Lefschetz Center for Dynamical Systems Seminar
Abstract: After an introductory blurb about calcium oscillations and waves in general, I shall briefly present a new model for calcium oscillations and waves in pancreatic acinar cells. I'll also discuss some of the experimental data we collected to validate this model. A bifurcation analysis of a simplified version of the model shows that travelling waves appear as homoclinic bifurcations from branches of periodic waves, and that the transition from isolated waves to periodic waves occurs at a T-point, where there is a heteroclinic cycle. Finally, I'll discuss some of the physiological implications of the bifurcation analysis.
Brown University Center for Statistical Sciences Seminar
Abstract: Some progress has been made on how to conceptualize the process of transferring (applying, generalizing) research results to various types of patients in the case of randomized trials of interventions. In the case of observational studies of diagnostic test performance, the process is less clear and there is increasing concern about the validity of some generally advocated approaches, such as the estimation of post-test probabilities using Bayes' theorem. This session will present for discussion a draft list of criteria for judging the transferability of test performance characteristics from research studies and explore the implications of these criteria for the design of future studies.
Center for Fluid Mechanics Seminar
Special PDE Seminar
Abstract: One version of the Maxwell-Bloch equations is a semilinear hyperbolic system with two characteristics. I will describe some asymptotic properties of these equations, emphasising the behaviour near a (realistic) singular limit. In this limit there are two widely separated time scales and one may use invariant manifold techniques to simplify the dynamics.
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: In the early 1990's, DeVore, Jawerth and Lucier developed, for wavelet-based image compression algorithms, image approximation error-versus-image size estimates in terms of the Besov space membership of the image.
The "localization" of the "DJL Theory" is a vehicle for extending that theory toward connections with image segmentation theory. An immediate applied result in this area is a new segmentation-compression algorithm whose estimates, for certain classes of images, provide asymptotic performance gains over a standard wavelet compression algorithm.
Another applied result (of the extension of the DJL Theory to cover segmentation also) is a new, generalized Mumford-Shah segmentation. The variance merge criterion is generalized into a smoothness energy criterion, corresponding to a Besov space semi-norm. A conservative generalization, this new energy collapses back to the ordinary M-S segmentation for an appropriate "vanilla case" in Hilbert space. Interpolation spaces seem to underpin this approach; the scheme apparently amounts to placing "the edge" of an intermediate space between the Besov spaces characterizing "object" and "background." One reason image segmentation algorithms are important is that segmentation is a critical algorithmic primitive for sensor fusion ( combining images originating from different sensor types to form a fused image conveying more information than any of the individual pictures convey ).
Brown Analysis Seminar
Brown University Graduate School Dissertation Defense
Applied Mathematics Colloquium
PDE Seminar
Department of Mathematics Colloquium
<--- 1999 Index