Scalable Domain Decomposed Monte Carlo Particle Transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

O'Brien, Matthew Joseph

2013-12-05

In this dissertation, we present the parallel algorithms necessary to run domain decomposed Monte Carlo particle transport on large numbers of processors (millions of processors). Previous algorithms were not scalable, and the parallel overhead became more computationally costly than the numerical simulation.

Mosaicing of airborne LiDAR bathymetry strips based on Monte Carlo matching

NASA Astrophysics Data System (ADS)

Yang, Fanlin; Su, Dianpeng; Zhang, Kai; Ma, Yue; Wang, Mingwei; Yang, Anxiu

2017-09-01

This study proposes a new methodology for mosaicing airborne light detection and ranging (LiDAR) bathymetry (ALB) data based on Monte Carlo matching. Various errors occur in ALB data due to imperfect system integration and other interference factors. To account for these errors, a Monte Carlo matching algorithm based on a nonlinear least-squares adjustment model is proposed. First, the raw data of strip overlap areas were filtered according to their relative drift of depths. Second, a Monte Carlo model and nonlinear least-squares adjustment model were combined to obtain seven transformation parameters. Then, the multibeam bathymetric data were used to correct the initial strip during strip mosaicing. Finally, to evaluate the proposed method, the experimental results were compared with the results of the Iterative Closest Points (ICP) and three-dimensional Normal Distributions Transform (3D-NDT) algorithms. The results demonstrate that the algorithm proposed in this study is more robust and effective. When the quality of the raw data is poor, the Monte Carlo matching algorithm can still achieve centimeter-level accuracy for overlapping areas, which meets the accuracy of bathymetry required by IHO Standards for Hydrographic Surveys Special Publication No.44.

Self-learning Monte Carlo method

DOE PAGES

Liu, Junwei; Qi, Yang; Meng, Zi Yang; ...

2017-01-04

Monte Carlo simulation is an unbiased numerical tool for studying classical and quantum many-body systems. One of its bottlenecks is the lack of a general and efficient update algorithm for large size systems close to the phase transition, for which local updates perform badly. In this Rapid Communication, we propose a general-purpose Monte Carlo method, dubbed self-learning Monte Carlo (SLMC), in which an efficient update algorithm is first learned from the training data generated in trial simulations and then used to speed up the actual simulation. Lastly, we demonstrate the efficiency of SLMC in a spin model at the phasemore » transition point, achieving a 10–20 times speedup.« less

Random Numbers and Monte Carlo Methods

NASA Astrophysics Data System (ADS)

Scherer, Philipp O. J.

Many-body problems often involve the calculation of integrals of very high dimension which cannot be treated by standard methods. For the calculation of thermodynamic averages Monte Carlo methods are very useful which sample the integration volume at randomly chosen points. After summarizing some basic statistics, we discuss algorithms for the generation of pseudo-random numbers with given probability distribution which are essential for all Monte Carlo methods. We show how the efficiency of Monte Carlo integration can be improved by sampling preferentially the important configurations. Finally the famous Metropolis algorithm is applied to classical many-particle systems. Computer experiments visualize the central limit theorem and apply the Metropolis method to the traveling salesman problem.

A High-Order Low-Order Algorithm with Exponentially Convergent Monte Carlo for Thermal Radiative Transfer

DOE PAGES

Bolding, Simon R.; Cleveland, Mathew Allen; Morel, Jim E.

2016-10-21

In this paper, we have implemented a new high-order low-order (HOLO) algorithm for solving thermal radiative transfer problems. The low-order (LO) system is based on the spatial and angular moments of the transport equation and a linear-discontinuous finite-element spatial representation, producing equations similar to the standard S 2 equations. The LO solver is fully implicit in time and efficiently resolves the nonlinear temperature dependence at each time step. The high-order (HO) solver utilizes exponentially convergent Monte Carlo (ECMC) to give a globally accurate solution for the angular intensity to a fixed-source pure-absorber transport problem. This global solution is used tomore » compute consistency terms, which require the HO and LO solutions to converge toward the same solution. The use of ECMC allows for the efficient reduction of statistical noise in the Monte Carlo solution, reducing inaccuracies introduced through the LO consistency terms. Finally, we compare results with an implicit Monte Carlo code for one-dimensional gray test problems and demonstrate the efficiency of ECMC over standard Monte Carlo in this HOLO algorithm.« less

Data decomposition of Monte Carlo particle transport simulations via tally servers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Romano, Paul K.; Siegel, Andrew R.; Forget, Benoit

An algorithm for decomposing large tally data in Monte Carlo particle transport simulations is developed, analyzed, and implemented in a continuous-energy Monte Carlo code, OpenMC. The algorithm is based on a non-overlapping decomposition of compute nodes into tracking processors and tally servers. The former are used to simulate the movement of particles through the domain while the latter continuously receive and update tally data. A performance model for this approach is developed, suggesting that, for a range of parameters relevant to LWR analysis, the tally server algorithm should perform with minimal overhead on contemporary supercomputers. An implementation of the algorithmmore » in OpenMC is then tested on the Intrepid and Titan supercomputers, supporting the key predictions of the model over a wide range of parameters. We thus conclude that the tally server algorithm is a successful approach to circumventing classical on-node memory constraints en route to unprecedentedly detailed Monte Carlo reactor simulations.« less

A novel algorithm for solving the true coincident counting issues in Monte Carlo simulations for radiation spectroscopy.

PubMed

Guan, Fada; Johns, Jesse M; Vasudevan, Latha; Zhang, Guoqing; Tang, Xiaobin; Poston, John W; Braby, Leslie A

2015-06-01

Coincident counts can be observed in experimental radiation spectroscopy. Accurate quantification of the radiation source requires the detection efficiency of the spectrometer, which is often experimentally determined. However, Monte Carlo analysis can be used to supplement experimental approaches to determine the detection efficiency a priori. The traditional Monte Carlo method overestimates the detection efficiency as a result of omitting coincident counts caused mainly by multiple cascade source particles. In this study, a novel "multi-primary coincident counting" algorithm was developed using the Geant4 Monte Carlo simulation toolkit. A high-purity Germanium detector for ⁶⁰Co gamma-ray spectroscopy problems was accurately modeled to validate the developed algorithm. The simulated pulse height spectrum agreed well qualitatively with the measured spectrum obtained using the high-purity Germanium detector. The developed algorithm can be extended to other applications, with a particular emphasis on challenging radiation fields, such as counting multiple types of coincident radiations released from nuclear fission or used nuclear fuel.

Optimization of the Monte Carlo code for modeling of photon migration in tissue.

PubMed

Zołek, Norbert S; Liebert, Adam; Maniewski, Roman

2006-10-01

The Monte Carlo method is frequently used to simulate light transport in turbid media because of its simplicity and flexibility, allowing to analyze complicated geometrical structures. Monte Carlo simulations are, however, time consuming because of the necessity to track the paths of individual photons. The time consuming computation is mainly associated with the calculation of the logarithmic and trigonometric functions as well as the generation of pseudo-random numbers. In this paper, the Monte Carlo algorithm was developed and optimized, by approximation of the logarithmic and trigonometric functions. The approximations were based on polynomial and rational functions, and the errors of these approximations are less than 1% of the values of the original functions. The proposed algorithm was verified by simulations of the time-resolved reflectance at several source-detector separations. The results of the calculation using the approximated algorithm were compared with those of the Monte Carlo simulations obtained with an exact computation of the logarithm and trigonometric functions as well as with the solution of the diffusion equation. The errors of the moments of the simulated distributions of times of flight of photons (total number of photons, mean time of flight and variance) are less than 2% for a range of optical properties, typical of living tissues. The proposed approximated algorithm allows to speed up the Monte Carlo simulations by a factor of 4. The developed code can be used on parallel machines, allowing for further acceleration.

Hybrid dose calculation: a dose calculation algorithm for microbeam radiation therapy

NASA Astrophysics Data System (ADS)

Donzelli, Mattia; Bräuer-Krisch, Elke; Oelfke, Uwe; Wilkens, Jan J.; Bartzsch, Stefan

2018-02-01

Microbeam radiation therapy (MRT) is still a preclinical approach in radiation oncology that uses planar micrometre wide beamlets with extremely high peak doses, separated by a few hundred micrometre wide low dose regions. Abundant preclinical evidence demonstrates that MRT spares normal tissue more effectively than conventional radiation therapy, at equivalent tumour control. In order to launch first clinical trials, accurate and efficient dose calculation methods are an inevitable prerequisite. In this work a hybrid dose calculation approach is presented that is based on a combination of Monte Carlo and kernel based dose calculation. In various examples the performance of the algorithm is compared to purely Monte Carlo and purely kernel based dose calculations. The accuracy of the developed algorithm is comparable to conventional pure Monte Carlo calculations. In particular for inhomogeneous materials the hybrid dose calculation algorithm out-performs purely convolution based dose calculation approaches. It is demonstrated that the hybrid algorithm can efficiently calculate even complicated pencil beam and cross firing beam geometries. The required calculation times are substantially lower than for pure Monte Carlo calculations.

Monte Carlo tests of the ELIPGRID-PC algorithm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Davidson, J.R.

1995-04-01

The standard tool for calculating the probability of detecting pockets of contamination called hot spots has been the ELIPGRID computer code of Singer and Wickman. The ELIPGRID-PC program has recently made this algorithm available for an IBM{reg_sign} PC. However, no known independent validation of the ELIPGRID algorithm exists. This document describes a Monte Carlo simulation-based validation of a modified version of the ELIPGRID-PC code. The modified ELIPGRID-PC code is shown to match Monte Carlo-calculated hot-spot detection probabilities to within {plus_minus}0.5% for 319 out of 320 test cases. The one exception, a very thin elliptical hot spot located within a rectangularmore » sampling grid, differed from the Monte Carlo-calculated probability by about 1%. These results provide confidence in the ability of the modified ELIPGRID-PC code to accurately predict hot-spot detection probabilities within an acceptable range of error.« less

The Impact of Monte Carlo Dose Calculations on Intensity-Modulated Radiation Therapy

NASA Astrophysics Data System (ADS)

Siebers, J. V.; Keall, P. J.; Mohan, R.

The effect of dose calculation accuracy for IMRT was studied by comparing different dose calculation algorithms. A head and neck IMRT plan was optimized using a superposition dose calculation algorithm. Dose was re-computed for the optimized plan using both Monte Carlo and pencil beam dose calculation algorithms to generate patient and phantom dose distributions. Tumor control probabilities (TCP) and normal tissue complication probabilities (NTCP) were computed to estimate the plan outcome. For the treatment plan studied, Monte Carlo best reproduces phantom dose measurements, the TCP was slightly lower than the superposition and pencil beam results, and the NTCP values differed little.

An unbiased Hessian representation for Monte Carlo PDFs.

PubMed

Carrazza, Stefano; Forte, Stefano; Kassabov, Zahari; Latorre, José Ignacio; Rojo, Juan

We develop a methodology for the construction of a Hessian representation of Monte Carlo sets of parton distributions, based on the use of a subset of the Monte Carlo PDF replicas as an unbiased linear basis, and of a genetic algorithm for the determination of the optimal basis. We validate the methodology by first showing that it faithfully reproduces a native Monte Carlo PDF set (NNPDF3.0), and then, that if applied to Hessian PDF set (MMHT14) which was transformed into a Monte Carlo set, it gives back the starting PDFs with minimal information loss. We then show that, when applied to a large Monte Carlo PDF set obtained as combination of several underlying sets, the methodology leads to a Hessian representation in terms of a rather smaller set of parameters (MC-H PDFs), thereby providing an alternative implementation of the recently suggested Meta-PDF idea and a Hessian version of the recently suggested PDF compression algorithm (CMC-PDFs). The mc2hessian conversion code is made publicly available together with (through LHAPDF6) a Hessian representations of the NNPDF3.0 set, and the MC-H PDF set.

The X-43A Six Degree of Freedom Monte Carlo Analysis

NASA Technical Reports Server (NTRS)

Baumann, Ethan; Bahm, Catherine; Strovers, Brian; Beck, Roger

2008-01-01

This report provides an overview of the Hyper-X research vehicle Monte Carlo analysis conducted with the six-degree-of-freedom simulation. The methodology and model uncertainties used for the Monte Carlo analysis are presented as permitted. In addition, the process used to select hardware validation test cases from the Monte Carlo data is described. The preflight Monte Carlo analysis indicated that the X-43A control system was robust to the preflight uncertainties and provided the Hyper-X project an important indication that the vehicle would likely be successful in accomplishing the mission objectives. The X-43A inflight performance is compared to the preflight Monte Carlo predictions and shown to exceed the Monte Carlo bounds in several instances. Possible modeling shortfalls are presented that may account for these discrepancies. The flight control laws and guidance algorithms were robust enough as a result of the preflight Monte Carlo analysis that the unexpected in-flight performance did not have undue consequences. Modeling and Monte Carlo analysis lessons learned are presented.

The X-43A Six Degree of Freedom Monte Carlo Analysis

NASA Technical Reports Server (NTRS)

Baumann, Ethan; Bahm, Catherine; Strovers, Brian; Beck, Roger; Richard, Michael

2007-01-01

This report provides an overview of the Hyper-X research vehicle Monte Carlo analysis conducted with the six-degree-of-freedom simulation. The methodology and model uncertainties used for the Monte Carlo analysis are presented as permitted. In addition, the process used to select hardware validation test cases from the Monte Carlo data is described. The preflight Monte Carlo analysis indicated that the X-43A control system was robust to the preflight uncertainties and provided the Hyper-X project an important indication that the vehicle would likely be successful in accomplishing the mission objectives. The X-43A in-flight performance is compared to the preflight Monte Carlo predictions and shown to exceed the Monte Carlo bounds in several instances. Possible modeling shortfalls are presented that may account for these discrepancies. The flight control laws and guidance algorithms were robust enough as a result of the preflight Monte Carlo analysis that the unexpected in-flight performance did not have undue consequences. Modeling and Monte Carlo analysis lessons learned are presented.

Metis: A Pure Metropolis Markov Chain Monte Carlo Bayesian Inference Library

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bates, Cameron Russell; Mckigney, Edward Allen

The use of Bayesian inference in data analysis has become the standard for large scienti c experiments [1, 2]. The Monte Carlo Codes Group(XCP-3) at Los Alamos has developed a simple set of algorithms currently implemented in C++ and Python to easily perform at-prior Markov Chain Monte Carlo Bayesian inference with pure Metropolis sampling. These implementations are designed to be user friendly and extensible for customization based on speci c application requirements. This document describes the algorithmic choices made and presents two use cases.

Finite element model updating using the shadow hybrid Monte Carlo technique

NASA Astrophysics Data System (ADS)

Boulkaibet, I.; Mthembu, L.; Marwala, T.; Friswell, M. I.; Adhikari, S.

2015-02-01

Recent research in the field of finite element model updating (FEM) advocates the adoption of Bayesian analysis techniques to dealing with the uncertainties associated with these models. However, Bayesian formulations require the evaluation of the Posterior Distribution Function which may not be available in analytical form. This is the case in FEM updating. In such cases sampling methods can provide good approximations of the Posterior distribution when implemented in the Bayesian context. Markov Chain Monte Carlo (MCMC) algorithms are the most popular sampling tools used to sample probability distributions. However, the efficiency of these algorithms is affected by the complexity of the systems (the size of the parameter space). The Hybrid Monte Carlo (HMC) offers a very important MCMC approach to dealing with higher-dimensional complex problems. The HMC uses the molecular dynamics (MD) steps as the global Monte Carlo (MC) moves to reach areas of high probability where the gradient of the log-density of the Posterior acts as a guide during the search process. However, the acceptance rate of HMC is sensitive to the system size as well as the time step used to evaluate the MD trajectory. To overcome this limitation we propose the use of the Shadow Hybrid Monte Carlo (SHMC) algorithm. The SHMC algorithm is a modified version of the Hybrid Monte Carlo (HMC) and designed to improve sampling for large-system sizes and time steps. This is done by sampling from a modified Hamiltonian function instead of the normal Hamiltonian function. In this paper, the efficiency and accuracy of the SHMC method is tested on the updating of two real structures; an unsymmetrical H-shaped beam structure and a GARTEUR SM-AG19 structure and is compared to the application of the HMC algorithm on the same structures.

Parallel Markov chain Monte Carlo - bridging the gap to high-performance Bayesian computation in animal breeding and genetics.

PubMed

Wu, Xiao-Lin; Sun, Chuanyu; Beissinger, Timothy M; Rosa, Guilherme Jm; Weigel, Kent A; Gatti, Natalia de Leon; Gianola, Daniel

2012-09-25

Most Bayesian models for the analysis of complex traits are not analytically tractable and inferences are based on computationally intensive techniques. This is true of Bayesian models for genome-enabled selection, which uses whole-genome molecular data to predict the genetic merit of candidate animals for breeding purposes. In this regard, parallel computing can overcome the bottlenecks that can arise from series computing. Hence, a major goal of the present study is to bridge the gap to high-performance Bayesian computation in the context of animal breeding and genetics. Parallel Monte Carlo Markov chain algorithms and strategies are described in the context of animal breeding and genetics. Parallel Monte Carlo algorithms are introduced as a starting point including their applications to computing single-parameter and certain multiple-parameter models. Then, two basic approaches for parallel Markov chain Monte Carlo are described: one aims at parallelization within a single chain; the other is based on running multiple chains, yet some variants are discussed as well. Features and strategies of the parallel Markov chain Monte Carlo are illustrated using real data, including a large beef cattle dataset with 50K SNP genotypes. Parallel Markov chain Monte Carlo algorithms are useful for computing complex Bayesian models, which does not only lead to a dramatic speedup in computing but can also be used to optimize model parameters in complex Bayesian models. Hence, we anticipate that use of parallel Markov chain Monte Carlo will have a profound impact on revolutionizing the computational tools for genomic selection programs.

Parallel Markov chain Monte Carlo - bridging the gap to high-performance Bayesian computation in animal breeding and genetics

PubMed Central

2012-01-01

Background Most Bayesian models for the analysis of complex traits are not analytically tractable and inferences are based on computationally intensive techniques. This is true of Bayesian models for genome-enabled selection, which uses whole-genome molecular data to predict the genetic merit of candidate animals for breeding purposes. In this regard, parallel computing can overcome the bottlenecks that can arise from series computing. Hence, a major goal of the present study is to bridge the gap to high-performance Bayesian computation in the context of animal breeding and genetics. Results Parallel Monte Carlo Markov chain algorithms and strategies are described in the context of animal breeding and genetics. Parallel Monte Carlo algorithms are introduced as a starting point including their applications to computing single-parameter and certain multiple-parameter models. Then, two basic approaches for parallel Markov chain Monte Carlo are described: one aims at parallelization within a single chain; the other is based on running multiple chains, yet some variants are discussed as well. Features and strategies of the parallel Markov chain Monte Carlo are illustrated using real data, including a large beef cattle dataset with 50K SNP genotypes. Conclusions Parallel Markov chain Monte Carlo algorithms are useful for computing complex Bayesian models, which does not only lead to a dramatic speedup in computing but can also be used to optimize model parameters in complex Bayesian models. Hence, we anticipate that use of parallel Markov chain Monte Carlo will have a profound impact on revolutionizing the computational tools for genomic selection programs. PMID:23009363

Self-Learning Monte Carlo Method

NASA Astrophysics Data System (ADS)

Liu, Junwei; Qi, Yang; Meng, Zi Yang; Fu, Liang

Monte Carlo simulation is an unbiased numerical tool for studying classical and quantum many-body systems. One of its bottlenecks is the lack of general and efficient update algorithm for large size systems close to phase transition or with strong frustrations, for which local updates perform badly. In this work, we propose a new general-purpose Monte Carlo method, dubbed self-learning Monte Carlo (SLMC), in which an efficient update algorithm is first learned from the training data generated in trial simulations and then used to speed up the actual simulation. We demonstrate the efficiency of SLMC in a spin model at the phase transition point, achieving a 10-20 times speedup. This work is supported by the DOE Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0010526.

A Christoffel function weighted least squares algorithm for collocation approximations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Narayan, Akil; Jakeman, John D.; Zhou, Tao

Here, we propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation framework. Our investigation is motivated by applications in the collocation approximation of parametric functions, which frequently entails construction of surrogates via orthogonal polynomials. A standard Monte Carlo approach would draw samples according to the density defining the orthogonal polynomial family. Our proposed algorithm instead samples with respect to the (weighted) pluripotential equilibrium measure of the domain, and subsequently solves a weighted least-squares problem, with weights given by evaluations of the Christoffel function. We present theoretical analysis tomore » motivate the algorithm, and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest.« less

A Christoffel function weighted least squares algorithm for collocation approximations

DOE PAGES

Narayan, Akil; Jakeman, John D.; Zhou, Tao

2016-11-28

Here, we propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation framework. Our investigation is motivated by applications in the collocation approximation of parametric functions, which frequently entails construction of surrogates via orthogonal polynomials. A standard Monte Carlo approach would draw samples according to the density defining the orthogonal polynomial family. Our proposed algorithm instead samples with respect to the (weighted) pluripotential equilibrium measure of the domain, and subsequently solves a weighted least-squares problem, with weights given by evaluations of the Christoffel function. We present theoretical analysis tomore » motivate the algorithm, and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest.« less

A Monte Carlo Approach for Adaptive Testing with Content Constraints

ERIC Educational Resources Information Center

Belov, Dmitry I.; Armstrong, Ronald D.; Weissman, Alexander

2008-01-01

This article presents a new algorithm for computerized adaptive testing (CAT) when content constraints are present. The algorithm is based on shadow CAT methodology to meet content constraints but applies Monte Carlo methods and provides the following advantages over shadow CAT: (a) lower maximum item exposure rates, (b) higher utilization of the…

Teaching Markov Chain Monte Carlo: Revealing the Basic Ideas behind the Algorithm

ERIC Educational Resources Information Center

Stewart, Wayne; Stewart, Sepideh

2014-01-01

For many scientists, researchers and students Markov chain Monte Carlo (MCMC) simulation is an important and necessary tool to perform Bayesian analyses. The simulation is often presented as a mathematical algorithm and then translated into an appropriate computer program. However, this can result in overlooking the fundamental and deeper…

Monte Carlo evaluation of Acuros XB dose calculation Algorithm for intensity modulated radiation therapy of nasopharyngeal carcinoma

NASA Astrophysics Data System (ADS)

Yeh, Peter C. Y.; Lee, C. C.; Chao, T. C.; Tung, C. J.

2017-11-01

Intensity-modulated radiation therapy is an effective treatment modality for the nasopharyngeal carcinoma. One important aspect of this cancer treatment is the need to have an accurate dose algorithm dealing with the complex air/bone/tissue interface in the head-neck region to achieve the cure without radiation-induced toxicities. The Acuros XB algorithm explicitly solves the linear Boltzmann transport equation in voxelized volumes to account for the tissue heterogeneities such as lungs, bone, air, and soft tissues in the treatment field receiving radiotherapy. With the single beam setup in phantoms, this algorithm has already been demonstrated to achieve the comparable accuracy with Monte Carlo simulations. In the present study, five nasopharyngeal carcinoma patients treated with the intensity-modulated radiation therapy were examined for their dose distributions calculated using the Acuros XB in the planning target volume and the organ-at-risk. Corresponding results of Monte Carlo simulations were computed from the electronic portal image data and the BEAMnrc/DOSXYZnrc code. Analysis of dose distributions in terms of the clinical indices indicated that the Acuros XB was in comparable accuracy with Monte Carlo simulations and better than the anisotropic analytical algorithm for dose calculations in real patients.

Automatic mesh adaptivity for hybrid Monte Carlo/deterministic neutronics modeling of difficult shielding problems

DOE PAGES

Ibrahim, Ahmad M.; Wilson, Paul P.H.; Sawan, Mohamed E.; ...

2015-06-30

The CADIS and FW-CADIS hybrid Monte Carlo/deterministic techniques dramatically increase the efficiency of neutronics modeling, but their use in the accurate design analysis of very large and geometrically complex nuclear systems has been limited by the large number of processors and memory requirements for their preliminary deterministic calculations and final Monte Carlo calculation. Three mesh adaptivity algorithms were developed to reduce the memory requirements of CADIS and FW-CADIS without sacrificing their efficiency improvement. First, a macromaterial approach enhances the fidelity of the deterministic models without changing the mesh. Second, a deterministic mesh refinement algorithm generates meshes that capture as muchmore » geometric detail as possible without exceeding a specified maximum number of mesh elements. Finally, a weight window coarsening algorithm decouples the weight window mesh and energy bins from the mesh and energy group structure of the deterministic calculations in order to remove the memory constraint of the weight window map from the deterministic mesh resolution. The three algorithms were used to enhance an FW-CADIS calculation of the prompt dose rate throughout the ITER experimental facility. Using these algorithms resulted in a 23.3% increase in the number of mesh tally elements in which the dose rates were calculated in a 10-day Monte Carlo calculation and, additionally, increased the efficiency of the Monte Carlo simulation by a factor of at least 3.4. The three algorithms enabled this difficult calculation to be accurately solved using an FW-CADIS simulation on a regular computer cluster, eliminating the need for a world-class super computer.« less

Forward and inverse uncertainty quantification using multilevel Monte Carlo algorithms for an elliptic non-local equation

DOE PAGES

Jasra, Ajay; Law, Kody J. H.; Zhou, Yan

2016-01-01

Our paper considers uncertainty quantification for an elliptic nonlocal equation. In particular, it is assumed that the parameters which define the kernel in the nonlocal operator are uncertain and a priori distributed according to a probability measure. It is shown that the induced probability measure on some quantities of interest arising from functionals of the solution to the equation with random inputs is well-defined,s as is the posterior distribution on parameters given observations. As the elliptic nonlocal equation cannot be solved approximate posteriors are constructed. The multilevel Monte Carlo (MLMC) and multilevel sequential Monte Carlo (MLSMC) sampling algorithms are usedmore » for a priori and a posteriori estimation, respectively, of quantities of interest. Furthermore, these algorithms reduce the amount of work to estimate posterior expectations, for a given level of error, relative to Monte Carlo and i.i.d. sampling from the posterior at a given level of approximation of the solution of the elliptic nonlocal equation.« less

Forward and inverse uncertainty quantification using multilevel Monte Carlo algorithms for an elliptic non-local equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jasra, Ajay; Law, Kody J. H.; Zhou, Yan

Our paper considers uncertainty quantification for an elliptic nonlocal equation. In particular, it is assumed that the parameters which define the kernel in the nonlocal operator are uncertain and a priori distributed according to a probability measure. It is shown that the induced probability measure on some quantities of interest arising from functionals of the solution to the equation with random inputs is well-defined,s as is the posterior distribution on parameters given observations. As the elliptic nonlocal equation cannot be solved approximate posteriors are constructed. The multilevel Monte Carlo (MLMC) and multilevel sequential Monte Carlo (MLSMC) sampling algorithms are usedmore » for a priori and a posteriori estimation, respectively, of quantities of interest. Furthermore, these algorithms reduce the amount of work to estimate posterior expectations, for a given level of error, relative to Monte Carlo and i.i.d. sampling from the posterior at a given level of approximation of the solution of the elliptic nonlocal equation.« less

High-efficiency wavefunction updates for large scale Quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Kent, Paul; McDaniel, Tyler; Li, Ying Wai; D'Azevedo, Ed

Within ab intio Quantum Monte Carlo (QMC) simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunctions. The evaluation of each Monte Carlo move requires finding the determinant of a dense matrix, which is traditionally iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. For calculations with thousands of electrons, this operation dominates the execution profile. We propose a novel rank- k delayed update scheme. This strategy enables probability evaluation for multiple successive Monte Carlo moves, with application of accepted moves to the matrices delayed until after a predetermined number of moves, k. Accepted events grouped in this manner are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency. This procedure does not change the underlying Monte Carlo sampling or the sampling efficiency. For large systems and algorithms such as diffusion Monte Carlo where the acceptance ratio is high, order of magnitude speedups can be obtained on both multi-core CPU and on GPUs, making this algorithm highly advantageous for current petascale and future exascale computations.

Experiences with Markov Chain Monte Carlo Convergence Assessment in Two Psychometric Examples

ERIC Educational Resources Information Center

Sinharay, Sandip

2004-01-01

There is an increasing use of Markov chain Monte Carlo (MCMC) algorithms for fitting statistical models in psychometrics, especially in situations where the traditional estimation techniques are very difficult to apply. One of the disadvantages of using an MCMC algorithm is that it is not straightforward to determine the convergence of the…

Exploring cluster Monte Carlo updates with Boltzmann machines

NASA Astrophysics Data System (ADS)

Wang, Lei

2017-11-01

Boltzmann machines are physics informed generative models with broad applications in machine learning. They model the probability distribution of an input data set with latent variables and generate new samples accordingly. Applying the Boltzmann machines back to physics, they are ideal recommender systems to accelerate the Monte Carlo simulation of physical systems due to their flexibility and effectiveness. More intriguingly, we show that the generative sampling of the Boltzmann machines can even give different cluster Monte Carlo algorithms. The latent representation of the Boltzmann machines can be designed to mediate complex interactions and identify clusters of the physical system. We demonstrate these findings with concrete examples of the classical Ising model with and without four-spin plaquette interactions. In the future, automatic searches in the algorithm space parametrized by Boltzmann machines may discover more innovative Monte Carlo updates.

Event-chain algorithm for the Heisenberg model: Evidence for z≃1 dynamic scaling.

PubMed

Nishikawa, Yoshihiko; Michel, Manon; Krauth, Werner; Hukushima, Koji

2015-12-01

We apply the event-chain Monte Carlo algorithm to the three-dimensional ferromagnetic Heisenberg model. The algorithm is rejection-free and also realizes an irreversible Markov chain that satisfies global balance. The autocorrelation functions of the magnetic susceptibility and the energy indicate a dynamical critical exponent z≈1 at the critical temperature, while that of the magnetization does not measure the performance of the algorithm. We show that the event-chain Monte Carlo algorithm substantially reduces the dynamical critical exponent from the conventional value of z≃2.

Monte Carlo uncertainty analysis of dose estimates in radiochromic film dosimetry with single-channel and multichannel algorithms.

PubMed

Vera-Sánchez, Juan Antonio; Ruiz-Morales, Carmen; González-López, Antonio

2018-03-01

To provide a multi-stage model to calculate uncertainty in radiochromic film dosimetry with Monte-Carlo techniques. This new approach is applied to single-channel and multichannel algorithms. Two lots of Gafchromic EBT3 are exposed in two different Varian linacs. They are read with an EPSON V800 flatbed scanner. The Monte-Carlo techniques in uncertainty analysis provide a numerical representation of the probability density functions of the output magnitudes. From this numerical representation, traditional parameters of uncertainty analysis as the standard deviations and bias are calculated. Moreover, these numerical representations are used to investigate the shape of the probability density functions of the output magnitudes. Also, another calibration film is read in four EPSON scanners (two V800 and two 10000XL) and the uncertainty analysis is carried out with the four images. The dose estimates of single-channel and multichannel algorithms show a Gaussian behavior and low bias. The multichannel algorithms lead to less uncertainty in the final dose estimates when the EPSON V800 is employed as reading device. In the case of the EPSON 10000XL, the single-channel algorithms provide less uncertainty in the dose estimates for doses higher than four Gy. A multi-stage model has been presented. With the aid of this model and the use of the Monte-Carlo techniques, the uncertainty of dose estimates for single-channel and multichannel algorithms are estimated. The application of the model together with Monte-Carlo techniques leads to a complete characterization of the uncertainties in radiochromic film dosimetry. Copyright © 2018 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Exact and Monte carlo resampling procedures for the Wilcoxon-Mann-Whitney and Kruskal-Wallis tests.

PubMed

Berry, K J; Mielke, P W

2000-12-01

Exact and Monte Carlo resampling FORTRAN programs are described for the Wilcoxon-Mann-Whitney rank sum test and the Kruskal-Wallis one-way analysis of variance for ranks test. The program algorithms compensate for tied values and do not depend on asymptotic approximations for probability values, unlike most algorithms contained in PC-based statistical software packages.

Pattern Recognition for a Flight Dynamics Monte Carlo Simulation

NASA Technical Reports Server (NTRS)

Restrepo, Carolina; Hurtado, John E.

2011-01-01

The design, analysis, and verification and validation of a spacecraft relies heavily on Monte Carlo simulations. Modern computational techniques are able to generate large amounts of Monte Carlo data but flight dynamics engineers lack the time and resources to analyze it all. The growing amounts of data combined with the diminished available time of engineers motivates the need to automate the analysis process. Pattern recognition algorithms are an innovative way of analyzing flight dynamics data efficiently. They can search large data sets for specific patterns and highlight critical variables so analysts can focus their analysis efforts. This work combines a few tractable pattern recognition algorithms with basic flight dynamics concepts to build a practical analysis tool for Monte Carlo simulations. Current results show that this tool can quickly and automatically identify individual design parameters, and most importantly, specific combinations of parameters that should be avoided in order to prevent specific system failures. The current version uses a kernel density estimation algorithm and a sequential feature selection algorithm combined with a k-nearest neighbor classifier to find and rank important design parameters. This provides an increased level of confidence in the analysis and saves a significant amount of time.

Path integral Monte Carlo ground state approach: formalism, implementation, and applications

NASA Astrophysics Data System (ADS)

Yan, Yangqian; Blume, D.

2017-11-01

Monte Carlo techniques have played an important role in understanding strongly correlated systems across many areas of physics, covering a wide range of energy and length scales. Among the many Monte Carlo methods applicable to quantum mechanical systems, the path integral Monte Carlo approach with its variants has been employed widely. Since semi-classical or classical approaches will not be discussed in this review, path integral based approaches can for our purposes be divided into two categories: approaches applicable to quantum mechanical systems at zero temperature and approaches applicable to quantum mechanical systems at finite temperature. While these two approaches are related to each other, the underlying formulation and aspects of the algorithm differ. This paper reviews the path integral Monte Carlo ground state (PIGS) approach, which solves the time-independent Schrödinger equation. Specifically, the PIGS approach allows for the determination of expectation values with respect to eigen states of the few- or many-body Schrödinger equation provided the system Hamiltonian is known. The theoretical framework behind the PIGS algorithm, implementation details, and sample applications for fermionic systems are presented.

Simulation of Nuclear Reactor Kinetics by the Monte Carlo Method

NASA Astrophysics Data System (ADS)

Gomin, E. A.; Davidenko, V. D.; Zinchenko, A. S.; Kharchenko, I. K.

2017-12-01

The KIR computer code intended for calculations of nuclear reactor kinetics using the Monte Carlo method is described. The algorithm implemented in the code is described in detail. Some results of test calculations are given.

Markov chain Monte Carlo techniques applied to parton distribution functions determination: Proof of concept

NASA Astrophysics Data System (ADS)

Gbedo, Yémalin Gabin; Mangin-Brinet, Mariane

2017-07-01

We present a new procedure to determine parton distribution functions (PDFs), based on Markov chain Monte Carlo (MCMC) methods. The aim of this paper is to show that we can replace the standard χ2 minimization by procedures grounded on statistical methods, and on Bayesian inference in particular, thus offering additional insight into the rich field of PDFs determination. After a basic introduction to these techniques, we introduce the algorithm we have chosen to implement—namely Hybrid (or Hamiltonian) Monte Carlo. This algorithm, initially developed for Lattice QCD, turns out to be very interesting when applied to PDFs determination by global analyses; we show that it allows us to circumvent the difficulties due to the high dimensionality of the problem, in particular concerning the acceptance. A first feasibility study is performed and presented, which indicates that Markov chain Monte Carlo can successfully be applied to the extraction of PDFs and of their uncertainties.

Scalable Domain Decomposed Monte Carlo Particle Transport

NASA Astrophysics Data System (ADS)

O'Brien, Matthew Joseph

In this dissertation, we present the parallel algorithms necessary to run domain decomposed Monte Carlo particle transport on large numbers of processors (millions of processors). Previous algorithms were not scalable, and the parallel overhead became more computationally costly than the numerical simulation. The main algorithms we consider are: • Domain decomposition of constructive solid geometry: enables extremely large calculations in which the background geometry is too large to fit in the memory of a single computational node. • Load Balancing: keeps the workload per processor as even as possible so the calculation runs efficiently. • Global Particle Find: if particles are on the wrong processor, globally resolve their locations to the correct processor based on particle coordinate and background domain. • Visualizing constructive solid geometry, sourcing particles, deciding that particle streaming communication is completed and spatial redecomposition. These algorithms are some of the most important parallel algorithms required for domain decomposed Monte Carlo particle transport. We demonstrate that our previous algorithms were not scalable, prove that our new algorithms are scalable, and run some of the algorithms up to 2 million MPI processes on the Sequoia supercomputer.

Discrete Diffusion Monte Carlo for Electron Thermal Transport

NASA Astrophysics Data System (ADS)

Chenhall, Jeffrey; Cao, Duc; Wollaeger, Ryan; Moses, Gregory

2014-10-01

The iSNB (implicit Schurtz Nicolai Busquet electron thermal transport method of Cao et al. is adapted to a Discrete Diffusion Monte Carlo (DDMC) solution method for eventual inclusion in a hybrid IMC-DDMC (Implicit Monte Carlo) method. The hybrid method will combine the efficiency of a diffusion method in short mean free path regions with the accuracy of a transport method in long mean free path regions. The Monte Carlo nature of the approach allows the algorithm to be massively parallelized. Work to date on the iSNB-DDMC method will be presented. This work was supported by Sandia National Laboratory - Albuquerque.

A histogram-free multicanonical Monte Carlo algorithm for the construction of analytical density of states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eisenbach, Markus; Li, Ying Wai

We report a new multicanonical Monte Carlo (MC) algorithm to obtain the density of states (DOS) for physical systems with continuous state variables in statistical mechanics. Our algorithm is able to obtain an analytical form for the DOS expressed in a chosen basis set, instead of a numerical array of finite resolution as in previous variants of this class of MC methods such as the multicanonical (MUCA) sampling and Wang-Landau (WL) sampling. This is enabled by storing the visited states directly in a data set and avoiding the explicit collection of a histogram. This practice also has the advantage ofmore » avoiding undesirable artificial errors caused by the discretization and binning of continuous state variables. Our results show that this scheme is capable of obtaining converged results with a much reduced number of Monte Carlo steps, leading to a significant speedup over existing algorithms.« less

Percentage depth dose evaluation in heterogeneous media using thermoluminescent dosimetry

PubMed Central

da Rosa, L.A.R.; Campos, L.T.; Alves, V.G.L.; Batista, D.V.S.; Facure, A.

2010-01-01

The purpose of this study is to investigate the influence of lung heterogeneity inside a soft tissue phantom on percentage depth dose (PDD). PDD curves were obtained experimentally using LiF:Mg,Ti (TLD‐100) thermoluminescent detectors and applying Eclipse treatment planning system algorithms Batho, modified Batho (M‐Batho or BMod), equivalent TAR (E‐TAR or EQTAR), and anisotropic analytical algorithm (AAA) for a 15 MV photon beam and field sizes of 1×1,2×2,5×5, and 10×10cm2. Monte Carlo simulations were performed using the DOSRZnrc user code of EGSnrc. The experimental results agree with Monte Carlo simulations for all irradiation field sizes. Comparisons with Monte Carlo calculations show that the AAA algorithm provides the best simulations of PDD curves for all field sizes investigated. However, even this algorithm cannot accurately predict PDD values in the lung for field sizes of 1×1 and 2×2cm2. An overdosage in the lung of about 40% and 20% is calculated by the AAA algorithm close to the interface soft tissue/lung for 1×1 and 2×2cm2 field sizes, respectively. It was demonstrated that differences of 100% between Monte Carlo results and the algorithms Batho, modified Batho, and equivalent TAR responses may exist inside the lung region for the 1×1cm2 field. PACS number: 87.55.kd

Monte Carlo treatment planning with modulated electron radiotherapy: framework development and application

NASA Astrophysics Data System (ADS)

Alexander, Andrew William

Within the field of medical physics, Monte Carlo radiation transport simulations are considered to be the most accurate method for the determination of dose distributions in patients. The McGill Monte Carlo treatment planning system (MMCTP), provides a flexible software environment to integrate Monte Carlo simulations with current and new treatment modalities. A developing treatment modality called energy and intensity modulated electron radiotherapy (MERT) is a promising modality, which has the fundamental capabilities to enhance the dosimetry of superficial targets. An objective of this work is to advance the research and development of MERT with the end goal of clinical use. To this end, we present the MMCTP system with an integrated toolkit for MERT planning and delivery of MERT fields. Delivery is achieved using an automated "few leaf electron collimator" (FLEC) and a controller. Aside from the MERT planning toolkit, the MMCTP system required numerous add-ons to perform the complex task of large-scale autonomous Monte Carlo simulations. The first was a DICOM import filter, followed by the implementation of DOSXYZnrc as a dose calculation engine and by logic methods for submitting and updating the status of Monte Carlo simulations. Within this work we validated the MMCTP system with a head and neck Monte Carlo recalculation study performed by a medical dosimetrist. The impact of MMCTP lies in the fact that it allows for systematic and platform independent large-scale Monte Carlo dose calculations for different treatment sites and treatment modalities. In addition to the MERT planning tools, various optimization algorithms were created external to MMCTP. The algorithms produced MERT treatment plans based on dose volume constraints that employ Monte Carlo pre-generated patient-specific kernels. The Monte Carlo kernels are generated from patient-specific Monte Carlo dose distributions within MMCTP. The structure of the MERT planning toolkit software and optimization algorithms are demonstrated. We investigated the clinical significance of MERT on spinal irradiation, breast boost irradiation, and a head and neck sarcoma cancer site using several parameters to analyze the treatment plans. Finally, we investigated the idea of mixed beam photon and electron treatment planning. Photon optimization treatment planning tools were included within the MERT planning toolkit for the purpose of mixed beam optimization. In conclusion, this thesis work has resulted in the development of an advanced framework for photon and electron Monte Carlo treatment planning studies and the development of an inverse planning system for photon, electron or mixed beam radiotherapy (MBRT). The justification and validation of this work is found within the results of the planning studies, which have demonstrated dosimetric advantages to using MERT or MBRT in comparison to clinical treatment alternatives.

Monte Carlo Transport for Electron Thermal Transport

NASA Astrophysics Data System (ADS)

Chenhall, Jeffrey; Cao, Duc; Moses, Gregory

2015-11-01

The iSNB (implicit Schurtz Nicolai Busquet multigroup electron thermal transport method of Cao et al. is adapted into a Monte Carlo transport method in order to better model the effects of non-local behavior. The end goal is a hybrid transport-diffusion method that combines Monte Carlo Transport with a discrete diffusion Monte Carlo (DDMC). The hybrid method will combine the efficiency of a diffusion method in short mean free path regions with the accuracy of a transport method in long mean free path regions. The Monte Carlo nature of the approach allows the algorithm to be massively parallelized. Work to date on the method will be presented. This work was supported by Sandia National Laboratory - Albuquerque and the University of Rochester Laboratory for Laser Energetics.

An empirical approach to estimate near-infra-red photon propagation and optically induced drug release in brain tissues

NASA Astrophysics Data System (ADS)

Prabhu Verleker, Akshay; Fang, Qianqian; Choi, Mi-Ran; Clare, Susan; Stantz, Keith M.

2015-03-01

The purpose of this study is to develop an alternate empirical approach to estimate near-infra-red (NIR) photon propagation and quantify optically induced drug release in brain metastasis, without relying on computationally expensive Monte Carlo techniques (gold standard). Targeted drug delivery with optically induced drug release is a noninvasive means to treat cancers and metastasis. This study is part of a larger project to treat brain metastasis by delivering lapatinib-drug-nanocomplexes and activating NIR-induced drug release. The empirical model was developed using a weighted approach to estimate photon scattering in tissues and calibrated using a GPU based 3D Monte Carlo. The empirical model was developed and tested against Monte Carlo in optical brain phantoms for pencil beams (width 1mm) and broad beams (width 10mm). The empirical algorithm was tested against the Monte Carlo for different albedos along with diffusion equation and in simulated brain phantoms resembling white-matter (μs'=8.25mm-1, μa=0.005mm-1) and gray-matter (μs'=2.45mm-1, μa=0.035mm-1) at wavelength 800nm. The goodness of fit between the two models was determined using coefficient of determination (R-squared analysis). Preliminary results show the Empirical algorithm matches Monte Carlo simulated fluence over a wide range of albedo (0.7 to 0.99), while the diffusion equation fails for lower albedo. The photon fluence generated by empirical code matched the Monte Carlo in homogeneous phantoms (R2=0.99). While GPU based Monte Carlo achieved 300X acceleration compared to earlier CPU based models, the empirical code is 700X faster than the Monte Carlo for a typical super-Gaussian laser beam.

Visual improvement for bad handwriting based on Monte-Carlo method

NASA Astrophysics Data System (ADS)

Shi, Cao; Xiao, Jianguo; Xu, Canhui; Jia, Wenhua

2014-03-01

A visual improvement algorithm based on Monte Carlo simulation is proposed in this paper, in order to enhance visual effects for bad handwriting. The whole improvement process is to use well designed typeface so as to optimize bad handwriting image. In this process, a series of linear operators for image transformation are defined for transforming typeface image to approach handwriting image. And specific parameters of linear operators are estimated by Monte Carlo method. Visual improvement experiments illustrate that the proposed algorithm can effectively enhance visual effect for handwriting image as well as maintain the original handwriting features, such as tilt, stroke order and drawing direction etc. The proposed visual improvement algorithm, in this paper, has a huge potential to be applied in tablet computer and Mobile Internet, in order to improve user experience on handwriting.

Instantons in Quantum Annealing: Thermally Assisted Tunneling Vs Quantum Monte Carlo Simulations

NASA Technical Reports Server (NTRS)

Jiang, Zhang; Smelyanskiy, Vadim N.; Boixo, Sergio; Isakov, Sergei V.; Neven, Hartmut; Mazzola, Guglielmo; Troyer, Matthias

2015-01-01

Recent numerical result (arXiv:1512.02206) from Google suggested that the D-Wave quantum annealer may have an asymptotic speed-up than simulated annealing, however, the asymptotic advantage disappears when it is compared to quantum Monte Carlo (a classical algorithm despite its name). We show analytically that the asymptotic scaling of quantum tunneling is exactly the same as the escape rate in quantum Monte Carlo for a class of problems. Thus, the Google result might be explained in our framework. We also found that the transition state in quantum Monte Carlo corresponds to the instanton solution in quantum tunneling problems, which is observed in numerical simulations.

Simulation-Based Model Checking for Nondeterministic Systems and Rare Events

DTIC Science & Technology

2016-03-24

year, we have investigated AO* search and Monte Carlo Tree Search algorithms to complement and enhance CMU’s SMCMDP. 1 Final Report, March 14... tree , so we can use it to find the probability of reachability for a property in PRISM’s Probabilistic LTL. By finding the maximum probability of...savings, particularly when handling very large models. 2.3 Monte Carlo Tree Search The Monte Carlo sampling process in SMCMDP can take a long time to

WARP

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bergmann, Ryan M.; Rowland, Kelly L.

2017-04-12

WARP, which can stand for ``Weaving All the Random Particles,'' is a three-dimensional (3D) continuous energy Monte Carlo neutron transport code developed at UC Berkeley to efficiently execute on NVIDIA graphics processing unit (GPU) platforms. WARP accelerates Monte Carlo simulations while preserving the benefits of using the Monte Carlo method, namely, that very few physical and geometrical simplifications are applied. WARP is able to calculate multiplication factors, neutron flux distributions (in both space and energy), and fission source distributions for time-independent neutron transport problems. It can run in both criticality or fixed source modes, but fixed source mode is currentlymore » not robust, optimized, or maintained in the newest version. WARP can transport neutrons in unrestricted arrangements of parallelepipeds, hexagonal prisms, cylinders, and spheres. The goal of developing WARP is to investigate algorithms that can grow into a full-featured, continuous energy, Monte Carlo neutron transport code that is accelerated by running on GPUs. The crux of the effort is to make Monte Carlo calculations faster while producing accurate results. Modern supercomputers are commonly being built with GPU coprocessor cards in their nodes to increase their computational efficiency and performance. GPUs execute efficiently on data-parallel problems, but most CPU codes, including those for Monte Carlo neutral particle transport, are predominantly task-parallel. WARP uses a data-parallel neutron transport algorithm to take advantage of the computing power GPUs offer.« less

Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo

DOE PAGES

McDaniel, Tyler; D’Azevedo, Ed F.; Li, Ying Wai; ...

2017-11-07

Within ab initio Quantum Monte Carlo simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunction. Each Monte Carlo step requires finding the determinant of a dense matrix. This is most commonly iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. The overall computational cost is therefore formally cubic in the number of electrons or matrix size. To improve the numerical efficiency of this procedure, we propose a novel multiple rank delayed update scheme. This strategy enables probability evaluation with applicationmore » of accepted moves to the matrices delayed until after a predetermined number of moves, K. The accepted events are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency via matrix-matrix operations instead of matrix-vector operations. Here this procedure does not change the underlying Monte Carlo sampling or its statistical efficiency. For calculations on large systems and algorithms such as diffusion Monte Carlo where the acceptance ratio is high, order of magnitude improvements in the update time can be obtained on both multi- core CPUs and GPUs.« less

Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo

DOE Office of Scientific and Technical Information (OSTI.GOV)

McDaniel, Tyler; D’Azevedo, Ed F.; Li, Ying Wai

Within ab initio Quantum Monte Carlo simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunction. Each Monte Carlo step requires finding the determinant of a dense matrix. This is most commonly iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. The overall computational cost is therefore formally cubic in the number of electrons or matrix size. To improve the numerical efficiency of this procedure, we propose a novel multiple rank delayed update scheme. This strategy enables probability evaluation with applicationmore » of accepted moves to the matrices delayed until after a predetermined number of moves, K. The accepted events are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency via matrix-matrix operations instead of matrix-vector operations. Here this procedure does not change the underlying Monte Carlo sampling or its statistical efficiency. For calculations on large systems and algorithms such as diffusion Monte Carlo where the acceptance ratio is high, order of magnitude improvements in the update time can be obtained on both multi- core CPUs and GPUs.« less

Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo.

PubMed

McDaniel, T; D'Azevedo, E F; Li, Y W; Wong, K; Kent, P R C

2017-11-07

Within ab initio Quantum Monte Carlo simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunction. Each Monte Carlo step requires finding the determinant of a dense matrix. This is most commonly iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. The overall computational cost is, therefore, formally cubic in the number of electrons or matrix size. To improve the numerical efficiency of this procedure, we propose a novel multiple rank delayed update scheme. This strategy enables probability evaluation with an application of accepted moves to the matrices delayed until after a predetermined number of moves, K. The accepted events are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency via matrix-matrix operations instead of matrix-vector operations. This procedure does not change the underlying Monte Carlo sampling or its statistical efficiency. For calculations on large systems and algorithms such as diffusion Monte Carlo, where the acceptance ratio is high, order of magnitude improvements in the update time can be obtained on both multi-core central processing units and graphical processing units.

Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo

NASA Astrophysics Data System (ADS)

McDaniel, T.; D'Azevedo, E. F.; Li, Y. W.; Wong, K.; Kent, P. R. C.

2017-11-01

Within ab initio Quantum Monte Carlo simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunction. Each Monte Carlo step requires finding the determinant of a dense matrix. This is most commonly iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. The overall computational cost is, therefore, formally cubic in the number of electrons or matrix size. To improve the numerical efficiency of this procedure, we propose a novel multiple rank delayed update scheme. This strategy enables probability evaluation with an application of accepted moves to the matrices delayed until after a predetermined number of moves, K. The accepted events are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency via matrix-matrix operations instead of matrix-vector operations. This procedure does not change the underlying Monte Carlo sampling or its statistical efficiency. For calculations on large systems and algorithms such as diffusion Monte Carlo, where the acceptance ratio is high, order of magnitude improvements in the update time can be obtained on both multi-core central processing units and graphical processing units.

High order methods for the integration of the Bateman equations and other problems of the form of y‧ = F(y,t)y

NASA Astrophysics Data System (ADS)

Josey, C.; Forget, B.; Smith, K.

2017-12-01

This paper introduces two families of A-stable algorithms for the integration of y‧ = F (y , t) y: the extended predictor-corrector (EPC) and the exponential-linear (EL) methods. The structure of the algorithm families are described, and the method of derivation of the coefficients presented. The new algorithms are then tested on a simple deterministic problem and a Monte Carlo isotopic evolution problem. The EPC family is shown to be only second order for systems of ODEs. However, the EPC-RK45 algorithm had the highest accuracy on the Monte Carlo test, requiring at least a factor of 2 fewer function evaluations to achieve a given accuracy than a second order predictor-corrector method (center extrapolation / center midpoint method) with regards to Gd-157 concentration. Members of the EL family can be derived to at least fourth order. The EL3 and the EL4 algorithms presented are shown to be third and fourth order respectively on the systems of ODE test. In the Monte Carlo test, these methods did not overtake the accuracy of EPC methods before statistical uncertainty dominated the error. The statistical properties of the algorithms were also analyzed during the Monte Carlo problem. The new methods are shown to yield smaller standard deviations on final quantities as compared to the reference predictor-corrector method, by up to a factor of 1.4.

How Monte Carlo heuristics aid to identify the physical processes of drug release kinetics.

PubMed

Lecca, Paola

2018-01-01

We implement a Monte Carlo heuristic algorithm to model drug release from a solid dosage form. We show that with Monte Carlo simulations it is possible to identify and explain the causes of the unsatisfactory predictive power of current drug release models. It is well known that the power-law, the exponential models, as well as those derived from or inspired by them accurately reproduce only the first 60% of the release curve of a drug from a dosage form. In this study, by using Monte Carlo simulation approaches, we show that these models fit quite accurately almost the entire release profile when the release kinetics is not governed by the coexistence of different physico-chemical mechanisms. We show that the accuracy of the traditional models are comparable with those of Monte Carlo heuristics when these heuristics approximate and oversimply the phenomenology of drug release. This observation suggests to develop and use novel Monte Carlo simulation heuristics able to describe the complexity of the release kinetics, and consequently to generate data more similar to those observed in real experiments. Implementing Monte Carlo simulation heuristics of the drug release phenomenology may be much straightforward and efficient than hypothesizing and implementing from scratch complex mathematical models of the physical processes involved in drug release. Identifying and understanding through simulation heuristics what processes of this phenomenology reproduce the observed data and then formalize them in mathematics may allow avoiding time-consuming, trial-error based regression procedures. Three bullet points, highlighting the customization of the procedure. •An efficient heuristics based on Monte Carlo methods for simulating drug release from solid dosage form encodes is presented. It specifies the model of the physical process in a simple but accurate way in the formula of the Monte Carlo Micro Step (MCS) time interval.•Given the experimentally observed curve of drug release, we point out how Monte Carlo heuristics can be integrated in an evolutionary algorithmic approach to infer the mode of MCS best fitting the observed data, and thus the observed release kinetics.•The software implementing the method is written in R language, the free most used language in the bioinformaticians community.

Using Stan for Item Response Theory Models

ERIC Educational Resources Information Center

Ames, Allison J.; Au, Chi Hang

2018-01-01

Stan is a flexible probabilistic programming language providing full Bayesian inference through Hamiltonian Monte Carlo algorithms. The benefits of Hamiltonian Monte Carlo include improved efficiency and faster inference, when compared to other MCMC software implementations. Users can interface with Stan through a variety of computing…

Dose specification for radiation therapy: dose to water or dose to medium?

NASA Astrophysics Data System (ADS)

Ma, C.-M.; Li, Jinsheng

2011-05-01

The Monte Carlo method enables accurate dose calculation for radiation therapy treatment planning and has been implemented in some commercial treatment planning systems. Unlike conventional dose calculation algorithms that provide patient dose information in terms of dose to water with variable electron density, the Monte Carlo method calculates the energy deposition in different media and expresses dose to a medium. This paper discusses the differences in dose calculated using water with different electron densities and that calculated for different biological media and the clinical issues on dose specification including dose prescription and plan evaluation using dose to water and dose to medium. We will demonstrate that conventional photon dose calculation algorithms compute doses similar to those simulated by Monte Carlo using water with different electron densities, which are close (<4% differences) to doses to media but significantly different (up to 11%) from doses to water converted from doses to media following American Association of Physicists in Medicine (AAPM) Task Group 105 recommendations. Our results suggest that for consistency with previous radiation therapy experience Monte Carlo photon algorithms report dose to medium for radiotherapy dose prescription, treatment plan evaluation and treatment outcome analysis.

Monte Carlo simulations in X-ray imaging

NASA Astrophysics Data System (ADS)

Giersch, Jürgen; Durst, Jürgen

2008-06-01

Monte Carlo simulations have become crucial tools in many fields of X-ray imaging. They help to understand the influence of physical effects such as absorption, scattering and fluorescence of photons in different detector materials on image quality parameters. They allow studying new imaging concepts like photon counting, energy weighting or material reconstruction. Additionally, they can be applied to the fields of nuclear medicine to define virtual setups studying new geometries or image reconstruction algorithms. Furthermore, an implementation of the propagation physics of electrons and photons allows studying the behavior of (novel) X-ray generation concepts. This versatility of Monte Carlo simulations is illustrated with some examples done by the Monte Carlo simulation ROSI. An overview of the structure of ROSI is given as an example of a modern, well-proven, object-oriented, parallel computing Monte Carlo simulation for X-ray imaging.

Hypothesis testing of scientific Monte Carlo calculations.

PubMed

Wallerberger, Markus; Gull, Emanuel

2017-11-01

The steadily increasing size of scientific Monte Carlo simulations and the desire for robust, correct, and reproducible results necessitates rigorous testing procedures for scientific simulations in order to detect numerical problems and programming bugs. However, the testing paradigms developed for deterministic algorithms have proven to be ill suited for stochastic algorithms. In this paper we demonstrate explicitly how the technique of statistical hypothesis testing, which is in wide use in other fields of science, can be used to devise automatic and reliable tests for Monte Carlo methods, and we show that these tests are able to detect some of the common problems encountered in stochastic scientific simulations. We argue that hypothesis testing should become part of the standard testing toolkit for scientific simulations.

Hypothesis testing of scientific Monte Carlo calculations

NASA Astrophysics Data System (ADS)

Wallerberger, Markus; Gull, Emanuel

2017-11-01

The steadily increasing size of scientific Monte Carlo simulations and the desire for robust, correct, and reproducible results necessitates rigorous testing procedures for scientific simulations in order to detect numerical problems and programming bugs. However, the testing paradigms developed for deterministic algorithms have proven to be ill suited for stochastic algorithms. In this paper we demonstrate explicitly how the technique of statistical hypothesis testing, which is in wide use in other fields of science, can be used to devise automatic and reliable tests for Monte Carlo methods, and we show that these tests are able to detect some of the common problems encountered in stochastic scientific simulations. We argue that hypothesis testing should become part of the standard testing toolkit for scientific simulations.

Online sequential Monte Carlo smoother for partially observed diffusion processes

NASA Astrophysics Data System (ADS)

Gloaguen, Pierre; Étienne, Marie-Pierre; Le Corff, Sylvain

2018-12-01

This paper introduces a new algorithm to approximate smoothed additive functionals of partially observed diffusion processes. This method relies on a new sequential Monte Carlo method which allows to compute such approximations online, i.e., as the observations are received, and with a computational complexity growing linearly with the number of Monte Carlo samples. The original algorithm cannot be used in the case of partially observed stochastic differential equations since the transition density of the latent data is usually unknown. We prove that it may be extended to partially observed continuous processes by replacing this unknown quantity by an unbiased estimator obtained for instance using general Poisson estimators. This estimator is proved to be consistent and its performance are illustrated using data from two models.

A surrogate accelerated multicanonical Monte Carlo method for uncertainty quantification

NASA Astrophysics Data System (ADS)

Wu, Keyi; Li, Jinglai

2016-09-01

In this work we consider a class of uncertainty quantification problems where the system performance or reliability is characterized by a scalar parameter y. The performance parameter y is random due to the presence of various sources of uncertainty in the system, and our goal is to estimate the probability density function (PDF) of y. We propose to use the multicanonical Monte Carlo (MMC) method, a special type of adaptive importance sampling algorithms, to compute the PDF of interest. Moreover, we develop an adaptive algorithm to construct local Gaussian process surrogates to further accelerate the MMC iterations. With numerical examples we demonstrate that the proposed method can achieve several orders of magnitudes of speedup over the standard Monte Carlo methods.

Testing trivializing maps in the Hybrid Monte Carlo algorithm

PubMed Central

Engel, Georg P.; Schaefer, Stefan

2011-01-01

We test a recent proposal to use approximate trivializing maps in a field theory to speed up Hybrid Monte Carlo simulations. Simulating the CPN−1 model, we find a small improvement with the leading order transformation, which is however compensated by the additional computational overhead. The scaling of the algorithm towards the continuum is not changed. In particular, the effect of the topological modes on the autocorrelation times is studied. PMID:21969733

Stochastic evaluation of second-order many-body perturbation energies.

PubMed

Willow, Soohaeng Yoo; Kim, Kwang S; Hirata, So

2012-11-28

With the aid of the Laplace transform, the canonical expression of the second-order many-body perturbation correction to an electronic energy is converted into the sum of two 13-dimensional integrals, the 12-dimensional parts of which are evaluated by Monte Carlo integration. Weight functions are identified that are analytically normalizable, are finite and non-negative everywhere, and share the same singularities as the integrands. They thus generate appropriate distributions of four-electron walkers via the Metropolis algorithm, yielding correlation energies of small molecules within a few mE(h) of the correct values after 10(8) Monte Carlo steps. This algorithm does away with the integral transformation as the hotspot of the usual algorithms, has a far superior size dependence of cost, does not suffer from the sign problem of some quantum Monte Carlo methods, and potentially easily parallelizable and extensible to other more complex electron-correlation theories.

GPU-powered Shotgun Stochastic Search for Dirichlet process mixtures of Gaussian Graphical Models

PubMed Central

Mukherjee, Chiranjit; Rodriguez, Abel

2016-01-01

Gaussian graphical models are popular for modeling high-dimensional multivariate data with sparse conditional dependencies. A mixture of Gaussian graphical models extends this model to the more realistic scenario where observations come from a heterogenous population composed of a small number of homogeneous sub-groups. In this paper we present a novel stochastic search algorithm for finding the posterior mode of high-dimensional Dirichlet process mixtures of decomposable Gaussian graphical models. Further, we investigate how to harness the massive thread-parallelization capabilities of graphical processing units to accelerate computation. The computational advantages of our algorithms are demonstrated with various simulated data examples in which we compare our stochastic search with a Markov chain Monte Carlo algorithm in moderate dimensional data examples. These experiments show that our stochastic search largely outperforms the Markov chain Monte Carlo algorithm in terms of computing-times and in terms of the quality of the posterior mode discovered. Finally, we analyze a gene expression dataset in which Markov chain Monte Carlo algorithms are too slow to be practically useful. PMID:28626348

GPU-powered Shotgun Stochastic Search for Dirichlet process mixtures of Gaussian Graphical Models.

PubMed

Mukherjee, Chiranjit; Rodriguez, Abel

2016-01-01

Gaussian graphical models are popular for modeling high-dimensional multivariate data with sparse conditional dependencies. A mixture of Gaussian graphical models extends this model to the more realistic scenario where observations come from a heterogenous population composed of a small number of homogeneous sub-groups. In this paper we present a novel stochastic search algorithm for finding the posterior mode of high-dimensional Dirichlet process mixtures of decomposable Gaussian graphical models. Further, we investigate how to harness the massive thread-parallelization capabilities of graphical processing units to accelerate computation. The computational advantages of our algorithms are demonstrated with various simulated data examples in which we compare our stochastic search with a Markov chain Monte Carlo algorithm in moderate dimensional data examples. These experiments show that our stochastic search largely outperforms the Markov chain Monte Carlo algorithm in terms of computing-times and in terms of the quality of the posterior mode discovered. Finally, we analyze a gene expression dataset in which Markov chain Monte Carlo algorithms are too slow to be practically useful.

SU-F-T-148: Are the Approximations in Analytic Semi-Empirical Dose Calculation Algorithms for Intensity Modulated Proton Therapy for Complex Heterogeneities of Head and Neck Clinically Significant?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yepes, P; UT MD Anderson Cancer Center, Houston, TX; Titt, U

2016-06-15

Purpose: Evaluate the differences in dose distributions between the proton analytic semi-empirical dose calculation algorithm used in the clinic and Monte Carlo calculations for a sample of 50 head-and-neck (H&N) patients and estimate the potential clinical significance of the differences. Methods: A cohort of 50 H&N patients, treated at the University of Texas Cancer Center with Intensity Modulated Proton Therapy (IMPT), were selected for evaluation of clinical significance of approximations in computed dose distributions. H&N site was selected because of the highly inhomogeneous nature of the anatomy. The Fast Dose Calculator (FDC), a fast track-repeating accelerated Monte Carlo algorithm formore » proton therapy, was utilized for the calculation of dose distributions delivered during treatment plans. Because of its short processing time, FDC allows for the processing of large cohorts of patients. FDC has been validated versus GEANT4, a full Monte Carlo system and measurements in water and for inhomogeneous phantoms. A gamma-index analysis, DVHs, EUDs, and TCP and NTCPs computed using published models were utilized to evaluate the differences between the Treatment Plan System (TPS) and FDC. Results: The Monte Carlo results systematically predict lower dose delivered in the target. The observed differences can be as large as 8 Gy, and should have a clinical impact. Gamma analysis also showed significant differences between both approaches, especially for the target volumes. Conclusion: Monte Carlo calculations with fast algorithms is practical and should be considered for the clinic, at least as a treatment plan verification tool.« less

The Metropolis Monte Carlo method with CUDA enabled Graphic Processing Units

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hall, Clifford; School of Physics, Astronomy, and Computational Sciences, George Mason University, 4400 University Dr., Fairfax, VA 22030; Ji, Weixiao

2014-02-01

We present a CPU–GPU system for runtime acceleration of large molecular simulations using GPU computation and memory swaps. The memory architecture of the GPU can be used both as container for simulation data stored on the graphics card and as floating-point code target, providing an effective means for the manipulation of atomistic or molecular data on the GPU. To fully take advantage of this mechanism, efficient GPU realizations of algorithms used to perform atomistic and molecular simulations are essential. Our system implements a versatile molecular engine, including inter-molecule interactions and orientational variables for performing the Metropolis Monte Carlo (MMC) algorithm,more » which is one type of Markov chain Monte Carlo. By combining memory objects with floating-point code fragments we have implemented an MMC parallel engine that entirely avoids the communication time of molecular data at runtime. Our runtime acceleration system is a forerunner of a new class of CPU–GPU algorithms exploiting memory concepts combined with threading for avoiding bus bandwidth and communication. The testbed molecular system used here is a condensed phase system of oligopyrrole chains. A benchmark shows a size scaling speedup of 60 for systems with 210,000 pyrrole monomers. Our implementation can easily be combined with MPI to connect in parallel several CPU–GPU duets. -- Highlights: •We parallelize the Metropolis Monte Carlo (MMC) algorithm on one CPU—GPU duet. •The Adaptive Tempering Monte Carlo employs MMC and profits from this CPU—GPU implementation. •Our benchmark shows a size scaling-up speedup of 62 for systems with 225,000 particles. •The testbed involves a polymeric system of oligopyrroles in the condensed phase. •The CPU—GPU parallelization includes dipole—dipole and Mie—Jones classic potentials.« less

A point kernel algorithm for microbeam radiation therapy

NASA Astrophysics Data System (ADS)

Debus, Charlotte; Oelfke, Uwe; Bartzsch, Stefan

2017-11-01

Microbeam radiation therapy (MRT) is a treatment approach in radiation therapy where the treatment field is spatially fractionated into arrays of a few tens of micrometre wide planar beams of unusually high peak doses separated by low dose regions of several hundred micrometre width. In preclinical studies, this treatment approach has proven to spare normal tissue more effectively than conventional radiation therapy, while being equally efficient in tumour control. So far dose calculations in MRT, a prerequisite for future clinical applications are based on Monte Carlo simulations. However, they are computationally expensive, since scoring volumes have to be small. In this article a kernel based dose calculation algorithm is presented that splits the calculation into photon and electron mediated energy transport, and performs the calculation of peak and valley doses in typical MRT treatment fields within a few minutes. Kernels are analytically calculated depending on the energy spectrum and material composition. In various homogeneous materials peak, valley doses and microbeam profiles are calculated and compared to Monte Carlo simulations. For a microbeam exposure of an anthropomorphic head phantom calculated dose values are compared to measurements and Monte Carlo calculations. Except for regions close to material interfaces calculated peak dose values match Monte Carlo results within 4% and valley dose values within 8% deviation. No significant differences are observed between profiles calculated by the kernel algorithm and Monte Carlo simulations. Measurements in the head phantom agree within 4% in the peak and within 10% in the valley region. The presented algorithm is attached to the treatment planning platform VIRTUOS. It was and is used for dose calculations in preclinical and pet-clinical trials at the biomedical beamline ID17 of the European synchrotron radiation facility in Grenoble, France.

