No abstract

Abstract.A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the Boltzmann equation in a strictly convex domain with the specular, bounce-back and diffuse boundary condition. With the aid of a distance function toward the grazing set, we construct weighted classical C 1 solutions away from the grazing set for all boundary conditions. For the diffuse boundary condition, we construct W 1,p solutions for 1 < p < 2 and weighted W 1,p solutions for 2 ≤ p ≤ ∞ as well. On the other hand, we show second derivatives do not exist up to the boundary in general by constructing counterexamples for all boundary conditions.

This paper presents a new feature extraction algorithm called Power Normalized Cepstral Coefficients (PNCC) that is based on auditory processing. Major new features of PNCC processing include the use of a power-law nonlinearity that replaces the traditional log nonlinearity used in MFCC coefficients, a noise-suppression algorithm based on asymmetric filtering that suppress background excitation, and a module that accomplishes temporal masking. We also propose the use of medium-time power analysis, in which environmental parameters are estimated over a longer duration than is commonly used for speech, as well as frequency smoothing. Experimental results demonstrate that PNCC processing provides substantial improvements in recognition accuracy compared to MFCC and PLP processing for speech in the presence of various types of additive noise and in reverberant environments, with only slightly greater computational cost than conventional MFCC processing, and without degrading the recognition accuracy that is observed while training and testing using clean speech. PNCC processing also provides better recognition accuracy in noisy environments than techniques such as Vector Taylor Series (VTS) and the ETSI Advanced Front End (AFE) while requiring much less computation. We describe an implementation of PNCC using "on-line processing" that does not require future knowledge of the input.

This paper describes the technical and system building advances made to the Google Home multichannel speech recognition system, which was launched in November 2016. Technical advances include an adaptive dereverberation frontend, the use of neural network models that do multichannel processing jointly with acoustic modeling, and Grid-LSTMs to model frequency variations. On the system level, improvements include adapting the model using Google Home specific data. We present results on a variety of multichannel sets. The combination of technical and system advances result in a reduction of WER of 8-28% relative compared to the current production system.

We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a general rigid bottom in a threedimensional horizontally periodic setting. We establish the global well-posedness of the problem both with and without surface tension. We prove that without surface tension the solution decays to the equilibrium state at an almost exponential rate; with surface tension, we show that the solution decays at an exponential rate. Our results include the case in which a heavier fluid lies above a lighter one, provided that the surface tension at the free internal interface is above a critical value, which we identify. This means that sufficiently large surface tension stabilizes the Rayleigh-Taylor instability in the nonlinear setting. As a part of our analysis, we establish elliptic estimates for the two-phase stationary Stokes problem.Notice that J = det ∇Θ is the Jacobian of the coordinate transformation. We also denote W = ∂ t Θ 3 K N = (−∂ 1 η, −∂ 2 η, 1)T i = e i + ∂ i ηe 3 for i = 1, 2 θ ij = ∂ j Θ i for i, j = 1, 2, 3.(1.23)