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 $\alpha$-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 $L^1$-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 $N_R$. We show that even a tiny mixing between the Higgs boson and a `decoupled' singlet scalar allows for Higgs-mediated pair production of $N_R$ without significant mixings between the active neutrinos and $N_R$, 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 $pp$-collision and can be a highly sensitive probe of the Higgs-singlet mixing at the current and future $pp$ 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