SU-F-T-444: Quality Improvement Review of Radiation Therapy Treatment Planning in the Presence of Dental Implants

DOE Office of Scientific and Technical Information (OSTI.GOV)

Parenica, H; Ford, J; Mavroidis, P

Purpose: To quantify and compare the effect of metallic dental implants (MDI) on dose distributions calculated using Collapsed Cone Convolution Superposition (CCCS) algorithm or a Monte Carlo algorithm (with and without correcting for the density of the MDI). Methods: Seven previously treated patients to the head and neck region were included in this study. The MDI and the streaking artifacts on the CT images were carefully contoured. For each patient a plan was optimized and calculated using the Pinnacle3 treatment planning system (TPS). For each patient two dose calculations were performed, a) with the densities of the MDI and CTmore » artifacts overridden (12 g/cc and 1 g/cc respectively) and b) without density overrides. The plans were then exported to the Monaco TPS and recalculated using Monte Carlo dose calculation algorithm. The changes in dose to PTVs and surrounding Regions of Interest (ROIs) were examined between all plans. Results: The Monte Carlo dose calculation indicated that PTVs received 6% lower dose than the CCCS algorithm predicted. In some cases, the Monte Carlo algorithm indicated that surrounding ROIs received higher dose (up to a factor of 2). Conclusion: Not properly accounting for dental implants can impact both the high dose regions (PTV) and the low dose regions (OAR). This study implies that if MDI and the artifacts are not appropriately contoured and given the correct density, there is potential significant impact on PTV coverage and OAR maximum doses.« less

Pushing the limits of Monte Carlo simulations for the three-dimensional Ising model

NASA Astrophysics Data System (ADS)

Ferrenberg, Alan M.; Xu, Jiahao; Landau, David P.

2018-04-01

While the three-dimensional Ising model has defied analytic solution, various numerical methods like Monte Carlo, Monte Carlo renormalization group, and series expansion have provided precise information about the phase transition. Using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators and data analysis with histogram reweighting and quadruple precision arithmetic, we have investigated the critical behavior of the simple cubic Ising Model, with lattice sizes ranging from 163 to 10243. By analyzing data with cross correlations between various thermodynamic quantities obtained from the same data pool, e.g., logarithmic derivatives of magnetization and derivatives of magnetization cumulants, we have obtained the critical inverse temperature Kc=0.221 654 626 (5 ) and the critical exponent of the correlation length ν =0.629 912 (86 ) with precision that exceeds all previous Monte Carlo estimates.

Markov Chain Monte Carlo Methods for Bayesian Data Analysis in Astronomy

NASA Astrophysics Data System (ADS)

Sharma, Sanjib

2017-08-01

Markov Chain Monte Carlo based Bayesian data analysis has now become the method of choice for analyzing and interpreting data in almost all disciplines of science. In astronomy, over the last decade, we have also seen a steady increase in the number of papers that employ Monte Carlo based Bayesian analysis. New, efficient Monte Carlo based methods are continuously being developed and explored. In this review, we first explain the basics of Bayesian theory and discuss how to set up data analysis problems within this framework. Next, we provide an overview of various Monte Carlo based methods for performing Bayesian data analysis. Finally, we discuss advanced ideas that enable us to tackle complex problems and thus hold great promise for the future. We also distribute downloadable computer software (available at https://github.com/sanjibs/bmcmc/ ) that implements some of the algorithms and examples discussed here.

QMCPACK: an open source ab initio quantum Monte Carlo package for the electronic structure of atoms, molecules and solids

NASA Astrophysics Data System (ADS)

Kim, Jeongnim; Baczewski, Andrew D.; Beaudet, Todd D.; Benali, Anouar; Chandler Bennett, M.; Berrill, Mark A.; Blunt, Nick S.; Josué Landinez Borda, Edgar; Casula, Michele; Ceperley, David M.; Chiesa, Simone; Clark, Bryan K.; Clay, Raymond C., III; Delaney, Kris T.; Dewing, Mark; Esler, Kenneth P.; Hao, Hongxia; Heinonen, Olle; Kent, Paul R. C.; Krogel, Jaron T.; Kylänpää, Ilkka; Li, Ying Wai; Lopez, M. Graham; Luo, Ye; Malone, Fionn D.; Martin, Richard M.; Mathuriya, Amrita; McMinis, Jeremy; Melton, Cody A.; Mitas, Lubos; Morales, Miguel A.; Neuscamman, Eric; Parker, William D.; Pineda Flores, Sergio D.; Romero, Nichols A.; Rubenstein, Brenda M.; Shea, Jacqueline A. R.; Shin, Hyeondeok; Shulenburger, Luke; Tillack, Andreas F.; Townsend, Joshua P.; Tubman, Norm M.; Van Der Goetz, Brett; Vincent, Jordan E.; ChangMo Yang, D.; Yang, Yubo; Zhang, Shuai; Zhao, Luning

2018-05-01

QMCPACK is an open source quantum Monte Carlo package for ab initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater–Jastrow type trial wavefunctions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary-field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit and graphical processing unit systems. We detail the program’s capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://qmcpack.org.

QMCPACK: an open source ab initio quantum Monte Carlo package for the electronic structure of atoms, molecules and solids.

PubMed

Kim, Jeongnim; Baczewski, Andrew T; Beaudet, Todd D; Benali, Anouar; Bennett, M Chandler; Berrill, Mark A; Blunt, Nick S; Borda, Edgar Josué Landinez; Casula, Michele; Ceperley, David M; Chiesa, Simone; Clark, Bryan K; Clay, Raymond C; Delaney, Kris T; Dewing, Mark; Esler, Kenneth P; Hao, Hongxia; Heinonen, Olle; Kent, Paul R C; Krogel, Jaron T; Kylänpää, Ilkka; Li, Ying Wai; Lopez, M Graham; Luo, Ye; Malone, Fionn D; Martin, Richard M; Mathuriya, Amrita; McMinis, Jeremy; Melton, Cody A; Mitas, Lubos; Morales, Miguel A; Neuscamman, Eric; Parker, William D; Pineda Flores, Sergio D; Romero, Nichols A; Rubenstein, Brenda M; Shea, Jacqueline A R; Shin, Hyeondeok; Shulenburger, Luke; Tillack, Andreas F; Townsend, Joshua P; Tubman, Norm M; Van Der Goetz, Brett; Vincent, Jordan E; Yang, D ChangMo; Yang, Yubo; Zhang, Shuai; Zhao, Luning

2018-05-16

QMCPACK is an open source quantum Monte Carlo package for ab initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wavefunctions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary-field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit and graphical processing unit systems. We detail the program's capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://qmcpack.org.

Exact Dynamics via Poisson Process: a unifying Monte Carlo paradigm

NASA Astrophysics Data System (ADS)

Gubernatis, James

2014-03-01

A common computational task is solving a set of ordinary differential equations (o.d.e.'s). A little known theorem says that the solution of any set of o.d.e.'s is exactly solved by the expectation value over a set of arbitary Poisson processes of a particular function of the elements of the matrix that defines the o.d.e.'s. The theorem thus provides a new starting point to develop real and imaginary-time continous-time solvers for quantum Monte Carlo algorithms, and several simple observations enable various quantum Monte Carlo techniques and variance reduction methods to transfer to a new context. I will state the theorem, note a transformation to a very simple computational scheme, and illustrate the use of some techniques from the directed-loop algorithm in context of the wavefunction Monte Carlo method that is used to solve the Lindblad master equation for the dynamics of open quantum systems. I will end by noting that as the theorem does not depend on the source of the o.d.e.'s coming from quantum mechanics, it also enables the transfer of continuous-time methods from quantum Monte Carlo to the simulation of various classical equations of motion heretofore only solved deterministically.

Probabilistic learning of nonlinear dynamical systems using sequential Monte Carlo

NASA Astrophysics Data System (ADS)

Schön, Thomas B.; Svensson, Andreas; Murray, Lawrence; Lindsten, Fredrik

2018-05-01

Probabilistic modeling provides the capability to represent and manipulate uncertainty in data, models, predictions and decisions. We are concerned with the problem of learning probabilistic models of dynamical systems from measured data. Specifically, we consider learning of probabilistic nonlinear state-space models. There is no closed-form solution available for this problem, implying that we are forced to use approximations. In this tutorial we will provide a self-contained introduction to one of the state-of-the-art methods-the particle Metropolis-Hastings algorithm-which has proven to offer a practical approximation. This is a Monte Carlo based method, where the particle filter is used to guide a Markov chain Monte Carlo method through the parameter space. One of the key merits of the particle Metropolis-Hastings algorithm is that it is guaranteed to converge to the "true solution" under mild assumptions, despite being based on a particle filter with only a finite number of particles. We will also provide a motivating numerical example illustrating the method using a modeling language tailored for sequential Monte Carlo methods. The intention of modeling languages of this kind is to open up the power of sophisticated Monte Carlo methods-including particle Metropolis-Hastings-to a large group of users without requiring them to know all the underlying mathematical details.

Quantum Monte Carlo Simulation of Frustrated Kondo Lattice Models

NASA Astrophysics Data System (ADS)

Sato, Toshihiro; Assaad, Fakher F.; Grover, Tarun

2018-03-01

The absence of the negative sign problem in quantum Monte Carlo simulations of spin and fermion systems has different origins. World-line based algorithms for spins require positivity of matrix elements whereas auxiliary field approaches for fermions depend on symmetries such as particle-hole symmetry. For negative-sign-free spin and fermionic systems, we show that one can formulate a negative-sign-free auxiliary field quantum Monte Carlo algorithm that allows Kondo coupling of fermions with the spins. Using this general approach, we study a half-filled Kondo lattice model on the honeycomb lattice with geometric frustration. In addition to the conventional Kondo insulator and antiferromagnetically ordered phases, we find a partial Kondo screened state where spins are selectively screened so as to alleviate frustration, and the lattice rotation symmetry is broken nematically.

Parameters Free Computational Characterization of Defects in Transition Metal Oxides with Diffusion Quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Santana, Juan A.; Krogel, Jaron T.; Kent, Paul R.; Reboredo, Fernando

Materials based on transition metal oxides (TMO's) are among the most challenging systems for computational characterization. Reliable and practical computations are possible by directly solving the many-body problem for TMO's with quantum Monte Carlo (QMC) methods. These methods are very computationally intensive, but recent developments in algorithms and computational infrastructures have enabled their application to real materials. We will show our efforts on the application of the diffusion quantum Monte Carlo (DMC) method to study the formation of defects in binary and ternary TMO and heterostructures of TMO. We will also outline current limitations in hardware and algorithms. This work is supported by the Materials Sciences & Engineering Division of the Office of Basic Energy Sciences, U.S. Department of Energy (DOE).

Quantifying the effect of air gap, depth, and range shifter thickness on TPS dosimetric accuracy in superficial PBS proton therapy.

PubMed

Shirey, Robert J; Wu, Hsinshun Terry

2018-01-01

This study quantifies the dosimetric accuracy of a commercial treatment planning system as functions of treatment depth, air gap, and range shifter thickness for superficial pencil beam scanning proton therapy treatments. The RayStation 6 pencil beam and Monte Carlo dose engines were each used to calculate the dose distributions for a single treatment plan with varying range shifter air gaps. Central axis dose values extracted from each of the calculated plans were compared to dose values measured with a calibrated PTW Markus chamber at various depths in RW3 solid water. Dose was measured at 12 depths, ranging from the surface to 5 cm, for each of the 18 different air gaps, which ranged from 0.5 to 28 cm. TPS dosimetric accuracy, defined as the ratio of calculated dose relative to the measured dose, was plotted as functions of depth and air gap for the pencil beam and Monte Carlo dose algorithms. The accuracy of the TPS pencil beam dose algorithm was found to be clinically unacceptable at depths shallower than 3 cm with air gaps wider than 10 cm, and increased range shifter thickness only added to the dosimetric inaccuracy of the pencil beam algorithm. Each configuration calculated with Monte Carlo was determined to be clinically acceptable. Further comparisons of the Monte Carlo dose algorithm to the measured spread-out Bragg Peaks of multiple fields used during machine commissioning verified the dosimetric accuracy of Monte Carlo in a variety of beam energies and field sizes. Discrepancies between measured and TPS calculated dose values can mainly be attributed to the ability (or lack thereof) of the TPS pencil beam dose algorithm to properly model secondary proton scatter generated in the range shifter. © 2017 The Authors. Journal of Applied Clinical Medical Physics published by Wiley Periodicals, Inc. on behalf of American Association of Physicists in Medicine.

Bayesian estimation of realized stochastic volatility model by Hybrid Monte Carlo algorithm

NASA Astrophysics Data System (ADS)

Takaishi, Tetsuya

2014-03-01

The hybrid Monte Carlo algorithm (HMCA) is applied for Bayesian parameter estimation of the realized stochastic volatility (RSV) model. Using the 2nd order minimum norm integrator (2MNI) for the molecular dynamics (MD) simulation in the HMCA, we find that the 2MNI is more efficient than the conventional leapfrog integrator. We also find that the autocorrelation time of the volatility variables sampled by the HMCA is very short. Thus it is concluded that the HMCA with the 2MNI is an efficient algorithm for parameter estimations of the RSV model.

Monte Carlo Simulations of Radiative and Neutrino Transport under Astrophysical Conditions

NASA Astrophysics Data System (ADS)

Krivosheyev, Yu. M.; Bisnovatyi-Kogan, G. S.

2018-05-01

Monte Carlo simulations are utilized to model radiative and neutrino transfer in astrophysics. An algorithm that can be used to study radiative transport in astrophysical plasma based on simulations of photon trajectories in a medium is described. Formation of the hard X-ray spectrum of the Galactic microquasar SS 433 is considered in detail as an example. Specific requirements for applying such simulations to neutrino transport in a densemedium and algorithmic differences compared to its application to photon transport are discussed.

Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kube, Susanna; Lasser, Caroline; Weber, Marcus

2009-04-01

The article addresses the achievable accuracy for a Monte Carlo sampling of Wigner functions in combination with a surface hopping algorithm for non-adiabatic quantum dynamics. The approximation of Wigner functions is realized by an adaption of the Metropolis algorithm for real-valued functions with disconnected support. The integration, which is necessary for computing values of the Wigner function, uses importance sampling with a Gaussian weight function. The numerical experiments agree with theoretical considerations and show an error of 2-3%.

Monte Carlo Calculations of Polarized Microwave Radiation Emerging from Cloud Structures

NASA Technical Reports Server (NTRS)

Kummerow, Christian; Roberti, Laura

1998-01-01

The last decade has seen tremendous growth in cloud dynamical and microphysical models that are able to simulate storms and storm systems with very high spatial resolution, typically of the order of a few kilometers. The fairly realistic distributions of cloud and hydrometeor properties that these models generate has in turn led to a renewed interest in the three-dimensional microwave radiative transfer modeling needed to understand the effect of cloud and rainfall inhomogeneities upon microwave observations. Monte Carlo methods, and particularly backwards Monte Carlo methods have shown themselves to be very desirable due to the quick convergence of the solutions. Unfortunately, backwards Monte Carlo methods are not well suited to treat polarized radiation. This study reviews the existing Monte Carlo methods and presents a new polarized Monte Carlo radiative transfer code. The code is based on a forward scheme but uses aliasing techniques to keep the computational requirements equivalent to the backwards solution. Radiative transfer computations have been performed using a microphysical-dynamical cloud model and the results are presented together with the algorithm description.

Asteroid mass estimation with Markov-chain Monte Carlo

NASA Astrophysics Data System (ADS)

Siltala, L.; Granvik, M.

2017-09-01

We have developed a new Markov-chain Monte Carlo-based algorithm for asteroid mass estimation based on mutual encounters and tested it for several different asteroids. Our results are in line with previous literature values but suggest that uncertainties of prior estimates may be misleading as a consequence of using linearized methods.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bolding, Simon R.; Cleveland, Mathew Allen; Morel, Jim E.

In this paper, we have implemented a new high-order low-order (HOLO) algorithm for solving thermal radiative transfer problems. The low-order (LO) system is based on the spatial and angular moments of the transport equation and a linear-discontinuous finite-element spatial representation, producing equations similar to the standard S 2 equations. The LO solver is fully implicit in time and efficiently resolves the nonlinear temperature dependence at each time step. The high-order (HO) solver utilizes exponentially convergent Monte Carlo (ECMC) to give a globally accurate solution for the angular intensity to a fixed-source pure-absorber transport problem. This global solution is used tomore » compute consistency terms, which require the HO and LO solutions to converge toward the same solution. The use of ECMC allows for the efficient reduction of statistical noise in the Monte Carlo solution, reducing inaccuracies introduced through the LO consistency terms. Finally, we compare results with an implicit Monte Carlo code for one-dimensional gray test problems and demonstrate the efficiency of ECMC over standard Monte Carlo in this HOLO algorithm.« less

SKIRT: The design of a suite of input models for Monte Carlo radiative transfer simulations

NASA Astrophysics Data System (ADS)

Baes, M.; Camps, P.

2015-09-01

The Monte Carlo method is the most popular technique to perform radiative transfer simulations in a general 3D geometry. The algorithms behind and acceleration techniques for Monte Carlo radiative transfer are discussed extensively in the literature, and many different Monte Carlo codes are publicly available. On the contrary, the design of a suite of components that can be used for the distribution of sources and sinks in radiative transfer codes has received very little attention. The availability of such models, with different degrees of complexity, has many benefits. For example, they can serve as toy models to test new physical ingredients, or as parameterised models for inverse radiative transfer fitting. For 3D Monte Carlo codes, this requires algorithms to efficiently generate random positions from 3D density distributions. We describe the design of a flexible suite of components for the Monte Carlo radiative transfer code SKIRT. The design is based on a combination of basic building blocks (which can be either analytical toy models or numerical models defined on grids or a set of particles) and the extensive use of decorators that combine and alter these building blocks to more complex structures. For a number of decorators, e.g. those that add spiral structure or clumpiness, we provide a detailed description of the algorithms that can be used to generate random positions. Advantages of this decorator-based design include code transparency, the avoidance of code duplication, and an increase in code maintainability. Moreover, since decorators can be chained without problems, very complex models can easily be constructed out of simple building blocks. Finally, based on a number of test simulations, we demonstrate that our design using customised random position generators is superior to a simpler design based on a generic black-box random position generator.

Comments on "Including the effects of temperature-dependent opacities in the implicit Monte Carlo algorithm" by N.A. Gentile [J. Comput. Phys. 230 (2011) 5100-5114

NASA Astrophysics Data System (ADS)

Ghosh, Karabi

2017-02-01

We briefly comment on a paper by N.A. Gentile [J. Comput. Phys. 230 (2011) 5100-5114] in which the Fleck factor has been modified to include the effects of temperature-dependent opacities in the implicit Monte Carlo algorithm developed by Fleck and Cummings [1,2]. Instead of the Fleck factor, f = 1 / (1 + βcΔtσP), the author derived the modified Fleck factor g = 1 / (1 + βcΔtσP - min [σP‧ (aTr4 - aT4)cΔt/ρCV, 0 ]) to be used in the Implicit Monte Carlo (IMC) algorithm in order to obtain more accurate solutions with much larger time steps. Here β = 4 aT3 / ρCV, σP is the Planck opacity and the derivative of Planck opacity w.r.t. the material temperature is σP‧ = dσP / dT.

Poster — Thur Eve — 14: Improving Tissue Segmentation for Monte Carlo Dose Calculation using DECT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Di Salvio, A.; Bedwani, S.; Carrier, J-F.

2014-08-15

Purpose: To improve Monte Carlo dose calculation accuracy through a new tissue segmentation technique with dual energy CT (DECT). Methods: Electron density (ED) and effective atomic number (EAN) can be extracted directly from DECT data with a stoichiometric calibration method. Images are acquired with Monte Carlo CT projections using the user code egs-cbct and reconstructed using an FDK backprojection algorithm. Calibration is performed using projections of a numerical RMI phantom. A weighted parameter algorithm then uses both EAN and ED to assign materials to voxels from DECT simulated images. This new method is compared to a standard tissue characterization frommore » single energy CT (SECT) data using a segmented calibrated Hounsfield unit (HU) to ED curve. Both methods are compared to the reference numerical head phantom. Monte Carlo simulations on uniform phantoms of different tissues using dosxyz-nrc show discrepancies in depth-dose distributions. Results: Both SECT and DECT segmentation methods show similar performance assigning soft tissues. Performance is however improved with DECT in regions with higher density, such as bones, where it assigns materials correctly 8% more often than segmentation with SECT, considering the same set of tissues and simulated clinical CT images, i.e. including noise and reconstruction artifacts. Furthermore, Monte Carlo results indicate that kV photon beam depth-dose distributions can double between two tissues of density higher than muscle. Conclusions: A direct acquisition of ED and the added information of EAN with DECT data improves tissue segmentation and increases the accuracy of Monte Carlo dose calculation in kV photon beams.« less

Dynamic load balancing for petascale quantum Monte Carlo applications: The Alias method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sudheer, C. D.; Krishnan, S.; Srinivasan, A.

Diffusion Monte Carlo is the most accurate widely used Quantum Monte Carlo method for the electronic structure of materials, but it requires frequent load balancing or population redistribution steps to maintain efficiency and avoid accumulation of systematic errors on parallel machines. The load balancing step can be a significant factor affecting performance, and will become more important as the number of processing elements increases. We propose a new dynamic load balancing algorithm, the Alias Method, and evaluate it theoretically and empirically. An important feature of the new algorithm is that the load can be perfectly balanced with each process receivingmore » at most one message. It is also optimal in the maximum size of messages received by any process. We also optimize its implementation to reduce network contention, a process facilitated by the low messaging requirement of the algorithm. Empirical results on the petaflop Cray XT Jaguar supercomputer at ORNL showing up to 30% improvement in performance on 120,000 cores. The load balancing algorithm may be straightforwardly implemented in existing codes. The algorithm may also be employed by any method with many near identical computational tasks that requires load balancing.« less

Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arampatzis, Giorgos, E-mail: garab@math.uoc.gr; Katsoulakis, Markos A., E-mail: markos@math.umass.edu; Plechac, Petr, E-mail: plechac@math.udel.edu

2012-10-01

We present a mathematical framework for constructing and analyzing parallel algorithms for lattice kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in spatially distributed, non-equilibrium physiochemical processes with complex chemistry and transport micro-mechanisms. Rather than focusing on constructing exactly the stochastic trajectories, our approach relies on approximating the evolution of observables, such as density, coverage, correlations and so on. More specifically, we develop a spatial domain decomposition of the Markov operator (generator) that describes the evolution of all observables according to the kinetic Monte Carlo algorithm. This domain decompositionmore » corresponds to a decomposition of the Markov generator into a hierarchy of operators and can be tailored to specific hierarchical parallel architectures such as multi-core processors or clusters of Graphical Processing Units (GPUs). Based on this operator decomposition, we formulate parallel Fractional step kinetic Monte Carlo algorithms by employing the Trotter Theorem and its randomized variants; these schemes, (a) are partially asynchronous on each fractional step time-window, and (b) are characterized by their communication schedule between processors. The proposed mathematical framework allows us to rigorously justify the numerical and statistical consistency of the proposed algorithms, showing the convergence of our approximating schemes to the original serial KMC. The approach also provides a systematic evaluation of different processor communicating schedules. We carry out a detailed benchmarking of the parallel KMC schemes using available exact solutions, for example, in Ising-type systems and we demonstrate the capabilities of the method to simulate complex spatially distributed reactions at very large scales on GPUs. Finally, we discuss work load balancing between processors and propose a re-balancing scheme based on probabilistic mass transport methods.« less

Modelling maximum river flow by using Bayesian Markov Chain Monte Carlo

NASA Astrophysics Data System (ADS)

Cheong, R. Y.; Gabda, D.

2017-09-01

Analysis of flood trends is vital since flooding threatens human living in terms of financial, environment and security. The data of annual maximum river flows in Sabah were fitted into generalized extreme value (GEV) distribution. Maximum likelihood estimator (MLE) raised naturally when working with GEV distribution. However, previous researches showed that MLE provide unstable results especially in small sample size. In this study, we used different Bayesian Markov Chain Monte Carlo (MCMC) based on Metropolis-Hastings algorithm to estimate GEV parameters. Bayesian MCMC method is a statistical inference which studies the parameter estimation by using posterior distribution based on Bayes’ theorem. Metropolis-Hastings algorithm is used to overcome the high dimensional state space faced in Monte Carlo method. This approach also considers more uncertainty in parameter estimation which then presents a better prediction on maximum river flow in Sabah.

Loading relativistic Maxwell distributions in particle simulations

NASA Astrophysics Data System (ADS)

Zenitani, S.

2015-12-01

In order to study energetic plasma phenomena by using particle-in-cell (PIC) and Monte-Carlo simulations, we need to deal with relativistic velocity distributions in these simulations. However, numerical algorithms to deal with relativistic distributions are not well known. In this contribution, we overview basic algorithms to load relativistic Maxwell distributions in PIC and Monte-Carlo simulations. For stationary relativistic Maxwellian, the inverse transform method and the Sobol algorithm are reviewed. To boost particles to obtain relativistic shifted-Maxwellian, two rejection methods are newly proposed in a physically transparent manner. Their acceptance efficiencies are 􏰅50% for generic cases and 100% for symmetric distributions. They can be combined with arbitrary base algorithms.

Monte Carlo calculation of large and small-angle electron scattering in air

NASA Astrophysics Data System (ADS)

Cohen, B. I.; Higginson, D. P.; Eng, C. D.; Farmer, W. A.; Friedman, A.; Grote, D. P.; Larson, D. J.

2017-11-01

A Monte Carlo method for angle scattering of electrons in air that accommodates the small-angle multiple scattering and larger-angle single scattering limits is introduced. The algorithm is designed for use in a particle-in-cell simulation of electron transport and electromagnetic wave effects in air. The method is illustrated in example calculations.

MC3: Multi-core Markov-chain Monte Carlo code

NASA Astrophysics Data System (ADS)

Cubillos, Patricio; Harrington, Joseph; Lust, Nate; Foster, AJ; Stemm, Madison; Loredo, Tom; Stevenson, Kevin; Campo, Chris; Hardin, Matt; Hardy, Ryan

2016-10-01

MC3 (Multi-core Markov-chain Monte Carlo) is a Bayesian statistics tool that can be executed from the shell prompt or interactively through the Python interpreter with single- or multiple-CPU parallel computing. It offers Markov-chain Monte Carlo (MCMC) posterior-distribution sampling for several algorithms, Levenberg-Marquardt least-squares optimization, and uniform non-informative, Jeffreys non-informative, or Gaussian-informative priors. MC3 can share the same value among multiple parameters and fix the value of parameters to constant values, and offers Gelman-Rubin convergence testing and correlated-noise estimation with time-averaging or wavelet-based likelihood estimation methods.

Accelerate quasi Monte Carlo method for solving systems of linear algebraic equations through shared memory

NASA Astrophysics Data System (ADS)

Lai, Siyan; Xu, Ying; Shao, Bo; Guo, Menghan; Lin, Xiaola

2017-04-01

In this paper we study on Monte Carlo method for solving systems of linear algebraic equations (SLAE) based on shared memory. Former research demostrated that GPU can effectively speed up the computations of this issue. Our purpose is to optimize Monte Carlo method simulation on GPUmemoryachritecture specifically. Random numbers are organized to storein shared memory, which aims to accelerate the parallel algorithm. Bank conflicts can be avoided by our Collaborative Thread Arrays(CTA)scheme. The results of experiments show that the shared memory based strategy can speed up the computaions over than 3X at most.

Monte Carlo charged-particle tracking and energy deposition on a Lagrangian mesh.

PubMed

Yuan, J; Moses, G A; McKenty, P W

2005-10-01

A Monte Carlo algorithm for alpha particle tracking and energy deposition on a cylindrical computational mesh in a Lagrangian hydrodynamics code used for inertial confinement fusion (ICF) simulations is presented. The straight line approximation is used to follow propagation of "Monte Carlo particles" which represent collections of alpha particles generated from thermonuclear deuterium-tritium (DT) reactions. Energy deposition in the plasma is modeled by the continuous slowing down approximation. The scheme addresses various aspects arising in the coupling of Monte Carlo tracking with Lagrangian hydrodynamics; such as non-orthogonal severely distorted mesh cells, particle relocation on the moving mesh and particle relocation after rezoning. A comparison with the flux-limited multi-group diffusion transport method is presented for a polar direct drive target design for the National Ignition Facility. Simulations show the Monte Carlo transport method predicts about earlier ignition than predicted by the diffusion method, and generates higher hot spot temperature. Nearly linear speed-up is achieved for multi-processor parallel simulations.

QMCPACK : an open source ab initio quantum Monte Carlo package for the electronic structure of atoms, molecules and solids

DOE PAGES

Kim, Jeongnim; Baczewski, Andrew T.; Beaudet, Todd D.; ...

2018-04-19

QMCPACK is an open source quantum Monte Carlo package for ab-initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wave functions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performancemore » computing architectures, including multicore central processing unit (CPU) and graphical processing unit (GPU) systems. We detail the program’s capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://www.qmcpack.org.« less

QMCPACK : an open source ab initio quantum Monte Carlo package for the electronic structure of atoms, molecules and solids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Jeongnim; Baczewski, Andrew T.; Beaudet, Todd D.

QMCPACK is an open source quantum Monte Carlo package for ab-initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wave functions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performancemore » computing architectures, including multicore central processing unit (CPU) and graphical processing unit (GPU) systems. We detail the program’s capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://www.qmcpack.org.« less

Direct simulation Monte Carlo method for the Uehling-Uhlenbeck-Boltzmann equation.

PubMed

Garcia, Alejandro L; Wagner, Wolfgang

2003-11-01

In this paper we describe a direct simulation Monte Carlo algorithm for the Uehling-Uhlenbeck-Boltzmann equation in terms of Markov processes. This provides a unifying framework for both the classical Boltzmann case as well as the Fermi-Dirac and Bose-Einstein cases. We establish the foundation of the algorithm by demonstrating its link to the kinetic equation. By numerical experiments we study its sensitivity to the number of simulation particles and to the discretization of the velocity space, when approximating the steady-state distribution.

A highly optimized vectorized code for Monte Carlo simulations of SU(3) lattice gauge theories

NASA Technical Reports Server (NTRS)

Barkai, D.; Moriarty, K. J. M.; Rebbi, C.

1984-01-01

New methods are introduced for improving the performance of the vectorized Monte Carlo SU(3) lattice gauge theory algorithm using the CDC CYBER 205. Structure, algorithm and programming considerations are discussed. The performance achieved for a 16(4) lattice on a 2-pipe system may be phrased in terms of the link update time or overall MFLOPS rates. For 32-bit arithmetic, it is 36.3 microsecond/link for 8 hits per iteration (40.9 microsecond for 10 hits) or 101.5 MFLOPS.

Path-integral Monte Carlo method for Rényi entanglement entropies.

PubMed

Herdman, C M; Inglis, Stephen; Roy, P-N; Melko, R G; Del Maestro, A

2014-07-01

We introduce a quantum Monte Carlo algorithm to measure the Rényi entanglement entropies in systems of interacting bosons in the continuum. This approach is based on a path-integral ground state method that can be applied to interacting itinerant bosons in any spatial dimension with direct relevance to experimental systems of quantum fluids. We demonstrate how it may be used to compute spatial mode entanglement, particle partitioned entanglement, and the entanglement of particles, providing insights into quantum correlations generated by fluctuations, indistinguishability, and interactions. We present proof-of-principle calculations and benchmark against an exactly soluble model of interacting bosons in one spatial dimension. As this algorithm retains the fundamental polynomial scaling of quantum Monte Carlo when applied to sign-problem-free models, future applications should allow for the study of entanglement entropy in large-scale many-body systems of interacting bosons.

MUSiC - A general search for deviations from monte carlo predictions in CMS

NASA Astrophysics Data System (ADS)

Biallass, Philipp A.; CMS Collaboration

2009-06-01

A model independent analysis approach in CMS is presented, systematically scanning the data for deviations from the Monte Carlo expectation. Such an analysis can contribute to the understanding of the detector and the tuning of the event generators. Furthermore, due to the minimal theoretical bias this approach is sensitive to a variety of models of new physics, including those not yet thought of. Events are classified into event classes according to their particle content (muons, electrons, photons, jets and missing transverse energy). A broad scan of various distributions is performed, identifying significant deviations from the Monte Carlo simulation. The importance of systematic uncertainties is outlined, which are taken into account rigorously within the algorithm. Possible detector effects and generator issues, as well as models involving Supersymmetry and new heavy gauge bosons are used as an input to the search algorithm.

MUSiC - A Generic Search for Deviations from Monte Carlo Predictions in CMS

NASA Astrophysics Data System (ADS)

Hof, Carsten

2009-05-01

We present a model independent analysis approach, systematically scanning the data for deviations from the Standard Model Monte Carlo expectation. Such an analysis can contribute to the understanding of the CMS detector and the tuning of the event generators. Furthermore, due to the minimal theoretical bias this approach is sensitive to a variety of models of new physics, including those not yet thought of. Events are classified into event classes according to their particle content (muons, electrons, photons, jets and missing transverse energy). A broad scan of various distributions is performed, identifying significant deviations from the Monte Carlo simulation. We outline the importance of systematic uncertainties, which are taken into account rigorously within the algorithm. Possible detector effects and generator issues, as well as models involving supersymmetry and new heavy gauge bosons have been used as an input to the search algorithm.

Monte Carlo calculation of large and small-angle electron scattering in air

DOE PAGES

Cohen, B. I.; Higginson, D. P.; Eng, C. D.; ...

2017-08-12

A Monte Carlo method for angle scattering of electrons in air that accommodates the small-angle multiple scattering and larger-angle single scattering limits is introduced. In this work, the algorithm is designed for use in a particle-in-cell simulation of electron transport and electromagnetic wave effects in air. The method is illustrated in example calculations.

Monte Carlo method for magnetic impurities in metals

NASA Technical Reports Server (NTRS)

Hirsch, J. E.; Fye, R. M.

1986-01-01

The paper discusses a Monte Carlo algorithm to study properties of dilute magnetic alloys; the method can treat a small number of magnetic impurities interacting wiith the conduction electrons in a metal. Results for the susceptibility of a single Anderson impurity in the symmetric case show the expected universal behavior at low temperatures. Some results for two Anderson impurities are also discussed.

An NCME Instructional Module on Estimating Item Response Theory Models Using Markov Chain Monte Carlo Methods

ERIC Educational Resources Information Center

Kim, Jee-Seon; Bolt, Daniel M.

2007-01-01

The purpose of this ITEMS module is to provide an introduction to Markov chain Monte Carlo (MCMC) estimation for item response models. A brief description of Bayesian inference is followed by an overview of the various facets of MCMC algorithms, including discussion of prior specification, sampling procedures, and methods for evaluating chain…

Modeling 2D and 3D diffusion.

PubMed

Saxton, Michael J

2007-01-01

Modeling obstructed diffusion is essential to the understanding of diffusion-mediated processes in the crowded cellular environment. Simple Monte Carlo techniques for modeling obstructed random walks are explained and related to Brownian dynamics and more complicated Monte Carlo methods. Random number generation is reviewed in the context of random walk simulations. Programming techniques and event-driven algorithms are discussed as ways to speed simulations.

A robust algorithm for automated target recognition using precomputed radar cross sections

NASA Astrophysics Data System (ADS)

Ehrman, Lisa M.; Lanterman, Aaron D.

2004-09-01

Passive radar is an emerging technology that offers a number of unique benefits, including covert operation. Many such systems are already capable of detecting and tracking aircraft. The goal of this work is to develop a robust algorithm for adding automated target recognition (ATR) capabilities to existing passive radar systems. In previous papers, we proposed conducting ATR by comparing the precomputed RCS of known targets to that of detected targets. To make the precomputed RCS as accurate as possible, a coordinated flight model is used to estimate aircraft orientation. Once the aircraft's position and orientation are known, it is possible to determine the incident and observed angles on the aircraft, relative to the transmitter and receiver. This makes it possible to extract the appropriate radar cross section (RCS) from our simulated database. This RCS is then scaled to account for propagation losses and the receiver's antenna gain. A Rician likelihood model compares these expected signals from different targets to the received target profile. We have previously employed Monte Carlo runs to gauge the probability of error in the ATR algorithm; however, generation of a statistically significant set of Monte Carlo runs is computationally intensive. As an alternative to Monte Carlo runs, we derive the relative entropy (also known as Kullback-Liebler distance) between two Rician distributions. Since the probability of Type II error in our hypothesis testing problem can be expressed as a function of the relative entropy via Stein's Lemma, this provides us with a computationally efficient method for determining an upper bound on our algorithm's performance. It also provides great insight into the types of classification errors we can expect from our algorithm. This paper compares the numerically approximated probability of Type II error with the results obtained from a set of Monte Carlo runs.

The impact of low-Z and high-Z metal implants in IMRT: A Monte Carlo study of dose inaccuracies in commercial dose algorithms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Spadea, Maria Francesca, E-mail: mfspadea@unicz.it; Verburg, Joost Mathias; Seco, Joao

2014-01-15

Purpose: The aim of the study was to evaluate the dosimetric impact of low-Z and high-Z metallic implants on IMRT plans. Methods: Computed tomography (CT) scans of three patients were analyzed to study effects due to the presence of Titanium (low-Z), Platinum and Gold (high-Z) inserts. To eliminate artifacts in CT images, a sinogram-based metal artifact reduction algorithm was applied. IMRT dose calculations were performed on both the uncorrected and corrected images using a commercial planning system (convolution/superposition algorithm) and an in-house Monte Carlo platform. Dose differences between uncorrected and corrected datasets were computed and analyzed using gamma index (Pγ{submore » <1}) and setting 2 mm and 2% as distance to agreement and dose difference criteria, respectively. Beam specific depth dose profiles across the metal were also examined. Results: Dose discrepancies between corrected and uncorrected datasets were not significant for low-Z material. High-Z materials caused under-dosage of 20%–25% in the region surrounding the metal and over dosage of 10%–15% downstream of the hardware. Gamma index test yielded Pγ{sub <1}>99% for all low-Z cases; while for high-Z cases it returned 91% < Pγ{sub <1}< 99%. Analysis of the depth dose curve of a single beam for low-Z cases revealed that, although the dose attenuation is altered inside the metal, it does not differ downstream of the insert. However, for high-Z metal implants the dose is increased up to 10%–12% around the insert. In addition, Monte Carlo method was more sensitive to the presence of metal inserts than superposition/convolution algorithm. Conclusions: The reduction in terms of dose of metal artifacts in CT images is relevant for high-Z implants. In this case, dose distribution should be calculated using Monte Carlo algorithms, given their superior accuracy in dose modeling in and around the metal. In addition, the knowledge of the composition of metal inserts improves the accuracy of the Monte Carlo dose calculation significantly.« less

Event-driven Monte Carlo: Exact dynamics at all time scales for discrete-variable models

NASA Astrophysics Data System (ADS)

Mendoza-Coto, Alejandro; Díaz-Méndez, Rogelio; Pupillo, Guido

2016-06-01

We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found, with no need to define any other phase-space construction. However, unlike existing methods, the present algorithm does not assume any particular statistical distribution to perform moves or to advance the time, and thus is a unique tool for the numerical exploration of fast and ultra-fast dynamical regimes. By decomposing the problem in a set of two-level subsystems, we find a natural variable step size, that is well defined from the normalization condition of the transition probabilities between the levels. We successfully test the algorithm with known exact solutions for non-equilibrium dynamics and equilibrium thermodynamical properties of Ising-spin models in one and two dimensions, and compare to standard implementations of kinetic Monte Carlo methods. The present algorithm is directly applicable to the study of the real-time dynamics of a large class of classical Markovian chains, and particularly to short-time situations where the exact evolution is relevant.

Geometrically Constructed Markov Chain Monte Carlo Study of Quantum Spin-phonon Complex Systems

NASA Astrophysics Data System (ADS)

Suwa, Hidemaro

2013-03-01

We have developed novel Monte Carlo methods for precisely calculating quantum spin-boson models and investigated the critical phenomena of the spin-Peierls systems. Three significant methods are presented. The first is a new optimization algorithm of the Markov chain transition kernel based on the geometric weight allocation. This algorithm, for the first time, satisfies the total balance generally without imposing the detailed balance and always minimizes the average rejection rate, being better than the Metropolis algorithm. The second is the extension of the worm (directed-loop) algorithm to non-conserved particles, which cannot be treated efficiently by the conventional methods. The third is the combination with the level spectroscopy. Proposing a new gap estimator, we are successful in eliminating the systematic error of the conventional moment method. Then we have elucidated the phase diagram and the universality class of the one-dimensional XXZ spin-Peierls system. The criticality is totally consistent with the J1 -J2 model, an effective model in the antiadiabatic limit. Through this research, we have succeeded in investigating the critical phenomena of the effectively frustrated quantum spin system by the quantum Monte Carlo method without the negative sign. JSPS Postdoctoral Fellow for Research Abroad

pyNSMC: A Python Module for Null-Space Monte Carlo Uncertainty Analysis

NASA Astrophysics Data System (ADS)

White, J.; Brakefield, L. K.

2015-12-01

The null-space monte carlo technique is a non-linear uncertainty analyses technique that is well-suited to high-dimensional inverse problems. While the technique is powerful, the existing workflow for completing null-space monte carlo is cumbersome, requiring the use of multiple commandline utilities, several sets of intermediate files and even a text editor. pyNSMC is an open-source python module that automates the workflow of null-space monte carlo uncertainty analyses. The module is fully compatible with the PEST and PEST++ software suites and leverages existing functionality of pyEMU, a python framework for linear-based uncertainty analyses. pyNSMC greatly simplifies the existing workflow for null-space monte carlo by taking advantage of object oriented design facilities in python. The core of pyNSMC is the ensemble class, which draws and stores realized random vectors and also provides functionality for exporting and visualizing results. By relieving users of the tedium associated with file handling and command line utility execution, pyNSMC instead focuses the user on the important steps and assumptions of null-space monte carlo analysis. Furthermore, pyNSMC facilitates learning through flow charts and results visualization, which are available at many points in the algorithm. The ease-of-use of the pyNSMC workflow is compared to the existing workflow for null-space monte carlo for a synthetic groundwater model with hundreds of estimable parameters.

An efficient Monte Carlo-based algorithm for scatter correction in keV cone-beam CT

NASA Astrophysics Data System (ADS)

Poludniowski, G.; Evans, P. M.; Hansen, V. N.; Webb, S.

2009-06-01

A new method is proposed for scatter-correction of cone-beam CT images. A coarse reconstruction is used in initial iteration steps. Modelling of the x-ray tube spectra and detector response are included in the algorithm. Photon diffusion inside the imaging subject is calculated using the Monte Carlo method. Photon scoring at the detector is calculated using forced detection to a fixed set of node points. The scatter profiles are then obtained by linear interpolation. The algorithm is referred to as the coarse reconstruction and fixed detection (CRFD) technique. Scatter predictions are quantitatively validated against a widely used general-purpose Monte Carlo code: BEAMnrc/EGSnrc (NRCC, Canada). Agreement is excellent. The CRFD algorithm was applied to projection data acquired with a Synergy XVI CBCT unit (Elekta Limited, Crawley, UK), using RANDO and Catphan phantoms (The Phantom Laboratory, Salem NY, USA). The algorithm was shown to be effective in removing scatter-induced artefacts from CBCT images, and took as little as 2 min on a desktop PC. Image uniformity was greatly improved as was CT-number accuracy in reconstructions. This latter improvement was less marked where the expected CT-number of a material was very different to the background material in which it was embedded.

Constant-pressure nested sampling with atomistic dynamics

NASA Astrophysics Data System (ADS)

Baldock, Robert J. N.; Bernstein, Noam; Salerno, K. Michael; Pártay, Lívia B.; Csányi, Gábor

2017-10-01

The nested sampling algorithm has been shown to be a general method for calculating the pressure-temperature-composition phase diagrams of materials. While the previous implementation used single-particle Monte Carlo moves, these are inefficient for condensed systems with general interactions where single-particle moves cannot be evaluated faster than the energy of the whole system. Here we enhance the method by using all-particle moves: either Galilean Monte Carlo or the total enthalpy Hamiltonian Monte Carlo algorithm, introduced in this paper. We show that these algorithms enable the determination of phase transition temperatures with equivalent accuracy to the previous method at 1 /N of the cost for an N -particle system with general interactions, or at equal cost when single-particle moves can be done in 1 /N of the cost of a full N -particle energy evaluation. We demonstrate this speed-up for the freezing and condensation transitions of the Lennard-Jones system and show the utility of the algorithms by calculating the order-disorder phase transition of a binary Lennard-Jones model alloy, the eutectic of copper-gold, the density anomaly of water, and the condensation and solidification of bead-spring polymers. The nested sampling method with all three algorithms is implemented in the pymatnest software.

A new moving strategy for the sequential Monte Carlo approach in optimizing the hydrological model parameters

NASA Astrophysics Data System (ADS)

Zhu, Gaofeng; Li, Xin; Ma, Jinzhu; Wang, Yunquan; Liu, Shaomin; Huang, Chunlin; Zhang, Kun; Hu, Xiaoli

2018-04-01

Sequential Monte Carlo (SMC) samplers have become increasing popular for estimating the posterior parameter distribution with the non-linear dependency structures and multiple modes often present in hydrological models. However, the explorative capabilities and efficiency of the sampler depends strongly on the efficiency in the move step of SMC sampler. In this paper we presented a new SMC sampler entitled the Particle Evolution Metropolis Sequential Monte Carlo (PEM-SMC) algorithm, which is well suited to handle unknown static parameters of hydrologic model. The PEM-SMC sampler is inspired by the works of Liang and Wong (2001) and operates by incorporating the strengths of the genetic algorithm, differential evolution algorithm and Metropolis-Hasting algorithm into the framework of SMC. We also prove that the sampler admits the target distribution to be a stationary distribution. Two case studies including a multi-dimensional bimodal normal distribution and a conceptual rainfall-runoff hydrologic model by only considering parameter uncertainty and simultaneously considering parameter and input uncertainty show that PEM-SMC sampler is generally superior to other popular SMC algorithms in handling the high dimensional problems. The study also indicated that it may be important to account for model structural uncertainty by using multiplier different hydrological models in the SMC framework in future study.

Monte Carlo algorithms for Brownian phylogenetic models.

PubMed

Horvilleur, Benjamin; Lartillot, Nicolas

2014-11-01

Brownian models have been introduced in phylogenetics for describing variation in substitution rates through time, with applications to molecular dating or to the comparative analysis of variation in substitution patterns among lineages. Thus far, however, the Monte Carlo implementations of these models have relied on crude approximations, in which the Brownian process is sampled only at the internal nodes of the phylogeny or at the midpoints along each branch, and the unknown trajectory between these sampled points is summarized by simple branchwise average substitution rates. A more accurate Monte Carlo approach is introduced, explicitly sampling a fine-grained discretization of the trajectory of the (potentially multivariate) Brownian process along the phylogeny. Generic Monte Carlo resampling algorithms are proposed for updating the Brownian paths along and across branches. Specific computational strategies are developed for efficient integration of the finite-time substitution probabilities across branches induced by the Brownian trajectory. The mixing properties and the computational complexity of the resulting Markov chain Monte Carlo sampler scale reasonably with the discretization level, allowing practical applications with up to a few hundred discretization points along the entire depth of the tree. The method can be generalized to other Markovian stochastic processes, making it possible to implement a wide range of time-dependent substitution models with well-controlled computational precision. The program is freely available at www.phylobayes.org. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

An Ensemble-Based Smoother with Retrospectively Updated Weights for Highly Nonlinear Systems

NASA Technical Reports Server (NTRS)

Chin, T. M.; Turmon, M. J.; Jewell, J. B.; Ghil, M.

2006-01-01

Monte Carlo computational methods have been introduced into data assimilation for nonlinear systems in order to alleviate the computational burden of updating and propagating the full probability distribution. By propagating an ensemble of representative states, algorithms like the ensemble Kalman filter (EnKF) and the resampled particle filter (RPF) rely on the existing modeling infrastructure to approximate the distribution based on the evolution of this ensemble. This work presents an ensemble-based smoother that is applicable to the Monte Carlo filtering schemes like EnKF and RPF. At the minor cost of retrospectively updating a set of weights for ensemble members, this smoother has demonstrated superior capabilities in state tracking for two highly nonlinear problems: the double-well potential and trivariate Lorenz systems. The algorithm does not require retrospective adaptation of the ensemble members themselves, and it is thus suited to a streaming operational mode. The accuracy of the proposed backward-update scheme in estimating non-Gaussian distributions is evaluated by comparison to the more accurate estimates provided by a Markov chain Monte Carlo algorithm.

Particle Communication and Domain Neighbor Coupling: Scalable Domain Decomposed Algorithms for Monte Carlo Particle Transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

O'Brien, M. J.; Brantley, P. S.

2015-01-20

In order to run Monte Carlo particle transport calculations on new supercomputers with hundreds of thousands or millions of processors, care must be taken to implement scalable algorithms. This means that the algorithms must continue to perform well as the processor count increases. In this paper, we examine the scalability of:(1) globally resolving the particle locations on the correct processor, (2) deciding that particle streaming communication has finished, and (3) efficiently coupling neighbor domains together with different replication levels. We have run domain decomposed Monte Carlo particle transport on up to 2 21 = 2,097,152 MPI processes on the IBMmore » BG/Q Sequoia supercomputer and observed scalable results that agree with our theoretical predictions. These calculations were carefully constructed to have the same amount of work on every processor, i.e. the calculation is already load balanced. We also examine load imbalanced calculations where each domain’s replication level is proportional to its particle workload. In this case we show how to efficiently couple together adjacent domains to maintain within workgroup load balance and minimize memory usage.« less

MDTS: automatic complex materials design using Monte Carlo tree search.

PubMed

M Dieb, Thaer; Ju, Shenghong; Yoshizoe, Kazuki; Hou, Zhufeng; Shiomi, Junichiro; Tsuda, Koji

2017-01-01

Complex materials design is often represented as a black-box combinatorial optimization problem. In this paper, we present a novel python library called MDTS (Materials Design using Tree Search). Our algorithm employs a Monte Carlo tree search approach, which has shown exceptional performance in computer Go game. Unlike evolutionary algorithms that require user intervention to set parameters appropriately, MDTS has no tuning parameters and works autonomously in various problems. In comparison to a Bayesian optimization package, our algorithm showed competitive search efficiency and superior scalability. We succeeded in designing large Silicon-Germanium (Si-Ge) alloy structures that Bayesian optimization could not deal with due to excessive computational cost. MDTS is available at https://github.com/tsudalab/MDTS.

MDTS: automatic complex materials design using Monte Carlo tree search

NASA Astrophysics Data System (ADS)

Dieb, Thaer M.; Ju, Shenghong; Yoshizoe, Kazuki; Hou, Zhufeng; Shiomi, Junichiro; Tsuda, Koji

2017-12-01

Complex materials design is often represented as a black-box combinatorial optimization problem. In this paper, we present a novel python library called MDTS (Materials Design using Tree Search). Our algorithm employs a Monte Carlo tree search approach, which has shown exceptional performance in computer Go game. Unlike evolutionary algorithms that require user intervention to set parameters appropriately, MDTS has no tuning parameters and works autonomously in various problems. In comparison to a Bayesian optimization package, our algorithm showed competitive search efficiency and superior scalability. We succeeded in designing large Silicon-Germanium (Si-Ge) alloy structures that Bayesian optimization could not deal with due to excessive computational cost. MDTS is available at https://github.com/tsudalab/MDTS.

Efficient kinetic Monte Carlo method for reaction-diffusion problems with spatially varying annihilation rates

NASA Astrophysics Data System (ADS)

Schwarz, Karsten; Rieger, Heiko

2013-03-01

We present an efficient Monte Carlo method to simulate reaction-diffusion processes with spatially varying particle annihilation or transformation rates as it occurs for instance in the context of motor-driven intracellular transport. Like Green's function reaction dynamics and first-passage time methods, our algorithm avoids small diffusive hops by propagating sufficiently distant particles in large hops to the boundaries of protective domains. Since for spatially varying annihilation or transformation rates the single particle diffusion propagator is not known analytically, we present an algorithm that generates efficiently either particle displacements or annihilations with the correct statistics, as we prove rigorously. The numerical efficiency of the algorithm is demonstrated with an illustrative example.

Note: A pure-sampling quantum Monte Carlo algorithm with independent Metropolis.

PubMed

Vrbik, Jan; Ospadov, Egor; Rothstein, Stuart M

2016-07-14

Recently, Ospadov and Rothstein published a pure-sampling quantum Monte Carlo algorithm (PSQMC) that features an auxiliary Path Z that connects the midpoints of the current and proposed Paths X and Y, respectively. When sufficiently long, Path Z provides statistical independence of Paths X and Y. Under those conditions, the Metropolis decision used in PSQMC is done without any approximation, i.e., not requiring microscopic reversibility and without having to introduce any G(x → x'; τ) factors into its decision function. This is a unique feature that contrasts with all competing reptation algorithms in the literature. An example illustrates that dependence of Paths X and Y has adverse consequences for pure sampling.

Note: A pure-sampling quantum Monte Carlo algorithm with independent Metropolis

NASA Astrophysics Data System (ADS)

Vrbik, Jan; Ospadov, Egor; Rothstein, Stuart M.

2016-07-01

Recently, Ospadov and Rothstein published a pure-sampling quantum Monte Carlo algorithm (PSQMC) that features an auxiliary Path Z that connects the midpoints of the current and proposed Paths X and Y, respectively. When sufficiently long, Path Z provides statistical independence of Paths X and Y. Under those conditions, the Metropolis decision used in PSQMC is done without any approximation, i.e., not requiring microscopic reversibility and without having to introduce any G(x → x'; τ) factors into its decision function. This is a unique feature that contrasts with all competing reptation algorithms in the literature. An example illustrates that dependence of Paths X and Y has adverse consequences for pure sampling.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sudhyadhom, A; McGuinness, C; Descovich, M

Purpose: To develop a methodology for validation of a Monte-Carlo dose calculation model for robotic small field SRS/SBRT deliveries. Methods: In a robotic treatment planning system, a Monte-Carlo model was iteratively optimized to match with beam data. A two-part analysis was developed to verify this model. 1) The Monte-Carlo model was validated in a simulated water phantom versus a Ray-Tracing calculation on a single beam collimator-by-collimator calculation. 2) The Monte-Carlo model was validated to be accurate in the most challenging situation, lung, by acquiring in-phantom measurements. A plan was created and delivered in a CIRS lung phantom with film insert.more » Separately, plans were delivered in an in-house created lung phantom with a PinPoint chamber insert within a lung simulating material. For medium to large collimator sizes, a single beam was delivered to the phantom. For small size collimators (10, 12.5, and 15mm), a robotically delivered plan was created to generate a uniform dose field of irradiation over a 2×2cm{sup 2} area. Results: Dose differences in simulated water between Ray-Tracing and Monte-Carlo were all within 1% at dmax and deeper. Maximum dose differences occurred prior to dmax but were all within 3%. Film measurements in a lung phantom show high correspondence of over 95% gamma at the 2%/2mm level for Monte-Carlo. Ion chamber measurements for collimator sizes of 12.5mm and above were within 3% of Monte-Carlo calculated values. Uniform irradiation involving the 10mm collimator resulted in a dose difference of ∼8% for both Monte-Carlo and Ray-Tracing indicating that there may be limitations with the dose calculation. Conclusion: We have developed a methodology to validate a Monte-Carlo model by verifying that it matches in water and, separately, that it corresponds well in lung simulating materials. The Monte-Carlo model and algorithm tested may have more limited accuracy for 10mm fields and smaller.« less

Polynomial complexity despite the fermionic sign

NASA Astrophysics Data System (ADS)

Rossi, R.; Prokof'ev, N.; Svistunov, B.; Van Houcke, K.; Werner, F.

2017-04-01

It is commonly believed that in unbiased quantum Monte Carlo approaches to fermionic many-body problems, the infamous sign problem generically implies prohibitively large computational times for obtaining thermodynamic-limit quantities. We point out that for convergent Feynman diagrammatic series evaluated with a recently introduced Monte Carlo algorithm (see Rossi R., arXiv:1612.05184), the computational time increases only polynomially with the inverse error on thermodynamic-limit quantities.

Hybrid Microgrid Configuration Optimization with Evolutionary Algorithms

NASA Astrophysics Data System (ADS)

Lopez, Nicolas

This dissertation explores the Renewable Energy Integration Problem, and proposes a Genetic Algorithm embedded with a Monte Carlo simulation to solve large instances of the problem that are impractical to solve via full enumeration. The Renewable Energy Integration Problem is defined as finding the optimum set of components to supply the electric demand to a hybrid microgrid. The components considered are solar panels, wind turbines, diesel generators, electric batteries, connections to the power grid and converters, which can be inverters and/or rectifiers. The methodology developed is explained as well as the combinatorial formulation. In addition, 2 case studies of a single objective optimization version of the problem are presented, in order to minimize cost and to minimize global warming potential (GWP) followed by a multi-objective implementation of the offered methodology, by utilizing a non-sorting Genetic Algorithm embedded with a monte Carlo Simulation. The method is validated by solving a small instance of the problem with known solution via a full enumeration algorithm developed by NREL in their software HOMER. The dissertation concludes that the evolutionary algorithms embedded with Monte Carlo simulation namely modified Genetic Algorithms are an efficient form of solving the problem, by finding approximate solutions in the case of single objective optimization, and by approximating the true Pareto front in the case of multiple objective optimization of the Renewable Energy Integration Problem.

Self-learning Monte Carlo with deep neural networks

NASA Astrophysics Data System (ADS)

Shen, Huitao; Liu, Junwei; Fu, Liang

2018-05-01

The self-learning Monte Carlo (SLMC) method is a general algorithm to speedup MC simulations. Its efficiency has been demonstrated in various systems by introducing an effective model to propose global moves in the configuration space. In this paper, we show that deep neural networks can be naturally incorporated into SLMC, and without any prior knowledge can learn the original model accurately and efficiently. Demonstrated in quantum impurity models, we reduce the complexity for a local update from O (β2) in Hirsch-Fye algorithm to O (β lnβ ) , which is a significant speedup especially for systems at low temperatures.

Monte Carlo sampling in diffusive dynamical systems

NASA Astrophysics Data System (ADS)

Tapias, Diego; Sanders, David P.; Altmann, Eduardo G.

2018-05-01

We introduce a Monte Carlo algorithm to efficiently compute transport properties of chaotic dynamical systems. Our method exploits the importance sampling technique that favors trajectories in the tail of the distribution of displacements, where deviations from a diffusive process are most prominent. We search for initial conditions using a proposal that correlates states in the Markov chain constructed via a Metropolis-Hastings algorithm. We show that our method outperforms the direct sampling method and also Metropolis-Hastings methods with alternative proposals. We test our general method through numerical simulations in 1D (box-map) and 2D (Lorentz gas) systems.

Vectorization of a Monte Carlo simulation scheme for nonequilibrium gas dynamics

NASA Technical Reports Server (NTRS)

Boyd, Iain D.

1991-01-01

Significant improvement has been obtained in the numerical performance of a Monte Carlo scheme for the analysis of nonequilibrium gas dynamics through an implementation of the algorithm which takes advantage of vector hardware, as presently demonstrated through application to three different problems. These are (1) a 1D standing-shock wave; (2) the flow of an expanding gas through an axisymmetric nozzle; and (3) the hypersonic flow of Ar gas over a 3D wedge. Problem (3) is illustrative of the greatly increased number of molecules which the simulation may involve, thanks to improved algorithm performance.

Multicanonical hybrid Monte Carlo algorithm: Boosting simulations of compact QED

NASA Astrophysics Data System (ADS)

Arnold, G.; Schilling, K.; Lippert, Th.

1999-03-01

We demonstrate that substantial progress can be achieved in the study of the phase structure of four-dimensional compact QED by a joint use of hybrid Monte Carlo and multicanonical algorithms through an efficient parallel implementation. This is borne out by the observation of considerable speedup of tunnelling between the metastable states, close to the phase transition, on the Wilson line. We estimate that the creation of adequate samples (with order 100 flip-flops) becomes a matter of half a year's run time at 2 Gflops sustained performance for lattices of size up to 244.

A novel Monte Carlo algorithm for simulating crystals with McStas

NASA Astrophysics Data System (ADS)

Alianelli, L.; Sánchez del Río, M.; Felici, R.; Andersen, K. H.; Farhi, E.

2004-07-01

We developed an original Monte Carlo algorithm for the simulation of Bragg diffraction by mosaic, bent and gradient crystals. It has practical applications, as it can be used for simulating imperfect crystals (monochromators, analyzers and perhaps samples) in neutron ray-tracing packages, like McStas. The code we describe here provides a detailed description of the particle interaction with the microscopic homogeneous regions composing the crystal, therefore it can be used also for the calculation of quantities having a conceptual interest, as multiple scattering, or for the interpretation of experiments aiming at characterizing crystals, like diffraction topographs.

Monte Carlo methods for multidimensional integration for European option pricing

NASA Astrophysics Data System (ADS)

Todorov, V.; Dimov, I. T.

2016-10-01

In this paper, we illustrate examples of highly accurate Monte Carlo and quasi-Monte Carlo methods for multiple integrals related to the evaluation of European style options. The idea is that the value of the option is formulated in terms of the expectation of some random variable; then the average of independent samples of this random variable is used to estimate the value of the option. First we obtain an integral representation for the value of the option using the risk neutral valuation formula. Then with an appropriations change of the constants we obtain a multidimensional integral over the unit hypercube of the corresponding dimensionality. Then we compare a specific type of lattice rules over one of the best low discrepancy sequence of Sobol for numerical integration. Quasi-Monte Carlo methods are compared with Adaptive and Crude Monte Carlo techniques for solving the problem. The four approaches are completely different thus it is a question of interest to know which one of them outperforms the other for evaluation multidimensional integrals in finance. Some of the advantages and disadvantages of the developed algorithms are discussed.

Monte Carlo-based Reconstruction in Water Cherenkov Detectors using Chroma

NASA Astrophysics Data System (ADS)

Seibert, Stanley; Latorre, Anthony

2012-03-01

We demonstrate the feasibility of event reconstruction---including position, direction, energy and particle identification---in water Cherenkov detectors with a purely Monte Carlo-based method. Using a fast optical Monte Carlo package we have written, called Chroma, in combination with several variance reduction techniques, we can estimate the value of a likelihood function for an arbitrary event hypothesis. The likelihood can then be maximized over the parameter space of interest using a form of gradient descent designed for stochastic functions. Although slower than more traditional reconstruction algorithms, this completely Monte Carlo-based technique is universal and can be applied to a detector of any size or shape, which is a major advantage during the design phase of an experiment. As a specific example, we focus on reconstruction results from a simulation of the 200 kiloton water Cherenkov far detector option for LBNE.

An improved target velocity sampling algorithm for free gas elastic scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Romano, Paul K.; Walsh, Jonathan A.

We present an improved algorithm for sampling the target velocity when simulating elastic scattering in a Monte Carlo neutron transport code that correctly accounts for the energy dependence of the scattering cross section. The algorithm samples the relative velocity directly, thereby avoiding a potentially inefficient rejection step based on the ratio of cross sections. Here, we have shown that this algorithm requires only one rejection step, whereas other methods of similar accuracy require two rejection steps. The method was verified against stochastic and deterministic reference results for upscattering percentages in 238U. Simulations of a light water reactor pin cell problemmore » demonstrate that using this algorithm results in a 3% or less penalty in performance when compared with an approximate method that is used in most production Monte Carlo codes« less

An improved target velocity sampling algorithm for free gas elastic scattering

DOE PAGES

Romano, Paul K.; Walsh, Jonathan A.

2018-02-03

We present an improved algorithm for sampling the target velocity when simulating elastic scattering in a Monte Carlo neutron transport code that correctly accounts for the energy dependence of the scattering cross section. The algorithm samples the relative velocity directly, thereby avoiding a potentially inefficient rejection step based on the ratio of cross sections. Here, we have shown that this algorithm requires only one rejection step, whereas other methods of similar accuracy require two rejection steps. The method was verified against stochastic and deterministic reference results for upscattering percentages in 238U. Simulations of a light water reactor pin cell problemmore » demonstrate that using this algorithm results in a 3% or less penalty in performance when compared with an approximate method that is used in most production Monte Carlo codes« less

A smart Monte Carlo procedure for production costing and uncertainty analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Parker, C.; Stremel, J.

1996-11-01

Electric utilities using chronological production costing models to decide whether to buy or sell power over the next week or next few weeks need to determine potential profits or losses under a number of uncertainties. A large amount of money can be at stake--often $100,000 a day or more--and one party of the sale must always take on the risk. In the case of fixed price ($/MWh) contracts, the seller accepts the risk. In the case of cost plus contracts, the buyer must accept the risk. So, modeling uncertainty and understanding the risk accurately can improve the competitive edge ofmore » the user. This paper investigates an efficient procedure for representing risks and costs from capacity outages. Typically, production costing models use an algorithm based on some form of random number generator to select resources as available or on outage. These algorithms allow experiments to be repeated and gains and losses to be observed in a short time. The authors perform several experiments to examine the capability of three unit outage selection methods and measures their results. Specifically, a brute force Monte Carlo procedure, a Monte Carlo procedure with Latin Hypercube sampling, and a Smart Monte Carlo procedure with cost stratification and directed sampling are examined.« less

Analysis of Monte Carlo accelerated iterative methods for sparse linear systems: Analysis of Monte Carlo accelerated iterative methods for sparse linear systems

DOE PAGES

Benzi, Michele; Evans, Thomas M.; Hamilton, Steven P.; ...

