Title: A Multi-scale Approach to  Limit Cycles with Random Perturbations Involving Fast Switching and Small Diffusion Abstract: This talk is devoted to multi-scale stochastic systems. The motivation is to treat limit cycles under random perturbations involving fast  random switching and small diffusion, which are represented by the use of two small parameters. Associated with the

Title: Optimal Transport on Finite Graphs with Applications Abstract: In this talk, I will discuss the optimal transport theory on discrete spaces. Various recent developments related to free energy, Fokker-Planck equations, as well as Wasserstein distance on graphs will be presented, some of them are rather surprising. Applications in game theory and robotics will be

Title: An overview of numerical algorithms for the Poisson-Boltzmann equation in biomolecular electrostatics Abstract: The Poisson-Boltzmann Equation (PBE) is a widely used implicit solvent model for the electrostatic analysis of solvated biomolecules. The numerical solution of the PBE is known to be challenging, due to the consideration of discontinuous coefficients, complex geometry of protein structures,

Title: A lower-order image denoising model for staircase reduction Abstract: In this talk, we will discuss a total-variation based lower-order image denoising model that is able to reduce the well-known staircasing phenomenon possessed by the Rudin-Osher-Fatemi model. To minimize the proposed variational model, we employ augmented Lagrangian method (ALM). Convergence analysis is established for the