**Lefschetz Center for Dynamical Systems Seminar**
See Thursday, March 9 LCDS Seminar The 2000 J.P. LaSalle Memorial Lecture
Lefschetz Center for Dynamical Systems Seminar
Brown University Center for Statistical Sciences Seminar
Abstract: The use of a truncation approximation to the Dirichlet process is utilized in a simple Gibbs sampling scheme for fitting a semiparametric generalized linear mixed model (GLMM). A novel aspect of this approach is that it generates draws directly from the posterior random measure, thus giving a method for directly infering the random effects distribution. The method is very flexible and can be used to fit the GLMM with non-normal random effects.
The approach will be llustrated by way of examples.
Center for Fluid Mechanics Seminar
Abstract: Recently derived solutions to the linearized thermocapillary, double diffusive, and binary fluid flow equations will be presented. The effects of residual accelerations, g-Jitter, on ``Benard type'' systems will then be considered in the context of parametric excitation externally imposed through time periodic accelerations. Using a one-term Galerkin expansion, the problem is also recast in terms of the Mathieu equation. Merits and limitations of the mechanical analogy with the viscously damped pendulum are discussed. Actual practices used to characterize g-Jitter effects of space-flight-fluid-physics experiments will be noted. Finally, preliminary results of a traveling wave instability predicted in a binary fluid are to be presented.
Brown Applied Mathematics Pattern Theory and Vision Seminar
- Wednesday, March 8, 2000,
Brown Applied Mathematics Pattern Theory and Vision Seminar Continued.....
Abstract: Multiscale methods in image processing allow both fast computations and the definition of large-scale features which are invisible to purely local processes. In our research we developed such fast methods for both curve completion and image segmentation. This talk will focus on the segmentation problem. The approach is applicable also to more general clustering problems.
Our algorithm uses modern numeric techniques to find an approximate solution to a normalized cut formulation of the segmentation problem in time that is linear in the size of the image with only a few dozen operations per pixel. In just one pass the algorithm provides a complete hierarchical decomposition of the image into segments. The algorithm detects the segments by applying a process of recursive coarsening in which the same minimization problem is represented with fewer and fewer variables, producing an irregular pyramid. At the coarser levels of this coarsening process we may compute additional internal statistics of the emerging segments and use these statistics to introduce new important segmentation quantities, which are invisible at the fine scale. Once the pyramid is completed it is scanned from the top down to associate pixels close to the boundaries of segments with the appropriate segment. The algorithm is inspired by algebraic multigrid (AMG) solvers of large-scale minimization problems. We demonstrate the algorithm by applying it to real images.
A joint work with Achi Brandt and Ronen Basri.
Brown Analysis Seminar
Lefschetz Center for Dynamical Systems Seminar
The 2000 J. P. LaSalle Memorial Lecture
*** LATE ANNOUNCEMENT ***
Brown University Center for Statistical Sciences Seminar
Abstract: The objective of this paper is twofold. The first is to find a Bayesian credible interval for the intraclass correlation coefficient in symmetric normal models based on some ``default'' or ``noninformative'' prior. Probability matching priors and reference priors along with Jeffreys' prior are considered, and the one-at-a-time reference prior emerges as the ``optimal'' according to several criteria. The second objective is to compare two nested models such as the intraclass and independence models using the distance or divergence between the two as the basis of comparison. A suitable criterion for this is the ``power divergence measure'' as introduced by Cressie and Read (1984). Such a measure includes the two Kullback-Leibler divergence measures and the Hellinger divergence measure as special cases. For the specific problem, the power divergence measure turns out to be a convex function solely of , the intraclass correlation coefficient with its minimum attained at =0. Thus the model comparison problem in this case amounts to testing the hypothesis H0 : =0. Due to the duality between hypothesis tests and set estimation, the hypothesis testing problem can also be solved by solving a corresponding set estimation problem. The present paper develops Bayesian methods based on the Kullback-Leibler and Hellinger divergence measures, rejecting H0 : =0 when the specified divergence measure exceeds some number d. This number d is so chosen that the resulting credible interval for the divergence measure has specified coverage probability 1-. The length of such an interval is compared with the (i) equal two-tailed credible interval and (ii) the HPD credible interval for , with the same coverage probability which can also be inverted into acceptance regions of H0 : =0. An example is considered where the HPD interval based on the one-at-a-time reference prior turns out to be the shortest credible interval having the same coverage probability.
Scientific Computing Seminar
Abstract: The analysis of wave propagation in diffractive optical elements (DOE's) poses a significant challenge because of the strong interplay between the material and the optical field. An introduction to the physics of diffractive optics will be given and two numerical methods suitable for the analysis of DOE's will be presented and compared.
PDE Seminar
No Speaker This Week
Department of Mathematics Colloquium
<--- 2000 Index