2017-03-05

Here, we consider hybrid deterministic-stochastic iterative algorithms for the solution of large, sparse linear systems. Starting from a convergent splitting of the coefficient matrix, we analyze various types of Monte Carlo acceleration schemes applied to the original preconditioned Richardson (stationary) iteration. We expect that these methods will have considerable potential for resiliency to faults when implemented on massively parallel machines. We also establish sufficient conditions for the convergence of the hybrid schemes, and we investigate different types of preconditioners including sparse approximate inverses. Numerical experiments on linear systems arising from the discretization of partial differential equations are presented.

Distance between configurations in Markov chain Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Fukuma, Masafumi; Matsumoto, Nobuyuki; Umeda, Naoya

2017-12-01

For a given Markov chain Monte Carlo algorithm we introduce a distance between two configurations that quantifies the difficulty of transition from one configuration to the other configuration. We argue that the distance takes a universal form for the class of algorithms which generate local moves in the configuration space. We explicitly calculate the distance for the Langevin algorithm, and show that it certainly has desired and expected properties as distance. We further show that the distance for a multimodal distribution gets dramatically reduced from a large value by the introduction of a tempering method. We also argue that, when the original distribution is highly multimodal with large number of degenerate vacua, an anti-de Sitter-like geometry naturally emerges in the extended configuration space.

Quantum-enhanced reinforcement learning for finite-episode games with discrete state spaces

NASA Astrophysics Data System (ADS)

Neukart, Florian; Von Dollen, David; Seidel, Christian; Compostella, Gabriele

2017-12-01

Quantum annealing algorithms belong to the class of metaheuristic tools, applicable for solving binary optimization problems. Hardware implementations of quantum annealing, such as the quantum annealing machines produced by D-Wave Systems, have been subject to multiple analyses in research, with the aim of characterizing the technology's usefulness for optimization and sampling tasks. Here, we present a way to partially embed both Monte Carlo policy iteration for finding an optimal policy on random observations, as well as how to embed n sub-optimal state-value functions for approximating an improved state-value function given a policy for finite horizon games with discrete state spaces on a D-Wave 2000Q quantum processing unit (QPU). We explain how both problems can be expressed as a quadratic unconstrained binary optimization (QUBO) problem, and show that quantum-enhanced Monte Carlo policy evaluation allows for finding equivalent or better state-value functions for a given policy with the same number episodes compared to a purely classical Monte Carlo algorithm. Additionally, we describe a quantum-classical policy learning algorithm. Our first and foremost aim is to explain how to represent and solve parts of these problems with the help of the QPU, and not to prove supremacy over every existing classical policy evaluation algorithm.

Development of reversible jump Markov Chain Monte Carlo algorithm in the Bayesian mixture modeling for microarray data in Indonesia

NASA Astrophysics Data System (ADS)

Astuti, Ani Budi; Iriawan, Nur; Irhamah, Kuswanto, Heri

2017-12-01

In the Bayesian mixture modeling requires stages the identification number of the most appropriate mixture components thus obtained mixture models fit the data through data driven concept. Reversible Jump Markov Chain Monte Carlo (RJMCMC) is a combination of the reversible jump (RJ) concept and the Markov Chain Monte Carlo (MCMC) concept used by some researchers to solve the problem of identifying the number of mixture components which are not known with certainty number. In its application, RJMCMC using the concept of the birth/death and the split-merge with six types of movement, that are w updating, θ updating, z updating, hyperparameter β updating, split-merge for components and birth/death from blank components. The development of the RJMCMC algorithm needs to be done according to the observed case. The purpose of this study is to know the performance of RJMCMC algorithm development in identifying the number of mixture components which are not known with certainty number in the Bayesian mixture modeling for microarray data in Indonesia. The results of this study represent that the concept RJMCMC algorithm development able to properly identify the number of mixture components in the Bayesian normal mixture model wherein the component mixture in the case of microarray data in Indonesia is not known for certain number.

Subtle Monte Carlo Updates in Dense Molecular Systems.

PubMed

Bottaro, Sandro; Boomsma, Wouter; E Johansson, Kristoffer; Andreetta, Christian; Hamelryck, Thomas; Ferkinghoff-Borg, Jesper

2012-02-14

Although Markov chain Monte Carlo (MC) simulation is a potentially powerful approach for exploring conformational space, it has been unable to compete with molecular dynamics (MD) in the analysis of high density structural states, such as the native state of globular proteins. Here, we introduce a kinetic algorithm, CRISP, that greatly enhances the sampling efficiency in all-atom MC simulations of dense systems. The algorithm is based on an exact analytical solution to the classic chain-closure problem, making it possible to express the interdependencies among degrees of freedom in the molecule as correlations in a multivariate Gaussian distribution. We demonstrate that our method reproduces structural variation in proteins with greater efficiency than current state-of-the-art Monte Carlo methods and has real-time simulation performance on par with molecular dynamics simulations. The presented results suggest our method as a valuable tool in the study of molecules in atomic detail, offering a potential alternative to molecular dynamics for probing long time-scale conformational transitions.

SU-E-T-202: Impact of Monte Carlo Dose Calculation Algorithm On Prostate SBRT Treatments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Venencia, C; Garrigo, E; Cardenas, J

2014-06-01

Purpose: The purpose of this work was to quantify the dosimetric impact of using Monte Carlo algorithm on pre calculated SBRT prostate treatment with pencil beam dose calculation algorithm. Methods: A 6MV photon beam produced by a Novalis TX (BrainLAB-Varian) linear accelerator equipped with HDMLC was used. Treatment plans were done using 9 fields with Iplanv4.5 (BrainLAB) and dynamic IMRT modality. Institutional SBRT protocol uses a total dose to the prostate of 40Gy in 5 fractions, every other day. Dose calculation is done by pencil beam (2mm dose resolution), heterogeneity correction and dose volume constraint (UCLA) for PTV D95%=40Gy andmore » D98%>39.2Gy, Rectum V20Gy<50%, V32Gy<20%, V36Gy<10% and V40Gy<5%, Bladder V20Gy<40% and V40Gy<10%, femoral heads V16Gy<5%, penile bulb V25Gy<3cc, urethra and overlap region between PTV and PRV Rectum Dmax<42Gy. 10 SBRT treatments plans were selected and recalculated using Monte Carlo with 2mm spatial resolution and mean variance of 2%. DVH comparisons between plans were done. Results: The average difference between PTV doses constraints were within 2%. However 3 plans have differences higher than 3% which does not meet the D98% criteria (>39.2Gy) and should have been renormalized. Dose volume constraint differences for rectum, bladder, femoral heads and penile bulb were les than 2% and within tolerances. Urethra region and overlapping between PTV and PRV Rectum shows increment of dose in all plans. The average difference for urethra region was 2.1% with a maximum of 7.8% and for the overlapping region 2.5% with a maximum of 8.7%. Conclusion: Monte Carlo dose calculation on dynamic IMRT treatments could affects on plan normalization. Dose increment in critical region of urethra and PTV overlapping region with PTV could have clinical consequences which need to be studied. The use of Monte Carlo dose calculation algorithm is limited because inverse planning dose optimization use only pencil beam.« less

Annealed Importance Sampling Reversible Jump MCMC algorithms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Karagiannis, Georgios; Andrieu, Christophe

2013-03-20

It will soon be 20 years since reversible jump Markov chain Monte Carlo (RJ-MCMC) algorithms have been proposed. They have significantly extended the scope of Markov chain Monte Carlo simulation methods, offering the promise to be able to routinely tackle transdimensional sampling problems, as encountered in Bayesian model selection problems for example, in a principled and flexible fashion. Their practical efficient implementation, however, still remains a challenge. A particular difficulty encountered in practice is in the choice of the dimension matching variables (both their nature and their distribution) and the reversible transformations which allow one to define the one-to-one mappingsmore » underpinning the design of these algorithms. Indeed, even seemingly sensible choices can lead to algorithms with very poor performance. The focus of this paper is the development and performance evaluation of a method, annealed importance sampling RJ-MCMC (aisRJ), which addresses this problem by mitigating the sensitivity of RJ-MCMC algorithms to the aforementioned poor design. As we shall see the algorithm can be understood as being an “exact approximation” of an idealized MCMC algorithm that would sample from the model probabilities directly in a model selection set-up. Such an idealized algorithm may have good theoretical convergence properties, but typically cannot be implemented, and our algorithms can approximate the performance of such idealized algorithms to an arbitrary degree while not introducing any bias for any degree of approximation. Our approach combines the dimension matching ideas of RJ-MCMC with annealed importance sampling and its Markov chain Monte Carlo implementation. We illustrate the performance of the algorithm with numerical simulations which indicate that, although the approach may at first appear computationally involved, it is in fact competitive.« less

Multigroup Monte Carlo on GPUs: Comparison of history- and event-based algorithms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hamilton, Steven P.; Slattery, Stuart R.; Evans, Thomas M.

This article presents an investigation of the performance of different multigroup Monte Carlo transport algorithms on GPUs with a discussion of both history-based and event-based approaches. Several algorithmic improvements are introduced for both approaches. By modifying the history-based algorithm that is traditionally favored in CPU-based MC codes to occasionally filter out dead particles to reduce thread divergence, performance exceeds that of either the pure history-based or event-based approaches. The impacts of several algorithmic choices are discussed, including performance studies on Kepler and Pascal generation NVIDIA GPUs for fixed source and eigenvalue calculations. Single-device performance equivalent to 20–40 CPU cores onmore » the K40 GPU and 60–80 CPU cores on the P100 GPU is achieved. Last, in addition, nearly perfect multi-device parallel weak scaling is demonstrated on more than 16,000 nodes of the Titan supercomputer.« less

Multigroup Monte Carlo on GPUs: Comparison of history- and event-based algorithms

DOE PAGES

Hamilton, Steven P.; Slattery, Stuart R.; Evans, Thomas M.

2017-12-22

This article presents an investigation of the performance of different multigroup Monte Carlo transport algorithms on GPUs with a discussion of both history-based and event-based approaches. Several algorithmic improvements are introduced for both approaches. By modifying the history-based algorithm that is traditionally favored in CPU-based MC codes to occasionally filter out dead particles to reduce thread divergence, performance exceeds that of either the pure history-based or event-based approaches. The impacts of several algorithmic choices are discussed, including performance studies on Kepler and Pascal generation NVIDIA GPUs for fixed source and eigenvalue calculations. Single-device performance equivalent to 20–40 CPU cores onmore » the K40 GPU and 60–80 CPU cores on the P100 GPU is achieved. Last, in addition, nearly perfect multi-device parallel weak scaling is demonstrated on more than 16,000 nodes of the Titan supercomputer.« less

Statistical hadronization and microcanonical ensemble

DOE PAGES

Becattini, F.; Ferroni, L.

2004-01-01

We present a Monte Carlo calculation of the microcanonical ensemble of the of the ideal hadron-resonance gas including all known states up to a mass of 1. 8 GeV, taking into account quantum statistics. The computing method is a development of a previous one based on a Metropolis Monte Carlo algorithm, with a the grand-canonical limit of the multi-species multiplicity distribution as proposal matrix. The microcanonical average multiplicities of the various hadron species are found to converge to the canonical ones for moderately low values of the total energy. This algorithm opens the way for event generators based for themore » statistical hadronization model.« less

Fast GPU-based Monte Carlo simulations for LDR prostate brachytherapy.

PubMed

Bonenfant, Éric; Magnoux, Vincent; Hissoiny, Sami; Ozell, Benoît; Beaulieu, Luc; Després, Philippe

2015-07-07

The aim of this study was to evaluate the potential of bGPUMCD, a Monte Carlo algorithm executed on Graphics Processing Units (GPUs), for fast dose calculations in permanent prostate implant dosimetry. It also aimed to validate a low dose rate brachytherapy source in terms of TG-43 metrics and to use this source to compute dose distributions for permanent prostate implant in very short times. The physics of bGPUMCD was reviewed and extended to include Rayleigh scattering and fluorescence from photoelectric interactions for all materials involved. The radial and anisotropy functions were obtained for the Nucletron SelectSeed in TG-43 conditions. These functions were compared to those found in the MD Anderson Imaging and Radiation Oncology Core brachytherapy source registry which are considered the TG-43 reference values. After appropriate calibration of the source, permanent prostate implant dose distributions were calculated for four patients and compared to an already validated Geant4 algorithm. The radial function calculated from bGPUMCD showed excellent agreement (differences within 1.3%) with TG-43 accepted values. The anisotropy functions at r = 1 cm and r = 4 cm were within 2% of TG-43 values for angles over 17.5°. For permanent prostate implants, Monte Carlo-based dose distributions with a statistical uncertainty of 1% or less for the target volume were obtained in 30 s or less for 1 × 1 × 1 mm(3) calculation grids. Dosimetric indices were very similar (within 2.7%) to those obtained with a validated, independent Monte Carlo code (Geant4) performing the calculations for the same cases in a much longer time (tens of minutes to more than a hour). bGPUMCD is a promising code that lets envision the use of Monte Carlo techniques in a clinical environment, with sub-minute execution times on a standard workstation. Future work will explore the use of this code with an inverse planning method to provide a complete Monte Carlo-based planning solution.

Fast GPU-based Monte Carlo simulations for LDR prostate brachytherapy

NASA Astrophysics Data System (ADS)

Bonenfant, Éric; Magnoux, Vincent; Hissoiny, Sami; Ozell, Benoît; Beaulieu, Luc; Després, Philippe

2015-07-01

The aim of this study was to evaluate the potential of bGPUMCD, a Monte Carlo algorithm executed on Graphics Processing Units (GPUs), for fast dose calculations in permanent prostate implant dosimetry. It also aimed to validate a low dose rate brachytherapy source in terms of TG-43 metrics and to use this source to compute dose distributions for permanent prostate implant in very short times. The physics of bGPUMCD was reviewed and extended to include Rayleigh scattering and fluorescence from photoelectric interactions for all materials involved. The radial and anisotropy functions were obtained for the Nucletron SelectSeed in TG-43 conditions. These functions were compared to those found in the MD Anderson Imaging and Radiation Oncology Core brachytherapy source registry which are considered the TG-43 reference values. After appropriate calibration of the source, permanent prostate implant dose distributions were calculated for four patients and compared to an already validated Geant4 algorithm. The radial function calculated from bGPUMCD showed excellent agreement (differences within 1.3%) with TG-43 accepted values. The anisotropy functions at r = 1 cm and r = 4 cm were within 2% of TG-43 values for angles over 17.5°. For permanent prostate implants, Monte Carlo-based dose distributions with a statistical uncertainty of 1% or less for the target volume were obtained in 30 s or less for 1 × 1 × 1 mm3 calculation grids. Dosimetric indices were very similar (within 2.7%) to those obtained with a validated, independent Monte Carlo code (Geant4) performing the calculations for the same cases in a much longer time (tens of minutes to more than a hour). bGPUMCD is a promising code that lets envision the use of Monte Carlo techniques in a clinical environment, with sub-minute execution times on a standard workstation. Future work will explore the use of this code with an inverse planning method to provide a complete Monte Carlo-based planning solution.

SU-E-T-171: Evaluation of the Analytical Anisotropic Algorithm in a Small Finger Joint Phantom Using Monte Carlo Simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chow, J; Owrangi, A; Jiang, R

2014-06-01

Purpose: This study investigated the performance of the anisotropic analytical algorithm (AAA) in dose calculation in radiotherapy concerning a small finger joint. Monte Carlo simulation (EGSnrc code) was used in this dosimetric evaluation. Methods: Heterogeneous finger joint phantom containing a vertical water layer (bone joint or cartilage) sandwiched by two bones with dimension 2 × 2 × 2 cm{sup 3} was irradiated by the 6 MV photon beams (field size = 4 × 4 cm{sup 2}). The central beam axis was along the length of the bone joint and the isocenter was set to the center of the joint. Themore » joint width and beam angle were varied from 0.5–2 mm and 0°–15°, respectively. Depth doses were calculated using the AAA and DOSXYZnrc. For dosimetric comparison and normalization, dose calculations were repeated in water phantom using the same beam geometry. Results: Our AAA and Monte Carlo results showed that the AAA underestimated the joint doses by 10%–20%, and could not predict joint dose variation with changes of joint width and beam angle. The calculated bone dose enhancement for the AAA was lower than Monte Carlo and the depth of maximum dose for the phantom was smaller than that for the water phantom. From Monte Carlo results, there was a decrease of joint dose as its width increased. This reflected the smaller the joint width, the more the bone scatter contributed to the depth dose. Moreover, the joint dose was found slightly decreased with an increase of beam angle. Conclusion: The AAA could not handle variations of joint dose well with changes of joint width and beam angle based on our finger joint phantom. Monte Carlo results showed that the joint dose decreased with increase of joint width and beam angle. This dosimetry comparison should be useful to radiation staff in radiotherapy related to small bone joint.« less

Fungible Correlation Matrices: A Method for Generating Nonsingular, Singular, and Improper Correlation Matrices for Monte Carlo Research.

PubMed

Waller, Niels G

2016-01-01

For a fixed set of standardized regression coefficients and a fixed coefficient of determination (R-squared), an infinite number of predictor correlation matrices will satisfy the implied quadratic form. I call such matrices fungible correlation matrices. In this article, I describe an algorithm for generating positive definite (PD), positive semidefinite (PSD), or indefinite (ID) fungible correlation matrices that have a random or fixed smallest eigenvalue. The underlying equations of this algorithm are reviewed from both algebraic and geometric perspectives. Two simulation studies illustrate that fungible correlation matrices can be profitably used in Monte Carlo research. The first study uses PD fungible correlation matrices to compare penalized regression algorithms. The second study uses ID fungible correlation matrices to compare matrix-smoothing algorithms. R code for generating fungible correlation matrices is presented in the supplemental materials.

A Monte Carlo method for the simulation of coagulation and nucleation based on weighted particles and the concepts of stochastic resolution and merging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kotalczyk, G., E-mail: Gregor.Kotalczyk@uni-due.de; Kruis, F.E.

Monte Carlo simulations based on weighted simulation particles can solve a variety of population balance problems and allow thus to formulate a solution-framework for many chemical engineering processes. This study presents a novel concept for the calculation of coagulation rates of weighted Monte Carlo particles by introducing a family of transformations to non-weighted Monte Carlo particles. The tuning of the accuracy (named ‘stochastic resolution’ in this paper) of those transformations allows the construction of a constant-number coagulation scheme. Furthermore, a parallel algorithm for the inclusion of newly formed Monte Carlo particles due to nucleation is presented in the scope ofmore » a constant-number scheme: the low-weight merging. This technique is found to create significantly less statistical simulation noise than the conventional technique (named ‘random removal’ in this paper). Both concepts are combined into a single GPU-based simulation method which is validated by comparison with the discrete-sectional simulation technique. Two test models describing a constant-rate nucleation coupled to a simultaneous coagulation in 1) the free-molecular regime or 2) the continuum regime are simulated for this purpose.« less

Monte Carlo: in the beginning and some great expectations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Metropolis, N.

1985-01-01

The central theme will be on the historical setting and origins of the Monte Carlo Method. The scene was post-war Los Alamos Scientific Laboratory. There was an inevitability about the Monte Carlo Event: the ENIAC had recently enjoyed its meteoric rise (on a classified Los Alamos problem); Stan Ulam had returned to Los Alamos; John von Neumann was a frequent visitor. Techniques, algorithms, and applications developed rapidly at Los Alamos. Soon, the fascination of the Method reached wider horizons. The first paper was submitted for publication in the spring of 1949. In the summer of 1949, the first open conferencemore » was held at the University of California at Los Angeles. Of some interst perhaps is an account of Fermi's earlier, independent application in neutron moderation studies while at the University of Rome. The quantum leap expected with the advent of massively parallel processors will provide stimuli for very ambitious applications of the Monte Carlo Method in disciplines ranging from field theories to cosmology, including more realistic models in the neurosciences. A structure of multi-instruction sets for parallel processing is ideally suited for the Monte Carlo approach. One may even hope for a modest hardening of the soft sciences.« less

On the utility of graphics cards to perform massively parallel simulation of advanced Monte Carlo methods

PubMed Central

Lee, Anthony; Yau, Christopher; Giles, Michael B.; Doucet, Arnaud; Holmes, Christopher C.

2011-01-01

We present a case-study on the utility of graphics cards to perform massively parallel simulation of advanced Monte Carlo methods. Graphics cards, containing multiple Graphics Processing Units (GPUs), are self-contained parallel computational devices that can be housed in conventional desktop and laptop computers and can be thought of as prototypes of the next generation of many-core processors. For certain classes of population-based Monte Carlo algorithms they offer massively parallel simulation, with the added advantage over conventional distributed multi-core processors that they are cheap, easily accessible, easy to maintain, easy to code, dedicated local devices with low power consumption. On a canonical set of stochastic simulation examples including population-based Markov chain Monte Carlo methods and Sequential Monte Carlo methods, we nd speedups from 35 to 500 fold over conventional single-threaded computer code. Our findings suggest that GPUs have the potential to facilitate the growth of statistical modelling into complex data rich domains through the availability of cheap and accessible many-core computation. We believe the speedup we observe should motivate wider use of parallelizable simulation methods and greater methodological attention to their design. PMID:22003276

Technical Note: A direct ray-tracing method to compute integral depth dose in pencil beam proton radiography with a multilayer ionization chamber.

PubMed

Farace, Paolo; Righetto, Roberto; Deffet, Sylvain; Meijers, Arturs; Vander Stappen, Francois

2016-12-01

To introduce a fast ray-tracing algorithm in pencil proton radiography (PR) with a multilayer ionization chamber (MLIC) for in vivo range error mapping. Pencil beam PR was obtained by delivering spots uniformly positioned in a square (45 × 45 mm 2 field-of-view) of 9 × 9 spots capable of crossing the phantoms (210 MeV). The exit beam was collected by a MLIC to sample the integral depth dose (IDD MLIC ). PRs of an electron-density and of a head phantom were acquired by moving the couch to obtain multiple 45 × 45 mm 2 frames. To map the corresponding range errors, the two-dimensional set of IDD MLIC was compared with (i) the integral depth dose computed by the treatment planning system (TPS) by both analytic (IDD TPS ) and Monte Carlo (IDD MC ) algorithms in a volume of water simulating the MLIC at the CT, and (ii) the integral depth dose directly computed by a simple ray-tracing algorithm (IDD direct ) through the same CT data. The exact spatial position of the spot pattern was numerically adjusted testing different in-plane positions and selecting the one that minimized the range differences between IDD direct and IDD MLIC . Range error mapping was feasible by both the TPS and the ray-tracing methods, but very sensitive to even small misalignments. In homogeneous regions, the range errors computed by the direct ray-tracing algorithm matched the results obtained by both the analytic and the Monte Carlo algorithms. In both phantoms, lateral heterogeneities were better modeled by the ray-tracing and the Monte Carlo algorithms than by the analytic TPS computation. Accordingly, when the pencil beam crossed lateral heterogeneities, the range errors mapped by the direct algorithm matched better the Monte Carlo maps than those obtained by the analytic algorithm. Finally, the simplicity of the ray-tracing algorithm allowed to implement a prototype procedure for automated spatial alignment. The ray-tracing algorithm can reliably replace the TPS method in MLIC PR for in vivo range verification and it can be a key component to develop software tools for spatial alignment and correction of CT calibration.

The Monte Carlo code MCPTV--Monte Carlo dose calculation in radiation therapy with carbon ions.

PubMed

Karg, Juergen; Speer, Stefan; Schmidt, Manfred; Mueller, Reinhold

2010-07-07

The Monte Carlo code MCPTV is presented. MCPTV is designed for dose calculation in treatment planning in radiation therapy with particles and especially carbon ions. MCPTV has a voxel-based concept and can perform a fast calculation of the dose distribution on patient CT data. Material and density information from CT are taken into account. Electromagnetic and nuclear interactions are implemented. Furthermore the algorithm gives information about the particle spectra and the energy deposition in each voxel. This can be used to calculate the relative biological effectiveness (RBE) for each voxel. Depth dose distributions are compared to experimental data giving good agreement. A clinical example is shown to demonstrate the capabilities of the MCPTV dose calculation.

Split Orthogonal Group: A Guiding Principle for Sign-Problem-Free Fermionic Simulations

NASA Astrophysics Data System (ADS)

Wang, Lei; Liu, Ye-Hua; Iazzi, Mauro; Troyer, Matthias; Harcos, Gergely

2015-12-01

We present a guiding principle for designing fermionic Hamiltonians and quantum Monte Carlo (QMC) methods that are free from the infamous sign problem by exploiting the Lie groups and Lie algebras that appear naturally in the Monte Carlo weight of fermionic QMC simulations. Specifically, rigorous mathematical constraints on the determinants involving matrices that lie in the split orthogonal group provide a guideline for sign-free simulations of fermionic models on bipartite lattices. This guiding principle not only unifies the recent solutions of the sign problem based on the continuous-time quantum Monte Carlo methods and the Majorana representation, but also suggests new efficient algorithms to simulate physical systems that were previously prohibitive because of the sign problem.

Transforming high-dimensional potential energy surfaces into sum-of-products form using Monte Carlo methods

NASA Astrophysics Data System (ADS)

Schröder, Markus; Meyer, Hans-Dieter

2017-08-01

We propose a Monte Carlo method, "Monte Carlo Potfit," for transforming high-dimensional potential energy surfaces evaluated on discrete grid points into a sum-of-products form, more precisely into a Tucker form. To this end we use a variational ansatz in which we replace numerically exact integrals with Monte Carlo integrals. This largely reduces the numerical cost by avoiding the evaluation of the potential on all grid points and allows a treatment of surfaces up to 15-18 degrees of freedom. We furthermore show that the error made with this ansatz can be controlled and vanishes in certain limits. We present calculations on the potential of HFCO to demonstrate the features of the algorithm. To demonstrate the power of the method, we transformed a 15D potential of the protonated water dimer (Zundel cation) in a sum-of-products form and calculated the ground and lowest 26 vibrationally excited states of the Zundel cation with the multi-configuration time-dependent Hartree method.

Semi-stochastic full configuration interaction quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Holmes, Adam; Petruzielo, Frank; Khadilkar, Mihir; Changlani, Hitesh; Nightingale, M. P.; Umrigar, C. J.

2012-02-01

In the recently proposed full configuration interaction quantum Monte Carlo (FCIQMC) [1,2], the ground state is projected out stochastically, using a population of walkers each of which represents a basis state in the Hilbert space spanned by Slater determinants. The infamous fermion sign problem manifests itself in the fact that walkers of either sign can be spawned on a given determinant. We propose an improvement on this method in the form of a hybrid stochastic/deterministic technique, which we expect will improve the efficiency of the algorithm by ameliorating the sign problem. We test the method on atoms and molecules, e.g., carbon, carbon dimer, N2 molecule, and stretched N2. [4pt] [1] Fermion Monte Carlo without fixed nodes: a Game of Life, death and annihilation in Slater Determinant space. George Booth, Alex Thom, Ali Alavi. J Chem Phys 131, 050106, (2009).[0pt] [2] Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo. Deidre Cleland, George Booth, and Ali Alavi. J Chem Phys 132, 041103 (2010).

Stochastic, real-space, imaginary-time evaluation of third-order Feynman-Goldstone diagrams

NASA Astrophysics Data System (ADS)

Willow, Soohaeng Yoo; Hirata, So

2014-01-01

A new, alternative set of interpretation rules of Feynman-Goldstone diagrams for many-body perturbation theory is proposed, which translates diagrams into algebraic expressions suitable for direct Monte Carlo integrations. A vertex of a diagram is associated with a Coulomb interaction (rather than a two-electron integral) and an edge with the trace of a Green's function in real space and imaginary time. With these, 12 diagrams of third-order many-body perturbation (MP3) theory are converted into 20-dimensional integrals, which are then evaluated by a Monte Carlo method. It uses redundant walkers for convergence acceleration and a weight function for importance sampling in conjunction with the Metropolis algorithm. The resulting Monte Carlo MP3 method has low-rank polynomial size dependence of the operation cost, a negligible memory cost, and a naturally parallel computational kernel, while reproducing the correct correlation energies of small molecules within a few mEh after 106 Monte Carlo steps.

The Linked Neighbour List (LNL) method for fast off-lattice Monte Carlo simulations of fluids

NASA Astrophysics Data System (ADS)

Mazzeo, M. D.; Ricci, M.; Zannoni, C.

2010-03-01

We present a new algorithm, called linked neighbour list (LNL), useful to substantially speed up off-lattice Monte Carlo simulations of fluids by avoiding the computation of the molecular energy before every attempted move. We introduce a few variants of the LNL method targeted to minimise memory footprint or augment memory coherence and cache utilisation. Additionally, we present a few algorithms which drastically accelerate neighbour finding. We test our methods on the simulation of a dense off-lattice Gay-Berne fluid subjected to periodic boundary conditions observing a speedup factor of about 2.5 with respect to a well-coded implementation based on a conventional link-cell. We provide several implementation details of the different key data structures and algorithms used in this work.

Multilevel Monte Carlo and improved timestepping methods in atmospheric dispersion modelling

NASA Astrophysics Data System (ADS)

Katsiolides, Grigoris; Müller, Eike H.; Scheichl, Robert; Shardlow, Tony; Giles, Michael B.; Thomson, David J.

2018-02-01

A common way to simulate the transport and spread of pollutants in the atmosphere is via stochastic Lagrangian dispersion models. Mathematically, these models describe turbulent transport processes with stochastic differential equations (SDEs). The computational bottleneck is the Monte Carlo algorithm, which simulates the motion of a large number of model particles in a turbulent velocity field; for each particle, a trajectory is calculated with a numerical timestepping method. Choosing an efficient numerical method is particularly important in operational emergency-response applications, such as tracking radioactive clouds from nuclear accidents or predicting the impact of volcanic ash clouds on international aviation, where accurate and timely predictions are essential. In this paper, we investigate the application of the Multilevel Monte Carlo (MLMC) method to simulate the propagation of particles in a representative one-dimensional dispersion scenario in the atmospheric boundary layer. MLMC can be shown to result in asymptotically superior computational complexity and reduced computational cost when compared to the Standard Monte Carlo (StMC) method, which is currently used in atmospheric dispersion modelling. To reduce the absolute cost of the method also in the non-asymptotic regime, it is equally important to choose the best possible numerical timestepping method on each level. To investigate this, we also compare the standard symplectic Euler method, which is used in many operational models, with two improved timestepping algorithms based on SDE splitting methods.

Parallel Algorithms for Monte Carlo Particle Transport Simulation on Exascale Computing Architectures

NASA Astrophysics Data System (ADS)

Romano, Paul Kollath

Monte Carlo particle transport methods are being considered as a viable option for high-fidelity simulation of nuclear reactors. While Monte Carlo methods offer several potential advantages over deterministic methods, there are a number of algorithmic shortcomings that would prevent their immediate adoption for full-core analyses. In this thesis, algorithms are proposed both to ameliorate the degradation in parallel efficiency typically observed for large numbers of processors and to offer a means of decomposing large tally data that will be needed for reactor analysis. A nearest-neighbor fission bank algorithm was proposed and subsequently implemented in the OpenMC Monte Carlo code. A theoretical analysis of the communication pattern shows that the expected cost is O( N ) whereas traditional fission bank algorithms are O(N) at best. The algorithm was tested on two supercomputers, the Intrepid Blue Gene/P and the Titan Cray XK7, and demonstrated nearly linear parallel scaling up to 163,840 processor cores on a full-core benchmark problem. An algorithm for reducing network communication arising from tally reduction was analyzed and implemented in OpenMC. The proposed algorithm groups only particle histories on a single processor into batches for tally purposes---in doing so it prevents all network communication for tallies until the very end of the simulation. The algorithm was tested, again on a full-core benchmark, and shown to reduce network communication substantially. A model was developed to predict the impact of load imbalances on the performance of domain decomposed simulations. The analysis demonstrated that load imbalances in domain decomposed simulations arise from two distinct phenomena: non-uniform particle densities and non-uniform spatial leakage. The dominant performance penalty for domain decomposition was shown to come from these physical effects rather than insufficient network bandwidth or high latency. The model predictions were verified with measured data from simulations in OpenMC on a full-core benchmark problem. Finally, a novel algorithm for decomposing large tally data was proposed, analyzed, and implemented/tested in OpenMC. The algorithm relies on disjoint sets of compute processes and tally servers. The analysis showed that for a range of parameters relevant to LWR analysis, the tally server algorithm should perform with minimal overhead. Tests were performed on Intrepid and Titan and demonstrated that the algorithm did indeed perform well over a wide range of parameters. (Copies available exclusively from MIT Libraries, libraries.mit.edu/docs - docs mit.edu)

Estimating rare events in biochemical systems using conditional sampling.

PubMed

Sundar, V S

2017-01-28

The paper focuses on development of variance reduction strategies to estimate rare events in biochemical systems. Obtaining this probability using brute force Monte Carlo simulations in conjunction with the stochastic simulation algorithm (Gillespie's method) is computationally prohibitive. To circumvent this, important sampling tools such as the weighted stochastic simulation algorithm and the doubly weighted stochastic simulation algorithm have been proposed. However, these strategies require an additional step of determining the important region to sample from, which is not straightforward for most of the problems. In this paper, we apply the subset simulation method, developed as a variance reduction tool in the context of structural engineering, to the problem of rare event estimation in biochemical systems. The main idea is that the rare event probability is expressed as a product of more frequent conditional probabilities. These conditional probabilities are estimated with high accuracy using Monte Carlo simulations, specifically the Markov chain Monte Carlo method with the modified Metropolis-Hastings algorithm. Generating sample realizations of the state vector using the stochastic simulation algorithm is viewed as mapping the discrete-state continuous-time random process to the standard normal random variable vector. This viewpoint opens up the possibility of applying more sophisticated and efficient sampling schemes developed elsewhere to problems in stochastic chemical kinetics. The results obtained using the subset simulation method are compared with existing variance reduction strategies for a few benchmark problems, and a satisfactory improvement in computational time is demonstrated.

Parallel Monte Carlo Search for Hough Transform

NASA Astrophysics Data System (ADS)

Lopes, Raul H. C.; Franqueira, Virginia N. L.; Reid, Ivan D.; Hobson, Peter R.

2017-10-01

We investigate the problem of line detection in digital image processing and in special how state of the art algorithms behave in the presence of noise and whether CPU efficiency can be improved by the combination of a Monte Carlo Tree Search, hierarchical space decomposition, and parallel computing. The starting point of the investigation is the method introduced in 1962 by Paul Hough for detecting lines in binary images. Extended in the 1970s to the detection of space forms, what came to be known as Hough Transform (HT) has been proposed, for example, in the context of track fitting in the LHC ATLAS and CMS projects. The Hough Transform transfers the problem of line detection, for example, into one of optimization of the peak in a vote counting process for cells which contain the possible points of candidate lines. The detection algorithm can be computationally expensive both in the demands made upon the processor and on memory. Additionally, it can have a reduced effectiveness in detection in the presence of noise. Our first contribution consists in an evaluation of the use of a variation of the Radon Transform as a form of improving theeffectiveness of line detection in the presence of noise. Then, parallel algorithms for variations of the Hough Transform and the Radon Transform for line detection are introduced. An algorithm for Parallel Monte Carlo Search applied to line detection is also introduced. Their algorithmic complexities are discussed. Finally, implementations on multi-GPU and multicore architectures are discussed.

A Comparison of Experimental EPMA Data and Monte Carlo Simulations

NASA Technical Reports Server (NTRS)

Carpenter, P. K.

2004-01-01

Monte Carlo (MC) modeling shows excellent prospects for simulating electron scattering and x-ray emission from complex geometries, and can be compared to experimental measurements using electron-probe microanalysis (EPMA) and phi(rho z) correction algorithms. Experimental EPMA measurements made on NIST SRM 481 (AgAu) and 482 (CuAu) alloys, at a range of accelerating potential and instrument take-off angles, represent a formal microanalysis data set that has been used to develop phi(rho z) correction algorithms. The accuracy of MC calculations obtained using the NIST, WinCasino, WinXray, and Penelope MC packages will be evaluated relative to these experimental data. There is additional information contained in the extended abstract.

Rényi information flow in the Ising model with single-spin dynamics.

PubMed

Deng, Zehui; Wu, Jinshan; Guo, Wenan

2014-12-01

The n-index Rényi mutual information and transfer entropies for the two-dimensional kinetic Ising model with arbitrary single-spin dynamics in the thermodynamic limit are derived as functions of ensemble averages of observables and spin-flip probabilities. Cluster Monte Carlo algorithms with different dynamics from the single-spin dynamics are thus applicable to estimate the transfer entropies. By means of Monte Carlo simulations with the Wolff algorithm, we calculate the information flows in the Ising model with the Metropolis dynamics and the Glauber dynamics, respectively. We find that not only the global Rényi transfer entropy, but also the pairwise Rényi transfer entropy, peaks in the disorder phase.

A hybrid multi-objective imperialist competitive algorithm and Monte Carlo method for robust safety design of a rail vehicle

NASA Astrophysics Data System (ADS)

Nejlaoui, Mohamed; Houidi, Ajmi; Affi, Zouhaier; Romdhane, Lotfi

2017-10-01

This paper deals with the robust safety design optimization of a rail vehicle system moving in short radius curved tracks. A combined multi-objective imperialist competitive algorithm and Monte Carlo method is developed and used for the robust multi-objective optimization of the rail vehicle system. This robust optimization of rail vehicle safety considers simultaneously the derailment angle and its standard deviation where the design parameters uncertainties are considered. The obtained results showed that the robust design reduces significantly the sensitivity of the rail vehicle safety to the design parameters uncertainties compared to the determinist one and to the literature results.

Tracking control of concentration profiles in a fed-batch bioreactor using a linear algebra methodology.

PubMed

Rómoli, Santiago; Serrano, Mario Emanuel; Ortiz, Oscar Alberto; Vega, Jorge Rubén; Eduardo Scaglia, Gustavo Juan

2015-07-01

Based on a linear algebra approach, this paper aims at developing a novel control law able to track reference profiles that were previously-determined in the literature. A main advantage of the proposed strategy is that the control actions are obtained by solving a system of linear equations. The optimal controller parameters are selected through Monte Carlo Randomized Algorithm in order to minimize a proposed cost index. The controller performance is evaluated through several tests, and compared with other controller reported in the literature. Finally, a Monte Carlo Randomized Algorithm is conducted to assess the performance of the proposed controller. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Improved Monte Carlo Scheme for Efficient Particle Transfer in Heterogeneous Systems in the Grand Canonical Ensemble: Application to Vapor-Liquid Nucleation.

PubMed

Loeffler, Troy D; Sepehri, Aliasghar; Chen, Bin

2015-09-08

Reformulation of existing Monte Carlo algorithms used in the study of grand canonical systems has yielded massive improvements in efficiency. Here we present an energy biasing scheme designed to address targeting issues encountered in particle swap moves using sophisticated algorithms such as the Aggregation-Volume-Bias and Unbonding-Bonding methods. Specifically, this energy biasing scheme allows a particle to be inserted to (or removed from) a region that is more acceptable. As a result, this new method showed a several-fold increase in insertion/removal efficiency in addition to an accelerated rate of convergence for the thermodynamic properties of the system.

Delving Into Dissipative Quantum Dynamics: From Approximate to Numerically Exact Approaches

NASA Astrophysics Data System (ADS)

Chen, Hsing-Ta

In this thesis, I explore dissipative quantum dynamics of several prototypical model systems via various approaches, ranging from approximate to numerically exact schemes. In particular, in the realm of the approximate I explore the accuracy of Pade-resummed master equations and the fewest switches surface hopping (FSSH) algorithm for the spin-boson model, and non-crossing approximations (NCA) for the Anderson-Holstein model. Next, I develop new and exact Monte Carlo approaches and test them on the spin-boson model. I propose well-defined criteria for assessing the accuracy of Pade-resummed quantum master equations, which correctly demarcate the regions of parameter space where the Pade approximation is reliable. I continue the investigation of spin-boson dynamics by benchmark comparisons of the semiclassical FSSH algorithm to exact dynamics over a wide range of parameters. Despite small deviations from golden-rule scaling in the Marcus regime, standard surface hopping algorithm is found to be accurate over a large portion of parameter space. The inclusion of decoherence corrections via the augmented FSSH algorithm improves the accuracy of dynamical behavior compared to exact simulations, but the effects are generally not dramatic for the cases I consider. Next, I introduce new methods for numerically exact real-time simulation based on real-time diagrammatic Quantum Monte Carlo (dQMC) and the inchworm algorithm. These methods optimally recycle Monte Carlo information from earlier times to greatly suppress the dynamical sign problem. In the context of the spin-boson model, I formulate the inchworm expansion in two distinct ways: the first with respect to an expansion in the system-bath coupling and the second as an expansion in the diabatic coupling. In addition, a cumulant version of the inchworm Monte Carlo method is motivated by the latter expansion, which allows for further suppression of the growth of the sign error. I provide a comprehensive comparison of the performance of the inchworm Monte Carlo algorithms to other exact methodologies as well as a discussion of the relative advantages and disadvantages of each. Finally, I investigate the dynamical interplay between the electron-electron interaction and the electron-phonon coupling within the Anderson-Holstein model via two complementary NCAs: the first is constructed around the weak-coupling limit and the second around the polaron limit. The influence of phonons on spectral and transport properties is explored in equilibrium, for non-equilibrium steady state and for transient dynamics after a quench. I find the two NCAs disagree in nontrivial ways, indicating that more reliable approaches to the problem are needed. The complementary frameworks used here pave the way for numerically exact methods based on inchworm dQMC algorithms capable of treating open systems simultaneously coupled to multiple fermionic and bosonic baths.

[Benchmark experiment to verify radiation transport calculations for dosimetry in radiation therapy].

PubMed

Renner, Franziska

2016-09-01

Monte Carlo simulations are regarded as the most accurate method of solving complex problems in the field of dosimetry and radiation transport. In (external) radiation therapy they are increasingly used for the calculation of dose distributions during treatment planning. In comparison to other algorithms for the calculation of dose distributions, Monte Carlo methods have the capability of improving the accuracy of dose calculations - especially under complex circumstances (e.g. consideration of inhomogeneities). However, there is a lack of knowledge of how accurate the results of Monte Carlo calculations are on an absolute basis. A practical verification of the calculations can be performed by direct comparison with the results of a benchmark experiment. This work presents such a benchmark experiment and compares its results (with detailed consideration of measurement uncertainty) with the results of Monte Carlo calculations using the well-established Monte Carlo code EGSnrc. The experiment was designed to have parallels to external beam radiation therapy with respect to the type and energy of the radiation, the materials used and the kind of dose measurement. Because the properties of the beam have to be well known in order to compare the results of the experiment and the simulation on an absolute basis, the benchmark experiment was performed using the research electron accelerator of the Physikalisch-Technische Bundesanstalt (PTB), whose beam was accurately characterized in advance. The benchmark experiment and the corresponding Monte Carlo simulations were carried out for two different types of ionization chambers and the results were compared. Considering the uncertainty, which is about 0.7 % for the experimental values and about 1.0 % for the Monte Carlo simulation, the results of the simulation and the experiment coincide. Copyright © 2015. Published by Elsevier GmbH.

Estimating statistical uncertainty of Monte Carlo efficiency-gain in the context of a correlated sampling Monte Carlo code for brachytherapy treatment planning with non-normal dose distribution.

PubMed

Mukhopadhyay, Nitai D; Sampson, Andrew J; Deniz, Daniel; Alm Carlsson, Gudrun; Williamson, Jeffrey; Malusek, Alexandr

2012-01-01

Correlated sampling Monte Carlo methods can shorten computing times in brachytherapy treatment planning. Monte Carlo efficiency is typically estimated via efficiency gain, defined as the reduction in computing time by correlated sampling relative to conventional Monte Carlo methods when equal statistical uncertainties have been achieved. The determination of the efficiency gain uncertainty arising from random effects, however, is not a straightforward task specially when the error distribution is non-normal. The purpose of this study is to evaluate the applicability of the F distribution and standardized uncertainty propagation methods (widely used in metrology to estimate uncertainty of physical measurements) for predicting confidence intervals about efficiency gain estimates derived from single Monte Carlo runs using fixed-collision correlated sampling in a simplified brachytherapy geometry. A bootstrap based algorithm was used to simulate the probability distribution of the efficiency gain estimates and the shortest 95% confidence interval was estimated from this distribution. It was found that the corresponding relative uncertainty was as large as 37% for this particular problem. The uncertainty propagation framework predicted confidence intervals reasonably well; however its main disadvantage was that uncertainties of input quantities had to be calculated in a separate run via a Monte Carlo method. The F distribution noticeably underestimated the confidence interval. These discrepancies were influenced by several photons with large statistical weights which made extremely large contributions to the scored absorbed dose difference. The mechanism of acquiring high statistical weights in the fixed-collision correlated sampling method was explained and a mitigation strategy was proposed. Copyright © 2011 Elsevier Ltd. All rights reserved.

Discrete range clustering using Monte Carlo methods

NASA Technical Reports Server (NTRS)

Chatterji, G. B.; Sridhar, B.

1993-01-01

For automatic obstacle avoidance guidance during rotorcraft low altitude flight, a reliable model of the nearby environment is needed. Such a model may be constructed by applying surface fitting techniques to the dense range map obtained by active sensing using radars. However, for covertness, passive sensing techniques using electro-optic sensors are desirable. As opposed to the dense range map obtained via active sensing, passive sensing algorithms produce reliable range at sparse locations, and therefore, surface fitting techniques to fill the gaps in the range measurement are not directly applicable. Both for automatic guidance and as a display for aiding the pilot, these discrete ranges need to be grouped into sets which correspond to objects in the nearby environment. The focus of this paper is on using Monte Carlo methods for clustering range points into meaningful groups. One of the aims of the paper is to explore whether simulated annealing methods offer significant advantage over the basic Monte Carlo method for this class of problems. We compare three different approaches and present application results of these algorithms to a laboratory image sequence and a helicopter flight sequence.

Hamiltonian Monte Carlo acceleration using surrogate functions with random bases.

PubMed

Zhang, Cheng; Shahbaba, Babak; Zhao, Hongkai

2017-11-01

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an efficient and scalable computational technique for a state-of-the-art Markov chain Monte Carlo methods, namely, Hamiltonian Monte Carlo. The key idea is to explore and exploit the structure and regularity in parameter space for the underlying probabilistic model to construct an effective approximation of its geometric properties. To this end, we build a surrogate function to approximate the target distribution using properly chosen random bases and an efficient optimization process. The resulting method provides a flexible, scalable, and efficient sampling algorithm, which converges to the correct target distribution. We show that by choosing the basis functions and optimization process differently, our method can be related to other approaches for the construction of surrogate functions such as generalized additive models or Gaussian process models. Experiments based on simulated and real data show that our approach leads to substantially more efficient sampling algorithms compared to existing state-of-the-art methods.

Estimating source parameters from deformation data, with an application to the March 1997 earthquake swarm off the Izu Peninsula, Japan

NASA Astrophysics Data System (ADS)

Cervelli, P.; Murray, M. H.; Segall, P.; Aoki, Y.; Kato, T.

2001-06-01

We have applied two Monte Carlo optimization techniques, simulated annealing and random cost, to the inversion of deformation data for fault and magma chamber geometry. These techniques involve an element of randomness that permits them to escape local minima and ultimately converge to the global minimum of misfit space. We have tested the Monte Carlo algorithms on two synthetic data sets. We have also compared them to one another in terms of their efficiency and reliability. We have applied the bootstrap method to estimate confidence intervals for the source parameters, including the correlations inherent in the data. Additionally, we present methods that use the information from the bootstrapping procedure to visualize the correlations between the different model parameters. We have applied these techniques to GPS, tilt, and leveling data from the March 1997 earthquake swarm off of the Izu Peninsula, Japan. Using the two Monte Carlo algorithms, we have inferred two sources, a dike and a fault, that fit the deformation data and the patterns of seismicity and that are consistent with the regional stress field.

Probabilistic analysis algorithm for UA slope software program.

DOT National Transportation Integrated Search

2013-12-01

A reliability-based computational algorithm for using a single row and equally spaced drilled shafts to : stabilize an unstable slope has been developed in this research. The Monte-Carlo simulation (MCS) : technique was used in the previously develop...

Coupled particle-in-cell and Monte Carlo transport modeling of intense radiographic sources

NASA Astrophysics Data System (ADS)

Rose, D. V.; Welch, D. R.; Oliver, B. V.; Clark, R. E.; Johnson, D. L.; Maenchen, J. E.; Menge, P. R.; Olson, C. L.; Rovang, D. C.

2002-03-01

Dose-rate calculations for intense electron-beam diodes using particle-in-cell (PIC) simulations along with Monte Carlo electron/photon transport calculations are presented. The electromagnetic PIC simulations are used to model the dynamic operation of the rod-pinch and immersed-B diodes. These simulations include algorithms for tracking electron scattering and energy loss in dense materials. The positions and momenta of photons created in these materials are recorded and separate Monte Carlo calculations are used to transport the photons to determine the dose in far-field detectors. These combined calculations are used to determine radiographer equations (dose scaling as a function of diode current and voltage) that are compared directly with measured dose rates obtained on the SABRE generator at Sandia National Laboratories.

Effective Online Bayesian Phylogenetics via Sequential Monte Carlo with Guided Proposals

PubMed Central

Fourment, Mathieu; Claywell, Brian C; Dinh, Vu; McCoy, Connor; Matsen IV, Frederick A; Darling, Aaron E

2018-01-01

Abstract Modern infectious disease outbreak surveillance produces continuous streams of sequence data which require phylogenetic analysis as data arrives. Current software packages for Bayesian phylogenetic inference are unable to quickly incorporate new sequences as they become available, making them less useful for dynamically unfolding evolutionary stories. This limitation can be addressed by applying a class of Bayesian statistical inference algorithms called sequential Monte Carlo (SMC) to conduct online inference, wherein new data can be continuously incorporated to update the estimate of the posterior probability distribution. In this article, we describe and evaluate several different online phylogenetic sequential Monte Carlo (OPSMC) algorithms. We show that proposing new phylogenies with a density similar to the Bayesian prior suffers from poor performance, and we develop “guided” proposals that better match the proposal density to the posterior. Furthermore, we show that the simplest guided proposals can exhibit pathological behavior in some situations, leading to poor results, and that the situation can be resolved by heating the proposal density. The results demonstrate that relative to the widely used MCMC-based algorithm implemented in MrBayes, the total time required to compute a series of phylogenetic posteriors as sequences arrive can be significantly reduced by the use of OPSMC, without incurring a significant loss in accuracy. PMID:29186587

Harnessing graphical structure in Markov chain Monte Carlo learning

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stolorz, P.E.; Chew P.C.

1996-12-31

The Monte Carlo method is recognized as a useful tool in learning and probabilistic inference methods common to many datamining problems. Generalized Hidden Markov Models and Bayes nets are especially popular applications. However, the presence of multiple modes in many relevant integrands and summands often renders the method slow and cumbersome. Recent mean field alternatives designed to speed things up have been inspired by experience gleaned from physics. The current work adopts an approach very similar to this in spirit, but focusses instead upon dynamic programming notions as a basis for producing systematic Monte Carlo improvements. The idea is tomore » approximate a given model by a dynamic programming-style decomposition, which then forms a scaffold upon which to build successively more accurate Monte Carlo approximations. Dynamic programming ideas alone fail to account for non-local structure, while standard Monte Carlo methods essentially ignore all structure. However, suitably-crafted hybrids can successfully exploit the strengths of each method, resulting in algorithms that combine speed with accuracy. The approach relies on the presence of significant {open_quotes}local{close_quotes} information in the problem at hand. This turns out to be a plausible assumption for many important applications. Example calculations are presented, and the overall strengths and weaknesses of the approach are discussed.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jakeman, John D.; Narayan, Akil; Zhou, Tao

We propose an algorithm for recovering sparse orthogonal polynomial expansions via collocation. A standard sampling approach for recovering sparse polynomials uses Monte Carlo sampling, from the density of orthogonality, which results in poor function recovery when the polynomial degree is high. Our proposed approach aims to mitigate this limitation by sampling with respect to the weighted equilibrium measure of the parametric domain and subsequently solves a preconditionedmore » $$\\ell^1$$-minimization problem, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function. Our algorithm can be applied to a wide class of orthogonal polynomial families on bounded and unbounded domains, including all classical families. We present theoretical analysis to motivate the algorithm and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. In conclusion, numerical examples are also provided to demonstrate that our proposed algorithm leads to comparable or improved accuracy even when compared with Legendre- and Hermite-specific algorithms.« less

Hybrid-optimization strategy for the communication of large-scale Kinetic Monte Carlo simulation

NASA Astrophysics Data System (ADS)

Wu, Baodong; Li, Shigang; Zhang, Yunquan; Nie, Ningming

2017-02-01

The parallel Kinetic Monte Carlo (KMC) algorithm based on domain decomposition has been widely used in large-scale physical simulations. However, the communication overhead of the parallel KMC algorithm is critical, and severely degrades the overall performance and scalability. In this paper, we present a hybrid optimization strategy to reduce the communication overhead for the parallel KMC simulations. We first propose a communication aggregation algorithm to reduce the total number of messages and eliminate the communication redundancy. Then, we utilize the shared memory to reduce the memory copy overhead of the intra-node communication. Finally, we optimize the communication scheduling using the neighborhood collective operations. We demonstrate the scalability and high performance of our hybrid optimization strategy by both theoretical and experimental analysis. Results show that the optimized KMC algorithm exhibits better performance and scalability than the well-known open-source library-SPPARKS. On 32-node Xeon E5-2680 cluster (total 640 cores), the optimized algorithm reduces the communication time by 24.8% compared with SPPARKS.

A Generalized Sampling and Preconditioning Scheme for Sparse Approximation of Polynomial Chaos Expansions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jakeman, John D.; Narayan, Akil; Zhou, Tao

We propose an algorithm for recovering sparse orthogonal polynomial expansions via collocation. A standard sampling approach for recovering sparse polynomials uses Monte Carlo sampling, from the density of orthogonality, which results in poor function recovery when the polynomial degree is high. Our proposed approach aims to mitigate this limitation by sampling with respect to the weighted equilibrium measure of the parametric domain and subsequently solves a preconditionedmore » $$\\ell^1$$-minimization problem, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function. Our algorithm can be applied to a wide class of orthogonal polynomial families on bounded and unbounded domains, including all classical families. We present theoretical analysis to motivate the algorithm and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. In conclusion, numerical examples are also provided to demonstrate that our proposed algorithm leads to comparable or improved accuracy even when compared with Legendre- and Hermite-specific algorithms.« less

A Generalized Sampling and Preconditioning Scheme for Sparse Approximation of Polynomial Chaos Expansions

DOE PAGES

Jakeman, John D.; Narayan, Akil; Zhou, Tao

2017-06-22

We propose an algorithm for recovering sparse orthogonal polynomial expansions via collocation. A standard sampling approach for recovering sparse polynomials uses Monte Carlo sampling, from the density of orthogonality, which results in poor function recovery when the polynomial degree is high. Our proposed approach aims to mitigate this limitation by sampling with respect to the weighted equilibrium measure of the parametric domain and subsequently solves a preconditionedmore » $$\\ell^1$$-minimization problem, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function. Our algorithm can be applied to a wide class of orthogonal polynomial families on bounded and unbounded domains, including all classical families. We present theoretical analysis to motivate the algorithm and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. In conclusion, numerical examples are also provided to demonstrate that our proposed algorithm leads to comparable or improved accuracy even when compared with Legendre- and Hermite-specific algorithms.« less

Water Oxidation Catalysis for NiOOH by a Metropolis Monte Carlo Algorithm.

PubMed

Hareli, Chen; Caspary Toroker, Maytal

2018-05-08

Understanding catalytic mechanisms is important for discovering better catalysts, particularly for water splitting reactions that are of great interest to the renewable energy field. One of the best performing catalysts for water oxidation is nickel oxyhydroxide (NiOOH). However, only one mechanism has been adopted so far for modeling catalysis of the active plane: β-NiOOH(01̅5). In order to understand how a second reaction mechanism affects catalysis, we perform Density Functional Theory + U (DFT+U) calculations of a second mechanism for water oxidation reaction of NiOOH. Then, we use a Metropolis Monte Carlo algorithm to calculate how many catalytic cycles are completed when two reaction mechanisms are competing. We find that within the Metropolis algorithm, the second mechanism has a higher overpotential and is therefore not active even for large applied biases.

Improved cache performance in Monte Carlo transport calculations using energy banding

NASA Astrophysics Data System (ADS)

Siegel, A.; Smith, K.; Felker, K.; Romano, P.; Forget, B.; Beckman, P.

2014-04-01

We present an energy banding algorithm for Monte Carlo (MC) neutral particle transport simulations which depend on large cross section lookup tables. In MC codes, read-only cross section data tables are accessed frequently, exhibit poor locality, and are typically too much large to fit in fast memory. Thus, performance is often limited by long latencies to RAM, or by off-node communication latencies when the data footprint is very large and must be decomposed on a distributed memory machine. The proposed energy banding algorithm allows maximal temporal reuse of data in band sizes that can flexibly accommodate different architectural features. The energy banding algorithm is general and has a number of benefits compared to the traditional approach. In the present analysis we explore its potential to achieve improvements in time-to-solution on modern cache-based architectures.

The kinetic activation-relaxation technique: an off-lattice, self-learning kinetic Monte Carlo algorithm with on-the-fly event search

NASA Astrophysics Data System (ADS)

Mousseau, Nomand

2012-02-01

While kinetic Monte Carlo algorithm has been proposed almost 40 years ago, its application in materials science has been mostly limited to lattice-based motion due to the difficulties associated with identifying new events and building usable catalogs when atoms moved into off-lattice position. Here, I present the kinetic activation-relaxation technique (kinetic ART) is an off-lattice, self-learning kinetic Monte Carlo algorithm with on-the-fly event search [1]. It combines ART nouveau [2], a very efficient unbiased open-ended activated method for finding transition states, with a topological classification [3] that allows a discrete cataloguing of local environments in complex systems, including disordered materials. In kinetic ART, local topologies are first identified for all atoms in a system. ART nouveau event searches are then launched for new topologies, building an extensive catalog of barriers and events. Next, all low energy events are fully reconstructed and relaxed, allowing to take complete account of elastic effects in the system's kinetics. Using standard kinetic Monte Carlo, the clock is brought forward and an event is then selected and applied before a new search for topologies is launched. In addition to presenting the various elements of the algorithm, I will discuss three recent applications to ion-bombarded silicon, defect diffusion in Fe and structural relaxation in amorphous silicon.[4pt] This work was done in collaboration with Laurent Karim B'eland, Peter Brommer, Fedwa El-Mellouhi, Jean-Francois Joly and Laurent Lewis.[4pt] [1] F. El-Mellouhi, N. Mousseau and L.J. Lewis, Phys. Rev. B. 78, 153202 (2008); L.K. B'eland et al., Phys. Rev. E 84, 046704 (2011).[2] G.T. Barkema and N. Mousseau, Phys. Rev. Lett. 77, 4358 (1996); E. Machado-Charry et al., J. Chem Phys. 135, 034102, (2011).[3] B.D. McKay, Congressus Numerantium 30, 45 (1981).

Bayesian Estimation of Multidimensional Item Response Models. A Comparison of Analytic and Simulation Algorithms

ERIC Educational Resources Information Center

Martin-Fernandez, Manuel; Revuelta, Javier

2017-01-01

This study compares the performance of two estimation algorithms of new usage, the Metropolis-Hastings Robins-Monro (MHRM) and the Hamiltonian MCMC (HMC), with two consolidated algorithms in the psychometric literature, the marginal likelihood via EM algorithm (MML-EM) and the Markov chain Monte Carlo (MCMC), in the estimation of multidimensional…

Kinetic Activation-Relaxation Technique and Self-Evolving Atomistic Kinetic Monte Carlo: Comparison of on-the-fly kinetic Monte Carlo algorithms

DOE PAGES

Beland, Laurent Karim; Osetskiy, Yury N.; Stoller, Roger E.; ...

2015-02-07

Here, we present a comparison of the Kinetic Activation–Relaxation Technique (k-ART) and the Self-Evolving Atomistic Kinetic Monte Carlo (SEAKMC), two off-lattice, on-the-fly Kinetic Monte Carlo (KMC) techniques that were recently used to solve several materials science problems. We show that if the initial displacements are localized the dimer method and the Activation–Relaxation Technique nouveau provide similar performance. We also show that k-ART and SEAKMC, although based on different approximations, are in agreement with each other, as demonstrated by the examples of 50 vacancies in a 1950-atom Fe box and of interstitial loops in 16,000-atom boxes. Generally speaking, k-ART’s treatment ofmore » geometry and flickers is more flexible, e.g. it can handle amorphous systems, and rigorous than SEAKMC’s, while the later’s concept of active volumes permits a significant speedup of simulations for the systems under consideration and therefore allows investigations of processes requiring large systems that are not accessible if not localizing calculations.« less

A novel Kinetic Monte Carlo algorithm for Non-Equilibrium Simulations

NASA Astrophysics Data System (ADS)

Jha, Prateek; Kuzovkov, Vladimir; Grzybowski, Bartosz; Olvera de La Cruz, Monica

2012-02-01

We have developed an off-lattice kinetic Monte Carlo simulation scheme for reaction-diffusion problems in soft matter systems. The definition of transition probabilities in the Monte Carlo scheme are taken identical to the transition rates in a renormalized master equation of the diffusion process and match that of the Glauber dynamics of Ising model. Our scheme provides several advantages over the Brownian dynamics technique for non-equilibrium simulations. Since particle displacements are accepted/rejected in a Monte Carlo fashion as opposed to moving particles following a stochastic equation of motion, nonphysical movements (e.g., violation of a hard core assumption) are not possible (these moves have zero acceptance). Further, the absence of a stochastic ``noise'' term resolves the computational difficulties associated with generating statistically independent trajectories with definitive mean properties. Finally, since the timestep is independent of the magnitude of the interaction forces, much longer time-steps can be employed than Brownian dynamics. We discuss the applications of this scheme for dynamic self-assembly of photo-switchable nanoparticles and dynamical problems in polymeric systems.

Performance and accuracy of criticality calculations performed using WARP – A framework for continuous energy Monte Carlo neutron transport in general 3D geometries on GPUs

DOE PAGES

Bergmann, Ryan M.; Rowland, Kelly L.; Radnović, Nikola; ...

2017-05-01

In this companion paper to "Algorithmic Choices in WARP - A Framework for Continuous Energy Monte Carlo Neutron Transport in General 3D Geometries on GPUs" (doi:10.1016/j.anucene.2014.10.039), the WARP Monte Carlo neutron transport framework for graphics processing units (GPUs) is benchmarked against production-level central processing unit (CPU) Monte Carlo neutron transport codes for both performance and accuracy. We compare neutron flux spectra, multiplication factors, runtimes, speedup factors, and costs of various GPU and CPU platforms running either WARP, Serpent 2.1.24, or MCNP 6.1. WARP compares well with the results of the production-level codes, and it is shown that on the newestmore » hardware considered, GPU platforms running WARP are between 0.8 to 7.6 times as fast as CPU platforms running production codes. Also, the GPU platforms running WARP were between 15% and 50% as expensive to purchase and between 80% to 90% as expensive to operate as equivalent CPU platforms performing at an equal simulation rate.« less

A Modified Monte Carlo Method for Carrier Transport in Germanium, Free of Isotropic Rates

NASA Astrophysics Data System (ADS)

Sundqvist, Kyle

2010-03-01

We present a new method for carrier transport simulation, relevant for high-purity germanium < 100 > at a temperature of 40 mK. In this system, the scattering of electrons and holes is dominated by spontaneous phonon emission. Free carriers are always out of equilibrium with the lattice. We must also properly account for directional effects due to band structure, but there are many cautions in the literature about treating germanium in particular. These objections arise because the germanium electron system is anisotropic to an extreme degree, while standard Monte Carlo algorithms maintain a reliance on isotropic, integrated rates. We re-examine Fermi's Golden Rule to produce a Monte Carlo method free of isotropic rates. Traditional Monte Carlo codes implement particle scattering based on an isotropically averaged rate, followed by a separate selection of the particle's final state via a momentum-dependent probability. In our method, the kernel of Fermi's Golden Rule produces analytical, bivariate rates which allow for the simultaneous choice of scatter and final state selection. Energy and momentum are automatically conserved. We compare our results to experimental data.

Performance and accuracy of criticality calculations performed using WARP – A framework for continuous energy Monte Carlo neutron transport in general 3D geometries on GPUs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bergmann, Ryan M.; Rowland, Kelly L.; Radnović, Nikola

In this companion paper to "Algorithmic Choices in WARP - A Framework for Continuous Energy Monte Carlo Neutron Transport in General 3D Geometries on GPUs" (doi:10.1016/j.anucene.2014.10.039), the WARP Monte Carlo neutron transport framework for graphics processing units (GPUs) is benchmarked against production-level central processing unit (CPU) Monte Carlo neutron transport codes for both performance and accuracy. We compare neutron flux spectra, multiplication factors, runtimes, speedup factors, and costs of various GPU and CPU platforms running either WARP, Serpent 2.1.24, or MCNP 6.1. WARP compares well with the results of the production-level codes, and it is shown that on the newestmore » hardware considered, GPU platforms running WARP are between 0.8 to 7.6 times as fast as CPU platforms running production codes. Also, the GPU platforms running WARP were between 15% and 50% as expensive to purchase and between 80% to 90% as expensive to operate as equivalent CPU platforms performing at an equal simulation rate.« less

Performance of quantum Monte Carlo for calculating molecular bond lengths

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cleland, Deidre M., E-mail: deidre.cleland@csiro.au; Per, Manolo C., E-mail: manolo.per@csiro.au

2016-03-28

This work investigates the accuracy of real-space quantum Monte Carlo (QMC) methods for calculating molecular geometries. We present the equilibrium bond lengths of a test set of 30 diatomic molecules calculated using variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) methods. The effect of different trial wavefunctions is investigated using single determinants constructed from Hartree-Fock (HF) and Density Functional Theory (DFT) orbitals with LDA, PBE, and B3LYP functionals, as well as small multi-configurational self-consistent field (MCSCF) multi-determinant expansions. When compared to experimental geometries, all DMC methods exhibit smaller mean-absolute deviations (MADs) than those given by HF, DFT, and MCSCF.more » The most accurate MAD of 3 ± 2 × 10{sup −3} Å is achieved using DMC with a small multi-determinant expansion. However, the more computationally efficient multi-determinant VMC method has a similar MAD of only 4.0 ± 0.9 × 10{sup −3} Å, suggesting that QMC forces calculated from the relatively simple VMC algorithm may often be sufficient for accurate molecular geometries.« less

The Development and Comparison of Molecular Dynamics Simulation and Monte Carlo Simulation

NASA Astrophysics Data System (ADS)

Chen, Jundong

2018-03-01

Molecular dynamics is an integrated technology that combines physics, mathematics and chemistry. Molecular dynamics method is a computer simulation experimental method, which is a powerful tool for studying condensed matter system. This technique not only can get the trajectory of the atom, but can also observe the microscopic details of the atomic motion. By studying the numerical integration algorithm in molecular dynamics simulation, we can not only analyze the microstructure, the motion of particles and the image of macroscopic relationship between them and the material, but can also study the relationship between the interaction and the macroscopic properties more conveniently. The Monte Carlo Simulation, similar to the molecular dynamics, is a tool for studying the micro-molecular and particle nature. In this paper, the theoretical background of computer numerical simulation is introduced, and the specific methods of numerical integration are summarized, including Verlet method, Leap-frog method and Velocity Verlet method. At the same time, the method and principle of Monte Carlo Simulation are introduced. Finally, similarities and differences of Monte Carlo Simulation and the molecular dynamics simulation are discussed.

