Results 1  10
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266
Sequential Monte Carlo Samplers
, 2002
"... In this paper, we propose a general algorithm to sample sequentially from a sequence of probability distributions known up to a normalizing constant and defined on a common space. A sequence of increasingly large artificial joint distributions is built; each of these distributions admits a marginal ..."
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Cited by 303 (44 self)
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In this paper, we propose a general algorithm to sample sequentially from a sequence of probability distributions known up to a normalizing constant and defined on a common space. A sequence of increasingly large artificial joint distributions is built; each of these distributions admits a marginal which is a distribution of interest. To sample from these distributions, we use sequential Monte Carlo methods. We show that these methods can be interpreted as interacting particle approximations of a nonlinear FeynmanKac flow in distribution space. One interpretation of the FeynmanKac flow corresponds to a nonlinear Markov kernel admitting a specified invariant distribution and is a natural nonlinear extension of the standard MetropolisHastings algorithm. Many theoretical results have already been established for such flows and their particle approximations. We demonstrate the use of these algorithms through simulation.
Annealed importance sampling
 In Statistics and Computing
, 2001
"... Abstract. Simulated annealing — moving from a tractable distribution to a distribution of interest via a sequence of intermediate distributions — has traditionally been used as an inexact method of handling isolated modes in Markov chain samplers. Here, it is shown how one can use the Markov chain t ..."
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Cited by 262 (5 self)
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Abstract. Simulated annealing — moving from a tractable distribution to a distribution of interest via a sequence of intermediate distributions — has traditionally been used as an inexact method of handling isolated modes in Markov chain samplers. Here, it is shown how one can use the Markov chain transitions for such an annealing sequence to define an importance sampler. The Markov chain aspect allows this method to perform acceptably even for highdimensional problems, where finding good importance sampling distributions would otherwise be very difficult, while the use of importance weights ensures that the estimates found converge to the correct values as the number of annealing runs increases. This annealed importance sampling procedure resembles the second half of the previouslystudied tempered transitions, and can be seen as a generalization of a recentlyproposed variant of sequential importance sampling. It is also related to thermodynamic integration methods for estimating ratios of normalizing constants. Annealed importance sampling is most attractive when isolated modes are present, or when estimates of normalizing constants are required, but it may also be more generally useful, since its independent sampling allows one to bypass some of the problems of assessing convergence and autocorrelation in Markov chain samplers. 1
Nonequilibrium measurements of free energy differences for microscopically reversible markovian systems
, 1998
"... An equality has recently been shown relating the free energy difference between two equilibrium ensembles of a system and an ensemble average of the work required to switch between these two configurations. In the present paper it is shown that this result can be derived under the assumption that th ..."
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Cited by 67 (1 self)
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An equality has recently been shown relating the free energy difference between two equilibrium ensembles of a system and an ensemble average of the work required to switch between these two configurations. In the present paper it is shown that this result can be derived under the assumption that the system's dynamics is Markovian and microscopically reversible. KEY WORDS: Nonequilibrium statistical mechanics; free energy; work; thermodynamic integration; thermodynamic perturbation.
Kinetics from nonequilibrium singlemolecule pulling experiments
 Biophys. J
"... ABSTRACT Mechanical forces exerted by laser tweezers or atomic force microscopes can be used to drive rare transitions in single molecules, such as unfolding of a protein or dissociation of a ligand. The phenomenological description of pulling experiments based on Bell’s expression for the forceind ..."
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Cited by 41 (0 self)
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ABSTRACT Mechanical forces exerted by laser tweezers or atomic force microscopes can be used to drive rare transitions in single molecules, such as unfolding of a protein or dissociation of a ligand. The phenomenological description of pulling experiments based on Bell’s expression for the forceinduced rupture rate is found to be inadequate when tested against computer simulations of a simple microscopic model of the dynamics. We introduce a new approach of comparable complexity to extract more accurate kinetic information about the molecular events from pulling experiments. Our procedure is based on the analysis of a simple stochastic model of pulling with a harmonic spring and encompasses the phenomenological approach, reducing to it in the appropriate limit. Our approach is tested against computer simulations of a multimodule titin model with anharmonic linkers and then an illustrative application is made to the forced unfolding of I27 subunits of the protein titin. Our procedure to extract kinetic information from pulling experiments is simple to implement and should prove useful in the analysis of experiments on a variety of systems.
