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Workshop on Recent Developments in Computer Simulation Studies in Condensed Matter Physics

作者： Mitsutake, Ayori Mori, Yoshiharu Okamoto, Yuko Nagoya Univ Dept Phys Aichi 4648602 Japan Keio Univ Dept Phys Kanagawa 2238522 Japan Nagoya Univ Dept Phys Nagoya Aichi 4648602 Japan Nagoya Univ Struct Biol Res Ctr Nagoya Aichi 4648602 Japan

We discuss multi-dimensional generalizations of multicanonical algorithm, simulated tempering, and replica-exchange method. We generalize the original potential energy function E-0 by adding any physical quantity V of interest as a new energy term with a coupling constant lambda. We then perform a multi-dimensional multicanonical simulation where a random walk in E-0 and V space is realized. We can alternately perform a multi-dimensional simulated-tempering simulation where a random walk in temperature T and parameter lambda is realized. The results of the multi-dimensional replica-exchange simulations can be used to determine the weight factors for these multi-dimensional multicanonical and simulated tempering simulations. Two examples of the above methods are presented for biomoleculr systems where the parameter lambda corresponds to the solvation parameter and the pressure. In the former, a random walk in the conformational energy and solvation free energy is performed, and in the latter, a random walk in the potential energy and volume is realized. (C) 2010 Published by Elsevier B.V.

关键词： Generalized-ensemble algorithms multicanonical algorithm simulated tempering replica-exchange method parallel tempering Mont Carlo molecular dynamics

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Multi-dimensional multicanonical algorithm, simulated tempering, replica-exchange method, and all that

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Physics Procedia 2010年 4卷 89-105页

作者： Ayori Mitsutake Yoshiharu Mori Yuko Okamoto Department of Physics Keio University Yokohama Kanagawa 223-8522 Japan Department of Physics Nagoya University Nagoya Aichi 464-8602 Japan Structural Biology Research Center Nagoya University Nagoya Aichi 464-8602 Japan

We discuss multi-dimensional generalizations of multicanonical algorithm, simulated tempering, and replica-exchange method. We generalize the original potential energy function E 0 by adding any physical quantity V of interest as a new energy term with a coupling constant λ . We then perform a multi-dimensional multicanonical simulation where a random walk in E 0 and V space is realized. We can alternately perform a multi-dimensional simulated-tempering simulation where a random walk in temperature T and parameter λ is realized. The results of the multi-dimensional replica-exchange simulations can be used to determine the weight factors for these multi-dimensional multicanonical and simulated tempering simulations. Two examples of the above methods are presented for biomoleculr systems where the parameter λ corresponds to the solvation parameter and the pressure. In the former, a random walk in the conformational energy and solvation free energy is performed, and in the latter, a random walk in the potential energy and volume is realized.

关键词： Generalized-ensemble algorithms multicanonical algorithm Simulated tempering Replica-exchange method Parallel tempering Mont Carlo Molecular dynamics

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Residual entropy of ordinary ice calculated from multicanonical Monte Carlo simulations

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MOLECULAR SIMULATION 2012年第11期38卷 856-860页

作者： Berg, Bernd A. Muguruma, Chizuru Okamoto, Yuko Nagoya Univ Grad Sch Sci Dept Phys Nagoya Aichi 4648602 Japan Nagoya Univ Grad Sch Sci Struct Biol Res Ctr Nagoya Aichi 4648602 Japan Nagoya Univ Grad Sch Engn Ctr Computat Sci Nagoya Aichi 4648603 Japan Chukyo Univ Dept Int Liberal Studies Toyota Aichi 4700393 Japan Florida State Univ Dept Phys Tallahassee FL 32306 USA

In this article, we calculated the residual entropy of ice I (ordinary ice) by multicanonical Monte Carlo simulations of two simple models with nearest neighbour interactions on 3D hexagonal lattices. Our estimate is found to be within 0.13% of an analytical approximation by Nagle, which is an improvement of Pauling's result from 1935. We pose it as a challenge to experimentalists to improve on the accuracy of a 1936 measurement by Giauque and Stout by about one order of magnitude, which would allow one to identify corrections to Pauling's value unambiguously. It is straightforward to transfer our methods to other crystal systems.

