Lefschetz Center for Dynamical Systems Seminar
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: Blake and Isard have introduced a non-parametric method of recursively estimating the conditional probability distribution on the position of a moving object in highly cluttered environments, which they call the CONDENSATION algorithm. Borrowing from ideas used in genetic algorithms, they maintain a family of samples from this distribution, which are updated by i) weighted sampling with replacement, ii) Langevin-style diffusion and iii) Kalman filtering-like reweighting using the next piece of data. I will do my best to describe their method, which is strikingly successful in tracking.
Applied Mathematics Colloquium
Coffee at 4:00 p.m., 182 George Street, Room 110 |
Abstract: Mathematical models of several modern-day optical telecommunication systems will be presented. Specific techniques such as dispersion compensation,distributed amplification and the use of dispersion decreasing fibers will be discussed. For these models non-trivial mathematical techniques such as the Lie transform, the method of multiple scales and the inverse scattering transform play a key role both in the formulation and solution. In particular, the novel concept of breathing pulses will be introduced. It will be shown that on short distances the dynamics of these objects are linear while on long distances they are nonlinear and governed by a class of equations that includes the nonlinear Schroedinger equation in special cases. These equations will be used to establish a criterion for the stability of breathing pulses in realistic cascaded optical transmission lines.
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