolated electrons, is presented and its advantages and limitations are
discussed.
|
It is well known that the outer parts of QSO accretion disks are prone to
selfgravity if heated solely by orbital dissipation. Such disks might be
expected to form stars rather than accrete onto the black hole. The arguments
leading to this conclusion are reviewed. Conversion of a part of the gas into
high-mass stars or stellar-mass black holes, and the release of energy in these
objects by fusion or accretion, may help to stabilize the remaining gas. If the
disk extends beyond a parsec, however, more energy is probably required for
stability than is available by turning half the gas into high-mass stars. Small
black holes are perhaps marginally viable energy sources, with important
implications (not pursued here) for the QSO spectral energy distribution, the
metallicity of the gas, microlensing of QSO disks, and perhaps
gravitational-wave searches. Other possible palliatives for selfgravity include
accretion driven by nonviscous torques that allow near-sonic accretion speeds
and hence lower surface densities for a given mass accretion rate. All such
modes of accretion face major theoretical difficulties, and in any case merely
postpone selfgravity. Alternatively, thin disks may not exist beyond a thousand
Schwarzshild radii or so (0.01 parsec), in which case QSOs must be fueled by
gas with small specific angular momentum.
|
Continuous-time Markovian evolution appears to be manifestly different in
classical and quantum worlds. We consider ensembles of random generators of
$N$-dimensional Markovian evolution, quantum and classical ones, and evaluate
their universal spectral properties. We then show how the two types of
generators can be related by superdecoherence. In analogy with the mechanism of
decoherence, which transforms a quantum state into a classical one,
superdecoherence can be used to transform a Lindblad operator (generator of
quantum evolution) into a Kolmogorov operator (generator of classical
evolution). We inspect spectra of random Lindblad operators undergoing
superdecoherence and demonstrate that, in the limit of complete
superdecoherence, the resulting operators exhibit spectral density typical to
random Kolmogorov operators. By gradually increasing strength of
superdecoherence, we observe a sharp quantum-to-classical transition.
Furthermore, we define an inverse procedure of supercoherification that is a
generalization of the scheme used to construct a quantum state out of a
classical one. Finally, we study microscopic correlation between neighbouring
eigenvalues through the complex spacing ratios and observe the horse-shoe
distribution, emblematic of the Ginibre universality class, for both types of
random generators. Remarkably, it survives superdecoherence and
supercoherification.
|
Single-zone synchrotron self-Compton and external Compton models are widely
used to explain broad-band Spectral Energy Distributions (SEDs) of blazars from
infrared to gamma-rays. These models bear obvious similarities to the
homogeneous synchrotron cloud model which is often applied to explain radio
emission from individual components of parsec-scale radio jets. The
parsec-scale core, typically the brightest and most compact feature of blazar
radio jet, could be the source of high-energy emission. We report on ongoing
work to test this hypothesis by deriving the physical properties of
parsec-scale radio emitting regions of twenty bright Fermi blazars using
dedicated 5-43 GHz VLBA observations and comparing these parameters to results
of SED modeling.
|
We investigate the instability of the ghost dark energy model against
perturbations in different cases. To this goal we use the squared sound speed
$v_s^2$ whose sign determines the stability of the model. When $v_s^2<0$ the
model is unstable against perturbation. At first we discuss the noninteracting
ghost dark energy model in a flat FRW universe and find out that such a model
is unstable due to the negativity of the $v_s^2$ in all epoches. The
interacting ghost dark energy model in both flat and non-flat universe are
studied in the next parts and in both cases we find that the squared sound
speed of ghost dark energy is always negative. This implies that the perfect
fluid for ghost dark energy is classically unstable against perturbations. In
both flat and non flat cases we find that the instability of the model
increases with increasing the value of the interacting coupling parameter.
|
We consider the 2D critical Ising model with spatially periodic boundary
conditions. It is shown that for a suitable reparametrization of the known
Boltzmann weights the transfer matrix becomes a polynomial in the variable
$\csc(4u)$, being $u$ the spectral parameter. The coefficients of this
polynomial are decomposed on the periodic Temperley-Lieb Algebra by introducing
a lattice version of the Local Integrals of Motion.
|
The aim of this work is to extend to finite potent endomorphisms the notion
of G-Drazin inverse of a finite square matrix. Accordingly, we determine the
structure and the properties of a G-Drazin inverse of a finite potent
endomorphism and, as an application, we offer an algorithm to compute the
explicit expression of all G-Drazin inverses of a finite square matrix.
|
Starting from a realistically sheared magnetic arcade connecting
chromospheric, transition region to coronal plasma, we simulate the in-situ
formation and sustained growth of a quiescent prominence in the solar corona.
