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Results for “Monte Carlo Method”

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PubMed1991

A Monte Carlo method for Bayesian inference in frailty models.

Many analyses in epidemiological and prognostic studies and in studies of event history data require methods that allow for unobserved covariates or "frailties." Clayton and Cuzick (1985, Journal of the Royal Statistical Society, Series A 148, 82-117) proposed a generalization of the proportional hazards model that implemented such random effects, but the proof of the asymptotic properties of the method remains elusive, and practical experience suggests that the likelihoods may be markedly nonquadratic. This paper sets out a Bayesian representation of the model in the spirit of Kalbfleisch (1978, Journal of the Royal Statistical Society, Series B 40, 214-221) and discusses inference using Monte Carlo methods.

Algorithms↗

PubMed1993

A Monte Carlo method for conformational analysis of saccharides.

A Metropolis Monte Carlo (MMC) algorithm was applied to explore conformational spaces spanned by the exocyclic dihedral angles of four disaccharides alpha-D-Man(1-->3)-alpha-D-Man(1-->O)Me (1), alpha-D-Man(1-->2)-alpha-D-Man(1-->O)Me (2), methyl beta-cellobioside (3), and methyl beta-maltoside (4). The simulation method uses the HSEA force field and randomly samples the conformational space with an automatic preference for low-energy states. In comparison to a systematic grid search, MMC offers a much more convenient and efficient protocol for the computation of ensemble average values of experimentally accessible NMR parameters such as NOE effects or 3J coupling constants. Energy barriers of a few kcal/mol were found to be surmounted easily when running the simulations with the temperature parameter set at room temperature, whereas passing significantly higher barriers required elevated temperature parameters. Ensemble average NOE values were calculated using the MMC technique and a conventional systematic grid search showing that the MMC method adequately samples the conformational spaces of 1-4. Theoretical NOEs derived for global or local minimum conformations are different from ensemble average values, and it is shown that averaged NOEs agree significantly better with experimental data. Ensemble average NOEs for 1 derived from MMC/HSEA, and previously reported MM2CARB and AMBER calculations all showed good agreement with experimental data, with MMC/HSEA giving the closest fit.

Algorithms↗

PubMed2005

Multi-Monte Carlo method for coagulation and condensation/evaporation in dispersed systems.

A new multi-Monte Carlo (MMC) method is promoted to consider general dynamic equation (GDE) for particle coagulation and condensation/evaporation. MMC method introduces the concept of a "weighted fictitious particle" and is based on time-driven Monte Carlo technique, constant number of fictitious particles technique, and constant volume technique. MMC method for independent coagulation, for independent condensation/evaporation, and for simultaneous coagulation and condensation/evaporation are validated by some special cases in which analytical solutions exist, in which numerical results agree with corresponding analytical solutions well. Furthermore, the computation cost of MMC method is low enough to be applied in engineering computation and general scientific quantitative analysis.

Journal Article↗

PubMed2005

Proton therapy analysis using the Monte Carlo method.

The range and straggling data obtained from the transport of ions in matter (TRIM) computer program were used to determine the trajectories of monoenergetic 60 MeV protons in muscle tissue by using the Monte Carlo technique. The appropriate profile for the shape of a proton pencil beam in proton therapy as well as the dose deposited in the tissue were computed. The good agreements between our results as compared with the corresponding experimental values are presented here to show the reliability of our Monte Carlo method.

Algorithms↗

PubMedDate not supplied

Cascade summing corrections for HPGe spectrometers by the Monte Carlo method.

Cascade summing corrections for application in HPGe gamma ray spectrometry have been calculated numerically by the Monte Carlo method. An algorithm has been developed which follows the path in the decay scheme from the starting state at the precursor radionuclide decay level, down to the ground state of the daughter radionuclide. With this procedure, it was possible to calculate the cascade summing correction for all gamma ray transitions present in the decay scheme. Since the cascade correction requires the values of peak and total detection efficiencies, another code has been developed in order to estimate these parameters for point and cylindrical sources. The radionuclides 60Co, 133Ba and 131I were used for testing the procedure. The results were in good agreement with values in the literature.

