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PubMed2004

Quantum Monte Carlo method for the ground state of many-boson systems.

We formulate a quantum Monte Carlo (QMC) method for calculating the ground state of many-boson systems. The method is based on a field-theoretical approach, and is closely related to existing fermion auxiliary-field QMC methods which are applied in several fields of physics. The ground-state projection is implemented as a branching random walk in the space of permanents consisting of identical single-particle orbitals. Any single-particle basis can be used, and the method is in principle exact. We illustrate this method with a trapped atomic boson gas, where the atoms interact via an attractive or repulsive contact two-body potential. We choose as the single-particle basis a real-space grid. We compare with exact results in small systems and arbitrarily sized systems of untrapped bosons with attractive interactions in one dimension, where analytical solutions exist. We also compare with the corresponding Gross-Pitaevskii (GP) mean-field calculations for trapped atoms, and discuss the close formal relation between our method and the GP approach. Our method provides a way to systematically improve upon GP while using the same framework, capturing interaction and correlation effects with a stochastic, coherent ensemble of noninteracting solutions. We discuss various algorithmic issues, including importance sampling and the back-propagation technique for computing observables, and illustrate them with numerical studies. We show results for systems with up to N approximately 400 bosons.

Journal Article↗
PubMed1996

Markov chain Monte Carlo methods in biostatistics.

Appropriate models in biostatistics are often quite complicated. Such models are typically most easily fit using Bayesian methods, which can often be implemented using simulation techniques. Markov chain Monte Carlo (MCMC) methods are an important set of tools for such simulations. We give an overview and references of this rapidly emerging technology along with a relatively simple example. MCMC techniques can be viewed as extensions of iterative maximization techniques, but with random jumps rather than maximizations at each step. Special care is needed when implementing iterative maximization procedures rather than closed-form methods, and even more care is needed with iterative simulation procedures: it is substantially more difficult to monitor convergence to a distribution than to a point. The most reliable implementations of MCMC build upon results from simpler models fit using combinations of maximization algorithms and noniterative simulations, so that the user has a rough idea of the location and scale of the posterior distribution of the quantities of interest under the more complicated model. These concerns with implementation, however, should not deter the biostatistician from using MCMC methods, but rather help to ensure wise use of these powerful techniques.

Algorithms↗
PubMed2005

Yet another application of the Monte Carlo method for modeling in the field of biomedicine.

By means of Monte Carlo simulations performed in the C programming language, an example of scientific programming for the generation of pseudorandom numbers relevant to both teaching and research in the field of biomedicine is presented. The relatively simple algorithm proposed makes possible the statistical analysis of sequences of random numbers. The following three generators of pseudorandom numbers were used: the rand function contained in the stdlib.h library of the C programming language, Marsaglia's generator, and a chaotic function. The statistical properties of the sequences generated were compared, identical parameter values being adopted for this purpose. The properties of two estimators in finite samples of the pseudorandom numbers were also evaluated and, under suitable conditions, both the maximum-likelihood and method of moments proved to be good estimators. The findings demonstrated that the proposed algorithm appears to be suitable for the analysis of data from random experiments, indicating that it has a large variety of possible applications in the clinical practice.

Algorithms↗
PubMed2004

Excited electronic state calculations by the transcorrelated variational Monte Carlo method: application to a helium atom.

We have implemented the excited electronic state calculations for a helium atom by the transcorrelated variational Monte Carlo (TC-VMC) method. In this method, Jastrow-Slater-type wave function is efficiently optimized not only for the Jastrow factor but also for the Slater determinant. Since the formalism for the TC-VMC method is based on the variance minimization, excited states as well as the ground state calculations are feasible. It is found that both the first and the second excitation energies given by TC-VMC are much closer to the experimental data than those given by the variational Monte Carlo method with using the Hartree-Fock orbitals. The successful results in the TC-VMC method are considered to be due to the nodal optimization of the wave functions.

Journal Article↗
PubMed2005

About estimation of fitted parameters' statistical uncertainties in EXAFS. Critical approach on usual and Monte Carlo methods.

An important step in X-ray absorption spectroscopy (XAS) analysis is the fitting of a model to the experimental spectra, with a view to obtaining structural parameters. It is important to estimate the errors on these parameters, and three methods are used for this purpose. This article presents the conditions for applying these methods. It is shown that the usual equation Sigma = 2H(-1) is not applicable for fitting in R space or on filtered XAS data; a formula is established to treat these cases, and the equivalence between the usual formula and the brute-force method is evidenced. Lastly, the problem of the nonlinearity of the XAS models and a comparison with Monte Carlo methods are addressed.