Contrary to previous works, our model captures all phases of the prominence
formation, including the loss of thermal equilibrium, its successive growth in
height and width to macroscopic dimensions, and the gradual bending of the
arched loops into dipped loops, as a result of the mass accumulation. Our
2.5-dimensional, fully thermodynamically and magnetohydrodynamically consistent
model mimics the magnetic topology of normal-polarity prominences above a
photospheric neutral line, and results in a curtain-like prominence above the
neutral line through which the ultimately dipped magnetic field lines protrude
at a finite angle. The formation results from concentrated heating in the
chromosphere, followed by plasma evaporation and later rapid condensation in
the corona due to thermal instability, as verified by linear instability
criteria. Concentrated heating in the lower atmosphere evaporates plasma from
below to accumulate at the top of coronal loops and supply mass to the later
prominence constantly. This is the first evaporation-condensation model study
where we can demonstrate how the formed prominence stays in a force balanced
state, which can be compared to the Kippenhahn-Schluter type magnetohydrostatic
model, all in a finite low-beta corona.
|
The $1/N$ expansion of matrix models is asymptotic, and it requires
non-perturbative corrections due to large $N$ instantons. Explicit expressions
for large $N$ instanton amplitudes are known in the case of Hermitian matrix
models with one cut, but not in the multi-cut case. We show that the recent
exact results on topological string instanton amplitudes provide the
non-perturbative contributions of large $N$ instantons in generic multi-cut,
Hermitian matrix models. We present a detailed test in the case of the cubic
matrix model by considering the asymptotics of its $1/N$ expansion, which we
obtain at relatively high genus for a generic two-cut background. These results
can be extended to certain non-conventional matrix models which admit a
topological string theory description. As an application, we determine the
large $N$ instanton corrections for the free energy of ABJM theory on the
three-sphere, which correspond to D-brane instanton corrections in superstring
theory. We also illustrate the applications of topological string instantons in
a more mathematical setting by considering orbifold Gromov-Witten invariants.
By focusing on the example of $\mathbb{C}^3/\mathbb{Z}_3$, we show that they
grow doubly-factorially with the genus and we obtain and test explicit
asymptotic formulae for them.
|
In this paper, we develop a new neural network family based on power series
expansion, which is proved to achieve a better approximation accuracy in
comparison with existing neural networks. This new set of neural networks
embeds the power series expansion (PSE) into the neural network structure. Then
it can improve the representation ability while preserving comparable
computational cost by increasing the degree of PSE instead of increasing the
depth or width. Both theoretical approximation and numerical results show the
advantages of this new neural network.
|
For optical waveguides with a layered background which itself is a slab
waveguide, a guided mode is a bound state in the continuum (BIC), if it
coexists with slab modes propagating outwards in the lateral direction; i.e.,
there are lateral leakage channels. It is known that generic BICs in optical
waveguides with lateral leakage channels are robust in the sense that they
still exist if the waveguide is perturbed arbitrarily. However, the theory is
not applicable to non-generic BICs which can be defined precisely. Near a BIC,
the waveguide supports resonant and leaky modes with a complex frequency and a
complex propagation constant, respectively. In this paper, we develop a
perturbation theory to show that the resonant and leaky modes near a
non-generic BIC have an ultra-high $Q$ factor and ultra-low leakage loss,
respectively. We also show that a merging-BIC obtained by tuning structural
parameters is always a non-generic BIC. Existing studies on merging-BICs are
concerned with specific examples and specific parameters. We analyze an
arbitrary structural perturbation (to a waveguide supporting a non-generic BIC)
given by $\delta F({\bf r})$, where $F({\bf r})$ is the perturbation profile
and $\delta$ is the amplitude, and show that the perturbed waveguide has two
BICs for $\delta>0$ (or $\delta<0$) and no BIC for $\delta<0$ (or $\delta>0$).
