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Results for “Monte Carlo Method”

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PubMed2000

Resolution of the phase-ambiguity problem in the centrosymmetric P [1] space group by Monte Carlo methods.

Simulated-annealing methods have been used to resolve the phase-ambiguity problem in the centrosymmetric P¿bar¿1¿ space group. First, an energy function based on the Sayre equation is introduced and a formal comparison with classical spin systems is drawn. The energy landscape is studied in detail and the validity of several energy criteria thoroughly tested. Classical Monte Carlo methods proved to be successful using a multistart optimization of the Sayre score, along with the additional monitoring of other energetic criteria. These involved the Terwilliger map quality index in reciprocal space in the absence of envelope information, and an envelope score if the shape of the molecule is known. The inherent phase-ambiguity problem of the P¿bar¿1¿ space group was therefore technically solved by Monte Carlo methods. The method should also work to resolve phase ambiguity in the SIR method of protein crystallography.

Computer Simulation↗

PubMed2004

Gaussian quantum Monte Carlo methods for fermions and bosons.

We introduce a new class of quantum Monte Carlo methods, based on a Gaussian quantum operator representation of fermionic states. The methods enable first-principles dynamical or equilibrium calculations in many-body Fermi systems, and, combined with the existing Gaussian representation for bosons, provide a unified method of simulating Bose-Fermi systems. As an application relevant to the Fermi sign problem, we calculate finite-temperature properties of the two dimensional Hubbard model and the dynamics in a simple model of coherent molecular dissociation.

Journal Article↗

PubMedDate not supplied

[Modeling of hydration of incorrect nucleic acid base pairs by the Monte Carlo method].

The hydration of water bridged base pairs of nucleic acids have been simulated via the Monte Carlo method. The simulation have shown that water molecules forming H-bonds with both bases preserve this H-bonding with large probability in the water surrounding. This fact supports the supposition about the important role of water molecules in wrong base pair formation and about the role of these base pairs in the structure and functioning of nucleic acids.

Base Composition↗

PubMedDate not supplied

[Hydration of the left spiral of the poly-L-proline type. Study by the Monte Carlo method].

The paper exhibits results of hydration shell Monte Carlo calculations in poly-L-proline II and extended helix conformation and in alpha-helical and beta-structural conformations for comparison. It was found that left-handed helix of poly-L-proline II type as well as epsilon-helix are characterized by very favorable hydration. Therefore this conformation has preference as compared to other standard conformations of the main polypeptide chain. This determined inevitability of cold denaturation of protein.

Amino Acid Sequence↗

PubMed2005

Estimation of the four-wave mixing noise probability-density function by the multicanonical Monte Carlo method.

The performance of high-powered wavelength-division multiplexed (WDM) optical networks can be severely degraded by four-wave-mixing- (FWM-) induced distortion. The multicanonical Monte Carlo method (MCMC) is used to calculate the probability-density function (PDF) of the decision variable of a receiver, limited by FWM noise. Compared with the conventional Monte Carlo method previously used to estimate this PDF, the MCMC method is much faster and can accurately estimate smaller error probabilities. The method takes into account the correlation between the components of the FWM noise, unlike the Gaussian model, which is shown not to provide accurate results.

Journal Article↗

PubMed1991

The electrostatically driven Monte Carlo method: application to conformational analysis of decaglycine.

The Electrostatically Driven Monte Carlo (EDMC) method was applied in a study of a decamer of glycine whose conformational behavior is described by the Empirical Conformational Energy Program for Peptides (ECEPP/2) potential energy model. When free neutral end groups were used, it was found that conformations that were not alpha-helical had significantly lower potential energies than fully alpha-helical ones. However, when the N- and C-termini were blocked by acetyl and methyl amide groups, respectively, the number of unsatisfied hydrogen-bond donors and acceptors at the helix termini was diminished from 8 to 6; in this case, the possibility of forming two additional alpha-helical hydrogen bonds was an important enough factor in making the alpha-helical conformation the one with the lowest energy. The EDMC method was used as a global energy optimizer since it does not often become trapped in high-energy local minima.

