Unbiased, scalable sampling of protein loop conformations from probabilistic priors

PubMed Central

2013-01-01

Background Protein loops are flexible structures that are intimately tied to function, but understanding loop motion and generating loop conformation ensembles remain significant computational challenges. Discrete search techniques scale poorly to large loops, optimization and molecular dynamics techniques are prone to local minima, and inverse kinematics techniques can only incorporate structural preferences in adhoc fashion. This paper presents Sub-Loop Inverse Kinematics Monte Carlo (SLIKMC), a new Markov chain Monte Carlo algorithm for generating conformations of closed loops according to experimentally available, heterogeneous structural preferences. Results Our simulation experiments demonstrate that the method computes high-scoring conformations of large loops (>10 residues) orders of magnitude faster than standard Monte Carlo and discrete search techniques. Two new developments contribute to the scalability of the new method. First, structural preferences are specified via a probabilistic graphical model (PGM) that links conformation variables, spatial variables (e.g., atom positions), constraints and prior information in a unified framework. The method uses a sparse PGM that exploits locality of interactions between atoms and residues. Second, a novel method for sampling sub-loops is developed to generate statistically unbiased samples of probability densities restricted by loop-closure constraints. Conclusion Numerical experiments confirm that SLIKMC generates conformation ensembles that are statistically consistent with specified structural preferences. Protein conformations with 100+ residues are sampled on standard PC hardware in seconds. Application to proteins involved in ion-binding demonstrate its potential as a tool for loop ensemble generation and missing structure completion. PMID:24565175

Monte Carlo sampling in diffusive dynamical systems

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Use of a Monte Carlo technique to complete a fragmented set of H2S emission rates from a wastewater treatment plant.

PubMed

Schauberger, Günther; Piringer, Martin; Baumann-Stanzer, Kathrin; Knauder, Werner; Petz, Erwin

2013-12-15

The impact of ambient concentrations in the vicinity of a plant can only be assessed if the emission rate is known. In this study, based on measurements of ambient H2S concentrations and meteorological parameters, the a priori unknown emission rates of a tannery wastewater treatment plant are calculated by an inverse dispersion technique. The calculations are determined using the Gaussian Austrian regulatory dispersion model. Following this method, emission data can be obtained, though only for a measurement station that is positioned such that the wind direction at the measurement station is leeward of the plant. Using the inverse transform sampling, which is a Monte Carlo technique, the dataset can also be completed for those wind directions for which no ambient concentration measurements are available. For the model validation, the measured ambient concentrations are compared with the calculated ambient concentrations obtained from the synthetic emission data of the Monte Carlo model. The cumulative frequency distribution of this new dataset agrees well with the empirical data. This inverse transform sampling method is thus a useful supplement for calculating emission rates using the inverse dispersion technique. Copyright © 2013 Elsevier B.V. All rights reserved.

Estimation of pressure-particle velocity impedance measurement uncertainty using the Monte Carlo method.

PubMed

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. © 2011 Acoustical Society of America

Application of a Monte Carlo framework with bootstrapping for quantification of uncertainty in baseline map of carbon emissions from deforestation in Tropical Regions

Treesearch

William Salas; Steve Hagen

2013-01-01

This presentation will provide an overview of an approach for quantifying uncertainty in spatial estimates of carbon emission from land use change. We generate uncertainty bounds around our final emissions estimate using a randomized, Monte Carlo (MC)-style sampling technique. This approach allows us to combine uncertainty from different sources without making...

Reactive Monte Carlo sampling with an ab initio potential

NASA Astrophysics Data System (ADS)

Leiding, Jeff; Coe, Joshua D.

2016-05-01

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

Use of randomized sampling for analysis of metabolic networks.

PubMed

Schellenberger, Jan; Palsson, Bernhard Ø

2009-02-27

Genome-scale metabolic network reconstructions in microorganisms have been formulated and studied for about 8 years. The constraint-based approach has shown great promise in analyzing the systemic properties of these network reconstructions. Notably, constraint-based models have been used successfully to predict the phenotypic effects of knock-outs and for metabolic engineering. The inherent uncertainty in both parameters and variables of large-scale models is significant and is well suited to study by Monte Carlo sampling of the solution space. These techniques have been applied extensively to the reaction rate (flux) space of networks, with more recent work focusing on dynamic/kinetic properties. Monte Carlo sampling as an analysis tool has many advantages, including the ability to work with missing data, the ability to apply post-processing techniques, and the ability to quantify uncertainty and to optimize experiments to reduce uncertainty. We present an overview of this emerging area of research in systems biology.

Some Small Sample Results for Maximum Likelihood Estimation in Multidimensional Scaling.

ERIC Educational Resources Information Center

Ramsay, J. O.

1980-01-01

Some aspects of the small sample behavior of maximum likelihood estimates in multidimensional scaling are investigated with Monte Carlo techniques. In particular, the chi square test for dimensionality is examined and a correction for bias is proposed and evaluated. (Author/JKS)

Density-based empirical likelihood procedures for testing symmetry of data distributions and K-sample comparisons.

PubMed

Vexler, Albert; Tanajian, Hovig; Hutson, Alan D

In practice, parametric likelihood-ratio techniques are powerful statistical tools. In this article, we propose and examine novel and simple distribution-free test statistics that efficiently approximate parametric likelihood ratios to analyze and compare distributions of K groups of observations. Using the density-based empirical likelihood methodology, we develop a Stata package that applies to a test for symmetry of data distributions and compares K -sample distributions. Recognizing that recent statistical software packages do not sufficiently address K -sample nonparametric comparisons of data distributions, we propose a new Stata command, vxdbel, to execute exact density-based empirical likelihood-ratio tests using K samples. To calculate p -values of the proposed tests, we use the following methods: 1) a classical technique based on Monte Carlo p -value evaluations; 2) an interpolation technique based on tabulated critical values; and 3) a new hybrid technique that combines methods 1 and 2. The third, cutting-edge method is shown to be very efficient in the context of exact-test p -value computations. This Bayesian-type method considers tabulated critical values as prior information and Monte Carlo generations of test statistic values as data used to depict the likelihood function. In this case, a nonparametric Bayesian method is proposed to compute critical values of exact tests.

Monte Carlo simulation of energy-dispersive x-ray fluorescence and applications

NASA Astrophysics Data System (ADS)

Li, Fusheng

Four key components with regards to Monte Carlo Library Least Squares (MCLLS) have been developed by the author. These include: a comprehensive and accurate Monte Carlo simulation code - CEARXRF5 with Differential Operators (DO) and coincidence sampling, Detector Response Function (DRF), an integrated Monte Carlo - Library Least-Squares (MCLLS) Graphical User Interface (GUI) visualization System (MCLLSPro) and a new reproducible and flexible benchmark experiment setup. All these developments or upgrades enable the MCLLS approach to be a useful and powerful tool for a tremendous variety of elemental analysis applications. CEARXRF, a comprehensive and accurate Monte Carlo code for simulating the total and individual library spectral responses of all elements, has been recently upgraded to version 5 by the author. The new version has several key improvements: input file format fully compatible with MCNP5, a new efficient general geometry tracking code, versatile source definitions, various variance reduction techniques (e.g. weight window mesh and splitting, stratifying sampling, etc.), a new cross section data storage and accessing method which improves the simulation speed by a factor of four and new cross section data, upgraded differential operators (DO) calculation capability, and also an updated coincidence sampling scheme which including K-L and L-L coincidence X-Rays, while keeping all the capabilities of the previous version. The new Differential Operators method is powerful for measurement sensitivity study and system optimization. For our Monte Carlo EDXRF elemental analysis system, it becomes an important technique for quantifying the matrix effect in near real time when combined with the MCLLS approach. An integrated visualization GUI system has been developed by the author to perform elemental analysis using iterated Library Least-Squares method for various samples when an initial guess is provided. This software was built on the Borland C++ Builder platform and has a user-friendly interface to accomplish all qualitative and quantitative tasks easily. That is to say, the software enables users to run the forward Monte Carlo simulation (if necessary) or use previously calculated Monte Carlo library spectra to obtain the sample elemental composition estimation within a minute. The GUI software is easy to use with user-friendly features and has the capability to accomplish all related tasks in a visualization environment. It can be a powerful tool for EDXRF analysts. A reproducible experiment setup has been built and experiments have been performed to benchmark the system. Two types of Standard Reference Materials (SRM), stainless steel samples from National Institute of Standards and Technology (NIST) and aluminum alloy samples from Alcoa Inc., with certified elemental compositions, are tested with this reproducible prototype system using a 109Cd radioisotope source (20mCi) and a liquid nitrogen cooled Si(Li) detector. The results show excellent agreement between the calculated sample compositions and their reference values and the approach is very fast.

Driven-dissipative quantum Monte Carlo method for open quantum systems

NASA Astrophysics Data System (ADS)

Nagy, Alexandra; Savona, Vincenzo

2018-05-01

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

RESPONDENT-DRIVEN SAMPLING AS MARKOV CHAIN MONTE CARLO

PubMed Central

GOEL, SHARAD; SALGANIK, MATTHEW J.

2013-01-01

Respondent-driven sampling (RDS) is a recently introduced, and now widely used, technique for estimating disease prevalence in hidden populations. RDS data are collected through a snowball mechanism, in which current sample members recruit future sample members. In this paper we present respondent-driven sampling as Markov chain Monte Carlo (MCMC) importance sampling, and we examine the effects of community structure and the recruitment procedure on the variance of RDS estimates. Past work has assumed that the variance of RDS estimates is primarily affected by segregation between healthy and infected individuals. We examine an illustrative model to show that this is not necessarily the case, and that bottlenecks anywhere in the networks can substantially affect estimates. We also show that variance is inflated by a common design feature in which sample members are encouraged to recruit multiple future sample members. The paper concludes with suggestions for implementing and evaluating respondent-driven sampling studies. PMID:19572381

Model-Averaged ℓ1 Regularization using Markov Chain Monte Carlo Model Composition

PubMed Central

Fraley, Chris; Percival, Daniel

2014-01-01

Bayesian Model Averaging (BMA) is an effective technique for addressing model uncertainty in variable selection problems. However, current BMA approaches have computational difficulty dealing with data in which there are many more measurements (variables) than samples. This paper presents a method for combining ℓ1 regularization and Markov chain Monte Carlo model composition techniques for BMA. By treating the ℓ1 regularization path as a model space, we propose a method to resolve the model uncertainty issues arising in model averaging from solution path point selection. We show that this method is computationally and empirically effective for regression and classification in high-dimensional datasets. We apply our technique in simulations, as well as to some applications that arise in genomics. PMID:25642001

Computer simulation of stochastic processes through model-sampling (Monte Carlo) techniques.

PubMed

Sheppard, C W.

1969-03-01

A simple Monte Carlo simulation program is outlined which can be used for the investigation of random-walk problems, for example in diffusion, or the movement of tracers in the blood circulation. The results given by the simulation are compared with those predicted by well-established theory, and it is shown how the model can be expanded to deal with drift, and with reflexion from or adsorption at a boundary.

PyMC: Bayesian Stochastic Modelling in Python

PubMed Central

Patil, Anand; Huard, David; Fonnesbeck, Christopher J.

2010-01-01

This user guide describes a Python package, PyMC, that allows users to efficiently code a probabilistic model and draw samples from its posterior distribution using Markov chain Monte Carlo techniques. PMID:21603108

An efficient interpolation technique for jump proposals in reversible-jump Markov chain Monte Carlo calculations

PubMed Central

Farr, W. M.; Mandel, I.; Stevens, D.

2015-01-01

Selection among alternative theoretical models given an observed dataset is an important challenge in many areas of physics and astronomy. Reversible-jump Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for performing Bayesian model selection, but it suffers from a fundamental difficulty and it requires jumps between model parameter spaces, but cannot efficiently explore both parameter spaces at once. Thus, a naive jump between parameter spaces is unlikely to be accepted in the Markov chain Monte Carlo (MCMC) algorithm and convergence is correspondingly slow. Here, we demonstrate an interpolation technique that uses samples from single-model MCMCs to propose intermodel jumps from an approximation to the single-model posterior of the target parameter space. The interpolation technique, based on a kD-tree data structure, is adaptive and efficient in modest dimensionality. We show that our technique leads to improved convergence over naive jumps in an RJMCMC, and compare it to other proposals in the literature to improve the convergence of RJMCMCs. We also demonstrate the use of the same interpolation technique as a way to construct efficient ‘global’ proposal distributions for single-model MCMCs without prior knowledge of the structure of the posterior distribution, and discuss improvements that permit the method to be used in higher dimensional spaces efficiently. PMID:26543580

Monte Carlo method for computing density of states and quench probability of potential energy and enthalpy landscapes.

PubMed

Mauro, John C; Loucks, Roger J; Balakrishnan, Jitendra; Raghavan, Srikanth

2007-05-21

The thermodynamics and kinetics of a many-body system can be described in terms of a potential energy landscape in multidimensional configuration space. The partition function of such a landscape can be written in terms of a density of states, which can be computed using a variety of Monte Carlo techniques. In this paper, a new self-consistent Monte Carlo method for computing density of states is described that uses importance sampling and a multiplicative update factor to achieve rapid convergence. The technique is then applied to compute the equilibrium quench probability of the various inherent structures (minima) in the landscape. The quench probability depends on both the potential energy of the inherent structure and the volume of its corresponding basin in configuration space. Finally, the methodology is extended to the isothermal-isobaric ensemble in order to compute inherent structure quench probabilities in an enthalpy landscape.

Respondent-driven sampling as Markov chain Monte Carlo.

PubMed

Goel, Sharad; Salganik, Matthew J

2009-07-30

Respondent-driven sampling (RDS) is a recently introduced, and now widely used, technique for estimating disease prevalence in hidden populations. RDS data are collected through a snowball mechanism, in which current sample members recruit future sample members. In this paper we present RDS as Markov chain Monte Carlo importance sampling, and we examine the effects of community structure and the recruitment procedure on the variance of RDS estimates. Past work has assumed that the variance of RDS estimates is primarily affected by segregation between healthy and infected individuals. We examine an illustrative model to show that this is not necessarily the case, and that bottlenecks anywhere in the networks can substantially affect estimates. We also show that variance is inflated by a common design feature in which the sample members are encouraged to recruit multiple future sample members. The paper concludes with suggestions for implementing and evaluating RDS studies.

Bold Diagrammatic Monte Carlo for Fermionic and Fermionized Systems

NASA Astrophysics Data System (ADS)

Svistunov, Boris

2013-03-01

In three different fermionic cases--repulsive Hubbard model, resonant fermions, and fermionized spins-1/2 (on triangular lattice)--we observe the phenomenon of sign blessing: Feynman diagrammatic series features finite convergence radius despite factorial growth of the number of diagrams with diagram order. Bold diagrammatic Monte Carlo technique allows us to sample millions of skeleton Feynman diagrams. With the universal fermionization trick we can fermionize essentially any (bosonic, spin, mixed, etc.) lattice system. The combination of fermionization and Bold diagrammatic Monte Carlo yields a universal first-principle approach to strongly correlated lattice systems, provided the sign blessing is a generic fermionic phenomenon. Supported by NSF and DARPA

Reactive Monte Carlo sampling with an ab initio potential

DOE PAGES

Leiding, Jeff; Coe, Joshua D.

2016-05-04

Here, we present the first application of reactive Monte Carlo in a first-principles context. The algorithm samples in a modified NVT ensemble in which the volume, temperature, and total number of atoms of a given type are held fixed, but molecular composition is allowed to evolve through stochastic variation of chemical connectivity. We also discuss general features of the method, as well as techniques needed to enhance the efficiency of Boltzmann sampling. Finally, we compare the results of simulation of NH 3 to those of ab initio molecular dynamics (AIMD). Furthermore, we find that there are regions of state spacemore » for which RxMC sampling is much more efficient than AIMD due to the “rare-event” character of chemical reactions.« less

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Decomposition of Some Well-Known Variance Reduction Techniques. Revision.

DTIC Science & Technology

1985-05-01

34use a family of transformatlom to convert given samples into samples conditioned on a given characteristic (p. 04)." Dub and Horowitz (1979), Granovsky ...34Antithetic Varlates Revisited," Commun. ACM 26, 11, 064-971. Granovsky , B.L. (1981), "Optimal Formulae of the Conditional Monte Carlo," SIAM J. Alg

Quantum speedup of Monte Carlo methods.

PubMed

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.

Quantum speedup of Monte Carlo methods

PubMed Central

Montanaro, Ashley

2015-01-01

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. PMID:26528079

A microstructural lattice model for strain oriented problems: A combined Monte Carlo finite element technique

NASA Technical Reports Server (NTRS)

Gayda, J.; Srolovitz, D. J.

1987-01-01

A specialized, microstructural lattice model, termed MCFET for combined Monte Carlo Finite Element Technique, was developed which simulates microstructural evolution in material systems where modulated phases occur and the directionality of the modulation is influenced by internal and external stresses. In this approach, the microstructure is discretized onto a fine lattice. Each element in the lattice is labelled in accordance with its microstructural identity. Diffusion of material at elevated temperatures is simulated by allowing exchanges of neighboring elements if the exchange lowers the total energy of the system. A Monte Carlo approach is used to select the exchange site while the change in energy associated with stress fields is computed using a finite element technique. The MCFET analysis was validated by comparing this approach with a closed form, analytical method for stress assisted, shape changes of a single particle in an infinite matrix. Sample MCFET analytical for multiparticle problems were also run and in general the resulting microstructural changes associated with the application of an external stress are similar to that observed in Ni-Al-Cr alloys at elevated temperature.

Accuracy of remotely sensed data: Sampling and analysis procedures

NASA Technical Reports Server (NTRS)

Congalton, R. G.; Oderwald, R. G.; Mead, R. A.

1982-01-01

A review and update of the discrete multivariate analysis techniques used for accuracy assessment is given. A listing of the computer program written to implement these techniques is given. New work on evaluating accuracy assessment using Monte Carlo simulation with different sampling schemes is given. The results of matrices from the mapping effort of the San Juan National Forest is given. A method for estimating the sample size requirements for implementing the accuracy assessment procedures is given. A proposed method for determining the reliability of change detection between two maps of the same area produced at different times is given.

Depletion Calculations Based on Perturbations. Application to the Study of a Rep-Like Assembly at Beginning of Cycle with TRIPOLI-4®.

NASA Astrophysics Data System (ADS)

Dieudonne, Cyril; Dumonteil, Eric; Malvagi, Fausto; M'Backé Diop, Cheikh

2014-06-01

For several years, Monte Carlo burnup/depletion codes have appeared, which couple Monte Carlo codes to simulate the neutron transport to deterministic methods, which handle the medium depletion due to the neutron flux. Solving Boltzmann and Bateman equations in such a way allows to track fine 3-dimensional effects and to get rid of multi-group hypotheses done by deterministic solvers. The counterpart is the prohibitive calculation time due to the Monte Carlo solver called at each time step. In this paper we present a methodology to avoid the repetitive and time-expensive Monte Carlo simulations, and to replace them by perturbation calculations: indeed the different burnup steps may be seen as perturbations of the isotopic concentration of an initial Monte Carlo simulation. In a first time we will present this method, and provide details on the perturbative technique used, namely the correlated sampling. In a second time the implementation of this method in the TRIPOLI-4® code will be discussed, as well as the precise calculation scheme a meme to bring important speed-up of the depletion calculation. Finally, this technique will be used to calculate the depletion of a REP-like assembly, studied at beginning of its cycle. After having validated the method with a reference calculation we will show that it can speed-up by nearly an order of magnitude standard Monte-Carlo depletion codes.

The Effect of Unequal Samples, Heterogeneity of Covariance Matrices, and Number of Variables on Discriminant Analysis Classification Tables and Related Statistics.

ERIC Educational Resources Information Center

Spearing, Debra; Woehlke, Paula

To assess the effect on discriminant analysis in terms of correct classification into two groups, the following parameters were systematically altered using Monte Carlo techniques: sample sizes; proportions of one group to the other; number of independent variables; and covariance matrices. The pairing of the off diagonals (or covariances) with…

Improved importance sampling technique for efficient simulation of digital communication systems

NASA Technical Reports Server (NTRS)

Lu, Dingqing; Yao, Kung

1988-01-01

A new, improved importance sampling (IIS) approach to simulation is considered. Some basic concepts of IS are introduced, and detailed evolutions of simulation estimation variances for Monte Carlo (MC) and IS simulations are given. The general results obtained from these evolutions are applied to the specific previously known conventional importance sampling (CIS) technique and the new IIS technique. The derivation for a linear system with no signal random memory is considered in some detail. For the CIS technique, the optimum input scaling parameter is found, while for the IIS technique, the optimum translation parameter is found. The results are generalized to a linear system with memory and signals. Specific numerical and simulation results are given which show the advantages of CIS over MC and IIS over CIS for simulations of digital communications systems.

Slice sampling technique in Bayesian extreme of gold price modelling

NASA Astrophysics Data System (ADS)

Rostami, Mohammad; Adam, Mohd Bakri; Ibrahim, Noor Akma; Yahya, Mohamed Hisham

2013-09-01

In this paper, a simulation study of Bayesian extreme values by using Markov Chain Monte Carlo via slice sampling algorithm is implemented. We compared the accuracy of slice sampling with other methods for a Gumbel model. This study revealed that slice sampling algorithm offers more accurate and closer estimates with less RMSE than other methods . Finally we successfully employed this procedure to estimate the parameters of Malaysia extreme gold price from 2000 to 2011.

Invited review article: physics and Monte Carlo techniques as relevant to cryogenic, phonon, and ionization readout of Cryogenic Dark Matter Search radiation detectors.

PubMed

Leman, Steven W

2012-09-01

This review discusses detector physics and Monte Carlo techniques for cryogenic, radiation detectors that utilize combined phonon and ionization readout. A general review of cryogenic phonon and charge transport is provided along with specific details of the Cryogenic Dark Matter Search detector instrumentation. In particular, this review covers quasidiffusive phonon transport, which includes phonon focusing, anharmonic decay, and isotope scattering. The interaction of phonons in the detector surface is discussed along with the downconversion of phonons in superconducting films. The charge transport physics include a mass tensor which results from the crystal band structure and is modeled with a Herring-Vogt transformation. Charge scattering processes involve the creation of Neganov-Luke phonons. Transition-edge-sensor (TES) simulations include a full electric circuit description and all thermal processes including Joule heating, cooling to the substrate, and thermal diffusion within the TES, the latter of which is necessary to model normal-superconducting phase separation. Relevant numerical constants are provided for these physical processes in germanium, silicon, aluminum, and tungsten. Random number sampling methods including inverse cumulative distribution function (CDF) and rejection techniques are reviewed. To improve the efficiency of charge transport modeling, an additional second order inverse CDF method is developed here along with an efficient barycentric coordinate sampling method of electric fields. Results are provided in a manner that is convenient for use in Monte Carlo and references are provided for validation of these models.

Application of Enhanced Sampling Monte Carlo Methods for High-Resolution Protein-Protein Docking in Rosetta

PubMed Central

Zhang, Zhe; Schindler, Christina E. M.; Lange, Oliver F.; Zacharias, Martin

2015-01-01

The high-resolution refinement of docked protein-protein complexes can provide valuable structural and mechanistic insight into protein complex formation complementing experiment. Monte Carlo (MC) based approaches are frequently applied to sample putative interaction geometries of proteins including also possible conformational changes of the binding partners. In order to explore efficiency improvements of the MC sampling, several enhanced sampling techniques, including temperature or Hamiltonian replica exchange and well-tempered ensemble approaches, have been combined with the MC method and were evaluated on 20 protein complexes using unbound partner structures. The well-tempered ensemble method combined with a 2-dimensional temperature and Hamiltonian replica exchange scheme (WTE-H-REMC) was identified as the most efficient search strategy. Comparison with prolonged MC searches indicates that the WTE-H-REMC approach requires approximately 5 times fewer MC steps to identify near native docking geometries compared to conventional MC searches. PMID:26053419

A novel hybrid scattering order-dependent variance reduction method for Monte Carlo simulations of radiative transfer in cloudy atmosphere

NASA Astrophysics Data System (ADS)

Wang, Zhen; Cui, Shengcheng; Yang, Jun; Gao, Haiyang; Liu, Chao; Zhang, Zhibo

2017-03-01

We present a novel hybrid scattering order-dependent variance reduction method to accelerate the convergence rate in both forward and backward Monte Carlo radiative transfer simulations involving highly forward-peaked scattering phase function. This method is built upon a newly developed theoretical framework that not only unifies both forward and backward radiative transfer in scattering-order-dependent integral equation, but also generalizes the variance reduction formalism in a wide range of simulation scenarios. In previous studies, variance reduction is achieved either by using the scattering phase function forward truncation technique or the target directional importance sampling technique. Our method combines both of them. A novel feature of our method is that all the tuning parameters used for phase function truncation and importance sampling techniques at each order of scattering are automatically optimized by the scattering order-dependent numerical evaluation experiments. To make such experiments feasible, we present a new scattering order sampling algorithm by remodeling integral radiative transfer kernel for the phase function truncation method. The presented method has been implemented in our Multiple-Scaling-based Cloudy Atmospheric Radiative Transfer (MSCART) model for validation and evaluation. The main advantage of the method is that it greatly improves the trade-off between numerical efficiency and accuracy order by order.

Optimizing the implementation of the target motion sampling temperature treatment technique - How fast can it get?

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

Tuomas, V.; Jaakko, L.

This article discusses the optimization of the target motion sampling (TMS) temperature treatment method, previously implemented in the Monte Carlo reactor physics code Serpent 2. The TMS method was introduced in [1] and first practical results were presented at the PHYSOR 2012 conference [2]. The method is a stochastic method for taking the effect of thermal motion into account on-the-fly in a Monte Carlo neutron transport calculation. It is based on sampling the target velocities at collision sites and then utilizing the 0 K cross sections at target-at-rest frame for reaction sampling. The fact that the total cross section becomesmore » a distributed quantity is handled using rejection sampling techniques. The original implementation of the TMS requires 2.0 times more CPU time in a PWR pin-cell case than a conventional Monte Carlo calculation relying on pre-broadened effective cross sections. In a HTGR case examined in this paper the overhead factor is as high as 3.6. By first changing from a multi-group to a continuous-energy implementation and then fine-tuning a parameter affecting the conservativity of the majorant cross section, it is possible to decrease the overhead factors to 1.4 and 2.3, respectively. Preliminary calculations are also made using a new and yet incomplete optimization method in which the temperature of the basis cross section is increased above 0 K. It seems that with the new approach it may be possible to decrease the factors even as low as 1.06 and 1.33, respectively, but its functionality has not yet been proven. Therefore, these performance measures should be considered preliminary. (authors)« less

Adaptive polynomial chaos techniques for uncertainty quantification of a gas cooled fast reactor transient

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

Perko, Z.; Gilli, L.; Lathouwers, D.

2013-07-01

Uncertainty quantification plays an increasingly important role in the nuclear community, especially with the rise of Best Estimate Plus Uncertainty methodologies. Sensitivity analysis, surrogate models, Monte Carlo sampling and several other techniques can be used to propagate input uncertainties. In recent years however polynomial chaos expansion has become a popular alternative providing high accuracy at affordable computational cost. This paper presents such polynomial chaos (PC) methods using adaptive sparse grids and adaptive basis set construction, together with an application to a Gas Cooled Fast Reactor transient. Comparison is made between a new sparse grid algorithm and the traditionally used techniquemore » proposed by Gerstner. An adaptive basis construction method is also introduced and is proved to be advantageous both from an accuracy and a computational point of view. As a demonstration the uncertainty quantification of a 50% loss of flow transient in the GFR2400 Gas Cooled Fast Reactor design was performed using the CATHARE code system. The results are compared to direct Monte Carlo sampling and show the superior convergence and high accuracy of the polynomial chaos expansion. Since PC techniques are easy to implement, they can offer an attractive alternative to traditional techniques for the uncertainty quantification of large scale problems. (authors)« less

Accuracy and convergence of coupled finite-volume/Monte Carlo codes for plasma edge simulations of nuclear fusion reactors

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

Ghoos, K., E-mail: kristel.ghoos@kuleuven.be; Dekeyser, W.; Samaey, G.

2016-10-01

The plasma and neutral transport in the plasma edge of a nuclear fusion reactor is usually simulated using coupled finite volume (FV)/Monte Carlo (MC) codes. However, under conditions of future reactors like ITER and DEMO, convergence issues become apparent. This paper examines the convergence behaviour and the numerical error contributions with a simplified FV/MC model for three coupling techniques: Correlated Sampling, Random Noise and Robbins Monro. Also, practical procedures to estimate the errors in complex codes are proposed. Moreover, first results with more complex models show that an order of magnitude speedup can be achieved without any loss in accuracymore » by making use of averaging in the Random Noise coupling technique.« less

Binding Modes of Ligands Using Enhanced Sampling (BLUES): Rapid Decorrelation of Ligand Binding Modes via Nonequilibrium Candidate Monte Carlo.

PubMed

Gill, Samuel C; Lim, Nathan M; Grinaway, Patrick B; Rustenburg, Ariën S; Fass, Josh; Ross, Gregory A; Chodera, John D; Mobley, David L

2018-05-31

Accurately predicting protein-ligand binding affinities and binding modes is a major goal in computational chemistry, but even the prediction of ligand binding modes in proteins poses major challenges. Here, we focus on solving the binding mode prediction problem for rigid fragments. That is, we focus on computing the dominant placement, conformation, and orientations of a relatively rigid, fragment-like ligand in a receptor, and the populations of the multiple binding modes which may be relevant. This problem is important in its own right, but is even more timely given the recent success of alchemical free energy calculations. Alchemical calculations are increasingly used to predict binding free energies of ligands to receptors. However, the accuracy of these calculations is dependent on proper sampling of the relevant ligand binding modes. Unfortunately, ligand binding modes may often be uncertain, hard to predict, and/or slow to interconvert on simulation time scales, so proper sampling with current techniques can require prohibitively long simulations. We need new methods which dramatically improve sampling of ligand binding modes. Here, we develop and apply a nonequilibrium candidate Monte Carlo (NCMC) method to improve sampling of ligand binding modes. In this technique, the ligand is rotated and subsequently allowed to relax in its new position through alchemical perturbation before accepting or rejecting the rotation and relaxation as a nonequilibrium Monte Carlo move. When applied to a T4 lysozyme model binding system, this NCMC method shows over 2 orders of magnitude improvement in binding mode sampling efficiency compared to a brute force molecular dynamics simulation. This is a first step toward applying this methodology to pharmaceutically relevant binding of fragments and, eventually, drug-like molecules. We are making this approach available via our new Binding modes of ligands using enhanced sampling (BLUES) package which is freely available on GitHub.

Resonance line transfer calculations by doubling thin layers. I - Comparison with other techniques. II - The use of the R-parallel redistribution function. [planetary atmospheres

NASA Technical Reports Server (NTRS)

Yelle, Roger V.; Wallace, Lloyd

1989-01-01

A versatile and efficient technique for the solution of the resonance line scattering problem with frequency redistribution in planetary atmospheres is introduced. Similar to the doubling approach commonly used in monochromatic scattering problems, the technique has been extended to include the frequency dependence of the radiation field. Methods for solving problems with external or internal sources and coupled spectral lines are presented, along with comparison of some sample calculations with results from Monte Carlo and Feautrier techniques. The doubling technique has also been applied to the solution of resonance line scattering problems where the R-parallel redistribution function is appropriate, both neglecting and including polarization as developed by Yelle and Wallace (1989). With the constraint that the atmosphere is illuminated from the zenith, the only difficulty of consequence is that of performing precise frequency integrations over the line profiles. With that problem solved, it is no longer necessary to use the Monte Carlo method to solve this class of problem.

Impact of multicollinearity on small sample hydrologic regression models

NASA Astrophysics Data System (ADS)

Kroll, Charles N.; Song, Peter

2013-06-01

Often hydrologic regression models are developed with ordinary least squares (OLS) procedures. The use of OLS with highly correlated explanatory variables produces multicollinearity, which creates highly sensitive parameter estimators with inflated variances and improper model selection. It is not clear how to best address multicollinearity in hydrologic regression models. Here a Monte Carlo simulation is developed to compare four techniques to address multicollinearity: OLS, OLS with variance inflation factor screening (VIF), principal component regression (PCR), and partial least squares regression (PLS). The performance of these four techniques was observed for varying sample sizes, correlation coefficients between the explanatory variables, and model error variances consistent with hydrologic regional regression models. The negative effects of multicollinearity are magnified at smaller sample sizes, higher correlations between the variables, and larger model error variances (smaller R2). The Monte Carlo simulation indicates that if the true model is known, multicollinearity is present, and the estimation and statistical testing of regression parameters are of interest, then PCR or PLS should be employed. If the model is unknown, or if the interest is solely on model predictions, is it recommended that OLS be employed since using more complicated techniques did not produce any improvement in model performance. A leave-one-out cross-validation case study was also performed using low-streamflow data sets from the eastern United States. Results indicate that OLS with stepwise selection generally produces models across study regions with varying levels of multicollinearity that are as good as biased regression techniques such as PCR and PLS.

Multilevel Mixture Kalman Filter

NASA Astrophysics Data System (ADS)

Guo, Dong; Wang, Xiaodong; Chen, Rong

2004-12-01

The mixture Kalman filter is a general sequential Monte Carlo technique for conditional linear dynamic systems. It generates samples of some indicator variables recursively based on sequential importance sampling (SIS) and integrates out the linear and Gaussian state variables conditioned on these indicators. Due to the marginalization process, the complexity of the mixture Kalman filter is quite high if the dimension of the indicator sampling space is high. In this paper, we address this difficulty by developing a new Monte Carlo sampling scheme, namely, the multilevel mixture Kalman filter. The basic idea is to make use of the multilevel or hierarchical structure of the space from which the indicator variables take values. That is, we draw samples in a multilevel fashion, beginning with sampling from the highest-level sampling space and then draw samples from the associate subspace of the newly drawn samples in a lower-level sampling space, until reaching the desired sampling space. Such a multilevel sampling scheme can be used in conjunction with the delayed estimation method, such as the delayed-sample method, resulting in delayed multilevel mixture Kalman filter. Examples in wireless communication, specifically the coherent and noncoherent 16-QAM over flat-fading channels, are provided to demonstrate the performance of the proposed multilevel mixture Kalman filter.

POWER ANALYSIS FOR COMPLEX MEDIATIONAL DESIGNS USING MONTE CARLO METHODS

PubMed Central

Thoemmes, Felix; MacKinnon, David P.; Reiser, Mark R.

2013-01-01

Applied researchers often include mediation effects in applications of advanced methods such as latent variable models and linear growth curve models. Guidance on how to estimate statistical power to detect mediation for these models has not yet been addressed in the literature. We describe a general framework for power analyses for complex mediational models. The approach is based on the well known technique of generating a large number of samples in a Monte Carlo study, and estimating power as the percentage of cases in which an estimate of interest is significantly different from zero. Examples of power calculation for commonly used mediational models are provided. Power analyses for the single mediator, multiple mediators, three-path mediation, mediation with latent variables, moderated mediation, and mediation in longitudinal designs are described. Annotated sample syntax for Mplus is appended and tabled values of required sample sizes are shown for some models. PMID:23935262

The Direct Lighting Computation in Global Illumination Methods

NASA Astrophysics Data System (ADS)

Wang, Changyaw Allen

1994-01-01

Creating realistic images is a computationally expensive process, but it is very important for applications such as interior design, product design, education, virtual reality, and movie special effects. To generate realistic images, state-of-art rendering techniques are employed to simulate global illumination, which accounts for the interreflection of light among objects. In this document, we formalize the global illumination problem into a eight -dimensional integral and discuss various methods that can accelerate the process of approximating this integral. We focus on the direct lighting computation, which accounts for the light reaching the viewer from the emitting sources after exactly one reflection, Monte Carlo sampling methods, and light source simplification. Results include a new sample generation method, a framework for the prediction of the total number of samples used in a solution, and a generalized Monte Carlo approach for computing the direct lighting from an environment which for the first time makes ray tracing feasible for highly complex environments.

Monte Carlo methods for multidimensional integration for European option pricing

NASA Astrophysics Data System (ADS)

Todorov, V.; Dimov, I. T.

2016-10-01

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

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

NASA Astrophysics Data System (ADS)

Yan, Yangqian; Blume, D.

2017-11-01

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

A 3-D Coupled CFD-DSMC Solution Method With Application to the Mars Sample Return Orbiter

NASA Technical Reports Server (NTRS)

Glass, Christopher E.; Gnoffo, Peter A.

2000-01-01

A method to obtain coupled Computational Fluid Dynamics-Direct Simulation Monte Carlo (CFD-DSMC), 3-D flow field solutions for highly blunt bodies at low incidence is presented and applied to one concept of the Mars Sample Return Orbiter vehicle as a demonstration of the technique. CFD is used to solve the high-density blunt forebody flow defining an inflow boundary condition for a DSMC solution of the afterbody wake flow. By combining the two techniques in flow regions where most applicable, the entire mixed flow field is modeled in an appropriate manner.

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

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

Badal, A; Zbijewski, W; Bolch, W

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

Approximation of Failure Probability Using Conditional Sampling

NASA Technical Reports Server (NTRS)

Giesy. Daniel P.; Crespo, Luis G.; Kenney, Sean P.

2008-01-01

In analyzing systems which depend on uncertain parameters, one technique is to partition the uncertain parameter domain into a failure set and its complement, and judge the quality of the system by estimating the probability of failure. If this is done by a sampling technique such as Monte Carlo and the probability of failure is small, accurate approximation can require so many sample points that the computational expense is prohibitive. Previous work of the authors has shown how to bound the failure event by sets of such simple geometry that their probabilities can be calculated analytically. In this paper, it is shown how to make use of these failure bounding sets and conditional sampling within them to substantially reduce the computational burden of approximating failure probability. It is also shown how the use of these sampling techniques improves the confidence intervals for the failure probability estimate for a given number of sample points and how they reduce the number of sample point analyses needed to achieve a given level of confidence.

Sensitivity analysis for oblique incidence reflectometry using Monte Carlo simulations.

PubMed

Kamran, Faisal; Andersen, Peter E

2015-08-10

Oblique incidence reflectometry has developed into an effective, noncontact, and noninvasive measurement technology for the quantification of both the reduced scattering and absorption coefficients of a sample. The optical properties are deduced by analyzing only the shape of the reflectance profiles. This article presents a sensitivity analysis of the technique in turbid media. Monte Carlo simulations are used to investigate the technique and its potential to distinguish the small changes between different levels of scattering. We present various regions of the dynamic range of optical properties in which system demands vary to be able to detect subtle changes in the structure of the medium, translated as measured optical properties. Effects of variation in anisotropy are discussed and results presented. Finally, experimental data of milk products with different fat content are considered as examples for comparison.

A Monte Carlo Simulation of Brownian Motion in the Freshman Laboratory

ERIC Educational Resources Information Center

Anger, C. D.; Prescott, J. R.

1970-01-01

Describes a dry- lab" experiment for the college freshman laboratory, in which the essential features of Browian motion are given principles, using the Monte Carlo technique. Calculations principles, using the Monte Carlo technique. Calculations are carried out by a computation sheme based on computer language. Bibliography. (LC)

A Monte Carlo study of Weibull reliability analysis for space shuttle main engine components

NASA Technical Reports Server (NTRS)

Abernethy, K.

1986-01-01

The incorporation of a number of additional capabilities into an existing Weibull analysis computer program and the results of Monte Carlo computer simulation study to evaluate the usefulness of the Weibull methods using samples with a very small number of failures and extensive censoring are discussed. Since the censoring mechanism inherent in the Space Shuttle Main Engine (SSME) data is hard to analyze, it was decided to use a random censoring model, generating censoring times from a uniform probability distribution. Some of the statistical techniques and computer programs that are used in the SSME Weibull analysis are described. The methods documented in were supplemented by adding computer calculations of approximate (using iteractive methods) confidence intervals for several parameters of interest. These calculations are based on a likelihood ratio statistic which is asymptotically a chisquared statistic with one degree of freedom. The assumptions built into the computer simulations are described. The simulation program and the techniques used in it are described there also. Simulation results are tabulated for various combinations of Weibull shape parameters and the numbers of failures in the samples.

Deterministic alternatives to the full configuration interaction quantum Monte Carlo method for strongly correlated systems

NASA Astrophysics Data System (ADS)

Tubman, Norm; Whaley, Birgitta

The development of exponential scaling methods has seen great progress in tackling larger systems than previously thought possible. One such technique, full configuration interaction quantum Monte Carlo, allows exact diagonalization through stochastically sampling of determinants. The method derives its utility from the information in the matrix elements of the Hamiltonian, together with a stochastic projected wave function, which are used to explore the important parts of Hilbert space. However, a stochastic representation of the wave function is not required to search Hilbert space efficiently and new deterministic approaches have recently been shown to efficiently find the important parts of determinant space. We shall discuss the technique of Adaptive Sampling Configuration Interaction (ASCI) and the related heat-bath Configuration Interaction approach for ground state and excited state simulations. We will present several applications for strongly correlated Hamiltonians. This work was supported through the Scientific Discovery through Advanced Computing (SciDAC) program funded by the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences.

Quantitative characterization of the atomic-scale structure of oxyhydroxides in rusts formed on steel surfaces

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

Saito, M.; Suzuki, S.; Kimura, M.

Quantitative X-ray structural analysis coupled with anomalous X-ray scattering has been used for characterizing the atomic-scale structure of rust formed on steel surfaces. Samples were prepared from rust layers formed on the surfaces of two commercial steels. X-ray scattered intensity profiles of the two samples showed that the rusts consisted mainly of two types of ferric oxyhydroxide, {alpha}-FeOOH and {gamma}-FeOOH. The amounts of these rust components and the realistic atomic arrangements in the components were estimated by fitting both the ordinary and the environmental interference functions with a model structure calculated using the reverse Monte Carlo simulation technique. The twomore » rust components were found to be the network structure formed by FeO{sub 6} octahedral units, the network structure itself deviating from the ideal case. The present results also suggest that the structural analysis method using anomalous X-ray scattering and the reverse Monte Carlo technique is very successful in determining the atomic-scale structure of rusts formed on the steel surfaces.« less

Hamiltonian Monte Carlo acceleration using surrogate functions with random bases.

PubMed

Zhang, Cheng; Shahbaba, Babak; Zhao, Hongkai

2017-11-01

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

Progressive Stochastic Reconstruction Technique (PSRT) for cryo electron tomography.

PubMed

Turoňová, Beata; Marsalek, Lukas; Davidovič, Tomáš; Slusallek, Philipp

2015-03-01

Cryo Electron Tomography (cryoET) plays an essential role in Structural Biology, as it is the only technique that allows to study the structure of large macromolecular complexes in their close to native environment in situ. The reconstruction methods currently in use, such as Weighted Back Projection (WBP) or Simultaneous Iterative Reconstruction Technique (SIRT), deliver noisy and low-contrast reconstructions, which complicates the application of high-resolution protocols, such as Subtomogram Averaging (SA). We propose a Progressive Stochastic Reconstruction Technique (PSRT) - a novel iterative approach to tomographic reconstruction in cryoET based on Monte Carlo random walks guided by Metropolis-Hastings sampling strategy. We design a progressive reconstruction scheme to suit the conditions present in cryoET and apply it successfully to reconstructions of macromolecular complexes from both synthetic and experimental datasets. We show how to integrate PSRT into SA, where it provides an elegant solution to the region-of-interest problem and delivers high-contrast reconstructions that significantly improve template-based localization without any loss of high-resolution structural information. Furthermore, the locality of SA is exploited to design an importance sampling scheme which significantly speeds up the otherwise slow Monte Carlo approach. Finally, we design a new memory efficient solution for the specimen-level interior problem of cryoET, removing all associated artifacts. Copyright © 2015 Elsevier Inc. All rights reserved.

Uncertainty Analysis Based on Sparse Grid Collocation and Quasi-Monte Carlo Sampling with Application in Groundwater Modeling

NASA Astrophysics Data System (ADS)

Zhang, G.; Lu, D.; Ye, M.; Gunzburger, M.

2011-12-01

Markov Chain Monte Carlo (MCMC) methods have been widely used in many fields of uncertainty analysis to estimate the posterior distributions of parameters and credible intervals of predictions in the Bayesian framework. However, in practice, MCMC may be computationally unaffordable due to slow convergence and the excessive number of forward model executions required, especially when the forward model is expensive to compute. Both disadvantages arise from the curse of dimensionality, i.e., the posterior distribution is usually a multivariate function of parameters. Recently, sparse grid method has been demonstrated to be an effective technique for coping with high-dimensional interpolation or integration problems. Thus, in order to accelerate the forward model and avoid the slow convergence of MCMC, we propose a new method for uncertainty analysis based on sparse grid interpolation and quasi-Monte Carlo sampling. First, we construct a polynomial approximation of the forward model in the parameter space by using the sparse grid interpolation. This approximation then defines an accurate surrogate posterior distribution that can be evaluated repeatedly at minimal computational cost. Second, instead of using MCMC, a quasi-Monte Carlo method is applied to draw samples in the parameter space. Then, the desired probability density function of each prediction is approximated by accumulating the posterior density values of all the samples according to the prediction values. Our method has the following advantages: (1) the polynomial approximation of the forward model on the sparse grid provides a very efficient evaluation of the surrogate posterior distribution; (2) the quasi-Monte Carlo method retains the same accuracy in approximating the PDF of predictions but avoids all disadvantages of MCMC. The proposed method is applied to a controlled numerical experiment of groundwater flow modeling. The results show that our method attains the same accuracy much more efficiently than traditional MCMC.

Multilevel sequential Monte Carlo: Mean square error bounds under verifiable conditions

DOE PAGES

Del Moral, Pierre; Jasra, Ajay; Law, Kody J. H.

2017-01-09

We consider the multilevel sequential Monte Carlo (MLSMC) method of Beskos et al. (Stoch. Proc. Appl. [to appear]). This technique is designed to approximate expectations w.r.t. probability laws associated to a discretization. For instance, in the context of inverse problems, where one discretizes the solution of a partial differential equation. The MLSMC approach is especially useful when independent, coupled sampling is not possible. Beskos et al. show that for MLSMC the computational effort to achieve a given error, can be less than independent sampling. In this article we significantly weaken the assumptions of Beskos et al., extending the proofs tomore » non-compact state-spaces. The assumptions are based upon multiplicative drift conditions as in Kontoyiannis and Meyn (Electron. J. Probab. 10 [2005]: 61–123). The assumptions are verified for an example.« less

Multilevel sequential Monte Carlo: Mean square error bounds under verifiable conditions

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

Del Moral, Pierre; Jasra, Ajay; Law, Kody J. H.

We consider the multilevel sequential Monte Carlo (MLSMC) method of Beskos et al. (Stoch. Proc. Appl. [to appear]). This technique is designed to approximate expectations w.r.t. probability laws associated to a discretization. For instance, in the context of inverse problems, where one discretizes the solution of a partial differential equation. The MLSMC approach is especially useful when independent, coupled sampling is not possible. Beskos et al. show that for MLSMC the computational effort to achieve a given error, can be less than independent sampling. In this article we significantly weaken the assumptions of Beskos et al., extending the proofs tomore » non-compact state-spaces. The assumptions are based upon multiplicative drift conditions as in Kontoyiannis and Meyn (Electron. J. Probab. 10 [2005]: 61–123). The assumptions are verified for an example.« less

Status of the Monte Carlo library least-squares (MCLLS) approach for non-linear radiation analyzer problems

NASA Astrophysics Data System (ADS)

Gardner, Robin P.; Xu, Libai

2009-10-01

The Center for Engineering Applications of Radioisotopes (CEAR) has been working for over a decade on the Monte Carlo library least-squares (MCLLS) approach for treating non-linear radiation analyzer problems including: (1) prompt gamma-ray neutron activation analysis (PGNAA) for bulk analysis, (2) energy-dispersive X-ray fluorescence (EDXRF) analyzers, and (3) carbon/oxygen tool analysis in oil well logging. This approach essentially consists of using Monte Carlo simulation to generate the libraries of all the elements to be analyzed plus any other required background libraries. These libraries are then used in the linear library least-squares (LLS) approach with unknown sample spectra to analyze for all elements in the sample. Iterations of this are used until the LLS values agree with the composition used to generate the libraries. The current status of the methods (and topics) necessary to implement the MCLLS approach is reported. This includes: (1) the Monte Carlo codes such as CEARXRF, CEARCPG, and CEARCO for forward generation of the necessary elemental library spectra for the LLS calculation for X-ray fluorescence, neutron capture prompt gamma-ray analyzers, and carbon/oxygen tools; (2) the correction of spectral pulse pile-up (PPU) distortion by Monte Carlo simulation with the code CEARIPPU; (3) generation of detector response functions (DRF) for detectors with linear and non-linear responses for Monte Carlo simulation of pulse-height spectra; and (4) the use of the differential operator (DO) technique to make the necessary iterations for non-linear responses practical. In addition to commonly analyzed single spectra, coincidence spectra or even two-dimensional (2-D) coincidence spectra can also be used in the MCLLS approach and may provide more accurate results.

