Showing papers on "Monte Carlo molecular modeling published in 1998"
TL;DR: In this paper, the authors presented an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction techniques, and showed Monte Carlo to be very robust but also slow.
Abstract: Monte Carlo is one of the most versatile and widely used numerical methods. Its convergence rate, O(N−1/2), is independent of dimension, which shows Monte Carlo to be very robust but also slow. This article presents an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction techniques. Accelerated convergence for Monte Carlo quadrature is attained using quasi-random (also called low-discrepancy) sequences, which are a deterministic alternative to random or pseudo-random sequences. The points in a quasi-random sequence are correlated to provide greater uniformity. The resulting quadrature method, called quasi-Monte Carlo, has a convergence rate of approximately O((logN)kN−1). For quasi-Monte Carlo, both theoretical error estimates and practical limitations are presented. Although the emphasis in this article is on integration, Monte Carlo simulation of rarefied gas dynamics is also discussed. In the limit of small mean free path (that is, the fluid dynamic limit), Monte Carlo loses its effectiveness because the collisional distance is much less than the fluid dynamic length scale. Computational examples are presented throughout the text to illustrate the theory. A number of open problems are described.
1,708 citations
TL;DR: It is proved that the minimalworst case error of quasi-Monte Carlo algorithms does not depend on the dimensiondiff the sum of the weights is finite, and the minimal number of function values in the worst case setting needed to reduce the initial error by ? is bounded byC??p, where the exponentp? 1, 2], andCdepends exponentially on thesum of weights.
686 citations
26 Mar 1998
TL;DR: In this paper, a sequence of Monte Carlo methods, namely importance sampling, rejection sampling, the Metropolis method, and Gibbs sampling, are described and a discussion of advanced methods, including methods for reducing random walk behaviour is presented.
Abstract: This chapter describes a sequence of Monte Carlo methods: importance sampling, rejection sampling, the Metropolis method, and Gibbs sampling. For each method, we discuss whether the method is expected to be useful for high—dimensional problems such as arise in inference with graphical models. After the methods have been described, the terminology of Markov chain Monte Carlo methods is presented. The chapter concludes with a discussion of advanced methods, including methods for reducing random walk behaviour.
590 citations
TL;DR: In this paper, the Monte Carlo maximum likelihood (MCMCMC) method is used to estimate stochastic volatility (SV) models, which can be expressed as a linear state space model with log chi-square disturbances and decompose it into a Gaussian part, constructed by the Kalman filter, and a remainder function whose expectation is evaluated by simulation.
347 citations
TL;DR: In this article, the relationship between Monte Carlo and quasi-Monte Carlo methods is analyzed from both theoretical and practical points of view with special emphasis on high-dimensional integration with a focus on high dimensional integration.
274 citations
Journal Article•
229 citations
TL;DR: In this paper, Monte Carlo methods for simulation of the dynamic behavior of surface reactions are developed, based on the chemical master equation, in a general framework which makes them applicable to a variety of models.
Abstract: Monte Carlo methods for the simulation of the dynamic behavior of surface reactions are developed, based on the chemical master equation. The methods are stated in a general framework which makes them applicable to a variety of models. Three methods are developed. A comparative analysis of the performance of the three methods, both theoretically and empirically, is included.
211 citations
TL;DR: The Monte Carlo complexity, i.e., the complexity of the stochastic solution of this problem, is analyzed and the results show that even in the global case Monte Carlo algorithms can perform better than deterministic ones, although the difference is not as large as in the local case.
209 citations
TL;DR: In this paper, the dependence of the viscosity and thermal conductivity on cell size for stochastic particle methods such as direct simulation Monte Carlo (DSMC) and its generalization, the consistent Boltzmann algorithm (CBA) was investigated.
Abstract: Using the Green–Kubo theory, the dependence of the viscosity and thermal conductivity on cell size is obtained explicitly for stochastic particle methods such as direct simulation Monte Carlo (DSMC) and its generalization, the consistent Boltzmann algorithm (CBA). These analytical results confirm empirical observations that significant errors occur when the cell dimensions are larger than a mean free path.
204 citations
TL;DR: In this paper, the supersymmetric Yang-Mills theory was dimensionally reduced to zero dimensions and the SU 2 and.. SU 3 partition functions were obtained by Monte Carlo methods.
200 citations
11 Nov 1998-Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment
TL;DR: In this article, a new simulation of nuclear γ cascades by the Monte Carlo method is described, which makes it possible to generate artificially individual events of the γ-cascade decay of an isolated, highly excited initial level in a medium and heavy nucleus.