Learning of state-space models with highly informative observations: A tempered sequential Monte Carlo solution

NASA Astrophysics Data System (ADS)

Svensson, Andreas; Schön, Thomas B.; Lindsten, Fredrik

2018-05-01

Probabilistic (or Bayesian) modeling and learning offers interesting possibilities for systematic representation of uncertainty using probability theory. However, probabilistic learning often leads to computationally challenging problems. Some problems of this type that were previously intractable can now be solved on standard personal computers thanks to recent advances in Monte Carlo methods. In particular, for learning of unknown parameters in nonlinear state-space models, methods based on the particle filter (a Monte Carlo method) have proven very useful. A notoriously challenging problem, however, still occurs when the observations in the state-space model are highly informative, i.e. when there is very little or no measurement noise present, relative to the amount of process noise. The particle filter will then struggle in estimating one of the basic components for probabilistic learning, namely the likelihood p (data | parameters). To this end we suggest an algorithm which initially assumes that there is substantial amount of artificial measurement noise present. The variance of this noise is sequentially decreased in an adaptive fashion such that we, in the end, recover the original problem or possibly a very close approximation of it. The main component in our algorithm is a sequential Monte Carlo (SMC) sampler, which gives our proposed method a clear resemblance to the SMC2 method. Another natural link is also made to the ideas underlying the approximate Bayesian computation (ABC). We illustrate it with numerical examples, and in particular show promising results for a challenging Wiener-Hammerstein benchmark problem.

Improving multivariate Horner schemes with Monte Carlo tree search

NASA Astrophysics Data System (ADS)

Kuipers, J.; Plaat, A.; Vermaseren, J. A. M.; van den Herik, H. J.

2013-11-01

Optimizing the cost of evaluating a polynomial is a classic problem in computer science. For polynomials in one variable, Horner's method provides a scheme for producing a computationally efficient form. For multivariate polynomials it is possible to generalize Horner's method, but this leaves freedom in the order of the variables. Traditionally, greedy schemes like most-occurring variable first are used. This simple textbook algorithm has given remarkably efficient results. Finding better algorithms has proved difficult. In trying to improve upon the greedy scheme we have implemented Monte Carlo tree search, a recent search method from the field of artificial intelligence. This results in better Horner schemes and reduces the cost of evaluating polynomials, sometimes by factors up to two.

Self-learning Monte Carlo method and cumulative update in fermion systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Junwei; Shen, Huitao; Qi, Yang

2017-06-07

In this study, we develop the self-learning Monte Carlo (SLMC) method, a general-purpose numerical method recently introduced to simulate many-body systems, for studying interacting fermion systems. Our method uses a highly efficient update algorithm, which we design and dub “cumulative update”, to generate new candidate configurations in the Markov chain based on a self-learned bosonic effective model. From a general analysis and a numerical study of the double exchange model as an example, we find that the SLMC with cumulative update drastically reduces the computational cost of the simulation, while remaining statistically exact. Remarkably, its computational complexity is far lessmore » than the conventional algorithm with local updates.« less

Collective translational and rotational Monte Carlo cluster move for general pairwise interaction

NASA Astrophysics Data System (ADS)

Růžička, Štěpán; Allen, Michael P.

2014-09-01

Virtual move Monte Carlo is a cluster algorithm which was originally developed for strongly attractive colloidal, molecular, or atomistic systems in order to both approximate the collective dynamics and avoid sampling of unphysical kinetic traps. In this paper, we present the algorithm in the form, which selects the moving cluster through a wider class of virtual states and which is applicable to general pairwise interactions, including hard-core repulsion. The newly proposed way of selecting the cluster increases the acceptance probability by up to several orders of magnitude, especially for rotational moves. The results have their applications in simulations of systems interacting via anisotropic potentials both to enhance the sampling of the phase space and to approximate the dynamics.

Improvement of Simulation Method in Validation of Software of the Coordinate Measuring Systems

NASA Astrophysics Data System (ADS)

Nieciąg, Halina

2015-10-01

Software is used in order to accomplish various tasks at each stage of the functioning of modern measuring systems. Before metrological confirmation of measuring equipment, the system has to be validated. This paper discusses the method for conducting validation studies of a fragment of software to calculate the values of measurands. Due to the number and nature of the variables affecting the coordinate measurement results and the complex character and multi-dimensionality of measurands, the study used the Monte Carlo method of numerical simulation. The article presents an attempt of possible improvement of results obtained by classic Monte Carlo tools. The algorithm LHS (Latin Hypercube Sampling) was implemented as alternative to the simple sampling schema of classic algorithm.

Assessing the performance of a covert automatic target recognition algorithm

NASA Astrophysics Data System (ADS)

Ehrman, Lisa M.; Lanterman, Aaron D.

2005-05-01

Passive radar systems exploit illuminators of opportunity, such as TV and FM radio, to illuminate potential targets. Doing so allows them to operate covertly and inexpensively. Our research seeks to enhance passive radar systems by adding automatic target recognition (ATR) capabilities. In previous papers we proposed conducting ATR by comparing the radar cross section (RCS) of aircraft detected by a passive radar system to the precomputed RCS of aircraft in the target class. To effectively model the low-frequency setting, the comparison is made via a Rician likelihood model. Monte Carlo simulations indicate that the approach is viable. This paper builds on that work by developing a method for quickly assessing the potential performance of the ATR algorithm without using exhaustive Monte Carlo trials. This method exploits the relation between the probability of error in a binary hypothesis test under the Bayesian framework to the Chernoff information. Since the data are well-modeled as Rician, we begin by deriving a closed-form approximation for the Chernoff information between two Rician densities. This leads to an approximation for the probability of error in the classification algorithm that is a function of the number of available measurements. We conclude with an application that would be particularly cumbersome to accomplish via Monte Carlo trials, but that can be quickly addressed using the Chernoff information approach. This application evaluates the length of time that an aircraft must be tracked before the probability of error in the ATR algorithm drops below a desired threshold.

LLNL Mercury Project Trinity Open Science Final Report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brantley, Patrick; Dawson, Shawn; McKinley, Scott

2016-04-20

The Mercury Monte Carlo particle transport code developed at Lawrence Livermore National Laboratory (LLNL) is used to simulate the transport of radiation through urban environments. These challenging calculations include complicated geometries and require significant computational resources to complete. As a result, a question arises as to the level of convergence of the calculations with Monte Carlo simulation particle count. In the Trinity Open Science calculations, one main focus was to investigate convergence of the relevant simulation quantities with Monte Carlo particle count to assess the current simulation methodology. Both for this application space but also of more general applicability, wemore » also investigated the impact of code algorithms on parallel scaling on the Trinity machine as well as the utilization of the Trinity DataWarp burst buffer technology in Mercury via the LLNL Scalable Checkpoint/Restart (SCR) library.« less

A calibrated Monte Carlo approach to quantify the impacts of misorientation and different driving forces on texture development

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liangzhe Zhang; Anthony D. Rollett; Timothy Bartel

2012-02-01

A calibrated Monte Carlo (cMC) approach, which quantifies grain boundary kinetics within a generic setting, is presented. The influence of misorientation is captured by adding a scaling coefficient in the spin flipping probability equation, while the contribution of different driving forces is weighted using a partition function. The calibration process relies on the established parametric links between Monte Carlo (MC) and sharp-interface models. The cMC algorithm quantifies microstructural evolution under complex thermomechanical environments and remedies some of the difficulties associated with conventional MC models. After validation, the cMC approach is applied to quantify the texture development of polycrystalline materials withmore » influences of misorientation and inhomogeneous bulk energy across grain boundaries. The results are in good agreement with theory and experiments.« less

Simulated Stochastic Approximation Annealing for Global Optimization with a Square-Root Cooling Schedule

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liang, Faming; Cheng, Yichen; Lin, Guang

2014-06-13

Simulated annealing has been widely used in the solution of optimization problems. As known by many researchers, the global optima cannot be guaranteed to be located by simulated annealing unless a logarithmic cooling schedule is used. However, the logarithmic cooling schedule is so slow that no one can afford to have such a long CPU time. This paper proposes a new stochastic optimization algorithm, the so-called simulated stochastic approximation annealing algorithm, which is a combination of simulated annealing and the stochastic approximation Monte Carlo algorithm. Under the framework of stochastic approximation Markov chain Monte Carlo, it is shown that themore » new algorithm can work with a cooling schedule in which the temperature can decrease much faster than in the logarithmic cooling schedule, e.g., a square-root cooling schedule, while guaranteeing the global optima to be reached when the temperature tends to zero. The new algorithm has been tested on a few benchmark optimization problems, including feed-forward neural network training and protein-folding. The numerical results indicate that the new algorithm can significantly outperform simulated annealing and other competitors.« less

Goal-oriented sensitivity analysis for lattice kinetic Monte Carlo simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arampatzis, Georgios, E-mail: garab@math.uoc.gr; Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003; Katsoulakis, Markos A., E-mail: markos@math.umass.edu

2014-03-28

In this paper we propose a new class of coupling methods for the sensitivity analysis of high dimensional stochastic systems and in particular for lattice Kinetic Monte Carlo (KMC). Sensitivity analysis for stochastic systems is typically based on approximating continuous derivatives with respect to model parameters by the mean value of samples from a finite difference scheme. Instead of using independent samples the proposed algorithm reduces the variance of the estimator by developing a strongly correlated-“coupled”- stochastic process for both the perturbed and unperturbed stochastic processes, defined in a common state space. The novelty of our construction is that themore » new coupled process depends on the targeted observables, e.g., coverage, Hamiltonian, spatial correlations, surface roughness, etc., hence we refer to the proposed method as goal-oriented sensitivity analysis. In particular, the rates of the coupled Continuous Time Markov Chain are obtained as solutions to a goal-oriented optimization problem, depending on the observable of interest, by considering the minimization functional of the corresponding variance. We show that this functional can be used as a diagnostic tool for the design and evaluation of different classes of couplings. Furthermore, the resulting KMC sensitivity algorithm has an easy implementation that is based on the Bortz–Kalos–Lebowitz algorithm's philosophy, where events are divided in classes depending on level sets of the observable of interest. Finally, we demonstrate in several examples including adsorption, desorption, and diffusion Kinetic Monte Carlo that for the same confidence interval and observable, the proposed goal-oriented algorithm can be two orders of magnitude faster than existing coupling algorithms for spatial KMC such as the Common Random Number approach. We also provide a complete implementation of the proposed sensitivity analysis algorithms, including various spatial KMC examples, in a supplementary MATLAB source code.« less

Extraction of diffuse correlation spectroscopy flow index by integration of Nth-order linear model with Monte Carlo simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shang, Yu; Lin, Yu; Yu, Guoqiang, E-mail: guoqiang.yu@uky.edu

2014-05-12

Conventional semi-infinite solution for extracting blood flow index (BFI) from diffuse correlation spectroscopy (DCS) measurements may cause errors in estimation of BFI (αD{sub B}) in tissues with small volume and large curvature. We proposed an algorithm integrating Nth-order linear model of autocorrelation function with the Monte Carlo simulation of photon migrations in tissue for the extraction of αD{sub B}. The volume and geometry of the measured tissue were incorporated in the Monte Carlo simulation, which overcome the semi-infinite restrictions. The algorithm was tested using computer simulations on four tissue models with varied volumes/geometries and applied on an in vivo strokemore » model of mouse. Computer simulations shows that the high-order (N ≥ 5) linear algorithm was more accurate in extracting αD{sub B} (errors < ±2%) from the noise-free DCS data than the semi-infinite solution (errors: −5.3% to −18.0%) for different tissue models. Although adding random noises to DCS data resulted in αD{sub B} variations, the mean values of errors in extracting αD{sub B} were similar to those reconstructed from the noise-free DCS data. In addition, the errors in extracting the relative changes of αD{sub B} using both linear algorithm and semi-infinite solution were fairly small (errors < ±2.0%) and did not rely on the tissue volume/geometry. The experimental results from the in vivo stroke mice agreed with those in simulations, demonstrating the robustness of the linear algorithm. DCS with the high-order linear algorithm shows the potential for the inter-subject comparison and longitudinal monitoring of absolute BFI in a variety of tissues/organs with different volumes/geometries.« less

RNA inverse folding using Monte Carlo tree search.

PubMed

Yang, Xiufeng; Yoshizoe, Kazuki; Taneda, Akito; Tsuda, Koji

2017-11-06

Artificially synthesized RNA molecules provide important ways for creating a variety of novel functional molecules. State-of-the-art RNA inverse folding algorithms can design simple and short RNA sequences of specific GC content, that fold into the target RNA structure. However, their performance is not satisfactory in complicated cases. We present a new inverse folding algorithm called MCTS-RNA, which uses Monte Carlo tree search (MCTS), a technique that has shown exceptional performance in Computer Go recently, to represent and discover the essential part of the sequence space. To obtain high accuracy, initial sequences generated by MCTS are further improved by a series of local updates. Our algorithm has an ability to control the GC content precisely and can deal with pseudoknot structures. Using common benchmark datasets for evaluation, MCTS-RNA showed a lot of promise as a standard method of RNA inverse folding. MCTS-RNA is available at https://github.com/tsudalab/MCTS-RNA .

Modified Monte Carlo method for study of electron transport in degenerate electron gas in the presence of electron-electron interactions, application to graphene

NASA Astrophysics Data System (ADS)

Borowik, Piotr; Thobel, Jean-Luc; Adamowicz, Leszek

2017-07-01

Standard computational methods used to take account of the Pauli Exclusion Principle into Monte Carlo (MC) simulations of electron transport in semiconductors may give unphysical results in low field regime, where obtained electron distribution function takes values exceeding unity. Modified algorithms were already proposed and allow to correctly account for electron scattering on phonons or impurities. Present paper extends this approach and proposes improved simulation scheme allowing including Pauli exclusion principle for electron-electron (e-e) scattering into MC simulations. Simulations with significantly reduced computational cost recreate correct values of the electron distribution function. Proposed algorithm is applied to study transport properties of degenerate electrons in graphene with e-e interactions. This required adapting the treatment of e-e scattering in the case of linear band dispersion relation. Hence, this part of the simulation algorithm is described in details.

ALGEBRA: ALgorithm for the heterogeneous dosimetry based on GEANT4 for BRAchytherapy.

PubMed

Afsharpour, H; Landry, G; D'Amours, M; Enger, S; Reniers, B; Poon, E; Carrier, J-F; Verhaegen, F; Beaulieu, L

2012-06-07

Task group 43 (TG43)-based dosimetry algorithms are efficient for brachytherapy dose calculation in water. However, human tissues have chemical compositions and densities different than water. Moreover, the mutual shielding effect of seeds on each other (interseed attenuation) is neglected in the TG43-based dosimetry platforms. The scientific community has expressed the need for an accurate dosimetry platform in brachytherapy. The purpose of this paper is to present ALGEBRA, a Monte Carlo platform for dosimetry in brachytherapy which is sufficiently fast and accurate for clinical and research purposes. ALGEBRA is based on the GEANT4 Monte Carlo code and is capable of handling the DICOM RT standard to recreate a virtual model of the treated site. Here, the performance of ALGEBRA is presented for the special case of LDR brachytherapy in permanent prostate and breast seed implants. However, the algorithm is also capable of handling other treatments such as HDR brachytherapy.

Communication: Calculation of interatomic forces and optimization of molecular geometry with auxiliary-field quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Motta, Mario; Zhang, Shiwei

2018-05-01

We propose an algorithm for accurate, systematic, and scalable computation of interatomic forces within the auxiliary-field quantum Monte Carlo (AFQMC) method. The algorithm relies on the Hellmann-Feynman theorem and incorporates Pulay corrections in the presence of atomic orbital basis sets. We benchmark the method for small molecules by comparing the computed forces with the derivatives of the AFQMC potential energy surface and by direct comparison with other quantum chemistry methods. We then perform geometry optimizations using the steepest descent algorithm in larger molecules. With realistic basis sets, we obtain equilibrium geometries in agreement, within statistical error bars, with experimental values. The increase in computational cost for computing forces in this approach is only a small prefactor over that of calculating the total energy. This paves the way for a general and efficient approach for geometry optimization and molecular dynamics within AFQMC.

Communication: An efficient and accurate perturbative correction to initiator full configuration interaction quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Blunt, Nick S.

2018-06-01

We present a perturbative correction within initiator full configuration interaction quantum Monte Carlo (i-FCIQMC). In the existing i-FCIQMC algorithm, a significant number of spawned walkers are discarded due to the initiator criteria. Here we show that these discarded walkers have a form that allows the calculation of a second-order Epstein-Nesbet correction, which may be accumulated in a trivial and inexpensive manner, yet substantially improves i-FCIQMC results. The correction is applied to the Hubbard model and the uniform electron gas and molecular systems.

Object-Oriented/Data-Oriented Design of a Direct Simulation Monte Carlo Algorithm

NASA Technical Reports Server (NTRS)

Liechty, Derek S.

2014-01-01

Over the past decade, there has been much progress towards improved phenomenological modeling and algorithmic updates for the direct simulation Monte Carlo (DSMC) method, which provides a probabilistic physical simulation of gas Rows. These improvements have largely been based on the work of the originator of the DSMC method, Graeme Bird. Of primary importance are improved chemistry, internal energy, and physics modeling and a reduction in time to solution. These allow for an expanded range of possible solutions In altitude and velocity space. NASA's current production code, the DSMC Analysis Code (DAC), is well-established and based on Bird's 1994 algorithms written in Fortran 77 and has proven difficult to upgrade. A new DSMC code is being developed in the C++ programming language using object-oriented and data-oriented design paradigms to facilitate the inclusion of the recent improvements and future development activities. The development efforts on the new code, the Multiphysics Algorithm with Particles (MAP), are described, and performance comparisons are made with DAC.

A global reaction route mapping-based kinetic Monte Carlo algorithm

NASA Astrophysics Data System (ADS)

Mitchell, Izaac; Irle, Stephan; Page, Alister J.

2016-07-01

We propose a new on-the-fly kinetic Monte Carlo (KMC) method that is based on exhaustive potential energy surface searching carried out with the global reaction route mapping (GRRM) algorithm. Starting from any given equilibrium state, this GRRM-KMC algorithm performs a one-step GRRM search to identify all surrounding transition states. Intrinsic reaction coordinate pathways are then calculated to identify potential subsequent equilibrium states. Harmonic transition state theory is used to calculate rate constants for all potential pathways, before a standard KMC accept/reject selection is performed. The selected pathway is then used to propagate the system forward in time, which is calculated on the basis of 1st order kinetics. The GRRM-KMC algorithm is validated here in two challenging contexts: intramolecular proton transfer in malonaldehyde and surface carbon diffusion on an iron nanoparticle. We demonstrate that in both cases the GRRM-KMC method is capable of reproducing the 1st order kinetics observed during independent quantum chemical molecular dynamics simulations using the density-functional tight-binding potential.

Efficiency in nonequilibrium molecular dynamics Monte Carlo simulations

DOE PAGES

Radak, Brian K.; Roux, Benoît

2016-10-07

Hybrid algorithms combining nonequilibrium molecular dynamics and Monte Carlo (neMD/MC) offer a powerful avenue for improving the sampling efficiency of computer simulations of complex systems. These neMD/MC algorithms are also increasingly finding use in applications where conventional approaches are impractical, such as constant-pH simulations with explicit solvent. However, selecting an optimal nonequilibrium protocol for maximum efficiency often represents a non-trivial challenge. This work evaluates the efficiency of a broad class of neMD/MC algorithms and protocols within the theoretical framework of linear response theory. The approximations are validated against constant pH-MD simulations and shown to provide accurate predictions of neMD/MC performance.more » An assessment of a large set of protocols confirms (both theoretically and empirically) that a linear work protocol gives the best neMD/MC performance. Lastly, a well-defined criterion for optimizing the time parameters of the protocol is proposed and demonstrated with an adaptive algorithm that improves the performance on-the-fly with minimal cost.« less

A global reaction route mapping-based kinetic Monte Carlo algorithm.

PubMed

Mitchell, Izaac; Irle, Stephan; Page, Alister J

2016-07-14

We propose a new on-the-fly kinetic Monte Carlo (KMC) method that is based on exhaustive potential energy surface searching carried out with the global reaction route mapping (GRRM) algorithm. Starting from any given equilibrium state, this GRRM-KMC algorithm performs a one-step GRRM search to identify all surrounding transition states. Intrinsic reaction coordinate pathways are then calculated to identify potential subsequent equilibrium states. Harmonic transition state theory is used to calculate rate constants for all potential pathways, before a standard KMC accept/reject selection is performed. The selected pathway is then used to propagate the system forward in time, which is calculated on the basis of 1st order kinetics. The GRRM-KMC algorithm is validated here in two challenging contexts: intramolecular proton transfer in malonaldehyde and surface carbon diffusion on an iron nanoparticle. We demonstrate that in both cases the GRRM-KMC method is capable of reproducing the 1st order kinetics observed during independent quantum chemical molecular dynamics simulations using the density-functional tight-binding potential.

Application of genetic algorithms to focal mechanism determination

NASA Astrophysics Data System (ADS)

Kobayashi, Reiji; Nakanishi, Ichiro

1994-04-01

Genetic algorithms are a new class of methods for global optimization. They resemble Monte Carlo techniques, but search for solutions more efficiently than uniform Monte Carlo sampling. In the field of geophysics, genetic algorithms have recently been used to solve some non-linear inverse problems (e.g., earthquake location, waveform inversion, migration velocity estimation). We present an application of genetic algorithms to focal mechanism determination from first-motion polarities of P-waves and apply our method to two recent large events, the Kushiro-oki earthquake of January 15, 1993 and the SW Hokkaido (Japan Sea) earthquake of July 12, 1993. Initial solution and curvature information of the objective function that gradient methods need are not required in our approach. Moreover globally optimal solutions can be efficiently obtained. Calculation of polarities based on double-couple models is the most time-consuming part of the source mechanism determination. The amount of calculations required by the method designed in this study is much less than that of previous grid search methods.

Excited states from quantum Monte Carlo in the basis of Slater determinants

DOE Office of Scientific and Technical Information (OSTI.GOV)

Humeniuk, Alexander; Mitrić, Roland, E-mail: roland.mitric@uni-wuerzburg.de

2014-11-21

Building on the full configuration interaction quantum Monte Carlo (FCIQMC) algorithm introduced recently by Booth et al. [J. Chem. Phys. 131, 054106 (2009)] to compute the ground state of correlated many-electron systems, an extension to the computation of excited states (exFCIQMC) is presented. The Hilbert space is divided into a large part consisting of pure Slater determinants and a much smaller orthogonal part (the size of which is controlled by a cut-off threshold), from which the lowest eigenstates can be removed efficiently. In this way, the quantum Monte Carlo algorithm is restricted to the orthogonal complement of the lower excitedmore » states and projects out the next highest excited state. Starting from the ground state, higher excited states can be found one after the other. The Schrödinger equation in imaginary time is solved by the same population dynamics as in the ground state algorithm with modified probabilities and matrix elements, for which working formulae are provided. As a proof of principle, the method is applied to lithium hydride in the 3-21G basis set and to the helium dimer in the aug-cc-pVDZ basis set. It is shown to give the correct electronic structure for all bond lengths. Much more testing will be required before the applicability of this method to electron correlation problems of interesting size can be assessed.« less

A fast Monte Carlo EM algorithm for estimation in latent class model analysis with an application to assess diagnostic accuracy for cervical neoplasia in women with AGC

PubMed Central

Kang, Le; Carter, Randy; Darcy, Kathleen; Kauderer, James; Liao, Shu-Yuan

2013-01-01

In this article we use a latent class model (LCM) with prevalence modeled as a function of covariates to assess diagnostic test accuracy in situations where the true disease status is not observed, but observations on three or more conditionally independent diagnostic tests are available. A fast Monte Carlo EM (MCEM) algorithm with binary (disease) diagnostic data is implemented to estimate parameters of interest; namely, sensitivity, specificity, and prevalence of the disease as a function of covariates. To obtain standard errors for confidence interval construction of estimated parameters, the missing information principle is applied to adjust information matrix estimates. We compare the adjusted information matrix based standard error estimates with the bootstrap standard error estimates both obtained using the fast MCEM algorithm through an extensive Monte Carlo study. Simulation demonstrates that the adjusted information matrix approach estimates the standard error similarly with the bootstrap methods under certain scenarios. The bootstrap percentile intervals have satisfactory coverage probabilities. We then apply the LCM analysis to a real data set of 122 subjects from a Gynecologic Oncology Group (GOG) study of significant cervical lesion (S-CL) diagnosis in women with atypical glandular cells of undetermined significance (AGC) to compare the diagnostic accuracy of a histology-based evaluation, a CA-IX biomarker-based test and a human papillomavirus (HPV) DNA test. PMID:24163493

A kMC-MD method with generalized move-sets for the simulation of folding of α-helical and β-stranded peptides.

PubMed

Peter, Emanuel K; Pivkin, Igor V; Shea, Joan-Emma

2015-04-14

In Monte-Carlo simulations of protein folding, pathways and folding times depend on the appropriate choice of the Monte-Carlo move or process path. We developed a generalized set of process paths for a hybrid kinetic Monte Carlo-Molecular dynamics algorithm, which makes use of a novel constant time-update and allows formation of α-helical and β-stranded secondary structures. We apply our new algorithm to the folding of 3 different proteins: TrpCage, GB1, and TrpZip4. All three systems are seen to fold within the range of the experimental folding times. For the β-hairpins, we observe that loop formation is the rate-determining process followed by collapse and formation of the native core. Cluster analysis of both peptides reveals that GB1 folds with equal likelihood along a zipper or a hydrophobic collapse mechanism, while TrpZip4 follows primarily a zipper pathway. The difference observed in the folding behavior of the two proteins can be attributed to the different arrangements of their hydrophobic core, strongly packed, and dry in case of TrpZip4, and partially hydrated in the case of GB1.

An off-lattice, self-learning kinetic Monte Carlo method using local environments.

PubMed

Konwar, Dhrubajit; Bhute, Vijesh J; Chatterjee, Abhijit

2011-11-07

We present a method called local environment kinetic Monte Carlo (LE-KMC) method for efficiently performing off-lattice, self-learning kinetic Monte Carlo (KMC) simulations of activated processes in material systems. Like other off-lattice KMC schemes, new atomic processes can be found on-the-fly in LE-KMC. However, a unique feature of LE-KMC is that as long as the assumption that all processes and rates depend only on the local environment is satisfied, LE-KMC provides a general algorithm for (i) unambiguously describing a process in terms of its local atomic environments, (ii) storing new processes and environments in a catalog for later use with standard KMC, and (iii) updating the system based on the local information once a process has been selected for a KMC move. Search, classification, storage and retrieval steps needed while employing local environments and processes in the LE-KMC method are discussed. The advantages and computational cost of LE-KMC are discussed. We assess the performance of the LE-KMC algorithm by considering test systems involving diffusion in a submonolayer Ag and Ag-Cu alloy films on Ag(001) surface.

A new concept of pencil beam dose calculation for 40-200 keV photons using analytical dose kernels.

PubMed

Bartzsch, Stefan; Oelfke, Uwe

2013-11-01

The advent of widespread kV-cone beam computer tomography in image guided radiation therapy and special therapeutic application of keV photons, e.g., in microbeam radiation therapy (MRT) require accurate and fast dose calculations for photon beams with energies between 40 and 200 keV. Multiple photon scattering originating from Compton scattering and the strong dependence of the photoelectric cross section on the atomic number of the interacting tissue render these dose calculations by far more challenging than the ones established for corresponding MeV beams. That is why so far developed analytical models of kV photon dose calculations fail to provide the required accuracy and one has to rely on time consuming Monte Carlo simulation techniques. In this paper, the authors introduce a novel analytical approach for kV photon dose calculations with an accuracy that is almost comparable to the one of Monte Carlo simulations. First, analytical point dose and pencil beam kernels are derived for homogeneous media and compared to Monte Carlo simulations performed with the Geant4 toolkit. The dose contributions are systematically separated into contributions from the relevant orders of multiple photon scattering. Moreover, approximate scaling laws for the extension of the algorithm to inhomogeneous media are derived. The comparison of the analytically derived dose kernels in water showed an excellent agreement with the Monte Carlo method. Calculated values deviate less than 5% from Monte Carlo derived dose values, for doses above 1% of the maximum dose. The analytical structure of the kernels allows adaption to arbitrary materials and photon spectra in the given energy range of 40-200 keV. The presented analytical methods can be employed in a fast treatment planning system for MRT. In convolution based algorithms dose calculation times can be reduced to a few minutes.

Monte Carlo verification of radiotherapy treatments with CloudMC.

PubMed

Miras, Hector; Jiménez, Rubén; Perales, Álvaro; Terrón, José Antonio; Bertolet, Alejandro; Ortiz, Antonio; Macías, José

2018-06-27

A new implementation has been made on CloudMC, a cloud-based platform presented in a previous work, in order to provide services for radiotherapy treatment verification by means of Monte Carlo in a fast, easy and economical way. A description of the architecture of the application and the new developments implemented is presented together with the results of the tests carried out to validate its performance. CloudMC has been developed over Microsoft Azure cloud. It is based on a map/reduce implementation for Monte Carlo calculations distribution over a dynamic cluster of virtual machines in order to reduce calculation time. CloudMC has been updated with new methods to read and process the information related to radiotherapy treatment verification: CT image set, treatment plan, structures and dose distribution files in DICOM format. Some tests have been designed in order to determine, for the different tasks, the most suitable type of virtual machines from those available in Azure. Finally, the performance of Monte Carlo verification in CloudMC is studied through three real cases that involve different treatment techniques, linac models and Monte Carlo codes. Considering computational and economic factors, D1_v2 and G1 virtual machines were selected as the default type for the Worker Roles and the Reducer Role respectively. Calculation times up to 33 min and costs of 16 € were achieved for the verification cases presented when a statistical uncertainty below 2% (2σ) was required. The costs were reduced to 3-6 € when uncertainty requirements are relaxed to 4%. Advantages like high computational power, scalability, easy access and pay-per-usage model, make Monte Carlo cloud-based solutions, like the one presented in this work, an important step forward to solve the long-lived problem of truly introducing the Monte Carlo algorithms in the daily routine of the radiotherapy planning process.

An Efficient MCMC Algorithm to Sample Binary Matrices with Fixed Marginals

ERIC Educational Resources Information Center

Verhelst, Norman D.

2008-01-01

Uniform sampling of binary matrices with fixed margins is known as a difficult problem. Two classes of algorithms to sample from a distribution not too different from the uniform are studied in the literature: importance sampling and Markov chain Monte Carlo (MCMC). Existing MCMC algorithms converge slowly, require a long burn-in period and yield…

MontePython 3: Parameter inference code for cosmology

NASA Astrophysics Data System (ADS)

Brinckmann, Thejs; Lesgourgues, Julien; Audren, Benjamin; Benabed, Karim; Prunet, Simon

2018-05-01

MontePython 3 provides numerous ways to explore parameter space using Monte Carlo Markov Chain (MCMC) sampling, including Metropolis-Hastings, Nested Sampling, Cosmo Hammer, and a Fisher sampling method. This improved version of the Monte Python (ascl:1307.002) parameter inference code for cosmology offers new ingredients that improve the performance of Metropolis-Hastings sampling, speeding up convergence and offering significant time improvement in difficult runs. Additional likelihoods and plotting options are available, as are post-processing algorithms such as Importance Sampling and Adding Derived Parameter.

Accurate condensed history Monte Carlo simulation of electron transport. II. Application to ion chamber response simulations.

PubMed

Kawrakow, I

2000-03-01

In this report the condensed history Monte Carlo simulation of electron transport and its application to the calculation of ion chamber response is discussed. It is shown that the strong step-size dependencies and lack of convergence to the correct answer previously observed are the combined effect of the following artifacts caused by the EGS4/PRESTA implementation of the condensed history technique: dose underprediction due to PRESTA'S pathlength correction and lateral correlation algorithm; dose overprediction due to the boundary crossing algorithm; dose overprediction due to the breakdown of the fictitious cross section method for sampling distances between discrete interaction and the inaccurate evaluation of energy-dependent quantities. These artifacts are now understood quantitatively and analytical expressions for their effect are given.

Parameters estimation for reactive transport: A way to test the validity of a reactive model

NASA Astrophysics Data System (ADS)

Aggarwal, Mohit; Cheikh Anta Ndiaye, Mame; Carrayrou, Jérôme

The chemical parameters used in reactive transport models are not known accurately due to the complexity and the heterogeneous conditions of a real domain. We will present an efficient algorithm in order to estimate the chemical parameters using Monte-Carlo method. Monte-Carlo methods are very robust for the optimisation of the highly non-linear mathematical model describing reactive transport. Reactive transport of tributyltin (TBT) through natural quartz sand at seven different pHs is taken as the test case. Our algorithm will be used to estimate the chemical parameters of the sorption of TBT onto the natural quartz sand. By testing and comparing three models of surface complexation, we show that the proposed adsorption model cannot explain the experimental data.

TH-E-18A-01: Developments in Monte Carlo Methods for Medical Imaging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Badal, A; Zbijewski, W; Bolch, W

Monte Carlo simulation methods are widely used in medical physics research and are starting to be implemented in clinical applications such as radiation therapy planning systems. Monte Carlo simulations offer the capability to accurately estimate quantities of interest that are challenging to measure experimentally while taking into account the realistic anatomy of an individual patient. Traditionally, practical application of Monte Carlo simulation codes in diagnostic imaging was limited by the need for large computational resources or long execution times. However, recent advancements in high-performance computing hardware, combined with a new generation of Monte Carlo simulation algorithms and novel postprocessing methods,more » are allowing for the computation of relevant imaging parameters of interest such as patient organ doses and scatter-to-primaryratios in radiographic projections in just a few seconds using affordable computational resources. Programmable Graphics Processing Units (GPUs), for example, provide a convenient, affordable platform for parallelized Monte Carlo executions that yield simulation times on the order of 10{sup 7} xray/ s. Even with GPU acceleration, however, Monte Carlo simulation times can be prohibitive for routine clinical practice. To reduce simulation times further, variance reduction techniques can be used to alter the probabilistic models underlying the x-ray tracking process, resulting in lower variance in the results without biasing the estimates. Other complementary strategies for further reductions in computation time are denoising of the Monte Carlo estimates and estimating (scoring) the quantity of interest at a sparse set of sampling locations (e.g. at a small number of detector pixels in a scatter simulation) followed by interpolation. Beyond reduction of the computational resources required for performing Monte Carlo simulations in medical imaging, the use of accurate representations of patient anatomy is crucial to the virtual generation of medical images and accurate estimation of radiation dose and other imaging parameters. For this, detailed computational phantoms of the patient anatomy must be utilized and implemented within the radiation transport code. Computational phantoms presently come in one of three format types, and in one of four morphometric categories. Format types include stylized (mathematical equation-based), voxel (segmented CT/MR images), and hybrid (NURBS and polygon mesh surfaces). Morphometric categories include reference (small library of phantoms by age at 50th height/weight percentile), patient-dependent (larger library of phantoms at various combinations of height/weight percentiles), patient-sculpted (phantoms altered to match the patient's unique outer body contour), and finally, patient-specific (an exact representation of the patient with respect to both body contour and internal anatomy). The existence and availability of these phantoms represents a very important advance for the simulation of realistic medical imaging applications using Monte Carlo methods. New Monte Carlo simulation codes need to be thoroughly validated before they can be used to perform novel research. Ideally, the validation process would involve comparison of results with those of an experimental measurement, but accurate replication of experimental conditions can be very challenging. It is very common to validate new Monte Carlo simulations by replicating previously published simulation results of similar experiments. This process, however, is commonly problematic due to the lack of sufficient information in the published reports of previous work so as to be able to replicate the simulation in detail. To aid in this process, the AAPM Task Group 195 prepared a report in which six different imaging research experiments commonly performed using Monte Carlo simulations are described and their results provided. The simulation conditions of all six cases are provided in full detail, with all necessary data on material composition, source, geometry, scoring and other parameters provided. The results of these simulations when performed with the four most common publicly available Monte Carlo packages are also provided in tabular form. The Task Group 195 Report will be useful for researchers needing to validate their Monte Carlo work, and for trainees needing to learn Monte Carlo simulation methods. In this symposium we will review the recent advancements in highperformance computing hardware enabling the reduction in computational resources needed for Monte Carlo simulations in medical imaging. We will review variance reduction techniques commonly applied in Monte Carlo simulations of medical imaging systems and present implementation strategies for efficient combination of these techniques with GPU acceleration. Trade-offs involved in Monte Carlo acceleration by means of denoising and “sparse sampling” will be discussed. A method for rapid scatter correction in cone-beam CT (<5 min/scan) will be presented as an illustration of the simulation speeds achievable with optimized Monte Carlo simulations. We will also discuss the development, availability, and capability of the various combinations of computational phantoms for Monte Carlo simulation of medical imaging systems. Finally, we will review some examples of experimental validation of Monte Carlo simulations and will present the AAPM Task Group 195 Report. Learning Objectives: Describe the advances in hardware available for performing Monte Carlo simulations in high performance computing environments. Explain variance reduction, denoising and sparse sampling techniques available for reduction of computational time needed for Monte Carlo simulations of medical imaging. List and compare the computational anthropomorphic phantoms currently available for more accurate assessment of medical imaging parameters in Monte Carlo simulations. Describe experimental methods used for validation of Monte Carlo simulations in medical imaging. Describe the AAPM Task Group 195 Report and its use for validation and teaching of Monte Carlo simulations in medical imaging.« less

An Improved Elastic and Nonelastic Neutron Transport Algorithm for Space Radiation

NASA Technical Reports Server (NTRS)

Clowdsley, Martha S.; Wilson, John W.; Heinbockel, John H.; Tripathi, R. K.; Singleterry, Robert C., Jr.; Shinn, Judy L.

2000-01-01

A neutron transport algorithm including both elastic and nonelastic particle interaction processes for use in space radiation protection for arbitrary shield material is developed. The algorithm is based upon a multiple energy grouping and analysis of the straight-ahead Boltzmann equation by using a mean value theorem for integrals. The algorithm is then coupled to the Langley HZETRN code through a bidirectional neutron evaporation source term. Evaluation of the neutron fluence generated by the solar particle event of February 23, 1956, for an aluminum water shield-target configuration is then compared with MCNPX and LAHET Monte Carlo calculations for the same shield-target configuration. With the Monte Carlo calculation as a benchmark, the algorithm developed in this paper showed a great improvement in results over the unmodified HZETRN solution. In addition, a high-energy bidirectional neutron source based on a formula by Ranft showed even further improvement of the fluence results over previous results near the front of the water target where diffusion out the front surface is important. Effects of improved interaction cross sections are modest compared with the addition of the high-energy bidirectional source terms.

Monte Carlo investigation of transient acoustic fields in partially or completely bounded medium. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Thanedar, B. D.

1972-01-01

A simple repetitive calculation was used to investigate what happens to the field in terms of the signal paths of disturbances originating from the energy source. The computation allowed the field to be reconstructed as a function of space and time on a statistical basis. The suggested Monte Carlo method is in response to the need for a numerical method to supplement analytical methods of solution which are only valid when the boundaries have simple shapes, rather than for a medium that is bounded. For the analysis, a suitable model was created from which was developed an algorithm for the estimation of acoustic pressure variations in the region under investigation. The validity of the technique was demonstrated by analysis of simple physical models with the aid of a digital computer. The Monte Carlo method is applicable to a medium which is homogeneous and is enclosed by either rectangular or curved boundaries.

High-Precision Monte Carlo Simulation of the Ising Models on the Penrose Lattice and the Dual Penrose Lattice

NASA Astrophysics Data System (ADS)

Komura, Yukihiro; Okabe, Yutaka

2016-04-01

We study the Ising models on the Penrose lattice and the dual Penrose lattice by means of the high-precision Monte Carlo simulation. Simulating systems up to the total system size N = 20633239, we estimate the critical temperatures on those lattices with high accuracy. For high-speed calculation, we use the generalized method of the single-GPU-based computation for the Swendsen-Wang multi-cluster algorithm of Monte Carlo simulation. As a result, we estimate the critical temperature on the Penrose lattice as Tc/J = 2.39781 ± 0.00005 and that of the dual Penrose lattice as Tc*/J = 2.14987 ± 0.00005. Moreover, we definitely confirm the duality relation between the critical temperatures on the dual pair of quasilattices with a high degree of accuracy, sinh (2J/Tc)sinh (2J/Tc*) = 1.00000 ± 0.00004.

Auxiliary field diffusion Monte Carlo calculations of light and medium-mass nuclei with local chiral interactions

NASA Astrophysics Data System (ADS)

Lonardoni, D.; Gandolfi, S.; Lynn, J. E.; Petrie, C.; Carlson, J.; Schmidt, K. E.; Schwenk, A.

2018-04-01

Quantum Monte Carlo methods have recently been employed to study properties of nuclei and infinite matter using local chiral effective-field-theory interactions. In this work, we present a detailed description of the auxiliary field diffusion Monte Carlo algorithm for nuclei in combination with local chiral two- and three-nucleon interactions up to next-to-next-to-leading order. We show results for the binding energy, charge radius, charge form factor, and Coulomb sum rule in nuclei with 3 ≤A ≤16 . Particular attention is devoted to the effect of different operator structures in the three-body force for different cutoffs. The outcomes suggest that local chiral interactions fit to few-body observables give a very good description of the ground-state properties of nuclei up to 16O, with the exception of one fit for the softer cutoff which predicts overbinding in larger nuclei.

A Monte Carlo simulation study for the gamma-ray/neutron dual-particle imager using rotational modulation collimator (RMC).

PubMed

Kim, Hyun Suk; Choi, Hong Yeop; Lee, Gyemin; Ye, Sung-Joon; Smith, Martin B; Kim, Geehyun

2018-03-01

The aim of this work is to develop a gamma-ray/neutron dual-particle imager, based on rotational modulation collimators (RMCs) and pulse shape discrimination (PSD)-capable scintillators, for possible applications for radioactivity monitoring as well as nuclear security and safeguards. A Monte Carlo simulation study was performed to design an RMC system for the dual-particle imaging, and modulation patterns were obtained for gamma-ray and neutron sources in various configurations. We applied an image reconstruction algorithm utilizing the maximum-likelihood expectation-maximization method based on the analytical modeling of source-detector configurations, to the Monte Carlo simulation results. Both gamma-ray and neutron source distributions were reconstructed and evaluated in terms of signal-to-noise ratio, showing the viability of developing an RMC-based gamma-ray/neutron dual-particle imager using PSD-capable scintillators.

Application of the three-component bidirectional reflectance distribution function model to Monte Carlo calculation of spectral effective emissivities of nonisothermal blackbody cavities.

PubMed

Prokhorov, Alexander; Prokhorova, Nina I

2012-11-20

We applied the bidirectional reflectance distribution function (BRDF) model consisting of diffuse, quasi-specular, and glossy components to the Monte Carlo modeling of spectral effective emissivities for nonisothermal cavities. A method for extension of a monochromatic three-component (3C) BRDF model to a continuous spectral range is proposed. The initial data for this method are the BRDFs measured in the plane of incidence at a single wavelength and several incidence angles and directional-hemispherical reflectance measured at one incidence angle within a finite spectral range. We proposed the Monte Carlo algorithm for calculation of spectral effective emissivities for nonisothermal cavities whose internal surface is described by the wavelength-dependent 3C BRDF model. The results obtained for a cylindroconical nonisothermal cavity are discussed and compared with results obtained using the conventional specular-diffuse model.

SU-E-T-405: Evaluation of the Raystation Electron Monte Carlo Algorithm for Varian Linear Accelerators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sansourekidou, P; Allen, C

2015-06-15

Purpose: To evaluate the Raystation v4.51 Electron Monte Carlo algorithm for Varian Trilogy, IX and 2100 series linear accelerators and commission for clinical use. Methods: Seventy two water and forty air scans were acquired with a water tank in the form of profiles and depth doses, as requested by vendor. Data was imported into Rayphysics beam modeling module. Energy spectrum was modeled using seven parameters. Contamination photons were modeled using five parameters. Source phase space was modeled using six parameters. Calculations were performed in clinical version 4.51 and percent depth dose curves and profiles were extracted to be compared tomore » water tank measurements. Sensitivity tests were performed for all parameters. Grid size and particle histories were evaluated per energy for statistical uncertainty performance. Results: Model accuracy for air profiles is poor in the shoulder and penumbra region. However, model accuracy for water scans is acceptable. All energies and cones are within 2%/2mm for 90% of the points evaluated. Source phase space parameters have a cumulative effect. To achieve distributions with satisfactory smoothness level a 0.1cm grid and 3,000,000 particle histories were used for commissioning calculations. Calculation time was approximately 3 hours per energy. Conclusion: Raystation electron Monte Carlo is acceptable for clinical use for the Varian accelerators listed. Results are inferior to Elekta Electron Monte Carlo modeling. Known issues were reported to Raysearch and will be resolved in upcoming releases. Auto-modeling is limited to open cone depth dose curves and needs expansion.« less

Reconstruction of Human Monte Carlo Geometry from Segmented Images

NASA Astrophysics Data System (ADS)

Zhao, Kai; Cheng, Mengyun; Fan, Yanchang; Wang, Wen; Long, Pengcheng; Wu, Yican

2014-06-01

Human computational phantoms have been used extensively for scientific experimental analysis and experimental simulation. This article presented a method for human geometry reconstruction from a series of segmented images of a Chinese visible human dataset. The phantom geometry could actually describe detailed structure of an organ and could be converted into the input file of the Monte Carlo codes for dose calculation. A whole-body computational phantom of Chinese adult female has been established by FDS Team which is named Rad-HUMAN with about 28.8 billion voxel number. For being processed conveniently, different organs on images were segmented with different RGB colors and the voxels were assigned with positions of the dataset. For refinement, the positions were first sampled. Secondly, the large sums of voxels inside the organ were three-dimensional adjacent, however, there were not thoroughly mergence methods to reduce the cell amounts for the description of the organ. In this study, the voxels on the organ surface were taken into consideration of the mergence which could produce fewer cells for the organs. At the same time, an indexed based sorting algorithm was put forward for enhancing the mergence speed. Finally, the Rad-HUMAN which included a total of 46 organs and tissues was described by the cuboids into the Monte Carlo Monte Carlo Geometry for the simulation. The Monte Carlo geometry was constructed directly from the segmented images and the voxels was merged exhaustively. Each organ geometry model was constructed without ambiguity and self-crossing, its geometry information could represent the accuracy appearance and precise interior structure of the organs. The constructed geometry largely retaining the original shape of organs could easily be described into different Monte Carlo codes input file such as MCNP. Its universal property was testified and high-performance was experimentally verified

Fast multipurpose Monte Carlo simulation for proton therapy using multi- and many-core CPU architectures.

PubMed

Souris, Kevin; Lee, John Aldo; Sterpin, Edmond

2016-04-01

Accuracy in proton therapy treatment planning can be improved using Monte Carlo (MC) simulations. However the long computation time of such methods hinders their use in clinical routine. This work aims to develop a fast multipurpose Monte Carlo simulation tool for proton therapy using massively parallel central processing unit (CPU) architectures. A new Monte Carlo, called MCsquare (many-core Monte Carlo), has been designed and optimized for the last generation of Intel Xeon processors and Intel Xeon Phi coprocessors. These massively parallel architectures offer the flexibility and the computational power suitable to MC methods. The class-II condensed history algorithm of MCsquare provides a fast and yet accurate method of simulating heavy charged particles such as protons, deuterons, and alphas inside voxelized geometries. Hard ionizations, with energy losses above a user-specified threshold, are simulated individually while soft events are regrouped in a multiple scattering theory. Elastic and inelastic nuclear interactions are sampled from ICRU 63 differential cross sections, thereby allowing for the computation of prompt gamma emission profiles. MCsquare has been benchmarked with the gate/geant4 Monte Carlo application for homogeneous and heterogeneous geometries. Comparisons with gate/geant4 for various geometries show deviations within 2%-1 mm. In spite of the limited memory bandwidth of the coprocessor simulation time is below 25 s for 10(7) primary 200 MeV protons in average soft tissues using all Xeon Phi and CPU resources embedded in a single desktop unit. MCsquare exploits the flexibility of CPU architectures to provide a multipurpose MC simulation tool. Optimized code enables the use of accurate MC calculation within a reasonable computation time, adequate for clinical practice. MCsquare also simulates prompt gamma emission and can thus be used also for in vivo range verification.

WE-AB-204-11: Development of a Nuclear Medicine Dosimetry Module for the GPU-Based Monte Carlo Code ARCHER

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, T; Lin, H; Xu, X

Purpose: To develop a nuclear medicine dosimetry module for the GPU-based Monte Carlo code ARCHER. Methods: We have developed a nuclear medicine dosimetry module for the fast Monte Carlo code ARCHER. The coupled electron-photon Monte Carlo transport kernel included in ARCHER is built upon the Dose Planning Method code (DPM). The developed module manages the radioactive decay simulation by consecutively tracking several types of radiation on a per disintegration basis using the statistical sampling method. Optimization techniques such as persistent threads and prefetching are studied and implemented. The developed module is verified against the VIDA code, which is based onmore » Geant4 toolkit and has previously been verified against OLINDA/EXM. A voxelized geometry is used in the preliminary test: a sphere made of ICRP soft tissue is surrounded by a box filled with water. Uniform activity distribution of I-131 is assumed in the sphere. Results: The self-absorption dose factors (mGy/MBqs) of the sphere with varying diameters are calculated by ARCHER and VIDA respectively. ARCHER’s result is in agreement with VIDA’s that are obtained from a previous publication. VIDA takes hours of CPU time to finish the computation, while it takes ARCHER 4.31 seconds for the 12.4-cm uniform activity sphere case. For a fairer CPU-GPU comparison, more effort will be made to eliminate the algorithmic differences. Conclusion: The coupled electron-photon Monte Carlo code ARCHER has been extended to radioactive decay simulation for nuclear medicine dosimetry. The developed code exhibits good performance in our preliminary test. The GPU-based Monte Carlo code is developed with grant support from the National Institute of Biomedical Imaging and Bioengineering through an R01 grant (R01EB015478)« less

An evaluation of solution algorithms and numerical approximation methods for modeling an ion exchange process

NASA Astrophysics Data System (ADS)

Bu, Sunyoung; Huang, Jingfang; Boyer, Treavor H.; Miller, Cass T.

2010-07-01

The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte-Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward difference formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte-Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications.

SU-F-SPS-11: The Dosimetric Comparison of Truebeam 2.0 and Cyberknife M6 Treatment Plans for Brain SRS Treatment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mabhouti, H; Sanli, E; Cebe, M

Purpose: Brain stereotactic radiosurgery involves the use of precisely directed, single session radiation to create a desired radiobiologic response within the brain target with acceptable minimal effects on surrounding structures or tissues. In this study, the dosimetric comparison of Truebeam 2.0 and Cyberknife M6 treatment plans were made. Methods: For Truebeam 2.0 machine, treatment planning were done using 2 full arc VMAT technique with 6 FFF beam on the CT scan of Randophantom simulating the treatment of sterotactic treatments for one brain metastasis. The dose distribution were calculated using Eclipse treatment planning system with Acuros XB algorithm. The treatment planningmore » of the same target were also done for Cyberknife M6 machine with Multiplan treatment planning system using Monte Carlo algorithm. Using the same film batch, the net OD to dose calibration curve was obtained using both machine by delivering 0- 800 cGy. Films were scanned 48 hours after irradiation using an Epson 1000XL flatbed scanner. Dose distribution were measured using EBT3 film dosimeter. The measured and calculated doses were compared. Results: The dose distribution in the target and 2 cm beyond the target edge were calculated on TPSs and measured using EBT3 film. For cyberknife plans, the gamma analysis passing rates between measured and calculated dose distributions were 99.2% and 96.7% for target and peripheral region of target respectively. For Truebeam plans, the gamma analysis passing rates were 99.1% and 95.5% for target and peripheral region of target respectively. Conclusion: Although, target dose distribution calculated accurately by Acuros XB and Monte Carlo algorithms, Monte carlo calculation algorithm predicts dose distribution around the peripheral region of target more accurately than Acuros algorithm.« less

Improved algorithm for estimating optical properties of food and biological materials using spatially-resolved diffuse reflectance

USDA-ARS?s Scientific Manuscript database

In this research, the inverse algorithm for estimating optical properties of food and biological materials from spatially-resolved diffuse reflectance was optimized in terms of data smoothing, normalization and spatial region of reflectance profile for curve fitting. Monte Carlo simulation was used ...

Monte Carlo simulations of time-of-flight PET with double-ended readout: calibration, coincidence resolving times and statistical lower bounds

PubMed Central

Derenzo, Stephen E

2017-01-01

This paper demonstrates through Monte Carlo simulations that a practical positron emission tomograph with (1) deep scintillators for efficient detection, (2) double-ended readout for depth-of-interaction information, (3) fixed-level analog triggering, and (4) accurate calibration and timing data corrections can achieve a coincidence resolving time (CRT) that is not far above the statistical lower bound. One Monte Carlo algorithm simulates a calibration procedure that uses data from a positron point source. Annihilation events with an interaction near the entrance surface of one scintillator are selected, and data from the two photodetectors on the other scintillator provide depth-dependent timing corrections. Another Monte Carlo algorithm simulates normal operation using these corrections and determines the CRT. A third Monte Carlo algorithm determines the CRT statistical lower bound by generating a series of random interaction depths, and for each interaction a set of random photoelectron times for each of the two photodetectors. The most likely interaction times are determined by shifting the depth-dependent probability density function to maximize the joint likelihood for all the photoelectron times in each set. Example calculations are tabulated for different numbers of photoelectrons and photodetector time jitters for three 3 × 3 × 30 mm3 scintillators: Lu2SiO5:Ce,Ca (LSO), LaBr3:Ce, and a hypothetical ultra-fast scintillator. To isolate the factors that depend on the scintillator length and the ability to estimate the DOI, CRT values are tabulated for perfect scintillator-photodetectors. For LSO with 4000 photoelectrons and single photoelectron time jitter of the photodetector J = 0.2 ns (FWHM), the CRT value using the statistically weighted average of corrected trigger times is 0.098 ns FWHM and the statistical lower bound is 0.091 ns FWHM. For LaBr3:Ce with 8000 photoelectrons and J = 0.2 ns FWHM, the CRT values are 0.070 and 0.063 ns FWHM, respectively. For the ultra-fast scintillator with 1 ns decay time, 4000 photoelectrons, and J = 0.2 ns FWHM, the CRT values are 0.021 and 0.017 ns FWHM, respectively. The examples also show that calibration and correction for depth-dependent variations in pulse height and in annihilation and optical photon transit times are necessary to achieve these CRT values. PMID:28327464

Monte Carlo simulations of time-of-flight PET with double-ended readout: calibration, coincidence resolving times and statistical lower bounds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Derenzo, Stephen E.

Here, this paper demonstrates through Monte Carlo simulations that a practical positron emission tomograph with (1) deep scintillators for efficient detection, (2) double-ended readout for depth-of-interaction information, (3) fixed-level analog triggering, and (4) accurate calibration and timing data corrections can achieve a coincidence resolving time (CRT) that is not far above the statistical lower bound. One Monte Carlo algorithm simulates a calibration procedure that uses data from a positron point source. Annihilation events with an interaction near the entrance surface of one scintillator are selected, and data from the two photodetectors on the other scintillator provide depth-dependent timing corrections. Anothermore » Monte Carlo algorithm simulates normal operation using these corrections and determines the CRT. A third Monte Carlo algorithm determines the CRT statistical lower bound by generating a series of random interaction depths, and for each interaction a set of random photoelectron times for each of the two photodetectors. The most likely interaction times are determined by shifting the depth-dependent probability density function to maximize the joint likelihood for all the photoelectron times in each set. Example calculations are tabulated for different numbers of photoelectrons and photodetector time jitters for three 3 × 3 × 30 mm 3 scintillators: Lu 2SiO 5 :Ce,Ca (LSO), LaBr 3:Ce, and a hypothetical ultra-fast scintillator. To isolate the factors that depend on the scintillator length and the ability to estimate the DOI, CRT values are tabulated for perfect scintillator-photodetectors. For LSO with 4000 photoelectrons and single photoelectron time jitter of the photodetector J = 0.2 ns (FWHM), the CRT value using the statistically weighted average of corrected trigger times is 0.098 ns FWHM and the statistical lower bound is 0.091 ns FWHM. For LaBr 3:Ce with 8000 photoelectrons and J = 0.2 ns FWHM, the CRT values are 0.070 and 0.063 ns FWHM, respectively. For the ultra-fast scintillator with 1 ns decay time, 4000 photoelectrons, and J = 0.2 ns FWHM, the CRT values are 0.021 and 0.017 ns FWHM, respectively. Lastly, the examples also show that calibration and correction for depth-dependent variations in pulse height and in annihilation and optical photon transit times are necessary to achieve these CRT values.« less

Monte Carlo simulations of time-of-flight PET with double-ended readout: calibration, coincidence resolving times and statistical lower bounds

DOE PAGES

Derenzo, Stephen E.

2017-04-11

Here, this paper demonstrates through Monte Carlo simulations that a practical positron emission tomograph with (1) deep scintillators for efficient detection, (2) double-ended readout for depth-of-interaction information, (3) fixed-level analog triggering, and (4) accurate calibration and timing data corrections can achieve a coincidence resolving time (CRT) that is not far above the statistical lower bound. One Monte Carlo algorithm simulates a calibration procedure that uses data from a positron point source. Annihilation events with an interaction near the entrance surface of one scintillator are selected, and data from the two photodetectors on the other scintillator provide depth-dependent timing corrections. Anothermore » Monte Carlo algorithm simulates normal operation using these corrections and determines the CRT. A third Monte Carlo algorithm determines the CRT statistical lower bound by generating a series of random interaction depths, and for each interaction a set of random photoelectron times for each of the two photodetectors. The most likely interaction times are determined by shifting the depth-dependent probability density function to maximize the joint likelihood for all the photoelectron times in each set. Example calculations are tabulated for different numbers of photoelectrons and photodetector time jitters for three 3 × 3 × 30 mm 3 scintillators: Lu 2SiO 5 :Ce,Ca (LSO), LaBr 3:Ce, and a hypothetical ultra-fast scintillator. To isolate the factors that depend on the scintillator length and the ability to estimate the DOI, CRT values are tabulated for perfect scintillator-photodetectors. For LSO with 4000 photoelectrons and single photoelectron time jitter of the photodetector J = 0.2 ns (FWHM), the CRT value using the statistically weighted average of corrected trigger times is 0.098 ns FWHM and the statistical lower bound is 0.091 ns FWHM. For LaBr 3:Ce with 8000 photoelectrons and J = 0.2 ns FWHM, the CRT values are 0.070 and 0.063 ns FWHM, respectively. For the ultra-fast scintillator with 1 ns decay time, 4000 photoelectrons, and J = 0.2 ns FWHM, the CRT values are 0.021 and 0.017 ns FWHM, respectively. Lastly, the examples also show that calibration and correction for depth-dependent variations in pulse height and in annihilation and optical photon transit times are necessary to achieve these CRT values.« less

Monte Carlo MP2 on Many Graphical Processing Units.

PubMed

Doran, Alexander E; Hirata, So

2016-10-11

In the Monte Carlo second-order many-body perturbation (MC-MP2) method, the long sum-of-product matrix expression of the MP2 energy, whose literal evaluation may be poorly scalable, is recast into a single high-dimensional integral of functions of electron pair coordinates, which is evaluated by the scalable method of Monte Carlo integration. The sampling efficiency is further accelerated by the redundant-walker algorithm, which allows a maximal reuse of electron pairs. Here, a multitude of graphical processing units (GPUs) offers a uniquely ideal platform to expose multilevel parallelism: fine-grain data-parallelism for the redundant-walker algorithm in which millions of threads compute and share orbital amplitudes on each GPU; coarse-grain instruction-parallelism for near-independent Monte Carlo integrations on many GPUs with few and infrequent interprocessor communications. While the efficiency boost by the redundant-walker algorithm on central processing units (CPUs) grows linearly with the number of electron pairs and tends to saturate when the latter exceeds the number of orbitals, on a GPU it grows quadratically before it increases linearly and then eventually saturates at a much larger number of pairs. This is because the orbital constructions are nearly perfectly parallelized on a GPU and thus completed in a near-constant time regardless of the number of pairs. In consequence, an MC-MP2/cc-pVDZ calculation of a benzene dimer is 2700 times faster on 256 GPUs (using 2048 electron pairs) than on two CPUs, each with 8 cores (which can use only up to 256 pairs effectively). We also numerically determine that the cost to achieve a given relative statistical uncertainty in an MC-MP2 energy increases as O(n 3 ) or better with system size n, which may be compared with the O(n 5 ) scaling of the conventional implementation of deterministic MP2. We thus establish the scalability of MC-MP2 with both system and computer sizes.

An Improved Method of Heterogeneity Compensation for the Convolution / Superposition Algorithm

NASA Astrophysics Data System (ADS)

Jacques, Robert; McNutt, Todd

2014-03-01

Purpose: To improve the accuracy of convolution/superposition (C/S) in heterogeneous material by developing a new algorithm: heterogeneity compensated superposition (HCS). Methods: C/S has proven to be a good estimator of the dose deposited in a homogeneous volume. However, near heterogeneities electron disequilibrium occurs, leading to the faster fall-off and re-buildup of dose. We propose to filter the actual patient density in a position and direction sensitive manner, allowing the dose deposited near interfaces to be increased or decreased relative to C/S. We implemented the effective density function as a multivariate first-order recursive filter and incorporated it into GPU-accelerated, multi-energetic C/S implementation. We compared HCS against C/S using the ICCR 2000 Monte-Carlo accuracy benchmark, 23 similar accuracy benchmarks and 5 patient cases. Results: Multi-energetic HCS increased the dosimetric accuracy for the vast majority of voxels; in many cases near Monte-Carlo results were achieved. We defined the per-voxel error, %|mm, as the minimum of the distance to agreement in mm and the dosimetric percentage error relative to the maximum MC dose. HCS improved the average mean error by 0.79 %|mm for the patient volumes; reducing the average mean error from 1.93 %|mm to 1.14 %|mm. Very low densities (i.e. < 0.1 g / cm3) remained problematic, but may be solvable with a better filter function. Conclusions: HCS improved upon C/S's density scaled heterogeneity correction with a position and direction sensitive density filter. This method significantly improved the accuracy of the GPU based algorithm reaching the accuracy levels of Monte Carlo based methods with performance in a few tenths of seconds per beam. Acknowledgement: Funding for this research was provided by the NSF Cooperative Agreement EEC9731748, Elekta / IMPAC Medical Systems, Inc. and the Johns Hopkins University. James Satterthwaite provided the Monte Carlo benchmark simulations.

TU-F-CAMPUS-T-05: A Cloud-Based Monte Carlo Dose Calculation for Electron Cutout Factors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mitchell, T; Bush, K

Purpose: For electron cutouts of smaller sizes, it is necessary to verify electron cutout factors due to perturbations in electron scattering. Often, this requires a physical measurement using a small ion chamber, diode, or film. The purpose of this study is to develop a fast Monte Carlo based dose calculation framework that requires only a smart phone photograph of the cutout and specification of the SSD and energy to determine the electron cutout factor, with the ultimate goal of making this cloud-based calculation widely available to the medical physics community. Methods: The algorithm uses a pattern recognition technique to identifymore » the corners of the cutout in the photograph as shown in Figure 1. It then corrects for variations in perspective, scaling, and translation of the photograph introduced by the user’s positioning of the camera. Blob detection is used to identify the portions of the cutout which comprise the aperture and the portions which are cutout material. This information is then used define physical densities of the voxels used in the Monte Carlo dose calculation algorithm as shown in Figure 2, and select a particle source from a pre-computed library of phase-spaces scored above the cutout. The electron cutout factor is obtained by taking a ratio of the maximum dose delivered with the cutout in place to the dose delivered under calibration/reference conditions. Results: The algorithm has been shown to successfully identify all necessary features of the electron cutout to perform the calculation. Subsequent testing will be performed to compare the Monte Carlo results with a physical measurement. Conclusion: A simple, cloud-based method of calculating electron cutout factors could eliminate the need for physical measurements and substantially reduce the time required to properly assure accurate dose delivery.« less

Virtual Network Embedding via Monte Carlo Tree Search.

PubMed

Haeri, Soroush; Trajkovic, Ljiljana

2018-02-01

Network virtualization helps overcome shortcomings of the current Internet architecture. The virtualized network architecture enables coexistence of multiple virtual networks (VNs) on an existing physical infrastructure. VN embedding (VNE) problem, which deals with the embedding of VN components onto a physical network, is known to be -hard. In this paper, we propose two VNE algorithms: MaVEn-M and MaVEn-S. MaVEn-M employs the multicommodity flow algorithm for virtual link mapping while MaVEn-S uses the shortest-path algorithm. They formalize the virtual node mapping problem by using the Markov decision process (MDP) framework and devise action policies (node mappings) for the proposed MDP using the Monte Carlo tree search algorithm. Service providers may adjust the execution time of the MaVEn algorithms based on the traffic load of VN requests. The objective of the algorithms is to maximize the profit of infrastructure providers. We develop a discrete event VNE simulator to implement and evaluate performance of MaVEn-M, MaVEn-S, and several recently proposed VNE algorithms. We introduce profitability as a new performance metric that captures both acceptance and revenue to cost ratios. Simulation results show that the proposed algorithms find more profitable solutions than the existing algorithms. Given additional computation time, they further improve embedding solutions.

New Tools to Prepare ACE Cross-section Files for MCNP Analytic Test Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brown, Forrest B.