Estimating the Earthquake Source Time Function by Markov Chain Monte Carlo Sampling

NASA Astrophysics Data System (ADS)

Dȩbski, Wojciech

2008-07-01

Many aspects of earthquake source dynamics like dynamic stress drop, rupture velocity and directivity, etc. are currently inferred from the source time functions obtained by a deconvolution of the propagation and recording effects from seismograms. The question of the accuracy of obtained results remains open. In this paper we address this issue by considering two aspects of the source time function deconvolution. First, we propose a new pseudo-spectral parameterization of the sought function which explicitly takes into account the physical constraints imposed on the sought functions. Such parameterization automatically excludes non-physical solutions and so improves the stability and uniqueness of the deconvolution. Secondly, we demonstrate that the Bayesian approach to the inverse problem at hand, combined with an efficient Markov Chain Monte Carlo sampling technique, is a method which allows efficient estimation of the source time function uncertainties. The key point of the approach is the description of the solution of the inverse problem by the a posteriori probability density function constructed according to the Bayesian (probabilistic) theory. Next, the Markov Chain Monte Carlo sampling technique is used to sample this function so the statistical estimator of a posteriori errors can be easily obtained with minimal additional computational effort with respect to modern inversion (optimization) algorithms. The methodological considerations are illustrated by a case study of the mining-induced seismic event of the magnitude M L ≈3.1 that occurred at Rudna (Poland) copper mine. The seismic P-wave records were inverted for the source time functions, using the proposed algorithm and the empirical Green function technique to approximate Green functions. The obtained solutions seem to suggest some complexity of the rupture process with double pulses of energy release. However, the error analysis shows that the hypothesis of source complexity is not justified at the 95% confidence level. On the basis of the analyzed event we also show that the separation of the source inversion into two steps introduces limitations on the completeness of the a posteriori error analysis.

Analytic score distributions for a spatially continuous tridirectional Monte Carol transport problem

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

Booth, T.E.

1996-01-01

The interpretation of the statistical error estimates produced by Monte Carlo transport codes is still somewhat of an art. Empirically, there are variance reduction techniques whose error estimates are almost always reliable, and there are variance reduction techniques whose error estimates are often unreliable. Unreliable error estimates usually result from inadequate large-score sampling from the score distribution`s tail. Statisticians believe that more accurate confidence interval statements are possible if the general nature of the score distribution can be characterized. Here, the analytic score distribution for the exponential transform applied to a simple, spatially continuous Monte Carlo transport problem is provided.more » Anisotropic scattering and implicit capture are included in the theory. In large part, the analytic score distributions that are derived provide the basis for the ten new statistical quality checks in MCNP.« less

Evaluation and optimization of sampling errors for the Monte Carlo Independent Column Approximation

NASA Astrophysics Data System (ADS)

Räisänen, Petri; Barker, W. Howard

2004-07-01

The Monte Carlo Independent Column Approximation (McICA) method for computing domain-average broadband radiative fluxes is unbiased with respect to the full ICA, but its flux estimates contain conditional random noise. McICA's sampling errors are evaluated here using a global climate model (GCM) dataset and a correlated-k distribution (CKD) radiation scheme. Two approaches to reduce McICA's sampling variance are discussed. The first is to simply restrict all of McICA's samples to cloudy regions. This avoids wasting precious few samples on essentially homogeneous clear skies. Clear-sky fluxes need to be computed separately for this approach, but this is usually done in GCMs for diagnostic purposes anyway. Second, accuracy can be improved by repeated sampling, and averaging those CKD terms with large cloud radiative effects. Although this naturally increases computational costs over the standard CKD model, random errors for fluxes and heating rates are reduced by typically 50% to 60%, for the present radiation code, when the total number of samples is increased by 50%. When both variance reduction techniques are applied simultaneously, globally averaged flux and heating rate random errors are reduced by a factor of #3.

Hybrid real-code ant colony optimisation for constrained mechanical design

NASA Astrophysics Data System (ADS)

Pholdee, Nantiwat; Bureerat, Sujin

2016-01-01

This paper proposes a hybrid meta-heuristic based on integrating a local search simplex downhill (SDH) method into the search procedure of real-code ant colony optimisation (ACOR). This hybridisation leads to five hybrid algorithms where a Monte Carlo technique, a Latin hypercube sampling technique (LHS) and a translational propagation Latin hypercube design (TPLHD) algorithm are used to generate an initial population. Also, two numerical schemes for selecting an initial simplex are investigated. The original ACOR and its hybrid versions along with a variety of established meta-heuristics are implemented to solve 17 constrained test problems where a fuzzy set theory penalty function technique is used to handle design constraints. The comparative results show that the hybrid algorithms are the top performers. Using the TPLHD technique gives better results than the other sampling techniques. The hybrid optimisers are a powerful design tool for constrained mechanical design problems.

Estimation variance bounds of importance sampling simulations in digital communication systems

NASA Technical Reports Server (NTRS)

Lu, D.; Yao, K.

1991-01-01

In practical applications of importance sampling (IS) simulation, two basic problems are encountered, that of determining the estimation variance and that of evaluating the proper IS parameters needed in the simulations. The authors derive new upper and lower bounds on the estimation variance which are applicable to IS techniques. The upper bound is simple to evaluate and may be minimized by the proper selection of the IS parameter. Thus, lower and upper bounds on the improvement ratio of various IS techniques relative to the direct Monte Carlo simulation are also available. These bounds are shown to be useful and computationally simple to obtain. Based on the proposed technique, one can readily find practical suboptimum IS parameters. Numerical results indicate that these bounding techniques are useful for IS simulations of linear and nonlinear communication systems with intersymbol interference in which bit error rate and IS estimation variances cannot be obtained readily using prior techniques.

Probability techniques for reliability analysis of composite materials

NASA Technical Reports Server (NTRS)

Wetherhold, Robert C.; Ucci, Anthony M.

1994-01-01

Traditional design approaches for composite materials have employed deterministic criteria for failure analysis. New approaches are required to predict the reliability of composite structures since strengths and stresses may be random variables. This report will examine and compare methods used to evaluate the reliability of composite laminae. The two types of methods that will be evaluated are fast probability integration (FPI) methods and Monte Carlo methods. In these methods, reliability is formulated as the probability that an explicit function of random variables is less than a given constant. Using failure criteria developed for composite materials, a function of design variables can be generated which defines a 'failure surface' in probability space. A number of methods are available to evaluate the integration over the probability space bounded by this surface; this integration delivers the required reliability. The methods which will be evaluated are: the first order, second moment FPI methods; second order, second moment FPI methods; the simple Monte Carlo; and an advanced Monte Carlo technique which utilizes importance sampling. The methods are compared for accuracy, efficiency, and for the conservativism of the reliability estimation. The methodology involved in determining the sensitivity of the reliability estimate to the design variables (strength distributions) and importance factors is also presented.

Advanced Navigation Strategies for an Asteroid Sample Return Mission

NASA Technical Reports Server (NTRS)

Bauman, J.; Getzandanner, K.; Williams, B.; Williams, K.

2011-01-01

The proximity operations phases of a sample return mission to an asteroid have been analyzed using advanced navigation techniques derived from experience gained in planetary exploration. These techniques rely on tracking types such as Earth-based radio metric Doppler and ranging, spacecraft-based ranging, and optical navigation using images of landmarks on the asteroid surface. Navigation strategies for the orbital phases leading up to sample collection, the touch down for collecting the sample, and the post sample collection phase at the asteroid are included. Options for successfully executing the phases are studied using covariance analysis and Monte Carlo simulations of an example mission to the near Earth asteroid 4660 Nereus. Two landing options were studied including trajectories with either one or two bums from orbit to the surface. Additionally, a comparison of post-sample collection strategies is presented. These strategies include remaining in orbit about the asteroid or standing-off a given distance until departure to Earth.

Propagating Mixed Uncertainties in Cyber Attacker Payoffs: Exploration of Two-Phase Monte Carlo Sampling and Probability Bounds Analysis

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

Chatterjee, Samrat; Tipireddy, Ramakrishna; Oster, Matthew R.

Securing cyber-systems on a continual basis against a multitude of adverse events is a challenging undertaking. Game-theoretic approaches, that model actions of strategic decision-makers, are increasingly being applied to address cybersecurity resource allocation challenges. Such game-based models account for multiple player actions and represent cyber attacker payoffs mostly as point utility estimates. Since a cyber-attacker’s payoff generation mechanism is largely unknown, appropriate representation and propagation of uncertainty is a critical task. In this paper we expand on prior work and focus on operationalizing the probabilistic uncertainty quantification framework, for a notional cyber system, through: 1) representation of uncertain attacker andmore » system-related modeling variables as probability distributions and mathematical intervals, and 2) exploration of uncertainty propagation techniques including two-phase Monte Carlo sampling and probability bounds analysis.« less

Relation Between Pore Size and the Compressibility of a Confined Fluid

PubMed Central

Gor, Gennady Y.; Siderius, Daniel W.; Rasmussen, Christopher J.; Krekelberg, William P.; Shen, Vincent K.; Bernstein, Noam

2015-01-01

When a fluid is confined to a nanopore, its thermodynamic properties differ from the properties of a bulk fluid, so measuring such properties of the confined fluid can provide information about the pore sizes. Here we report a simple relation between the pore size and isothermal compressibility of argon confined in these pores. Compressibility is calculated from the fluctuations of the number of particles in the grand canonical ensemble using two different simulation techniques: conventional grand-canonical Monte Carlo and grand-canonical ensemble transition-matrix Monte Carlo. Our results provide a theoretical framework for extracting the information on the pore sizes of fluid-saturated samples by measuring the compressibility from ultrasonic experiments. PMID:26590541

Solid-propellant rocket motor ballistic performance variation analyses

NASA Technical Reports Server (NTRS)

Sforzini, R. H.; Foster, W. A., Jr.

1975-01-01

Results are presented of research aimed at improving the assessment of off-nominal internal ballistic performance including tailoff and thrust imbalance of two large solid-rocket motors (SRMs) firing in parallel. Previous analyses using the Monte Carlo technique were refined to permit evaluation of the effects of radial and circumferential propellant temperature gradients. Sample evaluations of the effect of the temperature gradients are presented. A separate theoretical investigation of the effect of strain rate on the burning rate of propellant indicates that the thermoelastic coupling may cause substantial variations in burning rate during highly transient operating conditions. The Monte Carlo approach was also modified to permit the effects on performance of variation in the characteristics between lots of propellants and other materials to be evaluated. This permits the variabilities for the total SRM population to be determined. A sample case shows, however, that the effect of these between-lot variations on thrust imbalances within pairs of SRMs is minor in compariosn to the effect of the within-lot variations. The revised Monte Carlo and design analysis computer programs along with instructions including format requirements for preparation of input data and illustrative examples are presented.

Data re-arranging techniques leading to proper variable selections in high energy physics

NASA Astrophysics Data System (ADS)

Kůs, Václav; Bouř, Petr

2017-12-01

We introduce a new data based approach to homogeneity testing and variable selection carried out in high energy physics experiments, where one of the basic tasks is to test the homogeneity of weighted samples, mainly the Monte Carlo simulations (weighted) and real data measurements (unweighted). This technique is called ’data re-arranging’ and it enables variable selection performed by means of the classical statistical homogeneity tests such as Kolmogorov-Smirnov, Anderson-Darling, or Pearson’s chi-square divergence test. P-values of our variants of homogeneity tests are investigated and the empirical verification through 46 dimensional high energy particle physics data sets is accomplished under newly proposed (equiprobable) quantile binning. Particularly, the procedure of homogeneity testing is applied to re-arranged Monte Carlo samples and real DATA sets measured at the particle accelerator Tevatron in Fermilab at DØ experiment originating from top-antitop quark pair production in two decay channels (electron, muon) with 2, 3, or 4+ jets detected. Finally, the variable selections in the electron and muon channels induced by the re-arranging procedure for homogeneity testing are provided for Tevatron top-antitop quark data sets.

Adventures in Parallel Processing: Entry, Descent and Landing Simulation for the Genesis and Stardust Missions

NASA Technical Reports Server (NTRS)

Lyons, Daniel T.; Desai, Prasun N.

2005-01-01

This paper will describe the Entry, Descent and Landing simulation tradeoffs and techniques that were used to provide the Monte Carlo data required to approve entry during a critical period just before entry of the Genesis Sample Return Capsule. The same techniques will be used again when Stardust returns on January 15, 2006. Only one hour was available for the simulation which propagated 2000 dispersed entry states to the ground. Creative simulation tradeoffs combined with parallel processing were needed to provide the landing footprint statistics that were an essential part of the Go/NoGo decision that authorized release of the Sample Return Capsule a few hours before entry.

Study on the measuring distance for blood glucose infrared spectral measuring by Monte Carlo simulation

NASA Astrophysics Data System (ADS)

Li, Xiang

2016-10-01

Blood glucose monitoring is of great importance for controlling diabetes procedure and preventing the complications. At present, the clinical blood glucose concentration measurement is invasive and could be replaced by noninvasive spectroscopy analytical techniques. Among various parameters of optical fiber probe used in spectrum measuring, the measurement distance is the key one. The Monte Carlo technique is a flexible method for simulating light propagation in tissue. The simulation is based on the random walks that photons make as they travel through tissue, which are chosen by statistically sampling the probability distributions for step size and angular deflection per scattering event. The traditional method for determine the optimal distance between transmitting fiber and detector is using Monte Carlo simulation to find out the point where most photons come out. But there is a problem. In the epidermal layer there is no artery, vein or capillary vessel. Thus, when photons propagate and interactive with tissue in epidermal layer, no information is given to the photons. A new criterion is proposed to determine the optimal distance, which is named effective path length in this paper. The path length of each photons travelling in dermis is recorded when running Monte-Carlo simulation, which is the effective path length defined above. The sum of effective path length of every photon at each point is calculated. The detector should be place on the point which has most effective path length. Then the optimal measuring distance between transmitting fiber and detector is determined.

Cross hole GPR traveltime inversion using a fast and accurate neural network as a forward model

NASA Astrophysics Data System (ADS)

Mejer Hansen, Thomas

2017-04-01

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

Accurately modeling Gaussian beam propagation in the context of Monte Carlo techniques

NASA Astrophysics Data System (ADS)

Hokr, Brett H.; Winblad, Aidan; Bixler, Joel N.; Elpers, Gabriel; Zollars, Byron; Scully, Marlan O.; Yakovlev, Vladislav V.; Thomas, Robert J.

2016-03-01

Monte Carlo simulations are widely considered to be the gold standard for studying the propagation of light in turbid media. However, traditional Monte Carlo methods fail to account for diffraction because they treat light as a particle. This results in converging beams focusing to a point instead of a diffraction limited spot, greatly effecting the accuracy of Monte Carlo simulations near the focal plane. Here, we present a technique capable of simulating a focusing beam in accordance to the rules of Gaussian optics, resulting in a diffraction limited focal spot. This technique can be easily implemented into any traditional Monte Carlo simulation allowing existing models to be converted to include accurate focusing geometries with minimal effort. We will present results for a focusing beam in a layered tissue model, demonstrating that for different scenarios the region of highest intensity, thus the greatest heating, can change from the surface to the focus. The ability to simulate accurate focusing geometries will greatly enhance the usefulness of Monte Carlo for countless applications, including studying laser tissue interactions in medical applications and light propagation through turbid media.

Discrete Fractional Component Monte Carlo Simulation Study of Dilute Nonionic Surfactants at the Air-Water Interface.

PubMed

Yoo, Brian; Marin-Rimoldi, Eliseo; Mullen, Ryan Gotchy; Jusufi, Arben; Maginn, Edward J

2017-09-26

We present a newly developed Monte Carlo scheme to predict bulk surfactant concentrations and surface tensions at the air-water interface for various surfactant interfacial coverages. Since the concentration regimes of these systems of interest are typically very dilute (≪10 -5 mol. frac.), Monte Carlo simulations with the use of insertion/deletion moves can provide the ability to overcome finite system size limitations that often prohibit the use of modern molecular simulation techniques. In performing these simulations, we use the discrete fractional component Monte Carlo (DFCMC) method in the Gibbs ensemble framework, which allows us to separate the bulk and air-water interface into two separate boxes and efficiently swap tetraethylene glycol surfactants C 10 E 4 between boxes. Combining this move with preferential translations, volume biased insertions, and Wang-Landau biasing vastly enhances sampling and helps overcome the classical "insertion problem", often encountered in non-lattice Monte Carlo simulations. We demonstrate that this methodology is both consistent with the original molecular thermodynamic theory (MTT) of Blankschtein and co-workers, as well as their recently modified theory (MD/MTT), which incorporates the results of surfactant infinite dilution transfer free energies and surface tension calculations obtained from molecular dynamics simulations.

Free energy and phase equilibria for the restricted primitive model of ionic fluids from Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Orkoulas, Gerassimos; Panagiotopoulos, Athanassios Z.

1994-07-01

In this work, we investigate the liquid-vapor phase transition of the restricted primitive model of ionic fluids. We show that at the low temperatures where the phase transition occurs, the system cannot be studied by conventional molecular simulation methods because convergence to equilibrium is slow. To accelerate convergence, we propose cluster Monte Carlo moves capable of moving more than one particle at a time. We then address the issue of charged particle transfers in grand canonical and Gibbs ensemble Monte Carlo simulations, for which we propose a biased particle insertion/destruction scheme capable of sampling short interparticle distances. We compute the chemical potential for the restricted primitive model as a function of temperature and density from grand canonical Monte Carlo simulations and the phase envelope from Gibbs Monte Carlo simulations. Our calculated phase coexistence curve is in agreement with recent results of Caillol obtained on the four-dimensional hypersphere and our own earlier Gibbs ensemble simulations with single-ion transfers, with the exception of the critical temperature, which is lower in the current calculations. Our best estimates for the critical parameters are T*c=0.053, ρ*c=0.025. We conclude with possible future applications of the biased techniques developed here for phase equilibrium calculations for ionic fluids.

Bayesian linkage and segregation analysis: factoring the problem.

PubMed

Matthysse, S

2000-01-01

Complex segregation analysis and linkage methods are mathematical techniques for the genetic dissection of complex diseases. They are used to delineate complex modes of familial transmission and to localize putative disease susceptibility loci to specific chromosomal locations. The computational problem of Bayesian linkage and segregation analysis is one of integration in high-dimensional spaces. In this paper, three available techniques for Bayesian linkage and segregation analysis are discussed: Markov Chain Monte Carlo (MCMC), importance sampling, and exact calculation. The contribution of each to the overall integration will be explicitly discussed.

Monte Carlo simulation of X-ray imaging and spectroscopy experiments using quadric geometry and variance reduction techniques

NASA Astrophysics Data System (ADS)

Golosio, Bruno; Schoonjans, Tom; Brunetti, Antonio; Oliva, Piernicola; Masala, Giovanni Luca

2014-03-01

The simulation of X-ray imaging experiments is often performed using deterministic codes, which can be relatively fast and easy to use. However, such codes are generally not suitable for the simulation of even slightly more complex experimental conditions, involving, for instance, first-order or higher-order scattering, X-ray fluorescence emissions, or more complex geometries, particularly for experiments that combine spatial resolution with spectral information. In such cases, simulations are often performed using codes based on the Monte Carlo method. In a simple Monte Carlo approach, the interaction position of an X-ray photon and the state of the photon after an interaction are obtained simply according to the theoretical probability distributions. This approach may be quite inefficient because the final channels of interest may include only a limited region of space or photons produced by a rare interaction, e.g., fluorescent emission from elements with very low concentrations. In the field of X-ray fluorescence spectroscopy, this problem has been solved by combining the Monte Carlo method with variance reduction techniques, which can reduce the computation time by several orders of magnitude. In this work, we present a C++ code for the general simulation of X-ray imaging and spectroscopy experiments, based on the application of the Monte Carlo method in combination with variance reduction techniques, with a description of sample geometry based on quadric surfaces. We describe the benefits of the object-oriented approach in terms of code maintenance, the flexibility of the program for the simulation of different experimental conditions and the possibility of easily adding new modules. Sample applications in the fields of X-ray imaging and X-ray spectroscopy are discussed. Catalogue identifier: AERO_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERO_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 83617 No. of bytes in distributed program, including test data, etc.: 1038160 Distribution format: tar.gz Programming language: C++. Computer: Tested on several PCs and on Mac. Operating system: Linux, Mac OS X, Windows (native and cygwin). RAM: It is dependent on the input data but usually between 1 and 10 MB. Classification: 2.5, 21.1. External routines: XrayLib (https://github.com/tschoonj/xraylib/wiki) Nature of problem: Simulation of a wide range of X-ray imaging and spectroscopy experiments using different types of sources and detectors. Solution method: XRMC is a versatile program that is useful for the simulation of a wide range of X-ray imaging and spectroscopy experiments. It enables the simulation of monochromatic and polychromatic X-ray sources, with unpolarised or partially/completely polarised radiation. Single-element detectors as well as two-dimensional pixel detectors can be used in the simulations, with several acquisition options. In the current version of the program, the sample is modelled by combining convex three-dimensional objects demarcated by quadric surfaces, such as planes, ellipsoids and cylinders. The Monte Carlo approach makes XRMC able to accurately simulate X-ray photon transport and interactions with matter up to any order of interaction. The differential cross-sections and all other quantities related to the interaction processes (photoelectric absorption, fluorescence emission, elastic and inelastic scattering) are computed using the xraylib software library, which is currently the most complete and up-to-date software library for X-ray parameters. The use of variance reduction techniques makes XRMC able to reduce the simulation time by several orders of magnitude compared to other general-purpose Monte Carlo simulation programs. Running time: It is dependent on the complexity of the simulation. For the examples distributed with the code, it ranges from less than 1 s to a few minutes.

Probabilistic Magnetotelluric Inversion with Adaptive Regularisation Using the No-U-Turns Sampler

NASA Astrophysics Data System (ADS)

Conway, Dennis; Simpson, Janelle; Didana, Yohannes; Rugari, Joseph; Heinson, Graham

2018-04-01

We present the first inversion of magnetotelluric (MT) data using a Hamiltonian Monte Carlo algorithm. The inversion of MT data is an underdetermined problem which leads to an ensemble of feasible models for a given dataset. A standard approach in MT inversion is to perform a deterministic search for the single solution which is maximally smooth for a given data-fit threshold. An alternative approach is to use Markov Chain Monte Carlo (MCMC) methods, which have been used in MT inversion to explore the entire solution space and produce a suite of likely models. This approach has the advantage of assigning confidence to resistivity models, leading to better geological interpretations. Recent advances in MCMC techniques include the No-U-Turns Sampler (NUTS), an efficient and rapidly converging method which is based on Hamiltonian Monte Carlo. We have implemented a 1D MT inversion which uses the NUTS algorithm. Our model includes a fixed number of layers of variable thickness and resistivity, as well as probabilistic smoothing constraints which allow sharp and smooth transitions. We present the results of a synthetic study and show the accuracy of the technique, as well as the fast convergence, independence of starting models, and sampling efficiency. Finally, we test our technique on MT data collected from a site in Boulia, Queensland, Australia to show its utility in geological interpretation and ability to provide probabilistic estimates of features such as depth to basement.

A method of using cluster analysis to study statistical dependence in multivariate data

NASA Technical Reports Server (NTRS)

Borucki, W. J.; Card, D. H.; Lyle, G. C.

1975-01-01

A technique is presented that uses both cluster analysis and a Monte Carlo significance test of clusters to discover associations between variables in multidimensional data. The method is applied to an example of a noisy function in three-dimensional space, to a sample from a mixture of three bivariate normal distributions, and to the well-known Fisher's Iris data.

Monte Carlo isotopic inventory analysis for complex nuclear systems

NASA Astrophysics Data System (ADS)

Phruksarojanakun, Phiphat

Monte Carlo Inventory Simulation Engine (MCise) is a newly developed method for calculating isotopic inventory of materials. It offers the promise of modeling materials with complex processes and irradiation histories, which pose challenges for current, deterministic tools, and has strong analogies to Monte Carlo (MC) neutral particle transport. The analog method, including considerations for simple, complex and loop flows, is fully developed. In addition, six variance reduction tools provide unique capabilities of MCise to improve statistical precision of MC simulations. Forced Reaction forces an atom to undergo a desired number of reactions in a given irradiation environment. Biased Reaction Branching primarily focuses on improving statistical results of the isotopes that are produced from rare reaction pathways. Biased Source Sampling aims at increasing frequencies of sampling rare initial isotopes as the starting particles. Reaction Path Splitting increases the population by splitting the atom at each reaction point, creating one new atom for each decay or transmutation product. Delta Tracking is recommended for high-frequency pulsing to reduce the computing time. Lastly, Weight Window is introduced as a strategy to decrease large deviations of weight due to the uses of variance reduction techniques. A figure of merit is necessary to compare the efficiency of different variance reduction techniques. A number of possibilities for figure of merit are explored, two of which are robust and subsequently used. One is based on the relative error of a known target isotope (1/R 2T) and the other on the overall detection limit corrected by the relative error (1/DkR 2T). An automated Adaptive Variance-reduction Adjustment (AVA) tool is developed to iteratively define parameters for some variance reduction techniques in a problem with a target isotope. Sample problems demonstrate that AVA improves both precision and accuracy of a target result in an efficient manner. Potential applications of MCise include molten salt fueled reactors and liquid breeders in fusion blankets. As an example, the inventory analysis of a liquid actinide fuel in the In-Zinerator, a sub-critical power reactor driven by a fusion source, is examined. The result reassures MCise as a reliable tool for inventory analysis of complex nuclear systems.

Monte Carlo Simulation of Nonlinear Radiation Induced Plasmas. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Wang, B. S.

1972-01-01

A Monte Carlo simulation model for radiation induced plasmas with nonlinear properties due to recombination was, employing a piecewise linearized predict-correct iterative technique. Several important variance reduction techniques were developed and incorporated into the model, including an antithetic variates technique. This approach is especially efficient for plasma systems with inhomogeneous media, multidimensions, and irregular boundaries. The Monte Carlo code developed has been applied to the determination of the electron energy distribution function and related parameters for a noble gas plasma created by alpha-particle irradiation. The characteristics of the radiation induced plasma involved are given.

Improved inference in Bayesian segmentation using Monte Carlo sampling: application to hippocampal subfield volumetry.

PubMed

Iglesias, Juan Eugenio; Sabuncu, Mert Rory; Van Leemput, Koen

2013-10-01

Many segmentation algorithms in medical image analysis use Bayesian modeling to augment local image appearance with prior anatomical knowledge. Such methods often contain a large number of free parameters that are first estimated and then kept fixed during the actual segmentation process. However, a faithful Bayesian analysis would marginalize over such parameters, accounting for their uncertainty by considering all possible values they may take. Here we propose to incorporate this uncertainty into Bayesian segmentation methods in order to improve the inference process. In particular, we approximate the required marginalization over model parameters using computationally efficient Markov chain Monte Carlo techniques. We illustrate the proposed approach using a recently developed Bayesian method for the segmentation of hippocampal subfields in brain MRI scans, showing a significant improvement in an Alzheimer's disease classification task. As an additional benefit, the technique also allows one to compute informative "error bars" on the volume estimates of individual structures. Copyright © 2013 Elsevier B.V. All rights reserved.

Improved Inference in Bayesian Segmentation Using Monte Carlo Sampling: Application to Hippocampal Subfield Volumetry

PubMed Central

Iglesias, Juan Eugenio; Sabuncu, Mert Rory; Leemput, Koen Van

2013-01-01

Many segmentation algorithms in medical image analysis use Bayesian modeling to augment local image appearance with prior anatomical knowledge. Such methods often contain a large number of free parameters that are first estimated and then kept fixed during the actual segmentation process. However, a faithful Bayesian analysis would marginalize over such parameters, accounting for their uncertainty by considering all possible values they may take. Here we propose to incorporate this uncertainty into Bayesian segmentation methods in order to improve the inference process. In particular, we approximate the required marginalization over model parameters using computationally efficient Markov chain Monte Carlo techniques. We illustrate the proposed approach using a recently developed Bayesian method for the segmentation of hippocampal subfields in brain MRI scans, showing a significant improvement in an Alzheimer’s disease classification task. As an additional benefit, the technique also allows one to compute informative “error bars” on the volume estimates of individual structures. PMID:23773521

CosmoSIS: A system for MC parameter estimation

DOE PAGES

Bridle, S.; Dodelson, S.; Jennings, E.; ...

2015-12-23

CosmoSIS is a modular system for cosmological parameter estimation, based on Markov Chain Monte Carlo and related techniques. It provides a series of samplers, which drive the exploration of the parameter space, and a series of modules, which calculate the likelihood of the observed data for a given physical model, determined by the location of a sample in the parameter space. While CosmoSIS ships with a set of modules that calculate quantities of interest to cosmologists, there is nothing about the framework itself, nor in the Markov Chain Monte Carlo technique, that is specific to cosmology. Thus CosmoSIS could bemore » used for parameter estimation problems in other fields, including HEP. This paper describes the features of CosmoSIS and show an example of its use outside of cosmology. Furthermore, it also discusses how collaborative development strategies differ between two different communities: that of HEP physicists, accustomed to working in large collaborations, and that of cosmologists, who have traditionally not worked in large groups.« less

Determination of effective atomic number of biomedical samples using Gamma ray back-scattering

NASA Astrophysics Data System (ADS)

Singh, Inderjeet; Singh, Bhajan; Sandhu, B. S.; Sabharwal, Arvind D.

2018-05-01

The study of effective atomic number of biomedical sample has been carried out by using a non-destructive multiple back-scattering technique. Also radiation characterization method is used to compare the tissue equivalent material as human tissue. Response function of 3″ × 3″ NaI(Tl) scintillation detector is implemented on recorded pulse-height distribution to boost the counts under the photo-peak and help to reduce the uncertainty in the experimental result. Monte Carlo calculation for multiple back-scattered events supports the reported experimental work.

Recommender engine for continuous-time quantum Monte Carlo methods

NASA Astrophysics Data System (ADS)

Huang, Li; Yang, Yi-feng; Wang, Lei

2017-03-01

Recommender systems play an essential role in the modern business world. They recommend favorable items such as books, movies, and search queries to users based on their past preferences. Applying similar ideas and techniques to Monte Carlo simulations of physical systems boosts their efficiency without sacrificing accuracy. Exploiting the quantum to classical mapping inherent in the continuous-time quantum Monte Carlo methods, we construct a classical molecular gas model to reproduce the quantum distributions. We then utilize powerful molecular simulation techniques to propose efficient quantum Monte Carlo updates. The recommender engine approach provides a general way to speed up the quantum impurity solvers.

Statistical Symbolic Execution with Informed Sampling

NASA Technical Reports Server (NTRS)

Filieri, Antonio; Pasareanu, Corina S.; Visser, Willem; Geldenhuys, Jaco

2014-01-01

Symbolic execution techniques have been proposed recently for the probabilistic analysis of programs. These techniques seek to quantify the likelihood of reaching program events of interest, e.g., assert violations. They have many promising applications but have scalability issues due to high computational demand. To address this challenge, we propose a statistical symbolic execution technique that performs Monte Carlo sampling of the symbolic program paths and uses the obtained information for Bayesian estimation and hypothesis testing with respect to the probability of reaching the target events. To speed up the convergence of the statistical analysis, we propose Informed Sampling, an iterative symbolic execution that first explores the paths that have high statistical significance, prunes them from the state space and guides the execution towards less likely paths. The technique combines Bayesian estimation with a partial exact analysis for the pruned paths leading to provably improved convergence of the statistical analysis. We have implemented statistical symbolic execution with in- formed sampling in the Symbolic PathFinder tool. We show experimentally that the informed sampling obtains more precise results and converges faster than a purely statistical analysis and may also be more efficient than an exact symbolic analysis. When the latter does not terminate symbolic execution with informed sampling can give meaningful results under the same time and memory limits.

Comparison of internal dose estimates obtained using organ-level, voxel S value, and Monte Carlo techniques

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

Grimes, Joshua, E-mail: grimes.joshua@mayo.edu; Celler, Anna

2014-09-15

Purpose: The authors’ objective was to compare internal dose estimates obtained using the Organ Level Dose Assessment with Exponential Modeling (OLINDA/EXM) software, the voxel S value technique, and Monte Carlo simulation. Monte Carlo dose estimates were used as the reference standard to assess the impact of patient-specific anatomy on the final dose estimate. Methods: Six patients injected with{sup 99m}Tc-hydrazinonicotinamide-Tyr{sup 3}-octreotide were included in this study. A hybrid planar/SPECT imaging protocol was used to estimate {sup 99m}Tc time-integrated activity coefficients (TIACs) for kidneys, liver, spleen, and tumors. Additionally, TIACs were predicted for {sup 131}I, {sup 177}Lu, and {sup 90}Y assuming themore » same biological half-lives as the {sup 99m}Tc labeled tracer. The TIACs were used as input for OLINDA/EXM for organ-level dose calculation and voxel level dosimetry was performed using the voxel S value method and Monte Carlo simulation. Dose estimates for {sup 99m}Tc, {sup 131}I, {sup 177}Lu, and {sup 90}Y distributions were evaluated by comparing (i) organ-level S values corresponding to each method, (ii) total tumor and organ doses, (iii) differences in right and left kidney doses, and (iv) voxelized dose distributions calculated by Monte Carlo and the voxel S value technique. Results: The S values for all investigated radionuclides used by OLINDA/EXM and the corresponding patient-specific S values calculated by Monte Carlo agreed within 2.3% on average for self-irradiation, and differed by as much as 105% for cross-organ irradiation. Total organ doses calculated by OLINDA/EXM and the voxel S value technique agreed with Monte Carlo results within approximately ±7%. Differences between right and left kidney doses determined by Monte Carlo were as high as 73%. Comparison of the Monte Carlo and voxel S value dose distributions showed that each method produced similar dose volume histograms with a minimum dose covering 90% of the volume (D90) agreeing within ±3%, on average. Conclusions: Several aspects of OLINDA/EXM dose calculation were compared with patient-specific dose estimates obtained using Monte Carlo. Differences in patient anatomy led to large differences in cross-organ doses. However, total organ doses were still in good agreement since most of the deposited dose is due to self-irradiation. Comparison of voxelized doses calculated by Monte Carlo and the voxel S value technique showed that the 3D dose distributions produced by the respective methods are nearly identical.« less

Discrete ordinates-Monte Carlo coupling: A comparison of techniques in NERVA radiation analysis

NASA Technical Reports Server (NTRS)

Lindstrom, D. G.; Normand, E.; Wilcox, A. D.

1972-01-01

In the radiation analysis of the NERVA nuclear rocket system, two-dimensional discrete ordinates calculations are sufficient to provide detail in the pressure vessel and reactor assembly. Other parts of the system, however, require three-dimensional Monte Carlo analyses. To use these two methods in a single analysis, a means of coupling was developed whereby the results of a discrete ordinates calculation can be used to produce source data for a Monte Carlo calculation. Several techniques for producing source detail were investigated. Results of calculations on the NERVA system are compared and limitations and advantages of the coupling techniques discussed.

Quasi-Monte Carlo Methods Applied to Tau-Leaping in Stochastic Biological Systems.

PubMed

Beentjes, Casper H L; Baker, Ruth E

2018-05-25

Quasi-Monte Carlo methods have proven to be effective extensions of traditional Monte Carlo methods in, amongst others, problems of quadrature and the sample path simulation of stochastic differential equations. By replacing the random number input stream in a simulation procedure by a low-discrepancy number input stream, variance reductions of several orders have been observed in financial applications. Analysis of stochastic effects in well-mixed chemical reaction networks often relies on sample path simulation using Monte Carlo methods, even though these methods suffer from typical slow [Formula: see text] convergence rates as a function of the number of sample paths N. This paper investigates the combination of (randomised) quasi-Monte Carlo methods with an efficient sample path simulation procedure, namely [Formula: see text]-leaping. We show that this combination is often more effective than traditional Monte Carlo simulation in terms of the decay of statistical errors. The observed convergence rate behaviour is, however, non-trivial due to the discrete nature of the models of chemical reactions. We explain how this affects the performance of quasi-Monte Carlo methods by looking at a test problem in standard quadrature.

Postimplant dosimetry using a Monte Carlo dose calculation engine: a new clinical standard.

PubMed

Carrier, Jean-François; D'Amours, Michel; Verhaegen, Frank; Reniers, Brigitte; Martin, André-Guy; Vigneault, Eric; Beaulieu, Luc

2007-07-15

To use the Monte Carlo (MC) method as a dose calculation engine for postimplant dosimetry. To compare the results with clinically approved data for a sample of 28 patients. Two effects not taken into account by the clinical calculation, interseed attenuation and tissue composition, are being specifically investigated. An automated MC program was developed. The dose distributions were calculated for the target volume and organs at risk (OAR) for 28 patients. Additional MC techniques were developed to focus specifically on the interseed attenuation and tissue effects. For the clinical target volume (CTV) D(90) parameter, the mean difference between the clinical technique and the complete MC method is 10.7 Gy, with cases reaching up to 17 Gy. For all cases, the clinical technique overestimates the deposited dose in the CTV. This overestimation is mainly from a combination of two effects: the interseed attenuation (average, 6.8 Gy) and tissue composition (average, 4.1 Gy). The deposited dose in the OARs is also overestimated in the clinical calculation. The clinical technique systematically overestimates the deposited dose in the prostate and in the OARs. To reduce this systematic inaccuracy, the MC method should be considered in establishing a new standard for clinical postimplant dosimetry and dose-outcome studies in a near future.

Phonon Scattering and Confinement in Crystalline Films

NASA Astrophysics Data System (ADS)

Parrish, Kevin D.

The operating temperature of energy conversion and electronic devices affects their efficiency and efficacy. In many devices, however, the reference values of the thermal properties of the materials used are no longer applicable due to processing techniques performed. This leads to challenges in thermal management and thermal engineering that demand accurate predictive tools and high fidelity measurements. The thermal conductivity of strained, nanostructured, and ultra-thin dielectrics are predicted computationally using solutions to the Boltzmann transport equation. Experimental measurements of thermal diffusivity are performed using transient grating spectroscopy. The thermal conductivities of argon, modeled using the Lennard-Jones potential, and silicon, modeled using density functional theory, are predicted under compressive and tensile strain from lattice dynamics calculations. The thermal conductivity of silicon is found to be invariant with compression, a result that is in disagreement with previous computational efforts. This difference is attributed to the more accurate force constants calculated from density functional theory. The invariance is found to be a result of competing effects of increased phonon group velocities and decreased phonon lifetimes, demonstrating how the anharmonic contribution of the atomic potential can scale differently than the harmonic contribution. Using three Monte Carlo techniques, the phonon-boundary scattering and the subsequent thermal conductivity reduction are predicted for nanoporous silicon thin films. The Monte Carlo techniques used are free path sampling, isotropic ray-tracing, and a new technique, modal ray-tracing. The thermal conductivity predictions from all three techniques are observed to be comparable to previous experimental measurements on nanoporous silicon films. The phonon mean free paths predicted from isotropic ray-tracing, however, are unphysical as compared to those predicted by free path sampling. Removing the isotropic assumption, leading to the formulation of modal ray-tracing, corrects the mean free path distribution. The effect of phonon line-of-sight is investigated in nanoporous silicon films using free path sampling. When the line-of-sight is cut off there is a distinct change in thermal conductivity versus porosity. By analyzing the free paths of an obstructed phonon mode, it is concluded that the trend change is due to a hard upper limit on the free paths that can exist due to the nanopore geometry in the material. The transient grating technique is an optical contact-less laser based experiment for measuring the in-plane thermal diffusivity of thin films and membranes. The theory of operation and physical setup of a transient grating experiment is detailed. The procedure for extracting the thermal diffusivity from the raw experimental signal is improved upon by removing arbitrary user choice in the fitting parameters used and constructing a parameterless error minimizing procedure. The thermal conductivity of ultra-thin argon films modeled with the Lennard-Jones potential is calculated from both the Monte Carlo free path sampling technique and from explicit reduced dimensionality lattice dynamics calculations. In these ultra-thin films, the phonon properties are altered in more than a perturbative manner, referred to as the confinement regime. The free path sampling technique, which is a perturbative method, is compared to a reduced dimensionality lattice dynamics calculation where the entire film thickness is taken as the unit cell. Divergence in thermal conductivity magnitude and trend is found at few unit cell thick argon films. Although the phonon group velocities and lifetimes are affected, it is found that alterations to the phonon density of states are the primary cause of the deviation in thermal conductivity in the confinement regime.

Gadolinium as a Neutron Capture Therapy Agent

NASA Astrophysics Data System (ADS)

Shih, Jing-Luen Allen

The clinical results of treating brain tumors with boron neutron capture therapy are very encouraging and researchers around the world are once again making efforts to develop this therapeutic modality. Boron-10 is the agent receiving the most attention for neutron capture therapy but ^{157}Gd is a nuclide that also holds interesting properties of being a neutron capture therapy agent. The objective of this study is to evaluate ^{157}Gd as a neutron capture therapy agent. In this study it is determined that tumor concentrations of about 300 mug ^{157}Gd/g tumor can be achieved in brain tumors with some FDA approved MRI contrast agents such as Gd-DTPA and Gd-DOTA, and up to 628 mug ^{157 }Gd/g tumor can be established in bone tumors with Gd-EDTMP. Monte Carlo calculations show that with only 250 ppm of ^{157}Gd in tumor, neutron capture therapy can deliver 2,000 cGy to a tumor of 2 cm diameter or larger with 5 times 10^{12} n/cm ^2 fluence at the tumor. Dose measurements which were made with films and TLD's in phantoms verified these calculations. More extended Monte Carlo calculations demonstrate that neutron capture therapy with Gd possesses comparable dose distribution to B neutron capture therapy. With 5 times 10^{12 } n/cm^2 thermal neutrons at the tumor, Auger electrons from the Gd produced an optical density enhancement on the films that is similar to the effect caused by about 300 cGy of Gd prompt gamma dose which will further enhance the therapeutic effects. A technique that combines brachytherapy with Gd neutron capture therapy has been evaluated. Monte Carlo calculations show that 5,000 cGy of prompt gamma dose can be delivered to a treatment volume of 40 cm^3 with a 3-plane implant of a total of 9 Gd needles. The tumor to normal tissue advantage of this method is as good as ^{60} Co brachytherapy. Measurements of prompt gamma dose with films and TLD-700's in a lucite phantom verify the Monte Carlo evaluation. A technique which displays the Gd distribution and its relative concentration in samples has been developed. Concentrations of ^{157}Gd in samples range from 20 ppm to 500 ppm can be determined with this technique. The intrinsic spatial resolution of the imaging system in 70 mum.

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

NASA Astrophysics Data System (ADS)

White, J.; Brakefield, L. K.

2015-12-01

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

Energy dispersive X-ray fluorescence spectroscopy/Monte Carlo simulation approach for the non-destructive analysis of corrosion patina-bearing alloys in archaeological bronzes: The case of the bowl from the Fareleira 3 site (Vidigueira, South Portugal)

NASA Astrophysics Data System (ADS)

Bottaini, C.; Mirão, J.; Figuereido, M.; Candeias, A.; Brunetti, A.; Schiavon, N.

2015-01-01

Energy dispersive X-ray fluorescence (EDXRF) is a well-known technique for non-destructive and in situ analysis of archaeological artifacts both in terms of the qualitative and quantitative elemental composition because of its rapidity and non-destructiveness. In this study EDXRF and realistic Monte Carlo simulation using the X-ray Monte Carlo (XRMC) code package have been combined to characterize a Cu-based bowl from the Iron Age burial from Fareleira 3 (Southern Portugal). The artifact displays a multilayered structure made up of three distinct layers: a) alloy substrate; b) green oxidized corrosion patina; and c) brownish carbonate soil-derived crust. To assess the reliability of Monte Carlo simulation in reproducing the composition of the bulk metal of the objects without recurring to potentially damaging patina's and crust's removal, portable EDXRF analysis was performed on cleaned and patina/crust coated areas of the artifact. Patina has been characterized by micro X-ray Diffractometry (μXRD) and Back-Scattered Scanning Electron Microscopy + Energy Dispersive Spectroscopy (BSEM + EDS). Results indicate that the EDXRF/Monte Carlo protocol is well suited when a two-layered model is considered, whereas in areas where the patina + crust surface coating is too thick, X-rays from the alloy substrate are not able to exit the sample.

Improvement and performance evaluation of the perturbation source method for an exact Monte Carlo perturbation calculation in fixed source problems

NASA Astrophysics Data System (ADS)

Sakamoto, Hiroki; Yamamoto, Toshihiro

2017-09-01

This paper presents improvement and performance evaluation of the "perturbation source method", which is one of the Monte Carlo perturbation techniques. The formerly proposed perturbation source method was first-order accurate, although it is known that the method can be easily extended to an exact perturbation method. A transport equation for calculating an exact flux difference caused by a perturbation is solved. A perturbation particle representing a flux difference is explicitly transported in the perturbed system, instead of in the unperturbed system. The source term of the transport equation is defined by the unperturbed flux and the cross section (or optical parameter) changes. The unperturbed flux is provided by an "on-the-fly" technique during the course of the ordinary fixed source calculation for the unperturbed system. A set of perturbation particle is started at the collision point in the perturbed region and tracked until death. For a perturbation in a smaller portion of the whole domain, the efficiency of the perturbation source method can be improved by using a virtual scattering coefficient or cross section in the perturbed region, forcing collisions. Performance is evaluated by comparing the proposed method to other Monte Carlo perturbation methods. Numerical tests performed for a particle transport in a two-dimensional geometry reveal that the perturbation source method is less effective than the correlated sampling method for a perturbation in a larger portion of the whole domain. However, for a perturbation in a smaller portion, the perturbation source method outperforms the correlated sampling method. The efficiency depends strongly on the adjustment of the new virtual scattering coefficient or cross section.

A COMPARISON OF GALAXY COUNTING TECHNIQUES IN SPECTROSCOPICALLY UNDERSAMPLED REGIONS

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

Specian, Mike A.; Szalay, Alex S., E-mail: mspecia1@jhu.edu, E-mail: szalay@jhu.edu

2016-11-01

Accurate measures of galactic overdensities are invaluable for precision cosmology. Obtaining these measurements is complicated when members of one’s galaxy sample lack radial depths, most commonly derived via spectroscopic redshifts. In this paper, we utilize the Sloan Digital Sky Survey’s Main Galaxy Sample to compare seven methods of counting galaxies in cells when many of those galaxies lack redshifts. These methods fall into three categories: assigning galaxies discrete redshifts, scaling the numbers counted using regions’ spectroscopic completeness properties, and employing probabilistic techniques. We split spectroscopically undersampled regions into three types—those inside the spectroscopic footprint, those outside but adjacent to it,more » and those distant from it. Through Monte Carlo simulations, we demonstrate that the preferred counting techniques are a function of region type, cell size, and redshift. We conclude by reporting optimal counting strategies under a variety of conditions.« less

Statistical differences between relative quantitative molecular fingerprints from microbial communities.

PubMed

Portillo, M C; Gonzalez, J M

2008-08-01

Molecular fingerprints of microbial communities are a common method for the analysis and comparison of environmental samples. The significance of differences between microbial community fingerprints was analyzed considering the presence of different phylotypes and their relative abundance. A method is proposed by simulating coverage of the analyzed communities as a function of sampling size applying a Cramér-von Mises statistic. Comparisons were performed by a Monte Carlo testing procedure. As an example, this procedure was used to compare several sediment samples from freshwater ponds using a relative quantitative PCR-DGGE profiling technique. The method was able to discriminate among different samples based on their molecular fingerprints, and confirmed the lack of differences between aliquots from a single sample.