Abstract: A new simulation of nuclear γ cascades by the Monte Carlo method is described. It makes it possible to generate artificially individual events of the γ-cascade decay of an isolated, highly excited initial level in a medium and heavy nucleus. A broad class of quantities, associated with the process of γ-cascade de-excitation, can be modelled. The main advantage of the method is the possibility of a full quantitative control over the influence of the Porter–Thomas fluctuations of partial radiation widths on uncertainties of the modelled cascade-related quantities. For assessment of these uncertainties and a control over the accuracy of the method, a special statistical formalism has been developed.
TL;DR: In this paper, a quantum Monte Carlo scheme was proposed for the analysis of large disordered systems, using a pair of worldline discontinuities for sampling the extended configuration space of the system which includes both closed and disconnected worldlines.
TL;DR: In this paper, the correlation energy of the homogeneous three-dimensional interacting electron gas is calculated using the variational and fixed-node diffusion Monte Carlo methods, with trial functions that include backflow and three-body correlations.
Abstract: The correlation energy of the homogeneous three-dimensional interacting electron gas is calculated using the variational and fixed-node diffusion Monte Carlo methods, with trial functions that include backflow and three-body correlations. In the high-density regime ( r s<5) the effects of backflow dominate over those due to three-body correlations, but the relative importance of the latter increases as the density decreases. Since the backflow correlations vary the nodes of the trial function, this leads to improved energies in the fixed-node diffusion Monte Carlo calculations. The effects are comparable to those found for the two-dimensional electron gas, leading to much improved variational energies and fixed-node diffusion energies similar to the releasednode energies of Ceperley and Alder. @S0163-1829~98!00135-0#
TL;DR: Two methods for sequentially generating samples from filter densities and smoother densities by simple rejection algorithms are introduced in nonlinear and non-Gaussian state-space models.
Abstract: Nonlinear and non-Gaussian state-space models form a large and flexible model class in time series analysis. Two methods for sequentially generating samples from filter densities and smoother densities by simple rejection algorithms are introduced. We illustrate the behavior of our methods in several nonlinear and non-Gaussian examples and compare them with other well-known methods.
01 Jan 1998
TL;DR: In this article, the performance of ordinary Monte Carlo and quasi Monte Carlo methods in valuing moderate-and high-dimensional options was compared, where the dimensionality of the problems arises either from the number of time steps along a single path or from the underlying assets.
Abstract: This article compares the performance of ordinary Monte Carlo and quasi Monte Carlo methods in valuing moderate-and high-dimensional options The dimensionality of the problems arises either from the number of time steps along a single path or from the number of underlying assets We compare ordinary Monte Carlo with and without antithetic variates against Sobol’, Faure, and Generalized Faure sequences and three constructions of a discretely sampled Brownian path We test the standard random walk construction with all methods, a Brownian bridge construction proposed by Caflisch and Morokoff with Sobol’ points and an alternative construction based on principal components analysis also with Sobol’ points We find that the quasi Monte Carlo methods outperform ordinary Monte Carlo; the Brownian bridge construction generally outperforms the standard construction; and the principal components construction generally outperforms the Brownian bridge construction and is more widely applicable We interpret both the Brownian bridge and principal components constructions in terms of orthogonal expansions of Brownian motion and note an optimality property of the principal components construction
TL;DR: In this article, a new method for the stabilization of the sign problem in the Green Function Monte Carlo technique is devised for real lattice Hamiltonians and is based on an iterative ''stochastic reconfiguration'' scheme which introduces some bias but allows a stable simulation with constant sign.
Abstract: A new method for the stabilization of the sign problem in the Green Function Monte Carlo technique is proposed. The method is devised for real lattice Hamiltonians and is based on an iterative ''stochastic reconfiguration'' scheme which introduces some bias but allows a stable simulation with constant sign. The systematic reduction of this bias is in principle possible. The method is applied to the frustrated J1-J2 Heisenberg model, and tested against exact diagonalization data. Evidence of a finite spin gap for J2/J1 >~ 0.4 is found in the thermodynamic limit.
TL;DR: In this paper, a simple and efficient Green function Monte Carlo technique for computing both the ground state energy and ground state properties by the ''forward walking'' scheme is described. But this method is not suitable for the Heisenberg model.
Abstract: We describe in detail a simple and efficient Green function Monte Carlo technique for computing both the ground state energy and the ground state properties by the ``forward walking'' scheme. The simplicity of our reconfiguration process, used to maintain the walker population constant, allows us to control any source of systematic error in a rigorous and systematic way. We apply this method to the Heisenberg model and obtain accurate and reliable estimates of the ground state energy, the order parameter, and the static spin structure factor $S(q)$ for several momenta. For the latter quantity we also find very good agreement with available experimental data on the ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ antiferromagnet.
TL;DR: Comparisons of the performance (defined as the variance of the results multiplied by the CPU time required for solution) are presented for three common methods used in Monte Carlo solution.