Journal Article↗
PubMed2003

Voxel phantoms and Monte Carlo methods applied to in vivo measurements for simultaneous 241Am contamination in four body regions.

A Monte Carlo program, Visual Monte Carlo (VMC) in vivo, was written to simulate photon transport through an anthropomorphic phantom and to detect radiation emitted from the phantom. VMC in vivo uses a voxel phantom provided by Yale University and may be used to calibrate in vivo systems. This paper shows the application of VMC in vivo to the measurement of 241Am deposited simultaneously in the thoracic region, the bones, the liver and in the rest of the body. The percentages of 241Am in the four body regions were calculated using the biokinetic models established by the ICRP, for a single intake via inhalation. The four regions of the voxel phantom were then 'contaminated' in accordance with the calculated percentages. The calibration factor of the in vivo system was then obtained. This procedure was repeated for the radionuclide distributions obtained 5, 30, 120, 240 and 360 days after intake. VMC in vivo was also used to calculate the calibration factor of the in vivo system in which the radionuclide was assumed to be deposited only in the lung, as is normally done. The activities calculated with the radionuclide distributed in the four body regions as a factor of time, and the activities calculated with the radionuclide deposited in the lung only are compared.

Americium↗
PubMed2005

Quantifying and reducing uncertainty in life cycle assessment using the Bayesian Monte Carlo method.

The traditional life cycle assessment (LCA) does not perform quantitative uncertainty analysis. However, without characterizing the associated uncertainty, the reliability of assessment results cannot be understood or ascertained. In this study, the Bayesian method, in combination with the Monte Carlo technique, is used to quantify and update the uncertainty in LCA results. A case study of applying the method to comparison of alternative waste treatment options in terms of global warming potential due to greenhouse gas emissions is presented. In the case study, the prior distributions of the parameters used for estimating emission inventory and environmental impact in LCA were based on the expert judgment from the intergovernmental panel on climate change (IPCC) guideline and were subsequently updated using the likelihood distributions resulting from both national statistic and site-specific data. The posterior uncertainty distribution of the LCA results was generated using Monte Carlo simulations with posterior parameter probability distributions. The results indicated that the incorporation of quantitative uncertainty analysis into LCA revealed more information than the deterministic LCA method, and the resulting decision may thus be different. In addition, in combination with the Monte Carlo simulation, calculations of correlation coefficients facilitated the identification of important parameters that had major influence to LCA results. Finally, by using national statistic data and site-specific information to update the prior uncertainty distribution, the resultant uncertainty associated with the LCA results could be reduced. A better informed decision can therefore be made based on the clearer and more complete comparison of options.

Bayes Theorem↗
PubMed1993

An investigation of the possibilities of BNCT treatment planning with the Monte Carlo method.

The neutron fluence distribution inside two types of water phantom have been calculated with the Monte Carlo programme MCNP for the epithermal neutron beam at the Petten Low Flux Reactor. Comparison between the calculated and the measured neutron fluence distributions showed a reasonable agreement. The influence of beam and phantom geometry on the neutron fluence distribution has been calculated. An increase of the field size leads to a somewhat deeper position of the maximum of the thermal neutron fluence distribution in the cylindrical phantom. The possible use of beam modifying devices like wedges and blocks has been tested with this model. Blocks have been modelled that can locally reduce the fast neutron skin dose by 70%.

Boron Neutron Capture Therapy↗
PubMed2005

Adjoint Monte Carlo method for prostate external photon beam treatment planning: an application to 3D patient anatomy.

Recently, the theoretical framework of the adjoint Monte Carlo (AMC) method has been developed using a simplified patient geometry. In this study, we extended our previous work by applying the AMC framework to a 3D anatomical model called VIP-Man constructed from the Visible Human images. First, the adjoint fluxes for the prostate (PTV) and rectum and bladder (organs at risk (OARs)) were calculated on a spherical surface of 1 m radius, centred at the centre of gravity of PTV. An importance ratio, defined as the PTV dose divided by the weighted OAR doses, was calculated for each of the available beamlets to select the beam angles. Finally, the detailed doses in PTV and OAR were calculated using a forward Monte Carlo simulation to include the electron transport. The dose information was then used to generate dose volume histograms (DVHs). The Pinnacle treatment planning system was also used to generate DVHs for the 3D plans with beam angles obtained from the AMC (3D-AMC) and a standard six-field conformal radiation therapy plan (3D-CRT). Results show that the DVHs for prostate from 3D-AMC and the standard 3D-CRT are very similar, showing that both methods can deliver prescribed dose to the PTV. A substantial improvement in the DVHs for bladder and rectum was found for the 3D-AMC method in comparison to those obtained from 3D-CRT. However, the 3D-AMC plan is less conformal than the 3D-CRT plan because only bladder, rectum and PTV are considered for calculating the importance ratios. Nevertheless, this study clearly demonstrated the feasibility of the AMC in selecting the beam directions as a part of a treatment planning based on the anatomical information in a 3D and realistic patient anatomy.

