Showing papers on "Dynamic Monte Carlo method published in 1999"
TL;DR: In this paper, two new implementations of the EM algorithm are proposed for maximum likelihood fitting of generalized linear mixed models using random sampling to construct Monte Carlo approximations at the E-step.
Abstract: Summary. Two new implementations of the EM algorithm are proposed for maximum likelihood fitting of generalized linear mixed models. Both methods use random (independent and identically distributed) sampling to construct Monte Carlo approximations at the E-step. One approach involves generating random samples from the exact conditional distribution of the random effects (given the data) by rejection sampling, using the marginal distribution as a candidate. The second method uses a multivariate t importance sampling approximation. In many applications the two methods are complementary. Rejection sampling is more efficient when sample sizes are small, whereas importance sampling is better with larger sample sizes. Monte Carlo approximation using random samples allows the Monte Carlo error at each iteration to be assessed by using standard central limit theory combined with Taylor series methods. Specifically, we construct a sandwich variance estimate for the maximizer at each approximate E-step. This suggests a rule for automatically increasing the Monte Carlo sample size after iterations in which the true EM step is swamped by Monte Carlo error. In contrast, techniques for assessing Monte Carlo error have not been developed for use with alternative implementations of Monte Carlo EM algorithms utilizing Markov chain Monte Carlo E-step approximations. Three different data sets, including the infamous salamander data of McCullagh and Nelder, are used to illustrate the techniques and to compare them with the alternatives. The results show that the methods proposed can be considerably more efficient than those based on Markov chain Monte Carlo algorithms. However, the methods proposed may break down when the intractable integrals in the likelihood function are of high dimension.
585 citations
TL;DR: In this paper, a consistent two-step estimation procedure is proposed for a system of equations with limited dependent variables, and Monte Carlo simulation results suggest the procedure outperforms an existing two-stage method.
Abstract: A consistent two-step estimation procedure is proposed for a system of equations with limited dependent variables. Monte Carlo simulation results suggest the procedure outperforms an existing two-step method.
579 citations
TL;DR: This new version of VMC (now called XVMC) is more efficient than EGS4/PRESTA photon dose calculation by a factor of 15-20, so a standard treatment plan for photons can be calculated by Monte Carlo in about 20 min. on a "normal" personal computer.
Abstract: A new Monte Carlo algorithm for 3D photondose calculation in radiation therapy is presented, which is based on the previously developed Voxel Monte Carlo (VMC) for electron beams. The main result is that this new version of VMC (now called XVMC) is more efficient than EGS4/PRESTA photondose calculation by a factor of 15–20. Therefore, a standard treatment plan for photons can be calculated by Monte Carlo in about 20 min. on a “normal” personal computer. The improvement is caused mainly by the fast electron transport algorithm and ray tracing technique, and an initial ray tracing method to calculate the number of electrons created in each voxel by the primary photon beam. The model was tested in comparison to calculations by EGS4 using several fictive phantoms. In most cases a good coincidence has been found between both codes. Only within lung substitute dose differences have been observed.
354 citations
TL;DR: The effectiveness of the new generalized hyper-parallel tempering Monte Carlo simulation method is demonstrated by implementing it in a grand canonical ensemble for the Lennard-Jones fluid and the restricted primitive model.
Abstract: A new generalized hyper-parallel tempering Monte Carlo simulation method is presented. The method is particularly useful for simulation of many-molecule complex systems, where rough energy landscapes and inherently long characteristic relaxation times can pose formidable obstacles to effective sampling of relevant regions of configuration space. In this paper, we demonstrate the effectiveness of the new method by implementing it in a grand canonical ensemble for the Lennard-Jones fluid and the restricted primitive model. Coexistence curves and critical behavior have been explored by the new method. Our numerical results indicate that the new algorithm can be orders of magnitude more efficient than previously available techniques.
300 citations
TL;DR: In this article, a new biased Monte Carlo scheme was proposed to determine the crystal structures of zeolites from powder diffraction data, with success on all publicly known zeolite materials.
Abstract: We describe a new, biased Monte Carlo scheme to determine the crystal structures of zeolites from powder diffraction data. We test the method on all publicly known zeolite materials, with success in all cases. We show that the method of parallel tempering is a powerful supplement to the biased Monte Carlo.
282 citations
01 Jan 1999
TL;DR: In this paper, the authors present a round-trip tour from classical diffusion to quantum mechanics, with a focus on the application of Quantum Monte Carlo in nuclear physics and its application to Doped Fullerides.