Abstract: A review of various strategies for implementing Monte Carlo analysis of radiative media is presented. Comparisons of the performance (defined as the variance of the results multiplied by the CPU time required for solution) are presented for three common methods used in Monte Carlo solution. Methods of treating complex geometries are also explored and compared, and a ray-tracing technique based on finite-element models of the geometry is presented. The finite-element models allow use of commercial codes for describing complex geometries, and also allow efficient coupling of the Monte Carlo radiative model with other finite-element-based thermal models. The utility and performance of the direct simulation Monte Carlo ray-tracing methods in engineering problems involving realistic properties are examined. Strategies are compared for treating anisotropic scattering distributions, nonuniform temperatures and radiative properties, and spectral property variations. The effects of scattering on ray tracing and the necessary modifications to the algorithms are evaluated, and the performance and accuracy of these algorithms are evaluated and recommendations are suggested. The difficulties in handling inhomogeneous properties and spectrally dependent properties are presented, and some possible approaches are proposed and compared. Monte Carlo strategies for solving radiative transfer in participating media are described for use on parallel processors using different common architectures. An example benchmark problem is carried out to demonstrate the degree of speedup that can be obtained.
TL;DR: This work reviews and discusses some recent progress in the theory of Markov-chain Monte Carlo applications and attempts to assess the relevance of this theory for practical applications.
Abstract: We review and discuss some recent progress in the theory of Markov-chain Monte Carlo applications, particularly oriented to applications in statistics. We attempt to assess the relevance of this theory for practical applications.
TL;DR: The reliability and robustness of the new method should enable its routine application in model building protocols based on various (very sparse) experimentally derived structural restraints, and increasing the number of tertiary restraints improves the accuracy of the assembled structures.
Abstract: A new, efficient method for the assembly of protein tertiary structure from known, loosely encoded secondary structure restraints and sparse information about exact side chain contacts is proposed and evaluated. The method is based on a new, very simple method for the reduced modeling of protein structure and dynamics, where the protein is described as a lattice chain connecting side chain centers of mass rather than Calphas. The model has implicit built-in multibody correlations that simulate short- and long-range packing preferences, hydrogen bonding cooperativity and a mean force potential describing hydrophobic interactions. Due to the simplicity of the protein representation and definition of the model force field, the Monte Carlo algorithm is at least an order of magnitude faster than previously published Monte Carlo algorithms for structure assembly. In contrast to existing algorithms, the new method requires a smaller number of tertiary restraints for successful fold assembly; on average, one for every seven residues as compared to one for every four residues. For example, for smaller proteins such as the B domain of protein G, the resulting structures have a coordinate root mean square deviation (cRMSD), which is about 3 A from the experimental structure; for myoglobin, structures whose backbone cRMSD is 4.3 A are produced, and for a 247-residue TIM barrel, the cRMSD of the resulting folds is about 6 A. As would be expected, increasing the number of tertiary restraints improves the accuracy of the assembled structures. The reliability and robustness of the new method should enable its routine application in model building protocols based on various (very sparse) experimentally derived structural restraints.
TL;DR: In this article, the posterior probability density is used to estimate the probability of the existence of interesting Earth structures, such as discontinuities and flow patterns, in the model space.
Abstract: The general inverse problem is characterized by at least one of the following two complications: (1) data can only be computed from the model by means of a numerical algorithm, and (2) the a priori model constraints can only be expressed via numerical algorithms. For linear problems and the so-called `weakly nonlinear problems', which can be locally approximated by a linear problem, analytical methods can provide estimates of the best fitting model and measures of resolution (nonuniqueness and uncertainty of solutions). This is, however, not possible for general problems. The only way to proceed is to use sampling methods that collect information on the posterior probability density in the model space. One such method is the inverse Monte Carlo strategy for resolution analysis suggested by Mosegaard and Tarantola. This method allows sampling of the posterior probability density even in cases where prior information is only available as an algorithm that samples the prior probability density. Once a collection of models sampled according to the posterior is available, it is possible to estimate, not only posterior model parameter covariances, but also resolution measures that are more useful in many applications. For example, posterior probabilities of the existence of interesting Earth structures like discontinuities and flow patterns can be estimated. These extended possibilities for resolution analysis may also provide new insight into problems that are usually treated by means of analytical methods.
TL;DR: It is demonstrated that the recently proposed pruned‐enriched Rosenbluth method (PERM) leads to extremely efficient algorithms for the folding of simple model proteins and gives detailed information about the thermal spectrum and thus allows one to analyze thermodynamic aspects of the folding behavior of arbitrary sequences.