Dose-Response Relationship, Radiation↗
PubMed2003

Experimental evaluation of validity of simplified Monte Carlo method in proton dose calculations.

It is important for proton therapy to calculate dose distributions accurately in treatment planning. Dose calculations in the body for treatment planning are converted to dose distributions in water, and the converted calculations are then generally evaluated by the dose measurements in water. In this paper, proton dose calculations were realized for a phantom simulating a clinical heterogeneity. Both dose calculations in the phantom calculated by two dose calculation methods, the range-modulated pencil beam algorithm (RMPBA) and the simplified Monte Carlo (SMC) method, and dose calculations converted to dose distributions in water by the same two methods were verified experimentally through comparison with measured distributions, respectively. For the RMPBA, though the converted calculations in water agreed moderately well with the measured ones, the calculated results in the actual phantom produced large errors. This meant that dose calculations in treatment planning should be evaluated by the dose measurements not in water but in the body with heterogeneity. On the other hand, the results calculated in the phantom, even by the less rigorous SMC method, reproduced the experimental ones well. This finding showed that actual dose distributions in the body should be predicted by the SMC method.

Algorithms↗
PubMed2000

Monte Carlo methods for linkage analysis of two-locus disease models.

Parametric linkage analysis of simultaneous mapping of the two disease loci of a qualitative trait governed by a two-locus model has been shown to provide greater power in detecting linkage than standard lod-score analysis that maps a single disease locus. Despite its great potential for power gains, two-locus parametric analysis has not been used routinely in disease gene mapping. due to the computational intensity of currently available methods and programs. In this paper, we propose a Markov chain Monte Carlo (MCMC) method for performing lod-score analysis of qualitative traits governed by two-locus models. This method obtains lod-score estimates that can be arbitrarily close to their corresponding exact values. The algorithm implementing this MCMC method is linear in the number of markers. This feature enables us to perform two-locus analysis mapping each trait to a set of markers, instead of just to a single marker. We analyzed an alcohol dependence dataset composed of 105 pedigrees with various sizes and various degrees of missingness in the observed marker and disease data. The estimates from our MCMC procedure match up well with the lod scores from exact analysis, but it took much less time for the MCMC procedure to obtain the results. We also performed a simulation study to investigate power gains with additional markers. Our results indicate that an additional marker on each map can provide a great deal more information for linkage measured in terms of the magnitude of lod scores.

Alcoholism↗
PubMed2002

Determination and refinement of disordered crystal structures using evolutionary algorithms in combination with Monte Carlo methods.

An evolutionary algorithm called 'differential evolution' is combined with Monte Carlo simulation to determine and optimize models of disordered crystal structures. Requirements for successfully finding the parameters describing disorder from diffuse scattering data are discussed and the algorithm is applied to resolving the racemic and associated displacive disorder of the host substructure in a perhydrotriphenylene inclusion compound. Refinement resulted in a very good visual agreement between observed and calculated intensities and in a relatively low value of R(diffuse) = 0.148 (3). The computations for determining and refining the structure took 29 d with five to ten workstations running in parallel. Analysis of the progress of the structure determination shows that the essential information can be obtained within a few hours. Limits of the technique and strategies to optimize the procedure are discussed.

Journal Article↗
PubMed1998

A stochastic approximation algorithm with Markov chain Monte-carlo method for incomplete data estimation problems.

We propose a general procedure for solving incomplete data estimation problems. The procedure can be used to find the maximum likelihood estimate or to solve estimating equations in difficult cases such as estimation with the censored or truncated regression model, the nonlinear structural measurement error model, and the random effects model. The procedure is based on the general principle of stochastic approximation and the Markov chain Monte-Carlo method. Applying the theory on adaptive algorithms, we derive conditions under which the proposed procedure converges. Simulation studies also indicate that the proposed procedure consistently converges to the maximum likelihood estimate for the structural measurement error logistic regression model.

Journal Article↗