Abstract: Preface. 1. Basics, Quantum Monte Carlo and Statistical Mechanics M.P. Nightingale. 2. Stochastic Diagonalization H. de Raedt, et al. 3. World-Line Quantum Monte Carlo R.T. Scalettar. 4. Variational Monte Carlo in Solids S. Fahy. 5. Variational Monte Carlo Basics and Applications to Atoms and Molecules C.J. Umrigar. 6. Calculations of Exchange Frequencies with Path Integral Monte Carlo: Solid 3He Adsorbed on Graphite B. Bernu, D. Ceperley. 7. Static Response of Homogeneous Quantum Fluids by Diffusion Monte Carlo G. Senatore, et al. 8. Equilibrium and Dynamical Path Integral Methods: An Introduction J.D. Doll, et al. 9. Diffusion Monte Carlo L. Mitas. 10. Fermion Monte Carlo M.H. Kalos, F. Pederiva. 11. Quantum Monte Carlo in Nuclear Physics J. Carlson. 12. Reputation Quantum Monte Carlo: A Round-Trip Tour from Classical Diffusion to Quantum Mechanics S. Baroni, S. Moroni. 13. Quantum Monte Carlo for Lattice Fermions A. Muramatsu. 14. Phase Separation in the 2D Hubbard Model: A Challenging Application of Fixed-Node QMC G.B. Bachelet, A.C. Cosentini. 15. Constrained Path Monte Carlo for Fermions Shiwei Zhang. 16. Serial and Parallel Random Number Generation M. Mascagni. 17. Fixed-Node DMC for Fermions on a Lattice: Application to Doped Fullerides E. Koch, et al. 18. Index.
277 citations
TL;DR: In this article, the recently introduced end-bridging (EB) Monte Carlo move is revisited, and a thorough analysis of its geometric formulation and numerical implementation is given, along with detailed results from applying the move along with concerted rotation, in atomistic simulations of polyethylene (PE) melt systems with mean molecular lengths ranging from C78 up to C500, flat molecular weight distributions, and polydispersity indices I ranging from 1.02 to 1.12.
Abstract: The recently introduced end-bridging (EB) Monte Carlo move is revisited, and a thorough analysis of its geometric formulation and numerical implementation is given. Detailed results are presented from applying the move, along with concerted rotation, in atomistic simulations of polyethylene (PE) melt systems with mean molecular lengths ranging from C78 up to C500, flat molecular weight distributions, and polydispersity indices I ranging from 1.02 to 1.12. To avoid finite system-size effects, most simulations are executed in a superbox containing up to 5000 mers and special neighbor list strategies are implemented. For all chain lengths considered, excellent equilibration is observed of the thermodynamic and conformational properties of the melt at all length scales, from the level of the bond length to the level of the chain end-to-end vector. In sharp contrast, if no end bridging is allowed among the Monte Carlo moves, no equilibration is achieved, even for the C78 system. The polydispersity index I is f...
226 citations
TL;DR: The proof show that sequential updating schemes are correct, but also it establishes the correctness of a whole class of new methods that simply leave the Boltzmann distribution invariant.
Abstract: Detailed balance is an overly strict condition to ensure a valid Monte Carlo simulation. We show that, under fairly general assumptions, a Monte Carlo simulation need satisfy only the weaker balance condition. Not only does our proof show that sequential updating schemes are correct, but also it establishes the correctness of a whole class of new methods that simply leave the Boltzmann distribution invariant.
186 citations
TL;DR: In this article, a new stochastic method for calculating ground-state properties of quantum systems is introduced, where segments of a Langevin random walk guided by a trial wave function are subject to a Metropolis rejection test performed on the time integral of the local energy.
Abstract: We introduce a new stochastic method for calculating ground-state properties of quantum systems. Segments of a Langevin random walk guided by a trial wave function are subject to a Metropolis rejection test performed on the time integral of the local energy. The algorithm\char22{}which is as simple as variational Monte Carlo\char22{}for bosons provides exact expectation values of local observables, as well as their static and dynamic (in imaginary time) response functions, without mixed-estimate nor population-control biases. Our method is demonstrated with a few case applications to ${}^{4}\mathrm{He}$.
185 citations
TL;DR: In this paper, the authors present a general approach to greatly increase at little cost the efficiency of Monte Carlo algorithms by associating a renormalized observable (improved estimator) having the same average but a different variance.