Journal Article↗

PubMed2006

The use of a Monte Carlo method for uncertainty calculation, with an application to the measurement of neutron ambient dose equivalent rate.

This paper is concerned with the use of a Monte Carlo method for uncertainty calculation as an implementation of the propagation of distributions. It reviews the basic principles of the propagation of distributions and numerical aspects of a Monte Carlo implementation. It also discusses the possible advantages in some circumstances of the propagation of distributions over the GUM uncertainty framework, and how the results obtained in any particular instance can be compared with those provided by that framework. To illustrate these various aspects, an application to the measurement of neutron dose equivalent rate is given. A key consideration in this application is the manner in which the dominant source of uncertainty, namely that associated with the field-specific correction factor, is treated. The information available concerning this factor constitutes the correction factors for a set of fields of the same type as that in which a measurement is being made. This information is encoded as a probability density function (PDF) for the correction factor. This PDF constitutes an input to both methods of evaluation.

Anisotropy↗

PubMed1997

The study of the stability of Watson-Crick nucleic acid base pairs in water and dimethyl sulfoxide: computer simulation by the Monte Carlo method.

An extensive computer simulation of nucleic acid bases and Watson-Crick base pairs in a water cluster and DMSO cluster is performed by the Monte Carlo method. It is demonstrated that the unfavorable energetics of pair formation in a water cluster is determined by the significant destabilizing contribution of solvent to the energy of complex formation. It is shown that the formation of coplanar base pairs in a DMSO cluster is favorable. The DMSO cluster stabilizes A-U and A-T base pairs and the insignificant destabilization of the G-C base pair by a DMSO cluster is much less than the stabilization which occurs due to the attraction between bases.

Base Composition↗

PubMed2005

A scalable parallel Monte Carlo method for free energy simulations of molecular systems.

We present a method of parallelizing flat histogram Monte Carlo simulations, which give the free energy of a molecular system as an output. In the serial version, a constant probability distribution, as a function of any system parameter, is calculated by updating an external potential that is added to the system Hamiltonian. This external potential is related to the free energy. In the parallel implementation, the simulation is distributed on to different processors. With regular intervals the modifying potential is summed over all processors and distributed back to every processor, thus spreading the information of which parts of parameter space have been explored. This implementation is shown to decrease the execution time linearly with added number of processors.

Computer Simulation↗

PubMed1998

New developments of the electrostatically driven Monte Carlo method: test on the membrane-bound portion of melittin.

The electrostatically driven Monte Carlo (EDMC) method has been greatly improved by adding a series of new features, including a procedure for cluster analysis of the accepted conformations. This information is used to guide the search for the global energy minimum. Alternative procedures for generating perturbed conformations to sample the conformational space were also included. These procedures enhance the efficiency of the method by generating a larger number of low-energy conformations. The improved EDMC method has been used to explore the conformational space of a 20-residue polypeptide chain whose sequence corresponds to the membrane-bound portion of melittin. The ECEPP/3 (Empirical Conformational Energy Program for Peptides) algorithm was used to describe the conformational energy of the chain. After an exhaustive search involving 14 independent runs, the lowest energy conformation (LEC) (-91.0 kcal/mol) of the entire study was encountered in four of the runs, while conformations higher in energy by no more than 1.8 kcal/mol were found in the remaining runs with the exception of one of them (run 8). The LEC is identical to the conformation found recently by J. Lee, H. A. Scheraga, and S. Rackovsky [(1988) "Conformational Analysis of the 20-Residue Membrane-Bound Portion of Melittin by Conformational Space Annealing," Biopolymers, Vol. 46, pp. 103-115] as the lowest energy conformation obtained in their study using the conformational space annealing method. These results suggest that this conformation corresponds to the global energy minimum of the ECEPP/3 potential function for this specific sequence: it also appears to be the conformation of lowest free energy.

Amino Acid Sequence↗

PubMed1998

Correction factors for the NMi free-air ionization chamber for medium-energy x-rays calculated with the Monte Carlo method.

