48 research outputs found
Analysis and optimization of weighted ensemble sampling
We give a mathematical framework for weighted ensemble (WE) sampling, a
binning and resampling technique for efficiently computing probabilities in
molecular dynamics. We prove that WE sampling is unbiased in a very general
setting that includes adaptive binning. We show that when WE is used for
stationary calculations in tandem with a coarse model, the coarse model can be
used to optimize the allocation of replicas in the bins.Comment: 22 pages, 3 figure
On the phase transition curve in a directed exponential random graph model
We consider a family of directed exponential random graph models parametrized
by edges and outward stars. Much of the important statistical content of such
models is given by the normalization constant of the models, and in particular,
an appropriately scaled limit of the normalization, which is called the free
energy. We derive precise asymptotics for the normalization constant for finite
graphs. We use this to derive a formula for the free energy. The limit is
analytic everywhere except along a curve corresponding to a first order phase
transition. We examine unusual behavior of the model along the phase transition
curve.Comment: 31 pages, 2 figure
The parallel replica method for simulating long trajectories of Markov chains
The parallel replica dynamics, originally developed by A.F. Voter,
efficiently simulates very long trajectories of metastable Langevin dynamics.
We present an analogous algorithm for discrete time Markov processes. Such
Markov processes naturally arise, for example, from the time discretization of
a continuous time stochastic dynamics. Appealing to properties of
quasistationary distributions, we show that our algorithm reproduces exactly
(in some limiting regime) the law of the original trajectory, coarsened over
the metastable states.Comment: 13 pages, 6 figure