关键词： residual entropy ice ice rules multicanonical algorithm generalised-ensemble algorithms

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Enhanced Sampling algorithms

Enhanced Sampling Algorithms

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作者： Ayori Mitsutake Yoshiharu Mori Yuko Okamoto

In biomolecular systems (especially all-atom models) with many degrees of freedom such as proteins and nucleic acids, there exist an astronomically large number of local-minimum-energy states. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped in states of these energy local minima. Enhanced conformational sampling techniques are thus in great demand. A simulation in generalized ensemble performs a random walk in potential energy space and can overcome this difficulty. From only one simulation run, one can obtain canonical-ensemble averages of physical quantities as functions of temperature by the single-histogram and/or multiple-histogram reweighting techniques. In this article we review uses of the generalized-ensemble algorithms in biomolecular systems. Three well-known methods, namely, multicanonical algorithm, simulated tempering, and replica-exchange method, are described first. Both Monte Carlo and molecular dynamics versions of the algorithms are given. We then present various extensions of these three generalized-ensemble algorithms. The effectiveness of the methods is tested with short peptide and protein systems. less

关键词： Molecular Dynamics Simulation Monte Carlo Generalized-ensemble algorithm Replica-exchange method Simulated tempering multicanonical algorithm

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Molecular simulations in generalised ensemble

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MOLECULAR SIMULATION 2012年第14-15期38卷 1282-1296页

作者： Okamoto, Yuko Nagoya Univ Grad Sch Sci Dept Phys Nagoya Aichi 4648602 Japan Nagoya Univ Grad Sch Sci Struct Biol Res Ctr Nagoya Aichi 4648602 Japan Nagoya Univ Grad Sch Engn Ctr Computat Sci Nagoya Aichi 4648603 Japan

In this article, we review the generalised-ensemble algorithms. Three well-known methods, namely multicanonical algorithm, simulated tempering and replica-exchange method, are described first. Both Monte Carlo and molecular dynamics versions of the algorithms are presented. We then present further extensions of the above three methods. Finally, we discuss the relations among multicanonical algorithm, Wang-Landau method and metadynamics.

关键词： multicanonical algorithm simulated tempering replica-exchange method Wang-Landau method metadynamics

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Use of the weighted histogram analysis method for the analysis of simulated and parallel tempering simulations

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JOURNAL OF CHEMICAL THEORY AND COMPUTATION 2007年第1期3卷 26-41页

作者： Chodera, John D. Swope, William C. Pitera, Jed W. Seok, Chaok Dill, Ken A. Univ Calif San Francisco Grad Grp Biophys San Francisco CA 94143 USA Univ Calif San Francisco Dept Pharmaceut Chem San Francisco CA 94143 USA IBM Corp Almaden Res Ctr San Jose CA 95120 USA Seoul Natl Univ Coll Nat Sci Dept Chem Seoul 151747 South Korea

The growing adoption of generalized-ensemble algorithms for biomolecular simulation has resulted in a resurgence in the use of the weighted histogram analysis method (WHAM) to make use of all data generated by these simulations. Unfortunately, the original presentation of WHAM by Kumar et al. is not directly applicable to data generated by these methods. WHAM was originally formulated to combine data from independent samplings of the canonical ensemble, whereas many generalized-ensemble algorithms sample from mixtures of canonical ensembles at different temperatures. Sorting configurations generated from a parallel tempering simulation by temperature obscures the temporal correlation in the data and results in an improper treatment of the statistical uncertainties used in constructing the estimate of the density of states. Here we present variants of WHAM, STWHAM and PTWHAM, derived with the same set of assumptions, that can be directly applied to several generalized ensemble algorithms, including simulated tempering, parallel tempering (better known as replica-exchange among temperatures), and replica-exchange simulated tempering. We present methods that explicitly capture the considerable temporal correlation in sequentially generated configurations using autocorrelation analysis. This allows estimation of the statistical uncertainty in WHAM estimates of expectations for the canonical ensemble. We test the method with a one-dimensional model system and then apply it to the estimation of potentials of mean force from parallel tempering simulations of the alanine dipeptide in both implicit and explicit solvent.

关键词： MOLECULAR-DYNAMICS SIMULATIONS MONTE-CARLO REPLICA-EXCHANGE PHASE-TRANSITIONS multicanonical algorithm FREE-ENERGY ENSEMBLE SYSTEMS ERROR TEMPERATURE

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Generalized-ensemble algorithms for molecular dynamics simulations

Generalized-ensemble algorithms for molecular dynamics simul...