Abstract: We demonstrate that the recently proposed pruned-enriched Rosenbluth method (PERM) (Grassberger, Phys. Rev. E 56:3682, 1997) leads to extremely efficient algorithms for the folding of simple model proteins. We test it on several models for lattice heteropolymers, and compare it to published Monte Carlo studies of the properties of particular sequences. In all cases our method is faster than the previous ones, and in several cases we find new minimal energy states. In addition to producing more reliable candidates for ground states, our method gives detailed information about the thermal spectrum and thus allows one to analyze thermodynamic aspects of the folding behavior of arbitrary sequences. Proteins 32:52–66, 1998. © 1998 Wiley-Liss, Inc.
TL;DR: In this article, an efficient path-integral quantum Monte Carlo algorithm for the lattice polaron is presented, based on Feynman's integration of phonons and subsequent simulation of the resulting singleparticle self-interacting system.
Abstract: An efficient continuous-time path-integral quantum Monte Carlo algorithm for the lattice polaron is presented. It is based on Feynman's integration of phonons and subsequent simulation of the resulting single-particle self-interacting system. The method is free from the finite-size and finite-time-step errors and works in any dimensionality and for any range of electron-phonon interaction. The ground-state energy and effective mass of the polaron are calculated for several models. The polaron spectrum can be measured directly by Monte Carlo, which is of general interest.
TL;DR: In this paper, a new approach to cluster simulation is developed in the context of nucleation theory, which preferentially and automatically generates the physical clusters, defined as the density fluctuations that lead to nucleation, and determines their equilibrium distribution.
Abstract: A new approach to cluster simulation is developed in the context of nucleation theory. This approach is free of any arbitrariness involved in the definition of a cluster. Instead, it preferentially and automatically generates the physical clusters, defined as the density fluctuations that lead to nucleation, and determines their equilibrium distribution in a single simulation, thereby completely bypassing the computationally expensive free energy evaluation that is necessary in a conventional approach. The validity of the method is demonstrated for a single component system using a model potential for water under several values of supersaturation.
TL;DR: It is demonstrated that the recently proposed pruned-enriched Rosenbluth method (PERM) leads to extremely efficient algorithms for the folding of simple model proteins and gives detailed information about the thermal spectrum and thus allows one to analyze thermodynamic aspects of the folding behavior of arbitrary sequences.
Abstract: We demonstrate that the recently introduced pruned-enriched Rosenbluth method leads to extremely efficient algorithms for the folding of simple model proteins. We test them on several models for lattice heteropolymers, and compare the results to published Monte Carlo studies. In all cases our algorithms are faster than previous ones, and in several cases we find new minimal energy states. In addition, our algorithms give estimates for the partition sum at finite temperatures.
TL;DR: This work presents a C++ Monte Carlo class library for the automatic parallelization of Monte Carlo simulations and discusses the advantages of object-oriented design in the development of this library.
Abstract: We discuss the parallelization and object-oriented implementation of Monte Carlo simulations for physical problems We present a C++ Monte Carlo class library for the automatic parallelization of Monte Carlo simulations Besides discussing the advantages of object-oriented design in the development of this library, we show examples how C++ template techniques have allowed very generic but still optimal algorithms to be implemented for wide classes of problems These parallel and object-oriented codes have allowed us to perform the largest quantum Monte Carlo simulations ever done in condensed matter physics
01 Apr 1998
TL;DR: In this paper, the authors focus on two aspects: (i) Opinions about the optimal choice of weights, and (ii) Recursive weight factor estimates for Monte Carlo simulations of many systems.
Abstract: Monte Carlo (MC) simulations of many systems, can be considerably speeded up by using multicanonical or related methods. I shall focus on two aspects: (i) Opinions about the optimal choice of weights. (ii) Recursive weight factor estimates.
TL;DR: In this article, a combination of the coupling constant integration technique and the quantum Monte Carlo method is used to investigate the most relevant quantities in Kohn-Sham density-functional theory.
Abstract: A combination of the coupling constant integration technique and the quantum Monte Carlo method is used to investigate the most relevant quantities in Kohn-Sham density-functional theory. Variational quantum Monte Carlo is used to construct realistic many-body wave functions for diamond-structure silicon at different values of the Coulomb coupling constant. The exchange-correlation energy density along with the coupling constant dependence and the coupling-constant-integrated form of the pair-correlation function, the exchangecorrelation hole, and the exchange-correlation energy are presented. Comparisons of these functions are made with results obtained from the local-density approximation, the average density approximation, the weighted density approximation, and the generalized gradient approximation. We discuss reasons for the success of the local-density approximation. The insights provided by this approach will make it possible to carry out stringent tests of the effectiveness of exchange-correlation functionals and in the long term aid in the search for better functionals. @S0163-1829~98!02115-8#