主 题: Mathematical Study of Milestoning
报告人: Dr Ling Lin (Freier University, Berlin)
时 间: 2014-12-23 16:00-17:00
地 点: 理科一号楼1418（主持人：李铁军）
Milestoning is a coarse-graining strategy that can serve both as an analysis tool to analyze time series of complicated activated processes and as a computational tool to accelerate the computation of these processes. In this talk, I would like to review the mathematical foundation of milestoning.
For systems displaying metastability, the assumption of Markovian milestoning can be justified asymptotically provided that the metastable states are taken as milestones. Practically, the set of the metastable states can be identified automatically as the set that minimizes a metastability index, and a continuous-time Markov jump process can be built on this set by applying maximum likelihood estimation and Bayesian sampling techniques.
For systems without the timescale separation, the assumption of optimal milestoning can still be justified for the set of milestones made of the forward isocommittor surfaces, which allows us to build a discrete-time Markov chain on the index set of milestones. For diffusion processes, under mild assumptions, by using a set of milestones made of the backward isocommittor surfaces,
the mean first passage times between these milestones can be calculated exactly.
In practice, the isocommittor surfaces can be identified approximately as the hyperplanes in the reaction tube by using the string method, and an accelerated sampling procedure based on the confined simulations in Voronoi cells can compute the required key objects in milestoning efficiently without the need to reinitialize simulations on milestones.