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Symposium on Progress and Future Prospects in Molecular Dynamics Simulation

作者： Itoh, Satoru G. Okumura, Hisashi Okamoto, Yuko Nagoya Univ Sch Sci Dept Phys Nagoya Aichi 4648602 Japan

In complex systems with many degrees of freedom such as biomolecular systems, conventional Monte Carlo and molecular dynamics simulations in canonical ensemble or isobaric-isothermal ensemble suffer from the multiple-minima problem, resulting in entrapment in states of energy local minima. A simulation in generalized ensemble performs a random walk in specified variables and overcomes this difficulty. In this article we review the generalized-ensemble algorithms. multicanonical algorithm is described first. In this method, a random walk in potential energy space is realized and the simulation can avoid the multiple-minima problem. We then present two new generalized-ensemble algorithms, namely multioverlap algorithm and multibaric-multithermal algorithm, which are multi-variable/multi-dimensional extensions of the multicanonical algorithm. In the former method, a random walk in overlap space is realized, and in the latter that in both potential energy space and volume space is obtained. Emphasis is laid in the description of the molecular dynamics versions of these algorithms.

关键词： molecular dynamics simulation generalized-ensemble algorithms multicanonical algorithm multioverlap algorithm multibaric-multithermal algorithm

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Generalized-ensemble algorithms for molecular dynamics simulations

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MOLECULAR SIMULATION 2007年第1-2期33卷 47-56页

作者： Itoh, Satoru G. Okumura, Hisashi Okamoto, Yuko Nagoya Univ Sch Sci Dept Phys Nagoya Aichi 4648602 Japan

关键词： molecular dynamics simulation generalized-ensemble algorithms multicanonical algorithm multioverlap algorithm multibaric-multithermal algorithm

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A generalized Wang-Landau algorithm for Monte Carlo computation

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2005年第472期100卷 1311-1327页

作者： Liang, FM Texas A&M Univ Dept Stat College Stn TX 77843 USA

Inference for a complex system with a rough energy landscape is a central topic in Monte Carlo computation. Motivated by the successes of the Wang-Landau algorithm in discrete systems, we generalize the algorithm to continuous systems. The generalized algorithm has some features that conventional Monte Carlo algorithms do not have. First, it provides a new method for Monte Carlo integration based on stochastic approximation;second, it is an excellent tool for Monte Carlo optimization. In an appropriate setting, the algorithm can lead to a random walk in the energy space, and thus it can sample relevant parts of the sample space, even in the presence of many local energy minima. The generalized algorithm can be conveniently used in many problems of Monte Carlo integration and optimization, for example, normalizing constant estimation, model selection, highest posterior density interval construction, and function optimization. Our numerical results show that the algorithm outperforms simulated annealing and parallel tempering in optimization for the system with a rough energy landscape. Some theoretical results on the convergence of the algorithm are provided.

关键词： 1/k-ensemble sampling importance sampling Markov chain Monte Carlo Monte Carlo integration Monte Carlo optimization multicanonical algorithm Wang-Landau algorithm

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Comparisons of force fields for proteins by generalized-ensemble simulations

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CHEMICAL PHYSICS LETTERS 2004年第4-6期386卷 460-467页

作者： Yoda, T Sugita, Y Okamoto, Y Inst Mol Sci Dept Theoret Studies Bunkyo Ku Okazaki Aichi 4448585 Japan Inst Mol Sci Dept Therapeut Studies Tokyo Japan Grad Univ Adv Studies Dept Funct Mol Sci Okazaki Aichi 4448585 Japan

Secondary structural characteristics of six commonly used force fields for protein systems developed by different research groups have been compared. We performed molecular dynamics simulations of an alpha-helical polypeptide and a beta-hairpin polypeptide with explicit water molecules. Two generalized-ensemble algorithms, replica-exchange multicanonical algorithm and multicanonical replica-exchange method, for efficient sampling of configurational space have been employed. Comparisons of the secondary structure content of polypeptides for different force fields highlighted differences of their structural tendency. The results imply that a-helix is favored for AMBER94 and AMBER99 and that beta-hairpin is favored for GROMOS96, while CHARNIM22, AMBER96, and OPLS-AA/L have intermediate tendency. (C) 2004 Published by Elsevier B.V.

关键词： Molecular-dynamics simulations Beta-hairpin formation Energy landscape multicanonical algorithm Solution conformations Phase-transitions Aqueous-solution Ribonuclease-a C-peptide Thermodynamics

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