30,765 research outputs found
Exponential convergence of 1-graph of the solution semigroup of contact Hamilton-Jacobi equations
Under certain assumptions, we show that for the solution semigroup of
evolutionary contact Hamilton-Jacobi equations, its 1-graph, as a pseudo
Legendrian graph, converges exponentially to the 1-graph of the viscosity
solution of stationary equations in the sense of certain Hausdorff metrics.
This result reveals an essential difference between certain dissipative systems
and conservative systems from weak KAM aspects
Snapshot light-field laryngoscope
The convergence of recent advances in optical fabrication and digital
processing yields a new generation of imaging technology: light-field cameras,
which bridge the realms of applied mathematics, optics, and high-performance
computing. Herein for the first time, we introduce the paradigm of light-field
imaging into laryngoscopy. The resultant probe can image the three-dimensional
(3D) shape of vocal folds within a single camera exposure. Furthermore, to
improve the spatial resolution, we developed an image fusion algorithm,
providing a simple solution to a long-standing problem in light-field imaging.Comment: 15 pages, 6 figures, 1 tabl
X-ray Radiation Mechanisms and Beaming Effect of Hot Spots and Knots in Active Galactic Nuclear Jets
The observed radio-optical-X-ray spectral energy distributions (SEDs) of 22
hot spots and 45 knots in the jets of 35 active galactic nuclei are complied
from literature and modeled with single-zone lepton models. It is found that
the observed luminosities at 5 GHz (L_5GHz) and at 1 keV (L_1keV) are tightly
correlated, and the two kinds of sources can be roughly separated with a
division of L_1keV=L_5GHz. Our SED fits show that the mechanisms of the X-rays
are diverse. Considering the sources at rest, the synchrotron-self-Compton
(SSC) scattering would dominate the IC process. This model can interpret the
X-rays of some hot spots with a magnetic field strength (B_ssc^delta=1) being
consistent with the equipartition magnetic field (B_eq^delta=1) in one order of
magnitude, but an unreasonably low B_ssc^delta=1 is required to model the
X-rays for all knots. The ratio R_B=B_eq^delta=1/B_ssc^delta=1 is greater than
1 and it is tightly anti-correlated with ratio R_L= L_1keV/L_5GHz for both the
knots and the hot spots. We propose that the deviation may be due to the
neglect of the relativistic bulk motion for these sources. Considering this
effect, we show that the IC/CMB model well explains the X-ray emission for most
sources. Both B_eq' and delta are tentatively correlated with R_L. Corrected by
the beaming effect, the L'_5GHz-L'_1keV relations for the two kinds of sources
are even tighter than the observed ones. These facts suggest that, under the
equipartition condition, the observational differences of the X-rays from the
knots and hot spots may be mainly due the differences on the Doppler boosting
effect and the co-moving magnetic field of the two kinds of sources. Our IC
scattering models predict a prominent GeV-TeV component in the SEDs for some
sources, which are detectable with H.E.S.S. and Fermi/LAT.Comment: 38 pages, including 2 tables and 9 figures. Accepted for publications
in Ap
An Ensemble EM Algorithm for Bayesian Variable Selection
We study the Bayesian approach to variable selection in the context of linear
regression. Motivated by a recent work by Rockova and George (2014), we propose
an EM algorithm that returns the MAP estimate of the set of relevant variables.
