Research

Title: Degenerate Diffusion in Phase Separations Abstract: Phase separations are widely observed phenomena in materials science. One model of phase separation is the Cahn-Hilliard equation with a smooth double-well potential, and with phase-dependent diffusion mobilities. The latter is a feature of many materials systems and makes the analysis and accurate numerical simulations challenging. In this […]

Title: Bayesian Nonparametric Models and Its Applications Abstract: Polya tree priors are random probability measures that are easily centered at standard parametric families, such as the normal. As such, they provide a convenient avenue toward creating a parametric/nonparametric model for data. Briefly, we center a Polya tree at an initial parametric guess on data; then […]

Title: Exact clustering by semidefinite programming under the heterogeneous planted cluster model. Abstract: Clustering, or the sorting of data into groups of similar items, is a fundamental task in machine learning and statistical analysis. Until recently, most computational methods for clustering relied on heuristics with no theoretical guarantee ensuring that clusters present in the data […]

Title: Mean field models for thin film droplet coarsening Abstract: A thin liquid film coating a solid substrate is unstable and the late stage morphology is essentially quasiequilibrium droplets connected by an ultra thin film. Droplets exchange mass and coarsening occurs — the total number of droplets N(t) decreases while the average size of droplets […]