Electrochemistry↗

PubMed1997

Bayesian phylogenetic inference using DNA sequences: a Markov Chain Monte Carlo Method.

An improved Bayesian method is presented for estimating phylogenetic trees using DNA sequence data. The birth-death process with species sampling is used to specify the prior distribution of phylogenies and ancestral speciation times, and the posterior probabilities of phylogenies are used to estimate the maximum posterior probability (MAP) tree. Monte Carlo integration is used to integrate over the ancestral speciation times for particular trees. A Markov Chain Monte Carlo method is used to generate the set of trees with the highest posterior probabilities. Methods are described for an empirical Bayesian analysis, in which estimates of the speciation and extinction rates are used in calculating the posterior probabilities, and a hierarchical Bayesian analysis, in which these parameters are removed from the model by an additional integration. The Markov Chain Monte Carlo method avoids the requirement of our earlier method for calculating MAP trees to sum over all possible topologies (which limited the number of taxa in an analysis to about five). The methods are applied to analyze DNA sequences for nine species of primates, and the MAP tree, which is identical to a maximum-likelihood estimate of topology, has a probability of approximately 95%.

Algorithms↗

PubMed1982

Calculation of x-ray grid characteristics by Monte Carlo methods.

The performance of x-ray grids has generally been evaluated experimentally. A theoretical method has been developed by which photon histories are generated by Monte Carlo methods. The probability of penetrating the grid is calculated for each photon escaping from the object towards the detector. The scatter transmission of the grid is determined as the average of these individual probabilities. Results for linear and cross grids are in good agreement with measurements. The method is applicable to arbitrary irradiation and grid parameters. The dependence of scatter transmission values on the irradiation parameters is shown. Grids with linear and zigzag strip patterns are compared in order to demonstrate that even grids that cannot at present be manufactured can nevertheless be evaluated.

Monte Carlo Method↗

PubMed2003

Quantum Monte Carlo method using phase-free random walks with slater determinants.

We develop a quantum Monte Carlo method for many fermions using random walks in the space of Slater determinants. An approximate approach is formulated with a trial wave function |Psi(T)> to control the phase problem. Using a plane-wave basis and nonlocal pseudopotentials, we apply the method to Be, Si, and P atoms and dimers, and to bulk Si supercells. Single-determinant wave functions from density functional theory calculations were used as |Psi(T)> with no additional optimization. The calculated binding energies of dimers and cohesive energy of bulk Si are in excellent agreement with experiments and are comparable to the best existing theoretical results.

Journal Article↗

PubMedDate not supplied

Many-body optimization using an ab initio monte carlo method.

Advances in computing power have made it possible to study solvated molecules using ab initio quantum chemistry. Inclusion of discrete solvent molecules is required to determine geometric information about solute/solvent clusters. Monte Carlo methods are well suited to finding minima in many-body systems, and ab initio methods are applicable to the widest range of systems. A first principles Monte Carlo (FPMC) method was developed to find minima in many-body systems, and emphasis was placed on implementing moves that increase the likelihood of finding minimum energy structures. Partial optimization and molecular interchange moves aid in finding minima and overcome the incomplete sampling that is unavoidable when using ab initio methods. FPMC was validated by studying the boron trifluoride-water system, and then the method was used to examine the methyl carbenium ion in water to demonstrate its application to solvation problems.

Journal Article↗

PubMed2002

Derivation of a Monte Carlo method for modeling heterodyne detection in optical coherence tomography systems.

