Lefschetz Center for Dynamical Systems Seminar
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: A visual form contains various geometric features with high redundancy for recognition. Here I report an attempt at analyzing salient geometric features for a set of complex visual forms by human psychophysical judgments, where multidimensional scaling techniques was used to derive the perceived similarity space of the patterns. The psychophysical similarity of forms thus obtained was also used to analyze the selectivity of single-neuron responses of monkeys performing a visual memory task. I also report the observation that inferior temporal neurons encode both learned association and object geometry, and integrate mnemonic and perceptual capability in vision. Background from neurophysiology will be introduced to make the talk more or less self-contained.
Brown Analysis Seminar
Applied Mathematics & Center for Statistical Sciences Joint Colloquium
Abstract:
Calculation of maximum likelihood estimates for hierarchical
generalized linear models is computationally difficult and a number of
alternate estimation techniques have been proposed. Many of the
alternatives are based on the related ideas of best linear unbiased
prediction, maximization of a joint likelihood of the data and unobserved
random effects, and penalized quasi-likelihood. I first will introduce and
give examples of hierarchical generalized linear models. I will then
compare and contrast the alternative estimation methods with maximum
likelihood, point out drawbacks, and suggest reasons for their poor
performance.
Scientific Computing Seminar
Abstract:
Some years ago, Friedrichs proposed a new criterion, the symmetric
positive equation, to treat mixed elliptic-hyperbolic equations independently
of type. The author has treated the finite difference and finite elements
methods for these equations. However, the criterion is rigid and difficult
to apply in practical problems.
This talk proposes a relaxed criterion and a different solution
procedure which will be more applicable to real problems. Typical
solutions are shown. Extension to nonlinear equations is indicated.
PDE Seminar
Abstract: We describe traveling hole solutions of the Complex Ginzburg-Landau (CGL) equation as singular perturbations of dark solitons of the Nonlinear Schroedinger Equation (NLS). Modulation of the free parameters of the NLS solutions leads to a dynamical system describing the CGL dynamics in the vicinity of a traveling hole solution. Applications to a convection experiment will be discussed.
Department of Mathematics Colloquium
<--- 1997 Index