讲座题目一：神奇的模式概率与 “鞅”

讲座人：李硕彦教授

讲座时间：3月9日下午2:30-5:30

讲座地点：学院行政楼C505

讲座摘要： This talk is presented in elementary language. It is a continuation of my previous talk on 概率的似是而非.

Toss a coin repeatedly until the pattern THTH appears in a run. The average waiting time is not 16 but rather 20. For the pattern HTHH, it is 18 instead. What are the odds when these two patterns compete against each other? Well, be ready for a big surprise.

Martingale, in layman’s term, means fair gamble. When applicable, martingales solve problems in simpler ways than markov chains. Applying the team gambling technique (in the “Martingale of Patterns paper,” Annals of Probability, 1980) over the martingale stopping theorem, martingales solve the general problem of pattern occurrence with almost no computation.

Computational biologists consider patterns over the DNA alphabet {A, T, G, C} instead of coin tossing. Financial engineers deal with patterns of ups and downs. In wireless ad hoc networks, some protocols use binary patterns of listen/talk for node discovery.

讲座题目二：Stochastic processes

讲座人：李硕彦教授

讲座时间：3月10日下午2:30-5:30

讲座地点：学院行政楼C505

讲座摘要： Previously I have presented talks pertaining to 概率的似是而非. Some of the facts therein have only been intuitively explained, but the complete explanation in rigorous logic requires the knowledge in various stochastic processes, such as markov chain, martingale, Poisson process, Brownian motion. In this talk as well as future talks in June, I shall go through such background knowledge in stochastic processes. In a way these talks constitute a short course that links up intuitive probability with mathematical underpinning.Like network coding and switching networks. Stochastic processes make a major part of “数学与工程的对话.”

讲座人简介：李硕彦教授1970 年毕业于台湾大学, 1974 年UC Berkeley 数学博士, 1974-76 年于 M.I.T. 教授应用数学。1976-79 年于UI Chicago 教授数学、统计学、计算机科学, 1979-89 年于Bell Labs研究通信理论、交换系统。1989-2014 年任香港中文大学信息工程讲座教授、曾兼任数学礼任教授、网络编码研究所所长。于2014年8月开始任电子科技大学Distinguished University Professor (特聘讲座教授)。