A Monte Carlo (MC) method for modeling optical coherence tomography (OCT) measurements of a diffusely reflecting discontinuity embedded in a scattering medium is presented. For the first time to the authors' knowledge it is shown analytically that the applicability of an MC approach to this optical geometry is firmly justified, because, as we show, in the conjugate image plane the field reflected from the sample is delta-correlated from which it follows that the heterodyne signal is calculated from the intensity distribution only. This is not a trivial result because, in general, the light from the sample will have a finite spatial coherence that cannot be accounted for by MC simulation. To estimate this intensity distribution adequately we have developed a novel method for modeling a focused Gaussian beam in MC simulation. This approach is valid for a softly as well as for a strongly focused beam, and it is shown that in free space the full three-dimensional intensity distribution of a Gaussian beam is obtained. The OCT signal and the intensity distribution in a scattering medium have been obtained for several geometries with the suggested MC method; when this model and a recently published analytical model based on the extended Huygens-Fresnel principle are compared, excellent agreement is found.

Computer Simulation↗

PubMed2004

The validation of organ dose calculations using voxel phantoms and Monte Carlo methods applied to point and water immersion sources.

The Monte Carlo program 'Visual Monte Carlo-dose calculation' (VMC-dc) uses a voxel phantom to simulate the body organs and tissues, transports photons through this phantom and reports the absorbed dose received by each organ and tissue relevant to the calculation of effective dose as defined in ICRP Publication 60. This paper shows the validation of VMC-dc by comparison with EGSnrc and with a physical phantom containing TLDs. The validation of VMC-dc by comparison with EGSnrc was made for a collimated beam of 0.662 MeV photons irradiating a cube of water. For the validation by comparison with the physical phantom, the case considered was a whole body irradiation with a point 137Cs source placed at a distance of 1 m from the thorax of an Alderson-RANDO phantom. The validation results show good agreement for the doses obtained using VMC-dc and EGSnrc calculations, and from VMC-dc and TLD measurements. The program VMC-dc was then applied to the calculation of doses due to immersion in water containing gamma emitters. The dose conversion coefficients for water immersion are compared with their equivalents in the literature.

Humans↗

PubMed1987

Studies on evolutionary and selective properties of hypercycles using a Monte Carlo method.

The most relevant properties of hypercycles were previously studied mainly from a theoretical point of view. We have developed a Monte Carlo method simulating hypercyclic organization to obtain information about the dynamics of this prebiotic organization. Nucleation, growth, and selective properties have been tested and the results obtained are in good agreement with those of the theoretical predictions. The influence of hypercyclic organization on the "error threshold" has also been studied. As a consequence of the emergence of a hypercycle, the value of this threshold decreases. The amount of this decrease depends on the population size. Moreover, for some interval of quality factor values, either the hypercycle organization or an error catastrophe can be produced, depending on the initial conditions. The influence of these phenomena on both the dynamic behavior and evolutionary advantages of the hypercycle, as well as their decisive roles on genome size, are discussed.

Biological Evolution↗

PubMed1994

Monte Carlo methods for exploring sensitivity to distributional assumptions in a Bayesian analysis of a series of 2 x 2 tables.

This paper develops Monte Carlo methods for a Bayesian analysis of a series of 2 x 2 tables under a variety of distributional assumptions. I assume that the data in each table were generated from a pair of binomial distributions and the logarithm of odds of a favourable response follows a bivariate distribution with means that are linear functions of covariates and an arbitrary covariance matrix. I use Gibbs and importance sampling methods to obtain various characteristics of the posterior distribution of the quantities of interest. I apply the method to analyse the data from a population case-control study. Given the size of the population at risk I also derive the posterior distribution of the risk difference defined as the difference in the probabilities of disease development in the exposed and unexposed groups.

Bayes Theorem↗

PubMed1989

[Use of the Monte Carlo method for predicting the outcome of hypertension].

