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Results for “Monte Carlo Method”

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PubMed1981

An interpretation of the binding of ethidium bromide to the core nucleosome, based on Monte Carlo calculations.

We propose a model of ethidium binding to the nucleosome core particle. Ligand molecules are assumed to intercalate between the base pairs of the DNA core particle. The DNA is assumed to be divided into a finite number of segments. In the native core particle, one segment only is accessible to ethidium. The other DNA segments become progressively accessible when the binding ratio is increased. The binding isotherm resulting from such a model has been determined by a Monte Carlo method. The computed Scatchard plot exhibits the shape characteristic of a cooperative process. By fitting this curve with the experimental data of Erard et al. [1] one finds that 130 over the 140 DNA base pairs are accessible to the ethidium binding. The full accessibility of these sites is obtained when 8 or 9 ethidium at least are already bound to the core particle.

DNA↗

PubMed1999

Translational diffusion of flexible lipid chains in a Langmuir monolayer: a dynamic Monte Carlo study.

We report a computer simulation study of the lateral diffusion of conformationally disordered lipid molecules in a monolayer structure. The simulations were carried out with dynamic Monte Carlo methods, employing two different representations of the internal motions of the lipid chains. The classical Cohen-Turnbull theory is found to provide a good description of the simulated lateral diffusion coefficients at moderate densities. The substantial deviations found at low densities are attributed to the small density fluctuations needed to create the free volume required for the lateral diffusion process.

Computer Simulation↗

PubMed1981

Monte Carlo calculations of x-ray scatter data for diagnostic radiology.

X-ray scatter data have been calculated by Monte Carlo methods for diagnostic radiology applications. The scatter intensities relative to the primary intensities are given for different detectors for various values of object thickness, field size, object-to-detector distance, and primary energy. The results are compared the those from previous investigations. The calculations made it possible to resolve contradictions in published measurements regarding the dependence of scatter intensities on primary X-ray energy and detector response.

Models, Theoretical↗

PubMed2005

Monte Carlo modelling of a simple accident dosemeter.

A simple dosemeter made of a sulphur tablet, bare and cadmium-covered indium foils and a cadmium-covered copper foil has been modelled using MCNP5. Studies of the model without phantoms or other confounding factors have shown that the cross sections and fluence-to-dose factors generated by the Monte Carlo method agree with those generated by analytic expressions for the high-energy component. In this study, the effect of location on phantoms is studied and an extension of this study to low and intermediate energies is done. The activities expected from exposure to four critical assemblies on phantom is calculated and compared with observations.

Computer Simulation↗

PubMed2002

[The mean energy of electron determined by atomic hydrogen emission line in EACVD].

The process of atomic hydrogen emission in EACVD is simulated by Monte Carlo method. A method of determining the mean energy of electron is given by the ratio of atomic hydrogen emission line. The result is of great importance to determining the mean energy of electron in situ in the process of diamond film deposited by EACVD. Then, high quality diamond films can be obtained by controlling the conditions of technology efficiently.

Chemical Phenomena↗

PubMed2005

A simulation algorithm based on Bloch equations and product operator matrix: application to dipolar and scalar couplings.

A product operator matrix is proposed to describe scalar couplings in liquid NMR. Combination of the product operator matrix and non-linear Bloch equations is employed to describe effects of chemical shift, translational diffusion, dipolar field, radiation damping, and relaxation in multiple spin systems with both scalar and dipolar couplings. A new simulation algorithm based on this approach is used to simulate NMR signals from dipolar field effects in the presence of scalar couplings. Several typical coupled spin systems with both intra-molecular scalar couplings and inter-molecular dipolar couplings are simulated. Monte Carlo methods are incorporated into simulations as well to analyze diffusion process in these complicated spin systems. The simulated results of diffusion and relaxation parameters and 2D NMR spectra are coincident with the experimental measurements, and agree with theoretical predictions as well. The simulation algorithm presented herein therefore provides a convenient means for designing pulse sequences and quantifying experimental results in complex coupled spin systems.

Algorithms↗

PubMed2005

Broad-beam transmission data for new brachytherapy sources, Tm-170 and Yb-169.

The characteristics of the radionuclides (170)Tm and (169)Yb are highly interesting for their use as high dose-rate brachytherapy sources. The introduction of brachytherapy equipment containing these sources will lead to smaller required thicknesses of the materials used in radiation protection barriers compared with the use of conventional sources such as (192)Ir and (137)Cs. The purpose of this study is to determine the required thicknesses of protection material for the design of the protecting walls. Using the Monte Carlo method, transmission data were derived for broad-beam geometries through lead and concrete barriers, from which the first half value layer and tenth value layer are obtained. In addition, the dose reduction in a simulated patient was studied to determine whether transmission in the patient is a relevant factor in radiation protection calculations.

