报告题目：Mathematical models and a theory of biological population dynamics: From cells to ecology, small and large systems

报告人：钱紘 教授 （华盛顿大学）

报告时间：2018年7月25日（周三） 下午15:00

报告地点：复杂系统研究所报告厅

报告摘要: Complex dynamics of interacting populations of intrinsically stochastic individuals can be mathematically represented by a discrete-state, continuous-time Markov jump process.  T. G. Kurtz's theorem establishes a relation between this stochastic process, in the limit of V tending infinity, and the traditional dynamical systems based on ODEs.  We apply this theory to several problems in current cell biology in terms of the biochemical constituents, and illustrate the emergent notions of epigenetic phenotypes and their switching, and relation to the classical idea of phase transition.  The mathematical origin of the latter in non-uniform convergence when time goes to infinity with respect to the parameter V is discussed, and a large deviations result based on WKB ansatz will be presented. We suggest some open questions and a set of computational issues as well.

报告人简介:  Hong Qian，美国华盛顿大学应用数学系教授，北京大学定量生物学中心兼职教授。1982年毕业于北大天体物理学 专业，1989年在华盛顿大学取得生物化学和生物物理博士学位，随后分别从事生物和生物数学方面的博士后 研究工作。研究方向为生命系统的随机动力学、系统生物学、生物物理化学、生物数学等。已在Physics Reports、Annual Review of Physical Chemistry等顶级综述期刊发表综述文章19篇，在Nature、PNAS、Physical Review Letters、Biophysical Journal、Journal of Chemical Physics、Physical Review E、SIAM Journal of Applied Mathematics、Journal of Mathematical Biology等杂志发表研究论文150余篇。

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