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How to lose at Monte Carlo: a simple dynamical system whose typical statistical behavior is non computable [article]

Cristobal Rojas, Michael Yampolsky
2019 arXiv   pre-print
In particular, the Monte Carlo method cannot be applied to study these dynamical systems.  ...  We show that there exist real parameters a∈ (0,4) for which almost every orbit of f_a has the same statistical distribution in [0,1], but this limiting distribution is not Turing computable.  ...  Our result raises a disturbing possibility that even for the most simple family of examples of non-linear dynamical systems the Monte Carlo method can fail.  ... 
arXiv:1910.09625v2 fatcat:pzi7ebkufffdtdu4wiuwrjcgp4

The Convergence of Markov chain Monte Carlo Methods: From the Metropolis method to Hamiltonian Monte Carlo [article]

Michael Betancourt
2018 arXiv   pre-print
From its inception in the 1950s to the modern frontiers of applied statistics, Markov chain Monte Carlo has been one of the most ubiquitous and successful methods in statistical computing.  ...  In this article I will review the history of Markov chain Monte Carlo from its inception with the Metropolis method to today's state-of-the-art in Hamiltonian Monte Carlo.  ...  For a system at constant temperature, T , that equilibrium behavior is completely characterized by the canonical probability distribution, π(q, p) ∝ exp(−H(q, p)/k T ), Michael Betancourt is a research  ... 
arXiv:1706.01520v2 fatcat:hpj42h66zrandovxmt7mn4biea

Comparative Monte Carlo efficiency by Monte Carlo analysis

B. M. Rubenstein, J. E. Gubernatis, J. D. Doll
2010 Physical Review E  
We present a simple procedure to solve this sign problem and then test our Monte Carlo methods by computing the λ_2 of various Markov chain transition matrices.  ...  We propose a modified power method for computing the subdominant eigenvalue λ_2 of a matrix or continuous operator. Here we focus on defining simple Monte Carlo methods for its application.  ...  INTRODUCTION When designing a Monte Carlo simulation, the computational scientist often must decide which of several algorithmic options is the most efficient or how to optimize a particular algorithm.  ... 
doi:10.1103/physreve.82.036701 pmid:21230207 fatcat:6pvohurvlbhsflzpzq5mzuox2a

Monte Carlo Based Statistical Model Checking of Cyber-Physical Systems: A Review

Angela Pappagallo, Annalisa Massini, Enrico Tronci
2020 Information  
Statistical Model Checking (SMC) is a simulation-based approach that holds the promise to overcome such an obstacle by using statistical methods in order to sample the set of scenarios.  ...  In this paper, we will overview Monte Carlo-based SMC tools in order to provide selection criteria based on Key Performance Indicators (KPIs) for the verification activity (e.g., minimize verification  ...  Acknowledgments: We thank Alberto Lluch Lafuente for his very useful remarks on a preliminary version of this paper. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/info11120588 fatcat:fur5l4427ff4zkbdxyqtfuk2fq

Monte Carlo Methods for the Self-Avoiding Walk [article]

Alan D. Sokal
1994 arXiv   pre-print
This article is a pedagogical review of Monte Carlo methods for the self-avoiding walk, with emphasis on the extraordinarily efficient algorithms developed over the past decade.  ...  Monte Carlo Methods: A Review Monte Carlo methods can be classi ed as static, quasi-static or dynamic.  ...  This means that the statistical errors can be computed reliably, in advance of performing the Monte Carlo simulation.  ... 
arXiv:hep-lat/9405016v1 fatcat:a25htu2hfjd25gbsa7isnrvh6q

Monte Carlo analysis of inverse problems

Klaus Mosegaard, Malcolm Sambridge
2002 Inverse Problems  
Apocrypha The idea of computing acceptable solutions to (highly) non-linear inverse problems by Monte Carlo methods is not new.  ...  This way of calculating π is, in many ways, a typical Monte Carlo algorithm: Using a random input (initial conditions of the needle tossed in the experiment), an estimate of a non-random number (here π  ...  Last, but not least, it contains a more satisfactory historic account of the development of Monte Carlo methods, than is presented in the first chapters of this dissertation.  ... 
doi:10.1088/0266-5611/18/3/201 fatcat:2kufm5ienrf2tjs2746b6fyaa4

First-passage kinetic Monte Carlo method

Tomas Oppelstrup, Vasily V. Bulatov, Aleksandar Donev, Malvin H. Kalos, George H. Gilmer, Babak Sadigh
2009 Physical Review E  
The algorithm reproduces the statistics of the underlying Monte-Carlo model exactly.  ...  We present a new efficient method for Monte Carlo simulations of diffusion-reaction processes. First introduced by us in [Phys. Rev.  ...  Kinetic Monte Carlo (KMC) is a simple and robust computational approach for simulations of systems evolving through random walks.  ... 
doi:10.1103/physreve.80.066701 pmid:20365296 fatcat:utmwhpyonrdw5l4eomv2gkbc54

