Title: Improving the Convergence Rate of the Distributed Gradient Descent Method Abstract: This talk presents our recent work on the accelerated Distributed Gradient Descent (DGD) method for distributed optimization problems. We observed that the inexact convergence of the DGD algorithm can be caused by the inaccuracy in the consensus procedure in a distributed optimization setting. […]
Read MoreTitle: Numerical simulations of macroscopic quantities for stochastic differential equations with alpha-stable processes Abstract: The mean first exit time, escape probability and transitional probability density are utilized to quantify dynamical behaviors of stochastic differential equations with non-Gaussian, $\alpha$-stable type L\’evy motions. Taking advantage of the Toeplitz matrix structure of the time-space discretization, a fast and […]
Read MoreTitle: 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 […]
Read MoreTUSCALOOSA, Ala. — The National Science Foundation has awarded The University of Alabama a $2.85 million grant to strengthen content knowledge, teaching practice and leadership among math teachers in the greater Tuscaloosa area. Of the total funding, nearly 70 percent is direct support to teachers selected to participate. UA researchers are recruiting full-time math teachers in […]
Read MoreTopic: Non-hexagonal lattices from a two species interacting system Abstract: A two species interacting system motivated by the density functional theory for triblock copolymers contains long range interaction that affects the two species differently. In a two species periodic assembly of discs, the two species appear alternately on a lattice. A minimal two species periodic assembly […]
Read MoreTitle: 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 […]
Read MoreTitle: Area Laws for the Entanglement in the XXZ spin chain Abstract: The question on how to rigorously define and prove Many-Body-Localization (MBL) phenomena has attracted significant interest over the recent years. In this talk, we will give a physical motivation for the so-called entanglement entropy (EE) and explain why an area law for the EE can be interpreted […]
Read MoreTitle: 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 […]
Read MoreTitle: 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 […]
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