A MONTE-CARLO METHOD FOR ESTIMATING THE CORRELATION EXPONENT
MIKOSCH, T; WANG, QA
1995-01-01
We propose a Monte Carlo method for estimating the correlation exponent of a stationary ergodic sequence. The estimator can be considered as a bootstrap version of the classical Hill estimator. A simulation study shows that the method yields reasonable estimates.
A MONTE-CARLO METHOD FOR ESTIMATING THE CORRELATION EXPONENT
MIKOSCH, T; WANG, QA
We propose a Monte Carlo method for estimating the correlation exponent of a stationary ergodic sequence. The estimator can be considered as a bootstrap version of the classical Hill estimator. A simulation study shows that the method yields reasonable estimates.
Using Supervised Learning to Improve Monte Carlo Integral Estimation
Tracey, Brendan; Alonso, Juan J
2011-01-01
Monte Carlo (MC) techniques are often used to estimate integrals of a multivariate function using randomly generated samples of the function. In light of the increasing interest in uncertainty quantification and robust design applications in aerospace engineering, the calculation of expected values of such functions (e.g. performance measures) becomes important. However, MC techniques often suffer from high variance and slow convergence as the number of samples increases. In this paper we present Stacked Monte Carlo (StackMC), a new method for post-processing an existing set of MC samples to improve the associated integral estimate. StackMC is based on the supervised learning techniques of fitting functions and cross validation. It should reduce the variance of any type of Monte Carlo integral estimate (simple sampling, importance sampling, quasi-Monte Carlo, MCMC, etc.) without adding bias. We report on an extensive set of experiments confirming that the StackMC estimate of an integral is more accurate than ...
Failure Probability Estimation of Wind Turbines by Enhanced Monte Carlo
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Nielsen, Søren R.K.; Naess, Arvid
2012-01-01
This paper discusses the estimation of the failure probability of wind turbines required by codes of practice for designing them. The Standard Monte Carlo (SMC) simulations may be used for this reason conceptually as an alternative to the popular Peaks-Over-Threshold (POT) method. However......, estimation of very low failure probabilities with SMC simulations leads to unacceptably high computational costs. In this study, an Enhanced Monte Carlo (EMC) method is proposed that overcomes this obstacle. The method has advantages over both POT and SMC in terms of its low computational cost and accuracy...... is controlled by the pitch controller. This provides a fair framework for comparison of the behavior and failure event of the wind turbine with emphasis on the effect of the pitch controller. The Enhanced Monte Carlo method is then applied to the model and the failure probabilities of the model are estimated...
Monte Carlo estimation of the conditional Rasch model
Akkermans, Wies M.W.
1994-01-01
In order to obtain conditional maximum likelihood estimates, the so-called conditioning estimates have to be calculated. In this paper a method is examined that does not calculate these constants exactly, but approximates them using Monte Carlo Markov Chains. As an example, the method is applied to
Monte Carlo estimation of the conditional Rasch model
Akkermans, W.
1998-01-01
In order to obtain conditional maximum likelihood estimates, the conditioning constants are needed. Geyer and Thompson (1992) proposed a Markov chain Monte Carlo method that can be used to approximate these constants when they are difficult to calculate exactly. In the present paper, their method is
Estimation of beryllium ground state energy by Monte Carlo simulation
Energy Technology Data Exchange (ETDEWEB)
Kabir, K. M. Ariful [Department of Physical Sciences, School of Engineering and Computer Science, Independent University, Bangladesh (IUB) Dhaka (Bangladesh); Halder, Amal [Department of Mathematics, University of Dhaka Dhaka (Bangladesh)
2015-05-15
Quantum Monte Carlo method represent a powerful and broadly applicable computational tool for finding very accurate solution of the stationary Schrödinger equation for atoms, molecules, solids and a variety of model systems. Using variational Monte Carlo method we have calculated the ground state energy of the Beryllium atom. Our calculation are based on using a modified four parameters trial wave function which leads to good result comparing with the few parameters trial wave functions presented before. Based on random Numbers we can generate a large sample of electron locations to estimate the ground state energy of Beryllium. Our calculation gives good estimation for the ground state energy of the Beryllium atom comparing with the corresponding exact data.
Estimating return period of landslide triggering by Monte Carlo simulation
Peres, D. J.; Cancelliere, A.
2016-10-01
Assessment of landslide hazard is a crucial step for landslide mitigation planning. Estimation of the return period of slope instability represents a quantitative method to map landslide triggering hazard on a catchment. The most common approach to estimate return periods consists in coupling a triggering threshold equation, derived from an hydrological and slope stability process-based model, with a rainfall intensity-duration-frequency (IDF) curve. Such a traditional approach generally neglects the effect of rainfall intensity variability within events, as well as the variability of initial conditions, which depend on antecedent rainfall. We propose a Monte Carlo approach for estimating the return period of shallow landslide triggering which enables to account for both variabilities. Synthetic hourly rainfall-landslide data generated by Monte Carlo simulations are analysed to compute return periods as the mean interarrival time of a factor of safety less than one. Applications are first conducted to map landslide triggering hazard in the Loco catchment, located in highly landslide-prone area of the Peloritani Mountains, Sicily, Italy. Then a set of additional simulations are performed in order to evaluate the traditional IDF-based method by comparison with the Monte Carlo one. Results show that return period is affected significantly by variability of both rainfall intensity within events and of initial conditions, and that the traditional IDF-based approach may lead to an overestimation of the return period of landslide triggering, or, in other words, a non-conservative assessment of landslide hazard.
Metrics for Diagnosing Undersampling in Monte Carlo Tally Estimates
Energy Technology Data Exchange (ETDEWEB)
Perfetti, Christopher M. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Reactor and Nuclear Systems Div.; Rearden, Bradley T. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Reactor and Nuclear Systems Div.
2015-01-01
This study explored the potential of using Markov chain convergence diagnostics to predict the prevalence and magnitude of biases due to undersampling in Monte Carlo eigenvalue and flux tally estimates. Five metrics were applied to two models of pressurized water reactor fuel assemblies and their potential for identifying undersampling biases was evaluated by comparing the calculated test metrics with known biases in the tallies. Three of the five undersampling metrics showed the potential to accurately predict the behavior of undersampling biases in the responses examined in this study.
Monte Carlo estimation of the number of tatami tilings
Kimura, Kenji
2016-01-01
Motivated by the way Japanese tatami mats are placed on the floor, we consider domino tilings with a constraint and estimate the number of such tilings of plane regions. We map the system onto a monomer-dimer model with a novel local interaction on the dual lattice. We use a variant of the Hamiltonian replica exchange Monte Carlo method and the multi-parameter reweighting technique to study the model. The properties of the quantity are studied beyond exact enumeration and combinatorial method. The logarithm of the number of the tilings is linear in the boundary length of the region for all the regions studied.
Non-analog Monte Carlo estimators for radiation momentum deposition
Energy Technology Data Exchange (ETDEWEB)
Densmore, Jeffery D [Los Alamos National Laboratory; Hykes, Joshua M [Los Alamos National Laboratory
2008-01-01
The standard method for calculating radiation momentum deposition in Monte Carlo simulations is the analog estimator, which tallies the change in a particle's momentum at each interaction with the matter. Unfortunately, the analog estimator can suffer from large amounts of statistical error. In this paper, we present three new non-analog techniques for estimating momentum deposition. Specifically, we use absorption, collision, and track-length estimators to evaluate a simple integral expression for momentum deposition that does not contain terms that can cause large amounts of statistical error in the analog scheme. We compare our new non-analog estimators to the analog estimator with a set of test problems that encompass a wide range of material properties and both isotropic and anisotropic scattering. In nearly all cases, the new non-analog estimators outperform the analog estimator. The track-length estimator consistently yields the highest performance gains, improving upon the analog-estimator figure of merit by factors of up to two orders of magnitude.
Monte Carlo estimation of the number of tatami tilings
Kimura, Kenji; Higuchi, Saburo
2016-04-01
Motivated by the way Japanese tatami mats are placed on the floor, we consider domino tilings with a constraint and estimate the number of such tilings of plane regions. We map the system onto a monomer-dimer model with a novel local interaction on the dual lattice. We make use of a variant of the Hamiltonian replica exchange Monte Carlo method where data for ferromagnetic and anti-ferromagnetic models are combined to make a single family of histograms. The properties of the density of states is studied beyond exact enumeration and combinatorial methods. The logarithm of the number of the tilings is linear in the boundary length of the region for all the regions studied.
Diagnosing Undersampling in Monte Carlo Eigenvalue and Flux Tally Estimates
Energy Technology Data Exchange (ETDEWEB)
Perfetti, Christopher M [ORNL; Rearden, Bradley T [ORNL
2015-01-01
This study explored the impact of undersampling on the accuracy of tally estimates in Monte Carlo (MC) calculations. Steady-state MC simulations were performed for models of several critical systems with varying degrees of spatial and isotopic complexity, and the impact of undersampling on eigenvalue and fuel pin flux/fission estimates was examined. This study observed biases in MC eigenvalue estimates as large as several percent and biases in fuel pin flux/fission tally estimates that exceeded tens, and in some cases hundreds, of percent. This study also investigated five statistical metrics for predicting the occurrence of undersampling biases in MC simulations. Three of the metrics (the Heidelberger-Welch RHW, the Geweke Z-Score, and the Gelman-Rubin diagnostics) are commonly used for diagnosing the convergence of Markov chains, and two of the methods (the Contributing Particles per Generation and Tally Entropy) are new convergence metrics developed in the course of this study. These metrics were implemented in the KENO MC code within the SCALE code system and were evaluated for their reliability at predicting the onset and magnitude of undersampling biases in MC eigenvalue and flux tally estimates in two of the critical models. Of the five methods investigated, the Heidelberger-Welch RHW, the Gelman-Rubin diagnostics, and Tally Entropy produced test metrics that correlated strongly to the size of the observed undersampling biases, indicating their potential to effectively predict the size and prevalence of undersampling biases in MC simulations.
Asteroid mass estimation using Markov-Chain Monte Carlo techniques
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.
Bayesian adaptive Markov chain Monte Carlo estimation of genetic parameters.
Mathew, B; Bauer, A M; Koistinen, P; Reetz, T C; Léon, J; Sillanpää, M J
2012-10-01
Accurate and fast estimation of genetic parameters that underlie quantitative traits using mixed linear models with additive and dominance effects is of great importance in both natural and breeding populations. Here, we propose a new fast adaptive Markov chain Monte Carlo (MCMC) sampling algorithm for the estimation of genetic parameters in the linear mixed model with several random effects. In the learning phase of our algorithm, we use the hybrid Gibbs sampler to learn the covariance structure of the variance components. In the second phase of the algorithm, we use this covariance structure to formulate an effective proposal distribution for a Metropolis-Hastings algorithm, which uses a likelihood function in which the random effects have been integrated out. Compared with the hybrid Gibbs sampler, the new algorithm had better mixing properties and was approximately twice as fast to run. Our new algorithm was able to detect different modes in the posterior distribution. In addition, the posterior mode estimates from the adaptive MCMC method were close to the REML (residual maximum likelihood) estimates. Moreover, our exponential prior for inverse variance components was vague and enabled the estimated mode of the posterior variance to be practically zero, which was in agreement with the support from the likelihood (in the case of no dominance). The method performance is illustrated using simulated data sets with replicates and field data in barley.
Quantum Monte Carlo simulation
Wang, Yazhen
2011-01-01
Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating analytically intractable quantities. We derive the bias and variance for the proposed Monte Carlo quantum simulation estimator and establish the asymptotic theory for the estimator. The theory is used to design a computational scheme for minimizing the mean square er...
Highly Efficient Monte-Carlo for Estimating the Unavailability of Markov Dynamic System1）
Institute of Scientific and Technical Information of China (English)
XIAOGang; DENGLi; ZHANGBen-Ai; ZHUJian-Shi
2004-01-01
Monte Carlo simulation has become an important tool for estimating the reliability andavailability of dynamic system, since conventional numerical methods are no longer efficient whenthe size of the system to solve is large. However, evaluating by a simulation the probability of oc-currence of very rare events means playing a very large number of histories of the system, whichleads to unacceptable computing time. Highly efficient Monte Carlo should be worked out. In thispaper, based on the integral equation describing state transitions of Markov dynamic system, a u-niform Monte Carlo for estimating unavailability is presented. Using free-flight estimator, directstatistical estimation Monte Carlo is achieved. Using both free-flight estimator and biased proba-bility space of sampling, weighted statistical estimation Monte Carlo is also achieved. Five MonteCarlo schemes, including crude simulation, analog simulation, statistical estimation based oncrude and analog simulation, and weighted statistical estimation, are used for calculating the un-availability of a repairable Con/3/30 : F system. Their efficiencies are compared with each other.The results show the weighted statistical estimation Monte Carlo has the smallest variance and thehighest efficiency in very rare events simulation.
A Monte Carlo Evaluation of Estimated Parameters of Five Shrinkage Estimate Formuli.
Newman, Isadore; And Others
1979-01-01
A Monte Carlo simulation was employed to determine the accuracy with which the shrinkage in R squared can be estimated by five different shrinkage formulas. The study dealt with the use of shrinkage formulas for various sample sizes, different R squared values, and different degrees of multicollinearity. (Author/JKS)
Directory of Open Access Journals (Sweden)
José Luiz Ferreira Martins
2011-09-01
Full Text Available O objetivo deste artigo é o de analisar a viabilidade da utilização do método de Monte Carlo para estimar a produtividade na soldagem de tubulações industriais de aço carbono com base em amostras pequenas. O estudo foi realizado através de uma análise de uma amostra de referência contendo dados de produtividade de 160 juntas soldadas pelo processo Eletrodo Revestido na REDUC (refinaria de Duque de Caxias, utilizando o software ControlTub 5.3. A partir desses dados foram retiradas de forma aleatória, amostras com, respectivamente, 10, 15 e 20 elementos e executadas simulações pelo método de Monte Carlo. Comparando-se os resultados da amostra com 160 elementos e os dados gerados por simulação se observa que bons resultados podem ser obtidos usando o método de Monte Carlo para estimativa da produtividade da soldagem. Por outro lado, na indústria da construção brasileira o valor da média de produtividade é normalmente usado como um indicador de produtividade e é baseado em dados históricos de outros projetos coletados e avaliados somente após a conclusão do projeto, o que é uma limitação. Este artigo apresenta uma ferramenta para avaliação da execução em tempo real, permitindo ajustes nas estimativas e monitoramento de produtividade durante o empreendimento. Da mesma forma, em licitações, orçamentos e estimativas de prazo, a utilização desta técnica permite a adoção de outras estimativas diferentes da produtividade média, que é comumente usada e como alternativa, se sugerem três critérios: produtividade otimista, média e pessimista.The aim of this article is to analyze the feasibility of using Monte Carlo method to estimate productivity in industrial pipes welding of carbon steel based on small samples. The study was carried out through an analysis of a reference sample containing productivity data of 160 welded joints by SMAW process in REDUC (Duque de Caxias Refinery, using ControlTub 5.3 software
A Monte Carlo estimation of effective dose in chest tomosynthesis.
Sabol, John M
2009-12-01
The recent introduction of digital tomosynthesis imaging into routine clinical use has enabled the acquisition of volumetric patient data within a standard radiographic examination. Tomosynthesis requires the acquisition of multiple projection views, requiring additional dose compared to a standard projection examination. Knowledge of the effective dose is needed to make an appropriate decision between standard projection, tomosynthesis, and CT for thoracic x-ray examinations. In this article, the effective dose to the patient of chest tomosynthesis is calculated and compared to a standard radiographic examination and to values published for thoracic CT. Radiographic technique data for posterior-anterior (PA) and left lateral (LAT) radiographic chest examinations of medium-sized adults was obtained from clinical sites. From these data, the average incident air kerma for the standard views was determined. A commercially available tomosynthesis system was used to define the acquisition technique and geometry for each projection view. Using Monte Carlo techniques, the effective dose of the PA, LAT, and each tomosynthesis projection view was calculated. The effective dose for all projections of the tomosynthesis sweep was summed and compared to the calculated PA and LAT values and to the published values for thoracic CT. The average incident air kerma for the PA and left lateral clinical radiographic examinations were found to be 0.10 and 0.40 mGy, respectively. The effective dose for the PA view of a patient of the size of an average adult male was determined to be 0.017 mSv (ICRP 60) [0.018 mSv (ICRP 103)]. For the left lateral view of the same sized patient, the effective dose was determined to be 0.039 mSv (ICRP 60) [0.050 mSv (ICRP 103)]. The cumulative mA s for a tomosynthesis examination is recommended to be ten times the mA s of the PA image. With this technique, the effective dose for an average tomosynthesis examination was calculated to be 0.124 mSv (ICRP60
Monte Carlo Estimation of the Conditional Rasch Model. Research Report 94-09.
Akkermans, Wies M. W.
In order to obtain conditional maximum likelihood estimates, the so-called conditioning estimates have to be calculated. In this paper a method is examined that does not calculate these constants exactly, but approximates them using Monte Carlo Markov Chains. As an example, the method is applied to the conditional estimation of both item and…
Iba, Yukito
2000-01-01
``Extended Ensemble Monte Carlo''is a generic term that indicates a set of algorithms which are now popular in a variety of fields in physics and statistical information processing. Exchange Monte Carlo (Metropolis-Coupled Chain, Parallel Tempering), Simulated Tempering (Expanded Ensemble Monte Carlo), and Multicanonical Monte Carlo (Adaptive Umbrella Sampling) are typical members of this family. Here we give a cross-disciplinary survey of these algorithms with special emphasis on the great f...
Estimating the parameters of dynamical systems from Big Data using Sequential Monte Carlo samplers
Green, P. L.; Maskell, S.
2017-09-01
In this paper the authors present a method which facilitates computationally efficient parameter estimation of dynamical systems from a continuously growing set of measurement data. It is shown that the proposed method, which utilises Sequential Monte Carlo samplers, is guaranteed to be fully parallelisable (in contrast to Markov chain Monte Carlo methods) and can be applied to a wide variety of scenarios within structural dynamics. Its ability to allow convergence of one's parameter estimates, as more data is analysed, sets it apart from other sequential methods (such as the particle filter).
Hall, Eric
2016-01-09
The Monte Carlo (and Multi-level Monte Carlo) finite element method can be used to approximate observables of solutions to diffusion equations with lognormal distributed diffusion coefficients, e.g. modeling ground water flow. Typical models use lognormal diffusion coefficients with H´ older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible and can be larger than the computable low frequency error. We address how the total error can be estimated by the computable error.
Sandberg, Mattias
2015-01-07
The Monte Carlo (and Multi-level Monte Carlo) finite element method can be used to approximate observables of solutions to diffusion equations with log normal distributed diffusion coefficients, e.g. modelling ground water flow. Typical models use log normal diffusion coefficients with H¨older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible and can be larger than the computable low frequency error. This talk will address how the total error can be estimated by the computable error.
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…
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…
Markov Chain Monte Carlo Estimation of Item Parameters for the Generalized Graded Unfolding Model
de la Torre, Jimmy; Stark, Stephen; Chernyshenko, Oleksandr S.
2006-01-01
The authors present a Markov Chain Monte Carlo (MCMC) parameter estimation procedure for the generalized graded unfolding model (GGUM) and compare it to the marginal maximum likelihood (MML) approach implemented in the GGUM2000 computer program, using simulated and real personality data. In the simulation study, test length, number of response…
Energy Technology Data Exchange (ETDEWEB)
Wollaber, Allan Benton [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-06-16
This is a powerpoint presentation which serves as lecture material for the Parallel Computing summer school. It goes over the fundamentals of the Monte Carlo calculation method. The material is presented according to the following outline: Introduction (background, a simple example: estimating π), Why does this even work? (The Law of Large Numbers, The Central Limit Theorem), How to sample (inverse transform sampling, rejection), and An example from particle transport.
Energy Technology Data Exchange (ETDEWEB)
Brown, F.B.; Sutton, T.M.
1996-02-01
This report is composed of the lecture notes from the first half of a 32-hour graduate-level course on Monte Carlo methods offered at KAPL. These notes, prepared by two of the principle developers of KAPL`s RACER Monte Carlo code, cover the fundamental theory, concepts, and practices for Monte Carlo analysis. In particular, a thorough grounding in the basic fundamentals of Monte Carlo methods is presented, including random number generation, random sampling, the Monte Carlo approach to solving transport problems, computational geometry, collision physics, tallies, and eigenvalue calculations. Furthermore, modern computational algorithms for vector and parallel approaches to Monte Carlo calculations are covered in detail, including fundamental parallel and vector concepts, the event-based algorithm, master/slave schemes, parallel scaling laws, and portability issues.
Bardenet, R.
2012-01-01
ISBN:978-2-7598-1032-1; International audience; Bayesian inference often requires integrating some function with respect to a posterior distribution. Monte Carlo methods are sampling algorithms that allow to compute these integrals numerically when they are not analytically tractable. We review here the basic principles and the most common Monte Carlo algorithms, among which rejection sampling, importance sampling and Monte Carlo Markov chain (MCMC) methods. We give intuition on the theoretic...
Monte Carlo and nonlinearities
Dauchet, Jérémi; Blanco, Stéphane; Caliot, Cyril; Charon, Julien; Coustet, Christophe; Hafi, Mouna El; Eymet, Vincent; Farges, Olivier; Forest, Vincent; Fournier, Richard; Galtier, Mathieu; Gautrais, Jacques; Khuong, Anaïs; Pelissier, Lionel; Piaud, Benjamin; Roger, Maxime; Terrée, Guillaume; Weitz, Sebastian
2016-01-01
The Monte Carlo method is widely used to numerically predict systems behaviour. However, its powerful incremental design assumes a strong premise which has severely limited application so far: the estimation process must combine linearly over dimensions. Here we show that this premise can be alleviated by projecting nonlinearities on a polynomial basis and increasing the configuration-space dimension. Considering phytoplankton growth in light-limited environments, radiative transfer in planetary atmospheres, electromagnetic scattering by particles and concentrated-solar-power-plant productions, we prove the real world usability of this advance on four test-cases that were so far regarded as impracticable by Monte Carlo approaches. We also illustrate an outstanding feature of our method when applied to sharp problems with interacting particles: handling rare events is now straightforward. Overall, our extension preserves the features that made the method popular: addressing nonlinearities does not compromise o...
Monte-Carlo Inversion of Travel-Time Data for the Estimation of Weld Model Parameters
Hunter, A. J.; Drinkwater, B. W.; Wilcox, P. D.
2011-06-01
The quality of ultrasonic array imagery is adversely affected by uncompensated variations in the medium properties. A method for estimating the parameters of a general model of an inhomogeneous anisotropic medium is described. The model is comprised of a number of homogeneous sub-regions with unknown anisotropy. Bayesian estimation of the unknown model parameters is performed via a Monte-Carlo Markov chain using the Metropolis-Hastings algorithm. Results are demonstrated using simulated weld data.
Estimation under Multicollinearity: A Comparative Approach Using Monte Carlo Methods
Directory of Open Access Journals (Sweden)
D. A. Agunbiade
2010-01-01
Full Text Available Problem statement: A comparative investigation was done experimentally for 6 different Estimation Techniques of a just-identified simultaneous three-equation econometric model with three multi-collinear exogenous variables. Approach: The aim is to explore in depth the effects of the problems of multicollinearity and examine the sensitivity of findings to increasing sample sizes and increasing number of replications using the mean and total absolute bias statistics. Results: Findings revealed that the estimates are virtually identical for three estimators: LIML, 2SLS and ILS, while the performances of the other categories are not uniformly affected by the three levels of multicollinearity considered. It was also observed that while the frequency distribution of average parameter estimates was rather symmetric under the OLS, the other estimators was either negatively or positively skewed with no clear pattern. Conclusion: The study had established that L2ILS estimators are best for estimating parameters of data plagued by the lower open interval negative level of multicollinearity while FIML and OLS respectively rank highest for estimating parameters of data characterized by closed interval and upper categories level of multicollinearity.
Dunn, William L
2012-01-01
Exploring Monte Carlo Methods is a basic text that describes the numerical methods that have come to be known as "Monte Carlo." The book treats the subject generically through the first eight chapters and, thus, should be of use to anyone who wants to learn to use Monte Carlo. The next two chapters focus on applications in nuclear engineering, which are illustrative of uses in other fields. Five appendices are included, which provide useful information on probability distributions, general-purpose Monte Carlo codes for radiation transport, and other matters. The famous "Buffon's needle proble
Estimation of magnetocaloric properties by using Monte Carlo method for AMRR cycle
Arai, R.; Tamura, R.; Fukuda, H.; Li, J.; Saito, A. T.; Kaji, S.; Nakagome, H.; Numazawa, T.
2015-12-01
In order to achieve a wide refrigerating temperature range in magnetic refrigeration, it is effective to layer multiple materials with different Curie temperatures. It is crucial to have a detailed understanding of physical properties of materials to optimize the material selection and the layered structure. In the present study, we discuss methods for estimating a change in physical properties, particularly the Curie temperature when some of the Gd atoms are substituted for non-magnetic elements for material design, based on Gd as a ferromagnetic material which is a typical magnetocaloric material. For this purpose, whilst making calculations using the S=7/2 Ising model and the Monte Carlo method, we made a specific heat measurement and a magnetization measurement of Gd-R alloy (R = Y, Zr) to compare experimental values and calculated ones. The results showed that the magnetic entropy change, specific heat, and Curie temperature can be estimated with good accuracy using the Monte Carlo method.
Estimation of background spectrum in a shielded HPGe detector using Monte Carlo simulations.
Medhat, M E; Wang, Yifang
2014-02-01
Monte Carlo simulations are powerful tools used to estimate the background γ-radiation detected by high-resolution gamma-ray spectrometry systems with a HPGe (high purity germanium) detector contained inside a lead shield. The purpose of this work was to examine the applicability of Monte Carlo simulations to predict the optimal lead thickness necessary to reduce the background effect in spectrometer measurements. GEANT4 code was applied to simulate the background radiation spectrum at different thicknesses of lead. The simulated results were compared with experimental measurements of background radiation taken at the same shielding thickness. The results show that the background radiation detected depends on the thickness, size and lining of the shield. Simulation showed that 12 cm lead thick is the optimal shielding thickness.
A Monte Carlo approach for estimating measurement uncertainty using standard spreadsheet software.
Chew, Gina; Walczyk, Thomas
2012-03-01
Despite the importance of stating the measurement uncertainty in chemical analysis, concepts are still not widely applied by the broader scientific community. The Guide to the expression of uncertainty in measurement approves the use of both the partial derivative approach and the Monte Carlo approach. There are two limitations to the partial derivative approach. Firstly, it involves the computation of first-order derivatives of each component of the output quantity. This requires some mathematical skills and can be tedious if the mathematical model is complex. Secondly, it is not able to predict the probability distribution of the output quantity accurately if the input quantities are not normally distributed. Knowledge of the probability distribution is essential to determine the coverage interval. The Monte Carlo approach performs random sampling from probability distributions of the input quantities; hence, there is no need to compute first-order derivatives. In addition, it gives the probability density function of the output quantity as the end result, from which the coverage interval can be determined. Here we demonstrate how the Monte Carlo approach can be easily implemented to estimate measurement uncertainty using a standard spreadsheet software program such as Microsoft Excel. It is our aim to provide the analytical community with a tool to estimate measurement uncertainty using software that is already widely available and that is so simple to apply that it can even be used by students with basic computer skills and minimal mathematical knowledge.
Risk Consideration and Cost Estimation in Construction Projects Using Monte Carlo Simulation
Directory of Open Access Journals (Sweden)
Claudius A. Peleskei
2015-06-01
Full Text Available Construction projects usually involve high investments. It is, therefore, a risky adventure for companies as actual costs of construction projects nearly always exceed the planed scenario. This is due to the various risks and the large uncertainty existing within this industry. Determination and quantification of risks and their impact on project costs within the construction industry is described to be one of the most difficult areas. This paper analyses how the cost of construction projects can be estimated using Monte Carlo Simulation. It investigates if the different cost elements in a construction project follow a specific probability distribution. The research examines the effect of correlation between different project costs on the result of the Monte Carlo Simulation. The paper finds out that Monte Carlo Simulation can be a helpful tool for risk managers and can be used for cost estimation of construction projects. The research has shown that cost distributions are positively skewed and cost elements seem to have some interdependent relationships.
Energy Technology Data Exchange (ETDEWEB)
Cramer, S.N.
1984-01-01
The MORSE code is a large general-use multigroup Monte Carlo code system. Although no claims can be made regarding its superiority in either theoretical details or Monte Carlo techniques, MORSE has been, since its inception at ORNL in the late 1960s, the most widely used Monte Carlo radiation transport code. The principal reason for this popularity is that MORSE is relatively easy to use, independent of any installation or distribution center, and it can be easily customized to fit almost any specific need. Features of the MORSE code are described.
Reducing Uncertainty of Monte Carlo Estimated Fatigue Damage in Offshore Wind Turbines Using FORM
DEFF Research Database (Denmark)
Jensen, Jørgen Juncher; H. Horn, Jan-Tore
2016-01-01
Uncertainties related to fatigue damage estimation of non-linear systems are highly dependent on the tail behaviour and extreme values of the stress range distribution. By using a combination of the First Order Reliability Method (FORM) and Monte Carlo simulations (MCS), the accuracy of the fatigue...... estimations may be improved for the same computational efforts.The method is applied to a bottom-fixed, monopile-supported large offshore wind turbine, which is a non-linear and dynamically sensitive system. Different curve fitting techniques to the fatigue damage distribution have been used depending...
Monte-Carlo Estimation of the Inflight Performance of the GEMS Satellite X-Ray Polarimeter
Kitaguchi, Takao; Tamagawa, Toru; Hayato, Asami; Enoto, Teruaki; Yoshikawa, Akifumi; Kaneko, Kenta; Takeuchi, Yoko; Black, Kevin; Hill, Joanne; Jahoda, Keith; Krizmanic, John; Sturner, Steve; Griffiths, Scott; Kaaret, Philip; Marlowe, Hannah
2014-01-01
We report a Monte-Carlo estimation of the in-orbit performance of a cosmic X-ray polarimeter designed to be installed on the focal plane of a small satellite. The simulation uses GEANT for the transport of photons and energetic particles and results from Magboltz for the transport of secondary electrons in the detector gas. We validated the simulation by comparing spectra and modulation curves with actual data taken with radioactive sources and an X-ray generator. We also estimated the in-orbit background induced by cosmic radiation in low Earth orbit.
Monte Carlo transition probabilities
Lucy, L. B.
2001-01-01
Transition probabilities governing the interaction of energy packets and matter are derived that allow Monte Carlo NLTE transfer codes to be constructed without simplifying the treatment of line formation. These probabilities are such that the Monte Carlo calculation asymptotically recovers the local emissivity of a gas in statistical equilibrium. Numerical experiments with one-point statistical equilibrium problems for Fe II and Hydrogen confirm this asymptotic behaviour. In addition, the re...
Directory of Open Access Journals (Sweden)
Jae Phil Park
2016-06-01
Full Text Available The typical experimental procedure for testing stress corrosion cracking initiation involves an interval-censored reliability test. Based on these test results, the parameters of a Weibull distribution, which is a widely accepted crack initiation model, can be estimated using maximum likelihood estimation or median rank regression. However, it is difficult to determine the appropriate number of test specimens and censoring intervals required to obtain sufficiently accurate Weibull estimators. In this study, we compare maximum likelihood estimation and median rank regression using a Monte Carlo simulation to examine the effects of the total number of specimens, test duration, censoring interval, and shape parameters of the true Weibull distribution on the estimator uncertainty. Finally, we provide the quantitative uncertainties of both Weibull estimators, compare them with the true Weibull parameters, and suggest proper experimental conditions for developing a probabilistic crack initiation model through crack initiation tests.
Energy Technology Data Exchange (ETDEWEB)
Burke, TImothy P. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Kiedrowski, Brian C. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Martin, William R. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Brown, Forrest B. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-11-19
Kernel Density Estimators (KDEs) are a non-parametric density estimation technique that has recently been applied to Monte Carlo radiation transport simulations. Kernel density estimators are an alternative to histogram tallies for obtaining global solutions in Monte Carlo tallies. With KDEs, a single event, either a collision or particle track, can contribute to the score at multiple tally points with the uncertainty at those points being independent of the desired resolution of the solution. Thus, KDEs show potential for obtaining estimates of a global solution with reduced variance when compared to a histogram. Previously, KDEs have been applied to neutronics for one-group reactor physics problems and fixed source shielding applications. However, little work was done to obtain reaction rates using KDEs. This paper introduces a new form of the MFP KDE that is capable of handling general geometries. Furthermore, extending the MFP KDE to 2-D problems in continuous energy introduces inaccuracies to the solution. An ad-hoc solution to these inaccuracies is introduced that produces errors smaller than 4% at material interfaces.
DYNAMIC PARAMETERS ESTIMATION OF INTERFEROMETRIC SIGNALS BASED ON SEQUENTIAL MONTE CARLO METHOD
Directory of Open Access Journals (Sweden)
M. A. Volynsky
2014-05-01
Full Text Available The paper deals with sequential Monte Carlo method applied to problem of interferometric signals parameters estimation. The method is based on the statistical approximation of the posterior probability density distribution of parameters. Detailed description of the algorithm is given. The possibility of using the residual minimum between prediction and observation as a criterion for the selection of multitude elements generated at each algorithm step is shown. Analysis of input parameters influence on performance of the algorithm has been conducted. It was found that the standard deviation of the amplitude estimation error for typical signals is about 10% of the maximum amplitude value. The phase estimation error was shown to have a normal distribution. Analysis of the algorithm characteristics depending on input parameters is done. In particular, the influence analysis for a number of selected vectors of parameters on evaluation results is carried out. On the basis of simulation results for the considered class of signals, it is recommended to select 30% of the generated vectors number. The increase of the generated vectors number over 150 does not give significant improvement of the obtained estimates quality. The sequential Monte Carlo method is recommended for usage in dynamic processing of interferometric signals for the cases when high immunity is required to non-linear changes of signal parameters and influence of random noise.
Estimating Super Heavy Element Event Random Probabilities Using Monte Carlo Methods
Stoyer, Mark; Henderson, Roger; Kenneally, Jacqueline; Moody, Kenton; Nelson, Sarah; Shaughnessy, Dawn; Wilk, Philip
2009-10-01
Because superheavy element (SHE) experiments involve very low event rates and low statistics, estimating the probability that a given event sequence is due to random events is extremely important in judging the validity of the data. A Monte Carlo method developed at LLNL [1] is used on recent SHE experimental data to calculate random event probabilities. Current SHE experimental activities in collaboration with scientists at Dubna, Russia will be discussed. [4pt] [1] N.J. Stoyer, et al., Nucl. Instrum. Methods Phys. Res. A 455 (2000) 433.
Jennings, E.; Madigan, M.
2017-04-01
Given the complexity of modern cosmological parameter inference where we are faced with non-Gaussian data and noise, correlated systematics and multi-probe correlated datasets,the Approximate Bayesian Computation (ABC) method is a promising alternative to traditional Markov Chain Monte Carlo approaches in the case where the Likelihood is intractable or unknown. The ABC method is called ;Likelihood free; as it avoids explicit evaluation of the Likelihood by using a forward model simulation of the data which can include systematics. We introduce astroABC, an open source ABC Sequential Monte Carlo (SMC) sampler for parameter estimation. A key challenge in astrophysics is the efficient use of large multi-probe datasets to constrain high dimensional, possibly correlated parameter spaces. With this in mind astroABC allows for massive parallelization using MPI, a framework that handles spawning of processes across multiple nodes. A key new feature of astroABC is the ability to create MPI groups with different communicators, one for the sampler and several others for the forward model simulation, which speeds up sampling time considerably. For smaller jobs the Python multiprocessing option is also available. Other key features of this new sampler include: a Sequential Monte Carlo sampler; a method for iteratively adapting tolerance levels; local covariance estimate using scikit-learn's KDTree; modules for specifying optimal covariance matrix for a component-wise or multivariate normal perturbation kernel and a weighted covariance metric; restart files output frequently so an interrupted sampling run can be resumed at any iteration; output and restart files are backed up at every iteration; user defined distance metric and simulation methods; a module for specifying heterogeneous parameter priors including non-standard prior PDFs; a module for specifying a constant, linear, log or exponential tolerance level; well-documented examples and sample scripts. This code is hosted
Error in Monte Carlo, quasi-error in Quasi-Monte Carlo
Kleiss, R. H. P.; Lazopoulos, A.
2006-01-01
While the Quasi-Monte Carlo method of numerical integration achieves smaller integration error than standard Monte Carlo, its use in particle physics phenomenology has been hindered by the abscence of a reliable way to estimate that error. The standard Monte Carlo error estimator relies on the assumption that the points are generated independently of each other and, therefore, fails to account for the error improvement advertised by the Quasi-Monte Carlo method. We advocate the construction o...
Multilevel sequential Monte Carlo samplers
Beskos, Alexandros
2016-08-29
In this article we consider the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice, one often has to solve the associated PDE numerically, using, for instance finite element methods which depend on the step-size level . hL. In addition, the expectation cannot be computed analytically and one often resorts to Monte Carlo methods. In the context of this problem, it is known that the introduction of the multilevel Monte Carlo (MLMC) method can reduce the amount of computational effort to estimate expectations, for a given level of error. This is achieved via a telescoping identity associated to a Monte Carlo approximation of a sequence of probability distributions with discretization levels . âˆž>h0>h1â‹¯>hL. In many practical problems of interest, one cannot achieve an i.i.d. sampling of the associated sequence and a sequential Monte Carlo (SMC) version of the MLMC method is introduced to deal with this problem. It is shown that under appropriate assumptions, the attractive property of a reduction of the amount of computational effort to estimate expectations, for a given level of error, can be maintained within the SMC context. That is, relative to exact sampling and Monte Carlo for the distribution at the finest level . hL. The approach is numerically illustrated on a Bayesian inverse problem. Â© 2016 Elsevier B.V.
Alpha Eigenvalue Estimation from Dynamic Monte Carlo Calculation for Subcritical Systems
Energy Technology Data Exchange (ETDEWEB)
Shaukat, Nadeem; Shim, Hyung Jin; Jang, Sang Hoon [Seoul National University, Seoul (Korea, Republic of)
2016-05-15
The dynamic Monte Carlo (DMC) method has been used in the TART code for the α eigenvalue calculations. A unique method has been equipped to measure the α in time-stepwise Monte Carlo simulations. For off-critical systems, the neutron population is allowed to change exponentially over a period of time. The neutron population is uniformly combed to return it to the neutron population started with at the beginning of time boundary. In this study, the conventional dynamic Monte Carlo method has been implemented in the McCARD. There is an exponential change of neutron population at the end of each time boundary for off-critical systems. In order to control this exponential change at the end of each time boundary, a conventional time cut-off controlling population strategy is included in the DMC module implemented in the McCARD. the conventional combing method to control the neutron population for off-critical systems is implemented. Instead of considering the cycles, the simulation is divided in time intervals. At the end of each time interval, neutron population control is applied on the banked neutrons. Randomly selected neutrons are discarded, until the size of neutron population matches the initial neutron histories at the beginning of time simulation. The prompt neutron decay constant α is estimated from DMC algorithm for subcritical systems. The effectiveness of the results is examined for two-group infinite homogeneous problems with varying the k-value. From the comparisons with the analytical solutions, it is observed that the results are quite comparable with each other for each k-value.
First Passage Probability Estimation of Wind Turbines by Markov Chain Monte Carlo
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Nielsen, Søren R.K.
2013-01-01
Markov Chain Monte Carlo simulation has received considerable attention within the past decade as reportedly one of the most powerful techniques for the first passage probability estimation of dynamic systems. A very popular method in this direction capable of estimating probability of rare events...... with low computation cost is the subset simulation (SS). The idea of the method is to break a rare event into a sequence of more probable events which are easy to be estimated based on the conditional simulation techniques. Recently, two algorithms have been proposed in order to increase the efficiency...... of the method by modifying the conditional sampler. In this paper, applicability of the original SS is compared to the recently introduced modifications of the method on a wind turbine model. The model incorporates a PID pitch controller which aims at keeping the rotational speed of the wind turbine rotor equal...
Hrivnacova, I; Berejnov, V V; Brun, R; Carminati, F; Fassò, A; Futo, E; Gheata, A; Caballero, I G; Morsch, Andreas
2003-01-01
The concept of Virtual Monte Carlo (VMC) has been developed by the ALICE Software Project to allow different Monte Carlo simulation programs to run without changing the user code, such as the geometry definition, the detector response simulation or input and output formats. Recently, the VMC classes have been integrated into the ROOT framework, and the other relevant packages have been separated from the AliRoot framework and can be used individually by any other HEP project. The general concept of the VMC and its set of base classes provided in ROOT will be presented. Existing implementations for Geant3, Geant4 and FLUKA and simple examples of usage will be described.
Yang, Bo; Qiu, Rui; Li, JunLi; Lu, Wei; Wu, Zhen; Li, Chunyan
2017-02-01
When a strong laser beam irradiates a solid target, a hot plasma is produced and high-energy electrons are usually generated (the so-called "hot electrons"). These energetic electrons subsequently generate hard X-rays in the solid target through the Bremsstrahlung process. To date, only limited studies have been conducted on this laser-induced radiological protection issue. In this study, extensive literature reviews on the physics and properties of hot electrons have been conducted. On the basis of these information, the photon dose generated by the interaction between hot electrons and a solid target was simulated with the Monte Carlo code FLUKA. With some reasonable assumptions, the calculated dose can be regarded as the upper boundary of the experimental results over the laser intensity ranging from 1019 to 1021 W/cm2. Furthermore, an equation to estimate the photon dose generated from ultraintense laser-solid interactions based on the normalized laser intensity is derived. The shielding effects of common materials including concrete and lead were also studied for the laser-driven X-ray source. The dose transmission curves and tenth-value layers (TVLs) in concrete and lead were calculated through Monte Carlo simulations. These results could be used to perform a preliminary and fast radiation safety assessment for the X-rays generated from ultraintense laser-solid interactions.
Jennings, Elise
2016-01-01
Given the complexity of modern cosmological parameter inference where we are faced with non-Gaussian data and noise, correlated systematics and multi-probe correlated data sets, the Approximate Bayesian Computation (ABC) method is a promising alternative to traditional Markov Chain Monte Carlo approaches in the case where the Likelihood is intractable or unknown. The ABC method is called "Likelihood free" as it avoids explicit evaluation of the Likelihood by using a forward model simulation of the data which can include systematics. We introduce astroABC, an open source ABC Sequential Monte Carlo (SMC) sampler for parameter estimation. A key challenge in astrophysics is the efficient use of large multi-probe datasets to constrain high dimensional, possibly correlated parameter spaces. With this in mind astroABC allows for massive parallelization using MPI, a framework that handles spawning of jobs across multiple nodes. A key new feature of astroABC is the ability to create MPI groups with different communica...
Hop-Diffusion Monte Carlo for Epipolar Geometry Estimation between Very Wide-Baseline Images.
Brahmachari, Aveek S; Sarkar, Sudeep
2013-03-01
We present a Monte Carlo approach for epipolar geometry estimation that efficiently searches for minimal sets of inlier correspondences in the presence of many outliers in the putative correspondence set, a condition that is prevalent when we have wide baselines, significant scale changes, rotations in depth, occlusion, and repeated patterns. The proposed Monte Carlo algorithm uses Balanced LOcal and Global Search (BLOGS) to find the best minimal set of correspondences. The local search is a diffusion process using Joint Feature Distributions that captures the dependencies among the correspondences. And, the global search is a hopping search process across the minimal set space controlled by photometric properties. Using a novel experimental protocol that involves computing errors for manually marked ground truth points and images with outlier rates as high as 90 percent, we find that BLOGS is better than related approaches such as MAPSAC, NAPSAC, and BEEM. BLOGS results are of similar quality as other approaches, but BLOGS generate them in 10 times fewer iterations. The time per iteration for BLOGS is also the lowest among the ones we studied.
Hickson, Kevin J; O'Keefe, Graeme J
2014-09-01
The scalable XCAT voxelised phantom was used with the GATE Monte Carlo toolkit to investigate the effect of voxel size on dosimetry estimates of internally distributed radionuclide calculated using direct Monte Carlo simulation. A uniformly distributed Fluorine-18 source was simulated in the Kidneys of the XCAT phantom with the organ self dose (kidney ← kidney) and organ cross dose (liver ← kidney) being calculated for a number of organ and voxel sizes. Patient specific dose factors (DF) from a clinically acquired FDG PET/CT study have also been calculated for kidney self dose and liver ← kidney cross dose. Using the XCAT phantom it was found that significantly small voxel sizes are required to achieve accurate calculation of organ self dose. It has also been used to show that a voxel size of 2 mm or less is suitable for accurate calculations of organ cross dose. To compensate for insufficient voxel sampling a correction factor is proposed. This correction factor is applied to the patient specific dose factors calculated with the native voxel size of the PET/CT study.
Markov Chain Monte Carlo (MCMC) methods for parameter estimation of a novel hybrid redundant robot
Energy Technology Data Exchange (ETDEWEB)
Wang Yongbo, E-mail: yongbo.wang@hotmail.com [Laboratory of Intelligent Machine, Lappeenranta University of Technology, FIN-53851 Lappeenranta (Finland); Wu Huapeng; Handroos, Heikki [Laboratory of Intelligent Machine, Lappeenranta University of Technology, FIN-53851 Lappeenranta (Finland)
2011-10-15
This paper presents a statistical method for the calibration of a redundantly actuated hybrid serial-parallel robot IWR (Intersector Welding Robot). The robot under study will be used to carry out welding, machining, and remote handing for the assembly of vacuum vessel of International Thermonuclear Experimental Reactor (ITER). The robot has ten degrees of freedom (DOF), among which six DOF are contributed by the parallel mechanism and the rest are from the serial mechanism. In this paper, a kinematic error model which involves 54 unknown geometrical error parameters is developed for the proposed robot. Based on this error model, the mean values of the unknown parameters are statistically analyzed and estimated by means of Markov Chain Monte Carlo (MCMC) approach. The computer simulation is conducted by introducing random geometric errors and measurement poses which represent the corresponding real physical behaviors. The simulation results of the marginal posterior distributions of the estimated model parameters indicate that our method is reliable and robust.
Institute of Scientific and Technical Information of China (English)
Jiang Wei; Xiang Haige
2004-01-01
This paper addresses the issues of channel estimation in a Multiple-Input/Multiple-Output (MIMO) system. Markov Chain Monte Carlo (MCMC) method is employed to jointly estimate the Channel State Information (CSI) and the transmitted signals. The deduced algorithms can work well under circumstances of low Signal-to-Noise Ratio (SNR). Simulation results are presented to demonstrate their effectiveness.
Energy Technology Data Exchange (ETDEWEB)
Lee, Choonsik; Kim, Kwang Pyo; Long, Daniel; Fisher, Ryan; Tien, Chris; Simon, Steven L.; Bouville, Andre; Bolch, Wesley E. [Division of Cancer Epidemiology and Genetics, National Cancer Institute, National Institute of Health, Bethesda, Maryland 20852 (United States); Department of Nuclear Engineering, Kyung Hee University, Yongin 446-701 (Korea, Republic of); Department of Nuclear and Radiological Engineering, University of Florida, Gainesville, Florida 32611 (United States); Division of Cancer Epidemiology and Genetics, National Cancer Institute, National Institute of Health, Bethesda, Maryland 20852 (United States); Department of Nuclear and Radiological Engineering, University of Florida, Gainesville, Florida 32611 (United States)
2011-03-15
Purpose: To develop a computed tomography (CT) organ dose estimation method designed to readily provide organ doses in a reference adult male and female for different scan ranges to investigate the degree to which existing commercial programs can reasonably match organ doses defined in these more anatomically realistic adult hybrid phantomsMethods: The x-ray fan beam in the SOMATOM Sensation 16 multidetector CT scanner was simulated within the Monte Carlo radiation transport code MCNPX2.6. The simulated CT scanner model was validated through comparison with experimentally measured lateral free-in-air dose profiles and computed tomography dose index (CTDI) values. The reference adult male and female hybrid phantoms were coupled with the established CT scanner model following arm removal to simulate clinical head and other body region scans. A set of organ dose matrices were calculated for a series of consecutive axial scans ranging from the top of the head to the bottom of the phantoms with a beam thickness of 10 mm and the tube potentials of 80, 100, and 120 kVp. The organ doses for head, chest, and abdomen/pelvis examinations were calculated based on the organ dose matrices and compared to those obtained from two commercial programs, CT-EXPO and CTDOSIMETRY. Organ dose calculations were repeated for an adult stylized phantom by using the same simulation method used for the adult hybrid phantom. Results: Comparisons of both lateral free-in-air dose profiles and CTDI values through experimental measurement with the Monte Carlo simulations showed good agreement to within 9%. Organ doses for head, chest, and abdomen/pelvis scans reported in the commercial programs exceeded those from the Monte Carlo calculations in both the hybrid and stylized phantoms in this study, sometimes by orders of magnitude. Conclusions: The organ dose estimation method and dose matrices established in this study readily provides organ doses for a reference adult male and female for different
IMPROVED ALGORITHM FOR ROAD REGION SEGMENTATION BASED ON SEQUENTIAL MONTE-CARLO ESTIMATION
Directory of Open Access Journals (Sweden)
Zdenek Prochazka
2014-12-01
Full Text Available In recent years, many researchers and car makers put a lot of intensive effort into development of autonomous driving systems. Since visual information is the main modality used by human driver, a camera mounted on moving platform is very important kind of sensor, and various computer vision algorithms to handle vehicle surrounding situation are under intensive research. Our final goal is to develop a vision based lane detection system with ability to handle various types of road shapes, working on both structured and unstructured roads, ideally under presence of shadows. This paper presents a modified road region segmentation algorithm based on sequential Monte-Carlo estimation. Detailed description of the algorithm is given, and evaluation results show that the proposed algorithm outperforms the segmentation algorithm developed as a part of our previous work, as well as an conventional algorithm based on colour histogram.
Worm-improved estimators in continuous-time quantum Monte Carlo
Gunacker, P.; Wallerberger, M.; Ribic, T.; Hausoel, A.; Sangiovanni, G.; Held, K.
2016-09-01
We derive the improved estimators for general interactions and employ these for the continuous-time quantum Monte Carlo method. Using a worm algorithm we show how measuring higher-ordered correlators leads to an improved high-frequency behavior in irreducible quantities such as the one-particle self-energy or the irreducible two-particle vertex for non-density-density interactions. A good knowledge of the asymptotics of the two-particle vertex is essential for calculating nonlocal electronic correlations using diagrammatic extensions to the dynamical mean field theory as well as for calculating susceptibilities. We test our algorithm against analytic results for the multiorbital atomic limit and the Falicov-Kimball model.
Ashton, D J; Sánchez-Gil, V; Wilding, N B
2013-10-14
We investigate Monte Carlo simulation strategies for determining the effective ("depletion") potential between a pair of hard spheres immersed in a dense sea of much smaller hard spheres. Two routes to the depletion potential are considered. The first is based on estimates of the insertion probability of one big sphere in the presence of the other; we describe and compare three such methods. The second route exploits collective (cluster) updating to sample the depletion potential as a function of the separation of the big particles; we describe two such methods. For both routes, we find that the sampling efficiency at high densities of small particles can be enhanced considerably by exploiting "geometrical shortcuts" that focus the computational effort on a subset of small particles. All the methods we describe are readily extendable to particles interacting via arbitrary potentials.
Lu, Dan; Zhang, Guannan; Webster, Clayton; Barbier, Charlotte
2016-12-01
In this work, we develop an improved multilevel Monte Carlo (MLMC) method for estimating cumulative distribution functions (CDFs) of a quantity of interest, coming from numerical approximation of large-scale stochastic subsurface simulations. Compared with Monte Carlo (MC) methods, that require a significantly large number of high-fidelity model executions to achieve a prescribed accuracy when computing statistical expectations, MLMC methods were originally proposed to significantly reduce the computational cost with the use of multifidelity approximations. The improved performance of the MLMC methods depends strongly on the decay of the variance of the integrand as the level increases. However, the main challenge in estimating CDFs is that the integrand is a discontinuous indicator function whose variance decays slowly. To address this difficult task, we approximate the integrand using a smoothing function that accelerates the decay of the variance. In addition, we design a novel a posteriori optimization strategy to calibrate the smoothing function, so as to balance the computational gain and the approximation error. The combined proposed techniques are integrated into a very general and practical algorithm that can be applied to a wide range of subsurface problems for high-dimensional uncertainty quantification, such as a fine-grid oil reservoir model considered in this effort. The numerical results reveal that with the use of the calibrated smoothing function, the improved MLMC technique significantly reduces the computational complexity compared to the standard MC approach. Finally, we discuss several factors that affect the performance of the MLMC method and provide guidance for effective and efficient usage in practice.
Directory of Open Access Journals (Sweden)
Cecilia Maya
2004-12-01
Full Text Available El método Monte Carlo se aplica a varios casos de valoración de opciones financieras. El método genera una buena aproximación al comparar su precisión con la de otros métodos numéricos. La estimación que produce la versión Cruda de Monte Carlo puede ser aún más exacta si se recurre a metodologías de reducción de la varianza entre las cuales se sugieren la variable antitética y de la variable de control. Sin embargo, dichas metodologías requieren un esfuerzo computacional mayor por lo cual las mismas deben ser evaluadas en términos no sólo de su precisión sino también de su eficiencia.
Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions
Binder, Kurt; Block, Benjamin; Das, Subir K.; Virnau, Peter; Winter, David
2011-08-01
Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal growth, etc.). This article reviews two methods to estimate both interfacial free energies and line tensions by Monte Carlo simulations of simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is based on thermodynamic integration. This method is useful to study flat and inclined interfaces for Ising lattices, allowing also the estimation of line tensions of three-phase contact lines, when the interfaces meet walls (where "surface fields" may act). A generalization to off-lattice systems is described as well. The second method is based on the sampling of the order parameter distribution of the system throughout the two-phase coexistence region of the model. Both the interface free energies of flat interfaces and of (spherical or cylindrical) droplets (or bubbles) can be estimated, including also systems with walls, where sphere-cap shaped wall-attached droplets occur. The curvature-dependence of the interfacial free energy is discussed, and estimates for the line tensions are compared to results from the thermodynamic integration method. Basic limitations of all these methods are critically discussed, and an outlook on other approaches is given.