Due to its particular updating scheme, our algorithm can be implemented
efficiently without inverting a large matrix in each iteration and therefore
can scale up with big data. We also show that the MAP estimate returned by our
EM algorithm achieves variable selection consistency even when diverges
with . In practice, our algorithm could get stuck with local modes, a common
problem with EM algorithms. To address this issue, we propose an ensemble EM
algorithm, in which we repeatedly apply the EM algorithm on a subset of the
samples with a subset of the covariates, and then aggregate the variable
selection results across those bootstrap replicates. Empirical studies have
demonstrated the superior performance of the ensemble EM algorithm
Extreme-Point Symmetric Mode Decomposition Method for Data Analysis
An extreme-point symmetric mode decomposition (ESMD) method is proposed to
improve the Hilbert-Huang Transform (HHT) through the following prospects: (1)
The sifting process is implemented by the aid of 1, 2, 3 or more inner
interpolating curves, which classifies the methods into ESMD_I, ESMD_II,
ESMD_III, and so on; (2) The last residual is defined as an optimal curve
possessing a certain number of extreme points, instead of general trend with at
most one extreme point, which allows the optimal sifting times and
decompositions; (3) The extreme-point symmetry is applied instead of the
envelop symmetry; (4) The data-based direct interpolating approach is developed
to compute the instantaneous frequency and amplitude. One advantage of the ESMD
method is to determine an optimal global mean curve in an adaptive way which is
better than the common least-square method and running-mean approach; another
one is to determine the instantaneous frequency and amplitude in a direct way
which is better than the Hilbert-spectrum method. These will improve the
adaptive analysis of the data from atmospheric and oceanic sciences,
informatics, economics, ecology, medicine, seismology, and so on.Comment: 40 pages, 28 figure
A representation formula of viscosity solutions to weakly coupled systems of Hamilton-Jacobi equations with applications to regularizing effect
Based on a fixed point argument, we give a {\it dynamical representation} of
the viscosity solution to Cauchy problem of certain weakly coupled systems of
Hamilton-Jacobi equations with continuous initial datum. Using this formula, we
obtain some regularity results related to the viscosity solution, including a
partial extension of Lions' regularizing effect \cite{L} to the case of weakly
coupled systems
A Variational Algorithm for Bayesian Variable Selection
There has been an intense development on the estimation of a sparse
regression coefficient vector in statistics, machine learning and related
fields. In this paper, we focus on the Bayesian approach to this problem, where
sparsity is incorporated by the so-called spike-and-slab prior on the
coefficients. Instead of replying on MCMC for posterior inference, we propose a
fast and scalable algorithm based on variational approximation to the posterior
distribution. The updating scheme employed by our algorithm is different from
the one proposed by Carbonetto and Stephens (2012). Those changes seem crucial
for us to show that our algorithm can achieve asymptotic consistency even when
the feature dimension diverges exponentially fast with the sample size.
Empirical results have demonstrated the effectiveness and efficiency of the
proposed algorithm
Coalescing Majorana edge modes in non-Hermitian PT-symmetric Kitaev chain
A single unit cell contains all the information about the bulk system,
including the topological feature. The topological invariant can be extracted
from a finite system, which consists of several unit cells under certain
environment, such as a non-Hermitian external field. We investigate a non-
Hermitian finite-size Kitaev chain with PT-symmetric chemical potentials. Exact
solution at the symmetric point shows that Majorana edge modes can emerge as
the coalescing states at exceptional points and PT symmetry breaking states.
The coalescing zero mode is the finite-size projection of the conventional
degenerate zero modes in a Hermitian infinite system with the open boundary
condition. It indicates a variant of the bulk-edge correspondence: The number
of Majorana edge modes in a finite non-Hermitian system can be the topological
invariant to identify the topological phase of the corresponding bulk Hermitian
system.Comment: 7 pages, 2 figure
On class A Lorentzian 2-tori with poles I: Closed geodesics pass through poles
In this paper, by studying certain isometries on globally hyperbolic planes,
we prove that if is a timelike pole on a class A Lorentzian 2-torus, then
there exists a closed timelike geodesic passing through with any
preassigned free homotopy class in the interior of the stable time cone. We
also show a non-rigid result when timelike poles appear
Hybrid Interference Induced Flat Band Localization in Bipartite Optomechanical Lattices
The flat band localization, as an important phenomenon in solid state
physics, is fundamentally interesting in the exploration of exotic ground
property of many-body system. Here we demonstrate the appearance of a flat band
in a general bipartite optomechanical lattice, which could have one or two
dimensional framework. Physically, it is induced by the hybrid interference
between the photon and phonon modes in optomechanical lattice, which is quite
different from the destructive interference resulted from the special geometry
structure in the normal lattice (e.g., Lieb lattice). Moreover, this novel flat
band is controllable and features a special local density of states (LDOS)
pattern, which makes it is detectable in experiments. This work offers an
alternative approach to control the flat band localization with optomechanical
interaction, which may substantially advance the fields of cavity optomechanics
and solid state physics.Comment: 7 pages, 9 figures, Published in Scientifc Reports 7, 15188 (2017
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