Topic: Introduction to cluster algebras Abstract: The theory of cluster algebras is one of the most mathematically well-studied areas in mathematical physics. Since its discovery in 2001, it has been shown that cluster algebras are related to diverse areas of mathematics such as algebraic geometry, commutative algebra, knot theory, total positivity, quiver representations, string theory, statistical
Title:Â Predict the Ligand-Receptor Binding/Unbinding Kinetics with the Variational Implicit-Solvent Model and the String Method Abstract: Â The ligand-receptor binding/unbinding is a complex biophysical process in which water plays a critical role. To understand the fundamental mechanisms of such a process, we have developed a new and efficient approach that combines our level-set variational implicit-solvent model
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
Title: Sufficient dimension reduction for high dimensional data Abstract: The high dimensional data generated from modern scientific discoveries introduces unique challenges to statistical modeling. Sufficient dimension reduction (SDR) is a useful tool to bridge the gap through projection subspace recovery. In this study, a new formulation is proposed based on the Hellinger integral of order
The William Lowell Putnam Mathematical Competition is the preeminent mathematics competition for undergraduate college students in the United States and Canada. The Putnam Competition takes place annually on the first Saturday of December. The competition consists of two 3-hour sessions, one in the morning and one in the afternoon. During each session, participants work individually