Input estimation for drug discovery using optimal control and Markov chain Monte Carlo approaches.
Trägårdh, Magnus; Chappell, Michael J; Ahnmark, Andrea; Lindén, Daniel; Evans, Neil D; Gennemark, Peter
2016-04-01
Input estimation is employed in cases where it is desirable to recover the form of an input function which cannot be directly observed and for which there is no model for the generating process. In pharmacokinetic and pharmacodynamic modelling, input estimation in linear systems (deconvolution) is well established, while the nonlinear case is largely unexplored. In this paper, a rigorous definition of the input-estimation problem is given, and the choices involved in terms of modelling assumptions and estimation algorithms are discussed. In particular, the paper covers Maximum a Posteriori estimates using techniques from optimal control theory, and full Bayesian estimation using Markov Chain Monte Carlo (MCMC) approaches. These techniques are implemented using the optimisation software CasADi, and applied to two example problems: one where the oral absorption rate and bioavailability of the drug eflornithine are estimated using pharmacokinetic data from rats, and one where energy intake is estimated from body-mass measurements of mice exposed to monoclonal antibodies targeting the fibroblast growth factor receptor (FGFR) 1c. The results from the analysis are used to highlight the strengths and weaknesses of the methods used when applied to sparsely sampled data. The presented methods for optimal control are fast and robust, and can be recommended for use in drug discovery. The MCMC-based methods can have long running times and require more expertise from the user. The rigorous definition together with the illustrative examples and suggestions for software serve as a highly promising starting point for application of input-estimation methods to problems in drug discovery.
Kieftenbeld, Vincent; Natesan, Prathiba
2012-01-01
Markov chain Monte Carlo (MCMC) methods enable a fully Bayesian approach to parameter estimation of item response models. In this simulation study, the authors compared the recovery of graded response model parameters using marginal maximum likelihood (MML) and Gibbs sampling (MCMC) under various latent trait distributions, test lengths, and…
We developed a sequential Monte Carlo filter to estimate the states and the parameters in a stochastic model of Japanese Encephalitis (JE) spread in the Philippines. This method is particularly important for its adaptability to the availability of new incidence data. This method can also capture the...
Hickey, J.M.; Veerkamp, R.F.; Calus, M.P.L.; Mulder, H.A.; Thompson, R.
2009-01-01
Calculation of the exact prediction error variance covariance matrix is often computationally too demanding, which limits its application in REML algorithms, the calculation of accuracies of estimated breeding values and the control of variance of response to selection. Alternatively Monte Carlo
Hickey, J.M.; Veerkamp, R.F.; Calus, M.P.L.; Mulder, H.A.; Thompson, R.
2009-01-01
Calculation of the exact prediction error variance covariance matrix is often computationally too demanding, which limits its application in REML algorithms, the calculation of accuracies of estimated breeding values and the control of variance of response to selection. Alternatively Monte Carlo sam
Error in Monte Carlo, quasi-error in Quasi-Monte Carlo
Kleiss, R H
2006-01-01
While the Quasi-Monte Carlo method of numerical integration achieves smaller integration error than standard Monte Carlo, its use in particle physics phenomenology has been hindered by the abscence of a reliable way to estimate that error. The standard Monte Carlo error estimator relies on the assumption that the points are generated independently of each other and, therefore, fails to account for the error improvement advertised by the Quasi-Monte Carlo method. We advocate the construction of an estimator of stochastic nature, based on the ensemble of pointsets with a particular discrepancy value. We investigate the consequences of this choice and give some first empirical results on the suggested estimators.
Energy Technology Data Exchange (ETDEWEB)
Dimitriadis, A; Gialousis, G; Karlatira, M; Karaiskos, P; Georgiou, E; Yakoumakis, E [Medical Physics Department, Medical School, University of Athens, 75 Mikras Asias Str., Goudi 11527, Athens (Greece); Makri, T; Papaodysseas, S, E-mail: anestisdim@yahoo.com [Radiological Imaging Department, Ag. Sofia Hospital, Lebadias and Thibon, Goudi 11527, Athens (Greece)
2011-01-21
Organ doses are important quantities in assessing the radiation risk. In the case of children, estimation of this risk is of particular concern due to their significant radiosensitivity and the greater health detriment. The purpose of this study is to estimate the organ doses to paediatric patients undergoing barium meal and micturating cystourethrography examinations by clinical measurements and Monte Carlo simulation. In clinical measurements, dose-area products (DAPs) were assessed during examination of 50 patients undergoing barium meal and 90 patients undergoing cystourethrography examinations, separated equally within three age categories: namely newborn, 1 year and 5 years old. Monte Carlo simulation of photon transport in male and female mathematical phantoms was applied using the MCNP5 code in order to estimate the equivalent organ doses. Regarding the micturating cystourethrography examinations, the organs receiving considerable amounts of radiation doses were the urinary bladder (1.87, 2.43 and 4.7 mSv, the first, second and third value in the parentheses corresponds to neonatal, 1 year old and 5 year old patients, respectively), the large intestines (1.54, 1.8, 3.1 mSv), the small intestines (1.34, 1.56, 2.78 mSv), the stomach (1.46, 1.02, 2.01 mSv) and the gall bladder (1.46, 1.66, 2.18 mSv), depending upon the age of the child. Organs receiving considerable amounts of radiation during barium meal examinations were the stomach (9.81, 9.92, 11.5 mSv), the gall bladder (3.05, 5.74, 7.15 mSv), the rib bones (9.82, 10.1, 11.1 mSv) and the pancreas (5.8, 5.93, 6.65 mSv), depending upon the age of the child. DAPs to organ/effective doses conversion factors were derived for each age and examination in order to be compared with other studies.
Depth-of-interaction estimates in pixelated scintillator sensors using Monte Carlo techniques
Sharma, Diksha; Sze, Christina; Bhandari, Harish; Nagarkar, Vivek; Badano, Aldo
2017-01-01
Image quality in thick scintillator detectors can be improved by minimizing parallax errors through depth-of-interaction (DOI) estimation. A novel sensor for low-energy single photon imaging having a thick, transparent, crystalline pixelated micro-columnar CsI:Tl scintillator structure has been described, with possible future application in small-animal single photon emission computed tomography (SPECT) imaging when using thicker structures under development. In order to understand the fundamental limits of this new structure, we introduce cartesianDETECT2, an open-source optical transport package that uses Monte Carlo methods to obtain estimates of DOI for improving spatial resolution of nuclear imaging applications. Optical photon paths are calculated as a function of varying simulation parameters such as columnar surface roughness, bulk, and top-surface absorption. We use scanning electron microscope images to estimate appropriate surface roughness coefficients. Simulation results are analyzed to model and establish patterns between DOI and photon scattering. The effect of varying starting locations of optical photons on the spatial response is studied. Bulk and top-surface absorption fractions were varied to investigate their effect on spatial response as a function of DOI. We investigated the accuracy of our DOI estimation model for a particular screen with various training and testing sets, and for all cases the percent error between the estimated and actual DOI over the majority of the detector thickness was ±5% with a maximum error of up to ±10% at deeper DOIs. In addition, we found that cartesianDETECT2 is computationally five times more efficient than MANTIS. Findings indicate that DOI estimates can be extracted from a double-Gaussian model of the detector response. We observed that our model predicts DOI in pixelated scintillator detectors reasonably well.
Energy Technology Data Exchange (ETDEWEB)
Graf, Peter A.; Stewart, Gordon; Lackner, Matthew; Dykes, Katherine; Veers, Paul
2016-05-01
Long-term fatigue loads for floating offshore wind turbines are hard to estimate because they require the evaluation of the integral of a highly nonlinear function over a wide variety of wind and wave conditions. Current design standards involve scanning over a uniform rectangular grid of metocean inputs (e.g., wind speed and direction and wave height and period), which becomes intractable in high dimensions as the number of required evaluations grows exponentially with dimension. Monte Carlo integration offers a potentially efficient alternative because it has theoretical convergence proportional to the inverse of the square root of the number of samples, which is independent of dimension. In this paper, we first report on the integration of the aeroelastic code FAST into NREL's systems engineering tool, WISDEM, and the development of a high-throughput pipeline capable of sampling from arbitrary distributions, running FAST on a large scale, and postprocessing the results into estimates of fatigue loads. Second, we use this tool to run a variety of studies aimed at comparing grid-based and Monte Carlo-based approaches with calculating long-term fatigue loads. We observe that for more than a few dimensions, the Monte Carlo approach can represent a large improvement in computational efficiency, but that as nonlinearity increases, the effectiveness of Monte Carlo is correspondingly reduced. The present work sets the stage for future research focusing on using advanced statistical methods for analysis of wind turbine fatigue as well as extreme loads.
Energy Technology Data Exchange (ETDEWEB)
Mukhopadhyay, Nitai D. [Department of Biostatistics, Virginia Commonwealth University, Richmond, VA 23298 (United States); Sampson, Andrew J. [Department of Radiation Oncology, Virginia Commonwealth University, Richmond, VA 23298 (United States); Deniz, Daniel; Alm Carlsson, Gudrun [Department of Radiation Physics, Faculty of Health Sciences, Linkoeping University, SE 581 85 (Sweden); Williamson, Jeffrey [Department of Radiation Oncology, Virginia Commonwealth University, Richmond, VA 23298 (United States); Malusek, Alexandr, E-mail: malusek@ujf.cas.cz [Department of Radiation Physics, Faculty of Health Sciences, Linkoeping University, SE 581 85 (Sweden); Department of Radiation Dosimetry, Nuclear Physics Institute AS CR v.v.i., Na Truhlarce 39/64, 180 86 Prague (Czech Republic)
2012-01-15
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.
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.
LMC: Logarithmantic Monte Carlo
Mantz, Adam B.
2017-06-01
LMC is a Markov Chain Monte Carlo engine in Python that implements adaptive Metropolis-Hastings and slice sampling, as well as the affine-invariant method of Goodman & Weare, in a flexible framework. It can be used for simple problems, but the main use case is problems where expensive likelihood evaluations are provided by less flexible third-party software, which benefit from parallelization across many nodes at the sampling level. The parallel/adaptive methods use communication through MPI, or alternatively by writing/reading files, and mostly follow the approaches pioneered by CosmoMC (ascl:1106.025).
Dynamic measurements and uncertainty estimation of clinical thermometers using Monte Carlo method
Ogorevc, Jaka; Bojkovski, Jovan; Pušnik, Igor; Drnovšek, Janko
2016-09-01
Clinical thermometers in intensive care units are used for the continuous measurement of body temperature. This study describes a procedure for dynamic measurement uncertainty evaluation in order to examine the requirements for clinical thermometer dynamic properties in standards and recommendations. In this study thermistors were used as temperature sensors, transient temperature measurements were performed in water and air and the measurement data were processed for the investigation of thermometer dynamic properties. The thermometers were mathematically modelled. A Monte Carlo method was implemented for dynamic measurement uncertainty evaluation. The measurement uncertainty was analysed for static and dynamic conditions. Results showed that dynamic uncertainty is much larger than steady-state uncertainty. The results of dynamic uncertainty analysis were applied on an example of clinical measurements and were compared to current requirements in ISO standard for clinical thermometers. It can be concluded that there was no need for dynamic evaluation of clinical thermometers for continuous measurement, while dynamic measurement uncertainty was within the demands of target uncertainty. Whereas in the case of intermittent predictive thermometers, the thermometer dynamic properties had a significant impact on the measurement result. Estimation of dynamic uncertainty is crucial for the assurance of traceable and comparable measurements.
Lee, Taewoong; Lee, Hyounggun; Kim, Younghak; Lee, Wonho
2017-07-01
The performance of a Compton imager using a single three-dimensional position-sensitive LYSO scintillator detector was estimated using a Monte Carlo simulation. The Compton imager consisted of a single LYSO scintillator with a pixelized structure. The size of the scintillator and each pixel were 1.3 × 1.3 × 1.3 cm3 and 0.3 × 0.3 × 0.3 cm3, respectively. The order of γ-ray interactions was determined based on the deposited energies in each detector. After the determination of the interaction sequence, various types of reconstruction algorithms such as simple back-projection, filtered back-projection, and list-mode maximum-likelihood expectation maximization (LM-MLEM) were applied and compared with each other in terms of their angular resolution and signal-to-noise ratio (SNR) for several γ-ray energies. The LM-MLEM reconstruction algorithm exhibited the best performance for Compton imaging in maintaining high angular resolution and SNR. The two sources of 137Cs (662 keV) could be distinguishable if they were more than 17° apart. The reconstructed Compton images showed the precise position and distribution of various radiation isotopes, which demonstrated the feasibility of the monitoring of nuclear materials in homeland security and radioactive waste management applications.
Kanjilal, Oindrila; Manohar, C. S.
2017-07-01
The study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems. Attention is focused on importance sampling strategies based on the application of Girsanov's transformation method. Controls which minimize the distance function, as in the first order reliability method (FORM), are shown to minimize a bound on the sampling variance of the estimator for the probability of failure. Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two-point nonlinear boundary value problem, and, the second explores the application of the Volterra series in characterizing the controls. The relative merits of these schemes, vis-à-vis the method based on ideas from the FORM, are discussed. Illustrative examples, involving archetypal single degree of freedom (dof) nonlinear oscillators, and a multi-degree of freedom nonlinear dynamical system, are presented. The credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct Monte Carlo simulations.
Ferreira, P; Baptista, M; Di Maria, S; Vaz, P
2016-05-01
The aim of this work was to estimate the risk of radiation induced cancer following the Portuguese breast screening recommendations for Digital Mammography (DM) when applied to Digital Breast Tomosynthesis (DBT) and to evaluate how the risk to induce cancer could influence the energy used in breast diagnostic exams. The organ doses were calculated by Monte Carlo simulations using a female voxel phantom and considering the acquisition of 25 projection images. Single organ cancer incidence risks were calculated in order to assess the total effective radiation induced cancer risk. The screening strategy techniques considered were: DBT in Cranio-Caudal (CC) view and two-view DM (CC and Mediolateral Oblique (MLO)). The risk of cancer incidence following the Portuguese screening guidelines (screening every two years in the age range of 50-80years) was calculated by assuming a single CC DBT acquisition view as standalone screening strategy and compared with two-view DM. The difference in the total effective risk between DBT and DM is quite low. Nevertheless in DBT an increase of risk for the lung is observed with respect to DM. The lung is also the organ that is mainly affected when non-optimal beam energy (in terms of image quality and absorbed dose) is used instead of an optimal one. The use of non-optimal energies could increase the risk of lung cancer incidence by a factor of about 2.
IVF cycle cost estimation using Activity Based Costing and Monte Carlo simulation.
Cassettari, Lucia; Mosca, Marco; Mosca, Roberto; Rolando, Fabio; Costa, Mauro; Pisaturo, Valerio
2016-03-01
The Authors present a new methodological approach in stochastic regime to determine the actual costs of an healthcare process. The paper specifically shows the application of the methodology for the determination of the cost of an Assisted reproductive technology (ART) treatment in Italy. The reason of this research comes from the fact that deterministic regime is inadequate to implement an accurate estimate of the cost of this particular treatment. In fact the durations of the different activities involved are unfixed and described by means of frequency distributions. Hence the need to determine in addition to the mean value of the cost, the interval within which it is intended to vary with a known confidence level. Consequently the cost obtained for each type of cycle investigated (in vitro fertilization and embryo transfer with or without intracytoplasmic sperm injection), shows tolerance intervals around the mean value sufficiently restricted as to make the data obtained statistically robust and therefore usable also as reference for any benchmark with other Countries. It should be noted that under a methodological point of view the approach was rigorous. In fact it was used both the technique of Activity Based Costing for determining the cost of individual activities of the process both the Monte Carlo simulation, with control of experimental error, for the construction of the tolerance intervals on the final result.
Quantum Monte Carlo for minimum energy structures
Wagner, Lucas K
2010-01-01
We present an efficient method to find minimum energy structures using energy estimates from accurate quantum Monte Carlo calculations. This method involves a stochastic process formed from the stochastic energy estimates from Monte Carlo that can be averaged to find precise structural minima while using inexpensive calculations with moderate statistical uncertainty. We demonstrate the applicability of the algorithm by minimizing the energy of the H2O-OH- complex and showing that the structural minima from quantum Monte Carlo calculations affect the qualitative behavior of the potential energy surface substantially.
Energy Technology Data Exchange (ETDEWEB)
Lee, Choonsik; Kim, Kwang Pyo; Long, Daniel J.; Bolch, Wesley E. [Division of Cancer Epidemiology and Genetics, National Cancer Institute, National Institute of Health, Bethesda, Maryland 20852 (United States); Department of Nuclear Engineering, Kyung Hee University, Gyeonggi-do, 446906 (Korea, Republic of); J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida, Gainesville, Florida 32611 (United States)
2012-04-15
Purpose: To establish an organ dose database for pediatric and adolescent reference individuals undergoing computed tomography (CT) examinations by using Monte Carlo simulation. The data will permit rapid estimates of organ and effective doses for patients of different age, gender, examination type, and CT scanner model. Methods: The Monte Carlo simulation model of a Siemens Sensation 16 CT scanner previously published was employed as a base CT scanner model. A set of absorbed doses for 33 organs/tissues normalized to the product of 100 mAs and CTDI{sub vol} (mGy/100 mAs mGy) was established by coupling the CT scanner model with age-dependent reference pediatric hybrid phantoms. A series of single axial scans from the top of head to the feet of the phantoms was performed at a slice thickness of 10 mm, and at tube potentials of 80, 100, and 120 kVp. Using the established CTDI{sub vol}- and 100 mAs-normalized dose matrix, organ doses for different pediatric phantoms undergoing head, chest, abdomen-pelvis, and chest-abdomen-pelvis (CAP) scans with the Siemens Sensation 16 scanner were estimated and analyzed. The results were then compared with the values obtained from three independent published methods: CT-Expo software, organ dose for abdominal CT scan derived empirically from patient abdominal circumference, and effective dose per dose-length product (DLP). Results: Organ and effective doses were calculated and normalized to 100 mAs and CTDI{sub vol} for different CT examinations. At the same technical setting, dose to the organs, which were entirely included in the CT beam coverage, were higher by from 40 to 80% for newborn phantoms compared to those of 15-year phantoms. An increase of tube potential from 80 to 120 kVp resulted in 2.5-2.9-fold greater brain dose for head scans. The results from this study were compared with three different published studies and/or techniques. First, organ doses were compared to those given by CT-Expo which revealed dose
Channon, H A; Hamilton, A J; D'Souza, D N; Dunshea, F R
2016-06-01
Monte Carlo simulation was investigated as a potential methodology to estimate sensory tenderness, flavour and juiciness scores of pork following the implementation of key pathway interventions known to influence eating quality. Correction factors were established using mean data from published studies investigating key production, processing and cooking parameters. Probability distributions of correction factors were developed for single pathway parameters only, due to lack of interaction data. Except for moisture infusion, ageing period, aitchbone hanging and cooking pork to an internal temperature of >74°C, only small shifts in the mean of the probability distributions of correction factors were observed for the majority of pathway parameters investigated in this study. Output distributions of sensory scores, generated from Monte Carlo simulations of input distributions of correction factors and for individual pigs, indicated that this methodology may be useful in estimating both the shift and variability in pork eating traits when different pathway interventions are applied.
Wollack, James A.; Bolt, Daniel M.; Cohen, Allan S.; Lee, Young-Sun
2002-01-01
Compared the quality of item parameter estimates for marginal maximum likelihood (MML) and Markov Chain Monte Carlo (MCMC) with the nominal response model using simulation. The quality of item parameter recovery was nearly identical for MML and MCMC, and both methods tended to produce good estimates. (SLD)
Energy Technology Data Exchange (ETDEWEB)
Marcus, Ryan C. [Los Alamos National Laboratory
2012-07-25
MCMini is a proof of concept that demonstrates the possibility for Monte Carlo neutron transport using OpenCL with a focus on performance. This implementation, written in C, shows that tracing particles and calculating reactions on a 3D mesh can be done in a highly scalable fashion. These results demonstrate a potential path forward for MCNP or other Monte Carlo codes.
Smart detectors for Monte Carlo radiative transfer
Baes, Maarten
2008-01-01
Many optimization techniques have been invented to reduce the noise that is inherent in Monte Carlo radiative transfer simulations. As the typical detectors used in Monte Carlo simulations do not take into account all the information contained in the impacting photon packages, there is still room to optimize this detection process and the corresponding estimate of the surface brightness distributions. We want to investigate how all the information contained in the distribution of impacting photon packages can be optimally used to decrease the noise in the surface brightness distributions and hence to increase the efficiency of Monte Carlo radiative transfer simulations. We demonstrate that the estimate of the surface brightness distribution in a Monte Carlo radiative transfer simulation is similar to the estimate of the density distribution in an SPH simulation. Based on this similarity, a recipe is constructed for smart detectors that take full advantage of the exact location of the impact of the photon pack...
SU-E-T-238: Monte Carlo Estimation of Cerenkov Dose for Photo-Dynamic Radiotherapy
Energy Technology Data Exchange (ETDEWEB)
Chibani, O; Price, R; Ma, C [Fox Chase Cancer Center, Philadelphia, PA (United States); Eldib, A [Fox Chase Cancer Center, Philadelphia, PA (United States); University Cairo (Egypt); Mora, G [de Lisboa, Codex, Lisboa (Portugal)
2014-06-01
Purpose: Estimation of Cerenkov dose from high-energy megavoltage photon and electron beams in tissue and its impact on the radiosensitization using Protoporphyrine IX (PpIX) for tumor targeting enhancement in radiotherapy. Methods: The GEPTS Monte Carlo code is used to generate dose distributions from 18MV Varian photon beam and generic high-energy (45-MV) photon and (45-MeV) electron beams in a voxel-based tissueequivalent phantom. In addition to calculating the ionization dose, the code scores Cerenkov energy released in the wavelength range 375–425 nm corresponding to the pick of the PpIX absorption spectrum (Fig. 1) using the Frank-Tamm formula. Results: The simulations shows that the produced Cerenkov dose suitable for activating PpIX is 4000 to 5500 times lower than the overall radiation dose for all considered beams (18MV, 45 MV and 45 MeV). These results were contradictory to the recent experimental studies by Axelsson et al. (Med. Phys. 38 (2011) p 4127), where Cerenkov dose was reported to be only two orders of magnitude lower than the radiation dose. Note that our simulation results can be corroborated by a simple model where the Frank and Tamm formula is applied for electrons with 2 MeV/cm stopping power generating Cerenkov photons in the 375–425 nm range and assuming these photons have less than 1mm penetration in tissue. Conclusion: The Cerenkov dose generated by high-energy photon and electron beams may produce minimal clinical effect in comparison with the photon fluence (or dose) commonly used for photo-dynamic therapy. At the present time, it is unclear whether Cerenkov radiation is a significant contributor to the recently observed tumor regression for patients receiving radiotherapy and PpIX versus patients receiving radiotherapy only. The ongoing study will include animal experimentation and investigation of dose rate effects on PpIX response.
Smekens, F.; Létang, J. M.; Noblet, C.; Chiavassa, S.; Delpon, G.; Freud, N.; Rit, S.; Sarrut, D.
2014-12-01
We propose the split exponential track length estimator (seTLE), a new kerma-based method combining the exponential variant of the TLE and a splitting strategy to speed up Monte Carlo (MC) dose computation for low energy photon beams. The splitting strategy is applied to both the primary and the secondary emitted photons, triggered by either the MC events generator for primaries or the photon interactions generator for secondaries. Split photons are replaced by virtual particles for fast dose calculation using the exponential TLE. Virtual particles are propagated by ray-tracing in voxelized volumes and by conventional MC navigation elsewhere. Hence, the contribution of volumes such as collimators, treatment couch and holding devices can be taken into account in the dose calculation. We evaluated and analysed the seTLE method for two realistic small animal radiotherapy treatment plans. The effect of the kerma approximation, i.e. the complete deactivation of electron transport, was investigated. The efficiency of seTLE against splitting multiplicities was also studied. A benchmark with analog MC and TLE was carried out in terms of dose convergence and efficiency. The results showed that the deactivation of electrons impacts the dose at the water/bone interface in high dose regions. The maximum and mean dose differences normalized to the dose at the isocenter were, respectively of 14% and 2% . Optimal splitting multiplicities were found to be around 300. In all situations, discrepancies in integral dose were below 0.5% and 99.8% of the voxels fulfilled a 1%/0.3 mm gamma index criterion. Efficiency gains of seTLE varied from 3.2 × 105 to 7.7 × 105 compared to analog MC and from 13 to 15 compared to conventional TLE. In conclusion, seTLE provides results similar to the TLE while increasing the efficiency by a factor between 13 and 15, which makes it particularly well-suited to typical small animal radiation therapy applications.
On the predictivity of pore-scale simulations: Estimating uncertainties with multilevel Monte Carlo
Icardi, Matteo; Boccardo, Gianluca; Tempone, Raúl
2016-09-01
A fast method with tunable accuracy is proposed to estimate errors and uncertainties in pore-scale and Digital Rock Physics (DRP) problems. The overall predictivity of these studies can be, in fact, hindered by many factors including sample heterogeneity, computational and imaging limitations, model inadequacy and not perfectly known physical parameters. The typical objective of pore-scale studies is the estimation of macroscopic effective parameters such as permeability, effective diffusivity and hydrodynamic dispersion. However, these are often non-deterministic quantities (i.e., results obtained for specific pore-scale sample and setup are not totally reproducible by another "equivalent" sample and setup). The stochastic nature can arise due to the multi-scale heterogeneity, the computational and experimental limitations in considering large samples, and the complexity of the physical models. These approximations, in fact, introduce an error that, being dependent on a large number of complex factors, can be modeled as random. We propose a general simulation tool, based on multilevel Monte Carlo, that can reduce drastically the computational cost needed for computing accurate statistics of effective parameters and other quantities of interest, under any of these random errors. This is, to our knowledge, the first attempt to include Uncertainty Quantification (UQ) in pore-scale physics and simulation. The method can also provide estimates of the discretization error and it is tested on three-dimensional transport problems in heterogeneous materials, where the sampling procedure is done by generation algorithms able to reproduce realistic consolidated and unconsolidated random sphere and ellipsoid packings and arrangements. A totally automatic workflow is developed in an open-source code [1], that include rigid body physics and random packing algorithms, unstructured mesh discretization, finite volume solvers, extrapolation and post-processing techniques. The
On the predictivity of pore-scale simulations: estimating uncertainties with multilevel Monte Carlo
Icardi, Matteo
2016-02-08
A fast method with tunable accuracy is proposed to estimate errors and uncertainties in pore-scale and Digital Rock Physics (DRP) problems. The overall predictivity of these studies can be, in fact, hindered by many factors including sample heterogeneity, computational and imaging limitations, model inadequacy and not perfectly known physical parameters. The typical objective of pore-scale studies is the estimation of macroscopic effective parameters such as permeability, effective diffusivity and hydrodynamic dispersion. However, these are often non-deterministic quantities (i.e., results obtained for specific pore-scale sample and setup are not totally reproducible by another “equivalent” sample and setup). The stochastic nature can arise due to the multi-scale heterogeneity, the computational and experimental limitations in considering large samples, and the complexity of the physical models. These approximations, in fact, introduce an error that, being dependent on a large number of complex factors, can be modeled as random. We propose a general simulation tool, based on multilevel Monte Carlo, that can reduce drastically the computational cost needed for computing accurate statistics of effective parameters and other quantities of interest, under any of these random errors. This is, to our knowledge, the first attempt to include Uncertainty Quantification (UQ) in pore-scale physics and simulation. The method can also provide estimates of the discretization error and it is tested on three-dimensional transport problems in heterogeneous materials, where the sampling procedure is done by generation algorithms able to reproduce realistic consolidated and unconsolidated random sphere and ellipsoid packings and arrangements. A totally automatic workflow is developed in an open-source code [2015. https://bitbucket.org/micardi/porescalemc.], that include rigid body physics and random packing algorithms, unstructured mesh discretization, finite volume solvers
Monte Carlo methods for electromagnetics
Sadiku, Matthew NO
2009-01-01
Until now, novices had to painstakingly dig through the literature to discover how to use Monte Carlo techniques for solving electromagnetic problems. Written by one of the foremost researchers in the field, Monte Carlo Methods for Electromagnetics provides a solid understanding of these methods and their applications in electromagnetic computation. Including much of his own work, the author brings together essential information from several different publications.Using a simple, clear writing style, the author begins with a historical background and review of electromagnetic theory. After addressing probability and statistics, he introduces the finite difference method as well as the fixed and floating random walk Monte Carlo methods. The text then applies the Exodus method to Laplace's and Poisson's equations and presents Monte Carlo techniques for handing Neumann problems. It also deals with whole field computation using the Markov chain, applies Monte Carlo methods to time-varying diffusion problems, and ...
Fast sequential Monte Carlo methods for counting and optimization
Rubinstein, Reuven Y; Vaisman, Radislav
2013-01-01
A comprehensive account of the theory and application of Monte Carlo methods Based on years of research in efficient Monte Carlo methods for estimation of rare-event probabilities, counting problems, and combinatorial optimization, Fast Sequential Monte Carlo Methods for Counting and Optimization is a complete illustration of fast sequential Monte Carlo techniques. The book provides an accessible overview of current work in the field of Monte Carlo methods, specifically sequential Monte Carlo techniques, for solving abstract counting and optimization problems. Written by authorities in the
CSIR Research Space (South Africa)
Bidgood, Peter M
2017-01-01
Full Text Available , 2 01 7 | ht tp: //a rc. aia a.o rg | D OI : 1 0.2 514 /6. 201 7-0 106 55th AIAA Aerospace Sciences Meeting 9 - 13 January 2017, Grapevine, Texas AIAA 2017-0106 Copyright © 2017 by CSIR-South Africa. Published by the American Institute... Tunnel Balance Calibration models using Monte Carlo to Propagate Elemental Errors from Calibration to Installation.” Paper presented at 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition : Grapevine, Texas : s...
Indian Academy of Sciences (India)
M E MEDHAT; S P SHIRMARDI; V P SINGH
2017-03-01
Monte Carlo N-particle (MCNP) code has been used to simulate the transport of gamma photon rays of different energies (22, 31, 59.5 and 81 keV) to estimate the iron content in solutions. In this study, MCNP simulation results are compared with experiment and XCOM theoretical data. The simulation shows that theobtained results are in good agreement with experimental data, and better than the theoretical XCOM values. The study indicates that MCNP simulation is an excellent tool to estimate the iron concentration in the blood samples. The MCNP code can also be utilized to estimate other trace elements in the blood samples.
Medhat, M. E.; Shirmardi, S. P.; Singh, V. P.
2017-03-01
Monte Carlo N-particle (MCNP) code has been used to simulate the transport of gamma photon rays of different energies (22, 31, 59.5 and 81 keV) to estimate the iron content in solutions. In this study, MCNP simulation results are compared with experiment and XCOM theoretical data. The simulation shows that the obtained results are in good agreement with experimental data, and better than the theoretical XCOM values. The study indicates that MCNP simulation is an excellent tool to estimate the iron concentration in the blood samples. The MCNP code can also be utilized to estimate other trace elements in the blood samples.
Metropolis Methods for Quantum Monte Carlo Simulations
Ceperley, D. M.
2003-01-01
Since its first description fifty years ago, the Metropolis Monte Carlo method has been used in a variety of different ways for the simulation of continuum quantum many-body systems. This paper will consider some of the generalizations of the Metropolis algorithm employed in quantum Monte Carlo: Variational Monte Carlo, dynamical methods for projector monte carlo ({\\it i.e.} diffusion Monte Carlo with rejection), multilevel sampling in path integral Monte Carlo, the sampling of permutations, ...
Monte Carlo Algorithms for Linear Problems
DIMOV, Ivan
2000-01-01
MSC Subject Classification: 65C05, 65U05. Monte Carlo methods are a powerful tool in many fields of mathematics, physics and engineering. It is known, that these methods give statistical estimates for the functional of the solution by performing random sampling of a certain chance variable whose mathematical expectation is the desired functional. Monte Carlo methods are methods for solving problems using random variables. In the book [16] edited by Yu. A. Shreider one can find the followin...
Lectures on Monte Carlo methods
Madras, Neal
2001-01-01
Monte Carlo methods form an experimental branch of mathematics that employs simulations driven by random number generators. These methods are often used when others fail, since they are much less sensitive to the "curse of dimensionality", which plagues deterministic methods in problems with a large number of variables. Monte Carlo methods are used in many fields: mathematics, statistics, physics, chemistry, finance, computer science, and biology, for instance. This book is an introduction to Monte Carlo methods for anyone who would like to use these methods to study various kinds of mathemati
Energy Technology Data Exchange (ETDEWEB)
Bootsma, G. J., E-mail: Gregory.Bootsma@rmp.uhn.on.ca [Radiation Medicine Program, Princess Margaret Cancer Centre, Toronto, Ontario M5G 2M9 (Canada); Verhaegen, F. [Department of Radiation Oncology - MAASTRO, GROW—School for Oncology and Developmental Biology, Maastricht University Medical Center, Maastricht 6201 BN (Netherlands); Medical Physics Unit, Department of Oncology, McGill University, Montreal, Quebec H3G 1A4 (Canada); Jaffray, D. A. [Radiation Medicine Program, Princess Margaret Cancer Centre, Toronto, Ontario M5G 2M9 (Canada); Ontario Cancer Institute, Princess Margaret Cancer Centre, Toronto, Ontario M5G 2M9 (Canada); Department of Radiation Oncology, University of Toronto, Toronto, Ontario M5G 2M9 (Canada)
2015-01-15
Purpose: X-ray scatter is a significant impediment to image quality improvements in cone-beam CT (CBCT). The authors present and demonstrate a novel scatter correction algorithm using a scatter estimation method that simultaneously combines multiple Monte Carlo (MC) CBCT simulations through the use of a concurrently evaluated fitting function, referred to as concurrent MC fitting (CMCF). Methods: The CMCF method uses concurrently run MC CBCT scatter projection simulations that are a subset of the projection angles used in the projection set, P, to be corrected. The scattered photons reaching the detector in each MC simulation are simultaneously aggregated by an algorithm which computes the scatter detector response, S{sub MC}. S{sub MC} is fit to a function, S{sub F}, and if the fit of S{sub F} is within a specified goodness of fit (GOF), the simulations are terminated. The fit, S{sub F}, is then used to interpolate the scatter distribution over all pixel locations for every projection angle in the set P. The CMCF algorithm was tested using a frequency limited sum of sines and cosines as the fitting function on both simulated and measured data. The simulated data consisted of an anthropomorphic head and a pelvis phantom created from CT data, simulated with and without the use of a compensator. The measured data were a pelvis scan of a phantom and patient taken on an Elekta Synergy platform. The simulated data were used to evaluate various GOF metrics as well as determine a suitable fitness value. The simulated data were also used to quantitatively evaluate the image quality improvements provided by the CMCF method. A qualitative analysis was performed on the measured data by comparing the CMCF scatter corrected reconstruction to the original uncorrected and corrected by a constant scatter correction reconstruction, as well as a reconstruction created using a set of projections taken with a small cone angle. Results: Pearson’s correlation, r, proved to be a
Barengoltz, Jack
2016-07-01
Monte Carlo (MC) is a common method to estimate probability, effectively by a simulation. For planetary protection, it may be used to estimate the probability of impact P{}_{I} by a launch vehicle (upper stage) of a protected planet. The object of the analysis is to provide a value for P{}_{I} with a given level of confidence (LOC) that the true value does not exceed the maximum allowed value of P{}_{I}. In order to determine the number of MC histories required, one must also guess the maximum number of hits that will occur in the analysis. This extra parameter is needed because a LOC is desired. If more hits occur, the MC analysis would indicate that the true value may exceed the specification value with a higher probability than the LOC. (In the worst case, even the mean value of the estimated P{}_{I} might exceed the specification value.) After the analysis is conducted, the actual number of hits is, of course, the mean. The number of hits arises from a small probability per history and a large number of histories; these are the classic requirements for a Poisson distribution. For a known Poisson distribution (the mean is the only parameter), the probability for some interval in the number of hits is calculable. Before the analysis, this is not possible. Fortunately, there are methods that can bound the unknown mean for a Poisson distribution. F. Garwoodfootnote{ F. Garwood (1936), ``Fiduciary limits for the Poisson distribution.'' Biometrika 28, 437-442.} published an appropriate method that uses the Chi-squared function, actually its inversefootnote{ The integral chi-squared function would yield probability α as a function of the mean µ and an actual value n.} (despite the notation used): This formula for the upper and lower limits of the mean μ with the two-tailed probability 1-α depends on the LOC α and an estimated value of the number of "successes" n. In a MC analysis for planetary protection, only the upper limit is of interest, i.e., the single
Iakovidis, S.; Apostolidis, C.; Samaras, T.
2015-04-01
The objective of the present work is the application of the Monte Carlo method (GUMS1) for evaluating uncertainty in electromagnetic field measurements and the comparison of the results with the ones obtained using the 'standard' method (GUM). In particular, the two methods are applied in order to evaluate the field measurement uncertainty using a frequency selective radiation meter and the Total Exposure Quotient (TEQ) uncertainty. Comparative results are presented in order to highlight cases where GUMS1 results deviate significantly from the ones obtained using GUM, such as the presence of a non-linear mathematical model connecting the inputs with the output quantity (case of the TEQ model) or the presence of a dominant nonnormal distribution of an input quantity (case of U-shaped mismatch uncertainty). The deviation of the results obtained from the two methods can even lead to different decisions regarding the conformance with the exposure reference levels.
Brandão, Eric; Flesch, Rodolfo C C; Lenzi, Arcanjo; Flesch, Carlos A
2011-07-01
The pressure-particle velocity (PU) impedance measurement technique is an experimental method used to measure the surface impedance and the absorption coefficient of acoustic samples in situ or under free-field conditions. In this paper, the measurement uncertainty of the the absorption coefficient determined using the PU technique is explored applying the Monte Carlo method. It is shown that because of the uncertainty, it is particularly difficult to measure samples with low absorption and that difficulties associated with the localization of the acoustic centers of the sound source and the PU sensor affect the quality of the measurement roughly to the same extent as the errors in the transfer function between pressure and particle velocity do.
Lee, G. W.; Kim, T. H.; Youn, J. I.
2016-03-01
Thermal treatment has been used for collagen tightening and tissue contour enhancement. It is important to monitor the condition of collagenous tissue during and immediately after thermal treatment. Collagen denaturation changes the optical properties such as scattering coefficient and anisotropy. In this study, Monte Carlo simulation of polarized light was used to calculate the degree of linear polarization (DOLP) of backscattered light from thermally damaged porcine skin, and the Mueller matrix was calculated to verify the result of DOLP. We observed a decrease in the DOLP and a significant change in the radial distribution of the Mueller matrix elements at temperatures ranging from 55 to 65°C. This could be attributed to the increase in scattering coefficient and decrease in anisotropy caused by thermal denaturation in the tissue. The DOLP method has a potential implementation as a real-time closed-loop feedback system for use in various thermal treatment methods through measuring changes in optical properties of target tissues.
Monte Carlo integration on GPU
Kanzaki, J.
2010-01-01
We use a graphics processing unit (GPU) for fast computations of Monte Carlo integrations. Two widely used Monte Carlo integration programs, VEGAS and BASES, are parallelized on GPU. By using $W^{+}$ plus multi-gluon production processes at LHC, we test integrated cross sections and execution time for programs in FORTRAN and C on CPU and those on GPU. Integrated results agree with each other within statistical errors. Execution time of programs on GPU run about 50 times faster than those in C...
A Markov Chain Monte Carlo Approach to Estimate AIDS after HIV Infection.
Apenteng, Ofosuhene O; Ismail, Noor Azina
2015-01-01
The spread of human immunodeficiency virus (HIV) infection and the resulting acquired immune deficiency syndrome (AIDS) is a major health concern in many parts of the world, and mathematical models are commonly applied to understand the spread of the HIV epidemic. To understand the spread of HIV and AIDS cases and their parameters in a given population, it is necessary to develop a theoretical framework that takes into account realistic factors. The current study used this framework to assess the interaction between individuals who developed AIDS after HIV infection and individuals who did not develop AIDS after HIV infection (pre-AIDS). We first investigated how probabilistic parameters affect the model in terms of the HIV and AIDS population over a period of time. We observed that there is a critical threshold parameter, R0, which determines the behavior of the model. If R0 ≤ 1, there is a unique disease-free equilibrium; if R0 1, the disease-free equilibrium is unstable. We also show how a Markov chain Monte Carlo (MCMC) approach could be used as a supplement to forecast the numbers of reported HIV and AIDS cases. An approach using a Monte Carlo analysis is illustrated to understand the impact of model-based predictions in light of uncertain parameters on the spread of HIV. Finally, to examine this framework and demonstrate how it works, a case study was performed of reported HIV and AIDS cases from an annual data set in Malaysia, and then we compared how these approaches complement each other. We conclude that HIV disease in Malaysia shows epidemic behavior, especially in the context of understanding and predicting emerging cases of HIV and AIDS.
Hickey, John M; Veerkamp, Roel F; Calus, Mario P L; Mulder, Han A; Thompson, Robin
2009-02-09
Calculation of the exact prediction error variance covariance matrix is often computationally too demanding, which limits its application in REML algorithms, the calculation of accuracies of estimated breeding values and the control of variance of response to selection. Alternatively Monte Carlo sampling can be used to calculate approximations of the prediction error variance, which converge to the true values if enough samples are used. However, in practical situations the number of samples, which are computationally feasible, is limited. The objective of this study was to compare the convergence rate of different formulations of the prediction error variance calculated using Monte Carlo sampling. Four of these formulations were published, four were corresponding alternative versions, and two were derived as part of this study. The different formulations had different convergence rates and these were shown to depend on the number of samples and on the level of prediction error variance. Four formulations were competitive and these made use of information on either the variance of the estimated breeding value and on the variance of the true breeding value minus the estimated breeding value or on the covariance between the true and estimated breeding values.
Quantum speedup of Monte Carlo methods.
Montanaro, Ashley
2015-09-08
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently.
O'Hagan, Anthony; Stevenson, Matt; Madan, Jason
2007-10-01
Probabilistic sensitivity analysis (PSA) is required to account for uncertainty in cost-effectiveness calculations arising from health economic models. The simplest way to perform PSA in practice is by Monte Carlo methods, which involves running the model many times using randomly sampled values of the model inputs. However, this can be impractical when the economic model takes appreciable amounts of time to run. This situation arises, in particular, for patient-level simulation models (also known as micro-simulation or individual-level simulation models), where a single run of the model simulates the health care of many thousands of individual patients. The large number of patients required in each run to achieve accurate estimation of cost-effectiveness means that only a relatively small number of runs is possible. For this reason, it is often said that PSA is not practical for patient-level models. We develop a way to reduce the computational burden of Monte Carlo PSA for patient-level models, based on the algebra of analysis of variance. Methods are presented to estimate the mean and variance of the model output, with formulae for determining optimal sample sizes. The methods are simple to apply and will typically reduce the computational demand very substantially.
Monte Carlo Planning Method Estimates Planning Horizons during Interactive Social Exchange.
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Andreas Hula
2015-06-01
Full Text Available 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.
Zou, Yonghong; Christensen, Erik R; Zheng, Wei; Wei, Hua; Li, An
2014-11-01
A stochastic process was developed to simulate the stepwise debromination pathways for polybrominated diphenyl ethers (PBDEs). The stochastic process uses an analogue Markov Chain Monte Carlo (AMCMC) algorithm to generate PBDE debromination profiles. The acceptance or rejection of the randomly drawn stepwise debromination reactions was determined by a maximum likelihood function. The experimental observations at certain time points were used as target profiles; therefore, the stochastic processes are capable of presenting the effects of reaction conditions on the selection of debromination pathways. The application of the model is illustrated by adopting the experimental results of decabromodiphenyl ether (BDE209) in hexane exposed to sunlight. Inferences that were not obvious from experimental data were suggested by model simulations. For example, BDE206 has much higher accumulation at the first 30 min of sunlight exposure. By contrast, model simulation suggests that, BDE206 and BDE207 had comparable yields from BDE209. The reason for the higher BDE206 level is that BDE207 has the highest depletion in producing octa products. Compared to a previous version of the stochastic model based on stochastic reaction sequences (SRS), the AMCMC approach was determined to be more efficient and robust. Due to the feature of only requiring experimental observations as input, the AMCMC model is expected to be applicable to a wide range of PBDE debromination processes, e.g. microbial, photolytic, or joint effects in natural environments.
Beyond histograms: Efficiently estimating radial distribution functions via spectral Monte Carlo
Patrone, Paul N.; Rosch, Thomas W.
2017-03-01
Despite more than 40 years of research in condensed-matter physics, state-of-the-art approaches for simulating the radial distribution function (RDF) g(r) still rely on binning pair-separations into a histogram. Such methods suffer from undesirable properties, including subjectivity, high uncertainty, and slow rates of convergence. Moreover, such problems go undetected by the metrics often used to assess RDFs. To address these issues, we propose (I) a spectral Monte Carlo (SMC) quadrature method that yields g(r) as an analytical series expansion and (II) a Sobolev norm that assesses the quality of RDFs by quantifying their fluctuations. Using the latter, we show that, relative to histogram-based approaches, SMC reduces by orders of magnitude both the noise in g(r) and the number of pair separations needed for acceptable convergence. Moreover, SMC reduces subjectivity and yields simple, differentiable formulas for the RDF, which are useful for tasks such as coarse-grained force-field calibration via iterative Boltzmann inversion.
On the use of stochastic approximation Monte Carlo for Monte Carlo integration
Liang, Faming
2009-03-01
The stochastic approximation Monte Carlo (SAMC) algorithm has recently been proposed as a dynamic optimization algorithm in the literature. In this paper, we show in theory that the samples generated by SAMC can be used for Monte Carlo integration via a dynamically weighted estimator by calling some results from the literature of nonhomogeneous Markov chains. Our numerical results indicate that SAMC can yield significant savings over conventional Monte Carlo algorithms, such as the Metropolis-Hastings algorithm, for the problems for which the energy landscape is rugged. © 2008 Elsevier B.V. All rights reserved.
Nestler, Steffen
2013-02-01
We conducted a Monte Carlo study to investigate the performance of the polychoric instrumental variable estimator (PIV) in comparison to unweighted least squares (ULS) and diagonally weighted least squares (DWLS) in the estimation of a confirmatory factor analysis model with dichotomous indicators. The simulation involved 144 conditions (1,000 replications per condition) that were defined by a combination of (a) two types of latent factor models, (b) four sample sizes (100, 250, 500, 1,000), (c) three factor loadings (low, moderate, strong), (d) three levels of non-normality (normal, moderately, and extremely non-normal), and (e) whether the factor model was correctly specified or misspecified. The results showed that when the model was correctly specified, PIV produced estimates that were as accurate as ULS and DWLS. Furthermore, the simulation showed that PIV was more robust to structural misspecifications than ULS and DWLS.
Equilibrium Statistics: Monte Carlo Methods
Kröger, Martin
Monte Carlo methods use random numbers, or ‘random’ sequences, to sample from a known shape of a distribution, or to extract distribution by other means. and, in the context of this book, to (i) generate representative equilibrated samples prior being subjected to external fields, or (ii) evaluate high-dimensional integrals. Recipes for both topics, and some more general methods, are summarized in this chapter. It is important to realize, that Monte Carlo should be as artificial as possible to be efficient and elegant. Advanced Monte Carlo ‘moves’, required to optimize the speed of algorithms for a particular problem at hand, are outside the scope of this brief introduction. One particular modern example is the wavelet-accelerated MC sampling of polymer chains [406].
Monte Carlo Hamiltonian: Linear Potentials
Institute of Scientific and Technical Information of China (English)
LUO Xiang-Qian; LIU Jin-Jiang; HUANG Chun-Qing; JIANG Jun-Qin; Helmut KROGER
2002-01-01
We further study the validity of the Monte Carlo Hamiltonian method. The advantage of the method,in comparison with the standard Monte Carlo Lagrangian approach, is its capability to study the excited states. Weconsider two quantum mechanical models: a symmetric one V(x) = |x|/2; and an asymmetric one V(x) = ∞, forx ＜ 0 and V(x) = x, for x ≥ 0. The results for the spectrum, wave functions and thermodynamical observables are inagreement with the analytical or Runge-Kutta calculations.
Proton Upset Monte Carlo Simulation
O'Neill, Patrick M.; Kouba, Coy K.; Foster, Charles C.
2009-01-01
The Proton Upset Monte Carlo Simulation (PROPSET) program calculates the frequency of on-orbit upsets in computer chips (for given orbits such as Low Earth Orbit, Lunar Orbit, and the like) from proton bombardment based on the results of heavy ion testing alone. The software simulates the bombardment of modern microelectronic components (computer chips) with high-energy (.200 MeV) protons. The nuclear interaction of the proton with the silicon of the chip is modeled and nuclear fragments from this interaction are tracked using Monte Carlo techniques to produce statistically accurate predictions.
Shinn, Judy L.; Wilson, John W.; Nealy, John E.; Cucinotta, Francis A.
1990-01-01
Continuing efforts toward validating the buildup factor method and the BRYNTRN code, which use the deterministic approach in solving radiation transport problems and are the candidate engineering tools in space radiation shielding analyses, are presented. A simplified theory of proton buildup factors assuming no neutron coupling is derived to verify a previously chosen form for parameterizing the dose conversion factor that includes the secondary particle buildup effect. Estimates of dose in tissue made by the two deterministic approaches and the Monte Carlo method are intercompared for cases with various thicknesses of shields and various types of proton spectra. The results are found to be in reasonable agreement but with some overestimation by the buildup factor method when the effect of neutron production in the shield is significant. Future improvement to include neutron coupling in the buildup factor theory is suggested to alleviate this shortcoming. Impressive agreement for individual components of doses, such as those from the secondaries and heavy particle recoils, are obtained between BRYNTRN and Monte Carlo results.
SMCTC: Sequential Monte Carlo in C++
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Adam M. Johansen
2009-04-01
Full Text Available Sequential Monte Carlo methods are a very general class of Monte Carlo methodsfor sampling from sequences of distributions. Simple examples of these algorithms areused very widely in the tracking and signal processing literature. Recent developmentsillustrate that these techniques have much more general applicability, and can be appliedvery eectively to statistical inference problems. Unfortunately, these methods are oftenperceived as being computationally expensive and dicult to implement. This articleseeks to address both of these problems.A C++ template class library for the ecient and convenient implementation of verygeneral Sequential Monte Carlo algorithms is presented. Two example applications areprovided: a simple particle lter for illustrative purposes and a state-of-the-art algorithmfor rare event estimation.
CosmoPMC: Cosmology Population Monte Carlo
Kilbinger, Martin; Cappe, Olivier; Cardoso, Jean-Francois; Fort, Gersende; Prunet, Simon; Robert, Christian P; Wraith, Darren
2011-01-01
We present the public release of the Bayesian sampling algorithm for cosmology, CosmoPMC (Cosmology Population Monte Carlo). CosmoPMC explores the parameter space of various cosmological probes, and also provides a robust estimate of the Bayesian evidence. CosmoPMC is based on an adaptive importance sampling method called Population Monte Carlo (PMC). Various cosmology likelihood modules are implemented, and new modules can be added easily. The importance-sampling algorithm is written in C, and fully parallelised using the Message Passing Interface (MPI). Due to very little overhead, the wall-clock time required for sampling scales approximately with the number of CPUs. The CosmoPMC package contains post-processing and plotting programs, and in addition a Monte-Carlo Markov chain (MCMC) algorithm. The sampling engine is implemented in the library pmclib, and can be used independently. The software is available for download at http://www.cosmopmc.info.
Variance Reduction Techniques in Monte Carlo Methods
Kleijnen, Jack P.C.; Ridder, A.A.N.; Rubinstein, R.Y.
2010-01-01
Monte Carlo methods are simulation algorithms to estimate a numerical quantity in a statistical model of a real system. These algorithms are executed by computer programs. Variance reduction techniques (VRT) are needed, even though computer speed has been increasing dramatically, ever since the intr
Variance Reduction Techniques in Monte Carlo Methods
Kleijnen, Jack P.C.; Ridder, A.A.N.; Rubinstein, R.Y.
2010-01-01
Monte Carlo methods are simulation algorithms to estimate a numerical quantity in a statistical model of a real system. These algorithms are executed by computer programs. Variance reduction techniques (VRT) are needed, even though computer speed has been increasing dramatically, ever since the intr
Monte Carlo Particle Lists: MCPL
Kittelmann, Thomas; Knudsen, Erik B; Willendrup, Peter; Cai, Xiao Xiao; Kanaki, Kalliopi
2016-01-01
A binary format with lists of particle state information, for interchanging particles between various Monte Carlo simulation applications, is presented. Portable C code for file manipulation is made available to the scientific community, along with converters and plugins for several popular simulation packages.
Ulanovsky, A V; Minenko, V F; Korneev, S V
1997-01-01
An approach for evaluating the influence of measurement geometry on estimates of 131(I) in the thyroid from measurements with survey meters was developed using Monte Carlo simulation of radiation transport in the human body and the radiation detector. The modified Monte Carlo code, EGS4, including a newly developed mathematical model of detector, thyroid gland, and neck, was used for the computations. The approach was tested by comparing calculated and measured differential and integral detector characteristics. This procedure was applied to estimate uncertainties in direct thyroid-measurement results due to geometrical errors.
Applications of Monte Carlo Methods in Calculus.
Gordon, Sheldon P.; Gordon, Florence S.
1990-01-01
Discusses the application of probabilistic ideas, especially Monte Carlo simulation, to calculus. Describes some applications using the Monte Carlo method: Riemann sums; maximizing and minimizing a function; mean value theorems; and testing conjectures. (YP)
Curis, Emmanuel; Bénazeth, Simone
2005-05-01
An important step in X-ray absorption spectroscopy (XAS) analysis is the fitting of a model to the experimental spectra, with a view to obtaining structural parameters. It is important to estimate the errors on these parameters, and three methods are used for this purpose. This article presents the conditions for applying these methods. It is shown that the usual equation Sigma = 2H(-1) is not applicable for fitting in R space or on filtered XAS data; a formula is established to treat these cases, and the equivalence between the usual formula and the brute-force method is evidenced. Lastly, the problem of the nonlinearity of the XAS models and a comparison with Monte Carlo methods are addressed.