Monte Carlo calculations using one-group cross sections, multigroup cross sections, or simple continuous energy cross sections are often used to: (1) verify production codes against known analytical solutions, (2) verify new methods and algorithms that do not involve detailed collision physics, (3) compare Monte Carlo calculation methods with deterministic methods, and (4) teach fundamentals to students. In this work we describe 2 new tools for preparing the ACE cross-section files to be used by MCNP ® for these analytic test problems, simple_ace.pl and simple_ace_mg.pl.

Monte Carlo errors with less errors

NASA Astrophysics Data System (ADS)

Wolff, Ulli; Alpha Collaboration

2004-01-01

We explain in detail how to estimate mean values and assess statistical errors for arbitrary functions of elementary observables in Monte Carlo simulations. The method is to estimate and sum the relevant autocorrelation functions, which is argued to produce more certain error estimates than binning techniques and hence to help toward a better exploitation of expensive simulations. An effective integrated autocorrelation time is computed which is suitable to benchmark efficiencies of simulation algorithms with regard to specific observables of interest. A Matlab code is offered for download that implements the method. It can also combine independent runs (replica) allowing to judge their consistency.

Markov Chain Monte Carlo Used in Parameter Inference of Magnetic Resonance Spectra

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hock, Kiel; Earle, Keith

2016-02-06

In this paper, we use Boltzmann statistics and the maximum likelihood distribution derived from Bayes’ Theorem to infer parameter values for a Pake Doublet Spectrum, a lineshape of historical significance and contemporary relevance for determining distances between interacting magnetic dipoles. A Metropolis Hastings Markov Chain Monte Carlo algorithm is implemented and designed to find the optimum parameter set and to estimate parameter uncertainties. In conclusion, the posterior distribution allows us to define a metric on parameter space that induces a geometry with negative curvature that affects the parameter uncertainty estimates, particularly for spectra with low signal to noise.

Driven-dissipative quantum Monte Carlo method for open quantum systems

NASA Astrophysics Data System (ADS)

Nagy, Alexandra; Savona, Vincenzo

2018-05-01

We develop a real-time full configuration-interaction quantum Monte Carlo approach to model driven-dissipative open quantum systems with Markovian system-bath coupling. The method enables stochastic sampling of the Liouville-von Neumann time evolution of the density matrix thanks to a massively parallel algorithm, thus providing estimates of observables on the nonequilibrium steady state. We present the underlying theory and introduce an initiator technique and importance sampling to reduce the statistical error. Finally, we demonstrate the efficiency of our approach by applying it to the driven-dissipative two-dimensional X Y Z spin-1/2 model on a lattice.

Wavelet Monte Carlo dynamics: A new algorithm for simulating the hydrodynamics of interacting Brownian particles

NASA Astrophysics Data System (ADS)

Dyer, Oliver T.; Ball, Robin C.

2017-03-01

We develop a new algorithm for the Brownian dynamics of soft matter systems that evolves time by spatially correlated Monte Carlo moves. The algorithm uses vector wavelets as its basic moves and produces hydrodynamics in the low Reynolds number regime propagated according to the Oseen tensor. When small moves are removed, the correlations closely approximate the Rotne-Prager tensor, itself widely used to correct for deficiencies in Oseen. We also include plane wave moves to provide the longest range correlations, which we detail for both infinite and periodic systems. The computational cost of the algorithm scales competitively with the number of particles simulated, N, scaling as N In N in homogeneous systems and as N in dilute systems. In comparisons to established lattice Boltzmann and Brownian dynamics algorithms, the wavelet method was found to be only a factor of order 1 times more expensive than the cheaper lattice Boltzmann algorithm in marginally semi-dilute simulations, while it is significantly faster than both algorithms at large N in dilute simulations. We also validate the algorithm by checking that it reproduces the correct dynamics and equilibrium properties of simple single polymer systems, as well as verifying the effect of periodicity on the mobility tensor.

CYBER 200 Applications Seminar

NASA Technical Reports Server (NTRS)

Gary, J. P. (Compiler)

1984-01-01

Applications suited for the CYBER 200 digital computer are discussed. Various areas of application including meteorology, algorithms, fluid dynamics, monte carlo methods, petroleum, electronic circuit simulation, biochemistry, lattice gauge theory, economics and ray tracing are discussed.

Reference hypernetted chain theory for ferrofluid bilayer: Distribution functions compared with Monte Carlo

NASA Astrophysics Data System (ADS)

Polyakov, Evgeny A.; Vorontsov-Velyaminov, Pavel N.

2014-08-01

Properties of ferrofluid bilayer (modeled as a system of two planar layers separated by a distance h and each layer carrying a soft sphere dipolar liquid) are calculated in the framework of inhomogeneous Ornstein-Zernike equations with reference hypernetted chain closure (RHNC). The bridge functions are taken from a soft sphere (1/r12) reference system in the pressure-consistent closure approximation. In order to make the RHNC problem tractable, the angular dependence of the correlation functions is expanded into special orthogonal polynomials according to Lado. The resulting equations are solved using the Newton-GRMES algorithm as implemented in the public-domain solver NITSOL. Orientational densities and pair distribution functions of dipoles are compared with Monte Carlo simulation results. A numerical algorithm for the Fourier-Hankel transform of any positive integer order on a uniform grid is presented.

Exploring Neutrino Oscillation Parameter Space with a Monte Carlo Algorithm

NASA Astrophysics Data System (ADS)

Espejel, Hugo; Ernst, David; Cogswell, Bernadette; Latimer, David

2015-04-01

The χ2 (or likelihood) function for a global analysis of neutrino oscillation data is first calculated as a function of the neutrino mixing parameters. A computational challenge is to obtain the minima or the allowed regions for the mixing parameters. The conventional approach is to calculate the χ2 (or likelihood) function on a grid for a large number of points, and then marginalize over the likelihood function. As the number of parameters increases with the number of neutrinos, making the calculation numerically efficient becomes necessary. We implement a new Monte Carlo algorithm (D. Foreman-Mackey, D. W. Hogg, D. Lang and J. Goodman, Publications of the Astronomical Society of the Pacific, 125 306 (2013)) to determine its computational efficiency at finding the minima and allowed regions. We examine a realistic example to compare the historical and the new methods.

Markov Chain Monte Carlo Bayesian Learning for Neural Networks

NASA Technical Reports Server (NTRS)

Goodrich, Michael S.

2011-01-01

Conventional training methods for neural networks involve starting al a random location in the solution space of the network weights, navigating an error hyper surface to reach a minimum, and sometime stochastic based techniques (e.g., genetic algorithms) to avoid entrapment in a local minimum. It is further typically necessary to preprocess the data (e.g., normalization) to keep the training algorithm on course. Conversely, Bayesian based learning is an epistemological approach concerned with formally updating the plausibility of competing candidate hypotheses thereby obtaining a posterior distribution for the network weights conditioned on the available data and a prior distribution. In this paper, we developed a powerful methodology for estimating the full residual uncertainty in network weights and therefore network predictions by using a modified Jeffery's prior combined with a Metropolis Markov Chain Monte Carlo method.

Bayesian forecasting and uncertainty quantifying of stream flows using Metropolis-Hastings Markov Chain Monte Carlo algorithm

NASA Astrophysics Data System (ADS)

Wang, Hongrui; Wang, Cheng; Wang, Ying; Gao, Xiong; Yu, Chen

2017-06-01

This paper presents a Bayesian approach using Metropolis-Hastings Markov Chain Monte Carlo algorithm and applies this method for daily river flow rate forecast and uncertainty quantification for Zhujiachuan River using data collected from Qiaotoubao Gage Station and other 13 gage stations in Zhujiachuan watershed in China. The proposed method is also compared with the conventional maximum likelihood estimation (MLE) for parameter estimation and quantification of associated uncertainties. While the Bayesian method performs similarly in estimating the mean value of daily flow rate, it performs over the conventional MLE method on uncertainty quantification, providing relatively narrower reliable interval than the MLE confidence interval and thus more precise estimation by using the related information from regional gage stations. The Bayesian MCMC method might be more favorable in the uncertainty analysis and risk management.

Experimental evaluation of a GPU-based Monte Carlo dose calculation algorithm in the Monaco treatment planning system.

PubMed

Paudel, Moti R; Kim, Anthony; Sarfehnia, Arman; Ahmad, Sayed B; Beachey, David J; Sahgal, Arjun; Keller, Brian M

2016-11-08

A new GPU-based Monte Carlo dose calculation algorithm (GPUMCD), devel-oped by the vendor Elekta for the Monaco treatment planning system (TPS), is capable of modeling dose for both a standard linear accelerator and an Elekta MRI linear accelerator. We have experimentally evaluated this algorithm for a standard Elekta Agility linear accelerator. A beam model was developed in the Monaco TPS (research version 5.09.06) using the commissioned beam data for a 6 MV Agility linac. A heterogeneous phantom representing several scenarios - tumor-in-lung, lung, and bone-in-tissue - was designed and built. Dose calculations in Monaco were done using both the current clinical Monte Carlo algorithm, XVMC, and the new GPUMCD algorithm. Dose calculations in a Pinnacle TPS were also produced using the collapsed cone convolution (CCC) algorithm with heterogeneity correc-tion. Calculations were compared with the measured doses using an ionization chamber (A1SL) and Gafchromic EBT3 films for 2 × 2 cm2, 5 × 5 cm2, and 10 × 10 cm2 field sizes. The percentage depth doses (PDDs) calculated by XVMC and GPUMCD in a homogeneous solid water phantom were within 2%/2 mm of film measurements and within 1% of ion chamber measurements. For the tumor-in-lung phantom, the calculated doses were within 2.5%/2.5 mm of film measurements for GPUMCD. For the lung phantom, doses calculated by all of the algorithms were within 3%/3 mm of film measurements, except for the 2 × 2 cm2 field size where the CCC algorithm underestimated the depth dose by ~ 5% in a larger extent of the lung region. For the bone phantom, all of the algorithms were equivalent and calculated dose to within 2%/2 mm of film measurements, except at the interfaces. Both GPUMCD and XVMC showed interface effects, which were more pronounced for GPUMCD and were comparable to film measurements, whereas the CCC algorithm showed these effects poorly. © 2016 The Authors.

A clinical study of lung cancer dose calculation accuracy with Monte Carlo simulation.

PubMed

Zhao, Yanqun; Qi, Guohai; Yin, Gang; Wang, Xianliang; Wang, Pei; Li, Jian; Xiao, Mingyong; Li, Jie; Kang, Shengwei; Liao, Xiongfei

2014-12-16

The accuracy of dose calculation is crucial to the quality of treatment planning and, consequently, to the dose delivered to patients undergoing radiation therapy. Current general calculation algorithms such as Pencil Beam Convolution (PBC) and Collapsed Cone Convolution (CCC) have shortcomings in regard to severe inhomogeneities, particularly in those regions where charged particle equilibrium does not hold. The aim of this study was to evaluate the accuracy of the PBC and CCC algorithms in lung cancer radiotherapy using Monte Carlo (MC) technology. Four treatment plans were designed using Oncentra Masterplan TPS for each patient. Two intensity-modulated radiation therapy (IMRT) plans were developed using the PBC and CCC algorithms, and two three-dimensional conformal therapy (3DCRT) plans were developed using the PBC and CCC algorithms. The DICOM-RT files of the treatment plans were exported to the Monte Carlo system to recalculate. The dose distributions of GTV, PTV and ipsilateral lung calculated by the TPS and MC were compared. For 3DCRT and IMRT plans, the mean dose differences for GTV between the CCC and MC increased with decreasing of the GTV volume. For IMRT, the mean dose differences were found to be higher than that of 3DCRT. The CCC algorithm overestimated the GTV mean dose by approximately 3% for IMRT. For 3DCRT plans, when the volume of the GTV was greater than 100 cm(3), the mean doses calculated by CCC and MC almost have no difference. PBC shows large deviations from the MC algorithm. For the dose to the ipsilateral lung, the CCC algorithm overestimated the dose to the entire lung, and the PBC algorithm overestimated V20 but underestimated V5; the difference in V10 was not statistically significant. PBC substantially overestimates the dose to the tumour, but the CCC is similar to the MC simulation. It is recommended that the treatment plans for lung cancer be developed using an advanced dose calculation algorithm other than PBC. MC can accurately calculate the dose distribution in lung cancer and can provide a notably effective tool for benchmarking the performance of other dose calculation algorithms within patients.

FitSKIRT: genetic algorithms to automatically fit dusty galaxies with a Monte Carlo radiative transfer code

NASA Astrophysics Data System (ADS)

De Geyter, G.; Baes, M.; Fritz, J.; Camps, P.

2013-02-01

We present FitSKIRT, a method to efficiently fit radiative transfer models to UV/optical images of dusty galaxies. These images have the advantage that they have better spatial resolution compared to FIR/submm data. FitSKIRT uses the GAlib genetic algorithm library to optimize the output of the SKIRT Monte Carlo radiative transfer code. Genetic algorithms prove to be a valuable tool in handling the multi- dimensional search space as well as the noise induced by the random nature of the Monte Carlo radiative transfer code. FitSKIRT is tested on artificial images of a simulated edge-on spiral galaxy, where we gradually increase the number of fitted parameters. We find that we can recover all model parameters, even if all 11 model parameters are left unconstrained. Finally, we apply the FitSKIRT code to a V-band image of the edge-on spiral galaxy NGC 4013. This galaxy has been modeled previously by other authors using different combinations of radiative transfer codes and optimization methods. Given the different models and techniques and the complexity and degeneracies in the parameter space, we find reasonable agreement between the different models. We conclude that the FitSKIRT method allows comparison between different models and geometries in a quantitative manner and minimizes the need of human intervention and biasing. The high level of automation makes it an ideal tool to use on larger sets of observed data.

High-Throughput Characterization of Porous Materials Using Graphics Processing Units

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Jihan; Martin, Richard L.; Rübel, Oliver

We have developed a high-throughput graphics processing units (GPU) code that can characterize a large database of crystalline porous materials. In our algorithm, the GPU is utilized to accelerate energy grid calculations where the grid values represent interactions (i.e., Lennard-Jones + Coulomb potentials) between gas molecules (i.e., CHmore » $$_{4}$$ and CO$$_{2}$$) and material's framework atoms. Using a parallel flood fill CPU algorithm, inaccessible regions inside the framework structures are identified and blocked based on their energy profiles. Finally, we compute the Henry coefficients and heats of adsorption through statistical Widom insertion Monte Carlo moves in the domain restricted to the accessible space. The code offers significant speedup over a single core CPU code and allows us to characterize a set of porous materials at least an order of magnitude larger than ones considered in earlier studies. For structures selected from such a prescreening algorithm, full adsorption isotherms can be calculated by conducting multiple grand canonical Monte Carlo simulations concurrently within the GPU.« less

Searching for efficient Markov chain Monte Carlo proposal kernels

PubMed Central

Yang, Ziheng; Rodríguez, Carlos E.

2013-01-01

Markov chain Monte Carlo (MCMC) or the Metropolis–Hastings algorithm is a simulation algorithm that has made modern Bayesian statistical inference possible. Nevertheless, the efficiency of different Metropolis–Hastings proposal kernels has rarely been studied except for the Gaussian proposal. Here we propose a unique class of Bactrian kernels, which avoid proposing values that are very close to the current value, and compare their efficiency with a number of proposals for simulating different target distributions, with efficiency measured by the asymptotic variance of a parameter estimate. The uniform kernel is found to be more efficient than the Gaussian kernel, whereas the Bactrian kernel is even better. When optimal scales are used for both, the Bactrian kernel is at least 50% more efficient than the Gaussian. Implementation in a Bayesian program for molecular clock dating confirms the general applicability of our results to generic MCMC algorithms. Our results refute a previous claim that all proposals had nearly identical performance and will prompt further research into efficient MCMC proposals. PMID:24218600

The Wang-Landau Sampling Algorithm

NASA Astrophysics Data System (ADS)

Landau, David P.

2003-03-01

Over the past several decades Monte Carlo simulations[1] have evolved into a powerful tool for the study of wide-ranging problems in statistical/condensed matter physics. Standard methods sample the probability distribution for the states of the system, usually in the canonical ensemble, and enormous improvements have been made in performance through the implementation of novel algorithms. Nonetheless, difficulties arise near phase transitions, either due to critical slowing down near 2nd order transitions or to metastability near 1st order transitions, thus limiting the applicability of the method. We shall describe a new and different Monte Carlo approach [2] that uses a random walk in energy space to determine the density of states directly. Once the density of states is estimated, all thermodynamic properties can be calculated at all temperatures. This approach can be extended to multi-dimensional parameter spaces and has already found use in classical models of interacting particles including systems with complex energy landscapes, e.g., spin glasses, protein folding models, etc., as well as for quantum models. 1. A Guide to Monte Carlo Simulations in Statistical Physics, D. P. Landau and K. Binder (Cambridge U. Press, Cambridge, 2000). 2. Fugao Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001); Phys. Rev. E64, 056101-1 (2001).

Accuracy of tree diameter estimation from terrestrial laser scanning by circle-fitting methods

NASA Astrophysics Data System (ADS)

Koreň, Milan; Mokroš, Martin; Bucha, Tomáš

2017-12-01

This study compares the accuracies of diameter at breast height (DBH) estimations by three initial (minimum bounding box, centroid, and maximum distance) and two refining (Monte Carlo and optimal circle) circle-fitting methods The circle-fitting algorithms were evaluated in multi-scan mode and a simulated single-scan mode on 157 European beech trees (Fagus sylvatica L.). DBH measured by a calliper was used as reference data. Most of the studied circle-fitting algorithms significantly underestimated the mean DBH in both scanning modes. Only the Monte Carlo method in the single-scan mode significantly overestimated the mean DBH. The centroid method proved to be the least suitable and showed significantly different results from the other circle-fitting methods in both scanning modes. In multi-scan mode, the accuracy of the minimum bounding box method was not significantly different from the accuracies of the refining methods The accuracy of the maximum distance method was significantly different from the accuracies of the refining methods in both scanning modes. The accuracy of the Monte Carlo method was significantly different from the accuracy of the optimal circle method in only single-scan mode. The optimal circle method proved to be the most accurate circle-fitting method for DBH estimation from point clouds in both scanning modes.

Limited Memory Block Krylov Subspace Optimization for Computing Dominant Singular Value Decompositions

DTIC Science & Technology

2012-03-22

with performance profiles, Math. Program., 91 (2002), pp. 201–213. [6] P. DRINEAS, R. KANNAN, AND M. W. MAHONEY , Fast Monte Carlo algorithms for matrices...computing invariant subspaces of non-Hermitian matri- ces, Numer. Math., 25 ( 1975 /76), pp. 123–136. [25] , Matrix algorithms Vol. II: Eigensystems

Using Computer-Based "Experiments" in the Analysis of Chemical Reaction Equilibria

ERIC Educational Resources Information Center

Li, Zhao; Corti, David S.

2018-01-01

The application of the Reaction Monte Carlo (RxMC) algorithm to standard textbook problems in chemical reaction equilibria is discussed. The RxMC method is a molecular simulation algorithm for studying the equilibrium properties of reactive systems, and therefore provides the opportunity to develop computer-based "experiments" for the…

“Skin-Core-Skin” Structure of Polymer Crystallization Investigated by Multiscale Simulation

PubMed Central

Ruan, Chunlei

2018-01-01

“Skin-core-skin” structure is a typical crystal morphology in injection products. Previous numerical works have rarely focused on crystal evolution; rather, they have mostly been based on the prediction of temperature distribution or crystallization kinetics. The aim of this work was to achieve the “skin-core-skin” structure and investigate the role of external flow and temperature fields on crystal morphology. Therefore, the multiscale algorithm was extended to the simulation of polymer crystallization in a pipe flow. The multiscale algorithm contains two parts: a collocated finite volume method at the macroscopic level and a morphological Monte Carlo method at the microscopic level. The SIMPLE (semi-implicit method for pressure linked equations) algorithm was used to calculate the polymeric model at the macroscopic level, while the Monte Carlo method with stochastic birth-growth process of spherulites and shish-kebabs was used at the microscopic level. Results show that our algorithm is valid to predict “skin-core-skin” structure, and the initial melt temperature and the maximum velocity of melt at the inlet mainly affects the morphology of shish-kebabs. PMID:29659516

A derivation and scalable implementation of the synchronous parallel kinetic Monte Carlo method for simulating long-time dynamics

NASA Astrophysics Data System (ADS)

Byun, Hye Suk; El-Naggar, Mohamed Y.; Kalia, Rajiv K.; Nakano, Aiichiro; Vashishta, Priya

2017-10-01

Kinetic Monte Carlo (KMC) simulations are used to study long-time dynamics of a wide variety of systems. Unfortunately, the conventional KMC algorithm is not scalable to larger systems, since its time scale is inversely proportional to the simulated system size. A promising approach to resolving this issue is the synchronous parallel KMC (SPKMC) algorithm, which makes the time scale size-independent. This paper introduces a formal derivation of the SPKMC algorithm based on local transition-state and time-dependent Hartree approximations, as well as its scalable parallel implementation based on a dual linked-list cell method. The resulting algorithm has achieved a weak-scaling parallel efficiency of 0.935 on 1024 Intel Xeon processors for simulating biological electron transfer dynamics in a 4.2 billion-heme system, as well as decent strong-scaling parallel efficiency. The parallel code has been used to simulate a lattice of cytochrome complexes on a bacterial-membrane nanowire, and it is broadly applicable to other problems such as computational synthesis of new materials.

A global reaction route mapping-based kinetic Monte Carlo algorithm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mitchell, Izaac; Page, Alister J., E-mail: sirle@chem.nagoya-u.ac.jp, E-mail: alister.page@newcastle.edu.au; Irle, Stephan, E-mail: sirle@chem.nagoya-u.ac.jp, E-mail: alister.page@newcastle.edu.au

2016-07-14

We propose a new on-the-fly kinetic Monte Carlo (KMC) method that is based on exhaustive potential energy surface searching carried out with the global reaction route mapping (GRRM) algorithm. Starting from any given equilibrium state, this GRRM-KMC algorithm performs a one-step GRRM search to identify all surrounding transition states. Intrinsic reaction coordinate pathways are then calculated to identify potential subsequent equilibrium states. Harmonic transition state theory is used to calculate rate constants for all potential pathways, before a standard KMC accept/reject selection is performed. The selected pathway is then used to propagate the system forward in time, which is calculatedmore » on the basis of 1st order kinetics. The GRRM-KMC algorithm is validated here in two challenging contexts: intramolecular proton transfer in malonaldehyde and surface carbon diffusion on an iron nanoparticle. We demonstrate that in both cases the GRRM-KMC method is capable of reproducing the 1st order kinetics observed during independent quantum chemical molecular dynamics simulations using the density-functional tight-binding potential.« less

Numerical heating in Particle-In-Cell simulations with Monte Carlo binary collisions

NASA Astrophysics Data System (ADS)

Alves, E. Paulo; Mori, Warren; Fiuza, Frederico

2017-10-01

The binary Monte Carlo collision (BMCC) algorithm is a robust and popular method to include Coulomb collision effects in Particle-in-Cell (PIC) simulations of plasmas. While a number of works have focused on extending the validity of the model to different physical regimes of temperature and density, little attention has been given to the fundamental coupling between PIC and BMCC algorithms. Here, we show that the coupling between PIC and BMCC algorithms can give rise to (nonphysical) numerical heating of the system, that can be far greater than that observed when these algorithms operate independently. This deleterious numerical heating effect can significantly impact the evolution of the simulated system particularly for long simulation times. In this work, we describe the source of this numerical heating, and derive scaling laws for the numerical heating rates based on the numerical parameters of PIC-BMCC simulations. We compare our theoretical scalings with PIC-BMCC numerical experiments, and discuss strategies to minimize this parasitic effect. This work is supported by DOE FES under FWP 100237 and 100182.

Development of a Monte Carlo Simulation for APD-Based PET Detectors Using a Continuous Scintillating Crystal

NASA Astrophysics Data System (ADS)

Clowes, P.; Mccallum, S.; Welch, A.

2006-10-01

We are currently developing a multilayer avalanche photodiode (APD)-based detector for use in positron emission tomography (PET), which utilizes thin continuous crystals. In this paper, we developed a Monte Carlo-based simulation to aid in the design of such detectors. We measured the performance of a detector comprising a single thin continuous crystal (3.1 mm times 9.5 mm times 9.5 mm) of lutetium yttrium ortho-silicate (LYSO) and an APD array (4times4) elements; each element 1.6 mm2 and on a 2.3 mm pitch. We showed that a spatial resolution of better than 2.12 mm is achievable throughout the crystal provided that we adopt a Statistics Based Positioning (SBP) Algorithm. We then used Monte Carlo simulation to model the behavior of the detector. The accuracy of the Monte Carlo simulation was verified by comparing measured and simulated parent datasets (PDS) for the SBP algorithm. These datasets consisted of data for point sources at 49 positions uniformly distributed over the detector area. We also calculated the noise in the detector circuit and verified this value by measurement. The noise value was included in the simulation. We show that the performance of the simulation closely matches the measured performance. The simulations were extended to investigate the effect of different noise levels on positioning accuracy. This paper showed that if modest improvements could be made in the circuit noise then positioning accuracy would be greatly improved. In summary, we have developed a model that can be used to simulate the performance of a variety of APD-based continuous crystal PET detectors

Development of Monte Carlo based real-time treatment planning system with fast calculation algorithm for boron neutron capture therapy.

PubMed

Takada, Kenta; Kumada, Hiroaki; Liem, Peng Hong; Sakurai, Hideyuki; Sakae, Takeji

2016-12-01

We simulated the effect of patient displacement on organ doses in boron neutron capture therapy (BNCT). In addition, we developed a faster calculation algorithm (NCT high-speed) to simulate irradiation more efficiently. We simulated dose evaluation for the standard irradiation position (reference position) using a head phantom. Cases were assumed where the patient body is shifted in lateral directions compared to the reference position, as well as in the direction away from the irradiation aperture. For three groups of neutron (thermal, epithermal, and fast), flux distribution using NCT high-speed with a voxelized homogeneous phantom was calculated. The three groups of neutron fluxes were calculated for the same conditions with Monte Carlo code. These calculated results were compared. In the evaluations of body movements, there were no significant differences even with shifting up to 9mm in the lateral directions. However, the dose decreased by about 10% with shifts of 9mm in a direction away from the irradiation aperture. When comparing both calculations in the phantom surface up to 3cm, the maximum differences between the fluxes calculated by NCT high-speed with those calculated by Monte Carlo code for thermal neutrons and epithermal neutrons were 10% and 18%, respectively. The time required for NCT high-speed code was about 1/10th compared to Monte Carlo calculation. In the evaluation, the longitudinal displacement has a considerable effect on the organ doses. We also achieved faster calculation of depth distribution of thermal neutron flux using NCT high-speed calculation code. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

TH-E-BRE-07: Development of Dose Calculation Error Predictors for a Widely Implemented Clinical Algorithm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Egan, A; Laub, W

2014-06-15

Purpose: Several shortcomings of the current implementation of the analytic anisotropic algorithm (AAA) may lead to dose calculation errors in highly modulated treatments delivered to highly heterogeneous geometries. Here we introduce a set of dosimetric error predictors that can be applied to a clinical treatment plan and patient geometry in order to identify high risk plans. Once a problematic plan is identified, the treatment can be recalculated with more accurate algorithm in order to better assess its viability. Methods: Here we focus on three distinct sources dosimetric error in the AAA algorithm. First, due to a combination of discrepancies inmore » smallfield beam modeling as well as volume averaging effects, dose calculated through small MLC apertures can be underestimated, while that behind small MLC blocks can overestimated. Second, due the rectilinear scaling of the Monte Carlo generated pencil beam kernel, energy is not properly transported through heterogeneities near, but not impeding, the central axis of the beamlet. And third, AAA overestimates dose in regions very low density (< 0.2 g/cm{sup 3}). We have developed an algorithm to detect the location and magnitude of each scenario within the patient geometry, namely the field-size index (FSI), the heterogeneous scatter index (HSI), and the lowdensity index (LDI) respectively. Results: Error indices successfully identify deviations between AAA and Monte Carlo dose distributions in simple phantom geometries. Algorithms are currently implemented in the MATLAB computing environment and are able to run on a typical RapidArc head and neck geometry in less than an hour. Conclusion: Because these error indices successfully identify each type of error in contrived cases, with sufficient benchmarking, this method can be developed into a clinical tool that may be able to help estimate AAA dose calculation errors and when it might be advisable to use Monte Carlo calculations.« less

Identification of moisture content in tobacco plant leaves using outlier sample eliminating algorithms and hyperspectral data.

PubMed

Sun, Jun; Zhou, Xin; Wu, Xiaohong; Zhang, Xiaodong; Li, Qinglin

2016-02-26

Fast identification of moisture content in tobacco plant leaves plays a key role in the tobacco cultivation industry and benefits the management of tobacco plant in the farm. In order to identify moisture content of tobacco plant leaves in a fast and nondestructive way, a method involving Mahalanobis distance coupled with Monte Carlo cross validation(MD-MCCV) was proposed to eliminate outlier sample in this study. The hyperspectral data of 200 tobacco plant leaf samples of 20 moisture gradients were obtained using FieldSpc(®) 3 spectrometer. Savitzky-Golay smoothing(SG), roughness penalty smoothing(RPS), kernel smoothing(KS) and median smoothing(MS) were used to preprocess the raw spectra. In addition, Mahalanobis distance(MD), Monte Carlo cross validation(MCCV) and Mahalanobis distance coupled to Monte Carlo cross validation(MD-MCCV) were applied to select the outlier sample of the raw spectrum and four smoothing preprocessing spectra. Successive projections algorithm (SPA) was used to extract the most influential wavelengths. Multiple Linear Regression (MLR) was applied to build the prediction models based on preprocessed spectra feature in characteristic wavelengths. The results showed that the preferably four prediction model were MD-MCCV-SG (Rp(2) = 0.8401 and RMSEP = 0.1355), MD-MCCV-RPS (Rp(2) = 0.8030 and RMSEP = 0.1274), MD-MCCV-KS (Rp(2) = 0.8117 and RMSEP = 0.1433), MD-MCCV-MS (Rp(2) = 0.9132 and RMSEP = 0.1162). MD-MCCV algorithm performed best among MD algorithm, MCCV algorithm and the method without sample pretreatment algorithm in the eliminating outlier sample from 20 different moisture gradients of tobacco plant leaves and MD-MCCV can be used to eliminate outlier sample in the spectral preprocessing. Copyright © 2016 Elsevier Inc. All rights reserved.

A comparison of Monte Carlo-based Bayesian parameter estimation methods for stochastic models of genetic networks

PubMed Central

Zaikin, Alexey; Míguez, Joaquín

2017-01-01

We compare three state-of-the-art Bayesian inference methods for the estimation of the unknown parameters in a stochastic model of a genetic network. In particular, we introduce a stochastic version of the paradigmatic synthetic multicellular clock model proposed by Ullner et al., 2007. By introducing dynamical noise in the model and assuming that the partial observations of the system are contaminated by additive noise, we enable a principled mechanism to represent experimental uncertainties in the synthesis of the multicellular system and pave the way for the design of probabilistic methods for the estimation of any unknowns in the model. Within this setup, we tackle the Bayesian estimation of a subset of the model parameters. Specifically, we compare three Monte Carlo based numerical methods for the approximation of the posterior probability density function of the unknown parameters given a set of partial and noisy observations of the system. The schemes we assess are the particle Metropolis-Hastings (PMH) algorithm, the nonlinear population Monte Carlo (NPMC) method and the approximate Bayesian computation sequential Monte Carlo (ABC-SMC) scheme. We present an extensive numerical simulation study, which shows that while the three techniques can effectively solve the problem there are significant differences both in estimation accuracy and computational efficiency. PMID:28797087

Inverse Monte Carlo method in a multilayered tissue model for diffuse reflectance spectroscopy

NASA Astrophysics Data System (ADS)

Fredriksson, Ingemar; Larsson, Marcus; Strömberg, Tomas

2012-04-01

Model based data analysis of diffuse reflectance spectroscopy data enables the estimation of optical and structural tissue parameters. The aim of this study was to present an inverse Monte Carlo method based on spectra from two source-detector distances (0.4 and 1.2 mm), using a multilayered tissue model. The tissue model variables include geometrical properties, light scattering properties, tissue chromophores such as melanin and hemoglobin, oxygen saturation and average vessel diameter. The method utilizes a small set of presimulated Monte Carlo data for combinations of different levels of epidermal thickness and tissue scattering. The path length distributions in the different layers are stored and the effect of the other parameters is added in the post-processing. The accuracy of the method was evaluated using Monte Carlo simulations of tissue-like models containing discrete blood vessels, evaluating blood tissue fraction and oxygenation. It was also compared to a homogeneous model. The multilayer model performed better than the homogeneous model and all tissue parameters significantly improved spectral fitting. Recorded in vivo spectra were fitted well at both distances, which we previously found was not possible with a homogeneous model. No absolute intensity calibration is needed and the algorithm is fast enough for real-time processing.

Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: a path for the optimization of low-energy many-body bases.

PubMed

Reboredo, Fernando A; Kim, Jeongnim

2014-02-21

A statistical method is derived for the calculation of thermodynamic properties of many-body systems at low temperatures. This method is based on the self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo, J. Chem. Phys. 136, 204101 (2012)] and some ideas of the correlation function Monte Carlo approach [D. M. Ceperley and B. Bernu, J. Chem. Phys. 89, 6316 (1988)]. In order to allow the evolution in imaginary time to describe the density matrix, we remove the fixed-node restriction using complex antisymmetric guiding wave functions. In the process we obtain a parallel algorithm that optimizes a small subspace of the many-body Hilbert space to provide maximum overlap with the subspace spanned by the lowest-energy eigenstates of a many-body Hamiltonian. We show in a model system that the partition function is progressively maximized within this subspace. We show that the subspace spanned by the small basis systematically converges towards the subspace spanned by the lowest energy eigenstates. Possible applications of this method for calculating the thermodynamic properties of many-body systems near the ground state are discussed. The resulting basis can also be used to accelerate the calculation of the ground or excited states with quantum Monte Carlo.

Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: A path for the optimization of low-energy many-body bases

NASA Astrophysics Data System (ADS)

Reboredo, Fernando A.; Kim, Jeongnim

2014-02-01

A statistical method is derived for the calculation of thermodynamic properties of many-body systems at low temperatures. This method is based on the self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo, J. Chem. Phys. 136, 204101 (2012)] and some ideas of the correlation function Monte Carlo approach [D. M. Ceperley and B. Bernu, J. Chem. Phys. 89, 6316 (1988)]. In order to allow the evolution in imaginary time to describe the density matrix, we remove the fixed-node restriction using complex antisymmetric guiding wave functions. In the process we obtain a parallel algorithm that optimizes a small subspace of the many-body Hilbert space to provide maximum overlap with the subspace spanned by the lowest-energy eigenstates of a many-body Hamiltonian. We show in a model system that the partition function is progressively maximized within this subspace. We show that the subspace spanned by the small basis systematically converges towards the subspace spanned by the lowest energy eigenstates. Possible applications of this method for calculating the thermodynamic properties of many-body systems near the ground state are discussed. The resulting basis can also be used to accelerate the calculation of the ground or excited states with quantum Monte Carlo.

CPMC-Lab: A MATLAB package for Constrained Path Monte Carlo calculations

NASA Astrophysics Data System (ADS)

Nguyen, Huy; Shi, Hao; Xu, Jie; Zhang, Shiwei

2014-12-01

We describe CPMC-Lab, a MATLAB program for the constrained-path and phaseless auxiliary-field Monte Carlo methods. These methods have allowed applications ranging from the study of strongly correlated models, such as the Hubbard model, to ab initio calculations in molecules and solids. The present package implements the full ground-state constrained-path Monte Carlo (CPMC) method in MATLAB with a graphical interface, using the Hubbard model as an example. The package can perform calculations in finite supercells in any dimensions, under periodic or twist boundary conditions. Importance sampling and all other algorithmic details of a total energy calculation are included and illustrated. This open-source tool allows users to experiment with various model and run parameters and visualize the results. It provides a direct and interactive environment to learn the method and study the code with minimal overhead for setup. Furthermore, the package can be easily generalized for auxiliary-field quantum Monte Carlo (AFQMC) calculations in many other models for correlated electron systems, and can serve as a template for developing a production code for AFQMC total energy calculations in real materials. Several illustrative studies are carried out in one- and two-dimensional lattices on total energy, kinetic energy, potential energy, and charge- and spin-gaps.

A simplified analytical dose calculation algorithm accounting for tissue heterogeneity for low-energy brachytherapy sources.

PubMed

Mashouf, Shahram; Lechtman, Eli; Beaulieu, Luc; Verhaegen, Frank; Keller, Brian M; Ravi, Ananth; Pignol, Jean-Philippe

2013-09-21

The American Association of Physicists in Medicine Task Group No. 43 (AAPM TG-43) formalism is the standard for seeds brachytherapy dose calculation. But for breast seed implants, Monte Carlo simulations reveal large errors due to tissue heterogeneity. Since TG-43 includes several factors to account for source geometry, anisotropy and strength, we propose an additional correction factor, called the inhomogeneity correction factor (ICF), accounting for tissue heterogeneity for Pd-103 brachytherapy. This correction factor is calculated as a function of the media linear attenuation coefficient and mass energy absorption coefficient, and it is independent of the source internal structure. Ultimately the dose in heterogeneous media can be calculated as a product of dose in water as calculated by TG-43 protocol times the ICF. To validate the ICF methodology, dose absorbed in spherical phantoms with large tissue heterogeneities was compared using the TG-43 formalism corrected for heterogeneity versus Monte Carlo simulations. The agreement between Monte Carlo simulations and the ICF method remained within 5% in soft tissues up to several centimeters from a Pd-103 source. Compared to Monte Carlo, the ICF methods can easily be integrated into a clinical treatment planning system and it does not require the detailed internal structure of the source or the photon phase-space.

Understanding quantum tunneling using diffusion Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Inack, E. M.; Giudici, G.; Parolini, T.; Santoro, G.; Pilati, S.

2018-03-01

In simple ferromagnetic quantum Ising models characterized by an effective double-well energy landscape the characteristic tunneling time of path-integral Monte Carlo (PIMC) simulations has been shown to scale as the incoherent quantum-tunneling time, i.e., as 1 /Δ2 , where Δ is the tunneling gap. Since incoherent quantum tunneling is employed by quantum annealers (QAs) to solve optimization problems, this result suggests that there is no quantum advantage in using QAs with respect to quantum Monte Carlo (QMC) simulations. A counterexample is the recently introduced shamrock model (Andriyash and Amin, arXiv:1703.09277), where topological obstructions cause an exponential slowdown of the PIMC tunneling dynamics with respect to incoherent quantum tunneling, leaving open the possibility for potential quantum speedup, even for stoquastic models. In this work we investigate the tunneling time of projective QMC simulations based on the diffusion Monte Carlo (DMC) algorithm without guiding functions, showing that it scales as 1 /Δ , i.e., even more favorably than the incoherent quantum-tunneling time, both in a simple ferromagnetic system and in the more challenging shamrock model. However, a careful comparison between the DMC ground-state energies and the exact solution available for the transverse-field Ising chain indicates an exponential scaling of the computational cost required to keep a fixed relative error as the system size increases.

Efficient Monte Carlo Methods for Biomolecular Simulations.

NASA Astrophysics Data System (ADS)

Bouzida, Djamal

A new approach to efficient Monte Carlo simulations of biological molecules is presented. By relaxing the usual restriction to Markov processes, we are able to optimize performance while dealing directly with the inhomogeneity and anisotropy inherent in these systems. The advantage of this approach is that we can introduce a wide variety of Monte Carlo moves to deal with complicated motions of the molecule, while maintaining full optimization at every step. This enables the use of a variety of collective rotational moves that relax long-wavelength modes. We were able to show by explicit simulations that the resulting algorithms substantially increase the speed of the simulation while reproducing the correct equilibrium behavior. This approach is particularly intended for simulations of macromolecules, although we expect it to be useful in other situations. The dynamic optimization of the new Monte Carlo methods makes them very suitable for simulated annealing experiments on all systems whose state space is continuous in general, and to the protein folding problem in particular. We introduce an efficient annealing schedule using preferential bias moves. Our simulated annealing experiments yield structures whose free energies were lower than the equilibrated X-ray structure, which leads us to believe that the empirical energy function used does not fully represent the interatomic interactions. Furthermore, we believe that the largest discrepancies involve the solvent effects in particular.

On recontamination and directional-bias problems in Monte Carlo simulation of PDF turbulence models. [probability density function

NASA Technical Reports Server (NTRS)

Hsu, Andrew T.

1992-01-01

Turbulent combustion can not be simulated adequately by conventional moment closure turbulent models. The probability density function (PDF) method offers an attractive alternative: in a PDF model, the chemical source terms are closed and do not require additional models. Because the number of computational operations grows only linearly in the Monte Carlo scheme, it is chosen over finite differencing schemes. A grid dependent Monte Carlo scheme following J.Y. Chen and W. Kollmann has been studied in the present work. It was found that in order to conserve the mass fractions absolutely, one needs to add further restrictions to the scheme, namely alpha(sub j) + gamma(sub j) = alpha(sub j - 1) + gamma(sub j + 1). A new algorithm was devised that satisfied this restriction in the case of pure diffusion or uniform flow problems. Using examples, it is shown that absolute conservation can be achieved. Although for non-uniform flows absolute conservation seems impossible, the present scheme has reduced the error considerably.

The Multiple-Minima Problem in Protein Folding

NASA Astrophysics Data System (ADS)

Scheraga, Harold A.

1991-10-01

The conformational energy surface of a polypeptide or protein has many local minima, and conventional energy minimization procedures reach only a local minimum (near the starting point of the optimization algorithm) instead of the global minimum (the multiple-minima problem). Several procedures have been developed to surmount this problem, the most promising of which are: (a) build up procedure, (b) optimization of electrostatics, (c) Monte Carlo-plus-energy minimization, (d) electrostatically-driven Monte Carlo, (e) inclusion of distance restraints, (f) adaptive importance-sampling Monte Carlo, (g) relaxation of dimensionality, (h) pattern-recognition, and (i) diffusion equation method. These procedures have been applied to a variety of polypeptide structural problems, and the results of such computations are presented. These include the computation of the structures of open-chain and cyclic peptides, fibrous proteins and globular proteins. Present efforts are being devoted to scaling up these procedures from small polypeptides to proteins, to try to compute the three-dimensional structure of a protein from its amino sequence.

Solutions of the two-dimensional Hubbard model: Benchmarks and results from a wide range of numerical algorithms

DOE PAGES

LeBlanc, J. P. F.; Antipov, Andrey E.; Becca, Federico; ...

2015-12-14

Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification ofmore » uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Furthermore, cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.« less

Auxiliary field diffusion Monte Carlo calculations of light and medium-mass nuclei with local chiral interactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lonardoni, D.; Gandolfi, S.; Lynn, J. E.

Quantum Monte Carlo methods have recently been employed to study properties of nuclei and infinite matter using local chiral effective-field-theory interactions. In this paper, we present a detailed description of the auxiliary field diffusion Monte Carlo algorithm for nuclei in combination with local chiral two- and three-nucleon interactions up to next-to-next-to-leading order. We show results for the binding energy, charge radius, charge form factor, and Coulomb sum rule in nuclei withmore » $$3{\\le}A{\\le}16$$. Particular attention is devoted to the effect of different operator structures in the three-body force for different cutoffs. Finally, the outcomes suggest that local chiral interactions fit to few-body observables give a very good description of the ground-state properties of nuclei up to $$^{16}\\mathrm{O}$$, with the exception of one fit for the softer cutoff which predicts overbinding in larger nuclei.« less

The Monte Carlo photoionization and moving-mesh radiation hydrodynamics code CMACIONIZE

NASA Astrophysics Data System (ADS)

Vandenbroucke, B.; Wood, K.

2018-04-01

We present the public Monte Carlo photoionization and moving-mesh radiation hydrodynamics code CMACIONIZE, which can be used to simulate the self-consistent evolution of HII regions surrounding young O and B stars, or other sources of ionizing radiation. The code combines a Monte Carlo photoionization algorithm that uses a complex mix of hydrogen, helium and several coolants in order to self-consistently solve for the ionization and temperature balance at any given type, with a standard first order hydrodynamics scheme. The code can be run as a post-processing tool to get the line emission from an existing simulation snapshot, but can also be used to run full radiation hydrodynamical simulations. Both the radiation transfer and the hydrodynamics are implemented in a general way that is independent of the grid structure that is used to discretize the system, allowing it to be run both as a standard fixed grid code, but also as a moving-mesh code.

Hybrid Monte Carlo approach to the entanglement entropy of interacting fermions

NASA Astrophysics Data System (ADS)

Drut, Joaquín E.; Porter, William J.

2015-09-01

The Monte Carlo calculation of Rényi entanglement entropies Sn of interacting fermions suffers from a well-known signal-to-noise problem, even for a large number of situations in which the infamous sign problem is absent. A few methods have been proposed to overcome this issue, such as ensemble switching and the use of auxiliary partition-function ratios. Here, we present an approach that builds on the recently proposed free-fermion decomposition method; it incorporates entanglement in the probability measure in a natural way; it takes advantage of the hybrid Monte Carlo algorithm (an essential tool in lattice quantum chromodynamics and other gauge theories with dynamical fermions); and it does not suffer from noise problems. This method displays no sign problem for the same cases as other approaches and is therefore useful for a wide variety of systems. As a proof of principle, we calculate S2 for the one-dimensional, half-filled Hubbard model and compare with results from exact diagonalization and the free-fermion decomposition method.

OWL: A scalable Monte Carlo simulation suite for finite-temperature study of materials

NASA Astrophysics Data System (ADS)

Li, Ying Wai; Yuk, Simuck F.; Cooper, Valentino R.; Eisenbach, Markus; Odbadrakh, Khorgolkhuu

The OWL suite is a simulation package for performing large-scale Monte Carlo simulations. Its object-oriented, modular design enables it to interface with various external packages for energy evaluations. It is therefore applicable to study the finite-temperature properties for a wide range of systems: from simple classical spin models to materials where the energy is evaluated by ab initio methods. This scheme not only allows for the study of thermodynamic properties based on first-principles statistical mechanics, it also provides a means for massive, multi-level parallelism to fully exploit the capacity of modern heterogeneous computer architectures. We will demonstrate how improved strong and weak scaling is achieved by employing novel, parallel and scalable Monte Carlo algorithms, as well as the applications of OWL to a few selected frontier materials research problems. This research was supported by the Office of Science of the Department of Energy under contract DE-AC05-00OR22725.

Auxiliary field diffusion Monte Carlo calculations of light and medium-mass nuclei with local chiral interactions

DOE PAGES

Lonardoni, D.; Gandolfi, S.; Lynn, J. E.; ...

2018-04-24

Quantum Monte Carlo methods have recently been employed to study properties of nuclei and infinite matter using local chiral effective-field-theory interactions. In this paper, we present a detailed description of the auxiliary field diffusion Monte Carlo algorithm for nuclei in combination with local chiral two- and three-nucleon interactions up to next-to-next-to-leading order. We show results for the binding energy, charge radius, charge form factor, and Coulomb sum rule in nuclei withmore » $$3{\\le}A{\\le}16$$. Particular attention is devoted to the effect of different operator structures in the three-body force for different cutoffs. Finally, the outcomes suggest that local chiral interactions fit to few-body observables give a very good description of the ground-state properties of nuclei up to $$^{16}\\mathrm{O}$$, with the exception of one fit for the softer cutoff which predicts overbinding in larger nuclei.« less

Efficient Monte Carlo sampling of inverse problems using a neural network-based forward—applied to GPR crosshole traveltime inversion

NASA Astrophysics Data System (ADS)

Hansen, T. M.; Cordua, K. S.

2017-12-01

Probabilistically formulated inverse problems can be solved using Monte Carlo-based sampling methods. In principle, both advanced prior information, based on for example, complex geostatistical models and non-linear forward models can be considered using such methods. However, Monte Carlo methods may be associated with huge computational costs that, in practice, limit their application. This is not least due to the computational requirements related to solving the forward problem, where the physical forward response of some earth model has to be evaluated. Here, it is suggested to replace a numerical complex evaluation of the forward problem, with a trained neural network that can be evaluated very fast. This will introduce a modeling error that is quantified probabilistically such that it can be accounted for during inversion. This allows a very fast and efficient Monte Carlo sampling of the solution to an inverse problem. We demonstrate the methodology for first arrival traveltime inversion of crosshole ground penetrating radar data. An accurate forward model, based on 2-D full-waveform modeling followed by automatic traveltime picking, is replaced by a fast neural network. This provides a sampling algorithm three orders of magnitude faster than using the accurate and computationally expensive forward model, and also considerably faster and more accurate (i.e. with better resolution), than commonly used approximate forward models. The methodology has the potential to dramatically change the complexity of non-linear and non-Gaussian inverse problems that have to be solved using Monte Carlo sampling techniques.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Malone, Fionn D., E-mail: f.malone13@imperial.ac.uk; Lee, D. K. K.; Foulkes, W. M. C.

The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N-body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures. We demonstrate that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system of much recent interest: the uniform electron gas in the warm dense regime. The basis set incompleteness error at finite temperature is investigated and extrapolated via a simple Monte Carlo sampling procedure. Finally, we provide benchmark calculations for a four-electron system, comparing ourmore » results to previous work where possible.« less

Scalable and massively parallel Monte Carlo photon transport simulations for heterogeneous computing platforms

NASA Astrophysics Data System (ADS)

Yu, Leiming; Nina-Paravecino, Fanny; Kaeli, David; Fang, Qianqian

2018-01-01

We present a highly scalable Monte Carlo (MC) three-dimensional photon transport simulation platform designed for heterogeneous computing systems. Through the development of a massively parallel MC algorithm using the Open Computing Language framework, this research extends our existing graphics processing unit (GPU)-accelerated MC technique to a highly scalable vendor-independent heterogeneous computing environment, achieving significantly improved performance and software portability. A number of parallel computing techniques are investigated to achieve portable performance over a wide range of computing hardware. Furthermore, multiple thread-level and device-level load-balancing strategies are developed to obtain efficient simulations using multiple central processing units and GPUs.

Stochastic Investigation of Natural Frequency for Functionally Graded Plates

NASA Astrophysics Data System (ADS)

Karsh, P. K.; Mukhopadhyay, T.; Dey, S.

2018-03-01

This paper presents the stochastic natural frequency analysis of functionally graded plates by applying artificial neural network (ANN) approach. Latin hypercube sampling is utilised to train the ANN model. The proposed algorithm for stochastic natural frequency analysis of FGM plates is validated and verified with original finite element method and Monte Carlo simulation (MCS). The combined stochastic variation of input parameters such as, elastic modulus, shear modulus, Poisson ratio, and mass density are considered. Power law is applied to distribute the material properties across the thickness. The present ANN model reduces the sample size and computationally found efficient as compared to conventional Monte Carlo simulation.

A Monte-Carlo method which is not based on Markov chain algorithm, used to study electrostatic screening of ion potential

NASA Astrophysics Data System (ADS)

Šantić, Branko; Gracin, Davor

2017-12-01

A new simple Monte Carlo method is introduced for the study of electrostatic screening by surrounding ions. The proposed method is not based on the generally used Markov chain method for sample generation. Each sample is pristine and there is no correlation with other samples. As the main novelty, the pairs of ions are gradually added to a sample provided that the energy of each ion is within the boundaries determined by the temperature and the size of ions. The proposed method provides reliable results, as demonstrated by the screening of ion in plasma and in water.

Monte Carlo simulation of a noisy quantum channel with memory.

PubMed

Akhalwaya, Ismail; Moodley, Mervlyn; Petruccione, Francesco

2015-10-01

The classical capacity of quantum channels is well understood for channels with uncorrelated noise. For the case of correlated noise, however, there are still open questions. We calculate the classical capacity of a forgetful channel constructed by Markov switching between two depolarizing channels. Techniques have previously been applied to approximate the output entropy of this channel and thus its capacity. In this paper, we use a Metropolis-Hastings Monte Carlo approach to numerically calculate the entropy. The algorithm is implemented in parallel and its performance is studied and optimized. The effects of memory on the capacity are explored and previous results are confirmed to higher precision.

Effective emissivities of isothermal blackbody cavities calculated by the Monte Carlo method using the three-component bidirectional reflectance distribution function model.

PubMed

Prokhorov, Alexander

2012-05-01

This paper proposes a three-component bidirectional reflectance distribution function (3C BRDF) model consisting of diffuse, quasi-specular, and glossy components for calculation of effective emissivities of blackbody cavities and then investigates the properties of the new reflection model. The particle swarm optimization method is applied for fitting a 3C BRDF model to measured BRDFs. The model is incorporated into the Monte Carlo ray-tracing algorithm for isothermal cavities. Finally, the paper compares the results obtained using the 3C model and the conventional specular-diffuse model of reflection.

Using the Metropolis Algorithm to Calculate Thermodynamic Quantities: An Undergraduate Computational Experiment

ERIC Educational Resources Information Center

Beddard, Godfrey S.

2011-01-01

Thermodynamic quantities such as the average energy, heat capacity, and entropy are calculated using a Monte Carlo method based on the Metropolis algorithm. This method is illustrated with reference to the harmonic oscillator but is particularly useful when the partition function cannot be evaluated; an example using a one-dimensional spin system…

Bayesian forecasting and uncertainty quantifying of stream flows using Metropolis–Hastings Markov Chain Monte Carlo algorithm

DOE PAGES

Wang, Hongrui; Wang, Cheng; Wang, Ying; ...

2017-04-05

This paper presents a Bayesian approach using Metropolis-Hastings Markov Chain Monte Carlo algorithm and applies this method for daily river flow rate forecast and uncertainty quantification for Zhujiachuan River using data collected from Qiaotoubao Gage Station and other 13 gage stations in Zhujiachuan watershed in China. The proposed method is also compared with the conventional maximum likelihood estimation (MLE) for parameter estimation and quantification of associated uncertainties. While the Bayesian method performs similarly in estimating the mean value of daily flow rate, it performs over the conventional MLE method on uncertainty quantification, providing relatively narrower reliable interval than the MLEmore » confidence interval and thus more precise estimation by using the related information from regional gage stations. As a result, the Bayesian MCMC method might be more favorable in the uncertainty analysis and risk management.« less

Marathon: An Open Source Software Library for the Analysis of Markov-Chain Monte Carlo Algorithms

PubMed Central

Rechner, Steffen; Berger, Annabell

2016-01-01

We present the software library marathon, which is designed to support the analysis of sampling algorithms that are based on the Markov-Chain Monte Carlo principle. The main application of this library is the computation of properties of so-called state graphs, which represent the structure of Markov chains. We demonstrate applications and the usefulness of marathon by investigating the quality of several bounding methods on four well-known Markov chains for sampling perfect matchings and bipartite graphs. In a set of experiments, we compute the total mixing time and several of its bounds for a large number of input instances. We find that the upper bound gained by the famous canonical path method is often several magnitudes larger than the total mixing time and deteriorates with growing input size. In contrast, the spectral bound is found to be a precise approximation of the total mixing time. PMID:26824442

Methods for Monte Carlo simulations of biomacromolecules

PubMed Central

Vitalis, Andreas; Pappu, Rohit V.

2010-01-01

The state-of-the-art for Monte Carlo (MC) simulations of biomacromolecules is reviewed. Available methodologies for sampling conformational equilibria and associations of biomacromolecules in the canonical ensemble, given a continuum description of the solvent environment, are reviewed. Detailed sections are provided dealing with the choice of degrees of freedom, the efficiencies of MC algorithms and algorithmic peculiarities, as well as the optimization of simple movesets. The issue of introducing correlations into elementary MC moves, and the applicability of such methods to simulations of biomacromolecules is discussed. A brief discussion of multicanonical methods and an overview of recent simulation work highlighting the potential of MC methods are also provided. It is argued that MC simulations, while underutilized biomacromolecular simulation community, hold promise for simulations of complex systems and phenomena that span multiple length scales, especially when used in conjunction with implicit solvation models or other coarse graining strategies. PMID:20428473

SALUTE Grid Application using Message-Oriented Middleware

NASA Astrophysics Data System (ADS)

Atanassov, E.; Dimitrov, D. Sl.; Gurov, T.

2009-10-01

Stochastic ALgorithms for Ultra-fast Transport in sEmiconductors (SALUTE) is a grid application developed for solving various computationally intensive problems which describe ultra-fast carrier transport in semiconductors. SALUTE studies memory and quantum effects during the relaxation process due to electronphonon interaction in one-band semiconductors or quantum wires. Formally, SALUTE integrates a set of novel Monte Carlo, quasi-Monte Carlo and hybrid algorithms for solving various computationally intensive problems which describe the femtosecond relaxation process of optically excited carriers in one-band semiconductors or quantum wires. In this paper we present application-specific job submission and reservation management tool named a Job Track Server (JTS). It is developed using Message-Oriented middleware to implement robust, versatile job submission and tracing mechanism, which can be tailored to application specific failover and quality of service requirements. Experience from using the JTS for submission of SALUTE jobs is presented.

Statistical methods for launch vehicle guidance, navigation, and control (GN&C) system design and analysis

NASA Astrophysics Data System (ADS)

Rose, Michael Benjamin

A novel trajectory and attitude control and navigation analysis tool for powered ascent is developed. The tool is capable of rapid trade-space analysis and is designed to ultimately reduce turnaround time for launch vehicle design, mission planning, and redesign work. It is streamlined to quickly determine trajectory and attitude control dispersions, propellant dispersions, orbit insertion dispersions, and navigation errors and their sensitivities to sensor errors, actuator execution uncertainties, and random disturbances. The tool is developed by applying both Monte Carlo and linear covariance analysis techniques to a closed-loop, launch vehicle guidance, navigation, and control (GN&C) system. The nonlinear dynamics and flight GN&C software models of a closed-loop, six-degree-of-freedom (6-DOF), Monte Carlo simulation are formulated and developed. The nominal reference trajectory (NRT) for the proposed lunar ascent trajectory is defined and generated. The Monte Carlo truth models and GN&C algorithms are linearized about the NRT, the linear covariance equations are formulated, and the linear covariance simulation is developed. The performance of the launch vehicle GN&C system is evaluated using both Monte Carlo and linear covariance techniques and their trajectory and attitude control dispersion, propellant dispersion, orbit insertion dispersion, and navigation error results are validated and compared. Statistical results from linear covariance analysis are generally within 10% of Monte Carlo results, and in most cases the differences are less than 5%. This is an excellent result given the many complex nonlinearities that are embedded in the ascent GN&C problem. Moreover, the real value of this tool lies in its speed, where the linear covariance simulation is 1036.62 times faster than the Monte Carlo simulation. Although the application and results presented are for a lunar, single-stage-to-orbit (SSTO), ascent vehicle, the tools, techniques, and mathematical formulations that are discussed are applicable to ascent on Earth or other planets as well as other rocket-powered systems such as sounding rockets and ballistic missiles.

SU-E-T-586: Field Size Dependence of Output Factor for Uniform Scanning Proton Beams: A Comparison of TPS Calculation, Measurement and Monte Carlo Simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zheng, Y; Singh, H; Islam, M

2014-06-01

Purpose: Output dependence on field size for uniform scanning beams, and the accuracy of treatment planning system (TPS) calculation are not well studied. The purpose of this work is to investigate the dependence of output on field size for uniform scanning beams and compare it among TPS calculation, measurements and Monte Carlo simulations. Methods: Field size dependence was studied using various field sizes between 2.5 cm diameter to 10 cm diameter. The field size factor was studied for a number of proton range and modulation combinations based on output at the center of spread out Bragg peak normalized to amore » 10 cm diameter field. Three methods were used and compared in this study: 1) TPS calculation, 2) ionization chamber measurement, and 3) Monte Carlos simulation. The XiO TPS (Electa, St. Louis) was used to calculate the output factor using a pencil beam algorithm; a pinpoint ionization chamber was used for measurements; and the Fluka code was used for Monte Carlo simulations. Results: The field size factor varied with proton beam parameters, such as range, modulation, and calibration depth, and could decrease over 10% from a 10 cm to 3 cm diameter field for a large range proton beam. The XiO TPS predicted the field size factor relatively well at large field size, but could differ from measurements by 5% or more for small field and large range beams. Monte Carlo simulations predicted the field size factor within 1.5% of measurements. Conclusion: Output factor can vary largely with field size, and needs to be accounted for accurate proton beam delivery. This is especially important for small field beams such as in stereotactic proton therapy, where the field size dependence is large and TPS calculation is inaccurate. Measurements or Monte Carlo simulations are recommended for output determination for such cases.« less

A measurement-based generalized source model for Monte Carlo dose simulations of CT scans

PubMed Central

Ming, Xin; Feng, Yuanming; Liu, Ransheng; Yang, Chengwen; Zhou, Li; Zhai, Hezheng; Deng, Jun

2018-01-01

The goal of this study is to develop a generalized source model (GSM) for accurate Monte Carlo dose simulations of CT scans based solely on the measurement data without a priori knowledge of scanner specifications. The proposed generalized source model consists of an extended circular source located at x-ray target level with its energy spectrum, source distribution and fluence distribution derived from a set of measurement data conveniently available in the clinic. Specifically, the central axis percent depth dose (PDD) curves measured in water and the cone output factors measured in air were used to derive the energy spectrum and the source distribution respectively with a Levenberg-Marquardt algorithm. The in-air film measurement of fan-beam dose profiles at fixed gantry was back-projected to generate the fluence distribution of the source model. A benchmarked Monte Carlo user code was used to simulate the dose distributions in water with the developed source model as beam input. The feasibility and accuracy of the proposed source model was tested on a GE LightSpeed and a Philips Brilliance Big Bore multi-detector CT (MDCT) scanners available in our clinic. In general, the Monte Carlo simulations of the PDDs in water and dose profiles along lateral and longitudinal directions agreed with the measurements within 4%/1mm for both CT scanners. The absolute dose comparison using two CTDI phantoms (16 cm and 32 cm in diameters) indicated a better than 5% agreement between the Monte Carlo-simulated and the ion chamber-measured doses at a variety of locations for the two scanners. Overall, this study demonstrated that a generalized source model can be constructed based only on a set of measurement data and used for accurate Monte Carlo dose simulations of patients’ CT scans, which would facilitate patient-specific CT organ dose estimation and cancer risk management in the diagnostic and therapeutic radiology. PMID:28079526

A measurement-based generalized source model for Monte Carlo dose simulations of CT scans

NASA Astrophysics Data System (ADS)

Ming, Xin; Feng, Yuanming; Liu, Ransheng; Yang, Chengwen; Zhou, Li; Zhai, Hezheng; Deng, Jun

2017-03-01

The goal of this study is to develop a generalized source model for accurate Monte Carlo dose simulations of CT scans based solely on the measurement data without a priori knowledge of scanner specifications. The proposed generalized source model consists of an extended circular source located at x-ray target level with its energy spectrum, source distribution and fluence distribution derived from a set of measurement data conveniently available in the clinic. Specifically, the central axis percent depth dose (PDD) curves measured in water and the cone output factors measured in air were used to derive the energy spectrum and the source distribution respectively with a Levenberg-Marquardt algorithm. The in-air film measurement of fan-beam dose profiles at fixed gantry was back-projected to generate the fluence distribution of the source model. A benchmarked Monte Carlo user code was used to simulate the dose distributions in water with the developed source model as beam input. The feasibility and accuracy of the proposed source model was tested on a GE LightSpeed and a Philips Brilliance Big Bore multi-detector CT (MDCT) scanners available in our clinic. In general, the Monte Carlo simulations of the PDDs in water and dose profiles along lateral and longitudinal directions agreed with the measurements within 4%/1 mm for both CT scanners. The absolute dose comparison using two CTDI phantoms (16 cm and 32 cm in diameters) indicated a better than 5% agreement between the Monte Carlo-simulated and the ion chamber-measured doses at a variety of locations for the two scanners. Overall, this study demonstrated that a generalized source model can be constructed based only on a set of measurement data and used for accurate Monte Carlo dose simulations of patients’ CT scans, which would facilitate patient-specific CT organ dose estimation and cancer risk management in the diagnostic and therapeutic radiology.

Loading relativistic Maxwell distributions in particle simulations

NASA Astrophysics Data System (ADS)

Zenitani, Seiji

2015-04-01

Numerical algorithms to load relativistic Maxwell distributions in particle-in-cell (PIC) and Monte-Carlo simulations are presented. For stationary relativistic Maxwellian, the inverse transform method and the Sobol algorithm are reviewed. To boost particles to obtain relativistic shifted-Maxwellian, two rejection methods are proposed in a physically transparent manner. Their acceptance efficiencies are ≈50 % for generic cases and 100% for symmetric distributions. They can be combined with arbitrary base algorithms.

Monte Carlo simulations of time-of-flight PET with double-ended readout: calibration, coincidence resolving times and statistical lower bounds

NASA Astrophysics Data System (ADS)

E Derenzo, Stephen

2017-05-01

This paper demonstrates through Monte Carlo simulations that a practical positron emission tomograph with (1) deep scintillators for efficient detection, (2) double-ended readout for depth-of-interaction information, (3) fixed-level analog triggering, and (4) accurate calibration and timing data corrections can achieve a coincidence resolving time (CRT) that is not far above the statistical lower bound. One Monte Carlo algorithm simulates a calibration procedure that uses data from a positron point source. Annihilation events with an interaction near the entrance surface of one scintillator are selected, and data from the two photodetectors on the other scintillator provide depth-dependent timing corrections. Another Monte Carlo algorithm simulates normal operation using these corrections and determines the CRT. A third Monte Carlo algorithm determines the CRT statistical lower bound by generating a series of random interaction depths, and for each interaction a set of random photoelectron times for each of the two photodetectors. The most likely interaction times are determined by shifting the depth-dependent probability density function to maximize the joint likelihood for all the photoelectron times in each set. Example calculations are tabulated for different numbers of photoelectrons and photodetector time jitters for three 3  ×  3  ×  30 mm3 scintillators: Lu2SiO5:Ce,Ca (LSO), LaBr3:Ce, and a hypothetical ultra-fast scintillator. To isolate the factors that depend on the scintillator length and the ability to estimate the DOI, CRT values are tabulated for perfect scintillator-photodetectors. For LSO with 4000 photoelectrons and single photoelectron time jitter of the photodetector J  =  0.2 ns (FWHM), the CRT value using the statistically weighted average of corrected trigger times is 0.098 ns FWHM and the statistical lower bound is 0.091 ns FWHM. For LaBr3:Ce with 8000 photoelectrons and J  =  0.2 ns FWHM, the CRT values are 0.070 and 0.063 ns FWHM, respectively. For the ultra-fast scintillator with 1 ns decay time, 4000 photoelectrons, and J  =  0.2 ns FWHM, the CRT values are 0.021 and 0.017 ns FWHM, respectively. The examples also show that calibration and correction for depth-dependent variations in pulse height and in annihilation and optical photon transit times are necessary to achieve these CRT values.

Quantum Monte Carlo with very large multideterminant wavefunctions.