Abstract: We present a general approach to greatly increase at little cost the efficiency of Monte Carlo algorithms. To each observable to be computed we associate a renormalized observable (improved estimator) having the same average but a different variance. By writing down the zero-variance condition a fundamental equation determining the optimal choice for the renormalized observable is derived (zero-variance principle for each observable separately). We show, with several examples including classical and quantum Monte Carlo calculations, that the method can be very powerful.
161 citations
TL;DR: In this paper, configurational-bias Monte Carlo sampling techniques have been developed which overcome the difficulties of sampling configuration space efficiently for all-atom molecular models and for branched species represented with united atom models.
Abstract: Configurational-bias Monte Carlo sampling techniques have been developed which overcome the difficulties of sampling configuration space efficiently for all-atom molecular models and for branched species represented with united atom models. Implementation details of this sampling scheme are discussed. The accuracy of a united atom forcefield with non-bond parameters optimized for zeolite adsorption and a widely used all-atom forcefield are evaluated by comparison with experimental sorption isotherms of linear and branched hydrocarbons.
TL;DR: In this paper, a quantum Monte Carlo method for tensor and other spin interactions such as those that are commonly encountered in nuclear structure calculations is described. But the main ingredients are a Hubbard-Stratonovich transformation to uncouple the spin degrees of freedom along with a fixed node approximation to maintain stability.
TL;DR: In this article, a molecular simulation study of freezing transitions for simple fluids in narrow slit pores was performed using the grand canonical Monte Carlo simulation method, which indicated a first order fluid to solid transition.
Abstract: We report a molecular simulation study of freezing transitions for simple fluids in narrow slit pores. A major stumbling block in previous studies of freezing in pores has been the lack of any method for calculating the free energy difference between the confined solid and liquid phases. Conventional thermodynamic integration methods often fail for confined systems, due to the difficulty in choosing a suitable path of integration. We use a different approach that involves calculating the Landau free energy as a function of a suitable order parameter, using the grand canonical Monte Carlo simulation method. The grand free energy for each phase can then be obtained by one-dimensional integration of the Landau free energy over the order parameter. These calculations are carried out for two types of wall—fluid interaction, a hard wall and a strongly attractive wall modelled on carbon. The grand free energy results for both cases clearly indicate a first order fluid to solid transition. In the case of the attr...
TL;DR: In this article, an induced dynamics in the space of energy of single-spin-flip Monte Carlo algorithm was studied and the relaxation times were shown to have relaxation times proportional to the specific heat.
Abstract: We study an induced dynamics in the space of energy of single-spin-flip Monte Carlo algorithm. The method gives an efficient reweighting technique. This dynamics is shown to have relaxation times proportional to the specific heat. From this we argue for a logarithmic factor in the correlation time of the standard 2D Ising local dynamics.
TL;DR: In this paper, an extended version of the 3D Monte Carlo edge plasma transport code EMC3 including more complex physics is presented, and the balance equations for mass, momentum and energies are formulated in a general conservation form suited for direct application of the Monte Carlo solving algorithm.
TL;DR: New intermolecular potential models for benzene and cyclohexane have been developed, parameterized to the vapor–liquid coexistence properties, utilizing the Buckingham exponential-6 potential to describe nonbonded interactions.
Abstract: New intermolecular potential models for benzene and cyclohexane have been developed, parameterized to the vapor–liquid coexistence properties. The models utilize the Buckingham exponential-6 potential to describe nonbonded interactions. Histograms reweighting grand canonical Monte Carlo methods were used to obtain the model parameters. A new algorithm for insertion of molecules with complex molecular architectures or stiff intramolecular constraints has been developed. The algorithm is based on the creation of a reservoir of ideal chains from which structures are selected for insertion during a simulation run. The new potential models reproduce the experimental saturated liquid densities and vapor pressures to within average absolute deviations of 0.3% and 2.2%, respectively. Critical parameters are also in good agreement with experiment. The infinite dilution behavior of these two cyclic molecules in water was studied. A combination of Widom insertion and expanded ensemble techniques were used to determine the Henry’s law constant of benzene and cyclohexane in water. The results obtained have qualitatively correct temperature dependence. However, the Henry’s constant of benzene in water is overestimated and that of cyclohexane is underestimated at all temperatures by approximately a factor of 3.