This implies that a non-generic BIC is a merging-BIC (for any perturbation
profile $F$) when $\delta$ is regarded as a parameter. Our study indicates that
non-generic BICs have interesting special properties that are useful in
applications.
|
Object detection with Unmanned Aerial Vehicles (UAVs) has attracted much
attention in the research field of computer vision. However, not easy to
accurately detect objects with data obtained from UAVs, which capture images
from very high altitudes, making the image dominated by small object sizes,
that difficult to detect. Motivated by that challenge, we aim to improve the
performance of the one-stage detector YOLOv3 by adding a Spatial Pyramid
Pooling (SPP) layer on the end of the backbone darknet-53 to obtain more
efficient feature extraction process in object detection tasks with UAVs. We
also conducted an evaluation study on different versions of YOLOv3 methods.
Includes YOLOv3 with SPP, YOLOv3, and YOLOv3-tiny, which we analyzed with the
VisDrone2019-Det dataset. Here we show that YOLOv3 with SPP can get results mAP
0.6% higher than YOLOv3 and 26.6% than YOLOv3-Tiny at 640x640 input scale and
is even able to maintain accuracy at different input image scales than other
versions of the YOLOv3 method. Those results prove that the addition of SPP
layers to YOLOv3 can be an efficient solution for improving the performance of
the object detection method with data obtained from UAVs.
|
We propose a model to explain a puzzling 3:2 frequency ratio of high
frequency quasi-periodic oscillations (HFQPOs) in black hole (BH) X-ray
binaries, GRO J1655-40, GRS 1915+105 and XTE J1550-564. In our model a
non-axisymmetric magnetic coupling (MC) of a rotating black hole (BH) with its
surrounding accretion disc coexists with the Blandford-Znajek (BZ) process. The
upper frequency is fitted by a rotating hotspot near the inner edge of the
disc, which is produced by the energy transferred from the BH to the disc, and
the lower frequency is fitted by another rotating hotspot somewhere away from
the inner edge of the disc, which arises from the screw instability of the
magnetic field on the disc. It turns out that the 3:2 frequency ratio of HFQPOs
in these X-ray binaries could be well fitted to the observational data with a
much narrower range of the BH spin. In addition, the spectral properties of
HFQPOs are discussed. The correlation of HFQPOs with jets from microquasars is
contained naturally in our model.
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Higher-order unification (HOU) concerns unification of (extensions of)
$\lambda$-calculus and can be seen as an instance of equational unification
($E$-unification) modulo $\beta\eta$-equivalence of $\lambda$-terms. We study
equational unification of terms in languages with arbitrary variable binding
constructions modulo arbitrary second-order equational theories. Abstract
syntax with general variable binding and parametrised metavariables allows us
to work with arbitrary binders without committing to $\lambda$-calculus or use
inconvenient and error-prone term encodings, leading to a more flexible
framework. In this paper, we introduce $E$-unification for second-order
abstract syntax and describe a unification procedure for such problems, merging
ideas from both full HOU and general $E$-unification. We prove that the
procedure is sound and complete.
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We develop a theory of G-dimension for modules over local homomorphisms which
encompasses the classical theory of G-dimension for finite modules over local
rings. As an application, we prove that a local ring R of characteristic p is
Gorenstein if and only if it possesses a nonzero finite module of finite
projective dimension that has finite G-dimension when considered as an R-module
via some power of the Frobenius endomorphism of R. We also prove results that
track the behavior of Gorenstein properties of local homomorphisms under
(de)composition.
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We report on a search for nuclear recoil signals from solar $^8$B neutrinos
elastically scattering off xenon nuclei in XENON1T data, lowering the energy
threshold from 2.6 keV to 1.6 keV. We develop a variety of novel techniques to
limit the resulting increase in backgrounds near the threshold. No significant
$^8$B neutrino-like excess is found in an exposure of 0.6 t $\times$ y. For the
first time, we use the non-detection of solar neutrinos to constrain the light
yield from 1-2 keV nuclear recoils in liquid xenon, as well as non-standard
neutrino-quark interactions. Finally, we improve upon world-leading constraints
on dark matter-nucleus interactions for dark matter masses between 3 GeV/c$^2$
and 11 GeV/c$^2$ by as much as an order of magnitude.