PubMed

Scemama, Anthony; Applencourt, Thomas; Giner, Emmanuel; Caffarel, Michel

2016-07-01

An algorithm to compute efficiently the first two derivatives of (very) large multideterminant wavefunctions for quantum Monte Carlo calculations is presented. The calculation of determinants and their derivatives is performed using the Sherman-Morrison formula for updating the inverse Slater matrix. An improved implementation based on the reduction of the number of column substitutions and on a very efficient implementation of the calculation of the scalar products involved is presented. It is emphasized that multideterminant expansions contain in general a large number of identical spin-specific determinants: for typical configuration interaction-type wavefunctions the number of unique spin-specific determinants Ndetσ ( σ=↑,↓) with a non-negligible weight in the expansion is of order O(Ndet). We show that a careful implementation of the calculation of the Ndet -dependent contributions can make this step negligible enough so that in practice the algorithm scales as the total number of unique spin-specific determinants,  Ndet↑+Ndet↓, over a wide range of total number of determinants (here, Ndet up to about one million), thus greatly reducing the total computational cost. Finally, a new truncation scheme for the multideterminant expansion is proposed so that larger expansions can be considered without increasing the computational time. The algorithm is illustrated with all-electron fixed-node diffusion Monte Carlo calculations of the total energy of the chlorine atom. Calculations using a trial wavefunction including about 750,000 determinants with a computational increase of ∼400 compared to a single-determinant calculation are shown to be feasible. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Simulation and performance of an artificial retina for 40 MHz track reconstruction

DOE PAGES

Abba, A.; Bedeschi, F.; Citterio, M.; ...

2015-03-05

We present the results of a detailed simulation of the artificial retina pattern-recognition algorithm, designed to reconstruct events with hundreds of charged-particle tracks in pixel and silicon detectors at LHCb with LHC crossing frequency of 40 MHz. Performances of the artificial retina algorithm are assessed using the official Monte Carlo samples of the LHCb experiment. We found performances for the retina pattern-recognition algorithm comparable with the full LHCb reconstruction algorithm.

Testing algorithms for critical slowing down

NASA Astrophysics Data System (ADS)

Cossu, Guido; Boyle, Peter; Christ, Norman; Jung, Chulwoo; Jüttner, Andreas; Sanfilippo, Francesco

2018-03-01

We present the preliminary tests on two modifications of the Hybrid Monte Carlo (HMC) algorithm. Both algorithms are designed to travel much farther in the Hamiltonian phase space for each trajectory and reduce the autocorrelations among physical observables thus tackling the critical slowing down towards the continuum limit. We present a comparison of costs of the new algorithms with the standard HMC evolution for pure gauge fields, studying the autocorrelation times for various quantities including the topological charge.

Reconstruction of 2D PET data with Monte Carlo generated system matrix for generalized natural pixels

NASA Astrophysics Data System (ADS)

Vandenberghe, Stefaan; Staelens, Steven; Byrne, Charles L.; Soares, Edward J.; Lemahieu, Ignace; Glick, Stephen J.

2006-06-01

In discrete detector PET, natural pixels are image basis functions calculated from the response of detector pairs. By using reconstruction with natural pixel basis functions, the discretization of the object into a predefined grid can be avoided. Here, we propose to use generalized natural pixel reconstruction. Using this approach, the basis functions are not the detector sensitivity functions as in the natural pixel case but uniform parallel strips. The backprojection of the strip coefficients results in the reconstructed image. This paper proposes an easy and efficient way to generate the matrix M directly by Monte Carlo simulation. Elements of the generalized natural pixel system matrix are formed by calculating the intersection of a parallel strip with the detector sensitivity function. These generalized natural pixels are easier to use than conventional natural pixels because the final step from solution to a square pixel representation is done by simple backprojection. Due to rotational symmetry in the PET scanner, the matrix M is block circulant and only the first blockrow needs to be stored. Data were generated using a fast Monte Carlo simulator using ray tracing. The proposed method was compared to a listmode MLEM algorithm, which used ray tracing for doing forward and backprojection. Comparison of the algorithms with different phantoms showed that an improved resolution can be obtained using generalized natural pixel reconstruction with accurate system modelling. In addition, it was noted that for the same resolution a lower noise level is present in this reconstruction. A numerical observer study showed the proposed method exhibited increased performance as compared to a standard listmode EM algorithm. In another study, more realistic data were generated using the GATE Monte Carlo simulator. For these data, a more uniform contrast recovery and a better contrast-to-noise performance were observed. It was observed that major improvements in contrast recovery were obtained with MLEM when the correct system matrix was used instead of simple ray tracing. The correct modelling was the major cause of improved contrast for the same background noise. Less important factors were the choice of the algorithm (MLEM performed better than ART) and the basis functions (generalized natural pixels gave better results than pixels).

SU-E-T-344: Validation and Clinical Experience of Eclipse Electron Monte Carlo Algorithm (EMC)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pokharel, S; Rana, S

2014-06-01

Purpose: The purpose of this study is to validate Eclipse Electron Monte Carlo (Algorithm for routine clinical uses. Methods: The PTW inhomogeneity phantom (T40037) with different combination of heterogeneous slabs has been CT-scanned with Philips Brilliance 16 slice scanner. The phantom contains blocks of Rando Alderson materials mimicking lung, Polystyrene (Tissue), PTFE (Bone) and PMAA. The phantom has 30×30×2.5 cm base plate with 2cm recesses to insert inhomogeneity. The detector systems used in this study are diode, tlds and Gafchromic EBT2 films. The diode and tlds were included in CT scans. The CT sets are transferred to Eclipse treatment planningmore » system. Several plans have been created with Eclipse Monte Carlo (EMC) algorithm 11.0.21. Measurements have been carried out in Varian TrueBeam machine for energy from 6–22mev. Results: The measured and calculated doses agreed very well for tissue like media. The agreement was reasonably okay for the presence of lung inhomogeneity. The point dose agreement was within 3.5% and Gamma passing rate at 3%/3mm was greater than 93% except for 6Mev(85%). The disagreement can reach as high as 10% in the presence of bone inhomogeneity. This is due to eclipse reporting dose to the medium as opposed to the dose to the water as in conventional calculation engines. Conclusion: Care must be taken when using Varian Eclipse EMC algorithm for dose calculation for routine clinical uses. The algorithm dose not report dose to water in which most of the clinical experiences are based on rather it just reports dose to medium directly. In the presence of inhomogeneity such as bone, the dose discrepancy can be as high as 10% or even more depending on the location of normalization point or volume. As Radiation oncology as an empirical science, care must be taken before using EMC reported monitor units for clinical uses.« less

Characterisation of mega-voltage electron pencil beam dose distributions: viability of a measurement-based approach.

PubMed

Barnes, M P; Ebert, M A

2008-03-01

The concept of electron pencil-beam dose distributions is central to pencil-beam algorithms used in electron beam radiotherapy treatment planning. The Hogstrom algorithm, which is a common algorithm for electron treatment planning, models large electron field dose distributions by the superposition of a series of pencil beam dose distributions. This means that the accurate characterisation of an electron pencil beam is essential for the accuracy of the dose algorithm. The aim of this study was to evaluate a measurement based approach for obtaining electron pencil-beam dose distributions. The primary incentive for the study was the accurate calculation of dose distributions for narrow fields as traditional electron algorithms are generally inaccurate for such geometries. Kodak X-Omat radiographic film was used in a solid water phantom to measure the dose distribution of circular 12 MeV beams from a Varian 21EX linear accelerator. Measurements were made for beams of diameter, 1.5, 2, 4, 8, 16 and 32 mm. A blocked-field technique was used to subtract photon contamination in the beam. The "error function" derived from Fermi-Eyges Multiple Coulomb Scattering (MCS) theory for corresponding square fields was used to fit resulting dose distributions so that extrapolation down to a pencil beam distribution could be made. The Monte Carlo codes, BEAM and EGSnrc were used to simulate the experimental arrangement. The 8 mm beam dose distribution was also measured with TLD-100 microcubes. Agreement between film, TLD and Monte Carlo simulation results were found to be consistent with the spatial resolution used. The study has shown that it is possible to extrapolate narrow electron beam dose distributions down to a pencil beam dose distribution using the error function. However, due to experimental uncertainties and measurement difficulties, Monte Carlo is recommended as the method of choice for characterising electron pencil-beam dose distributions.

A Configurational-Bias-Monte-Carlo Back-Mapping Algorithm for Efficient and Rapid Conversion of Coarse-Grained Water Structures Into Atomistic Models.

PubMed

Loeffler, Troy David; Chan, Henry; Narayanan, Badri; Cherukara, Mathew J; Gray, Stephen K; Sankaranarayanan, Subramanian K R S

2018-06-20

Coarse-grained molecular dynamics (MD) simulations represent a powerful approach to simulate longer time scale and larger length scale phenomena than those accessible to all-atom models. The gain in efficiency, however, comes at the cost of atomistic details. The reverse transformation, also known as back-mapping, of coarse grained beads into their atomistic constituents represents a major challenge. Most existing approaches are limited to specific molecules or specific force-fields and often rely on running a long time atomistic MD of the back-mapped configuration to arrive at an optimal solution. Such approaches are problematic when dealing with systems with high diffusion barriers. Here, we introduce a new extension of the configurational-bias-Monte-Carlo (CBMC) algorithm, which we term the crystalline-configurational-bias-Monte-Carlo (C-CBMC) algortihm, that allows rapid and efficient conversion of a coarse-grained model back into its atomistic representation. Although the method is generic, we use a coarse-grained water model as a representative example and demonstrate the back-mapping or reverse transformation for model systems ranging from the ice-liquid water interface to amorphous and crystalline ice configurations. A series of simulations using the TIP4P/Ice model are performed to compare the new CBMC method to several other standard Monte Carlo and Molecular Dynamics based back-mapping techniques. In all the cases, the C-CBMC algorithm is able to find optimal hydrogen bonded configuration many thousand evaluations/steps sooner than the other methods compared within this paper. For crystalline ice structures such as a hexagonal, cubic, and cubic-hexagonal stacking disorder structures, the C-CBMC was able to find structures that were between 0.05 and 0.1 eV/water molecule lower in energy than the ground state energies predicted by the other methods. Detailed analysis of the atomistic structures show a significantly better global hydrogen positioning when contrasted with the existing simpler back-mapping methods. Our results demonstrate the efficiency and efficacy of our new back-mapping approach, especially for crystalline systems where simple force-field based relaxations have a tendency to get trapped in local minima.

Infinite variance in fermion quantum Monte Carlo calculations.

PubMed

Shi, Hao; Zhang, Shiwei

2016-03-01

For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, and lattice quantum chromodynamics calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied on to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple subareas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calculation unreliable or meaningless. We discuss how to identify the infinite variance problem. An approach is then proposed to solve the problem. The solution does not require major modifications to standard algorithms, adding a "bridge link" to the imaginary-time path integral. The general idea is applicable to a variety of situations where the infinite variance problem may be present. Illustrative results are presented for the ground state of the Hubbard model at half-filling.

A non-stochastic iterative computational method to model light propagation in turbid media

NASA Astrophysics Data System (ADS)

McIntyre, Thomas J.; Zemp, Roger J.

2015-03-01

Monte Carlo models are widely used to model light transport in turbid media, however their results implicitly contain stochastic variations. These fluctuations are not ideal, especially for inverse problems where Jacobian matrix errors can lead to large uncertainties upon matrix inversion. Yet Monte Carlo approaches are more computationally favorable than solving the full Radiative Transport Equation. Here, a non-stochastic computational method of estimating fluence distributions in turbid media is proposed, which is called the Non-Stochastic Propagation by Iterative Radiance Evaluation method (NSPIRE). Rather than using stochastic means to determine a random walk for each photon packet, the propagation of light from any element to all other elements in a grid is modelled simultaneously. For locally homogeneous anisotropic turbid media, the matrices used to represent scattering and projection are shown to be block Toeplitz, which leads to computational simplifications via convolution operators. To evaluate the accuracy of the algorithm, 2D simulations were done and compared against Monte Carlo models for the cases of an isotropic point source and a pencil beam incident on a semi-infinite turbid medium. The model was shown to have a mean percent error less than 2%. The algorithm represents a new paradigm in radiative transport modelling and may offer a non-stochastic alternative to modeling light transport in anisotropic scattering media for applications where the diffusion approximation is insufficient.

Ant colony algorithm implementation in electron and photon Monte Carlo transport: application to the commissioning of radiosurgery photon beams.

PubMed

García-Pareja, S; Galán, P; Manzano, F; Brualla, L; Lallena, A M

2010-07-01

In this work, the authors describe an approach which has been developed to drive the application of different variance-reduction techniques to the Monte Carlo simulation of photon and electron transport in clinical accelerators. The new approach considers the following techniques: Russian roulette, splitting, a modified version of the directional bremsstrahlung splitting, and the azimuthal particle redistribution. Their application is controlled by an ant colony algorithm based on an importance map. The procedure has been applied to radiosurgery beams. Specifically, the authors have calculated depth-dose profiles, off-axis ratios, and output factors, quantities usually considered in the commissioning of these beams. The agreement between Monte Carlo results and the corresponding measurements is within approximately 3%/0.3 mm for the central axis percentage depth dose and the dose profiles. The importance map generated in the calculation can be used to discuss simulation details in the different parts of the geometry in a simple way. The simulation CPU times are comparable to those needed within other approaches common in this field. The new approach is competitive with those previously used in this kind of problems (PSF generation or source models) and has some practical advantages that make it to be a good tool to simulate the radiation transport in problems where the quantities of interest are difficult to obtain because of low statistics.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Costa, Liborio I., E-mail: liborio78@gmail.com

A new Markov Chain Monte Carlo method for simulating the dynamics of particle systems characterized by hard-core interactions is introduced. In contrast to traditional Kinetic Monte Carlo approaches, where the state of the system is associated with minima in the energy landscape, in the proposed method, the state of the system is associated with the set of paths traveled by the atoms and the transition probabilities for an atom to be displaced are proportional to the corresponding velocities. In this way, the number of possible state-to-state transitions is reduced to a discrete set, and a direct link between the Montemore » Carlo time step and true physical time is naturally established. The resulting rejection-free algorithm is validated against event-driven molecular dynamics: the equilibrium and non-equilibrium dynamics of hard disks converge to the exact results with decreasing displacement size.« less

Comparison of normal tissue dose calculation methods for epidemiological studies of radiotherapy patients.

PubMed

Mille, Matthew M; Jung, Jae Won; Lee, Choonik; Kuzmin, Gleb A; Lee, Choonsik

2018-06-01

Radiation dosimetry is an essential input for epidemiological studies of radiotherapy patients aimed at quantifying the dose-response relationship of late-term morbidity and mortality. Individualised organ dose must be estimated for all tissues of interest located in-field, near-field, or out-of-field. Whereas conventional measurement approaches are limited to points in water or anthropomorphic phantoms, computational approaches using patient images or human phantoms offer greater flexibility and can provide more detailed three-dimensional dose information. In the current study, we systematically compared four different dose calculation algorithms so that dosimetrists and epidemiologists can better understand the advantages and limitations of the various approaches at their disposal. The four dose calculations algorithms considered were as follows: the (1) Analytical Anisotropic Algorithm (AAA) and (2) Acuros XB algorithm (Acuros XB), as implemented in the Eclipse treatment planning system (TPS); (3) a Monte Carlo radiation transport code, EGSnrc; and (4) an accelerated Monte Carlo code, the x-ray Voxel Monte Carlo (XVMC). The four algorithms were compared in terms of their accuracy and appropriateness in the context of dose reconstruction for epidemiological investigations. Accuracy in peripheral dose was evaluated first by benchmarking the calculated dose profiles against measurements in a homogeneous water phantom. Additional simulations in a heterogeneous cylinder phantom evaluated the performance of the algorithms in the presence of tissue heterogeneity. In general, we found that the algorithms contained within the commercial TPS (AAA and Acuros XB) were fast and accurate in-field or near-field, but not acceptable out-of-field. Therefore, the TPS is best suited for epidemiological studies involving large cohorts and where the organs of interest are located in-field or partially in-field. The EGSnrc and XVMC codes showed excellent agreement with measurements both in-field and out-of-field. The EGSnrc code was the most accurate dosimetry approach, but was too slow to be used for large-scale epidemiological cohorts. The XVMC code showed similar accuracy to EGSnrc, but was significantly faster, and thus epidemiological applications seem feasible, especially when the organs of interest reside far away from the field edge.

A Monte Carlo comparison of the recovery of winds near upwind and downwind from the SASS-1 model function by means of the sum of squares algorithm and a maximum likelihood estimator

NASA Technical Reports Server (NTRS)

Pierson, W. J., Jr.

1984-01-01

Backscatter measurements at upwind and crosswind are simulated for five incidence angles by means of the SASS-1 model function. The effects of communication noise and attitude errors are simulated by Monte Carlo methods, and the winds are recovered by both the Sum of Square (SOS) algorithm and a Maximum Likelihood Estimater (MLE). The SOS algorithm is shown to fail for light enough winds at all incidence angles and to fail to show areas of calm because backscatter estimates that were negative or that produced incorrect values of K sub p greater than one were discarded. The MLE performs well for all input backscatter estimates and returns calm when both are negative. The use of the SOS algorithm is shown to have introduced errors in the SASS-1 model function that, in part, cancel out the errors that result from using it, but that also cause disagreement with other data sources such as the AAFE circle flight data at light winds. Implications for future scatterometer systems are given.

Asteroid mass estimation using Markov-chain Monte Carlo

NASA Astrophysics Data System (ADS)

Siltala, Lauri; Granvik, Mikael

2017-11-01

Estimates for asteroid masses are based on their gravitational perturbations on the orbits of other objects such as Mars, spacecraft, or other asteroids and/or their satellites. In the case of asteroid-asteroid perturbations, this leads to an inverse problem in at least 13 dimensions where the aim is to derive the mass of the perturbing asteroid(s) and six orbital elements for both the perturbing asteroid(s) and the test asteroid(s) based on astrometric observations. We have developed and implemented three different mass estimation algorithms utilizing asteroid-asteroid perturbations: the very rough 'marching' approximation, in which the asteroids' orbital elements are not fitted, thereby reducing the problem to a one-dimensional estimation of the mass, an implementation of the Nelder-Mead simplex method, and most significantly, a Markov-chain Monte Carlo (MCMC) approach. We describe each of these algorithms with particular focus on the MCMC algorithm, and present example results using both synthetic and real data. Our results agree with the published mass estimates, but suggest that the published uncertainties may be misleading as a consequence of using linearized mass-estimation methods. Finally, we discuss remaining challenges with the algorithms as well as future plans.

North Alabama Lightning Mapping Array (LMA): VHF Source Retrieval Algorithm and Error Analyses

NASA Technical Reports Server (NTRS)

Koshak, W. J.; Solakiewicz, R. J.; Blakeslee, R. J.; Goodman, S. J.; Christian, H. J.; Hall, J.; Bailey, J.; Krider, E. P.; Bateman, M. G.; Boccippio, D.

2003-01-01

Two approaches are used to characterize how accurately the North Alabama Lightning Mapping Array (LMA) is able to locate lightning VHF sources in space and in time. The first method uses a Monte Carlo computer simulation to estimate source retrieval errors. The simulation applies a VHF source retrieval algorithm that was recently developed at the NASA Marshall Space Flight Center (MSFC) and that is similar, but not identical to, the standard New Mexico Tech retrieval algorithm. The second method uses a purely theoretical technique (i.e., chi-squared Curvature Matrix Theory) to estimate retrieval errors. Both methods assume that the LMA system has an overall rms timing error of 50 ns, but all other possible errors (e.g., multiple sources per retrieval attempt) are neglected. The detailed spatial distributions of retrieval errors are provided. Given that the two methods are completely independent of one another, it is shown that they provide remarkably similar results. However, for many source locations, the Curvature Matrix Theory produces larger altitude error estimates than the (more realistic) Monte Carlo simulation.

Commissioning and initial acceptance tests for a commercial convolution dose calculation algorithm for radiotherapy treatment planning in comparison with Monte Carlo simulation and measurement

PubMed Central

Moradi, Farhad; Mahdavi, Seyed Rabi; Mostaar, Ahmad; Motamedi, Mohsen

2012-01-01

In this study the commissioning of a dose calculation algorithm in a currently used treatment planning system was performed and the calculation accuracy of two available methods in the treatment planning system i.e., collapsed cone convolution (CCC) and equivalent tissue air ratio (ETAR) was verified in tissue heterogeneities. For this purpose an inhomogeneous phantom (IMRT thorax phantom) was used and dose curves obtained by the TPS (treatment planning system) were compared with experimental measurements and Monte Carlo (MCNP code) simulation. Dose measurements were performed by using EDR2 radiographic films within the phantom. Dose difference (DD) between experimental results and two calculation methods was obtained. Results indicate maximum difference of 12% in the lung and 3% in the bone tissue of the phantom between two methods and the CCC algorithm shows more accurate depth dose curves in tissue heterogeneities. Simulation results show the accurate dose estimation by MCNP4C in soft tissue region of the phantom and also better results than ETAR method in bone and lung tissues. PMID:22973081

Effective optimization using sample persistence: A case study on quantum annealers and various Monte Carlo optimization methods

NASA Astrophysics Data System (ADS)

Karimi, Hamed; Rosenberg, Gili; Katzgraber, Helmut G.

2017-10-01

We present and apply a general-purpose, multistart algorithm for improving the performance of low-energy samplers used for solving optimization problems. The algorithm iteratively fixes the value of a large portion of the variables to values that have a high probability of being optimal. The resulting problems are smaller and less connected, and samplers tend to give better low-energy samples for these problems. The algorithm is trivially parallelizable since each start in the multistart algorithm is independent, and could be applied to any heuristic solver that can be run multiple times to give a sample. We present results for several classes of hard problems solved using simulated annealing, path-integral quantum Monte Carlo, parallel tempering with isoenergetic cluster moves, and a quantum annealer, and show that the success metrics and the scaling are improved substantially. When combined with this algorithm, the quantum annealer's scaling was substantially improved for native Chimera graph problems. In addition, with this algorithm the scaling of the time to solution of the quantum annealer is comparable to the Hamze-de Freitas-Selby algorithm on the weak-strong cluster problems introduced by Boixo et al. Parallel tempering with isoenergetic cluster moves was able to consistently solve three-dimensional spin glass problems with 8000 variables when combined with our method, whereas without our method it could not solve any.

Fast analytical scatter estimation using graphics processing units.

PubMed

Ingleby, Harry; Lippuner, Jonas; Rickey, Daniel W; Li, Yue; Elbakri, Idris

2015-01-01

To develop a fast patient-specific analytical estimator of first-order Compton and Rayleigh scatter in cone-beam computed tomography, implemented using graphics processing units. The authors developed an analytical estimator for first-order Compton and Rayleigh scatter in a cone-beam computed tomography geometry. The estimator was coded using NVIDIA's CUDA environment for execution on an NVIDIA graphics processing unit. Performance of the analytical estimator was validated by comparison with high-count Monte Carlo simulations for two different numerical phantoms. Monoenergetic analytical simulations were compared with monoenergetic and polyenergetic Monte Carlo simulations. Analytical and Monte Carlo scatter estimates were compared both qualitatively, from visual inspection of images and profiles, and quantitatively, using a scaled root-mean-square difference metric. Reconstruction of simulated cone-beam projection data of an anthropomorphic breast phantom illustrated the potential of this method as a component of a scatter correction algorithm. The monoenergetic analytical and Monte Carlo scatter estimates showed very good agreement. The monoenergetic analytical estimates showed good agreement for Compton single scatter and reasonable agreement for Rayleigh single scatter when compared with polyenergetic Monte Carlo estimates. For a voxelized phantom with dimensions 128 × 128 × 128 voxels and a detector with 256 × 256 pixels, the analytical estimator required 669 seconds for a single projection, using a single NVIDIA 9800 GX2 video card. Accounting for first order scatter in cone-beam image reconstruction improves the contrast to noise ratio of the reconstructed images. The analytical scatter estimator, implemented using graphics processing units, provides rapid and accurate estimates of single scatter and with further acceleration and a method to account for multiple scatter may be useful for practical scatter correction schemes.

Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: A path for the optimization of low-energy many-body bases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reboredo, Fernando A.; Kim, Jeongnim

A statistical method is derived for the calculation of thermodynamic properties of many-body systems at low temperatures. This method is based on the self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo, J. Chem. Phys. 136, 204101 (2012)] and some ideas of the correlation function Monte Carlo approach [D. M. Ceperley and B. Bernu, J. Chem. Phys. 89, 6316 (1988)]. In order to allow the evolution in imaginary time to describe the density matrix, we remove the fixed-node restriction using complex antisymmetric guiding wave functions. In the process we obtain a parallel algorithm that optimizes a small subspacemore » of the many-body Hilbert space to provide maximum overlap with the subspace spanned by the lowest-energy eigenstates of a many-body Hamiltonian. We show in a model system that the partition function is progressively maximized within this subspace. We show that the subspace spanned by the small basis systematically converges towards the subspace spanned by the lowest energy eigenstates. Possible applications of this method for calculating the thermodynamic properties of many-body systems near the ground state are discussed. The resulting basis can also be used to accelerate the calculation of the ground or excited states with quantum Monte Carlo.« less

Million-body star cluster simulations: comparisons between Monte Carlo and direct N-body

NASA Astrophysics Data System (ADS)

Rodriguez, Carl L.; Morscher, Meagan; Wang, Long; Chatterjee, Sourav; Rasio, Frederic A.; Spurzem, Rainer

2016-12-01

We present the first detailed comparison between million-body globular cluster simulations computed with a Hénon-type Monte Carlo code, CMC, and a direct N-body code, NBODY6++GPU. Both simulations start from an identical cluster model with 106 particles, and include all of the relevant physics needed to treat the system in a highly realistic way. With the two codes `frozen' (no fine-tuning of any free parameters or internal algorithms of the codes) we find good agreement in the overall evolution of the two models. Furthermore, we find that in both models, large numbers of stellar-mass black holes (>1000) are retained for 12 Gyr. Thus, the very accurate direct N-body approach confirms recent predictions that black holes can be retained in present-day, old globular clusters. We find only minor disagreements between the two models and attribute these to the small-N dynamics driving the evolution of the cluster core for which the Monte Carlo assumptions are less ideal. Based on the overwhelming general agreement between the two models computed using these vastly different techniques, we conclude that our Monte Carlo approach, which is more approximate, but dramatically faster compared to the direct N-body, is capable of producing an accurate description of the long-term evolution of massive globular clusters even when the clusters contain large populations of stellar-mass black holes.

Cross-platform validation and analysis environment for particle physics

NASA Astrophysics Data System (ADS)

Chekanov, S. V.; Pogrebnyak, I.; Wilbern, D.

2017-11-01

A multi-platform validation and analysis framework for public Monte Carlo simulation for high-energy particle collisions is discussed. The front-end of this framework uses the Python programming language, while the back-end is written in Java, which provides a multi-platform environment that can be run from a web browser and can easily be deployed at the grid sites. The analysis package includes all major software tools used in high-energy physics, such as Lorentz vectors, jet algorithms, histogram packages, graphic canvases, and tools for providing data access. This multi-platform software suite, designed to minimize OS-specific maintenance and deployment time, is used for online validation of Monte Carlo event samples through a web interface.

PBMC: Pre-conditioned Backward Monte Carlo code for radiative transport in planetary atmospheres

NASA Astrophysics Data System (ADS)

García Muñoz, A.; Mills, F. P.

2017-08-01

PBMC (Pre-Conditioned Backward Monte Carlo) solves the vector Radiative Transport Equation (vRTE) and can be applied to planetary atmospheres irradiated from above. The code builds the solution by simulating the photon trajectories from the detector towards the radiation source, i.e. in the reverse order of the actual photon displacements. In accounting for the polarization in the sampling of photon propagation directions and pre-conditioning the scattering matrix with information from the scattering matrices of prior (in the BMC integration order) photon collisions, PBMC avoids the unstable and biased solutions of classical BMC algorithms for conservative, optically-thick, strongly-polarizing media such as Rayleigh atmospheres.

Reactive Monte Carlo sampling with an ab initio potential

NASA Astrophysics Data System (ADS)

Leiding, Jeff; Coe, Joshua D.

2016-05-01

We present the first application of reactive Monte Carlo in a first-principles context. The algorithm samples in a modified NVT ensemble in which the volume, temperature, and total number of atoms of a given type are held fixed, but molecular composition is allowed to evolve through stochastic variation of chemical connectivity. We discuss general features of the method, as well as techniques needed to enhance the efficiency of Boltzmann sampling. Finally, we compare the results of simulation of NH3 to those of ab initio molecular dynamics (AIMD). We find that there are regions of state space for which RxMC sampling is much more efficient than AIMD due to the "rare-event" character of chemical reactions.

Kinetic Monte Carlo simulations of thermally activated magnetization reversal in dual-layer Exchange Coupled Composite recording media

NASA Astrophysics Data System (ADS)

Plumer, M. L.; Almudallal, A. M.; Mercer, J. I.; Whitehead, J. P.; Fal, T. J.

The kinetic Monte Carlo (KMC) method developed for thermally activated magnetic reversal processes in single-layer recording media has been extended to study dual-layer Exchange Coupled Composition (ECC) media used in current and next generations of disc drives. The attempt frequency is derived from the Langer formalism with the saddle point determined using a variant of Bellman Ford algorithm. Complication (such as stagnation) arising from coupled grains having metastable states are addressed. MH-hysteresis loops are calculated over a wide range of anisotropy ratios, sweep rates and inter-layer coupling parameter. Results are compared with standard micromagnetics at fast sweep rates and experimental results at slow sweep rates.

Monte Carlo Study of Four-Dimensional Self-avoiding Walks of up to One Billion Steps

NASA Astrophysics Data System (ADS)

Clisby, Nathan

2018-04-01

We study self-avoiding walks on the four-dimensional hypercubic lattice via Monte Carlo simulations of walks with up to one billion steps. We study the expected logarithmic corrections to scaling, and find convincing evidence in support the scaling form predicted by the renormalization group, with an estimate for the power of the logarithmic factor of 0.2516(14), which is consistent with the predicted value of 1/4. We also characterize the behaviour of the pivot algorithm for sampling four dimensional self-avoiding walks, and conjecture that the probability of a pivot move being successful for an N-step walk is O([ log N ]^{-1/4}).

Accuracy of Reaction Cross Section for Exotic Nuclei in Glauber Model Based on MCMC Diagnostics

NASA Astrophysics Data System (ADS)

Rueter, Keiti; Novikov, Ivan

2017-01-01

Parameters of a nuclear density distribution for an exotic nuclei with halo or skin structures can be determined from the experimentally measured reaction cross-section. In the presented work, to extract parameters such as nuclear size information for a halo and core, we compare experimental data on reaction cross-sections with values obtained using expressions of the Glauber Model. These calculations are performed using a Markov Chain Monte Carlo algorithm. We discuss the accuracy of the Monte Carlo approach and its dependence on k*, the power law turnover point in the discreet power spectrum of the random number sequence and on the lag-1 autocorrelation time of the random number sequence.

Trigeminal neuralgia treatment dosimetry of the Cyberknife

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ho, Anthony; Lo, Anthony T., E-mail: tonyho22003@yahoo.com; Dieterich, Sonja

2012-04-01

There are 2 Cyberknife units at Stanford University. The robot of 1 Cyberknife is positioned on the patient's right, whereas the second is on the patient's left. The present study examines whether there is any difference in dosimetry when we are treating patients with trigeminal neuralgia when the target is on the right side or the left side of the patient. In addition, we also study whether Monte Carlo dose calculation has any effect on the dosimetry. We concluded that the clinical and dosimetric outcomes of CyberKnife treatment for trigeminal neuralgia are independent of the robot position. Monte Carlo calculationmore » algorithm may be useful in deriving the dose necessary for trigeminal neuralgia treatments.« less

A brief history of the introduction of generalized ensembles to Markov chain Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Berg, Bernd A.

2017-03-01

The most efficient weights for Markov chain Monte Carlo calculations of physical observables are not necessarily those of the canonical ensemble. Generalized ensembles, which do not exist in nature but can be simulated on computers, lead often to a much faster convergence. In particular, they have been used for simulations of first order phase transitions and for simulations of complex systems in which conflicting constraints lead to a rugged free energy landscape. Starting off with the Metropolis algorithm and Hastings' extension, I present a minireview which focuses on the explosive use of generalized ensembles in the early 1990s. Illustrations are given, which range from spin models to peptides.

Multiscale Monte Carlo equilibration: Two-color QCD with two fermion flavors

DOE PAGES

Detmold, William; Endres, Michael G.

2016-12-02

In this study, we demonstrate the applicability of a recently proposed multiscale thermalization algorithm to two-color quantum chromodynamics (QCD) with two mass-degenerate fermion flavors. The algorithm involves refining an ensemble of gauge configurations that had been generated using a renormalization group (RG) matched coarse action, thereby producing a fine ensemble that is close to the thermalized distribution of a target fine action; the refined ensemble is subsequently rethermalized using conventional algorithms. Although the generalization of this algorithm from pure Yang-Mills theory to QCD with dynamical fermions is straightforward, we find that in the latter case, the method is susceptible tomore » numerical instabilities during the initial stages of rethermalization when using the hybrid Monte Carlo algorithm. We find that these instabilities arise from large fermion forces in the evolution, which are attributed to an accumulation of spurious near-zero modes of the Dirac operator. We propose a simple strategy for curing this problem, and demonstrate that rapid thermalization--as probed by a variety of gluonic and fermionic operators--is possible with the use of this solution. Also, we study the sensitivity of rethermalization rates to the RG matching of the coarse and fine actions, and identify effective matching conditions based on a variety of measured scales.« less

The Development of WARP - A Framework for Continuous Energy Monte Carlo Neutron Transport in General 3D Geometries on GPUs

NASA Astrophysics Data System (ADS)

Bergmann, Ryan

Graphics processing units, or GPUs, have gradually increased in computational power from the small, job-specific boards of the early 1990s to the programmable powerhouses of today. Compared to more common central processing units, or CPUs, GPUs have a higher aggregate memory bandwidth, much higher floating-point operations per second (FLOPS), and lower energy consumption per FLOP. Because one of the main obstacles in exascale computing is power consumption, many new supercomputing platforms are gaining much of their computational capacity by incorporating GPUs into their compute nodes. Since CPU-optimized parallel algorithms are not directly portable to GPU architectures (or at least not without losing substantial performance), transport codes need to be rewritten to execute efficiently on GPUs. Unless this is done, reactor simulations cannot take full advantage of these new supercomputers. WARP, which can stand for ``Weaving All the Random Particles,'' is a three-dimensional (3D) continuous energy Monte Carlo neutron transport code developed in this work as to efficiently implement a continuous energy Monte Carlo neutron transport algorithm on a GPU. WARP accelerates Monte Carlo simulations while preserving the benefits of using the Monte Carlo Method, namely, very few physical and geometrical simplifications. WARP is able to calculate multiplication factors, flux tallies, and fission source distributions for time-independent problems, and can run in both criticality or fixed source modes. WARP can transport neutrons in unrestricted arrangements of parallelepipeds, hexagonal prisms, cylinders, and spheres. WARP uses an event-based algorithm, but with some important differences. Moving data is expensive, so WARP uses a remapping vector of pointer/index pairs to direct GPU threads to the data they need to access. The remapping vector is sorted by reaction type after every transport iteration using a high-efficiency parallel radix sort, which serves to keep the reaction types as contiguous as possible and removes completed histories from the transport cycle. The sort reduces the amount of divergence in GPU ``thread blocks,'' keeps the SIMD units as full as possible, and eliminates using memory bandwidth to check if a neutron in the batch has been terminated or not. Using a remapping vector means the data access pattern is irregular, but this is mitigated by using large batch sizes where the GPU can effectively eliminate the high cost of irregular global memory access. WARP modifies the standard unionized energy grid implementation to reduce memory traffic. Instead of storing a matrix of pointers indexed by reaction type and energy, WARP stores three matrices. The first contains cross section values, the second contains pointers to angular distributions, and a third contains pointers to energy distributions. This linked list type of layout increases memory usage, but lowers the number of data loads that are needed to determine a reaction by eliminating a pointer load to find a cross section value. Optimized, high-performance GPU code libraries are also used by WARP wherever possible. The CUDA performance primitives (CUDPP) library is used to perform the parallel reductions, sorts and sums, the CURAND library is used to seed the linear congruential random number generators, and the OptiX ray tracing framework is used for geometry representation. OptiX is a highly-optimized library developed by NVIDIA that automatically builds hierarchical acceleration structures around user-input geometry so only surfaces along a ray line need to be queried in ray tracing. WARP also performs material and cell number queries with OptiX by using a point-in-polygon like algorithm. WARP has shown that GPUs are an effective platform for performing Monte Carlo neutron transport with continuous energy cross sections. Currently, WARP is the most detailed and feature-rich program in existence for performing continuous energy Monte Carlo neutron transport in general 3D geometries on GPUs, but compared to production codes like Serpent and MCNP, WARP has limited capabilities. Despite WARP's lack of features, its novel algorithm implementations show that high performance can be achieved on a GPU despite the inherently divergent program flow and sparse data access patterns. WARP is not ready for everyday nuclear reactor calculations, but is a good platform for further development of GPU-accelerated Monte Carlo neutron transport. In it's current state, it may be a useful tool for multiplication factor searches, i.e. determining reactivity coefficients by perturbing material densities or temperatures, since these types of calculations typically do not require many flux tallies. (Abstract shortened by UMI.)

Neutrino oscillation parameter sampling with MonteCUBES

NASA Astrophysics Data System (ADS)

Blennow, Mattias; Fernandez-Martinez, Enrique

2010-01-01

We present MonteCUBES ("Monte Carlo Utility Based Experiment Simulator"), a software package designed to sample the neutrino oscillation parameter space through Markov Chain Monte Carlo algorithms. MonteCUBES makes use of the GLoBES software so that the existing experiment definitions for GLoBES, describing long baseline and reactor experiments, can be used with MonteCUBES. MonteCUBES consists of two main parts: The first is a C library, written as a plug-in for GLoBES, implementing the Markov Chain Monte Carlo algorithm to sample the parameter space. The second part is a user-friendly graphical Matlab interface to easily read, analyze, plot and export the results of the parameter space sampling. Program summaryProgram title: MonteCUBES (Monte Carlo Utility Based Experiment Simulator) Catalogue identifier: AEFJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFJ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence No. of lines in distributed program, including test data, etc.: 69 634 No. of bytes in distributed program, including test data, etc.: 3 980 776 Distribution format: tar.gz Programming language: C Computer: MonteCUBES builds and installs on 32 bit and 64 bit Linux systems where GLoBES is installed Operating system: 32 bit and 64 bit Linux RAM: Typically a few MBs Classification: 11.1 External routines: GLoBES [1,2] and routines/libraries used by GLoBES Subprograms used:Cat Id ADZI_v1_0, Title GLoBES, Reference CPC 177 (2007) 439 Nature of problem: Since neutrino masses do not appear in the standard model of particle physics, many models of neutrino masses also induce other types of new physics, which could affect the outcome of neutrino oscillation experiments. In general, these new physics imply high-dimensional parameter spaces that are difficult to explore using classical methods such as multi-dimensional projections and minimizations, such as those used in GLoBES [1,2]. Solution method: MonteCUBES is written as a plug-in to the GLoBES software [1,2] and provides the necessary methods to perform Markov Chain Monte Carlo sampling of the parameter space. This allows an efficient sampling of the parameter space and has a complexity which does not grow exponentially with the parameter space dimension. The integration of the MonteCUBES package with the GLoBES software makes sure that the experimental definitions already in use by the community can also be used with MonteCUBES, while also lowering the learning threshold for users who already know GLoBES. Additional comments: A Matlab GUI for interpretation of results is included in the distribution. Running time: The typical running time varies depending on the dimensionality of the parameter space, the complexity of the experiment, and how well the parameter space should be sampled. The running time for our simulations [3] with 15 free parameters at a Neutrino Factory with O(10) samples varied from a few hours to tens of hours. References:P. Huber, M. Lindner, W. Winter, Comput. Phys. Comm. 167 (2005) 195, hep-ph/0407333. P. Huber, J. Kopp, M. Lindner, M. Rolinec, W. Winter, Comput. Phys. Comm. 177 (2007) 432, hep-ph/0701187. S. Antusch, M. Blennow, E. Fernandez-Martinez, J. Lopez-Pavon, arXiv:0903.3986 [hep-ph].

EDITORIAL: Special section: Selected papers from the Second European Workshop on Monte Carlo Treatment Planning (MCTP2009) Special section: Selected papers from the Second European Workshop on Monte Carlo Treatment Planning (MCTP2009)

NASA Astrophysics Data System (ADS)

Spezi, Emiliano

2010-08-01

Sixty years after the paper 'The Monte Carlo method' by N Metropolis and S Ulam in The Journal of the American Statistical Association (Metropolis and Ulam 1949), use of the most accurate algorithm for computer modelling of radiotherapy linear accelerators, radiation detectors and three dimensional patient dose was discussed in Wales (UK). The Second European Workshop on Monte Carlo Treatment Planning (MCTP2009) was held at the National Museum of Wales in Cardiff. The event, organized by Velindre NHS Trust, Cardiff University and Cancer Research Wales, lasted two and a half days, during which leading experts and contributing authors presented and discussed the latest advances in the field of Monte Carlo treatment planning (MCTP). MCTP2009 was highly successful, judging from the number of participants which was in excess of 140. Of the attendees, 24% came from the UK, 46% from the rest of Europe, 12% from North America and 18% from the rest of the World. Fifty-three oral presentations and 24 posters were delivered in a total of 12 scientific sessions. MCTP2009 follows the success of previous similar initiatives (Verhaegen and Seuntjens 2005, Reynaert 2007, Verhaegen and Seuntjens 2008), and confirms the high level of interest in Monte Carlo technology for radiotherapy treatment planning. The 13 articles selected for this special section (following Physics in Medicine and Biology's usual rigorous peer-review procedure) give a good picture of the high quality of the work presented at MCTP2009. The book of abstracts can be downloaded from http://www.mctp2009.org. I wish to thank the IOP Medical Physics and Computational Physics Groups for their financial support, Elekta Ltd and Dosisoft for sponsoring MCTP2009, and leading manufacturers such as BrainLab, Nucletron and Varian for showcasing their latest MC-based radiotherapy solutions during a dedicated technical session. I am also very grateful to the eight invited speakers who kindly accepted to give keynote presentations which contributed significantly to raising the quality of the event and capturing the interest of the medical physics community. I also wish to thank all those who contributed to the success of MCTP2009: the members of the local Organizing Committee and the Workshop Management Team who managed the event very efficiently, the members of the European Working Group in Monte Carlo Treatment Planning (EWG-MCTP) who acted as Guest Associate Editors for the MCTP2009 abstracts reviewing process, and all the authors who generated new, high quality work. Finally, I hope that you find the contents of this special section enjoyable and informative. Emiliano Spezi Chairman of MCTP2009 Organizing Committee and Guest Editor References Metropolis N and Ulam S 1949 The Monte Carlo method J. Amer. Stat. Assoc. 44 335-41 Reynaert N 2007 First European Workshop on Monte Carlo Treatment Planning J. Phys.: Conf. Ser. 74 011001 Verhaegen F and Seuntjens J 2005 International Workshop on Current Topics in Monte Carlo Treatment Planning Phys. Med. Biol. 50 Verhaegen F and Seuntjens J 2008 International Workshop on Monte Carlo Techniques in Radiotherapy Delivery and Verification J. Phys.: Conf. Ser. 102 011001

SU-E-T-519: Investigation of the CyberKnife MultiPlan Monte Carlo Dose Calculation Using EBT3 Film Absolute Dosimetry for Delivery in a Heterogeneous Thorax Phantom

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lamberto, M; Chen, H; Huang, K

2015-06-15

Purpose To characterize the Cyberknife (CK) robotic system’s dosimetric accuracy of the delivery of MultiPlan’s Monte Carlo dose calculations using EBT3 radiochromic film inserted in a thorax phantom. Methods The CIRS XSight Lung Tracking (XLT) Phantom (model 10823) was used in this study with custom cut EBT3 film inserted in the horizontal (coronal) plane inside the lung tissue equivalent phantom. CK MultiPlan v3.5.3 with Monte Carlo dose calculation algorithm (1.5 mm grid size, 2% statistical uncertainty) was used to calculate a clinical plan for a 25-mm lung tumor lesion, as contoured by the physician, and then imported onto the XLTmore » phantom CT. Using the same film batch, the net OD to dose calibration curve was obtained using CK with the 60 mm fixed cone by delivering 0– 800 cGy. The test films (n=3) were irradiated using 325 cGy to the prescription point. Films were scanned 48 hours after irradiation using an Epson v700 scanner (48 bits color scan, extracted red channel only, 96 dpi). Percent absolute dose and relative isodose distribution difference relative to the planned dose were quantified using an in-house QA software program. Multiplan Monte Carlo dose calculation was validated using RCF dosimetry (EBT3) and gamma index criteria of 3%/3mm and 2%/2mm for absolute dose and relative isodose distribution measurement comparisons. Results EBT3 film measurements of the patient plans calculated with Monte Carlo in MultiPlan resulted in an absolute dose passing rate of 99.6±0.4% for the Gamma Index of 3%/3mm, 10% dose threshold, and 95.6±4.4% for 2%/2mm, 10% threshold criteria. The measured central axis absolute dose was within 1.2% (329.0±2.5 cGy) of the Monte Carlo planned dose (325.0±6.5 cGy) for that same point. Conclusion MultiPlan’s Monte Carlo dose calculation was validated using the EBT3 film absolute dosimetry for delivery in a heterogeneous thorax phantom.« less

EFFICIENT MODEL-FITTING AND MODEL-COMPARISON FOR HIGH-DIMENSIONAL BAYESIAN GEOSTATISTICAL MODELS. (R826887)

EPA Science Inventory

Geostatistical models are appropriate for spatially distributed data measured at irregularly spaced locations. We propose an efficient Markov chain Monte Carlo (MCMC) algorithm for fitting Bayesian geostatistical models with substantial numbers of unknown parameters to sizable...

Monte Carlo simulation of dynamic phase transitions and frequency dispersions of hysteresis curves in core/shell ferrimagnetic cubic nanoparticle

NASA Astrophysics Data System (ADS)

Vatansever, Erol

2017-05-01

By means of Monte Carlo simulation method with Metropolis algorithm, we elucidate the thermal and magnetic phase transition behaviors of a ferrimagnetic core/shell nanocubic system driven by a time dependent magnetic field. The particle core is composed of ferromagnetic spins, and it is surrounded by an antiferromagnetic shell. At the interface of the core/shell particle, we use antiferromagnetic spin-spin coupling. We simulate the nanoparticle using classical Heisenberg spins. After a detailed analysis, our Monte Carlo simulation results suggest that present system exhibits unusual and interesting magnetic behaviors. For example, at the relatively lower temperature regions, an increment in the amplitude of the external field destroys the antiferromagnetism in the shell part of the nanoparticle, leading to a ground state with ferromagnetic character. Moreover, particular attention has been dedicated to the hysteresis behaviors of the system. For the first time, we show that frequency dispersions can be categorized into three groups for a fixed temperature for finite core/shell systems, as in the case of the conventional bulk systems under the influence of an oscillating magnetic field.

Radiative transfer and spectroscopic databases: A line-sampling Monte Carlo approach

NASA Astrophysics Data System (ADS)

Galtier, Mathieu; Blanco, Stéphane; Dauchet, Jérémi; El Hafi, Mouna; Eymet, Vincent; Fournier, Richard; Roger, Maxime; Spiesser, Christophe; Terrée, Guillaume

2016-03-01

Dealing with molecular-state transitions for radiative transfer purposes involves two successive steps that both reach the complexity level at which physicists start thinking about statistical approaches: (1) constructing line-shaped absorption spectra as the result of very numerous state-transitions, (2) integrating over optical-path domains. For the first time, we show here how these steps can be addressed simultaneously using the null-collision concept. This opens the door to the design of Monte Carlo codes directly estimating radiative transfer observables from spectroscopic databases. The intermediate step of producing accurate high-resolution absorption spectra is no longer required. A Monte Carlo algorithm is proposed and applied to six one-dimensional test cases. It allows the computation of spectrally integrated intensities (over 25 cm-1 bands or the full IR range) in a few seconds, regardless of the retained database and line model. But free parameters need to be selected and they impact the convergence. A first possible selection is provided in full detail. We observe that this selection is highly satisfactory for quite distinct atmospheric and combustion configurations, but a more systematic exploration is still in progress.

A Monte Carlo model for 3D grain evolution during welding

NASA Astrophysics Data System (ADS)

Rodgers, Theron M.; Mitchell, John A.; Tikare, Veena

2017-09-01

Welding is one of the most wide-spread processes used in metal joining. However, there are currently no open-source software implementations for the simulation of microstructural evolution during a weld pass. Here we describe a Potts Monte Carlo based model implemented in the SPPARKS kinetic Monte Carlo computational framework. The model simulates melting, solidification and solid-state microstructural evolution of material in the fusion and heat-affected zones of a weld. The model does not simulate thermal behavior, but rather utilizes user input parameters to specify weld pool and heat-affect zone properties. Weld pool shapes are specified by Bézier curves, which allow for the specification of a wide range of pool shapes. Pool shapes can range from narrow and deep to wide and shallow representing different fluid flow conditions within the pool. Surrounding temperature gradients are calculated with the aide of a closest point projection algorithm. The model also allows simulation of pulsed power welding through time-dependent variation of the weld pool size. Example simulation results and comparisons with laboratory weld observations demonstrate microstructural variation with weld speed, pool shape, and pulsed-power.

Radiative transfer calculated from a Markov chain formalism

NASA Technical Reports Server (NTRS)

Esposito, L. W.; House, L. L.

1978-01-01

The theory of Markov chains is used to formulate the radiative transport problem in a general way by modeling the successive interactions of a photon as a stochastic process. Under the minimal requirement that the stochastic process is a Markov chain, the determination of the diffuse reflection or transmission from a scattering atmosphere is equivalent to the solution of a system of linear equations. This treatment is mathematically equivalent to, and thus has many of the advantages of, Monte Carlo methods, but can be considerably more rapid than Monte Carlo algorithms for numerical calculations in particular applications. We have verified the speed and accuracy of this formalism for the standard problem of finding the intensity of scattered light from a homogeneous plane-parallel atmosphere with an arbitrary phase function for scattering. Accurate results over a wide range of parameters were obtained with computation times comparable to those of a standard 'doubling' routine. The generality of this formalism thus allows fast, direct solutions to problems that were previously soluble only by Monte Carlo methods. Some comparisons are made with respect to integral equation methods.

Tolerance allocation for an electronic system using neural network/Monte Carlo approach

NASA Astrophysics Data System (ADS)

Al-Mohammed, Mohammed; Esteve, Daniel; Boucher, Jaque

2001-12-01

The intense global competition to produce quality products at a low cost has led many industrial nations to consider tolerances as a key factor to bring about cost as well as to remain competitive. In actually, Tolerance allocation stays widely applied on the Mechanic System. It is known that to study the tolerances in an electronic domain, Monte-Carlo method well be used. But the later method spends a long time. This paper reviews several methods (Worst-case, Statistical Method, Least Cost Allocation by Optimization methods) that can be used for treating the tolerancing problem for an Electronic System and explains their advantages and their limitations. Then, it proposes an efficient method based on the Neural Networks associated with Monte-Carlo method as basis data. The network is trained using the Error Back Propagation Algorithm to predict the individual part tolerances, minimizing the total cost of the system by a method of optimization. This proposed approach has been applied on Small-Signal Amplifier Circuit as an example. This method can be easily extended to a complex system of n-components.

Analysis of Optogalvanic Transients at 621.7 nm, 633.4 nm and 640.2 nm of Neon in a Discharge Plasma Fitted with a Monte Carlo Mathematical Model.

NASA Astrophysics Data System (ADS)

Ogungbemi, Kayode; Han, Xianming; Blosser, Micheal; Misra, Prabhakar; LASER Spectroscopy Group Collaboration

2014-03-01

Optogalvanic transitions have been recorded and fitted for 1s5 - 2p7\\ (621.7 nm), 1s5 - 2p8 (633.4 nm) and 1s5 - 2p9 (640.2 nm) transitions of neon in a Fe-Ne hollow cathode plasma discharge as a function of current (2-19 mA) and time evolution (0-50 microsec). The optogalvanic waveforms have been fitted to a Monte carlo mathematical model. The variation in the excited population of neon is governed by the rate of collision of the atoms involving the common metastable state (1s5) for the three transitions investigated. The concomitant changes in amplitudes and intensities of the optogalvanic signal waveforms associated with these transitions have been studied rigorously and the fitted parameters obtained using the Monte Carlo algorithm to help better understand the physics of the hollow cathode discharge. Thanks to Laser Spectroscopy group in Physics and Astronomy Dept. Howard University Washington DC.

A reversible-jump Markov chain Monte Carlo algorithm for 1D inversion of magnetotelluric data

NASA Astrophysics Data System (ADS)

Mandolesi, Eric; Ogaya, Xenia; Campanyà, Joan; Piana Agostinetti, Nicola

2018-04-01

This paper presents a new computer code developed to solve the 1D magnetotelluric (MT) inverse problem using a Bayesian trans-dimensional Markov chain Monte Carlo algorithm. MT data are sensitive to the depth-distribution of rock electric conductivity (or its reciprocal, resistivity). The solution provided is a probability distribution - the so-called posterior probability distribution (PPD) for the conductivity at depth, together with the PPD of the interface depths. The PPD is sampled via a reversible-jump Markov Chain Monte Carlo (rjMcMC) algorithm, using a modified Metropolis-Hastings (MH) rule to accept or discard candidate models along the chains. As the optimal parameterization for the inversion process is generally unknown a trans-dimensional approach is used to allow the dataset itself to indicate the most probable number of parameters needed to sample the PPD. The algorithm is tested against two simulated datasets and a set of MT data acquired in the Clare Basin (County Clare, Ireland). For the simulated datasets the correct number of conductive layers at depth and the associated electrical conductivity values is retrieved, together with reasonable estimates of the uncertainties on the investigated parameters. Results from the inversion of field measurements are compared with results obtained using a deterministic method and with well-log data from a nearby borehole. The PPD is in good agreement with the well-log data, showing as a main structure a high conductive layer associated with the Clare Shale formation. In this study, we demonstrate that our new code go beyond algorithms developend using a linear inversion scheme, as it can be used: (1) to by-pass the subjective choices in the 1D parameterizations, i.e. the number of horizontal layers in the 1D parameterization, and (2) to estimate realistic uncertainties on the retrieved parameters. The algorithm is implemented using a simple MPI approach, where independent chains run on isolated CPU, to take full advantage of parallel computer architectures. In case of a large number of data, a master/slave appoach can be used, where the master CPU samples the parameter space and the slave CPUs compute forward solutions.

Computational characterization of HPGe detectors usable for a wide variety of source geometries by using Monte Carlo simulation and a multi-objective evolutionary algorithm

NASA Astrophysics Data System (ADS)

Guerra, J. G.; Rubiano, J. G.; Winter, G.; Guerra, A. G.; Alonso, H.; Arnedo, M. A.; Tejera, A.; Martel, P.; Bolivar, J. P.

2017-06-01

In this work, we have developed a computational methodology for characterizing HPGe detectors by implementing in parallel a multi-objective evolutionary algorithm, together with a Monte Carlo simulation code. The evolutionary algorithm is used for searching the geometrical parameters of a model of detector by minimizing the differences between the efficiencies calculated by Monte Carlo simulation and two reference sets of Full Energy Peak Efficiencies (FEPEs) corresponding to two given sample geometries, a beaker of small diameter laid over the detector window and a beaker of large capacity which wrap the detector. This methodology is a generalization of a previously published work, which was limited to beakers placed over the window of the detector with a diameter equal or smaller than the crystal diameter, so that the crystal mount cap (which surround the lateral surface of the crystal), was not considered in the detector model. The generalization has been accomplished not only by including such a mount cap in the model, but also using multi-objective optimization instead of mono-objective, with the aim of building a model sufficiently accurate for a wider variety of beakers commonly used for the measurement of environmental samples by gamma spectrometry, like for instance, Marinellis, Petris, or any other beaker with a diameter larger than the crystal diameter, for which part of the detected radiation have to pass through the mount cap. The proposed methodology has been applied to an HPGe XtRa detector, providing a model of detector which has been successfully verificated for different source-detector geometries and materials and experimentally validated using CRMs.

Predicting patchy particle crystals: variable box shape simulations and evolutionary algorithms.

PubMed

Bianchi, Emanuela; Doppelbauer, Günther; Filion, Laura; Dijkstra, Marjolein; Kahl, Gerhard

2012-06-07

We consider several patchy particle models that have been proposed in literature and we investigate their candidate crystal structures in a systematic way. We compare two different algorithms for predicting crystal structures: (i) an approach based on Monte Carlo simulations in the isobaric-isothermal ensemble and (ii) an optimization technique based on ideas of evolutionary algorithms. We show that the two methods are equally successful and provide consistent results on crystalline phases of patchy particle systems.

Small-Noise Analysis and Symmetrization of Implicit Monte Carlo Samplers

DOE PAGES

Goodman, Jonathan; Lin, Kevin K.; Morzfeld, Matthias

2015-07-06

Implicit samplers are algorithms for producing independent, weighted samples from multivariate probability distributions. These are often applied in Bayesian data assimilation algorithms. We use Laplace asymptotic expansions to analyze two implicit samplers in the small noise regime. Our analysis suggests a symmetrization of the algorithms that leads to improved implicit sampling schemes at a relatively small additional cost. Here, computational experiments confirm the theory and show that symmetrization is effective for small noise sampling problems.

Calculated X-ray Intensities Using Monte Carlo Algorithms: A Comparison to Experimental EPMA Data

NASA Technical Reports Server (NTRS)

Carpenter, P. K.

2005-01-01

Monte Carlo (MC) modeling has been used extensively to simulate electron scattering and x-ray emission from complex geometries. Here are presented comparisons between MC results and experimental electron-probe microanalysis (EPMA) measurements as well as phi(rhoz) correction algorithms. Experimental EPMA measurements made on NIST SRM 481 (AgAu) and 482 (CuAu) alloys, at a range of accelerating potential and instrument take-off angles, represent a formal microanalysis data set that has been widely used to develop phi(rhoz) correction algorithms. X-ray intensity data produced by MC simulations represents an independent test of both experimental and phi(rhoz) correction algorithms. The alpha-factor method has previously been used to evaluate systematic errors in the analysis of semiconductor and silicate minerals, and is used here to compare the accuracy of experimental and MC-calculated x-ray data. X-ray intensities calculated by MC are used to generate a-factors using the certificated compositions in the CuAu binary relative to pure Cu and Au standards. MC simulations are obtained using the NIST, WinCasino, and WinXray algorithms; derived x-ray intensities have a built-in atomic number correction, and are further corrected for absorption and characteristic fluorescence using the PAP phi(rhoz) correction algorithm. The Penelope code additionally simulates both characteristic and continuum x-ray fluorescence and thus requires no further correction for use in calculating alpha-factors.

Energy modulated electron therapy: Design, implementation, and evaluation of a novel method of treatment planning and delivery

NASA Astrophysics Data System (ADS)

Al-Yahya, Khalid

Energy modulated electron therapy (EMET) is a promising treatment modality that has the fundamental capabilities to enhance the treatment planning and delivery of superficially located targets. Although it offers advantages over x-ray intensity modulated radiation therapy (IMRT), EMET has not been widely implemented to the same level of accuracy, automation, and clinical routine as its x-ray counterpart. This lack of implementation is attributed to the absence of a remotely automated beam shaping system as well as the deficiency in dosimetric accuracy of clinical electron pencil beam algorithms in the presence of beam modifiers and tissue heterogeneities. In this study, we present a novel technique for treatment planning and delivery of EMET. The delivery is achieved using a prototype of an automated "few leaf electron collimator" (FLEC). It consists of four copper leaves driven by stepper motors which are synchronized with the x-ray jaws in order to form a series of collimated rectangular openings or "fieldlets". Based on Monte Carlo studies, the FLEC has been designed to serve as an accessory tool to the current accelerator equipment. The FLEC was constructed and its operation was fully automated and integrated with the accelerator through an in-house assembled control unit. The control unit is a portable computer system accompanied with customized software that delivers EMET plans after acquiring them from the optimization station. EMET plans are produced based on dose volume constraints that employ Monte Carlo pre-generated and patient-specific kernels which are utilized by an in-house developed optimization algorithm. The structure of the optimization software is demonstrated. Using Monte Carlo techniques to calculate dose allows for accurate modeling of the collimation system as well as the patient heterogeneous geometry and take into account their impact on optimization. The Monte Carlo calculations were validated by comparing them against output measurements with an ionization chamber. Comparisons with measurements using nearly energy-independent radiochromic films were performed to confirm the Monte Carlo calculation accuracy for 1-D and 2-D dose distributions. We investigated the clinical significance of EMET on cancer sites that are inherently difficult to plan with IMRT. Several parameters were used to analyze treatment plans where they show that EMET provides significant overall improvements over IMRT.

Monte Carlo based, patient-specific RapidArc QA using Linac log files.

PubMed

Teke, Tony; Bergman, Alanah M; Kwa, William; Gill, Bradford; Duzenli, Cheryl; Popescu, I Antoniu

2010-01-01

A Monte Carlo (MC) based QA process to validate the dynamic beam delivery accuracy for Varian RapidArc (Varian Medical Systems, Palo Alto, CA) using Linac delivery log files (DynaLog) is presented. Using DynaLog file analysis and MC simulations, the goal of this article is to (a) confirm that adequate sampling is used in the RapidArc optimization algorithm (177 static gantry angles) and (b) to assess the physical machine performance [gantry angle and monitor unit (MU) delivery accuracy]. Ten clinically acceptable RapidArc treatment plans were generated for various tumor sites and delivered to a water-equivalent cylindrical phantom on the treatment unit. Three Monte Carlo simulations were performed to calculate dose to the CT phantom image set: (a) One using a series of static gantry angles defined by 177 control points with treatment planning system (TPS) MLC control files (planning files), (b) one using continuous gantry rotation with TPS generated MLC control files, and (c) one using continuous gantry rotation with actual Linac delivery log files. Monte Carlo simulated dose distributions are compared to both ionization chamber point measurements and with RapidArc TPS calculated doses. The 3D dose distributions were compared using a 3D gamma-factor analysis, employing a 3%/3 mm distance-to-agreement criterion. The dose difference between MC simulations, TPS, and ionization chamber point measurements was less than 2.1%. For all plans, the MC calculated 3D dose distributions agreed well with the TPS calculated doses (gamma-factor values were less than 1 for more than 95% of the points considered). Machine performance QA was supplemented with an extensive DynaLog file analysis. A DynaLog file analysis showed that leaf position errors were less than 1 mm for 94% of the time and there were no leaf errors greater than 2.5 mm. The mean standard deviation in MU and gantry angle were 0.052 MU and 0.355 degrees, respectively, for the ten cases analyzed. The accuracy and flexibility of the Monte Carlo based RapidArc QA system were demonstrated. Good machine performance and accurate dose distribution delivery of RapidArc plans were observed. The sampling used in the TPS optimization algorithm was found to be adequate.

A Bootstrap Metropolis-Hastings Algorithm for Bayesian Analysis of Big Data.

PubMed

Liang, Faming; Kim, Jinsu; Song, Qifan

2016-01-01

Markov chain Monte Carlo (MCMC) methods have proven to be a very powerful tool for analyzing data of complex structures. However, their computer-intensive nature, which typically require a large number of iterations and a complete scan of the full dataset for each iteration, precludes their use for big data analysis. In this paper, we propose the so-called bootstrap Metropolis-Hastings (BMH) algorithm, which provides a general framework for how to tame powerful MCMC methods to be used for big data analysis; that is to replace the full data log-likelihood by a Monte Carlo average of the log-likelihoods that are calculated in parallel from multiple bootstrap samples. The BMH algorithm possesses an embarrassingly parallel structure and avoids repeated scans of the full dataset in iterations, and is thus feasible for big data problems. Compared to the popular divide-and-combine method, BMH can be generally more efficient as it can asymptotically integrate the whole data information into a single simulation run. The BMH algorithm is very flexible. Like the Metropolis-Hastings algorithm, it can serve as a basic building block for developing advanced MCMC algorithms that are feasible for big data problems. This is illustrated in the paper by the tempering BMH algorithm, which can be viewed as a combination of parallel tempering and the BMH algorithm. BMH can also be used for model selection and optimization by combining with reversible jump MCMC and simulated annealing, respectively.

A Bootstrap Metropolis–Hastings Algorithm for Bayesian Analysis of Big Data

PubMed Central

Kim, Jinsu; Song, Qifan

2016-01-01

Markov chain Monte Carlo (MCMC) methods have proven to be a very powerful tool for analyzing data of complex structures. However, their computer-intensive nature, which typically require a large number of iterations and a complete scan of the full dataset for each iteration, precludes their use for big data analysis. In this paper, we propose the so-called bootstrap Metropolis-Hastings (BMH) algorithm, which provides a general framework for how to tame powerful MCMC methods to be used for big data analysis; that is to replace the full data log-likelihood by a Monte Carlo average of the log-likelihoods that are calculated in parallel from multiple bootstrap samples. The BMH algorithm possesses an embarrassingly parallel structure and avoids repeated scans of the full dataset in iterations, and is thus feasible for big data problems. Compared to the popular divide-and-combine method, BMH can be generally more efficient as it can asymptotically integrate the whole data information into a single simulation run. The BMH algorithm is very flexible. Like the Metropolis-Hastings algorithm, it can serve as a basic building block for developing advanced MCMC algorithms that are feasible for big data problems. This is illustrated in the paper by the tempering BMH algorithm, which can be viewed as a combination of parallel tempering and the BMH algorithm. BMH can also be used for model selection and optimization by combining with reversible jump MCMC and simulated annealing, respectively. PMID:29033469

Performances of the New Real Time Tsunami Detection Algorithm applied to tide gauges data

NASA Astrophysics Data System (ADS)

Chierici, F.; Embriaco, D.; Morucci, S.

2017-12-01

Real-time tsunami detection algorithms play a key role in any Tsunami Early Warning System. We have developed a new algorithm for tsunami detection (TDA) based on the real-time tide removal and real-time band-pass filtering of seabed pressure time series acquired by Bottom Pressure Recorders. The TDA algorithm greatly increases the tsunami detection probability, shortens the detection delay and enhances detection reliability with respect to the most widely used tsunami detection algorithm, while containing the computational cost. The algorithm is designed to be used also in autonomous early warning systems with a set of input parameters and procedures which can be reconfigured in real time. We have also developed a methodology based on Monte Carlo simulations to test the tsunami detection algorithms. The algorithm performance is estimated by defining and evaluating statistical parameters, namely the detection probability, the detection delay, which are functions of the tsunami amplitude and wavelength, and the occurring rate of false alarms. In this work we present the performance of the TDA algorithm applied to tide gauge data. We have adapted the new tsunami detection algorithm and the Monte Carlo test methodology to tide gauges. Sea level data acquired by coastal tide gauges in different locations and environmental conditions have been used in order to consider real working scenarios in the test. We also present an application of the algorithm to the tsunami event generated by Tohoku earthquake on March 11th 2011, using data recorded by several tide gauges scattered all over the Pacific area.

