|Colloquium, 臺灣大學資訊工程學系 李彥寰教授|
Thursday, September 24, 16:10—17:00 數學系3174
Title: Non-Asymptotic Analysis of EM in Poisson Inverse Problems
Abstract:Poisson inverse problems arise in many real-world applications, such as positron emission tomography and astronomical image deblurring. Expectation maximization (EM) is a standard---and perhaps the most popular---approach to solving a Poisson inverse problem. Vardi et al. proved EM asymptotically converges more than three decades ago; however, it was unclear how fast EM converges. In this talk, I will present a non-asymptotic convergence guarantee for EM. Our analysis exploits an interesting connection between EM and a portfolio selection method due to Cover.
|Colloquium, 淡江大學數學系 楊定揮教授|
Thursday, October 8, 15:10—17:00 數學系3174
Title: Some Recent Works on the Dynamics and Traveling Wave Solutions of Non-Monotone Three Species Food Web Models
Abstract: Three species food web models are fundamental building blocks of large scale ecosystems. To clarify the local or global and short-term or long-term behavior of ecosystems, it is essential to understand the interacting dynamics of three species food web models. A monotone ecosystem whose interactions among n-species are all cooperative or competitive (n = 2) have been well studied in the past three decades by the theory of monotone dynamical systems. However, for a non-monotone system whose interactions are blended at least with one consumption (i.e. herbivory, predation or parasitism), most known results are constrained on two species cases since the classical Poincare-Bendixson Theorem can be applied. Hence recent attention has been attracted to the dynamics of a non-monotone ecosystem with at least three species. In this talk, we will first survey some recent progress on the non-diffusive predator-prey food web models. Then, with diffusion, the existence of traveling wave solutions by upper lower solutions/shooting method are investigated. Finally, some open problems of these topics are proposed.