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Tolerance against failures and errors is an important feature of many complex
networked systems [1,2]. It has been shown that a class of inhomogeneously
wired networks called scale-free[1,3] networks can be surprisingly robust to
failures, suggesting that socially self-organized systems such as the
World-Wide Web, the Internet, and other kinds of social networks [4] may have
significant tolerance against failures by virtue of their scale-free degree
distribution. I show that this finding only holds on the assumption that the
diffusion process supported by the network is a simple one, requiring only a
single contact in order for transmission to be successful.
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A maximum stellar surface density $\Sigma_{max} \sim 3 \times 10^5\,{\rm
M_\odot\,pc^{-2}}$ is observed across all classes of dense stellar systems
(e.g. star clusters, galactic nuclei, etc.), spanning $\sim 8$ orders of
magnitude in mass. It has been proposed that this characteristic scale is set
by some dynamical feedback mechanism preventing collapse beyond a certain
surface density. However, simple analytic models and detailed simulations of
star formation moderated by feedback from massive stars argue that feedback
becomes {\it less} efficient at higher surface densities (with the star
formation efficiency increasing as $\sim \Sigma/\Sigma_{crit}$). We therefore
propose an alternative model wherein stellar feedback becomes ineffective at
moderating star formation above some $\Sigma_{crit}$, so the supply of
star-forming gas is rapidly converted to stars before the system can contract
to higher surface density. We show that such a model -- with $\Sigma_{crit}$
taken directly from the theory -- naturally predicts the observed
$\Sigma_{max}$. $\Sigma_{max}\sim 100\Sigma_{crit}$ because the gas consumption
time is longer than the global freefall time even when feedback is ineffective.
Moreover the predicted $\Sigma_{max}$ is robust to spatial scale and
metallicity, and is preserved even if multiple episodes of star formation/gas
inflow occur. In this context, the observed $\Sigma_{max}$ directly tells us
where feedback fails.
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We study the Liouville metric associated to an approximation of a
log-correlated Gaussian field with short range correlation. We show that below
a parameter $\gamma_c >0$, the left-right length of rectangles for the
Riemannian metric $e^{\gamma \phi_{0,n}} ds^2$ with various aspect ratio is
concentrated with quasi-lognormal tails, that the renormalized metric is tight
when $\gamma < \min ( \gamma_c, 0.4)$ and that subsequential limits are
consistent with the Weyl scaling.
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We present nonlocal integrable reductions of super AKNS coupled equations. By
the use of nonlocal reductions of Ablowitz and Musslimani we find new super
integrable equations. In particular we introduce nonlocal super NLS equations
and the nonlocal super mKdV equations.
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An attempt to extract critical exponents gamma, beta and tau from data on
gold nuclei fragmentation due to interactions with nuclear emulsion at energies
4.0 A GeV and 10.6 A GeV is presented. Based on analysis of Campi's 2nd charge
moments, two subsets of data at each energy are selected from the inclusive
data, corresponding to 'liquid' and 'gas' phases. The extracted values of
critical exponents from the selected data sets are in agreement with
predictions of 'liquid-gas' model of phase transition.
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The first underground data run of the ZEPLIN-II experiment has set a limit on
the nuclear recoil rate in the two-phase xenon detector for direct dark matter
searches. In this paper the results from this run are converted into the limits
on spin-dependent WIMP-proton and WIMP-neutron cross-sections. The minimum of
the curve for WIMP-neutron cross-section corresponds to 0.07 pb at a WIMP mass
of around 65 GeV.
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A novel space-discretized Finite Differences-based model reduction,
introduced in (Liu,Guo,2020) is extended to the partial differential equations
(PDE) model of a multi-layer Mead-Marcus-type sandwich beam with clamped-free
boundary conditions. The PDE model describes transverse vibrations for a
sandwich beam whose alternating outer elastic layers constrain viscoelastic
core layers, which allow transverse shear. The major goal of this project is to
design a single tip velocity sensor to control the overall dynamics on the
beam. Since the spectrum of the PDE can not be constructed analytically, the
so-called multipliers approach is adopted to prove that the PDE model is
exactly observable with sub-optimal observation time. Next, the PDE model is
reduced by the ``order-reduced'' Finite-Differences technique. This method does
not require any type of filtering though the exact observability as $h\to 0$ is
achieved by a constraint on the material constants. The main challenge here is
the strong coupling of the shear dynamics of the middle layer with overall
bending dynamics. This complicates the absorption of coupling terms in the
discrete energy estimates. This is sharply different from a single-layer
(Euler-Bernoulli) beam.