Continuous-time quantum Monte Carlo impurity solvers

NASA Astrophysics Data System (ADS)

Gull, Emanuel; Werner, Philipp; Fuchs, Sebastian; Surer, Brigitte; Pruschke, Thomas; Troyer, Matthias

2011-04-01

Continuous-time quantum Monte Carlo impurity solvers are algorithms that sample the partition function of an impurity model using diagrammatic Monte Carlo techniques. The present paper describes codes that implement the interaction expansion algorithm originally developed by Rubtsov, Savkin, and Lichtenstein, as well as the hybridization expansion method developed by Werner, Millis, Troyer, et al. These impurity solvers are part of the ALPS-DMFT application package and are accompanied by an implementation of dynamical mean-field self-consistency equations for (single orbital single site) dynamical mean-field problems with arbitrary densities of states. Program summaryProgram title: dmft Catalogue identifier: AEIL_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIL_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: ALPS LIBRARY LICENSE version 1.1 No. of lines in distributed program, including test data, etc.: 899 806 No. of bytes in distributed program, including test data, etc.: 32 153 916 Distribution format: tar.gz Programming language: C++ Operating system: The ALPS libraries have been tested on the following platforms and compilers: Linux with GNU Compiler Collection (g++ version 3.1 and higher), and Intel C++ Compiler (icc version 7.0 and higher) MacOS X with GNU Compiler (g++ Apple-version 3.1, 3.3 and 4.0) IBM AIX with Visual Age C++ (xlC version 6.0) and GNU (g++ version 3.1 and higher) compilers Compaq Tru64 UNIX with Compq C++ Compiler (cxx) SGI IRIX with MIPSpro C++ Compiler (CC) HP-UX with HP C++ Compiler (aCC) Windows with Cygwin or coLinux platforms and GNU Compiler Collection (g++ version 3.1 and higher) RAM: 10 MB-1 GB Classification: 7.3 External routines: ALPS [1], BLAS/LAPACK, HDF5 Nature of problem: (See [2].) Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as representations of quantum dots and molecular conductors and play an increasingly important role in the theory of "correlated electron" materials as auxiliary problems whose solution gives the "dynamical mean field" approximation to the self-energy and local correlation functions. Solution method: Quantum impurity models require a method of solution which provides access to both high and low energy scales and is effective for wide classes of physically realistic models. The continuous-time quantum Monte Carlo algorithms for which we present implementations here meet this challenge. Continuous-time quantum impurity methods are based on partition function expansions of quantum impurity models that are stochastically sampled to all orders using diagrammatic quantum Monte Carlo techniques. For a review of quantum impurity models and their applications and of continuous-time quantum Monte Carlo methods for impurity models we refer the reader to [2]. Additional comments: Use of dmft requires citation of this paper. Use of any ALPS program requires citation of the ALPS [1] paper. Running time: 60 s-8 h per iteration.

Accelerating Monte Carlo simulations with an NVIDIA ® graphics processor

NASA Astrophysics Data System (ADS)

Martinsen, Paul; Blaschke, Johannes; Künnemeyer, Rainer; Jordan, Robert

2009-10-01

Modern graphics cards, commonly used in desktop computers, have evolved beyond a simple interface between processor and display to incorporate sophisticated calculation engines that can be applied to general purpose computing. The Monte Carlo algorithm for modelling photon transport in turbid media has been implemented on an NVIDIA ® 8800 GT graphics card using the CUDA toolkit. The Monte Carlo method relies on following the trajectory of millions of photons through the sample, often taking hours or days to complete. The graphics-processor implementation, processing roughly 110 million scattering events per second, was found to run more than 70 times faster than a similar, single-threaded implementation on a 2.67 GHz desktop computer. Program summaryProgram title: Phoogle-C/Phoogle-G Catalogue identifier: AEEB_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEB_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 51 264 No. of bytes in distributed program, including test data, etc.: 2 238 805 Distribution format: tar.gz Programming language: C++ Computer: Designed for Intel PCs. Phoogle-G requires a NVIDIA graphics card with support for CUDA 1.1 Operating system: Windows XP Has the code been vectorised or parallelized?: Phoogle-G is written for SIMD architectures RAM: 1 GB Classification: 21.1 External routines: Charles Karney Random number library. Microsoft Foundation Class library. NVIDA CUDA library [1]. Nature of problem: The Monte Carlo technique is an effective algorithm for exploring the propagation of light in turbid media. However, accurate results require tracing the path of many photons within the media. The independence of photons naturally lends the Monte Carlo technique to implementation on parallel architectures. Generally, parallel computing can be expensive, but recent advances in consumer grade graphics cards have opened the possibility of high-performance desktop parallel-computing. Solution method: In this pair of programmes we have implemented the Monte Carlo algorithm described by Prahl et al. [2] for photon transport in infinite scattering media to compare the performance of two readily accessible architectures: a standard desktop PC and a consumer grade graphics card from NVIDIA. Restrictions: The graphics card implementation uses single precision floating point numbers for all calculations. Only photon transport from an isotropic point-source is supported. The graphics-card version has no user interface. The simulation parameters must be set in the source code. The desktop version has a simple user interface; however some properties can only be accessed through an ActiveX client (such as Matlab). Additional comments: The random number library used has a LGPL ( http://www.gnu.org/copyleft/lesser.html) licence. Running time: Runtime can range from minutes to months depending on the number of photons simulated and the optical properties of the medium. References:http://www.nvidia.com/object/cuda_home.html. S. Prahl, M. Keijzer, Sl. Jacques, A. Welch, SPIE Institute Series 5 (1989) 102.

Application of Monte Carlo algorithms to the Bayesian analysis of the Cosmic Microwave Background

NASA Technical Reports Server (NTRS)

Jewell, J.; Levin, S.; Anderson, C. H.

2004-01-01

Power spectrum estimation and evaluation of associated errors in the presence of incomplete sky coverage; nonhomogeneous, correlated instrumental noise; and foreground emission are problems of central importance for the extraction of cosmological information from the cosmic microwave background (CMB).

Error Analyses of the North Alabama Lightning Mapping Array (LMA)

NASA Technical Reports Server (NTRS)

Koshak, W. J.; Solokiewicz, R. J.; Blakeslee, R. J.; Goodman, S. J.; Christian, H. J.; Hall, J. M.; Bailey, J. C.; Krider, E. P.; Bateman, M. G.; Boccippio, D. J.

2003-01-01

Two approaches are used to characterize how accurately the North Alabama Lightning Mapping Array (LMA) is able to locate lightning VHF sources in space and in time. The first method uses a Monte Carlo computer simulation to estimate source retrieval errors. The simulation applies a VHF source retrieval algorithm that was recently developed at the NASA-MSFC and that is similar, but not identical to, the standard New Mexico Tech retrieval algorithm. The second method uses a purely theoretical technique (i.e., chi-squared Curvature Matrix theory) to estimate retrieval errors. Both methods assume that the LMA system has an overall rms timing error of 50ns, but all other possible errors (e.g., multiple sources per retrieval attempt) are neglected. The detailed spatial distributions of retrieval errors are provided. Given that the two methods are completely independent of one another, it is shown that they provide remarkably similar results, except that the chi-squared theory produces larger altitude error estimates than the (more realistic) Monte Carlo simulation.

Chemical application of diffusion quantum Monte Carlo

NASA Technical Reports Server (NTRS)

Reynolds, P. J.; Lester, W. A., Jr.

1984-01-01

The diffusion quantum Monte Carlo (QMC) method gives a stochastic solution to the Schroedinger equation. This approach is receiving increasing attention in chemical applications as a result of its high accuracy. However, reducing statistical uncertainty remains a priority because chemical effects are often obtained as small differences of large numbers. As an example, the single-triplet splitting of the energy of the methylene molecule CH sub 2 is given. The QMC algorithm was implemented on the CYBER 205, first as a direct transcription of the algorithm running on the VAX 11/780, and second by explicitly writing vector code for all loops longer than a crossover length C. The speed of the codes relative to one another as a function of C, and relative to the VAX, are discussed. The computational time dependence obtained versus the number of basis functions is discussed and this is compared with that obtained from traditional quantum chemistry codes and that obtained from traditional computer architectures.

New approach for absolute fluence distribution calculations in Monte Carlo simulations of light propagation in turbid media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Böcklin, Christoph, E-mail: boecklic@ethz.ch; Baumann, Dirk; Fröhlich, Jürg

A novel way to attain three dimensional fluence rate maps from Monte-Carlo simulations of photon propagation is presented in this work. The propagation of light in a turbid medium is described by the radiative transfer equation and formulated in terms of radiance. For many applications, particularly in biomedical optics, the fluence rate is a more useful quantity and directly derived from the radiance by integrating over all directions. Contrary to the usual way which calculates the fluence rate from absorbed photon power, the fluence rate in this work is directly calculated from the photon packet trajectory. The voxel based algorithmmore » works in arbitrary geometries and material distributions. It is shown that the new algorithm is more efficient and also works in materials with a low or even zero absorption coefficient. The capabilities of the new algorithm are demonstrated on a curved layered structure, where a non-scattering, non-absorbing layer is sandwiched between two highly scattering layers.« less

Auxiliary-field-based trial wave functions in quantum Monte Carlo calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chang, Chia -Chen; Rubenstein, Brenda M.; Morales, Miguel A.

2016-12-19

Quantum Monte Carlo (QMC) algorithms have long relied on Jastrow factors to incorporate dynamic correlation into trial wave functions. While Jastrow-type wave functions have been widely employed in real-space algorithms, they have seen limited use in second-quantized QMC methods, particularly in projection methods that involve a stochastic evolution of the wave function in imaginary time. Here we propose a scheme for generating Jastrow-type correlated trial wave functions for auxiliary-field QMC methods. The method is based on decoupling the two-body Jastrow into one-body projectors coupled to auxiliary fields, which then operate on a single determinant to produce a multideterminant trial wavemore » function. We demonstrate that intelligent sampling of the most significant determinants in this expansion can produce compact trial wave functions that reduce errors in the calculated energies. Lastly, our technique may be readily generalized to accommodate a wide range of two-body Jastrow factors and applied to a variety of model and chemical systems.« less

A comparative study of history-based versus vectorized Monte Carlo methods in the GPU/CUDA environment for a simple neutron eigenvalue problem

NASA Astrophysics Data System (ADS)

Liu, Tianyu; Du, Xining; Ji, Wei; Xu, X. George; Brown, Forrest B.

2014-06-01

For nuclear reactor analysis such as the neutron eigenvalue calculations, the time consuming Monte Carlo (MC) simulations can be accelerated by using graphics processing units (GPUs). However, traditional MC methods are often history-based, and their performance on GPUs is affected significantly by the thread divergence problem. In this paper we describe the development of a newly designed event-based vectorized MC algorithm for solving the neutron eigenvalue problem. The code was implemented using NVIDIA's Compute Unified Device Architecture (CUDA), and tested on a NVIDIA Tesla M2090 GPU card. We found that although the vectorized MC algorithm greatly reduces the occurrence of thread divergence thus enhancing the warp execution efficiency, the overall simulation speed is roughly ten times slower than the history-based MC code on GPUs. Profiling results suggest that the slow speed is probably due to the memory access latency caused by the large amount of global memory transactions. Possible solutions to improve the code efficiency are discussed.

TH-A-19A-06: Site-Specific Comparison of Analytical and Monte Carlo Based Dose Calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schuemann, J; Grassberger, C; Paganetti, H

2014-06-15

Purpose: To investigate the impact of complex patient geometries on the capability of analytical dose calculation algorithms to accurately predict dose distributions and to verify currently used uncertainty margins in proton therapy. Methods: Dose distributions predicted by an analytical pencilbeam algorithm were compared with Monte Carlo simulations (MCS) using TOPAS. 79 complete patient treatment plans were investigated for 7 disease sites (liver, prostate, breast, medulloblastoma spine and whole brain, lung and head and neck). A total of 508 individual passively scattered treatment fields were analyzed for field specific properties. Comparisons based on target coverage indices (EUD, D95, D90 and D50)more » were performed. Range differences were estimated for the distal position of the 90% dose level (R90) and the 50% dose level (R50). Two-dimensional distal dose surfaces were calculated and the root mean square differences (RMSD), average range difference (ARD) and average distal dose degradation (ADD), the distance between the distal position of the 80% and 20% dose levels (R80- R20), were analyzed. Results: We found target coverage indices calculated by TOPAS to generally be around 1–2% lower than predicted by the analytical algorithm. Differences in R90 predicted by TOPAS and the planning system can be larger than currently applied range margins in proton therapy for small regions distal to the target volume. We estimate new site-specific range margins (R90) for analytical dose calculations considering total range uncertainties and uncertainties from dose calculation alone based on the RMSD. Our results demonstrate that a reduction of currently used uncertainty margins is feasible for liver, prostate and whole brain fields even without introducing MC dose calculations. Conclusion: Analytical dose calculation algorithms predict dose distributions within clinical limits for more homogeneous patients sites (liver, prostate, whole brain). However, we recommend treatment plan verification using Monte Carlo simulations for patients with complex geometries.« less

Monte Carlo closure for moment-based transport schemes in general relativistic radiation hydrodynamic simulations

NASA Astrophysics Data System (ADS)

Foucart, Francois

2018-04-01

General relativistic radiation hydrodynamic simulations are necessary to accurately model a number of astrophysical systems involving black holes and neutron stars. Photon transport plays a crucial role in radiatively dominated accretion discs, while neutrino transport is critical to core-collapse supernovae and to the modelling of electromagnetic transients and nucleosynthesis in neutron star mergers. However, evolving the full Boltzmann equations of radiative transport is extremely expensive. Here, we describe the implementation in the general relativistic SPEC code of a cheaper radiation hydrodynamic method that theoretically converges to a solution of Boltzmann's equation in the limit of infinite numerical resources. The algorithm is based on a grey two-moment scheme, in which we evolve the energy density and momentum density of the radiation. Two-moment schemes require a closure that fills in missing information about the energy spectrum and higher order moments of the radiation. Instead of the approximate analytical closure currently used in core-collapse and merger simulations, we complement the two-moment scheme with a low-accuracy Monte Carlo evolution. The Monte Carlo results can provide any or all of the missing information in the evolution of the moments, as desired by the user. As a first test of our methods, we study a set of idealized problems demonstrating that our algorithm performs significantly better than existing analytical closures. We also discuss the current limitations of our method, in particular open questions regarding the stability of the fully coupled scheme.

Probabilistic Magnetotelluric Inversion with Adaptive Regularisation Using the No-U-Turns Sampler

NASA Astrophysics Data System (ADS)

Conway, Dennis; Simpson, Janelle; Didana, Yohannes; Rugari, Joseph; Heinson, Graham

2018-04-01

We present the first inversion of magnetotelluric (MT) data using a Hamiltonian Monte Carlo algorithm. The inversion of MT data is an underdetermined problem which leads to an ensemble of feasible models for a given dataset. A standard approach in MT inversion is to perform a deterministic search for the single solution which is maximally smooth for a given data-fit threshold. An alternative approach is to use Markov Chain Monte Carlo (MCMC) methods, which have been used in MT inversion to explore the entire solution space and produce a suite of likely models. This approach has the advantage of assigning confidence to resistivity models, leading to better geological interpretations. Recent advances in MCMC techniques include the No-U-Turns Sampler (NUTS), an efficient and rapidly converging method which is based on Hamiltonian Monte Carlo. We have implemented a 1D MT inversion which uses the NUTS algorithm. Our model includes a fixed number of layers of variable thickness and resistivity, as well as probabilistic smoothing constraints which allow sharp and smooth transitions. We present the results of a synthetic study and show the accuracy of the technique, as well as the fast convergence, independence of starting models, and sampling efficiency. Finally, we test our technique on MT data collected from a site in Boulia, Queensland, Australia to show its utility in geological interpretation and ability to provide probabilistic estimates of features such as depth to basement.

Macroion solutions in the cell model studied by field theory and Monte Carlo simulations.

PubMed

Lue, Leo; Linse, Per

2011-12-14

Aqueous solutions of charged spherical macroions with variable dielectric permittivity and their associated counterions are examined within the cell model using a field theory and Monte Carlo simulations. The field theory is based on separation of fields into short- and long-wavelength terms, which are subjected to different statistical-mechanical treatments. The simulations were performed by using a new, accurate, and fast algorithm for numerical evaluation of the electrostatic polarization interaction. The field theory provides counterion distributions outside a macroion in good agreement with the simulation results over the full range from weak to strong electrostatic coupling. A low-dielectric macroion leads to a displacement of the counterions away from the macroion. © 2011 American Institute of Physics

Monte Carlo Sampling in Fractal Landscapes

NASA Astrophysics Data System (ADS)

Leitão, Jorge C.; Lopes, J. M. Viana Parente; Altmann, Eduardo G.

2013-05-01

We design a random walk to explore fractal landscapes such as those describing chaotic transients in dynamical systems. We show that the random walk moves efficiently only when its step length depends on the height of the landscape via the largest Lyapunov exponent of the chaotic system. We propose a generalization of the Wang-Landau algorithm which constructs not only the density of states (transient time distribution) but also the correct step length. As a result, we obtain a flat-histogram Monte Carlo method which samples fractal landscapes in polynomial time, a dramatic improvement over the exponential scaling of traditional uniform-sampling methods. Our results are not limited by the dimensionality of the landscape and are confirmed numerically in chaotic systems with up to 30 dimensions.

Advances in Monte-Carlo code TRIPOLI-4®'s treatment of the electromagnetic cascade

NASA Astrophysics Data System (ADS)

Mancusi, Davide; Bonin, Alice; Hugot, François-Xavier; Malouch, Fadhel

2018-01-01

TRIPOLI-4® is a Monte-Carlo particle-transport code developed at CEA-Saclay (France) that is employed in the domains of nuclear-reactor physics, criticality-safety, shielding/radiation protection and nuclear instrumentation. The goal of this paper is to report on current developments, validation and verification made in TRIPOLI-4 in the electron/positron/photon sector. The new capabilities and improvements concern refinements to the electron transport algorithm, the introduction of a charge-deposition score, the new thick-target bremsstrahlung option, the upgrade of the bremsstrahlung model and the improvement of electron angular straggling at low energy. The importance of each of the developments above is illustrated by comparisons with calculations performed with other codes and with experimental data.

Continuous-time quantum Monte Carlo calculation of multiorbital vertex asymptotics

NASA Astrophysics Data System (ADS)

Kaufmann, Josef; Gunacker, Patrik; Held, Karsten

2017-07-01

We derive the equations for calculating the high-frequency asymptotics of the local two-particle vertex function for a multiorbital impurity model. These relate the asymptotics for a general local interaction to equal-time two-particle Green's functions, which we sample using continuous-time quantum Monte Carlo simulations with a worm algorithm. As specific examples we study the single-orbital Hubbard model and the three t2 g orbitals of SrVO3 within dynamical mean-field theory (DMFT). We demonstrate how the knowledge of the high-frequency asymptotics reduces the statistical uncertainties of the vertex and further eliminates finite-box-size effects. The proposed method benefits the calculation of nonlocal susceptibilities in DMFT and diagrammatic extensions of DMFT.

Miming the cancer-immune system competition by kinetic Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Bianca, Carlo; Lemarchand, Annie

2016-10-01

In order to mimic the interactions between cancer and the immune system at cell scale, we propose a minimal model of cell interactions that is similar to a chemical mechanism including autocatalytic steps. The cells are supposed to bear a quantity called activity that may increase during the interactions. The fluctuations of cell activity are controlled by a so-called thermostat. We develop a kinetic Monte Carlo algorithm to simulate the cell interactions and thermalization of cell activity. The model is able to reproduce the well-known behavior of tumors treated by immunotherapy: the first apparent elimination of the tumor by the immune system is followed by a long equilibrium period and the final escape of cancer from immunosurveillance.

Importance Sampling of Word Patterns in DNA and Protein Sequences

PubMed Central

Chan, Hock Peng; Chen, Louis H.Y.

2010-01-01

Abstract Monte Carlo methods can provide accurate p-value estimates of word counting test statistics and are easy to implement. They are especially attractive when an asymptotic theory is absent or when either the search sequence or the word pattern is too short for the application of asymptotic formulae. Naive direct Monte Carlo is undesirable for the estimation of small probabilities because the associated rare events of interest are seldom generated. We propose instead efficient importance sampling algorithms that use controlled insertion of the desired word patterns on randomly generated sequences. The implementation is illustrated on word patterns of biological interest: palindromes and inverted repeats, patterns arising from position-specific weight matrices (PSWMs), and co-occurrences of pairs of motifs. PMID:21128856

Cross-platform validation and analysis environment for particle physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chekanov, S. V.; Pogrebnyak, I.; Wilbern, D.

A multi-platform validation and analysis framework for public Monte Carlo simulation for high-energy particle collisions is discussed. The front-end of this framework uses the Python programming language, while the back-end is written in Java, which provides a multi-platform environment that can be run from a web browser and can easily be deployed at the grid sites. The analysis package includes all major software tools used in high-energy physics, such as Lorentz vectors, jet algorithms, histogram packages, graphic canvases, and tools for providing data access. This multi-platform software suite, designed to minimize OS-specific maintenance and deployment time, is used for onlinemore » validation of Monte Carlo event samples through a web interface.« less

Acting Irrationally to Improve Performance in Stochastic Worlds

NASA Astrophysics Data System (ADS)

Belavkin, Roman V.

Despite many theories and algorithms for decision-making, after estimating the utility function the choice is usually made by maximising its expected value (the max EU principle). This traditional and 'rational' conclusion of the decision-making process is compared in this paper with several 'irrational' techniques that make choice in Monte-Carlo fashion. The comparison is made by evaluating the performance of simple decision-theoretic agents in stochastic environments. It is shown that not only the random choice strategies can achieve performance comparable to the max EU method, but under certain conditions the Monte-Carlo choice methods perform almost two times better than the max EU. The paper concludes by quoting evidence from recent cognitive modelling works as well as the famous decision-making paradoxes.

A GPU-based large-scale Monte Carlo simulation method for systems with long-range interactions

NASA Astrophysics Data System (ADS)

Liang, Yihao; Xing, Xiangjun; Li, Yaohang

2017-06-01

In this work we present an efficient implementation of Canonical Monte Carlo simulation for Coulomb many body systems on graphics processing units (GPU). Our method takes advantage of the GPU Single Instruction, Multiple Data (SIMD) architectures, and adopts the sequential updating scheme of Metropolis algorithm. It makes no approximation in the computation of energy, and reaches a remarkable 440-fold speedup, compared with the serial implementation on CPU. We further use this method to simulate primitive model electrolytes, and measure very precisely all ion-ion pair correlation functions at high concentrations. From these data, we extract the renormalized Debye length, renormalized valences of constituent ions, and renormalized dielectric constants. These results demonstrate unequivocally physics beyond the classical Poisson-Boltzmann theory.

Wang-Landau method for calculating Rényi entropies in finite-temperature quantum Monte Carlo simulations.

PubMed

Inglis, Stephen; Melko, Roger G

2013-01-01

We implement a Wang-Landau sampling technique in quantum Monte Carlo (QMC) simulations for the purpose of calculating the Rényi entanglement entropies and associated mutual information. The algorithm converges an estimate for an analog to the density of states for stochastic series expansion QMC, allowing a direct calculation of Rényi entropies without explicit thermodynamic integration. We benchmark results for the mutual information on two-dimensional (2D) isotropic and anisotropic Heisenberg models, a 2D transverse field Ising model, and a three-dimensional Heisenberg model, confirming a critical scaling of the mutual information in cases with a finite-temperature transition. We discuss the benefits and limitations of broad sampling techniques compared to standard importance sampling methods.

Double differential neutron spectra generated by the interaction of a 12 MeV/nucleon 36S beam on a thick natCu target

NASA Astrophysics Data System (ADS)

Trinh, N. D.; Fadil, M.; Lewitowicz, M.; Ledoux, X.; Laurent, B.; Thomas, J.-C.; Clerc, T.; Desmezières, V.; Dupuis, M.; Madeline, A.; Dessay, E.; Grinyer, G. F.; Grinyer, J.; Menard, N.; Porée, F.; Achouri, L.; Delaunay, F.; Parlog, M.

2018-07-01

Double differential neutron spectra (energy, angle) originating from a thick natCu target bombarded by a 12 MeV/nucleon 36S16+ beam were measured by the activation method and the Time-of-flight technique at the Grand Accélérateur National d'Ions Lourds (GANIL). A neutron spectrum unfolding algorithm combining the SAND-II iterative method and Monte-Carlo techniques was developed for the analysis of the activation results that cover a wide range of neutron energies. It was implemented into a graphical user interface program, called GanUnfold. The experimental neutron spectra are compared to Monte-Carlo simulations performed using the PHITS and FLUKA codes.

Monte-Carlo simulation of a stochastic differential equation

NASA Astrophysics Data System (ADS)

Arif, ULLAH; Majid, KHAN; M, KAMRAN; R, KHAN; Zhengmao, SHENG

2017-12-01

For solving higher dimensional diffusion equations with an inhomogeneous diffusion coefficient, Monte Carlo (MC) techniques are considered to be more effective than other algorithms, such as finite element method or finite difference method. The inhomogeneity of diffusion coefficient strongly limits the use of different numerical techniques. For better convergence, methods with higher orders have been kept forward to allow MC codes with large step size. The main focus of this work is to look for operators that can produce converging results for large step sizes. As a first step, our comparative analysis has been applied to a general stochastic problem. Subsequently, our formulization is applied to the problem of pitch angle scattering resulting from Coulomb collisions of charge particles in the toroidal devices.

Accuracy control in Monte Carlo radiative calculations

NASA Technical Reports Server (NTRS)

Almazan, P. Planas

1993-01-01

The general accuracy law that rules the Monte Carlo, ray-tracing algorithms used commonly for the calculation of the radiative entities in the thermal analysis of spacecraft are presented. These entities involve transfer of radiative energy either from a single source to a target (e.g., the configuration factors). or from several sources to a target (e.g., the absorbed heat fluxes). In fact, the former is just a particular case of the latter. The accuracy model is later applied to the calculation of some specific radiative entities. Furthermore, some issues related to the implementation of such a model in a software tool are discussed. Although only the relative error is considered through the discussion, similar results can be derived for the absolute error.

Simple formalism for efficient derivatives and multi-determinant expansions in quantum Monte Carlo

DOE Office of Scientific and Technical Information (OSTI.GOV)

Filippi, Claudia, E-mail: c.filippi@utwente.nl; Assaraf, Roland, E-mail: assaraf@lct.jussieu.fr; Moroni, Saverio, E-mail: moroni@democritos.it

2016-05-21

We present a simple and general formalism to compute efficiently the derivatives of a multi-determinant Jastrow-Slater wave function, the local energy, the interatomic forces, and similar quantities needed in quantum Monte Carlo. Through a straightforward manipulation of matrices evaluated on the occupied and virtual orbitals, we obtain an efficiency equivalent to algorithmic differentiation in the computation of the interatomic forces and the optimization of the orbital parameters. Furthermore, for a large multi-determinant expansion, the significant computational gain afforded by a recently introduced table method is here extended to the local value of any one-body operator and to its derivatives, inmore » both all-electron and pseudopotential calculations.« less

McSKY: A hybrid Monte-Carlo lime-beam code for shielded gamma skyshine calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shultis, J.K.; Faw, R.E.; Stedry, M.H.

1994-07-01

McSKY evaluates skyshine dose from an isotropic, monoenergetic, point photon source collimated into either a vertical cone or a vertical structure with an N-sided polygon cross section. The code assumes an overhead shield of two materials, through the user can specify zero shield thickness for an unshielded calculation. The code uses a Monte-Carlo algorithm to evaluate transport through source shields and the integral line source to describe photon transport through the atmosphere. The source energy must be between 0.02 and 100 MeV. For heavily shielded sources with energies above 20 MeV, McSKY results must be used cautiously, especially at detectormore » locations near the source.« less

New approach based on tetrahedral-mesh geometry for accurate 4D Monte Carlo patient-dose calculation

NASA Astrophysics Data System (ADS)

Han, Min Cheol; Yeom, Yeon Soo; Kim, Chan Hyeong; Kim, Seonghoon; Sohn, Jason W.

2015-02-01

In the present study, to achieve accurate 4D Monte Carlo dose calculation in radiation therapy, we devised a new approach that combines (1) modeling of the patient body using tetrahedral-mesh geometry based on the patient’s 4D CT data, (2) continuous movement/deformation of the tetrahedral patient model by interpolation of deformation vector fields acquired through deformable image registration, and (3) direct transportation of radiation particles during the movement and deformation of the tetrahedral patient model. The results of our feasibility study show that it is certainly possible to construct 4D patient models (= phantoms) with sufficient accuracy using the tetrahedral-mesh geometry and to directly transport radiation particles during continuous movement and deformation of the tetrahedral patient model. This new approach not only produces more accurate dose distribution in the patient but also replaces the current practice of using multiple 3D voxel phantoms and combining multiple dose distributions after Monte Carlo simulations. For routine clinical application of our new approach, the use of fast automatic segmentation algorithms is a must. In order to achieve, simultaneously, both dose accuracy and computation speed, the number of tetrahedrons for the lungs should be optimized. Although the current computation speed of our new 4D Monte Carlo simulation approach is slow (i.e. ~40 times slower than that of the conventional dose accumulation approach), this problem is resolvable by developing, in Geant4, a dedicated navigation class optimized for particle transportation in tetrahedral-mesh geometry.

Monte Carlo simulations of precise timekeeping in the Milstar communication satellite system

NASA Technical Reports Server (NTRS)

Camparo, James C.; Frueholz, R. P.

1995-01-01

The Milstar communications satellite system will provide secure antijam communication capabilities for DOD operations into the next century. In order to accomplish this task, the Milstar system will employ precise timekeeping on its satellites and at its ground control stations. The constellation will consist of four satellites in geosynchronous orbit, each carrying a set of four rubidium (Rb) atomic clocks. Several times a day, during normal operation, the Mission Control Element (MCE) will collect timing information from the constellation, and after several days use this information to update the time and frequency of the satellite clocks. The MCE will maintain precise time with a cesium (Cs) atomic clock, synchronized to UTC(USNO) via a GPS receiver. We have developed a Monte Carlo simulation of Milstar's space segment timekeeping. The simulation includes the effects of: uplink/downlink time transfer noise; satellite crosslink time transfer noise; satellite diurnal temperature variations; satellite and ground station atomic clock noise; and also quantization limits regarding satellite time and frequency corrections. The Monte Carlo simulation capability has proven to be an invaluable tool in assessing the performance characteristics of various timekeeping algorithms proposed for Milstar, and also in highlighting the timekeeping capabilities of the system. Here, we provide a brief overview of the basic Milstar timekeeping architecture as it is presently envisioned. We then describe the Monte Carlo simulation of space segment timekeeping, and provide examples of the simulation's efficacy in resolving timekeeping issues.

Multi-particle phase space integration with arbitrary set of singularities in CompHEP

NASA Astrophysics Data System (ADS)

Kovalenko, D. N.; Pukhov, A. E.

1997-02-01

We describe an algorithm of multi-particle phase space integration for collision and decay processes realized in CompHEP package version 3.2. In the framework of this algorithm it is possible to regularize an arbitrary set of singularities caused by virtual particle propagators. The algorithm is based on the method of the recursive representation of kinematics and on the multichannel Monte Carlo approach. CompHEP package is available by WWW: http://theory.npi.msu.su/pukhov/comphep.html

Monte Carlo simulation of Ising models by multispin coding on a vector computer

NASA Astrophysics Data System (ADS)

Wansleben, Stephan; Zabolitzky, John G.; Kalle, Claus

1984-11-01

Rebbi's efficient multispin coding algorithm for Ising models is combined with the use of the vector computer CDC Cyber 205. A speed of 21.2 million updates per second is reached. This is comparable to that obtained by special- purpose computers.

Fast and unbiased estimator of the time-dependent Hurst exponent.

PubMed

Pianese, Augusto; Bianchi, Sergio; Palazzo, Anna Maria

2018-03-01

We combine two existing estimators of the local Hurst exponent to improve both the goodness of fit and the computational speed of the algorithm. An application with simulated time series is implemented, and a Monte Carlo simulation is performed to provide evidence of the improvement.

Fast and unbiased estimator of the time-dependent Hurst exponent

NASA Astrophysics Data System (ADS)

Pianese, Augusto; Bianchi, Sergio; Palazzo, Anna Maria

2018-03-01

We combine two existing estimators of the local Hurst exponent to improve both the goodness of fit and the computational speed of the algorithm. An application with simulated time series is implemented, and a Monte Carlo simulation is performed to provide evidence of the improvement.

Asteroid mass estimation using Markov-Chain Monte Carlo techniques

NASA Astrophysics Data System (ADS)

Siltala, Lauri; Granvik, Mikael

2016-10-01

Estimates for asteroid masses are based on their gravitational perturbations on the orbits of other objects such as Mars, spacecraft, or other asteroids and/or their satellites. In the case of asteroid-asteroid perturbations, this leads to a 13-dimensional inverse problem where the aim is to derive the mass of the perturbing asteroid and six orbital elements for both the perturbing asteroid and the test asteroid using astrometric observations. We have developed and implemented three different mass estimation algorithms utilizing asteroid-asteroid perturbations into the OpenOrb asteroid-orbit-computation software: the very rough 'marching' approximation, in which the asteroid orbits are fixed at a given epoch, reducing the problem to a one-dimensional estimation of the mass, an implementation of the Nelder-Mead simplex method, and most significantly, a Markov-Chain Monte Carlo (MCMC) approach. We will introduce each of these algorithms with particular focus on the MCMC algorithm, and present example results for both synthetic and real data. Our results agree with the published mass estimates, but suggest that the published uncertainties may be misleading as a consequence of using linearized mass-estimation methods. Finally, we discuss remaining challenges with the algorithms as well as future plans, particularly in connection with ESA's Gaia mission.

Assessment of mean-field microkinetic models for CO methanation on stepped metal surfaces using accelerated kinetic Monte Carlo

NASA Astrophysics Data System (ADS)

Andersen, Mie; Plaisance, Craig P.; Reuter, Karsten

2017-10-01

First-principles screening studies aimed at predicting the catalytic activity of transition metal (TM) catalysts have traditionally been based on mean-field (MF) microkinetic models, which neglect the effect of spatial correlations in the adsorbate layer. Here we critically assess the accuracy of such models for the specific case of CO methanation over stepped metals by comparing to spatially resolved kinetic Monte Carlo (kMC) simulations. We find that the typical low diffusion barriers offered by metal surfaces can be significantly increased at step sites, which results in persisting correlations in the adsorbate layer. As a consequence, MF models may overestimate the catalytic activity of TM catalysts by several orders of magnitude. The potential higher accuracy of kMC models comes at a higher computational cost, which can be especially challenging for surface reactions on metals due to a large disparity in the time scales of different processes. In order to overcome this issue, we implement and test a recently developed algorithm for achieving temporal acceleration of kMC simulations. While the algorithm overall performs quite well, we identify some challenging cases which may lead to a breakdown of acceleration algorithms and discuss possible directions for future algorithm development.

Validation of a track repeating algorithm for intensity modulated proton therapy: clinical cases study

NASA Astrophysics Data System (ADS)

Yepes, Pablo P.; Eley, John G.; Liu, Amy; Mirkovic, Dragan; Randeniya, Sharmalee; Titt, Uwe; Mohan, Radhe

2016-04-01

Monte Carlo (MC) methods are acknowledged as the most accurate technique to calculate dose distributions. However, due its lengthy calculation times, they are difficult to utilize in the clinic or for large retrospective studies. Track-repeating algorithms, based on MC-generated particle track data in water, accelerate dose calculations substantially, while essentially preserving the accuracy of MC. In this study, we present the validation of an efficient dose calculation algorithm for intensity modulated proton therapy, the fast dose calculator (FDC), based on a track-repeating technique. We validated the FDC algorithm for 23 patients, which included 7 brain, 6 head-and-neck, 5 lung, 1 spine, 1 pelvis and 3 prostate cases. For validation, we compared FDC-generated dose distributions with those from a full-fledged Monte Carlo based on GEANT4 (G4). We compared dose-volume-histograms, 3D-gamma-indices and analyzed a series of dosimetric indices. More than 99% of the voxels in the voxelized phantoms describing the patients have a gamma-index smaller than unity for the 2%/2 mm criteria. In addition the difference relative to the prescribed dose between the dosimetric indices calculated with FDC and G4 is less than 1%. FDC reduces the calculation times from 5 ms per proton to around 5 μs.

A New Algorithm with Plane Waves and Wavelets for Random Velocity Fields with Many Spatial Scales

NASA Astrophysics Data System (ADS)

Elliott, Frank W.; Majda, Andrew J.

1995-03-01

A new Monte Carlo algorithm for constructing and sampling stationary isotropic Gaussian random fields with power-law energy spectrum, infrared divergence, and fractal self-similar scaling is developed here. The theoretical basis for this algorithm involves the fact that such a random field is well approximated by a superposition of random one-dimensional plane waves involving a fixed finite number of directions. In general each one-dimensional plane wave is the sum of a random shear layer and a random acoustical wave. These one-dimensional random plane waves are then simulated by a wavelet Monte Carlo method for a single space variable developed recently by the authors. The computational results reported in this paper demonstrate remarkable low variance and economical representation of such Gaussian random fields through this new algorithm. In particular, the velocity structure function for an imcorepressible isotropic Gaussian random field in two space dimensions with the Kolmogoroff spectrum can be simulated accurately over 12 decades with only 100 realizations of the algorithm with the scaling exponent accurate to 1.1% and the constant prefactor accurate to 6%; in fact, the exponent of the velocity structure function can be computed over 12 decades within 3.3% with only 10 realizations. Furthermore, only 46,592 active computational elements are utilized in each realization to achieve these results for 12 decades of scaling behavior.

Developing a cosmic ray muon sampling capability for muon tomography and monitoring applications

NASA Astrophysics Data System (ADS)

Chatzidakis, S.; Chrysikopoulou, S.; Tsoukalas, L. H.

2015-12-01

In this study, a cosmic ray muon sampling capability using a phenomenological model that captures the main characteristics of the experimentally measured spectrum coupled with a set of statistical algorithms is developed. The "muon generator" produces muons with zenith angles in the range 0-90° and energies in the range 1-100 GeV and is suitable for Monte Carlo simulations with emphasis on muon tomographic and monitoring applications. The muon energy distribution is described by the Smith and Duller (1959) [35] phenomenological model. Statistical algorithms are then employed for generating random samples. The inverse transform provides a means to generate samples from the muon angular distribution, whereas the Acceptance-Rejection and Metropolis-Hastings algorithms are employed to provide the energy component. The predictions for muon energies 1-60 GeV and zenith angles 0-90° are validated with a series of actual spectrum measurements and with estimates from the software library CRY. The results confirm the validity of the phenomenological model and the applicability of the statistical algorithms to generate polyenergetic-polydirectional muons. The response of the algorithms and the impact of critical parameters on computation time and computed results were investigated. Final output from the proposed "muon generator" is a look-up table that contains the sampled muon angles and energies and can be easily integrated into Monte Carlo particle simulation codes such as Geant4 and MCNP.

Stan : A Probabilistic Programming Language

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carpenter, Bob; Gelman, Andrew; Hoffman, Matthew D.

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Stan is also a platform for computing log densities and their gradients and Hessians, which can be used in alternative algorithms such as variational Bayes, expectationmore » propagation, and marginal inference using approximate integration. To this end, Stan is set up so that the densities, gradients, and Hessians, along with intermediate quantities of the algorithm such as acceptance probabilities, are easily accessible. Stan can also be called from the command line using the cmdstan package, through R using the rstan package, and through Python using the pystan package. All three interfaces support sampling and optimization-based inference with diagnostics and posterior analysis. rstan and pystan also provide access to log probabilities, gradients, Hessians, parameter transforms, and specialized plotting.« less

Many-body calculations of low energy eigenstates in magnetic and periodic systems with self healing diffusion Monte Carlo: steps beyond the fixed-phase

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reboredo, Fernando A.

The self-healing diffusion Monte Carlo algorithm (SHDMC) [Reboredo, Hood and Kent, Phys. Rev. B {\\bf 79}, 195117 (2009), Reboredo, {\\it ibid.} {\\bf 80}, 125110 (2009)] is extended to study the ground and excited states of magnetic and periodic systems. A recursive optimization algorithm is derived from the time evolution of the mixed probability density. The mixed probability density is given by an ensemble of electronic configurations (walkers) with complex weight. This complex weigh allows the amplitude of the fix-node wave function to move away from the trial wave function phase. This novel approach is both a generalization of SHDMC andmore » the fixed-phase approximation [Ortiz, Ceperley and Martin Phys Rev. Lett. {\\bf 71}, 2777 (1993)]. When used recursively it improves simultaneously the node and phase. The algorithm is demonstrated to converge to the nearly exact solutions of model systems with periodic boundary conditions or applied magnetic fields. The method is also applied to obtain low energy excitations with magnetic field or periodic boundary conditions. The potential applications of this new method to study periodic, magnetic, and complex Hamiltonians are discussed.« less

Simulating polarized light scattering in terrestrial snow based on bicontinuous random medium and Monte Carlo ray tracing

NASA Astrophysics Data System (ADS)

Xiong, Chuan; Shi, Jiancheng

2014-01-01

To date, the light scattering models of snow consider very little about the real snow microstructures. The ideal spherical or other single shaped particle assumptions in previous snow light scattering models can cause error in light scattering modeling of snow and further cause errors in remote sensing inversion algorithms. This paper tries to build up a snow polarized reflectance model based on bicontinuous medium, with which the real snow microstructure is considered. The accurate specific surface area of bicontinuous medium can be analytically derived. The polarized Monte Carlo ray tracing technique is applied to the computer generated bicontinuous medium. With proper algorithms, the snow surface albedo, bidirectional reflectance distribution function (BRDF) and polarized BRDF can be simulated. The validation of model predicted spectral albedo and bidirectional reflectance factor (BRF) using experiment data shows good results. The relationship between snow surface albedo and snow specific surface area (SSA) were predicted, and this relationship can be used for future improvement of snow specific surface area (SSA) inversion algorithms. The model predicted polarized reflectance is validated and proved accurate, which can be further applied in polarized remote sensing.

Multiple Time-Step Dual-Hamiltonian Hybrid Molecular Dynamics — Monte Carlo Canonical Propagation Algorithm

PubMed Central

Weare, Jonathan; Dinner, Aaron R.; Roux, Benoît

2016-01-01

A multiple time-step integrator based on a dual Hamiltonian and a hybrid method combining molecular dynamics (MD) and Monte Carlo (MC) is proposed to sample systems in the canonical ensemble. The Dual Hamiltonian Multiple Time-Step (DHMTS) algorithm is based on two similar Hamiltonians: a computationally expensive one that serves as a reference and a computationally inexpensive one to which the workload is shifted. The central assumption is that the difference between the two Hamiltonians is slowly varying. Earlier work has shown that such dual Hamiltonian multiple time-step schemes effectively precondition nonlinear differential equations for dynamics by reformulating them into a recursive root finding problem that can be solved by propagating a correction term through an internal loop, analogous to RESPA. Of special interest in the present context, a hybrid MD-MC version of the DHMTS algorithm is introduced to enforce detailed balance via a Metropolis acceptance criterion and ensure consistency with the Boltzmann distribution. The Metropolis criterion suppresses the discretization errors normally associated with the propagation according to the computationally inexpensive Hamiltonian, treating the discretization error as an external work. Illustrative tests are carried out to demonstrate the effectiveness of the method. PMID:26918826

Stan : A Probabilistic Programming Language

DOE PAGES

Carpenter, Bob; Gelman, Andrew; Hoffman, Matthew D.; ...

2017-01-01

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Stan is also a platform for computing log densities and their gradients and Hessians, which can be used in alternative algorithms such as variational Bayes, expectationmore » propagation, and marginal inference using approximate integration. To this end, Stan is set up so that the densities, gradients, and Hessians, along with intermediate quantities of the algorithm such as acceptance probabilities, are easily accessible. Stan can also be called from the command line using the cmdstan package, through R using the rstan package, and through Python using the pystan package. All three interfaces support sampling and optimization-based inference with diagnostics and posterior analysis. rstan and pystan also provide access to log probabilities, gradients, Hessians, parameter transforms, and specialized plotting.« less

SU-E-T-397: Evaluation of Planned Dose Distributions by Monte Carlo (0.5%) and Ray Tracing Algorithm for the Spinal Tumors with CyberKnife

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cho, H; Brindle, J; Hepel, J

2015-06-15

Purpose: To analyze and evaluate dose distribution between Ray Tracing (RT) and Monte Carlo (MC) algorithms of 0.5% uncertainty on a critical structure of spinal cord and gross target volume and planning target volume. Methods: Twenty four spinal tumor patients were treated with stereotactic body radiotherapy (SBRT) by CyberKnife in 2013 and 2014. The MC algorithm with 0.5% of uncertainty is used to recalculate the dose distribution for the treatment plan of the patients using the same beams, beam directions, and monitor units (MUs). Results: The prescription doses are uniformly larger for MC plans than RT except one case. Upmore » to a factor of 1.19 for 0.25cc threshold volume and 1.14 for 1.2cc threshold volume of dose differences are observed for the spinal cord. Conclusion: The MC recalculated dose distributions are larger than the original MC calculations for the spinal tumor cases. Based on the accuracy of the MC calculations, more radiation dose might be delivered to the tumor targets and spinal cords with the increase prescription dose.« less

Monte Carlo Simulation for Perusal and Practice.

ERIC Educational Resources Information Center

Brooks, Gordon P.; Barcikowski, Robert S.; Robey, Randall R.

The meaningful investigation of many problems in statistics can be solved through Monte Carlo methods. Monte Carlo studies can help solve problems that are mathematically intractable through the analysis of random samples from populations whose characteristics are known to the researcher. Using Monte Carlo simulation, the values of a statistic are…

(U) Introduction to Monte Carlo Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hungerford, Aimee L.

2017-03-20

Monte Carlo methods are very valuable for representing solutions to particle transport problems. Here we describe a “cook book” approach to handling the terms in a transport equation using Monte Carlo methods. Focus is on the mechanics of a numerical Monte Carlo code, rather than the mathematical foundations of the method.

Maximum Likelihood and Minimum Distance Applied to Univariate Mixture Distributions.

ERIC Educational Resources Information Center

Wang, Yuh-Yin Wu; Schafer, William D.

This Monte-Carlo study compared modified Newton (NW), expectation-maximization algorithm (EM), and minimum Cramer-von Mises distance (MD), used to estimate parameters of univariate mixtures of two components. Data sets were fixed at size 160 and manipulated by mean separation, variance ratio, component proportion, and non-normality. Results…

An Introduction to Computational Physics

NASA Astrophysics Data System (ADS)

Pang, Tao

2010-07-01

Preface to first edition; Preface; Acknowledgements; 1. Introduction; 2. Approximation of a function; 3. Numerical calculus; 4. Ordinary differential equations; 5. Numerical methods for matrices; 6. Spectral analysis; 7. Partial differential equations; 8. Molecular dynamics simulations; 9. Modeling continuous systems; 10. Monte Carlo simulations; 11. Genetic algorithm and programming; 12. Numerical renormalization; References; Index.

Software for Demonstration of Features of Chain Polymerization Processes

ERIC Educational Resources Information Center

Sosnowski, Stanislaw

2013-01-01

Free software for the demonstration of the features of homo- and copolymerization processes (free radical, controlled radical, and living) is described. The software is based on the Monte Carlo algorithms and offers insight into the kinetics, molecular weight distribution, and microstructure of the macromolecules formed in those processes. It also…

Monte Carlo Algorithms for a Bayesian Analysis of the Cosmic Microwave Background

NASA Technical Reports Server (NTRS)

Jewell, Jeffrey B.; Eriksen, H. K.; ODwyer, I. J.; Wandelt, B. D.; Gorski, K.; Knox, L.; Chu, M.

2006-01-01

A viewgraph presentation on the review of Bayesian approach to Cosmic Microwave Background (CMB) analysis, numerical implementation with Gibbs sampling, a summary of application to WMAP I and work in progress with generalizations to polarization, foregrounds, asymmetric beams, and 1/f noise is given.

Progress in lattice gauge theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Creutz, M.

1983-01-01

These lectures first provide an overview of the current status of lattice gauge theory calculations. They then review some technical points on group integration, gauge fixing, and order parameters. Various Monte Carlo algorithms are discussed. Finally, alternatives to the Wilson action are considered in the context of universality for the continuum limit. 41 references.

Parallelization and implementation of approximate root isolation for nonlinear system by Monte Carlo

NASA Astrophysics Data System (ADS)

Khosravi, Ebrahim

1998-12-01

This dissertation solves a fundamental problem of isolating the real roots of nonlinear systems of equations by Monte-Carlo that were published by Bush Jones. This algorithm requires only function values and can be applied readily to complicated systems of transcendental functions. The implementation of this sequential algorithm provides scientists with the means to utilize function analysis in mathematics or other fields of science. The algorithm, however, is so computationally intensive that the system is limited to a very small set of variables, and this will make it unfeasible for large systems of equations. Also a computational technique was needed for investigating a metrology of preventing the algorithm structure from converging to the same root along different paths of computation. The research provides techniques for improving the efficiency and correctness of the algorithm. The sequential algorithm for this technique was corrected and a parallel algorithm is presented. This parallel method has been formally analyzed and is compared with other known methods of root isolation. The effectiveness, efficiency, enhanced overall performance of the parallel processing of the program in comparison to sequential processing is discussed. The message passing model was used for this parallel processing, and it is presented and implemented on Intel/860 MIMD architecture. The parallel processing proposed in this research has been implemented in an ongoing high energy physics experiment: this algorithm has been used to track neutrinoes in a super K detector. This experiment is located in Japan, and data can be processed on-line or off-line locally or remotely.

Minimal model for the secondary structures and conformational conversions in proteins

NASA Astrophysics Data System (ADS)

Imamura, Hideo

Better understanding of protein folding process can provide physical insights on the function of proteins and makes it possible to benefit from genetic information accumulated so far. Protein folding process normally takes place in less than seconds but even seconds are beyond reach of current computational power for simulations on a system of all-atom detail. Hence, to model and explore protein folding process it is crucial to construct a proper model that can adequately describe the physical process and mechanism for the relevant time scale. We discuss the reduced off-lattice model that can express _-helix and ?-hairpin conformations defined solely by a given sequence in order to investigate a protein folding mechanism of conformations such as a ?-hairpin and also to investigate conformational conversions in proteins. The first two chapters introduce and review essential concepts in protein folding modelling physical interaction in proteins, various simple models, and also review computational methods, in particular, the Metropolis Monte Carlo method, its dynamic interpretation and thermodynamic Monte Carlo algorithms. Chapter 3 describes the minimalist model that represents both _-helix and ?-sheet conformations using simple potentials. The native conformation can be specified by the sequence without particular conformational biases to a reference state. In Chapter 4, the model is used to investigate the folding mechanism of ?-hairpins exhaustively using the dynamic Monte Carlo and a thermodynamic Monte Carlo method an effcient combination of the multicanonical Monte Carlo and the weighted histogram analysis method. We show that the major folding pathways and folding rate depend on the location of a hydrophobic. The conformational conversions between _-helix and ?-sheet conformations are examined in Chapter 5 and 6. First, the conformational conversion due to mutation in a non-hydrophobic system and then the conformational conversion due to mutation with a hydrophobic pair at a different position at various temperatures are examined.

Kinetic Monte Carlo simulations of the effect of the exchange control layer thickness in CoPtCrB/CoPtCrSiO granular media

NASA Astrophysics Data System (ADS)

Almudallal, Ahmad M.; Mercer, J. I.; Whitehead, J. P.; Plumer, M. L.; van Ek, J.

2018-05-01

A hybrid Landau Lifshitz Gilbert/kinetic Monte Carlo algorithm is used to simulate experimental magnetic hysteresis loops for dual layer exchange coupled composite media. The calculation of the rate coefficients and difficulties arising from low energy barriers, a fundamental problem of the kinetic Monte Carlo method, are discussed and the methodology used to treat them in the present work is described. The results from simulations are compared with experimental vibrating sample magnetometer measurements on dual layer CoPtCrB/CoPtCrSiO media and a quantitative relationship between the thickness of the exchange control layer separating the layers and the effective exchange constant between the layers is obtained. Estimates of the energy barriers separating magnetically reversed states of the individual grains in zero applied field as well as the saturation field at sweep rates relevant to the bit write speeds in magnetic recording are also presented. The significance of this comparison between simulations and experiment and the estimates of the material parameters obtained from it are discussed in relation to optimizing the performance of magnetic storage media.

Verification of unfold error estimates in the UFO code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fehl, D.L.; Biggs, F.

Spectral unfolding is an inverse mathematical operation which attempts to obtain spectral source information from a set of tabulated response functions and data measurements. Several unfold algorithms have appeared over the past 30 years; among them is the UFO (UnFold Operator) code. In addition to an unfolded spectrum, UFO also estimates the unfold uncertainty (error) induced by running the code in a Monte Carlo fashion with prescribed data distributions (Gaussian deviates). In the problem studied, data were simulated from an arbitrarily chosen blackbody spectrum (10 keV) and a set of overlapping response functions. The data were assumed to have anmore » imprecision of 5% (standard deviation). 100 random data sets were generated. The built-in estimate of unfold uncertainty agreed with the Monte Carlo estimate to within the statistical resolution of this relatively small sample size (95% confidence level). A possible 10% bias between the two methods was unresolved. The Monte Carlo technique is also useful in underdetemined problems, for which the error matrix method does not apply. UFO has been applied to the diagnosis of low energy x rays emitted by Z-Pinch and ion-beam driven hohlraums.« less

Monte Carlo modeling of time-resolved fluorescence for depth-selective interrogation of layered tissue.

PubMed

Pfefer, T Joshua; Wang, Quanzeng; Drezek, Rebekah A

2011-11-01

Computational approaches for simulation of light-tissue interactions have provided extensive insight into biophotonic procedures for diagnosis and therapy. However, few studies have addressed simulation of time-resolved fluorescence (TRF) in tissue and none have combined Monte Carlo simulations with standard TRF processing algorithms to elucidate approaches for cancer detection in layered biological tissue. In this study, we investigate how illumination-collection parameters (e.g., collection angle and source-detector separation) influence the ability to measure fluorophore lifetime and tissue layer thickness. Decay curves are simulated with a Monte Carlo TRF light propagation model. Multi-exponential iterative deconvolution is used to determine lifetimes and fractional signal contributions. The ability to detect changes in mucosal thickness is optimized by probes that selectively interrogate regions superficial to the mucosal-submucosal boundary. Optimal accuracy in simultaneous determination of lifetimes in both layers is achieved when each layer contributes 40-60% of the signal. These results indicate that depth-selective approaches to TRF have the potential to enhance disease detection in layered biological tissue and that modeling can play an important role in probe design optimization. Published by Elsevier Ireland Ltd.

A Hybrid Monte Carlo importance sampling of rare events in Turbulence and in Turbulent Models

NASA Astrophysics Data System (ADS)

Margazoglou, Georgios; Biferale, Luca; Grauer, Rainer; Jansen, Karl; Mesterhazy, David; Rosenow, Tillmann; Tripiccione, Raffaele

2017-11-01

Extreme and rare events is a challenging topic in the field of turbulence. Trying to investigate those instances through the use of traditional numerical tools turns to be a notorious task, as they fail to systematically sample the fluctuations around them. On the other hand, we propose that an importance sampling Monte Carlo method can selectively highlight extreme events in remote areas of the phase space and induce their occurrence. We present a brand new computational approach, based on the path integral formulation of stochastic dynamics, and employ an accelerated Hybrid Monte Carlo (HMC) algorithm for this purpose. Through the paradigm of stochastic one-dimensional Burgers' equation, subjected to a random noise that is white-in-time and power-law correlated in Fourier space, we will prove our concept and benchmark our results with standard CFD methods. Furthermore, we will present our first results of constrained sampling around saddle-point instanton configurations (optimal fluctuations). The research leading to these results has received funding from the EU Horizon 2020 research and innovation programme under Grant Agreement No. 642069, and from the EU Seventh Framework Programme (FP7/2007-2013) under ERC Grant Agreement No. 339032.

A Monte Carlo model for 3D grain evolution during welding

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rodgers, Theron M.; Mitchell, John A.; Tikare, Veena

Welding is one of the most wide-spread processes used in metal joining. However, there are currently no open-source software implementations for the simulation of microstructural evolution during a weld pass. Here we describe a Potts Monte Carlo based model implemented in the SPPARKS kinetic Monte Carlo computational framework. The model simulates melting, solidification and solid-state microstructural evolution of material in the fusion and heat-affected zones of a weld. The model does not simulate thermal behavior, but rather utilizes user input parameters to specify weld pool and heat-affect zone properties. Weld pool shapes are specified by Bezier curves, which allow formore » the specification of a wide range of pool shapes. Pool shapes can range from narrow and deep to wide and shallow representing different fluid flow conditions within the pool. Surrounding temperature gradients are calculated with the aide of a closest point projection algorithm. Furthermore, the model also allows simulation of pulsed power welding through time-dependent variation of the weld pool size. Example simulation results and comparisons with laboratory weld observations demonstrate microstructural variation with weld speed, pool shape, and pulsed-power.« less

A Monte Carlo model for 3D grain evolution during welding

DOE PAGES

Rodgers, Theron M.; Mitchell, John A.; Tikare, Veena

2017-08-04

Welding is one of the most wide-spread processes used in metal joining. However, there are currently no open-source software implementations for the simulation of microstructural evolution during a weld pass. Here we describe a Potts Monte Carlo based model implemented in the SPPARKS kinetic Monte Carlo computational framework. The model simulates melting, solidification and solid-state microstructural evolution of material in the fusion and heat-affected zones of a weld. The model does not simulate thermal behavior, but rather utilizes user input parameters to specify weld pool and heat-affect zone properties. Weld pool shapes are specified by Bezier curves, which allow formore » the specification of a wide range of pool shapes. Pool shapes can range from narrow and deep to wide and shallow representing different fluid flow conditions within the pool. Surrounding temperature gradients are calculated with the aide of a closest point projection algorithm. Furthermore, the model also allows simulation of pulsed power welding through time-dependent variation of the weld pool size. Example simulation results and comparisons with laboratory weld observations demonstrate microstructural variation with weld speed, pool shape, and pulsed-power.« less

Apparatus and method for tracking a molecule or particle in three dimensions

DOEpatents

Werner, James H [Los Alamos, NM; Goodwin, Peter M [Los Alamos, NM; Lessard, Guillaume [Santa Fe, NM

2009-03-03

An apparatus and method were used to track the movement of fluorescent particles in three dimensions. Control software was used with the apparatus to implement a tracking algorithm for tracking the motion of the individual particles in glycerol/water mixtures. Monte Carlo simulations suggest that the tracking algorithms in combination with the apparatus may be used for tracking the motion of single fluorescent or fluorescently labeled biomolecules in three dimensions.

Reactive Monte Carlo sampling with an ab initio potential

DOE PAGES

Leiding, Jeff; Coe, Joshua D.

2016-05-04

Here, we present the first application of reactive Monte Carlo in a first-principles context. The algorithm samples in a modified NVT ensemble in which the volume, temperature, and total number of atoms of a given type are held fixed, but molecular composition is allowed to evolve through stochastic variation of chemical connectivity. We also discuss general features of the method, as well as techniques needed to enhance the efficiency of Boltzmann sampling. Finally, we compare the results of simulation of NH 3 to those of ab initio molecular dynamics (AIMD). Furthermore, we find that there are regions of state spacemore » for which RxMC sampling is much more efficient than AIMD due to the “rare-event” character of chemical reactions.« less

Analysis and Assessment of Operation Risk for Hybrid AC/DC Power System based on the Monte Carlo Method

NASA Astrophysics Data System (ADS)

Hu, Xiaojing; Li, Qiang; Zhang, Hao; Guo, Ziming; Zhao, Kun; Li, Xinpeng

2018-06-01

Based on the Monte Carlo method, an improved risk assessment method for hybrid AC/DC power system with VSC station considering the operation status of generators, converter stations, AC lines and DC lines is proposed. According to the sequential AC/DC power flow algorithm, node voltage and line active power are solved, and then the operation risk indices of node voltage over-limit and line active power over-limit are calculated. Finally, an improved two-area IEEE RTS-96 system is taken as a case to analyze and assessment its operation risk. The results show that the proposed model and method can intuitively and directly reflect the weak nodes and weak lines of the system, which can provide some reference for the dispatching department.

Microstructure engineering of Pt-Al alloy thin films through Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Harris, R. A.; Terblans, J. J.; Swart, H. C.

2014-06-01

A kinetic algorithm, based on the regular solution model, was used in conjunction with the Monte Carlo method to simulate the evolution of a micro-scaled thin film system during exposure to a high temperature environment. Pt-Al thin films were prepared via electron beam physical vapor deposition (EB-PVD) with an atomic concentration ratio of Pt63:Al37. These films were heat treated at an annealing temperature of 400 °C for 16 and 49 minutes. Scanning Auger Microscopy (SAM) (PHI 700) was used to obtain elemental maps while sputtering through the thin films. Simulations were run for the same annealing temperatures and thin-film composition. From these simulations theoretical depth profiles and simulated microstructures were obtained. These were compared to the experimentally measured depth profiles and elemental maps.

Population Annealing Monte Carlo for Frustrated Systems

NASA Astrophysics Data System (ADS)

Amey, Christopher; Machta, Jonathan

Population annealing is a sequential Monte Carlo algorithm that efficiently simulates equilibrium systems with rough free energy landscapes such as spin glasses and glassy fluids. A large population of configurations is initially thermalized at high temperature and then cooled to low temperature according to an annealing schedule. The population is kept in thermal equilibrium at every annealing step via resampling configurations according to their Boltzmann weights. Population annealing is comparable to parallel tempering in terms of efficiency, but has several distinct and useful features. In this talk I will give an introduction to population annealing and present recent progress in understanding its equilibration properties and optimizing it for spin glasses. Results from large-scale population annealing simulations for the Ising spin glass in 3D and 4D will be presented. NSF Grant DMR-1507506.

Parallelized Stochastic Cutoff Method for Long-Range Interacting Systems

NASA Astrophysics Data System (ADS)

Endo, Eishin; Toga, Yuta; Sasaki, Munetaka

2015-07-01

We present a method of parallelizing the stochastic cutoff (SCO) method, which is a Monte-Carlo method for long-range interacting systems. After interactions are eliminated by the SCO method, we subdivide a lattice into noninteracting interpenetrating sublattices. This subdivision enables us to parallelize the Monte-Carlo calculation in the SCO method. Such subdivision is found by numerically solving the vertex coloring of a graph created by the SCO method. We use an algorithm proposed by Kuhn and Wattenhofer to solve the vertex coloring by parallel computation. This method was applied to a two-dimensional magnetic dipolar system on an L × L square lattice to examine its parallelization efficiency. The result showed that, in the case of L = 2304, the speed of computation increased about 102 times by parallel computation with 288 processors.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Serin, E.; Codel, G.; Mabhouti, H.

Purpose: In small field geometries, the electronic equilibrium can be lost, making it challenging for the dose-calculation algorithm to accurately predict the dose, especially in the presence of tissue heterogeneities. In this study, dosimetric accuracy of Monte Carlo (MC) advanced dose calculation and sequential algorithms of Multiplan treatment planning system were investigated for small radiation fields incident on homogeneous and heterogeneous geometries. Methods: Small open fields of fixed cones of Cyberknife M6 unit 100 to 500 mm2 were used for this study. The fields were incident on in house phantom containing lung, air, and bone inhomogeneities and also homogeneous phantom.more » Using the same film batch, the net OD to dose calibration curve was obtained using CK with the 60 mm fixed cone by delivering 0- 800 cGy. Films were scanned 48 hours after irradiation using an Epson 1000XL flatbed scanner. The dosimetric accuracy of MC and sequential algorithms in the presence of the inhomogeneities was compared against EBT3 film dosimetry Results: Open field tests in a homogeneous phantom showed good agreement between two algorithms and film measurement For MC algorithm, the minimum gamma analysis passing rates between measured and calculated dose distributions were 99.7% and 98.3% for homogeneous and inhomogeneous fields in the case of lung and bone respectively. For sequential algorithm, the minimum gamma analysis passing rates were 98.9% and 92.5% for for homogeneous and inhomogeneous fields respectively for used all cone sizes. In the case of the air heterogeneity, the differences were larger for both calculation algorithms. Overall, when compared to measurement, the MC had better agreement than sequential algorithm. Conclusion: The Monte Carlo calculation algorithm in the Multiplan treatment planning system is an improvement over the existing sequential algorithm. Dose discrepancies were observed for in the presence of air inhomogeneities.« less

Monte Carlo generator ELRADGEN 2.0 for simulation of radiative events in elastic ep-scattering of polarized particles

NASA Astrophysics Data System (ADS)

Akushevich, I.; Filoti, O. F.; Ilyichev, A.; Shumeiko, N.

2012-07-01

The structure and algorithms of the Monte Carlo generator ELRADGEN 2.0 designed to simulate radiative events in polarized ep-scattering are presented. The full set of analytical expressions for the QED radiative corrections is presented and discussed in detail. Algorithmic improvements implemented to provide faster simulation of hard real photon events are described. Numerical tests show high quality of generation of photonic variables and radiatively corrected cross section. The comparison of the elastic radiative tail simulated within the kinematical conditions of the BLAST experiment at MIT BATES shows a good agreement with experimental data. Catalogue identifier: AELO_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELO_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1299 No. of bytes in distributed program, including test data, etc.: 11 348 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: All Operating system: Any RAM: 1 MB Classification: 11.2, 11.4 Nature of problem: Simulation of radiative events in polarized ep-scattering. Solution method: Monte Carlo simulation according to the distributions of the real photon kinematic variables that are calculated by the covariant method of QED radiative correction estimation. The approach provides rather fast and accurate generation. Running time: The simulation of 108 radiative events for itest:=1 takes up to 52 seconds on Pentium(R) Dual-Core 2.00 GHz processor.

Comparison of statistical sampling methods with ScannerBit, the GAMBIT scanning module

NASA Astrophysics Data System (ADS)

Martinez, Gregory D.; McKay, James; Farmer, Ben; Scott, Pat; Roebber, Elinore; Putze, Antje; Conrad, Jan

2017-11-01

We introduce ScannerBit, the statistics and sampling module of the public, open-source global fitting framework GAMBIT. ScannerBit provides a standardised interface to different sampling algorithms, enabling the use and comparison of multiple computational methods for inferring profile likelihoods, Bayesian posteriors, and other statistical quantities. The current version offers random, grid, raster, nested sampling, differential evolution, Markov Chain Monte Carlo (MCMC) and ensemble Monte Carlo samplers. We also announce the release of a new standalone differential evolution sampler, Diver, and describe its design, usage and interface to ScannerBit. We subject Diver and three other samplers (the nested sampler MultiNest, the MCMC GreAT, and the native ScannerBit implementation of the ensemble Monte Carlo algorithm T-Walk) to a battery of statistical tests. For this we use a realistic physical likelihood function, based on the scalar singlet model of dark matter. We examine the performance of each sampler as a function of its adjustable settings, and the dimensionality of the sampling problem. We evaluate performance on four metrics: optimality of the best fit found, completeness in exploring the best-fit region, number of likelihood evaluations, and total runtime. For Bayesian posterior estimation at high resolution, T-Walk provides the most accurate and timely mapping of the full parameter space. For profile likelihood analysis in less than about ten dimensions, we find that Diver and MultiNest score similarly in terms of best fit and speed, outperforming GreAT and T-Walk; in ten or more dimensions, Diver substantially outperforms the other three samplers on all metrics.