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

PubMed

Kawrakow, I

2000-03-01

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

BATSE analysis techniques for probing the GRB spatial and luminosity distributions

NASA Technical Reports Server (NTRS)

Hakkila, Jon; Meegan, Charles A.

1992-01-01

The Burst And Transient Source Experiment (BATSE) has measured homogeneity and isotropy parameters from an increasingly large sample of observed gamma-ray bursts (GRBs), while also maintaining a summary of the way in which the sky has been sampled. Measurement of both of these are necessary for any study of the BATSE data statistically, as they take into account the most serious observational selection effects known in the study of GRBs: beam-smearing and inhomogeneous, anisotropic sky sampling. Knowledge of these effects is important to analysis of GRB angular and intensity distributions. In addition to determining that the bursts are local, it is hoped that analysis of such distributions will allow boundaries to be placed on the true GRB spatial distribution and luminosity function. The technique for studying GRB spatial and luminosity distributions is direct. Results of BATSE analyses are compared to Monte Carlo models parameterized by a variety of spatial and luminosity characteristics.

[Accuracy Check of Monte Carlo Simulation in Particle Therapy Using Gel Dosimeters].

PubMed

Furuta, Takuya

2017-01-01

Gel dosimeters are a three-dimensional imaging tool for dose distribution induced by radiations. They can be used for accuracy check of Monte Carlo simulation in particle therapy. An application was reviewed in this article. An inhomogeneous biological sample placing a gel dosimeter behind it was irradiated by carbon beam. The recorded dose distribution in the gel dosimeter reflected the inhomogeneity of the biological sample. Monte Carlo simulation was conducted by reconstructing the biological sample from its CT image. The accuracy of the particle transport by Monte Carlo simulation was checked by comparing the dose distribution in the gel dosimeter between simulation and experiment.

Procedure for Adapting Direct Simulation Monte Carlo Meshes

NASA Technical Reports Server (NTRS)

Woronowicz, Michael S.; Wilmoth, Richard G.; Carlson, Ann B.; Rault, Didier F. G.

1992-01-01

A technique is presented for adapting computational meshes used in the G2 version of the direct simulation Monte Carlo method. The physical ideas underlying the technique are discussed, and adaptation formulas are developed for use on solutions generated from an initial mesh. The effect of statistical scatter on adaptation is addressed, and results demonstrate the ability of this technique to achieve more accurate results without increasing necessary computational resources.

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

DOE PAGES

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

2015-02-07

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

Thermal analysis of combinatorial solid geometry models using SINDA

NASA Technical Reports Server (NTRS)

Gerencser, Diane; Radke, George; Introne, Rob; Klosterman, John; Miklosovic, Dave

1993-01-01

Algorithms have been developed using Monte Carlo techniques to determine the thermal network parameters necessary to perform a finite difference analysis on Combinatorial Solid Geometry (CSG) models. Orbital and laser fluxes as well as internal heat generation are modeled to facilitate satellite modeling. The results of the thermal calculations are used to model the infrared (IR) images of targets and assess target vulnerability. Sample analyses and validation are presented which demonstrate code products.

Monte Carlo analysis of neutron diffuse scattering data

NASA Astrophysics Data System (ADS)

Goossens, D. J.; Heerdegen, A. P.; Welberry, T. R.; Gutmann, M. J.

2006-11-01

This paper presents a discussion of a technique developed for the analysis of neutron diffuse scattering data. The technique involves processing the data into reciprocal space sections and modelling the diffuse scattering in these sections. A Monte Carlo modelling approach is used in which the crystal energy is a function of interatomic distances between molecules and torsional rotations within molecules. The parameters of the model are the spring constants governing the interactions, as they determine the correlations which evolve when the model crystal structure is relaxed at finite temperature. When the model crystal has reached equilibrium its diffraction pattern is calculated and a χ2 goodness-of-fit test between observed and calculated data slices is performed. This allows a least-squares refinement of the fit parameters and so automated refinement can proceed. The first application of this methodology to neutron, rather than X-ray, data is outlined. The sample studied was deuterated benzil, d-benzil, C14D10O2, for which data was collected using time-of-flight Laue diffraction on SXD at ISIS.

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

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

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

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

Spectrum simulation in DTSA-II.

PubMed

Ritchie, Nicholas W M

2009-10-01

Spectrum simulation is a useful practical and pedagogical tool. Particularly with complex samples or trace constituents, a simulation can help to understand the limits of the technique and the instrument parameters for the optimal measurement. DTSA-II, software for electron probe microanalysis, provides both easy to use and flexible tools for simulating common and less common sample geometries and materials. Analytical models based on (rhoz) curves provide quick simulations of simple samples. Monte Carlo models based on electron and X-ray transport provide more sophisticated models of arbitrarily complex samples. DTSA-II provides a broad range of simulation tools in a framework with many different interchangeable physical models. In addition, DTSA-II provides tools for visualizing, comparing, manipulating, and quantifying simulated and measured spectra.

Adjoint acceleration of Monte Carlo simulations using TORT/MCNP coupling approach: a case study on the shielding improvement for the cyclotron room of the Buddhist Tzu Chi General Hospital.

PubMed

Sheu, R J; Sheu, R D; Jiang, S H; Kao, C H

2005-01-01

Full-scale Monte Carlo simulations of the cyclotron room of the Buddhist Tzu Chi General Hospital were carried out to improve the original inadequate maze design. Variance reduction techniques are indispensable in this study to facilitate the simulations for testing a variety of configurations of shielding modification. The TORT/MCNP manual coupling approach based on the Consistent Adjoint Driven Importance Sampling (CADIS) methodology has been used throughout this study. The CADIS utilises the source and transport biasing in a consistent manner. With this method, the computational efficiency was increased significantly by more than two orders of magnitude and the statistical convergence was also improved compared to the unbiased Monte Carlo run. This paper describes the shielding problem encountered, the procedure for coupling the TORT and MCNP codes to accelerate the calculations and the calculation results for the original and improved shielding designs. In order to verify the calculation results and seek additional accelerations, sensitivity studies on the space-dependent and energy-dependent parameters were also conducted.

Estimating air chemical emissions from research activities using stack measurement data.

PubMed

Ballinger, Marcel Y; Duchsherer, Cheryl J; Woodruff, Rodger K; Larson, Timothy V

2013-03-01

Current methods of estimating air emissions from research and development (R&D) activities use a wide range of release fractions or emission factors with bases ranging from empirical to semi-empirical. Although considered conservative, the uncertainties and confidence levels of the existing methods have not been reported. Chemical emissions were estimated from sampling data taken from four research facilities over 10 years. The approach was to use a Monte Carlo technique to create distributions of annual emission estimates for target compounds detected in source test samples. Distributions were created for each year and building sampled for compounds with sufficient detection frequency to qualify for the analysis. The results using the Monte Carlo technique without applying a filter to remove negative emission values showed almost all distributions spanning zero, and 40% of the distributions having a negative mean. This indicates that emissions are so low as to be indistinguishable from building background. Application of a filter to allow only positive values in the distribution provided a more realistic value for emissions and increased the distribution mean by an average of 16%. Release fractions were calculated by dividing the emission estimates by a building chemical inventory quantity. Two variations were used for this quantity: chemical usage, and chemical usage plus one-half standing inventory. Filters were applied so that only release fraction values from zero to one were included in the resulting distributions. Release fractions had a wide range among chemicals and among data sets for different buildings and/or years for a given chemical. Regressions of release fractions to molecular weight and vapor pressure showed weak correlations. Similarly, regressions of mean emissions to chemical usage, chemical inventory, molecular weight, and vapor pressure also gave weak correlations. These results highlight the difficulties in estimating emissions from R&D facilities using chemical inventory data. Air emissions from research operations are difficult to estimate because of the changing nature of research processes and the small quantity and wide variety of chemicals used. Analysis of stack measurements taken over multiple facilities and a 10-year period using a Monte Carlo technique provided a method to quantify the low emissions and to estimate release fractions based on chemical inventories. The variation in release fractions did not correlate well with factors investigated, confirming the complexities in estimating R&D emissions.

Simulation and statistics: Like rhythm and song

NASA Astrophysics Data System (ADS)

Othman, Abdul Rahman

2013-04-01

Simulation has been introduced to solve problems in the form of systems. By using this technique the following two problems can be overcome. First, a problem that has an analytical solution but the cost of running an experiment to solve is high in terms of money and lives. Second, a problem exists but has no analytical solution. In the field of statistical inference the second problem is often encountered. With the advent of high-speed computing devices, a statistician can now use resampling techniques such as the bootstrap and permutations to form pseudo sampling distribution that will lead to the solution of the problem that cannot be solved analytically. This paper discusses how a Monte Carlo simulation was and still being used to verify the analytical solution in inference. This paper also discusses the resampling techniques as simulation techniques. The misunderstandings about these two techniques are examined. The successful usages of both techniques are also explained.

Coarse kMC-based replica exchange algorithms for the accelerated simulation of protein folding in explicit solvent.

PubMed

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

2016-05-14

In this paper, we present a coarse replica exchange molecular dynamics (REMD) approach, based on kinetic Monte Carlo (kMC). The new development significantly can reduce the amount of replicas and the computational cost needed to enhance sampling in protein simulations. We introduce 2 different methods which primarily differ in the exchange scheme between the parallel ensembles. We apply this approach on folding of 2 different β-stranded peptides: the C-terminal β-hairpin fragment of GB1 and TrpZip4. Additionally, we use the new simulation technique to study the folding of TrpCage, a small fast folding α-helical peptide. Subsequently, we apply the new methodology on conformation changes in signaling of the light-oxygen voltage (LOV) sensitive domain from Avena sativa (AsLOV2). Our results agree well with data reported in the literature. In simulations of dialanine, we compare the statistical sampling of the 2 techniques with conventional REMD and analyze their performance. The new techniques can reduce the computational cost of REMD significantly and can be used in enhanced sampling simulations of biomolecules.

Solving the master equation without kinetic Monte Carlo: Tensor train approximations for a CO oxidation model

NASA Astrophysics Data System (ADS)

Gelß, Patrick; Matera, Sebastian; Schütte, Christof

2016-06-01

In multiscale modeling of heterogeneous catalytic processes, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. Usually, this is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO2(110) surface. We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness.

Hydrologic Model Selection using Markov chain Monte Carlo methods

NASA Astrophysics Data System (ADS)

Marshall, L.; Sharma, A.; Nott, D.

2002-12-01

Estimation of parameter uncertainty (and in turn model uncertainty) allows assessment of the risk in likely applications of hydrological models. Bayesian statistical inference provides an ideal means of assessing parameter uncertainty whereby prior knowledge about the parameter is combined with information from the available data to produce a probability distribution (the posterior distribution) that describes uncertainty about the parameter and serves as a basis for selecting appropriate values for use in modelling applications. Widespread use of Bayesian techniques in hydrology has been hindered by difficulties in summarizing and exploring the posterior distribution. These difficulties have been largely overcome by recent advances in Markov chain Monte Carlo (MCMC) methods that involve random sampling of the posterior distribution. This study presents an adaptive MCMC sampling algorithm which has characteristics that are well suited to model parameters with a high degree of correlation and interdependence, as is often evident in hydrological models. The MCMC sampling technique is used to compare six alternative configurations of a commonly used conceptual rainfall-runoff model, the Australian Water Balance Model (AWBM), using 11 years of daily rainfall runoff data from the Bass river catchment in Australia. The alternative configurations considered fall into two classes - those that consider model errors to be independent of prior values, and those that model the errors as an autoregressive process. Each such class consists of three formulations that represent increasing levels of complexity (and parameterisation) of the original model structure. The results from this study point both to the importance of using Bayesian approaches in evaluating model performance, as well as the simplicity of the MCMC sampling framework that has the ability to bring such approaches within the reach of the applied hydrological community.

Monte Carlo Simulation for Perusal and Practice.

ERIC Educational Resources Information Center

Brooks, Gordon P.; Barcikowski, Robert S.; Robey, Randall R.

The meaningful investigation of many problems in statistics can be solved through Monte Carlo methods. Monte Carlo studies can help solve problems that are mathematically intractable through the analysis of random samples from populations whose characteristics are known to the researcher. Using Monte Carlo simulation, the values of a statistic are…

Modeling 2D and 3D diffusion.

PubMed

Saxton, Michael J

2007-01-01

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

Advanced statistical methods for improved data analysis of NASA astrophysics missions

NASA Technical Reports Server (NTRS)

Feigelson, Eric D.

1992-01-01

The investigators under this grant studied ways to improve the statistical analysis of astronomical data. They looked at existing techniques, the development of new techniques, and the production and distribution of specialized software to the astronomical community. Abstracts of nine papers that were produced are included, as well as brief descriptions of four software packages. The articles that are abstracted discuss analytical and Monte Carlo comparisons of six different linear least squares fits, a (second) paper on linear regression in astronomy, two reviews of public domain software for the astronomer, subsample and half-sample methods for estimating sampling distributions, a nonparametric estimation of survival functions under dependent competing risks, censoring in astronomical data due to nondetections, an astronomy survival analysis computer package called ASURV, and improving the statistical methodology of astronomical data analysis.

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

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

Liu, T; Lin, H; Xu, X

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

Calculating phase equilibrium properties of plasma pseudopotential model using hybrid Gibbs statistical ensemble Monte-Carlo technique

NASA Astrophysics Data System (ADS)

Butlitsky, M. A.; Zelener, B. B.; Zelener, B. V.

2015-11-01

Earlier a two-component pseudopotential plasma model, which we called a “shelf Coulomb” model has been developed. A Monte-Carlo study of canonical NVT ensemble with periodic boundary conditions has been undertaken to calculate equations of state, pair distribution functions, internal energies and other thermodynamics properties of the model. In present work, an attempt is made to apply so-called hybrid Gibbs statistical ensemble Monte-Carlo technique to this model. First simulation results data show qualitatively similar results for critical point region for both methods. Gibbs ensemble technique let us to estimate the melting curve position and a triple point of the model (in reduced temperature and specific volume coordinates): T* ≈ 0.0476, v* ≈ 6 × 10-4.

Determining the nuclear data uncertainty on MONK10 and WIMS10 criticality calculations

NASA Astrophysics Data System (ADS)

Ware, Tim; Dobson, Geoff; Hanlon, David; Hiles, Richard; Mason, Robert; Perry, Ray

2017-09-01

The ANSWERS Software Service is developing a number of techniques to better understand and quantify uncertainty on calculations of the neutron multiplication factor, k-effective, in nuclear fuel and other systems containing fissile material. The uncertainty on the calculated k-effective arises from a number of sources, including nuclear data uncertainties, manufacturing tolerances, modelling approximations and, for Monte Carlo simulation, stochastic uncertainty. For determining the uncertainties due to nuclear data, a set of application libraries have been generated for use with the MONK10 Monte Carlo and the WIMS10 deterministic criticality and reactor physics codes. This paper overviews the generation of these nuclear data libraries by Latin hypercube sampling of JEFF-3.1.2 evaluated data based upon a library of covariance data taken from JEFF, ENDF/B, JENDL and TENDL evaluations. Criticality calculations have been performed with MONK10 and WIMS10 using these sampled libraries for a number of benchmark models of fissile systems. Results are presented which show the uncertainty on k-effective for these systems arising from the uncertainty on the input nuclear data.

Analytic nuclear forces and molecular properties from full configuration interaction quantum Monte Carlo

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

Thomas, Robert E.; Overy, Catherine; Opalka, Daniel

Unbiased stochastic sampling of the one- and two-body reduced density matrices is achieved in full configuration interaction quantum Monte Carlo with the introduction of a second, “replica” ensemble of walkers, whose population evolves in imaginary time independently from the first and which entails only modest additional computational overheads. The matrices obtained from this approach are shown to be representative of full configuration-interaction quality and hence provide a realistic opportunity to achieve high-quality results for a range of properties whose operators do not necessarily commute with the Hamiltonian. A density-matrix formulated quasi-variational energy estimator having been already proposed and investigated, themore » present work extends the scope of the theory to take in studies of analytic nuclear forces, molecular dipole moments, and polarisabilities, with extensive comparison to exact results where possible. These new results confirm the suitability of the sampling technique and, where sufficiently large basis sets are available, achieve close agreement with experimental values, expanding the scope of the method to new areas of investigation.« less

Sample Size and Power Estimates for a Confirmatory Factor Analytic Model in Exercise and Sport: A Monte Carlo Approach

ERIC Educational Resources Information Center

Myers, Nicholas D.; Ahn, Soyeon; Jin, Ying

2011-01-01

Monte Carlo methods can be used in data analytic situations (e.g., validity studies) to make decisions about sample size and to estimate power. The purpose of using Monte Carlo methods in a validity study is to improve the methodological approach within a study where the primary focus is on construct validity issues and not on advancing…

E Pluribus Analysis: Applying a Superforecasting Methodology to the Detection of Homegrown Violence

DTIC Science & Technology

2018-03-01

actor violence and a set of predefined decision-making protocols. This research included running four simulations using the Monte Carlo technique, which...actor violence and a set of predefined decision-making protocols. This research included running four simulations using the Monte Carlo technique...PREDICTING RANDOMNESS.............................................................24 1. Using a “ Runs Test” to Determine a Temporal Pattern in Lone

Calibrating and training of neutron based NSA techniques with less SNM standards

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

Geist, William H; Swinhoe, Martyn T; Bracken, David S

2010-01-01

Accessing special nuclear material (SNM) standards for the calibration of and training on nondestructive assay (NDA) instruments has become increasingly difficult in light of enhanced safeguards and security regulations. Limited or nonexistent access to SNM has affected neutron based NDA techniques more than gamma ray techniques because the effects of multiplication require a range of masses to accurately measure the detector response. Neutron based NDA techniques can also be greatly affected by the matrix and impurity characteristics of the item. The safeguards community has been developing techniques for calibrating instrumentation and training personnel with dwindling numbers of SNM standards. Montemore » Carlo methods have become increasingly important for design and calibration of instrumentation. Monte Carlo techniques have the ability to accurately predict the detector response for passive techniques. The Monte Carlo results are usually benchmarked to neutron source measurements such as californium. For active techniques, the modeling becomes more difficult because of the interaction of the interrogation source with the detector and nuclear material; and the results cannot be simply benchmarked with neutron sources. A Monte Carlo calculated calibration curve for a training course in Indonesia of material test reactor (MTR) fuel elements assayed with an active well coincidence counter (AWCC) will be presented as an example. Performing training activities with reduced amounts of nuclear material makes it difficult to demonstrate how the multiplication and matrix properties of the item affects the detector response and limits the knowledge that can be obtained with hands-on training. A neutron pulse simulator (NPS) has been developed that can produce a pulse stream representative of a real pulse stream output from a detector measuring SNM. The NPS has been used by the International Atomic Energy Agency (IAEA) for detector testing and training applications at the Agency due to the lack of appropriate SNM standards. This paper will address the effect of reduced access to SNM for calibration and training of neutron NDA applications along with the advantages and disadvantages of some solutions that do not use standards, such as the Monte Carlo techniques and the NPS.« less

Rare Event Simulation in Radiation Transport

NASA Astrophysics Data System (ADS)

Kollman, Craig

This dissertation studies methods for estimating extremely small probabilities by Monte Carlo simulation. Problems in radiation transport typically involve estimating very rare events or the expected value of a random variable which is with overwhelming probability equal to zero. These problems often have high dimensional state spaces and irregular geometries so that analytic solutions are not possible. Monte Carlo simulation must be used to estimate the radiation dosage being transported to a particular location. If the area is well shielded the probability of any one particular particle getting through is very small. Because of the large number of particles involved, even a tiny fraction penetrating the shield may represent an unacceptable level of radiation. It therefore becomes critical to be able to accurately estimate this extremely small probability. Importance sampling is a well known technique for improving the efficiency of rare event calculations. Here, a new set of probabilities is used in the simulation runs. The results are multiplied by the likelihood ratio between the true and simulated probabilities so as to keep our estimator unbiased. The variance of the resulting estimator is very sensitive to which new set of transition probabilities are chosen. It is shown that a zero variance estimator does exist, but that its computation requires exact knowledge of the solution. A simple random walk with an associated killing model for the scatter of neutrons is introduced. Large deviation results for optimal importance sampling in random walks are extended to the case where killing is present. An adaptive "learning" algorithm for implementing importance sampling is given for more general Markov chain models of neutron scatter. For finite state spaces this algorithm is shown to give, with probability one, a sequence of estimates converging exponentially fast to the true solution. In the final chapter, an attempt to generalize this algorithm to a continuous state space is made. This involves partitioning the space into a finite number of cells. There is a tradeoff between additional computation per iteration and variance reduction per iteration that arises in determining the optimal grid size. All versions of this algorithm can be thought of as a compromise between deterministic and Monte Carlo methods, capturing advantages of both techniques.

Space shuttle solid rocket booster recovery system definition, volume 1

NASA Technical Reports Server (NTRS)

1973-01-01

The performance requirements, preliminary designs, and development program plans for an airborne recovery system for the space shuttle solid rocket booster are discussed. The analyses performed during the study phase of the program are presented. The basic considerations which established the system configuration are defined. A Monte Carlo statistical technique using random sampling of the probability distribution for the critical water impact parameters was used to determine the failure probability of each solid rocket booster component as functions of impact velocity and component strength capability.

E-Area LLWF Vadose Zone Model: Probabilistic Model for Estimating Subsided-Area Infiltration Rates

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

Dyer, J.; Flach, G.

A probabilistic model employing a Monte Carlo sampling technique was developed in Python to generate statistical distributions of the upslope-intact-area to subsided-area ratio (Area UAi/Area SAi) for closure cap subsidence scenarios that differ in assumed percent subsidence and the total number of intact plus subsided compartments. The plan is to use this model as a component in the probabilistic system model for the E-Area Performance Assessment (PA), contributing uncertainty in infiltration estimates.

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

PubMed

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

2012-01-01

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

Optimizing the triple-axis spectrometer PANDA at the MLZ for small samples and complex sample environment conditions

NASA Astrophysics Data System (ADS)

Utschick, C.; Skoulatos, M.; Schneidewind, A.; Böni, P.

2016-11-01

The cold-neutron triple-axis spectrometer PANDA at the neutron source FRM II has been serving an international user community studying condensed matter physics problems. We report on a new setup, improving the signal-to-noise ratio for small samples and pressure cell setups. Analytical and numerical Monte Carlo methods are used for the optimization of elliptic and parabolic focusing guides. They are placed between the monochromator and sample positions, and the flux at the sample is compared to the one achieved by standard monochromator focusing techniques. A 25 times smaller spot size is achieved, associated with a factor of 2 increased intensity, within the same divergence limits, ± 2 ° . This optional neutron focusing guide shall establish a top-class spectrometer for studying novel exotic properties of matter in combination with more stringent sample environment conditions such as extreme pressures associated with small sample sizes.

Investigation of the SCS-CN initial abstraction ratio using a Monte Carlo simulation for the derived flood frequency curves

NASA Astrophysics Data System (ADS)

Caporali, E.; Chiarello, V.; Galeati, G.

2014-12-01

Peak discharges estimates for a given return period are of primary importance in engineering practice for risk assessment and hydraulic structure design. Different statistical methods are chosen here for the assessment of flood frequency curve: one indirect technique based on the extreme rainfall event analysis, the Peak Over Threshold (POT) model and the Annual Maxima approach as direct techniques using river discharge data. In the framework of the indirect method, a Monte Carlo simulation approach is adopted to determine a derived frequency distribution of peak runoff using a probabilistic formulation of the SCS-CN method as stochastic rainfall-runoff model. A Monte Carlo simulation is used to generate a sample of different runoff events from different stochastic combination of rainfall depth, storm duration, and initial loss inputs. The distribution of the rainfall storm events is assumed to follow the GP law whose parameters are estimated through GEV's parameters of annual maximum data. The evaluation of the initial abstraction ratio is investigated since it is one of the most questionable assumption in the SCS-CN model and plays a key role in river basin characterized by high-permeability soils, mainly governed by infiltration excess mechanism. In order to take into account the uncertainty of the model parameters, this modified approach, that is able to revise and re-evaluate the original value of the initial abstraction ratio, is implemented. In the POT model the choice of the threshold has been an essential issue, mainly based on a compromise between bias and variance. The Generalized Extreme Value (GEV) distribution fitted to the annual maxima discharges is therefore compared with the Pareto distributed peaks to check the suitability of the frequency of occurrence representation. The methodology is applied to a large dam in the Serchio river basin, located in the Tuscany Region. The application has shown as Monte Carlo simulation technique can be a useful tool to provide more robust estimation of the results obtained by direct statistical methods.

Improved spatial resolution in PET scanners using sampling techniques

PubMed Central

Surti, Suleman; Scheuermann, Ryan; Werner, Matthew E.; Karp, Joel S.

2009-01-01

Increased focus towards improved detector spatial resolution in PET has led to the use of smaller crystals in some form of light sharing detector design. In this work we evaluate two sampling techniques that can be applied during calibrations for pixelated detector designs in order to improve the reconstructed spatial resolution. The inter-crystal positioning technique utilizes sub-sampling in the crystal flood map to better sample the Compton scatter events in the detector. The Compton scatter rejection technique, on the other hand, rejects those events that are located further from individual crystal centers in the flood map. We performed Monte Carlo simulations followed by measurements on two whole-body scanners for point source data. The simulations and measurements were performed for scanners using scintillators with Zeff ranging from 46.9 to 63 for LaBr3 and LYSO, respectively. Our results show that near the center of the scanner, inter-crystal positioning technique leads to a gain of about 0.5-mm in reconstructed spatial resolution (FWHM) for both scanner designs. In a small animal LYSO scanner the resolution improves from 1.9-mm to 1.6-mm with the inter-crystal technique. The Compton scatter rejection technique shows higher gains in spatial resolution but at the cost of reduction in scanner sensitivity. The inter-crystal positioning technique represents a modest acquisition software modification for an improvement in spatial resolution, but at a cost of potentially longer data correction and reconstruction times. The Compton scatter rejection technique, while also requiring a modest acquisition software change with no increased data correction and reconstruction times, will be useful in applications where the scanner sensitivity is very high and larger improvements in spatial resolution are desirable. PMID:19779586

Potential, velocity, and density fields from sparse and noisy redshift-distance samples - Method

NASA Technical Reports Server (NTRS)

Dekel, Avishai; Bertschinger, Edmund; Faber, Sandra M.

1990-01-01

A method for recovering the three-dimensional potential, velocity, and density fields from large-scale redshift-distance samples is described. Galaxies are taken as tracers of the velocity field, not of the mass. The density field and the initial conditions are calculated using an iterative procedure that applies the no-vorticity assumption at an initial time and uses the Zel'dovich approximation to relate initial and final positions of particles on a grid. The method is tested using a cosmological N-body simulation 'observed' at the positions of real galaxies in a redshift-distance sample, taking into account their distance measurement errors. Malmquist bias and other systematic and statistical errors are extensively explored using both analytical techniques and Monte Carlo simulations.

Solving the master equation without kinetic Monte Carlo: Tensor train approximations for a CO oxidation model

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

Gelß, Patrick, E-mail: p.gelss@fu-berlin.de; Matera, Sebastian, E-mail: matera@math.fu-berlin.de; Schütte, Christof, E-mail: schuette@mi.fu-berlin.de

2016-06-01

In multiscale modeling of heterogeneous catalytic processes, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. Usually, this is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO{sub 2}(110) surface.more » We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness.« less

Molecular Dynamics, Monte Carlo Simulations, and Langevin Dynamics: A Computational Review

PubMed Central

Paquet, Eric; Viktor, Herna L.

2015-01-01

Macromolecular structures, such as neuraminidases, hemagglutinins, and monoclonal antibodies, are not rigid entities. Rather, they are characterised by their flexibility, which is the result of the interaction and collective motion of their constituent atoms. This conformational diversity has a significant impact on their physicochemical and biological properties. Among these are their structural stability, the transport of ions through the M2 channel, drug resistance, macromolecular docking, binding energy, and rational epitope design. To assess these properties and to calculate the associated thermodynamical observables, the conformational space must be efficiently sampled and the dynamic of the constituent atoms must be simulated. This paper presents algorithms and techniques that address the abovementioned issues. To this end, a computational review of molecular dynamics, Monte Carlo simulations, Langevin dynamics, and free energy calculation is presented. The exposition is made from first principles to promote a better understanding of the potentialities, limitations, applications, and interrelations of these computational methods. PMID:25785262

The specific purpose Monte Carlo code McENL for simulating the response of epithermal neutron lifetime well logging tools

NASA Astrophysics Data System (ADS)

Prettyman, T. H.; Gardner, R. P.; Verghese, K.

1993-08-01

A new specific purpose Monte Carlo code called McENL for modeling the time response of epithermal neutron lifetime tools is described. The weight windows technique, employing splitting and Russian roulette, is used with an automated importance function based on the solution of an adjoint diffusion model to improve the code efficiency. Complete composition and density correlated sampling is also included in the code, and can be used to study the effect on tool response of small variations in the formation, borehole, or logging tool composition and density. An illustration of the latter application is given for the density of a thermal neutron filter. McENL was benchmarked against test-pit data for the Mobil pulsed neutron porosity tool and was found to be very accurate. Results of the experimental validation and details of code performance are presented.

The unbiasedness of a generalized mirage boundary correction method for Monte Carlo integration estimators of volume

Treesearch

Thomas B. Lynch; Jeffrey H. Gove

2014-01-01

The typical "double counting" application of the mirage method of boundary correction cannot be applied to sampling systems such as critical height sampling (CHS) that are based on a Monte Carlo sample of a tree (or debris) attribute because the critical height (or other random attribute) sampled from a mirage point is generally not equal to the critical...

Monte Carlo Method for Determining Earthquake Recurrence Parameters from Short Paleoseismic Catalogs: Example Calculations for California

USGS Publications Warehouse

Parsons, Tom

2008-01-01

Paleoearthquake observations often lack enough events at a given site to directly define a probability density function (PDF) for earthquake recurrence. Sites with fewer than 10-15 intervals do not provide enough information to reliably determine the shape of the PDF using standard maximum-likelihood techniques [e.g., Ellsworth et al., 1999]. In this paper I present a method that attempts to fit wide ranges of distribution parameters to short paleoseismic series. From repeated Monte Carlo draws, it becomes possible to quantitatively estimate most likely recurrence PDF parameters, and a ranked distribution of parameters is returned that can be used to assess uncertainties in hazard calculations. In tests on short synthetic earthquake series, the method gives results that cluster around the mean of the input distribution, whereas maximum likelihood methods return the sample means [e.g., NIST/SEMATECH, 2006]. For short series (fewer than 10 intervals), sample means tend to reflect the median of an asymmetric recurrence distribution, possibly leading to an overestimate of the hazard should they be used in probability calculations. Therefore a Monte Carlo approach may be useful for assessing recurrence from limited paleoearthquake records. Further, the degree of functional dependence among parameters like mean recurrence interval and coefficient of variation can be established. The method is described for use with time-independent and time-dependent PDF?s, and results from 19 paleoseismic sequences on strike-slip faults throughout the state of California are given.

Monte Carlo method for determining earthquake recurrence parameters from short paleoseismic catalogs: Example calculations for California

USGS Publications Warehouse

Parsons, T.

2008-01-01

Paleoearthquake observations often lack enough events at a given site to directly define a probability density function (PDF) for earthquake recurrence. Sites with fewer than 10-15 intervals do not provide enough information to reliably determine the shape of the PDF using standard maximum-likelihood techniques (e.g., Ellsworth et al., 1999). In this paper I present a method that attempts to fit wide ranges of distribution parameters to short paleoseismic series. From repeated Monte Carlo draws, it becomes possible to quantitatively estimate most likely recurrence PDF parameters, and a ranked distribution of parameters is returned that can be used to assess uncertainties in hazard calculations. In tests on short synthetic earthquake series, the method gives results that cluster around the mean of the input distribution, whereas maximum likelihood methods return the sample means (e.g., NIST/SEMATECH, 2006). For short series (fewer than 10 intervals), sample means tend to reflect the median of an asymmetric recurrence distribution, possibly leading to an overestimate of the hazard should they be used in probability calculations. Therefore a Monte Carlo approach may be useful for assessing recurrence from limited paleoearthquake records. Further, the degree of functional dependence among parameters like mean recurrence interval and coefficient of variation can be established. The method is described for use with time-independent and time-dependent PDFs, and results from 19 paleoseismic sequences on strike-slip faults throughout the state of California are given.

Off-diagonal expansion quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Albash, Tameem; Wagenbreth, Gene; Hen, Itay

2017-12-01

We propose a Monte Carlo algorithm designed to simulate quantum as well as classical systems at equilibrium, bridging the algorithmic gap between quantum and classical thermal simulation algorithms. The method is based on a decomposition of the quantum partition function that can be viewed as a series expansion about its classical part. We argue that the algorithm not only provides a theoretical advancement in the field of quantum Monte Carlo simulations, but is optimally suited to tackle quantum many-body systems that exhibit a range of behaviors from "fully quantum" to "fully classical," in contrast to many existing methods. We demonstrate the advantages, sometimes by orders of magnitude, of the technique by comparing it against existing state-of-the-art schemes such as path integral quantum Monte Carlo and stochastic series expansion. We also illustrate how our method allows for the unification of quantum and classical thermal parallel tempering techniques into a single algorithm and discuss its practical significance.

Monte Carlo-based Reconstruction in Water Cherenkov Detectors using Chroma

NASA Astrophysics Data System (ADS)

Seibert, Stanley; Latorre, Anthony

2012-03-01

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

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

NASA Astrophysics Data System (ADS)

Gbedo, Yémalin Gabin; Mangin-Brinet, Mariane

2017-07-01

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

Off-diagonal expansion quantum Monte Carlo.

PubMed

Albash, Tameem; Wagenbreth, Gene; Hen, Itay

2017-12-01

We propose a Monte Carlo algorithm designed to simulate quantum as well as classical systems at equilibrium, bridging the algorithmic gap between quantum and classical thermal simulation algorithms. The method is based on a decomposition of the quantum partition function that can be viewed as a series expansion about its classical part. We argue that the algorithm not only provides a theoretical advancement in the field of quantum Monte Carlo simulations, but is optimally suited to tackle quantum many-body systems that exhibit a range of behaviors from "fully quantum" to "fully classical," in contrast to many existing methods. We demonstrate the advantages, sometimes by orders of magnitude, of the technique by comparing it against existing state-of-the-art schemes such as path integral quantum Monte Carlo and stochastic series expansion. We also illustrate how our method allows for the unification of quantum and classical thermal parallel tempering techniques into a single algorithm and discuss its practical significance.

An adaptive Bayesian inference algorithm to estimate the parameters of a hazardous atmospheric release

NASA Astrophysics Data System (ADS)

Rajaona, Harizo; Septier, François; Armand, Patrick; Delignon, Yves; Olry, Christophe; Albergel, Armand; Moussafir, Jacques

2015-12-01

In the eventuality of an accidental or intentional atmospheric release, the reconstruction of the source term using measurements from a set of sensors is an important and challenging inverse problem. A rapid and accurate estimation of the source allows faster and more efficient action for first-response teams, in addition to providing better damage assessment. This paper presents a Bayesian probabilistic approach to estimate the location and the temporal emission profile of a pointwise source. The release rate is evaluated analytically by using a Gaussian assumption on its prior distribution, and is enhanced with a positivity constraint to improve the estimation. The source location is obtained by the means of an advanced iterative Monte-Carlo technique called Adaptive Multiple Importance Sampling (AMIS), which uses a recycling process at each iteration to accelerate its convergence. The proposed methodology is tested using synthetic and real concentration data in the framework of the Fusion Field Trials 2007 (FFT-07) experiment. The quality of the obtained results is comparable to those coming from the Markov Chain Monte Carlo (MCMC) algorithm, a popular Bayesian method used for source estimation. Moreover, the adaptive processing of the AMIS provides a better sampling efficiency by reusing all the generated samples.

Verification of unfold error estimates in the UFO code

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

Fehl, D.L.; Biggs, F.

Spectral unfolding is an inverse mathematical operation which attempts to obtain spectral source information from a set of tabulated response functions and data measurements. Several unfold algorithms have appeared over the past 30 years; among them is the UFO (UnFold Operator) code. In addition to an unfolded spectrum, UFO also estimates the unfold uncertainty (error) induced by running the code in a Monte Carlo fashion with prescribed data distributions (Gaussian deviates). In the problem studied, data were simulated from an arbitrarily chosen blackbody spectrum (10 keV) and a set of overlapping response functions. The data were assumed to have anmore » imprecision of 5% (standard deviation). 100 random data sets were generated. The built-in estimate of unfold uncertainty agreed with the Monte Carlo estimate to within the statistical resolution of this relatively small sample size (95% confidence level). A possible 10% bias between the two methods was unresolved. The Monte Carlo technique is also useful in underdetemined problems, for which the error matrix method does not apply. UFO has been applied to the diagnosis of low energy x rays emitted by Z-Pinch and ion-beam driven hohlraums.« less

Simulating the Generalized Gibbs Ensemble (GGE): A Hilbert space Monte Carlo approach

NASA Astrophysics Data System (ADS)

Alba, Vincenzo

By combining classical Monte Carlo and Bethe ansatz techniques we devise a numerical method to construct the Truncated Generalized Gibbs Ensemble (TGGE) for the spin-1/2 isotropic Heisenberg (XXX) chain. The key idea is to sample the Hilbert space of the model with the appropriate GGE probability measure. The method can be extended to other integrable systems, such as the Lieb-Liniger model. We benchmark the approach focusing on GGE expectation values of several local observables. As finite-size effects decay exponentially with system size, moderately large chains are sufficient to extract thermodynamic quantities. The Monte Carlo results are in agreement with both the Thermodynamic Bethe Ansatz (TBA) and the Quantum Transfer Matrix approach (QTM). Remarkably, it is possible to extract in a simple way the steady-state Bethe-Gaudin-Takahashi (BGT) roots distributions, which encode complete information about the GGE expectation values in the thermodynamic limit. Finally, it is straightforward to simulate extensions of the GGE, in which, besides the local integral of motion (local charges), one includes arbitrary functions of the BGT roots. As an example, we include in the GGE the first non-trivial quasi-local integral of motion.

Efficient Simulation of Secondary Fluorescence Via NIST DTSA-II Monte Carlo.

PubMed

Ritchie, Nicholas W M

2017-06-01

Secondary fluorescence, the final term in the familiar matrix correction triumvirate Z·A·F, is the most challenging for Monte Carlo models to simulate. In fact, only two implementations of Monte Carlo models commonly used to simulate electron probe X-ray spectra can calculate secondary fluorescence-PENEPMA and NIST DTSA-II a (DTSA-II is discussed herein). These two models share many physical models but there are some important differences in the way each implements X-ray emission including secondary fluorescence. PENEPMA is based on PENELOPE, a general purpose software package for simulation of both relativistic and subrelativistic electron/positron interactions with matter. On the other hand, NIST DTSA-II was designed exclusively for simulation of X-ray spectra generated by subrelativistic electrons. NIST DTSA-II uses variance reduction techniques unsuited to general purpose code. These optimizations help NIST DTSA-II to be orders of magnitude more computationally efficient while retaining detector position sensitivity. Simulations execute in minutes rather than hours and can model differences that result from detector position. Both PENEPMA and NIST DTSA-II are capable of handling complex sample geometries and we will demonstrate that both are of similar accuracy when modeling experimental secondary fluorescence data from the literature.

Hyper-Parallel Tempering Monte Carlo Method and It's Applications

NASA Astrophysics Data System (ADS)

Yan, Qiliang; de Pablo, Juan

2000-03-01

A new generalized hyper-parallel tempering Monte Carlo molecular simulation method is presented for study of complex fluids. The method is particularly useful for simulation of many-molecule complex systems, where rough energy landscapes and inherently long characteristic relaxation times can pose formidable obstacles to effective sampling of relevant regions of configuration space. The method combines several key elements from expanded ensemble formalisms, parallel-tempering, open ensemble simulations, configurational bias techniques, and histogram reweighting analysis of results. It is found to accelerate significantly the diffusion of a complex system through phase-space. In this presentation, we demonstrate the effectiveness of the new method by implementing it in grand canonical ensembles for a Lennard-Jones fluid, for the restricted primitive model of electrolyte solutions (RPM), and for polymer solutions and blends. Our results indicate that the new algorithm is capable of overcoming the large free energy barriers associated with phase transitions, thereby greatly facilitating the simulation of coexistence properties. It is also shown that the method can be orders of magnitude more efficient than previously available techniques. More importantly, the method is relatively simple and can be incorporated into existing simulation codes with minor efforts.

Random Numbers and Monte Carlo Methods

NASA Astrophysics Data System (ADS)

Scherer, Philipp O. J.

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

Sample size guidelines for fitting a lognormal probability distribution to censored most probable number data with a Markov chain Monte Carlo method.

PubMed

Williams, Michael S; Cao, Yong; Ebel, Eric D

2013-07-15

Levels of pathogenic organisms in food and water have steadily declined in many parts of the world. A consequence of this reduction is that the proportion of samples that test positive for the most contaminated product-pathogen pairings has fallen to less than 0.1. While this is unequivocally beneficial to public health, datasets with very few enumerated samples present an analytical challenge because a large proportion of the observations are censored values. One application of particular interest to risk assessors is the fitting of a statistical distribution function to datasets collected at some point in the farm-to-table continuum. The fitted distribution forms an important component of an exposure assessment. A number of studies have compared different fitting methods and proposed lower limits on the proportion of samples where the organisms of interest are identified and enumerated, with the recommended lower limit of enumerated samples being 0.2. This recommendation may not be applicable to food safety risk assessments for a number of reasons, which include the development of new Bayesian fitting methods, the use of highly sensitive screening tests, and the generally larger sample sizes found in surveys of food commodities. This study evaluates the performance of a Markov chain Monte Carlo fitting method when used in conjunction with a screening test and enumeration of positive samples by the Most Probable Number technique. The results suggest that levels of contamination for common product-pathogen pairs, such as Salmonella on poultry carcasses, can be reliably estimated with the proposed fitting method and samples sizes in excess of 500 observations. The results do, however, demonstrate that simple guidelines for this application, such as the proportion of positive samples, cannot be provided. Published by Elsevier B.V.

Solving large-scale PDE-constrained Bayesian inverse problems with Riemann manifold Hamiltonian Monte Carlo

NASA Astrophysics Data System (ADS)

Bui-Thanh, T.; Girolami, M.

2014-11-01

We consider the Riemann manifold Hamiltonian Monte Carlo (RMHMC) method for solving statistical inverse problems governed by partial differential equations (PDEs). The Bayesian framework is employed to cast the inverse problem into the task of statistical inference whose solution is the posterior distribution in infinite dimensional parameter space conditional upon observation data and Gaussian prior measure. We discretize both the likelihood and the prior using the H1-conforming finite element method together with a matrix transfer technique. The power of the RMHMC method is that it exploits the geometric structure induced by the PDE constraints of the underlying inverse problem. Consequently, each RMHMC posterior sample is almost uncorrelated/independent from the others providing statistically efficient Markov chain simulation. However this statistical efficiency comes at a computational cost. This motivates us to consider computationally more efficient strategies for RMHMC. At the heart of our construction is the fact that for Gaussian error structures the Fisher information matrix coincides with the Gauss-Newton Hessian. We exploit this fact in considering a computationally simplified RMHMC method combining state-of-the-art adjoint techniques and the superiority of the RMHMC method. Specifically, we first form the Gauss-Newton Hessian at the maximum a posteriori point and then use it as a fixed constant metric tensor throughout RMHMC simulation. This eliminates the need for the computationally costly differential geometric Christoffel symbols, which in turn greatly reduces computational effort at a corresponding loss of sampling efficiency. We further reduce the cost of forming the Fisher information matrix by using a low rank approximation via a randomized singular value decomposition technique. This is efficient since a small number of Hessian-vector products are required. The Hessian-vector product in turn requires only two extra PDE solves using the adjoint technique. Various numerical results up to 1025 parameters are presented to demonstrate the ability of the RMHMC method in exploring the geometric structure of the problem to propose (almost) uncorrelated/independent samples that are far away from each other, and yet the acceptance rate is almost unity. The results also suggest that for the PDE models considered the proposed fixed metric RMHMC can attain almost as high a quality performance as the original RMHMC, i.e. generating (almost) uncorrelated/independent samples, while being two orders of magnitude less computationally expensive.

Scan Order in Gibbs Sampling: Models in Which it Matters and Bounds on How Much.

PubMed

He, Bryan; De Sa, Christopher; Mitliagkas, Ioannis; Ré, Christopher

2016-01-01

Gibbs sampling is a Markov Chain Monte Carlo sampling technique that iteratively samples variables from their conditional distributions. There are two common scan orders for the variables: random scan and systematic scan. Due to the benefits of locality in hardware, systematic scan is commonly used, even though most statistical guarantees are only for random scan. While it has been conjectured that the mixing times of random scan and systematic scan do not differ by more than a logarithmic factor, we show by counterexample that this is not the case, and we prove that that the mixing times do not differ by more than a polynomial factor under mild conditions. To prove these relative bounds, we introduce a method of augmenting the state space to study systematic scan using conductance.

Scan Order in Gibbs Sampling: Models in Which it Matters and Bounds on How Much

PubMed Central

He, Bryan; De Sa, Christopher; Mitliagkas, Ioannis; Ré, Christopher

2016-01-01

Gibbs sampling is a Markov Chain Monte Carlo sampling technique that iteratively samples variables from their conditional distributions. There are two common scan orders for the variables: random scan and systematic scan. Due to the benefits of locality in hardware, systematic scan is commonly used, even though most statistical guarantees are only for random scan. While it has been conjectured that the mixing times of random scan and systematic scan do not differ by more than a logarithmic factor, we show by counterexample that this is not the case, and we prove that that the mixing times do not differ by more than a polynomial factor under mild conditions. To prove these relative bounds, we introduce a method of augmenting the state space to study systematic scan using conductance. PMID:28344429

Determination of output factor for 6 MV small photon beam: comparison between Monte Carlo simulation technique and microDiamond detector

NASA Astrophysics Data System (ADS)

Krongkietlearts, K.; Tangboonduangjit, P.; Paisangittisakul, N.

2016-03-01

In order to improve the life's quality for a cancer patient, the radiation techniques are constantly evolving. Especially, the two modern techniques which are intensity modulated radiation therapy (IMRT) and volumetric modulated arc therapy (VMAT) are quite promising. They comprise of many small beam sizes (beamlets) with various intensities to achieve the intended radiation dose to the tumor and minimal dose to the nearby normal tissue. The study investigates whether the microDiamond detector (PTW manufacturer), a synthetic single crystal diamond detector, is suitable for small field output factor measurement. The results were compared with those measured by the stereotactic field detector (SFD) and the Monte Carlo simulation (EGSnrc/BEAMnrc/DOSXYZ). The calibration of Monte Carlo simulation was done using the percentage depth dose and dose profile measured by the photon field detector (PFD) of the 10×10 cm2 field size with 100 cm SSD. Comparison of the values obtained from the calculations and measurements are consistent, no more than 1% difference. The output factors obtained from the microDiamond detector have been compared with those of SFD and Monte Carlo simulation, the results demonstrate the percentage difference of less than 2%.

Specific and Non-Specific Protein Association in Solution: Computation of Solvent Effects and Prediction of First-Encounter Modes for Efficient Configurational Bias Monte Carlo Simulations

PubMed Central

Cardone, Antonio; Pant, Harish; Hassan, Sergio A.