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In this article, non-linear Equal Width-Wave (EW) equation will be
numerically solved . For this aim, the non-linear term in the equation is
firstly linearized by Rubin-Graves type approach. After that, to reduce the
equation into a solvable discretized linear algebraic equation system which is
the essential part of this study, the Crank-Nicolson type approximation and
cubic Hermite collocation method are respectively applied to obtain the
integration in the temporal and spatial domain directions. To be able to
illustrate the validity and accuracy of the proposed method, six test model
problems that is single solitary wave, the interaction of two solitary waves,
the interaction of three solitary waves, the Maxwellian initial condition,
undular bore and finally soliton collision will be taken into consideration and
solved. Since only the single solitary wave has an analytical solution among
these solitary waves, the error norms Linf and L2 are computed and compared to
a few of the previous works available in the literature. Furthermore, the
widely used three invariants I1, I2 and I3 of the proposed problems during the
simulations are computed and presented. Beside those, the relative changes in
those invariants are presented. Also, a comparison of the error norms Linf and
L2 and these invariants obviously shows that the proposed scheme produces
better and compatible results than most of the previous works using the same
parameters. Finally, von Neumann analysis has shown that the present scheme is
unconditionally stable.
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Vascular adhesion of circulating tumor cells (CTCs) is a key step in cancer
spreading. If inflammation is recognized to favor the formation of vascular
metastatic niches, little is known about the contribution of blood rheology to
CTC deposition. Herein, a microfluidic chip, covered by a confluent monolayer
of endothelial cells, is used for analyzing the adhesion and rolling of
colorectal (HCT 15) and breast (MDA MB 231) cancer cells under different
biophysical conditions. These include the analysis of cell transport in a
physiological solution and whole blood; over a healthy and a TNF alpha inflamed
endothelium; with a flow rate of 50 and 100 nL/min. Upon stimulation of the
endothelial monolayer with TNF alpha (25 ng/mL), CTC adhesion increases by 2 to
4 times whilst cell rolling velocity only slightly reduces. Notably, whole
blood also enhances cancer cell deposition by 2 to 3 times, but only on the
unstimulated vasculature. For all tested conditions, no statistically
significant difference is observed between the two cancer cell types. Finally,
a computational model for CTC transport demonstrates that a rigid cell
approximation reasonably predicts rolling velocities while cell deformability
is needed to model adhesion. These results would suggest that, within
microvascular networks, blood rheology and inflammation contribute similarly to
CTC deposition thereby facilitating the formation of metastatic niches along
the entire network, including the healthy endothelium. In microfluidic based
assays, neglecting blood rheology would significantly underestimate the
metastatic potential of cancer cells.
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We prove that every finitely presented self-similar group embeds in a
finitely presented simple group. This establishes that every group embedding in
a finitely presented self-similar group satisfies the Boone-Higman conjecture.
The simple groups in question are certain commutator subgroups of
R\"over-Nekrashevych groups, and the difficulty lies in the fact that even if a
R\"over-Nekrashevych group is finitely presented, its commutator subgroup might
not be. We also discuss a general example involving matrix groups over certain
rings, which in particular establishes that every finitely generated subgroup
of $\mathrm{GL}_n(\mathbb{Q})$ satisfies the Boone-Higman conjecture.
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Optical rigidity in aLIGO gravitational-wave detector, operated on dark port
regime, is unstable. We show that the same interferometer with excluded
symmetric mechanical mode but with unbalanced arms allows to get stable optical
spring for antisymmetric mechanical mode. Arm detuning necessary to get
stability is shown to be a small one - it corresponds to small power in signal
port. We show that stable optical spring may be also obtained in
Michelson-Sagnac interferometer with both power and signal recycling mirrors
and unbalanced arms.
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Midrapidity nucleon elliptic flow is studied within the Boltzmann-equation
simulations of symmetric heavy-ion collisions. The simulations follow a lattice
Hamiltonian extended to relativistic transport. It is demonstrated that in the
peripheral heavy-ion collisions the high-momentum elliptic flow is strongly
sensitive to the momentum dependence of mean field at supranormal densities.
