A Special Applied Mathematics Colloquium
Special Announcement
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: The problem of discrete denoising arises in various scenarios including channel decoding, hidden Markov model state estimation, image enhancement, biomolecular sequence analysis, text correction, and many more. We propose a discrete denoising algorithm, that, based on the observation of the output of a known Discrete Memoryless Channel (DMC), estimates the input sequence to minimize a given fidelity criterion. The algorithm is universal in the sense that it requires no knowledge of the input sequence or its statistical properties. Yet, asymptotically it performs as well as the optimum distribution-dependent scheme. The proposed denoising algorithm is practical, and can be implemented in O(n log n) time and linear storage complexity.
Based on joint work with Erik Ordentlich, Gadiel Seroussi, Sergio Verdu, and Marcelo Weinberger.
Brown Analysis Seminar
Scientific Computing Seminar
University of Michigan - Ann Arbor | |
Abstract: Multimaterial flows are of great interest in a wide spectrum of physical problems, ranging from studying the dynamics and stability of interfaces, through mixing processes, the dynamics of bubbles,to liquid suspensions and bubbly flows. Different types of flows call for different assumptions, and lead to flow models which raise computational issues of different flavor. Stratified flows dominated by propagating material fronts are often described by one-velocity one-pressure models. Unexpectedly, numerical methods for these models have proved difficult, often producing material fronts contaminated by nonphysical oscillations. In dispersed flows, such as liquid suspensions, tracking individual interfaces is not of interest for the macroscopic flow description. A common practice is to average the equations, yielding models that are inherently nonconservative due to momentum and energy exchange terms between the phases. They require closure relations which are not available from first physical principles, and even when motivated by physical considerations yield controversial results. Most notoriously, assuming a single (equilibrium) pressure for all species, leads to loss of time-hyperbolicity of the governing equations, often referred to as the ill-posedness of the multiphase flow equations.
The talk will discuss the numerical issues raised by multimaterial flow computations, will present strategies in the design of suitable numerical algorithms and a host of numerical results.
Scientific Computing Seminar
PDE Seminar
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