Analysis Seminar
Abstract: I discuss a recent joint work with J. Pipher about a generalization of a theorem of Journe-Jones to the case of multiparamter Hardy spaces. The result says that any bounded sequence of H^1 functions converging a.e. also converges in weak-star topology of H^1 to the same function. Generalization of this result to the multiparameter situation is far from trivial: it requires a clever induction in the number of parameters argument.
Brown University Center for Statistical Sciences Seminar
Abstract: We propose a novel alternative to case-control sampling for the estimation of individual-level risk in spatial epidemiology. Our approach uses weighted estimating equations to estimate regression parameters in the intensity function of an inhomogeneous spatial point process, when information on risk factors is available at the individual level for cases, but only at a spatially aggregated level for the population at risk. We develop data-driven methods to select the weights used in the estimating equations and show through simulation that the choice of weights can have a major impact on efficiency of estimation. We develop a formal test to detect non-Poisson behavior in the underlying point process and assess the performance of the test using simulations of Poisson and Poisson-cluster point processes. We apply our methods to data on the spatial distribution of childhood meningococcal disease cases in Merseyside, UK between 1981 and 2007.
Joint Lefschetz Center for Dynamical Systems/PDE Seminar
Abstract: We will begin by considering the second initial boundary problem in narrow domains of width ?? 1 for linear second order differential equations with nonlinear boundary conditions. The solution of such a problem converges as ? ? 0 to the solution of a standard reaction-diffusion equation in a domain of reduced dimension. This reduction allows to obtain some results concerning wave front propagation in smooth narrow domains. However, if the domain is asymptotically non-smooth then the situation is a lot more involved and one is led to study the large deviations principle (LDP) for continuous, homogeneous, strong Markov processes that do not necessarily behave locally as a Wiener process. Any strong Markov process Xt in R that is continuous with probability one, under some minimal regularity conditions, is governed by a generalized elliptic operator DvDu, where v and u are two strictly increasing functions, v is right continuous and u is continuous. Here, we shall consider the LDP for Markov processes whose infinitesimal generator is ? DvDu where 0
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract:
Coreference resolution is the task of linking a nominal expression (such as a pronoun) to its antecedent in text or speech data. We propose a maximum entropy model which ranks the syntactic environments in which antecedents tend to occur. We learn this model in an unsupervised way using the Expectation/Maximization (EM) algorithm. As an initial application, we describe a consistent, probabilistic reformulation of the pronoun resolution model given in (Charniak+Elsner 09); we then extend this to a high-precision model predicting coreference between noun phrases with the same head word. This is joint work with Eugene Charniak and Mark Johnson; it is very much still in progress, so comments and suggestions are welcome.
[pizza will be provided]