A group of 764 out-patients (359 men and 405 women) was studied 10-24 years after having received clinical treatment for hypertension. After discharge from the clinic 455 patients died. The degree of the disease development was defined in 164 out of 178 survivals. The fate of 131 subjects was unknown. By using the theory of probability and Monte Carlo method we calculated mean times of progress from one class to another (according to Tochowicz's classification) and mean survival times at particular stages of the disease. Hypertension progress from class II to class III was 11.4 years, and survival time measured from the diagnosis to the manifestation of class II was 12.3 years. Progress from class III to class IV was 8.0 years, and survival time of patients with class III was 7.3 years. In class IV patients mean survival time was only 2.5 years. In patients died of hypertension complications mean survival time was 17.1 years. A single control study by using the Monte Carlo method permits a definition of the dynamics in the development of hypertension and duration of its successive stages.

Female↗

PubMed2002

Using Monte Carlo methods to commission electron beams: a feasibility study.

The purpose of this study was to investigate the feasibility of using Monte Carlo methods to assist in the commissioning of electron beams for a medical linear accelerator. The EGS4/BEAM code system was used to model an installed linear accelerator at this institution. Following an initial tuning of the input parameters, dosimetry data normally measured during the machine commissioning was calculated using the Monte Carlo code. All commissioning data was calculated for 6- and 12-MeV electron beams, and a subset of the commissioning data was calculated for the 20-MeV electron beams. On central axis, calculated percentage depth dose, cross-beam profiles, cone-insert ratios, and air-gap factors were generally within 2% of Dmax or 1 mm of the measured commissioning data; however, calculated open-cone ratios were not within 2%, in most cases. Calculated off-axis dose profiles for small fields were generally within the 2% (1-mm) criteria; however, calculated dose profiles for larger (open cone) fields frequently failed the 2% (1-mm) criteria. The remaining discrepancies between Monte Carlo calculations and measurement could be due to flaws in the Monte Carlo code, inaccuracies in the simulation geometry, the approximation of the initial source configuration, or a combination of the above. Although agreement between Monte Carlo calculated and measured doses was impressive and similar to previously published comparisons, our results did not prove our hypothesis that Monte Carlo calculations can generate electron commissioning data that is accurate within 2% of Dmax or 0.1 cm over the entire range of clinical treatment parameters. Although we believe that this hypothesis can be proved, it remains a challenge for the medical physics community. We intend to pursue this further by developing systematic methods for isolating causes of these differences.

Air↗

PubMedDate not supplied

Amino acid similarity matrix for homology modeling derived from structural alignment and optimized by the Monte Carlo method.

In this paper, we obtained a similarity matrix for homology modeling based on the structure of proteins in a structural alignment. The alignment procedure was executed within dynamic programming generally used in alignment methods. An initial matrix derived from the structural alignment was optimized by the Markov chain Monte Carlo method at low temperature to fit its sequence alignment to the structural alignment. Structural alignment was performed on the basis of the superposition of C alpha atoms for two protein structures. The objective function in the Monte Carlo procedure was defined by entropy in the information theory, allowing us to show that the amino acid similarity matrix aligned accurately. When compared with the structural alignment, the average number of incorrect amino acid residues in the sequence alignment was 22.6 for all residues and about 3.7 for residues in structurally conserved regions. The alignment with our matrix was more similar to structural alignment than to sequence alignments using other amino acid substitution matrices.

Algorithms↗

PubMed2005

Metabolic flux distribution analysis by 13C-tracer experiments using the Markov chain-Monte Carlo method.

Metabolic flux analysis using 13C-tracer experiments is an important tool in metabolic engineering since intracellular fluxes are non-measurable quantities in vivo. Current metabolic flux analysis approaches are fully based on stoichiometric constraints and carbon atom balances, where the over-determined system is iteratively solved by a parameter estimation approach. However, the unavoidable measurement noises involved in the fractional enrichment data obtained by 13C-enrichment experiment and the possible existence of unknown pathways prevent a simple parameter estimation method for intracellular flux quantification. The MCMC (Markov chain-Monte Carlo) method, which obtains intracellular flux distributions through delicately constructed Markov chains, is shown to be an effective approach for deep understanding of the intracellular metabolic network. Its application is illustrated through the simulation of an example metabolic network.

Carbon Isotopes↗