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Numerical schemes are presented for dynamical systems with multiple timescales. Two classes of methods are discussed, depending on the time interval on which the evolution of the slow variables in the system is sought. On rather short time intervals, the slow variables satisfy ordinary differential equations. On longer time intervals, however, fluctuations(More)
We study the action minimization problem that is formally associated to phase transformation in the stochastically perturbed Allen-Cahn equation. The sharp-interface limit is related to (but different from) the sharp-interface limits of the related energy functional and deterministic gradient flows. In the sharp-interface limit of the action minimization(More)
We analyze a class of numerical schemes proposed in [26] for stochastic differential equations with multiple time scales. Both advective and diffusive time scales are considered. Weak as well as strong convergence theorems are proven. Most of our results are optimal. They in turn allow us to provide a thorough discussion on the efficiency as well as optimal(More)
This paper gives a systematic introduction to HMM, the heterogeneous multiscale methods, including the fundamental design principles behind the HMM philosophy and the main obstacles that have to be overcome when using HMM for a particular problem. This is illustrated by examples from several application areas, including complex fluids, micro-fluidics,(More)
We give a new formula expressing the components of the mean force in terms of a conditional expectation which can be computed by Blue Moon sampling. This generalizes to the vectorial case a formula first derived by Ruiz-Montero et al. for a scalar reaction coordinate. We also discuss how to compute this conditional average by means of constrained stochastic(More)
An efficient simulation algorithm for chemical kinetic systems with disparate rates is proposed. This new algorithm is quite general, and it amounts to a simple and seamless modification of the classical stochastic simulation algorithm (SSA), also known as the Gillespie [J. Comput. Phys. 22, 403 (1976); J. Phys. Chem. 81, 2340 (1977)] algorithm. The basic(More)
BACKGROUND Many current works aiming to learn regulatory networks from systems biology data must balance model complexity with respect to data availability and quality. Methods that learn regulatory associations based on unit-less metrics, such as Mutual Information, are attractive in that they scale well and reduce the number of free parameters (model(More)
This paper gives a systematic introduction to HMM, the heterogeneous multiscale method, including the fundamental design principles behind the HMM philosophy and the main obstacles that have to be overcome when using HMM for a particular problem. This is illustrated by examples from several application areas, including complex fluids, micro-fluidics,(More)