19 January 2012
Quenching Phenomena for Parabolic Problems Having Concentrated Nonlinear Sources
C.Y. Chan
Department of Mathematics
University of Louisiana at Lafayette

A criterion for the quenching of the solution for a one-dimensional semi-linear parabolic first initial-boundary value problem with a concentrated nonlinear source situated at b is given. The locations of b for global existence of the solution and for the quenching of the solution are investigated. A correct formulation of the problem in multi-dimensions is discussed, and a quenching criterion is given.
 
The talk should be of interest to a general audience.

9 February 2012
Bayesian graphical models for multivariate functional data
Hongxiao Zhu
Department of Statistical Science
Duke University

In a broad variety of application areas there is interest in inferring the dependence structure in multivariate functional data. For data in vector form, conditional independence relationships between variables can be inferred through allowing zeros in the precision matrix through a Gaussian graphical model. Bayesian methods can be used to allow unknown locations of zeros, with a hyper inverse-Wishart prior chosen for the covariance. We generalize these methods to define a new class of Gaussian process graphical models for multivariate functional data. We focus on models with decomposable graph structures with a single precision matrix encoding the conditional independence between the functions. We also discuss the more general class of non-decomposable graphs. Properties of the proposed process are considered, and two efficient Algorithms are developed for posterior computation relying on Markov chain Monte Carlo. The methods are evaluated through simulation studies and applied to Electroencephalography (EEG) data in neuroscience.

13 February 2012 (MONDAY 4:00)
Distribution-Free Estimators of Variance Components for Multivariate Linear Mixed Model
Jun Han
Department of Mathematics and Statistics
Georgia State University

Non-iterative, distribution-free, and unbiased estimators of variance components, including minimum norm quadratic unbiased estimator and method of moments estimator, are derived for multivariate mixed model. A general cluster-wise covariance and a same-member-only response-wise covariance are assumed. Some properties of the proposed estimators such as unbiasedness and existence are discussed, and related computational issues are addressed. A simulation study shows that the proposed computationally efficient estimators are comparable with iterative Gaussian (restricted) maximum likelihood estimator in terms of bias and mean square error. An application of gene expression family data is presented to illustrate the proposed estimators.

15 March 2012
Dispersal in Heterogeneous Landscapes
Yuan Lou
Department of Mathematics
Ohio State University

From habitat degradation and climate change to spatial spread of invasive species, dispersal plays a central role in determining how organisms cope with a changing environment. How should organisms disperse "optimally" in heterogeneous environments? The dispersal of many organisms depends upon local biotic and abiotic factors and as such are often biased. In contrast with unbiased movements which are well understood from theoretical perspectives, we have limited knowledge of the consequences of biased dispersal, especially in the context of the spatial dynamics of interacting species. This talk will focus on the effects of biased dispersal on two competing species in spatially varying environments. The talk is mainly based upon joint works with Steve Cantrell and Chris Cosner of University of Miami.