The high transverse-momentum particles are directly and exclusively emitted
from the high-density zone in the collisions, while remaining particles
primarily continue along the beam axis. The elliptic flow was measured by the
KaoS Collaboration as a function of the transverse momentum at a number of
impact parameters in Bi + Bi collisions at 400, 700, and 1000 MeV/nucleon. The
observed elliptic anisotropies in peripheral collisions, which quickly rise
with momentum, can only be explained in simulations when assuming a strong
momentum dependence of nucleonic mean field. This momentum dependence must
strengthen with the rise of density above normal. The mean-field
parametrizations, which describe the data in simulations with various success,
are confronted with mean fields from microscopic nuclear-matter calculations.
Two of the microscopic potentials in the comparisons have unacceptably weak
momentum-dependencies at supranormal densities. The optical potentials from the
Dirac-Brueckner-Hartree-Fock calculations, on the other hand, together with the
UV14 + TNI potential from variational calculations, agree rather well within
the region of sensitivity with the parametrized potentials that best describe
the data.
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We propose an integrability setup for the computation of correlation
functions of gauge-invariant operators in $\mathcal{N}=4$ supersymmetric
Yang-Mills theory at higher orders in the large $N_{\text{c}}$ genus expansion
and at any order in the 't Hooft coupling $g_{\text{YM}}^2N_{\text{c}}$. In
this multi-step proposal, one polygonizes the string worldsheet in all possible
ways, hexagonalizes all resulting polygons, and sprinkles mirror particles over
all hexagon junctions to obtain the full correlator. We test our
integrability-based conjecture against a non-planar four-point correlator of
large half-BPS operators at one and two loops.
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The social Web is transforming the way information is created and
distributed. Blog authoring tools enable users to publish content, while sites
such as Digg and Del.icio.us are used to distribute content to a wider
audience. With content fast becoming a commodity, interest in using social
networks to promote and find content has grown, both on the side of content
producers (viral marketing) and consumers (recommendation). Here we study the
role of social networks in promoting content on Digg, a social news aggregator
that allows users to submit links to and vote on news stories. Digg's goal is
to feature the most interesting stories on its front page, and it aggregates
opinions of its many users to identify them. Like other social networking
sites, Digg allows users to designate other users as ``friends'' and see what
stories they found interesting. We studied the spread of interest in news
stories submitted to Digg in June 2006. Our results suggest that pattern of the
spread of interest in a story on the network is indicative of how popular the
story will become. Stories that spread mainly outside of the submitter's
neighborhood go on to be very popular, while stories that spread mainly through
submitter's social neighborhood prove not to be very popular. This effect is
visible already in the early stages of voting, and one can make a prediction
about the potential audience of a story simply by analyzing where the initial
votes come from.
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Thermal fluctuations in cell membranes manifest as an excess area (${\cal
A}_{\rm ex}$) which governs a multitude of physical process at the sub-micron
scale. We present a theoretical framework, based on an in silico tether pulling
method, which may be used to reliably estimate ${\cal A}_{\rm ex}$ in live
cells. The tether forces estimated from our simulations compare well with our
experimental measurements for tethers extracted from ruptured GUVs and HeLa
cells. We demonstrate the significance and validity of our method by showing
that all our calculations along with experiments of tether extraction in 15
different cell types collapse onto two unified scaling relationships mapping
tether force, tether radius, bending stiffness $\kappa$, and membrane tension
$\sigma$. We show that $R_{\rm bead}$, the size of the wetting region, is an
important determinant of the radius of the extracted tether, which is equal to
$\xi=\sqrt{\kappa/2\sigma}$ (a characteristic length scale of the membrane) for
$R_{\rm bead}<\xi$, and is equal to $R_{\rm bead}$ for $R_{\rm bead}>\xi$. We
also find that the estimated excess area follows a linear scaling behavior that
only depends on the true value of ${\cal A}_{\rm ex}$ for the membrane, based
on which we propose a self-consistent technique to estimate the range of excess
membrane areas in a cell.
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We present a self-supervised learning approach for optical flow. Our method
distills reliable flow estimations from non-occluded pixels, and uses these
predictions as ground truth to learn optical flow for hallucinated occlusions.
