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The weighted ensemble method, introduced by Huber and Kim, [G. A. Huber and S. Kim, Biophys. J. 70, 97 (1996)], is one of a handful of rigorous approaches to path sampling of rare events. Expanding earlier discussions, we show that the technique is statistically exact for a wide class of Markovian and non-Markovian dynamics. The derivation is based on standard path-integral (path probability) ideas, but recasts the weighted-ensemble approach as simple resampling in path space. Similar reasoning indicates that arbitrary nonstatic binning procedures, which merely guide the resampling process, are also valid. Numerical examples confirm the claims, including the use of bins which can adaptively find the target state in a simple model.
Because biological processes can make different loci have different evolutionary histories, species tree estimation requires multiple loci from across the genome. While many processes can result in discord between gene trees and species trees, incomp
Recent advances in selected CI, including the adaptive sampling configuration interaction (ASCI) algorithm and its heat bath extension, have made the ASCI approach competitive with the most accurate techniques available, and hence an increasingly pow
We consider a direct optimization approach for ensemble density functional theory electronic structure calculations. The update operator for the electronic orbitals takes the structure of the Stiefel manifold into account and we present an optimizati
The development of enhanced sampling methods has greatly extended the scope of atomistic simulations, allowing long-time phenomena to be studied with accessible computational resources. Many such methods rely on the identification of an appropriate s
The detail structure of the wave function is analyzed at various refinement levels using the methods of wavelet analysis. The eigenvalue problem of a model system is solved in granular Hilbert spaces, and the trajectory of the eigenstates is traced i