Brachytherapy↗

PubMed1999

[Molecular mechanics study on Conformation of a homooligopeptide constituted by isovalin].

Conformational energy computations on a homo-hexapeptide of (S)-isovaline were performed using molecular mechanics on MacroModel. Conformational search calculations were carried out by Monte Carlo method. AMBER* was used as the force field. The global minimum energy conformation was found to be a 3(10)-helix coordinated by four hydrogen bonds. The results of the theoretical analysis of the conformation of the peptide are in agreement with its reported conformational properties in the solid state determined by X-ray crystallographic analysis.

Crystallography, X-Ray↗

PubMed2005

Pseudo-likelihood analysis of codon substitution models with neighbor-dependent rates.

Recently, Markov processes for the evolution of coding DNA with neighbor dependence in the instantaneous substitution rates have been considered. The neighbor dependency makes the models analytically intractable, and previously Markov chain Monte Carlo methods have been used for statistical inference. Using a pseudo-likelihood idea, we introduce in this paper an approximative estimation method which is fast to compute. The pseudo-likelihood estimates are shown to be very accurate, and from analyzing 348 human-mouse coding sequences we conclude that the incorporation of a CpG effect improves the fit of the model considerably.

Algorithms↗

PubMed2000

Shock wave profiles in the burnett approximation

This paper is devoted to a discussion of the profiles of shock waves using the full nonlinear Burnett equations of hydrodynamics as they appear from the Chapman-Enskog solution to the Boltzmann equation. The system considered is a dilute gas composed of rigid spheres. The numerical analysis is carried out by transforming the hydrodynamic equations into a set of four first-order equations in four dimensions. We compare the numerical solutions of the Burnett equations, obtained using Adam's method, with the well known direct simulation Monte Carlo method for different Mach numbers. An exhaustive mathematical analysis of the results offered here has been done mainly in connection with the existence of heteroclinic trajectories between the two stationary points located upflow and downflow. The main result of this study is that such a trajectory exists for the Burnett equations for Mach numbers greater than 1. Our numerical calculations suggest that heteroclinic trajectories exist up to a critical Mach number ( approximately 2.69) where local mathematical analysis and numerical computations reveal a saddle-node-Hopf bifurcation. This upper limit for the existence of heteroclinic trajectories deserves further clarification.

Journal Article↗

PubMed1980

Estimation of the reliability of parameters obtained by non-linear regression.

Four methods for estimating the reliability of parameters obtained by non-linear regression are compared. Matrix inversion demands the lest computational effort, but can be unreliable for overdetermined models. The 'jack-knife' technique was found to give results of the right magnitude, but some unexplained discrepancies suggest that this method should be used with caution. A Monte Carlo method and the method of support planes were found to be in good agreement with matrix inversion, but both involve a substantial computational investment. The method of support planes is preferred as it gives information on the degree of non-linearity of the equation which is fitted to the data.

Computers↗

PubMed1998

Extraction of the photon spectra from measured beam parameters.

Knowledge of the photon spectrum of a radiotherapy beam is often needed for three-dimensional (3-D) dose calculations using Monte Carlo methods and/or algorithms employing energy deposition kernels. Direct measurement of the x-ray energy fluence spectrum is not feasible for the high-energy photon beams used clinically. In this paper, the spectrum is extracted from basic beam data that are readily obtained for a clinical beam. We describe the photon spectrum using just two parameters. One parameter, which determines the high-energy part of the spectrum, is obtained using the measured dose in the buildup region for a small field, where electron contamination of the beam can be neglected. The other parameter is extracted from the photon beam attenuation in water. The results compare favorably to spectra generated from Monte Carlo simulations.

Algorithms↗

PubMed2006

Dynamic partitioning for hybrid simulation of the bistable HIV-1 transactivation network.

MOTIVATION: The stochastic kinetics of a well-mixed chemical system, governed by the chemical Master equation, can be simulated using the exact methods of Gillespie. However, these methods do not scale well as systems become more complex and larger models are built to include reactions with widely varying rates, since the computational burden of simulation increases with the number of reaction events. Continuous models may provide an approximate solution and are computationally less costly, but they fail to capture the stochastic behavior of small populations of macromolecules. RESULTS: In this article we present a hybrid simulation algorithm that dynamically partitions the system into subsets of continuous and discrete reactions, approximates the continuous reactions deterministically as a system of ordinary differential equations (ODE) and uses a Monte Carlo method for generating discrete reaction events according to a time-dependent propensity. Our approach to partitioning is improved such that we dynamically partition the system of reactions, based on a threshold relative to the distribution of propensities in the discrete subset. We have implemented the hybrid algorithm in an extensible framework, utilizing two rigorous ODE solvers to approximate the continuous reactions, and use an example model to illustrate the accuracy and potential speedup of the algorithm when compared with exact stochastic simulation. AVAILABILITY: Software and benchmark models used for this publication can be made available upon request from the authors.

