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Results for “Monte Carlo Method”

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PubMed2006

Efficiency of rejection-free dynamic Monte Carlo methods for homogeneous spin models, hard disk systems, and hard sphere systems.

We construct asymptotic arguments for the relative efficiency of rejection-free Monte Carlo (MC) methods compared to the standard MC method. We find that the efficiency is proportional to exp(constbeta) in the Ising, sqrt[beta] in the classical XY, and beta in the classical Heisenberg spin systems with inverse temperature beta, regardless of the dimension. The efficiency in hard particle systems is also obtained, and found to be proportional to (rho(cp)-rho)(-d) with the closest packing density rho(cp), density rho, and dimension d of the systems. We construct and implement a rejection-free Monte Carlo method for the hard-disk system. The RFMC has a greater computational efficiency at high densities, and the density dependence of the efficiency is as predicted by our arguments.

Journal Article↗

PubMed1997

Protein-nucleic acid recognition: simulation of base and "model" amino acids complexes in DMSO by the Monte Carlo method.

A computer simulation of guanine (G), cytosine (C), the G-C base pair, protonated C (CH+), acetic acid in neutral (AcOH) and deprotonated (AcO-) forms, G-AcO-, C-AcOH, and CH(+)-AcO- complexes, solvated in DMSO was carried out by the Monte Carlo method. It is shown that the G-C base pair formation in DMSO is energetically favorable. The G-AcO- complex formation is comparable with the formation of G-C base pair in energetically favorability. In this case the acetate anion can replace C in the G-C base pair. The formation of the C-AcOH complex is much less favorable than the formation of the G-C pair. However proton transfer from AcOH to C leads to the formation of the CH(+)-AcO- complex, which is the most favorable of all complexes studied. Here the acetic acid can replace G in a G-C base pair. The formation of G-AcO- and CH(+)-AcO- specific complexes detected in DMSO with the help of experiment and theory is a competitive process with respect to the formation of G-C base pairs, and can be considered the primary step in the real mechanism of protein-nucleic acid recognition.

Amino Acids↗

PubMed1996

Interpretation of pooling experiments using the Markov chain Monte Carlo method.

This paper describes an effective method for extracting as much information as possible from pooling experiments for library screening. Pools are collections of clones, and screening a pool with a probe determines whether any of these clones are positive for the probe. The results of the pool screenings are interpreted, or decoded, to infer which clones are candidates to be positive. These candidate positives are subjected to confirmatory testing. Decoding the pool screening results is complicated by the presence of errors, which typically lead to ambiguities in the inference of positive clones. However, in many applications there are reasonable models for the prior distributions for positives and for errors, and Bayes inference is the preferred method for ranking candidate positives. Because of the combinatoric complexity of the Bayes formulation, we implemented a decoding algorithm using a Markov chain Monte Carlo method. The algorithm was used in screening a library with 1298 clones using 47 pools. We corroborated the posterior probabilities for positives with results from confirmatory screening. We also simulated the screening of a 10-fold coverage library of 33,000 clones using 253 pools. The use of our algorithm, effective under conditions where combinatorial decoding techniques are imprudent, allows the use of fewer pools and also introduces needed robustness.

Algorithms↗

PubMed2005

Imaginary-chemical-potential quantum Monte Carlo method for Hubbard molecules.

We generalize the imaginary-chemical-potential quantum Monte Carlo (QMC) method proposed by Dagotto [Phys. Rev. B 41, R811 (1990)] to systems without particle-hole symmetry. The generalized method is tested by comparing the results of the QMC simulations and exact diagonalization on small Hubbard molecules, such as tetrahedron and truncated tetrahedron. Results of the application of the method to the C60 Hubbard molecule are discussed.

Journal Article↗

PubMedDate not supplied

[Study of the hydration characteristics of nucleic acid bases and their complementary pairs using the Monte-Carlo method].

To elucidate the role of certain atomic groups in the formation of the nucleic acid hydrate shell, we simulated the systems involving a base or a complementary pair (the base molecules are methylated in N9 of purines and in N1 of pyrimidines) and 25 water molecules using the Monte-Carlo method. All hydrophilic centers, except for N1 purines and N3 pyrimidines in complementary pairs, form hydrogen bonds (H-bonds) with water molecules. The mean numbers of H-bonds formed by different centers, and distributions of the geometric characteristics of these bonds, which appeared similar to those in crystals, have been calculated. The formation of bridges of one, two of three water molecules between hydrophilic centers was shown. The probabilities of formation of these bridges have been calculated.

DNA↗

PubMed1999

Relativistic calculations using Monte Carlo methods: one-electron systems.

