Decay estimates of solutions to the compressible Euler-Maxwell system in R3

We study the large time behavior of solutions near a constant equilibrium to the compressible Euler-Maxwell system in $\r3$. We first refine a global existence theorem by assuming that the $H^3$ norm of the initial data is small, but the higher order derivatives can be arbitrarily large. If the initial data belongs to \Dot{H}^{-s} ($0\le s<3/2$) or $\dot{B}_{2,\infty}^{-s}$ ($0<s\le3/2$), by a regularity interpolation trick, we obtain the various decay rates of the solution and its higher order derivatives. As an immediate byproduct, the usual $L^p$--$L^2$ $(1\le p\le 2)$ type of the decay rates follow without requiring that the $L^p$ norm of initial data is small.Comment: 22 pages, typos are fixed, Journal of Differential Equations (2015

Stability of steady states of the Navier-Stokes-Poisson equations with non-flat doping profile

We consider the stability of the steady state of the compressible Navier-Stokes-Poisson equations with the non-flat doping profile. We prove the global existence of classical solutions near the steady state for the large doping profile. For the small doping profile, we prove the time decay rates of the solution provided that the initial perturbation belongs to $L^p$ with $1\le p< 3/2$

Bayesian Neighbourhood Component Analysis

Learning a good distance metric in feature space potentially improves the performance of the KNN classifier and is useful in many real-world applications. Many metric learning algorithms are however based on the point estimation of a quadratic optimization problem, which is time-consuming, susceptible to overfitting, and lack a natural mechanism to reason with parameter uncertainty, an important property useful especially when the training set is small and/or noisy. To deal with these issues, we present a novel Bayesian metric learning method, called Bayesian NCA, based on the well-known Neighbourhood Component Analysis method, in which the metric posterior is characterized by the local label consistency constraints of observations, encoded with a similarity graph instead of independent pairwise constraints. For efficient Bayesian optimization, we explore the variational lower bound over the log-likelihood of the original NCA objective. Experiments on several publicly available datasets demonstrate that the proposed method is able to learn robust metric measures from small size dataset and/or from challenging training set with labels contaminated by errors. The proposed method is also shown to outperform a previous pairwise constrained Bayesian metric learning method

Bridging the Gap Between Monaural Speech Enhancement and Recognition with Distortion-Independent Acoustic Modeling

Monaural speech enhancement has made dramatic advances since the introduction of deep learning a few years ago. Although enhanced speech has been demonstrated to have better intelligibility and quality for human listeners, feeding it directly to automatic speech recognition (ASR) systems trained with noisy speech has not produced expected improvements in ASR performance. The lack of an enhancement benefit on recognition, or the gap between monaural speech enhancement and recognition, is often attributed to speech distortions introduced in the enhancement process. In this study, we analyze the distortion problem, compare different acoustic models, and investigate a distortion-independent training scheme for monaural speech recognition. Experimental results suggest that distortion-independent acoustic modeling is able to overcome the distortion problem. Such an acoustic model can also work with speech enhancement models different from the one used during training. Moreover, the models investigated in this paper outperform the previous best system on the CHiME-2 corpus

On Piterbarg's max-discretisation theorem for homogeneous Gaussian random fields

Motivated by the papers of Piterbarg (2004) and H\"{u}sler (2004), in this paper the asymptotic relation between the maximum of a continuous dependent homogeneous Gaussian random field and the maximum of this field sampled at discrete time points is studied. It is shown that, for the weakly dependent case, these two maxima are asymptotically independent, dependent and coincide when the grid of the discrete time points is a sparse grid, Pickands grid and dense grid, respectively, while for the strongly dependent case, these two maxima are asymptotically totally dependent if the grid of the discrete time points is sufficiently dense, and asymptotically dependent if the the grid points are sparse or Pickands grids.Comment:

Global well-posedness of the compressible bipolar Euler-Maxwell system in R^3

We first construct the global unique solution by assuming that the initial data is small in the H^3 norm but its higher order derivatives could be large. If further the initial data belongs to \Dot{H}^{-s} (0\le s<3/2) or \dot{B}_{2,\infty}^{-s} (0< s\le3/2), we obtain the various decay rates of the solution and its higher order derivatives. As an immediate byproduct, the L^p-L^2 (1\le p\le 2) type of the decay rates follow without requiring the smallness for L^p norm of initial data. In particular, the decay rate for the difference of densities could reach to (1+t)^{-13/4} in L^2 norm.Comment: 24 pages. arXiv admin note: substantial text overlap with arXiv:1211.5034, arXiv:1207.220

sWSI: A Low-cost and Commercial-quality Whole Slide Imaging System on Android and iOS Smartphones

In this paper, scalable Whole Slide Imaging (sWSI), a novel high-throughput, cost-effective and robust whole slide imaging system on both Android and iOS platforms is introduced and analyzed. With sWSI, most mainstream smartphone connected to a optical eyepiece of any manually controlled microscope can be automatically controlled to capture sequences of mega-pixel fields of views that are synthesized into giga-pixel virtual slides. Remote servers carry out the majority of computation asynchronously to support clients running at satisfying frame rates without sacrificing image quality nor robustness. A typical 15x15mm sample can be digitized in 30 seconds with 4X or in 3 minutes with 10X object magnification, costing under $1. The virtual slide quality is considered comparable to existing high-end scanners thus satisfying for clinical usage by surveyed pathologies. The scan procedure with features such as supporting magnification up to 100x, recoding z-stacks, specimen-type-neutral and giving real-time feedback, is deemed work-flow-friendly and reliable

Zero surface tension limit of viscous surface waves

We consider the free boundary problem for a layer of viscous, incompressible fluid in a uniform gravitational field, lying above a rigid bottom and below the atmosphere. For the "semi-small" initial data, we prove the zero surface tension limit of the problem within a local time interval. The unique local strong solution with surface tension is constructed as the limit of a sequence of approximate solutions to a special parabolic regularization. For the small initial data, we prove the global-in-time zero surface tension limit of the problem.Comment: 57pp. arXiv admin note: substantial text overlap with arXiv:1011.5179, arXiv:1109.179

Global well-posedness of an initial-boundary value problem for viscous non-resistive MHD systems

This paper concerns the viscous and non-resistive MHD systems which govern the motion of electrically conducting fluids interacting with magnetic fields. We consider an initial-boundary value problem for both compressible and (nonhomogeneous and homogeneous) incompressible fluids in an infinite flat layer. We prove the global well-posedness of the systems around a uniform magnetic field which is vertical to the layer. Moreover, the solution converges to the steady state at an almost exponential rate as time goes to infinity. Our proof relies on a two-tier energy method for the reformulated systems in Lagrangian coordinates.Comment: 31 pages. Add some more remarks and explanation

The well-posedness of the compressible non-isentropic Euler-Maxwell system in R^3

We first construct the global unique solution by assuming that the initial data is small in the $H^3$ norm but the higher order derivatives could be large. If further the initial data belongs to \Dot{H}^{-s} ($0\le s<3/2$) or $\dot{B}_{2,\infty}^{-s}$ ($0< s\le3/2$), we obtain the various decay rates of the solution and its higher order derivatives. In particular, the decay rates of the density and temperature of electron could reach to $(1+t)^{-13/4}$ in $L^2$ norm.Comment: arXiv admin note: substantial text overlap with arXiv:1207.220