TL;DR: In this paper, a diffusion Monte Carlo method was used to calculate the lowest energy state of a uniform gas of bosons interacting through different model potentials, both strictly repulsive and with an attractive well.
Abstract: We use a diffusion Monte Carlo method to calculate the lowest-energy state of a uniform gas of bosons interacting through different model potentials, both strictly repulsive and with an attractive well. We explicitly verify that at low density the energy per particle follows a universal behavior fixed by the gas parameter ${\mathrm{na}}^{3}.$ In the regime of densities typical for experiments in trapped Bose-condensed gases, the corrections to the mean-field energy greatly exceed the differences due to the details of the potential.
TL;DR: Incremental estimation of the reduction in variance, in conjunction with statistical normalization of interpixel color distances, yields an energy-preserving algorithm that converges to a spatially nonconstant steady state.
Abstract: Monte Carlo sampling can be used to estimate solutions to global light transport and other rendering problems. However, a large number of observations may be needed to reduce the variance to acceptable levels. Rather than computing more observations within each pixel, if spatial coherence exists in image space it can be used to reduce visual error by averaging estimators in adjacent pixels. Anisotropic diffusion is a space-variant noise reduction technique that can selectively preserve texture, edges, and other details using a map of image coherence. The coherence map can be estimated from depth and normal information as well as interpixel color distance. Incremental estimation of the reduction in variance, in conjunction with statistical normalization of interpixel color distances, yields an energy-preserving algorithm that converges to a spatially nonconstant steady state.
TL;DR: In this article, a new method for employed electron-electron (e-e) and electron-ion (ei) interactions in Monte Carlo particle based simulators is presented.
Abstract: A new method for employed electron-electron (e-e) and electron-ion (e-i) interactions in Monte Carlo particle based simulators is presented. By using a corrected Coulomb force in conjunction with a proper cutoff range, the "double" counting of the long range interaction is eliminated while reducing the simulation time for molecular dynamics by a factor of 1000. The proposed method naturally incorporated the multi-ion contributions, local distortions in the scattering potential due to the movement of the free charges, and carrier-density fluctuations. The doping dependence of the low-field mobility obtained from three-dimensional (3-D) resistor simulation closely follows experimental results, thus proving the correctness of the proposed approach.
TL;DR: An optimal algorithm is developed on the basis of a multigrid variance reduction technique that attains a higher convergence rate than any deterministic algorithm and also higher than that of previously developed Monte Carlo algorithms for parametric integration.
TL;DR: In this article, Monte Carlo energy and variance minimization techniques for optimizing many-body wave functions were investigated, including limiting the variations in the weighting factors that arise in correlated sampling estimations of the energy and its variance.
Abstract: We investigate Monte Carlo energy and variance-minimization techniques for optimizing many-body wave functions. Several variants of the basic techniques are studied, including limiting the variations in the weighting factors that arise in correlated sampling estimations of the energy and its variance. We investigate the numerical stability of the techniques and identify two reasons why variance minimization exhibits superior numerical stability to energy minimization. The characteristics of each method are studied using a noninteracting 64-electron model of crystalline silicon. While our main interest is in solid-state systems, the issues investigated are relevant to Monte Carlo studies of atoms, molecules, and solids. We identify a robust and efficient variance-minimization scheme for optimizing wave functions for large systems.
TL;DR: In this article, a Monte Carlo study of the two-component 4 model on the simple cubic lattice in three dimensions was presented, where suitable tuning of the coupling constant was found to eliminate leading-order corrections to scaling.
Abstract: We present a Monte Carlo study of the two-component 4 model on the simple cubic lattice in three dimensions By suitable tuning of the coupling constant, , we eliminate leading-order corrections to scaling High-statistics simulations using finite-size scaling techniques yield = 06723(3)[8] and = 00381(2)[2], where the statistical and systematical errors are given in the first and second bracket, respectively These results are more precise than any previous theoretical estimate of the critical exponents for the 3D XY universality class
TL;DR: In this article, the n/v-Stillinger cluster was applied to the condensation of supersaturated argon vapor, in a preliminary calculation of the rate of nucleation for a single set of conditions (temperature=85 K, pressure=2500 Torr).
