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We present a kinetic Monte Carlo method for simulating chemical transformations specified by reaction rules, which can be viewed as generators of chemical reactions, or equivalently, definitions of reaction classes. A rule identifies the…
The multiple-try Metropolis (MTM) algorithm is a generalization of the Metropolis-Hastings algorithm in which the transition kernel uses a compound proposal consisting of multiple candidate draws. Since its seminal paper there have been…
We present an efficient Monte Carlo method to simulate reaction-diffusion processes with spatially varying particle annihilation or transformation rates as it occurs for instance in the context of motor-driven intracellular transport. Like…
In this work, we present, analyze, and implement a class of Multi-Level Markov chain Monte Carlo (ML-MCMC) algorithms based on independent Metropolis-Hastings proposals for Bayesian inverse problems. In this context, the likelihood function…
A first-order, Monte Carlo ensemble method has been recently introduced for solving parabolic equations with random coefficients in [26], which is a natural synthesis of the ensemble-based, Monte Carlo sampling algorithm and the…
Molecular dynamics algorithms are subject to some amount of error dependent on the size of the time step that is used. This error can be corrected by periodically updating the system with a Metropolis criteria, where the integration step is…
The multilevel Monte Carlo (MLMC) method has been used for a wide variety of stochastic applications. In this paper we consider its use in situations in which input random variables can be replaced by similar approximate random variables…
Considering the issue of estimating small probabilities p, ie. measuring a rare domain F = {x | g(x) > q} with respect to the distribution of a random vector X, Multilevel Splitting strategies (also called Subset Simulation) aim at writing…
The term ``sequential Monte Carlo methods'' or, equivalently, ``particle filters,'' refers to a general class of iterative algorithms that performs Monte Carlo approximations of a given sequence of distributions of interest (\pi_t). We…
In this paper we propose a methodology for the efficient implementation of Machine Learning (ML)-based methods in particle-in-cell (PIC) codes, with a focus on Monte-Carlo or statistical extensions to the PIC algorithm. The presented…
This work introduces two Monte Carlo (MC)-based sampling methods, known as line sampling and subset simulation, to improve the performance of standard MC analyses in the context of asteroid impact risk assessment. Both techniques sample the…
We generalize the rejection-free event-chain Monte Carlo algorithm from many particle systems with pairwise interactions to systems with arbitrary three- or many-particle interactions. We introduce generalized lifting probabilities between…
Biological tissues are complex structures composed of many elements which make light-based tissue diagnostics challenging. Over the past decades, Monte Carlo technique has been used as a fundamental and versatile approach toward modeling…
We introduce a powerful Monte Carlo (MC) algorithm for the atomistic simulation of bulk models of oligo- and poly-thiophenes by redesigning MC moves originally developed for considerably simpler polymer structures and architectures, such as…
We propose a new sampling algorithm combining two quite powerful ideas in the Markov chain Monte Carlo literature -- adaptive Metropolis sampler and two-stage Metropolis-Hastings sampler. The proposed sampling method will be particularly…
Metropolis Monte Carlo simulation is used to investigate the elasticity of torsionally stressed double-stranded DNA, in which twist and supercoiling are incorporated as a natural result of base-stacking interaction and backbone bending…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
We present a method to model the interaction and the dynamics of atoms excited to Rydberg states. We show a way to solve the optical Bloch equations for laser excitation of the frozen gas in good agreement with the experiment. A second…
Elastic systems that are spatially heterogeneous in their mechanical response pose special challenges for molecular simulations. Standard methods for sampling thermal fluctuations of a system's size and shape proceed through a series of…
The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a {\bf fixed}…