Herbei, Radu; Kubatko, Laura
2013-03-26
Markov chains are widely used for modeling in many areas of molecular biology and genetics. As the complexity of such models advances, it becomes increasingly important to assess the rate at which a Markov chain converges to its stationary distribution in order to carry out accurate inference. A common measure of convergence to the stationary distribution is the total variation distance, but this measure can be difficult to compute when the state space of the chain is large. We propose a Monte Carlo method to estimate the total variation distance that can be applied in this situation, and we demonstrate how the method can be efficiently implemented by taking advantage of GPU computing techniques. We apply the method to two Markov chains on the space of phylogenetic trees, and discuss the implications of our findings for the development of algorithms for phylogenetic inference.
Nagamine, Shuji; Fujibuchi, Toshioh; Umezu, Yoshiyuki; Himuro, Kazuhiko; Awamoto, Shinichi; Tsutsui, Yuji; Nakamura, Yasuhiko
2017-03-01
In this study, we estimated the ambient dose equivalent rate (hereafter "dose rate") in the fluoro-2-deoxy-D-glucose (FDG) administration room in our hospital using Monte Carlo simulations, and examined the appropriate medical-personnel locations and a shielding method to reduce the dose rate during FDG injection using a lead glass shield. The line source was assumed to be the FDG feed tube and the patient a cube source. The dose rate distribution was calculated with a composite source that combines the line and cube sources. The dose rate distribution was also calculated when a lead glass shield was placed in the rear section of the lead-acrylic shield. The dose rate behind the automatic administration device decreased by 87 % with respect to that behind the lead-acrylic shield. Upon positioning a 2.8-cm-thick lead glass shield, the dose rate behind the lead-acrylic shield decreased by 67 %.
Institute of Scientific and Technical Information of China (English)
罗正鸿; 詹晓力; 阳永荣
2006-01-01
The application of Monte Carlo method in estimating rate constants for polymerization was described.A general program for Monte Carlo simulation was determined first according to the elementary reactions, after which the rate constants could be automatically adjusted and optimized through comparing of experimental and simulated data with an error expression that meeted a given minimum criterion.Such a process made the rate constants to be estimated without kinetic model in advance.The technique was applied to estimate the rate constants of the bulk polymerization of styrene catalyzed by the rare earth catalyst.The estimated results showed the Monte Carlo method was feasible and effective for estimating rate constants in polymerization engineering.
(U) Introduction to Monte Carlo Methods
Energy Technology Data Exchange (ETDEWEB)
Hungerford, Aimee L. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
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.
Comparative Dosimetric Estimates of a 25 keV Electron Micro-beam with three Monte Carlo Codes
Energy Technology Data Exchange (ETDEWEB)
Mainardi, Enrico; Donahue, Richard J.; Blakely, Eleanor A.
2002-09-11
The calculations presented compare the different performances of the three Monte Carlo codes PENELOPE-1999, MCNP-4C and PITS, for the evaluation of Dose profiles from a 25 keV electron micro-beam traversing individual cells. The overall model of a cell is a water cylinder equivalent for the three codes but with a different internal scoring geometry: hollow cylinders for PENELOPE and MCNP, whereas spheres are used for the PITS code. A cylindrical cell geometry with scoring volumes with the shape of hollow cylinders was initially selected for PENELOPE and MCNP because of its superior simulation of the actual shape and dimensions of a cell and for its improved computer-time efficiency if compared to spherical internal volumes. Some of the transfer points and energy transfer that constitute a radiation track may actually fall in the space between spheres, that would be outside the spherical scoring volume. This internal geometry, along with the PENELOPE algorithm, drastically reduced the computer time when using this code if comparing with event-by-event Monte Carlo codes like PITS. This preliminary work has been important to address dosimetric estimates at low electron energies. It demonstrates that codes like PENELOPE can be used for Dose evaluation, even with such small geometries and energies involved, which are far below the normal use for which the code was created. Further work (initiated in Summer 2002) is still needed however, to create a user-code for PENELOPE that allows uniform comparison of exact cell geometries, integral volumes and also microdosimetric scoring quantities, a field where track-structure codes like PITS, written for this purpose, are believed to be superior.
Energy Technology Data Exchange (ETDEWEB)
Han, Gi Young; Seo, Bo Kyun [Korea Institute of Nuclear Safety,, Daejeon (Korea, Republic of); Kim, Do Hyun; Shin, Chang Ho; Kim, Song Hyun [Dept. of Nuclear Engineering, Hanyang University, Seoul (Korea, Republic of); Sun, Gwang Min [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2016-06-15
In analyzing residual radiation, researchers generally use a two-step Monte Carlo (MC) simulation. The first step (MC1) simulates neutron transport, and the second step (MC2) transports the decay photons emitted from the activated materials. In this process, the stochastic uncertainty estimated by the MC2 appears only as a final result, but it is underestimated because the stochastic error generated in MC1 cannot be directly included in MC2. Hence, estimating the true stochastic uncertainty requires quantifying the propagation degree of the stochastic error in MC1. The brute force technique is a straightforward method to estimate the true uncertainty. However, it is a costly method to obtain reliable results. Another method, called the adjoint-based method, can reduce the computational time needed to evaluate the true uncertainty; however, there are limitations. To address those limitations, we propose a new strategy to estimate uncertainty propagation without any additional calculations in two-step MC simulations. To verify the proposed method, we applied it to activation benchmark problems and compared the results with those of previous methods. The results show that the proposed method increases the applicability and user-friendliness preserving accuracy in quantifying uncertainty propagation. We expect that the proposed strategy will contribute to efficient and accurate two-step MC calculations.
Density matrix quantum Monte Carlo
Blunt, N S; Spencer, J S; Foulkes, W M C
2013-01-01
This paper describes a quantum Monte Carlo method capable of sampling the full density matrix of a many-particle system, thus granting access to arbitrary reduced density matrices and allowing expectation values of complicated non-local operators to be evaluated easily. The direct sampling of the density matrix also raises the possibility of calculating previously inaccessible entanglement measures. The algorithm closely resembles the recently introduced full configuration interaction quantum Monte Carlo method, but works all the way from infinite to zero temperature. We explain the theory underlying the method, describe the algorithm, and introduce an importance-sampling procedure to improve the stochastic efficiency. To demonstrate the potential of our approach, the energy and staggered magnetization of the isotropic antiferromagnetic Heisenberg model on small lattices and the concurrence of one-dimensional spin rings are compared to exact or well-established results. Finally, the nature of the sign problem...
Efficient kinetic Monte Carlo simulation
Schulze, Tim P.
2008-02-01
This paper concerns kinetic Monte Carlo (KMC) algorithms that have a single-event execution time independent of the system size. Two methods are presented—one that combines the use of inverted-list data structures with rejection Monte Carlo and a second that combines inverted lists with the Marsaglia-Norman-Cannon algorithm. The resulting algorithms apply to models with rates that are determined by the local environment but are otherwise arbitrary, time-dependent and spatially heterogeneous. While especially useful for crystal growth simulation, the algorithms are presented from the point of view that KMC is the numerical task of simulating a single realization of a Markov process, allowing application to a broad range of areas where heterogeneous random walks are the dominate simulation cost.
Adaptive Multilevel Monte Carlo Simulation
Hoel, H
2011-08-23
This work generalizes a multilevel forward Euler Monte Carlo method introduced in Michael B. Giles. (Michael Giles. Oper. Res. 56(3):607–617, 2008.) for the approximation of expected values depending on the solution to an Itô stochastic differential equation. The work (Michael Giles. Oper. Res. 56(3):607– 617, 2008.) proposed and analyzed a forward Euler multilevelMonte Carlo method based on a hierarchy of uniform time discretizations and control variates to reduce the computational effort required by a standard, single level, Forward Euler Monte Carlo method. This work introduces an adaptive hierarchy of non uniform time discretizations, generated by an adaptive algorithmintroduced in (AnnaDzougoutov et al. Raùl Tempone. Adaptive Monte Carlo algorithms for stopped diffusion. In Multiscale methods in science and engineering, volume 44 of Lect. Notes Comput. Sci. Eng., pages 59–88. Springer, Berlin, 2005; Kyoung-Sook Moon et al. Stoch. Anal. Appl. 23(3):511–558, 2005; Kyoung-Sook Moon et al. An adaptive algorithm for ordinary, stochastic and partial differential equations. In Recent advances in adaptive computation, volume 383 of Contemp. Math., pages 325–343. Amer. Math. Soc., Providence, RI, 2005.). This form of the adaptive algorithm generates stochastic, path dependent, time steps and is based on a posteriori error expansions first developed in (Anders Szepessy et al. Comm. Pure Appl. Math. 54(10):1169– 1214, 2001). Our numerical results for a stopped diffusion problem, exhibit savings in the computational cost to achieve an accuracy of ϑ(TOL),from(TOL−3), from using a single level version of the adaptive algorithm to ϑ(((TOL−1)log(TOL))2).
Directory of Open Access Journals (Sweden)
Christelle Garnier
2008-05-01
Full Text Available We address the problem of phase noise (PHN and carrier frequency offset (CFO mitigation in multicarrier receivers. In multicarrier systems, phase distortions cause two effects: the common phase error (CPE and the intercarrier interference (ICI which severely degrade the accuracy of the symbol detection stage. Here, we propose a non-pilot-aided scheme to jointly estimate PHN, CFO, and multicarrier signal in time domain. Unlike existing methods, non-pilot-based estimation is performed without any decision-directed scheme. Our approach to the problem is based on Bayesian estimation using sequential Monte Carlo filtering commonly referred to as particle filtering. The particle filter is efficiently implemented by combining the principles of the Rao-Blackwellization technique and an approximate optimal importance function for phase distortion sampling. Moreover, in order to fully benefit from time-domain processing, we propose a multicarrier signal model which includes the redundancy information induced by the cyclic prefix, thus leading to a significant performance improvement. Simulation results are provided in terms of bit error rate (BER and mean square error (MSE to illustrate the efficiency and the robustness of the proposed algorithm.
Nightingale, M.P.; Blöte , H.W.J.
1996-01-01
The principle and the efficiency of the Monte Carlo transfer-matrix algorithm are discussed. Enhancements of this algorithm are illustrated by applications to several phase transitions in lattice spin models. We demonstrate how the statistical noise can be reduced considerably by a similarity transf
Nightingale, M.P.; Blöte , H.W.J.
1996-01-01
The principle and the efficiency of the Monte Carlo transfer-matrix algorithm are discussed. Enhancements of this algorithm are illustrated by applications to several phase transitions in lattice spin models. We demonstrate how the statistical noise can be reduced considerably by a similarity
Directory of Open Access Journals (Sweden)
Miguel Arias Albornoz
2008-09-01
Full Text Available En este trabajo se aplica el método de simulación de Monte Carlo (MC para estimar el número de depresiones rápidas de tensión (dips esperados en barras de una red eléctrica. Las estimaciones obtenidas a través de MC se comparan con los resultados de otro método de cálculo conocido como Método de Posiciones de Falla (MPF. Entre los resultados se muestra tanto la convergencia del algoritmo MC a los valores de largo plazo del método MPF como la distribución completa de frecuencias para diferentes eventos, lo cual representa información valiosa para apoyar la toma de decisiones sobre el empleo de equipos sensibles a este tipo de perturbación.In this work, the Monte Carlo simulation method (MC is applied to estimate the number of expected voltage dips in the nodes of an electric network. The estimations obtained through MC are compared with the results of another method of calculation, known as Failure Position Method (MPF. In the results, both the convergence of the algorithm with the long-term values of the MPF method and the complete distribution of frequencies for different events are shown. This represents valuable information to support the decision-making process for equipment that is sensitive to this type of perturbation.
Ng, C M
2013-10-01
The development of a population PK/PD model, an essential component for model-based drug development, is both time- and labor-intensive. A graphical-processing unit (GPU) computing technology has been proposed and used to accelerate many scientific computations. The objective of this study was to develop a hybrid GPU-CPU implementation of parallelized Monte Carlo parametric expectation maximization (MCPEM) estimation algorithm for population PK data analysis. A hybrid GPU-CPU implementation of the MCPEM algorithm (MCPEMGPU) and identical algorithm that is designed for the single CPU (MCPEMCPU) were developed using MATLAB in a single computer equipped with dual Xeon 6-Core E5690 CPU and a NVIDIA Tesla C2070 GPU parallel computing card that contained 448 stream processors. Two different PK models with rich/sparse sampling design schemes were used to simulate population data in assessing the performance of MCPEMCPU and MCPEMGPU. Results were analyzed by comparing the parameter estimation and model computation times. Speedup factor was used to assess the relative benefit of parallelized MCPEMGPU over MCPEMCPU in shortening model computation time. The MCPEMGPU consistently achieved shorter computation time than the MCPEMCPU and can offer more than 48-fold speedup using a single GPU card. The novel hybrid GPU-CPU implementation of parallelized MCPEM algorithm developed in this study holds a great promise in serving as the core for the next-generation of modeling software for population PK/PD analysis.
Hybrid Monte Carlo with Chaotic Mixing
Kadakia, Nirag
2016-01-01
We propose a hybrid Monte Carlo (HMC) technique applicable to high-dimensional multivariate normal distributions that effectively samples along chaotic trajectories. The method is predicated on the freedom of choice of the HMC momentum distribution, and due to its mixing properties, exhibits sample-to-sample autocorrelations that decay far faster than those in the traditional hybrid Monte Carlo algorithm. We test the methods on distributions of varying correlation structure, finding that the proposed technique produces superior covariance estimates, is less reliant on step-size tuning, and can even function with sparse or no momentum re-sampling. The method presented here is promising for more general distributions, such as those that arise in Bayesian learning of artificial neural networks and in the state and parameter estimation of dynamical systems.
Multilevel sequential Monte-Carlo samplers
Jasra, Ajay
2016-01-05
Multilevel Monte-Carlo methods provide a powerful computational technique for reducing the computational cost of estimating expectations for a given computational effort. They are particularly relevant for computational problems when approximate distributions are determined via a resolution parameter h, with h=0 giving the theoretical exact distribution (e.g. SDEs or inverse problems with PDEs). The method provides a benefit by coupling samples from successive resolutions, and estimating differences of successive expectations. We develop a methodology that brings Sequential Monte-Carlo (SMC) algorithms within the framework of the Multilevel idea, as SMC provides a natural set-up for coupling samples over different resolutions. We prove that the new algorithm indeed preserves the benefits of the multilevel principle, even if samples at all resolutions are now correlated.
Russo, S; Mariani, T T; Migliorini, R; Marcellusi, A; Mennini, F S
2015-09-16
The aim of the study is to estimate the pension costs incurred for patients with musculoskeletal disorders (MDs) and specifically with rheumatoid arthritis (RA) and ankylosing spondylitis (AS) in Italy between 2009 and 2012. We analyzed the database of the Italian National Social Security Institute (Istituto Nazionale Previdenza Sociale i.e. INPS) to estimate the total costs of three types of social security benefits granted to patients with MDs, RA and AS: disability benefits (for people with reduced working ability), disability pensions (for people who cannot qualify as workers) and incapacity pensions (for people without working ability). We developed a probabilistic model with a Monte Carlo simulation to estimate the total costs for each type of benefit associated with MDs, RA and AS. We also estimated the productivity loss resulting from RA in 2013. From 2009 to 2012 about 393 thousand treatments were paid for a total of approximately €2.7 billion. The annual number of treatments was on average 98 thousand and cost in total €674 million per year. In particular, the total pension burden was about €99 million for RA and €26 million for AS. The productivity loss for AR in 2013 was equal to €707,425,191 due to 9,174,221 working days lost. Our study is the fi rst to estimate the burden of social security pensions for MDs based on data of both approved claims and benefits paid by the national security system. From 2009 to 2012, in Italy, the highest indirect costs were associated with disability pensions (54% of the total indirect cost), followed by disability benefits (44.1% of cost) and incapacity pensions (1.8% of cost). In conclusion, MDs are chronic and highly debilitating diseases with a strong female predominance and very significant economic and social costs that are set to increase due to the aging of the population.
Directory of Open Access Journals (Sweden)
S. Russo
2015-09-01
Full Text Available The aim of the study is to estimate the pension costs incurred for patients with musculoskeletal disorders (MDs and specifi cally with rheumatoid arthritis (RA and ankylosing spondylitis (AS in Italy between 2009 and 2012. We analyzed the database of the Italian National Social Security Institute (Istituto Nazionale Previdenza Sociale i.e. INPS to estimate the total costs of three types of social security benefi ts granted to patients with MDs, RA and AS: disability benefi ts (for people with reduced working ability, disability pensions (for people who cannot qualify as workers and incapacity pensions (for people without working ability. We developed a probabilistic model with a Monte Carlo simulation to estimate the total costs for each type of benefi t associated with MDs, RA and AS. We also estimated the productivity loss resulting from RA in 2013. From 2009 to 2012 about 393 thousand treatments were paid for a total of approximately €2.7 billion. The annual number of treatments was on average 98 thousand and cost in total €674 million per year. In particular, the total pension burden was about €99 million for RA and €26 million for AS. The productivity loss for AR in 2013 was equal to €707,425,191 due to 9,174,221 working days lost. Our study is the fi rst to estimate the burden of social security pensions for MDs based on data of both approved claims and benefi ts paid by the national security system. From 2009 to 2012, in Italy, the highest indirect costs were associated with disability pensions (54% of the total indirect cost, followed by disability benefi ts (44.1% of cost and incapacity pensions (1.8% of cost. In conclusion, MDs are chronic and highly debilitating diseases with a strong female predominance and very signifi cant economic and social costs that are set to increase due to the aging of the population.
DEFF Research Database (Denmark)
Blasone, Roberta-Serena; Vrugt, Jasper A.; Madsen, Henrik
2008-01-01
estimate of the associated uncertainty. This uncertainty arises from incomplete process representation, uncertainty in initial conditions, input, output and parameter error. The generalized likelihood uncertainty estimation (GLUE) framework was one of the first attempts to represent prediction uncertainty...
Directory of Open Access Journals (Sweden)
Md Nabiul Islam Khan
Full Text Available In the Point-Centred Quarter Method (PCQM, the mean distance of the first nearest plants in each quadrant of a number of random sample points is converted to plant density. It is a quick method for plant density estimation. In recent publications the estimator equations of simple PCQM (PCQM1 and higher order ones (PCQM2 and PCQM3, which uses the distance of the second and third nearest plants, respectively show discrepancy. This study attempts to review PCQM estimators in order to find the most accurate equation form. We tested the accuracy of different PCQM equations using Monte Carlo Simulations in simulated (having 'random', 'aggregated' and 'regular' spatial patterns plant populations and empirical ones.PCQM requires at least 50 sample points to ensure a desired level of accuracy. PCQM with a corrected estimator is more accurate than with a previously published estimator. The published PCQM versions (PCQM1, PCQM2 and PCQM3 show significant differences in accuracy of density estimation, i.e. the higher order PCQM provides higher accuracy. However, the corrected PCQM versions show no significant differences among them as tested in various spatial patterns except in plant assemblages with a strong repulsion (plant competition. If N is number of sample points and R is distance, the corrected estimator of PCQM1 is 4(4N - 1/(π ∑ R2 but not 12N/(π ∑ R2, of PCQM2 is 4(8N - 1/(π ∑ R2 but not 28N/(π ∑ R2 and of PCQM3 is 4(12N - 1/(π ∑ R2 but not 44N/(π ∑ R2 as published.If the spatial pattern of a plant association is random, PCQM1 with a corrected equation estimator and over 50 sample points would be sufficient to provide accurate density estimation. PCQM using just the nearest tree in each quadrant is therefore sufficient, which facilitates sampling of trees, particularly in areas with just a few hundred trees per hectare. PCQM3 provides the best density estimations for all types of plant assemblages including the repulsion process
Matilainen, Kaarina; Mäntysaari, Esa A; Lidauer, Martin H; Strandén, Ismo; Thompson, Robin
2013-01-01
Estimation of variance components by Monte Carlo (MC) expectation maximization (EM) restricted maximum likelihood (REML) is computationally efficient for large data sets and complex linear mixed effects models. However, efficiency may be lost due to the need for a large number of iterations of the EM algorithm. To decrease the computing time we explored the use of faster converging Newton-type algorithms within MC REML implementations. The implemented algorithms were: MC Newton-Raphson (NR), where the information matrix was generated via sampling; MC average information(AI), where the information was computed as an average of observed and expected information; and MC Broyden's method, where the zero of the gradient was searched using a quasi-Newton-type algorithm. Performance of these algorithms was evaluated using simulated data. The final estimates were in good agreement with corresponding analytical ones. MC NR REML and MC AI REML enhanced convergence compared to MC EM REML and gave standard errors for the estimates as a by-product. MC NR REML required a larger number of MC samples, while each MC AI REML iteration demanded extra solving of mixed model equations by the number of parameters to be estimated. MC Broyden's method required the largest number of MC samples with our small data and did not give standard errors for the parameters directly. We studied the performance of three different convergence criteria for the MC AI REML algorithm. Our results indicate the importance of defining a suitable convergence criterion and critical value in order to obtain an efficient Newton-type method utilizing a MC algorithm. Overall, use of a MC algorithm with Newton-type methods proved feasible and the results encourage testing of these methods with different kinds of large-scale problem settings.
Saccomandi, Paola; Larocca, Enza Stefania; Rendina, Veneranda; Schena, Emiliano; D'Ambrosio, Roberto; Crescenzi, Anna; Di Matteo, Francesco Maria; Silvestri, Sergio
2016-08-01
The investigation of laser-tissue interaction is crucial for diagnostics and therapeutics. In particular, the estimation of tissue optical properties allows developing predictive models for defining organ-specific treatment planning tool. With regard to laser ablation (LA), optical properties are among the main responsible for the therapy efficacy, as they globally affect the heating process of the tissue, due to its capability to absorb and scatter laser energy. The recent introduction of LA for pancreatic tumor treatment in clinical studies has fostered the need to assess the laser-pancreas interaction and hence to find its optical properties in the wavelength of interest. This work aims at estimating optical properties (i.e., absorption, μ a , scattering, μ s , anisotropy, g, coefficients) of neuroendocrine pancreas tumor at 1064 nm. Experiments were performed using two popular sample storage methods; the optical properties of frozen and paraffin-embedded neuroendocrine tumor of the pancreas are estimated by employing a double-integrating-sphere system and inverse Monte Carlo algorithm. Results show that paraffin-embedded tissue is characterized by absorption and scattering coefficients significantly higher than frozen samples (μ a of 56 cm(-1) vs 0.9 cm(-1), μ s of 539 cm(-1) vs 130 cm(-1), respectively). Simulations show that such different optical features strongly influence the pancreas temperature distribution during LA. This result may affect the prediction of therapeutic outcome. Therefore, the choice of the appropriate preparation technique of samples for optical property estimation is crucial for the performances of the mathematical models which predict LA thermal outcome on the tissue and lead the selection of optimal LA settings.
Directory of Open Access Journals (Sweden)
Kaarina Matilainen
Full Text Available Estimation of variance components by Monte Carlo (MC expectation maximization (EM restricted maximum likelihood (REML is computationally efficient for large data sets and complex linear mixed effects models. However, efficiency may be lost due to the need for a large number of iterations of the EM algorithm. To decrease the computing time we explored the use of faster converging Newton-type algorithms within MC REML implementations. The implemented algorithms were: MC Newton-Raphson (NR, where the information matrix was generated via sampling; MC average information(AI, where the information was computed as an average of observed and expected information; and MC Broyden's method, where the zero of the gradient was searched using a quasi-Newton-type algorithm. Performance of these algorithms was evaluated using simulated data. The final estimates were in good agreement with corresponding analytical ones. MC NR REML and MC AI REML enhanced convergence compared to MC EM REML and gave standard errors for the estimates as a by-product. MC NR REML required a larger number of MC samples, while each MC AI REML iteration demanded extra solving of mixed model equations by the number of parameters to be estimated. MC Broyden's method required the largest number of MC samples with our small data and did not give standard errors for the parameters directly. We studied the performance of three different convergence criteria for the MC AI REML algorithm. Our results indicate the importance of defining a suitable convergence criterion and critical value in order to obtain an efficient Newton-type method utilizing a MC algorithm. Overall, use of a MC algorithm with Newton-type methods proved feasible and the results encourage testing of these methods with different kinds of large-scale problem settings.
Monte Carlo approach to turbulence
Energy Technology Data Exchange (ETDEWEB)
Dueben, P.; Homeier, D.; Muenster, G. [Muenster Univ. (Germany). Inst. fuer Theoretische Physik; Jansen, K. [DESY, Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Mesterhazy, D. [Humboldt Univ., Berlin (Germany). Inst. fuer Physik
2009-11-15
The behavior of the one-dimensional random-force-driven Burgers equation is investigated in the path integral formalism on a discrete space-time lattice. We show that by means of Monte Carlo methods one may evaluate observables, such as structure functions, as ensemble averages over different field realizations. The regularization of shock solutions to the zero-viscosity limit (Hopf-equation) eventually leads to constraints on lattice parameters required for the stability of the simulations. Insight into the formation of localized structures (shocks) and their dynamics is obtained. (orig.)
Zhang, Ying; Feng, Yuanming; Wang, Wei; Yang, Chengwen; Wang, Ping
2017-01-01
A novel and versatile “bottom-up” approach is developed to estimate the radiobiological effect of clinic radiotherapy. The model consists of multi-scale Monte Carlo simulations from organ to cell levels. At cellular level, accumulated damages are computed using a spectrum-based accumulation algorithm and predefined cellular damage database. The damage repair mechanism is modeled by an expanded reaction-rate two-lesion kinetic model, which were calibrated through replicating a radiobiological experiment. Multi-scale modeling is then performed on a lung cancer patient under conventional fractionated irradiation. The cell killing effects of two representative voxels (isocenter and peripheral voxel of the tumor) are computed and compared. At microscopic level, the nucleus dose and damage yields vary among all nucleuses within the voxels. Slightly larger percentage of cDSB yield is observed for the peripheral voxel (55.0%) compared to the isocenter one (52.5%). For isocenter voxel, survival fraction increase monotonically at reduced oxygen environment. Under an extreme anoxic condition (0.001%), survival fraction is calculated to be 80% and the hypoxia reduction factor reaches a maximum value of 2.24. In conclusion, with biological-related variations, the proposed multi-scale approach is more versatile than the existing approaches for evaluating personalized radiobiological effects in radiotherapy. PMID:28322329
Zhang, Ying; Feng, Yuanming; Wang, Wei; Yang, Chengwen; Wang, Ping
2017-03-01
A novel and versatile “bottom-up” approach is developed to estimate the radiobiological effect of clinic radiotherapy. The model consists of multi-scale Monte Carlo simulations from organ to cell levels. At cellular level, accumulated damages are computed using a spectrum-based accumulation algorithm and predefined cellular damage database. The damage repair mechanism is modeled by an expanded reaction-rate two-lesion kinetic model, which were calibrated through replicating a radiobiological experiment. Multi-scale modeling is then performed on a lung cancer patient under conventional fractionated irradiation. The cell killing effects of two representative voxels (isocenter and peripheral voxel of the tumor) are computed and compared. At microscopic level, the nucleus dose and damage yields vary among all nucleuses within the voxels. Slightly larger percentage of cDSB yield is observed for the peripheral voxel (55.0%) compared to the isocenter one (52.5%). For isocenter voxel, survival fraction increase monotonically at reduced oxygen environment. Under an extreme anoxic condition (0.001%), survival fraction is calculated to be 80% and the hypoxia reduction factor reaches a maximum value of 2.24. In conclusion, with biological-related variations, the proposed multi-scale approach is more versatile than the existing approaches for evaluating personalized radiobiological effects in radiotherapy.
Directory of Open Access Journals (Sweden)
Jalid Abdelilah
2016-01-01
Full Text Available In engineering industry, control of manufactured parts is usually done on a coordinate measuring machine (CMM, a sensor mounted at the end of the machine probes a set of points on the surface to be inspected. Data processing is performed subsequently using software, and the result of this measurement process either validates or not the conformity of the part. Measurement uncertainty is a crucial parameter for making the right decisions, and not taking into account this parameter can, therefore, sometimes lead to aberrant decisions. The determination of the uncertainty measurement on CMM is a complex task for the variety of influencing factors. Through this study, we aim to check if the uncertainty propagation model developed according to the guide to the expression of uncertainty in measurement (GUM approach is valid, we present here a comparison of the GUM and Monte Carlo methods. This comparison is made to estimate a flatness deviation of a surface belonging to an industrial part and the uncertainty associated to the measurement result.
Energy Technology Data Exchange (ETDEWEB)
Kanjilal, Oindrila, E-mail: oindrila@civil.iisc.ernet.in; Manohar, C.S., E-mail: manohar@civil.iisc.ernet.in
2017-07-15
The study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems. Attention is focused on importance sampling strategies based on the application of Girsanov's transformation method. Controls which minimize the distance function, as in the first order reliability method (FORM), are shown to minimize a bound on the sampling variance of the estimator for the probability of failure. Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two-point nonlinear boundary value problem, and, the second explores the application of the Volterra series in characterizing the controls. The relative merits of these schemes, vis-à-vis the method based on ideas from the FORM, are discussed. Illustrative examples, involving archetypal single degree of freedom (dof) nonlinear oscillators, and a multi-degree of freedom nonlinear dynamical system, are presented. The credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct Monte Carlo simulations. - Highlights: • The distance minimizing control forces minimize a bound on the sampling variance. • Establishing Girsanov controls via solution of a two-point boundary value problem. • Girsanov controls via Volterra's series representation for the transfer functions.
Directory of Open Access Journals (Sweden)
J. A. Vrugt
2011-04-01
Full Text Available Formal and informal Bayesian approaches are increasingly being used to treat forcing, model structural, parameter and calibration data uncertainty, and summarize hydrologic prediction uncertainty. This requires posterior sampling methods that approximate the (evolving posterior distribution. We recently introduced the DiffeRential Evolution Adaptive Metropolis (DREAM algorithm, an adaptive Markov Chain Monte Carlo (MCMC method that is especially designed to solve complex, high-dimensional and multimodal posterior probability density functions. The method runs multiple chains in parallel, and maintains detailed balance and ergodicity. Here, I present the latest algorithmic developments, and introduce a discrete sampling variant of DREAM that samples the parameter space at fixed points. The development of this new code, DREAM(D, has been inspired by the existing class of integer optimization problems, and emerging class of experimental design problems. Such non-continuous parameter estimation problems are of considerable theoretical and practical interest. The theory developed herein is applicable to DREAM(ZS (Vrugt et al., 2011 and MT-DREAM(ZS (Laloy and Vrugt, 2011 as well. Two case studies involving a sudoku puzzle and rainfall – runoff model calibration problem are used to illustrate DREAM(D.
Nortey, Ezekiel N N; Ansah-Narh, Theophilus; Asah-Asante, Richard; Minkah, Richard
2015-01-01
Although, there exists numerous literature on the procedure for forecasting or predicting election results, in Ghana only opinion poll strategies have been used. To fill this gap, the paper develops Markov chain models for forecasting the 2016 presidential election results at the Regional, Zonal (i.e. Savannah, Coastal and Forest) and the National levels using past presidential election results of Ghana. The methodology develops a model for prediction of the 2016 presidential election results in Ghana using the Markov chains Monte Carlo (MCMC) methodology with bootstrap estimates. The results were that the ruling NDC may marginally win the 2016 Presidential Elections but would not obtain the more than 50 % votes to be declared an outright winner. This means that there is going to be a run-off election between the two giant political parties: the ruling NDC and the major opposition party, NPP. The prediction for the 2016 Presidential run-off election between the NDC and the NPP was rather in favour of the major opposition party, the NPP with a little over the 50 % votes obtained.
Directory of Open Access Journals (Sweden)
Lecouey Jean-Luc
2015-01-01
Full Text Available The GUINEVERE project was launched in 2006, within the 6th Euratom Framework Program IP-EUROTRANS, in order to study the feasibility of transmutation in Accelerator Driven subcritical Systems (ADS. This zero-power facility hosted at the SCK·CEN site in Mol (Belgium couples the fast subcritical lead reactor VENUS-F with an external neutron source provided by interaction of deuterons delivered by the GENEPI-3C accelerator and a tritiated target located at the reactor core center. In order to test on-line subcriticality monitoring techniques, the reactivity of all the VENUS-F configurations used must be known beforehand to serve as benchmark values. That is why the Modified Source Multiplication Method (MSM is under consideration to estimate the reactivity worth of the control rods when the reactor is largely subcritical as well as near-critical. The MSM method appears to be a technique well adapted to measure control rod worth over a large range of subcriticality levels. The MSM factors which are required to account for spatial effects in the reactor can be successfully calculated using a Monte Carlo neutron transport code.
Markov chain Monte Carlo approach to parameter estimation in the FitzHugh-Nagumo model.
Jensen, Anders Chr; Ditlevsen, Susanne; Kessler, Mathieu; Papaspiliopoulos, Omiros
2012-10-01
Excitability is observed in a variety of natural systems, such as neuronal dynamics, cardiovascular tissues, or climate dynamics. The stochastic FitzHugh-Nagumo model is a prominent example representing an excitable system. To validate the practical use of a model, the first step is to estimate model parameters from experimental data. This is not an easy task because of the inherent nonlinearity necessary to produce the excitable dynamics, and because the two coordinates of the model are moving on different time scales. Here we propose a Bayesian framework for parameter estimation, which can handle multidimensional nonlinear diffusions with large time scale separation. The estimation method is illustrated on simulated data.
Monte Carlo techniques in radiation therapy
Verhaegen, Frank
2013-01-01
Modern cancer treatment relies on Monte Carlo simulations to help radiotherapists and clinical physicists better understand and compute radiation dose from imaging devices as well as exploit four-dimensional imaging data. With Monte Carlo-based treatment planning tools now available from commercial vendors, a complete transition to Monte Carlo-based dose calculation methods in radiotherapy could likely take place in the next decade. Monte Carlo Techniques in Radiation Therapy explores the use of Monte Carlo methods for modeling various features of internal and external radiation sources, including light ion beams. The book-the first of its kind-addresses applications of the Monte Carlo particle transport simulation technique in radiation therapy, mainly focusing on external beam radiotherapy and brachytherapy. It presents the mathematical and technical aspects of the methods in particle transport simulations. The book also discusses the modeling of medical linacs and other irradiation devices; issues specific...
Absorbed dose estimations of 131I for critical organs using the GEANT4 Monte Carlo simulation code
Institute of Scientific and Technical Information of China (English)
Ziaur Rahman; Shakeel ur Rehman; Waheed Arshed; Nasir M Mirza; Abdul Rashid; Jahan Zeb
2012-01-01
The aim of this study is to compare the absorbed doses of critical organs of 131I using the MIRD (Medical Internal Radiation Dose) with the corresponding predictions made by GEANT4 simulations.S-values (mean absorbed dose rate per unit activity) and energy deposition per decay for critical organs of 131I for various ages,using standard cylindrical phantom comprising water and ICRP soft-tissue material,have also been estimated.In this study the effect of volume reduction of thyroid,during radiation therapy,on the calculation of absorbed dose is also being estimated using GEANT4.Photon specific energy deposition in the other organs of the neck,due to 131I decay in the thyroid organ,has also been estimated.The maximum relative difference of MIRD with the GEANT4 simulated results is 5.64％ for an adult's critical organs of 131I.Excellent agreement was found between the results of water and ICRP soft tissue using the cylindrical model.S-values are tabulated for critical organs of 131I,using 1,5,10,15 and 18 years (adults) individuals.S-values for a cylindrical thyroid of different sizes,having 3.07％ relative differences of GEANT4 with Siegel & Stabin results.Comparison of the experimentally measured values at 0.5 and 1 m away from neck of the ionization chamber with GEANT4 based Monte Carlo simulations results show good agreement.This study shows that GEANT4 code is an important tool for the internal dosimetry calculations.
Charon, Julien; Blanco, Stéphane; Cornet, Jean-François; Dauchet, Jérémi; El Hafi, Mouna; Fournier, Richard; Abboud, Mira Kaissar; Weitz, Sebastian
2016-03-01
In the present paper, Schiff's approximation is applied to the study of light scattering by large and optically-soft axisymmetric particles, with special attention to cylindrical and spheroidal photosynthetic micro-organisms. This approximation is similar to the anomalous diffraction approximation but includes a description of phase functions. Resulting formulations for the radiative properties are multidimensional integrals, the numerical resolution of which requires close attention. It is here argued that strong benefits can be expected from a statistical resolution by the Monte Carlo method. But designing such efficient Monte Carlo algorithms requires the development of non-standard algorithmic tricks using careful mathematical analysis of the integral formulations: the codes that we develop (and make available) include an original treatment of the nonlinearity in the differential scattering cross-section (squared modulus of the scattering amplitude) thanks to a double sampling procedure. This approach makes it possible to take advantage of recent methodological advances in the field of Monte Carlo methods, illustrated here by the estimation of sensitivities to parameters. Comparison with reference solutions provided by the T-Matrix method is presented whenever possible. Required geometric calculations are closely similar to those used in standard Monte Carlo codes for geometric optics by the computer-graphics community, i.e. calculation of intersections between rays and surfaces, which opens interesting perspectives for the treatment of particles with complex shapes.
Approaching Chemical Accuracy with Quantum Monte Carlo
Petruzielo, Frank R.; Toulouse, Julien; Umrigar, C. J.
2012-01-01
International audience; A quantum Monte Carlo study of the atomization energies for the G2 set of molecules is presented. Basis size dependence of diffusion Monte Carlo atomization energies is studied with a single determinant Slater-Jastrow trial wavefunction formed from Hartree-Fock orbitals. With the largest basis set, the mean absolute deviation from experimental atomization energies for the G2 set is 3.0 kcal/mol. Optimizing the orbitals within variational Monte Carlo improves the agreem...
Mean field simulation for Monte Carlo integration
Del Moral, Pierre
2013-01-01
In the last three decades, there has been a dramatic increase in the use of interacting particle methods as a powerful tool in real-world applications of Monte Carlo simulation in computational physics, population biology, computer sciences, and statistical machine learning. Ideally suited to parallel and distributed computation, these advanced particle algorithms include nonlinear interacting jump diffusions; quantum, diffusion, and resampled Monte Carlo methods; Feynman-Kac particle models; genetic and evolutionary algorithms; sequential Monte Carlo methods; adaptive and interacting Marko
Estimation of stochastic frontier models with fixed-effects through Monte Carlo Maximum Likelihood
Emvalomatis, G.; Stefanou, S.E.; Oude Lansink, A.G.J.M.
2011-01-01
Estimation of nonlinear fixed-effects models is plagued by the incidental parameters problem. This paper proposes a procedure for choosing appropriate densities for integrating the incidental parameters from the likelihood function in a general context. The densities are based on priors that are
Markov chain Monte Carlo approach to parameter estimation in the FitzHugh-Nagumo model
DEFF Research Database (Denmark)
Jensen, Anders Christian; Ditlevsen, Susanne; Kessler, Mathieu
2012-01-01
Excitability is observed in a variety of natural systems, such as neuronal dynamics, cardiovascular tissues, or climate dynamics. The stochastic FitzHugh-Nagumo model is a prominent example representing an excitable system. To validate the practical use of a model, the first step is to estimate m...
Estimation of stochastic frontier models with fixed-effects through Monte Carlo Maximum Likelihood
Emvalomatis, G.; Stefanou, S.E.; Oude Lansink, A.G.J.M.
2011-01-01
Estimation of nonlinear fixed-effects models is plagued by the incidental parameters problem. This paper proposes a procedure for choosing appropriate densities for integrating the incidental parameters from the likelihood function in a general context. The densities are based on priors that are upd
Monte Carlo Treatment Planning for Advanced Radiotherapy
DEFF Research Database (Denmark)
Cronholm, Rickard
and validation of a Monte Carlo model of a medical linear accelerator (i), converting a CT scan of a patient to a Monte Carlo compliant phantom (ii) and translating the treatment plan parameters (including beam energy, angles of incidence, collimator settings etc) to a Monte Carlo input file (iii). A protocol...... previous algorithms since it uses delineations of structures in order to include and/or exclude certain media in various anatomical regions. This method has the potential to reduce anatomically irrelevant media assignment. In house MATLAB scripts translating the treatment plan parameters to Monte Carlo...
1-D EQUILIBRIUM DISCRETE DIFFUSION MONTE CARLO
Energy Technology Data Exchange (ETDEWEB)
T. EVANS; ET AL
2000-08-01
We present a new hybrid Monte Carlo method for 1-D equilibrium diffusion problems in which the radiation field coexists with matter in local thermodynamic equilibrium. This method, the Equilibrium Discrete Diffusion Monte Carlo (EqDDMC) method, combines Monte Carlo particles with spatially discrete diffusion solutions. We verify the EqDDMC method with computational results from three slab problems. The EqDDMC method represents an incremental step toward applying this hybrid methodology to non-equilibrium diffusion, where it could be simultaneously coupled to Monte Carlo transport.
Fast Estimator of jacobians in Monte Carlo Integration on Lefschetz Thimbles
Alexandru, Andrei; Bedaque, Paulo F; Ridgway, Gregory W; Warrington, Neill C
2016-01-01
A solution to the sign problem is the so-called "Lefschetz thimble approach" where the domain of integration for field variables in the path integral is deformed from the real axis to a sub-manifold in the complex space. For properly chosen sub-manifolds ("thimbles") the sign problem disappears or is drastically alleviated. The parametrization of the thimble by real coordinates require the calculation of a jacobian with a computational cost of order O(V^3), where V is proportional to the spacetime volume. In this note we propose two estimators for this jacobian with a computational cost of order O(V). We discuss analytically the regimes where we expect the estimator to work and show numerical examples in two different models.
Probabilistic parameter estimation of activated sludge processes using Markov Chain Monte Carlo.
Sharifi, Soroosh; Murthy, Sudhir; Takács, Imre; Massoudieh, Arash
2014-03-01
One of the most important challenges in making activated sludge models (ASMs) applicable to design problems is identifying the values of its many stoichiometric and kinetic parameters. When wastewater characteristics data from full-scale biological treatment systems are used for parameter estimation, several sources of uncertainty, including uncertainty in measured data, external forcing (e.g. influent characteristics), and model structural errors influence the value of the estimated parameters. This paper presents a Bayesian hierarchical modeling framework for the probabilistic estimation of activated sludge process parameters. The method provides the joint probability density functions (JPDFs) of stoichiometric and kinetic parameters by updating prior information regarding the parameters obtained from expert knowledge and literature. The method also provides the posterior correlations between the parameters, as well as a measure of sensitivity of the different constituents with respect to the parameters. This information can be used to design experiments to provide higher information content regarding certain parameters. The method is illustrated using the ASM1 model to describe synthetically generated data from a hypothetical biological treatment system. The results indicate that data from full-scale systems can narrow down the ranges of some parameters substantially whereas the amount of information they provide regarding other parameters is small, due to either large correlations between some of the parameters or a lack of sensitivity with respect to the parameters.
Reducing uncertainty of Monte Carlo estimated fatigue damage in offshore wind turbines using FORM
DEFF Research Database (Denmark)
H. Horn, Jan-Tore; Jensen, Jørgen Juncher
2016-01-01
on the sea-state dependent response characteristics, and the effect of a bi-linear S-N curve isdiscussed. Finally, analyses are performed on several environmental conditions to investigate the long-term applicability of this multistep method. Wave loads are calculated using state-of-the-art theory, while...... estimations may be improved for the same computational efforts.The method is applied to a bottom-fixed, monopilesupported large offshore wind turbine, which is a nonlinear and dynamically sensitive system. Different curve fitting techniques to the fatigue damage distribution have been used depending...
Jadoon, K. Z.; Altaf, M. U.; McCabe, M. F.; Hoteit, I.; Moghadas, D.
2014-12-01
In arid and semi-arid regions, soil salinity has a major impact on agro-ecosystems, agricultural productivity, environment and sustainability. High levels of soil salinity adversely affect plant growth and productivity, soil and water quality, and may eventually result in soil erosion and land degradation. Being essentially a hazard, it's important to monitor and map soil salinity at an early stage to effectively use soil resources and maintain soil salinity level below the salt tolerance of crops. In this respect, low frequency electromagnetic induction (EMI) systems can be used as a noninvasive method to map the distribution of soil salinity at the field scale and at a high spatial resolution. In this contribution, an EMI system (the CMD Mini-Explorer) is used to estimate soil salinity using a Bayesian approach implemented via a Markov chain Monte Carlo (MCMC) sampling for inversion of multi-configuration EMI measurements. In-situ and EMI measurements were conducted across a farm where Acacia trees are irrigated with brackish water using a drip irrigation system. The electromagnetic forward model is based on the full solution of Maxwell's equation, and the subsurface is considered as a three-layer problem. In total, five parameters (electrical conductivity of three layers and thickness of top two layers) were inverted and modeled electrical conductivities were converted into the universal standard of soil salinity measurement (i.e. using the method of electrical conductivity of a saturated soil paste extract). Simulation results demonstrate that the proposed scheme successfully recovers soil salinity and reduces the uncertainties in the prior estimate. Analysis of the resulting posterior distribution of parameters indicates that electrical conductivity of the top two layers and the thickness of the first layer are well constrained by the EMI measurements. The proposed approach allows for quantitative mapping and monitoring of the spatial electrical conductivity
Institute of Scientific and Technical Information of China (English)
ZHOU Jie; TANG Aiping; FENG Hailin
2016-01-01
The statistical inference for generalized mixed-effects state space models (MESSM) are investigated when the random effects are unknown.Two filtering algorithms are designed both of which are based on mixture Kalman filter.These algorithms are particularly useful when the longitudinal measurements are sparse.The authors also propose a globally convergent algorithm for parameter estimation of MESSM which can be used to locate the initial value of parameters for local while more efficient algorithms.Simulation examples are carried out which validate the efficacy of the proposed approaches.A data set from the clinical trial is investigated and a smaller mean square error is achieved compared to the existing results in literatures.
Deshayes, Yannick; Verdier, Frederic; Bechou, Laurent; Tregon, Bernard; Danto, Yves; Laffitte, Dominique; Goudard, Jean Luc
2004-09-01
High performance and high reliability are two of the most important goals driving the penetration of optical transmission into telecommunication systems ranging from 880 nm to 1550 nm. Lifetime prediction defined as the time at which a parameter reaches its maximum acceptable shirt still stays the main result in terms of reliability estimation for a technology. For optoelectronic emissive components, selection tests and life testing are specifically used for reliability evaluation according to Telcordia GR-468 CORE requirements. This approach is based on extrapolation of degradation laws, based on physics of failure and electrical or optical parameters, allowing both strong test time reduction and long-term reliability prediction. Unfortunately, in the case of mature technology, there is a growing complexity to calculate average lifetime and failure rates (FITs) using ageing tests in particular due to extremely low failure rates. For present laser diode technologies, time to failure tend to be 106 hours aged under typical conditions (Popt=10 mW and T=80°C). These ageing tests must be performed on more than 100 components aged during 10000 hours mixing different temperatures and drive current conditions conducting to acceleration factors above 300-400. These conditions are high-cost, time consuming and cannot give a complete distribution of times to failure. A new approach consists in use statistic computations to extrapolate lifetime distribution and failure rates in operating conditions from physical parameters of experimental degradation laws. In this paper, Distributed Feedback single mode laser diodes (DFB-LD) used for 1550 nm telecommunication network working at 2.5 Gbit/s transfer rate are studied. Electrical and optical parameters have been measured before and after ageing tests, performed at constant current, according to Telcordia GR-468 requirements. Cumulative failure rates and lifetime distributions are computed using statistic calculations and
DEFF Research Database (Denmark)
Jensen, Jørgen Juncher
2015-01-01
For non-linear systems the estimation of fatigue damage under stochastic loadings can be rather time-consuming. Usually Monte Carlo simulation (MCS) is applied, but the coefficient-of-variation (COV) can be large if only a small set of simulations can be done due to otherwise excessive CPU time. ...... the COV. For a specific example dealing with stresses in a tendon in a tension leg platform the COV is thereby reduced by a factor of three....
Monte Carlo Simulation Program from the World Petroleum Assessment 2000, DDS-60 (Emc2.xls)
U.S. Geological Survey, Department of the Interior — Monte Carlo programs described in chapter MC, Monte Carlo Simulation Method. Emc2.xls was the program used to calculate the estimates of undiscovered resources for...
Mont Carlo Simulation Program from the World Petroleum Assessment 2000, DDS-60 (emcee.xls).xml
U.S. Geological Survey, Department of the Interior — Monte Carlo programs described in chapter MC, Monte Carlo Simulation Method. Emc2.xls was the program used to calculate the estimates of undiscovered resources for...
Monte Carlo Simulation Program from the World Petroleum Assessment 2000, DDS-60 (Emc2.xls).
U.S. Geological Survey, Department of the Interior — Monte Carlo programs described in chapter MC, Monte Carlo Simulation Method. Emc2.xls was the program used to calculate the estimates of undiscovered resources for...
Mont Carlo Simulation Program from the World Petroleum Assessment 2000, DDS-60 (emcee.xls)
U.S. Geological Survey, Department of the Interior — Monte Carlo programs described in chapter MC, Monte Carlo Simulation Method. Emc2.xls was the program used to calculate the estimates of undiscovered resources for...
Wang, Wenjing; Qiu, Rui; Ren, Li; Liu, Huan; Wu, Zhen; Li, Chunyan; Niu, Yantao; Li, Junli
2017-06-01
At present, the Chinese specification for testing of quality control in x-ray mammography is based on a simple breast model, and does not consider the glandular tissue distribution in the breast. In order to more precisely estimate the mean glandular dose (MGD) in mammography for Chinese women, a three-dimensional (3D) detailed breast model based on realistic structures in the breast and Chinese female breast parameters was built and applied in this study. To characterize the Chinese female breast, Chinese female breast parameters including breast size, compressed breast thickness (CBT), and glandular content were investigated in this study. A mathematical model with the detailed breast structures was constructed based on the Chinese female breast parameters. The mathematical model was then converted to a voxel model with voxels. The voxel model was compressed in craniocaudal (CC) view to obtain a deformation model. The compressed breast model was combined with the Chinese reference adult female whole-body voxel phantom (CRAF) to study the effects of backscatter from the female body. Monte Carlo simulations of the glandular dose in mammography were performed with Geant 4. The glandular tissue dose conversion coefficients for breasts with different glandular contents (5%, 25%, 50%, 75%, and 100% glandularity) and CBTs (3 cm, 4 cm, 5 cm, and 6 cm) were calculated, respectively, at various x-ray tube voltages (25 kV, 28 kV, 30 kV, 32 kV, and 35 kV) for various target/filter combinations (Mo/Mo, Mo/Rh, Rh/Rh, and W/Rh). A series of glandular tissue dose conversion coefficients for dose estimation in mammography were calculated. The conversion coefficients calculated in this study were compared with those estimated with the simple breast model. A discrepancy of 5.4-38.0% was observed. This was consistent with the results obtained from the realistic breast models in the literature. A 3D detailed breast model with realistic structures in the breast was constructed
Sargeant, Glen A.; Sovada, Marsha A.; Slivinski, Christiane C.; Johnson, Douglas H.
2005-01-01
Accurate maps of species distributions are essential tools for wildlife research and conservation. Unfortunately, biologists often are forced to rely on maps derived from observed occurrences recorded opportunistically during observation periods of variable length. Spurious inferences are likely to result because such maps are profoundly affected by the duration and intensity of observation and by methods used to delineate distributions, especially when detection is uncertain. We conducted a systematic survey of swift fox (Vulpes velox) distribution in western Kansas, USA, and used Markov chain Monte Carlo (MCMC) image restoration to rectify these problems. During 1997–1999, we searched 355 townships (ca. 93 km) 1–3 times each for an average cost of $7,315 per year and achieved a detection rate (probability of detecting swift foxes, if present, during a single search) of = 0.69 (95% Bayesian confidence interval [BCI] = [0.60, 0.77]). Our analysis produced an estimate of the underlying distribution, rather than a map of observed occurrences, that reflected the uncertainty associated with estimates of model parameters. To evaluate our results, we analyzed simulated data with similar properties. Results of our simulations suggest negligible bias and good precision when probabilities of detection on ≥1 survey occasions (cumulative probabilities of detection) exceed 0.65. Although the use of MCMC image restoration has been limited by theoretical and computational complexities, alternatives do not possess the same advantages. Image models accommodate uncertain detection, do not require spatially independent data or a census of map units, and can be used to estimate species distributions directly from observations without relying on habitat covariates or parameters that must be estimated subjectively. These features facilitate economical surveys of large regions, the detection of temporal trends in distribution, and assessments of landscape-level relations between
Langevin Monte Carlo filtering for target tracking
Iglesias Garcia, Fernando; Bocquel, Melanie; Driessen, Hans
2015-01-01
This paper introduces the Langevin Monte Carlo Filter (LMCF), a particle filter with a Markov chain Monte Carlo algorithm which draws proposals by simulating Hamiltonian dynamics. This approach is well suited to non-linear filtering problems in high dimensional state spaces where the bootstrap filte
An introduction to Monte Carlo methods
Walter, J. -C.; Barkema, G. T.
2015-01-01
Monte Carlo simulations are methods for simulating statistical systems. The aim is to generate a representative ensemble of configurations to access thermodynamical quantities without the need to solve the system analytically or to perform an exact enumeration. The main principles of Monte Carlo sim
An introduction to Monte Carlo methods
Walter, J. -C.; Barkema, G. T.
2015-01-01
Monte Carlo simulations are methods for simulating statistical systems. The aim is to generate a representative ensemble of configurations to access thermodynamical quantities without the need to solve the system analytically or to perform an exact enumeration. The main principles of Monte Carlo sim
Challenges of Monte Carlo Transport
Energy Technology Data Exchange (ETDEWEB)
Long, Alex Roberts [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-06-10
These are slides from a presentation for Parallel Summer School at Los Alamos National Laboratory. Solving discretized partial differential equations (PDEs) of interest can require a large number of computations. We can identify concurrency to allow parallel solution of discrete PDEs. Simulated particles histories can be used to solve the Boltzmann transport equation. Particle histories are independent in neutral particle transport, making them amenable to parallel computation. Physical parameters and method type determine the data dependencies of particle histories. Data requirements shape parallel algorithms for Monte Carlo. Then, Parallel Computational Physics and Parallel Monte Carlo are discussed and, finally, the results are given. The mesh passing method greatly simplifies the IMC implementation and allows simple load-balancing. Using MPI windows and passive, one-sided RMA further simplifies the implementation by removing target synchronization. The author is very interested in implementations of PGAS that may allow further optimization for one-sided, read-only memory access (e.g. Open SHMEM). The MPICH_RMA_OVER_DMAPP option and library is required to make one-sided messaging scale on Trinitite - Moonlight scales poorly. Interconnect specific libraries or functions are likely necessary to ensure performance. BRANSON has been used to directly compare the current standard method to a proposed method on idealized problems. The mesh passing algorithm performs well on problems that are designed to show the scalability of the particle passing method. BRANSON can now run load-imbalanced, dynamic problems. Potential avenues of improvement in the mesh passing algorithm will be implemented and explored. A suite of test problems that stress DD methods will elucidate a possible path forward for production codes.