Algorithms↗

PubMed2003

Markov chain Monte Carlo without likelihoods.

Many stochastic simulation approaches for generating observations from a posterior distribution depend on knowing a likelihood function. However, for many complex probability models, such likelihoods are either impossible or computationally prohibitive to obtain. Here we present a Markov chain Monte Carlo method for generating observations from a posterior distribution without the use of likelihoods. It can also be used in frequentist applications, in particular for maximum-likelihood estimation. The approach is illustrated by an example of ancestral inference in population genetics. A number of open problems are highlighted in the discussion.

Algorithms↗

PubMed2005

Robust tests for the multivariate Behrens-Fisher problem.

Hotelling's T2 procedure is used to test the equality of means in two-group multivariate designs when covariances are homogeneous. A number of alternatives to T2, which are robust to covariance heterogeneity, have been proposed in the literature. However, all are sensitive to departures from multivariate normality. We demonstrate how to obtain multivariate tests that are robust to covariance heterogeneity and non-normality with estimators of location and scale based on trimming and Winsorizing. The performance of six alternatives to T2 was examined via Monte Carlo methods when characteristics of the research design, degree of covariance heterogeneity, and degree of non-normality were manipulated. We have recently developed a program written in the SAS/IML language that can be used to implement these robust multivariate tests. Recommendations are provided on the specific data-analytic conditions under which these tests should be adopted.

Analysis of Variance↗

PubMed2004

The effect of unrealistic thyroid vertical position on thyroid dose in the MIRD phantom.

Anatomically, the thyroid gland is placed in the lower neck, extending from the level of the fifth cervical vertebra down to the first thoracic vertebra. However, the thyroid of the Medical Internal Radiation Dose (MIRD) phantom, which has been widely used for dosimetric calculation, is located right above the top of the torso and is completely included in the neck region. To investigate the effect of the unrealistic position of the thyroid in the MIRD phantom on dose calculation, thyroid absorbed doses at various vertical positions were calculated for the idealized external broad parallel photon beam from anterior-posterior, posterior-anterior, right lateral (RLAT), and left lateral (LLAT) direction using the Monte Carlo method. The thyroid absorbed dose decreased by as much as about 60% for 0.05 MeV photon in both RLAT and LLAT irradiations when the thyroid was relocated to realistic position (inserted into the torso). The effective dose also decreased by 10%, consequently. The thyroid dose of the widely accepted stylized model, the MIRD phantom, is overestimated in RLAT and LLAT irradiation geometries.

Algorithms↗

PubMed2006

[Markov Chain Monte Carlo scheme for parameter uncertainty analysis in water quality model].

Parameter identification plays an important role in environmental model application. Markov Chain Monte Carlo method was introduced to estimate parameter uncertainty, since usual Bayes discrete methods were not applicable to produce posterior distribution of complicated environmental model due to the limit of computation. In order to study the performance and efficiency of MCMC, two case studies were used. Results indicate that, either sampling performance or sampling efficiency, MCMC method both has its special advantages in producing posterior distribution. Moreover, results of Gelman convergence diagnostics indicate that sampling sequence can converge to a stationary distribution. A key finding was that the MCMC scheme presented herein provided a powerful means of parameter identification and uncertainty analysis.

Models, Theoretical↗

PubMed2003

MCMC genome rearrangement.

MOTIVATION: As more and more genomes have been sequenced, genomic data is rapidly accumulating. Genome-wide mutations are believed more neutral than local mutations such as substitutions, insertions and deletions, therefore phylogenetic investigations based on inversions, transpositions and inverted transpositions are less biased by the hypothesis on neutral evolution. Although efficient algorithms exist for obtaining the inversion distance of two signed permutations, there is no reliable algorithm when both inversions and transpositions are considered. Moreover, different type of mutations happen with different rates, and it is not clear how to weight them in a distance based approach. RESULTS: We introduce a Markov Chain Monte Carlo method to genome rearrangement based on a stochastic model of evolution, which can estimate the number of different evolutionary events needed to sort a signed permutation. The performance of the method was tested on simulated data, and the estimated numbers of different types of mutations were reliable. Human and Drosophila mitochondrial data were also analysed with the new method. The mixing time of the Markov Chain is short both in terms of CPU times and number of proposals. AVAILABILITY: The source code in C is available on request from the author.

Algorithms↗