Variance minimization and Monte Carlo integration are used to evaluate the four-component Dirac equation for a number of one-electron atomic and diatomic systems. This combination produces accurate energies, is relatively simple to implement, and exhibits few of the problems associated with traditional techniques.

Journal Article↗

PubMed2005

Calculation of the entropy and free energy by the hypothetical scanning Monte Carlo method: application to peptides.

A new approach, the hypothetical scanning Monte Carlo (HSMC), for calculating the absolute entropy, S, and free energy, F, has been introduced recently and applied first to fluids (argon and water) and later to peptides. In this paper the method is further developed for peptide chains in vacuum. S is calculated from a given MC sample by reconstructing each sample conformation i step-by-step, i.e., calculating transition probabilities (TPs) for the dihedral and bond angles and fixing the related atoms at their positions. At step k of the process the chain's coordinates that have already been determined are kept fixed (the "frozen past") and TP(k) is obtained from a MC simulation of the "future" part of the chain whose TPs as yet have not been determined; when the process is completed the contribution of conformation i to the entropy is, S(i) approximately -ln Pi(k) TP(k). In a recent paper we studied polyglycine chains, modeled by the AMBER force field with constant bond lengths and bond angles (the rigid model). Decaglycine [(Gly)(10)] was studied in the helical, extended, and hairpin microstates, while (Gly)(16) was treated only in the first two microstates. In this paper the samples are increased and restudied, (Gly)(16) is also investigated in the hairpin microstate, and for (Gly)(10) approximations are tested where only part of the future is considered for calculating the TPs. We calculate upper and lower bounds for F and demonstrate that like for fluids, F can be obtained from multiple reconstructions of a single conformation. We also test a more realistic model of (Gly)(10) where the bond angles are allowed to move (the flexible model). Very accurate results for S and F are obtained which are compared to results obtained by the quasiharmonic approximation and the local states method. Thus, differences in entropy and free energy between the three microstates are obtained within errors of 0.1-0.3 kcal/mol. The HSMC method can be applied to a macromolecule with any degree of flexibility, ranging from local fluctuations to a random coil. The present results demonstrate that the difference in stability, DeltaF(mn)=F(m)-F(n) between significantly different microstates m and n, can be obtained from two simulations only without the need to resort to thermodynamic integration. Our long-term goal is to extend this method to any peptide and apply it to a peptide immersed in a box with explicit water.

Computer Simulation↗

PubMed2005

Bayesian models and Markov chain Monte Carlo methods for protein motifs with the secondary characteristics.

Statistical methods have been developed for finding local patterns, also called motifs, in multiple protein sequences. The aligned segments may imply functional or structural core regions. However, the existing methods often have difficulties in aligning multiple proteins when sequence residue identities are low (e.g., less than 25%). In this article, we develop a Bayesian model and Markov chain Monte Carlo (MCMC) methods for identifying subtle motifs in protein sequences. Specifically, a motif is defined not only in terms of specific sites characterized by amino acid frequency vectors, but also as a combination of secondary characteristics such as hydrophobicity, polarity, etc. Markov chain Monte Carlo methods are proposed to search for a motif pattern with high posterior probability under the new model. A special MCMC algorithm is developed, involving transitions between state spaces of different dimensions. The proposed methods were supported by a simulated study. It was then tested by two real datasets, including a group of helix-turn-helix proteins, and one set from the CATH Protein Structure Classification Database. Statistical comparisons showed that the new approach worked better than a typical Gibbs sampling approach which is based only on an amino acid model.

Amino Acid Motifs↗

PubMed2006

Oscillator strengths of helium computed using Monte Carlo methods.

We have optimized trial wave functions for the three lowest states of the helium atom with symmetry 1S, 1P, 1D, 3S, 3P, and 3D using variational Monte Carlo methods. With these wave functions we then computed dipole oscillator strengths for the 1S-1P, 1P-1D, 3S-3P, and 3P-3D transitions using the length, velocity, and acceleration forms. Our values are in good agreement with the best results found in the literature.

Journal Article↗

PubMed2004

A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method.

RATIONALE AND OBJECTIVES: As an important part of bioluminescence tomography, which is a newly developed optical imaging modality, mouse optical simulation environment (MOSE) is developed to simulate bioluminescent phenomena in the living mouse and to predict bioluminescent signals detectable outside the mouse. This simulator is dedicated to small animal optical imaging based on bioluminescence. MATERIALS AND METHODS: With the parameters of biological tissues, bioluminescent sources, and charge coupled device (CCD) detectors, the 2-dimensional/3-dimensional MOSE simulates the whole process of the light propagation in 2-dimensional/3-dimensional biological tissues using the Monte Carlo method. Both the implementation details and the software architecture are described in this article. RESULTS: The software system is implemented in the Visual C++ programming language with the OpenGL techniques and has a user-friendly interface facilitating interactions relevant to bioluminescent imaging. The accuracy of the system is verified by comparing the MOSE results with independent data from analytic solutions and commercial software. CONCLUSION: As shown in our simulation and analysis, the MOSE is accurate, flexible, and efficient to simulate the photon propagation for bioluminescence tomography. With graduate refinements and enhancements, it is hoped that the MOSE will become a standard tool for bioluminescence tomography.