The MC21 Monte Carlo Transport Code
Energy Technology Data Exchange (ETDEWEB)
Sutton TM, Donovan TJ, Trumbull TH, Dobreff PS, Caro E, Griesheimer DP, Tyburski LJ, Carpenter DC, Joo H
2007-01-09
MC21 is a new Monte Carlo neutron and photon transport code currently under joint development at the Knolls Atomic Power Laboratory and the Bettis Atomic Power Laboratory. MC21 is the Monte Carlo transport kernel of the broader Common Monte Carlo Design Tool (CMCDT), which is also currently under development. The vision for CMCDT is to provide an automated, computer-aided modeling and post-processing environment integrated with a Monte Carlo solver that is optimized for reactor analysis. CMCDT represents a strategy to push the Monte Carlo method beyond its traditional role as a benchmarking tool or ''tool of last resort'' and into a dominant design role. This paper describes various aspects of the code, including the neutron physics and nuclear data treatments, the geometry representation, and the tally and depletion capabilities.
A note on simultaneous Monte Carlo tests
DEFF Research Database (Denmark)
Hahn, Ute
In this short note, Monte Carlo tests of goodness of fit for data of the form X(t), t ∈ I are considered, that reject the null hypothesis if X(t) leaves an acceptance region bounded by an upper and lower curve for some t in I. A construction of the acceptance region is proposed that complies to a...... to a given target level of rejection, and yields exact p-values. The construction is based on pointwise quantiles, estimated from simulated realizations of X(t) under the null hypothesis....
Spike Inference from Calcium Imaging using Sequential Monte Carlo Methods
NeuroData; Paninski, L
2015-01-01
Vogelstein JT, Paninski L. Spike Inference from Calcium Imaging using Sequential Monte Carlo Methods. Statistical and Applied Mathematical Sciences Institute (SAMSI) Program on Sequential Monte Carlo Methods, 2008
Monte Carlo methods for light propagation in biological tissues
Vinckenbosch, Laura; Lacaux, Céline; Tindel, Samy; Thomassin, Magalie; Obara, Tiphaine
2016-01-01
Light propagation in turbid media is driven by the equation of radiative transfer. We give a formal probabilistic representation of its solution in the framework of biological tissues and we implement algorithms based on Monte Carlo methods in order to estimate the quantity of light that is received by a homogeneous tissue when emitted by an optic fiber. A variance reduction method is studied and implemented, as well as a Markov chain Monte Carlo method based on the Metropolis–Hastings algori...
Nasir, M.; Pratama, D.; Anam, C.; Haryanto, F.
2016-03-01
The aim of this research was to calculate Size Specific Dose Estimates (SSDE) generated by the varian OBI CBCT v1.4 X-ray tube working at 100 kV using EGSnrc Monte Carlo simulations. The EGSnrc Monte Carlo code used in this simulation was divided into two parts. Phase space file data resulted by the first part simulation became an input to the second part. This research was performed with varying phantom diameters of 5 to 35 cm and varying phantom lengths of 10 to 25 cm. Dose distribution data were used to calculate SSDE values using trapezoidal rule (trapz) function in a Matlab program. SSDE obtained from this calculation was compared to that in AAPM report and experimental data. It was obtained that the normalization of SSDE value for each phantom diameter was between 1.00 and 3.19. The normalization of SSDE value for each phantom length was between 0.96 and 1.07. The statistical error in this simulation was 4.98% for varying phantom diameters and 5.20% for varying phantom lengths. This study demonstrated the accuracy of the Monte Carlo technique in simulating the dose calculation. In the future, the influence of cylindrical phantom material to SSDE would be studied.
Energy Technology Data Exchange (ETDEWEB)
Cho, S H [Department of Radiation Physics, University of Texas M D Anderson Cancer Center, 1515 Holcombe Blvd, Unit 94, Houston, TX 77030 (United States)
2005-08-07
A recent mice study demonstrated that gold nanoparticles could be safely administered and used to enhance the tumour dose during radiation therapy. The use of gold nanoparticles seems more promising than earlier methods because of the high atomic number of gold and because nanoparticles can more easily penetrate the tumour vasculature. However, to date, possible dose enhancement due to the use of gold nanoparticles has not been well quantified, especially for common radiation treatment situations. Therefore, the current preliminary study estimated this dose enhancement by Monte Carlo calculations for several phantom test cases representing radiation treatments with the following modalities: 140 kVp x-rays, 4 and 6 MV photon beams, and {sup 192}Ir gamma rays. The current study considered three levels of gold concentration within the tumour, two of which are based on the aforementioned mice study, and assumed either no gold or a single gold concentration level outside the tumour. The dose enhancement over the tumour volume considered for the 140 kVp x-ray case can be at least a factor of 2 at an achievable gold concentration of 7 mg Au/g tumour assuming no gold outside the tumour. The tumour dose enhancement for the cases involving the 4 and 6 MV photon beams based on the same assumption ranged from about 1% to 7%, depending on the amount of gold within the tumour and photon beam qualities. For the {sup 192}Ir cases, the dose enhancement within the tumour region ranged from 5% to 31%, depending on radial distance and gold concentration level within the tumour. For the 7 mg Au/g tumour cases, the loading of gold into surrounding normal tissue at 2 mg Au/g resulted in an increase in the normal tissue dose, up to 30%, negligible, and about 2% for the 140 kVp x-rays, 6 MV photon beam, and {sup 192}Ir gamma rays, respectively, while the magnitude of dose enhancement within the tumour was essentially unchanged. (note)
Cho, Sang Hyun
2005-08-07
A recent mice study demonstrated that gold nanoparticles could be safely administered and used to enhance the tumour dose during radiation therapy. The use of gold nanoparticles seems more promising than earlier methods because of the high atomic number of gold and because nanoparticles can more easily penetrate the tumour vasculature. However, to date, possible dose enhancement due to the use of gold nanoparticles has not been well quantified, especially for common radiation treatment situations. Therefore, the current preliminary study estimated this dose enhancement by Monte Carlo calculations for several phantom test cases representing radiation treatments with the following modalities: 140 kVp x-rays, 4 and 6 MV photon beams, and 192Ir gamma rays. The current study considered three levels of gold concentration within the tumour, two of which are based on the aforementioned mice study, and assumed either no gold or a single gold concentration level outside the tumour. The dose enhancement over the tumour volume considered for the 140 kVp x-ray case can be at least a factor of 2 at an achievable gold concentration of 7 mg Au/g tumour assuming no gold outside the tumour. The tumour dose enhancement for the cases involving the 4 and 6 MV photon beams based on the same assumption ranged from about 1% to 7%, depending on the amount of gold within the tumour and photon beam qualities. For the 192Ir cases, the dose enhancement within the tumour region ranged from 5% to 31%, depending on radial distance and gold concentration level within the tumour. For the 7 mg Au/g tumour cases, the loading of gold into surrounding normal tissue at 2 mg Au/g resulted in an increase in the normal tissue dose, up to 30%, negligible, and about 2% for the 140 kVp x-rays, 6 MV photon beam, and 192Ir gamma rays, respectively, while the magnitude of dose enhancement within the tumour was essentially unchanged.
Monte Carlo approaches to light nuclei
Energy Technology Data Exchange (ETDEWEB)
Carlson, J.
1990-01-01
Significant progress has been made recently in the application of Monte Carlo methods to the study of light nuclei. We review new Green's function Monte Carlo results for the alpha particle, Variational Monte Carlo studies of {sup 16}O, and methods for low-energy scattering and transitions. Through these calculations, a coherent picture of the structure and electromagnetic properties of light nuclei has arisen. In particular, we examine the effect of the three-nucleon interaction and the importance of exchange currents in a variety of experimentally measured properties, including form factors and capture cross sections. 29 refs., 7 figs.
Monte carlo simulation for soot dynamics
Zhou, Kun
2012-01-01
A new Monte Carlo method termed Comb-like frame Monte Carlo is developed to simulate the soot dynamics. Detailed stochastic error analysis is provided. Comb-like frame Monte Carlo is coupled with the gas phase solver Chemkin II to simulate soot formation in a 1-D premixed burner stabilized flame. The simulated soot number density, volume fraction, and particle size distribution all agree well with the measurement available in literature. The origin of the bimodal distribution of particle size distribution is revealed with quantitative proof.
Lattice gauge theories and Monte Carlo simulations
Rebbi, Claudio
1983-01-01
This volume is the most up-to-date review on Lattice Gauge Theories and Monte Carlo Simulations. It consists of two parts. Part one is an introductory lecture on the lattice gauge theories in general, Monte Carlo techniques and on the results to date. Part two consists of important original papers in this field. These selected reprints involve the following: Lattice Gauge Theories, General Formalism and Expansion Techniques, Monte Carlo Simulations. Phase Structures, Observables in Pure Gauge Theories, Systems with Bosonic Matter Fields, Simulation of Systems with Fermions.
Fast quantum Monte Carlo on a GPU
Lutsyshyn, Y
2013-01-01
We present a scheme for the parallelization of quantum Monte Carlo on graphical processing units, focusing on bosonic systems and variational Monte Carlo. We use asynchronous execution schemes with shared memory persistence, and obtain an excellent acceleration. Comparing with single core execution, GPU-accelerated code runs over x100 faster. The CUDA code is provided along with the package that is necessary to execute variational Monte Carlo for a system representing liquid helium-4. The program was benchmarked on several models of Nvidia GPU, including Fermi GTX560 and M2090, and the latest Kepler architecture K20 GPU. Kepler-specific optimization is discussed.
Jalayer, Fatemeh; Ebrahimian, Hossein
2014-05-01
Introduction The first few days elapsed after the occurrence of a strong earthquake and in the presence of an ongoing aftershock sequence are quite critical for emergency decision-making purposes. Epidemic Type Aftershock Sequence (ETAS) models are used frequently for forecasting the spatio-temporal evolution of seismicity in the short-term (Ogata, 1988). The ETAS models are epidemic stochastic point process models in which every earthquake is a potential triggering event for subsequent earthquakes. The ETAS model parameters are usually calibrated a priori and based on a set of events that do not belong to the on-going seismic sequence (Marzocchi and Lombardi 2009). However, adaptive model parameter estimation, based on the events in the on-going sequence, may have several advantages such as, tuning the model to the specific sequence characteristics, and capturing possible variations in time of the model parameters. Simulation-based methods can be employed in order to provide a robust estimate for the spatio-temporal seismicity forecasts in a prescribed forecasting time interval (i.e., a day) within a post-main shock environment. This robust estimate takes into account the uncertainty in the model parameters expressed as the posterior joint probability distribution for the model parameters conditioned on the events that have already occurred (i.e., before the beginning of the forecasting interval) in the on-going seismic sequence. The Markov Chain Monte Carlo simulation scheme is used herein in order to sample directly from the posterior probability distribution for ETAS model parameters. Moreover, the sequence of events that is going to occur during the forecasting interval (and hence affecting the seismicity in an epidemic type model like ETAS) is also generated through a stochastic procedure. The procedure leads to two spatio-temporal outcomes: (1) the probability distribution for the forecasted number of events, and (2) the uncertainty in estimating the
Bayesian phylogeny analysis via stochastic approximation Monte Carlo
Cheon, Sooyoung
2009-11-01
Monte Carlo methods have received much attention in the recent literature of phylogeny analysis. However, the conventional Markov chain Monte Carlo algorithms, such as the Metropolis-Hastings algorithm, tend to get trapped in a local mode in simulating from the posterior distribution of phylogenetic trees, rendering the inference ineffective. In this paper, we apply an advanced Monte Carlo algorithm, the stochastic approximation Monte Carlo algorithm, to Bayesian phylogeny analysis. Our method is compared with two popular Bayesian phylogeny software, BAMBE and MrBayes, on simulated and real datasets. The numerical results indicate that our method outperforms BAMBE and MrBayes. Among the three methods, SAMC produces the consensus trees which have the highest similarity to the true trees, and the model parameter estimates which have the smallest mean square errors, but costs the least CPU time. © 2009 Elsevier Inc. All rights reserved.
Bayesian phylogeny analysis via stochastic approximation Monte Carlo.
Cheon, Sooyoung; Liang, Faming
2009-11-01
Monte Carlo methods have received much attention in the recent literature of phylogeny analysis. However, the conventional Markov chain Monte Carlo algorithms, such as the Metropolis-Hastings algorithm, tend to get trapped in a local mode in simulating from the posterior distribution of phylogenetic trees, rendering the inference ineffective. In this paper, we apply an advanced Monte Carlo algorithm, the stochastic approximation Monte Carlo algorithm, to Bayesian phylogeny analysis. Our method is compared with two popular Bayesian phylogeny software, BAMBE and MrBayes, on simulated and real datasets. The numerical results indicate that our method outperforms BAMBE and MrBayes. Among the three methods, SAMC produces the consensus trees which have the highest similarity to the true trees, and the model parameter estimates which have the smallest mean square errors, but costs the least CPU time.
Monte Carlo techniques for analyzing deep penetration problems
Energy Technology Data Exchange (ETDEWEB)
Cramer, S.N.; Gonnord, J.; Hendricks, J.S.
1985-01-01
A review of current methods and difficulties in Monte Carlo deep-penetration calculations is presented. Statistical uncertainty is discussed, and recent adjoint optimization of splitting, Russian roulette, and exponential transformation biasing is reviewed. Other aspects of the random walk and estimation processes are covered, including the relatively new DXANG angular biasing technique. Specific items summarized are albedo scattering, Monte Carlo coupling techniques with discrete ordinates and other methods, adjoint solutions, and multi-group Monte Carlo. The topic of code-generated biasing parameters is presented, including the creation of adjoint importance functions from forward calculations. Finally, current and future work in the area of computer learning and artificial intelligence is discussed in connection with Monte Carlo applications. 29 refs.
Quantum Monte Carlo for vibrating molecules
Energy Technology Data Exchange (ETDEWEB)
Brown, W.R. [Univ. of California, Berkeley, CA (United States). Chemistry Dept.]|[Lawrence Berkeley National Lab., CA (United States). Chemical Sciences Div.
1996-08-01
Quantum Monte Carlo (QMC) has successfully computed the total electronic energies of atoms and molecules. The main goal of this work is to use correlation function quantum Monte Carlo (CFQMC) to compute the vibrational state energies of molecules given a potential energy surface (PES). In CFQMC, an ensemble of random walkers simulate the diffusion and branching processes of the imaginary-time time dependent Schroedinger equation in order to evaluate the matrix elements. The program QMCVIB was written to perform multi-state VMC and CFQMC calculations and employed for several calculations of the H{sub 2}O and C{sub 3} vibrational states, using 7 PES`s, 3 trial wavefunction forms, two methods of non-linear basis function parameter optimization, and on both serial and parallel computers. In order to construct accurate trial wavefunctions different wavefunctions forms were required for H{sub 2}O and C{sub 3}. In order to construct accurate trial wavefunctions for C{sub 3}, the non-linear parameters were optimized with respect to the sum of the energies of several low-lying vibrational states. In order to stabilize the statistical error estimates for C{sub 3} the Monte Carlo data was collected into blocks. Accurate vibrational state energies were computed using both serial and parallel QMCVIB programs. Comparison of vibrational state energies computed from the three C{sub 3} PES`s suggested that a non-linear equilibrium geometry PES is the most accurate and that discrete potential representations may be used to conveniently determine vibrational state energies.
11th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing
Nuyens, Dirk
2016-01-01
This book presents the refereed proceedings of the Eleventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Leuven (Belgium) in April 2014. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising, in particular, in finance, statistics and computer graphics.
Simulation and the Monte Carlo method
Rubinstein, Reuven Y
2016-01-01
Simulation and the Monte Carlo Method, Third Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the major topics that have emerged in Monte Carlo simulation since the publication of the classic First Edition over more than a quarter of a century ago. While maintaining its accessible and intuitive approach, this revised edition features a wealth of up-to-date information that facilitates a deeper understanding of problem solving across a wide array of subject areas, such as engineering, statistics, computer science, mathematics, and the physical and life sciences. The book begins with a modernized introduction that addresses the basic concepts of probability, Markov processes, and convex optimization. Subsequent chapters discuss the dramatic changes that have occurred in the field of the Monte Carlo method, with coverage of many modern topics including: Markov Chain Monte Carlo, variance reduction techniques such as the transform likelihood ratio...
Monte Carlo simulations for plasma physics
Energy Technology Data Exchange (ETDEWEB)
Okamoto, M.; Murakami, S.; Nakajima, N.; Wang, W.X. [National Inst. for Fusion Science, Toki, Gifu (Japan)
2000-07-01
Plasma behaviours are very complicated and the analyses are generally difficult. However, when the collisional processes play an important role in the plasma behaviour, the Monte Carlo method is often employed as a useful tool. For examples, in neutral particle injection heating (NBI heating), electron or ion cyclotron heating, and alpha heating, Coulomb collisions slow down high energetic particles and pitch angle scatter them. These processes are often studied by the Monte Carlo technique and good agreements can be obtained with the experimental results. Recently, Monte Carlo Method has been developed to study fast particle transports associated with heating and generating the radial electric field. Further it is applied to investigating the neoclassical transport in the plasma with steep gradients of density and temperatures which is beyong the conventional neoclassical theory. In this report, we briefly summarize the researches done by the present authors utilizing the Monte Carlo method. (author)
Quantum Monte Carlo Calculations of Light Nuclei
Pieper, Steven C
2007-01-01
During the last 15 years, there has been much progress in defining the nuclear Hamiltonian and applying quantum Monte Carlo methods to the calculation of light nuclei. I describe both aspects of this work and some recent results.
Improved Monte Carlo Renormalization Group Method
Gupta, R.; Wilson, K. G.; Umrigar, C.
1985-01-01
An extensive program to analyze critical systems using an Improved Monte Carlo Renormalization Group Method (IMCRG) being undertaken at LANL and Cornell is described. Here we first briefly review the method and then list some of the topics being investigated.
Monte Carlo methods for particle transport
Haghighat, Alireza
2015-01-01
The Monte Carlo method has become the de facto standard in radiation transport. Although powerful, if not understood and used appropriately, the method can give misleading results. Monte Carlo Methods for Particle Transport teaches appropriate use of the Monte Carlo method, explaining the method's fundamental concepts as well as its limitations. Concise yet comprehensive, this well-organized text: * Introduces the particle importance equation and its use for variance reduction * Describes general and particle-transport-specific variance reduction techniques * Presents particle transport eigenvalue issues and methodologies to address these issues * Explores advanced formulations based on the author's research activities * Discusses parallel processing concepts and factors affecting parallel performance Featuring illustrative examples, mathematical derivations, computer algorithms, and homework problems, Monte Carlo Methods for Particle Transport provides nuclear engineers and scientists with a practical guide ...
Quantum Monte Carlo approaches for correlated systems
Becca, Federico
2017-01-01
Over the past several decades, computational approaches to studying strongly-interacting systems have become increasingly varied and sophisticated. This book provides a comprehensive introduction to state-of-the-art quantum Monte Carlo techniques relevant for applications in correlated systems. Providing a clear overview of variational wave functions, and featuring a detailed presentation of stochastic samplings including Markov chains and Langevin dynamics, which are developed into a discussion of Monte Carlo methods. The variational technique is described, from foundations to a detailed description of its algorithms. Further topics discussed include optimisation techniques, real-time dynamics and projection methods, including Green's function, reptation and auxiliary-field Monte Carlo, from basic definitions to advanced algorithms for efficient codes, and the book concludes with recent developments on the continuum space. Quantum Monte Carlo Approaches for Correlated Systems provides an extensive reference ...
Monte Carlo scatter correction for SPECT
Liu, Zemei
The goal of this dissertation is to present a quantitatively accurate and computationally fast scatter correction method that is robust and easily accessible for routine applications in SPECT imaging. A Monte Carlo based scatter estimation method is investigated and developed further. The Monte Carlo simulation program SIMIND (Simulating Medical Imaging Nuclear Detectors), was specifically developed to simulate clinical SPECT systems. The SIMIND scatter estimation (SSE) method was developed further using a multithreading technique to distribute the scatter estimation task across multiple threads running concurrently on multi-core CPU's to accelerate the scatter estimation process. An analytical collimator that ensures less noise was used during SSE. The research includes the addition to SIMIND of charge transport modeling in cadmium zinc telluride (CZT) detectors. Phenomena associated with radiation-induced charge transport including charge trapping, charge diffusion, charge sharing between neighboring detector pixels, as well as uncertainties in the detection process are addressed. Experimental measurements and simulation studies were designed for scintillation crystal based SPECT and CZT based SPECT systems to verify and evaluate the expanded SSE method. Jaszczak Deluxe and Anthropomorphic Torso Phantoms (Data Spectrum Corporation, Hillsborough, NC, USA) were used for experimental measurements and digital versions of the same phantoms employed during simulations to mimic experimental acquisitions. This study design enabled easy comparison of experimental and simulated data. The results have consistently shown that the SSE method performed similarly or better than the triple energy window (TEW) and effective scatter source estimation (ESSE) methods for experiments on all the clinical SPECT systems. The SSE method is proven to be a viable method for scatter estimation for routine clinical use.
Bartalini, P.; Kryukov, A.; Selyuzhenkov, Ilya V.; Sherstnev, A.; Vologdin, A.
2004-01-01
We present the Monte-Carlo events Data Base (MCDB) project and its development plans. MCDB facilitates communication between authors of Monte-Carlo generators and experimental users. It also provides a convenient book-keeping and an easy access to generator level samples. The first release of MCDB is now operational for the CMS collaboration. In this paper we review the main ideas behind MCDB and discuss future plans to develop this Data Base further within the CERN LCG framework.
The Feynman Path Goes Monte Carlo
Sauer, Tilman
2001-01-01
Path integral Monte Carlo (PIMC) simulations have become an important tool for the investigation of the statistical mechanics of quantum systems. I discuss some of the history of applying the Monte Carlo method to non-relativistic quantum systems in path-integral representation. The principle feasibility of the method was well established by the early eighties, a number of algorithmic improvements have been introduced in the last two decades.
Monte Carlo Hamiltonian:Inverse Potential
Institute of Scientific and Technical Information of China (English)
LUO Xiang-Qian; CHENG Xiao-Ni; Helmut KR(O)GER
2004-01-01
The Monte Carlo Hamiltonian method developed recently allows to investigate the ground state and low-lying excited states of a quantum system,using Monte Carlo(MC)algorithm with importance sampling.However,conventional MC algorithm has some difficulties when applied to inverse potentials.We propose to use effective potential and extrapolation method to solve the problem.We present examples from the hydrogen system.
Self-consistent kinetic lattice Monte Carlo
Energy Technology Data Exchange (ETDEWEB)
Horsfield, A.; Dunham, S.; Fujitani, Hideaki
1999-07-01
The authors present a brief description of a formalism for modeling point defect diffusion in crystalline systems using a Monte Carlo technique. The main approximations required to construct a practical scheme are briefly discussed, with special emphasis on the proper treatment of charged dopants and defects. This is followed by tight binding calculations of the diffusion barrier heights for charged vacancies. Finally, an application of the kinetic lattice Monte Carlo method to vacancy diffusion is presented.
Quantum Monte Carlo Calculations of Neutron Matter
Carlson, J; Ravenhall, D G
2003-01-01
Uniform neutron matter is approximated by a cubic box containing a finite number of neutrons, with periodic boundary conditions. We report variational and Green's function Monte Carlo calculations of the ground state of fourteen neutrons in a periodic box using the Argonne $\\vep $ two-nucleon interaction at densities up to one and half times the nuclear matter density. The effects of the finite box size are estimated using variational wave functions together with cluster expansion and chain summation techniques. They are small at subnuclear densities. We discuss the expansion of the energy of low-density neutron gas in powers of its Fermi momentum. This expansion is strongly modified by the large nn scattering length, and does not begin with the Fermi-gas kinetic energy as assumed in both Skyrme and relativistic mean field theories. The leading term of neutron gas energy is ~ half the Fermi-gas kinetic energy. The quantum Monte Carlo results are also used to calibrate the accuracy of variational calculations ...
Implications of Monte Carlo Statistical Errors in Criticality Safety Assessments
Energy Technology Data Exchange (ETDEWEB)
Pevey, Ronald E.
2005-09-15
Most criticality safety calculations are performed using Monte Carlo techniques because of Monte Carlo's ability to handle complex three-dimensional geometries. For Monte Carlo calculations, the more histories sampled, the lower the standard deviation of the resulting estimates. The common intuition is, therefore, that the more histories, the better; as a result, analysts tend to run Monte Carlo analyses as long as possible (or at least to a minimum acceptable uncertainty). For Monte Carlo criticality safety analyses, however, the optimization situation is complicated by the fact that procedures usually require that an extra margin of safety be added because of the statistical uncertainty of the Monte Carlo calculations. This additional safety margin affects the impact of the choice of the calculational standard deviation, both on production and on safety. This paper shows that, under the assumptions of normally distributed benchmarking calculational errors and exact compliance with the upper subcritical limit (USL), the standard deviation that optimizes production is zero, but there is a non-zero value of the calculational standard deviation that minimizes the risk of inadvertently labeling a supercritical configuration as subcritical. Furthermore, this value is shown to be a simple function of the typical benchmarking step outcomes--the bias, the standard deviation of the bias, the upper subcritical limit, and the number of standard deviations added to calculated k-effectives before comparison to the USL.
Comparative Dosimetric Estimates of a 25 keV Electron Micro-beam with three Monte Carlo Codes
Mainardi, E; Donahue, R J
2002-01-01
The calculations presented compare the different performances of the three Monte Carlo codes PENELOPE-1999, MCNP-4C and PITS, for the evaluation of Dose profiles from a 25 keV electron micro-beam traversing individual cells. The overall model of a cell is a water cylinder equivalent for the three codes but with a different internal scoring geometry: hollow cylinders for PENELOPE and MCNP, whereas spheres are used for the PITS code. A cylindrical cell geometry with scoring volumes with the shape of hollow cylinders was initially selected for PENELOPE and MCNP because of its superior simulation of the actual shape and dimensions of a cell and for its improved computer-time efficiency if compared to spherical internal volumes. Some of the transfer points and energy transfer that constitute a radiation track may actually fall in the space between spheres, that would be outside the spherical scoring volume. This internal geometry, along with the PENELOPE algorithm, drastically reduced the computer time when using ...
Approaching Chemical Accuracy with Quantum Monte Carlo
Petruzielo, F R; Umrigar, C J
2012-01-01
A quantum Monte Carlo study of the atomization energies for the G2 set of molecules is presented. Basis size dependence of diffusion Monte Carlo atomization energies is studied with a single determinant Slater-Jastrow trial wavefunction formed from Hartree-Fock orbitals. With the largest basis set, the mean absolute deviation from experimental atomization energies for the G2 set is 3.0 kcal/mol. Optimizing the orbitals within variational Monte Carlo improves the agreement between diffusion Monte Carlo and experiment, reducing the mean absolute deviation to 2.1 kcal/mol. Moving beyond a single determinant Slater-Jastrow trial wavefunction, diffusion Monte Carlo with a small complete active space Slater-Jastrow trial wavefunction results in near chemical accuracy. In this case, the mean absolute deviation from experimental atomization energies is 1.2 kcal/mol. It is shown from calculations on systems containing phosphorus that the accuracy can be further improved by employing a larger active space.
Utilising Monte Carlo Simulation for the Valuation of Mining Concessions
Directory of Open Access Journals (Sweden)
Rosli Said
2005-12-01
Full Text Available Valuation involves the analyses of various input data to produce an estimated value. Since each input is itself often an estimate, there is an element of uncertainty in the input. This leads to uncertainty in the resultant output value. It is argued that a valuation must also convey information on the uncertainty, so as to be more meaningful and informative to the user. The Monte Carlo simulation technique can generate the information on uncertainty and is therefore potentially useful to valuation. This paper reports on the investigation that has been conducted to apply Monte Carlo simulation technique in mineral valuation, more specifically, in the valuation of a quarry concession.
Monte Carlo EM加速算法%Acceleration of Monte Carlo EM Algorithm
Institute of Scientific and Technical Information of China (English)
罗季
2008-01-01
EM算法是近年来常用的求后验众数的估计的一种数据增广算法,但由于求出其E步中积分的显示表达式有时很困难,甚至不可能,限制了其应用的广泛性.而Monte Carlo EM算法很好地解决了这个问题,将EM算法中E步的积分用Monte Carlo模拟来有效实现,使其适用性大大增强.但无论是EM算法,还是Monte Carlo EM算法,其收敛速度都是线性的,被缺损信息的倒数所控制,当缺损数据的比例很高时,收敛速度就非常缓慢.而Newton-Raphson算法在后验众数的附近具有二次收敛速率.本文提出Monte Carlo EM加速算法,将Monte Carlo EM算法与Newton-Raphson算法结合,既使得EM算法中的E步用Monte Carlo模拟得以实现,又证明了该算法在后验众数附近具有二次收敛速度.从而使其保留了Monte Carlo EM算法的优点,并改进了Monte Carlo EM算法的收敛速度.本文通过数值例子,将Monte Carlo EM加速算法的结果与EM算法、Monte Carlo EM算法的结果进行比较,进一步说明了Monte Carlo EM加速算法的优良性.
Monte Carlo systems used for treatment planning and dose verification
Energy Technology Data Exchange (ETDEWEB)
Brualla, Lorenzo [Universitaetsklinikum Essen, NCTeam, Strahlenklinik, Essen (Germany); Rodriguez, Miguel [Centro Medico Paitilla, Balboa (Panama); Lallena, Antonio M. [Universidad de Granada, Departamento de Fisica Atomica, Molecular y Nuclear, Granada (Spain)
2017-04-15
General-purpose radiation transport Monte Carlo codes have been used for estimation of the absorbed dose distribution in external photon and electron beam radiotherapy patients since several decades. Results obtained with these codes are usually more accurate than those provided by treatment planning systems based on non-stochastic methods. Traditionally, absorbed dose computations based on general-purpose Monte Carlo codes have been used only for research, owing to the difficulties associated with setting up a simulation and the long computation time required. To take advantage of radiation transport Monte Carlo codes applied to routine clinical practice, researchers and private companies have developed treatment planning and dose verification systems that are partly or fully based on fast Monte Carlo algorithms. This review presents a comprehensive list of the currently existing Monte Carlo systems that can be used to calculate or verify an external photon and electron beam radiotherapy treatment plan. Particular attention is given to those systems that are distributed, either freely or commercially, and that do not require programming tasks from the end user. These systems are compared in terms of features and the simulation time required to compute a set of benchmark calculations. (orig.) [German] Seit mehreren Jahrzehnten werden allgemein anwendbare Monte-Carlo-Codes zur Simulation des Strahlungstransports benutzt, um die Verteilung der absorbierten Dosis in der perkutanen Strahlentherapie mit Photonen und Elektronen zu evaluieren. Die damit erzielten Ergebnisse sind meist akkurater als solche, die mit nichtstochastischen Methoden herkoemmlicher Bestrahlungsplanungssysteme erzielt werden koennen. Wegen des damit verbundenen Arbeitsaufwands und der langen Dauer der Berechnungen wurden Monte-Carlo-Simulationen von Dosisverteilungen in der konventionellen Strahlentherapie in der Vergangenheit im Wesentlichen in der Forschung eingesetzt. Im Bemuehen, Monte-Carlo
Random Numbers and Monte Carlo Methods
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.
Shell model the Monte Carlo way
Energy Technology Data Exchange (ETDEWEB)
Ormand, W.E.
1995-03-01
The formalism for the auxiliary-field Monte Carlo approach to the nuclear shell model is presented. The method is based on a linearization of the two-body part of the Hamiltonian in an imaginary-time propagator using the Hubbard-Stratonovich transformation. The foundation of the method, as applied to the nuclear many-body problem, is discussed. Topics presented in detail include: (1) the density-density formulation of the method, (2) computation of the overlaps, (3) the sign of the Monte Carlo weight function, (4) techniques for performing Monte Carlo sampling, and (5) the reconstruction of response functions from an imaginary-time auto-correlation function using MaxEnt techniques. Results obtained using schematic interactions, which have no sign problem, are presented to demonstrate the feasibility of the method, while an extrapolation method for realistic Hamiltonians is presented. In addition, applications at finite temperature are outlined.
Quantum Monte Carlo with variable spins.
Melton, Cody A; Bennett, M Chandler; Mitas, Lubos
2016-06-28
We investigate the inclusion of variable spins in electronic structure quantum Monte Carlo, with a focus on diffusion Monte Carlo with Hamiltonians that include spin-orbit interactions. Following our previous introduction of fixed-phase spin-orbit diffusion Monte Carlo, we thoroughly discuss the details of the method and elaborate upon its technicalities. We present a proof for an upper-bound property for complex nonlocal operators, which allows for the implementation of T-moves to ensure the variational property. We discuss the time step biases associated with our particular choice of spin representation. Applications of the method are also presented for atomic and molecular systems. We calculate the binding energies and geometry of the PbH and Sn2 molecules, as well as the electron affinities of the 6p row elements in close agreement with experiments.
A brief introduction to Monte Carlo simulation.
Bonate, P L
2001-01-01
Simulation affects our life every day through our interactions with the automobile, airline and entertainment industries, just to name a few. The use of simulation in drug development is relatively new, but its use is increasing in relation to the speed at which modern computers run. One well known example of simulation in drug development is molecular modelling. Another use of simulation that is being seen recently in drug development is Monte Carlo simulation of clinical trials. Monte Carlo simulation differs from traditional simulation in that the model parameters are treated as stochastic or random variables, rather than as fixed values. The purpose of this paper is to provide a brief introduction to Monte Carlo simulation methods.
Quantum Monte Carlo with Variable Spins
Melton, Cody A; Mitas, Lubos
2016-01-01
We investigate the inclusion of variable spins in electronic structure quantum Monte Carlo, with a focus on diffusion Monte Carlo with Hamiltonians that include spin-orbit interactions. Following our previous introduction of fixed-phase spin-orbit diffusion Monte Carlo (FPSODMC), we thoroughly discuss the details of the method and elaborate upon its technicalities. We present a proof for an upper-bound property for complex nonlocal operators, which allows for the implementation of T-moves to ensure the variational property. We discuss the time step biases associated with our particular choice of spin representation. Applications of the method are also presented for atomic and molecular systems. We calculate the binding energies and geometry of the PbH and Sn$_2$ molecules, as well as the electron affinities of the 6$p$ row elements in close agreement with experiments.
Adiabatic optimization versus diffusion Monte Carlo methods
Jarret, Michael; Jordan, Stephen P.; Lackey, Brad
2016-10-01
Most experimental and theoretical studies of adiabatic optimization use stoquastic Hamiltonians, whose ground states are expressible using only real nonnegative amplitudes. This raises a question as to whether classical Monte Carlo methods can simulate stoquastic adiabatic algorithms with polynomial overhead. Here we analyze diffusion Monte Carlo algorithms. We argue that, based on differences between L1 and L2 normalized states, these algorithms suffer from certain obstructions preventing them from efficiently simulating stoquastic adiabatic evolution in generality. In practice however, we obtain good performance by introducing a method that we call Substochastic Monte Carlo. In fact, our simulations are good classical optimization algorithms in their own right, competitive with the best previously known heuristic solvers for MAX-k -SAT at k =2 ,3 ,4 .
Self-learning Monte Carlo method
Liu, Junwei; Qi, Yang; Meng, Zi Yang; Fu, Liang
2017-01-01
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. We demonstrate the efficiency of SLMC in a spin model at the phase transition point, achieving a 10-20 times speedup.
Monte Carlo strategies in scientific computing
Liu, Jun S
2008-01-01
This paperback edition is a reprint of the 2001 Springer edition This book provides a self-contained and up-to-date treatment of the Monte Carlo method and develops a common framework under which various Monte Carlo techniques can be "standardized" and compared Given the interdisciplinary nature of the topics and a moderate prerequisite for the reader, this book should be of interest to a broad audience of quantitative researchers such as computational biologists, computer scientists, econometricians, engineers, probabilists, and statisticians It can also be used as the textbook for a graduate-level course on Monte Carlo methods Many problems discussed in the alter chapters can be potential thesis topics for masters’ or PhD students in statistics or computer science departments Jun Liu is Professor of Statistics at Harvard University, with a courtesy Professor appointment at Harvard Biostatistics Department Professor Liu was the recipient of the 2002 COPSS Presidents' Award, the most prestigious one for sta...
A continuation multilevel Monte Carlo algorithm
Collier, Nathan
2014-09-05
We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the required error tolerance is satisfied. CMLMC assumes discretization hierarchies that are defined a priori for each level and are geometrically refined across levels. The actual choice of computational work across levels is based on parametric models for the average cost per sample and the corresponding variance and weak error. These parameters are calibrated using Bayesian estimation, taking particular notice of the deepest levels of the discretization hierarchy, where only few realizations are available to produce the estimates. The resulting CMLMC estimator exhibits a non-trivial splitting between bias and statistical contributions. We also show the asymptotic normality of the statistical error in the MLMC estimator and justify in this way our error estimate that allows prescribing both required accuracy and confidence in the final result. Numerical results substantiate the above results and illustrate the corresponding computational savings in examples that are described in terms of differential equations either driven by random measures or with random coefficients. © 2014, Springer Science+Business Media Dordrecht.
Lunt, Mark F.; Rigby, Matt; Ganesan, Anita L.; Manning, Alistair J.
2016-09-01
Atmospheric trace gas inversions often attempt to attribute fluxes to a high-dimensional grid using observations. To make this problem computationally feasible, and to reduce the degree of under-determination, some form of dimension reduction is usually performed. Here, we present an objective method for reducing the spatial dimension of the parameter space in atmospheric trace gas inversions. In addition to solving for a set of unknowns that govern emissions of a trace gas, we set out a framework that considers the number of unknowns to itself be an unknown. We rely on the well-established reversible-jump Markov chain Monte Carlo algorithm to use the data to determine the dimension of the parameter space. This framework provides a single-step process that solves for both the resolution of the inversion grid, as well as the magnitude of fluxes from this grid. Therefore, the uncertainty that surrounds the choice of aggregation is accounted for in the posterior parameter distribution. The posterior distribution of this transdimensional Markov chain provides a naturally smoothed solution, formed from an ensemble of coarser partitions of the spatial domain. We describe the form of the reversible-jump algorithm and how it may be applied to trace gas inversions. We build the system into a hierarchical Bayesian framework in which other unknown factors, such as the magnitude of the model uncertainty, can also be explored. A pseudo-data example is used to show the usefulness of this approach when compared to a subjectively chosen partitioning of a spatial domain. An inversion using real data is also shown to illustrate the scales at which the data allow for methane emissions over north-west Europe to be resolved.
Dokania, N; Mathimalar, S; Garai, A; Nanal, V; Pillay, R G; Bhushan, K G
2015-01-01
The neutron flux at low energy ($E_n\\leq15$ MeV) resulting from the radioactivity of the rock in the underground cavern of the India-based Neutrino Observatory is estimated using Geant4-based Monte Carlo simulations. The neutron production rate due to the spontaneous fission of U, Th and ($\\alpha, n$) interactions in the rock is determined employing the actual rock composition. It has been demonstrated that the total flux is equivalent to a finite size cylindrical rock ($D=L=140$ cm) element. The energy integrated neutron flux thus obtained at the center of the underground tunnel is 2.76 (0.47) $\\times 10^{-6}\\rm~n ~cm^{-2}~s^{-1}$. The estimated neutron flux is of the same order ($\\sim10^{-6}\\rm~n ~cm^{-2}~s^{-1}$)~as measured in other underground laboratories.
Parallel Markov chain Monte Carlo simulations.
Ren, Ruichao; Orkoulas, G
2007-06-07
With strict detailed balance, parallel Monte Carlo simulation through domain decomposition cannot be validated with conventional Markov chain theory, which describes an intrinsically serial stochastic process. In this work, the parallel version of Markov chain theory and its role in accelerating Monte Carlo simulations via cluster computing is explored. It is shown that sequential updating is the key to improving efficiency in parallel simulations through domain decomposition. A parallel scheme is proposed to reduce interprocessor communication or synchronization, which slows down parallel simulation with increasing number of processors. Parallel simulation results for the two-dimensional lattice gas model show substantial reduction of simulation time for systems of moderate and large size.
Monte Carlo Hamiltonian：Linear Potentials
Institute of Scientific and Technical Information of China (English)
LUOXiang－Qian; HelmutKROEGER; 等
2002-01-01
We further study the validity of the Monte Carlo Hamiltonian method .The advantage of the method,in comparison with the standard Monte Carlo Lagrangian approach,is its capability to study the excited states.We consider two quantum mechanical models:a symmetric one V(x)=/x/2;and an asymmetric one V(x)==∞,for x<0 and V(x)=2,for x≥0.The results for the spectrum,wave functions and thermodynamical observables are in agreement with the analytical or Runge-Kutta calculations.
Monte Carlo dose distributions for radiosurgery
Energy Technology Data Exchange (ETDEWEB)
Perucha, M.; Leal, A.; Rincon, M.; Carrasco, E. [Sevilla Univ. (Spain). Dept. Fisiologia Medica y Biofisica; Sanchez-Doblado, F. [Sevilla Univ. (Spain). Dept. Fisiologia Medica y Biofisica]|[Hospital Univ. Virgen Macarena, Sevilla (Spain). Servicio de Oncologia Radioterapica; Nunez, L. [Clinica Puerta de Hierro, Madrid (Spain). Servicio de Radiofisica; Arrans, R.; Sanchez-Calzado, J.A.; Errazquin, L. [Hospital Univ. Virgen Macarena, Sevilla (Spain). Servicio de Oncologia Radioterapica; Sanchez-Nieto, B. [Royal Marsden NHS Trust (United Kingdom). Joint Dept. of Physics]|[Inst. of Cancer Research, Sutton, Surrey (United Kingdom)
2001-07-01
The precision of Radiosurgery Treatment planning systems is limited by the approximations of their algorithms and by their dosimetrical input data. This fact is especially important in small fields. However, the Monte Carlo methods is an accurate alternative as it considers every aspect of particle transport. In this work an acoustic neurinoma is studied by comparing the dose distribution of both a planning system and Monte Carlo. Relative shifts have been measured and furthermore, Dose-Volume Histograms have been calculated for target and adjacent organs at risk. (orig.)
Monte carlo simulations of organic photovoltaics.
Groves, Chris; Greenham, Neil C
2014-01-01
Monte Carlo simulations are a valuable tool to model the generation, separation, and collection of charges in organic photovoltaics where charges move by hopping in a complex nanostructure and Coulomb interactions between charge carriers are important. We review the Monte Carlo techniques that have been applied to this problem, and describe the results of simulations of the various recombination processes that limit device performance. We show how these processes are influenced by the local physical and energetic structure of the material, providing information that is useful for design of efficient photovoltaic systems.
Monte Carlo simulation of neutron scattering instruments
Energy Technology Data Exchange (ETDEWEB)
Seeger, P.A.
1995-12-31
A library of Monte Carlo subroutines has been developed for the purpose of design of neutron scattering instruments. Using small-angle scattering as an example, the philosophy and structure of the library are described and the programs are used to compare instruments at continuous wave (CW) and long-pulse spallation source (LPSS) neutron facilities. The Monte Carlo results give a count-rate gain of a factor between 2 and 4 using time-of-flight analysis. This is comparable to scaling arguments based on the ratio of wavelength bandwidth to resolution width.
The Rational Hybrid Monte Carlo Algorithm
Clark, M A
2006-01-01
The past few years have seen considerable progress in algorithmic development for the generation of gauge fields including the effects of dynamical fermions. The Rational Hybrid Monte Carlo (RHMC) algorithm, where Hybrid Monte Carlo is performed using a rational approximation in place the usual inverse quark matrix kernel is one of these developments. This algorithm has been found to be extremely beneficial in many areas of lattice QCD (chiral fermions, finite temperature, Wilson fermions etc.). We review the algorithm and some of these benefits, and we compare against other recent algorithm developements. We conclude with an update of the Berlin wall plot comparing costs of all popular fermion formulations.
The Rational Hybrid Monte Carlo algorithm
Clark, Michael
2006-12-01
The past few years have seen considerable progress in algorithmic development for the generation of gauge fields including the effects of dynamical fermions. The Rational Hybrid Monte Carlo (RHMC) algorithm, where Hybrid Monte Carlo is performed using a rational approximation in place the usual inverse quark matrix kernel is one of these developments. This algorithm has been found to be extremely beneficial in many areas of lattice QCD (chiral fermions, finite temperature, Wilson fermions etc.). We review the algorithm and some of these benefits, and we compare against other recent algorithm developements. We conclude with an update of the Berlin wall plot comparing costs of all popular fermion formulations.
Energy Technology Data Exchange (ETDEWEB)
Authier, N
1998-12-01
One of the questions asked in radiation shielding problems is the estimation of the radiation level in particular to determine accessibility of working persons in controlled area (nuclear power plants, nuclear fuel reprocessing plants) or to study the dose gradients encountered in material (iron nuclear vessel, medical therapy, electronics in satellite). The flux and reaction rate estimators used in Monte Carlo codes give average values in volumes or on surfaces of the geometrical description of the system. But in certain configurations, the knowledge of punctual deposited energy and dose estimates are necessary. The Monte Carlo estimate of the flux at a point of interest is a calculus which presents an unbounded variance. The central limit theorem cannot be applied thus no easy confidencelevel may be calculated. The convergence rate is then very poor. We propose in this study a new solution for the photon flux at a point estimator. The method is based on the 'once more collided flux estimator' developed earlier for neutron calculations. It solves the problem of the unbounded variance and do not add any bias to the estimation. We show however that our new sampling schemes specially developed to treat the anisotropy of the photon coherent scattering is necessary for a good and regular behavior of the estimator. This developments integrated in the TRIPOLI-4 Monte Carlo code add the possibility of an unbiased punctual estimate on media interfaces. (author)
Monte Carlo methods in AB initio quantum chemistry quantum Monte Carlo for molecules
Lester, William A; Reynolds, PJ
1994-01-01
This book presents the basic theory and application of the Monte Carlo method to the electronic structure of atoms and molecules. It assumes no previous knowledge of the subject, only a knowledge of molecular quantum mechanics at the first-year graduate level. A working knowledge of traditional ab initio quantum chemistry is helpful, but not essential.Some distinguishing features of this book are: Clear exposition of the basic theory at a level to facilitate independent study. Discussion of the various versions of the theory: diffusion Monte Carlo, Green's function Monte Carlo, and release n
Use of Monte Carlo Methods in brachytherapy; Uso del metodo de Monte Carlo en braquiterapia
Energy Technology Data Exchange (ETDEWEB)
Granero Cabanero, D.
2015-07-01
The Monte Carlo method has become a fundamental tool for brachytherapy dosimetry mainly because no difficulties associated with experimental dosimetry. In brachytherapy the main handicap of experimental dosimetry is the high dose gradient near the present sources making small uncertainties in the positioning of the detectors lead to large uncertainties in the dose. This presentation will review mainly the procedure for calculating dose distributions around a fountain using the Monte Carlo method showing the difficulties inherent in these calculations. In addition we will briefly review other applications of the method of Monte Carlo in brachytherapy dosimetry, as its use in advanced calculation algorithms, calculating barriers or obtaining dose applicators around. (Author)
Monte Carlo methods and models in finance and insurance
Korn, Ralf
2010-01-01
Offering a unique balance between applications and calculations, this book incorporates the application background of finance and insurance with the theory and applications of Monte Carlo methods. It presents recent methods and algorithms, including the multilevel Monte Carlo method, the statistical Romberg method, and the Heath-Platen estimator, as well as recent financial and actuarial models, such as the Cheyette and dynamic mortality models. The book enables readers to find the right algorithm for a desired application and illustrates complicated methods and algorithms with simple applicat
Accuracy Analysis of Assembly Success Rate with Monte Carlo Simulations
Institute of Scientific and Technical Information of China (English)
仲昕; 杨汝清; 周兵
2003-01-01
Monte Carlo simulation was applied to Assembly Success Rate (ASR) analyses.ASR of two peg-in-hole robot assemblies was used as an example by taking component parts' sizes,manufacturing tolerances and robot repeatability into account.A statistic arithmetic expression was proposed and deduced in this paper,which offers an alternative method of estimating the accuracy of ASR,without having to repeat the simulations.This statistic method also helps to choose a suitable sample size,if error reduction is desired.Monte Carlo simulation results demonstrated the feasibility of the method.
Wilson, J. A.; Richardson, J. A.
2015-12-01
Traditional methods used to calculate recurrence rate of volcanism, such as linear regression, maximum likelihood and Weibull-Poisson distributions, are effective at estimating recurrence rate and confidence level, but these methods are unable to estimate uncertainty in recurrence rate through time. We propose a new model for estimating recurrence rate and uncertainty, Volcanic Event Recurrence Rate Model. VERRM is an algorithm that incorporates radiometric ages, volcanic stratigraphy and paleomagnetic data into a Monte Carlo simulation, generating acceptable ages for each event. Each model run is used to calculate recurrence rate using a moving average window. These rates are binned into discrete time intervals and plotted using the 5th, 50th and 95th percentiles. We present recurrence rates from Cima Volcanic Field (CA), Yucca Mountain (NV) and Arsia Mons (Mars). Results from Cima Volcanic Field illustrate how several K-Ar ages with large uncertainties obscure three well documented volcanic episodes. Yucca Mountain results are similar to published rates and illustrate the use of using the same radiometric age for multiple events in a spatially defined cluster. Arsia Mons results show a clear waxing/waning of volcanism through time. VERRM output may be used for a spatio-temporal model or to plot uncertainty in quantifiable parameters such as eruption volume or geochemistry. Alternatively, the algorithm may be reworked to constrain geomagnetic chrons. VERRM is implemented in Python 2.7 and takes advantage of NumPy, SciPy and matplotlib libraries for optimization and quality plotting presentation. A typical Monte Carlo simulation of 40 volcanic events takes a few minutes to couple hours to complete, depending on the bin size used to assign ages.
Monte Carlo Methods for Tempo Tracking and Rhythm Quantization
Cemgil, A T; 10.1613/jair.1121
2011-01-01
We present a probabilistic generative model for timing deviations in expressive music performance. The structure of the proposed model is equivalent to a switching state space model. The switch variables correspond to discrete note locations as in a musical score. The continuous hidden variables denote the tempo. We formulate two well known music recognition problems, namely tempo tracking and automatic transcription (rhythm quantization) as filtering and maximum a posteriori (MAP) state estimation tasks. Exact computation of posterior features such as the MAP state is intractable in this model class, so we introduce Monte Carlo methods for integration and optimization. We compare Markov Chain Monte Carlo (MCMC) methods (such as Gibbs sampling, simulated annealing and iterative improvement) and sequential Monte Carlo methods (particle filters). Our simulation results suggest better results with sequential methods. The methods can be applied in both online and batch scenarios such as tempo tracking and transcr...
Introduction to the variational and diffusion Monte Carlo methods
Toulouse, Julien; Umrigar, C J
2015-01-01
We provide a pedagogical introduction to the two main variants of real-space quantum Monte Carlo methods for electronic-structure calculations: variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). Assuming no prior knowledge on the subject, we review in depth the Metropolis-Hastings algorithm used in VMC for sampling the square of an approximate wave function, discussing details important for applications to electronic systems. We also review in detail the more sophisticated DMC algorithm within the fixed-node approximation, introduced to avoid the infamous Fermionic sign problem, which allows one to sample a more accurate approximation to the ground-state wave function. Throughout this review, we discuss the statistical methods used for evaluating expectation values and statistical uncertainties. In particular, we show how to estimate nonlinear functions of expectation values and their statistical uncertainties.
Monte Carlo Simulation in Statistical Physics An Introduction
Binder, Kurt
2010-01-01
Monte Carlo Simulation in Statistical Physics deals with the computer simulation of many-body systems in condensed-matter physics and related fields of physics, chemistry and beyond, to traffic flows, stock market fluctuations, etc.). Using random numbers generated by a computer, probability distributions are calculated, allowing the estimation of the thermodynamic properties of various systems. This book describes the theoretical background to several variants of these Monte Carlo methods and gives a systematic presentation from which newcomers can learn to perform such simulations and to analyze their results. The fifth edition covers Classical as well as Quantum Monte Carlo methods. Furthermore a new chapter on the sampling of free-energy landscapes has been added. To help students in their work a special web server has been installed to host programs and discussion groups (http://wwwcp.tphys.uni-heidelberg.de). Prof. Binder was awarded the Berni J. Alder CECAM Award for Computational Physics 2001 as well ...
SPANDY: a Monte Carlo program for gas target scattering geometry
Energy Technology Data Exchange (ETDEWEB)
Jarmie, N.; Jett, J.H.; Niethammer, A.C.
1977-02-01
A Monte Carlo computer program is presented that simulates a two-slit gas target scattering geometry. The program is useful in estimating effects due to finite geometry and multiple scattering in the target foil. Details of the program are presented and experience with a specific example is discussed.
Tackling the premature convergence problem in Monte-Carlo localization
Kootstra, G.; de Boer, B.
2009-01-01
Monte-Carlo localization uses particle filtering to estimate the position of the robot. The method is known to suffer from the loss of potential positions when there is ambiguity present in the environment. Since many indoor environments are highly symmetric, this problem of premature convergence is
Testing Dependent Correlations with Nonoverlapping Variables: A Monte Carlo Simulation
Silver, N. Clayton; Hittner, James B.; May, Kim
2004-01-01
The authors conducted a Monte Carlo simulation of 4 test statistics or comparing dependent correlations with no variables in common. Empirical Type 1 error rates and power estimates were determined for K. Pearson and L. N. G. Filon's (1898) z, O. J. Dunn and V. A. Clark's (1969) z, J. H. Steiger's (1980) original modification of Dunn and Clark's…
A comparison of Monte Carlo generators
Golan, Tomasz
2014-01-01
A comparison of GENIE, NEUT, NUANCE, and NuWro Monte Carlo neutrino event generators is presented using a set of four observables: protons multiplicity, total visible energy, most energetic proton momentum, and $\\pi^+$ two-dimensional energy vs cosine distribution.