A survey of sequential Monte Carlo methods for economics and finance
, 2009
"... This paper serves as an introduction and survey for economists to the field of sequential Monte Carlo methods which are also known as particle filters. Sequential Monte Carlo methods are simulation based algorithms used to compute the highdimensional and/or complex integrals that arise regularly in ..."
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Cited by 34 (7 self)
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This paper serves as an introduction and survey for economists to the field of sequential Monte Carlo methods which are also known as particle filters. Sequential Monte Carlo methods are simulation based algorithms used to compute the highdimensional and/or complex integrals that arise regularly in applied work. These methods are becoming increasingly popular in economics and finance; from dynamic stochastic general equilibrium models in macroeconomics to option pricing. The objective of this paper is to explain the basics of the methodology, provide references to the literature, and cover some of the theoretical results that justify the methods in practice.
Artificial Brownian motors: Controlling transport on the nanoscale
 REV MOD. PHYS
, 2009
"... In systems possessing spatial or dynamical symmetry breaking, Brownian motion combined with unbiased external input signals, deterministic and random alike, can assist directed motion of particles at submicron scales. In such cases, one speaks of “Brownian motors. ” In this review the constructive r ..."
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Cited by 31 (4 self)
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In systems possessing spatial or dynamical symmetry breaking, Brownian motion combined with unbiased external input signals, deterministic and random alike, can assist directed motion of particles at submicron scales. In such cases, one speaks of “Brownian motors. ” In this review the constructive role of Brownian motion is exemplified for various physical and technological setups, which are inspired by the cellular molecular machinery: the working principles and characteristics of stylized devices are discussed to show how fluctuations, either thermal or extrinsic, can be used to control diffusive particle transport. Recent experimental demonstrations of this concept are surveyed with particular attention to transport in artificial, i.e., nonbiological, nanopores, lithographic tracks, and optical traps, where singleparticle currents were first measured. Much emphasis is given to two and threedimensional devices containing many interacting particles of one or more species; for this class of artificial motors, noise rectification results also from the interplay of particle Brownian motion and geometric constraints. Recently, selective control and optimization of the transport of interacting colloidal particles and magnetic vortices have been successfully achieved, thus leading to the new generation of microfluidic and superconducting devices presented here. The field has recently been enriched with impressive experimental achievements in building artificial Brownian motor devices that even operate within the quantum domain by harvesting quantum Brownian motion. Sundry akin topics include activities aimed at noiseassisted shuttling other degrees of freedom such as charge, spin, or even heat and the assembly of chemical synthetic molecular motors. This review ends with a perspective for future pathways and potential new applications.
FluctuationDissipation: Response Theory in Statistical Physics
 PHYSICS REPORTS 461 (2008) 111195
, 2008
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Wijland: Thermodynamic formalism for systems with Markov dynamics
 J. Stat. Phys
, 2008
"... The thermodynamic formalism allows one to access the chaotic properties of equilibrium and outofequilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function within the framework of discrete time Markov chains was not sui ..."
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Cited by 21 (3 self)
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The thermodynamic formalism allows one to access the chaotic properties of equilibrium and outofequilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function within the framework of discrete time Markov chains was not suitable for continuous time Markov dynamics. Here we propose another interpretation of the definition that allows us to apply the thermodynamic formalism to continuous time. We also generalize the formalism –a dynamical Gibbs ensemble construction– to a whole family of observables and their associated large deviation functions. This allows us to make the connection between the thermodynamic formalism and the observable involved in the muchstudied fluctuation theorem. We illustrate our approach on various physical systems: random walks, exclusion processes, an Ising model and the contact process. In the latter cases, we identify a signature of the occurrence of dynamical phase transitions. We show that this signature can already be unraveled using the simplest dynamical ensemble one could define, based on the number of configuration changes a system has undergone over an asymptotically large time window. 1 1
Fluctuation relations for diffusion process
 Commun. Math. Phys
"... The paper presents a unified approach to different fluctuation relations for classical nonequilibrium dynamics described by diffusion processes. Such relations compare the statistics of fluctuations of the entropy production or work in the original process to the similar statistics in the timerever ..."
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Cited by 21 (6 self)
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The paper presents a unified approach to different fluctuation relations for classical nonequilibrium dynamics described by diffusion processes. Such relations compare the statistics of fluctuations of the entropy production or work in the original process to the similar statistics in the timereversed process. The origin of a variety of fluctuation relations is traced to the use of different time reversals. It is also shown how the application of the presented approach to the tangent process describing the joint evolution of infinitesimally close trajectories of the original process leads to a multiplicative extension of the fluctuation relations. 1