A new method is described for the determination of x-ray quality dependent correction factors for free-air ionization chambers. The method is based on weighting correction factors for mono-energetic photons, which are calculated using the Monte Carlo method, with measured air kerma spectra. With this method, correction factors for electron loss, scatter inside the chamber and transmission through the diaphragm and front wall have been calculated for the NMi free-air chamber for medium-energy x-rays for a wide range of x-ray qualities in use at NMi. The newly obtained correction factors were compared with the values in use at present, which are based on interpolation of experimental data for a specific set of x-ray qualities. For x-ray qualities which are similar to this specific set, the agreement between the correction factors determined with the new method and those based on the experimental data is better than 0.1%, except for heavily filtered x-rays generated at 250 kV. For x-ray qualities dissimilar to the specific set, differences up to 0.4% exist, which can be explained by uncertainties in the interpolation procedure of the experimental data. Since the new method does not depend on experimental data for a specific set of x-ray qualities, the new method allows for a more flexible use of the free-air chamber as a primary standard for air kerma for any x-ray quality in the medium-energy x-ray range.

Air↗

PubMed2001

Quantum Monte Carlo method for attractive Coulomb potentials.

Starting from an exact lower bound on the imaginary-time propagator, we present a path-integral quantum Monte Carlo method that can handle singular attractive potentials. We illustrate the basic ideas of this quantum Monte Carlo algorithm by simulating the ground state of hydrogen and helium.

Journal Article↗

PubMed2002

Hybrid monte carlo method for simulation of two-component aerosol coagulation and phase segregation.

The paper presents the development of a hybrid Monte Carlo (MC) method for the simulation of the simultaneous coagulation and phase segregation of an immiscible two-component binary aerosol. The model is intended to qualitatively model our prior studies of the synthesis of mixed metal oxides for which phase-segregated domains have been observed in molten nanodroplets. In our previous works (J. Aerosol Sci.32, 1479 (2001); Chem. Eng. Sci.56, 5763 (2001); submitted for publication) we developed sectional and monodisperse models where the internal state of the aerosol particles was described. These methods have certain limitations and it is difficult to include additional physical effects into the framework. Our new approach combines both constant volume and constant number Monte Carlo methods. Similar to our previous models, we assume that the phase segregation is kinetically controlled. The MC approach allows us to compute the mean number of enclosures (minor phase) per droplet, average enclosure volume, and the width of the enclosure size distribution. The results show that asymptotic behavior of enclosure distribution exists that is independent of initial conditions, which is very close to the continuum self-preserving distribution. Temperature is a key parameter because it allows for a significant change in the internal transport rate within each droplet. In particular, increasing the temperature significantly enhances the Brownian coagulation rate and lowers the number of enclosures per droplet. As a result, the MC results indicate that the growth of the minor phase can be moderated quite dramatically by small changes in system temperature. These results serve to illustrate the utility of this synthesis approach to the controlled growth of nanoparticles through the use of a majority matrix to slow down the encounter frequency of the minor phase and therefore its particle size.

Journal Article↗

PubMed2002

Parallel Monte Carlo methods for physical mapping of chromosomes.

Reconstructing a physical map of a chromosome from a genomic library presents a central computational problem in genetics. Physical map reconstruction in the presence of errors is a problem of high computational complexity. Parallel Monte Carlo methods for a maximum likelihood estimation-based approach to physical map reconstruction are presented. The estimation procedure entails gradient descent search for determining the optimal spacings between probes for a given probe ordering. The optimal probe ordering is determined using a simulated Monte Carlo algorithm. A two-tier parallelization strategy is proposed wherein the gradient descent search is parallelized at the lower level and the simulated Monte Carlo algorithm is simultaneously parallelized at the higher level. Implementation and experimental results on a network of shared-memory symmetric multiprocessors (SMPs) are presented.

Algorithms↗

PubMed1989

The multiple-minima problem in the conformational analysis of polypeptides. III. An electrostatically driven Monte Carlo method: tests on enkephalin.