Monte Carlo Tools for Jet Quenching
Zapp, Korinna
2011-01-01
A thorough understanding of jet quenching on the basis of multi-particle final states and jet observables requires new theoretical tools. This talk summarises the status and propects of the theoretical description of jet quenching in terms of Monte Carlo generators.
An Introduction to Monte Carlo Methods
Raeside, D. E.
1974-01-01
Reviews the principles of Monte Carlo calculation and random number generation in an attempt to introduce the direct and the rejection method of sampling techniques as well as the variance-reduction procedures. Indicates that the increasing availability of computers makes it possible for a wider audience to learn about these powerful methods. (CC)
Scalable Domain Decomposed Monte Carlo Particle Transport
Energy Technology Data Exchange (ETDEWEB)
O' Brien, Matthew Joseph [Univ. of California, Davis, CA (United States)
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.
Monte Carlo methods beyond detailed balance
Schram, Raoul D.; Barkema, Gerard T.
2015-01-01
Monte Carlo algorithms are nearly always based on the concept of detailed balance and ergodicity. In this paper we focus on algorithms that do not satisfy detailed balance. We introduce a general method for designing non-detailed balance algorithms, starting from a conventional algorithm satisfying
An analysis of Monte Carlo tree search
CSIR Research Space (South Africa)
James, S
2017-02-01
Full Text Available Monte Carlo Tree Search (MCTS) is a family of directed search algorithms that has gained widespread attention in recent years. Despite the vast amount of research into MCTS, the effect of modifications on the algorithm, as well as the manner...
Monte Carlo Simulation of Counting Experiments.
Ogden, Philip M.
A computer program to perform a Monte Carlo simulation of counting experiments was written. The program was based on a mathematical derivation which started with counts in a time interval. The time interval was subdivided to form a binomial distribution with no two counts in the same subinterval. Then the number of subintervals was extended to…
Energy Technology Data Exchange (ETDEWEB)
Lima, Alexandre Roza de
2014-07-01
The International Commission on Radiological Protection, ICRP, in its publication 103, reviewed recent epidemiological evidence and indicated that, for the eye lens, the absorbed dose threshold for induction of late detriment is around 0.5 Gy. On this basis, on April 21, 2011, the ICRP recommended changes to the occupational dose limit in planned exposure situations, reducing the eye lens equivalent dose limit from 150 mSv to 20 mSv per year, on average, during the period of 5 years, with exposure not to exceed 50 mSv in a single year. This paper presents the dose estimation to eye lens, H{sub p}(10), effective dose and doses to important organs in the body, received by industrial gamma radiography workers, during planned or accidental exposure situations. The computer program Visual Monte Carlo was used and two relevant scenarios were postulated. The first is a planned exposure situation scenario where the operator is directly exposed to radiation during the operation. 12 radiographic exposures per day for 250 days per year, which leads to an exposure of 36,000 seconds or 10 hours per year were considered. The simulation was carried out using the following parameters: a {sup 192}Ir source with 1.0 TBq of activity, the source/operator distance varying from 5 m to 10 m at three different heights of 0.2 m, 1.0 m and 2.0 m. The eyes lens doses were estimated as being between 16.9 mSv/year and 66.9 mSv/year and for H{sub p}(10) the doses were between 17.7 mSv/year and 74.2 mSv/year. For the accidental exposure situation scenario, the same radionuclide and activity were used, but in this case the doses were calculated with and without a collimator. The heights above ground considered were 1.0 m, 1.5 m e 2.0 m, the source/operator distance was 40 cm and, the exposure time 74 seconds. The eyes lens doses, for 1.5 m, were 12.3 mGy and 0.28 mGy without and with a collimator, respectively. Three conclusions resulted from this work. The first was that the estimated doses show
Global Monte Carlo Simulation with High Order Polynomial Expansions
Energy Technology Data Exchange (ETDEWEB)
William R. Martin; James Paul Holloway; Kaushik Banerjee; Jesse Cheatham; Jeremy Conlin
2007-12-13
The functional expansion technique (FET) was recently developed for Monte Carlo simulation. The basic idea of the FET is to expand a Monte Carlo tally in terms of a high order expansion, the coefficients of which can be estimated via the usual random walk process in a conventional Monte Carlo code. If the expansion basis is chosen carefully, the lowest order coefficient is simply the conventional histogram tally, corresponding to a flat mode. This research project studied the applicability of using the FET to estimate the fission source, from which fission sites can be sampled for the next generation. The idea is that individual fission sites contribute to expansion modes that may span the geometry being considered, possibly increasing the communication across a loosely coupled system and thereby improving convergence over the conventional fission bank approach used in most production Monte Carlo codes. The project examined a number of basis functions, including global Legendre polynomials as well as “local” piecewise polynomials such as finite element hat functions and higher order versions. The global FET showed an improvement in convergence over the conventional fission bank approach. The local FET methods showed some advantages versus global polynomials in handling geometries with discontinuous material properties. The conventional finite element hat functions had the disadvantage that the expansion coefficients could not be estimated directly but had to be obtained by solving a linear system whose matrix elements were estimated. An alternative fission matrix-based response matrix algorithm was formulated. Studies were made of two alternative applications of the FET, one based on the kernel density estimator and one based on Arnoldi’s method of minimized iterations. Preliminary results for both methods indicate improvements in fission source convergence. These developments indicate that the FET has promise for speeding up Monte Carlo fission source
Monte Carlo radiation transport in external beam radiotherapy
Çeçen, Yiğit
2013-01-01
The use of Monte Carlo in radiation transport is an effective way to predict absorbed dose distributions. Monte Carlo modeling has contributed to a better understanding of photon and electron transport by radiotherapy physicists. The aim of this review is to introduce Monte Carlo as a powerful radiation transport tool. In this review, photon and electron transport algorithms for Monte Carlo techniques are investigated and a clinical linear accelerator model is studied for external beam radiot...
DeMarco, J J; Cagnon, C H; Cody, D D; Stevens, D M; McCollough, C H; Zankl, M; Angel, E; McNitt-Gray, M F
2007-05-07
The purpose of this work is to examine the effects of patient size on radiation dose from CT scans. To perform these investigations, we used Monte Carlo simulation methods with detailed models of both patients and multidetector computed tomography (MDCT) scanners. A family of three-dimensional, voxelized patient models previously developed and validated by the GSF was implemented as input files using the Monte Carlo code MCNPX. These patient models represent a range of patient sizes and ages (8 weeks to 48 years) and have all radiosensitive organs previously identified and segmented, allowing the estimation of dose to any individual organ and calculation of patient effective dose. To estimate radiation dose, every voxel in each patient model was assigned both a specific organ index number and an elemental composition and mass density. Simulated CT scans of each voxelized patient model were performed using a previously developed MDCT source model that includes scanner specific spectra, including bowtie filter, scanner geometry and helical source path. The scan simulations in this work include a whole-body scan protocol and a thoracic CT scan protocol, each performed with fixed tube current. The whole-body scan simulation yielded a predictable decrease in effective dose as a function of increasing patient weight. Results from analysis of individual organs demonstrated similar trends, but with some individual variations. A comparison with a conventional dose estimation method using the ImPACT spreadsheet yielded an effective dose of 0.14 mSv mAs(-1) for the whole-body scan. This result is lower than the simulations on the voxelized model designated 'Irene' (0.15 mSv mAs(-1)) and higher than the models 'Donna' and 'Golem' (0.12 mSv mAs(-1)). For the thoracic scan protocol, the ImPACT spreadsheet estimates an effective dose of 0.037 mSv mAs(-1), which falls between the calculated values for Irene (0.042 mSv mAs(-1)) and Donna (0.031 mSv mAs(-1)) and is higher relative
Li, Ruochen; Englehardt, James D; Li, Xiaoguang
2012-02-01
Multivariate probability distributions, such as may be used for mixture dose-response assessment, are typically highly parameterized and difficult to fit to available data. However, such distributions may be useful in analyzing the large electronic data sets becoming available, such as dose-response biomarker and genetic information. In this article, a new two-stage computational approach is introduced for estimating multivariate distributions and addressing parameter uncertainty. The proposed first stage comprises a gradient Markov chain Monte Carlo (GMCMC) technique to find Bayesian posterior mode estimates (PMEs) of parameters, equivalent to maximum likelihood estimates (MLEs) in the absence of subjective information. In the second stage, these estimates are used to initialize a Markov chain Monte Carlo (MCMC) simulation, replacing the conventional burn-in period to allow convergent simulation of the full joint Bayesian posterior distribution and the corresponding unconditional multivariate distribution (not conditional on uncertain parameter values). When the distribution of parameter uncertainty is such a Bayesian posterior, the unconditional distribution is termed predictive. The method is demonstrated by finding conditional and unconditional versions of the recently proposed emergent dose-response function (DRF). Results are shown for the five-parameter common-mode and seven-parameter dissimilar-mode models, based on published data for eight benzene-toluene dose pairs. The common mode conditional DRF is obtained with a 21-fold reduction in data requirement versus MCMC. Example common-mode unconditional DRFs are then found using synthetic data, showing a 71% reduction in required data. The approach is further demonstrated for a PCB 126-PCB 153 mixture. Applicability is analyzed and discussed. Matlab(®) computer programs are provided.
Monte Carlo Euler approximations of HJM term structure financial models
Björk, Tomas
2012-11-22
We present Monte Carlo-Euler methods for a weak approximation problem related to the Heath-Jarrow-Morton (HJM) term structure model, based on Itô stochastic differential equations in infinite dimensional spaces, and prove strong and weak error convergence estimates. The weak error estimates are based on stochastic flows and discrete dual backward problems, and they can be used to identify different error contributions arising from time and maturity discretization as well as the classical statistical error due to finite sampling. Explicit formulas for efficient computation of sharp error approximation are included. Due to the structure of the HJM models considered here, the computational effort devoted to the error estimates is low compared to the work to compute Monte Carlo solutions to the HJM model. Numerical examples with known exact solution are included in order to show the behavior of the estimates. © 2012 Springer Science+Business Media Dordrecht.
Monte Carlo simulations of the NIMROD diffractometer
Energy Technology Data Exchange (ETDEWEB)
Botti, A. [University of Roma TRE, Rome (Italy)]. E-mail: botti@fis.uniroma3.it; Ricci, M.A. [University of Roma TRE, Rome (Italy); Bowron, D.T. [ISIS-Rutherford Appleton Laboratory, Chilton (United Kingdom); Soper, A.K. [ISIS-Rutherford Appleton Laboratory, Chilton (United Kingdom)
2006-11-15
The near and intermediate range order diffractometer (NIMROD) has been selected as a day one instrument on the second target station at ISIS. Uniquely, NIMROD will provide continuous access to particle separations ranging from the interatomic (<1A) to the mesoscopic (<300A). This instrument is mainly designed for structural investigations, although the possibility of putting a Fermi chopper (and corresponding NIMONIC chopper) in the incident beam line, will potentially allow the performance of low resolution inelastic scattering measurements. The performance characteristics of the TOF diffractometer have been simulated by means of a series of Monte Carlo calculations. In particular, the flux as a function of the transferred momentum Q as well as the resolution in Q and transferred energy have been estimated. Moreover, the possibility of including a honeycomb collimator in order to achieve better resolution has been tested. Here, we want to present the design of this diffractometer that will bridge the gap between wide- and small-angle neutron scattering experiments.
Monte Carlo study of real time dynamics
Alexandru, Andrei; Bedaque, Paulo F; Vartak, Sohan; Warrington, Neill C
2016-01-01
Monte Carlo studies involving real time dynamics are severely restricted by the sign problem that emerges from highly oscillatory phase of the path integral. In this letter, we present a new method to compute real time quantities on the lattice using the Schwinger-Keldysh formalism via Monte Carlo simulations. The key idea is to deform the path integration domain to a complex manifold where the phase oscillations are mild and the sign problem is manageable. We use the previously introduced "contraction algorithm" to create a Markov chain on this alternative manifold. We substantiate our approach by analyzing the quantum mechanical anharmonic oscillator. Our results are in agreement with the exact ones obtained by diagonalization of the Hamiltonian. The method we introduce is generic and in principle applicable to quantum field theory albeit very slow. We discuss some possible improvements that should speed up the algorithm.
Monte Carlo Simulation for Particle Detectors
Pia, Maria Grazia
2012-01-01
Monte Carlo simulation is an essential component of experimental particle physics in all the phases of its life-cycle: the investigation of the physics reach of detector concepts, the design of facilities and detectors, the development and optimization of data reconstruction software, the data analysis for the production of physics results. This note briefly outlines some research topics related to Monte Carlo simulation, that are relevant to future experimental perspectives in particle physics. The focus is on physics aspects: conceptual progress beyond current particle transport schemes, the incorporation of materials science knowledge relevant to novel detection technologies, functionality to model radiation damage, the capability for multi-scale simulation, quantitative validation and uncertainty quantification to determine the predictive power of simulation. The R&D on simulation for future detectors would profit from cooperation within various components of the particle physics community, and synerg...
An enhanced Monte Carlo outlier detection method.
Zhang, Liangxiao; Li, Peiwu; Mao, Jin; Ma, Fei; Ding, Xiaoxia; Zhang, Qi
2015-09-30
Outlier detection is crucial in building a highly predictive model. In this study, we proposed an enhanced Monte Carlo outlier detection method by establishing cross-prediction models based on determinate normal samples and analyzing the distribution of prediction errors individually for dubious samples. One simulated and three real datasets were used to illustrate and validate the performance of our method, and the results indicated that this method outperformed Monte Carlo outlier detection in outlier diagnosis. After these outliers were removed, the value of validation by Kovats retention indices and the root mean square error of prediction decreased from 3.195 to 1.655, and the average cross-validation prediction error decreased from 2.0341 to 1.2780. This method helps establish a good model by eliminating outliers. © 2015 Wiley Periodicals, Inc.
Composite biasing in Monte Carlo radiative transfer
Baes, Maarten; Lunttila, Tuomas; Bianchi, Simone; Camps, Peter; Juvela, Mika; Kuiper, Rolf
2016-01-01
Biasing or importance sampling is a powerful technique in Monte Carlo radiative transfer, and can be applied in different forms to increase the accuracy and efficiency of simulations. One of the drawbacks of the use of biasing is the potential introduction of large weight factors. We discuss a general strategy, composite biasing, to suppress the appearance of large weight factors. We use this composite biasing approach for two different problems faced by current state-of-the-art Monte Carlo radiative transfer codes: the generation of photon packages from multiple components, and the penetration of radiation through high optical depth barriers. In both cases, the implementation of the relevant algorithms is trivial and does not interfere with any other optimisation techniques. Through simple test models, we demonstrate the general applicability, accuracy and efficiency of the composite biasing approach. In particular, for the penetration of high optical depths, the gain in efficiency is spectacular for the spe...
Multilevel Monte Carlo Approaches for Numerical Homogenization
Efendiev, Yalchin R.
2015-10-01
In this article, we study the application of multilevel Monte Carlo (MLMC) approaches to numerical random homogenization. Our objective is to compute the expectation of some functionals of the homogenized coefficients, or of the homogenized solutions. This is accomplished within MLMC by considering different sizes of representative volumes (RVEs). Many inexpensive computations with the smallest RVE size are combined with fewer expensive computations performed on larger RVEs. Likewise, when it comes to homogenized solutions, different levels of coarse-grid meshes are used to solve the homogenized equation. We show that, by carefully selecting the number of realizations at each level, we can achieve a speed-up in the computations in comparison to a standard Monte Carlo method. Numerical results are presented for both one-dimensional and two-dimensional test-cases that illustrate the efficiency of the approach.
Monte Carlo simulations on SIMD computer architectures
Energy Technology Data Exchange (ETDEWEB)
Burmester, C.P.; Gronsky, R. [Lawrence Berkeley Lab., CA (United States); Wille, L.T. [Florida Atlantic Univ., Boca Raton, FL (United States). Dept. of Physics
1992-03-01
Algorithmic considerations regarding the implementation of various materials science applications of the Monte Carlo technique to single instruction multiple data (SMM) computer architectures are presented. In particular, implementation of the Ising model with nearest, next nearest, and long range screened Coulomb interactions on the SIMD architecture MasPar MP-1 (DEC mpp-12000) series of massively parallel computers is demonstrated. Methods of code development which optimize processor array use and minimize inter-processor communication are presented including lattice partitioning and the use of processor array spanning tree structures for data reduction. Both geometric and algorithmic parallel approaches are utilized. Benchmarks in terms of Monte Carlo updates per second for the MasPar architecture are presented and compared to values reported in the literature from comparable studies on other architectures.
Inhomogeneous Monte Carlo simulations of dermoscopic spectroscopy
Gareau, Daniel S.; Li, Ting; Jacques, Steven; Krueger, James
2012-03-01
Clinical skin-lesion diagnosis uses dermoscopy: 10X epiluminescence microscopy. Skin appearance ranges from black to white with shades of blue, red, gray and orange. Color is an important diagnostic criteria for diseases including melanoma. Melanin and blood content and distribution impact the diffuse spectral remittance (300-1000nm). Skin layers: immersion medium, stratum corneum, spinous epidermis, basal epidermis and dermis as well as laterally asymmetric features (eg. melanocytic invasion) were modeled in an inhomogeneous Monte Carlo model.
Handbook of Markov chain Monte Carlo
Brooks, Steve
2011-01-01
""Handbook of Markov Chain Monte Carlo"" brings together the major advances that have occurred in recent years while incorporating enough introductory material for new users of MCMC. Along with thorough coverage of the theoretical foundations and algorithmic and computational methodology, this comprehensive handbook includes substantial realistic case studies from a variety of disciplines. These case studies demonstrate the application of MCMC methods and serve as a series of templates for the construction, implementation, and choice of MCMC methodology.
Accelerated Monte Carlo by Embedded Cluster Dynamics
Brower, R. C.; Gross, N. A.; Moriarty, K. J. M.
1991-07-01
We present an overview of the new methods for embedding Ising spins in continuous fields to achieve accelerated cluster Monte Carlo algorithms. The methods of Brower and Tamayo and Wolff are summarized and variations are suggested for the O( N) models based on multiple embedded Z2 spin components and/or correlated projections. Topological features are discussed for the XY model and numerical simulations presented for d=2, d=3 and mean field theory lattices.
An introduction to Monte Carlo methods
Walter, J.-C.; Barkema, G. T.
2015-01-01
Monte Carlo simulations are methods for simulating statistical systems. The aim is to generate a representative ensemble of configurations to access thermodynamical quantities without the need to solve the system analytically or to perform an exact enumeration. The main principles of Monte Carlo simulations are ergodicity and detailed balance. The Ising model is a lattice spin system with nearest neighbor interactions that is appropriate to illustrate different examples of Monte Carlo simulations. It displays a second order phase transition between disordered (high temperature) and ordered (low temperature) phases, leading to different strategies of simulations. The Metropolis algorithm and the Glauber dynamics are efficient at high temperature. Close to the critical temperature, where the spins display long range correlations, cluster algorithms are more efficient. We introduce the rejection free (or continuous time) algorithm and describe in details an interesting alternative representation of the Ising model using graphs instead of spins with the so-called Worm algorithm. We conclude with an important discussion of the dynamical effects such as thermalization and correlation time.
Monte Carlo methods for multidimensional integration for European option pricing
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 methods for light propagation in biological tissues.
Vinckenbosch, Laura; Lacaux, Céline; Tindel, Samy; Thomassin, Magalie; Obara, Tiphaine
2015-11-01
Light propagation in turbid media is driven by the equation of radiative transfer. We give a formal probabilistic representation of its solution in the framework of biological tissues and we implement algorithms based on Monte Carlo methods in order to estimate the quantity of light that is received by a homogeneous tissue when emitted by an optic fiber. A variance reduction method is studied and implemented, as well as a Markov chain Monte Carlo method based on the Metropolis-Hastings algorithm. The resulting estimating methods are then compared to the so-called Wang-Prahl (or Wang) method. Finally, the formal representation allows to derive a non-linear optimization algorithm close to Levenberg-Marquardt that is used for the estimation of the scattering and absorption coefficients of the tissue from measurements.
Monte Carlo Study on Singly Tagged D Mesons at BES-Ⅲ
Institute of Scientific and Technical Information of China (English)
ZHAO Ming-Gang; YU Chun-Xu; LI Xue-Qian
2009-01-01
We present Monte Carlo studies on the singly tagged D mesons,which are crucial in the absolute measurements of D meson decays,based on a full Monte Carlo simulation for the BES-Ⅲ detector,with the BES-Ⅲ Offline Software System.The expected detection efficiencies and mass resolutions of the tagged D mesons are well estimated.
A zero-variance based scheme for Monte Carlo criticality simulations
Christoforou, S.
2010-01-01
The ability of the Monte Carlo method to solve particle transport problems by simulating the particle behaviour makes it a very useful technique in nuclear reactor physics. However, the statistical nature of Monte Carlo implies that there will always be a variance associated with the estimate obtain
Institute of Scientific and Technical Information of China (English)
万文应; 夏庆
2015-01-01
With the illustration of a specific problem, this paper demonstrates that using Monte Carlo Simulation technology will improve intuitive effect of teaching Probability and Mathematical Statistics course, and save instructors’ effort as well.And it is estimated that Monte Carlo Simulation technology will be one of the major teaching methods for Probability and Mathematical Statistics course in the future.
Strategies for CT tissue segmentation for Monte Carlo calculations in nuclear medicine dosimetry
DEFF Research Database (Denmark)
Braad, Poul-Erik; Andersen, Thomas; Hansen, Søren Baarsgaard;
2016-01-01
Purpose: CT images are used for patient specific Monte Carlo treatment planning in radionuclide therapy. The authors investigated the impact of tissue classification, CT image segmentation, and CT errors on Monte Carlo calculated absorbed dose estimates in nuclear medicine. Methods: CT errors...... patient specific dosimetry in nuclear medicine. Accurate dosimetry was obtained with a 13-tissue ramp that included five different bone types....
Guideline of Monte Carlo calculation. Neutron/gamma ray transport simulation by Monte Carlo method
2002-01-01
This report condenses basic theories and advanced applications of neutron/gamma ray transport calculations in many fields of nuclear energy research. Chapters 1 through 5 treat historical progress of Monte Carlo methods, general issues of variance reduction technique, cross section libraries used in continuous energy Monte Carlo codes. In chapter 6, the following issues are discussed: fusion benchmark experiments, design of ITER, experiment analyses of fast critical assembly, core analyses of JMTR, simulation of pulsed neutron experiment, core analyses of HTTR, duct streaming calculations, bulk shielding calculations, neutron/gamma ray transport calculations of the Hiroshima atomic bomb. Chapters 8 and 9 treat function enhancements of MCNP and MVP codes, and a parallel processing of Monte Carlo calculation, respectively. An important references are attached at the end of this report.
Díez, A; Largo, J; Solana, J R
2006-08-21
Computer simulations have been performed for fluids with van der Waals potential, that is, hard spheres with attractive inverse power tails, to determine the equation of state and the excess energy. On the other hand, the first- and second-order perturbative contributions to the energy and the zero- and first-order perturbative contributions to the compressibility factor have been determined too from Monte Carlo simulations performed on the reference hard-sphere system. The aim was to test the reliability of this "exact" perturbation theory. It has been found that the results obtained from the Monte Carlo perturbation theory for these two thermodynamic properties agree well with the direct Monte Carlo simulations. Moreover, it has been found that results from the Barker-Henderson [J. Chem. Phys. 47, 2856 (1967)] perturbation theory are in good agreement with those from the exact perturbation theory.
Energy Technology Data Exchange (ETDEWEB)
Richet, Y
2006-12-15
Criticality Monte Carlo calculations aim at estimating the effective multiplication factor (k-effective) for a fissile system through iterations simulating neutrons propagation (making a Markov chain). Arbitrary initialization of the neutron population can deeply bias the k-effective estimation, defined as the mean of the k-effective computed at each iteration. A simplified model of this cycle k-effective sequence is built, based on characteristics of industrial criticality Monte Carlo calculations. Statistical tests, inspired by Brownian bridge properties, are designed to discriminate stationarity of the cycle k-effective sequence. The initial detected transient is, then, suppressed in order to improve the estimation of the system k-effective. The different versions of this methodology are detailed and compared, firstly on a plan of numerical tests fitted on criticality Monte Carlo calculations, and, secondly on real criticality calculations. Eventually, the best methodologies observed in these tests are selected and allow to improve industrial Monte Carlo criticality calculations. (author)
Directory of Open Access Journals (Sweden)
Archana V
2014-05-01
Full Text Available Co-efficient of variation is a unitless measure of dispersion and is very frequently used in scientific investigations. This has motivated several researchers to propose estimators and tests concerning the co-efficient of variation of normal distribution(s. While proposing a class of estimators for the co-efficient of variation of a finite population, Tripathi et al., (2002 suggested that the estimator of co-efficient of variation of a finite population can also be used as an estimator of C.V for any distribution when the sampling design is SRSWR. This has motivated us to propose 28 estimators of finite population co-efficient of variation as estimators of co-efficient of variation of one component of a bivariate normal distribution when prior information is available regarding the second component. Cramer Rao type lower bound is derived to the mean square error of these estimators. Extensive simulation is carried out to compare these estimators. The results indicate that out of these 28 estimators, eight estimators have larger relative efficiency compared to the sample co-efficient of variation. The asymptotic mean square errors of the best estimators are derived to the order of for the benefit of users of co-efficient of variation.
Monte Carlo evaluation of derivative-based global sensitivity measures
Energy Technology Data Exchange (ETDEWEB)
Kucherenko, S. [Centre for Process Systems Engineering, Imperial College London, London SW7 2AZ (United Kingdom)], E-mail: s.kucherenko@ic.ac.uk; Rodriguez-Fernandez, M. [Process Engineering Group, Instituto de Investigaciones Marinas, Spanish Council for Scientific Research (C.S.I.C.), C/ Eduardo Cabello, 6, 36208 Vigo (Spain); Pantelides, C.; Shah, N. [Centre for Process Systems Engineering, Imperial College London, London SW7 2AZ (United Kingdom)
2009-07-15
A novel approach for evaluation of derivative-based global sensitivity measures (DGSM) is presented. It is compared with the Morris and the Sobol' sensitivity indices methods. It is shown that there is a link between DGSM and Sobol' sensitivity indices. DGSM are very easy to implement and evaluate numerically. The computational time required for numerical evaluation of DGSM is many orders of magnitude lower than that for estimation of the Sobol' sensitivity indices. It is also lower than that for the Morris method. Efficiencies of Monte Carlo (MC) and quasi-Monte Carlo (QMC) sampling methods for calculation of DGSM are compared. It is shown that the superiority of QMC over MC depends on the problem's effective dimension, which can also be estimated using DGSM.
Archana V; Aruna Rao K
2014-01-01
Co-efficient of variation is a unitless measure of dispersion and is very frequently used in scientific investigations. This has motivated several researchers to propose estimators and tests concerning the co-efficient of variation of normal distribution(s). While proposing a class of estimators for the co-efficient of variation of a finite population, Tripathi et al., (2002) suggested that the estimator of co-efficient of variation of a finite population can also be used as an estimator of C...
Quantum Monte Carlo with directed loops.
Syljuåsen, Olav F; Sandvik, Anders W
2002-10-01
We introduce the concept of directed loops in stochastic series expansion and path-integral quantum Monte Carlo methods. Using the detailed balance rules for directed loops, we show that it is possible to smoothly connect generally applicable simulation schemes (in which it is necessary to include backtracking processes in the loop construction) to more restricted loop algorithms that can be constructed only for a limited range of Hamiltonians (where backtracking can be avoided). The "algorithmic discontinuities" between general and special points (or regions) in parameter space can hence be eliminated. As a specific example, we consider the anisotropic S=1/2 Heisenberg antiferromagnet in an external magnetic field. We show that directed-loop simulations are very efficient for the full range of magnetic fields (zero to the saturation point) and anisotropies. In particular, for weak fields and anisotropies, the autocorrelations are significantly reduced relative to those of previous approaches. The back-tracking probability vanishes continuously as the isotropic Heisenberg point is approached. For the XY model, we show that back tracking can be avoided for all fields extending up to the saturation field. The method is hence particularly efficient in this case. We use directed-loop simulations to study the magnetization process in the two-dimensional Heisenberg model at very low temperatures. For LxL lattices with L up to 64, we utilize the step structure in the magnetization curve to extract gaps between different spin sectors. Finite-size scaling of the gaps gives an accurate estimate of the transverse susceptibility in the thermodynamic limit: chi( perpendicular )=0.0659+/-0.0002.
Planning Tunnel Construction Using Markov Chain Monte Carlo (MCMC)
Vargas, Juan P.; Koppe,Jair C.; Sebastián Pérez; Hurtado, Juan P.
2015-01-01
Tunnels, drifts, drives, and other types of underground excavation are very common in mining as well as in the construction of roads, railways, dams, and other civil engineering projects. Planning is essential to the success of tunnel excavation, and construction time is one of the most important factors to be taken into account. This paper proposes a simulation algorithm based on a stochastic numerical method, the Markov chain Monte Carlo method, that can provide the best estimate of the ope...
A simple introduction to Markov Chain Monte-Carlo sampling.
van Ravenzwaaij, Don; Cassey, Pete; Brown, Scott D
2016-03-11
Markov Chain Monte-Carlo (MCMC) is an increasingly popular method for obtaining information about distributions, especially for estimating posterior distributions in Bayesian inference. This article provides a very basic introduction to MCMC sampling. It describes what MCMC is, and what it can be used for, with simple illustrative examples. Highlighted are some of the benefits and limitations of MCMC sampling, as well as different approaches to circumventing the limitations most likely to trouble cognitive scientists.
Monte-Carlo Method for Coalbed Methane Resource Assessment in Key Coal Mining Areas of China
Institute of Scientific and Technical Information of China (English)
Yang Yongguo; Chen Yuhua; Qin Yong; Cheng Qiuming
2008-01-01
Monte-Carlo method is used for estimating coalbed methane (CBM) resources in key coal mining areas of China. Monte-Carlo method is shown to be superior to the traditional volumetric method with constant parameters in the calculation of CBM resources. The focus of the article is to introduce the main algorithm and the realization of functions estimated by Monte-Carlo method, including selection of parameters, determination of distribution function, generation of pseudo-random numbers, and evaluation of the parameters corresponding to pseudo-random numbers. A specified software on the basis of Monte-Carlo method is developed using Visual C++ for the assessment of the CBM resources. A case study shows that calculation results using Monte-Carlo method have smaller error range in comparison with those using volumetric method.
Seichter, Felicia; Vogt, Josef; Radermacher, Peter; Mizaikoff, Boris
2017-01-25
The calibration of analytical systems is time-consuming and the effort for daily calibration routines should therefore be minimized, while maintaining the analytical accuracy and precision. The 'calibration transfer' approach proposes to combine calibration data already recorded with actual calibrations measurements. However, this strategy was developed for the multivariate, linear analysis of spectroscopic data, and thus, cannot be applied to sensors with a single response channel and/or a non-linear relationship between signal and desired analytical concentration. To fill this gap for a non-linear calibration equation, we assume that the coefficients for the equation, collected over several calibration runs, are normally distributed. Considering that coefficients of an actual calibration are a sample of this distribution, only a few standards are needed for a complete calibration data set. The resulting calibration transfer approach is demonstrated for a fluorescence oxygen sensor and implemented as a hierarchical Bayesian model, combined with a Lagrange Multipliers technique and Monte-Carlo Markov-Chain sampling. The latter provides realistic estimates for coefficients and prediction together with accurate error bounds by simulating known measurement errors and system fluctuations. Performance criteria for validation and optimal selection of a reduced set of calibration samples were developed and lead to a setup which maintains the analytical performance of a full calibration. Strategies for a rapid determination of problems occurring in a daily calibration routine, are proposed, thereby opening the possibility of correcting the problem just in time.
Status of Monte-Carlo Event Generators
Energy Technology Data Exchange (ETDEWEB)
Hoeche, Stefan; /SLAC
2011-08-11
Recent progress on general-purpose Monte-Carlo event generators is reviewed with emphasis on the simulation of hard QCD processes and subsequent parton cascades. Describing full final states of high-energy particle collisions in contemporary experiments is an intricate task. Hundreds of particles are typically produced, and the reactions involve both large and small momentum transfer. The high-dimensional phase space makes an exact solution of the problem impossible. Instead, one typically resorts to regarding events as factorized into different steps, ordered descending in the mass scales or invariant momentum transfers which are involved. In this picture, a hard interaction, described through fixed-order perturbation theory, is followed by multiple Bremsstrahlung emissions off initial- and final-state and, finally, by the hadronization process, which binds QCD partons into color-neutral hadrons. Each of these steps can be treated independently, which is the basic concept inherent to general-purpose event generators. Their development is nowadays often focused on an improved description of radiative corrections to hard processes through perturbative QCD. In this context, the concept of jets is introduced, which allows to relate sprays of hadronic particles in detectors to the partons in perturbation theory. In this talk, we briefly review recent progress on perturbative QCD in event generation. The main focus lies on the general-purpose Monte-Carlo programs HERWIG, PYTHIA and SHERPA, which will be the workhorses for LHC phenomenology. A detailed description of the physics models included in these generators can be found in [8]. We also discuss matrix-element generators, which provide the parton-level input for general-purpose Monte Carlo.
Haba, Tomonobu; Koyama, Shuji; Ida, Yoshihiro
2014-01-01
The longitudinal dose profile in a computed tomography dose index (CTDI) phantom had been studied by many researchers. The cross-sectional dose profile in the CTDI phantom, however, has not been studied. It is also important to understand the cross-sectional dose profile in the CTDI phantom for dose estimation in X-ray CT. In this study, the cross-sectional dose profile in the CTDI phantom was calculated by use of a Monte Carlo (MC) simulation method. A helical or a 320-detector-row cone-beam X-ray CT scanner was simulated. The cross-sectional dose profile in the CTDI phantom from surface to surface through the center point was calculated by MC simulation. The shape of the calculation region was a cylinder of 1-mm-diameter. The length of the cylinder was 23, 100, or 300 mm to represent various CT ionization chamber lengths. Detailed analyses of the energy depositions demonstrated that the cross-sectional dose profile was different in measurement methods and phantom sizes. In this study, we also focused on the validation of the weighting factor used in weighted CTDI (CTDI w ). As it stands now, the weighting factor used in CTDI w is (1/3, 2/3) for the (central, peripheral) axes. Our results showed that an equal weighting factor, which is (1/2, 1/2) for the (central, peripheral) axes, is more suitable to estimate the average cross-sectional dose when X-ray CT dose estimation is performed.
A Monte Carlo algorithm for degenerate plasmas
Energy Technology Data Exchange (ETDEWEB)
Turrell, A.E., E-mail: a.turrell09@imperial.ac.uk; Sherlock, M.; Rose, S.J.
2013-09-15
A procedure for performing Monte Carlo calculations of plasmas with an arbitrary level of degeneracy is outlined. It has possible applications in inertial confinement fusion and astrophysics. Degenerate particles are initialised according to the Fermi–Dirac distribution function, and scattering is via a Pauli blocked binary collision approximation. The algorithm is tested against degenerate electron–ion equilibration, and the degenerate resistivity transport coefficient from unmagnetised first order transport theory. The code is applied to the cold fuel shell and alpha particle equilibration problem of inertial confinement fusion.
Archimedes, the Free Monte Carlo simulator
Sellier, Jean Michel D
2012-01-01
Archimedes is the GNU package for Monte Carlo simulations of electron transport in semiconductor devices. The first release appeared in 2004 and since then it has been improved with many new features like quantum corrections, magnetic fields, new materials, GUI, etc. This document represents the first attempt to have a complete manual. Many of the Physics models implemented are described and a detailed description is presented to make the user able to write his/her own input deck. Please, feel free to contact the author if you want to contribute to the project.
Cluster hybrid Monte Carlo simulation algorithms
Plascak, J. A.; Ferrenberg, Alan M.; Landau, D. P.
2002-06-01
We show that addition of Metropolis single spin flips to the Wolff cluster-flipping Monte Carlo procedure leads to a dramatic increase in performance for the spin-1/2 Ising model. We also show that adding Wolff cluster flipping to the Metropolis or heat bath algorithms in systems where just cluster flipping is not immediately obvious (such as the spin-3/2 Ising model) can substantially reduce the statistical errors of the simulations. A further advantage of these methods is that systematic errors introduced by the use of imperfect random-number generation may be largely healed by hybridizing single spin flips with cluster flipping.
Introduction to Cluster Monte Carlo Algorithms
Luijten, E.
This chapter provides an introduction to cluster Monte Carlo algorithms for classical statistical-mechanical systems. A brief review of the conventional Metropolis algorithm is given, followed by a detailed discussion of the lattice cluster algorithm developed by Swendsen and Wang and the single-cluster variant introduced by Wolff. For continuum systems, the geometric cluster algorithm of Dress and Krauth is described. It is shown how their geometric approach can be generalized to incorporate particle interactions beyond hardcore repulsions, thus forging a connection between the lattice and continuum approaches. Several illustrative examples are discussed.
Monte Carlo simulation for the transport beamline
Energy Technology Data Exchange (ETDEWEB)
Romano, F.; Cuttone, G.; Jia, S. B.; Varisano, A. [INFN, Laboratori Nazionali del Sud, Via Santa Sofia 62, Catania (Italy); Attili, A.; Marchetto, F.; Russo, G. [INFN, Sezione di Torino, Via P.Giuria, 1 10125 Torino (Italy); Cirrone, G. A. P.; Schillaci, F.; Scuderi, V. [INFN, Laboratori Nazionali del Sud, Via Santa Sofia 62, Catania, Italy and Institute of Physics Czech Academy of Science, ELI-Beamlines project, Na Slovance 2, Prague (Czech Republic); Carpinelli, M. [INFN Sezione di Cagliari, c/o Dipartimento di Fisica, Università di Cagliari, Cagliari (Italy); Tramontana, A. [INFN, Laboratori Nazionali del Sud, Via Santa Sofia 62, Catania, Italy and Università di Catania, Dipartimento di Fisica e Astronomia, Via S. Sofia 64, Catania (Italy)
2013-07-26
In the framework of the ELIMED project, Monte Carlo (MC) simulations are widely used to study the physical transport of charged particles generated by laser-target interactions and to preliminarily evaluate fluence and dose distributions. An energy selection system and the experimental setup for the TARANIS laser facility in Belfast (UK) have been already simulated with the GEANT4 (GEometry ANd Tracking) MC toolkit. Preliminary results are reported here. Future developments are planned to implement a MC based 3D treatment planning in order to optimize shots number and dose delivery.
Mosaic crystal algorithm for Monte Carlo simulations
Seeger, P A
2002-01-01
An algorithm is presented for calculating reflectivity, absorption, and scattering of mosaic crystals in Monte Carlo simulations of neutron instruments. The algorithm uses multi-step transport through the crystal with an exact solution of the Darwin equations at each step. It relies on the kinematical model for Bragg reflection (with parameters adjusted to reproduce experimental data). For computation of thermal effects (the Debye-Waller factor and coherent inelastic scattering), an expansion of the Debye integral as a rapidly converging series of exponential terms is also presented. Any crystal geometry and plane orientation may be treated. The algorithm has been incorporated into the neutron instrument simulation package NISP. (orig.)
Diffusion quantum Monte Carlo for molecules
Energy Technology Data Exchange (ETDEWEB)
Lester, W.A. Jr.
1986-07-01
A quantum mechanical Monte Carlo method has been used for the treatment of molecular problems. The imaginary-time Schroedinger equation written with a shift in zero energy (E/sub T/ - V(R)) can be interpreted as a generalized diffusion equation with a position-dependent rate or branching term. Since diffusion is the continuum limit of a random walk, one may simulate the Schroedinger equation with a function psi (note, not psi/sup 2/) as a density of ''walks.'' The walks undergo an exponential birth and death as given by the rate term. 16 refs., 2 tabs.
Energy Technology Data Exchange (ETDEWEB)
Marcus, Ryan C. [Los Alamos National Laboratory
2012-07-24
Overview of this presentation is (1) Exascale computing - different technologies, getting there; (2) high-performance proof-of-concept MCMini - features and results; and (3) OpenCL toolkit - Oatmeal (OpenCL Automatic Memory Allocation Library) - purpose and features. Despite driver issues, OpenCL seems like a good, hardware agnostic tool. MCMini demonstrates the possibility for GPGPU-based Monte Carlo methods - it shows great scaling for HPC application and algorithmic equivalence. Oatmeal provides a flexible framework to aid in the development of scientific OpenCL codes.
State-of-the-art Monte Carlo 1988
Energy Technology Data Exchange (ETDEWEB)
Soran, P.D.
1988-06-28
Particle transport calculations in highly dimensional and physically complex geometries, such as detector calibration, radiation shielding, space reactors, and oil-well logging, generally require Monte Carlo transport techniques. Monte Carlo particle transport can be performed on a variety of computers ranging from APOLLOs to VAXs. Some of the hardware and software developments, which now permit Monte Carlo methods to be routinely used, are reviewed in this paper. The development of inexpensive, large, fast computer memory, coupled with fast central processing units, permits Monte Carlo calculations to be performed on workstations, minicomputers, and supercomputers. The Monte Carlo renaissance is further aided by innovations in computer architecture and software development. Advances in vectorization and parallelization architecture have resulted in the development of new algorithms which have greatly reduced processing times. Finally, the renewed interest in Monte Carlo has spawned new variance reduction techniques which are being implemented in large computer codes. 45 refs.
Dai, Yunyun
2013-01-01
Mixtures of item response theory (IRT) models have been proposed as a technique to explore response patterns in test data related to cognitive strategies, instructional sensitivity, and differential item functioning (DIF). Estimation proves challenging due to difficulties in identification and questions of effect size needed to recover underlying…
Schabel, Matthias C; Fluckiger, Jacob U; DiBella, Edward V R
2010-08-21
Widespread adoption of quantitative pharmacokinetic modeling methods in conjunction with dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) has led to increased recognition of the importance of obtaining accurate patient-specific arterial input function (AIF) measurements. Ideally, DCE-MRI studies use an AIF directly measured in an artery local to the tissue of interest, along with measured tissue concentration curves, to quantitatively determine pharmacokinetic parameters. However, the numerous technical and practical difficulties associated with AIF measurement have made the use of population-averaged AIF data a popular, if sub-optimal, alternative to AIF measurement. In this work, we present and characterize a new algorithm for determining the AIF solely from the measured tissue concentration curves. This Monte Carlo blind estimation (MCBE) algorithm estimates the AIF from the subsets of D concentration-time curves drawn from a larger pool of M candidate curves via nonlinear optimization, doing so for multiple (Q) subsets and statistically averaging these repeated estimates. The MCBE algorithm can be viewed as a generalization of previously published methods that employ clustering of concentration-time curves and only estimate the AIF once. Extensive computer simulations were performed over physiologically and experimentally realistic ranges of imaging and tissue parameters, and the impact of choosing different values of D and Q was investigated. We found the algorithm to be robust, computationally efficient and capable of accurately estimating the AIF even for relatively high noise levels, long sampling intervals and low diversity of tissue curves. With the incorporation of bootstrapping initialization, we further demonstrated the ability to blindly estimate AIFs that deviate substantially in shape from the population-averaged initial guess. Pharmacokinetic parameter estimates for K(trans), k(ep), v(p) and v(e) all showed relative biases and
Monte Carlo Simulations: Number of Iterations and Accuracy
2015-07-01
Jessica Schultheis for her editorial review. vi INTENTIONALLY LEFT BLANK. 1 1. Introduction Monte Carlo (MC) methods1 are often used...ARL-TN-0684 ● JULY 2015 US Army Research Laboratory Monte Carlo Simulations: Number of Iterations and Accuracy by William...needed. Do not return it to the originator. ARL-TN-0684 ● JULY 2015 US Army Research Laboratory Monte Carlo Simulations: Number
Discrete diffusion Monte Carlo for frequency-dependent radiative transfer
Energy Technology Data Exchange (ETDEWEB)
Densmore, Jeffrey D [Los Alamos National Laboratory; Kelly, Thompson G [Los Alamos National Laboratory; Urbatish, Todd J [Los Alamos National Laboratory
2010-11-17
Discrete Diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Implicit Monte Carlo radiative-transfer simulations. In this paper, we develop an extension of DDMC for frequency-dependent radiative transfer. We base our new DDMC method on a frequency-integrated diffusion equation for frequencies below a specified threshold. Above this threshold we employ standard Monte Carlo. With a frequency-dependent test problem, we confirm the increased efficiency of our new DDMC technique.
Alternative Monte Carlo Approach for General Global Illumination
Institute of Scientific and Technical Information of China (English)
徐庆; 李朋; 徐源; 孙济洲
2004-01-01
An alternative Monte Carlo strategy for the computation of global illumination problem was presented.The proposed approach provided a new and optimal way for solving Monte Carlo global illumination based on the zero variance importance sampling procedure. A new importance driven Monte Carlo global illumination algorithm in the framework of the new computing scheme was developed and implemented. Results, which were obtained by rendering test scenes, show that this new framework and the newly derived algorithm are effective and promising.
Validation of Compton Scattering Monte Carlo Simulation Models
Weidenspointner, Georg; Hauf, Steffen; Hoff, Gabriela; Kuster, Markus; Pia, Maria Grazia; Saracco, Paolo
2014-01-01
Several models for the Monte Carlo simulation of Compton scattering on electrons are quantitatively evaluated with respect to a large collection of experimental data retrieved from the literature. Some of these models are currently implemented in general purpose Monte Carlo systems; some have been implemented and evaluated for possible use in Monte Carlo particle transport for the first time in this study. Here we present first and preliminary results concerning total and differential Compton scattering cross sections.
Cluster Monte Carlo methods for the FePt Hamiltonian
Lyberatos, A.; Parker, G. J.
2016-02-01
Cluster Monte Carlo methods for the classical spin Hamiltonian of FePt with long range exchange interactions are presented. We use a combination of the Swendsen-Wang (or Wolff) and Metropolis algorithms that satisfies the detailed balance condition and ergodicity. The algorithms are tested by calculating the temperature dependence of the magnetization, susceptibility and heat capacity of L10-FePt nanoparticles in a range including the critical region. The cluster models yield numerical results in good agreement within statistical error with the standard single-spin flipping Monte Carlo method. The variation of the spin autocorrelation time with grain size is used to deduce the dynamic exponent of the algorithms. Our cluster models do not provide a more accurate estimate of the magnetic properties at equilibrium.
Multiple Monte Carlo Testing with Applications in Spatial Point Processes
DEFF Research Database (Denmark)
Mrkvička, Tomáš; Myllymäki, Mari; Hahn, Ute
with a function as the test statistic, 3) several Monte Carlo tests with functions as test statistics. The rank test has correct (global) type I error in each case and it is accompanied with a p-value and with a graphical interpretation which shows which subtest or which distances of the used test function......The rank envelope test (Myllym\\"aki et al., Global envelope tests for spatial processes, arXiv:1307.0239 [stat.ME]) is proposed as a solution to multiple testing problem for Monte Carlo tests. Three different situations are recognized: 1) a few univariate Monte Carlo tests, 2) a Monte Carlo test...
Thorn, Graeme J; King, John R
2016-01-01
The Gram-positive bacterium Clostridium acetobutylicum is an anaerobic endospore-forming species which produces acetone, butanol and ethanol via the acetone-butanol (AB) fermentation process, leading to biofuels including butanol. In previous work we looked to estimate the parameters in an ordinary differential equation model of the glucose metabolism network using data from pH-controlled continuous culture experiments. Here we combine two approaches, namely the approximate Bayesian computation via an existing sequential Monte Carlo (ABC-SMC) method (to compute credible intervals for the parameters), and the profile likelihood estimation (PLE) (to improve the calculation of confidence intervals for the same parameters), the parameters in both cases being derived from experimental data from forward shift experiments. We also apply the ABC-SMC method to investigate which of the models introduced previously (one non-sporulation and four sporulation models) have the greatest strength of evidence. We find that the joint approximate posterior distribution of the parameters determines the same parameters as previously, including all of the basal and increased enzyme production rates and enzyme reaction activity parameters, as well as the Michaelis-Menten kinetic parameters for glucose ingestion, while other parameters are not as well-determined, particularly those connected with the internal metabolites acetyl-CoA, acetoacetyl-CoA and butyryl-CoA. We also find that the approximate posterior is strongly non-Gaussian, indicating that our previous assumption of elliptical contours of the distribution is not valid, which has the effect of reducing the numbers of pairs of parameters that are (linearly) correlated with each other. Calculations of confidence intervals using the PLE method back this up. Finally, we find that all five of our models are equally likely, given the data available at present. Copyright © 2015 Elsevier Inc. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Yakoumakis, Emmanuel; Kostopoulou, Helen; Dimitriadis, Anastastios; Georgiou, Evaggelos [University of Athens, Medical Physics Department, Medical School, Athens (Greece); Makri, Triantafilia [' Agia Sofia' Hospital, Medical Physics Unit, Athens (Greece); Tsalafoutas, Ioannis [Anticancer-Oncology Hospital of Athens ' Agios Savvas' , Medical Physics Department, Athens (Greece)
2013-03-15
Children diagnosed with congenital heart disease often undergo cardiac catheterization for their treatment, which involves the use of ionizing radiation and therefore a risk of radiation-induced cancer. The purpose of this study was to calculate the effective and equivalent organ doses (H{sub T}) in those children and estimate the risk of exposure-induced death. Fifty-three children were divided into three groups: atrial septal defect (ASD), ventricular septal defect (VSD) and patent ductus arteriosus (PDA). In all procedures, the exposure conditions and the dose-area product meters readings were recorded for each individual acquisition. Monte Carlo simulations were run using the PCXMC 2.0 code and mathematical phantoms simulating a child's anatomy. The H{sub T} values to all irradiated organs and the resulting E and risk of exposure-induced death values were calculated. The average dose-area product values were, respectively, 40 {+-} 12 Gy.cm{sup 2} for the ASD, 17.5 {+-} 0.7 Gy.cm{sup 2} for the VSD and 9.5 {+-} 1 Gy.cm{sup 2} for the PDA group. The average E values were 40 {+-} 12, 22 {+-} 2.5 and 17 {+-} 3.6 mSv for ASD, VSD and PDA groups, respectively. The respective estimated risk of exposure-induced death values per procedure were 0.109, 0.106 and 0.067%. Cardiac catheterizations in children involve a considerable risk for radiation-induced cancer that has to be further reduced. (orig.)
Legchenko, Anatoly; Comte, Jean-Christophe; Ofterdinger, Ulrich; Vouillamoz, Jean-Michel; Lawson, Fabrice Messan Amen; Walsh, John
2017-09-01
We propose a simple and robust approach for investigating uncertainty in the results of inversion in geophysics. We apply this approach to inversion of Surface Nuclear Magnetic Resonance (SNMR) data, which is also known as Magnetic Resonance Sounding (MRS). Solution of this inverse problem is known to be non-unique. We inverse MRS data using the well-known Tikhonov regularization method, which provides an optimal solution as a trade-off between the stability and accuracy. Then, we perturb this model by random values and compute the fitting error for the perturbed models. The magnitude of these perturbations is limited by the uncertainty estimated with the singular value decomposition (SVD) and taking into account experimental errors. We use 106 perturbed models and show that the large majority of these models, which have all the water content within the variations given by the SVD estimate, do not fit data with an acceptable accuracy. Thus, we may limit the solution space by only the equivalent inverse models that fit data with the accuracy close to that of the initial inverse model. For representing inversion results, we use three equivalent solutions instead of the only one: the ;best; solution given by the regularization or other inversion technic and the extreme variations of this solution corresponding to the equivalent models with the minimum and the maximum volume of water. For demonstrating our approach, we use synthetic data sets and experimental data acquired in the framework of investigation of a hard rock aquifer in the Ireland (County Donegal).
THE MCNPX MONTE CARLO RADIATION TRANSPORT CODE
Energy Technology Data Exchange (ETDEWEB)
WATERS, LAURIE S. [Los Alamos National Laboratory; MCKINNEY, GREGG W. [Los Alamos National Laboratory; DURKEE, JOE W. [Los Alamos National Laboratory; FENSIN, MICHAEL L. [Los Alamos National Laboratory; JAMES, MICHAEL R. [Los Alamos National Laboratory; JOHNS, RUSSELL C. [Los Alamos National Laboratory; PELOWITZ, DENISE B. [Los Alamos National Laboratory
2007-01-10
MCNPX (Monte Carlo N-Particle eXtended) is a general-purpose Monte Carlo radiation transport code with three-dimensional geometry and continuous-energy transport of 34 particles and light ions. It contains flexible source and tally options, interactive graphics, and support for both sequential and multi-processing computer platforms. MCNPX is based on MCNP4B, and has been upgraded to most MCNP5 capabilities. MCNP is a highly stable code tracking neutrons, photons and electrons, and using evaluated nuclear data libraries for low-energy interaction probabilities. MCNPX has extended this base to a comprehensive set of particles and light ions, with heavy ion transport in development. Models have been included to calculate interaction probabilities when libraries are not available. Recent additions focus on the time evolution of residual nuclei decay, allowing calculation of transmutation and delayed particle emission. MCNPX is now a code of great dynamic range, and the excellent neutronics capabilities allow new opportunities to simulate devices of interest to experimental particle physics; particularly calorimetry. This paper describes the capabilities of the current MCNPX version 2.6.C, and also discusses ongoing code development.
Multi-Index Monte Carlo (MIMC)
Haji Ali, Abdul Lateef
2015-01-07
We propose and analyze a novel Multi-Index Monte Carlo (MIMC) method for weak approximation of stochastic models that are described in terms of differential equations either driven by random measures or with random coefficients. The MIMC method is both a stochastic version of the combination technique introduced by Zenger, Griebel and collaborators and an extension of the Multilevel Monte Carlo (MLMC) method first described by Heinrich and Giles. Inspired by Giles’s seminal work, instead of using first-order differences as in MLMC, we use in MIMC high-order mixed differences to reduce the variance of the hierarchical differences dramatically. Under standard assumptions on the convergence rates of the weak error, variance and work per sample, the optimal index set turns out to be of Total Degree (TD) type. When using such sets, MIMC yields new and improved complexity results, which are natural generalizations of Giles’s MLMC analysis, and which increase the domain of problem parameters for which we achieve the optimal convergence.