Abstract: The molecular theory of the homogeneous nucleation rate based on the n/v-Stillinger cluster, and developed in the preceding paper (paper I), is applied to the condensation of supersaturated argon vapor, in a preliminary calculation of the rate of nucleation for a single set of conditions (temperature=85 K, pressure=2500 Torr). Free energies are obtained by means of Monte Carlo simulation. Upper and lower bounds differing by only two orders of magnitude are obtained. Since the best current measurements of vapor phase nucleation rates are accurate to within about a single order of magnitude, this result is considered promising. The direction of future work to improve the accuracy of the predicted rate is clear, and considerable improvement should be possible. These directions are discussed in the paper. Also, the essentially non ad hoc nature of the n/v-Stillinger cluster is demonstrated by the appearance of a range of connectivity distances (in a predicted location) within which the calculated nucleation r...
TL;DR: It is demonstrated that stochastic global optimization algorithms of the first order, i.e., with local minimization after each iteration (e.g., Monte Carlo-Minimization), have a greater chance of finding the global minimum after a fixed number of function evaluations.
TL;DR: A Monte Carlo based inverse treatment planning system (MCI) has been developed which combines arguably the most accurate dose calculation method (Monte Carlo particle transport) with a 'guaranteed' optimization method (simulated annealing).
Abstract: A Monte Carlo-based inverse treatment planning system (MCI) has been developed which combines arguably the most accurate dose calculation method (Monte Carlo particle transport) with a `guaranteed' optimization method (simulated annealing). A distribution of photons is specified in the tumour volume; they are transported using an adjoint calculation method to outside the patient surface to build up an intensity distribution. This intensity distribution is used as the initial input into an optimization algorithm. The dose distribution from each beam element from a number of fields is pre-calculated using Monte Carlo transport. Simulated annealing optimization is then used to find the weighting of each beam element, to yield the optimal dose distribution for the given criteria and constraints. MCI plans have been generated in various theoretical phantoms and patient geometries. These plans show conformation of the dose to the target volume and avoidance of critical structures. To verify the code, an experiment was performed on an anthropomorphic phantom.
TL;DR: In this paper, the formation free energy of clusters in a supersaturated vapor is obtained by a constrained Monte Carlo technique, where the key feature is to set an upper limit to the size of cluster, which serves essentially as an extra thermodynamic variable that constrains the system.
Abstract: The formation free energy of clusters in a supersaturated vapor is obtained by a constrained Monte Carlo technique. A key feature of this approach is to set an upper limit to the size of cluster. This maximum cluster size serves essentially as an extra thermodynamic variable that constrains the system. As a result, clusters larger than the critical cluster of nucleation in the supersaturated vapor can no longer grow beyond the limiting size. Like changing the overall density of the system, changing the maximum cluster size also results in a different supersaturation and thereby a different formation free energy. However, at the same supersaturation and temperature it is found that the formation free energy has a unique value, independent of the upper limit of cluster size. The predicted size of critical cluster of nucleation is found to be consistent with the nucleation theorem as well as previous results using different simulation approaches.
TL;DR: In this article, a particle number reprojection method in the shell model Monte Carlo was introduced to calculate nuclear level densities in the complete (pf+g{sub 9/2}) -shell using a good-sign Hamiltonian.
Abstract: We introduce a particle-number reprojection method in the shell model Monte Carlo that enables the calculation of observables for a series of nuclei using a Monte Carlo sampling for a single nucleus. The method is applied to calculate nuclear level densities in the complete (pf+g{sub 9/2}) -shell using a good-sign Hamiltonian. Level densities of odd-A and odd-odd nuclei are reliably extracted despite an additional sign problem. Both the mass and the T{sub z} dependence of the experimental level densities are well described without any adjustable parameters. The odd-even staggering observed in the calculated backshift parameter follows the experimental data more closely than do empirical formulas. (c) 1999 The American Physical Society.
TL;DR: A new method, the analytical rebridging scheme, is presented, for Monte Carlo simulation of proline-containing, cyclic peptides, which achieves effective equilibration and agrees well with experimental data in all cases.
Abstract: We present a new method, the analytical rebridging scheme, for Monte Carlo simulation of proline-containing, cyclic peptides. The cis/trans isomerization is accommodated by allowing for two states of the amide bond. We apply our method to five peptides that have previously been characterized by nuclear magnetic resonance methods. Our simulations achieve effective equilibration and agree well with experimental data in all cases. We discuss the importance of effective equilibration as well as the role of bond flexibility and solvent effects in the prediction of equilibrium properties.
TL;DR: In this article, a Monte Carlo simulation of a three-dimensional Heisenberg model with a finite uniaxial anisotropy was used to study the crossover from coherent rotation to nucleation.