Ab Initio Molecular Dynamics with Quantum Monte Carlo

Ye Luo, Sandro Sorella
2015 Frontiers in Materials  
A Solutions to the second order Langevin dynamics 91 A.  ...  The typical flow chart of variational Monte Carlo is described as algorithm 1.  ...  Antisymmetrized geminal power wavefunction H 2 is a very simple example to show how a chemical bond forms.  ... 
doi:10.3389/fmats.2015.00029 fatcat:jh6ew6m4uze6hkqrfwdkvrfo2i

Monte Carlo Studies of Quantum Critical Metals

Erez Berg, Samuel Lederer, Yoni Schattner, Simon Trebst
2019 Annual Review of Condensed Matter Physics  
However, it has recently been realized that many models used to describe such systems are amenable to numerically exact solution by quantum Monte Carlo (QMC) techniques, without suffering from the fermion  ...  We describe the results obtained so far, and their implications for superconductivity, non-Fermi liquid behavior, and transport in the vicinity of metallic quantum critical points.  ...  Acknowledgements It is a pleasure to thank C. Bauer, S. Chatterjee, D. Chowdhury, A. Chubokov, R. Fernandes, M. Gerlach, S. Kivelson, A. Klein, M. Metlitski, S.  ... 
doi:10.1146/annurev-conmatphys-031218-013339 fatcat:e74yol4vxrh5lmwreq4kfnynxq

Chapter 3 Methods for Monte Carlo Simulations of Biomacromolecules [chapter]

Andreas Vitalis, Rohit V. Pappu
2009 Annual Reports in Computational Chemistry  
The state-of-the-art for Monte Carlo (MC) simulations of biomacromolecules is reviewed.  ...  The issue of introducing correlations into elementary MC moves, and the applicability of such methods to simulations of biomacromolecules is discussed.  ...  earlier versions of this package) that helped guide our thinking regarding Monte Carlo simulations.  ... 
doi:10.1016/s1574-1400(09)00503-9 pmid:20428473 pmcid:PMC2860296 fatcat:rogy3kwucbgovbjpv776jf3v5u

Clustering and heterogeneous dynamics in a kinetic Monte Carlo model of self-propelled hard disks

Demian Levis, Ludovic Berthier
2014 Physical Review E  
We introduce a kinetic Monte-Carlo model for self-propelled hard disks to capture with minimal ingredients the interplay between thermal fluctuations, excluded volume and self-propulsion in large assemblies  ...  As density is increased, the nonequilibrium clusters percolate to form a ramified structure reminiscent of a physical gel.  ...  The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. 306845.  ... 
doi:10.1103/physreve.89.062301 pmid:25019770 fatcat:rgk2no4bpzgxnkjh6rnobikfx4

Dynamical Monte Carlo study of equilibrium polymers: Static properties

J. P. Wittmer, A. Milchev, M. E. Cates
1998 Journal of Chemical Physics  
Using a novel algorithm we are able to describe efficiently both static and dynamic properties of systems in which the mean chain length is effectively comparable to that of laboratory experiments (up  ...  We report results of extensive Dynamical Monte Carlo investigations on self-assembled Equilibrium Polymers (EP) without loops in good solvent.  ...  Acknowledgement The authors are indebted to J. P. Desplat, Y. Rouault  ... 
doi:10.1063/1.476623 fatcat:wzlo5tuiendftg67i2fhkr7mdm

Path Weight Sampling: Exact Monte Carlo Computation of the Mutual Information between Stochastic Trajectories [article]

Manuel Reinhardt, Gašper Tkačik, Pieter Rein ten Wolde
2022 arXiv   pre-print
The principal idea is to use the master equation to evaluate the exact conditional probability of an individual output trajectory for a given input trajectory, and average this via Monte Carlo sampling  ...  system that is described by a master equation.  ...  This work is part of the Dutch Research Council (NWO) and was performed at the research institute AMOLF.  ... 
arXiv:2203.03461v1 fatcat:4h77agcryrdstedzynmobn5y7e

Fluid simulations with localized boltzmann upscaling by direct simulation Monte-Carlo

Pierre Degond, Giacomo Dimarco
2012 Journal of Computational Physics  
In this paper we extend the idea of buffer zones and dynamic coupling to the case of the Monte Carlo methods.  ...  In the present work, we present a novel numerical algorithm to couple the Direct Simulation Monte Carlo method (DSMC) for the solution of the Boltzmann equation with a finite volume like method for the  ...  On the other hand, the solutions contain large statistical errors which are the typical drawback of Monte Carlo methods.  ... 
doi:10.1016/j.jcp.2011.11.030 fatcat:wwvo42m64jb5hpu6tdxfjbxga4

Optimal Prediction in Molecular Dynamics

Benjamin Seibold
2004 Monte Carlo Methods and Applications  
We present how optimal prediction can be applied to a typical problem in the field of molecular dynamics, in order to reduce the number of particles to be tracked in the computations.  ...  The comparison is carried out by Monte-Carlo simulations, and it is shown under which conditions optimal prediction yields a valid approximation to the original system.  ...  Acknowledgements In the end I wish to thank . ..  ... 
doi:10.1515/156939604323091199 fatcat:szqxcjkrwvay7inqrm5wszj2ae
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