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Institute
In recent years Markov State Models (MSMs) have attracted a consid-
erable amount of attention with regard to modelling conformation changes
and associated function of biomolecular systems. They have been used
successfully, e.g., for peptides including time-resolved spectroscopic ex-
periments, protein function and protein folding , DNA and RNA, and
ligand-receptor interaction in drug design and more complicated multi-
valent scenarios. In this article a novel reweighting scheme is introduced
that allows to construct an MSM for certain molecular system out of an
MSM for a similar system. This permits studying how molecular proper-
ties on long timescales differ between similar molecular systems without
performing full molecular dynamics simulations for each system under con-
sideration. The performance of the reweighting scheme is illustrated for
simple test cases including one where the main wells of the respective en-
ergy landscapes are located differently and an alchemical transformation
of butane to pentane where the dimension of the state space is changed.
Reversible Markov chains are the basis of many applications. However, computing transition probabilities by a finite sampling of a Markov chain can lead to truncation errors. Even if the original Markov chain is reversible, the approximated Markov chain might be non-reversible and will lose important properties, like the real valued spectrum. In this paper, we show how to find the closest reversible Markov chain to a given transition matrix. It turns out that this matrix can be computed by solving a convex minimization problem.
Applications of the cross-entropy method to importance sampling and optimal control of diffusions
(2014)
We study the cross-entropy method for diffusions. One of the results is a versatile cross-entropy algorithm that can be used to design efficient importance sampling strategies for rare events or to solve optimal control problems. The approach is based on the minimization of a suitable cross-entropy functional, with a parametric family of exponentially tilted probability distributions. We illustrate the new algorithm with several numerical examples and discuss algorithmic issues and possible extensions of the method.