We further design a simple CNN to utilize temporal information from multiple
frames for better flow estimation. These two principles lead to an approach
that yields the best performance for unsupervised optical flow learning on the
challenging benchmarks including MPI Sintel, KITTI 2012 and 2015. More notably,
our self-supervised pre-trained model provides an excellent initialization for
supervised fine-tuning. Our fine-tuned models achieve state-of-the-art results
on all three datasets. At the time of writing, we achieve EPE=4.26 on the
Sintel benchmark, outperforming all submitted methods.
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For an object classification system, the most critical obstacles towards
real-world applications are often caused by large intra-class variability,
arising from different lightings, occlusion and corruption, in limited sample
sets. Most methods in the literature would fail when the training samples are
heavily occluded, corrupted or have significant illumination or viewpoint
variations. Besides, most of the existing methods and especially deep
learning-based methods, need large training sets to achieve a satisfactory
recognition performance. Although using the pre-trained network on a generic
large-scale dataset and fine-tune it to the small-sized target dataset is a
widely used technique, this would not help when the content of base and target
datasets are very different. To address these issues, we propose a joint
projection and low-rank dictionary learning method using dual graph constraints
(JP-LRDL). The proposed joint learning method would enable us to learn the
features on top of which dictionaries can be better learned, from the data with
large intra-class variability. Specifically, a structured class-specific
dictionary is learned and the discrimination is further improved by imposing a
graph constraint on the coding coefficients, that maximizes the intra-class
compactness and inter-class separability. We also enforce low-rank and
structural incoherence constraints on sub-dictionaries to make them more
compact and robust to variations and outliers and reduce the redundancy among
them, respectively. To preserve the intrinsic structure of data and penalize
unfavourable relationship among training samples simultaneously, we introduce a
projection graph into the framework, which significantly enhances the
discriminative ability of the projection matrix and makes the method robust to
small-sized and high-dimensional datasets.
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We consider tree-level off-shell currents of two massive particles and $n$
massless bosons in the classical limit, which can be fused into the classical
limit of $n+2$ scattering amplitudes. We show that dressing up the current with
coherent wave-functions associated with the massive particles leads to the
recently proposed Worldline Quantum Field Theory (WQFT) path integral. The
currents thus constructed encode solutions of classical equations of motion so
they can be applied to contexts where the classical limit is relevant,
including hard thermal loops. We give several examples of these currents in
scalar, gauge and gravitational theories.
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Multisource image analysis that leverages complementary spectral, spatial,
and structural information benefits fine-grained object recognition that aims
to classify an object into one of many similar subcategories. However, for
multisource tasks that involve relatively small objects, even the smallest
registration errors can introduce high uncertainty in the classification
process. We approach this problem from a weakly supervised learning perspective
in which the input images correspond to larger neighborhoods around the
expected object locations where an object with a given class label is present
in the neighborhood without any knowledge of its exact location. The proposed
method uses a single-source deep instance attention model with parallel
branches for joint localization and classification of objects, and extends this
model into a multisource setting where a reference source that is assumed to
have no location uncertainty is used to aid the fusion of multiple sources in
four different levels: probability level, logit level, feature level, and pixel
level. We show that all levels of fusion provide higher accuracies compared to
the state-of-the-art, with the best performing method of feature-level fusion
resulting in 53% accuracy for the recognition of 40 different types of trees,
corresponding to an improvement of 5.7% over the best performing baseline when
RGB, multispectral, and LiDAR data are used. We also provide an in-depth
comparison by evaluating each model at various parameter complexity settings,
where the increased model capacity results in a further improvement of 6.3%
over the default capacity setting.
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We prove that static black holes in n-dimensional asymptotically flat
spacetime cannot support non-trivial electric p-form field strengths when
(n+1)/2<= p <= n-1. This implies in particular that static black holes cannot
possess dipole hair under these fields.
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The topic of this conference is ``The Chaotic Universe''. One of the main
achievements of last century has been to relate chaos in fluids to their
thermodynamics. It is our purpose to make connection between chaos in
gravitation and standard thermodynamics. Though there have been many previous
steps and attempts, so far no convincing conclusion has been reached.
After explaining how the approach works for glasses, we shall discuss the
thermodynamics of two specific systems: black holes and globular star clusters.
In both cases we point out that the dynamics satisfies the first and second law
of thermodynamics, though negative specific heats occur.
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This paper is devoted to the characterization of the lack of compactness of
the Sobolev embedding of $H^N(R^{2N})$ into the Orlicz space using Fourier
analysis.
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Subsets and Splits