The three-dimensional conformation of Met-enkephalin, corresponding to the lowest minimum of the empirical potential energy function ECEPP/2 (empirical conformational energy program for peptides), has been determined using a new algorithm, viz. the Electrostatically Driven Monte Carlo Method. This methodology assumes that a polypeptide or protein molecule is driven toward the native structure by the combined action of electrostatic interactions and stochastic conformational changes associated with thermal movements. These features are included in the algorithm that produces a Monte Carlo search in the conformational hyperspace of the polypeptide, using electrostatic predictions and a random sampling technique to locate low-energy conformations. In addition, we have incorporated an alternative mechanism that allows the structure to escape from some conformational regions representing metastable local energy minima and even from regions of the conformational space with great stability. In 33 test calculations on Met-enkephalin, starting from arbitrary or completely random conformations, the structure corresponding to the global energy minimum was found in all the cases analyzed, with a relatively small search of the conformational space. Some of these starting conformations were right or left-handed alpha-helices, characterized by good electrostatic interactions involving their backbone peptide dipoles; nevertheless, the procedure was able to convert such locally stable structures to the global-minimum conformation.

Electrochemistry↗

PubMed1992

The management of small abdominal aortic aneurysms: a computer simulation using Monte Carlo methods.

Many small abdominal aortic aneurysms can now be identified by ultrasound screening and it is necessary to decide whether the risks of enlargement and rupture justify elective surgery. A computer simulation of the behaviour of small aneurysms has been constructed using Monte Carlo methods to model patterns of enlargement and rupture. The effect of policy with regard to the observation and timing of intervention has been evaluated for different patient groups. The results demonstrate the value of early intervention in otherwise fit patients with expected operative mortality rates of 5% or below, whereas, for older patients (over 70 years old) 6-monthly screening and operation if the aneurysm exceeds 5 cm is suggested. Higher risk patients with expected operative mortality of over 10% may be better treated conservatively up to an aneurysm diameter of 7 or 8 cm. The method used for simulation is flexible, being easily adjusted to take account of new information, and may have applications in other areas of clinical decision making.

Aged↗

PubMed2005

A practical treatment for the three-body interactions in the transcorrelated variational Monte Carlo method: application to atoms from lithium to neon.

We suggest a practical solution to dealing with the three-body interactions in the transcorrelated variational Monte Carlo method (TC-VMC). In the TC-VMC method, which was suggested in our previous paper [N. Umezawa and S. Tsuneyuki, J. Chem. Phys. 119, 10015 (2003)], the Jastrow-Slater-type wave function is efficiently optimized through a self-consistent procedure by minimizing the variance of the local energy. The three-body terms in the transcorrelated self-consistent-field equation, which have been simply ignored in our previous works, are efficiently calculated by the Monte Carlo numerical integration. We found that our treatment for the three-body interactions is successful for atoms from Li to Ne.

Journal Article↗

PubMed2003

The use of a Monte Carlo method to calculate the average solid angle subtended by a detector to source in a non-parallel plane.

In a previous scientific note, a short computer program for a personal computer was described that calculated the average solid angle subtended by a circular or rectangular detector window to a circular or rectangular source in a parallel plane by a Monte Carlo method. This note describes the development of the program for conditions where the detector window is not parallel to the plane of the source, and in particular looks at a method of analysing orientations that relates straightforwardly to practical measurement.

Algorithms↗

PubMed2003

Nonideal gas flow and heat transfer in micro- and nanochannels using the direct simulation Monte Carlo method.

Subsonic nonideal gas flow and heat transfer in micro- and nanochannels for different Knudsen numbers are investigated numerically using the direct simulation Monte Carlo method modified with a consistent Boltzmann algorithm. The van der Waals equation is used as the equation of state. The collision rate is also modified based on the Enskog theory for dense gas. It is shown that the nonideal gas effect becomes significant when the gas becomes so dense that the ideal gas assumption breaks down. The results also show that the nonideal gas effect is dependent not only on the gas density, but also on the channel size. A higher gas density and a smaller channel size lead to a more significant nonideal gas effect. The nonideal gas effect also causes lower skin friction coefficients and different heat transfer flux distributions at the wall surface. The simulations presented in this work are helpful for a better understanding of micro- and nanoscale gas flows.

Journal Article↗