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

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: 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: 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: Understanding Manifold-structured Data via Geometric Modeling and Learning Abstract: Analyzing and inferring the underlying global intrinsic structures of data from its local information are critical in many fields. In practice, coherent structures of data allow us to model data as low dimensional manifolds, represented as point clouds, in a possible high dimensional space. Different