3,322 research outputs found
Density-Dependent Analysis of Nonequilibrium Paths Improves Free Energy Estimates II. A Feynman-Kac Formalism
The nonequilibrium fluctuation theorems have paved the way for estimating
equilibrium thermodynamic properties, such as free energy differences, using
trajectories from driven nonequilibrium processes. While many statistical
estimators may be derived from these identities, some are more efficient than
others. It has recently been suggested that trajectories sampled using a
particular time-dependent protocol for perturbing the Hamiltonian may be
analyzed with another one. Choosing an analysis protocol based on the
nonequilibrium density was empirically demonstrated to reduce the variance and
bias of free energy estimates. Here, we present an alternate mathematical
formalism for protocol postprocessing based on the Feynmac-Kac theorem. The
estimator that results from this formalism is demonstrated on a few
low-dimensional model systems. It is found to have reduced bias compared to
both the standard form of Jarzynski's equality and the previous protocol
postprocessing formalism.Comment: 21 pages, 5 figure
Universally Consistent Latent Position Estimation and Vertex Classification for Random Dot Product Graphs
In this work we show that, using the eigen-decomposition of the adjacency
matrix, we can consistently estimate latent positions for random dot product
graphs provided the latent positions are i.i.d. from some distribution. If
class labels are observed for a number of vertices tending to infinity, then we
show that the remaining vertices can be classified with error converging to
Bayes optimal using the -nearest-neighbors classification rule. We evaluate
the proposed methods on simulated data and a graph derived from Wikipedia
Nonequilibrium candidate Monte Carlo: A new tool for efficient equilibrium simulation
Metropolis Monte Carlo simulation is a powerful tool for studying the
equilibrium properties of matter. In complex condensed-phase systems, however,
it is difficult to design Monte Carlo moves with high acceptance probabilities
that also rapidly sample uncorrelated configurations. Here, we introduce a new
class of moves based on nonequilibrium dynamics: candidate configurations are
generated through a finite-time process in which a system is actively driven
out of equilibrium, and accepted with criteria that preserve the equilibrium
distribution. The acceptance rule is similar to the Metropolis acceptance
probability, but related to the nonequilibrium work rather than the
instantaneous energy difference. Our method is applicable to sampling from both
a single thermodynamic state or a mixture of thermodynamic states, and allows
both coordinates and thermodynamic parameters to be driven in nonequilibrium
proposals. While generating finite-time switching trajectories incurs an
additional cost, driving some degrees of freedom while allowing others to
evolve naturally can lead to large enhancements in acceptance probabilities,
greatly reducing structural correlation times. Using nonequilibrium driven
processes vastly expands the repertoire of useful Monte Carlo proposals in
simulations of dense solvated systems
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