Chemical application of diffusion quantum Monte Carlo
Reynolds, P. J.; Lester, W. A., Jr.
1983-10-01
The diffusion quantum Monte Carlo (QMC) method gives a stochastic solution to the Schroedinger equation. As an example the singlet-triplet splitting of the energy of the methylene molecule CH2 is given. The QMC algorithm was implemented on the CYBER 205, first as a direct transcription of the algorithm running on our 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 is discussed. Since CH2 has only eight electrons, most of the loops in this application are fairly short. The longest inner loops run over the set of atomic basis functions. The CPU time dependence obtained versus the number of basis functions is discussed and compared with that obtained from traditional quantum chemistry codes and that obtained from traditional computer architectures. Finally, preliminary work on restructuring the algorithm to compute the separate Monte Carlo realizations in parallel is discussed.
Multi-Index Monte Carlo (MIMC)
Haji Ali, Abdul Lateef
2016-01-06
We propose and analyze a novel Multi-Index Monte Carlo (MIMC) method for weak approximation of stochastic models that are described in terms of differential equations either driven by random measures or with random coefficients. The MIMC method is both a stochastic version of the combination technique introduced by Zenger, Griebel and collaborators and an extension of the Multilevel Monte Carlo (MLMC) method first described by Heinrich and Giles. Inspired by Giles s seminal work, instead of using first-order differences as in MLMC, we use in MIMC high-order mixed differences to reduce the variance of the hierarchical differences dramatically. Under standard assumptions on the convergence rates of the weak error, variance and work per sample, the optimal index set turns out to be of Total Degree (TD) type. When using such sets, MIMC yields new and improved complexity results, which are natural generalizations of Giles s MLMC analysis, and which increase the domain of problem parameters for which we achieve the optimal convergence, O(TOL-2).
Discrete range clustering using Monte Carlo methods
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.
Information Geometry and Sequential Monte Carlo
Sim, Aaron; Stumpf, Michael P H
2012-01-01
This paper explores the application of methods from information geometry to the sequential Monte Carlo (SMC) sampler. In particular the Riemannian manifold Metropolis-adjusted Langevin algorithm (mMALA) is adapted for the transition kernels in SMC. Similar to its function in Markov chain Monte Carlo methods, the mMALA is a fully adaptable kernel which allows for efficient sampling of high-dimensional and highly correlated parameter spaces. We set up the theoretical framework for its use in SMC with a focus on the application to the problem of sequential Bayesian inference for dynamical systems as modelled by sets of ordinary differential equations. In addition, we argue that defining the sequence of distributions on geodesics optimises the effective sample sizes in the SMC run. We illustrate the application of the methodology by inferring the parameters of simulated Lotka-Volterra and Fitzhugh-Nagumo models. In particular we demonstrate that compared to employing a standard adaptive random walk kernel, the SM...
Ivančič, Matic; Naglič, Peter; Likar, Boštjan; Pernuš, Franjo; Bürmen, Miran
2017-02-01
For a given experimental setting, the measured spatially resolved reflectance rapidly drops with decreasing numerical aperture of the detection scheme. Consequently, for detection schemes with small numerical apertures, the computational time of MC simulations required to obtain adequate signal-to-noise ratio of the spatially resolved reflectance can become very long. We mitigate the issue by virtually increasing the numerical aperture of the detection scheme in MC simulations and devise a criterion for robust estimation of its maximum value. By using the proposed methodology, we show that the acceptance angle of a selected imaging system can be virtually increased from 3 to 11 while preserving a low relative error of the simulated spatially resolved reflectance over a wide range of tissue-like optical properties. As a result, a more than eightfold improvement in the computation time is attained.
Quantum Monte Carlo Endstation for Petascale Computing
Energy Technology Data Exchange (ETDEWEB)
Lubos Mitas
2011-01-26
NCSU research group has been focused on accomplising the key goals of this initiative: establishing new generation of quantum Monte Carlo (QMC) computational tools as a part of Endstation petaflop initiative for use at the DOE ORNL computational facilities and for use by computational electronic structure community at large; carrying out high accuracy quantum Monte Carlo demonstration projects in application of these tools to the forefront electronic structure problems in molecular and solid systems; expanding the impact of QMC methods and approaches; explaining and enhancing the impact of these advanced computational approaches. In particular, we have developed quantum Monte Carlo code (QWalk, www.qwalk.org) which was significantly expanded and optimized using funds from this support and at present became an actively used tool in the petascale regime by ORNL researchers and beyond. These developments have been built upon efforts undertaken by the PI's group and collaborators over the period of the last decade. The code was optimized and tested extensively on a number of parallel architectures including petaflop ORNL Jaguar machine. We have developed and redesigned a number of code modules such as evaluation of wave functions and orbitals, calculations of pfaffians and introduction of backflow coordinates together with overall organization of the code and random walker distribution over multicore architectures. We have addressed several bottlenecks such as load balancing and verified efficiency and accuracy of the calculations with the other groups of the Endstation team. The QWalk package contains about 50,000 lines of high quality object-oriented C++ and includes also interfaces to data files from other conventional electronic structure codes such as Gamess, Gaussian, Crystal and others. This grant supported PI for one month during summers, a full-time postdoc and partially three graduate students over the period of the grant duration, it has resulted in 13
Chemical accuracy from quantum Monte Carlo for the benzene dimer
Energy Technology Data Exchange (ETDEWEB)
Azadi, Sam, E-mail: s.azadi@ucl.ac.uk [Department of Earth Science and Thomas Young Centre, University College London, London WC1E 6BT (United Kingdom); Cohen, R. E. [London Centre for Nanotechnology, University College London, London WC1E 6BT, United Kingdom and Extreme Materials Initiative, Geophysical Laboratory, Carnegie Institution of Washington, Washington, D.C. 20015 (United States)
2015-09-14
We report an accurate study of interactions between benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory using different van der Waals functionals. In our quantum Monte Carlo (QMC) calculations, we use accurate correlated trial wave functions including three-body Jastrow factors and backflow transformations. We consider two benzene molecules in the parallel displaced geometry, and find that by highly optimizing the wave function and introducing more dynamical correlation into the wave function, we compute the weak chemical binding energy between aromatic rings accurately. We find optimal VMC and DMC binding energies of −2.3(4) and −2.7(3) kcal/mol, respectively. The best estimate of the coupled-cluster theory through perturbative triplets/complete basis set limit is −2.65(2) kcal/mol [Miliordos et al., J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate that QMC methods give chemical accuracy for weakly bound van der Waals molecular interactions, comparable to results from the best quantum chemistry methods.
A semianalytic Monte Carlo code for modelling LIDAR measurements
Palazzi, Elisa; Kostadinov, Ivan; Petritoli, Andrea; Ravegnani, Fabrizio; Bortoli, Daniele; Masieri, Samuele; Premuda, Margherita; Giovanelli, Giorgio
2007-10-01
LIDAR (LIght Detection and Ranging) is an optical active remote sensing technology with many applications in atmospheric physics. Modelling of LIDAR measurements appears useful approach for evaluating the effects of various environmental variables and scenarios as well as of different measurement geometries and instrumental characteristics. In this regard a Monte Carlo simulation model can provide a reliable answer to these important requirements. A semianalytic Monte Carlo code for modelling LIDAR measurements has been developed at ISAC-CNR. The backscattered laser signal detected by the LIDAR system is calculated in the code taking into account the contributions due to the main atmospheric molecular constituents and aerosol particles through processes of single and multiple scattering. The contributions by molecular absorption, ground and clouds reflection are evaluated too. The code can perform simulations of both monostatic and bistatic LIDAR systems. To enhance the efficiency of the Monte Carlo simulation, analytical estimates and expected value calculations are performed. Artificial devices (such as forced collision, local forced collision, splitting and russian roulette) are moreover foreseen by the code, which can enable the user to drastically reduce the variance of the calculation.
FAST CONVERGENT MONTE CARLO RECEIVER FOR OFDM SYSTEMS
Institute of Scientific and Technical Information of China (English)
Wu Lili; Liao Guisheng; Bao Zheng; Shang Yong
2005-01-01
The paper investigates the problem of the design of an optimal Orthogonal Frequency Division Multiplexing (OFDM) receiver against unknown frequency selective fading. A fast convergent Monte Carlo receiver is proposed. In the proposed method, the Markov Chain Monte Carlo (MCMC) methods are employed for the blind Bayesian detection without channel estimation. Meanwhile, with the exploitation of the characteristics of OFDM systems, two methods are employed to improve the convergence rate and enhance the efficiency of MCMC algorithms.One is the integration of the posterior distribution function with respect to the associated channel parameters, which is involved in the derivation of the objective distribution function; the other is the intra-symbol differential coding for the elimination of the bimodality problem resulting from the presence of unknown fading channels. Moreover, no matrix inversion is needed with the use of the orthogonality property of OFDM modulation and hence the computational load is significantly reduced. Computer simulation results show the effectiveness of the fast convergent Monte Carlo receiver.
Cluster Monte Carlo methods for the FePt Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Lyberatos, A., E-mail: lyb@materials.uoc.gr [Materials Science and Technology Department, P.O. Box 2208, 71003 Heraklion (Greece); Parker, G.J. [HGST, A Western Digital Company, 3403 Yerba Buena Road, San Jose, CA 95135 (United States)
2016-02-15
Cluster Monte Carlo methods for the classical spin Hamiltonian of FePt with long range exchange interactions are presented. We use a combination of the Swendsen–Wang (or Wolff) and Metropolis algorithms that satisfies the detailed balance condition and ergodicity. The algorithms are tested by calculating the temperature dependence of the magnetization, susceptibility and heat capacity of L1{sub 0}-FePt nanoparticles in a range including the critical region. The cluster models yield numerical results in good agreement within statistical error with the standard single-spin flipping Monte Carlo method. The variation of the spin autocorrelation time with grain size is used to deduce the dynamic exponent of the algorithms. Our cluster models do not provide a more accurate estimate of the magnetic properties at equilibrium. - Highlights: • A new cluster Monte Carlo algorithm was applied to FePt nanoparticles. • Magnetic anisotropy imposes a restriction on cluster moves. • Inclusion of Metropolis steps is required to satisfy ergodicity. • In the critical region a percolating cluster occurs for any grain size. • Critical slowing down is not solved by the new cluster algorithms.
Haba, Tomonobu; Koyama, Shuji; Kinomura, Yutaka; Ida, Yoshihiro; Kobayashi, Masanao
2016-09-01
The American Association of Physicists in Medicine (AAPM) task group 204 has recommended the use of size-dependent conversion factors to calculate size-specific dose estimate (SSDE) values from volume computed tomography dose index (CTDIvol) values. However, these conversion factors do not consider the effects of 320-detector-row volume computed tomography (CT) examinations or the new CT dosimetry metrics proposed by AAPM task group 111. This study aims to investigate the influence of these examinations and metrics on the conversion factors reported by AAPM task group 204, using Monte Carlo simulations. Simulations were performed modelling a Toshiba Aquilion ONE CT scanner, in order to compute dose values in water for cylindrical phantoms with 8-40-cm diameters at 2-cm intervals for each scanning parameter (tube voltage, bow-tie filter, longitudinal beam width). Then, the conversion factors were obtained by applying exponential regression analysis between the dose values for a given phantom diameter and the phantom diameter combined with various scanning parameters. The conversion factors for each scanning method (helical, axial, or volume scanning) and CT dosimetry method (i.e., the CTDI100 method or the AAPM task group 111 method) were in agreement with those reported by AAPM task group 204, within a percentage error of 14.2 % for phantom diameters ≥11.2 cm. The results obtained in this study indicate that the conversion factors previously presented by AAPM task group 204 can be used to provide appropriate SSDE values for 320-detector-row volume CT examinations and the CT dosimetry metrics proposed by the AAPM task group 111.
A Monte Carlo study on multiple output stochastic frontiers
DEFF Research Database (Denmark)
Henningsen, Geraldine; Henningsen, Arne; Jensen, Uwe
2015-01-01
In the estimation of multiple output technologies in a primal approach, the mainquestion is how to handle the multiple outputs. Often, an output distance function is used,where the classical approach is to exploit its homogeneity property by selecting one outputquantity as the dependent variable...... as directional components asregressors. A number of studies have compared these specifications using real world dataand have found significant differences in the inefficiency estimates. However, in order to getto the bottom of these differences, we apply a Monte-Carlo simulation. We test the robustnessof both...
Directory of Open Access Journals (Sweden)
Marcelo Angelo Cirillo
2010-07-01
Full Text Available A inferencia estatistica em populacoes binomiais contaminadas esta sujeita a erros grosseiros de estimacao, uma vez que as amostras nao sao identicamente distribuidas. Por esse problema, este trabalho tem por objetivo determinar qual a melhor constante de afinidade (c1 que proporcione melhor desempenho em um estimador pertencente a classedos estimadores-E. Com esse proposito, neste trabalho, foi utilizada a metodologia, considerando-se o metodo de simulacao Monte Carlo, no qual diferentes configuracoes descritas pela combinacao de valores parametricos, niveis de contaminacao e tamanhos de amostra foram avaliados. Concluiu-se que, para alta probabilidade de mistura (ƒÁ = 0,40, recomenda-se assumir c1 = 0,1 nas situacoes de grandes amostras (n = 50 e n = 80. The statistical inference in binomial population is subject to gross errors of estimate, as the samples are not identically distributed. Due to this problem, this work aims to determine which is the best affinity constant (c1 that provides the best performance in the estimator, belonging to the class of E-estimators. With that purpose, the methodology used in this work was applied considering the Monte Carlo simulation method, in which different configurations described by combination of parametric values, levels of contamination and sample sizes were appraised. It was concluded that for the high probability of contamination (ƒÁ = 0.40, c1 = 0.1 is recommended in cases with large samples (n = 50 and n = 80.
Momennezhad, Mehdi; Nasseri, Shahrokh; Zakavi, Seyed Rasoul; Parach, Ali Asghar; Ghorbani, Mahdi; Asl, Ruhollah Ghahraman
2016-01-01
Single-photon emission computed tomography (SPECT)-based tracers are easily available and more widely used than positron emission tomography (PET)-based tracers, and SPECT imaging still remains the most prevalent nuclear medicine imaging modality worldwide. The aim of this study is to implement an image-based Monte Carlo method for patient-specific three-dimensional (3D) absorbed dose calculation in patients after injection of (99m)Tc-hydrazinonicotinamide (hynic)-Tyr(3)-octreotide as a SPECT radiotracer. (99m)Tc patient-speciﬁc S values and the absorbed doses were calculated with GATE code for each source-target organ pair in four patients who were imaged for suspected neuroendocrine tumors. Each patient underwent multiple whole-body planar scans as well as SPECT imaging over a period of 1-24 h after intravenous injection of (99m)hynic-Tyr(3)-octreotide. The patient-specific S values calculated by GATE Monte Carlo code and the corresponding S values obtained by MIRDOSE program differed within 4.3% on an average for self-irradiation, and differed within 69.6% on an average for cross-irradiation. However, the agreement between total organ doses calculated by GATE code and MIRDOSE program for all patients was reasonably well (percentage difference was about 4.6% on an average). Normal and tumor absorbed doses calculated with GATE were slightly higher than those calculated with MIRDOSE program. The average ratio of GATE absorbed doses to MIRDOSE was 1.07 ± 0.11 (ranging from 0.94 to 1.36). According to the results, it is proposed that when cross-organ irradiation is dominant, a comprehensive approach such as GATE Monte Carlo dosimetry be used since it provides more reliable dosimetric results.
Stochastic simulation and Monte-Carlo methods; Simulation stochastique et methodes de Monte-Carlo
Energy Technology Data Exchange (ETDEWEB)
Graham, C. [Centre National de la Recherche Scientifique (CNRS), 91 - Gif-sur-Yvette (France); Ecole Polytechnique, 91 - Palaiseau (France); Talay, D. [Institut National de Recherche en Informatique et en Automatique (INRIA), 78 - Le Chesnay (France); Ecole Polytechnique, 91 - Palaiseau (France)
2011-07-01
This book presents some numerical probabilistic methods of simulation with their convergence speed. It combines mathematical precision and numerical developments, each proposed method belonging to a precise theoretical context developed in a rigorous and self-sufficient manner. After some recalls about the big numbers law and the basics of probabilistic simulation, the authors introduce the martingales and their main properties. Then, they develop a chapter on non-asymptotic estimations of Monte-Carlo method errors. This chapter gives a recall of the central limit theorem and precises its convergence speed. It introduces the Log-Sobolev and concentration inequalities, about which the study has greatly developed during the last years. This chapter ends with some variance reduction techniques. In order to demonstrate in a rigorous way the simulation results of stochastic processes, the authors introduce the basic notions of probabilities and of stochastic calculus, in particular the essential basics of Ito calculus, adapted to each numerical method proposed. They successively study the construction and important properties of the Poisson process, of the jump and deterministic Markov processes (linked to transport equations), and of the solutions of stochastic differential equations. Numerical methods are then developed and the convergence speed results of algorithms are rigorously demonstrated. In passing, the authors describe the probabilistic interpretation basics of the parabolic partial derivative equations. Non-trivial applications to real applied problems are also developed. (J.S.)
Morse Monte Carlo Radiation Transport Code System
Energy Technology Data Exchange (ETDEWEB)
Emmett, M.B.
1975-02-01
The report contains sections containing descriptions of the MORSE and PICTURE codes, input descriptions, sample problems, deviations of the physical equations and explanations of the various error messages. The MORSE code is a multipurpose neutron and gamma-ray transport Monte Carlo code. Time dependence for both shielding and criticality problems is provided. General three-dimensional geometry may be used with an albedo option available at any material surface. The PICTURE code provide aid in preparing correct input data for the combinatorial geometry package CG. It provides a printed view of arbitrary two-dimensional slices through the geometry. By inspecting these pictures one may determine if the geometry specified by the input cards is indeed the desired geometry. 23 refs. (WRF)
Variational Monte Carlo study of pentaquark states
Energy Technology Data Exchange (ETDEWEB)
Mark W. Paris
2005-07-01
Accurate numerical solution of the five-body Schrodinger equation is effected via variational Monte Carlo. The spectrum is assumed to exhibit a narrow resonance with strangeness S=+1. A fully antisymmetrized and pair-correlated five-quark wave function is obtained for the assumed non-relativistic Hamiltonian which has spin, isospin, and color dependent pair interactions and many-body confining terms which are fixed by the non-exotic spectra. Gauge field dynamics are modeled via flux tube exchange factors. The energy determined for the ground states with J=1/2 and negative (positive) parity is 2.22 GeV (2.50 GeV). A lower energy negative parity state is consistent with recent lattice results. The short-range structure of the state is analyzed via its diquark content.
Monte Carlo simulation of neutron scattering instruments
Energy Technology Data Exchange (ETDEWEB)
Seeger, P.A.; Daemen, L.L.; Hjelm, R.P. Jr.
1998-12-01
A code package consisting of the Monte Carlo Library MCLIB, the executing code MC{_}RUN, the web application MC{_}Web, and various ancillary codes is proposed as an open standard for simulation of neutron scattering instruments. The architecture of the package includes structures to define surfaces, regions, and optical elements contained in regions. A particle is defined by its vector position and velocity, its time of flight, its mass and charge, and a polarization vector. The MC{_}RUN code handles neutron transport and bookkeeping, while the action on the neutron within any region is computed using algorithms that may be deterministic, probabilistic, or a combination. Complete versatility is possible because the existing library may be supplemented by any procedures a user is able to code. Some examples are shown.
Atomistic Monte Carlo simulation of lipid membranes
DEFF Research Database (Denmark)
Wüstner, Daniel; Sklenar, Heinz
2014-01-01
, as assessed by calculation of molecular energies and entropies. We also show transition from a crystalline-like to a fluid DPPC bilayer by the CBC local-move MC method, as indicated by the electron density profile, head group orientation, area per lipid, and whole-lipid displacements. We discuss the potential......Biological membranes are complex assemblies of many different molecules of which analysis demands a variety of experimental and computational approaches. In this article, we explain challenges and advantages of atomistic Monte Carlo (MC) simulation of lipid membranes. We provide an introduction...... into the various move sets that are implemented in current MC methods for efficient conformational sampling of lipids and other molecules. In the second part, we demonstrate for a concrete example, how an atomistic local-move set can be implemented for MC simulations of phospholipid monomers and bilayer patches...
Experimental Monte Carlo Quantum Process Certification
Steffen, L; Fedorov, A; Baur, M; Wallraff, A
2012-01-01
Experimental implementations of quantum information processing have now reached a level of sophistication where quantum process tomography is impractical. The number of experimental settings as well as the computational cost of the data post-processing now translates to days of effort to characterize even experiments with as few as 8 qubits. Recently a more practical approach to determine the fidelity of an experimental quantum process has been proposed, where the experimental data is compared directly to an ideal process using Monte Carlo sampling. Here we present an experimental implementation of this scheme in a circuit quantum electrodynamics setup to determine the fidelity of two qubit gates, such as the cphase and the cnot gate, and three qubit gates, such as the Toffoli gate and two sequential cphase gates.
Gas discharges modeling by Monte Carlo technique
Directory of Open Access Journals (Sweden)
Savić Marija
2010-01-01
Full Text Available The basic assumption of the Townsend theory - that ions produce secondary electrons - is valid only in a very narrow range of the reduced electric field E/N. In accordance with the revised Townsend theory that was suggested by Phelps and Petrović, secondary electrons are produced in collisions of ions, fast neutrals, metastable atoms or photons with the cathode, or in gas phase ionizations by fast neutrals. In this paper we tried to build up a Monte Carlo code that can be used to calculate secondary electron yields for different types of particles. The obtained results are in good agreement with the analytical results of Phelps and. Petrović [Plasma Sourc. Sci. Technol. 8 (1999 R1].
On nonlinear Markov chain Monte Carlo
Andrieu, Christophe; Doucet, Arnaud; Del Moral, Pierre; 10.3150/10-BEJ307
2011-01-01
Let $\\mathscr{P}(E)$ be the space of probability measures on a measurable space $(E,\\mathcal{E})$. In this paper we introduce a class of nonlinear Markov chain Monte Carlo (MCMC) methods for simulating from a probability measure $\\pi\\in\\mathscr{P}(E)$. Nonlinear Markov kernels (see [Feynman--Kac Formulae: Genealogical and Interacting Particle Systems with Applications (2004) Springer]) $K:\\mathscr{P}(E)\\times E\\rightarrow\\mathscr{P}(E)$ can be constructed to, in some sense, improve over MCMC methods. However, such nonlinear kernels cannot be simulated exactly, so approximations of the nonlinear kernels are constructed using auxiliary or potentially self-interacting chains. Several nonlinear kernels are presented and it is demonstrated that, under some conditions, the associated approximations exhibit a strong law of large numbers; our proof technique is via the Poisson equation and Foster--Lyapunov conditions. We investigate the performance of our approximations with some simulations.
Monte Carlo exploration of warped Higgsless models
Energy Technology Data Exchange (ETDEWEB)
Hewett, JoAnne L.; Lillie, Benjamin; Rizzo, Thomas Gerard [Stanford Linear Accelerator Center, 2575 Sand Hill Rd., Menlo Park, CA, 94025 (United States)]. E-mail: rizzo@slac.stanford.edu
2004-10-01
We have performed a detailed Monte Carlo exploration of the parameter space for a warped Higgsless model of electroweak symmetry breaking in 5 dimensions. This model is based on the SU(2){sub L} x SU(2){sub R} x U(1){sub B-L} gauge group in an AdS{sub 5} bulk with arbitrary gauge kinetic terms on both the Planck and TeV branes. Constraints arising from precision electroweak measurements and collider data are found to be relatively easy to satisfy. We show, however, that the additional requirement of perturbative unitarity up to the cut-off, {approx_equal} 10 TeV, in W{sub L}{sup +}W{sub L}{sup -} elastic scattering in the absence of dangerous tachyons eliminates all models. If successful models of this class exist, they must be highly fine-tuned. (author)
Monte Carlo Exploration of Warped Higgsless Models
Hewett, J L; Rizzo, T G
2004-01-01
We have performed a detailed Monte Carlo exploration of the parameter space for a warped Higgsless model of electroweak symmetry breaking in 5 dimensions. This model is based on the $SU(2)_L\\times SU(2)_R\\times U(1)_{B-L}$ gauge group in an AdS$_5$ bulk with arbitrary gauge kinetic terms on both the Planck and TeV branes. Constraints arising from precision electroweak measurements and collider data are found to be relatively easy to satisfy. We show, however, that the additional requirement of perturbative unitarity up to the cut-off, $\\simeq 10$ TeV, in $W_L^+W_L^-$ elastic scattering in the absence of dangerous tachyons eliminates all models. If successful models of this class exist, they must be highly fine-tuned.
Monte Carlo Implementation of Polarized Hadronization
Matevosyan, Hrayr H; Thomas, Anthony W
2016-01-01
We study the polarized quark hadronization in a Monte Carlo (MC) framework based on the recent extension of the quark-jet framework, where a self-consistent treatment of the quark polarization transfer in a sequential hadronization picture has been presented. Here, we first adopt this approach for MC simulations of hadronization process with finite number of produced hadrons, expressing the relevant probabilities in terms of the eight leading twist quark-to-quark transverse momentum dependent (TMD) splitting functions (SFs) for elementary $q \\to q'+h$ transition. We present explicit expressions for the unpolarized and Collins fragmentation functions (FFs) of unpolarized hadrons emitted at rank two. Further, we demonstrate that all the current spectator-type model calculations of the leading twist quark-to-quark TMD SFs violate the positivity constraints, and propose quark model based ansatz for these input functions that circumvents the problem. We validate our MC framework by explicitly proving the absence o...
Commensurabilities between ETNOs: a Monte Carlo survey
Marcos, C de la Fuente
2016-01-01
Many asteroids in the main and trans-Neptunian belts are trapped in mean motion resonances with Jupiter and Neptune, respectively. As a side effect, they experience accidental commensurabilities among themselves. These commensurabilities define characteristic patterns that can be used to trace the source of the observed resonant behaviour. Here, we explore systematically the existence of commensurabilities between the known ETNOs using their heliocentric and barycentric semimajor axes, their uncertainties, and Monte Carlo techniques. We find that the commensurability patterns present in the known ETNO population resemble those found in the main and trans-Neptunian belts. Although based on small number statistics, such patterns can only be properly explained if most, if not all, of the known ETNOs are subjected to the resonant gravitational perturbations of yet undetected trans-Plutonian planets. We show explicitly that some of the statistically significant commensurabilities are compatible with the Planet Nin...
Variable length trajectory compressible hybrid Monte Carlo
Nishimura, Akihiko
2016-01-01
Hybrid Monte Carlo (HMC) generates samples from a prescribed probability distribution in a configuration space by simulating Hamiltonian dynamics, followed by the Metropolis (-Hastings) acceptance/rejection step. Compressible HMC (CHMC) generalizes HMC to a situation in which the dynamics is reversible but not necessarily Hamiltonian. This article presents a framework to further extend the algorithm. Within the existing framework, each trajectory of the dynamics must be integrated for the same amount of (random) time to generate a valid Metropolis proposal. Our generalized acceptance/rejection mechanism allows a more deliberate choice of the integration time for each trajectory. The proposed algorithm in particular enables an effective application of variable step size integrators to HMC-type sampling algorithms based on reversible dynamics. The potential of our framework is further demonstrated by another extension of HMC which reduces the wasted computations due to unstable numerical approximations and corr...
Lunar Regolith Albedos Using Monte Carlos
Wilson, T. L.; Andersen, V.; Pinsky, L. S.
2003-01-01
The analysis of planetary regoliths for their backscatter albedos produced by cosmic rays (CRs) is important for space exploration and its potential contributions to science investigations in fundamental physics and astrophysics. Albedos affect all such experiments and the personnel that operate them. Groups have analyzed the production rates of various particles and elemental species by planetary surfaces when bombarded with Galactic CR fluxes, both theoretically and by means of various transport codes, some of which have emphasized neutrons. Here we report on the preliminary results of our current Monte Carlo investigation into the production of charged particles, neutrons, and neutrinos by the lunar surface using FLUKA. In contrast to previous work, the effects of charm are now included.
Nuclear reactions in Monte Carlo codes.
Ferrari, A; Sala, P R
2002-01-01
The physics foundations of hadronic interactions as implemented in most Monte Carlo codes are presented together with a few practical examples. The description of the relevant physics is presented schematically split into the major steps in order to stress the different approaches required for the full understanding of nuclear reactions at intermediate and high energies. Due to the complexity of the problem, only a few semi-qualitative arguments are developed in this paper. The description will be necessarily schematic and somewhat incomplete, but hopefully it will be useful for a first introduction into this topic. Examples are shown mostly for the high energy regime, where all mechanisms mentioned in the paper are at work and to which perhaps most of the readers are less accustomed. Examples for lower energies can be found in the references.
Atomistic Monte Carlo simulation of lipid membranes
DEFF Research Database (Denmark)
Wüstner, Daniel; Sklenar, Heinz
2014-01-01
Biological membranes are complex assemblies of many different molecules of which analysis demands a variety of experimental and computational approaches. In this article, we explain challenges and advantages of atomistic Monte Carlo (MC) simulation of lipid membranes. We provide an introduction......, as assessed by calculation of molecular energies and entropies. We also show transition from a crystalline-like to a fluid DPPC bilayer by the CBC local-move MC method, as indicated by the electron density profile, head group orientation, area per lipid, and whole-lipid displacements. We discuss the potential...... of local-move MC methods in combination with molecular dynamics simulations, for example, for studying multi-component lipid membranes containing cholesterol....
Geometric Monte Carlo and Black Janus Geometries
Bak, Dongsu; Kim, Kyung Kiu; Min, Hyunsoo; Song, Jeong-Pil
2016-01-01
We describe an application of the Monte Carlo method to the Janus deformation of the black brane background. We present numerical results for three and five dimensional black Janus geometries with planar and spherical interfaces. In particular, we argue that the 5D geometry with a spherical interface has an application in understanding the finite temperature bag-like QCD model via the AdS/CFT correspondence. The accuracy and convergence of the algorithm are evaluated with respect to the grid spacing. The systematic errors of the method are determined using an exact solution of 3D black Janus. This numerical approach for solving linear problems is unaffected initial guess of a trial solution and can handle an arbitrary geometry under various boundary conditions in the presence of source fields.
Modeling neutron guides using Monte Carlo simulations
Wang, D Q; Crow, M L; Wang, X L; Lee, W T; Hubbard, C R
2002-01-01
Four neutron guide geometries, straight, converging, diverging and curved, were characterized using Monte Carlo ray-tracing simulations. The main areas of interest are the transmission of the guides at various neutron energies and the intrinsic time-of-flight (TOF) peak broadening. Use of a delta-function time pulse from a uniform Lambert neutron source allows one to quantitatively simulate the effect of guides' geometry on the TOF peak broadening. With a converging guide, the intensity and the beam divergence increases while the TOF peak width decreases compared with that of a straight guide. By contrast, use of a diverging guide decreases the intensity and the beam divergence, and broadens the width (in TOF) of the transmitted neutron pulse.
Accurate barrier heights using diffusion Monte Carlo
Krongchon, Kittithat; Wagner, Lucas K
2016-01-01
Fixed node diffusion Monte Carlo (DMC) has been performed on a test set of forward and reverse barrier heights for 19 non-hydrogen-transfer reactions, and the nodal error has been assessed. The DMC results are robust to changes in the nodal surface, as assessed by using different mean-field techniques to generate single determinant wave functions. Using these single determinant nodal surfaces, DMC results in errors of 1.5(5) kcal/mol on barrier heights. Using the large data set of DMC energies, we attempted to find good descriptors of the fixed node error. It does not correlate with a number of descriptors including change in density, but does correlate with the gap between the highest occupied and lowest unoccupied orbital energies in the mean-field calculation.
Recent Developments in Quantum Monte Carlo: Methods and Applications
Aspuru-Guzik, Alan; Austin, Brian; Domin, Dominik; Galek, Peter T. A.; Handy, Nicholas; Prasad, Rajendra; Salomon-Ferrer, Romelia; Umezawa, Naoto; Lester, William A.
2007-12-01
The quantum Monte Carlo method in the diffusion Monte Carlo form has become recognized for its capability of describing the electronic structure of atomic, molecular and condensed matter systems to high accuracy. This talk will briefly outline the method with emphasis on recent developments connected with trial function construction, linear scaling, and applications to selected systems.
QUANTUM MONTE-CARLO SIMULATIONS - ALGORITHMS, LIMITATIONS AND APPLICATIONS
DERAEDT, H
1992-01-01
A survey is given of Quantum Monte Carlo methods currently used to simulate quantum lattice models. The formalisms employed to construct the simulation algorithms are sketched. The origin of fundamental (minus sign) problems which limit the applicability of the Quantum Monte Carlo approach is shown
QWalk: A Quantum Monte Carlo Program for Electronic Structure
Wagner, Lucas K; Mitas, Lubos
2007-01-01
We describe QWalk, a new computational package capable of performing Quantum Monte Carlo electronic structure calculations for molecules and solids with many electrons. We describe the structure of the program and its implementation of Quantum Monte Carlo methods. It is open-source, licensed under the GPL, and available at the web site http://www.qwalk.org
Quantum Monte Carlo Simulations : Algorithms, Limitations and Applications
Raedt, H. De
1992-01-01
A survey is given of Quantum Monte Carlo methods currently used to simulate quantum lattice models. The formalisms employed to construct the simulation algorithms are sketched. The origin of fundamental (minus sign) problems which limit the applicability of the Quantum Monte Carlo approach is shown
Reporting Monte Carlo Studies in Structural Equation Modeling
Boomsma, Anne
2013-01-01
In structural equation modeling, Monte Carlo simulations have been used increasingly over the last two decades, as an inventory from the journal Structural Equation Modeling illustrates. Reaching out to a broad audience, this article provides guidelines for reporting Monte Carlo studies in that fiel
Practical schemes for accurate forces in quantum Monte Carlo
Moroni, S.; Saccani, S.; Filippi, Claudia
2014-01-01
While the computation of interatomic forces has become a well-established practice within variational Monte Carlo (VMC), the use of the more accurate Fixed-Node Diffusion Monte Carlo (DMC) method is still largely limited to the computation of total energies on structures obtained at a lower level of
Efficiency and accuracy of Monte Carlo (importance) sampling
Waarts, P.H.
2003-01-01
Monte Carlo Analysis is often regarded as the most simple and accurate reliability method. Be-sides it is the most transparent method. The only problem is the accuracy in correlation with the efficiency. Monte Carlo gets less efficient or less accurate when very low probabilities are to be computed
The Monte Carlo Method. Popular Lectures in Mathematics.
Sobol', I. M.
The Monte Carlo Method is a method of approximately solving mathematical and physical problems by the simulation of random quantities. The principal goal of this booklet is to suggest to specialists in all areas that they will encounter problems which can be solved by the Monte Carlo Method. Part I of the booklet discusses the simulation of random…
Forest canopy BRDF simulation using Monte Carlo method
Huang, J.; Wu, B.; Zeng, Y.; Tian, Y.
2006-01-01
Monte Carlo method is a random statistic method, which has been widely used to simulate the Bidirectional Reflectance Distribution Function (BRDF) of vegetation canopy in the field of visible remote sensing. The random process between photons and forest canopy was designed using Monte Carlo method.
Sensitivity of Monte Carlo simulations to input distributions
Energy Technology Data Exchange (ETDEWEB)
RamoRao, B. S.; Srikanta Mishra, S.; McNeish, J.; Andrews, R. W.
2001-07-01
The sensitivity of the results of a Monte Carlo simulation to the shapes and moments of the probability distributions of the input variables is studied. An economical computational scheme is presented as an alternative to the replicate Monte Carlo simulations and is explained with an illustrative example. (Author) 4 refs.
Quantum Monte Carlo using a Stochastic Poisson Solver
Energy Technology Data Exchange (ETDEWEB)
Das, D; Martin, R M; Kalos, M H
2005-05-06
Quantum Monte Carlo (QMC) is an extremely powerful method to treat many-body systems. Usually quantum Monte Carlo has been applied in cases where the interaction potential has a simple analytic form, like the 1/r Coulomb potential. However, in a complicated environment as in a semiconductor heterostructure, the evaluation of the interaction itself becomes a non-trivial problem. Obtaining the potential from any grid-based finite-difference method, for every walker and every step is unfeasible. We demonstrate an alternative approach of solving the Poisson equation by a classical Monte Carlo within the overall quantum Monte Carlo scheme. We have developed a modified ''Walk On Spheres'' algorithm using Green's function techniques, which can efficiently account for the interaction energy of walker configurations, typical of quantum Monte Carlo algorithms. This stochastically obtained potential can be easily incorporated within popular quantum Monte Carlo techniques like variational Monte Carlo (VMC) or diffusion Monte Carlo (DMC). We demonstrate the validity of this method by studying a simple problem, the polarization of a helium atom in the electric field of an infinite capacitor.
Further experience in Bayesian analysis using Monte Carlo Integration
H.K. van Dijk (Herman); T. Kloek (Teun)
1980-01-01
textabstractAn earlier paper [Kloek and Van Dijk (1978)] is extended in three ways. First, Monte Carlo integration is performed in a nine-dimensional parameter space of Klein's model I [Klein (1950)]. Second, Monte Carlo is used as a tool for the elicitation of a uniform prior on a finite region by
New Approaches and Applications for Monte Carlo Perturbation Theory
Energy Technology Data Exchange (ETDEWEB)
Aufiero, Manuele; Bidaud, Adrien; Kotlyar, Dan; Leppänen, Jaakko; Palmiotti, Giuseppe; Salvatores, Massimo; Sen, Sonat; Shwageraus, Eugene; Fratoni, Massimiliano
2017-02-01
This paper presents some of the recent and new advancements in the extension of Monte Carlo Perturbation Theory methodologies and application. In particular, the discussed problems involve Brunup calculation, perturbation calculation based on continuous energy functions, and Monte Carlo Perturbation Theory in loosely coupled systems.
Forest canopy BRDF simulation using Monte Carlo method
Huang, J.; Wu, B.; Zeng, Y.; Tian, Y.
2006-01-01
Monte Carlo method is a random statistic method, which has been widely used to simulate the Bidirectional Reflectance Distribution Function (BRDF) of vegetation canopy in the field of visible remote sensing. The random process between photons and forest canopy was designed using Monte Carlo method.
Practical schemes for accurate forces in quantum Monte Carlo
Moroni, S.; Saccani, S.; Filippi, C.
2014-01-01
While the computation of interatomic forces has become a well-established practice within variational Monte Carlo (VMC), the use of the more accurate Fixed-Node Diffusion Monte Carlo (DMC) method is still largely limited to the computation of total energies on structures obtained at a lower level of
CERN Summer Student Report 2016 Monte Carlo Data Base Improvement
Caciulescu, Alexandru Razvan
2016-01-01
During my Summer Student project I worked on improving the Monte Carlo Data Base and MonALISA services for the ALICE Collaboration. The project included learning the infrastructure for tracking and monitoring of the Monte Carlo productions as well as developing a new RESTful API for seamless integration with the JIRA issue tracking framework.
Accelerated GPU based SPECT Monte Carlo simulations
Garcia, Marie-Paule; Bert, Julien; Benoit, Didier; Bardiès, Manuel; Visvikis, Dimitris
2016-06-01
Monte Carlo (MC) modelling is widely used in the field of single photon emission computed tomography (SPECT) as it is a reliable technique to simulate very high quality scans. This technique provides very accurate modelling of the radiation transport and particle interactions in a heterogeneous medium. Various MC codes exist for nuclear medicine imaging simulations. Recently, new strategies exploiting the computing capabilities of graphical processing units (GPU) have been proposed. This work aims at evaluating the accuracy of such GPU implementation strategies in comparison to standard MC codes in the context of SPECT imaging. GATE was considered the reference MC toolkit and used to evaluate the performance of newly developed GPU Geant4-based Monte Carlo simulation (GGEMS) modules for SPECT imaging. Radioisotopes with different photon energies were used with these various CPU and GPU Geant4-based MC codes in order to assess the best strategy for each configuration. Three different isotopes were considered: 99m Tc, 111In and 131I, using a low energy high resolution (LEHR) collimator, a medium energy general purpose (MEGP) collimator and a high energy general purpose (HEGP) collimator respectively. Point source, uniform source, cylindrical phantom and anthropomorphic phantom acquisitions were simulated using a model of the GE infinia II 3/8" gamma camera. Both simulation platforms yielded a similar system sensitivity and image statistical quality for the various combinations. The overall acceleration factor between GATE and GGEMS platform derived from the same cylindrical phantom acquisition was between 18 and 27 for the different radioisotopes. Besides, a full MC simulation using an anthropomorphic phantom showed the full potential of the GGEMS platform, with a resulting acceleration factor up to 71. The good agreement with reference codes and the acceleration factors obtained support the use of GPU implementation strategies for improving computational efficiency
Monte Carlo modelling of TRIGA research reactor
El Bakkari, B.; Nacir, B.; El Bardouni, T.; El Younoussi, C.; Merroun, O.; Htet, A.; Boulaich, Y.; Zoubair, M.; Boukhal, H.; Chakir, M.
2010-10-01
The Moroccan 2 MW TRIGA MARK II research reactor at Centre des Etudes Nucléaires de la Maâmora (CENM) achieved initial criticality on May 2, 2007. The reactor is designed to effectively implement the various fields of basic nuclear research, manpower training, and production of radioisotopes for their use in agriculture, industry, and medicine. This study deals with the neutronic analysis of the 2-MW TRIGA MARK II research reactor at CENM and validation of the results by comparisons with the experimental, operational, and available final safety analysis report (FSAR) values. The study was prepared in collaboration between the Laboratory of Radiation and Nuclear Systems (ERSN-LMR) from Faculty of Sciences of Tetuan (Morocco) and CENM. The 3-D continuous energy Monte Carlo code MCNP (version 5) was used to develop a versatile and accurate full model of the TRIGA core. The model represents in detailed all components of the core with literally no physical approximation. Continuous energy cross-section data from the more recent nuclear data evaluations (ENDF/B-VI.8, ENDF/B-VII.0, JEFF-3.1, and JENDL-3.3) as well as S( α, β) thermal neutron scattering functions distributed with the MCNP code were used. The cross-section libraries were generated by using the NJOY99 system updated to its more recent patch file "up259". The consistency and accuracy of both the Monte Carlo simulation and neutron transport physics were established by benchmarking the TRIGA experiments. Core excess reactivity, total and integral control rods worth as well as power peaking factors were used in the validation process. Results of calculations are analysed and discussed.
Accelerated GPU based SPECT Monte Carlo simulations.
Garcia, Marie-Paule; Bert, Julien; Benoit, Didier; Bardiès, Manuel; Visvikis, Dimitris
2016-06-07
Monte Carlo (MC) modelling is widely used in the field of single photon emission computed tomography (SPECT) as it is a reliable technique to simulate very high quality scans. This technique provides very accurate modelling of the radiation transport and particle interactions in a heterogeneous medium. Various MC codes exist for nuclear medicine imaging simulations. Recently, new strategies exploiting the computing capabilities of graphical processing units (GPU) have been proposed. This work aims at evaluating the accuracy of such GPU implementation strategies in comparison to standard MC codes in the context of SPECT imaging. GATE was considered the reference MC toolkit and used to evaluate the performance of newly developed GPU Geant4-based Monte Carlo simulation (GGEMS) modules for SPECT imaging. Radioisotopes with different photon energies were used with these various CPU and GPU Geant4-based MC codes in order to assess the best strategy for each configuration. Three different isotopes were considered: (99m) Tc, (111)In and (131)I, using a low energy high resolution (LEHR) collimator, a medium energy general purpose (MEGP) collimator and a high energy general purpose (HEGP) collimator respectively. Point source, uniform source, cylindrical phantom and anthropomorphic phantom acquisitions were simulated using a model of the GE infinia II 3/8" gamma camera. Both simulation platforms yielded a similar system sensitivity and image statistical quality for the various combinations. The overall acceleration factor between GATE and GGEMS platform derived from the same cylindrical phantom acquisition was between 18 and 27 for the different radioisotopes. Besides, a full MC simulation using an anthropomorphic phantom showed the full potential of the GGEMS platform, with a resulting acceleration factor up to 71. The good agreement with reference codes and the acceleration factors obtained support the use of GPU implementation strategies for improving computational
Fission Matrix Capability for MCNP Monte Carlo
Energy Technology Data Exchange (ETDEWEB)
Carney, Sean E. [Los Alamos National Laboratory; Brown, Forrest B. [Los Alamos National Laboratory; Kiedrowski, Brian C. [Los Alamos National Laboratory; Martin, William R. [Los Alamos National Laboratory
2012-09-05
In a Monte Carlo criticality calculation, before the tallying of quantities can begin, a converged fission source (the fundamental eigenvector of the fission kernel) is required. Tallies of interest may include powers, absorption rates, leakage rates, or the multiplication factor (the fundamental eigenvalue of the fission kernel, k{sub eff}). Just as in the power iteration method of linear algebra, if the dominance ratio (the ratio of the first and zeroth eigenvalues) is high, many iterations of neutron history simulations are required to isolate the fundamental mode of the problem. Optically large systems have large dominance ratios, and systems containing poor neutron communication between regions are also slow to converge. The fission matrix method, implemented into MCNP[1], addresses these problems. When Monte Carlo random walk from a source is executed, the fission kernel is stochastically applied to the source. Random numbers are used for: distances to collision, reaction types, scattering physics, fission reactions, etc. This method is used because the fission kernel is a complex, 7-dimensional operator that is not explicitly known. Deterministic methods use approximations/discretization in energy, space, and direction to the kernel. Consequently, they are faster. Monte Carlo directly simulates the physics, which necessitates the use of random sampling. Because of this statistical noise, common convergence acceleration methods used in deterministic methods do not work. In the fission matrix method, we are using the random walk information not only to build the next-iteration fission source, but also a spatially-averaged fission kernel. Just like in deterministic methods, this involves approximation and discretization. The approximation is the tallying of the spatially-discretized fission kernel with an incorrect fission source. We address this by making the spatial mesh fine enough that this error is negligible. As a consequence of discretization we get a
Vectorized Monte Carlo methods for reactor lattice analysis
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.
Quantum Monte Carlo methods algorithms for lattice models
Gubernatis, James; Werner, Philipp
2016-01-01
Featuring detailed explanations of the major algorithms used in quantum Monte Carlo simulations, this is the first textbook of its kind to provide a pedagogical overview of the field and its applications. The book provides a comprehensive introduction to the Monte Carlo method, its use, and its foundations, and examines algorithms for the simulation of quantum many-body lattice problems at finite and zero temperature. These algorithms include continuous-time loop and cluster algorithms for quantum spins, determinant methods for simulating fermions, power methods for computing ground and excited states, and the variational Monte Carlo method. Also discussed are continuous-time algorithms for quantum impurity models and their use within dynamical mean-field theory, along with algorithms for analytically continuing imaginary-time quantum Monte Carlo data. The parallelization of Monte Carlo simulations is also addressed. This is an essential resource for graduate students, teachers, and researchers interested in ...
Non-Boltzmann Ensembles and Monte Carlo Simulations
Murthy, K. P. N.
2016-10-01
Boltzmann sampling based on Metropolis algorithm has been extensively used for simulating a canonical ensemble and for calculating macroscopic properties of a closed system at desired temperatures. An estimate of a mechanical property, like energy, of an equilibrium system, is made by averaging over a large number microstates generated by Boltzmann Monte Carlo methods. This is possible because we can assign a numerical value for energy to each microstate. However, a thermal property like entropy, is not easily accessible to these methods. The reason is simple. We can not assign a numerical value for entropy, to a microstate. Entropy is not a property associated with any single microstate. It is a collective property of all the microstates. Toward calculating entropy and other thermal properties, a non-Boltzmann Monte Carlo technique called Umbrella sampling was proposed some forty years ago. Umbrella sampling has since undergone several metamorphoses and we have now, multi-canonical Monte Carlo, entropic sampling, flat histogram methods, Wang-Landau algorithm etc. This class of methods generates non-Boltzmann ensembles which are un-physical. However, physical quantities can be calculated as follows. First un-weight a microstates of the entropic ensemble; then re-weight it to the desired physical ensemble. Carry out weighted average over the entropic ensemble to estimate physical quantities. In this talk I shall tell you of the most recent non- Boltzmann Monte Carlo method and show how to calculate free energy for a few systems. We first consider estimation of free energy as a function of energy at different temperatures to characterize phase transition in an hairpin DNA in the presence of an unzipping force. Next we consider free energy as a function of order parameter and to this end we estimate density of states g(E, M), as a function of both energy E, and order parameter M. This is carried out in two stages. We estimate g(E) in the first stage. Employing g
Baräo, Fernando; Nakagawa, Masayuki; Távora, Luis; Vaz, Pedro
2001-01-01
This book focusses on the state of the art of Monte Carlo methods in radiation physics and particle transport simulation and applications, the latter involving in particular, the use and development of electron--gamma, neutron--gamma and hadronic codes. Besides the basic theory and the methods employed, special attention is paid to algorithm development for modeling, and the analysis of experiments and measurements in a variety of fields ranging from particle to medical physics.
Baumgartner, Andreas; Steurer, Andreas; Maringer, Franz Josef
2009-11-01
Photon energy spectra of Varian Clinac 2100C and 2300C/D treatment heads were calculated with PENELOPE-2006, using simplified Monte Carlo models. These spectra constitute the basis of beam models used for the calculation of correction factors required for the Austrian absorbed dose to water primary standard. To validate the models, simulated depth dose curves in water and calculated radiation quality factors (TPR(20,10)) were compared with ionization chamber measurements. In addition the results are discussed in context with detailed Monte Carlo studies from the literature in reference to mean spectral photon energy and degree of equivalence between simulated and calculated percentage-depth-dose curves. Mean absolute deviations between measured and simulated depth dose curves smaller than 2.0% were found. The differences between simulation and measurement of TPR(20,10) were smaller than 2.6%. This shows the usefulness of the simplified beam models in applications since their dependence on energy spectra and radiation quality is small in comparison to its energy range.
Novel Extrapolation Method in the Monte Carlo Shell Model
Shimizu, Noritaka; Mizusaki, Takahiro; Otsuka, Takaharu; Abe, Takashi; Honma, Michio
2010-01-01
We propose an extrapolation method utilizing energy variance in the Monte Carlo shell model in order to estimate the energy eigenvalue and observables accurately. We derive a formula for the energy variance with deformed Slater determinants, which enables us to calculate the energy variance efficiently. The feasibility of the method is demonstrated for the full $pf$-shell calculation of $^{56}$Ni, and the applicability of the method to a system beyond current limit of exact diagonalization is shown for the $pf$+$g_{9/2}$-shell calculation of $^{64}$Ge.
On adaptive resampling strategies for sequential Monte Carlo methods
Del Moral, Pierre; Jasra, Ajay; 10.3150/10-BEJ335
2012-01-01
Sequential Monte Carlo (SMC) methods are a class of techniques to sample approximately from any sequence of probability distributions using a combination of importance sampling and resampling steps. This paper is concerned with the convergence analysis of a class of SMC methods where the times at which resampling occurs are computed online using criteria such as the effective sample size. This is a popular approach amongst practitioners but there are very few convergence results available for these methods. By combining semigroup techniques with an original coupling argument, we obtain functional central limit theorems and uniform exponential concentration estimates for these algorithms.
Cluster Monte Carlo simulations of the nematic-isotropic transition
Priezjev, N. V.; Pelcovits, Robert A.
2001-06-01
We report the results of simulations of the three-dimensional Lebwohl-Lasher model of the nematic-isotropic transition using a single cluster Monte Carlo algorithm. The algorithm, first introduced by Kunz and Zumbach to study two-dimensional nematics, is a modification of the Wolff algorithm for spin systems, and greatly reduces critical slowing down. We calculate the free energy in the neighborhood of the transition for systems up to linear size 70. We find a double well structure with a barrier that grows with increasing system size. We thus obtain an upper estimate of the value of the transition temperature in the thermodynamic limit.
Communication: Water on hexagonal boron nitride from diffusion Monte Carlo
Energy Technology Data Exchange (ETDEWEB)
Al-Hamdani, Yasmine S.; Ma, Ming; Michaelides, Angelos, E-mail: angelos.michaelides@ucl.ac.uk [Thomas Young Centre and London Centre for Nanotechnology, 17–19 Gordon Street, London WC1H 0AH (United Kingdom); Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ (United Kingdom); Alfè, Dario [Thomas Young Centre and London Centre for Nanotechnology, 17–19 Gordon Street, London WC1H 0AH (United Kingdom); Department of Earth Sciences, University College London, Gower Street, London WC1E 6BT (United Kingdom); Lilienfeld, O. Anatole von [Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials, Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel (Switzerland); Argonne Leadership Computing Facility, Argonne National Laboratories, 9700 S. Cass Avenue Argonne, Lemont, Illinois 60439 (United States)
2015-05-14
Despite a recent flurry of experimental and simulation studies, an accurate estimate of the interaction strength of water molecules with hexagonal boron nitride is lacking. Here, we report quantum Monte Carlo results for the adsorption of a water monomer on a periodic hexagonal boron nitride sheet, which yield a water monomer interaction energy of −84 ± 5 meV. We use the results to evaluate the performance of several widely used density functional theory (DFT) exchange correlation functionals and find that they all deviate substantially. Differences in interaction energies between different adsorption sites are however better reproduced by DFT.
Quantifying uncertainties in primordial nucleosynthesis without Monte Carlo simulations
Fiorentini, G; Sarkar, S; Villante, F L
1998-01-01
We present a simple method for determining the (correlated) uncertainties of the light element abundances expected from big bang nucleosynthesis, which avoids the need for lengthy Monte Carlo simulations. Our approach helps to clarify the role of the different nuclear reactions contributing to a particular elemental abundance and makes it easy to implement energy-independent changes in the measured reaction rates. As an application, we demonstrate how this method simplifies the statistical estimation of the nucleon-to-photon ratio through comparison of the standard BBN predictions with the observationally inferred abundances.
Iterative acceleration methods for Monte Carlo and deterministic criticality calculations
Energy Technology Data Exchange (ETDEWEB)
Urbatsch, T.J.