2013-01-01

Weak and ultra-weak protein-protein association play a role in molecular recognition, and can drive spontaneous self-assembly and aggregation. Such interactions are difficult to detect experimentally, and are a challenge to the force field and sampling technique. A method is proposed to identify low-population protein-protein binding modes in aqueous solution. The method is designed to identify preferential first-encounter complexes from which the final complex(es) at equilibrium evolves. A continuum model is used to represent the effects of the solvent, which accounts for short- and long-range effects of water exclusion and for liquid-structure forces at protein/liquid interfaces. These effects control the behavior of proteins in close proximity and are optimized based on binding enthalpy data and simulations. An algorithm is described to construct a biasing function for self-adaptive configurational-bias Monte Carlo of a set of interacting proteins. The function allows mixing large and local changes in the spatial distribution of proteins, thereby enhancing sampling of relevant microstates. The method is applied to three binary systems. Generalization to multiprotein complexes is discussed. PMID:24044772

Comparison of VRX CT scanners geometries

NASA Astrophysics Data System (ADS)

DiBianca, Frank A.; Melnyk, Roman; Duckworth, Christopher N.; Russ, Stephan; Jordan, Lawrence M.; Laughter, Joseph S.

2001-06-01

A technique called Variable-Resolution X-ray (VRX) detection greatly increases the spatial resolution in computed tomography (CT) and digital radiography (DR) as the field size decreases. The technique is based on a principle called `projective compression' that allows both the resolution element and the sampling distance of a CT detector to scale with the subject or field size. For very large (40 - 50 cm) field sizes, resolution exceeding 2 cy/mm is possible and for very small fields, microscopy is attainable with resolution exceeding 100 cy/mm. This paper compares the benefits obtainable with two different VRX detector geometries: the single-arm geometry and the dual-arm geometry. The analysis is based on Monte Carlo simulations and direct calculations. The results of this study indicate that the dual-arm system appears to have more advantages than the single-arm technique.

A Monte Carlo Study of Levene's Test of Homogeneity of Variance: Empirical Frequencies of Type I Error in Normal Distributions.

ERIC Educational Resources Information Center

Neel, John H.; Stallings, William M.

An influential statistics test recommends a Levene text for homogeneity of variance. A recent note suggests that Levene's test is upwardly biased for small samples. Another report shows inflated Alpha estimates and low power. Neither study utilized more than two sample sizes. This Monte Carlo study involved sampling from a normal population for…

Radiotherapy Monte Carlo simulation using cloud computing technology.

PubMed

Poole, C M; Cornelius, I; Trapp, J V; Langton, C M

2012-12-01

Cloud computing allows for vast computational resources to be leveraged quickly and easily in bursts as and when required. Here we describe a technique that allows for Monte Carlo radiotherapy dose calculations to be performed using GEANT4 and executed in the cloud, with relative simulation cost and completion time evaluated as a function of machine count. As expected, simulation completion time decreases as 1/n for n parallel machines, and relative simulation cost is found to be optimal where n is a factor of the total simulation time in hours. Using the technique, we demonstrate the potential usefulness of cloud computing as a solution for rapid Monte Carlo simulation for radiotherapy dose calculation without the need for dedicated local computer hardware as a proof of principal.

Radiation doses in volume-of-interest breast computed tomography—A Monte Carlo simulation study

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

Lai, Chao-Jen, E-mail: cjlai3711@gmail.com; Zhong, Yuncheng; Yi, Ying

2015-06-15

Purpose: Cone beam breast computed tomography (breast CT) with true three-dimensional, nearly isotropic spatial resolution has been developed and investigated over the past decade to overcome the problem of lesions overlapping with breast anatomical structures on two-dimensional mammographic images. However, the ability of breast CT to detect small objects, such as tissue structure edges and small calcifications, is limited. To resolve this problem, the authors proposed and developed a volume-of-interest (VOI) breast CT technique to image a small VOI using a higher radiation dose to improve that region’s visibility. In this study, the authors performed Monte Carlo simulations to estimatemore » average breast dose and average glandular dose (AGD) for the VOI breast CT technique. Methods: Electron–Gamma-Shower system code-based Monte Carlo codes were used to simulate breast CT. The Monte Carlo codes estimated were validated using physical measurements of air kerma ratios and point doses in phantoms with an ion chamber and optically stimulated luminescence dosimeters. The validated full cone x-ray source was then collimated to simulate half cone beam x-rays to image digital pendant-geometry, hemi-ellipsoidal, homogeneous breast phantoms and to estimate breast doses with full field scans. 13-cm in diameter, 10-cm long hemi-ellipsoidal homogeneous phantoms were used to simulate median breasts. Breast compositions of 25% and 50% volumetric glandular fractions (VGFs) were used to investigate the influence on breast dose. The simulated half cone beam x-rays were then collimated to a narrow x-ray beam with an area of 2.5 × 2.5 cm{sup 2} field of view at the isocenter plane and to perform VOI field scans. The Monte Carlo results for the full field scans and the VOI field scans were then used to estimate the AGD for the VOI breast CT technique. Results: The ratios of air kerma ratios and dose measurement results from the Monte Carlo simulation to those from the physical measurements were 0.97 ± 0.03 and 1.10 ± 0.13, respectively, indicating that the accuracy of the Monte Carlo simulation was adequate. The normalized AGD with VOI field scans was substantially reduced by a factor of about 2 over the VOI region and by a factor of 18 over the entire breast for both 25% and 50% VGF simulated breasts compared with the normalized AGD with full field scans. The normalized AGD for the VOI breast CT technique can be kept the same as or lower than that for a full field scan with the exposure level for the VOI field scan increased by a factor of as much as 12. Conclusions: The authors’ Monte Carlo estimates of normalized AGDs for the VOI breast CT technique show that this technique can be used to markedly increase the dose to the breast and thus the visibility of the VOI region without increasing the dose to the breast. The results of this investigation should be helpful for those interested in using VOI breast CT technique to image small calcifications with dose concern.« less

Radiation doses in volume-of-interest breast computed tomography—A Monte Carlo simulation study

PubMed Central

Lai, Chao-Jen; Zhong, Yuncheng; Yi, Ying; Wang, Tianpeng; Shaw, Chris C.

2015-01-01

Purpose: Cone beam breast computed tomography (breast CT) with true three-dimensional, nearly isotropic spatial resolution has been developed and investigated over the past decade to overcome the problem of lesions overlapping with breast anatomical structures on two-dimensional mammographic images. However, the ability of breast CT to detect small objects, such as tissue structure edges and small calcifications, is limited. To resolve this problem, the authors proposed and developed a volume-of-interest (VOI) breast CT technique to image a small VOI using a higher radiation dose to improve that region’s visibility. In this study, the authors performed Monte Carlo simulations to estimate average breast dose and average glandular dose (AGD) for the VOI breast CT technique. Methods: Electron–Gamma-Shower system code-based Monte Carlo codes were used to simulate breast CT. The Monte Carlo codes estimated were validated using physical measurements of air kerma ratios and point doses in phantoms with an ion chamber and optically stimulated luminescence dosimeters. The validated full cone x-ray source was then collimated to simulate half cone beam x-rays to image digital pendant-geometry, hemi-ellipsoidal, homogeneous breast phantoms and to estimate breast doses with full field scans. 13-cm in diameter, 10-cm long hemi-ellipsoidal homogeneous phantoms were used to simulate median breasts. Breast compositions of 25% and 50% volumetric glandular fractions (VGFs) were used to investigate the influence on breast dose. The simulated half cone beam x-rays were then collimated to a narrow x-ray beam with an area of 2.5 × 2.5 cm2 field of view at the isocenter plane and to perform VOI field scans. The Monte Carlo results for the full field scans and the VOI field scans were then used to estimate the AGD for the VOI breast CT technique. Results: The ratios of air kerma ratios and dose measurement results from the Monte Carlo simulation to those from the physical measurements were 0.97 ± 0.03 and 1.10 ± 0.13, respectively, indicating that the accuracy of the Monte Carlo simulation was adequate. The normalized AGD with VOI field scans was substantially reduced by a factor of about 2 over the VOI region and by a factor of 18 over the entire breast for both 25% and 50% VGF simulated breasts compared with the normalized AGD with full field scans. The normalized AGD for the VOI breast CT technique can be kept the same as or lower than that for a full field scan with the exposure level for the VOI field scan increased by a factor of as much as 12. Conclusions: The authors’ Monte Carlo estimates of normalized AGDs for the VOI breast CT technique show that this technique can be used to markedly increase the dose to the breast and thus the visibility of the VOI region without increasing the dose to the breast. The results of this investigation should be helpful for those interested in using VOI breast CT technique to image small calcifications with dose concern. PMID:26127058

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

PubMed

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

2018-03-01

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

A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields

DOE PAGES

Osborn, Sarah; Vassilevski, Panayot S.; Villa, Umberto

2017-10-26

In this paper, we propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the Karhunen--Loève (KL) decomposition. However, the KL expansion requires solving a dense eigenvalue problem and is therefore computationally infeasible for large-scale problems. Sampling methods based on stochastic partial differential equations provide a highly scalable way to sample Gaussian fields, but the resulting parametrization is mesh dependent. We propose a multilevel decomposition of the stochastic field to allow for scalable, hierarchical sampling based on solving amore » mixed finite element formulation of a stochastic reaction-diffusion equation with a random, white noise source function. Lastly, numerical experiments are presented to demonstrate the scalability of the sampling method as well as numerical results of multilevel Monte Carlo simulations for a subsurface porous media flow application using the proposed sampling method.« less

A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields

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

Osborn, Sarah; Vassilevski, Panayot S.; Villa, Umberto

In this paper, we propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the Karhunen--Loève (KL) decomposition. However, the KL expansion requires solving a dense eigenvalue problem and is therefore computationally infeasible for large-scale problems. Sampling methods based on stochastic partial differential equations provide a highly scalable way to sample Gaussian fields, but the resulting parametrization is mesh dependent. We propose a multilevel decomposition of the stochastic field to allow for scalable, hierarchical sampling based on solving amore » mixed finite element formulation of a stochastic reaction-diffusion equation with a random, white noise source function. Lastly, numerical experiments are presented to demonstrate the scalability of the sampling method as well as numerical results of multilevel Monte Carlo simulations for a subsurface porous media flow application using the proposed sampling method.« less

Diabat Interpolation for Polymorph Free-Energy Differences.

PubMed

Kamat, Kartik; Peters, Baron

2017-02-02

Existing methods to compute free-energy differences between polymorphs use harmonic approximations, advanced non-Boltzmann bias sampling techniques, and/or multistage free-energy perturbations. This work demonstrates how Bennett's diabat interpolation method ( J. Comput. Phys. 1976, 22, 245 ) can be combined with energy gaps from lattice-switch Monte Carlo techniques ( Phys. Rev. E 2000, 61, 906 ) to swiftly estimate polymorph free-energy differences. The new method requires only two unbiased molecular dynamics simulations, one for each polymorph. To illustrate the new method, we compute the free-energy difference between face-centered cubic and body-centered cubic polymorphs for a Gaussian core solid. We discuss the justification for parabolic models of the free-energy diabats and similarities to methods that have been used in studies of electron transfer.

i-TED: A novel concept for high-sensitivity (n,γ) cross-section measurements

NASA Astrophysics Data System (ADS)

Domingo-Pardo, C.

2016-07-01

A new method for measuring (n , γ) cross-sections aiming at enhanced signal-to-background ratio is presented. This new approach is based on the combination of the pulse-height weighting technique with a total energy detection system that features γ-ray imaging capability (i-TED). The latter allows one to exploit Compton imaging techniques to discriminate between true capture γ-rays arising from the sample under study and background γ-rays coming from contaminant neutron (prompt or delayed) captures in the surrounding environment. A general proof-of-concept detection system for this application is presented in this paper together with a description of the imaging method and a conceptual demonstration based on Monte Carlo simulations.

Application of the A.C. Admittance Technique to Double Layer Studies on Polycrystalline Gold Electrodes

DTIC Science & Technology

1992-02-24

AVAiLABILITY STATEMENT 12b. DISTRIBUTION CODE Unclassified 1 . %Bsr’RACT , 3’ um . Crl) A detailed examination of the dependence of the a.c. admittance...NUMBER OF PAGES double layer at gold/solution interface, a.c. admittance techniques, constant phase element model 1 . PRCE CODE 17. SECURITY...Chemistry University of California Davis, CA 95616 U.S.A. tOn leave from the Instituto de Fisica e Quimica de Sao Carlos, USP, Sao Carlos, SP 13560

A simple methodology for characterization of germanium coaxial detectors by using Monte Carlo simulation and evolutionary algorithms.

PubMed

Guerra, J G; Rubiano, J G; Winter, G; Guerra, A G; Alonso, H; Arnedo, M A; Tejera, A; Gil, J M; Rodríguez, R; Martel, P; Bolivar, J P

2015-11-01

The determination in a sample of the activity concentration of a specific radionuclide by gamma spectrometry needs to know the full energy peak efficiency (FEPE) for the energy of interest. The difficulties related to the experimental calibration make it advisable to have alternative methods for FEPE determination, such as the simulation of the transport of photons in the crystal by the Monte Carlo method, which requires an accurate knowledge of the characteristics and geometry of the detector. The characterization process is mainly carried out by Canberra Industries Inc. using proprietary techniques and methodologies developed by that company. It is a costly procedure (due to shipping and to the cost of the process itself) and for some research laboratories an alternative in situ procedure can be very useful. The main goal of this paper is to find an alternative to this costly characterization process, by establishing a method for optimizing the parameters of characterizing the detector, through a computational procedure which could be reproduced at a standard research lab. This method consists in the determination of the detector geometric parameters by using Monte Carlo simulation in parallel with an optimization process, based on evolutionary algorithms, starting from a set of reference FEPEs determined experimentally or computationally. The proposed method has proven to be effective and simple to implement. It provides a set of characterization parameters which it has been successfully validated for different source-detector geometries, and also for a wide range of environmental samples and certified materials. Copyright © 2015 Elsevier Ltd. All rights reserved.

A path integral methodology for obtaining thermodynamic properties of nonadiabatic systems using Gaussian mixture distributions

NASA Astrophysics Data System (ADS)

Raymond, Neil; Iouchtchenko, Dmitri; Roy, Pierre-Nicholas; Nooijen, Marcel

2018-05-01

We introduce a new path integral Monte Carlo method for investigating nonadiabatic systems in thermal equilibrium and demonstrate an approach to reducing stochastic error. We derive a general path integral expression for the partition function in a product basis of continuous nuclear and discrete electronic degrees of freedom without the use of any mapping schemes. We separate our Hamiltonian into a harmonic portion and a coupling portion; the partition function can then be calculated as the product of a Monte Carlo estimator (of the coupling contribution to the partition function) and a normalization factor (that is evaluated analytically). A Gaussian mixture model is used to evaluate the Monte Carlo estimator in a computationally efficient manner. Using two model systems, we demonstrate our approach to reduce the stochastic error associated with the Monte Carlo estimator. We show that the selection of the harmonic oscillators comprising the sampling distribution directly affects the efficiency of the method. Our results demonstrate that our path integral Monte Carlo method's deviation from exact Trotter calculations is dominated by the choice of the sampling distribution. By improving the sampling distribution, we can drastically reduce the stochastic error leading to lower computational cost.

Convergence and Efficiency of Adaptive Importance Sampling Techniques with Partial Biasing

NASA Astrophysics Data System (ADS)

Fort, G.; Jourdain, B.; Lelièvre, T.; Stoltz, G.

2018-04-01

We propose a new Monte Carlo method to efficiently sample a multimodal distribution (known up to a normalization constant). We consider a generalization of the discrete-time Self Healing Umbrella Sampling method, which can also be seen as a generalization of well-tempered metadynamics. The dynamics is based on an adaptive importance technique. The importance function relies on the weights (namely the relative probabilities) of disjoint sets which form a partition of the space. These weights are unknown but are learnt on the fly yielding an adaptive algorithm. In the context of computational statistical physics, the logarithm of these weights is, up to an additive constant, the free-energy, and the discrete valued function defining the partition is called the collective variable. The algorithm falls into the general class of Wang-Landau type methods, and is a generalization of the original Self Healing Umbrella Sampling method in two ways: (i) the updating strategy leads to a larger penalization strength of already visited sets in order to escape more quickly from metastable states, and (ii) the target distribution is biased using only a fraction of the free-energy, in order to increase the effective sample size and reduce the variance of importance sampling estimators. We prove the convergence of the algorithm and analyze numerically its efficiency on a toy example.

The Use of Monte Carlo Techniques to Teach Probability.

ERIC Educational Resources Information Center

Newell, G. J.; MacFarlane, J. D.

1985-01-01

Presents sports-oriented examples (cricket and football) in which Monte Carlo methods are used on microcomputers to teach probability concepts. Both examples include computer programs (with listings) which utilize the microcomputer's random number generator. Instructional strategies, with further challenges to help students understand the role of…

Profile-likelihood Confidence Intervals in Item Response Theory Models.

PubMed

Chalmers, R Philip; Pek, Jolynn; Liu, Yang

2017-01-01

Confidence intervals (CIs) are fundamental inferential devices which quantify the sampling variability of parameter estimates. In item response theory, CIs have been primarily obtained from large-sample Wald-type approaches based on standard error estimates, derived from the observed or expected information matrix, after parameters have been estimated via maximum likelihood. An alternative approach to constructing CIs is to quantify sampling variability directly from the likelihood function with a technique known as profile-likelihood confidence intervals (PL CIs). In this article, we introduce PL CIs for item response theory models, compare PL CIs to classical large-sample Wald-type CIs, and demonstrate important distinctions among these CIs. CIs are then constructed for parameters directly estimated in the specified model and for transformed parameters which are often obtained post-estimation. Monte Carlo simulation results suggest that PL CIs perform consistently better than Wald-type CIs for both non-transformed and transformed parameters.

Steady-State Electrodiffusion from the Nernst-Planck Equation Coupled to Local Equilibrium Monte Carlo Simulations.

PubMed

Boda, Dezső; Gillespie, Dirk

2012-03-13

We propose a procedure to compute the steady-state transport of charged particles based on the Nernst-Planck (NP) equation of electrodiffusion. To close the NP equation and to establish a relation between the concentration and electrochemical potential profiles, we introduce the Local Equilibrium Monte Carlo (LEMC) method. In this method, Grand Canonical Monte Carlo simulations are performed using the electrochemical potential specified for the distinct volume elements. An iteration procedure that self-consistently solves the NP and flux continuity equations with LEMC is shown to converge quickly. This NP+LEMC technique can be used in systems with diffusion of charged or uncharged particles in complex three-dimensional geometries, including systems with low concentrations and small applied voltages that are difficult for other particle simulation techniques.

Comparison of UWCC MOX fuel measurements to MCNP-REN calculations

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

Abhold, M.; Baker, M.; Jie, R.

1998-12-31

The development of neutron coincidence counting has greatly improved the accuracy and versatility of neutron-based techniques to assay fissile materials. Today, the shift register analyzer connected to either a passive or active neutron detector is widely used by both domestic and international safeguards organizations. The continued development of these techniques and detectors makes extensive use of the predictions of detector response through the use of Monte Carlo techniques in conjunction with the point reactor model. Unfortunately, the point reactor model, as it is currently used, fails to accurately predict detector response in highly multiplying mediums such as mixed-oxide (MOX) lightmore » water reactor fuel assemblies. For this reason, efforts have been made to modify the currently used Monte Carlo codes and to develop new analytical methods so that this model is not required to predict detector response. The authors describe their efforts to modify a widely used Monte Carlo code for this purpose and also compare calculational results with experimental measurements.« less

Probabilistic safety analysis for urgent situations following the accidental release of a pollutant in the atmosphere

NASA Astrophysics Data System (ADS)

Armand, P.; Brocheton, F.; Poulet, D.; Vendel, F.; Dubourg, V.; Yalamas, T.

2014-10-01

This paper is an original contribution to uncertainty quantification in atmospheric transport & dispersion (AT&D) at the local scale (1-10 km). It is proposed to account for the imprecise knowledge of the meteorological and release conditions in the case of an accidental hazardous atmospheric emission. The aim is to produce probabilistic risk maps instead of a deterministic toxic load map in order to help the stakeholders making their decisions. Due to the urge attached to such situations, the proposed methodology is able to produce such maps in a limited amount of time. It resorts to a Lagrangian particle dispersion model (LPDM) using wind fields interpolated from a pre-established database that collects the results from a computational fluid dynamics (CFD) model. This enables a decoupling of the CFD simulations from the dispersion analysis, thus a considerable saving of computational time. In order to make the Monte-Carlo-sampling-based estimation of the probability field even faster, it is also proposed to recourse to the use of a vector Gaussian process surrogate model together with high performance computing (HPC) resources. The Gaussian process (GP) surrogate modelling technique is coupled with a probabilistic principal component analysis (PCA) for reducing the number of GP predictors to fit, store and predict. The design of experiments (DOE) from which the surrogate model is built, is run over a cluster of PCs for making the total production time as short as possible. The use of GP predictors is validated by comparing the results produced by this technique with those obtained by crude Monte Carlo sampling.

High-resolution Monte Carlo simulation of flow and conservative transport in heterogeneous porous media: 2. Transport results

USGS Publications Warehouse

Naff, R.L.; Haley, D.F.; Sudicky, E.A.

1998-01-01

In this, the second of two papers concerned with the use of numerical simulation to examine flow and transport parameters in heterogeneous porous media via Monte Carlo methods, results from the transport aspect of these simulations are reported on. Transport simulations contained herein assume a finite pulse input of conservative tracer, and the numerical technique endeavors to realistically simulate tracer spreading as the cloud moves through a heterogeneous medium. Medium heterogeneity is limited to the hydraulic conductivity field, and generation of this field assumes that the hydraulic-conductivity process is second-order stationary. Methods of estimating cloud moments, and the interpretation of these moments, are discussed. Techniques for estimation of large-time macrodispersivities from cloud second-moment data, and for the approximation of the standard errors associated with these macrodispersivities, are also presented. These moment and macrodispersivity estimation techniques were applied to tracer clouds resulting from transport scenarios generated by specific Monte Carlo simulations. Where feasible, moments and macrodispersivities resulting from the Monte Carlo simulations are compared with first- and second-order perturbation analyses. Some limited results concerning the possible ergodic nature of these simulations, and the presence of non-Gaussian behavior of the mean cloud, are reported on as well.

Performance evaluation of an importance sampling technique in a Jackson network

NASA Astrophysics Data System (ADS)

brahim Mahdipour, E.; Masoud Rahmani, Amir; Setayeshi, Saeed

2014-03-01

Importance sampling is a technique that is commonly used to speed up Monte Carlo simulation of rare events. However, little is known regarding the design of efficient importance sampling algorithms in the context of queueing networks. The standard approach, which simulates the system using an a priori fixed change of measure suggested by large deviation analysis, has been shown to fail in even the simplest network settings. Estimating probabilities associated with rare events has been a topic of great importance in queueing theory, and in applied probability at large. In this article, we analyse the performance of an importance sampling estimator for a rare event probability in a Jackson network. This article carries out strict deadlines to a two-node Jackson network with feedback whose arrival and service rates are modulated by an exogenous finite state Markov process. We have estimated the probability of network blocking for various sets of parameters, and also the probability of missing the deadline of customers for different loads and deadlines. We have finally shown that the probability of total population overflow may be affected by various deadline values, service rates and arrival rates.

HepSim: A repository with predictions for high-energy physics experiments

DOE PAGES

Chekanov, S. V.

2015-02-03

A file repository for calculations of cross sections and kinematic distributions using Monte Carlo generators for high-energy collisions is discussed. The repository is used to facilitate effective preservation and archiving of data from theoretical calculations and for comparisons with experimental data. The HepSim data library is publicly accessible and includes a number of Monte Carlo event samples with Standard Model predictions for current and future experiments. The HepSim project includes a software package to automate the process of downloading and viewing online Monte Carlo event samples. Data streaming over a network for end-user analysis is discussed.

Three-dimensional light-tissue interaction models for bioluminescence tomography

NASA Astrophysics Data System (ADS)

Côté, D.; Allard, M.; Henkelman, R. M.; Vitkin, I. A.

2005-09-01

Many diagnostic and therapeutic approaches in medical physics today take advantage of the unique properties of light and its interaction with tissues. Because light scatters in tissue, our ability to develop these techniques depends critically on our knowledge of the distribution of light in tissue. Solutions to the diffusion equation can provide such information, but often lack the flexibility required for more general problems that involve, for instance, inhomogeneous optical properties, light polarization, arbitrary three-dimensional geometries, or arbitrary scattering. Monte Carlo techniques, which statistically sample the light distribution in tissue, offer a better alternative to analytical models. First, we discuss our implementation of a validated three-dimensional polarization-sensitive Monte Carlo algorithm and demonstrate its generality with respect to the geometry and scattering models it can treat. Second, we apply our model to bioluminescence tomography. After appropriate genetic modifications to cell lines, bioluminescence can be used as an indicator of cell activity, and is often used to study tumour growth and treatment in animal models. However, the amount of light escaping the animal is strongly dependent on the position and size of the tumour. Using forward models and structural data from magnetic resonance imaging, we show how the models can help to determine the location and size of tumour made of bioluminescent cancer cells in the brain of a mouse.

Deterministic theory of Monte Carlo variance

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

Ueki, T.; Larsen, E.W.

1996-12-31

The theoretical estimation of variance in Monte Carlo transport simulations, particularly those using variance reduction techniques, is a substantially unsolved problem. In this paper, the authors describe a theory that predicts the variance in a variance reduction method proposed by Dwivedi. Dwivedi`s method combines the exponential transform with angular biasing. The key element of this theory is a new modified transport problem, containing the Monte Carlo weight w as an extra independent variable, which simulates Dwivedi`s Monte Carlo scheme. The (deterministic) solution of this modified transport problem yields an expression for the variance. The authors give computational results that validatemore » this theory.« less

Multivariate stochastic simulation with subjective multivariate normal distributions

Treesearch

P. J. Ince; J. Buongiorno

1991-01-01

In many applications of Monte Carlo simulation in forestry or forest products, it may be known that some variables are correlated. However, for simplicity, in most simulations it has been assumed that random variables are independently distributed. This report describes an alternative Monte Carlo simulation technique for subjectively assesed multivariate normal...

Using Monte Carlo Techniques to Demonstrate the Meaning and Implications of Multicollinearity

ERIC Educational Resources Information Center

Vaughan, Timothy S.; Berry, Kelly E.

2005-01-01

This article presents an in-class Monte Carlo demonstration, designed to demonstrate to students the implications of multicollinearity in a multiple regression study. In the demonstration, students already familiar with multiple regression concepts are presented with a scenario in which the "true" relationship between the response and…

Auxiliary-field-based trial wave functions in quantum Monte Carlo calculations

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

Chang, Chia -Chen; Rubenstein, Brenda M.; Morales, Miguel A.

2016-12-19

Quantum Monte Carlo (QMC) algorithms have long relied on Jastrow factors to incorporate dynamic correlation into trial wave functions. While Jastrow-type wave functions have been widely employed in real-space algorithms, they have seen limited use in second-quantized QMC methods, particularly in projection methods that involve a stochastic evolution of the wave function in imaginary time. Here we propose a scheme for generating Jastrow-type correlated trial wave functions for auxiliary-field QMC methods. The method is based on decoupling the two-body Jastrow into one-body projectors coupled to auxiliary fields, which then operate on a single determinant to produce a multideterminant trial wavemore » function. We demonstrate that intelligent sampling of the most significant determinants in this expansion can produce compact trial wave functions that reduce errors in the calculated energies. Lastly, our technique may be readily generalized to accommodate a wide range of two-body Jastrow factors and applied to a variety of model and chemical systems.« less

Application of genetic algorithms to focal mechanism determination

NASA Astrophysics Data System (ADS)

Kobayashi, Reiji; Nakanishi, Ichiro

1994-04-01

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

Raman scattering from phonons and magnons in magnetic semiconductors, MnTe

NASA Technical Reports Server (NTRS)

Mobasser, S. R.; Hart, T. R.

1985-01-01

Comparisons are made between theoretical and experimental data on laser Raman scattering by phonons and two-magnons in antiferromagnetic and paramagnetic phases of MnTe. The study was performed specifically to characterize the magnetic exchange coupling constants of the Mn ions in the samples. Crystal MnTe samples were bombarded with an Ar ion laser beam to obtain spectrometer and photon counter data. One E(2g) phonon with a room temperature energy of 178/cm and a two-magnon peak of 360/cm were observed in the Raman spectrum. A spin wave dispersion relation is presented for the spectrum. Finally, a Monte Carlo technique was used to calculate the two-magnon joint density of states that best fits the experimental data.

Comparison of Methods for Estimating Low Flow Characteristics of Streams

USGS Publications Warehouse

Tasker, Gary D.

1987-01-01

Four methods for estimating the 7-day, 10-year and 7-day, 20-year low flows for streams are compared by the bootstrap method. The bootstrap method is a Monte Carlo technique in which random samples are drawn from an unspecified sampling distribution defined from observed data. The nonparametric nature of the bootstrap makes it suitable for comparing methods based on a flow series for which the true distribution is unknown. Results show that the two methods based on hypothetical distribution (Log-Pearson III and Weibull) had lower mean square errors than did the G. E. P. Box-D. R. Cox transformation method or the Log-W. C. Boughton method which is based on a fit of plotting positions.

Techniques for detecting effects of urban and rural land-use practices on stream-water chemistry in selected watersheds in Texas, Minnesota,and Illinois

USGS Publications Warehouse

Walker, J.F.

1993-01-01

Selected statistical techniques were applied to three urban watersheds in Texas and Minnesota and three rural watersheds in Illinois. For the urban watersheds, single- and paired-site data-collection strategies were considered. The paired-site strategy was much more effective than the singlesite strategy for detecting changes. Analysis of storm load regression residuals demonstrated the potential utility of regressions for variability reduction. For the rural watersheds, none of the selected techniques were effective at identifying changes, primarily due to a small degree of management-practice implementation, potential errors introduced through the estimation of storm load, and small sample sizes. A Monte Carlo sensitivity analysis was used to determine the percent change in water chemistry that could be detected for each watershed. In most instances, the use of regressions improved the ability to detect changes.

Multiscale Monte Carlo equilibration: Pure Yang-Mills theory

DOE PAGES

Endres, Michael G.; Brower, Richard C.; Orginos, Kostas; ...

2015-12-29

In this study, 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.

Probabilistic calibration of the distributed hydrological model RIBS applied to real-time flood forecasting: the Harod river basin case study (Israel)

NASA Astrophysics Data System (ADS)

Nesti, Alice; Mediero, Luis; Garrote, Luis; Caporali, Enrica

2010-05-01

An automatic probabilistic calibration method for distributed rainfall-runoff models is presented. The high number of parameters in hydrologic distributed models makes special demands on the optimization procedure to estimate model parameters. With the proposed technique it is possible to reduce the complexity of calibration while maintaining adequate model predictions. The first step of the calibration procedure of the main model parameters is done manually with the aim to identify their variation range. Afterwards a Monte-Carlo technique is applied, which consists on repetitive model simulations with randomly generated parameters. The Monte Carlo Analysis Toolbox (MCAT) includes a number of analysis methods to evaluate the results of these Monte Carlo parameter sampling experiments. The study investigates the use of a global sensitivity analysis as a screening tool to reduce the parametric dimensionality of multi-objective hydrological model calibration problems, while maximizing the information extracted from hydrological response data. The method is applied to the calibration of the RIBS flood forecasting model in the Harod river basin, placed on Israel. The Harod basin has an extension of 180 km2. The catchment has a Mediterranean climate and it is mainly characterized by a desert landscape, with a soil that is able to absorb large quantities of rainfall and at the same time is capable to generate high peaks of discharge. Radar rainfall data with 6 minute temporal resolution are available as input to the model. The aim of the study is the validation of the model for real-time flood forecasting, in order to evaluate the benefits of improved precipitation forecasting within the FLASH European project.

Structure of Nano-sized CeO 2 Materials: Combined Scattering and Spectroscopic Investigations

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

Marchbank, Huw R.; Clark, Adam H.; Hyde, Timothy I.

Here, the nature of nano-sized ceria, CeO 2, systems were investigated using neutron and X-ray diffraction and X-ray absorption spectroscopy. Whilst both diffraction andtotal pair distribution functions (PDFs) revealed that in all the samples the occupancy of both Ce 4+ and O 2- are very close to the ideal stoichiometry, the analysis using reverse Monte Carlo technique revealedsignificant disorder around oxygen atoms in the nano sized ceria samples in comparison to the highly crystalline NIST standard.In addition, the analysis reveal that the main differences observed in the pair correlations from various X-ray and neutron diffraction techniques were attributed to themore » particle size of the CeO 2 prepared by the reported three methods. Furthermore, detailed analysis of the Ce L 3– and K-edge EXAFS data support this finding; in particular the decrease in higher shell coordination numbers with respect to the NIST standard, are attributed to differences in particle size.« less

Structure of Nano-sized CeO 2 Materials: Combined Scattering and Spectroscopic Investigations

DOE PAGES

Marchbank, Huw R.; Clark, Adam H.; Hyde, Timothy I.; ...

2016-08-29

Here, the nature of nano-sized ceria, CeO 2, systems were investigated using neutron and X-ray diffraction and X-ray absorption spectroscopy. Whilst both diffraction andtotal pair distribution functions (PDFs) revealed that in all the samples the occupancy of both Ce 4+ and O 2- are very close to the ideal stoichiometry, the analysis using reverse Monte Carlo technique revealedsignificant disorder around oxygen atoms in the nano sized ceria samples in comparison to the highly crystalline NIST standard.In addition, the analysis reveal that the main differences observed in the pair correlations from various X-ray and neutron diffraction techniques were attributed to themore » particle size of the CeO 2 prepared by the reported three methods. Furthermore, detailed analysis of the Ce L 3– and K-edge EXAFS data support this finding; in particular the decrease in higher shell coordination numbers with respect to the NIST standard, are attributed to differences in particle size.« less

Continuous-time quantum Monte Carlo impurity solvers

NASA Astrophysics Data System (ADS)

Gull, Emanuel; Werner, Philipp; Fuchs, Sebastian; Surer, Brigitte; Pruschke, Thomas; Troyer, Matthias

2011-04-01

Continuous-time quantum Monte Carlo impurity solvers are algorithms that sample the partition function of an impurity model using diagrammatic Monte Carlo techniques. The present paper describes codes that implement the interaction expansion algorithm originally developed by Rubtsov, Savkin, and Lichtenstein, as well as the hybridization expansion method developed by Werner, Millis, Troyer, et al. These impurity solvers are part of the ALPS-DMFT application package and are accompanied by an implementation of dynamical mean-field self-consistency equations for (single orbital single site) dynamical mean-field problems with arbitrary densities of states. Program summaryProgram title: dmft Catalogue identifier: AEIL_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIL_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: ALPS LIBRARY LICENSE version 1.1 No. of lines in distributed program, including test data, etc.: 899 806 No. of bytes in distributed program, including test data, etc.: 32 153 916 Distribution format: tar.gz Programming language: C++ Operating system: The ALPS libraries have been tested on the following platforms and compilers: Linux with GNU Compiler Collection (g++ version 3.1 and higher), and Intel C++ Compiler (icc version 7.0 and higher) MacOS X with GNU Compiler (g++ Apple-version 3.1, 3.3 and 4.0) IBM AIX with Visual Age C++ (xlC version 6.0) and GNU (g++ version 3.1 and higher) compilers Compaq Tru64 UNIX with Compq C++ Compiler (cxx) SGI IRIX with MIPSpro C++ Compiler (CC) HP-UX with HP C++ Compiler (aCC) Windows with Cygwin or coLinux platforms and GNU Compiler Collection (g++ version 3.1 and higher) RAM: 10 MB-1 GB Classification: 7.3 External routines: ALPS [1], BLAS/LAPACK, HDF5 Nature of problem: (See [2].) Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as representations of quantum dots and molecular conductors and play an increasingly important role in the theory of "correlated electron" materials as auxiliary problems whose solution gives the "dynamical mean field" approximation to the self-energy and local correlation functions. Solution method: Quantum impurity models require a method of solution which provides access to both high and low energy scales and is effective for wide classes of physically realistic models. The continuous-time quantum Monte Carlo algorithms for which we present implementations here meet this challenge. Continuous-time quantum impurity methods are based on partition function expansions of quantum impurity models that are stochastically sampled to all orders using diagrammatic quantum Monte Carlo techniques. For a review of quantum impurity models and their applications and of continuous-time quantum Monte Carlo methods for impurity models we refer the reader to [2]. Additional comments: Use of dmft requires citation of this paper. Use of any ALPS program requires citation of the ALPS [1] paper. Running time: 60 s-8 h per iteration.

A two-stage Monte Carlo approach to the expression of uncertainty with finite sample sizes.

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

Crowder, Stephen Vernon; Moyer, Robert D.

2005-05-01

Proposed supplement I to the GUM outlines a 'propagation of distributions' approach to deriving the distribution of a measurand for any non-linear function and for any set of random inputs. The supplement's proposed Monte Carlo approach assumes that the distributions of the random inputs are known exactly. This implies that the sample sizes are effectively infinite. In this case, the mean of the measurand can be determined precisely using a large number of Monte Carlo simulations. In practice, however, the distributions of the inputs will rarely be known exactly, but must be estimated using possibly small samples. If these approximatedmore » distributions are treated as exact, the uncertainty in estimating the mean is not properly taken into account. In this paper, we propose a two-stage Monte Carlo procedure that explicitly takes into account the finite sample sizes used to estimate parameters of the input distributions. We will illustrate the approach with a case study involving the efficiency of a thermistor mount power sensor. The performance of the proposed approach will be compared to the standard GUM approach for finite samples using simple non-linear measurement equations. We will investigate performance in terms of coverage probabilities of derived confidence intervals.« less

Poster — Thur Eve — 45: Comparison of different Monte Carlo methods of scoring linear energy transfer in modulated proton therapy beams

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

Granville, DA; Sawakuchi, GO

2014-08-15

In this work, we demonstrate inconsistencies in commonly used Monte Carlo methods of scoring linear energy transfer (LET) in proton therapy beams. In particle therapy beams, the LET is an important parameter because the relative biological effectiveness (RBE) depends on it. LET is often determined using Monte Carlo techniques. We used a realistic Monte Carlo model of a proton therapy nozzle to score proton LET in spread-out Bragg peak (SOBP) depth-dose distributions. We used three different scoring and calculation techniques to determine average LET at varying depths within a 140 MeV beam with a 4 cm SOBP and a 250more » MeV beam with a 10 cm SOBP. These techniques included fluence-weighted (Φ-LET) and dose-weighted average (D-LET) LET calculations from: 1) scored energy spectra converted to LET spectra through a lookup table, 2) directly scored LET spectra and 3) accumulated LET scored ‘on-the-fly’ during simulations. All protons (primary and secondary) were included in the scoring. Φ-LET was found to be less sensitive to changes in scoring technique than D-LET. In addition, the spectral scoring methods were sensitive to low-energy (high-LET) cutoff values in the averaging. Using cutoff parameters chosen carefully for consistency between techniques, we found variations in Φ-LET values of up to 1.6% and variations in D-LET values of up to 11.2% for the same irradiation conditions, depending on the method used to score LET. Variations were largest near the end of the SOBP, where the LET and energy spectra are broader.« less

Nuclear risk analysis of the Ulysses mission

NASA Astrophysics Data System (ADS)

Bartram, Bart W.; Vaughan, Frank R.; Englehart, Richard W.

An account is given of the method used to quantify the risks accruing to the use of a radioisotope thermoelectric generator fueled by Pu-238 dioxide aboard the Space Shuttle-launched Ulysses mission. After using a Monte Carlo technique to develop probability distributions for the radiological consequences of a range of accident scenarios throughout the mission, factors affecting those consequences are identified in conjunction with their probability distributions. The functional relationship among all the factors is then established, and probability distributions for all factor effects are combined by means of a Monte Carlo technique.

Monte Carlo technique for very large ising models

NASA Astrophysics Data System (ADS)

Kalle, C.; Winkelmann, V.

1982-08-01

Rebbi's multispin coding technique is improved and applied to the kinetic Ising model with size 600*600*600. We give the central part of our computer program (for a CDC Cyber 76), which will be helpful also in a simulation of smaller systems, and describe the other tricks necessary to go to large lattices. The magnetization M at T=1.4* T c is found to decay asymptotically as exp(-t/2.90) if t is measured in Monte Carlo steps per spin, and M( t = 0) = 1 initially.

Skin fluorescence model based on the Monte Carlo technique

NASA Astrophysics Data System (ADS)

Churmakov, Dmitry Y.; Meglinski, Igor V.; Piletsky, Sergey A.; Greenhalgh, Douglas A.

2003-10-01

The novel Monte Carlo technique of simulation of spatial fluorescence distribution within the human skin is presented. The computational model of skin takes into account spatial distribution of fluorophores following the collagen fibers packing, whereas in epidermis and stratum corneum the distribution of fluorophores assumed to be homogeneous. The results of simulation suggest that distribution of auto-fluorescence is significantly suppressed in the NIR spectral region, while fluorescence of sensor layer embedded in epidermis is localized at the adjusted depth. The model is also able to simulate the skin fluorescence spectra.

Exact Dynamics via Poisson Process: a unifying Monte Carlo paradigm

NASA Astrophysics Data System (ADS)

Gubernatis, James

2014-03-01

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

Accelerating Sequences in the Presence of Metal by Exploiting the Spatial Distribution of Off-Resonance

PubMed Central

Smith, Matthew R.; Artz, Nathan S.; Koch, Kevin M.; Samsonov, Alexey; Reeder, Scott B.

2014-01-01

Purpose To demonstrate feasibility of exploiting the spatial distribution of off-resonance surrounding metallic implants for accelerating multispectral imaging techniques. Theory Multispectral imaging (MSI) techniques perform time-consuming independent 3D acquisitions with varying RF frequency offsets to address the extreme off-resonance from metallic implants. Each off-resonance bin provides a unique spatial sensitivity that is analogous to the sensitivity of a receiver coil, and therefore provides a unique opportunity for acceleration. Methods Fully sampled MSI was performed to demonstrate retrospective acceleration. A uniform sampling pattern across off-resonance bins was compared to several adaptive sampling strategies using a total hip replacement phantom. Monte Carlo simulations were performed to compare noise propagation of two of these strategies. With a total knee replacement phantom, positive and negative off-resonance bins were strategically sampled with respect to the B0 field to minimize aliasing. Reconstructions were performed with a parallel imaging framework to demonstrate retrospective acceleration. Results An adaptive sampling scheme dramatically improved reconstruction quality, which was supported by the noise propagation analysis. Independent acceleration of negative and positive off-resonance bins demonstrated reduced overlapping of aliased signal to improve the reconstruction. Conclusion This work presents the feasibility of acceleration in the presence of metal by exploiting the spatial sensitivities of off-resonance bins. PMID:24431210

High-efficiency wavefunction updates for large scale Quantum Monte Carlo

NASA Astrophysics Data System (ADS)

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

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

Exploring cluster Monte Carlo updates with Boltzmann machines

NASA Astrophysics Data System (ADS)

Wang, Lei

2017-11-01

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

Logistic regression applied to natural hazards: rare event logistic regression with replications

NASA Astrophysics Data System (ADS)

Guns, M.; Vanacker, V.

2012-06-01

Statistical analysis of natural hazards needs particular attention, as most of these phenomena are rare events. This study shows that the ordinary rare event logistic regression, as it is now commonly used in geomorphologic studies, does not always lead to a robust detection of controlling factors, as the results can be strongly sample-dependent. In this paper, we introduce some concepts of Monte Carlo simulations in rare event logistic regression. This technique, so-called rare event logistic regression with replications, combines the strength of probabilistic and statistical methods, and allows overcoming some of the limitations of previous developments through robust variable selection. This technique was here developed for the analyses of landslide controlling factors, but the concept is widely applicable for statistical analyses of natural hazards.

Variance in binary stellar population synthesis

NASA Astrophysics Data System (ADS)

Breivik, Katelyn; Larson, Shane L.

2016-03-01

In the years preceding LISA, Milky Way compact binary population simulations can be used to inform the science capabilities of the mission. Galactic population simulation efforts generally focus on high fidelity models that require extensive computational power to produce a single simulated population for each model. Each simulated population represents an incomplete sample of the functions governing compact binary evolution, thus introducing variance from one simulation to another. We present a rapid Monte Carlo population simulation technique that can simulate thousands of populations in less than a week, thus allowing a full exploration of the variance associated with a binary stellar evolution model.

Studying Variance in the Galactic Ultra-compact Binary Population

NASA Astrophysics Data System (ADS)

Larson, Shane L.; Breivik, Katelyn

2017-01-01

In the years preceding LISA, Milky Way compact binary population simulations can be used to inform the science capabilities of the mission. Galactic population simulation efforts generally focus on high fidelity models that require extensive computational power to produce a single simulated population for each model. Each simulated population represents an incomplete sample of the functions governing compact binary evolution, thus introducing variance from one simulation to another. We present a rapid Monte Carlo population simulation technique that can simulate thousands of populations on week-long timescales, thus allowing a full exploration of the variance associated with a binary stellar evolution model.

A Novel Implementation of Massively Parallel Three Dimensional Monte Carlo Radiation Transport

NASA Astrophysics Data System (ADS)

Robinson, P. B.; Peterson, J. D. L.

2005-12-01

The goal of our summer project was to implement the difference formulation for radiation transport into Cosmos++, a multidimensional, massively parallel, magneto hydrodynamics code for astrophysical applications (Peter Anninos - AX). The difference formulation is a new method for Symbolic Implicit Monte Carlo thermal transport (Brooks and Szöke - PAT). Formerly, simultaneous implementation of fully implicit Monte Carlo radiation transport in multiple dimensions on multiple processors had not been convincingly demonstrated. We found that a combination of the difference formulation and the inherent structure of Cosmos++ makes such an implementation both accurate and straightforward. We developed a "nearly nearest neighbor physics" technique to allow each processor to work independently, even with a fully implicit code. This technique coupled with the increased accuracy of an implicit Monte Carlo solution and the efficiency of parallel computing systems allows us to demonstrate the possibility of massively parallel thermal transport. This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48

Comparison of the Results of MISSE 6 Atomic Oxygen Erosion Yields of Layered Kapton H Films with Monte Carlo Computational Predictions

NASA Technical Reports Server (NTRS)

Banks, Bruce A.; Groh, Kim De; Kneubel, Christian A.

2014-01-01

A space experiment flown as part of the Materials International Space Station Experiment 6B (MISSE 6B) was designed to compare the atomic oxygen erosion yield (Ey) of layers of Kapton H polyimide with no spacers between layers with that of layers of Kapton H with spacers between layers. The results were compared to a solid Kapton H (DuPont, Wilmington, DE) sample. Monte Carlo computational modeling was performed to optimize atomic oxygen interaction parameter values to match the results of both the MISSE 6B multilayer experiment and the undercut erosion profile from a crack defect in an aluminized Kapton H sample flown on the Long Duration Exposure Facility (LDEF). The Monte Carlo modeling produced credible agreement with space results of increased Ey for all samples with spacers as well as predicting the space-observed enhancement in erosion near the edges of samples due to scattering from the beveled edges of the sample holders.

Monte Carlo simulation of the resolution volume for the SEQUOIA spectrometer

NASA Astrophysics Data System (ADS)

Granroth, G. E.; Hahn, S. E.

2015-01-01

Monte Carlo ray tracing simulations, of direct geometry spectrometers, have been particularly useful in instrument design and characterization. However, these tools can also be useful for experiment planning and analysis. To this end, the McStas Monte Carlo ray tracing model of SEQUOIA, the fine resolution fermi chopper spectrometer at the Spallation Neutron Source (SNS) of Oak Ridge National Laboratory (ORNL), has been modified to include the time of flight resolution sample and detector components. With these components, the resolution ellipsoid can be calculated for any detector pixel and energy bin of the instrument. The simulation is split in two pieces. First, the incident beamline up to the sample is simulated for 1 × 1011 neutron packets (4 days on 30 cores). This provides a virtual source for the backend that includes the resolution sample and monitor components. Next, a series of detector and energy pixels are computed in parallel. It takes on the order of 30 s to calculate a single resolution ellipsoid on a single core. Python scripts have been written to transform the ellipsoid into the space of an oriented single crystal, and to characterize the ellipsoid in various ways. Though this tool is under development as a planning tool, we have successfully used it to provide the resolution function for convolution with theoretical models. Specifically, theoretical calculations of the spin waves in YFeO3 were compared to measurements taken on SEQUOIA. Though the overall features of the spectra can be explained while neglecting resolution effects, the variation in intensity of the modes is well described once the resolution is included. As this was a single sharp mode, the simulated half intensity value of the resolution ellipsoid was used to provide the resolution width. A description of the simulation, its use, and paths forward for this technique will be discussed.

