Nonlinear Waves Seminar
Lefschetz Center for Dynamical Systems Seminar
Abstract: It is well known that, generically, homo and heteroclinic solutions do not survive singular perturbations. We adjusted the method of Kruscal and Segur (known as asymptotics beyond all orders) to discuss singular perturbations of periodic solutions.
Brown University Center for Statistical Sciences Seminar
Abstract: Clinical trials often include interim analyses that compare treatment groups with respect to the mean function of a response process. Sometimes it is unclear how the mean functions of the groups might differ, and thus one cannot confidently prespecify a simple metric upon which a stopping rule or repeated confidence interval can be based. This motivated us to extend the repeated confidence interval approach for a finite-dimensional parameter (Jennison & Turnbull, 1989) to the use of repeated confidence bands for the mean function of a response process. Formal tests of hypotheses are easily constructed from the repeated confidence bands. We also describe how inferences for the mean function can be adaptively restriced to different subsets of its domain at different interim analyses. An example is given involving an AIDS clinical trial.
Special Lefschetz Center for Dynamical Systems Seminar
Brown Analysis Seminar
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: I will compare simulations of some simple neuron models as a base for modelling Hebbian assemblies distributed over a few cortical areas. The discussion of this may be relevant to the following topics: Hebbian assemblies in the cortex, oscillations and binding in visual cortical areas, rate code versus exact timing of spikes, minimal complexity of single neuron models.
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: How does the nervous system achieve the fundamental task of perceptual organization? Both theoretical and empirical investigations point to the mechanism of oscillatory correlation as a potential representational framework. In this talk, I will describe a class of locally excitatory, globally inhibitory oscillator networks (LEGION). We show both analytically and by computer simulation that LEGION networks rapidly achieve both synchronization within blocks of oscillators and desynchronization between different blocks. The model has been applied to segmenting a variety of imagery, and provides a neurocomputational framework for addressing perceptual organization and figure/ground segregation in visual perception.
Brown University Center for Statistical Sciences Seminar
Abstract: Hierarchical models provide a mechanism for stabilizing disease rate estimates from small areas, while maintaining geographic resolution. Spatial correlation among rates is possible, often due to unobserved covariates such as environmental or socio-economic effects. One typically incorporates spatial variation into hierarchical models through random effects with a pairwise difference prior structure. In such a model, the rate estimate for a given small area is conditionally dependent on the rate estimates from neighboring areas. In many part applications, the definition of neighbors was fixed a priori. In this presentation, two methods are compared for generalizing the notion of "neighbor" within spatial hierarchical models for regional disease rates. The first method involves variable weights defining the contribution of rates in pooled estimates; the second involves weights induced by direct modeling of spatial correlation. Implementation, interpretation, and model fit are compared for the various approaches using two data sets with differing types of regionalization. The first data set involves lung cancer mortality in Ohio, the second involves lip cancer incidence in Scotland.
PDE Seminar
Department of Mathematics Colloquium
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