Computer Simulation↗

PubMed2002

A cumulative sum test for a peri-stimulus time histogram using the Monte Carlo method.

We have established a cumulative sum (CUSUM) test for a peri-stimulus time histogram (PSTH) for the case where a conditioning stimulus is delivered at a fixed interval after previous discharge of a motor unit. (We refer to this kind of PSTH as an 'arranged PSTH'). Expectations of the firing probability after the conditioning stimulus vary among the bins in this arranged PSTH, while the expectations among the bins are all the same in the original PSTH; thus, we could not apply conventional tests for statistical analysis. We, therefore, propose a novel CUSUM test that uses the Monte Carlo method. With this method, the range of the statistical scattering noise on a CUSUM is computationally found by simulating the statistical process in order to calculate the confidence interval. We verified this CUSUM test using both simulated and actual experiments. This paper presents the procedure for performing this new method, along with an example of its application.

Membrane Potentials↗

PubMedDate not supplied

Bayesian analysis of ROC curves using Markov-chain Monte Carlo methods.

The authors introduce a Bayesian approach to generalized linear regression models for rating data observed in the evaluation of a diagnostic technology. Such models were previously studied using a non-Bayesian approach. In a Bayesian analysis, the difficulties inherent in an ordinal rating scale are circumvented by using data-augmentation techniques. Posterior distributions for the regression parameters- and thereby for receiver operating characteristic (ROC) curve parameters and values, for the area under a ROC curve, differences between areas, etc.-may then be computed by Markov-chain Monte Carlo methods. Inferences are made in standard Bayesian ways. The methods are exemplified by a study of ultrasonography rating data for the detection of hepatic metastases in patients with colon or breast cancer (previously analyzed) and the results compared.

Bayes Theorem↗

PubMed2001

Genomewide multipoint linkage analysis of seven extended Palauan pedigrees with schizophrenia, by a Markov-chain Monte Carlo method.

Palauans are an isolated population in Micronesia with lifetime prevalence of schizophrenia (SCZD) of 2%, compared to the world rate of approximately 1%. The possible enrichment for SCZD genes, in conjunction with the potential for reduced etiological heterogeneity and the opportunity to ascertain statistically powerful extended pedigrees, makes Palauans a population of choice for the mapping of SCZD genes. We have used a Markov-chain Monte Carlo method to perform a genomewide multipoint analysis in seven extended pedigrees from Palau. Robust multipoint parametric and nonparametric linkage (NPL) analyses were performed under three nested diagnostic classifications-core, spectrum, and broad. We observed four regions of interest across the genome. Two of these regions-on chromosomes 2p13-14 (for which, under core diagnostic classification, NPL=6.5 and parametric LOD=4.8) and 13q12-22 (for which, under broad diagnostic classification, parametric LOD=3.6, and, under spectrum diagnostic classification, parametric LOD=3.5)-had evidence for linkage with genomewide significance, after correction for multiple testing; with the current pedigree resource and genotyping, these regions are estimated to be 4.3 cM and 19.75 cM in size, respectively. A third region, with intermediate evidence for linkage, was identified on chromosome 5q22-qter (for which, under broad diagnostic classification, parametric LOD=2.5). The fourth region of interest had only borderline suggestive evidence for linkage (on 3q24-28; for this region, under broad diagnostic classification, parametric LOD=2.0). All regions exhibited evidence for genetic heterogeneity. Our findings provide significant evidence for susceptibility loci on chromosomes 2p13-14 and 13q12-22 and support both a model of genetic heterogeneity and the utility of a broader set of diagnostic classifications in the population from Palau.

Chromosome Mapping↗

PubMed2005

Analysis of QUADOS problem on TLD-ALBEDO personal dosemeter responses using discrete ordinates and Monte Carlo methods.