FASTER 3: A generalized-geometry Monte Carlo computer program for the transport of neutrons and gamma rays. Volume 2: Users manual

NASA Technical Reports Server (NTRS)

Jordan, T. M.

1970-01-01

A description of the FASTER-III program for Monte Carlo Carlo calculation of photon and neutron transport in complex geometries is presented. Major revisions include the capability of calculating minimum weight shield configurations for primary and secondary radiation and optimal importance sampling parameters. The program description includes a users manual describing the preparation of input data cards, the printout from a sample problem including the data card images, definitions of Fortran variables, the program logic, and the control cards required to run on the IBM 7094, IBM 360, UNIVAC 1108 and CDC 6600 computers.

TiOx deposited by magnetron sputtering: a joint modelling and experimental study

NASA Astrophysics Data System (ADS)

Tonneau, R.; Moskovkin, P.; Pflug, A.; Lucas, S.

2018-05-01

This paper presents a 3D multiscale simulation approach to model magnetron reactive sputter deposition of TiOx⩽2 at various O2 inlets and its validation against experimental results. The simulation first involves the transport of sputtered material in a vacuum chamber by means of a three-dimensional direct simulation Monte Carlo (DSMC) technique. Second, the film growth at different positions on a 3D substrate is simulated using a kinetic Monte Carlo (kMC) method. When simulating the transport of species in the chamber, wall chemistry reactions are taken into account in order to get the proper content of the reactive species in the volume. Angular and energy distributions of particles are extracted from DSMC and used for film growth modelling by kMC. Along with the simulation, experimental deposition of TiOx coatings on silicon samples placed at different positions on a curved sample holder was performed. The experimental results are in agreement with the simulated ones. For a given coater, the plasma phase hysteresis behaviour, film composition and film morphology are predicted. The used methodology can be applied to any coater and any films. This paves the way to the elaboration of a virtual coater allowing a user to predict composition and morphology of films deposited in silico.

Monte Carlo method for calculating the radiation skyshine produced by electron accelerators

NASA Astrophysics Data System (ADS)

Kong, Chaocheng; Li, Quanfeng; Chen, Huaibi; Du, Taibin; Cheng, Cheng; Tang, Chuanxiang; Zhu, Li; Zhang, Hui; Pei, Zhigang; Ming, Shenjin

2005-06-01

Using the MCNP4C Monte Carlo code, the X-ray skyshine produced by 9 MeV, 15 MeV and 21 MeV electron linear accelerators were calculated respectively with a new two-step method combined with the split and roulette variance reduction technique. Results of the Monte Carlo simulation, the empirical formulas used for skyshine calculation and the dose measurements were analyzed and compared. In conclusion, the skyshine dose measurements agreed reasonably with the results computed by the Monte Carlo method, but deviated from computational results given by empirical formulas. The effect on skyshine dose caused by different structures of accelerator head is also discussed in this paper.

Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics

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

Kube, Susanna; Lasser, Caroline; Weber, Marcus

2009-04-01

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

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

NASA Astrophysics Data System (ADS)

Rose, Michael Benjamin

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

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

Marshall, William BJ J; Rearden, Bradley T

The validation of neutron transport methods used in nuclear criticality safety analyses is required by consensus American National Standards Institute/American Nuclear Society (ANSI/ANS) standards. In the last decade, there has been an increased interest in correlations among critical experiments used in validation that have shared physical attributes and which impact the independence of each measurement. The statistical methods included in many of the frequently cited guidance documents on performing validation calculations incorporate the assumption that all individual measurements are independent, so little guidance is available to practitioners on the topic. Typical guidance includes recommendations to select experiments from multiple facilitiesmore » and experiment series in an attempt to minimize the impact of correlations or common-cause errors in experiments. Recent efforts have been made both to determine the magnitude of such correlations between experiments and to develop and apply methods for adjusting the bias and bias uncertainty to account for the correlations. This paper describes recent work performed at Oak Ridge National Laboratory using the Sampler sequence from the SCALE code system to develop experimental correlations using a Monte Carlo sampling technique. Sampler will be available for the first time with the release of SCALE 6.2, and a brief introduction to the methods used to calculate experiment correlations within this new sequence is presented in this paper. Techniques to utilize these correlations in the establishment of upper subcritical limits are the subject of a companion paper and will not be discussed here. Example experimental uncertainties and correlation coefficients are presented for a variety of low-enriched uranium water-moderated lattice experiments selected for use in a benchmark exercise by the Working Party on Nuclear Criticality Safety Subgroup on Uncertainty Analysis in Criticality Safety Analyses. The results include studies on the effect of fuel rod pitch on the correlations, and some observations are also made regarding difficulties in determining experimental correlations using the Monte Carlo sampling technique.« less

Reconciling a geophysical model to data using a Markov chain Monte Carlo algorithm: An application to the Yellow Sea-Korean Peninsula region

NASA Astrophysics Data System (ADS)

Pasyanos, Michael E.; Franz, Gregory A.; Ramirez, Abelardo L.

2006-03-01

In an effort to build seismic models that are the most consistent with multiple data sets we have applied a new probabilistic inverse technique. This method uses a Markov chain Monte Carlo (MCMC) algorithm to sample models from a prior distribution and test them against multiple data types to generate a posterior distribution. While computationally expensive, this approach has several advantages over deterministic models, notably the seamless reconciliation of different data types that constrain the model, the proper handling of both data and model uncertainties, and the ability to easily incorporate a variety of prior information, all in a straightforward, natural fashion. A real advantage of the technique is that it provides a more complete picture of the solution space. By mapping out the posterior probability density function, we can avoid simplistic assumptions about the model space and allow alternative solutions to be identified, compared, and ranked. Here we use this method to determine the crust and upper mantle structure of the Yellow Sea and Korean Peninsula region. The model is parameterized as a series of seven layers in a regular latitude-longitude grid, each of which is characterized by thickness and seismic parameters (Vp, Vs, and density). We use surface wave dispersion and body wave traveltime data to drive the model. We find that when properly tuned (i.e., the Markov chains have had adequate time to fully sample the model space and the inversion has converged), the technique behaves as expected. The posterior model reflects the prior information at the edge of the model where there is little or no data to constrain adjustments, but the range of acceptable models is significantly reduced in data-rich regions, producing values of sediment thickness, crustal thickness, and upper mantle velocities consistent with expectations based on knowledge of the regional tectonic setting.

The use of Monte Carlo simulations for accurate dose determination with thermoluminescence dosemeters in radiation therapy beams.

PubMed

Mobit, P

2002-01-01

The energy responses of LiF-TLDs irradiated in megavoltage electron and photon beams have been determined experimentally by many investigators over the past 35 years but the results vary considerably. General cavity theory has been used to model some of the experimental findings but the predictions of these cavity theories differ from each other and from measurements by more than 13%. Recently, two groups or investigators using Monte Carlo simulations and careful experimental techniques showed that the energy response of 1 mm or 2 mm thick LiF-TLD irradiated by megavoltage photon and electron beams is not more than 5% less than unity for low-Z phantom materials like water or Perspex. However, when the depth of irradiation is significantly different from dmax and the TLD size is more than 5 mm, then the energy response is up to 12% less than unity for incident electron beams. Monte Carlo simulations of some of the experiments reported in the literature showed that some of the contradictory experimental results are reproducible with Monte Carlo simulations. Monte Carlo simulations show that the energy response of LiF-TLDs depends on the size of detector used in electron beams, the depth of irradiation and the incident electron energy. Other differences can be attributed to absolute dose determination and precision of the TL technique. Monte Carlo simulations have also been used to evaluate some of the published general cavity theories. The results show that some of the parameters used to evaluate Burlin's general cavity theory are wrong by factor of 3. Despite this, the estimation of the energy response for most clinical situations using Burlin's cavity equation agrees with Monte Carlo simulations within 1%.

A quantitative and non-contact technique to characterise microstructural variations of skin tissues during photo-damaging process based on Mueller matrix polarimetry.

PubMed

Dong, Yang; He, Honghui; Sheng, Wei; Wu, Jian; Ma, Hui

2017-10-31

Skin tissue consists of collagen and elastic fibres, which are highly susceptible to damage when exposed to ultraviolet radiation (UVR), leading to skin aging and cancer. However, a lack of non-invasive detection methods makes determining the degree of UVR damage to skin in real time difficult. As one of the fundamental features of light, polarization can be used to develop imaging techniques capable of providing structural information about tissues. In particular, Mueller matrix polarimetry is suitable for detecting changes in collagen and elastic fibres. Here, we demonstrate a novel, quantitative, non-contact and in situ technique based on Mueller matrix polarimetry for monitoring the microstructural changes of skin tissues during UVR-induced photo-damaging. We measured the Mueller matrices of nude mouse skin samples, then analysed the transformed parameters to characterise microstructural changes during the skin photo-damaging and self-repairing processes. Comparisons between samples with and without the application of a sunscreen showed that the Mueller matrix-derived parameters are potential indicators for fibrous microstructure in skin tissues. Histological examination and Monte Carlo simulations confirmed the relationship between the Mueller matrix parameters and changes to fibrous structures. This technique paves the way for non-contact evaluation of skin structure in cosmetics and dermatological health.

Noise in Neuronal and Electronic Circuits: A General Modeling Framework and Non-Monte Carlo Simulation Techniques.

PubMed

Kilinc, Deniz; Demir, Alper

2017-08-01

The brain is extremely energy efficient and remarkably robust in what it does despite the considerable variability and noise caused by the stochastic mechanisms in neurons and synapses. Computational modeling is a powerful tool that can help us gain insight into this important aspect of brain mechanism. A deep understanding and computational design tools can help develop robust neuromorphic electronic circuits and hybrid neuroelectronic systems. In this paper, we present a general modeling framework for biological neuronal circuits that systematically captures the nonstationary stochastic behavior of ion channels and synaptic processes. In this framework, fine-grained, discrete-state, continuous-time Markov chain models of both ion channels and synaptic processes are treated in a unified manner. Our modeling framework features a mechanism for the automatic generation of the corresponding coarse-grained, continuous-state, continuous-time stochastic differential equation models for neuronal variability and noise. Furthermore, we repurpose non-Monte Carlo noise analysis techniques, which were previously developed for analog electronic circuits, for the stochastic characterization of neuronal circuits both in time and frequency domain. We verify that the fast non-Monte Carlo analysis methods produce results with the same accuracy as computationally expensive Monte Carlo simulations. We have implemented the proposed techniques in a prototype simulator, where both biological neuronal and analog electronic circuits can be simulated together in a coupled manner.

Effectiveness of different rescanning techniques for scanned proton radiotherapy in lung cancer patients

NASA Astrophysics Data System (ADS)

Engwall, E.; Glimelius, L.; Hynning, E.

2018-05-01

Non-small cell lung cancer (NSCLC) is a tumour type thought to be well-suited for proton radiotherapy. However, the lung region poses many problems related to organ motion and can for actively scanned beams induce severe interplay effects. In this study we investigate four mitigating rescanning techniques: (1) volumetric rescanning, (2) layered rescanning, (3) breath-sampled (BS) layered rescanning, and (4) continuous breath-sampled (CBS) layered rescanning. The breath-sampled methods will spread the layer rescans over a full breathing cycle, resulting in an improved averaging effect at the expense of longer treatment times. In CBS, we aim at further improving the averaging by delivering as many rescans as possible within one breathing cycle. The interplay effect was evaluated for 4D robustly optimized treatment plans (with and without rescanning) for seven NSCLC patients in the treatment planning system RayStation. The optimization and final dose calculation used a Monte Carlo dose engine to account for the density heterogeneities in the lung region. A realistic treatment delivery time structure given from the IBA ScanAlgo simulation tool served as basis for the interplay evaluation. Both slow (2.0 s) and fast (0.1 s) energy switching times were simulated. For all seven studied patients, rescanning improves the dose conformity to the target. The general trend is that the breath-sampled techniques are superior to layered and volumetric rescanning with respect to both target coverage and variability in dose to OARs. The spacing between rescans in our breath-sampled techniques is set at planning, based on the average breathing cycle length obtained in conjunction with CT acquisition. For moderately varied breathing cycle lengths between planning and delivery (up to 15%), the breath-sampled techniques still mitigate the interplay effect well. This shows the potential for smooth implementation at the clinic without additional motion monitoring equipment.

Proton Upset Monte Carlo Simulation

NASA Technical Reports Server (NTRS)

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.

A Dasymetric-Based Monte Carlo Simulation Approach to the Probabilistic Analysis of Spatial Variables

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

Morton, April M; Piburn, Jesse O; McManamay, Ryan A

2017-01-01

Monte Carlo simulation is a popular numerical experimentation technique used in a range of scientific fields to obtain the statistics of unknown random output variables. Despite its widespread applicability, it can be difficult to infer required input probability distributions when they are related to population counts unknown at desired spatial resolutions. To overcome this challenge, we propose a framework that uses a dasymetric model to infer the probability distributions needed for a specific class of Monte Carlo simulations which depend on population counts.

Discrete range clustering using Monte Carlo methods

NASA Technical Reports Server (NTRS)

Chatterji, G. B.; Sridhar, B.

1993-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2001-06-01

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

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

ERIC Educational Resources Information Center

Sinharay, Sandip

2004-01-01

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

Coupled multi-group neutron photon transport for the simulation of high-resolution gamma-ray spectroscopy applications

NASA Astrophysics Data System (ADS)

Burns, Kimberly Ann

The accurate and efficient simulation of coupled neutron-photon problems is necessary for several important radiation detection applications. Examples include the detection of nuclear threats concealed in cargo containers and prompt gamma neutron activation analysis for nondestructive determination of elemental composition of unknown samples. In these applications, high-resolution gamma-ray spectrometers are used to preserve as much information as possible about the emitted photon flux, which consists of both continuum and characteristic gamma rays with discrete energies. Monte Carlo transport is the most commonly used modeling tool for this type of problem, but computational times for many problems can be prohibitive. This work explores the use of coupled Monte Carlo-deterministic methods for the simulation of neutron-induced photons for high-resolution gamma-ray spectroscopy applications. RAdiation Detection Scenario Analysis Toolbox (RADSAT), a code which couples deterministic and Monte Carlo transport to perform radiation detection scenario analysis in three dimensions [1], was used as the building block for the methods derived in this work. RADSAT was capable of performing coupled deterministic-Monte Carlo simulations for gamma-only and neutron-only problems. The purpose of this work was to develop the methodology necessary to perform coupled neutron-photon calculations and add this capability to RADSAT. Performing coupled neutron-photon calculations requires four main steps: the deterministic neutron transport calculation, the neutron-induced photon spectrum calculation, the deterministic photon transport calculation, and the Monte Carlo detector response calculation. The necessary requirements for each of these steps were determined. A major challenge in utilizing multigroup deterministic transport methods for neutron-photon problems was maintaining the discrete neutron-induced photon signatures throughout the simulation. Existing coupled neutron-photon cross-section libraries and the methods used to produce neutron-induced photons were unsuitable for high-resolution gamma-ray spectroscopy applications. Central to this work was the development of a method for generating multigroup neutron-photon cross-sections in a way that separates the discrete and continuum photon emissions so the neutron-induced photon signatures were preserved. The RADSAT-NG cross-section library was developed as a specialized multigroup neutron-photon cross-section set for the simulation of high-resolution gamma-ray spectroscopy applications. The methodology and cross sections were tested using code-to-code comparison with MCNP5 [2] and NJOY [3]. A simple benchmark geometry was used for all cases compared with MCNP. The geometry consists of a cubical sample with a 252Cf neutron source on one side and a HPGe gamma-ray spectrometer on the opposing side. Different materials were examined in the cubical sample: polyethylene (C2H4), P, N, O, and Fe. The cross sections for each of the materials were compared to cross sections collapsed using NJOY. Comparisons of the volume-averaged neutron flux within the sample, volume-averaged photon flux within the detector, and high-purity gamma-ray spectrometer response (only for polyethylene) were completed using RADSAT and MCNP. The code-to-code comparisons show promising results for the coupled Monte Carlo-deterministic method. The RADSAT-NG cross-section production method showed good agreement with NJOY for all materials considered although some additional work is needed in the resonance region and in the first and last energy bin. Some cross section discrepancies existed in the lowest and highest energy bin, but the overall shape and magnitude of the two methods agreed. For the volume-averaged photon flux within the detector, typically the five most intense lines agree to within approximately 5% of the MCNP calculated flux for all of materials considered. The agreement in the code-to-code comparisons cases demonstrates a proof-of-concept of the method for use in RADSAT for coupled neutron-photon problems in high-resolution gamma-ray spectroscopy applications. One of the primary motivators for using the coupled method over pure Monte Carlo method is the potential for significantly lower computational times. For the code-to-code comparison cases, the run times for RADSAT were approximately 25--500 times shorter than for MCNP, as shown in Table 1. This was assuming a 40 mCi 252Cf neutron source and 600 seconds of "real-world" measurement time. The only variance reduction technique implemented in the MCNP calculation was forward biasing of the source toward the sample target. Improved MCNP runtimes could be achieved with the addition of more advanced variance reduction techniques.

Acceleration of Monte Carlo simulation of photon migration in complex heterogeneous media using Intel many-integrated core architecture.

PubMed

Gorshkov, Anton V; Kirillin, Mikhail Yu

2015-08-01

Over two decades, the Monte Carlo technique has become a gold standard in simulation of light propagation in turbid media, including biotissues. Technological solutions provide further advances of this technique. The Intel Xeon Phi coprocessor is a new type of accelerator for highly parallel general purpose computing, which allows execution of a wide range of applications without substantial code modification. We present a technical approach of porting our previously developed Monte Carlo (MC) code for simulation of light transport in tissues to the Intel Xeon Phi coprocessor. We show that employing the accelerator allows reducing computational time of MC simulation and obtaining simulation speed-up comparable to GPU. We demonstrate the performance of the developed code for simulation of light transport in the human head and determination of the measurement volume in near-infrared spectroscopy brain sensing.

Bulk substrate porosity verification by applying Monte Carlo modeling and Castaing's formula using energy-dispersive x-rays

NASA Astrophysics Data System (ADS)

Yung, Lai Chin; Fei, Cheong Choke; Mandeep, Jit Singh; Amin, Nowshad; Lai, Khin Wee

2015-11-01

The leadframe fabrication process normally involves additional thin-metal layer plating on the bulk copper substrate surface for wire bonding purposes. Silver, tin, and copper flakes are commonly adopted as plating materials. It is critical to assess the density of the plated metal layer, and in particular to look for porosity or voids underneath the layer, which may reduce the reliability during high-temperature stress. A fast, reliable inspection technique is needed to assess the porosity or void weakness. To this end, the characteristics of x-rays generated from bulk samples were examined using an energy-dispersive x-ray (EDX) detector to examine the porosity percentage. Monte Carlo modeling was integrated with Castaing's formula to verify the integrity of the experimental data. Samples with different porosity percentages were considered to test the correlation between the intensity of the collected x-ray signal and the material density. To further verify the integrity of the model, conventional cross-sectional samples were also taken to observe the porosity percentage using Image J software measurement. A breakthrough in bulk substrate assessment was achieved by applying EDX for the first time to nonelemental analysis. The experimental data showed that the EDX features were not only useful for elemental analysis, but also applicable to thin-film metal layer thickness measurement and bulk material density determination. A detailed experiment was conducted using EDX to assess the plating metal layer and bulk material porosity.

Uncertainty quantification for constitutive model calibration of brain tissue.

PubMed

Brewick, Patrick T; Teferra, Kirubel

2018-05-31

The results of a study comparing model calibration techniques for Ogden's constitutive model that describes the hyperelastic behavior of brain tissue are presented. One and two-term Ogden models are fit to two different sets of stress-strain experimental data for brain tissue using both least squares optimization and Bayesian estimation. For the Bayesian estimation, the joint posterior distribution of the constitutive parameters is calculated by employing Hamiltonian Monte Carlo (HMC) sampling, a type of Markov Chain Monte Carlo method. The HMC method is enriched in this work to intrinsically enforce the Drucker stability criterion by formulating a nonlinear parameter constraint function, which ensures the constitutive model produces physically meaningful results. Through application of the nested sampling technique, 95% confidence bounds on the constitutive model parameters are identified, and these bounds are then propagated through the constitutive model to produce the resultant bounds on the stress-strain response. The behavior of the model calibration procedures and the effect of the characteristics of the experimental data are extensively evaluated. It is demonstrated that increasing model complexity (i.e., adding an additional term in the Ogden model) improves the accuracy of the best-fit set of parameters while also increasing the uncertainty via the widening of the confidence bounds of the calibrated parameters. Despite some similarity between the two data sets, the resulting distributions are noticeably different, highlighting the sensitivity of the calibration procedures to the characteristics of the data. For example, the amount of uncertainty reported on the experimental data plays an essential role in how data points are weighted during the calibration, and this significantly affects how the parameters are calibrated when combining experimental data sets from disparate sources. Published by Elsevier Ltd.

Diffuse reflectance imaging for non-melanoma skin cancer detection using laser feedback interferometry

NASA Astrophysics Data System (ADS)

Mowla, Alireza; Taimre, Thomas; Lim, Yah L.; Bertling, Karl; Wilson, Stephen J.; Prow, Tarl W.; Soyer, H. P.; Rakić, Aleksandar D.

2016-04-01

We propose a compact, self-aligned, low-cost, and versatile infrared diffuse-reflectance laser imaging system using a laser feedback interferometry technique with possible applications in in vivo biological tissue imaging and skin cancer detection. We examine the proposed technique experimentally using a three-layer agar skin phantom. A cylindrical region with a scattering rate lower than that of the surrounding normal tissue was used as a model for a non-melanoma skin tumour. The same structure was implemented in a Monte Carlo computational model. The experimental results agree well with the Monte Carlo simulations validating the theoretical basis of the technique. Results prove the applicability of the proposed technique for biological tissue imaging, with the capability of depth sectioning and a penetration depth of well over 1.2 mm into the skin phantom.

Comparison of sampling techniques for Bayesian parameter estimation

NASA Astrophysics Data System (ADS)

Allison, Rupert; Dunkley, Joanna

2014-02-01

The posterior probability distribution for a set of model parameters encodes all that the data have to tell us in the context of a given model; it is the fundamental quantity for Bayesian parameter estimation. In order to infer the posterior probability distribution we have to decide how to explore parameter space. Here we compare three prescriptions for how parameter space is navigated, discussing their relative merits. We consider Metropolis-Hasting sampling, nested sampling and affine-invariant ensemble Markov chain Monte Carlo (MCMC) sampling. We focus on their performance on toy-model Gaussian likelihoods and on a real-world cosmological data set. We outline the sampling algorithms themselves and elaborate on performance diagnostics such as convergence time, scope for parallelization, dimensional scaling, requisite tunings and suitability for non-Gaussian distributions. We find that nested sampling delivers high-fidelity estimates for posterior statistics at low computational cost, and should be adopted in favour of Metropolis-Hastings in many cases. Affine-invariant MCMC is competitive when computing clusters can be utilized for massive parallelization. Affine-invariant MCMC and existing extensions to nested sampling naturally probe multimodal and curving distributions.

Hybrid Monte Carlo/deterministic methods for radiation shielding problems

NASA Astrophysics Data System (ADS)

Becker, Troy L.

For the past few decades, the most common type of deep-penetration (shielding) problem simulated using Monte Carlo methods has been the source-detector problem, in which a response is calculated at a single location in space. Traditionally, the nonanalog Monte Carlo methods used to solve these problems have required significant user input to generate and sufficiently optimize the biasing parameters necessary to obtain a statistically reliable solution. It has been demonstrated that this laborious task can be replaced by automated processes that rely on a deterministic adjoint solution to set the biasing parameters---the so-called hybrid methods. The increase in computational power over recent years has also led to interest in obtaining the solution in a region of space much larger than a point detector. In this thesis, we propose two methods for solving problems ranging from source-detector problems to more global calculations---weight windows and the Transform approach. These techniques employ sonic of the same biasing elements that have been used previously; however, the fundamental difference is that here the biasing techniques are used as elements of a comprehensive tool set to distribute Monte Carlo particles in a user-specified way. The weight window achieves the user-specified Monte Carlo particle distribution by imposing a particular weight window on the system, without altering the particle physics. The Transform approach introduces a transform into the neutron transport equation, which results in a complete modification of the particle physics to produce the user-specified Monte Carlo distribution. These methods are tested in a three-dimensional multigroup Monte Carlo code. For a basic shielding problem and a more realistic one, these methods adequately solved source-detector problems and more global calculations. Furthermore, they confirmed that theoretical Monte Carlo particle distributions correspond to the simulated ones, implying that these methods can be used to achieve user-specified Monte Carlo distributions. Overall, the Transform approach performed more efficiently than the weight window methods, but it performed much more efficiently for source-detector problems than for global problems.

Application of dynamic Monte Carlo technique in proton beam radiotherapy using Geant4 simulation toolkit

NASA Astrophysics Data System (ADS)

Guan, Fada

Monte Carlo method has been successfully applied in simulating the particles transport problems. Most of the Monte Carlo simulation tools are static and they can only be used to perform the static simulations for the problems with fixed physics and geometry settings. Proton therapy is a dynamic treatment technique in the clinical application. In this research, we developed a method to perform the dynamic Monte Carlo simulation of proton therapy using Geant4 simulation toolkit. A passive-scattering treatment nozzle equipped with a rotating range modulation wheel was modeled in this research. One important application of the Monte Carlo simulation is to predict the spatial dose distribution in the target geometry. For simplification, a mathematical model of a human body is usually used as the target, but only the average dose over the whole organ or tissue can be obtained rather than the accurate spatial dose distribution. In this research, we developed a method using MATLAB to convert the medical images of a patient from CT scanning into the patient voxel geometry. Hence, if the patient voxel geometry is used as the target in the Monte Carlo simulation, the accurate spatial dose distribution in the target can be obtained. A data analysis tool---root was used to score the simulation results during a Geant4 simulation and to analyze the data and plot results after simulation. Finally, we successfully obtained the accurate spatial dose distribution in part of a human body after treating a patient with prostate cancer using proton therapy.

An Energy-Dispersive X-Ray Fluorescence Spectrometry and Monte Carlo simulation study of Iron-Age Nuragic small bronzes ("Navicelle") from Sardinia, Italy

NASA Astrophysics Data System (ADS)

Schiavon, Nick; de Palmas, Anna; Bulla, Claudio; Piga, Giampaolo; Brunetti, Antonio

2016-09-01

A spectrometric protocol combining Energy Dispersive X-Ray Fluorescence Spectrometry with Monte Carlo simulations of experimental spectra using the XRMC code package has been applied for the first time to characterize the elemental composition of a series of famous Iron Age small scale archaeological bronze replicas of ships (known as the ;Navicelle;) from the Nuragic civilization in Sardinia, Italy. The proposed protocol is a useful, nondestructive and fast analytical tool for Cultural Heritage sample. In Monte Carlo simulations, each sample was modeled as a multilayered object composed by two or three layers depending on the sample: when all present, the three layers are the original bronze substrate, the surface corrosion patina and an outermost protective layer (Paraloid) applied during past restorations. Monte Carlo simulations were able to account for the presence of the patina/corrosion layer as well as the presence of the Paraloid protective layer. It also accounted for the roughness effect commonly found at the surface of corroded metal archaeological artifacts. In this respect, the Monte Carlo simulation approach adopted here was, to the best of our knowledge, unique and enabled to determine the bronze alloy composition together with the thickness of the surface layers without the need for previously removing the surface patinas, a process potentially threatening preservation of precious archaeological/artistic artifacts for future generations.

Concepts and Plans towards fast large scale Monte Carlo production for the ATLAS Experiment

NASA Astrophysics Data System (ADS)

Ritsch, E.; Atlas Collaboration

2014-06-01

The huge success of the physics program of the ATLAS experiment at the Large Hadron Collider (LHC) during Run 1 relies upon a great number of simulated Monte Carlo events. This Monte Carlo production takes the biggest part of the computing resources being in use by ATLAS as of now. In this document we describe the plans to overcome the computing resource limitations for large scale Monte Carlo production in the ATLAS Experiment for Run 2, and beyond. A number of fast detector simulation, digitization and reconstruction techniques are being discussed, based upon a new flexible detector simulation framework. To optimally benefit from these developments, a redesigned ATLAS MC production chain is presented at the end of this document.

Advances in the Assessment of Wind Turbine Operating Extreme Loads via More Efficient Calculation Approaches

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

Graf, Peter; Damiani, Rick R.; Dykes, Katherine

2017-01-09

A new adaptive stratified importance sampling (ASIS) method is proposed as an alternative approach for the calculation of the 50 year extreme load under operational conditions, as in design load case 1.1 of the the International Electrotechnical Commission design standard. ASIS combines elements of the binning and extrapolation technique, currently described by the standard, and of the importance sampling (IS) method to estimate load probability of exceedances (POEs). Whereas a Monte Carlo (MC) approach would lead to the sought level of POE with a daunting number of simulations, IS-based techniques are promising as they target the sampling of the inputmore » parameters on the parts of the distributions that are most responsible for the extreme loads, thus reducing the number of runs required. We compared the various methods on select load channels as output from FAST, an aero-hydro-servo-elastic tool for the design and analysis of wind turbines developed by the National Renewable Energy Laboratory (NREL). Our newly devised method, although still in its infancy in terms of tuning of the subparameters, is comparable to the others in terms of load estimation and its variance versus computational cost, and offers great promise going forward due to the incorporation of adaptivity into the already powerful importance sampling concept.« less

A Quantitative Three-Dimensional Image Analysis Tool for Maximal Acquisition of Spatial Heterogeneity Data.

PubMed

Allenby, Mark C; Misener, Ruth; Panoskaltsis, Nicki; Mantalaris, Athanasios

2017-02-01

Three-dimensional (3D) imaging techniques provide spatial insight into environmental and cellular interactions and are implemented in various fields, including tissue engineering, but have been restricted by limited quantification tools that misrepresent or underutilize the cellular phenomena captured. This study develops image postprocessing algorithms pairing complex Euclidean metrics with Monte Carlo simulations to quantitatively assess cell and microenvironment spatial distributions while utilizing, for the first time, the entire 3D image captured. Although current methods only analyze a central fraction of presented confocal microscopy images, the proposed algorithms can utilize 210% more cells to calculate 3D spatial distributions that can span a 23-fold longer distance. These algorithms seek to leverage the high sample cost of 3D tissue imaging techniques by extracting maximal quantitative data throughout the captured image.

An Educational MONTE CARLO Simulation/Animation Program for the Cosmic Rays Muons and a Prototype Computer-Driven Hardware Display.

ERIC Educational Resources Information Center

Kalkanis, G.; Sarris, M. M.

1999-01-01

Describes an educational software program for the study of and detection methods for the cosmic ray muons passing through several light transparent materials (i.e., water, air, etc.). Simulates muons and Cherenkov photons' paths and interactions and visualizes/animates them on the computer screen using Monte Carlo methods/techniques which employ…

Use of Empirical Estimates of Shrinkage in Multiple Regression: A Caution.

ERIC Educational Resources Information Center

Kromrey, Jeffrey D.; Hines, Constance V.

1995-01-01

The accuracy of four empirical techniques to estimate shrinkage in multiple regression was studied through Monte Carlo simulation. None of the techniques provided unbiased estimates of the population squared multiple correlation coefficient, but the normalized jackknife and bootstrap techniques demonstrated marginally acceptable performance with…

Improvements in sub-grid, microphysics averages using quadrature based approaches

NASA Astrophysics Data System (ADS)

Chowdhary, K.; Debusschere, B.; Larson, V. E.

2013-12-01

Sub-grid variability in microphysical processes plays a critical role in atmospheric climate models. In order to account for this sub-grid variability, Larson and Schanen (2013) propose placing a probability density function on the sub-grid cloud microphysics quantities, e.g. autoconversion rate, essentially interpreting the cloud microphysics quantities as a random variable in each grid box. Random sampling techniques, e.g. Monte Carlo and Latin Hypercube, can be used to calculate statistics, e.g. averages, on the microphysics quantities, which then feed back into the model dynamics on the coarse scale. We propose an alternate approach using numerical quadrature methods based on deterministic sampling points to compute the statistical moments of microphysics quantities in each grid box. We have performed a preliminary test on the Kessler autoconversion formula, and, upon comparison with Latin Hypercube sampling, our approach shows an increased level of accuracy with a reduction in sample size by almost two orders of magnitude. Application to other microphysics processes is the subject of ongoing research.

Cathodoluminescence Study of Hafnium Oxide

NASA Astrophysics Data System (ADS)

Purcell, Emily; Hengehold, Robert; McClory, John

2011-10-01

Hafnium dioxide (HfO2) is increasingly being used in place of silicon oxide as a gate insulator in field effect transistors. This is primarily due to its high dielectric constant, κ, of 25. Samples of HfO2 were grown by either atomic layer deposition (ALD) or pulsed laser deposition (PLD), with the PLD samples having assorted substrate temperatures during deposition (300 C, 500 C, and 750 C). Cathodoluminescence (CL) was chosen as the technique used for studying these HfO2 samples. The CL system used was capable of beam energies ranging from 1 keV to 20 keV and beam currents ranging from 10 μA to 50 μA. A Monte Carlo calculation using CASINO software was performed in order to determine the beam energy for the desired depth of penetration. Measurements were taken at sample temperatures ranging from 7K (closed cycled cryostat) to 300K (room temperature), as well as at various beam energies and beam currents. Comparison will be made between the PLD and ALD spectra.

Numerical simulations of strongly correlated electron and spin systems

NASA Astrophysics Data System (ADS)

Changlani, Hitesh Jaiprakash

Developing analytical and numerical tools for strongly correlated systems is a central challenge for the condensed matter physics community. In the absence of exact solutions and controlled analytical approximations, numerical techniques have often contributed to our understanding of these systems. Exact Diagonalization (ED) requires the storage of at least two vectors the size of the Hilbert space under consideration (which grows exponentially with system size) which makes it affordable only for small systems. The Density Matrix Renormalization Group (DMRG) uses an intelligent Hilbert space truncation procedure to significantly reduce this cost, but in its present formulation is limited to quasi-1D systems. Quantum Monte Carlo (QMC) maps the Schrodinger equation to the diffusion equation (in imaginary time) and only samples the eigenvector over time, thereby avoiding the memory limitation. However, the stochasticity involved in the method gives rise to the "sign problem" characteristic of fermion and frustrated spin systems. The first part of this thesis is an effort to make progress in the development of a numerical technique which overcomes the above mentioned problems. We consider novel variational wavefunctions, christened "Correlator Product States" (CPS), that have a general functional form which hopes to capture essential correlations in the ground states of spin and fermion systems in any dimension. We also consider a recent proposal to modify projector (Green's Function) Quantum Monte Carlo to ameliorate the sign problem for realistic and model Hamiltonians (such as the Hubbard model). This exploration led to our own set of improvements, primarily a semistochastic formulation of projector Quantum Monte Carlo. Despite their limitations, existing numerical techniques can yield physical insights into a wide variety of problems. The second part of this thesis considers one such numerical technique - DMRG - and adapts it to study the Heisenberg antiferromagnet on a generic tree graph. Our attention turns to a systematic numerical and semi-analytical study of the effect of local even/odd sublattice imbalance on the low energy spectrum of antiferromagnets on regular Cayley trees. Finally, motivated by previous experiments and theories of randomly diluted antiferromagnets (where an even/odd sublattice imbalance naturally occurs), we present our study of the Heisenberg antiferromagnet on the Cayley tree at the percolation threshold. Our work shows how to detect "emergent" low energy degrees of freedom and compute the effective interactions between them by using data from DMRG calculations.

Generating moment matching scenarios using optimization techniques

DOE PAGES

Mehrotra, Sanjay; Papp, Dávid

2013-05-16

An optimization based method is proposed to generate moment matching scenarios for numerical integration and its use in stochastic programming. The main advantage of the method is its flexibility: it can generate scenarios matching any prescribed set of moments of the underlying distribution rather than matching all moments up to a certain order, and the distribution can be defined over an arbitrary set. This allows for a reduction in the number of scenarios and allows the scenarios to be better tailored to the problem at hand. The method is based on a semi-infinite linear programming formulation of the problem thatmore » is shown to be solvable with polynomial iteration complexity. A practical column generation method is implemented. The column generation subproblems are polynomial optimization problems; however, they need not be solved to optimality. It is found that the columns in the column generation approach can be efficiently generated by random sampling. The number of scenarios generated matches a lower bound of Tchakaloff's. The rate of convergence of the approximation error is established for continuous integrands, and an improved bound is given for smooth integrands. Extensive numerical experiments are presented in which variants of the proposed method are compared to Monte Carlo and quasi-Monte Carlo methods on both numerical integration problems and stochastic optimization problems. The benefits of being able to match any prescribed set of moments, rather than all moments up to a certain order, is also demonstrated using optimization problems with 100-dimensional random vectors. Here, empirical results show that the proposed approach outperforms Monte Carlo and quasi-Monte Carlo based approaches on the tested problems.« less

A comparative study of Conroy and Monte Carlo methods applied to multiple quadratures and multiple scattering

NASA Technical Reports Server (NTRS)

Deepak, A.; Fluellen, A.

1978-01-01

An efficient numerical method of multiple quadratures, the Conroy method, is applied to the problem of computing multiple scattering contributions in the radiative transfer through realistic planetary atmospheres. A brief error analysis of the method is given and comparisons are drawn with the more familiar Monte Carlo method. Both methods are stochastic problem-solving models of a physical or mathematical process and utilize the sampling scheme for points distributed over a definite region. In the Monte Carlo scheme the sample points are distributed randomly over the integration region. In the Conroy method, the sample points are distributed systematically, such that the point distribution forms a unique, closed, symmetrical pattern which effectively fills the region of the multidimensional integration. The methods are illustrated by two simple examples: one, of multidimensional integration involving two independent variables, and the other, of computing the second order scattering contribution to the sky radiance.

Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics

NASA Technical Reports Server (NTRS)

Pohorille, Andrew

2006-01-01

The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described by rate constants. These problems are isomorphic with chemical kinetics problems. Recently, several efficient techniques for this purpose have been developed based on the approach originally proposed by Gillespie. Although the utility of the techniques mentioned above for Bayesian problems has not been determined, further research along these lines is warranted

Molecular detection of Toxoplasma gondii in water samples from Scotland and a comparison between the 529bp real-time PCR and ITS1 nested PCR.

PubMed

Wells, Beth; Shaw, Hannah; Innocent, Giles; Guido, Stefano; Hotchkiss, Emily; Parigi, Maria; Opsteegh, Marieke; Green, James; Gillespie, Simon; Innes, Elisabeth A; Katzer, Frank

2015-12-15

Waterborne transmission of Toxoplasma gondii is a potential public health risk and there are currently no agreed optimised methods for the recovery, processing and detection of T. gondii oocysts in water samples. In this study modified methods of T. gondii oocyst recovery and DNA extraction were applied to 1427 samples collected from 147 public water supplies throughout Scotland. T. gondii DNA was detected, using real time PCR (qPCR) targeting the 529bp repeat element, in 8.79% of interpretable samples (124 out of 1411 samples). The samples which were positive for T. gondii DNA originated from a third of the sampled water sources. The samples which were positive by qPCR and some of the negative samples were reanalysed using ITS1 nested PCR (nPCR) and results compared. The 529bp qPCR was the more sensitive technique and a full analysis of assay performance, by Bayesian analysis using a Markov Chain Monte Carlo method, was completed which demonstrated the efficacy of this method for the detection of T. gondii in water samples. Copyright © 2015 The Authors. Published by Elsevier Ltd.. All rights reserved.

Microscale and nanoscale strain mapping techniques applied to creep of rocks

NASA Astrophysics Data System (ADS)

Quintanilla-Terminel, Alejandra; Zimmerman, Mark E.; Evans, Brian; Kohlstedt, David L.

2017-07-01

Usually several deformation mechanisms interact to accommodate plastic deformation. Quantifying the contribution of each to the total strain is necessary to bridge the gaps from observations of microstructures, to geomechanical descriptions, to extrapolating from laboratory data to field observations. Here, we describe the experimental and computational techniques involved in microscale strain mapping (MSSM), which allows strain produced during high-pressure, high-temperature deformation experiments to be tracked with high resolution. MSSM relies on the analysis of the relative displacement of initially regularly spaced markers after deformation. We present two lithography techniques used to pattern rock substrates at different scales: photolithography and electron-beam lithography. Further, we discuss the challenges of applying the MSSM technique to samples used in high-temperature and high-pressure experiments. We applied the MSSM technique to a study of strain partitioning during creep of Carrara marble and grain boundary sliding in San Carlos olivine, synthetic forsterite, and Solnhofen limestone at a confining pressure, Pc, of 300 MPa and homologous temperatures, T/Tm, of 0.3 to 0.6. The MSSM technique works very well up to temperatures of 700 °C. The experimental developments described here show promising results for higher-temperature applications.

Monte Carlo simulations of particle acceleration at oblique shocks

NASA Technical Reports Server (NTRS)

Baring, Matthew G.; Ellison, Donald C.; Jones, Frank C.

1994-01-01

The Fermi shock acceleration mechanism may be responsible for the production of high-energy cosmic rays in a wide variety of environments. Modeling of this phenomenon has largely focused on plane-parallel shocks, and one of the most promising techniques for its study is the Monte Carlo simulation of particle transport in shocked fluid flows. One of the principal problems in shock acceleration theory is the mechanism and efficiency of injection of particles from the thermal gas into the accelerated population. The Monte Carlo technique is ideally suited to addressing the injection problem directly, and previous applications of it to the quasi-parallel Earth bow shock led to very successful modeling of proton and heavy ion spectra, as well as other observed quantities. Recently this technique has been extended to oblique shock geometries, in which the upstream magnetic field makes a significant angle Theta(sub B1) to the shock normal. Spectral resutls from test particle Monte Carlo simulations of cosmic-ray acceleration at oblique, nonrelativistic shocks are presented. The results show that low Mach number shocks have injection efficiencies that are relatively insensitive to (though not independent of) the shock obliquity, but that there is a dramatic drop in efficiency for shocks of Mach number 30 or more as the obliquity increases above 15 deg. Cosmic-ray distributions just upstream of the shock reveal prominent bumps at energies below the thermal peak; these disappear far upstream but might be observable features close to astrophysical shocks.

Uncertainty importance analysis using parametric moment ratio functions.

PubMed

Wei, Pengfei; Lu, Zhenzhou; Song, Jingwen

2014-02-01

This article presents a new importance analysis framework, called parametric moment ratio function, for measuring the reduction of model output uncertainty when the distribution parameters of inputs are changed, and the emphasis is put on the mean and variance ratio functions with respect to the variances of model inputs. The proposed concepts efficiently guide the analyst to achieve a targeted reduction on the model output mean and variance by operating on the variances of model inputs. The unbiased and progressive unbiased Monte Carlo estimators are also derived for the parametric mean and variance ratio functions, respectively. Only a set of samples is needed for implementing the proposed importance analysis by the proposed estimators, thus the computational cost is free of input dimensionality. An analytical test example with highly nonlinear behavior is introduced for illustrating the engineering significance of the proposed importance analysis technique and verifying the efficiency and convergence of the derived Monte Carlo estimators. Finally, the moment ratio function is applied to a planar 10-bar structure for achieving a targeted 50% reduction of the model output variance. © 2013 Society for Risk Analysis.

Monte Carlo investigation of thrust imbalance of solid rocket motor pairs

NASA Technical Reports Server (NTRS)

Sforzini, R. H.; Foster, W. A., Jr.

1976-01-01

The Monte Carlo method of statistical analysis is used to investigate the theoretical thrust imbalance of pairs of solid rocket motors (SRMs) firing in parallel. Sets of the significant variables are selected using a random sampling technique and the imbalance calculated for a large number of motor pairs using a simplified, but comprehensive, model of the internal ballistics. The treatment of burning surface geometry allows for the variations in the ovality and alignment of the motor case and mandrel as well as those arising from differences in the basic size dimensions and propellant properties. The analysis is used to predict the thrust-time characteristics of 130 randomly selected pairs of Titan IIIC SRMs. A statistical comparison of the results with test data for 20 pairs shows the theory underpredicts the standard deviation in maximum thrust imbalance by 20% with variability in burning times matched within 2%. The range in thrust imbalance of Space Shuttle type SRM pairs is also estimated using applicable tolerances and variabilities and a correction factor based on the Titan IIIC analysis.

Monte Carlo simulations of product distributions and contained metal estimates

USGS Publications Warehouse

Gettings, Mark E.

2013-01-01

Estimation of product distributions of two factors was simulated by conventional Monte Carlo techniques using factor distributions that were independent (uncorrelated). Several simulations using uniform distributions of factors show that the product distribution has a central peak approximately centered at the product of the medians of the factor distributions. Factor distributions that are peaked, such as Gaussian (normal) produce an even more peaked product distribution. Piecewise analytic solutions can be obtained for independent factor distributions and yield insight into the properties of the product distribution. As an example, porphyry copper grades and tonnages are now available in at least one public database and their distributions were analyzed. Although both grade and tonnage can be approximated with lognormal distributions, they are not exactly fit by them. The grade shows some nonlinear correlation with tonnage for the published database. Sampling by deposit from available databases of grade, tonnage, and geological details of each deposit specifies both grade and tonnage for that deposit. Any correlation between grade and tonnage is then preserved and the observed distribution of grades and tonnages can be used with no assumption of distribution form.

Markov Chain Monte Carlo Joint Analysis of Chandra X-Ray Imaging Spectroscopy and Sunyaev-Zel'dovich Effect Data

NASA Technical Reports Server (NTRS)

Bonamente, Massimillano; Joy, Marshall K.; Carlstrom, John E.; Reese, Erik D.; LaRoque, Samuel J.

2004-01-01

X-ray and Sunyaev-Zel'dovich effect data can be combined to determine the distance to galaxy clusters. High-resolution X-ray data are now available from Chandra, which provides both spatial and spectral information, and Sunyaev-Zel'dovich effect data were obtained from the BIMA and Owens Valley Radio Observatory (OVRO) arrays. We introduce a Markov Chain Monte Carlo procedure for the joint analysis of X-ray and Sunyaev- Zel'dovich effect data. The advantages of this method are the high computational efficiency and the ability to measure simultaneously the probability distribution of all parameters of interest, such as the spatial and spectral properties of the cluster gas and also for derivative quantities such as the distance to the cluster. We demonstrate this technique by applying it to the Chandra X-ray data and the OVRO radio data for the galaxy cluster A611. Comparisons with traditional likelihood ratio methods reveal the robustness of the method. This method will be used in follow-up paper to determine the distances to a large sample of galaxy cluster.

Acceleration and sensitivity analysis of lattice kinetic Monte Carlo simulations using parallel processing and rate constant rescaling

NASA Astrophysics Data System (ADS)

Núñez, M.; Robie, T.; Vlachos, D. G.

2017-10-01

Kinetic Monte Carlo (KMC) simulation provides insights into catalytic reactions unobtainable with either experiments or mean-field microkinetic models. Sensitivity analysis of KMC models assesses the robustness of the predictions to parametric perturbations and identifies rate determining steps in a chemical reaction network. Stiffness in the chemical reaction network, a ubiquitous feature, demands lengthy run times for KMC models and renders efficient sensitivity analysis based on the likelihood ratio method unusable. We address the challenge of efficiently conducting KMC simulations and performing accurate sensitivity analysis in systems with unknown time scales by employing two acceleration techniques: rate constant rescaling and parallel processing. We develop statistical criteria that ensure sufficient sampling of non-equilibrium steady state conditions. Our approach provides the twofold benefit of accelerating the simulation itself and enabling likelihood ratio sensitivity analysis, which provides further speedup relative to finite difference sensitivity analysis. As a result, the likelihood ratio method can be applied to real chemistry. We apply our methodology to the water-gas shift reaction on Pt(111).

