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in this introductory talk, I will give an overview of the network sciences, and in particular, some basic metrics and models to analyze and model social networks.

For bootstrap sample sums resulting from a sequences of random variables , a very general central limit theorem is established. The random variables do not need to be independent or identically distributed or to be of any particular dependence structure. Furthermore, no conditions, including moment conditions, are imposed in general on the marginal distributions of the . As a special case of the main result, a result of Liu (1988) concerning independent but not identically distributed is extended to a larger class of parent sequences.

We generalize the P(N)-graded Lie super algebras of Martinez-Zelmanov. This generalization is not so restrictive but sufficient enough so that we are able to have a classification for this generalized P(N)-graded Lie super-algebras. The upshot is that the generalized P(N)-graded Lie super-algebra L is centrally isogenous to a matrix Lie super-algebra coordinated by an associative super-algebra with a super- involution. Moreover, L is P(N)-graded if and only if the coordinate algebra R is commutative and the super-involution is trivial. This recovers Martinez-Zelmanov’s theorem for type P(N). The motivation of this generalization comes from the fermionic-bosonic module construction.

题目：PDE Free Boundary Problems from Biology报告人：Prof Bei Hu (Notre Dame University, USA)时间：2017年6月16日 （周五） 下午2：00-- 3：00地点：宁静楼104室欢迎各位参加

In this talk，a new model which describes the vegetation pattern formation in ecological evolution system will be discussed. The mathematical model consists of a degenerate reaction-diffusion system with a cross diffusion. It shows that the system has a global solution. Some other properties of weak solutions will be also discussed.

The presentation includes two parts. The first part is a brief introduction of adaptive designs in clinical trials. The second part presents a specific adaptive design, namely Bayesian optimal randomized design, summarized as follows. Consider a clinical trial with two or more treatments. Assignment of n patients to the treatments is sequential.

题目: A Parallel Projection Method for Minimizing a Finite Sum of Convex Functions报告人：徐洪坤 教授（第三世界科学院院士、杭州电子科大特聘教授）地点：教学北楼北108室时间：2017年6月7日(星期三) 下午2：30—3：30欢迎各位参

题目: 基于配对交易策略的动态资产配置问题研究报告人：张寄洲教授（上海师范大学）地点：教学北楼北108室时间：2017年6月7日(星期三)下午3：30—4：30欢迎各位参加