1995-11-01
If you have ever given up on a nuclear criticality calculation and terminated it because it took so long to converge, you might find this thesis of interest. The author develops three methods for improving the fission source convergence in nuclear criticality calculations for physical systems with high dominance ratios for which convergence is slow. The Fission Matrix Acceleration Method and the Fission Diffusion Synthetic Acceleration (FDSA) Method are acceleration methods that speed fission source convergence for both Monte Carlo and deterministic methods. The third method is a hybrid Monte Carlo method that also converges for difficult problems where the unaccelerated Monte Carlo method fails. The author tested the feasibility of all three methods in a test bed consisting of idealized problems. He has successfully accelerated fission source convergence in both deterministic and Monte Carlo criticality calculations. By filtering statistical noise, he has incorporated deterministic attributes into the Monte Carlo calculations in order to speed their source convergence. He has used both the fission matrix and a diffusion approximation to perform unbiased accelerations. The Fission Matrix Acceleration method has been implemented in the production code MCNP and successfully applied to a real problem. When the unaccelerated calculations are unable to converge to the correct solution, they cannot be accelerated in an unbiased fashion. A Hybrid Monte Carlo method weds Monte Carlo and a modified diffusion calculation to overcome these deficiencies. The Hybrid method additionally possesses reduced statistical errors.
Flow in Random Microstructures: a Multilevel Monte Carlo Approach
Icardi, Matteo
2016-01-06
In this work we are interested in the fast estimation of effective parameters of random heterogeneous materials using Multilevel Monte Carlo (MLMC). MLMC is an efficient and flexible solution for the propagation of uncertainties in complex models, where an explicit parametrisation of the input randomness is not available or too expensive. We propose a general-purpose algorithm and computational code for the solution of Partial Differential Equations (PDEs) on random heterogeneous materials. We make use of the key idea of MLMC, based on different discretization levels, extending it in a more general context, making use of a hierarchy of physical resolution scales, solvers, models and other numerical/geometrical discretisation parameters. Modifications of the classical MLMC estimators are proposed to further reduce variance in cases where analytical convergence rates and asymptotic regimes are not available. Spheres, ellipsoids and general convex-shaped grains are placed randomly in the domain with different placing/packing algorithms and the effective properties of the heterogeneous medium are computed. These are, for example, effective diffusivities, conductivities, and reaction rates. The implementation of the Monte-Carlo estimators, the statistical samples and each single solver is done efficiently in parallel. The method is tested and applied for pore-scale simulations of random sphere packings.
Evolutionary Sequential Monte Carlo Samplers for Change-Point Models
Directory of Open Access Journals (Sweden)
Arnaud Dufays
2016-03-01
Full Text Available Sequential Monte Carlo (SMC methods are widely used for non-linear filtering purposes. However, the SMC scope encompasses wider applications such as estimating static model parameters so much that it is becoming a serious alternative to Markov-Chain Monte-Carlo (MCMC methods. Not only do SMC algorithms draw posterior distributions of static or dynamic parameters but additionally they provide an estimate of the marginal likelihood. The tempered and time (TNT algorithm, developed in this paper, combines (off-line tempered SMC inference with on-line SMC inference for drawing realizations from many sequential posterior distributions without experiencing a particle degeneracy problem. Furthermore, it introduces a new MCMC rejuvenation step that is generic, automated and well-suited for multi-modal distributions. As this update relies on the wide heuristic optimization literature, numerous extensions are readily available. The algorithm is notably appropriate for estimating change-point models. As an example, we compare several change-point GARCH models through their marginal log-likelihoods over time.
Information-Geometric Markov Chain Monte Carlo Methods Using Diffusions
Directory of Open Access Journals (Sweden)
Samuel Livingstone
2014-06-01
Full Text Available Recent work incorporating geometric ideas in Markov chain Monte Carlo is reviewed in order to highlight these advances and their possible application in a range of domains beyond statistics. A full exposition of Markov chains and their use in Monte Carlo simulation for statistical inference and molecular dynamics is provided, with particular emphasis on methods based on Langevin diffusions. After this, geometric concepts in Markov chain Monte Carlo are introduced. A full derivation of the Langevin diffusion on a Riemannian manifold is given, together with a discussion of the appropriate Riemannian metric choice for different problems. A survey of applications is provided, and some open questions are discussed.
The Monte Carlo method the method of statistical trials
Shreider, YuA
1966-01-01
The Monte Carlo Method: The Method of Statistical Trials is a systematic account of the fundamental concepts and techniques of the Monte Carlo method, together with its range of applications. Some of these applications include the computation of definite integrals, neutron physics, and in the investigation of servicing processes. This volume is comprised of seven chapters and begins with an overview of the basic features of the Monte Carlo method and typical examples of its application to simple problems in computational mathematics. The next chapter examines the computation of multi-dimensio
Quantifying the Effect of Undersampling in Monte Carlo Simulations Using SCALE
Energy Technology Data Exchange (ETDEWEB)
Perfetti, Christopher M [ORNL; Rearden, Bradley T [ORNL
2014-01-01
This study explores the effect of undersampling in Monte Carlo calculations on tally estimates and tally variance estimates for burnup credit applications. Steady-state Monte Carlo simulations were performed for models of several critical systems with varying degrees of spatial and isotopic complexity and the impact of undersampling on eigenvalue and flux estimates was examined. Using an inadequate number of particle histories in each generation was found to produce an approximately 100 pcm bias in the eigenvalue estimates, and biases that exceeded 10% in fuel pin flux estimates.
Monte Carlo simulations for heavy ion dosimetry
Energy Technology Data Exchange (ETDEWEB)
Geithner, O.
2006-07-26
Water-to-air stopping power ratio (s{sub w,air}) calculations for the ionization chamber dosimetry of clinically relevant ion beams with initial energies from 50 to 450 MeV/u have been performed using the Monte Carlo technique. To simulate the transport of a particle in water the computer code SHIELD-HIT v2 was used which is a substantially modified version of its predecessor SHIELD-HIT v1. The code was partially rewritten, replacing formerly used single precision variables with double precision variables. The lowest particle transport specific energy was decreased from 1 MeV/u down to 10 keV/u by modifying the Bethe- Bloch formula, thus widening its range for medical dosimetry applications. Optional MSTAR and ICRU-73 stopping power data were included. The fragmentation model was verified using all available experimental data and some parameters were adjusted. The present code version shows excellent agreement with experimental data. Additional to the calculations of stopping power ratios, s{sub w,air}, the influence of fragments and I-values on s{sub w,air} for carbon ion beams was investigated. The value of s{sub w,air} deviates as much as 2.3% at the Bragg peak from the recommended by TRS-398 constant value of 1.130 for an energy of 50 MeV/u. (orig.)
Rare event simulation using Monte Carlo methods
Rubino, Gerardo
2009-01-01
In a probabilistic model, a rare event is an event with a very small probability of occurrence. The forecasting of rare events is a formidable task but is important in many areas. For instance a catastrophic failure in a transport system or in a nuclear power plant, the failure of an information processing system in a bank, or in the communication network of a group of banks, leading to financial losses. Being able to evaluate the probability of rare events is therefore a critical issue. Monte Carlo Methods, the simulation of corresponding models, are used to analyze rare events. This book sets out to present the mathematical tools available for the efficient simulation of rare events. Importance sampling and splitting are presented along with an exposition of how to apply these tools to a variety of fields ranging from performance and dependability evaluation of complex systems, typically in computer science or in telecommunications, to chemical reaction analysis in biology or particle transport in physics. ...
Monte Carlo Simulations of the Photospheric Process
Santana, Rodolfo; Hernandez, Roberto A; Kumar, Pawan
2015-01-01
We present a Monte Carlo (MC) code we wrote to simulate the photospheric process and to study the photospheric spectrum above the peak energy. Our simulations were performed with a photon to electron ratio $N_{\\gamma}/N_{e} = 10^{5}$, as determined by observations of the GRB prompt emission. We searched an exhaustive parameter space to determine if the photospheric process can match the observed high-energy spectrum of the prompt emission. If we do not consider electron re-heating, we determined that the best conditions to produce the observed high-energy spectrum are low photon temperatures and high optical depths. However, for these simulations, the spectrum peaks at an energy below 300 keV by a factor $\\sim 10$. For the cases we consider with higher photon temperatures and lower optical depths, we demonstrate that additional energy in the electrons is required to produce a power-law spectrum above the peak-energy. By considering electron re-heating near the photosphere, the spectrum for these simulations h...
Finding Planet Nine: a Monte Carlo approach
Marcos, C de la Fuente
2016-01-01
Planet Nine is a hypothetical planet located well beyond Pluto that has been proposed in an attempt to explain the observed clustering in physical space of the perihelia of six extreme trans-Neptunian objects or ETNOs. The predicted approximate values of its orbital elements include a semimajor axis of 700 au, an eccentricity of 0.6, an inclination of 30 degrees, and an argument of perihelion of 150 degrees. Searching for this putative planet is already under way. Here, we use a Monte Carlo approach to create a synthetic population of Planet Nine orbits and study its visibility statistically in terms of various parameters and focusing on the aphelion configuration. Our analysis shows that, if Planet Nine exists and is at aphelion, it might be found projected against one out of four specific areas in the sky. Each area is linked to a particular value of the longitude of the ascending node and two of them are compatible with an apsidal antialignment scenario. In addition and after studying the current statistic...
Atomistic Monte Carlo simulation of lipid membranes.
Wüstner, Daniel; Sklenar, Heinz
2014-01-24
Biological membranes are complex assemblies of many different molecules of which analysis demands a variety of experimental and computational approaches. In this article, we explain challenges and advantages of atomistic Monte Carlo (MC) simulation of lipid membranes. We provide an introduction into the various move sets that are implemented in current MC methods for efficient conformational sampling of lipids and other molecules. In the second part, we demonstrate for a concrete example, how an atomistic local-move set can be implemented for MC simulations of phospholipid monomers and bilayer patches. We use our recently devised chain breakage/closure (CBC) local move set in the bond-/torsion angle space with the constant-bond-length approximation (CBLA) for the phospholipid dipalmitoylphosphatidylcholine (DPPC). We demonstrate rapid conformational equilibration for a single DPPC molecule, as assessed by calculation of molecular energies and entropies. We also show transition from a crystalline-like to a fluid DPPC bilayer by the CBC local-move MC method, as indicated by the electron density profile, head group orientation, area per lipid, and whole-lipid displacements. We discuss the potential of local-move MC methods in combination with molecular dynamics simulations, for example, for studying multi-component lipid membranes containing cholesterol.
Parallel Monte Carlo Simulation of Aerosol Dynamics
Directory of Open Access Journals (Sweden)
Kun Zhou
2014-02-01
Full Text Available A highly efficient Monte Carlo (MC algorithm is developed for the numerical simulation of aerosol dynamics, that is, nucleation, surface growth, and coagulation. Nucleation and surface growth are handled with deterministic means, while coagulation is simulated with a stochastic method (Marcus-Lushnikov stochastic process. Operator splitting techniques are used to synthesize the deterministic and stochastic parts in the algorithm. The algorithm is parallelized using the Message Passing Interface (MPI. The parallel computing efficiency is investigated through numerical examples. Near 60% parallel efficiency is achieved for the maximum testing case with 3.7 million MC particles running on 93 parallel computing nodes. The algorithm is verified through simulating various testing cases and comparing the simulation results with available analytical and/or other numerical solutions. Generally, it is found that only small number (hundreds or thousands of MC particles is necessary to accurately predict the aerosol particle number density, volume fraction, and so forth, that is, low order moments of the Particle Size Distribution (PSD function. Accurately predicting the high order moments of the PSD needs to dramatically increase the number of MC particles.
Monte Carlo simulations of Protein Adsorption
Sharma, Sumit; Kumar, Sanat K.; Belfort, Georges
2008-03-01
Amyloidogenic diseases, such as, Alzheimer's are caused by adsorption and aggregation of partially unfolded proteins. Adsorption of proteins is a concern in design of biomedical devices, such as dialysis membranes. Protein adsorption is often accompanied by conformational rearrangements in protein molecules. Such conformational rearrangements are thought to affect many properties of adsorbed protein molecules such as their adhesion strength to the surface, biological activity, and aggregation tendency. It has been experimentally shown that many naturally occurring proteins, upon adsorption to hydrophobic surfaces, undergo a helix to sheet or random coil secondary structural rearrangement. However, to better understand the equilibrium structural complexities of this phenomenon, we have performed Monte Carlo (MC) simulations of adsorption of a four helix bundle, modeled as a lattice protein, and studied the adsorption behavior and equilibrium protein conformations at different temperatures and degrees of surface hydrophobicity. To study the free energy and entropic effects on adsorption, Canonical ensemble MC simulations have been combined with Weighted Histogram Analysis Method(WHAM). Conformational transitions of proteins on surfaces will be discussed as a function of surface hydrophobicity and compared to analogous bulk transitions.
Monte Carlo Simulation of River Meander Modelling
Posner, A. J.; Duan, J. G.
2010-12-01
This study first compares the first order analytical solutions for flow field by Ikeda et. al. (1981) and Johanesson and Parker (1989b). Ikeda et. al.’s (1981) linear bank erosion model was implemented to predict the rate of bank erosion in which the bank erosion coefficient is treated as a stochastic variable that varies with physical properties of the bank (e.g. cohesiveness, stratigraphy, vegetation density). The developed model was used to predict the evolution of meandering planforms. Then, the modeling results were analyzed and compared to the observed data. Since the migration of meandering channel consists of downstream translation, lateral expansion, and downstream or upstream rotations. Several measures are formulated in order to determine which of the resulting planform is closest to the experimental measured one. Results from the deterministic model highly depend on the calibrated erosion coefficient. Since field measurements are always limited, the stochastic model yielded more realistic predictions of meandering planform evolutions. Due to the random nature of bank erosion coefficient, the meandering planform evolution is a stochastic process that can only be accurately predicted by a stochastic model. Quasi-2D Ikeda (1989) flow solution with Monte Carlo Simulation of Bank Erosion Coefficient.
Commensurabilities between ETNOs: a Monte Carlo survey
de la Fuente Marcos, C.; de la Fuente Marcos, R.
2016-07-01
Many asteroids in the main and trans-Neptunian belts are trapped in mean motion resonances with Jupiter and Neptune, respectively. As a side effect, they experience accidental commensurabilities among themselves. These commensurabilities define characteristic patterns that can be used to trace the source of the observed resonant behaviour. Here, we explore systematically the existence of commensurabilities between the known ETNOs using their heliocentric and barycentric semimajor axes, their uncertainties, and Monte Carlo techniques. We find that the commensurability patterns present in the known ETNO population resemble those found in the main and trans-Neptunian belts. Although based on small number statistics, such patterns can only be properly explained if most, if not all, of the known ETNOs are subjected to the resonant gravitational perturbations of yet undetected trans-Plutonian planets. We show explicitly that some of the statistically significant commensurabilities are compatible with the Planet Nine hypothesis; in particular, a number of objects may be trapped in the 5:3 and 3:1 mean motion resonances with a putative Planet Nine with semimajor axis ˜700 au.
Diffusion Monte Carlo in internal coordinates.
Petit, Andrew S; McCoy, Anne B
2013-08-15
An internal coordinate extension of diffusion Monte Carlo (DMC) is described as a first step toward a generalized reduced-dimensional DMC approach. The method places no constraints on the choice of internal coordinates other than the requirement that they all be independent. Using H(3)(+) and its isotopologues as model systems, the methodology is shown to be capable of successfully describing the ground state properties of molecules that undergo large amplitude, zero-point vibrational motions. Combining the approach developed here with the fixed-node approximation allows vibrationally excited states to be treated. Analysis of the ground state probability distribution is shown to provide important insights into the set of internal coordinates that are less strongly coupled and therefore more suitable for use as the nodal coordinates for the fixed-node DMC calculations. In particular, the curvilinear normal mode coordinates are found to provide reasonable nodal surfaces for the fundamentals of H(2)D(+) and D(2)H(+) despite both molecules being highly fluxional.
Monte Carlo simulations for focusing elliptical guides
Energy Technology Data Exchange (ETDEWEB)
Valicu, Roxana [FRM2 Garching, Muenchen (Germany); Boeni, Peter [E20, TU Muenchen (Germany)
2009-07-01
The aim of the Monte Carlo simulations using McStas Programme was to improve the focusing of the neutron beam existing at PGAA (FRM II) by prolongation of the existing elliptic guide (coated now with supermirrors with m=3) with a new part. First we have tried with an initial length of the additional guide of 7,5cm and coatings for the neutron guide of supermirrors with m=4,5 and 6. The gain (calculated by dividing the intensity in the focal point after adding the guide by the intensity at the focal point with the initial guide) obtained for this coatings indicated that a coating with m=5 would be appropriate for a first trial. The next step was to vary the length of the additional guide for this m value and therefore choosing the appropriate length for the maximal gain. With the m value and the length of the guide fixed we have introduced an aperture 1 cm before the focal point and we have varied the radius of this aperture in order to obtain a focused beam. We have observed a dramatic decrease in the size of the beam in the focal point after introducing this aperture. The simulation results, the gains obtained and the evolution of the beam size will be presented.
Monte Carlo Production Management at CMS
Boudoul, G.; Pol, A; Srimanobhas, P; Vlimant, J R; Franzoni, Giovanni
2015-01-01
The analysis of the LHC data at the Compact Muon Solenoid (CMS) experiment requires the production of a large number of simulated events.During the runI of LHC (2010-2012), CMS has produced over 12 Billion simulated events,organized in approximately sixty different campaigns each emulating specific detector conditions and LHC running conditions (pile up).In order toaggregate the information needed for the configuration and prioritization of the events production,assure the book-keeping and of all the processing requests placed by the physics analysis groups,and to interface with the CMS production infrastructure,the web-based service Monte Carlo Management (McM) has been developed and put in production in 2012.McM is based on recent server infrastructure technology (CherryPy + java) and relies on a CouchDB database back-end.This contribution will coverthe one and half year of operational experience managing samples of simulated events for CMS,the evolution of its functionalitiesand the extension of its capabi...
Monte Carlo models of dust coagulation
Zsom, Andras
2010-01-01
The thesis deals with the first stage of planet formation, namely dust coagulation from micron to millimeter sizes in circumstellar disks. For the first time, we collect and compile the recent laboratory experiments on dust aggregates into a collision model that can be implemented into dust coagulation models. We put this model into a Monte Carlo code that uses representative particles to simulate dust evolution. Simulations are performed using three different disk models in a local box (0D) located at 1 AU distance from the central star. We find that the dust evolution does not follow the previously assumed growth-fragmentation cycle, but growth is halted by bouncing before the fragmentation regime is reached. We call this the bouncing barrier which is an additional obstacle during the already complex formation process of planetesimals. The absence of the growth-fragmentation cycle and the halted growth has two important consequences for planet formation. 1) It is observed that disk atmospheres are dusty thr...
Atomistic Monte Carlo Simulation of Lipid Membranes
Directory of Open Access Journals (Sweden)
Daniel Wüstner
2014-01-01
Full Text Available Biological membranes are complex assemblies of many different molecules of which analysis demands a variety of experimental and computational approaches. In this article, we explain challenges and advantages of atomistic Monte Carlo (MC simulation of lipid membranes. We provide an introduction into the various move sets that are implemented in current MC methods for efficient conformational sampling of lipids and other molecules. In the second part, we demonstrate for a concrete example, how an atomistic local-move set can be implemented for MC simulations of phospholipid monomers and bilayer patches. We use our recently devised chain breakage/closure (CBC local move set in the bond-/torsion angle space with the constant-bond-length approximation (CBLA for the phospholipid dipalmitoylphosphatidylcholine (DPPC. We demonstrate rapid conformational equilibration for a single DPPC molecule, as assessed by calculation of molecular energies and entropies. We also show transition from a crystalline-like to a fluid DPPC bilayer by the CBC local-move MC method, as indicated by the electron density profile, head group orientation, area per lipid, and whole-lipid displacements. We discuss the potential of local-move MC methods in combination with molecular dynamics simulations, for example, for studying multi-component lipid membranes containing cholesterol.
Parallel Monte Carlo simulation of aerosol dynamics
Zhou, K.
2014-01-01
A highly efficient Monte Carlo (MC) algorithm is developed for the numerical simulation of aerosol dynamics, that is, nucleation, surface growth, and coagulation. Nucleation and surface growth are handled with deterministic means, while coagulation is simulated with a stochastic method (Marcus-Lushnikov stochastic process). Operator splitting techniques are used to synthesize the deterministic and stochastic parts in the algorithm. The algorithm is parallelized using the Message Passing Interface (MPI). The parallel computing efficiency is investigated through numerical examples. Near 60% parallel efficiency is achieved for the maximum testing case with 3.7 million MC particles running on 93 parallel computing nodes. The algorithm is verified through simulating various testing cases and comparing the simulation results with available analytical and/or other numerical solutions. Generally, it is found that only small number (hundreds or thousands) of MC particles is necessary to accurately predict the aerosol particle number density, volume fraction, and so forth, that is, low order moments of the Particle Size Distribution (PSD) function. Accurately predicting the high order moments of the PSD needs to dramatically increase the number of MC particles. 2014 Kun Zhou et al.
Measuring Berry curvature with quantum Monte Carlo
Kolodrubetz, Michael
2014-01-01
The Berry curvature and its descendant, the Berry phase, play an important role in quantum mechanics. They can be used to understand the Aharonov-Bohm effect, define topological Chern numbers, and generally to investigate the geometric properties of a quantum ground state manifold. While Berry curvature has been well-studied in the regimes of few-body physics and non-interacting particles, its use in the regime of strong interactions is hindered by the lack of numerical methods to solve it. In this paper we fill this gap by implementing a quantum Monte Carlo method to solve for the Berry curvature, based on interpreting Berry curvature as a leading correction to imaginary time ramps. We demonstrate our algorithm using the transverse-field Ising model in one and two dimensions, the latter of which is non-integrable. Despite the fact that the Berry curvature gives information about the phase of the wave function, we show that our algorithm has no sign or phase problem for standard sign-problem-free Hamiltonians...
Morton, S E; Chiew, Y S; Pretty, C; Moltchanova, E; Scarrott, C; Redmond, D; Shaw, G M; Chase, J G
2017-02-01
Randomised control trials have sought to seek to improve mechanical ventilation treatment. However, few trials to date have shown clinical significance. It is hypothesised that aside from effective treatment, the outcome metrics and sample sizes of the trial also affect the significance, and thus impact trial design. In this study, a Monte-Carlo simulation method was developed and used to investigate several outcome metrics of ventilation treatment, including 1) length of mechanical ventilation (LoMV); 2) Ventilator Free Days (VFD); and 3) LoMV-28, a combination of the other metrics. As these metrics have highly skewed distributions, it also investigated the impact of imposing clinically relevant exclusion criteria on study power to enable better design for significance. Data from invasively ventilated patients from a single intensive care unit were used in this analysis to demonstrate the method. Use of LoMV as an outcome metric required 160 patients/arm to reach 80% power with a clinically expected intervention difference of 25% LoMV if clinically relevant exclusion criteria were applied to the cohort, but 400 patients/arm if they were not. However, only 130 patients/arm would be required for the same statistical significance at the same intervention difference if VFD was used. A Monte-Carlo simulation approach using local cohort data combined with objective patient selection criteria can yield better design of ventilation studies to desired power and significance, with fewer patients per arm than traditional trial design methods, which in turn reduces patient risk. Outcome metrics, such as VFD, should be used when a difference in mortality is also expected between the two cohorts. Finally, the non-parametric approach taken is readily generalisable to a range of trial types where outcome data is similarly skewed.
Hu, Shuming; Mitas, Lubos
2012-02-01
Thorium dioxide solid is a unique optical and heat-resistant actinide material with large gap and cohesion. It is a diamagnet, unlike a number of other similar actinide oxides. We investigate the electronic structure of ThO2 using Density Functional Theory (DFT) and quantum Monte Carlo (QMC) methods. We adopt Stuttgart RLC and RSC effective core potentials (pseudopotentials) for the Th atom. In the DFT calculations, some of the properties are verified in all-electron calculations using the FLAPW techniques. Using the fixed-node diffusion Monte Carlo we calculate the ground state and several excited states from which we estimate the cohesion and the band gap. Simulation cells of several sizes are used to estimate/reduce the finite size effects. We compare the QMC results with recent DFT calculations with several types of functionals which include hybrids such as PBE0 and HSE. Insights from QMC calculations give us understanding of the correlations beyond the DFT approaches and pave the way for accurate electronic structure calculations of other actinide materials.
Fourier Monte Carlo renormalization-group approach to crystalline membranes.
Tröster, A
2015-02-01
The computation of the critical exponent η characterizing the universal elastic behavior of crystalline membranes in the flat phase continues to represent challenges to theorists as well as computer simulators that manifest themselves in a considerable spread of numerical results for η published in the literature. We present additional insight into this problem that results from combining Wilson's momentum shell renormalization-group method with the power of modern computer simulations based on the Fourier Monte Carlo algorithm. After discussing the ideas and difficulties underlying this combined scheme, we present a calculation of the renormalization-group flow of the effective two-dimensional Young modulus for momentum shells of different thickness. Extrapolation to infinite shell thickness allows us to produce results in reasonable agreement with those obtained by functional renormalization group or by Fourier Monte Carlo simulations in combination with finite-size scaling. Moreover, our method allows us to obtain a decent estimate for the value of the Wegner exponent ω that determines the leading correction to scaling, which in turn allows us to refine our numerical estimate for η previously obtained from precise finite-size scaling data.
Evaluation of atomic electron binding energies for Monte Carlo particle transport
Pia, Maria Grazia; Batic, Matej; Begalli, Marcia; Kim, Chan Hyeong; Quintieri, Lina; Saracco, Paolo
2011-01-01
A survey of atomic binding energies used by general purpose Monte Carlo systems is reported. Various compilations of these parameters have been evaluated; their accuracy is estimated with respect to experimental data. Their effects on physics quantities relevant to Monte Carlo particle transport are highlighted: X-ray fluorescence emission, electron and proton ionization cross sections, and Doppler broadening in Compton scattering. The effects due to different binding energies are quantified with respect to experimental data. The results of the analysis provide quantitative ground for the selection of binding energies to optimize the accuracy of Monte Carlo simulation in experimental use cases. Recommendations on software design dealing with these parameters and on the improvement of data libraries for Monte Carlo simulation are discussed.
Schabel, Matthias C.; DiBella, Edward V. R.; Jensen, Randy L.; Salzman, Karen L.
2010-08-01
Accurate quantification of pharmacokinetic model parameters in tracer kinetic imaging experiments requires correspondingly accurate determination of the arterial input function (AIF). Despite significant effort expended on methods of directly measuring patient-specific AIFs in modalities as diverse as dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), dynamic positron emission tomography (PET), and perfusion computed tomography (CT), fundamental and technical difficulties have made consistent and reliable achievement of that goal elusive. Here, we validate a new algorithm for AIF determination, the Monte Carlo blind estimation (MCBE) method (which is described in detail and characterized by extensive simulations in a companion paper), by comparing AIFs measured in DCE-MRI studies of eight brain tumor patients with results of blind estimation. Blind AIFs calculated with the MCBE method using a pool of concentration-time curves from a region of normal brain tissue were found to be quite similar to the measured AIFs, with statistically significant decreases in fit residuals observed in six of eight patients. Biases between the blind and measured pharmacokinetic parameters were the dominant source of error. Averaged over all eight patients, the mean biases were +7% in K trans, 0% in kep, -11% in vp and +10% in ve. Corresponding uncertainties (median absolute deviation from the best fit line) were 0.0043 min-1 in K trans, 0.0491 min-1 in kep, 0.29% in vp and 0.45% in ve. The use of a published population-averaged AIF resulted in larger mean biases in three of the four parameters (-23% in K trans, -22% in kep, -63% in vp), with the bias in ve unchanged, and led to larger uncertainties in all four parameters (0.0083 min-1 in K trans, 0.1038 min-1 in kep, 0.31% in vp and 0.95% in ve). When blind AIFs were calculated from a region of tumor tissue, statistically significant decreases in fit residuals were observed in all eight patients despite larger
Energy Technology Data Exchange (ETDEWEB)
Lima, Gabriel A.C. [Universidade Estadual de Campinas (UNICAMP), SP (Brazil). Inst. de Geociencias. Lab. de Analises Geoeconomicas de Recursos Minerais]. E-mail: gabriel@ige.unicamp.br; Vidal, Alexandre C.; Suslick, Saul B. [Universidade Estadual de Campinas (UNICAMP), SP (Brazil) Inst. de Geociencias. Dept. de Geologia e Recursos Naturais]. E-mails: vidal@ige.unicamp.br; suslick@ige.unicamp.br
2006-04-15
In many papers dealing with estimation of oil reserves, engineers usually assume that well porosity can be modeled as a Gaussian distribution, that is, under this assumption the expected value of porosity can be estimated from the average porosity values from well log and petrophysical data. But, other distributions can be used to model local porosity when Gaussian distribution cannot fit sample data. In this paper, using actual porosity data of a 3-NA-002-RJS well from the Campos Basin, it is shown that for a selected interval, the logistic distribution fits the data better than other distributions and its expected value should be used to estimate the well porosities of the entire population. In such cases, as numerical analysis shows, using arithmetic mean instead of expected value may give rise to errors. The data shows that using an average as porosity estimator will overestimate the P90 and underestimate the P10 estimates. (author)
Monte-Carlo simulation-based statistical modeling
Chen, John
2017-01-01
This book brings together expert researchers engaged in Monte-Carlo simulation-based statistical modeling, offering them a forum to present and discuss recent issues in methodological development as well as public health applications. It is divided into three parts, with the first providing an overview of Monte-Carlo techniques, the second focusing on missing data Monte-Carlo methods, and the third addressing Bayesian and general statistical modeling using Monte-Carlo simulations. The data and computer programs used here will also be made publicly available, allowing readers to replicate the model development and data analysis presented in each chapter, and to readily apply them in their own research. Featuring highly topical content, the book has the potential to impact model development and data analyses across a wide spectrum of fields, and to spark further research in this direction.
EXTENDED MONTE CARLO LOCALIZATION ALGORITHM FOR MOBILE SENSOR NETWORKS
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
A real-world localization system for wireless sensor networks that adapts for mobility and irregular radio propagation model is considered.The traditional range-based techniques and recent range-free localization schemes are not welt competent for localization in mobile sensor networks,while the probabilistic approach of Bayesian filtering with particle-based density representations provides a comprehensive solution to such localization problem.Monte Carlo localization is a Bayesian filtering method that approximates the mobile node’S location by a set of weighted particles.In this paper,an enhanced Monte Carlo localization algorithm-Extended Monte Carlo Localization (Ext-MCL) is suitable for the practical wireless network environment where the radio propagation model is irregular.Simulation results show the proposal gets better localization accuracy and higher localizable node number than previously proposed Monte Carlo localization schemes not only for ideal radio model,but also for irregular one.
On the Markov Chain Monte Carlo (MCMC) method
Indian Academy of Sciences (India)
Rajeeva L Karandikar
2006-04-01
Markov Chain Monte Carlo (MCMC) is a popular method used to generate samples from arbitrary distributions, which may be speciﬁed indirectly. In this article, we give an introduction to this method along with some examples.
Monte Carlo simulations: Hidden errors from ``good'' random number generators
Ferrenberg, Alan M.; Landau, D. P.; Wong, Y. Joanna
1992-12-01
The Wolff algorithm is now accepted as the best cluster-flipping Monte Carlo algorithm for beating ``critical slowing down.'' We show how this method can yield incorrect answers due to subtle correlations in ``high quality'' random number generators.
An Introduction to Multilevel Monte Carlo for Option Valuation
Higham, Desmond J
2015-01-01
Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation. In 2008, Giles proposed a remarkable improvement to the approach of discretizing with a numerical method and applying standard Monte Carlo. His multilevel Monte Carlo method offers an order of speed up given by the inverse of epsilon, where epsilon is the required accuracy. So computations can run 100 times more quickly when two digits of accuracy are required. The multilevel philosophy has since been adopted by a range of researchers and a wealth of practically significant results has arisen, most of which have yet to make their way into the expository literature. In this work, we give a brief, accessible, introduction to multilevel Monte Carlo and summarize recent results applicable to the task of option evaluation.
MODELING LEACHING OF VIRUSES BY THE MONTE CARLO METHOD
A predictive screening model was developed for fate and transport of viruses in the unsaturated zone. A database of input parameters allowed Monte Carlo analysis with the model. The resulting kernel densities of predicted attenuation during percolation indicated very ...
Accelerating Monte Carlo Renderers by Ray Histogram Fusion
Directory of Open Access Journals (Sweden)
Mauricio Delbracio
2015-03-01
Full Text Available This paper details the recently introduced Ray Histogram Fusion (RHF filter for accelerating Monte Carlo renderers [M. Delbracio et al., Boosting Monte Carlo Rendering by Ray Histogram Fusion, ACM Transactions on Graphics, 33 (2014]. In this filter, each pixel in the image is characterized by the colors of the rays that reach its surface. Pixels are compared using a statistical distance on the associated ray color distributions. Based on this distance, it decides whether two pixels can share their rays or not. The RHF filter is consistent: as the number of samples increases, more evidence is required to average two pixels. The algorithm provides a significant gain in PSNR, or equivalently accelerates the rendering process by using many fewer Monte Carlo samples without observable bias. Since the RHF filter depends only on the Monte Carlo samples color values, it can be naturally combined with all rendering effects.
Monte Carlo methods and applications in nuclear physics
Energy Technology Data Exchange (ETDEWEB)
Carlson, J.
1990-01-01
Monte Carlo methods for studying few- and many-body quantum systems are introduced, with special emphasis given to their applications in nuclear physics. Variational and Green's function Monte Carlo methods are presented in some detail. The status of calculations of light nuclei is reviewed, including discussions of the three-nucleon-interaction, charge and magnetic form factors, the coulomb sum rule, and studies of low-energy radiative transitions. 58 refs., 12 figs.
Public Infrastructure for Monte Carlo Simulation: publicMC@BATAN
Waskita, A A; Akbar, Z; Handoko, L T; 10.1063/1.3462759
2010-01-01
The first cluster-based public computing for Monte Carlo simulation in Indonesia is introduced. The system has been developed to enable public to perform Monte Carlo simulation on a parallel computer through an integrated and user friendly dynamic web interface. The beta version, so called publicMC@BATAN, has been released and implemented for internal users at the National Nuclear Energy Agency (BATAN). In this paper the concept and architecture of publicMC@BATAN are presented.
Radiative Equilibrium and Temperature Correction in Monte Carlo Radiation Transfer
Bjorkman, J. E.; Wood, Kenneth
2001-01-01
We describe a general radiative equilibrium and temperature correction procedure for use in Monte Carlo radiation transfer codes with sources of temperature-independent opacity, such as astrophysical dust. The technique utilizes the fact that Monte Carlo simulations track individual photon packets, so we may easily determine where their energy is absorbed. When a packet is absorbed, it heats a particular cell within the envelope, raising its temperature. To enforce radiative equilibrium, the ...
Chemical accuracy from quantum Monte Carlo for the Benzene Dimer
Azadi, Sam; Cohen, R. E
2015-01-01
We report an accurate study of interactions between Benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory (DFT) using different van der Waals (vdW) functionals. In our QMC calculations, we use accurate correlated trial wave functions including three-body Jastrow factors, and backflow transformations. We consider two benzene molecules in the parallel displaced (PD) geometry, and fin...
de Finetti Priors using Markov chain Monte Carlo computations.
Bacallado, Sergio; Diaconis, Persi; Holmes, Susan
2015-07-01
Recent advances in Monte Carlo methods allow us to revisit work by de Finetti who suggested the use of approximate exchangeability in the analyses of contingency tables. This paper gives examples of computational implementations using Metropolis Hastings, Langevin and Hamiltonian Monte Carlo to compute posterior distributions for test statistics relevant for testing independence, reversible or three way models for discrete exponential families using polynomial priors and Gröbner bases.
Event-chain Monte Carlo for classical continuous spin models
Michel, Manon; Mayer, Johannes; Krauth, Werner
2015-10-01
We apply the event-chain Monte Carlo algorithm to classical continuum spin models on a lattice and clarify the condition for its validity. In the two-dimensional XY model, it outperforms the local Monte Carlo algorithm by two orders of magnitude, although it remains slower than the Wolff cluster algorithm. In the three-dimensional XY spin glass model at low temperature, the event-chain algorithm is far superior to the other algorithms.
Confidence and efficiency scaling in Variational Quantum Monte Carlo calculations
Delyon, François; Holzmann, Markus
2016-01-01
Based on the central limit theorem, we discuss the problem of evaluation of the statistical error of Monte Carlo calculations using a time discretized diffusion process. We present a robust and practical method to determine the effective variance of general observables and show how to verify the equilibrium hypothesis by the Kolmogorov-Smirnov test. We then derive scaling laws of the efficiency illustrated by Variational Monte Carlo calculations on the two dimensional electron gas.
Study of the Transition Flow Regime using Monte Carlo Methods
Hassan, H. A.
1999-01-01
This NASA Cooperative Agreement presents a study of the Transition Flow Regime Using Monte Carlo Methods. The topics included in this final report are: 1) New Direct Simulation Monte Carlo (DSMC) procedures; 2) The DS3W and DS2A Programs; 3) Papers presented; 4) Miscellaneous Applications and Program Modifications; 5) Solution of Transitional Wake Flows at Mach 10; and 6) Turbulence Modeling of Shock-Dominated Fows with a k-Enstrophy Formulation.
Monte Carlo Simulation of Optical Properties of Wake Bubbles
Institute of Scientific and Technical Information of China (English)
CAO Jing; WANG Jiang-An; JIANG Xing-Zhou; SHI Sheng-Wei
2007-01-01
Based on Mie scattering theory and the theory of multiple light scattering, the light scattering properties of air bubbles in a wake are analysed by Monte Carlo simulation. The results show that backscattering is enhanced obviously due to the existence of bubbles, especially with the increase of bubble density, and that it is feasible to use the Monte Carlo method to study the properties of light scattering by air bubbles.
Successful combination of the stochastic linearization and Monte Carlo methods
Elishakoff, I.; Colombi, P.
1993-01-01
A combination of a stochastic linearization and Monte Carlo techniques is presented for the first time in literature. A system with separable nonlinear damping and nonlinear restoring force is considered. The proposed combination of the energy-wise linearization with the Monte Carlo method yields an error under 5 percent, which corresponds to the error reduction associated with the conventional stochastic linearization by a factor of 4.6.
Confidence and efficiency scaling in variational quantum Monte Carlo calculations
Delyon, F.; Bernu, B.; Holzmann, Markus
2017-02-01
Based on the central limit theorem, we discuss the problem of evaluation of the statistical error of Monte Carlo calculations using a time-discretized diffusion process. We present a robust and practical method to determine the effective variance of general observables and show how to verify the equilibrium hypothesis by the Kolmogorov-Smirnov test. We then derive scaling laws of the efficiency illustrated by variational Monte Carlo calculations on the two-dimensional electron gas.
Multiscale Monte Carlo equilibration: pure Yang-Mills theory
Endres, Michael G; Detmold, William; Orginos, Kostas; Pochinsky, Andrew V
2015-01-01
We present a multiscale thermalization algorithm for lattice gauge theory, which enables efficient parallel generation of uncorrelated gauge field configurations. The algorithm combines standard Monte Carlo techniques with ideas drawn from real space renormalization group and multigrid methods. We demonstrate the viability of the algorithm for pure Yang-Mills gauge theory for both heat bath and hybrid Monte Carlo evolution, and show that it ameliorates the problem of topological freezing up to controllable lattice spacing artifacts.
Geometrical and Monte Carlo projectors in 3D PET reconstruction
Aguiar, Pablo; Rafecas López, Magdalena; Ortuno, Juan Enrique; Kontaxakis, George; Santos, Andrés; Pavía, Javier; Ros, Domènec
2010-01-01
Purpose: In the present work, the authors compare geometrical and Monte Carlo projectors in detail. The geometrical projectors considered were the conventional geometrical Siddon ray-tracer (S-RT) and the orthogonal distance-based ray-tracer (OD-RT), based on computing the orthogonal distance from the center of image voxel to the line-of-response. A comparison of these geometrical projectors was performed using different point spread function (PSF) models. The Monte Carlo-based method under c...
Monte Carlo method for solving a parabolic problem
Directory of Open Access Journals (Sweden)
Tian Yi
2016-01-01
Full Text Available In this paper, we present a numerical method based on random sampling for a parabolic problem. This method combines use of the Crank-Nicolson method and Monte Carlo method. In the numerical algorithm, we first discretize governing equations by Crank-Nicolson method, and obtain a large sparse system of linear algebraic equations, then use Monte Carlo method to solve the linear algebraic equations. To illustrate the usefulness of this technique, we apply it to some test problems.
MONTE CARLO SIMULATION OF CHARGED PARTICLE IN AN ELECTRONEGATIVE PLASMA
Directory of Open Access Journals (Sweden)
L SETTAOUTI
2003-12-01
Full Text Available Interest in radio frequency (rf discharges has grown tremendously in recent years due to their importance in microelectronic technologies. Especially interesting are the properties of discharges in electronegative gases which are most frequently used for technological applications. Monte Carlo simulation have become increasingly important as a simulation tool particularly in the area of plasma physics. In this work, we present some detailed properties of rf plasmas obtained by Monte Carlo simulation code, in SF6
Application of Monte Carlo methods in tomotherapy and radiation biophysics
Hsiao, Ya-Yun
Helical tomotherapy is an attractive treatment for cancer therapy because highly conformal dose distributions can be achieved while the on-board megavoltage CT provides simultaneous images for accurate patient positioning. The convolution/superposition (C/S) dose calculation methods typically used for Tomotherapy treatment planning may overestimate skin (superficial) doses by 3-13%. Although more accurate than C/S methods, Monte Carlo (MC) simulations are too slow for routine clinical treatment planning. However, the computational requirements of MC can be reduced by developing a source model for the parts of the accelerator that do not change from patient to patient. This source model then becomes the starting point for additional simulations of the penetration of radiation through patient. In the first section of this dissertation, a source model for a helical tomotherapy is constructed by condensing information from MC simulations into series of analytical formulas. The MC calculated percentage depth dose and beam profiles computed using the source model agree within 2% of measurements for a wide range of field sizes, which suggests that the proposed source model provides an adequate representation of the tomotherapy head for dose calculations. Monte Carlo methods are a versatile technique for simulating many physical, chemical and biological processes. In the second major of this thesis, a new methodology is developed to simulate of the induction of DNA damage by low-energy photons. First, the PENELOPE Monte Carlo radiation transport code is used to estimate the spectrum of initial electrons produced by photons. The initial spectrum of electrons are then combined with DNA damage yields for monoenergetic electrons from the fast Monte Carlo damage simulation (MCDS) developed earlier by Semenenko and Stewart (Purdue University). Single- and double-strand break yields predicted by the proposed methodology are in good agreement (1%) with the results of published
Maucec, M; de Meijer, RJ; van der Klis, MMIP; Hendriks, Peter; Jones, DG
2004-01-01
This paper represents a supplementary study to Part I: Monte Carlo assessment of detection depth limits, aimed at estimating the acquisition times, required to detect radioactive particles offshore by towed gamma-ray spectrometry. Using Monte Carlo simulations, sets of measuring conditions were cove
Sechopoulos, I.; Ali, E.S.; Badal, A.; Badano, A.; Boone, J.M.; Kyprianou, I.S.; Mainegra-Hing, E.; McMillan, K.L.; McNitt-Gray, M.F.; Rogers, D.W.; Samei, E.; Turner, A.C.
2015-01-01
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 a
Monte Carlo Volcano Seismic Moment Tensors
Waite, G. P.; Brill, K. A.; Lanza, F.
2015-12-01
Inverse modeling of volcano seismic sources can provide insight into the geometry and dynamics of volcanic conduits. But given the logistical challenges of working on an active volcano, seismic networks are typically deficient in spatial and temporal coverage; this potentially leads to large errors in source models. In addition, uncertainties in the centroid location and moment-tensor components, including volumetric components, are difficult to constrain from the linear inversion results, which leads to a poor understanding of the model space. In this study, we employ a nonlinear inversion using a Monte Carlo scheme with the objective of defining robustly resolved elements of model space. The model space is randomized by centroid location and moment tensor eigenvectors. Point sources densely sample the summit area and moment tensors are constrained to a randomly chosen geometry within the inversion; Green's functions for the random moment tensors are all calculated from modeled single forces, making the nonlinear inversion computationally reasonable. We apply this method to very-long-period (VLP) seismic events that accompany minor eruptions at Fuego volcano, Guatemala. The library of single force Green's functions is computed with a 3D finite-difference modeling algorithm through a homogeneous velocity-density model that includes topography, for a 3D grid of nodes, spaced 40 m apart, within the summit region. The homogenous velocity and density model is justified by long wavelength of VLP data. The nonlinear inversion reveals well resolved model features and informs the interpretation through a better understanding of the possible models. This approach can also be used to evaluate possible station geometries in order to optimize networks prior to deployment.
Monte Carlo simulation of large electron fields
Faddegon, Bruce A.; Perl, Joseph; Asai, Makoto
2008-03-01
Two Monte Carlo systems, EGSnrc and Geant4, the latter with two different 'physics lists,' were used to calculate dose distributions in large electron fields used in radiotherapy. Source and geometry parameters were adjusted to match calculated results to measurement. Both codes were capable of accurately reproducing the measured dose distributions of the six electron beams available on the accelerator. Depth penetration matched the average measured with a diode and parallel-plate chamber to 0.04 cm or better. Calculated depth dose curves agreed to 2% with diode measurements in the build-up region, although for the lower beam energies there was a discrepancy of up to 5% in this region when calculated results are compared to parallel-plate measurements. Dose profiles at the depth of maximum dose matched to 2-3% in the central 25 cm of the field, corresponding to the field size of the largest applicator. A 4% match was obtained outside the central region. The discrepancy observed in the bremsstrahlung tail in published results that used EGS4 is no longer evident. Simulations with the different codes and physics lists used different source energies, incident beam angles, thicknesses of the primary foils, and distance between the primary and secondary foil. The true source and geometry parameters were not known with sufficient accuracy to determine which parameter set, including the energy of the source, was closest to the truth. These results underscore the requirement for experimental benchmarks of depth penetration and electron scatter for beam energies and foils relevant to radiotherapy.
Dosimetry applications in GATE Monte Carlo toolkit.
Papadimitroulas, Panagiotis
2017-02-21
Monte Carlo (MC) simulations are a well-established method for studying physical processes in medical physics. The purpose of this review is to present GATE dosimetry applications on diagnostic and therapeutic simulated protocols. There is a significant need for accurate quantification of the absorbed dose in several specific applications such as preclinical and pediatric studies. GATE is an open-source MC toolkit for simulating imaging, radiotherapy (RT) and dosimetry applications in a user-friendly environment, which is well validated and widely accepted by the scientific community. In RT applications, during treatment planning, it is essential to accurately assess the deposited energy and the absorbed dose per tissue/organ of interest, as well as the local statistical uncertainty. Several types of realistic dosimetric applications are described including: molecular imaging, radio-immunotherapy, radiotherapy and brachytherapy. GATE has been efficiently used in several applications, such as Dose Point Kernels, S-values, Brachytherapy parameters, and has been compared against various MC codes which are considered as standard tools for decades. Furthermore, the presented studies show reliable modeling of particle beams when comparing experimental with simulated data. Examples of different dosimetric protocols are reported for individualized dosimetry and simulations combining imaging and therapy dose monitoring, with the use of modern computational phantoms. Personalization of medical protocols can be achieved by combining GATE MC simulations with anthropomorphic computational models and clinical anatomical data. This is a review study, covering several dosimetric applications of GATE, and the different tools used for modeling realistic clinical acquisitions with accurate dose assessment. Copyright © 2017 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
Monte Carlo implementation of polarized hadronization
Matevosyan, Hrayr H.; Kotzinian, Aram; Thomas, Anthony W.
2017-01-01
We study the polarized quark hadronization in a Monte Carlo (MC) framework based on the recent extension of the quark-jet framework, where a self-consistent treatment of the quark polarization transfer in a sequential hadronization picture has been presented. Here, we first adopt this approach for MC simulations of the hadronization process with a finite number of produced hadrons, expressing the relevant probabilities in terms of the eight leading twist quark-to-quark transverse-momentum-dependent (TMD) splitting functions (SFs) for elementary q →q'+h transition. We present explicit expressions for the unpolarized and Collins fragmentation functions (FFs) of unpolarized hadrons emitted at rank 2. Further, we demonstrate that all the current spectator-type model calculations of the leading twist quark-to-quark TMD SFs violate the positivity constraints, and we propose a quark model based ansatz for these input functions that circumvents the problem. We validate our MC framework by explicitly proving the absence of unphysical azimuthal modulations of the computed polarized FFs, and by precisely reproducing the earlier derived explicit results for rank-2 pions. Finally, we present the full results for pion unpolarized and Collins FFs, as well as the corresponding analyzing powers from high statistics MC simulations with a large number of produced hadrons for two different model input elementary SFs. The results for both sets of input functions exhibit the same general features of an opposite signed Collins function for favored and unfavored channels at large z and, at the same time, demonstrate the flexibility of the quark-jet framework by producing significantly different dependences of the results at mid to low z for the two model inputs.
kmos: A lattice kinetic Monte Carlo framework
Hoffmann, Max J.; Matera, Sebastian; Reuter, Karsten
2014-07-01
Kinetic Monte Carlo (kMC) simulations have emerged as a key tool for microkinetic modeling in heterogeneous catalysis and other materials applications. Systems, where site-specificity of all elementary reactions allows a mapping onto a lattice of discrete active sites, can be addressed within the particularly efficient lattice kMC approach. To this end we describe the versatile kmos software package, which offers a most user-friendly implementation, execution, and evaluation of lattice kMC models of arbitrary complexity in one- to three-dimensional lattice systems, involving multiple active sites in periodic or aperiodic arrangements, as well as site-resolved pairwise and higher-order lateral interactions. Conceptually, kmos achieves a maximum runtime performance which is essentially independent of lattice size by generating code for the efficiency-determining local update of available events that is optimized for a defined kMC model. For this model definition and the control of all runtime and evaluation aspects kmos offers a high-level application programming interface. Usage proceeds interactively, via scripts, or a graphical user interface, which visualizes the model geometry, the lattice occupations and rates of selected elementary reactions, while allowing on-the-fly changes of simulation parameters. We demonstrate the performance and scaling of kmos with the application to kMC models for surface catalytic processes, where for given operation conditions (temperature and partial pressures of all reactants) central simulation outcomes are catalytic activity and selectivities, surface composition, and mechanistic insight into the occurrence of individual elementary processes in the reaction network.
Perturbation Monte Carlo methods for tissue structure alterations.
Nguyen, Jennifer; Hayakawa, Carole K; Mourant, Judith R; Spanier, Jerome
2013-01-01
This paper describes an extension of the perturbation Monte Carlo method to model light transport when the phase function is arbitrarily perturbed. Current perturbation Monte Carlo methods allow perturbation of both the scattering and absorption coefficients, however, the phase function can not be varied. The more complex method we develop and test here is not limited in this way. We derive a rigorous perturbation Monte Carlo extension that can be applied to a large family of important biomedical light transport problems and demonstrate its greater computational efficiency compared with using conventional Monte Carlo simulations to produce forward transport problem solutions. The gains of the perturbation method occur because only a single baseline Monte Carlo simulation is needed to obtain forward solutions to other closely related problems whose input is described by perturbing one or more parameters from the input of the baseline problem. The new perturbation Monte Carlo methods are tested using tissue light scattering parameters relevant to epithelia where many tumors originate. The tissue model has parameters for the number density and average size of three classes of scatterers; whole nuclei, organelles such as lysosomes and mitochondria, and small particles such as ribosomes or large protein complexes. When these parameters or the wavelength is varied the scattering coefficient and the phase function vary. Perturbation calculations give accurate results over variations of ∼15-25% of the scattering parameters.
A Survey on Multilevel Monte Carlo for European Options
Directory of Open Access Journals (Sweden)
Masoud Moharamnejad
2016-03-01
Full Text Available One of the most applicable and common methods for pricing options is the Monte Carlo simulation. Among the advantages of this method we can name ease of use, being suitable for different types of options including vanilla options and exotic options. On one hand, convergence rate of Monte Carlo's variance is , which has a slow convergence in responding problems, such that for achieving accuracy of ε for a d dimensional problem, computation complexity would be . Thus, various methods have been proposed in Monte Carlo framework to increase the convergence rate of variance as variance reduction methods. One of the recent methods was proposed by Gills in 2006, is the multilevel Monte Carlo method. This method besides reducing the computationcomplexity to while being used in Euler discretizing and to while being used in Milsteindiscretizing method, has the capacity to be combined with other variance reduction methods. In this article, multilevel Monte Carlo using Euler and Milsteindiscretizing methods is adopted for comparing computation complexity with standard Monte Carlo method in pricing European call options.
Bayesian Optimal Experimental Design Using Multilevel Monte Carlo
Issaid, Chaouki Ben
2015-01-07
Experimental design is very important since experiments are often resource-exhaustive and time-consuming. We carry out experimental design in the Bayesian framework. To measure the amount of information, which can be extracted from the data in an experiment, we use the expected information gain as the utility function, which specifically is the expected logarithmic ratio between the posterior and prior distributions. Optimizing this utility function enables us to design experiments that yield the most informative data for our purpose. One of the major difficulties in evaluating the expected information gain is that the integral is nested and can be high dimensional. We propose using Multilevel Monte Carlo techniques to accelerate the computation of the nested high dimensional integral. The advantages are twofold. First, the Multilevel Monte Carlo can significantly reduce the cost of the nested integral for a given tolerance, by using an optimal sample distribution among different sample averages of the inner integrals. Second, the Multilevel Monte Carlo method imposes less assumptions, such as the concentration of measures, required by Laplace method. We test our Multilevel Monte Carlo technique using a numerical example on the design of sensor deployment for a Darcy flow problem governed by one dimensional Laplace equation. We also compare the performance of the Multilevel Monte Carlo, Laplace approximation and direct double loop Monte Carlo.
Longitudinal functional principal component modelling via Stochastic Approximation Monte Carlo
Martinez, Josue G.