Multi-scale modeling of spin transport in organic semiconductors

NASA Astrophysics Data System (ADS)

Hemmatiyan, Shayan; Souza, Amaury; Kordt, Pascal; McNellis, Erik; Andrienko, Denis; Sinova, Jairo

In this work, we present our theoretical framework to simulate simultaneously spin and charge transport in amorphous organic semiconductors. By combining several techniques e.g. molecular dynamics, density functional theory and kinetic Monte Carlo, we are be able to study spin transport in the presence of anisotropy, thermal effects, magnetic and electric field effects in a realistic morphologies of amorphous organic systems. We apply our multi-scale approach to investigate the spin transport in amorphous Alq3 (Tris(8-hydroxyquinolinato)aluminum) and address the underlying spin relaxation mechanism in this system as a function of temperature, bias voltage, magnetic field and sample thickness.

Enhanced configurational sampling with hybrid non-equilibrium molecular dynamics-Monte Carlo propagator

NASA Astrophysics Data System (ADS)

Suh, Donghyuk; Radak, Brian K.; Chipot, Christophe; Roux, Benoît

2018-01-01

Molecular dynamics (MD) trajectories based on classical equations of motion can be used to sample the configurational space of complex molecular systems. However, brute-force MD often converges slowly due to the ruggedness of the underlying potential energy surface. Several schemes have been proposed to address this problem by effectively smoothing the potential energy surface. However, in order to recover the proper Boltzmann equilibrium probability distribution, these approaches must then rely on statistical reweighting techniques or generate the simulations within a Hamiltonian tempering replica-exchange scheme. The present work puts forth a novel hybrid sampling propagator combining Metropolis-Hastings Monte Carlo (MC) with proposed moves generated by non-equilibrium MD (neMD). This hybrid neMD-MC propagator comprises three elementary elements: (i) an atomic system is dynamically propagated for some period of time using standard equilibrium MD on the correct potential energy surface; (ii) the system is then propagated for a brief period of time during what is referred to as a "boosting phase," via a time-dependent Hamiltonian that is evolved toward the perturbed potential energy surface and then back to the correct potential energy surface; (iii) the resulting configuration at the end of the neMD trajectory is then accepted or rejected according to a Metropolis criterion before returning to step 1. A symmetric two-end momentum reversal prescription is used at the end of the neMD trajectories to guarantee that the hybrid neMD-MC sampling propagator obeys microscopic detailed balance and rigorously yields the equilibrium Boltzmann distribution. The hybrid neMD-MC sampling propagator is designed and implemented to enhance the sampling by relying on the accelerated MD and solute tempering schemes. It is also combined with the adaptive biased force sampling algorithm to examine. Illustrative tests with specific biomolecular systems indicate that the method can yield a significant speedup.

Enhanced configurational sampling with hybrid non-equilibrium molecular dynamics-Monte Carlo propagator.

PubMed

Suh, Donghyuk; Radak, Brian K; Chipot, Christophe; Roux, Benoît

2018-01-07

Molecular dynamics (MD) trajectories based on classical equations of motion can be used to sample the configurational space of complex molecular systems. However, brute-force MD often converges slowly due to the ruggedness of the underlying potential energy surface. Several schemes have been proposed to address this problem by effectively smoothing the potential energy surface. However, in order to recover the proper Boltzmann equilibrium probability distribution, these approaches must then rely on statistical reweighting techniques or generate the simulations within a Hamiltonian tempering replica-exchange scheme. The present work puts forth a novel hybrid sampling propagator combining Metropolis-Hastings Monte Carlo (MC) with proposed moves generated by non-equilibrium MD (neMD). This hybrid neMD-MC propagator comprises three elementary elements: (i) an atomic system is dynamically propagated for some period of time using standard equilibrium MD on the correct potential energy surface; (ii) the system is then propagated for a brief period of time during what is referred to as a "boosting phase," via a time-dependent Hamiltonian that is evolved toward the perturbed potential energy surface and then back to the correct potential energy surface; (iii) the resulting configuration at the end of the neMD trajectory is then accepted or rejected according to a Metropolis criterion before returning to step 1. A symmetric two-end momentum reversal prescription is used at the end of the neMD trajectories to guarantee that the hybrid neMD-MC sampling propagator obeys microscopic detailed balance and rigorously yields the equilibrium Boltzmann distribution. The hybrid neMD-MC sampling propagator is designed and implemented to enhance the sampling by relying on the accelerated MD and solute tempering schemes. It is also combined with the adaptive biased force sampling algorithm to examine. Illustrative tests with specific biomolecular systems indicate that the method can yield a significant speedup.

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

NASA Astrophysics Data System (ADS)

Šantić, Branko; Gracin, Davor

2017-12-01

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

Method and program product for determining a radiance field in an optical environment

NASA Technical Reports Server (NTRS)

Reinersman, Phillip N. (Inventor); Carder, Kendall L. (Inventor)

2007-01-01

A hybrid method is presented by which Monte Carlo techniques are combined with iterative relaxation techniques to solve the Radiative Transfer Equation in arbitrary one-, two- or three-dimensional optical environments. The optical environments are first divided into contiguous regions, or elements, with Monte Carlo techniques then being employed to determine the optical response function of each type of element. The elements are combined, and the iterative relaxation techniques are used to determine simultaneously the radiance field on the boundary and throughout the interior of the modeled environment. This hybrid model is capable of providing estimates of the under-water light field needed to expedite inspection of ship hulls and port facilities. It is also capable of providing estimates of the subaerial light field for structured, absorbing or non-absorbing environments such as shadows of mountain ranges within and without absorption spectral bands such as water vapor or CO.sub.2 bands.

Extension of the Viscous Collision Limiting Direct Simulation Monte Carlo Technique to Multiple Species

NASA Technical Reports Server (NTRS)

Liechty, Derek S.; Burt, Jonathan M.

2016-01-01

There are many flows fields that span a wide range of length scales where regions of both rarefied and continuum flow exist and neither direct simulation Monte Carlo (DSMC) nor computational fluid dynamics (CFD) provide the appropriate solution everywhere. Recently, a new viscous collision limited (VCL) DSMC technique was proposed to incorporate effects of physical diffusion into collision limiter calculations to make the low Knudsen number regime normally limited to CFD more tractable for an all-particle technique. This original work had been derived for a single species gas. The current work extends the VCL-DSMC technique to gases with multiple species. Similar derivations were performed to equate numerical and physical transport coefficients. However, a more rigorous treatment of determining the mixture viscosity is applied. In the original work, consideration was given to internal energy non-equilibrium, and this is also extended in the current work to chemical non-equilibrium.

Identification of high transverse momentum top quarks in pp collisions at $$ \\sqrt{s}=8 $$ TeV with the ATLAS detector

DOE PAGES

Aad, G.; Abbott, B.; Abdallah, J.; ...

2016-06-16

This study presents studies of the performance of several jet-substructure techniques, which are used to identify hadronically decaying top quarks with high transverse momentum contained in large-radius jets. The efficiency of identifying top quarks is measured using a sample of top-quark pairs and the rate of wrongly identifying jets from other quarks or gluons as top quarks is measured using multijet events collected with the ATLAS experiment in 20.3 fb -1 of 8 TeV proton-proton collisions at the Large Hadron Collider. Predictions from Monte Carlo simulations are found to provide an accurate description of the performance. The techniques are comparedmore » in terms of signal efficiency and background rejection using simulations, covering a larger range in jet transverse momenta than accessible in the dataset. Finally and additionally, a novel technique is developed that is optimized to reconstruct top quarks in events with many jets.« less

Comparison of a 3-D CFD-DSMC Solution Methodology With a Wind Tunnel Experiment

NASA Technical Reports Server (NTRS)

Glass, Christopher E.; Horvath, Thomas J.

2002-01-01

A solution method for problems that contain both continuum and rarefied flow regions is presented. The methodology is applied to flow about the 3-D Mars Sample Return Orbiter (MSRO) that has a highly compressed forebody flow, a shear layer where the flow separates from a forebody lip, and a low density wake. Because blunt body flow fields contain such disparate regions, employing a single numerical technique to solve the entire 3-D flow field is often impractical, or the technique does not apply. Direct simulation Monte Carlo (DSMC) could be employed to solve the entire flow field; however, the technique requires inordinate computational resources for continuum and near-continuum regions, and is best suited for the wake region. Computational fluid dynamics (CFD) will solve the high-density forebody flow, but continuum assumptions do not apply in the rarefied wake region. The CFD-DSMC approach presented herein may be a suitable way to obtain a higher fidelity solution.

Mapping local anisotropy axis for scattering media using backscattering Mueller matrix imaging

NASA Astrophysics Data System (ADS)

He, Honghui; Sun, Minghao; Zeng, Nan; Du, E.; Guo, Yihong; He, Yonghong; Ma, Hui

2014-03-01

Mueller matrix imaging techniques can be used to detect the micro-structure variations of superficial biological tissues, including the sizes and shapes of cells, the structures in cells, and the densities of the organelles. Many tissues contain anisotropic fibrous micro-structures, such as collagen fibers, elastin fibers, and muscle fibers. Changes of these fibrous structures are potentially good indicators for some pathological variations. In this paper, we propose a quantitative analysis technique based on Mueller matrix for mapping local anisotropy axis of scattering media. By conducting both experiments on silk sample and Monte Carlo simulation based on the sphere-cylinder scattering model (SCSM), we extract anisotropy axis parameters from different backscattering Mueller matrix elements. Moreover, we testify the possible applications of these parameters for biological tissues. The preliminary experimental results of human cancerous samples show that, these parameters are capable to map the local axis of fibers. Since many pathological changes including early stage cancers affect the well aligned structures for tissues, the experimental results indicate that these parameters can be used as potential tools in clinical applications for biomedical diagnosis purposes.

State Tracking and Fault Diagnosis for Dynamic Systems Using Labeled Uncertainty Graph.

PubMed

Zhou, Gan; Feng, Wenquan; Zhao, Qi; Zhao, Hongbo

2015-11-05

Cyber-physical systems such as autonomous spacecraft, power plants and automotive systems become more vulnerable to unanticipated failures as their complexity increases. Accurate tracking of system dynamics and fault diagnosis are essential. This paper presents an efficient state estimation method for dynamic systems modeled as concurrent probabilistic automata. First, the Labeled Uncertainty Graph (LUG) method in the planning domain is introduced to describe the state tracking and fault diagnosis processes. Because the system model is probabilistic, the Monte Carlo technique is employed to sample the probability distribution of belief states. In addition, to address the sample impoverishment problem, an innovative look-ahead technique is proposed to recursively generate most likely belief states without exhaustively checking all possible successor modes. The overall algorithms incorporate two major steps: a roll-forward process that estimates system state and identifies faults, and a roll-backward process that analyzes possible system trajectories once the faults have been detected. We demonstrate the effectiveness of this approach by applying it to a real world domain: the power supply control unit of a spacecraft.

Reconstruction of Laser-Induced Surface Topography from Electron Backscatter Diffraction Patterns.

PubMed

Callahan, Patrick G; Echlin, McLean P; Pollock, Tresa M; De Graef, Marc

2017-08-01

We demonstrate that the surface topography of a sample can be reconstructed from electron backscatter diffraction (EBSD) patterns collected with a commercial EBSD system. This technique combines the location of the maximum background intensity with a correction from Monte Carlo simulations to determine the local surface normals at each point in an EBSD scan. A surface height map is then reconstructed from the local surface normals. In this study, a Ni sample was machined with a femtosecond laser, which causes the formation of a laser-induced periodic surface structure (LIPSS). The topography of the LIPSS was analyzed using atomic force microscopy (AFM) and reconstructions from EBSD patterns collected at 5 and 20 kV. The LIPSS consisted of a combination of low frequency waviness due to curtaining and high frequency ridges. The morphology of the reconstructed low frequency waviness and high frequency ridges matched the AFM data. The reconstruction technique does not require any modification to existing EBSD systems and so can be particularly useful for measuring topography and its evolution during in situ experiments.

Using MathCad to Evaluate Exact Integral Formulations of Spacecraft Orbital Heats for Primitive Surfaces at Any Orientation

NASA Technical Reports Server (NTRS)

Pinckney, John

2010-01-01

With the advent of high speed computing Monte Carlo ray tracing techniques has become the preferred method for evaluating spacecraft orbital heats. Monte Carlo has its greatest advantage where there are many interacting surfaces. However Monte Carlo programs are specialized programs that suffer from some inaccuracy, long calculation times and high purchase cost. A general orbital heating integral is presented here that is accurate, fast and runs on MathCad, a generally available engineering mathematics program. The integral is easy to read, understand and alter. The integral can be applied to unshaded primitive surfaces at any orientation. The method is limited to direct heating calculations. This integral formulation can be used for quick orbit evaluations and spot checking Monte Carlo results.

Monte Carlo Calculations of Polarized Microwave Radiation Emerging from Cloud Structures

NASA Technical Reports Server (NTRS)

Kummerow, Christian; Roberti, Laura

1998-01-01

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

EDITORIAL: International Workshop on Monte Carlo Techniques in Radiotherapy Delivery and Verification

NASA Astrophysics Data System (ADS)

Verhaegen, Frank; Seuntjens, Jan

2008-03-01

Monte Carlo particle transport techniques offer exciting tools for radiotherapy research, where they play an increasingly important role. Topics of research related to clinical applications range from treatment planning, motion and registration studies, brachytherapy, verification imaging and dosimetry. The International Workshop on Monte Carlo Techniques in Radiotherapy Delivery and Verification took place in a hotel in Montreal in French Canada, from 29 May-1 June 2007, and was the third workshop to be held on a related topic, which now seems to have become a tri-annual event. About one hundred workers from many different countries participated in the four-day meeting. Seventeen experts in the field were invited to review topics and present their latest work. About half of the audience was made up by young graduate students. In a very full program, 57 papers were presented and 10 posters were on display during most of the meeting. On the evening of the third day a boat trip around the island of Montreal allowed participants to enjoy the city views, and to sample the local cuisine. The topics covered at the workshop included the latest developments in the most popular Monte Carlo transport algorithms, fast Monte Carlo, statistical issues, source modeling, MC treatment planning, modeling of imaging devices for treatment verification, registration and deformation of images and a sizeable number of contributions on brachytherapy. In this volume you will find 27 short papers resulting from the workshop on a variety of topics, some of them on very new stuff such as graphics processing units for fast computing, PET modeling, dual-energy CT, calculations in dynamic phantoms, tomotherapy devices, . . . . We acknowledge the financial support of the National Cancer Institute of Canada, the Institute of Cancer Research of the Canadian Institutes of Health Research, the Association Québécoise des Physicien(ne)s Médicaux Clinique, the Institute of Physics, and MedicalPhysicsWeb. At McGill we thank the following departments for support: the Cancer Axis of the Research Institute of the McGill University Health Center, the Faculties of Medicine and Science, the Departments of Oncology and Physics and the Medical Physics Unit. The following companies are thanked: TomoTherapy and Standard Imaging. The American Association of Physicists in Medicine and the International Atomic Energy Agency are gratefully acknowledged for endorsing the meeting. A final word of thanks goes out to all of those who contributed to the successful Workshop: first of all our administrative assistant Ms Margery Knewstubb, the website developer Dr François DeBlois, the two heads of the logistics team, Ms Emily Poon and Ms Emily Heath, our local medical physics students and staff, the IOP staff and the authors who shared their new and exciting work with us. Editors: Frank Verhaegen and Jan Seuntjens (McGill University) Associate editors: Luc Beaulieu, Iwan Kawrakow, Tony Popescu and David Rogers

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

DOE PAGES

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

2016-01-01

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

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

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

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

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

Entanglement and the fermion sign problem in auxiliary field quantum Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Broecker, Peter; Trebst, Simon

2016-08-01

Quantum Monte Carlo simulations of fermions are hampered by the notorious sign problem whose most striking manifestation is an exponential growth of sampling errors with the number of particles. With the sign problem known to be an NP-hard problem and any generic solution thus highly elusive, the Monte Carlo sampling of interacting many-fermion systems is commonly thought to be restricted to a small class of model systems for which a sign-free basis has been identified. Here we demonstrate that entanglement measures, in particular the so-called Rényi entropies, can intrinsically exhibit a certain robustness against the sign problem in auxiliary-field quantum Monte Carlo approaches and possibly allow for the identification of global ground-state properties via their scaling behavior even in the presence of a strong sign problem. We corroborate these findings via numerical simulations of fermionic quantum phase transitions of spinless fermions on the honeycomb lattice at and below half filling.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Simulation-Based Model Checking for Nondeterministic Systems and Rare Events

DTIC Science & Technology

2016-03-24

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

Discrepancy-based error estimates for Quasi-Monte Carlo III. Error distributions and central limits

NASA Astrophysics Data System (ADS)

Hoogland, Jiri; Kleiss, Ronald

1997-04-01

In Quasi-Monte Carlo integration, the integration error is believed to be generally smaller than in classical Monte Carlo with the same number of integration points. Using an appropriate definition of an ensemble of quasi-random point sets, we derive various results on the probability distribution of the integration error, which can be compared to the standard Central Limit Theorem for normal stochastic sampling. In many cases, a Gaussian error distribution is obtained.

Fast alternative Monte Carlo formalism for a class of problems in biophotonics

NASA Astrophysics Data System (ADS)

Miller, Steven D.

1997-12-01

A practical and effective, alternative Monte Carlo formalism is presented that rapidly finds flux solutions to the radiative transport equation for a class of problems in biophotonics; namely, wide-beam irradiance of finite, optically anisotropic homogeneous or heterogeneous biomedias, which both strongly scatter and absorb light. Such biomedias include liver, tumors, blood, or highly blood perfused tissues. As Fermat rays comprising a wide coherent (laser) beam enter the tissue, they evolve into a bundle of random optical paths or trajectories due to scattering. Overall, this can be physically interpreted as a bundle of Markov trajectories traced out by a 'gas' of Brownian-like point photons being successively scattered and absorbed. By considering the cumulative flow of a statistical bundle of trajectories through interior data planes, the effective equivalent information of the (generally unknown) analytical flux solutions of the transfer equation rapidly emerges. Unlike the standard Monte Carlo techniques, which evaluate scalar fluence, this technique is faster, more efficient, and simpler to apply for this specific class of optical situations. Other analytical or numerical techniques can either become unwieldy or lack viability or are simply more difficult to apply. Illustrative flux calculations are presented for liver, blood, and tissue-tumor-tissue systems.

Deep learning ensemble with asymptotic techniques for oscillometric blood pressure estimation.

PubMed

Lee, Soojeong; Chang, Joon-Hyuk

2017-11-01

This paper proposes a deep learning based ensemble regression estimator with asymptotic techniques, and offers a method that can decrease uncertainty for oscillometric blood pressure (BP) measurements using the bootstrap and Monte-Carlo approach. While the former is used to estimate SBP and DBP, the latter attempts to determine confidence intervals (CIs) for SBP and DBP based on oscillometric BP measurements. This work originally employs deep belief networks (DBN)-deep neural networks (DNN) to effectively estimate BPs based on oscillometric measurements. However, there are some inherent problems with these methods. First, it is not easy to determine the best DBN-DNN estimator, and worthy information might be omitted when selecting one DBN-DNN estimator and discarding the others. Additionally, our input feature vectors, obtained from only five measurements per subject, represent a very small sample size; this is a critical weakness when using the DBN-DNN technique and can cause overfitting or underfitting, depending on the structure of the algorithm. To address these problems, an ensemble with an asymptotic approach (based on combining the bootstrap with the DBN-DNN technique) is utilized to generate the pseudo features needed to estimate the SBP and DBP. In the first stage, the bootstrap-aggregation technique is used to create ensemble parameters. Afterward, the AdaBoost approach is employed for the second-stage SBP and DBP estimation. We then use the bootstrap and Monte-Carlo techniques in order to determine the CIs based on the target BP estimated using the DBN-DNN ensemble regression estimator with the asymptotic technique in the third stage. The proposed method can mitigate the estimation uncertainty such as large the standard deviation of error (SDE) on comparing the proposed DBN-DNN ensemble regression estimator with the DBN-DNN single regression estimator, we identify that the SDEs of the SBP and DBP are reduced by 0.58 and 0.57  mmHg, respectively. These indicate that the proposed method actually enhances the performance by 9.18% and 10.88% compared with the DBN-DNN single estimator. The proposed methodology improves the accuracy of BP estimation and reduces the uncertainty for BP estimation. Copyright © 2017 Elsevier B.V. All rights reserved.

Monte Carlo simulation of air sampling methods for the measurement of radon decay products.

PubMed

Sima, Octavian; Luca, Aurelian; Sahagia, Maria

2017-08-01

A stochastic model of the processes involved in the measurement of the activity of the 222 Rn decay products was developed. The distributions of the relevant factors, including air sampling and radionuclide collection, are propagated using Monte Carlo simulation to the final distribution of the measurement results. The uncertainties of the 222 Rn decay products concentrations in the air are realistically evaluated. Copyright © 2017 Elsevier Ltd. All rights reserved.

Kinetic Monte Carlo simulation of intermixing during semiconductor heteroepitaxy

NASA Astrophysics Data System (ADS)

Rouhani, M. Djafari; Kassem, H.; Dalla Torre, J.; Landa, G.; Estève, D.

2002-03-01

We have used the kinetic Monte Carlo technique to investigate the intermixing mechanisms during the heteroepitaxial growth of semiconductors. We have shown that the temperature increases the intermixing between the substrate and deposited film, while an increasing growth rate inhibits this intermixing. We have also observed that intermixing is reduced when the energetics becomes unfavorable, i.e. with high lattice mismatches or hard-deposited materials.

Monte Carlo algorithms for Brownian phylogenetic models.

PubMed

Horvilleur, Benjamin; Lartillot, Nicolas

2014-11-01

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

Near-infrared optical properties of ex-vivo human skin and subcutaneous tissues using reflectance and transmittance measurements

NASA Astrophysics Data System (ADS)

Simpson, Rebecca; Laufer, Jan G.; Kohl-Bareis, Matthias; Essenpreis, Matthias; Cope, Mark

1997-08-01

The vast majority of 'non-invasive' measurements of human tissues using near infrared spectroscopy rely on passing light through the dermis and subdermis of the skin. Accurate knowledge of the optical properties of these tissues is essential to put into models of light transport and predict the effects of skin perfusion on measurements of deep tissue. Additionally, the skin could be a useful accessible organ for non-invasively determining the constituents of blood flowing through it. Samples of abdominal human skin (including subdermal tissue) were obtained from either post mortem examinations or plastic surgery. The samples were separated into a dermal layer (epidermis and dermis, 1.5 to 2 mm tick), and a sub-cutaneous layer comprised largely of fat. They were enclosed between two glass coverslips and placed in an integrating sphere to measure their reflectance and transmittance over a range of wavelengths from 600 to 1000 nm. The reflectance and transmittance values were converted into average absorption and reduced scattering coefficients by comparison with a Monte Carlo model of light transport. Improvements to the Monte Carlo model and measurement technique removed some previous uncertainties. The results show excellent separation of reduced scattering and absorption coefficient, with clear absorption peaks of hemoglobin, water and lipid. The effect of tissue storage upon measured optical properties was investigated.

Probabilistic dietary exposure assessment taking into account variability in both amount and frequency of consumption.

PubMed

Slob, Wout

2006-07-01

Probabilistic dietary exposure assessments that are fully based on Monte Carlo sampling from the raw intake data may not be appropriate. This paper shows that the data should first be analysed by using a statistical model that is able to take the various dimensions of food consumption patterns into account. A (parametric) model is discussed that takes into account the interindividual variation in (daily) consumption frequencies, as well as in amounts consumed. Further, the model can be used to include covariates, such as age, sex, or other individual attributes. Some illustrative examples show how this model may be used to estimate the probability of exceeding an (acute or chronic) exposure limit. These results are compared with the results based on directly counting the fraction of observed intakes exceeding the limit value. This comparison shows that the latter method is not adequate, in particular for the acute exposure situation. A two-step approach for probabilistic (acute) exposure assessment is proposed: first analyse the consumption data by a (parametric) statistical model as discussed in this paper, and then use Monte Carlo techniques for combining the variation in concentrations with the variation in consumption (by sampling from the statistical model). This approach results in an estimate of the fraction of the population as a function of the fraction of days at which the exposure limit is exceeded by the individual.

Deterministic and reliability based optimization of integrated thermal protection system composite panel using adaptive sampling techniques

NASA Astrophysics Data System (ADS)

Ravishankar, Bharani

Conventional space vehicles have thermal protection systems (TPS) that provide protection to an underlying structure that carries the flight loads. In an attempt to save weight, there is interest in an integrated TPS (ITPS) that combines the structural function and the TPS function. This has weight saving potential, but complicates the design of the ITPS that now has both thermal and structural failure modes. The main objectives of this dissertation was to optimally design the ITPS subjected to thermal and mechanical loads through deterministic and reliability based optimization. The optimization of the ITPS structure requires computationally expensive finite element analyses of 3D ITPS (solid) model. To reduce the computational expenses involved in the structural analysis, finite element based homogenization method was employed, homogenizing the 3D ITPS model to a 2D orthotropic plate. However it was found that homogenization was applicable only for panels that are much larger than the characteristic dimensions of the repeating unit cell in the ITPS panel. Hence a single unit cell was used for the optimization process to reduce the computational cost. Deterministic and probabilistic optimization of the ITPS panel required evaluation of failure constraints at various design points. This further demands computationally expensive finite element analyses which was replaced by efficient, low fidelity surrogate models. In an optimization process, it is important to represent the constraints accurately to find the optimum design. Instead of building global surrogate models using large number of designs, the computational resources were directed towards target regions near constraint boundaries for accurate representation of constraints using adaptive sampling strategies. Efficient Global Reliability Analyses (EGRA) facilitates sequentially sampling of design points around the region of interest in the design space. EGRA was applied to the response surface construction of the failure constraints in the deterministic and reliability based optimization of the ITPS panel. It was shown that using adaptive sampling, the number of designs required to find the optimum were reduced drastically, while improving the accuracy. System reliability of ITPS was estimated using Monte Carlo Simulation (MCS) based method. Separable Monte Carlo method was employed that allowed separable sampling of the random variables to predict the probability of failure accurately. The reliability analysis considered uncertainties in the geometry, material properties, loading conditions of the panel and error in finite element modeling. These uncertainties further increased the computational cost of MCS techniques which was also reduced by employing surrogate models. In order to estimate the error in the probability of failure estimate, bootstrapping method was applied. This research work thus demonstrates optimization of the ITPS composite panel with multiple failure modes and large number of uncertainties using adaptive sampling techniques.

Statistical Evaluation of Time Series Analysis Techniques

NASA Technical Reports Server (NTRS)

Benignus, V. A.

1973-01-01

The performance of a modified version of NASA's multivariate spectrum analysis program is discussed. A multiple regression model was used to make the revisions. Performance improvements were documented and compared to the standard fast Fourier transform by Monte Carlo techniques.

Bayesian Probability Theory

NASA Astrophysics Data System (ADS)

von der Linden, Wolfgang; Dose, Volker; von Toussaint, Udo

2014-06-01

Preface; Part I. Introduction: 1. The meaning of probability; 2. Basic definitions; 3. Bayesian inference; 4. Combinatrics; 5. Random walks; 6. Limit theorems; 7. Continuous distributions; 8. The central limit theorem; 9. Poisson processes and waiting times; Part II. Assigning Probabilities: 10. Transformation invariance; 11. Maximum entropy; 12. Qualified maximum entropy; 13. Global smoothness; Part III. Parameter Estimation: 14. Bayesian parameter estimation; 15. Frequentist parameter estimation; 16. The Cramer-Rao inequality; Part IV. Testing Hypotheses: 17. The Bayesian way; 18. The frequentist way; 19. Sampling distributions; 20. Bayesian vs frequentist hypothesis tests; Part V. Real World Applications: 21. Regression; 22. Inconsistent data; 23. Unrecognized signal contributions; 24. Change point problems; 25. Function estimation; 26. Integral equations; 27. Model selection; 28. Bayesian experimental design; Part VI. Probabilistic Numerical Techniques: 29. Numerical integration; 30. Monte Carlo methods; 31. Nested sampling; Appendixes; References; Index.

High-Fidelity Coupled Monte-Carlo/Thermal-Hydraulics Calculations

NASA Astrophysics Data System (ADS)

Ivanov, Aleksandar; Sanchez, Victor; Ivanov, Kostadin

2014-06-01

Monte Carlo methods have been used as reference reactor physics calculation tools worldwide. The advance in computer technology allows the calculation of detailed flux distributions in both space and energy. In most of the cases however, those calculations are done under the assumption of homogeneous material density and temperature distributions. The aim of this work is to develop a consistent methodology for providing realistic three-dimensional thermal-hydraulic distributions by coupling the in-house developed sub-channel code SUBCHANFLOW with the standard Monte-Carlo transport code MCNP. In addition to the innovative technique of on-the fly material definition, a flux-based weight-window technique has been introduced to improve both the magnitude and the distribution of the relative errors. Finally, a coupled code system for the simulation of steady-state reactor physics problems has been developed. Besides the problem of effective feedback data interchange between the codes, the treatment of temperature dependence of the continuous energy nuclear data has been investigated.

A comprehensive evaluation of various sensitivity analysis methods: A case study with a hydrological model

DOE PAGES

Gan, Yanjun; Duan, Qingyun; Gong, Wei; ...

2014-01-01

Sensitivity analysis (SA) is a commonly used approach for identifying important parameters that dominate model behaviors. We use a newly developed software package, a Problem Solving environment for Uncertainty Analysis and Design Exploration (PSUADE), to evaluate the effectiveness and efficiency of ten widely used SA methods, including seven qualitative and three quantitative ones. All SA methods are tested using a variety of sampling techniques to screen out the most sensitive (i.e., important) parameters from the insensitive ones. The Sacramento Soil Moisture Accounting (SAC-SMA) model, which has thirteen tunable parameters, is used for illustration. The South Branch Potomac River basin nearmore » Springfield, West Virginia in the U.S. is chosen as the study area. The key findings from this study are: (1) For qualitative SA methods, Correlation Analysis (CA), Regression Analysis (RA), and Gaussian Process (GP) screening methods are shown to be not effective in this example. Morris One-At-a-Time (MOAT) screening is the most efficient, needing only 280 samples to identify the most important parameters, but it is the least robust method. Multivariate Adaptive Regression Splines (MARS), Delta Test (DT) and Sum-Of-Trees (SOT) screening methods need about 400–600 samples for the same purpose. Monte Carlo (MC), Orthogonal Array (OA) and Orthogonal Array based Latin Hypercube (OALH) are appropriate sampling techniques for them; (2) For quantitative SA methods, at least 2777 samples are needed for Fourier Amplitude Sensitivity Test (FAST) to identity parameter main effect. McKay method needs about 360 samples to evaluate the main effect, more than 1000 samples to assess the two-way interaction effect. OALH and LPτ (LPTAU) sampling techniques are more appropriate for McKay method. For the Sobol' method, the minimum samples needed are 1050 to compute the first-order and total sensitivity indices correctly. These comparisons show that qualitative SA methods are more efficient but less accurate and robust than quantitative ones.« less

Honest Importance Sampling with Multiple Markov Chains

PubMed Central

Tan, Aixin; Doss, Hani; Hobert, James P.

2017-01-01

Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π1, is used to estimate an expectation with respect to another, π. The importance sampling estimator is strongly consistent and, as long as two simple moment conditions are satisfied, it obeys a central limit theorem (CLT). Moreover, there is a simple consistent estimator for the asymptotic variance in the CLT, which makes for routine computation of standard errors. Importance sampling can also be used in the Markov chain Monte Carlo (MCMC) context. Indeed, if the random sample from π1 is replaced by a Harris ergodic Markov chain with invariant density π1, then the resulting estimator remains strongly consistent. There is a price to be paid however, as the computation of standard errors becomes more complicated. First, the two simple moment conditions that guarantee a CLT in the iid case are not enough in the MCMC context. Second, even when a CLT does hold, the asymptotic variance has a complex form and is difficult to estimate consistently. In this paper, we explain how to use regenerative simulation to overcome these problems. Actually, we consider a more general set up, where we assume that Markov chain samples from several probability densities, π1, …, πk, are available. We construct multiple-chain importance sampling estimators for which we obtain a CLT based on regeneration. We show that if the Markov chains converge to their respective target distributions at a geometric rate, then under moment conditions similar to those required in the iid case, the MCMC-based importance sampling estimator obeys a CLT. Furthermore, because the CLT is based on a regenerative process, there is a simple consistent estimator of the asymptotic variance. We illustrate the method with two applications in Bayesian sensitivity analysis. The first concerns one-way random effects models under different priors. The second involves Bayesian variable selection in linear regression, and for this application, importance sampling based on multiple chains enables an empirical Bayes approach to variable selection. PMID:28701855

Honest Importance Sampling with Multiple Markov Chains.

PubMed

Tan, Aixin; Doss, Hani; Hobert, James P

2015-01-01

Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π 1 , is used to estimate an expectation with respect to another, π . The importance sampling estimator is strongly consistent and, as long as two simple moment conditions are satisfied, it obeys a central limit theorem (CLT). Moreover, there is a simple consistent estimator for the asymptotic variance in the CLT, which makes for routine computation of standard errors. Importance sampling can also be used in the Markov chain Monte Carlo (MCMC) context. Indeed, if the random sample from π 1 is replaced by a Harris ergodic Markov chain with invariant density π 1 , then the resulting estimator remains strongly consistent. There is a price to be paid however, as the computation of standard errors becomes more complicated. First, the two simple moment conditions that guarantee a CLT in the iid case are not enough in the MCMC context. Second, even when a CLT does hold, the asymptotic variance has a complex form and is difficult to estimate consistently. In this paper, we explain how to use regenerative simulation to overcome these problems. Actually, we consider a more general set up, where we assume that Markov chain samples from several probability densities, π 1 , …, π k , are available. We construct multiple-chain importance sampling estimators for which we obtain a CLT based on regeneration. We show that if the Markov chains converge to their respective target distributions at a geometric rate, then under moment conditions similar to those required in the iid case, the MCMC-based importance sampling estimator obeys a CLT. Furthermore, because the CLT is based on a regenerative process, there is a simple consistent estimator of the asymptotic variance. We illustrate the method with two applications in Bayesian sensitivity analysis. The first concerns one-way random effects models under different priors. The second involves Bayesian variable selection in linear regression, and for this application, importance sampling based on multiple chains enables an empirical Bayes approach to variable selection.

Monte Carlo and Molecular Dynamics in the Multicanonical Ensemble: Connections between Wang-Landau Sampling and Metadynamics

NASA Astrophysics Data System (ADS)

Vogel, Thomas; Perez, Danny; Junghans, Christoph

2014-03-01

We show direct formal relationships between the Wang-Landau iteration [PRL 86, 2050 (2001)], metadynamics [PNAS 99, 12562 (2002)] and statistical temperature molecular dynamics [PRL 97, 050601 (2006)], the major Monte Carlo and molecular dynamics work horses for sampling from a generalized, multicanonical ensemble. We aim at helping to consolidate the developments in the different areas by indicating how methodological advancements can be transferred in a straightforward way, avoiding the parallel, largely independent, developments tracks observed in the past.

Validation of a Monte Carlo Simulation of Binary Time Series.

DTIC Science & Technology

1981-09-18

the probability distribution corresponding to the population from which the n sample vectors are generated. Simple unbiased estimators were chosen for...Cowcept A s*us Agew Bethesd, Marylnd H. L. Wauom Am D. RoQuE SymMS Reserch Brach , p" Ssms Delsbian September 18, 1981 DTIC EL E C T E SEP 24 =I98ST...is generated from the sample of such vectors produced by several independent replications of the Monte Carlo simulation. Then the validity of the

Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain

NASA Astrophysics Data System (ADS)

Beck, Joakim; Dia, Ben Mansour; Espath, Luis F. R.; Long, Quan; Tempone, Raúl

2018-06-01

In calculating expected information gain in optimal Bayesian experimental design, the computation of the inner loop in the classical double-loop Monte Carlo requires a large number of samples and suffers from underflow if the number of samples is small. These drawbacks can be avoided by using an importance sampling approach. We present a computationally efficient method for optimal Bayesian experimental design that introduces importance sampling based on the Laplace method to the inner loop. We derive the optimal values for the method parameters in which the average computational cost is minimized according to the desired error tolerance. We use three numerical examples to demonstrate the computational efficiency of our method compared with the classical double-loop Monte Carlo, and a more recent single-loop Monte Carlo method that uses the Laplace method as an approximation of the return value of the inner loop. The first example is a scalar problem that is linear in the uncertain parameter. The second example is a nonlinear scalar problem. The third example deals with the optimal sensor placement for an electrical impedance tomography experiment to recover the fiber orientation in laminate composites.

A partially reflecting random walk on spheres algorithm for electrical impedance tomography

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

Maire, Sylvain, E-mail: maire@univ-tln.fr; Simon, Martin, E-mail: simon@math.uni-mainz.de

2015-12-15

In this work, we develop a probabilistic estimator for the voltage-to-current map arising in electrical impedance tomography. This novel so-called partially reflecting random walk on spheres estimator enables Monte Carlo methods to compute the voltage-to-current map in an embarrassingly parallel manner, which is an important issue with regard to the corresponding inverse problem. Our method uses the well-known random walk on spheres algorithm inside subdomains where the diffusion coefficient is constant and employs replacement techniques motivated by finite difference discretization to deal with both mixed boundary conditions and interface transmission conditions. We analyze the global bias and the variance ofmore » the new estimator both theoretically and experimentally. Subsequently, the variance of the new estimator is considerably reduced via a novel control variate conditional sampling technique which yields a highly efficient hybrid forward solver coupling probabilistic and deterministic algorithms.« less

Secondary signal imaging (SSI) electron tomography (SSI-ET): A new three-dimensional metrology for mesoscale specimens in transmission electron microscope.

PubMed

Han, Chang Wan; Ortalan, Volkan

2015-09-01

We have demonstrated a new electron tomography technique utilizing the secondary signals (secondary electrons and backscattered electrons) for ultra thick (a few μm) specimens. The Monte Carlo electron scattering simulations reveal that the amount of backscattered electrons generated by 200 and 300keV incident electrons is a monotonic function of the sample thickness and this causes the thickness contrast satisfying the projection requirement for the tomographic reconstruction. Additional contribution of the secondary electrons emitted from the edges of the specimens enhances the visibility of the surface features. The acquired SSI tilt series of the specimen having mesoscopic dimensions are successfully reconstructed verifying that this new technique, so called the secondary signal imaging electron tomography (SSI-ET), can directly be utilized for 3D structural analysis of mesoscale structures. Published by Elsevier Ltd.

Applying Monte-Carlo simulations to optimize an inelastic neutron scattering system for soil carbon analysis

USDA-ARS?s Scientific Manuscript database

Computer Monte-Carlo (MC) simulations (Geant4) of neutron propagation and acquisition of gamma response from soil samples was applied to evaluate INS system performance characteristic [sensitivity, minimal detectable level (MDL)] for soil carbon measurement. The INS system model with best performanc...

SIMCA T 1.0: A SAS Computer Program for Simulating Computer Adaptive Testing

ERIC Educational Resources Information Center

Raiche, Gilles; Blais, Jean-Guy

2006-01-01

Monte Carlo methodologies are frequently applied to study the sampling distribution of the estimated proficiency level in adaptive testing. These methods eliminate real situational constraints. However, these Monte Carlo methodologies are not currently supported by the available software programs, and when these programs are available, their…

A Christoffel function weighted least squares algorithm for collocation approximations

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

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

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

A Christoffel function weighted least squares algorithm for collocation approximations

DOE PAGES

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

2016-11-28

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

Verification of unfold error estimates in the unfold operator code

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

Fehl, D.L.; Biggs, F.

Spectral unfolding is an inverse mathematical operation that attempts to obtain spectral source information from a set of response functions and data measurements. Several unfold algorithms have appeared over the past 30 years; among them is the unfold operator (UFO) code written at Sandia National Laboratories. In addition to an unfolded spectrum, the UFO code also estimates the unfold uncertainty (error) induced by estimated random uncertainties in the data. In UFO the unfold uncertainty is obtained from the error matrix. This built-in estimate has now been compared to error estimates obtained by running the code in a Monte Carlo fashionmore » with prescribed data distributions (Gaussian deviates). In the test problem studied, data were simulated from an arbitrarily chosen blackbody spectrum (10 keV) and a set of overlapping response functions. The data were assumed to have an imprecision of 5{percent} (standard deviation). One hundred random data sets were generated. The built-in estimate of unfold uncertainty agreed with the Monte Carlo estimate to within the statistical resolution of this relatively small sample size (95{percent} confidence level). A possible 10{percent} bias between the two methods was unresolved. The Monte Carlo technique is also useful in underdetermined problems, for which the error matrix method does not apply. UFO has been applied to the diagnosis of low energy x rays emitted by Z-pinch and ion-beam driven hohlraums. {copyright} {ital 1997 American Institute of Physics.}« less

Efficient sampling of parsimonious inversion histories with application to genome rearrangement in Yersinia.

PubMed

Miklós, István; Darling, Aaron E

2009-06-22

Inversions are among the most common mutations acting on the order and orientation of genes in a genome, and polynomial-time algorithms exist to obtain a minimal length series of inversions that transform one genome arrangement to another. However, the minimum length series of inversions (the optimal sorting path) is often not unique as many such optimal sorting paths exist. If we assume that all optimal sorting paths are equally likely, then statistical inference on genome arrangement history must account for all such sorting paths and not just a single estimate. No deterministic polynomial algorithm is known to count the number of optimal sorting paths nor sample from the uniform distribution of optimal sorting paths. Here, we propose a stochastic method that uniformly samples the set of all optimal sorting paths. Our method uses a novel formulation of parallel Markov chain Monte Carlo. In practice, our method can quickly estimate the total number of optimal sorting paths. We introduce a variant of our approach in which short inversions are modeled to be more likely, and we show how the method can be used to estimate the distribution of inversion lengths and breakpoint usage in pathogenic Yersinia pestis. The proposed method has been implemented in a program called "MC4Inversion." We draw comparison of MC4Inversion to the sampler implemented in BADGER and a previously described importance sampling (IS) technique. We find that on high-divergence data sets, MC4Inversion finds more optimal sorting paths per second than BADGER and the IS technique and simultaneously avoids bias inherent in the IS technique.

Methods and Tools for Evaluating Uncertainty in Ecological Models: A Survey

EPA Science Inventory

Poster presented at the Ecological Society of America Meeting. Ecologists are familiar with a variety of uncertainty techniques, particularly in the intersection of maximum likelihood parameter estimation and Monte Carlo analysis techniques, as well as a recent increase in Baye...

Markov chain Monte Carlo techniques and spatial-temporal modelling for medical EIT.

PubMed

West, Robert M; Aykroyd, Robert G; Meng, Sha; Williams, Richard A

2004-02-01

Many imaging problems such as imaging with electrical impedance tomography (EIT) can be shown to be inverse problems: that is either there is no unique solution or the solution does not depend continuously on the data. As a consequence solution of inverse problems based on measured data alone is unstable, particularly if the mapping between the solution distribution and the measurements is also nonlinear as in EIT. To deliver a practical stable solution, it is necessary to make considerable use of prior information or regularization techniques. The role of a Bayesian approach is therefore of fundamental importance, especially when coupled with Markov chain Monte Carlo (MCMC) sampling to provide information about solution behaviour. Spatial smoothing is a commonly used approach to regularization. In the human thorax EIT example considered here nonlinearity increases the difficulty of imaging, using only boundary data, leading to reconstructions which are often rather too smooth. In particular, in medical imaging the resistivity distribution usually contains substantial jumps at the boundaries of different anatomical regions. With spatial smoothing these boundaries can be masked by blurring. This paper focuses on the medical application of EIT to monitor lung and cardiac function and uses explicit geometric information regarding anatomical structure and incorporates temporal correlation. Some simple properties are assumed known, or at least reliably estimated from separate studies, whereas others are estimated from the voltage measurements. This structural formulation will also allow direct estimation of clinically important quantities, such as ejection fraction and residual capacity, along with assessment of precision.

Probabilistic treatment of the uncertainty from the finite size of weighted Monte Carlo data

NASA Astrophysics Data System (ADS)

Glüsenkamp, Thorsten

2018-06-01

Parameter estimation in HEP experiments often involves Monte Carlo simulation to model the experimental response function. A typical application are forward-folding likelihood analyses with re-weighting, or time-consuming minimization schemes with a new simulation set for each parameter value. Problematically, the finite size of such Monte Carlo samples carries intrinsic uncertainty that can lead to a substantial bias in parameter estimation if it is neglected and the sample size is small. We introduce a probabilistic treatment of this problem by replacing the usual likelihood functions with novel generalized probability distributions that incorporate the finite statistics via suitable marginalization. These new PDFs are analytic, and can be used to replace the Poisson, multinomial, and sample-based unbinned likelihoods, which covers many use cases in high-energy physics. In the limit of infinite statistics, they reduce to the respective standard probability distributions. In the general case of arbitrary Monte Carlo weights, the expressions involve the fourth Lauricella function FD, for which we find a new finite-sum representation in a certain parameter setting. The result also represents an exact form for Carlson's Dirichlet average Rn with n > 0, and thereby an efficient way to calculate the probability generating function of the Dirichlet-multinomial distribution, the extended divided difference of a monomial, or arbitrary moments of univariate B-splines. We demonstrate the bias reduction of our approach with a typical toy Monte Carlo problem, estimating the normalization of a peak in a falling energy spectrum, and compare the results with previously published methods from the literature.

Molecular Modeling of Nucleic Acid Structure: Electrostatics and Solvation

PubMed Central

Bergonzo, Christina; Galindo-Murillo, Rodrigo; Cheatham, Thomas E.

2014-01-01

This unit presents an overview of computer simulation techniques as applied to nucleic acid systems, ranging from simple in vacuo molecular modeling techniques to more complete all-atom molecular dynamics treatments that include an explicit representation of the environment. The third in a series of four units, this unit focuses on critical issues in solvation and the treatment of electrostatics. UNITS 7.5 & 7.8 introduced the modeling of nucleic acid structure at the molecular level. This included a discussion of how to generate an initial model, how to evaluate the utility or reliability of a given model, and ultimately how to manipulate this model to better understand the structure, dynamics, and interactions. Subject to an appropriate representation of the energy, such as a specifically parameterized empirical force field, the techniques of minimization and Monte Carlo simulation, as well as molecular dynamics (MD) methods, were introduced as means to sample conformational space for a better understanding of the relevance of a given model. From this discussion, the major limitations with modeling, in general, were highlighted. These are the difficult issues in sampling conformational space effectively—the multiple minima or conformational sampling problems—and accurately representing the underlying energy of interaction. In order to provide a realistic model of the underlying energetics for nucleic acids in their native environments, it is crucial to include some representation of solvation (by water) and also to properly treat the electrostatic interactions. These are discussed in detail in this unit. PMID:18428877

Molecular modeling of nucleic Acid structure: electrostatics and solvation.

PubMed

Bergonzo, Christina; Galindo-Murillo, Rodrigo; Cheatham, Thomas E

2014-12-19

This unit presents an overview of computer simulation techniques as applied to nucleic acid systems, ranging from simple in vacuo molecular modeling techniques to more complete all-atom molecular dynamics treatments that include an explicit representation of the environment. The third in a series of four units, this unit focuses on critical issues in solvation and the treatment of electrostatics. UNITS 7.5 & 7.8 introduced the modeling of nucleic acid structure at the molecular level. This included a discussion of how to generate an initial model, how to evaluate the utility or reliability of a given model, and ultimately how to manipulate this model to better understand its structure, dynamics, and interactions. Subject to an appropriate representation of the energy, such as a specifically parameterized empirical force field, the techniques of minimization and Monte Carlo simulation, as well as molecular dynamics (MD) methods, were introduced as a way of sampling conformational space for a better understanding of the relevance of a given model. This discussion highlighted the major limitations with modeling in general. When sampling conformational space effectively, difficult issues are encountered, such as multiple minima or conformational sampling problems, and accurately representing the underlying energy of interaction. In order to provide a realistic model of the underlying energetics for nucleic acids in their native environments, it is crucial to include some representation of solvation (by water) and also to properly treat the electrostatic interactions. These subjects are discussed in detail in this unit. Copyright © 2014 John Wiley & Sons, Inc.

Robustness of survival estimates for radio-marked animals

USGS Publications Warehouse

Bunck, C.M.; Chen, C.-L.