A simple methodology for characterization of germanium coaxial detectors by using Monte Carlo simulation and evolutionary algorithms.

PubMed

Guerra, J G; Rubiano, J G; Winter, G; Guerra, A G; Alonso, H; Arnedo, M A; Tejera, A; Gil, J M; Rodríguez, R; Martel, P; Bolivar, J P

2015-11-01

The determination in a sample of the activity concentration of a specific radionuclide by gamma spectrometry needs to know the full energy peak efficiency (FEPE) for the energy of interest. The difficulties related to the experimental calibration make it advisable to have alternative methods for FEPE determination, such as the simulation of the transport of photons in the crystal by the Monte Carlo method, which requires an accurate knowledge of the characteristics and geometry of the detector. The characterization process is mainly carried out by Canberra Industries Inc. using proprietary techniques and methodologies developed by that company. It is a costly procedure (due to shipping and to the cost of the process itself) and for some research laboratories an alternative in situ procedure can be very useful. The main goal of this paper is to find an alternative to this costly characterization process, by establishing a method for optimizing the parameters of characterizing the detector, through a computational procedure which could be reproduced at a standard research lab. This method consists in the determination of the detector geometric parameters by using Monte Carlo simulation in parallel with an optimization process, based on evolutionary algorithms, starting from a set of reference FEPEs determined experimentally or computationally. The proposed method has proven to be effective and simple to implement. It provides a set of characterization parameters which it has been successfully validated for different source-detector geometries, and also for a wide range of environmental samples and certified materials. Copyright © 2015 Elsevier Ltd. All rights reserved.

NVIDIA OptiX ray-tracing engine as a new tool for modelling medical imaging systems

NASA Astrophysics Data System (ADS)

Pietrzak, Jakub; Kacperski, Krzysztof; Cieślar, Marek

2015-03-01

The most accurate technique to model the X- and gamma radiation path through a numerically defined object is the Monte Carlo simulation which follows single photons according to their interaction probabilities. A simplified and much faster approach, which just integrates total interaction probabilities along selected paths, is known as ray tracing. Both techniques are used in medical imaging for simulating real imaging systems and as projectors required in iterative tomographic reconstruction algorithms. These approaches are ready for massive parallel implementation e.g. on Graphics Processing Units (GPU), which can greatly accelerate the computation time at a relatively low cost. In this paper we describe the application of the NVIDIA OptiX ray-tracing engine, popular in professional graphics and rendering applications, as a new powerful tool for X- and gamma ray-tracing in medical imaging. It allows the implementation of a variety of physical interactions of rays with pixel-, mesh- or nurbs-based objects, and recording any required quantities, like path integrals, interaction sites, deposited energies, and others. Using the OptiX engine we have implemented a code for rapid Monte Carlo simulations of Single Photon Emission Computed Tomography (SPECT) imaging, as well as the ray-tracing projector, which can be used in reconstruction algorithms. The engine generates efficient, scalable and optimized GPU code, ready to run on multi GPU heterogeneous systems. We have compared the results our simulations with the GATE package. With the OptiX engine the computation time of a Monte Carlo simulation can be reduced from days to minutes.

Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: a path for the optimization of low-energy many-body basis expansions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Jeongnim; Reboredo, Fernando A.

The self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo J. Chem. Phys. {\\bf 136}, 204101 (2012)] and some ideas of the correlation function Monte Carlo approach [D. M. Ceperley and B. Bernu, J. Chem. Phys. {\\bf 89}, 6316 (1988)] are blended to obtain a method for the calculation of thermodynamic properties of many-body systems at low temperatures. In order to allow the evolution in imaginary time to describe the density matrix, we remove the fixed-node restriction using complex antisymmetric trial wave functions. A statistical method is derived for the calculation of finite temperature properties of many-body systemsmore » near the ground state. In the process we also obtain a parallel algorithm that optimizes the many-body basis of a small subspace of the many-body Hilbert space. This small subspace is optimized to have maximum overlap with the one expanded by the lower energy eigenstates of a many-body Hamiltonian. We show in a model system that the Helmholtz free energy is minimized within this subspace as the iteration number increases. We show that the subspace expanded by the small basis systematically converges towards the subspace expanded by the lowest energy eigenstates. Possible applications of this method to calculate the thermodynamic properties of many-body systems near the ground state are discussed. The resulting basis can be also used to accelerate the calculation of the ground or excited states with Quantum Monte Carlo.« less

Neural network simulation of the atmospheric point spread function for the adjacency effect research

NASA Astrophysics Data System (ADS)

Ma, Xiaoshan; Wang, Haidong; Li, Ligang; Yang, Zhen; Meng, Xin

2016-10-01

Adjacency effect could be regarded as the convolution of the atmospheric point spread function (PSF) and the surface leaving radiance. Monte Carlo is a common method to simulate the atmospheric PSF. But it can't obtain analytic expression and the meaningful results can be only acquired by statistical analysis of millions of data. A backward Monte Carlo algorithm was employed to simulate photon emitting and propagating in the atmosphere under different conditions. The PSF was determined by recording the photon-receiving numbers in fixed bin at different position. A multilayer feed-forward neural network with a single hidden layer was designed to learn the relationship between the PSF's and the input condition parameters. The neural network used the back-propagation learning rule for training. Its input parameters involved atmosphere condition, spectrum range, observing geometry. The outputs of the network were photon-receiving numbers in the corresponding bin. Because the output units were too many to be allowed by neural network, the large network was divided into a collection of smaller ones. These small networks could be ran simultaneously on many workstations and/or PCs to speed up the training. It is important to note that the simulated PSF's by Monte Carlo technique in non-nadir viewing angles are more complicated than that in nadir conditions which brings difficulties in the design of the neural network. The results obtained show that the neural network approach could be very useful to compute the atmospheric PSF based on the simulated data generated by Monte Carlo method.

IMRT head and neck treatment planning with a commercially available Monte Carlo based planning system

NASA Astrophysics Data System (ADS)

Boudreau, C.; Heath, E.; Seuntjens, J.; Ballivy, O.; Parker, W.

2005-03-01

The PEREGRINE Monte Carlo dose-calculation system (North American Scientific, Cranberry Township, PA) is the first commercially available Monte Carlo dose-calculation code intended specifically for intensity modulated radiotherapy (IMRT) treatment planning and quality assurance. In order to assess the impact of Monte Carlo based dose calculations for IMRT clinical cases, dose distributions for 11 head and neck patients were evaluated using both PEREGRINE and the CORVUS (North American Scientific, Cranberry Township, PA) finite size pencil beam (FSPB) algorithm with equivalent path-length (EPL) inhomogeneity correction. For the target volumes, PEREGRINE calculations predict, on average, a less than 2% difference in the calculated mean and maximum doses to the gross tumour volume (GTV) and clinical target volume (CTV). An average 16% ± 4% and 12% ± 2% reduction in the volume covered by the prescription isodose line was observed for the GTV and CTV, respectively. Overall, no significant differences were noted in the doses to the mandible and spinal cord. For the parotid glands, PEREGRINE predicted a 6% ± 1% increase in the volume of tissue receiving a dose greater than 25 Gy and an increase of 4% ± 1% in the mean dose. Similar results were noted for the brainstem where PEREGRINE predicted a 6% ± 2% increase in the mean dose. The observed differences between the PEREGRINE and CORVUS calculated dose distributions are attributed to secondary electron fluence perturbations, which are not modelled by the EPL correction, issues of organ outlining, particularly in the vicinity of air cavities, and differences in dose reporting (dose to water versus dose to tissue type).

A response to Yu et al. "A forward-backward fragment assembling algorithm for the identification of genomic amplification and deletion breakpoints using high-density single nucleotide polymorphism (SNP) array", BMC Bioinformatics 2007, 8: 145.

PubMed

Rueda, Oscar M; Diaz-Uriarte, Ramon

2007-10-16

Yu et al. (BMC Bioinformatics 2007,8: 145+) have recently compared the performance of several methods for the detection of genomic amplification and deletion breakpoints using data from high-density single nucleotide polymorphism arrays. One of the methods compared is our non-homogenous Hidden Markov Model approach. Our approach uses Markov Chain Monte Carlo for inference, but Yu et al. ran the sampler for a severely insufficient number of iterations for a Markov Chain Monte Carlo-based method. Moreover, they did not use the appropriate reference level for the non-altered state. We rerun the analysis in Yu et al. using appropriate settings for both the Markov Chain Monte Carlo iterations and the reference level. Additionally, to show how easy it is to obtain answers to additional specific questions, we have added a new analysis targeted specifically to the detection of breakpoints. The reanalysis shows that the performance of our method is comparable to that of the other methods analyzed. In addition, we can provide probabilities of a given spot being a breakpoint, something unique among the methods examined. Markov Chain Monte Carlo methods require using a sufficient number of iterations before they can be assumed to yield samples from the distribution of interest. Running our method with too small a number of iterations cannot be representative of its performance. Moreover, our analysis shows how our original approach can be easily adapted to answer specific additional questions (e.g., identify edges).

Analysis of the penumbra enlargement in lung versus the quality index of photon beams: a methodology to check the dose calculation algorithm.

PubMed

Tsiakalos, Miltiadis F; Theodorou, Kiki; Kappas, Constantin; Zefkili, Sofia; Rosenwold, Jean-Claude

2004-04-01

It is well known that considerable underdosage can occur at the edges of a tumor inside the lung because of the degradation of penumbra due to lack of lateral electronic equilibrium. Although present even at smaller energies, this phenomenon is more pronounced for higher energies. Apart from Monte Carlo calculation, most of the existing Treatment Planning Systems (TPSs) cannot deal at all, or with acceptable accuracy, with this effect. A methodology has been developed for assessing the dose calculation algorithms in the lung region where lateral electronic disequilibrium exists, based on the Quality Index (QI) of the incident beam. A phantom, consisting of layers of polystyrene and lung material, has been irradiated using photon beams of 4, 6, 15, and 20 MV. The cross-plane profiles of each beam for 5x5, 10x10, and 25x10 fields have been measured at the middle of the phantom with the use of films. The penumbra (20%-80%) and fringe (50%-90%) enlargement was measured and the ratio of the widths for the lung to that of polystyrene was defined as the Correction Factor (CF). Monte Carlo calculations in the two phantoms have also been performed for energies of 6, 15, and 20 MV. Five commercial TPS's algorithms were tested for their ability to predict the penumbra and fringe enlargement. A linear relationship has been found between the QI of the beams and the CF of the penumbra and fringe enlargement for all the examined fields. Monte Carlo calculations agree very well (less than 1% difference) with the film measurements. The CF values range between 1.1 for 4 MV (QI 0.620) and 2.28 for 20 MV (QI 0.794). Three of the tested TPS's algorithms could not predict any enlargement at all for all energies and all fields and two of them could predict the penumbra enlargement to some extent. The proposed methodology can help any user or developer to check the accuracy of its algorithm for lung cases, based on a simple phantom geometry and the QI of the incident beam. This check is very important especially when higher energies are used, as the inaccuracies in existing algorithms can lead to an incorrect choice of energy for lung treatment and consequently to a failure in tumor control.

Computer Simulation of Electron Positron Annihilation Processes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, y

2003-10-02

With the launching of the Next Linear Collider coming closer and closer, there is a pressing need for physicists to develop a fully-integrated computer simulation of e{sup +}e{sup -} annihilation process at center-of-mass energy of 1TeV. A simulation program acts as the template for future experiments. Either new physics will be discovered, or current theoretical uncertainties will shrink due to more accurate higher-order radiative correction calculations. The existence of an efficient and accurate simulation will help us understand the new data and validate (or veto) some of the theoretical models developed to explain new physics. It should handle well interfacesmore » between different sectors of physics, e.g., interactions happening at parton levels well above the QCD scale which are described by perturbative QCD, and interactions happening at much lower energy scale, which combine partons into hadrons. Also it should achieve competitive speed in real time when the complexity of the simulation increases. This thesis contributes some tools that will be useful for the development of such simulation programs. We begin our study by the development of a new Monte Carlo algorithm intended to perform efficiently in selecting weight-1 events when multiple parameter dimensions are strongly correlated. The algorithm first seeks to model the peaks of the distribution by features, adapting these features to the function using the EM algorithm. The representation of the distribution provided by these features is then improved using the VEGAS algorithm for the Monte Carlo integration. The two strategies mesh neatly into an effective multi-channel adaptive representation. We then present a new algorithm for the simulation of parton shower processes in high energy QCD. We want to find an algorithm which is free of negative weights, produces its output as a set of exclusive events, and whose total rate exactly matches the full Feynman amplitude calculation. Our strategy is to create the whole QCD shower as a tree structure generated by a multiple Poisson process. Working with the whole shower allows us to include correlations between gluon emissions from different sources. QCD destructive interference is controlled by the implementation of ''angular-ordering,'' as in the HERWIG Monte Carlo program. We discuss methods for systematic improvement of the approach to include higher order QCD effects.« less

Photon beam dosimetry with EBT3 film in heterogeneous regions: Application to the evaluation of dose-calculation algorithms

NASA Astrophysics Data System (ADS)

Jung, Hyunuk; Kum, Oyeon; Han, Youngyih; Park, Byungdo; Cheong, Kwang-Ho

2014-12-01

For a better understanding of the accuracy of state-of-the-art-radiation therapies, 2-dimensional dosimetry in a patient-like environment will be helpful. Therefore, the dosimetry of EBT3 films in non-water-equivalent tissues was investigated, and the accuracy of commercially-used dose-calculation algorithms was evaluated with EBT3 measurement. Dose distributions were measured with EBT3 films for an in-house-designed phantom that contained a lung or a bone substitute, i.e., an air cavity (3 × 3 × 3 cm3) or teflon (2 × 2 × 2 cm3 or 3 × 3 × 3 cm3), respectively. The phantom was irradiated with 6-MV X-rays with field sizes of 2 × 2, 3 × 3, and 5 × 5 cm2. The accuracy of EBT3 dosimetry was evaluated by comparing the measured dose with the dose obtained from Monte Carlo (MC) simulations. A dose-to-bone-equivalent material was obtained by multiplying the EBT3 measurements by the stopping power ratio (SPR). The EBT3 measurements were then compared with the predictions from four algorithms: Monte Carlo (MC) in iPlan, acuros XB (AXB), analytical anisotropic algorithm (AAA) in Eclipse, and superposition-convolution (SC) in Pinnacle. For the air cavity, the EBT3 measurements agreed with the MC calculation to within 2% on average. For teflon, the EBT3 measurements differed by 9.297% (±0.9229%) on average from the Monte Carlo calculation before dose conversion, and by 0.717% (±0.6546%) after applying the SPR. The doses calculated by using the MC, AXB, AAA, and SC algorithms for the air cavity differed from the EBT3 measurements on average by 2.174, 2.863, 18.01, and 8.391%, respectively; for teflon, the average differences were 3.447, 4.113, 7.589, and 5.102%. The EBT3 measurements corrected with the SPR agreed with 2% on average both within and beyond the heterogeneities with MC results, thereby indicating that EBT3 dosimetry can be used in heterogeneous media. The MC and the AXB dose calculation algorithms exhibited clinically-acceptable accuracy (<5%) in heterogeneities.

Recent advances and future prospects for Monte Carlo

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brown, Forrest B

2010-01-01

The history of Monte Carlo methods is closely linked to that of computers: The first known Monte Carlo program was written in 1947 for the ENIAC; a pre-release of the first Fortran compiler was used for Monte Carlo In 1957; Monte Carlo codes were adapted to vector computers in the 1980s, clusters and parallel computers in the 1990s, and teraflop systems in the 2000s. Recent advances include hierarchical parallelism, combining threaded calculations on multicore processors with message-passing among different nodes. With the advances In computmg, Monte Carlo codes have evolved with new capabilities and new ways of use. Production codesmore » such as MCNP, MVP, MONK, TRIPOLI and SCALE are now 20-30 years old (or more) and are very rich in advanced featUres. The former 'method of last resort' has now become the first choice for many applications. Calculations are now routinely performed on office computers, not just on supercomputers. Current research and development efforts are investigating the use of Monte Carlo methods on FPGAs. GPUs, and many-core processors. Other far-reaching research is exploring ways to adapt Monte Carlo methods to future exaflop systems that may have 1M or more concurrent computational processes.« less

First-Order Phase Transition in the Quantum Adiabatic Algorithm

DTIC Science & Technology

2010-01-14

London) 400, 133 (1999). [19] T. Jörg, F. Krzakala, G . Semerjian, and F. Zamponi, arXiv:0911.3438. PRL 104, 020502 (2010) P HY S I CA L R EV I EW LE T T E R S week ending 15 JANUARY 2010 020502-4 ...Box 12211 Research Triangle Park, NC 27709-2211 15. SUBJECT TERMS Quantum Adiabatic Algorithm, Monte Carlo, Quantum Phase Transition A. P . Young, V...documentation. Approved for public release; distribution is unlimited. ... 56290.2-PH-QC First-Order Phase Transition in the Quantum Adiabatic Algorithm A. P

PyMercury: Interactive Python for the Mercury Monte Carlo Particle Transport Code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Iandola, F N; O'Brien, M J; Procassini, R J

2010-11-29

Monte Carlo particle transport applications are often written in low-level languages (C/C++) for optimal performance on clusters and supercomputers. However, this development approach often sacrifices straightforward usability and testing in the interest of fast application performance. To improve usability, some high-performance computing applications employ mixed-language programming with high-level and low-level languages. In this study, we consider the benefits of incorporating an interactive Python interface into a Monte Carlo application. With PyMercury, a new Python extension to the Mercury general-purpose Monte Carlo particle transport code, we improve application usability without diminishing performance. In two case studies, we illustrate how PyMercury improvesmore » usability and simplifies testing and validation in a Monte Carlo application. In short, PyMercury demonstrates the value of interactive Python for Monte Carlo particle transport applications. In the future, we expect interactive Python to play an increasingly significant role in Monte Carlo usage and testing.« less

An Introduction to Computational Physics - 2nd Edition

NASA Astrophysics Data System (ADS)

Pang, Tao

2006-01-01

Preface to first edition; Preface; Acknowledgements; 1. Introduction; 2. Approximation of a function; 3. Numerical calculus; 4. Ordinary differential equations; 5. Numerical methods for matrices; 6. Spectral analysis; 7. Partial differential equations; 8. Molecular dynamics simulations; 9. Modeling continuous systems; 10. Monte Carlo simulations; 11. Genetic algorithm and programming; 12. Numerical renormalization; References; Index.

Algebraic, geometric, and stochastic aspects of genetic operators

NASA Technical Reports Server (NTRS)

Foo, N. Y.; Bosworth, J. L.

1972-01-01

Genetic algorithms for function optimization employ genetic operators patterned after those observed in search strategies employed in natural adaptation. Two of these operators, crossover and inversion, are interpreted in terms of their algebraic and geometric properties. Stochastic models of the operators are developed which are employed in Monte Carlo simulations of their behavior.

Automatic crown cover mapping to improve forest inventory

Treesearch

Claude Vidal; Jean-Guy Boureau; Nicolas Robert; Nicolas Py; Josiane Zerubia; Xavier Descombes; Guillaume Perrin

2009-01-01

To automatically analyze near infrared aerial photographs, the French National Institute for Research in Computer Science and Control developed together with the French National Forest Inventory (NFI) a method for automatic crown cover mapping. This method uses a Reverse Jump Monte Carlo Markov Chain algorithm to locate the crowns and describe those using ellipses or...

Effects of Missing Data Methods in Structural Equation Modeling with Nonnormal Longitudinal Data

ERIC Educational Resources Information Center

Shin, Tacksoo; Davison, Mark L.; Long, Jeffrey D.

2009-01-01

The purpose of this study is to investigate the effects of missing data techniques in longitudinal studies under diverse conditions. A Monte Carlo simulation examined the performance of 3 missing data methods in latent growth modeling: listwise deletion (LD), maximum likelihood estimation using the expectation and maximization algorithm with a…

Accelerated Monte Carlo Methods for Coulomb Collisions

NASA Astrophysics Data System (ADS)

Rosin, Mark; Ricketson, Lee; Dimits, Andris; Caflisch, Russel; Cohen, Bruce

2014-03-01

We present a new highly efficient multi-level Monte Carlo (MLMC) simulation algorithm for Coulomb collisions in a plasma. The scheme, initially developed and used successfully for applications in financial mathematics, is applied here to kinetic plasmas for the first time. The method is based on a Langevin treatment of the Landau-Fokker-Planck equation and has a rich history derived from the works of Einstein and Chandrasekhar. The MLMC scheme successfully reduces the computational cost of achieving an RMS error ɛ in the numerical solution to collisional plasma problems from (ɛ-3) - for the standard state-of-the-art Langevin and binary collision algorithms - to a theoretically optimal (ɛ-2) scaling, when used in conjunction with an underlying Milstein discretization to the Langevin equation. In the test case presented here, the method accelerates simulations by factors of up to 100. We summarize the scheme, present some tricks for improving its efficiency yet further, and discuss the method's range of applicability. Work performed for US DOE by LLNL under contract DE-AC52- 07NA27344 and by UCLA under grant DE-FG02-05ER25710.

Surface excitations in electron spectroscopy. Part I: dielectric formalism and Monte Carlo algorithm

PubMed Central

Salvat-Pujol, F; Werner, W S M

2013-01-01

The theory describing energy losses of charged non-relativistic projectiles crossing a planar interface is derived on the basis of the Maxwell equations, outlining the physical assumptions of the model in great detail. The employed approach is very general in that various common models for surface excitations (such as the specular reflection model) can be obtained by an appropriate choice of parameter values. The dynamics of charged projectiles near surfaces is examined by calculations of the induced surface charge and the depth- and direction-dependent differential inelastic inverse mean free path (DIIMFP) and stopping power. The effect of several simplifications frequently encountered in the literature is investigated: differences of up to 100% are found in heights, widths, and positions of peaks in the DIIMFP. The presented model is implemented in a Monte Carlo algorithm for the simulation of the electron transport relevant for surface electron spectroscopy. Simulated reflection electron energy loss spectra are in good agreement with experiment on an absolute scale. Copyright © 2012 John Wiley & Sons, Ltd. PMID:23794766

Non-Cartesian MRI Reconstruction With Automatic Regularization Via Monte-Carlo SURE

PubMed Central

Weller, Daniel S.; Nielsen, Jon-Fredrik; Fessler, Jeffrey A.

2013-01-01

Magnetic resonance image (MRI) reconstruction from undersampled k-space data requires regularization to reduce noise and aliasing artifacts. Proper application of regularization however requires appropriate selection of associated regularization parameters. In this work, we develop a data-driven regularization parameter adjustment scheme that minimizes an estimate (based on the principle of Stein’s unbiased risk estimate—SURE) of a suitable weighted squared-error measure in k-space. To compute this SURE-type estimate, we propose a Monte-Carlo scheme that extends our previous approach to inverse problems (e.g., MRI reconstruction) involving complex-valued images. Our approach depends only on the output of a given reconstruction algorithm and does not require knowledge of its internal workings, so it is capable of tackling a wide variety of reconstruction algorithms and nonquadratic regularizers including total variation and those based on the ℓ1-norm. Experiments with simulated and real MR data indicate that the proposed approach is capable of providing near mean squared-error (MSE) optimal regularization parameters for single-coil undersampled non-Cartesian MRI reconstruction. PMID:23591478

Optimal processing for gel electrophoresis images: Applying Monte Carlo Tree Search in GelApp.

PubMed

Nguyen, Phi-Vu; Ghezal, Ali; Hsueh, Ya-Chih; Boudier, Thomas; Gan, Samuel Ken-En; Lee, Hwee Kuan

2016-08-01

In biomedical research, gel band size estimation in electrophoresis analysis is a routine process. To facilitate and automate this process, numerous software have been released, notably the GelApp mobile app. However, the band detection accuracy is limited due to a band detection algorithm that cannot adapt to the variations in input images. To address this, we used the Monte Carlo Tree Search with Upper Confidence Bound (MCTS-UCB) method to efficiently search for optimal image processing pipelines for the band detection task, thereby improving the segmentation algorithm. Incorporating this into GelApp, we report a significant enhancement of gel band detection accuracy by 55.9 ± 2.0% for protein polyacrylamide gels, and 35.9 ± 2.5% for DNA SYBR green agarose gels. This implementation is a proof-of-concept in demonstrating MCTS-UCB as a strategy to optimize general image segmentation. The improved version of GelApp-GelApp 2.0-is freely available on both Google Play Store (for Android platform), and Apple App Store (for iOS platform). © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Monte Carlo Planning Method Estimates Planning Horizons during Interactive Social Exchange.

PubMed

Hula, Andreas; Montague, P Read; Dayan, Peter

2015-06-01

Reciprocating interactions represent a central feature of all human exchanges. They have been the target of various recent experiments, with healthy participants and psychiatric populations engaging as dyads in multi-round exchanges such as a repeated trust task. Behaviour in such exchanges involves complexities related to each agent's preference for equity with their partner, beliefs about the partner's appetite for equity, beliefs about the partner's model of their partner, and so on. Agents may also plan different numbers of steps into the future. Providing a computationally precise account of the behaviour is an essential step towards understanding what underlies choices. A natural framework for this is that of an interactive partially observable Markov decision process (IPOMDP). However, the various complexities make IPOMDPs inordinately computationally challenging. Here, we show how to approximate the solution for the multi-round trust task using a variant of the Monte-Carlo tree search algorithm. We demonstrate that the algorithm is efficient and effective, and therefore can be used to invert observations of behavioural choices. We use generated behaviour to elucidate the richness and sophistication of interactive inference.

Sequential Markov chain Monte Carlo filter with simultaneous model selection for electrocardiogram signal modeling.

PubMed

Edla, Shwetha; Kovvali, Narayan; Papandreou-Suppappola, Antonia

2012-01-01

Constructing statistical models of electrocardiogram (ECG) signals, whose parameters can be used for automated disease classification, is of great importance in precluding manual annotation and providing prompt diagnosis of cardiac diseases. ECG signals consist of several segments with different morphologies (namely the P wave, QRS complex and the T wave) in a single heart beat, which can vary across individuals and diseases. Also, existing statistical ECG models exhibit a reliance upon obtaining a priori information from the ECG data by using preprocessing algorithms to initialize the filter parameters, or to define the user-specified model parameters. In this paper, we propose an ECG modeling technique using the sequential Markov chain Monte Carlo (SMCMC) filter that can perform simultaneous model selection, by adaptively choosing from different representations depending upon the nature of the data. Our results demonstrate the ability of the algorithm to track various types of ECG morphologies, including intermittently occurring ECG beats. In addition, we use the estimated model parameters as the feature set to classify between ECG signals with normal sinus rhythm and four different types of arrhythmia.

MONTE CARLO SIMULATIONS OF PERIODIC PULSED REACTOR WITH MOVING GEOMETRY PARTS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cao, Yan; Gohar, Yousry

2015-11-01

In a periodic pulsed reactor, the reactor state varies periodically from slightly subcritical to slightly prompt supercritical for producing periodic power pulses. Such periodic state change is accomplished by a periodic movement of specific reactor parts, such as control rods or reflector sections. The analysis of such reactor is difficult to perform with the current reactor physics computer programs. Based on past experience, the utilization of the point kinetics approximations gives considerable errors in predicting the magnitude and the shape of the power pulse if the reactor has significantly different neutron life times in different zones. To accurately simulate themore » dynamics of this type of reactor, a Monte Carlo procedure using the transfer function TRCL/TR of the MCNP/MCNPX computer programs is utilized to model the movable reactor parts. In this paper, two algorithms simulating the geometry part movements during a neutron history tracking have been developed. Several test cases have been developed to evaluate these procedures. The numerical test cases have shown that the developed algorithms can be utilized to simulate the reactor dynamics with movable geometry parts.« less

Ion-Stockmayer clusters: Minima, classical thermodynamics, and variational ground state estimates of Li+(CH3NO2)n (n = 1-20)

NASA Astrophysics Data System (ADS)

Curotto, E.

2015-12-01

Structural optimizations, classical NVT ensemble, and variational Monte Carlo simulations of ion Stockmayer clusters parameterized to approximate the Li+(CH3NO2)n (n = 1-20) systems are performed. The Metropolis algorithm enhanced by the parallel tempering strategy is used to measure internal energies and heat capacities, and a parallel version of the genetic algorithm is employed to obtain the most important minima. The first solvation sheath is octahedral and this feature remains the dominant theme in the structure of clusters with n ≥ 6. The first "magic number" is identified using the adiabatic solvent dissociation energy, and it marks the completion of the second solvation layer for the lithium ion-nitromethane clusters. It corresponds to the n = 18 system, a solvated ion with the first sheath having octahedral symmetry, weakly bound to an eight-membered and a four-membered ring crowning a vertex of the octahedron. Variational Monte Carlo estimates of the adiabatic solvent dissociation energy reveal that quantum effects further enhance the stability of the n = 18 system relative to its neighbors.

Comparisons between MCNP, EGS4 and experiment for clinical electron beams.

PubMed

Jeraj, R; Keall, P J; Ostwald, P M

1999-03-01

Understanding the limitations of Monte Carlo codes is essential in order to avoid systematic errors in simulations, and to suggest further improvement of the codes. MCNP and EGS4, Monte Carlo codes commonly used in medical physics, were compared and evaluated against electron depth dose data and experimental backscatter results obtained using clinical radiotherapy beams. Different physical models and algorithms used in the codes give significantly different depth dose curves and electron backscattering factors. The default version of MCNP calculates electron depth dose curves which are too penetrating. The MCNP results agree better with experiment if the ITS-style energy-indexing algorithm is used. EGS4 underpredicts electron backscattering for high-Z materials. The results slightly improve if optimal PRESTA-I parameters are used. MCNP simulates backscattering well even for high-Z materials. To conclude the comparison, a timing study was performed. EGS4 is generally faster than MCNP and use of a large number of scoring voxels dramatically slows down the MCNP calculation. However, use of a large number of geometry voxels in MCNP only slightly affects the speed of the calculation.

Monte Carlo Planning Method Estimates Planning Horizons during Interactive Social Exchange

PubMed Central

Hula, Andreas; Montague, P. Read; Dayan, Peter

2015-01-01

Reciprocating interactions represent a central feature of all human exchanges. They have been the target of various recent experiments, with healthy participants and psychiatric populations engaging as dyads in multi-round exchanges such as a repeated trust task. Behaviour in such exchanges involves complexities related to each agent’s preference for equity with their partner, beliefs about the partner’s appetite for equity, beliefs about the partner’s model of their partner, and so on. Agents may also plan different numbers of steps into the future. Providing a computationally precise account of the behaviour is an essential step towards understanding what underlies choices. A natural framework for this is that of an interactive partially observable Markov decision process (IPOMDP). However, the various complexities make IPOMDPs inordinately computationally challenging. Here, we show how to approximate the solution for the multi-round trust task using a variant of the Monte-Carlo tree search algorithm. We demonstrate that the algorithm is efficient and effective, and therefore can be used to invert observations of behavioural choices. We use generated behaviour to elucidate the richness and sophistication of interactive inference. PMID:26053429

TU-F-17A-08: The Relative Accuracy of 4D Dose Accumulation for Lung Radiotherapy Using Rigid Dose Projection Versus Dose Recalculation On Every Breathing Phase

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lamb, J; Lee, C; Tee, S

2014-06-15

Purpose: To investigate the accuracy of 4D dose accumulation using projection of dose calculated on the end-exhalation, mid-ventilation, or average intensity breathing phase CT scan, versus dose accumulation performed using full Monte Carlo dose recalculation on every breathing phase. Methods: Radiotherapy plans were analyzed for 10 patients with stage I-II lung cancer planned using 4D-CT. SBRT plans were optimized using the dose calculated by a commercially-available Monte Carlo algorithm on the end-exhalation 4D-CT phase. 4D dose accumulations using deformable registration were performed with a commercially available tool that projected the planned dose onto every breathing phase without recalculation, as wellmore » as with a Monte Carlo recalculation of the dose on all breathing phases. The 3D planned dose (3D-EX), the 3D dose calculated on the average intensity image (3D-AVE), and the 4D accumulations of the dose calculated on the end-exhalation phase CT (4D-PR-EX), the mid-ventilation phase CT (4D-PR-MID), and the average intensity image (4D-PR-AVE), respectively, were compared against the accumulation of the Monte Carlo dose recalculated on every phase. Plan evaluation metrics relating to target volumes and critical structures relevant for lung SBRT were analyzed. Results: Plan evaluation metrics tabulated using 4D-PR-EX, 4D-PR-MID, and 4D-PR-AVE differed from those tabulated using Monte Carlo recalculation on every phase by an average of 0.14±0.70 Gy, - 0.11±0.51 Gy, and 0.00±0.62 Gy, respectively. Deviations of between 8 and 13 Gy were observed between the 4D-MC calculations and both 3D methods for the proximal bronchial trees of 3 patients. Conclusions: 4D dose accumulation using projection without re-calculation may be sufficiently accurate compared to 4D dose accumulated from Monte Carlo recalculation on every phase, depending on institutional protocols. Use of 4D dose accumulation should be considered when evaluating normal tissue complication probabilities as well as in clinical situations where target volumes are directly inferior to mobile critical structures.« less

Minimizing the Discrepancy between Simulated and Historical Failures in Turbine Engines: A Simulation-Based Optimization Method (Postprint)

DTIC Science & Technology

2015-01-01

Procedure. The simulated annealing (SA) algorithm is a well-known local search metaheuristic used to address discrete, continuous, and multiobjective...design of experiments (DOE) to tune the parameters of the optimiza- tion algorithm . Section 5 shows the results of the case study. Finally, concluding... metaheuristic . The proposed method is broken down into two phases. Phase I consists of a Monte Carlo simulation to obtain the simulated percentage of failure

Light reflection models for computer graphics.

PubMed

Greenberg, D P

1989-04-14

During the past 20 years, computer graphic techniques for simulating the reflection of light have progressed so that today images of photorealistic quality can be produced. Early algorithms considered direct lighting only, but global illumination phenomena with indirect lighting, surface interreflections, and shadows can now be modeled with ray tracing, radiosity, and Monte Carlo simulations. This article describes the historical development of computer graphic algorithms for light reflection and pictorially illustrates what will be commonly available in the near future.

Slice sampling technique in Bayesian extreme of gold price modelling

NASA Astrophysics Data System (ADS)

Rostami, Mohammad; Adam, Mohd Bakri; Ibrahim, Noor Akma; Yahya, Mohamed Hisham

2013-09-01

In this paper, a simulation study of Bayesian extreme values by using Markov Chain Monte Carlo via slice sampling algorithm is implemented. We compared the accuracy of slice sampling with other methods for a Gumbel model. This study revealed that slice sampling algorithm offers more accurate and closer estimates with less RMSE than other methods . Finally we successfully employed this procedure to estimate the parameters of Malaysia extreme gold price from 2000 to 2011.

Crystal-structure prediction via the Floppy-Box Monte Carlo algorithm: Method and application to hard (non)convex particles

NASA Astrophysics Data System (ADS)

de Graaf, Joost; Filion, Laura; Marechal, Matthieu; van Roij, René; Dijkstra, Marjolein

2012-12-01

In this paper, we describe the way to set up the floppy-box Monte Carlo (FBMC) method [L. Filion, M. Marechal, B. van Oorschot, D. Pelt, F. Smallenburg, and M. Dijkstra, Phys. Rev. Lett. 103, 188302 (2009), 10.1103/PhysRevLett.103.188302] to predict crystal-structure candidates for colloidal particles. The algorithm is explained in detail to ensure that it can be straightforwardly implemented on the basis of this text. The handling of hard-particle interactions in the FBMC algorithm is given special attention, as (soft) short-range and semi-long-range interactions can be treated in an analogous way. We also discuss two types of algorithms for checking for overlaps between polyhedra, the method of separating axes and a triangular-tessellation based technique. These can be combined with the FBMC method to enable crystal-structure prediction for systems composed of highly shape-anisotropic particles. Moreover, we present the results for the dense crystal structures predicted using the FBMC method for 159 (non)convex faceted particles, on which the findings in [J. de Graaf, R. van Roij, and M. Dijkstra, Phys. Rev. Lett. 107, 155501 (2011), 10.1103/PhysRevLett.107.155501] were based. Finally, we comment on the process of crystal-structure prediction itself and the choices that can be made in these simulations.

Modeling of light distribution in the brain for topographical imaging

NASA Astrophysics Data System (ADS)

Okada, Eiji; Hayashi, Toshiyuki; Kawaguchi, Hiroshi

2004-07-01

Multi-channel optical imaging system can obtain a topographical distribution of the activated region in the brain cortex by a simple mapping algorithm. Near-infrared light is strongly scattered in the head and the volume of tissue that contributes to the change in the optical signal detected with source-detector pair on the head surface is broadly distributed in the brain. This scattering effect results in poor resolution and contrast in the topographic image of the brain activity. We report theoretical investigations on the spatial resolution of the topographic imaging of the brain activity. The head model for the theoretical study consists of five layers that imitate the scalp, skull, subarachnoid space, gray matter and white matter. The light propagation in the head model is predicted by Monte Carlo simulation to obtain the spatial sensitivity profile for a source-detector pair. The source-detector pairs are one dimensionally arranged on the surface of the model and the distance between the adjoining source-detector pairs are varied from 4 mm to 32 mm. The change in detected intensity caused by the absorption change is obtained by Monte Carlo simulation. The position of absorption change is reconstructed by the conventional mapping algorithm and the reconstruction algorithm using the spatial sensitivity profiles. We discuss the effective interval between the source-detector pairs and the choice of reconstruction algorithms to improve the topographic images of brain activity.

Variance-reduced simulation of lattice discrete-time Markov chains with applications in reaction networks

NASA Astrophysics Data System (ADS)

Maginnis, P. A.; West, M.; Dullerud, G. E.

2016-10-01

We propose an algorithm to accelerate Monte Carlo simulation for a broad class of stochastic processes. Specifically, the class of countable-state, discrete-time Markov chains driven by additive Poisson noise, or lattice discrete-time Markov chains. In particular, this class includes simulation of reaction networks via the tau-leaping algorithm. To produce the speedup, we simulate pairs of fair-draw trajectories that are negatively correlated. Thus, when averaged, these paths produce an unbiased Monte Carlo estimator that has reduced variance and, therefore, reduced error. Numerical results for three example systems included in this work demonstrate two to four orders of magnitude reduction of mean-square error. The numerical examples were chosen to illustrate different application areas and levels of system complexity. The areas are: gene expression (affine state-dependent rates), aerosol particle coagulation with emission and human immunodeficiency virus infection (both with nonlinear state-dependent rates). Our algorithm views the system dynamics as a ;black-box;, i.e., we only require control of pseudorandom number generator inputs. As a result, typical codes can be retrofitted with our algorithm using only minor changes. We prove several analytical results. Among these, we characterize the relationship of covariances between paths in the general nonlinear state-dependent intensity rates case, and we prove variance reduction of mean estimators in the special case of affine intensity rates.

Monte Carlo reference data sets for imaging research: Executive summary of the report of AAPM Research Committee Task Group 195.

PubMed

Sechopoulos, Ioannis; Ali, Elsayed S M; Badal, Andreu; Badano, Aldo; Boone, John M; Kyprianou, Iacovos S; Mainegra-Hing, Ernesto; McMillan, Kyle L; McNitt-Gray, Michael F; Rogers, D W O; Samei, Ehsan; Turner, Adam C

2015-10-01

The use of Monte Carlo simulations in diagnostic medical imaging research is widespread due to its flexibility and ability to estimate quantities that are challenging to measure empirically. However, any new Monte Carlo simulation code needs to be validated before it can be used reliably. The type and degree of validation required depends on the goals of the research project, but, typically, such validation involves either comparison of simulation results to physical measurements or to previously published results obtained with established Monte Carlo codes. The former is complicated due to nuances of experimental conditions and uncertainty, while the latter is challenging due to typical graphical presentation and lack of simulation details in previous publications. In addition, entering the field of Monte Carlo simulations in general involves a steep learning curve. It is not a simple task to learn how to program and interpret a Monte Carlo simulation, even when using one of the publicly available code packages. This Task Group report provides a common reference for benchmarking Monte Carlo simulations across a range of Monte Carlo codes and simulation scenarios. In the report, all simulation conditions are provided for six different Monte Carlo simulation cases that involve common x-ray based imaging research areas. The results obtained for the six cases using four publicly available Monte Carlo software packages are included in tabular form. In addition to a full description of all simulation conditions and results, a discussion and comparison of results among the Monte Carlo packages and the lessons learned during the compilation of these results are included. This abridged version of the report includes only an introductory description of the six cases and a brief example of the results of one of the cases. This work provides an investigator the necessary information to benchmark his/her Monte Carlo simulation software against the reference cases included here before performing his/her own novel research. In addition, an investigator entering the field of Monte Carlo simulations can use these descriptions and results as a self-teaching tool to ensure that he/she is able to perform a specific simulation correctly. Finally, educators can assign these cases as learning projects as part of course objectives or training programs.

Monte Carlo Modeling of the Initial Radiation Emitted by a Nuclear Device in the National Capital Region

DTIC Science & Technology

2013-07-01

also simulated in the models. Data was derived from calculations using the three-dimensional Monte Carlo radiation transport code MCNP (Monte Carlo N...32  B.  MCNP PHYSICS OPTIONS ......................................................................................... 33  C.  HAZUS...input deck’) for the MCNP , Monte Carlo N-Particle, radiation transport code. MCNP is a general-purpose code designed to simulate neutron, photon

The energy-dependent electron loss model: backscattering and application to heterogeneous slab media.

PubMed

Lee, Tae Kyu; Sandison, George A

2003-01-21

Electron backscattering has been incorporated into the energy-dependent electron loss (EL) model and the resulting algorithm is applied to predict dose deposition in slab heterogeneous media. This algorithm utilizes a reflection coefficient from the interface that is computed on the basis of Goudsmit-Saunderson theory and an average energy for the backscattered electrons based on Everhart's theory. Predictions of dose deposition in slab heterogeneous media are compared to the Monte Carlo based dose planning method (DPM) and a numerical discrete ordinates method (DOM). The slab media studied comprised water/Pb, water/Al, water/bone, water/bone/water, and water/lung/water, and incident electron beam energies of 10 MeV and 18 MeV. The predicted dose enhancement due to backscattering is accurate to within 3% of dose maximum even for lead as the backscattering medium. Dose discrepancies at large depths beyond the interface were as high as 5% of dose maximum and we speculate that this error may be attributed to the EL model assuming a Gaussian energy distribution for the electrons at depth. The computational cost is low compared to Monte Carlo simulations making the EL model attractive as a fast dose engine for dose optimization algorithms. The predictive power of the algorithm demonstrates that the small angle scattering restriction on the EL model can be overcome while retaining dose calculation accuracy and requiring only one free variable, chi, in the algorithm to be determined in advance of calculation.

A hybrid multiscale Monte Carlo algorithm (HyMSMC) to cope with disparity in time scales and species populations in intracellular networks.

PubMed

Samant, Asawari; Ogunnaike, Babatunde A; Vlachos, Dionisios G

2007-05-24

The fundamental role that intrinsic stochasticity plays in cellular functions has been shown via numerous computational and experimental studies. In the face of such evidence, it is important that intracellular networks are simulated with stochastic algorithms that can capture molecular fluctuations. However, separation of time scales and disparity in species population, two common features of intracellular networks, make stochastic simulation of such networks computationally prohibitive. While recent work has addressed each of these challenges separately, a generic algorithm that can simultaneously tackle disparity in time scales and population scales in stochastic systems is currently lacking. In this paper, we propose the hybrid, multiscale Monte Carlo (HyMSMC) method that fills in this void. The proposed HyMSMC method blends stochastic singular perturbation concepts, to deal with potential stiffness, with a hybrid of exact and coarse-grained stochastic algorithms, to cope with separation in population sizes. In addition, we introduce the computational singular perturbation (CSP) method as a means of systematically partitioning fast and slow networks and computing relaxation times for convergence. We also propose a new criteria of convergence of fast networks to stochastic low-dimensional manifolds, which further accelerates the algorithm. We use several prototype and biological examples, including a gene expression model displaying bistability, to demonstrate the efficiency, accuracy and applicability of the HyMSMC method. Bistable models serve as stringent tests for the success of multiscale MC methods and illustrate limitations of some literature methods.

The energy-dependent electron loss model: backscattering and application to heterogeneous slab media

NASA Astrophysics Data System (ADS)

Lee, Tae Kyu; Sandison, George A.

2003-01-01

Electron backscattering has been incorporated into the energy-dependent electron loss (EL) model and the resulting algorithm is applied to predict dose deposition in slab heterogeneous media. This algorithm utilizes a reflection coefficient from the interface that is computed on the basis of Goudsmit-Saunderson theory and an average energy for the backscattered electrons based on Everhart's theory. Predictions of dose deposition in slab heterogeneous media are compared to the Monte Carlo based dose planning method (DPM) and a numerical discrete ordinates method (DOM). The slab media studied comprised water/Pb, water/Al, water/bone, water/bone/water, and water/lung/water, and incident electron beam energies of 10 MeV and 18 MeV. The predicted dose enhancement due to backscattering is accurate to within 3% of dose maximum even for lead as the backscattering medium. Dose discrepancies at large depths beyond the interface were as high as 5% of dose maximum and we speculate that this error may be attributed to the EL model assuming a Gaussian energy distribution for the electrons at depth. The computational cost is low compared to Monte Carlo simulations making the EL model attractive as a fast dose engine for dose optimization algorithms. The predictive power of the algorithm demonstrates that the small angle scattering restriction on the EL model can be overcome while retaining dose calculation accuracy and requiring only one free variable, χ, in the algorithm to be determined in advance of calculation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Y; Liu, B; Liang, B

Purpose: Current CyberKnife treatment planning system (TPS) provided two dose calculation algorithms: Ray-tracing and Monte Carlo. Ray-tracing algorithm is fast, but less accurate, and also can’t handle irregular fields since a multi-leaf collimator system was recently introduced to CyberKnife M6 system. Monte Carlo method has well-known accuracy, but the current version still takes a long time to finish dose calculations. The purpose of this paper is to develop a GPU-based fast C/S dose engine for CyberKnife system to achieve both accuracy and efficiency. Methods: The TERMA distribution from a poly-energetic source was calculated based on beam’s eye view coordinate system,more » which is GPU friendly and has linear complexity. The dose distribution was then computed by inversely collecting the energy depositions from all TERMA points along 192 collapsed-cone directions. EGSnrc user code was used to pre-calculate energy deposition kernels (EDKs) for a series of mono-energy photons The energy spectrum was reconstructed based on measured tissue maximum ratio (TMR) curve, the TERMA averaged cumulative kernels was then calculated. Beam hardening parameters and intensity profiles were optimized based on measurement data from CyberKnife system. Results: The difference between measured and calculated TMR are less than 1% for all collimators except in the build-up regions. The calculated profiles also showed good agreements with the measured doses within 1% except in the penumbra regions. The developed C/S dose engine was also used to evaluate four clinical CyberKnife treatment plans, the results showed a better dose calculation accuracy than Ray-tracing algorithm compared with Monte Carlo method for heterogeneous cases. For the dose calculation time, it takes about several seconds for one beam depends on collimator size and dose calculation grids. Conclusion: A GPU-based C/S dose engine has been developed for CyberKnife system, which was proven to be efficient and accurate for clinical purpose, and can be easily implemented in TPS.« less

GPU-accelerated Monte Carlo convolution/superposition implementation for dose calculation.

PubMed

Zhou, Bo; Yu, Cedric X; Chen, Danny Z; Hu, X Sharon

2010-11-01

Dose calculation is a key component in radiation treatment planning systems. Its performance and accuracy are crucial to the quality of treatment plans as emerging advanced radiation therapy technologies are exerting ever tighter constraints on dose calculation. A common practice is to choose either a deterministic method such as the convolution/superposition (CS) method for speed or a Monte Carlo (MC) method for accuracy. The goal of this work is to boost the performance of a hybrid Monte Carlo convolution/superposition (MCCS) method by devising a graphics processing unit (GPU) implementation so as to make the method practical for day-to-day usage. Although the MCCS algorithm combines the merits of MC fluence generation and CS fluence transport, it is still not fast enough to be used as a day-to-day planning tool. To alleviate the speed issue of MC algorithms, the authors adopted MCCS as their target method and implemented a GPU-based version. In order to fully utilize the GPU computing power, the MCCS algorithm is modified to match the GPU hardware architecture. The performance of the authors' GPU-based implementation on an Nvidia GTX260 card is compared to a multithreaded software implementation on a quad-core system. A speedup in the range of 6.7-11.4x is observed for the clinical cases used. The less than 2% statistical fluctuation also indicates that the accuracy of the authors' GPU-based implementation is in good agreement with the results from the quad-core CPU implementation. This work shows that GPU is a feasible and cost-efficient solution compared to other alternatives such as using cluster machines or field-programmable gate arrays for satisfying the increasing demands on computation speed and accuracy of dose calculation. But there are also inherent limitations of using GPU for accelerating MC-type applications, which are also analyzed in detail in this article.

An improved random walk algorithm for the implicit Monte Carlo method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Keady, Kendra P., E-mail: keadyk@lanl.gov; Cleveland, Mathew A.

In this work, we introduce a modified Implicit Monte Carlo (IMC) Random Walk (RW) algorithm, which increases simulation efficiency for multigroup radiative transfer problems with strongly frequency-dependent opacities. To date, the RW method has only been implemented in “fully-gray” form; that is, the multigroup IMC opacities are group-collapsed over the full frequency domain of the problem to obtain a gray diffusion problem for RW. This formulation works well for problems with large spatial cells and/or opacities that are weakly dependent on frequency; however, the efficiency of the RW method degrades when the spatial cells are thin or the opacities aremore » a strong function of frequency. To address this inefficiency, we introduce a RW frequency group cutoff in each spatial cell, which divides the frequency domain into optically thick and optically thin components. In the modified algorithm, opacities for the RW diffusion problem are obtained by group-collapsing IMC opacities below the frequency group cutoff. Particles with frequencies above the cutoff are transported via standard IMC, while particles below the cutoff are eligible for RW. This greatly increases the total number of RW steps taken per IMC time-step, which in turn improves the efficiency of the simulation. We refer to this new method as Partially-Gray Random Walk (PGRW). We present numerical results for several multigroup radiative transfer problems, which show that the PGRW method is significantly more efficient than standard RW for several problems of interest. In general, PGRW decreases runtimes by a factor of ∼2–4 compared to standard RW, and a factor of ∼3–6 compared to standard IMC. While PGRW is slower than frequency-dependent Discrete Diffusion Monte Carlo (DDMC), it is also easier to adapt to unstructured meshes and can be used in spatial cells where DDMC is not applicable. This suggests that it may be optimal to employ both DDMC and PGRW in a single simulation.« less

Fixed-node quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Anderson, James B.

Quantum Monte Carlo methods cannot at present provide exact solutions of the Schrödinger equation for systems with more than a few electrons. But, quantum Monte Carlo calculations can provide very low energy, highly accurate solutions for many systems ranging up to several hundred electrons. These systems include atoms such as Be and Fe, molecules such as H2O, CH4, and HF, and condensed materials such as solid N2 and solid silicon. The quantum Monte Carlo predictions of their energies and structures may not be `exact', but they are the best available. Most of the Monte Carlo calculations for these systems have been carried out using approximately correct fixed nodal hypersurfaces and they have come to be known as `fixed-node quantum Monte Carlo' calculations. In this paper we review these `fixed node' calculations and the accuracies they yield.

Vectorized Monte Carlo methods for reactor lattice analysis

NASA Technical Reports Server (NTRS)

Brown, F. B.

1984-01-01

Some of the new computational methods and equivalent mathematical representations of physics models used in the MCV code, a vectorized continuous-enery Monte Carlo code for use on the CYBER-205 computer are discussed. While the principal application of MCV is the neutronics analysis of repeating reactor lattices, the new methods used in MCV should be generally useful for vectorizing Monte Carlo for other applications. For background, a brief overview of the vector processing features of the CYBER-205 is included, followed by a discussion of the fundamentals of Monte Carlo vectorization. The physics models used in the MCV vectorized Monte Carlo code are then summarized. The new methods used in scattering analysis are presented along with details of several key, highly specialized computational routines. Finally, speedups relative to CDC-7600 scalar Monte Carlo are discussed.

Limits on the Efficiency of Event-Based Algorithms for Monte Carlo Neutron Transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Romano, Paul K.; Siegel, Andrew R.

The traditional form of parallelism in Monte Carlo particle transport simulations, wherein each individual particle history is considered a unit of work, does not lend itself well to data-level parallelism. Event-based algorithms, which were originally used for simulations on vector processors, may offer a path toward better utilizing data-level parallelism in modern computer architectures. In this study, a simple model is developed for estimating the efficiency of the event-based particle transport algorithm under two sets of assumptions. Data collected from simulations of four reactor problems using OpenMC was then used in conjunction with the models to calculate the speedup duemore » to vectorization as a function of the size of the particle bank and the vector width. When each event type is assumed to have constant execution time, the achievable speedup is directly related to the particle bank size. We observed that the bank size generally needs to be at least 20 times greater than vector size to achieve vector efficiency greater than 90%. Lastly, when the execution times for events are allowed to vary, the vector speedup is also limited by differences in execution time for events being carried out in a single event-iteration.« less

Limits on the Efficiency of Event-Based Algorithms for Monte Carlo Neutron Transport

DOE PAGES

Romano, Paul K.; Siegel, Andrew R.

2017-07-01

The traditional form of parallelism in Monte Carlo particle transport simulations, wherein each individual particle history is considered a unit of work, does not lend itself well to data-level parallelism. Event-based algorithms, which were originally used for simulations on vector processors, may offer a path toward better utilizing data-level parallelism in modern computer architectures. In this study, a simple model is developed for estimating the efficiency of the event-based particle transport algorithm under two sets of assumptions. Data collected from simulations of four reactor problems using OpenMC was then used in conjunction with the models to calculate the speedup duemore » to vectorization as a function of the size of the particle bank and the vector width. When each event type is assumed to have constant execution time, the achievable speedup is directly related to the particle bank size. We observed that the bank size generally needs to be at least 20 times greater than vector size to achieve vector efficiency greater than 90%. Lastly, when the execution times for events are allowed to vary, the vector speedup is also limited by differences in execution time for events being carried out in a single event-iteration.« less

Efficient stochastic approaches for sensitivity studies of an Eulerian large-scale air pollution model

NASA Astrophysics Data System (ADS)

Dimov, I.; Georgieva, R.; Todorov, V.; Ostromsky, Tz.

2017-10-01

Reliability of large-scale mathematical models is an important issue when such models are used to support decision makers. Sensitivity analysis of model outputs to variation or natural uncertainties of model inputs is crucial for improving the reliability of mathematical models. A comprehensive experimental study of Monte Carlo algorithms based on Sobol sequences for multidimensional numerical integration has been done. A comparison with Latin hypercube sampling and a particular quasi-Monte Carlo lattice rule based on generalized Fibonacci numbers has been presented. The algorithms have been successfully applied to compute global Sobol sensitivity measures corresponding to the influence of several input parameters (six chemical reactions rates and four different groups of pollutants) on the concentrations of important air pollutants. The concentration values have been generated by the Unified Danish Eulerian Model. The sensitivity study has been done for the areas of several European cities with different geographical locations. The numerical tests show that the stochastic algorithms under consideration are efficient for multidimensional integration and especially for computing small by value sensitivity indices. It is a crucial element since even small indices may be important to be estimated in order to achieve a more accurate distribution of inputs influence and a more reliable interpretation of the mathematical model results.

Rare Event Simulation in Radiation Transport

NASA Astrophysics Data System (ADS)

Kollman, Craig

This dissertation studies methods for estimating extremely small probabilities by Monte Carlo simulation. Problems in radiation transport typically involve estimating very rare events or the expected value of a random variable which is with overwhelming probability equal to zero. These problems often have high dimensional state spaces and irregular geometries so that analytic solutions are not possible. Monte Carlo simulation must be used to estimate the radiation dosage being transported to a particular location. If the area is well shielded the probability of any one particular particle getting through is very small. Because of the large number of particles involved, even a tiny fraction penetrating the shield may represent an unacceptable level of radiation. It therefore becomes critical to be able to accurately estimate this extremely small probability. Importance sampling is a well known technique for improving the efficiency of rare event calculations. Here, a new set of probabilities is used in the simulation runs. The results are multiplied by the likelihood ratio between the true and simulated probabilities so as to keep our estimator unbiased. The variance of the resulting estimator is very sensitive to which new set of transition probabilities are chosen. It is shown that a zero variance estimator does exist, but that its computation requires exact knowledge of the solution. A simple random walk with an associated killing model for the scatter of neutrons is introduced. Large deviation results for optimal importance sampling in random walks are extended to the case where killing is present. An adaptive "learning" algorithm for implementing importance sampling is given for more general Markov chain models of neutron scatter. For finite state spaces this algorithm is shown to give, with probability one, a sequence of estimates converging exponentially fast to the true solution. In the final chapter, an attempt to generalize this algorithm to a continuous state space is made. This involves partitioning the space into a finite number of cells. There is a tradeoff between additional computation per iteration and variance reduction per iteration that arises in determining the optimal grid size. All versions of this algorithm can be thought of as a compromise between deterministic and Monte Carlo methods, capturing advantages of both techniques.

Prompt Radiation Protection Factors

DTIC Science & Technology

2018-02-01

dimensional Monte-Carlo radiation transport code MCNP (Monte Carlo N-Particle) and the evaluation of the protection factors (ratio of dose in the open to...radiation was performed using the three dimensional Monte- Carlo radiation transport code MCNP (Monte Carlo N-Particle) and the evaluation of the protection...by detonation of a nuclear device have placed renewed emphasis on evaluation of the consequences in case of such an event. The Defense Threat

Analysis of estimation algorithms for CDTI and CAS applications

NASA Technical Reports Server (NTRS)

Goka, T.

1985-01-01

Estimation algorithms for Cockpit Display of Traffic Information (CDTI) and Collision Avoidance System (CAS) applications were analyzed and/or developed. The algorithms are based on actual or projected operational and performance characteristics of an Enhanced TCAS II traffic sensor developed by Bendix and the Federal Aviation Administration. Three algorithm areas are examined and discussed. These are horizontal x and y, range and altitude estimation algorithms. Raw estimation errors are quantified using Monte Carlo simulations developed for each application; the raw errors are then used to infer impacts on the CDTI and CAS applications. Applications of smoothing algorithms to CDTI problems are also discussed briefly. Technical conclusions are summarized based on the analysis of simulation results.

A 3DHZETRN Code in a Spherical Uniform Sphere with Monte Carlo Verification

NASA Technical Reports Server (NTRS)

Wilson, John W.; Slaba, Tony C.; Badavi, Francis F.; Reddell, Brandon D.; Bahadori, Amir A.

2014-01-01

The computationally efficient HZETRN code has been used in recent trade studies for lunar and Martian exploration and is currently being used in the engineering development of the next generation of space vehicles, habitats, and extra vehicular activity equipment. A new version (3DHZETRN) capable of transporting High charge (Z) and Energy (HZE) and light ions (including neutrons) under space-like boundary conditions with enhanced neutron and light ion propagation is under development. In the present report, new algorithms for light ion and neutron propagation with well-defined convergence criteria in 3D objects is developed and tested against Monte Carlo simulations to verify the solution methodology. The code will be available through the software system, OLTARIS, for shield design and validation and provides a basis for personal computer software capable of space shield analysis and optimization.

CMacIonize: Monte Carlo photoionisation and moving-mesh radiation hydrodynamics

NASA Astrophysics Data System (ADS)

Vandenbroucke, Bert; Wood, Kenneth

2018-02-01

CMacIonize simulates the self-consistent evolution of HII regions surrounding young O and B stars, or other sources of ionizing radiation. The code combines a Monte Carlo photoionization algorithm that uses a complex mix of hydrogen, helium and several coolants in order to self-consistently solve for the ionization and temperature balance at any given time, with a standard first order hydrodynamics scheme. The code can be run as a post-processing tool to get the line emission from an existing simulation snapshot, but can also be used to run full radiation hydrodynamical simulations. Both the radiation transfer and the hydrodynamics are implemented in a general way that is independent of the grid structure that is used to discretize the system, allowing it to be run both as a standard fixed grid code and also as a moving-mesh code.

Magnetocaloric effect in Sr2CrIrO6 double perovskite: Monte Carlo simulation

NASA Astrophysics Data System (ADS)

El Rhazouani, O.; Slassi, A.; Ziat, Y.; Benyoussef, A.

2017-05-01

Monte Carlo simulation (MCS) combined with the Metropolis algorithm has been performed to study the magnetocaloric effect (MCE) in the promising double perovskite (DP) Sr2CrIrO6 that has not so far been synthetized. This paper presents the global magneto-thermodynamic behavior of Sr2CrIrO6 compound in term of MCE and discusses the behavior in comparison to other DPs. Thermal dependence of the magnetization has been investigated for different values of reduced external magnetic field. Thermal magnetic entropy and its change have been obtained. The adiabatic temperature change and the relative cooling power have been established. Through the obtained results, Sr2CrIrO6 DP could have some potential applications for magnetic refrigeration over a wide temperature range above room temperature and at large magnetic fields.

Monte Carlo simulations of medical imaging modalities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Estes, G.P.

Because continuous-energy Monte Carlo radiation transport calculations can be nearly exact simulations of physical reality (within data limitations, geometric approximations, transport algorithms, etc.), it follows that one should be able to closely approximate the results of many experiments from first-principles computations. This line of reasoning has led to various MCNP studies that involve simulations of medical imaging modalities and other visualization methods such as radiography, Anger camera, computerized tomography (CT) scans, and SABRINA particle track visualization. It is the intent of this paper to summarize some of these imaging simulations in the hope of stimulating further work, especially as computermore » power increases. Improved interpretation and prediction of medical images should ultimately lead to enhanced medical treatments. It is also reasonable to assume that such computations could be used to design new or more effective imaging instruments.« less

Calculation of electron Dose Point Kernel in water with GEANT4 for medical application

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guimaraes, C. C.; Sene, F. F.; Martinelli, J. R.

2009-06-03

The rapid insertion of new technologies in medical physics in the last years, especially in nuclear medicine, has been followed by a great development of faster Monte Carlo algorithms. GEANT4 is a Monte Carlo toolkit that contains the tools to simulate the problems of particle transport through matter. In this work, GEANT4 was used to calculate the dose-point-kernel (DPK) for monoenergetic electrons in water, which is an important reference medium for nuclear medicine. The three different physical models of electromagnetic interactions provided by GEANT4 - Low Energy, Penelope and Standard - were employed. To verify the adequacy of these models,more » the results were compared with references from the literature. For all energies and physical models, the agreement between calculated DPKs and reported values is satisfactory.« less

Monte Carlo modeling of spatial coherence: free-space diffraction

PubMed Central

Fischer, David G.; Prahl, Scott A.; Duncan, Donald D.

2008-01-01

We present a Monte Carlo method for propagating partially coherent fields through complex deterministic optical systems. A Gaussian copula is used to synthesize a random source with an arbitrary spatial coherence function. Physical optics and Monte Carlo predictions of the first- and second-order statistics of the field are shown for coherent and partially coherent sources for free-space propagation, imaging using a binary Fresnel zone plate, and propagation through a limiting aperture. Excellent agreement between the physical optics and Monte Carlo predictions is demonstrated in all cases. Convergence criteria are presented for judging the quality of the Monte Carlo predictions. PMID:18830335

Study of multi-dimensional radiative energy transfer in molecular gases

NASA Technical Reports Server (NTRS)

Liu, Jiwen; Tiwari, S. N.

1993-01-01

The Monte Carlo method (MCM) is applied to analyze radiative heat transfer in nongray gases. The nongray model employed is based on the statistical arrow band model with an exponential-tailed inverse intensity distribution. Consideration of spectral correlation results in some distinguishing features of the Monte Carlo formulations. Validation of the Monte Carlo formulations has been conducted by comparing results of this method with other solutions. Extension of a one-dimensional problem to a multi-dimensional problem requires some special treatments in the Monte Carlo analysis. Use of different assumptions results in different sets of Monte Carlo formulations. The nongray narrow band formulations provide the most accurate results.

Recommendations for dose calculations of lung cancer treatment plans treated with stereotactic ablative body radiotherapy (SABR)

NASA Astrophysics Data System (ADS)

Devpura, S.; Siddiqui, M. S.; Chen, D.; Liu, D.; Li, H.; Kumar, S.; Gordon, J.; Ajlouni, M.; Movsas, B.; Chetty, I. J.

2014-03-01

The purpose of this study was to systematically evaluate dose distributions computed with 5 different dose algorithms for patients with lung cancers treated using stereotactic ablative body radiotherapy (SABR). Treatment plans for 133 lung cancer patients, initially computed with a 1D-pencil beam (equivalent-path-length, EPL-1D) algorithm, were recalculated with 4 other algorithms commissioned for treatment planning, including 3-D pencil-beam (EPL-3D), anisotropic analytical algorithm (AAA), collapsed cone convolution superposition (CCC), and Monte Carlo (MC). The plan prescription dose was 48 Gy in 4 fractions normalized to the 95% isodose line. Tumors were classified according to location: peripheral tumors surrounded by lung (lung-island, N=39), peripheral tumors attached to the rib-cage or chest wall (lung-wall, N=44), and centrally-located tumors (lung-central, N=50). Relative to the EPL-1D algorithm, PTV D95 and mean dose values computed with the other 4 algorithms were lowest for "lung-island" tumors with smallest field sizes (3-5 cm). On the other hand, the smallest differences were noted for lung-central tumors treated with largest field widths (7-10 cm). Amongst all locations, dose distribution differences were most strongly correlated with tumor size for lung-island tumors. For most cases, convolution/superposition and MC algorithms were in good agreement. Mean lung dose (MLD) values computed with the EPL-1D algorithm were highly correlated with that of the other algorithms (correlation coefficient =0.99). The MLD values were found to be ~10% lower for small lung-island tumors with the model-based (conv/superposition and MC) vs. the correction-based (pencil-beam) algorithms with the model-based algorithms predicting greater low dose spread within the lungs. This study suggests that pencil beam algorithms should be avoided for lung SABR planning. For the most challenging cases, small tumors surrounded entirely by lung tissue (lung-island type), a Monte-Carlo-based algorithm may be warranted.