Sampling from high-dimensional systems often suffers from the curse of dimensionality. In this paper, we explored the use of sequential structures in sampling from high-dimensional systems with an aim at eliminating the curse of dimensionality, and proposed an algorithm, so-called sequential parallel tempering as an extension of parallel tempering. The algorithm was tested with the witch's hat ...

We apply a recently developed adaptive algorithm that systematically improves the efficiency of parallel tempering or replica exchange methods in the numerical simulation of small proteins. Feedback iterations allow us to identify an optimal set of temperatures/replicas which are found to concentrate at the bottlenecks of the simulations. A measure of convergence for the equilibration of the pa...

Multicanonical MCMC (Multicanonical Markov Chain Monte Carlo; Multicanonical Monte Carlo) is discussed as a method of rare event sampling. Starting from a review of the generic framework of importance sampling, multicanonical MCMC is introduced, followed by applications in random matrices, random graphs, and chaotic dynamical systems. Replica exchange MCMC (also known as parallel tempering or M...

Simulated tempering (ST) is an established Markov Chain Monte Carlo (MCMC) methodology for sampling from a multimodal density π(θ). The technique involves introducing an auxiliary variable k taking values in a finite subset of [0, 1] and indexing a set of tempered distributions, say π k (θ) ∝ π(θ) k. Small values of k encourage better mixing, but samples from π are only obtained when the joint ...

This article provides a brief review of recent developments in Markov chain Monte Carlo methodology. The methods discussed include the standard Metropolis-Hastings algorithm, the Gibbs sampler, and various special cases of interest to practitioners. It also devotes a section on strategies for improving mixing rate of MCMC samplers, e.g., simulated tempering, parallel tempering, parameter expans...

By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small T's, it is possible to derive a generic analytic expression for appropriate order parameters, whose coefficients are obtained from simple simulations. Once in such regimes simulations by standard algorithms are not reliable; an enhanced tempering...

Many discrete-time predator-prey models possess three equilibria, corresponding to (1) extinction of both species, (2) extinction of the predator and survival of the prey at its carrying capacity, or (3) coexistence of both species. For a variety of such models, the equilibrium corresponding to coexistence may lose stability via a Hopf bifurcation, in which case trajectories approach an invaria...

We continued the study of the contact homology of subcritical Stein manifolds initiated by Mei-Lin Yau. With the technical assumption that the first Chern class of the Stein domain vanishes, we determined the full contact homology of the boundary of a subcritical Stein domain. Moreover we calculated the genus 0 correlators and descendants of one marked point for the Stein domain. As an applicat...

We consider the role played by subcritical bubbles during the electroweak phase transition, estimate their average size, amplitude and formation rate taking into account the crucial role played by thermalization. We also study the influence of subcritical bubbles on the formation of critical bubbles in the thin wall regime and show that, contrary to some recent claims, subcritical bubbles do no...