1992-01-01

Telemetry techniques are often used to study the survival of birds and mammals; particularly whcn mark-recapture approaches are unsuitable. Both parametric and nonparametric methods to estimate survival have becn developed or modified from other applications. An implicit assumption in these approaches is that the probability of re-locating an animal with a functioning transmitter is one. A Monte Carlo study was conducted to determine the bias and variance of the Kaplan-Meier estimator and an estimator based also on the assumption of constant hazard and to eva!uate the performance of the two-sample tests associated with each. Modifications of each estimator which allow a re-Iocation probability of less than one are described and evaluated. Generallv the unmodified estimators were biased but had lower variance. At low sample sizes all estimators performed poorly. Under the null hypothesis, the distribution of all test statistics reasonably approximated the null distribution when survival was low but not when it was high. The power of the two-sample tests were similar.

Monte Carlo uncertainty analyses of a bLS inverse-dispersion technique for measuring gas emissions from livestock operations

USDA-ARS?s Scientific Manuscript database

The backward Lagrangian stochastic (bLS) inverse-dispersion technique has been used to measure fugitive gas emissions from livestock operations. The accuracy of the bLS technique, as indicated by the percentages of gas recovery in various tracer-release experiments, has generally been within ± 10% o...

Deep learning beyond Lefschetz thimbles

NASA Astrophysics Data System (ADS)

Alexandru, Andrei; Bedaque, Paulo F.; Lamm, Henry; Lawrence, Scott

2017-11-01

The generalized thimble method to treat field theories with sign problems requires repeatedly solving the computationally expensive holomorphic flow equations. We present a machine learning technique to bypass this problem. The central idea is to obtain a few field configurations via the flow equations to train a feed-forward neural network. The trained network defines a new manifold of integration which reduces the sign problem and can be rapidly sampled. We present results for the 1 +1 dimensional Thirring model with Wilson fermions on sizable lattices. In addition to the gain in speed, the parametrization of the integration manifold we use avoids the "trapping" of Monte Carlo chains which plagues large-flow calculations, a considerable shortcoming of the previous attempts.

Eyeglasses Lens Contour Extraction from Facial Images Using an Efficient Shape Description

PubMed Central

Borza, Diana; Darabant, Adrian Sergiu; Danescu, Radu

2013-01-01

This paper presents a system that automatically extracts the position of the eyeglasses and the accurate shape and size of the frame lenses in facial images. The novelty brought by this paper consists in three key contributions. The first one is an original model for representing the shape of the eyeglasses lens, using Fourier descriptors. The second one is a method for generating the search space starting from a finite, relatively small number of representative lens shapes based on Fourier morphing. Finally, we propose an accurate lens contour extraction algorithm using a multi-stage Monte Carlo sampling technique. Multiple experiments demonstrate the effectiveness of our approach. PMID:24152926

A Monte Carlo Evaluation of Estimated Parameters of Five Shrinkage Estimate Formuli.

ERIC Educational Resources Information Center

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)

Extensions of the MCNP5 and TRIPOLI4 Monte Carlo Codes for Transient Reactor Analysis

NASA Astrophysics Data System (ADS)

Hoogenboom, J. Eduard; Sjenitzer, Bart L.

2014-06-01

To simulate reactor transients for safety analysis with the Monte Carlo method the generation and decay of delayed neutron precursors is implemented in the MCNP5 and TRIPOLI4 general purpose Monte Carlo codes. Important new variance reduction techniques like forced decay of precursors in each time interval and the branchless collision method are included to obtain reasonable statistics for the power production per time interval. For simulation of practical reactor transients also the feedback effect from the thermal-hydraulics must be included. This requires coupling of the Monte Carlo code with a thermal-hydraulics (TH) code, providing the temperature distribution in the reactor, which affects the neutron transport via the cross section data. The TH code also provides the coolant density distribution in the reactor, directly influencing the neutron transport. Different techniques for this coupling are discussed. As a demonstration a 3x3 mini fuel assembly with a moving control rod is considered for MCNP5 and a mini core existing of 3x3 PWR fuel assemblies with control rods and burnable poisons for TRIPOLI4. Results are shown for reactor transients due to control rod movement or withdrawal. The TRIPOLI4 transient calculation is started at low power and includes thermal-hydraulic feedback. The power rises about 10 decades and finally stabilises the reactor power at a much higher level than initial. The examples demonstrate that the modified Monte Carlo codes are capable of performing correct transient calculations, taking into account all geometrical and cross section detail.

Backscatter factors and mass energy-absorption coefficient ratios for diagnostic radiology dosimetry

NASA Astrophysics Data System (ADS)

Benmakhlouf, Hamza; Bouchard, Hugo; Fransson, Annette; Andreo, Pedro

2011-11-01

Backscatter factors, B, and mass energy-absorption coefficient ratios, (μen/ρ)w, air, for the determination of the surface dose in diagnostic radiology were calculated using Monte Carlo simulations. The main purpose was to extend the range of available data to qualities used in modern x-ray techniques, particularly for interventional radiology. A comprehensive database for mono-energetic photons between 4 and 150 keV and different field sizes was created for a 15 cm thick water phantom. Backscattered spectra were calculated with the PENELOPE Monte Carlo system, scoring track-length fluence differential in energy with negligible statistical uncertainty; using the Monte Carlo computed spectra, B factors and (μen/ρ)w, air were then calculated numerically for each energy. Weighted averaging procedures were subsequently used to convolve incident clinical spectra with mono-energetic data. The method was benchmarked against full Monte Carlo calculations of incident clinical spectra obtaining differences within 0.3-0.6%. The technique used enables the calculation of B and (μen/ρ)w, air for any incident spectrum without further time-consuming Monte Carlo simulations. The adequacy of the extended dosimetry data to a broader range of clinical qualities than those currently available, while keeping consistency with existing data, was confirmed through detailed comparisons. Mono-energetic and spectra-averaged values were compared with published data, including those in ICRU Report 74 and IAEA TRS-457, finding average differences of 0.6%. Results are provided in comprehensive tables appropriated for clinical use. Additional qualities can easily be calculated using a designed GUI interface in conjunction with software to generate incident photon spectra.

A New Monte Carlo Method for Estimating Marginal Likelihoods.

PubMed

Wang, Yu-Bo; Chen, Ming-Hui; Kuo, Lynn; Lewis, Paul O

2018-06-01

Evaluating the marginal likelihood in Bayesian analysis is essential for model selection. Estimators based on a single Markov chain Monte Carlo sample from the posterior distribution include the harmonic mean estimator and the inflated density ratio estimator. We propose a new class of Monte Carlo estimators based on this single Markov chain Monte Carlo sample. This class can be thought of as a generalization of the harmonic mean and inflated density ratio estimators using a partition weighted kernel (likelihood times prior). We show that our estimator is consistent and has better theoretical properties than the harmonic mean and inflated density ratio estimators. In addition, we provide guidelines on choosing optimal weights. Simulation studies were conducted to examine the empirical performance of the proposed estimator. We further demonstrate the desirable features of the proposed estimator with two real data sets: one is from a prostate cancer study using an ordinal probit regression model with latent variables; the other is for the power prior construction from two Eastern Cooperative Oncology Group phase III clinical trials using the cure rate survival model with similar objectives.

Monte Carlo Simulation of Effective Coordination Mechanisms for e-Commerce

NASA Astrophysics Data System (ADS)

Sakas, D. P.; Vlachos, D. S.; Simos, T. E.

2008-11-01

Making decisions in a dynamic environment is considered extremely important in today's market. Decision trees which can be used to model these systems, are not easily constructed and solved, especially in the case of infinite sets of consequences (for example, consider the case where only the mean and the variance of an outcome is known). In this work, discrete approximation and Monte Carlo techniques are used to overcome the aforementioned difficulties.

A Monte Carlo-based radiation safety assessment for astronauts in an environment with confined magnetic field shielding.

PubMed

Geng, Changran; Tang, Xiaobin; Gong, Chunhui; Guan, Fada; Johns, Jesse; Shu, Diyun; Chen, Da

2015-12-01

The active shielding technique has great potential for radiation protection in space exploration because it has the advantage of a significant mass saving compared with the passive shielding technique. This paper demonstrates a Monte Carlo-based approach to evaluating the shielding effectiveness of the active shielding technique using confined magnetic fields (CMFs). The International Commission on Radiological Protection reference anthropomorphic phantom, as well as the toroidal CMF, was modeled using the Monte Carlo toolkit Geant4. The penetrating primary particle fluence, organ-specific dose equivalent, and male effective dose were calculated for particles in galactic cosmic radiation (GCR) and solar particle events (SPEs). Results show that the SPE protons can be easily shielded against, even almost completely deflected, by the toroidal magnetic field. GCR particles can also be more effectively shielded against by increasing the magnetic field strength. Our results also show that the introduction of a structural Al wall in the CMF did not provide additional shielding for GCR; in fact it can weaken the total shielding effect of the CMF. This study demonstrated the feasibility of accurately determining the radiation field inside the environment and evaluating the organ dose equivalents for astronauts under active shielding using the CMF.

Self-consistent modelling of line-driven hot-star winds with Monte Carlo radiation hydrodynamics

NASA Astrophysics Data System (ADS)

Noebauer, U. M.; Sim, S. A.

2015-11-01

Radiative pressure exerted by line interactions is a prominent driver of outflows in astrophysical systems, being at work in the outflows emerging from hot stars or from the accretion discs of cataclysmic variables, massive young stars and active galactic nuclei. In this work, a new radiation hydrodynamical approach to model line-driven hot-star winds is presented. By coupling a Monte Carlo radiative transfer scheme with a finite volume fluid dynamical method, line-driven mass outflows may be modelled self-consistently, benefiting from the advantages of Monte Carlo techniques in treating multiline effects, such as multiple scatterings, and in dealing with arbitrary multidimensional configurations. In this work, we introduce our approach in detail by highlighting the key numerical techniques and verifying their operation in a number of simplified applications, specifically in a series of self-consistent, one-dimensional, Sobolev-type, hot-star wind calculations. The utility and accuracy of our approach are demonstrated by comparing the obtained results with the predictions of various formulations of the so-called CAK theory and by confronting the calculations with modern sophisticated techniques of predicting the wind structure. Using these calculations, we also point out some useful diagnostic capabilities our approach provides. Finally, we discuss some of the current limitations of our method, some possible extensions and potential future applications.

The Forecast Interpretation Tool—a Monte Carlo technique for blending climatic distributions with probabilistic forecasts

USGS Publications Warehouse

Husak, Gregory J.; Michaelsen, Joel; Kyriakidis, P.; Verdin, James P.; Funk, Chris; Galu, Gideon

2011-01-01

Probabilistic forecasts are produced from a variety of outlets to help predict rainfall, and other meteorological events, for periods of 1 month or more. Such forecasts are expressed as probabilities of a rainfall event, e.g. being in the upper, middle, or lower third of the relevant distribution of rainfall in the region. The impact of these forecasts on the expectation for the event is not always clear or easily conveyed. This article proposes a technique based on Monte Carlo simulation for adjusting existing climatologic statistical parameters to match forecast information, resulting in new parameters defining the probability of events for the forecast interval. The resulting parameters are shown to approximate the forecasts with reasonable accuracy. To show the value of the technique as an application for seasonal rainfall, it is used with consensus forecast developed for the Greater Horn of Africa for the 2009 March-April-May season. An alternative, analytical approach is also proposed, and discussed in comparison to the first simulation-based technique.

Dynamic Event Tree advancements and control logic improvements

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

Alfonsi, Andrea; Rabiti, Cristian; Mandelli, Diego

The RAVEN code has been under development at the Idaho National Laboratory since 2012. Its main goal is to create a multi-purpose platform for the deploying of all the capabilities needed for Probabilistic Risk Assessment, uncertainty quantification, data mining analysis and optimization studies. RAVEN is currently equipped with three different sampling categories: Forward samplers (Monte Carlo, Latin Hyper Cube, Stratified, Grid Sampler, Factorials, etc.), Adaptive Samplers (Limit Surface search, Adaptive Polynomial Chaos, etc.) and Dynamic Event Tree (DET) samplers (Deterministic and Adaptive Dynamic Event Trees). The main subject of this document is to report the activities that have been donemore » in order to: start the migration of the RAVEN/RELAP-7 control logic system into MOOSE, and develop advanced dynamic sampling capabilities based on the Dynamic Event Tree approach. In order to provide to all MOOSE-based applications a control logic capability, in this Fiscal Year an initial migration activity has been initiated, moving the control logic system, designed for RELAP-7 by the RAVEN team, into the MOOSE framework. In this document, a brief explanation of what has been done is going to be reported. The second and most important subject of this report is about the development of a Dynamic Event Tree (DET) sampler named “Hybrid Dynamic Event Tree” (HDET) and its Adaptive variant “Adaptive Hybrid Dynamic Event Tree” (AHDET). As other authors have already reported, among the different types of uncertainties, it is possible to discern two principle types: aleatory and epistemic uncertainties. The classical Dynamic Event Tree is in charge of treating the first class (aleatory) uncertainties; the dependence of the probabilistic risk assessment and analysis on the epistemic uncertainties are treated by an initial Monte Carlo sampling (MCDET). From each Monte Carlo sample, a DET analysis is run (in total, N trees). The Monte Carlo employs a pre-sampling of the input space characterized by epistemic uncertainties. The consequent Dynamic Event Tree performs the exploration of the aleatory space. In the RAVEN code, a more general approach has been developed, not limiting the exploration of the epistemic space through a Monte Carlo method but using all the forward sampling strategies RAVEN currently employs. The user can combine a Latin Hyper Cube, Grid, Stratified and Monte Carlo sampling in order to explore the epistemic space, without any limitation. From this pre-sampling, the Dynamic Event Tree sampler starts its aleatory space exploration. As reported by the authors, the Dynamic Event Tree is a good fit to develop a goal-oriented sampling strategy. The DET is used to drive a Limit Surface search. The methodology that has been developed by the authors last year, performs a Limit Surface search in the aleatory space only. This report documents how this approach has been extended in order to consider the epistemic space interacting with the Hybrid Dynamic Event Tree methodology.« less

Nonparametric Bayesian Segmentation of a Multivariate Inhomogeneous Space-Time Poisson Process.

PubMed

Ding, Mingtao; He, Lihan; Dunson, David; Carin, Lawrence

2012-12-01

A nonparametric Bayesian model is proposed for segmenting time-evolving multivariate spatial point process data. An inhomogeneous Poisson process is assumed, with a logistic stick-breaking process (LSBP) used to encourage piecewise-constant spatial Poisson intensities. The LSBP explicitly favors spatially contiguous segments, and infers the number of segments based on the observed data. The temporal dynamics of the segmentation and of the Poisson intensities are modeled with exponential correlation in time, implemented in the form of a first-order autoregressive model for uniformly sampled discrete data, and via a Gaussian process with an exponential kernel for general temporal sampling. We consider and compare two different inference techniques: a Markov chain Monte Carlo sampler, which has relatively high computational complexity; and an approximate and efficient variational Bayesian analysis. The model is demonstrated with a simulated example and a real example of space-time crime events in Cincinnati, Ohio, USA.

Simulation of 'hitch-hiking' genealogies.

PubMed

Slade, P F

2001-01-01

An ancestral influence graph is derived, an analogue of the coalescent and a composite of Griffiths' (1991) two-locus ancestral graph and Krone and Neuhauser's (1997) ancestral selection graph. This generalizes their use of branching-coalescing random graphs so as to incorporate both selection and recombination into gene genealogies. Qualitative understanding of a 'hitch-hiking' effect on genealogies is pursued via diagrammatic representation of the genealogical process in a two-locus, two-allele haploid model. Extending the simulation technique of Griffiths and Tavare (1996), computational estimation of expected times to the most recent common ancestor of samples of n genes under recombination and selection in two-locus, two-allele haploid and diploid models are presented. Such times are conditional on sample configuration. Monte Carlo simulations show that 'hitch-hiking' is a subtle effect that alters the conditional expected depth of the genealogy at the linked neutral locus depending on a mutation-selection-recombination balance.

Real-time absorption and scattering characterization of slab-shaped turbid samples obtained by a combination of angular and spatially resolved measurements.

PubMed

Dam, Jan S; Yavari, Nazila; Sørensen, Søren; Andersson-Engels, Stefan

2005-07-10

We present a fast and accurate method for real-time determination of the absorption coefficient, the scattering coefficient, and the anisotropy factor of thin turbid samples by using simple continuous-wave noncoherent light sources. The three optical properties are extracted from recordings of angularly resolved transmittance in addition to spatially resolved diffuse reflectance and transmittance. The applied multivariate calibration and prediction techniques are based on multiple polynomial regression in combination with a Newton--Raphson algorithm. The numerical test results based on Monte Carlo simulations showed mean prediction errors of approximately 0.5% for all three optical properties within ranges typical for biological media. Preliminary experimental results are also presented yielding errors of approximately 5%. Thus the presented methods show a substantial potential for simultaneous absorption and scattering characterization of turbid media.

The Joker: A Custom Monte Carlo Sampler for Binary-star and Exoplanet Radial Velocity Data

NASA Astrophysics Data System (ADS)

Price-Whelan, Adrian M.; Hogg, David W.; Foreman-Mackey, Daniel; Rix, Hans-Walter

2017-03-01

Given sparse or low-quality radial velocity measurements of a star, there are often many qualitatively different stellar or exoplanet companion orbit models that are consistent with the data. The consequent multimodality of the likelihood function leads to extremely challenging search, optimization, and Markov chain Monte Carlo (MCMC) posterior sampling over the orbital parameters. Here we create a custom Monte Carlo sampler for sparse or noisy radial velocity measurements of two-body systems that can produce posterior samples for orbital parameters even when the likelihood function is poorly behaved. The six standard orbital parameters for a binary system can be split into four nonlinear parameters (period, eccentricity, argument of pericenter, phase) and two linear parameters (velocity amplitude, barycenter velocity). We capitalize on this by building a sampling method in which we densely sample the prior probability density function (pdf) in the nonlinear parameters and perform rejection sampling using a likelihood function marginalized over the linear parameters. With sparse or uninformative data, the sampling obtained by this rejection sampling is generally multimodal and dense. With informative data, the sampling becomes effectively unimodal but too sparse: in these cases we follow the rejection sampling with standard MCMC. The method produces correct samplings in orbital parameters for data that include as few as three epochs. The Joker can therefore be used to produce proper samplings of multimodal pdfs, which are still informative and can be used in hierarchical (population) modeling. We give some examples that show how the posterior pdf depends sensitively on the number and time coverage of the observations and their uncertainties.

Renyi entanglement entropy of interacting fermions calculated using the continuous-time quantum Monte Carlo method.

PubMed

Wang, Lei; Troyer, Matthias

2014-09-12

We present a new algorithm for calculating the Renyi entanglement entropy of interacting fermions using the continuous-time quantum Monte Carlo method. The algorithm only samples the interaction correction of the entanglement entropy, which by design ensures the efficient calculation of weakly interacting systems. Combined with Monte Carlo reweighting, the algorithm also performs well for systems with strong interactions. We demonstrate the potential of this method by studying the quantum entanglement signatures of the charge-density-wave transition of interacting fermions on a square lattice.

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

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

Bates, Cameron Russell; Mckigney, Edward Allen

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

Monte Carlo modeling of atomic oxygen attack of polymers with protective coatings on LDEF

NASA Technical Reports Server (NTRS)

Banks, Bruce A.; Degroh, Kim K.; Sechkar, Edward A.

1992-01-01

Characterization of the behavior of atomic oxygen interaction with materials on the Long Duration Exposure Facility (LDEF) will assist in understanding the mechanisms involved, and will lead to improved reliability in predicting in-space durability of materials based on ground laboratory testing. A computational simulation of atomic oxygen interaction with protected polymers was developed using Monte Carlo techniques. Through the use of assumed mechanistic behavior of atomic oxygen and results of both ground laboratory and LDEF data, a predictive Monte Carlo model was developed which simulates the oxidation processes that occur on polymers with applied protective coatings that have defects. The use of high atomic oxygen fluence-directed ram LDEF results has enabled mechanistic implications to be made by adjusting Monte Carlo modeling assumptions to match observed results based on scanning electron microscopy. Modeling assumptions, implications, and predictions are presented, along with comparison of observed ground laboratory and LDEF results.

Finite-size scaling study of the two-dimensional Blume-Capel model

NASA Astrophysics Data System (ADS)

Beale, Paul D.

1986-02-01

The phase diagram of the two-dimensional Blume-Capel model is investigated by using the technique of phenomenological finite-size scaling. The location of the tricritical point and the values of the critical and tricritical exponents are determined. The location of the tricritical point (Tt=0.610+/-0.005, Dt=1.9655+/-0.0010) is well outside the error bars for the value quoted in previous Monte Carlo simulations but in excellent agreement with more recent Monte Carlo renormalization-group results. The values of the critical and tricritical exponents, with the exception of the leading thermal tricritical exponent, are in excellent agreement with previous calculations, conjectured values, and Monte Carlo renormalization-group studies.

An analysis on the theory of pulse oximetry by Monte Carlo simulation

NASA Astrophysics Data System (ADS)

Fan, Shangchun; Cai, Rui; Xing, Weiwei; Liu, Changting; Chen, Guangfei; Wang, Junfeng

2008-10-01

The pulse oximetry is a kind of electronic instrument that measures the oxygen saturation of arterial blood and pulse rate by non-invasive techniques. It enables prompt recognition of hypoxemia. In a conventional transmittance type pulse oximeter, the absorption of light by oxygenated and reduced hemoglobin is measured at two wavelength 660nm and 940nm. But the accuracy and measuring range of the pulse oximeter can not meet the requirement of clinical application. There are limitations in the theory of pulse oximetry, which is proved by Monte Carlo method. The mean paths are calculated in the Monte Carlo simulation. The results prove that the mean paths are not the same between the different wavelengths.

Multiple-time-stepping generalized hybrid Monte Carlo methods

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

Escribano, Bruno, E-mail: bescribano@bcamath.org; Akhmatskaya, Elena; IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao

2015-01-01

Performance of the generalized shadow hybrid Monte Carlo (GSHMC) method [1], which proved to be superior in sampling efficiency over its predecessors [2–4], molecular dynamics and hybrid Monte Carlo, can be further improved by combining it with multi-time-stepping (MTS) and mollification of slow forces. We demonstrate that the comparatively simple modifications of the method not only lead to better performance of GSHMC itself but also allow for beating the best performed methods, which use the similar force splitting schemes. In addition we show that the same ideas can be successfully applied to the conventional generalized hybrid Monte Carlo method (GHMC).more » The resulting methods, MTS-GHMC and MTS-GSHMC, provide accurate reproduction of thermodynamic and dynamical properties, exact temperature control during simulation and computational robustness and efficiency. MTS-GHMC uses a generalized momentum update to achieve weak stochastic stabilization to the molecular dynamics (MD) integrator. MTS-GSHMC adds the use of a shadow (modified) Hamiltonian to filter the MD trajectories in the HMC scheme. We introduce a new shadow Hamiltonian formulation adapted to force-splitting methods. The use of such Hamiltonians improves the acceptance rate of trajectories and has a strong impact on the sampling efficiency of the method. Both methods were implemented in the open-source MD package ProtoMol and were tested on a water and a protein systems. Results were compared to those obtained using a Langevin Molly (LM) method [5] on the same systems. The test results demonstrate the superiority of the new methods over LM in terms of stability, accuracy and sampling efficiency. This suggests that putting the MTS approach in the framework of hybrid Monte Carlo and using the natural stochasticity offered by the generalized hybrid Monte Carlo lead to improving stability of MTS and allow for achieving larger step sizes in the simulation of complex systems.« less

LMC: Logarithmantic Monte Carlo

NASA Astrophysics Data System (ADS)

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).

On the predictivity of pore-scale simulations: Estimating uncertainties with multilevel Monte Carlo

NASA Astrophysics Data System (ADS)

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 proposed method can be efficiently used in many porous media applications for problems such as stochastic homogenization/upscaling, propagation of uncertainty from microscopic fluid and rock properties to macro-scale parameters, robust estimation of Representative Elementary Volume size for arbitrary physics.

Analysis of dense-medium light scattering with applications to corneal tissue: experiments and Monte Carlo simulations.

PubMed

Kim, K B; Shanyfelt, L M; Hahn, D W

2006-01-01

Dense-medium scattering is explored in the context of providing a quantitative measurement of turbidity, with specific application to corneal haze. A multiple-wavelength scattering technique is proposed to make use of two-color scattering response ratios, thereby providing a means for data normalization. A combination of measurements and simulations are reported to assess this technique, including light-scattering experiments for a range of polystyrene suspensions. Monte Carlo (MC) simulations were performed using a multiple-scattering algorithm based on full Mie scattering theory. The simulations were in excellent agreement with the polystyrene suspension experiments, thereby validating the MC model. The MC model was then used to simulate multiwavelength scattering in a corneal tissue model. Overall, the proposed multiwavelength scattering technique appears to be a feasible approach to quantify dense-medium scattering such as the manifestation of corneal haze, although more complex modeling of keratocyte scattering, and animal studies, are necessary.

Efficient global biopolymer sampling with end-transfer configurational bias Monte Carlo

NASA Astrophysics Data System (ADS)

Arya, Gaurav; Schlick, Tamar

2007-01-01

We develop an "end-transfer configurational bias Monte Carlo" method for efficient thermodynamic sampling of complex biopolymers and assess its performance on a mesoscale model of chromatin (oligonucleosome) at different salt conditions compared to other Monte Carlo moves. Our method extends traditional configurational bias by deleting a repeating motif (monomer) from one end of the biopolymer and regrowing it at the opposite end using the standard Rosenbluth scheme. The method's sampling efficiency compared to local moves, pivot rotations, and standard configurational bias is assessed by parameters relating to translational, rotational, and internal degrees of freedom of the oligonucleosome. Our results show that the end-transfer method is superior in sampling every degree of freedom of the oligonucleosomes over other methods at high salt concentrations (weak electrostatics) but worse than the pivot rotations in terms of sampling internal and rotational sampling at low-to-moderate salt concentrations (strong electrostatics). Under all conditions investigated, however, the end-transfer method is several orders of magnitude more efficient than the standard configurational bias approach. This is because the characteristic sampling time of the innermost oligonucleosome motif scales quadratically with the length of the oligonucleosomes for the end-transfer method while it scales exponentially for the traditional configurational-bias method. Thus, the method we propose can significantly improve performance for global biomolecular applications, especially in condensed systems with weak nonbonded interactions and may be combined with local enhancements to improve local sampling.

Comparing Three Estimation Methods for the Three-Parameter Logistic IRT Model

ERIC Educational Resources Information Center

Lamsal, Sunil

2015-01-01

Different estimation procedures have been developed for the unidimensional three-parameter item response theory (IRT) model. These techniques include the marginal maximum likelihood estimation, the fully Bayesian estimation using Markov chain Monte Carlo simulation techniques, and the Metropolis-Hastings Robbin-Monro estimation. With each…

Space Object Collision Probability via Monte Carlo on the Graphics Processing Unit

NASA Astrophysics Data System (ADS)

Vittaldev, Vivek; Russell, Ryan P.

2017-09-01

Fast and accurate collision probability computations are essential for protecting space assets. Monte Carlo (MC) simulation is the most accurate but computationally intensive method. A Graphics Processing Unit (GPU) is used to parallelize the computation and reduce the overall runtime. Using MC techniques to compute the collision probability is common in literature as the benchmark. An optimized implementation on the GPU, however, is a challenging problem and is the main focus of the current work. The MC simulation takes samples from the uncertainty distributions of the Resident Space Objects (RSOs) at any time during a time window of interest and outputs the separations at closest approach. Therefore, any uncertainty propagation method may be used and the collision probability is automatically computed as a function of RSO collision radii. Integration using a fixed time step and a quartic interpolation after every Runge Kutta step ensures that no close approaches are missed. Two orders of magnitude speedups over a serial CPU implementation are shown, and speedups improve moderately with higher fidelity dynamics. The tool makes the MC approach tractable on a single workstation, and can be used as a final product, or for verifying surrogate and analytical collision probability methods.

A Hybrid Monte Carlo importance sampling of rare events in Turbulence and in Turbulent Models

NASA Astrophysics Data System (ADS)

Margazoglou, Georgios; Biferale, Luca; Grauer, Rainer; Jansen, Karl; Mesterhazy, David; Rosenow, Tillmann; Tripiccione, Raffaele

2017-11-01

Extreme and rare events is a challenging topic in the field of turbulence. Trying to investigate those instances through the use of traditional numerical tools turns to be a notorious task, as they fail to systematically sample the fluctuations around them. On the other hand, we propose that an importance sampling Monte Carlo method can selectively highlight extreme events in remote areas of the phase space and induce their occurrence. We present a brand new computational approach, based on the path integral formulation of stochastic dynamics, and employ an accelerated Hybrid Monte Carlo (HMC) algorithm for this purpose. Through the paradigm of stochastic one-dimensional Burgers' equation, subjected to a random noise that is white-in-time and power-law correlated in Fourier space, we will prove our concept and benchmark our results with standard CFD methods. Furthermore, we will present our first results of constrained sampling around saddle-point instanton configurations (optimal fluctuations). The research leading to these results has received funding from the EU Horizon 2020 research and innovation programme under Grant Agreement No. 642069, and from the EU Seventh Framework Programme (FP7/2007-2013) under ERC Grant Agreement No. 339032.

Parallel Monte Carlo transport modeling in the context of a time-dependent, three-dimensional multi-physics code

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

Procassini, R.J.

1997-12-31

The fine-scale, multi-space resolution that is envisioned for accurate simulations of complex weapons systems in three spatial dimensions implies flop-rate and memory-storage requirements that will only be obtained in the near future through the use of parallel computational techniques. Since the Monte Carlo transport models in these simulations usually stress both of these computational resources, they are prime candidates for parallelization. The MONACO Monte Carlo transport package, which is currently under development at LLNL, will utilize two types of parallelism within the context of a multi-physics design code: decomposition of the spatial domain across processors (spatial parallelism) and distribution ofmore » particles in a given spatial subdomain across additional processors (particle parallelism). This implementation of the package will utilize explicit data communication between domains (message passing). Such a parallel implementation of a Monte Carlo transport model will result in non-deterministic communication patterns. The communication of particles between subdomains during a Monte Carlo time step may require a significant level of effort to achieve a high parallel efficiency.« less

The structure of liquid water by polarized neutron diffraction and reverse Monte Carlo modelling.

PubMed

Temleitner, László; Pusztai, László; Schweika, Werner

2007-08-22

The coherent static structure factor of water has been investigated by polarized neutron diffraction. Polarization analysis allows us to separate the huge incoherent scattering background from hydrogen and to obtain high quality data of the coherent scattering from four different mixtures of liquid H(2)O and D(2)O. The information obtained by the variation of the scattering contrast confines the configurational space of water and is used by the reverse Monte Carlo technique to model the total structure factors. Structural characteristics have been calculated directly from the resulting sets of particle coordinates. Consistency with existing partial pair correlation functions, derived without the application of polarized neutrons, was checked by incorporating them into our reverse Monte Carlo calculations. We also performed Monte Carlo simulations of a hard sphere system, which provides an accurate estimate of the information content of the measured data. It is shown that the present combination of polarized neutron scattering and reverse Monte Carlo structural modelling is a promising approach towards a detailed understanding of the microscopic structure of water.

Metallic lithium by quantum Monte Carlo

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

Sugiyama, G.; Zerah, G.; Alder, B.J.

Lithium was chosen as the simplest known metal for the first application of quantum Monte Carlo methods in order to evaluate the accuracy of conventional one-electron band theories. Lithium has been extensively studied using such techniques. Band theory calculations have certain limitations in general and specifically in their application to lithium. Results depend on such factors as charge shape approximations (muffin tins), pseudopotentials (a special problem for lithium where the lack of rho core states requires a strong pseudopotential), and the form and parameters chosen for the exchange potential. The calculations are all one-electron methods in which the correlation effectsmore » are included in an ad hoc manner. This approximation may be particularly poor in the high compression regime, where the core states become delocalized. Furthermore, band theory provides only self-consistent results rather than strict limits on the energies. The quantum Monte Carlo method is a totally different technique using a many-body rather than a mean field approach which yields an upper bound on the energies. 18 refs., 4 figs., 1 tab.« less

Supernova Light Curves and Spectra from Two Different Codes: Supernu and Phoenix

NASA Astrophysics Data System (ADS)

Van Rossum, Daniel R; Wollaeger, Ryan T

2014-08-01

The observed similarities between light curve shapes from Type Ia supernovae, and in particular the correlation of light curve shape and brightness, have been actively studied for more than two decades. In recent years, hydronamic simulations of white dwarf explosions have advanced greatly, and multiple mechanisms that could potentially produce Type Ia supernovae have been explored in detail. The question which of the proposed mechanisms is (or are) possibly realized in nature remains challenging to answer, but detailed synthetic light curves and spectra from explosion simulations are very helpful and important guidelines towards answering this question.We present results from a newly developed radiation transport code, Supernu. Supernu solves the supernova radiation transfer problem uses a novel technique based on a hybrid between Implicit Monte Carlo and Discrete Diffusion Monte Carlo. This technique enhances the efficiency with respect to traditional implicit monte carlo codes and thus lends itself perfectly for multi-dimensional simulations. We show direct comparisons of light curves and spectra from Type Ia simulations with Supernu versus the legacy Phoenix code.

Conditional Monte Carlo randomization tests for regression models.

PubMed

Parhat, Parwen; Rosenberger, William F; Diao, Guoqing

2014-08-15

We discuss the computation of randomization tests for clinical trials of two treatments when the primary outcome is based on a regression model. We begin by revisiting the seminal paper of Gail, Tan, and Piantadosi (1988), and then describe a method based on Monte Carlo generation of randomization sequences. The tests based on this Monte Carlo procedure are design based, in that they incorporate the particular randomization procedure used. We discuss permuted block designs, complete randomization, and biased coin designs. We also use a new technique by Plamadeala and Rosenberger (2012) for simple computation of conditional randomization tests. Like Gail, Tan, and Piantadosi, we focus on residuals from generalized linear models and martingale residuals from survival models. Such techniques do not apply to longitudinal data analysis, and we introduce a method for computation of randomization tests based on the predicted rate of change from a generalized linear mixed model when outcomes are longitudinal. We show, by simulation, that these randomization tests preserve the size and power well under model misspecification. Copyright © 2014 John Wiley & Sons, Ltd.

Adaptive Monte Carlo methods

NASA Astrophysics Data System (ADS)

Fasnacht, Marc

We develop adaptive Monte Carlo methods for the calculation of the free energy as a function of a parameter of interest. The methods presented are particularly well-suited for systems with complex energy landscapes, where standard sampling techniques have difficulties. The Adaptive Histogram Method uses a biasing potential derived from histograms recorded during the simulation to achieve uniform sampling in the parameter of interest. The Adaptive Integration method directly calculates an estimate of the free energy from the average derivative of the Hamiltonian with respect to the parameter of interest and uses it as a biasing potential. We compare both methods to a state of the art method, and demonstrate that they compare favorably for the calculation of potentials of mean force of dense Lennard-Jones fluids. We use the Adaptive Integration Method to calculate accurate potentials of mean force for different types of simple particles in a Lennard-Jones fluid. Our approach allows us to separate the contributions of the solvent to the potential of mean force from the effect of the direct interaction between the particles. With contributions of the solvent determined, we can find the potential of mean force directly for any other direct interaction without additional simulations. We also test the accuracy of the Adaptive Integration Method on a thermodynamic cycle, which allows us to perform a consistency check between potentials of mean force and chemical potentials calculated using the Adaptive Integration Method. The results demonstrate a high degree of consistency of the method.

Propagating probability distributions of stand variables using sequential Monte Carlo methods

Treesearch

Jeffrey H. Gove

2009-01-01

A general probabilistic approach to stand yield estimation is developed based on sequential Monte Carlo filters, also known as particle filters. The essential steps in the development of the sampling importance resampling (SIR) particle filter are presented. The SIR filter is then applied to simulated and observed data showing how the 'predictor - corrector'...

Recovery of Graded Response Model Parameters: A Comparison of Marginal Maximum Likelihood and Markov Chain Monte Carlo Estimation

ERIC Educational Resources Information Center

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…

Multiple Regression with Varying Levels of Correlation among Predictors: Monte Carlo Sampling from Normal and Non-Normal Populations.

ERIC Educational Resources Information Center

Vasu, Ellen Storey

1978-01-01

The effects of the violation of the assumption of normality in the conditional distributions of the dependent variable, coupled with the condition of multicollinearity upon the outcome of testing the hypothesis that the regression coefficient equals zero, are investigated via a Monte Carlo study. (Author/JKS)

Biasing anisotropic scattering kernels for deep-penetration Monte Carlo calculations

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

Carter, L.L.; Hendricks, J.S.

1983-01-01

The exponential transform is often used to improve the efficiency of deep-penetration Monte Carlo calculations. This technique is usually implemented by biasing the distance-to-collision kernel of the transport equation, but leaving the scattering kernel unchanged. Dwivedi obtained significant improvements in efficiency by biasing an isotropic scattering kernel as well as the distance-to-collision kernel. This idea is extended to anisotropic scattering, particularly the highly forward Klein-Nishina scattering of gamma rays.

Hamiltonian Monte Carlo Inversion of Seismic Sources in Complex Media

NASA Astrophysics Data System (ADS)

Fichtner, A.; Simutė, S.

2017-12-01

We present a probabilistic seismic source inversion method that properly accounts for 3D heterogeneous Earth structure and provides full uncertainty information on the timing, location and mechanism of the event. Our method rests on two essential elements: (1) reciprocity and spectral-element simulations in complex media, and (2) Hamiltonian Monte Carlo sampling that requires only a small amount of test models. Using spectral-element simulations of 3D, visco-elastic, anisotropic wave propagation, we precompute a data base of the strain tensor in time and space by placing sources at the positions of receivers. Exploiting reciprocity, this receiver-side strain data base can be used to promptly compute synthetic seismograms at the receiver locations for any hypothetical source within the volume of interest. The rapid solution of the forward problem enables a Bayesian solution of the inverse problem. For this, we developed a variant of Hamiltonian Monte Carlo (HMC) sampling. Taking advantage of easily computable derivatives, HMC converges to the posterior probability density with orders of magnitude less samples than derivative-free Monte Carlo methods. (Exact numbers depend on observational errors and the quality of the prior). We apply our method to the Japanese Islands region where we previously constrained 3D structure of the crust and upper mantle using full-waveform inversion with a minimum period of around 15 s.

Biophotonics in diagnosis and modeling of tissue pathologies

NASA Astrophysics Data System (ADS)

Serafetinides, A. A.; Makropoulou, M.; Drakaki, E.

2008-12-01

Biophotonics techniques are applied to several fields in medicine and biology. The laser based techniques, such as the laser induced fluorescence (LIF) spectroscopy and the optical coherence tomography (OCT), are of particular importance in dermatology, where the laser radiation could be directly applied to the tissue target (e.g. skin). In addition, OCT resolves architectural tissue properties that might be useful as tumour discrimination parameters for skin as well as for ocular non-invasive visualization. Skin and ocular tissues are complex multilayered and inhomogeneous organs with spatially varying optical properties. This fact complicates the quantitative analysis of the fluorescence and/or light scattering spectra, even from the same tissue sample. To overcome this problem, mathematical simulation is applied for the investigation of the human tissue optical properties, in the visible/infrared range of the spectrum, resulting in a better discrimination of several tissue pathologies. In this work, we present i) a general view on biophotonics applications in diagnosis of human diseases, ii) some specific results on laser spectroscopy techniques, as LIF measurements, applied in arterial and skin pathologies and iii) some experimental and theoretical results on ocular OCT measurements. Regarding the LIF spectroscopy, we examined the autofluorescence properties of several human skin samples, excised from humans undergoing biopsy examination. A nitrogen laser was used as an excitation source, emitting at 337 nm (ultraviolet excitation). Histopathology examination of the samples was also performed, after the laser spectroscopy measurements and the results from the spectroscopic and medical analysis were compared, to differentiate malignancies, e.g. basal cell carcinoma tissue (BCC), from normal skin tissue. Regarding the OCT technique, we correlated human data, obtained from patients undergoing OCT examination, with Monte Carlo simulated cornea and retina tissues for diagnosis of ocular diseases.

LCG MCDB—a knowledgebase of Monte-Carlo simulated events

NASA Astrophysics Data System (ADS)

Belov, S.; Dudko, L.; Galkin, E.; Gusev, A.; Pokorski, W.; Sherstnev, A.

2008-02-01

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 dedicated 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. Program summaryProgram title: LCG Monte-Carlo Data Base Catalogue identifier: ADZX_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZX_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence No. of lines in distributed program, including test data, etc.: 30 129 No. of bytes in distributed program, including test data, etc.: 216 943 Distribution format: tar.gz Programming language: Perl Computer: CPU: Intel Pentium 4, RAM: 1 Gb, HDD: 100 Gb Operating system: Scientific Linux CERN 3/4 RAM: 1 073 741 824 bytes (1 Gb) Classification: 9 External routines:perl >= 5.8.5; Perl modules DBD-mysql >= 2.9004, File::Basename, GD::SecurityImage, GD::SecurityImage::AC, Linux::Statistics, XML::LibXML > 1.6, XML::SAX, XML::NamespaceSupport; Apache HTTP Server >= 2.0.59; mod auth external >= 2.2.9; edg-utils-system RPM package; gd >= 2.0.28; rpm package CASTOR-client >= 2.1.2-4; arc-server (optional) Nature of problem: Often, different groups of experimentalists prepare similar samples of particle collision events or turn to the same group of authors of Monte-Carlo (MC) generators to prepare the events. For example, the same MC samples of Standard Model (SM) processes can be employed for the investigations either in the SM analyses (as a signal) or in searches for new phenomena in Beyond Standard Model analyses (as a background). If the samples are made available publicly and equipped with corresponding and comprehensive documentation, it can speed up cross checks of the samples themselves and physical models applied. Some event samples require a lot of computing resources for preparation. So, a central storage of the samples prevents possible waste of researcher time and computing resources, which can be used to prepare the same events many times. Solution method: Creation of a special knowledgebase (MCDB) designed to keep event samples for the LHC experimental and phenomenological community. The knowledgebase is realized as a separate web-server ( http://mcdb.cern.ch). All event samples are kept on types at CERN. Documentation describing the events is the main contents of MCDB. Users can browse the knowledgebase, read and comment articles (documentation), and download event samples. Authors can upload new event samples, create new articles, and edit own articles. Restrictions: The software is adopted to solve the problems, described in the article and there are no any additional restrictions. Unusual features: The software provides a framework to store and document large files with flexible authentication and authorization system. Different external storages with large capacity can be used to keep the files. The WEB Content Management System provides all of the necessary interfaces for the authors of the files, end-users and administrators. Running time: Real time operations. References: [1] The main LCG MCDB server, http://mcdb.cern.ch/. [2] P. Bartalini, L. Dudko, A. Kryukov, I.V. Selyuzhenkov, A. Sherstnev, A. Vologdin, LCG Monte-Carlo data base, hep-ph/0404241. [3] J.P. Baud, B. Couturier, C. Curran, J.D. Durand, E. Knezo, S. Occhetti, O. Barring, CASTOR: status and evolution, cs.oh/0305047.

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

NASA Astrophysics Data System (ADS)

Baes, M.; Camps, P.

2015-09-01

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

Monte Carlo Simulation of Soil Moisture Effects on Anti-Tank Landmines Detection by Neutron Backscattering Technique

NASA Astrophysics Data System (ADS)

Mowlawi, Ali Asghar; Yazdani, Majed

The detection of landmines using available technologies is a time consuming, expensive, and extremely dangerous job, so that there is a need for technological breakthroughs in this field. One of the safest and most effective technologies to landmine and explosive detection is the neutron backscattering technique. The slowing-down of fast neutrons to the thermal energy is a direct measure of the concentration of hydrogen, one of the main elements present in explosive materials. The elastic scattering of fast neutrons is affected by the strong resonances in the cross-section of the three other elements of explosives: nitrogen, oxygen, and carbon. In this work, Monte Carlo estimations of the soil moisture effects on landmine detection are presented.

A determination of relativistic shock jump conditions using Monte Carlo techniques

NASA Technical Reports Server (NTRS)

Ellison, Donald C.; Reynolds, Stephen P.

1991-01-01

Monte Carlo techniques are used, assuming isotropic elastic scattering of all particles, to calculate jump conditions in parallel relativistic collisionless shocks in the absence of Fermi acceleration. The shock velocity and compression ratios are shown for arbitrary flow velocities and for any upstream temperature. Both single-component electron-positron plasma and two-component proton-electron plasmas are considered. It is shown that protons and electrons must share energy, directly or through the mediation of plasma waves, in order to satisfy the basic conservation conditions, and the electron and proton temperatures are determined for a particular microscopic, kinetic-theory model, namely, that protons always scatter elastically. The results are directly applicable to shocks in which waves of scattering superthermal particles are absent.

Double differential neutron spectra generated by the interaction of a 12 MeV/nucleon 36S beam on a thick natCu target

NASA Astrophysics Data System (ADS)

Trinh, N. D.; Fadil, M.; Lewitowicz, M.; Ledoux, X.; Laurent, B.; Thomas, J.-C.; Clerc, T.; Desmezières, V.; Dupuis, M.; Madeline, A.; Dessay, E.; Grinyer, G. F.; Grinyer, J.; Menard, N.; Porée, F.; Achouri, L.; Delaunay, F.; Parlog, M.

2018-07-01

Double differential neutron spectra (energy, angle) originating from a thick natCu target bombarded by a 12 MeV/nucleon 36S16+ beam were measured by the activation method and the Time-of-flight technique at the Grand Accélérateur National d'Ions Lourds (GANIL). A neutron spectrum unfolding algorithm combining the SAND-II iterative method and Monte-Carlo techniques was developed for the analysis of the activation results that cover a wide range of neutron energies. It was implemented into a graphical user interface program, called GanUnfold. The experimental neutron spectra are compared to Monte-Carlo simulations performed using the PHITS and FLUKA codes.

Monte-Carlo simulation of a stochastic differential equation

NASA Astrophysics Data System (ADS)

Arif, ULLAH; Majid, KHAN; M, KAMRAN; R, KHAN; Zhengmao, SHENG

2017-12-01

For solving higher dimensional diffusion equations with an inhomogeneous diffusion coefficient, Monte Carlo (MC) techniques are considered to be more effective than other algorithms, such as finite element method or finite difference method. The inhomogeneity of diffusion coefficient strongly limits the use of different numerical techniques. For better convergence, methods with higher orders have been kept forward to allow MC codes with large step size. The main focus of this work is to look for operators that can produce converging results for large step sizes. As a first step, our comparative analysis has been applied to a general stochastic problem. Subsequently, our formulization is applied to the problem of pitch angle scattering resulting from Coulomb collisions of charge particles in the toroidal devices.

Towards a framework for testing general relativity with extreme-mass-ratio-inspiral observations

NASA Astrophysics Data System (ADS)

Chua, A. J. K.; Hee, S.; Handley, W. J.; Higson, E.; Moore, C. J.; Gair, J. R.; Hobson, M. P.; Lasenby, A. N.

2018-07-01

Extreme-mass-ratio-inspiral observations from future space-based gravitational-wave detectors such as LISA will enable strong-field tests of general relativity with unprecedented precision, but at prohibitive computational cost if existing statistical techniques are used. In one such test that is currently employed for LIGO black hole binary mergers, generic deviations from relativity are represented by N deformation parameters in a generalized waveform model; the Bayesian evidence for each of its 2N combinatorial submodels is then combined into a posterior odds ratio for modified gravity over relativity in a null-hypothesis test. We adapt and apply this test to a generalized model for extreme-mass-ratio inspirals constructed on deformed black hole spacetimes, and focus our investigation on how computational efficiency can be increased through an evidence-free method of model selection. This method is akin to the algorithm known as product-space Markov chain Monte Carlo, but uses nested sampling and improved error estimates from a rethreading technique. We perform benchmarking and robustness checks for the method, and find order-of-magnitude computational gains over regular nested sampling in the case of synthetic data generated from the null model.

A Monte Carlo investigation of thrust imbalance of solid rocket motor pairs

NASA Technical Reports Server (NTRS)

Sforzini, R. H.; Foster, W. A., Jr.; Johnson, J. S., Jr.

