1,232 research outputs found
Spatial regularity of semigroups generated by L\'{e}vy type operators
We apply the probabilistic coupling approach to establish the spatial
regularity of semigroups associated with L\'{e}vy type operators, by assuming
that the martingale problem of L\'{e}vy type operators is well posed. In
particular, we can prove the Lipschitz continuity of the semigroups under
H\"{o}lder continuity of coefficients, even when the L\'evy kernel
corresponding to L\'{e}vy type operators is singular.Comment: 18 page
Gradient Estimates and Ergodicity for SDEs Driven by Multiplicative L\'{e}vy Noises via Coupling
We consider SDEs driven by multiplicative pure jump L\'{e}vy noises, where
L\'evy processes are not necessarily comparable to -stable-like
processes. By assuming that the SDE has a unique solution, we obtain gradient
estimates of the associated semigroup when the drift term is locally H\"{o}lder
continuous, and we establish the ergodicity of the process both in the
-Wasserstein distance and the total variation, when the coefficients are
dissipative for large distances. The proof is based on a new explicit Markov
coupling for SDEs driven by multiplicative pure jump L\'{e}vy noises, which is
derived for the first time in this paper.Comment: 34 page
The limit to rarefaction wave with vacuum for 1D compressible fluids with temperature-dependent viscosities
In this paper we study the zero dissipation limit of the one-dimensional full
compressible Navier-Stokes(CNS) equations with temperature-dependent viscosity
and heat-conduction coefficient. It is proved that given a rarefaction wave
with one-side vacuum state to the full compressible Euler equations, we can
construct a sequence of solutions to the full CNS equations which converge to
the above rarefaction wave with vacuum as the viscosity and the heat conduction
coefficient tend to zero. Moreover, the uniform convergence rate is obtained.
The main difficulty in our proof lies in the degeneracies of the density, the
temperature and the temperature-dependent viscosities at the vacuum region in
the zero dissipation limit.Comment: 31 pages. arXiv admin note: text overlap with arXiv:1011.199
Probing the Decoupled Seesaw Scalar in Rare Higgs Decay
The Higgs boson can mix with a singlet scalar that dynamically generates the
Majorana mass of the right-handed neutrino . We show that even a tiny
mixing between the Higgs boson and a `decoupled' singlet scalar allows for
Higgs-mediated pair production of without significant mixings between the
active neutrinos and , and thus testable at colliders via a characteristic
signal of two same-sign same-flavor lepton pairs, plus missing energy. We
demonstrate that this search channel is mostly background-free in
-collision and can be a highly sensitive probe of the Higgs-singlet mixing
at the current and future colliders. Such channel provides a clean signal
to discover the singlet scalar and explore the origin of neutrino masses.Comment: 16 pages, 7 figures, 2 table
Zero dissipation limit to rarefaction wave with vacuum for 1-D compressible Navier-Stokes equations
It is well-known that one-dimensional isentropic gas dynamics has two
elementary waves, i.e., shock wave and rarefaction wave. Among the two waves,
only the rarefaction wave can be connected with vacuum. Given a rarefaction
wave with one-side vacuum state to the compressible Euler equations, we can
construct a sequence of solutions to one-dimensional compressible isentropic
Navier-Stokes equations which converge to the above rarefaction wave with
vacuum as the viscosity tends to zero. Moreover, the uniform convergence rate
is obtained. The proof consists of a scaling argument and elementary energy
analysis based on the underlying rarefaction wave structures.Comment: 23 page
A Unified Approach to Coupling SDEs driven by L\'{e}vy Noise and Some Applications
We present a general method to construct couplings of stochastic differential
equations driven by L\'{e}vy noise in terms of coupling operators. This
approach covers both coupling by reflection and refined basic coupling which
are often discussed in the literature. As an application, we establish
regularity results for the transition semigroups of the solutions to stochastic
differential equations driven by additive L\'{e}vy noise.Comment: 21 page
Multi-scale Convolution Aggregation and Stochastic Feature Reuse for DenseNets
Recently, Convolution Neural Networks (CNNs) obtained huge success in
numerous vision tasks. In particular, DenseNets have demonstrated that feature
reuse via dense skip connections can effectively alleviate the difficulty of
training very deep networks and that reusing features generated by the initial
layers in all subsequent layers has strong impact on performance. To feed even
richer information into the network, a novel adaptive Multi-scale Convolution
Aggregation module is presented in this paper. Composed of layers for
multi-scale convolutions, trainable cross-scale aggregation, maxout, and
concatenation, this module is highly non-linear and can boost the accuracy of
DenseNet while using much fewer parameters. In addition, due to high model
complexity, the network with extremely dense feature reuse is prone to
overfitting. To address this problem, a regularization method named Stochastic
Feature Reuse is also presented. Through randomly dropping a set of feature
maps to be reused for each mini-batch during the training phase, this
regularization method reduces training costs and prevents co-adaptation.
Experimental results on CIFAR-10, CIFAR-100 and SVHN benchmarks demonstrated
the effectiveness of the proposed methods
Semi-dense Stereo Matching using Dual CNNs
A robust solution for semi-dense stereo matching is presented. It utilizes
two CNN models for computing stereo matching cost and performing
confidence-based filtering, respectively. Compared to existing CNNs-based
matching cost generation approaches, our method feeds additional global
information into the network so that the learned model can better handle
challenging cases, such as lighting changes and lack of textures. Through
utilizing non-parametric transforms, our method is also more self-reliant than
most existing semi-dense stereo approaches, which rely highly on the adjustment
of parameters. The experimental results based on Middlebury Stereo dataset
demonstrate that the proposed approach outperforms the state-of-the-art
semi-dense stereo approaches
Analytical Solution for Stochastic Unit Commitment Considering Wind Power Uncertainty with Gaussian Mixture Model
To capture the stochastic characteristics of renewable energy generation
output, the chance-constrained unit commitment (CCUC) model is widely used.
Conventionally, analytical solution for CCUC is usually based on simplified
probability assumption or neglecting some operational constraints, otherwise
scenar-io-based methods are used to approximate probability with heavy
computation burden. In this paper, Gaussian mixture model (GMM) is employed to
characterize the correlation between wind farms and probability distribution of
their forecast errors. In our model, chance constraints including reserve
sufficiency and branch power flow bounds are ensured to be satisfied with
pre-determined probability. To solve this CCUC problem, we propose a Newton
method based procedure to acquire the quantiles and transform chance
constraints into deterministic constraints. Therefore, the CCUC model is
efficiently solved as a mixed-integer quadratic programming problem. Numerical
tests are performed on several systems to illustrate efficiency and scalability
of the proposed method
Multiple periodic oscillations in the radio light curves of NRAO 530
In this paper, the time series analysis method CLEANest is employed to search
for characteristic periodicities in the radio light curves of the blazar NRAO
530 at 4.8, 8.0 and 14.5 GHz over a time baseline of three decades. Two
prominent periodicities on time scales of about 6.3 and 9.5 yr are identified
at all three frequencies, in agreement with previous results derived from
different numerical techniques, confirming the multiplicity of the
periodicities in NRAO 530. In addition to these two significant periods, there
is also evidence of shorter-timescale periodicities of about 5.0 yr, 4.2 yr,
3.4 yr and 2.8 yr showing lower amplitude in the periodograms. The physical
mechanisms responsible for the radio quasi-periodic oscillations and the
multiplicity of the periods are discussed.Comment: accepted for publication in SCIENCE CHINA (Physics, Mechanics &
Astronomy), 8 pages, 7 figure
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