In the scope of QUADOS, a Concerted Action of the European Commission, eight calculational problems were prepared in order to evaluate the use of computational codes for dosimetry in radiation protection and medical physics, and to disseminate "good practice" throughout the radiation dosimetry community. This paper focuses on the analysis of the P4 problem on the 'TLD-albedo dosemeter: neutron and/or photon response of a four-element TL-dosemeter mounted on a standard ISO slab phantom'. Altogether 17 solutions were received from the participants, 14 of those transported neutrons and 15 photons. Most participants (16 out of 17) used Monte Carlo methods. These calculations are time-consuming, requiring several days of CPU time to perform the whole set of calculations and achieve good statistical precision. The possibility of using deterministic discrete ordinates codes as an alternative to Monte Carlo was therefore investigated and is presented here. In particular the capacity of the adjoint mode calculations is shown.

Computer Simulation↗

PubMed2005

[Markov Chain Monte Carlo Method of multiple imputation for longitudinal data with missing values in the survey of maternal and children health].

OBJECTIVE: To deal with arbitrary missing pattern in longitudinal data of the Survey of Maternal and Child Health and make the most appropriate inferences with multiple imputation (MI) for further analysis. METHODS: SAS 9.0 was used for Markov Chain Monte Carlo (MCMC) method of MI procedure to impute missing values and combine inferences. RESULTS: The result is acceptable as the data set was imputed 5 times. CONCLUSION: MI is able to solve a variety of problems in missing data sets and to improve the statistical power, especially with the use of MCMC method, for complicated missing data sets.

Bias↗

PubMed2003

A Monte-Carlo method for interface dosimetry of beta emitters.

Biologically targeted radiotherapy optimization requires accurate dose estimation, from macroscopic to cellular/subcellular dimensions. In particular, dose perturbations produced at interfaces between dissimilar media could affect therapy outcome. The magnitude of these perturbations depends on a complex set of parameters. This study investigates perturbations on electron dose for materials with atomic numbers (Z) up to 79 (79Au) at their interface with water as a function of Z, energy, distance from interface and geometry. A Monte-Carlo method that produces absorbed dose distributions in a voxel geometry has been developed using EGSnrc transport routines. Heterogeneous media and activity distributions can be input into this code. The backscatter dose factor (BSDF), which quantifies interface dose perturbations, was estimated using this code. The BSDF magnitude ranged from approximately 3% to approximately 50%, depending on source energy and Z. The BSDF decreased with increasing energy and showed a logarithmic dependence on Z. Empirical functions were fit to the results, that could be used to correct dose calculations performed using dose-point-kernels estimated in water, to cases involving different scattering materials. The BSDF was found to be highly dependent on interface geometry and scoring volume; thus it is vital that BSDFs are used only in geometry conditions that are similar to those in which they were originally produced.

Beta Particles↗

PubMed1991

Simulation of the passage of fast electrons and the early stage of water radiolysis by the Monte Carlo method.

A numerical computer simulation of the processes of the interaction of electrons with liquid water and vapor was performed, beginning with the absorption of the energy of ionizing radiation and including the chemical changes in the medium. The specific features of the liquid phase compared with the gaseous phase were taken into account. Among them are the decrease of the ionization potential and collective excitations of the plasmon type. The mass stopping powers and ranges of electrons in liquid water and vapor were calculated. Within the frames of the stochastic model the kinetics of water radiolysis in the picosecond range of radiolysis was calculated by the Monte Carlo method. The mechanism of water radiolysis was found with the electron-ion recombination and the reactions of quasi-free and solvated electrons taken into account.

Computer Simulation↗

PubMed1994

Prediction of conformation of rat galanin in the presence and absence of water with the use of Monte Carlo methods and the ECEPP/3 force field.

The conformation of the 29-residue rat galanin neuropeptide was studied using the Monte Carlo with energy minimization (MCM) and electrostatically driven Monte Carlo (EDMC) methods. According to a previously elaborated procedure, the polypeptide chain was first treated in a united-residue approximation, in order to enable extensive exploration of the conformational space to be carried out (with the use of MCM). Then the low-energy united-residue conformations were converted to the all-atom representations, and EDMC simulations were carried out for the all-atom polypeptide chains, using the ECEPP/3 force field with hydration included. In order to estimate the effect of environment on galanin conformation, the low-energy conformations obtained as a result of these simulations were taken as starting structures for further EDMC runs that did not include hydration. The lowest-energy conformation obtained in aqueous solution calculations had a nonhelical N-terminal part packed against the nonpolar face of a residual helix that extended from Pro13 toward the C-terminus. One next lowest-energy structure was a nearly-all-helical conformation, but with a markedly higher energy. In contrast, all of the low-energy conformations in the absence of water were all-helical differing only by the extent to which the helix was kinked around Pro13. These results are in qualitative agreement with the available NMR and CD data of galanin in aqueous and nonaqueous solvents.

Amino Acid Sequence↗