2010-06-01
The authors consider the analysis of hierarchical longitudinal functional data based upon a functional principal components approach. In contrast to standard frequentist approaches to selecting the number of principal components, the authors do model averaging using a Bayesian formulation. A relatively straightforward reversible jump Markov Chain Monte Carlo formulation has poor mixing properties and in simulated data often becomes trapped at the wrong number of principal components. In order to overcome this, the authors show how to apply Stochastic Approximation Monte Carlo (SAMC) to this problem, a method that has the potential to explore the entire space and does not become trapped in local extrema. The combination of reversible jump methods and SAMC in hierarchical longitudinal functional data is simplified by a polar coordinate representation of the principal components. The approach is easy to implement and does well in simulated data in determining the distribution of the number of principal components, and in terms of its frequentist estimation properties. Empirical applications are also presented.
Chemical accuracy from quantum Monte Carlo for the Benzene Dimer
Azadi, Sam
2015-01-01
We report an accurate study of interactions between Benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory (DFT) using different van der Waals (vdW) functionals. In our QMC calculations, we use accurate correlated trial wave functions including three-body Jastrow factors, and backflow transformations. We consider two benzene molecules in the parallel displaced (PD) geometry, and find that by highly optimizing the wave function and introducing more dynamical correlation into the wave function, we compute the weak chemical binding energy between aromatic rings accurately. We find optimal VMC and DMC binding energies of -2.3(4) and -2.7(3) kcal/mol, respectively. The best estimate of the CCSD(T)/CBS limit is -2.65(2) kcal/mol [E. Miliordos et al, J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate that QMC methods give chemical accuracy for weakly bound van der Waals molecular interactions, compar...
Infinite variance in fermion quantum Monte Carlo calculations.
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.
Pore-scale uncertainty quantification with multilevel Monte Carlo
Icardi, Matteo
2014-01-06
Computational fluid dynamics (CFD) simulations of pore-scale transport processes in porous media have recently gained large popularity. However the geometrical details of the pore structures can be known only in a very low number of samples and the detailed flow computations can be carried out only on a limited number of cases. The explicit introduction of randomness in the geometry and in other setup parameters can be crucial for the optimization of pore-scale investigations for random homogenization. Since there are no generic ways to parametrize the randomness in the porescale structures, Monte Carlo techniques are the most accessible to compute statistics. We propose a multilevel Monte Carlo (MLMC) technique to reduce the computational cost of estimating quantities of interest within a prescribed accuracy constraint. Random samples of pore geometries with a hierarchy of geometrical complexities and grid refinements, are synthetically generated and used to propagate the uncertainties in the flow simulations and compute statistics of macro-scale effective parameters.
On the time scale associated with Monte Carlo simulations.
Bal, Kristof M; Neyts, Erik C
2014-11-28
Uniform-acceptance force-bias Monte Carlo (fbMC) methods have been shown to be a powerful technique to access longer timescales in atomistic simulations allowing, for example, phase transitions and growth. Recently, a new fbMC method, the time-stamped force-bias Monte Carlo (tfMC) method, was derived with inclusion of an estimated effective timescale; this timescale, however, does not seem able to explain some of the successes the method. In this contribution, we therefore explicitly quantify the effective timescale tfMC is able to access for a variety of systems, namely a simple single-particle, one-dimensional model system, the Lennard-Jones liquid, an adatom on the Cu(100) surface, a silicon crystal with point defects and a highly defected graphene sheet, in order to gain new insights into the mechanisms by which tfMC operates. It is found that considerable boosts, up to three orders of magnitude compared to molecular dynamics, can be achieved for solid state systems by lowering of the apparent activation barrier of occurring processes, while not requiring any system-specific input or modifications of the method. We furthermore address the pitfalls of using the method as a replacement or complement of molecular dynamics simulations, its ability to explicitly describe correct dynamics and reaction mechanisms, and the association of timescales to MC simulations in general.
On the time scale associated with Monte Carlo simulations
Energy Technology Data Exchange (ETDEWEB)
Bal, Kristof M., E-mail: kristof.bal@uantwerpen.be; Neyts, Erik C. [Department of Chemistry, University of Antwerp, Research Group PLASMANT, Universiteitsplein 1, 2610 Wilrijk, Antwerp (Belgium)
2014-11-28
Uniform-acceptance force-bias Monte Carlo (fbMC) methods have been shown to be a powerful technique to access longer timescales in atomistic simulations allowing, for example, phase transitions and growth. Recently, a new fbMC method, the time-stamped force-bias Monte Carlo (tfMC) method, was derived with inclusion of an estimated effective timescale; this timescale, however, does not seem able to explain some of the successes the method. In this contribution, we therefore explicitly quantify the effective timescale tfMC is able to access for a variety of systems, namely a simple single-particle, one-dimensional model system, the Lennard-Jones liquid, an adatom on the Cu(100) surface, a silicon crystal with point defects and a highly defected graphene sheet, in order to gain new insights into the mechanisms by which tfMC operates. It is found that considerable boosts, up to three orders of magnitude compared to molecular dynamics, can be achieved for solid state systems by lowering of the apparent activation barrier of occurring processes, while not requiring any system-specific input or modifications of the method. We furthermore address the pitfalls of using the method as a replacement or complement of molecular dynamics simulations, its ability to explicitly describe correct dynamics and reaction mechanisms, and the association of timescales to MC simulations in general.
Infinite Variance in Fermion Quantum Monte Carlo Calculations
Shi, Hao
2015-01-01
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, lattice QCD 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 upon to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple sub-areas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations turn out to 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 calc...
Infinite variance in fermion quantum Monte Carlo calculations
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.
Bayesian Inference in Monte-Carlo Tree Search
Tesauro, Gerald; Segal, Richard
2012-01-01
Monte-Carlo Tree Search (MCTS) methods are drawing great interest after yielding breakthrough results in computer Go. This paper proposes a Bayesian approach to MCTS that is inspired by distributionfree approaches such as UCT [13], yet significantly differs in important respects. The Bayesian framework allows potentially much more accurate (Bayes-optimal) estimation of node values and node uncertainties from a limited number of simulation trials. We further propose propagating inference in the tree via fast analytic Gaussian approximation methods: this can make the overhead of Bayesian inference manageable in domains such as Go, while preserving high accuracy of expected-value estimates. We find substantial empirical outperformance of UCT in an idealized bandit-tree test environment, where we can obtain valuable insights by comparing with known ground truth. Additionally we rigorously prove on-policy and off-policy convergence of the proposed methods.
Monte Carlo Registration and Its Application with Autonomous Robots
Directory of Open Access Journals (Sweden)
Christian Rink
2016-01-01
Full Text Available This work focuses on Monte Carlo registration methods and their application with autonomous robots. A streaming and an offline variant are developed, both based on a particle filter. The streaming registration is performed in real-time during data acquisition with a laser striper allowing for on-the-fly pose estimation. Thus, the acquired data can be instantly utilized, for example, for object modeling or robot manipulation, and the laser scan can be aborted after convergence. Curvature features are calculated online and the estimated poses are optimized in the particle weighting step. For sampling the pose particles, uniform, normal, and Bingham distributions are compared. The methods are evaluated with a high-precision laser striper attached to an industrial robot and with a noisy Time-of-Flight camera attached to service robots. The shown applications range from robot assisted teleoperation, over autonomous object modeling, to mobile robot localization.
Reversible jump Markov chain Monte Carlo for deconvolution.
Kang, Dongwoo; Verotta, Davide
2007-06-01
To solve the problem of estimating an unknown input function to a linear time invariant system we propose an adaptive non-parametric method based on reversible jump Markov chain Monte Carlo (RJMCMC). We use piecewise polynomial functions (splines) to represent the input function. The RJMCMC algorithm allows the exploration of a large space of competing models, in our case the collection of splines corresponding to alternative positions of breakpoints, and it is based on the specification of transition probabilities between the models. RJMCMC determines: the number and the position of the breakpoints, and the coefficients determining the shape of the spline, as well as the corresponding posterior distribution of breakpoints, number of breakpoints, coefficients and arbitrary statistics of interest associated with the estimation problem. Simulation studies show that the RJMCMC method can obtain accurate reconstructions of complex input functions, and obtains better results compared with standard non-parametric deconvolution methods. Applications to real data are also reported.
Cheon, Sooyoung
2013-02-16
Importance sampling and Markov chain Monte Carlo methods have been used in exact inference for contingency tables for a long time, however, their performances are not always very satisfactory. In this paper, we propose a stochastic approximation Monte Carlo importance sampling (SAMCIS) method for tackling this problem. SAMCIS is a combination of adaptive Markov chain Monte Carlo and importance sampling, which employs the stochastic approximation Monte Carlo algorithm (Liang et al., J. Am. Stat. Assoc., 102(477):305-320, 2007) to draw samples from an enlarged reference set with a known Markov basis. Compared to the existing importance sampling and Markov chain Monte Carlo methods, SAMCIS has a few advantages, such as fast convergence, ergodicity, and the ability to achieve a desired proportion of valid tables. The numerical results indicate that SAMCIS can outperform the existing importance sampling and Markov chain Monte Carlo methods: It can produce much more accurate estimates in much shorter CPU time than the existing methods, especially for the tables with high degrees of freedom. © 2013 Springer Science+Business Media New York.
pyNSMC: A Python Module for Null-Space Monte Carlo Uncertainty Analysis
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.
Monte Carlo Techniques for Nuclear Systems - Theory Lectures
Energy Technology Data Exchange (ETDEWEB)
Brown, Forrest B. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Monte Carlo Methods, Codes, and Applications Group; Univ. of New Mexico, Albuquerque, NM (United States). Nuclear Engineering Dept.
2016-11-29
These are lecture notes for a Monte Carlo class given at the University of New Mexico. The following topics are covered: course information; nuclear eng. review & MC; random numbers and sampling; computational geometry; collision physics; tallies and statistics; eigenvalue calculations I; eigenvalue calculations II; eigenvalue calculations III; variance reduction; parallel Monte Carlo; parameter studies; fission matrix and higher eigenmodes; doppler broadening; Monte Carlo depletion; HTGR modeling; coupled MC and T/H calculations; fission energy deposition. Solving particle transport problems with the Monte Carlo method is simple - just simulate the particle behavior. The devil is in the details, however. These lectures provide a balanced approach to the theory and practice of Monte Carlo simulation codes. The first lectures provide an overview of Monte Carlo simulation methods, covering the transport equation, random sampling, computational geometry, collision physics, and statistics. The next lectures focus on the state-of-the-art in Monte Carlo criticality simulations, covering the theory of eigenvalue calculations, convergence analysis, dominance ratio calculations, bias in Keff and tallies, bias in uncertainties, a case study of a realistic calculation, and Wielandt acceleration techniques. The remaining lectures cover advanced topics, including HTGR modeling and stochastic geometry, temperature dependence, fission energy deposition, depletion calculations, parallel calculations, and parameter studies. This portion of the class focuses on using MCNP to perform criticality calculations for reactor physics and criticality safety applications. It is an intermediate level class, intended for those with at least some familiarity with MCNP. Class examples provide hands-on experience at running the code, plotting both geometry and results, and understanding the code output. The class includes lectures & hands-on computer use for a variety of Monte Carlo calculations
Use of Monte Carlo methods in environmental risk assessments at the INEL: Applications and issues
Energy Technology Data Exchange (ETDEWEB)
Harris, G.; Van Horn, R.
1996-06-01
The EPA is increasingly considering the use of probabilistic risk assessment techniques as an alternative or refinement of the current point estimate of risk. This report provides an overview of the probabilistic technique called Monte Carlo Analysis. Advantages and disadvantages of implementing a Monte Carlo analysis over a point estimate analysis for environmental risk assessment are discussed. The general methodology is provided along with an example of its implementation. A phased approach to risk analysis that allows iterative refinement of the risk estimates is recommended for use at the INEL.
Reducing quasi-ergodicity in a double well potential by Tsallis Monte Carlo simulation
Iwamatsu, Masao; Okabe, Yutaka
2000-01-01
A new Monte Carlo scheme based on the system of Tsallis's generalized statistical mechanics is applied to a simple double well potential to calculate the canonical thermal average of potential energy. Although we observed serious quasi-ergodicity when using the standard Metropolis Monte Carlo algorithm, this problem is largely reduced by the use of the new Monte Carlo algorithm. Therefore the ergodicity is guaranteed even for short Monte Carlo steps if we use this new canonical Monte Carlo sc...
Finding organic vapors - a Monte Carlo approach
Vuollekoski, Henri; Boy, Michael; Kerminen, Veli-Matti; Kulmala, Markku
2010-05-01
drawbacks in accuracy, the inability to find diurnal variation and the lack of size resolution. Here, we aim to shed some light onto the problem by applying an ad hoc Monte Carlo algorithm to a well established aerosol dynamical model, the University of Helsinki Multicomponent Aerosol model (UHMA). By performing a side-by-side comparison with measurement data within the algorithm, this approach has the significant advantage of decreasing the amount of manual labor. But more importantly, by basing the comparison on particle number size distribution data - a quantity that can be quite reliably measured - the accuracy of the results is good.
Coherent Scattering Imaging Monte Carlo Simulation
Hassan, Laila Abdulgalil Rafik
Conventional mammography has poor contrast between healthy and cancerous tissues due to the small difference in attenuation properties. Coherent scatter potentially provides more information because interference of coherently scattered radiation depends on the average intermolecular spacing, and can be used to characterize tissue types. However, typical coherent scatter analysis techniques are not compatible with rapid low dose screening techniques. Coherent scatter slot scan imaging is a novel imaging technique which provides new information with higher contrast. In this work a simulation of coherent scatter was performed for slot scan imaging to assess its performance and provide system optimization. In coherent scatter imaging, the coherent scatter is exploited using a conventional slot scan mammography system with anti-scatter grids tilted at the characteristic angle of cancerous tissues. A Monte Carlo simulation was used to simulate the coherent scatter imaging. System optimization was performed across several parameters, including source voltage, tilt angle, grid distances, grid ratio, and shielding geometry. The contrast increased as the grid tilt angle increased beyond the characteristic angle for the modeled carcinoma. A grid tilt angle of 16 degrees yielded the highest contrast and signal to noise ratio (SNR). Also, contrast increased as the source voltage increased. Increasing grid ratio improved contrast at the expense of decreasing SNR. A grid ratio of 10:1 was sufficient to give a good contrast without reducing the intensity to a noise level. The optimal source to sample distance was determined to be such that the source should be located at the focal distance of the grid. A carcinoma lump of 0.5x0.5x0.5 cm3 in size was detectable which is reasonable considering the high noise due to the usage of relatively small number of incident photons for computational reasons. A further study is needed to study the effect of breast density and breast thickness
Kumar, Nagendra
2016-01-01
In earlier works, it was shown that the energy dependent soft time lags observed in kHz QPOs of neutron star low mass X-ray binaries (LMXBs) can be explained as being due to Comptonization lags provided a significant fraction ($\\eta \\sim 0.2$ - $0.8$) of the Comptonized photons impinge back into the soft photon source. Here we use a Monte Carlo scheme to verify if such a fraction is viable or not. In particular we consider three different Comptonizing medium geometries: (i) a spherical shell, (ii) a boundary layer like torus and (iii) a corona on top of an accretion disk. Two set of spectral parameters corresponding to the 'hot' and 'cold' seed photon models were explored. The general result of the study is that for a wide range of sizes, the fraction lies within $\\eta \\sim 0.3$ - $0.7$, and hence compatible with the range required to explain the soft time lags. Since there is a large uncertainty in the range, we cannot concretely rule out any of the geometries or spectral models, but the analysis suggests th...
Belinato, Walmir; Santos, William S.; Silva, Rogério M. V.; Souza, Divanizia N.
2014-03-01
The determination of dose conversion factors (S values) for the radionuclide fluorodeoxyglucose (18F-FDG) absorbed in the lungs during a positron emission tomography (PET) procedure was calculated using the Monte Carlo method (MCNPX version 2.7.0). For the obtained dose conversion factors of interest, it was considered a uniform absorption of radiopharmaceutical by the lung of a healthy adult human. The spectrum of fluorine was introduced in the input data file for the simulation. The simulation took place in two adult phantoms of both sexes, based on polygon mesh surfaces called FASH and MASH with anatomy and posture according to ICRP 89. The S values for the 22 internal organs/tissues, chosen from ICRP No. 110, for the FASH and MASH phantoms were compared with the results obtained from a MIRD V phantoms called ADAM and EVA used by the Committee on Medical Internal Radiation Dose (MIRD). We observed variation of more than 100% in S values due to structural anatomical differences in the internal organs of the MASH and FASH phantoms compared to the mathematical phantom.
Directory of Open Access Journals (Sweden)
Belinato Walmir
2014-03-01
Full Text Available The determination of dose conversion factors (S values for the radionuclide fluorodeoxyglucose (18F-FDG absorbed in the lungs during a positron emission tomography (PET procedure was calculated using the Monte Carlo method (MCNPX version 2.7.0. For the obtained dose conversion factors of interest, it was considered a uniform absorption of radiopharmaceutical by the lung of a healthy adult human. The spectrum of fluorine was introduced in the input data file for the simulation. The simulation took place in two adult phantoms of both sexes, based on polygon mesh surfaces called FASH and MASH with anatomy and posture according to ICRP 89. The S values for the 22 internal organs/tissues, chosen from ICRP No. 110, for the FASH and MASH phantoms were compared with the results obtained from a MIRD V phantoms called ADAM and EVA used by the Committee on Medical Internal Radiation Dose (MIRD. We observed variation of more than 100% in S values due to structural anatomical differences in the internal organs of the MASH and FASH phantoms compared to the mathematical phantom.
Kumar, Nagendra; Misra, Ranjeev
2016-10-01
In earlier works, it was shown that the energy-dependent soft time lags observed in kHz quasi-periodic oscillations of neutron star low-mass X-ray binaries can be explained as being due to Comptonization lags provided a significant fraction (η ˜ 0.2-0.8) of the Comptonized photons impinge back into the soft photon source. Here we use a Monte Carlo scheme to verify if such a fraction is viable or not. In particular we consider three different Comptonizing medium geometries: (i) a spherical shell, (ii) a boundary layer like torus and (iii) a corona on top of an accretion disc. Two sets of spectral parameters corresponding to the `hot' and `cold' seed photon models were explored. The general result of the study is that for a wide range of sizes, the fraction lies within η ˜ 0.3-0.7, and hence compatible with the range required to explain the soft time lags. Since there is a large uncertainty in the range, we cannot concretely rule out any of the geometries or spectral models, but the analysis suggests that a boundary layer type geometry with a `cold' seed spectral model is favoured over an accretion corona model. Better quality data will allow one to constrain the geometry more rigorously. Our results emphasize that there is significant heating of the soft photon source by the Comptonized photons and hence this effect needs to be taken into account for any detailed study of these sources.
Monte Carlo autofluorescence modeling of cervical intraepithelial neoplasm progression
Chu, S. C.; Chiang, H. K.; Wu, C. E.; He, S. Y.; Wang, D. Y.
2006-02-01
Monte Carlo fluorescence model has been developed to estimate the autofluorescent spectra associated with the progression of the Exo-Cervical Intraepithelial Neoplasm (CIN). We used double integrating spheres system and a tunable light source system, 380 to 600 nm, to measure the reflection and transmission spectra of a 50 μm thick tissue, and used Inverse Adding-Doubling (IAD) method to estimate the absorption (μa) and scattering (μs) coefficients. Human cervical tissue samples were sliced vertically (longitudinal) by the frozen section method. The results show that the absorption and scattering coefficients of cervical neoplasia are 2~3 times higher than normal tissues. We applied Monte Carlo method to estimate photon distribution and fluorescence emission in the tissue. By combining the intrinsic fluorescence information (collagen, NADH, and FAD), the anatomical information of the epithelium, CIN, stroma layers, and the fluorescence escape function, the autofluorescence spectra of CIN at different development stages were obtained.We have observed that the progression of the CIN results in gradually decreasing of the autofluorescence intensity of collagen peak intensity. In addition, the existence of the CIN layer formeda barrier that blocks the autofluorescence escaping from the stroma layer due to the strong extinction(scattering and absorption) of the CIN layer. To our knowledge, this is the first study measuring the CIN optical properties in the visible range; it also successfully demonstrates the fluorescence model forestimating autofluorescence spectra of cervical tissue associated with the progression of the CIN tissue;this model is very important in assisting the CIN diagnosis and treatment in clinical medicine.
Hybrid Multilevel Monte Carlo Simulation of Stochastic Reaction Networks
Moraes, Alvaro
2015-01-07
Stochastic reaction networks (SRNs) is a class of continuous-time Markov chains intended to describe, from the kinetic point of view, the time-evolution of chemical systems in which molecules of different chemical species undergo a finite set of reaction channels. This talk is based on articles [4, 5, 6], where we are interested in the following problem: given a SRN, X, defined though its set of reaction channels, and its initial state, x0, estimate E (g(X(T))); that is, the expected value of a scalar observable, g, of the process, X, at a fixed time, T. This problem lead us to define a series of Monte Carlo estimators, M, such that, with high probability can produce values close to the quantity of interest, E (g(X(T))). More specifically, given a user-selected tolerance, TOL, and a small confidence level, η, find an estimator, M, based on approximate sampled paths of X, such that, P (|E (g(X(T))) − M| ≤ TOL) ≥ 1 − η; even more, we want to achieve this objective with near optimal computational work. We first introduce a hybrid path-simulation scheme based on the well-known stochastic simulation algorithm (SSA)[3] and the tau-leap method [2]. Then, we introduce a Multilevel Monte Carlo strategy that allows us to achieve a computational complexity of order O(T OL−2), this is the same computational complexity as in an exact method but with a smaller constant. We provide numerical examples to show our results.
Applications guide to the MORSE Monte Carlo code
Energy Technology Data Exchange (ETDEWEB)
Cramer, S.N.
1985-08-01
A practical guide for the implementation of the MORESE-CG Monte Carlo radiation transport computer code system is presented. The various versions of the MORSE code are compared and contrasted, and the many references dealing explicitly with the MORSE-CG code are reviewed. The treatment of angular scattering is discussed, and procedures for obtaining increased differentiality of results in terms of reaction types and nuclides from a multigroup Monte Carlo code are explained in terms of cross-section and geometry data manipulation. Examples of standard cross-section data input and output are shown. Many other features of the code system are also reviewed, including (1) the concept of primary and secondary particles, (2) fission neutron generation, (3) albedo data capability, (4) DOMINO coupling, (5) history file use for post-processing of results, (6) adjoint mode operation, (7) variance reduction, and (8) input/output. In addition, examples of the combinatorial geometry are given, and the new array of arrays geometry feature (MARS) and its three-dimensional plotting code (JUNEBUG) are presented. Realistic examples of user routines for source, estimation, path-length stretching, and cross-section data manipulation are given. A deatiled explanation of the coupling between the random walk and estimation procedure is given in terms of both code parameters and physical analogies. The operation of the code in the adjoint mode is covered extensively. The basic concepts of adjoint theory and dimensionality are discussed and examples of adjoint source and estimator user routines are given for all common situations. Adjoint source normalization is explained, a few sample problems are given, and the concept of obtaining forward differential results from adjoint calculations is covered. Finally, the documentation of the standard MORSE-CG sample problem package is reviewed and on-going and future work is discussed.
Accuracy of Monte Carlo simulations compared to in-vivo MDCT dosimetry
Energy Technology Data Exchange (ETDEWEB)
Bostani, Maryam, E-mail: mbostani@mednet.ucla.edu; McMillan, Kyle; Cagnon, Chris H.; McNitt-Gray, Michael F. [Departments of Biomedical Physics and Radiology, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, California 90024 (United States); Mueller, Jonathon W. [United States Air Force, Keesler Air Force Base, Biloxi, Mississippi 39534 (United States); Cody, Dianna D. [University of Texas M.D. Anderson Cancer Center, Houston, Texas 77030 (United States); DeMarco, John J. [Departments of Biomedical Physics and Radiation Oncology, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, California 90024 (United States)
2015-02-15
Purpose: The purpose of this study was to assess the accuracy of a Monte Carlo simulation-based method for estimating radiation dose from multidetector computed tomography (MDCT) by comparing simulated doses in ten patients to in-vivo dose measurements. Methods: MD Anderson Cancer Center Institutional Review Board approved the acquisition of in-vivo rectal dose measurements in a pilot study of ten patients undergoing virtual colonoscopy. The dose measurements were obtained by affixing TLD capsules to the inner lumen of rectal catheters. Voxelized patient models were generated from the MDCT images of the ten patients, and the dose to the TLD for all exposures was estimated using Monte Carlo based simulations. The Monte Carlo simulation results were compared to the in-vivo dose measurements to determine accuracy. Results: The calculated mean percent difference between TLD measurements and Monte Carlo simulations was −4.9% with standard deviation of 8.7% and a range of −22.7% to 5.7%. Conclusions: The results of this study demonstrate very good agreement between simulated and measured doses in-vivo. Taken together with previous validation efforts, this work demonstrates that the Monte Carlo simulation methods can provide accurate estimates of radiation dose in patients undergoing CT examinations.
A Markov Chain Monte Carlo Approach to Confirmatory Item Factor Analysis
Edwards, Michael C.
2010-01-01
Item factor analysis has a rich tradition in both the structural equation modeling and item response theory frameworks. The goal of this paper is to demonstrate a novel combination of various Markov chain Monte Carlo (MCMC) estimation routines to estimate parameters of a wide variety of confirmatory item factor analysis models. Further, I show…
A study of Monte Carlo radiative transfer through fractal clouds
Energy Technology Data Exchange (ETDEWEB)
Gautier, C.; Lavallec, D.; O`Hirok, W.; Ricchiazzi, P. [Univ. of California, Santa Barbara, CA (United States)] [and others
1996-04-01
An understanding of radiation transport (RT) through clouds is fundamental to studies of the earth`s radiation budget and climate dynamics. The transmission through horizontally homogeneous clouds has been studied thoroughly using accurate, discreet ordinates radiative transfer models. However, the applicability of these results to general problems of global radiation budget is limited by the plane parallel assumption and the fact that real clouds fields show variability, both vertically and horizontally, on all size scales. To understand how radiation interacts with realistic clouds, we have used a Monte Carlo radiative transfer model to compute the details of the photon-cloud interaction on synthetic cloud fields. Synthetic cloud fields, generated by a cascade model, reproduce the scaling behavior, as well as the cloud variability observed and estimated from cloud satellite data.
Markov Chain Monte Carlo Bayesian Learning for Neural Networks
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.
Measuring Renyi entanglement entropy in quantum Monte Carlo simulations.
Hastings, Matthew B; González, Iván; Kallin, Ann B; Melko, Roger G
2010-04-16
We develop a quantum Monte Carlo procedure, in the valence bond basis, to measure the Renyi entanglement entropy of a many-body ground state as the expectation value of a unitary Swap operator acting on two copies of the system. An improved estimator involving the ratio of Swap operators for different subregions enables convergence of the entropy in a simulation time polynomial in the system size. We demonstrate convergence of the Renyi entropy to exact results for a Heisenberg chain. Finally, we calculate the scaling of the Renyi entropy in the two-dimensional Heisenberg model and confirm that the Néel ground state obeys the expected area law for systems up to linear size L=32.
Continuous-time quantum Monte Carlo using worm sampling
Gunacker, P.; Wallerberger, M.; Gull, E.; Hausoel, A.; Sangiovanni, G.; Held, K.
2015-10-01
We present a worm sampling method for calculating one- and two-particle Green's functions using continuous-time quantum Monte Carlo simulations in the hybridization expansion (CT-HYB). Instead of measuring Green's functions by removing hybridization lines from partition function configurations, as in conventional CT-HYB, the worm algorithm directly samples the Green's function. We show that worm sampling is necessary to obtain general two-particle Green's functions which are not of density-density type and that it improves the sampling efficiency when approaching the atomic limit. Such two-particle Green's functions are needed to compute off-diagonal elements of susceptibilities and occur in diagrammatic extensions of the dynamical mean-field theory and in efficient estimators for the single-particle self-energy.
New Monte Carlo method for the self-avoiding walk
Berretti, Alberto; Sokal, Alan D.
1985-08-01
We introduce a new Monte Carlo algorithm for the self-avoiding walk (SAW), and show that it is particularly efficient in the critical region (long chains). We also introduce new and more efficient statistical techniques. We employ these methods to extract numerical estimates for the critical parameters of the SAW on the square lattice. We find μ=2.63820 ± 0.00004 ± 0.00030 γ=1.352 ± 0.006 ± 0.025 νv=0.7590 ± 0.0062 ± 0.0042 where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second bar represents statistical error (classical 95% confidence limits). These results are based on SAWs of average length ≈ 166, using 340 hours CPU time on a CDC Cyber 170-730. We compare our results to previous work and indicate some directions for future research.
CORPORATE VALUATION USING TWO-DIMENSIONAL MONTE CARLO SIMULATION
Directory of Open Access Journals (Sweden)
Toth Reka
2010-12-01
Full Text Available In this paper, we have presented a corporate valuation model. The model combine several valuation methods in order to get more accurate results. To determine the corporate asset value we have used the Gordon-like two-stage asset valuation model based on the calculation of the free cash flow to the firm. We have used the free cash flow to the firm to determine the corporate market value, which was calculated with use of the Black-Scholes option pricing model in frame of the two-dimensional Monte Carlo simulation method. The combined model and the use of the two-dimensional simulation model provides a better opportunity for the corporate value estimation.
Quantitative application of Monte Carlo simulation in Fire-PSA
Energy Technology Data Exchange (ETDEWEB)
Mangs, J.; Hostikka, S.; Korhonen, T. [Valtion Teknillinen Tutkimuskeskus, Espoo (Finland); Keski-Rahkonen, O.
2007-05-15
In a power plant a fire cell forms the basic subunit. Since the fire is initially located there, the full-scale time dependent fire simulation and estimation of target response must be performed within the fire cell. Conditional, time dependent damage probabilities in a fire cell can now be calculated for arbitrary targets (component or a subsystem) combining probabilistic (Monte Carlo) and deterministic simulation. For the latter a spectrum from simple correlations up to latest computational fluid dynamics models is available. Selection of the code is made according to the requirements form the target cell. Although calculations are numerically heavy, it is now economically possible and feasible to carry out quantitative fire-PSA for a complete plant iteratively with the main PSA. From real applications examples are shown on assessment of fire spread possibility in a relay room, and potential of fire spread on cables in a tunnel. (orig.)
An unbiased Hessian representation for Monte Carlo PDFs
Energy Technology Data Exchange (ETDEWEB)
Carrazza, Stefano; Forte, Stefano [Universita di Milano, TIF Lab, Dipartimento di Fisica, Milan (Italy); INFN, Sezione di Milano (Italy); Kassabov, Zahari [Universita di Milano, TIF Lab, Dipartimento di Fisica, Milan (Italy); Universita di Torino, Dipartimento di Fisica, Turin (Italy); INFN, Sezione di Torino (Italy); Latorre, Jose Ignacio [Universitat de Barcelona, Departament d' Estructura i Constituents de la Materia, Barcelona (Spain); Rojo, Juan [University of Oxford, Rudolf Peierls Centre for Theoretical Physics, Oxford (United Kingdom)
2015-08-15
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. (orig.)
An Unbiased Hessian Representation for Monte Carlo PDFs
Carrazza, Stefano; Kassabov, Zahari; Latorre, Jose Ignacio; Rojo, Juan
2015-01-01
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 (CMC-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 togethe...
Monte Carlo evaluation of kerma in an HDR brachytherapy bunker
Energy Technology Data Exchange (ETDEWEB)
Perez-Calatayud, J [Department of Atomic, Molecular and Nuclear Physics, and IFIC, CSIC-University of Valencia, Burjassot (Spain); Granero, D [Department of Atomic, Molecular and Nuclear Physics, and IFIC, CSIC-University of Valencia, Burjassot (Spain); Ballester, F [Department of Atomic, Molecular and Nuclear Physics, and IFIC, CSIC-University of Valencia, Burjassot (Spain); Casal, E [Department of Atomic, Molecular and Nuclear Physics, and IFIC, CSIC-University of Valencia, Burjassot (Spain); Crispin, V [FIVO, Fundacion Instituto Valenciano De OncologIa, Valencia (Spain); Puchades, V [Grupo IMO-SFA, Madrid (Spain); Leon, A [Department of Chemistry and Nuclear Engineering, Polytechnic University of Valencia, Valencia (Spain); Verdu, G [Department of Chemistry and Nuclear Engineering, Polytechnic University of Valencia, Valencia (Spain)
2004-12-21
In recent years, the use of high dose rate (HDR) after-loader machines has greatly increased due to the shift from traditional Cs-137/Ir-192 low dose rate (LDR) to HDR brachytherapy. The method used to calculate the required concrete and, where appropriate, lead shielding in the door is based on analytical methods provided by documents published by the ICRP, the IAEA and the NCRP. The purpose of this study is to perform a more realistic kerma evaluation at the entrance maze door of an HDR bunker using the Monte Carlo code GEANT4. The Monte Carlo results were validated experimentally. The spectrum at the maze entrance door, obtained with Monte Carlo, has an average energy of about 110 keV, maintaining a similar value along the length of the maze. The comparison of results from the aforementioned values with the Monte Carlo ones shows that results obtained using the albedo coefficient from the ICRP document more closely match those given by the Monte Carlo method, although the maximum value given by MC calculations is 30% greater. (note)
Calculation Aspects of the European Rebalanced Basket Option using Monte Carlo Methods: Valuation
Directory of Open Access Journals (Sweden)
CJ van der Merwe
2012-06-01
Full Text Available Extra premiums can be charged to a client to guarantee a minimum payout of a contract on a portfolio that gets rebalanced on a regular basis back to fixed proportions. The valuation of this premium can be changed to that of the pricing of a European put option with underlying rebalanced portfolio. This article finds the most efficient estimators for the value of this path-dependant multi-asset put option using different Monte Carlo methods. With the help of a refined method, computing time of the value decreased significantly. Furthermore, Variance Reduction Techniques and Quasi-Monte Carlo methods delivered more accurate and faster converging estimates as well.
Monte Carlo studies of model Langmuir monolayers.
Opps, S B; Yang, B; Gray, C G; Sullivan, D E
2001-04-01
This paper examines some of the basic properties of a model Langmuir monolayer, consisting of surfactant molecules deposited onto a water subphase. The surfactants are modeled as rigid rods composed of a head and tail segment of diameters sigma(hh) and sigma(tt), respectively. The tails consist of n(t) approximately 4-7 effective monomers representing methylene groups. These rigid rods interact via site-site Lennard-Jones potentials with different interaction parameters for the tail-tail, head-tail, and head-head interactions. In a previous paper, we studied the ground-state properties of this system using a Landau approach. In the present paper, Monte Carlo simulations were performed in the canonical ensemble to elucidate the finite-temperature behavior of this system. Simulation techniques, incorporating a system of dynamic filters, allow us to decrease CPU time with negligible statistical error. This paper focuses on several of the key parameters, such as density, head-tail diameter mismatch, and chain length, responsible for driving transitions from uniformly tilted to untilted phases and between different tilt-ordered phases. Upon varying the density of the system, with sigma(hh)=sigma(tt), we observe a transition from a tilted (NNN)-condensed phase to an untilted-liquid phase and, upon comparison with recent experiments with fatty acid-alcohol and fatty acid-ester mixtures [M. C. Shih, M. K. Durbin, A. Malik, P. Zschack, and P. Dutta, J. Chem. Phys. 101, 9132 (1994); E. Teer, C. M. Knobler, C. Lautz, S. Wurlitzer, J. Kildae, and T. M. Fischer, J. Chem. Phys. 106, 1913 (1997)], we identify this as the L'(2)/Ov-L1 phase boundary. By varying the head-tail diameter ratio, we observe a decrease in T(c) with increasing mismatch. However, as the chain length was increased we observed that the transition temperatures increased and differences in T(c) due to head-tail diameter mismatch were diminished. In most of the present research, the water was treated as a hard
Quantitative Monte Carlo-based holmium-166 SPECT reconstruction
Energy Technology Data Exchange (ETDEWEB)
Elschot, Mattijs; Smits, Maarten L. J.; Nijsen, Johannes F. W.; Lam, Marnix G. E. H.; Zonnenberg, Bernard A.; Bosch, Maurice A. A. J. van den; Jong, Hugo W. A. M. de [Department of Radiology and Nuclear Medicine, University Medical Center Utrecht, Heidelberglaan 100, 3584 CX Utrecht (Netherlands); Viergever, Max A. [Image Sciences Institute, University Medical Center Utrecht, Heidelberglaan 100, 3584 CX Utrecht (Netherlands)
2013-11-15
Purpose: Quantitative imaging of the radionuclide distribution is of increasing interest for microsphere radioembolization (RE) of liver malignancies, to aid treatment planning and dosimetry. For this purpose, holmium-166 ({sup 166}Ho) microspheres have been developed, which can be visualized with a gamma camera. The objective of this work is to develop and evaluate a new reconstruction method for quantitative {sup 166}Ho SPECT, including Monte Carlo-based modeling of photon contributions from the full energy spectrum.Methods: A fast Monte Carlo (MC) simulator was developed for simulation of {sup 166}Ho projection images and incorporated in a statistical reconstruction algorithm (SPECT-fMC). Photon scatter and attenuation for all photons sampled from the full {sup 166}Ho energy spectrum were modeled during reconstruction by Monte Carlo simulations. The energy- and distance-dependent collimator-detector response was modeled using precalculated convolution kernels. Phantom experiments were performed to quantitatively evaluate image contrast, image noise, count errors, and activity recovery coefficients (ARCs) of SPECT-fMC in comparison with those of an energy window-based method for correction of down-scattered high-energy photons (SPECT-DSW) and a previously presented hybrid method that combines MC simulation of photopeak scatter with energy window-based estimation of down-scattered high-energy contributions (SPECT-ppMC+DSW). Additionally, the impact of SPECT-fMC on whole-body recovered activities (A{sup est}) and estimated radiation absorbed doses was evaluated using clinical SPECT data of six {sup 166}Ho RE patients.Results: At the same noise level, SPECT-fMC images showed substantially higher contrast than SPECT-DSW and SPECT-ppMC+DSW in spheres ≥17 mm in diameter. The count error was reduced from 29% (SPECT-DSW) and 25% (SPECT-ppMC+DSW) to 12% (SPECT-fMC). ARCs in five spherical volumes of 1.96–106.21 ml were improved from 32%–63% (SPECT-DSW) and 50%–80
Combined experimental and Monte Carlo verification of brachytherapy plans for vaginal applicators
Sloboda, Ron S.; Wang, Ruqing
1998-12-01
Dose rates in a phantom around a shielded and an unshielded vaginal applicator containing Selectron low-dose-rate sources were determined by experiment and Monte Carlo simulation. Measurements were performed with thermoluminescent dosimeters in a white polystyrene phantom using an experimental protocol geared for precision. Calculations for the same set-up were done using a version of the EGS4 Monte Carlo code system modified for brachytherapy applications into which a new combinatorial geometry package developed by Bielajew was recently incorporated. Measured dose rates agree with Monte Carlo estimates to within 5% (1 SD) for the unshielded applicator, while highlighting some experimental uncertainties for the shielded applicator. Monte Carlo calculations were also done to determine a value for the effective transmission of the shield required for clinical treatment planning, and to estimate the dose rate in water at points in axial and sagittal planes transecting the shielded applicator. Comparison with dose rates generated by the planning system indicates that agreement is better than 5% (1 SD) at most positions. The precision thermoluminescent dosimetry protocol and modified Monte Carlo code are effective complementary tools for brachytherapy applicator dosimetry.
Calibration and Monte Carlo modelling of neutron long counters
Tagziria, H
2000-01-01
The Monte Carlo technique has become a very powerful tool in radiation transport as full advantage is taken of enhanced cross-section data, more powerful computers and statistical techniques, together with better characterisation of neutron and photon source spectra. At the National Physical Laboratory, calculations using the Monte Carlo radiation transport code MCNP-4B have been combined with accurate measurements to characterise two long counters routinely used to standardise monoenergetic neutron fields. New and more accurate response function curves have been produced for both long counters. A novel approach using Monte Carlo methods has been developed, validated and used to model the response function of the counters and determine more accurately their effective centres, which have always been difficult to establish experimentally. Calculations and measurements agree well, especially for the De Pangher long counter for which details of the design and constructional material are well known. The sensitivit...
Vectorizing and macrotasking Monte Carlo neutral particle algorithms
Energy Technology Data Exchange (ETDEWEB)
Heifetz, D.B.
1987-04-01
Monte Carlo algorithms for computing neutral particle transport in plasmas have been vectorized and macrotasked. The techniques used are directly applicable to Monte Carlo calculations of neutron and photon transport, and Monte Carlo integration schemes in general. A highly vectorized code was achieved by calculating test flight trajectories in loops over arrays of flight data, isolating the conditional branches to as few a number of loops as possible. A number of solutions are discussed to the problem of gaps appearing in the arrays due to completed flights, which impede vectorization. A simple and effective implementation of macrotasking is achieved by dividing the calculation of the test flight profile among several processors. A tree of random numbers is used to ensure reproducible results. The additional memory required for each task may preclude using a larger number of tasks. In future machines, the limit of macrotasking may be possible, with each test flight, and split test flight, being a separate task.
Properties of Reactive Oxygen Species by Quantum Monte Carlo
Zen, Andrea; Guidoni, Leonardo
2014-01-01
The electronic properties of the oxygen molecule, in its singlet and triplet states, and of many small oxygen-containing radicals and anions have important roles in different fields of Chemistry, Biology and Atmospheric Science. Nevertheless, the electronic structure of such species is a challenge for ab-initio computational approaches because of the difficulties to correctly describe the statical and dynamical correlation effects in presence of one or more unpaired electrons. Only the highest-level quantum chemical approaches can yield reliable characterizations of their molecular properties, such as binding energies, equilibrium structures, molecular vibrations, charge distribution and polarizabilities. In this work we use the variational Monte Carlo (VMC) and the lattice regularized Monte Carlo (LRDMC) methods to investigate the equilibrium geometries and molecular properties of oxygen and oxygen reactive species. Quantum Monte Carlo methods are used in combination with the Jastrow Antisymmetrized Geminal ...
LCG MCDB - a Knowledgebase of Monte Carlo Simulated Events
Belov, S; Galkin, E; Gusev, A; Pokorski, Witold; Sherstnev, A V
2008-01-01
In this paper we report on LCG Monte Carlo Data Base (MCDB) and software which has been developed to operate MCDB. The main purpose of the LCG MCDB project is to provide a storage and documentation system for sophisticated event samples simulated for the LHC collaborations by experts. In many cases, the modern Monte Carlo simulation of physical processes requires expert knowledge in Monte Carlo generators or significant amount of CPU time to produce the events. MCDB is a knowledgebase mainly to accumulate simulated events of this type. The main motivation behind LCG MCDB is to make the sophisticated MC event samples available for various physical groups. All the data from MCDB is accessible in several convenient ways. LCG MCDB is being developed within the CERN LCG Application Area Simulation project.
The Monte Carlo method in quantum field theory
Morningstar, C
2007-01-01
This series of six lectures is an introduction to using the Monte Carlo method to carry out nonperturbative studies in quantum field theories. Path integrals in quantum field theory are reviewed, and their evaluation by the Monte Carlo method with Markov-chain based importance sampling is presented. Properties of Markov chains are discussed in detail and several proofs are presented, culminating in the fundamental limit theorem for irreducible Markov chains. The example of a real scalar field theory is used to illustrate the Metropolis-Hastings method and to demonstrate the effectiveness of an action-preserving (microcanonical) local updating algorithm in reducing autocorrelations. The goal of these lectures is to provide the beginner with the basic skills needed to start carrying out Monte Carlo studies in quantum field theories, as well as to present the underlying theoretical foundations of the method.
TAKING THE NEXT STEP WITH INTELLIGENT MONTE CARLO
Energy Technology Data Exchange (ETDEWEB)
Booth, T.E.; Carlson, J.A. [and others
2000-10-01
For many scientific calculations, Monte Carlo is the only practical method available. Unfortunately, standard Monte Carlo methods converge slowly as the square root of the computer time. We have shown, both numerically and theoretically, that the convergence rate can be increased dramatically if the Monte Carlo algorithm is allowed to adapt based on what it has learned from previous samples. As the learning continues, computational efficiency increases, often geometrically fast. The particle transport work achieved geometric convergence for a two-region problem as well as for problems with rapidly changing nuclear data. The statistics work provided theoretical proof of geometic convergence for continuous transport problems and promising initial results for airborne migration of particles. The statistical physics work applied adaptive methods to a variety of physical problems including the three-dimensional Ising glass, quantum scattering, and eigenvalue problems.
Optimised Iteration in Coupled Monte Carlo - Thermal-Hydraulics Calculations
Hoogenboom, J. Eduard; Dufek, Jan
2014-06-01
This paper describes an optimised iteration scheme for the number of neutron histories and the relaxation factor in successive iterations of coupled Monte Carlo and thermal-hydraulic reactor calculations based on the stochastic iteration method. The scheme results in an increasing number of neutron histories for the Monte Carlo calculation in successive iteration steps and a decreasing relaxation factor for the spatial power distribution to be used as input to the thermal-hydraulics calculation. The theoretical basis is discussed in detail and practical consequences of the scheme are shown, among which a nearly linear increase per iteration of the number of cycles in the Monte Carlo calculation. The scheme is demonstrated for a full PWR type fuel assembly. Results are shown for the axial power distribution during several iteration steps. A few alternative iteration method are also tested and it is concluded that the presented iteration method is near optimal.
Monte Carlo tests of the ELIPGRID-PC algorithm
Energy Technology Data Exchange (ETDEWEB)
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 rectangular 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.
Efficiency of Monte Carlo sampling in chaotic systems.
Leitão, Jorge C; Lopes, J M Viana Parente; Altmann, Eduardo G
2014-11-01
In this paper we investigate how the complexity of chaotic phase spaces affect the efficiency of importance sampling Monte Carlo simulations. We focus on flat-histogram simulations of the distribution of finite-time Lyapunov exponent in a simple chaotic system and obtain analytically that the computational effort: (i) scales polynomially with the finite time, a tremendous improvement over the exponential scaling obtained in uniform sampling simulations; and (ii) the polynomial scaling is suboptimal, a phenomenon known as critical slowing down. We show that critical slowing down appears because of the limited possibilities to issue a local proposal in the Monte Carlo procedure when it is applied to chaotic systems. These results show how generic properties of chaotic systems limit the efficiency of Monte Carlo simulations.
Sequential Monte Carlo on large binary sampling spaces
Schäfer, Christian
2011-01-01
A Monte Carlo algorithm is said to be adaptive if it automatically calibrates its current proposal distribution using past simulations. The choice of the parametric family that defines the set of proposal distributions is critical for a good performance. In this paper, we present such a parametric family for adaptive sampling on high-dimensional binary spaces. A practical motivation for this problem is variable selection in a linear regression context. We want to sample from a Bayesian posterior distribution on the model space using an appropriate version of Sequential Monte Carlo. Raw versions of Sequential Monte Carlo are easily implemented using binary vectors with independent components. For high-dimensional problems, however, these simple proposals do not yield satisfactory results. The key to an efficient adaptive algorithm are binary parametric families which take correlations into account, analogously to the multivariate normal distribution on continuous spaces. We provide a review of models for binar...
Monte Carlo simulation of laser attenuation characteristics in fog
Wang, Hong-Xia; Sun, Chao; Zhu, You-zhang; Sun, Hong-hui; Li, Pan-shi
2011-06-01
Based on the Mie scattering theory and the gamma size distribution model, the scattering extinction parameter of spherical fog-drop is calculated. For the transmission attenuation of the laser in the fog, a Monte Carlo simulation model is established, and the impact of attenuation ratio on visibility and field angle is computed and analysed using the program developed by MATLAB language. The results of the Monte Carlo method in this paper are compared with the results of single scattering method. The results show that the influence of multiple scattering need to be considered when the visibility is low, and single scattering calculations have larger errors. The phenomenon of multiple scattering can be interpreted more better when the Monte Carlo is used to calculate the attenuation ratio of the laser transmitting in the fog.
VARIATIONAL MONTE-CARLO APPROACH FOR ARTICULATED OBJECT TRACKING
Directory of Open Access Journals (Sweden)
Kartik Dwivedi
2013-12-01
Full Text Available In this paper, we describe a novel variational Monte Carlo approach for modeling and tracking body parts of articulated objects. An articulated object (human target is represented as a dynamic Markov network of the different constituent parts. The proposed approach combines local information of individual body parts and other spatial constraints influenced by neighboring parts. The movement of the relative parts of the articulated body is modeled with local information of displacements from the Markov network and the global information from other neighboring parts. We explore the effect of certain model parameters (including the number of parts tracked; number of Monte-Carlo cycles, etc. on system accuracy and show that ourvariational Monte Carlo approach achieves better efficiency and effectiveness compared to other methods on a number of real-time video datasets containing single targets.
Meaningful timescales from Monte Carlo simulations of molecular systems
Costa, Liborio I
2016-01-01
A new Markov Chain Monte Carlo method for simulating the dynamics of molecular systems with atomistic detail 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 Monte 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.
Applicability of Quasi-Monte Carlo for lattice systems
Ammon, Andreas; Jansen, Karl; Leovey, Hernan; Griewank, Andreas; Müller-Preussker, Micheal
2013-01-01
This project investigates the applicability of quasi-Monte Carlo methods to Euclidean lattice systems in order to improve the asymptotic error scaling of observables for such theories. The error of an observable calculated by averaging over random observations generated from ordinary Monte Carlo simulations scales like $N^{-1/2}$, where $N$ is the number of observations. By means of quasi-Monte Carlo methods it is possible to improve this scaling for certain problems to $N^{-1}$, or even further if the problems are regular enough. We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling of all investigated observables in both cases.
Implementation of Monte Carlo Simulations for the Gamma Knife System
Energy Technology Data Exchange (ETDEWEB)
Xiong, W [Memorial Sloan-Kettering Cancer Center/Mercy Medical Center, 1000 N Village Ave., Rockville Centre, NY 11570 (United States); Huang, D [Memorial Sloan-Kettering Cancer Center/Mercy Medical Center, 1000 N Village Ave., Rockville Centre, NY 11570 (United States); Lee, L [Memorial Sloan-Kettering Cancer Center/Mercy Medical Center, 1000 N Village Ave., Rockville Centre, NY 11570 (United States); Feng, J [Memorial Sloan-Kettering Cancer Center/Mercy Medical Center, 1000 N Village Ave., Rockville Centre, NY 11570 (United States); Morris, K [Memorial Sloan-Kettering Cancer Center/Mercy Medical Center, 1000 N Village Ave., Rockville Centre, NY 11570 (United States); Calugaru, E [Memorial Sloan-Kettering Cancer Center/Mercy Medical Center, 1000 N Village Ave., Rockville Centre, NY 11570 (United States); Burman, C [Memorial Sloan-Kettering Cancer Center/Mercy Medical Center, 1000 N Village Ave., Rockville Centre, NY 11570 (United States); Li, J [Fox Chase Cancer Center, 333 Cottman Ave., Philadelphia, PA 17111 (United States); Ma, C-M [Fox Chase Cancer Center, 333 Cottman Ave., Philadelphia, PA 17111 (United States)
2007-06-15
Currently the Gamma Knife system is accompanied with a treatment planning system, Leksell GammaPlan (LGP) which is a standard, computer-based treatment planning system for Gamma Knife radiosurgery. In LGP, the dose calculation algorithm does not consider the scatter dose contributions and the inhomogeneity effect due to the skull and air cavities. To improve the dose calculation accuracy, Monte Carlo simulations have been implemented for the Gamma Knife planning system. In this work, the 201 Cobalt-60 sources in the Gamma Knife unit are considered to have the same activity. Each Cobalt-60 source is contained in a cylindric stainless steel capsule. The particle phase space information is stored in four beam data files, which are collected in the inner sides of the 4 treatment helmets, after the Cobalt beam passes through the stationary and helmet collimators. Patient geometries are rebuilt from patient CT data. Twenty two Patients are included in the Monte Carlo simulation for this study. The dose is calculated using Monte Carlo in both homogenous and inhomogeneous geometries with identical beam parameters. To investigate the attenuation effect of the skull bone the dose in a 16cm diameter spherical QA phantom is measured with and without a 1.5mm Lead-covering and also simulated using Monte Carlo. The dose ratios with and without the 1.5mm Lead-covering are 89.8% based on measurements and 89.2% according to Monte Carlo for a 18mm-collimator Helmet. For patient geometries, the Monte Carlo results show that although the relative isodose lines remain almost the same with and without inhomogeneity corrections, the difference in the absolute dose is clinically significant. The average inhomogeneity correction is (3.9 {+-} 0.90) % for the 22 patients investigated. These results suggest that the inhomogeneity effect should be considered in the dose calculation for Gamma Knife treatment planning.
A standard Event Class for Monte Carlo Generators
Institute of Scientific and Technical Information of China (English)
L.A.Gerren; M.Fischler
2001-01-01
StdHepC++[1]is a CLHEP[2] Monte Carlo event class library which provides a common interface to Monte Carlo Event Generators,This work is an extensive redesign of the StdHep Fortran interface to use the full power of object oriented design,A generated event maps naturally onto the Directed Acyclic Graph concept and we have used the HepMC classes to implement this.The full implementation allows the user to combine events to simulate beam pileup and access them transparently as though they were a single event.
Parallelization of Monte Carlo codes MVP/GMVP
Energy Technology Data Exchange (ETDEWEB)
Nagaya, Yasunobu; Mori, Takamasa; Nakagawa, Masayuki [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment; Sasaki, Makoto
1998-03-01
General-purpose Monte Carlo codes MVP/GMVP are well-vectorized and thus enable us to perform high-speed Monte Carlo calculations. In order to achieve more speedups, we parallelized the codes on the different types of the parallel processing platforms. The platforms reported are a distributed-memory vector-parallel computer Fujitsu VPP500, a distributed-memory massively parallel computer Intel Paragon and a distributed-memory scalar-parallel computer Hitachi SR2201. As mentioned generally, ideal speedup could be obtained for large-scale problems but parallelization efficiency got worse as the batch size per a processing element (PE) was smaller. (author)
Parton distribution functions in Monte Carlo factorisation scheme
Jadach, S.; Płaczek, W.; Sapeta, S.; Siódmok, A.; Skrzypek, M.
2016-12-01
A next step in development of the KrkNLO method of including complete NLO QCD corrections to hard processes in a LO parton-shower Monte Carlo is presented. It consists of a generalisation of the method, previously used for the Drell-Yan process, to Higgs-boson production. This extension is accompanied with the complete description of parton distribution functions in a dedicated, Monte Carlo factorisation scheme, applicable to any process of production of one or more colour-neutral particles in hadron-hadron collisions.