1974-01-01

A technique is described for theoretical, statistical evaluation of the thrust imbalance of pairs of solid-propellant rocket motors (SRMs) firing in parallel. Sets of the significant variables, determined as a part of the research, are selected using a random sampling technique and the imbalance calculated for a large number of motor pairs. The performance model is upgraded to include the effects of statistical variations in the ovality and alignment of the motor case and mandrel. Effects of cross-correlations of variables are minimized by selecting for the most part completely independent input variables, over forty in number. The imbalance is evaluated in terms of six time - varying parameters as well as eleven single valued ones which themselves are subject to statistical analysis. A sample study of the thrust imbalance of 50 pairs of 146 in. dia. SRMs of the type to be used on the space shuttle is presented. The FORTRAN IV computer program of the analysis and complete instructions for its use are included. Performance computation time for one pair of SRMs is approximately 35 seconds on the IBM 370/155 using the FORTRAN H compiler.

Towards a framework for testing general relativity with extreme-mass-ratio-inspiral observations

NASA Astrophysics Data System (ADS)

Chua, A. J. K.; Hee, S.; Handley, W. J.; Higson, E.; Moore, C. J.; Gair, J. R.; Hobson, M. P.; Lasenby, A. N.

2018-04-01

Extreme-mass-ratio-inspiral observations from future space-based gravitational-wave detectors such as LISA will enable strong-field tests of general relativity with unprecedented precision, but at prohibitive computational cost if existing statistical techniques are used. In one such test that is currently employed for LIGO black-hole binary mergers, generic deviations from relativity are represented by N deformation parameters in a generalised waveform model; the Bayesian evidence for each of its 2N combinatorial submodels is then combined into a posterior odds ratio for modified gravity over relativity in a null-hypothesis test. We adapt and apply this test to a generalised model for extreme-mass-ratio inspirals constructed on deformed black-hole spacetimes, and focus our investigation on how computational efficiency can be increased through an evidence-free method of model selection. This method is akin to the algorithm known as product-space Markov chain Monte Carlo, but uses nested sampling and improved error estimates from a rethreading technique. We perform benchmarking and robustness checks for the method, and find order-of-magnitude computational gains over regular nested sampling in the case of synthetic data generated from the null model.

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

PubMed

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

2016-07-14

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

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

NASA Astrophysics Data System (ADS)

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

2016-07-01

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

Algorithmic developments of the kinetic activation-relaxation technique: Accessing long-time kinetics of larger and more complex systems

NASA Astrophysics Data System (ADS)

Trochet, Mickaël; Sauvé-Lacoursière, Alecsandre; Mousseau, Normand

2017-10-01

In spite of the considerable computer speed increase of the last decades, long-time atomic simulations remain a challenge and most molecular dynamical simulations are limited to 1 μ s at the very best in condensed matter and materials science. There is a need, therefore, for accelerated methods that can bridge the gap between the full dynamical description of molecular dynamics and experimentally relevant time scales. This is the goal of the kinetic Activation-Relaxation Technique (k-ART), an off-lattice kinetic Monte-Carlo method with on-the-fly catalog building capabilities based on the topological tool NAUTY and the open-ended search method Activation-Relaxation Technique (ART nouveau) that has been applied with success to the study of long-time kinetics of complex materials, including grain boundaries, alloys, and amorphous materials. We present a number of recent algorithmic additions, including the use of local force calculation, two-level parallelization, improved topological description, and biased sampling and show how they perform on two applications linked to defect diffusion and relaxation after ion bombardement in Si.

Quality of water and sediment in streams affected by historical mining, and quality of Mine Tailings, in the Rio Grande/Rio Bravo Basin, Big Bend Area of the United States and Mexico, August 2002

USGS Publications Warehouse

Lambert, Rebecca B.; Kolbe, Christine M.; Belzer, Wayne

2008-01-01

The U.S. Geological Survey, in cooperation with the International Boundary and Water Commission - U.S. and Mexican Sections, the National Park Service, the Texas Commission on Environmental Quality, the Secretaria de Medio Ambiente y Recursos Naturales in Mexico, the Area de Proteccion de Flora y Fauna Canon de Santa Elena in Mexico, and the Area de Proteccion de Flora y Fauna Maderas del Carmen in Mexico, collected samples of stream water, streambed sediment, and mine tailings during August 2002 for a study to determine whether trace elements from abandoned mines in the area in and around Big Bend National Park have affected the water and sediment quality in the Rio Grande/Rio Bravo Basin of the United States and Mexico. Samples were collected from eight sites on the main stem of the Rio Grande/Rio Bravo, four Rio Grande/Rio Bravo tributary sites downstream from abandoned mines or mine-tailing sites, and 11 mine-tailing sites. Mines in the area were operated to produce fluorite, germanium, iron, lead, mercury, silver, and zinc during the late 1800s through at least the late 1970s. Moderate (relatively neutral) pHs in stream-water samples collected at the 12 Rio Grande/Rio Bravo main-stem and tributary sites indicate that water is well mixed, diluted, and buffered with respect to the solubility of trace elements. The highest sulfate concentrations were in water samples from tributaries draining the Terlingua mining district. Only the sample from the Rough Run Draw site exceeded the Texas Surface Water Quality Standards general-use protection criterion for sulfate. All chloride and dissolved solids concentrations in water samples were less than the general-use protection criteria. Aluminum, copper, mercury, nickel, selenium, and zinc were detected in all water samples for which each element was analyzed. Cadmium, chromium, and lead were detected in samples less frequently, and silver was not detected in any of the samples. None of the sample concentrations of aluminum, cadmium, chromium, nickel, selenium, and zinc exceeded the Texas Surface Water Quality Standards criteria for aquatic life-use protection or human health. The only trace elements detected in the water samples at concentrations exceeding the Texas Surface Water Quality Standards criterion for human health (fish consumption use) was lead at one site and mercury at 10 of 12 sites. Relatively high mercury concentrations distributed throughout the area might indicate sources of mercury in addition to abandoned mining areas. Streambed-sediment samples were collected from 12 sites and analyzed for 44 major and trace elements. In general, the trace elements detected in streambed-sediment samples were low in concentration, interpreted as consistent with background concentrations. Concentrations at two sites, however, were elevated compared to Texas Commission on Environmental Quality criteria. Concentrations of antimony, arsenic, cadmium, lead, silver, and zinc in the sample from San Carlos Creek downstream from La Esperanza (San Carlos) Mine exceeded the Texas Commission on Environmental Quality screening levels for sediment. The sample from Rough Run Draw, downstream from the Study Butte Mine, also showed elevated concentrations of arsenic, cadmium, and lead, but these concentrations were much lower than those in the San Carlos Creek sample and did not exceed screening levels. Elevated concentrations of multiple trace elements in streambed-sediment samples from San Carlos Creek and Rough Run Draw indicate that San Carlos Creek, and probably Rough Run Draw, have been adversely affected by mining activities. Fourteen mine-tailing samples from 11 mines were analyzed for 25 major and trace elements. All trace elements except selenium and thallium were detected in one or more samples. The highest lead concentrations were detected in tailings samples from the Boquillas, Puerto Rico, La Esperanza (San Carlos), and Tres Marias Mines, as might be expected because the tailings ar

Rare event simulation in radiation transport

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

Kollman, Craig

1993-10-01

This dissertation studies methods for estimating extremely small probabilities by Monte Carlo simulation. Problems in radiation transport typically involve estimating very rare events or the expected value of a random variable which is with overwhelming probability equal to zero. These problems often have high dimensional state spaces and irregular geometries so that analytic solutions are not possible. Monte Carlo simulation must be used to estimate the radiation dosage being transported to a particular location. If the area is well shielded the probability of any one particular particle getting through is very small. Because of the large number of particles involved,more » even a tiny fraction penetrating the shield may represent an unacceptable level of radiation. It therefore becomes critical to be able to accurately estimate this extremely small probability. Importance sampling is a well known technique for improving the efficiency of rare event calculations. Here, a new set of probabilities is used in the simulation runs. The results are multiple by the likelihood ratio between the true and simulated probabilities so as to keep the estimator unbiased. The variance of the resulting estimator is very sensitive to which new set of transition probabilities are chosen. It is shown that a zero variance estimator does exist, but that its computation requires exact knowledge of the solution. A simple random walk with an associated killing model for the scatter of neutrons is introduced. Large deviation results for optimal importance sampling in random walks are extended to the case where killing is present. An adaptive ``learning`` algorithm for implementing importance sampling is given for more general Markov chain models of neutron scatter. For finite state spaces this algorithm is shown to give with probability one, a sequence of estimates converging exponentially fast to the true solution.« less

Implementation of Monte Carlo Dose calculation for CyberKnife treatment planning

NASA Astrophysics Data System (ADS)

Ma, C.-M.; Li, J. S.; Deng, J.; Fan, J.

2008-02-01

Accurate dose calculation is essential to advanced stereotactic radiosurgery (SRS) and stereotactic radiotherapy (SRT) especially for treatment planning involving heterogeneous patient anatomy. This paper describes the implementation of a fast Monte Carlo dose calculation algorithm in SRS/SRT treatment planning for the CyberKnife® SRS/SRT system. A superposition Monte Carlo algorithm is developed for this application. Photon mean free paths and interaction types for different materials and energies as well as the tracks of secondary electrons are pre-simulated using the MCSIM system. Photon interaction forcing and splitting are applied to the source photons in the patient calculation and the pre-simulated electron tracks are repeated with proper corrections based on the tissue density and electron stopping powers. Electron energy is deposited along the tracks and accumulated in the simulation geometry. Scattered and bremsstrahlung photons are transported, after applying the Russian roulette technique, in the same way as the primary photons. Dose calculations are compared with full Monte Carlo simulations performed using EGS4/MCSIM and the CyberKnife treatment planning system (TPS) for lung, head & neck and liver treatments. Comparisons with full Monte Carlo simulations show excellent agreement (within 0.5%). More than 10% differences in the target dose are found between Monte Carlo simulations and the CyberKnife TPS for SRS/SRT lung treatment while negligible differences are shown in head and neck and liver for the cases investigated. The calculation time using our superposition Monte Carlo algorithm is reduced up to 62 times (46 times on average for 10 typical clinical cases) compared to full Monte Carlo simulations. SRS/SRT dose distributions calculated by simple dose algorithms may be significantly overestimated for small lung target volumes, which can be improved by accurate Monte Carlo dose calculations.

A comparison of maximum likelihood and other estimators of eigenvalues from several correlated Monte Carlo samples

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

Beer, M.

1980-12-01

The maximum likelihood method for the multivariate normal distribution is applied to the case of several individual eigenvalues. Correlated Monte Carlo estimates of the eigenvalue are assumed to follow this prescription and aspects of the assumption are examined. Monte Carlo cell calculations using the SAM-CE and VIM codes for the TRX-1 and TRX-2 benchmark reactors, and SAM-CE full core results are analyzed with this method. Variance reductions of a few percent to a factor of 2 are obtained from maximum likelihood estimation as compared with the simple average and the minimum variance individual eigenvalue. The numerical results verify that themore » use of sample variances and correlation coefficients in place of the corresponding population statistics still leads to nearly minimum variance estimation for a sufficient number of histories and aggregates.« less

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

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

Eisenbach, Markus; Li, Ying Wai

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

The Joker: A custom Monte Carlo sampler for binary-star and exoplanet radial velocity data

NASA Astrophysics Data System (ADS)

Price-Whelan, Adrian M.; Hogg, David W.; Foreman-Mackey, Daniel; Rix, Hans-Walter

2017-01-01

Given sparse or low-quality radial-velocity measurements of a star, there are often many qualitatively different stellar or exoplanet companion orbit models that are consistent with the data. The consequent multimodality of the likelihood function leads to extremely challenging search, optimization, and MCMC posterior sampling over the orbital parameters. The Joker is a custom-built Monte Carlo sampler that can produce a posterior sampling for orbital parameters given sparse or noisy radial-velocity measurements, even when the likelihood function is poorly behaved. The method produces correct samplings in orbital parameters for data that include as few as three epochs. The Joker can therefore be used to produce proper samplings of multimodal pdfs, which are still highly informative and can be used in hierarchical (population) modeling.

Efficient Sampling of Parsimonious Inversion Histories with Application to Genome Rearrangement in Yersinia

PubMed Central

Darling, Aaron E.

2009-01-01

Inversions are among the most common mutations acting on the order and orientation of genes in a genome, and polynomial-time algorithms exist to obtain a minimal length series of inversions that transform one genome arrangement to another. However, the minimum length series of inversions (the optimal sorting path) is often not unique as many such optimal sorting paths exist. If we assume that all optimal sorting paths are equally likely, then statistical inference on genome arrangement history must account for all such sorting paths and not just a single estimate. No deterministic polynomial algorithm is known to count the number of optimal sorting paths nor sample from the uniform distribution of optimal sorting paths. Here, we propose a stochastic method that uniformly samples the set of all optimal sorting paths. Our method uses a novel formulation of parallel Markov chain Monte Carlo. In practice, our method can quickly estimate the total number of optimal sorting paths. We introduce a variant of our approach in which short inversions are modeled to be more likely, and we show how the method can be used to estimate the distribution of inversion lengths and breakpoint usage in pathogenic Yersinia pestis. The proposed method has been implemented in a program called “MC4Inversion.” We draw comparison of MC4Inversion to the sampler implemented in BADGER and a previously described importance sampling (IS) technique. We find that on high-divergence data sets, MC4Inversion finds more optimal sorting paths per second than BADGER and the IS technique and simultaneously avoids bias inherent in the IS technique. PMID:20333186

Fission matrix-based Monte Carlo criticality analysis of fuel storage pools

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

Farlotti, M.; Ecole Polytechnique, Palaiseau, F 91128; Larsen, E. W.

2013-07-01

Standard Monte Carlo transport procedures experience difficulties in solving criticality problems in fuel storage pools. Because of the strong neutron absorption between fuel assemblies, source convergence can be very slow, leading to incorrect estimates of the eigenvalue and the eigenfunction. This study examines an alternative fission matrix-based Monte Carlo transport method that takes advantage of the geometry of a storage pool to overcome this difficulty. The method uses Monte Carlo transport to build (essentially) a fission matrix, which is then used to calculate the criticality and the critical flux. This method was tested using a test code on a simplemore » problem containing 8 assemblies in a square pool. The standard Monte Carlo method gave the expected eigenfunction in 5 cases out of 10, while the fission matrix method gave the expected eigenfunction in all 10 cases. In addition, the fission matrix method provides an estimate of the error in the eigenvalue and the eigenfunction, and it allows the user to control this error by running an adequate number of cycles. Because of these advantages, the fission matrix method yields a higher confidence in the results than standard Monte Carlo. We also discuss potential improvements of the method, including the potential for variance reduction techniques. (authors)« less

Monte Carlo analysis for the determination of the conic constant of an aspheric micro lens based on a scanning white light interferometric measurement

NASA Astrophysics Data System (ADS)

Gugsa, Solomon A.; Davies, Angela

2005-08-01

Characterizing an aspheric micro lens is critical for understanding the performance and providing feedback to the manufacturing. We describe a method to find the best-fit conic of an aspheric micro lens using a least squares minimization and Monte Carlo analysis. Our analysis is based on scanning white light interferometry measurements, and we compare the standard rapid technique where a single measurement is taken of the apex of the lens to the more time-consuming stitching technique where more surface area is measured. Both are corrected for tip/tilt based on a planar fit to the substrate. Four major parameters and their uncertainties are estimated from the measurement and a chi-square minimization is carried out to determine the best-fit conic constant. The four parameters are the base radius of curvature, the aperture of the lens, the lens center, and the sag of the lens. A probability distribution is chosen for each of the four parameters based on the measurement uncertainties and a Monte Carlo process is used to iterate the minimization process. Eleven measurements were taken and data is also chosen randomly from the group during the Monte Carlo simulation to capture the measurement repeatability. A distribution of best-fit conic constants results, where the mean is a good estimate of the best-fit conic and the distribution width represents the combined measurement uncertainty. We also compare the Monte Carlo process for the stitched data and the not stitched data. Our analysis allows us to analyze the residual surface error in terms of Zernike polynomials and determine uncertainty estimates for each coefficient.

Automatic variance reduction for Monte Carlo simulations via the local importance function transform

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

Turner, S.A.

1996-02-01

The author derives a transformed transport problem that can be solved theoretically by analog Monte Carlo with zero variance. However, the Monte Carlo simulation of this transformed problem cannot be implemented in practice, so he develops a method for approximating it. The approximation to the zero variance method consists of replacing the continuous adjoint transport solution in the transformed transport problem by a piecewise continuous approximation containing local biasing parameters obtained from a deterministic calculation. He uses the transport and collision processes of the transformed problem to bias distance-to-collision and selection of post-collision energy groups and trajectories in a traditionalmore » Monte Carlo simulation of ``real`` particles. He refers to the resulting variance reduction method as the Local Importance Function Transform (LIFI) method. He demonstrates the efficiency of the LIFT method for several 3-D, linearly anisotropic scattering, one-group, and multigroup problems. In these problems the LIFT method is shown to be more efficient than the AVATAR scheme, which is one of the best variance reduction techniques currently available in a state-of-the-art Monte Carlo code. For most of the problems considered, the LIFT method produces higher figures of merit than AVATAR, even when the LIFT method is used as a ``black box``. There are some problems that cause trouble for most variance reduction techniques, and the LIFT method is no exception. For example, the author demonstrates that problems with voids, or low density regions, can cause a reduction in the efficiency of the LIFT method. However, the LIFT method still performs better than survival biasing and AVATAR in these difficult cases.« less

ACCELERATING FUSION REACTOR NEUTRONICS MODELING BY AUTOMATIC COUPLING OF HYBRID MONTE CARLO/DETERMINISTIC TRANSPORT ON CAD GEOMETRY

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

Biondo, Elliott D; Ibrahim, Ahmad M; Mosher, Scott W

2015-01-01

Detailed radiation transport calculations are necessary for many aspects of the design of fusion energy systems (FES) such as ensuring occupational safety, assessing the activation of system components for waste disposal, and maintaining cryogenic temperatures within superconducting magnets. Hybrid Monte Carlo (MC)/deterministic techniques are necessary for this analysis because FES are large, heavily shielded, and contain streaming paths that can only be resolved with MC. The tremendous complexity of FES necessitates the use of CAD geometry for design and analysis. Previous ITER analysis has required the translation of CAD geometry to MCNP5 form in order to use the AutomateD VAriaNcemore » reducTion Generator (ADVANTG) for hybrid MC/deterministic transport. In this work, ADVANTG was modified to support CAD geometry, allowing hybrid (MC)/deterministic transport to be done automatically and eliminating the need for this translation step. This was done by adding a new ray tracing routine to ADVANTG for CAD geometries using the Direct Accelerated Geometry Monte Carlo (DAGMC) software library. This new capability is demonstrated with a prompt dose rate calculation for an ITER computational benchmark problem using both the Consistent Adjoint Driven Importance Sampling (CADIS) method an the Forward Weighted (FW)-CADIS method. The variance reduction parameters produced by ADVANTG are shown to be the same using CAD geometry and standard MCNP5 geometry. Significant speedups were observed for both neutrons (as high as a factor of 7.1) and photons (as high as a factor of 59.6).« less

MC3: Multi-core Markov-chain Monte Carlo code

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

Electrical conductivity of San Carlos olivine along [100] under oxygen- and pyroxene-buffered conditions and implications for defect equilibria

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

Wanamaker, B.J.; Duba, A.G.

1993-01-10

The electrical conductivity along [100] of single crystal San Carlos olivine was measured as a function of temperature between 1100[degrees] and 1200[degrees]C and oxygen fugacity between 10[sup [minus]6] and 10[sup +0.5] Pa (at 1200[degrees]C), and either with (pyroxene-buffered) or without (self-buffered) an added natural pyroxene buffer from a San Carlos Iherzolite. Under these temperature and fO[sub 2] conditions, electrical conduction in the self-buffered sample is attributed to polarons (Fe[sup [sm bullet

Monte Carlo simulations of coherent backscatter for identification of the optical coefficients of biological tissues in vivo

NASA Astrophysics Data System (ADS)

Eddowes, M. H.; Mills, T. N.; Delpy, D. T.

1995-05-01

A Monte Carlo model of light backscattered from turbid media has been used to simulate the effects of weak localization in biological tissues. A validation technique is used that implies that for the scattering and absorption coefficients and for refractive index mismatches found in tissues, the Monte Carlo method is likely to provide more accurate results than the methods previously used. The model also has the ability to simulate the effects of various illumination profiles and other laboratory-imposed conditions. A curve-fitting routine has been developed that might be used to extract the optical coefficients from the angular intensity profiles seen in experiments on turbid biological tissues, data that could be obtained in vivo.

Hypothesis testing of scientific Monte Carlo calculations.

PubMed

Wallerberger, Markus; Gull, Emanuel

2017-11-01

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

Hypothesis testing of scientific Monte Carlo calculations

NASA Astrophysics Data System (ADS)

Wallerberger, Markus; Gull, Emanuel

2017-11-01

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

Monte Carlo Techniques for Calculations of Charge Deposition and Displacement Damage from Protons in Visible and Infrared Sensor Arrays

NASA Technical Reports Server (NTRS)

Marshall, Paul; Reed, Robert; Fodness, Bryan; Jordan, Tom; Pickel, Jim; Xapsos, Michael; Burke, Ed

2004-01-01

This slide presentation examines motivation for Monte Carlo methods, charge deposition in sensor arrays, displacement damage calculations, and future work. The discussion of charge deposition sensor arrays includes Si active pixel sensor APS arrays and LWIR HgCdTe FPAs. The discussion of displacement damage calculations includes nonionizing energy loss (NIEL), HgCdTe NIEL calculation results including variance, and implications for damage in HgCdTe detector arrays.

A Monte Carlo-finite element model for strain energy controlled microstructural evolution - 'Rafting' in superalloys

NASA Technical Reports Server (NTRS)

Gayda, J.; Srolovitz, D. J.

1989-01-01

This paper presents a specialized microstructural lattice model, MCFET (Monte Carlo finite element technique), which simulates microstructural evolution in materials in which strain energy has an important role in determining morphology. The model is capable of accounting for externally applied stress, surface tension, misfit, elastic inhomogeneity, elastic anisotropy, and arbitrary temperatures. The MCFET analysis was found to compare well with the results of analytical calculations of the equilibrium morphologies of isolated particles in an infinite matrix.

General Monte Carlo reliability simulation code including common mode failures and HARP fault/error-handling

NASA Technical Reports Server (NTRS)

Platt, M. E.; Lewis, E. E.; Boehm, F.

1991-01-01

A Monte Carlo Fortran computer program was developed that uses two variance reduction techniques for computing system reliability applicable to solving very large highly reliable fault-tolerant systems. The program is consistent with the hybrid automated reliability predictor (HARP) code which employs behavioral decomposition and complex fault-error handling models. This new capability is called MC-HARP which efficiently solves reliability models with non-constant failures rates (Weibull). Common mode failure modeling is also a specialty.

Improving the Ar I and II branching ratio calibration method: Monte Carlo simulations of effects from photon scattering/reflecting in hollow cathodes

NASA Astrophysics Data System (ADS)

Lawler, J. E.; Den Hartog, E. A.

2018-03-01

The Ar I and II branching ratio calibration method is discussed with the goal of improving the technique. This method of establishing a relative radiometric calibration is important in ongoing research to improve atomic transition probabilities for quantitative spectroscopy in astrophysics and other fields. Specific suggestions are presented along with Monte Carlo simulations of wavelength dependent effects from scattering/reflecting of photons in a hollow cathode.

Giant Steps in Cefalù

NASA Astrophysics Data System (ADS)

Jeffery, David J.; Mazzali, Paolo A.

2007-08-01

Giant steps is a technique to accelerate Monte Carlo radiative transfer in optically-thick cells (which are isotropic and homogeneous in matter properties and into which astrophysical atmospheres are divided) by greatly reducing the number of Monte Carlo steps needed to propagate photon packets through such cells. In an optically-thick cell, packets starting from any point (which can be regarded a point source) well away from the cell wall act essentially as packets diffusing from the point source in an infinite, isotropic, homogeneous atmosphere. One can replace many ordinary Monte Carlo steps that a packet diffusing from the point source takes by a randomly directed giant step whose length is slightly less than the distance to the nearest cell wall point from the point source. The giant step is assigned a time duration equal to the time for the RMS radius for a burst of packets diffusing from the point source to have reached the giant step length. We call assigning giant-step time durations this way RMS-radius (RMSR) synchronization. Propagating packets by series of giant steps in giant-steps random walks in the interiors of optically-thick cells constitutes the technique of giant steps. Giant steps effectively replaces the exact diffusion treatment of ordinary Monte Carlo radiative transfer in optically-thick cells by an approximate diffusion treatment. In this paper, we describe the basic idea of giant steps and report demonstration giant-steps flux calculations for the grey atmosphere. Speed-up factors of order 100 are obtained relative to ordinary Monte Carlo radiative transfer. In practical applications, speed-up factors of order ten and perhaps more are possible. The speed-up factor is likely to be significantly application-dependent and there is a trade-off between speed-up and accuracy. This paper and past work suggest that giant-steps error can probably be kept to a few percent by using sufficiently large boundary-layer optical depths while still maintaining large speed-up factors. Thus, giant steps can be characterized as a moderate accuracy radiative transfer technique. For many applications, the loss of some accuracy may be a tolerable price to pay for the speed-ups gained by using giant steps.

An Evaluation of a Markov Chain Monte Carlo Method for the Two-Parameter Logistic Model.

ERIC Educational Resources Information Center

Kim, Seock-Ho; Cohen, Allan S.

The accuracy of the Markov Chain Monte Carlo (MCMC) procedure Gibbs sampling was considered for estimation of item parameters of the two-parameter logistic model. Data for the Law School Admission Test (LSAT) Section 6 were analyzed to illustrate the MCMC procedure. In addition, simulated data sets were analyzed using the MCMC, marginal Bayesian…

Use of single scatter electron monte carlo transport for medical radiation sciences

DOEpatents

Svatos, Michelle M.

2001-01-01

The single scatter Monte Carlo code CREEP models precise microscopic interactions of electrons with matter to enhance physical understanding of radiation sciences. It is designed to simulate electrons in any medium, including materials important for biological studies. It simulates each interaction individually by sampling from a library which contains accurate information over a broad range of energies.

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

ERIC Educational Resources Information Center

Kim, Jee-Seon; Bolt, Daniel M.

2007-01-01

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

Replica-exchange Wang Landau sampling: pushing the limits of Monte Carlo simulations in materials sciences

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

Perera, Meewanage Dilina N; Li, Ying Wai; Eisenbach, Markus

We describe the study of thermodynamics of materials using replica-exchange Wang Landau (REWL) sampling, a generic framework for massively parallel implementations of the Wang Landau Monte Carlo method. To evaluate the performance and scalability of the method, we investigate the magnetic phase transition in body-centered cubic (bcc) iron using the classical Heisenberg model parameterized with first principles calculations. We demonstrate that our framework leads to a significant speedup without compromising the accuracy and precision and facilitates the study of much larger systems than is possible with its serial counterpart.

A Monte Carlo Program for Simulating Selection Decisions from Personnel Tests

ERIC Educational Resources Information Center

Petersen, Calvin R.; Thain, John W.

1976-01-01

Relative to test and criterion parameters and cutting scores, the correlation coefficient, sample size, and number of samples to be drawn (all inputs), this program calculates decision classification rates across samples and for combined samples. Several other related indices are also computed. (Author)

Time dependent variation of carrying capacity of prestressed precast beam

NASA Astrophysics Data System (ADS)

Le, Tuan D.; Konečný, Petr; Matečková, Pavlína

2018-04-01

The article deals with the evaluation of the precast concrete element time dependent carrying capacity. The variation of the resistance is inherited property of laboratory as well as in-situ members. Thus the specification of highest, yet possible, laboratory sample resistance is important with respect to evaluation of laboratory experiments based on the test machine loading capabilities. The ultimate capacity is evaluated through the bending moment resistance of a simply supported prestressed concrete beam. The probabilistic assessment is applied. Scatter of random variables of compressive strength of concrete and effective height of the cross section is considered. Monte Carlo simulation technique is used to investigate the performance of the cross section of the beam with changes of tendons’ positions and compressive strength of concrete.

Has the 2008 financial crisis affected stock market efficiency? The case of Eurozone

NASA Astrophysics Data System (ADS)

Anagnostidis, P.; Varsakelis, C.; Emmanouilides, C. J.

2016-04-01

In this paper, the impact of the 2008 financial crisis on the weak-form efficiency of twelve Eurozone stock markets is investigated empirically. Efficiency is tested via the Generalized Hurst Exponent method, while dynamic Hurst exponents are estimated by means of the rolling window technique. To account for biases associated with the finite sample size and the leptokurtosis of the financial data, the statistical significance of the Hurst exponent estimates is assessed through a series of Monte-Carlo simulations drawn from the class of α-stable distributions. According to our results, the 2008 crisis has adversely affected stock price efficiency in most of the Eurozone capital markets, leading to the emergence of significant mean-reverting patterns in stock price movements.

Accelerating Monte Carlo simulations with an NVIDIA ® graphics processor

NASA Astrophysics Data System (ADS)

Martinsen, Paul; Blaschke, Johannes; Künnemeyer, Rainer; Jordan, Robert

2009-10-01

Modern graphics cards, commonly used in desktop computers, have evolved beyond a simple interface between processor and display to incorporate sophisticated calculation engines that can be applied to general purpose computing. The Monte Carlo algorithm for modelling photon transport in turbid media has been implemented on an NVIDIA ® 8800 GT graphics card using the CUDA toolkit. The Monte Carlo method relies on following the trajectory of millions of photons through the sample, often taking hours or days to complete. The graphics-processor implementation, processing roughly 110 million scattering events per second, was found to run more than 70 times faster than a similar, single-threaded implementation on a 2.67 GHz desktop computer. Program summaryProgram title: Phoogle-C/Phoogle-G Catalogue identifier: AEEB_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEB_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 51 264 No. of bytes in distributed program, including test data, etc.: 2 238 805 Distribution format: tar.gz Programming language: C++ Computer: Designed for Intel PCs. Phoogle-G requires a NVIDIA graphics card with support for CUDA 1.1 Operating system: Windows XP Has the code been vectorised or parallelized?: Phoogle-G is written for SIMD architectures RAM: 1 GB Classification: 21.1 External routines: Charles Karney Random number library. Microsoft Foundation Class library. NVIDA CUDA library [1]. Nature of problem: The Monte Carlo technique is an effective algorithm for exploring the propagation of light in turbid media. However, accurate results require tracing the path of many photons within the media. The independence of photons naturally lends the Monte Carlo technique to implementation on parallel architectures. Generally, parallel computing can be expensive, but recent advances in consumer grade graphics cards have opened the possibility of high-performance desktop parallel-computing. Solution method: In this pair of programmes we have implemented the Monte Carlo algorithm described by Prahl et al. [2] for photon transport in infinite scattering media to compare the performance of two readily accessible architectures: a standard desktop PC and a consumer grade graphics card from NVIDIA. Restrictions: The graphics card implementation uses single precision floating point numbers for all calculations. Only photon transport from an isotropic point-source is supported. The graphics-card version has no user interface. The simulation parameters must be set in the source code. The desktop version has a simple user interface; however some properties can only be accessed through an ActiveX client (such as Matlab). Additional comments: The random number library used has a LGPL ( http://www.gnu.org/copyleft/lesser.html) licence. Running time: Runtime can range from minutes to months depending on the number of photons simulated and the optical properties of the medium. References:http://www.nvidia.com/object/cuda_home.html. S. Prahl, M. Keijzer, Sl. Jacques, A. Welch, SPIE Institute Series 5 (1989) 102.

Evaluation and characterization of thyroid-disrupting activities in soil samples along the Second Songhua River, China.

PubMed

Kong, Dongdong; Wang, Yafei; Wang, Jinsheng; Teng, Yanguo; Li, Na; Li, Jian

2016-11-01

In this study, a recombinant thyroid receptor (TR) gene yeast assay combined with Monte Carlo simulation were used to evaluate and characterize soil samples collected from Jilin (China) along the Second Songhua River, for their ant/agonist effect on TR. No TR agonistic activity was found in soils, but many soil samples exhibited TR antagonistic activities, and the bioassay-derived amiodarone hydrochloride equivalents, which was calculated based on Monte Carlo simulation, ranged from not detected (N.D.) to 35.5μg/g. Hydrophilic substance fractions were determined to be the contributors to TR antagonistic activity in these soil samples. Our results indicate that the novel calculation method is effective for the quantification and characterization of TR antagonists in soil samples, and these data could provide useful information for future management and remediation efforts for contaminated soils. Copyright © 2016 Elsevier Inc. All rights reserved.

Computational and theoretical studies of globular proteins

NASA Astrophysics Data System (ADS)

Pagan, Daniel L.

Protein crystallization is often achieved in experiment through a trial and error approach. To date, there exists a dearth of theoretical understanding of the initial conditions necessary to promote crystallization. While a better understanding of crystallization will help to create good crystals suitable for structure analysis, it will also allow us to prevent the onset of certain diseases. The core of this thesis is to model and, ultimately, understand the phase behavior of protein particles in solution. Toward this goal, we calculate the fluid-fluid coexistence curve in the vicinity of the metastable critical point of the modified Lennard-Jones potential, where it has been shown that nucleation is increased by many orders of magnitude. We use finite-size scaling techniques and grand canonical Monte Carlo simulation methods. This has allowed us to pinpoint the critical point and subcritical region with high accuracy in spite of the critical fluctuations that hinder sampling using other Monte Carlo techniques. We also attempt to model the phase behavior of the gamma-crystallins, mutations of which have been linked to genetic cataracts. The complete phase behavior of the square well potential at the ranges of attraction lambda = 1.15 and lambda = 1.25 is calculated and compared with that of the gammaII-crystallin. The role of solvent is also important in the crystallization process and affects the phase behavior of proteins in solution. We study a model that accounts for the contribution of the solvent free-energy to the free-energy of globular proteins. This model allows us to model phase behavior that includes solvent.

Monte Carlo Sampling in Fractal Landscapes

NASA Astrophysics Data System (ADS)

Leitão, Jorge C.; Lopes, J. M. Viana Parente; Altmann, Eduardo G.

2013-05-01

We design a random walk to explore fractal landscapes such as those describing chaotic transients in dynamical systems. We show that the random walk moves efficiently only when its step length depends on the height of the landscape via the largest Lyapunov exponent of the chaotic system. We propose a generalization of the Wang-Landau algorithm which constructs not only the density of states (transient time distribution) but also the correct step length. As a result, we obtain a flat-histogram Monte Carlo method which samples fractal landscapes in polynomial time, a dramatic improvement over the exponential scaling of traditional uniform-sampling methods. Our results are not limited by the dimensionality of the landscape and are confirmed numerically in chaotic systems with up to 30 dimensions.

Development and Validation of the Caring Loneliness Scale.

PubMed

Karhe, Liisa; Kaunonen, Marja; Koivisto, Anna-Maija

2016-12-01

The Caring Loneliness Scale (CARLOS) includes 5 categories derived from earlier qualitative research. This article assesses the reliability and construct validity of a scale designed to measure patient experiences of loneliness in a professional caring relationship. Statistical analysis with 4 different sample sizes included Cronbach's alpha and exploratory factor analysis with principal axis factoring extraction. The sample size of 250 gave the most useful and comprehensible structure, but all 4 samples yielded underlying content of loneliness experiences. The initial 5 categories were reduced to 4 factors with 24 items and Cronbach's alpha ranging from .77 to .90. The findings support the reliability and validity of CARLOS for the assessment of Finnish breast cancer and heart surgery patients' experiences but as all instruments, further validation is needed.

Following atomistic kinetics on experimental timescales with the kinetic Activation–Relaxation Technique

DOE PAGES

Mousseau, Normand; Béland, Laurent Karim; Brommer, Peter; ...

2014-12-24

The properties of materials, even at the atomic level, evolve on macroscopic time scales. Following this evolution through simulation has been a challenge for many years. For lattice-based activated diffusion, kinetic Monte Carlo has turned out to be an almost perfect solution. Various accelerated molecular dynamical schemes, for their part, have allowed the study on long time scale of relatively simple systems. There is still a desire and need, however, for methods able to handle complex materials such as alloys and disordered systems. In this paper, we review the kinetic Activation–Relaxation Technique (k-ART), one of a handful of off-lattice kineticmore » Monte Carlo methods, with on-the-fly cataloging, that have been proposed in the last few years.« less

DUAL STATE-PARAMETER UPDATING SCHEME ON A CONCEPTUAL HYDROLOGIC MODEL USING SEQUENTIAL MONTE CARLO FILTERS

NASA Astrophysics Data System (ADS)

Noh, Seong Jin; Tachikawa, Yasuto; Shiiba, Michiharu; Kim, Sunmin

Applications of data assimilation techniques have been widely used to improve upon the predictability of hydrologic modeling. Among various data assimilation techniques, sequential Monte Carlo (SMC) filters, known as "particle filters" provide the capability to handle non-linear and non-Gaussian state-space models. This paper proposes a dual state-parameter updating scheme (DUS) based on SMC methods to estimate both state and parameter variables of a hydrologic model. We introduce a kernel smoothing method for the robust estimation of uncertain model parameters in the DUS. The applicability of the dual updating scheme is illustrated using the implementation of the storage function model on a middle-sized Japanese catchment. We also compare performance results of DUS combined with various SMC methods, such as SIR, ASIR and RPF.

Coarse-grained computation for particle coagulation and sintering processes by linking Quadrature Method of Moments with Monte-Carlo

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

Zou Yu, E-mail: yzou@Princeton.ED; Kavousanakis, Michail E., E-mail: mkavousa@Princeton.ED; Kevrekidis, Ioannis G., E-mail: yannis@Princeton.ED

2010-07-20

The study of particle coagulation and sintering processes is important in a variety of research studies ranging from cell fusion and dust motion to aerosol formation applications. These processes are traditionally simulated using either Monte-Carlo methods or integro-differential equations for particle number density functions. In this paper, we present a computational technique for cases where we believe that accurate closed evolution equations for a finite number of moments of the density function exist in principle, but are not explicitly available. The so-called equation-free computational framework is then employed to numerically obtain the solution of these unavailable closed moment equations bymore » exploiting (through intelligent design of computational experiments) the corresponding fine-scale (here, Monte-Carlo) simulation. We illustrate the use of this method by accelerating the computation of evolving moments of uni- and bivariate particle coagulation and sintering through short simulation bursts of a constant-number Monte-Carlo scheme.« less

Semi-stochastic full configuration interaction quantum Monte Carlo

NASA Astrophysics Data System (ADS)

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

2012-02-01

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

Monte Carlo approaches to sampling forested tracts with lines or points

Treesearch

Harry T. Valentine; Jeffrey H. Gove; Timothy G. Gregoire

2001-01-01

Several line- and point-based sampling methods can be employed to estimate the aggregate dimensions of trees standing on a forested tract or pieces of coarse woody debris lying on the forest floor. Line methods include line intersect sampling, horizontal line sampling, and transect relascope sampling; point methods include variable- and fixed-radius plot sampling, and...

Importance Sampling Variance Reduction in GRESS ATMOSIM

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

Wakeford, Daniel Tyler

This document is intended to introduce the importance sampling method of variance reduction to a Geant4 user for application to neutral particle Monte Carlo transport through the atmosphere, as implemented in GRESS ATMOSIM.

Lognormal Approximations of Fault Tree Uncertainty Distributions.

PubMed

El-Shanawany, Ashraf Ben; Ardron, Keith H; Walker, Simon P

2018-01-26

Fault trees are used in reliability modeling to create logical models of fault combinations that can lead to undesirable events. The output of a fault tree analysis (the top event probability) is expressed in terms of the failure probabilities of basic events that are input to the model. Typically, the basic event probabilities are not known exactly, but are modeled as probability distributions: therefore, the top event probability is also represented as an uncertainty distribution. Monte Carlo methods are generally used for evaluating the uncertainty distribution, but such calculations are computationally intensive and do not readily reveal the dominant contributors to the uncertainty. In this article, a closed-form approximation for the fault tree top event uncertainty distribution is developed, which is applicable when the uncertainties in the basic events of the model are lognormally distributed. The results of the approximate method are compared with results from two sampling-based methods: namely, the Monte Carlo method and the Wilks method based on order statistics. It is shown that the closed-form expression can provide a reasonable approximation to results obtained by Monte Carlo sampling, without incurring the computational expense. The Wilks method is found to be a useful means of providing an upper bound for the percentiles of the uncertainty distribution while being computationally inexpensive compared with full Monte Carlo sampling. The lognormal approximation method and Wilks's method appear attractive, practical alternatives for the evaluation of uncertainty in the output of fault trees and similar multilinear models. © 2018 Society for Risk Analysis.

Distribution of the Determinant of the Sample Correlation Matrix: Monte Carlo Type One Error Rates.

ERIC Educational Resources Information Center

Reddon, John R.; And Others

1985-01-01

Computer sampling from a multivariate normal spherical population was used to evaluate the type one error rates for a test of sphericity based on the distribution of the determinant of the sample correlation matrix. (Author/LMO)

Integration of Fricke gel dosimetry with Ag nanoparticles for experimental dose enhancement determination in theranostics.

PubMed

Vedelago, J; Mattea, F; Valente, M

2018-03-01

The use and implementation of nanoparticles in medicine has grown exponentially in the last twenty years. Their main applications include drug delivery, theranostics, tissue engineering and magneto function. Dosimetry techniques can take advantage of inorganic nanoparticles properties and their combination with gel dosimetry techniques could be used as a first step for their later inclusion in radio-diagnostics or radiotherapy treatments. The present study presents preliminary results of properly synthesized and purified silver nanoparticles integration with Fricke gel dosimeters. Used nanoparticles presented mean sizes ranging from 2 to 20 nm, with a lognormal distribution. Xylenol orange concentration in Fricke gel dosimeter was adjust in order to allow sample's optical readout, accounting nanoparticles plasmon. Dose enhancement was assessed irradiating dosimeters setting X-ray beams energies below and above silver K-edge. Monte Carlo simulations were used to estimate the dose enhancement in the experiments and compare with the trend obtained in the experimental results. Copyright © 2018 Elsevier Ltd. All rights reserved.

Localisation of an Unknown Number of Land Mines Using a Network of Vapour Detectors

PubMed Central

Chhadé, Hiba Haj; Abdallah, Fahed; Mougharbel, Imad; Gning, Amadou; Julier, Simon; Mihaylova, Lyudmila

2014-01-01

We consider the problem of localising an unknown number of land mines using concentration information provided by a wireless sensor network. A number of vapour sensors/detectors, deployed in the region of interest, are able to detect the concentration of the explosive vapours, emanating from buried land mines. The collected data is communicated to a fusion centre. Using a model for the transport of the explosive chemicals in the air, we determine the unknown number of sources using a Principal Component Analysis (PCA)-based technique. We also formulate the inverse problem of determining the positions and emission rates of the land mines using concentration measurements provided by the wireless sensor network. We present a solution for this problem based on a probabilistic Bayesian technique using a Markov chain Monte Carlo sampling scheme, and we compare it to the least squares optimisation approach. Experiments conducted on simulated data show the effectiveness of the proposed approach. PMID:25384008

Gaussian process regression for sensor networks under localization uncertainty

USGS Publications Warehouse

Jadaliha, M.; Xu, Yunfei; Choi, Jongeun; Johnson, N.S.; Li, Weiming

2013-01-01

In this paper, we formulate Gaussian process regression with observations under the localization uncertainty due to the resource-constrained sensor networks. In our formulation, effects of observations, measurement noise, localization uncertainty, and prior distributions are all correctly incorporated in the posterior predictive statistics. The analytically intractable posterior predictive statistics are proposed to be approximated by two techniques, viz., Monte Carlo sampling and Laplace's method. Such approximation techniques have been carefully tailored to our problems and their approximation error and complexity are analyzed. Simulation study demonstrates that the proposed approaches perform much better than approaches without considering the localization uncertainty properly. Finally, we have applied the proposed approaches on the experimentally collected real data from a dye concentration field over a section of a river and a temperature field of an outdoor swimming pool to provide proof of concept tests and evaluate the proposed schemes in real situations. In both simulation and experimental results, the proposed methods outperform the quick-and-dirty solutions often used in practice.

A Monte Carlo approach applied to ultrasonic non-destructive testing

NASA Astrophysics Data System (ADS)

Mosca, I.; Bilgili, F.; Meier, T.; Sigloch, K.

2012-04-01

Non-destructive testing based on ultrasound allows us to detect, characterize and size discrete flaws in geotechnical and architectural structures and materials. This information is needed to determine whether such flaws can be tolerated in future service. In typical ultrasonic experiments, only the first-arriving P-wave is interpreted, and the remainder of the recorded waveform is neglected. Our work aims at understanding surface waves, which are strong signals in the later wave train, with the ultimate goal of full waveform tomography. At present, even the structural estimation of layered media is still challenging because material properties of the samples can vary widely, and good initial models for inversion do not often exist. The aim of the present study is to combine non-destructive testing with a theoretical data analysis and hence to contribute to conservation strategies of archaeological and architectural structures. We analyze ultrasonic waveforms measured at the surface of a variety of samples, and define the behaviour of surface waves in structures of increasing complexity. The tremendous potential of ultrasonic surface waves becomes an advantage only if numerical forward modelling tools are available to describe the waveforms accurately. We compute synthetic full seismograms as well as group and phase velocities for the data. We invert them for the elastic properties of the sample via a global search of the parameter space, using the Neighbourhood Algorithm. Such a Monte Carlo approach allows us to perform a complete uncertainty and resolution analysis, but the computational cost is high and increases quickly with the number of model parameters. Therefore it is practical only for defining the seismic properties of media with a limited number of degrees of freedom, such as layered structures. We have applied this approach to both synthetic layered structures and real samples. The former contributed to benchmark the propagation of ultrasonic surface waves in typical materials tested with a non-destructive technique (e.g., marble, unweathered and weathered concrete and natural stone).

A Monte Carlo approach applied to ultrasonic non-destructive testing

NASA Astrophysics Data System (ADS)

Mosca, I.; Bilgili, F.; Meier, T. M.; Sigloch, K.

2011-12-01

Non-destructive testing based on ultrasound allows us to detect, characterize and size discrete flaws in geotechnical and engineering structures and materials. This information is needed to determine whether such flaws can be tolerated in future service. In typical ultrasonic experiments, only the first-arriving P-wave is interpreted, and the remainder of the recorded waveform is neglected. Our work aims at understanding surface waves, which are strong signals in the later wave train, with the ultimate goal of full waveform tomography. At present, even the structural estimation of layered media is still challenging because material properties of the samples can vary widely, and good initial models for inversion do not often exist. The aim of the present study is to analyze ultrasonic waveforms measured at the surface of Plexiglas and rock samples, and to define the behaviour of surface waves in structures of increasing complexity. The tremendous potential of ultrasonic surface waves becomes an advantage only if numerical forward modelling tools are available to describe the waveforms accurately. We compute synthetic full seismograms as well as group and phase velocities for the data. We invert them for the elastic properties of the sample via a global search of the parameter space, using the Neighbourhood Algorithm. Such a Monte Carlo approach allows us to perform a complete uncertainty and resolution analysis, but the computational cost is high and increases quickly with the number of model parameters. Therefore it is practical only for defining the seismic properties of media with a limited number of degrees of freedom, such as layered structures. We have applied this approach to both synthetic layered structures and real samples. The former contributed to benchmark the propagation of ultrasonic surface waves in typical materials tested with a non-destructive technique (e.g., marble, unweathered and weathered concrete and natural stone).

Tunable Coarse Graining for Monte Carlo Simulations of Proteins via Smoothed Energy Tables: Direct and Exchange Simulations

PubMed Central

2015-01-01

Many commonly used coarse-grained models for proteins are based on simplified interaction sites and consequently may suffer from significant limitations, such as the inability to properly model protein secondary structure without the addition of restraints. Recent work on a benzene fluid (LettieriS.; ZuckermanD. M.J. Comput. Chem.2012, 33, 268−27522120971) suggested an alternative strategy of tabulating and smoothing fully atomistic orientation-dependent interactions among rigid molecules or fragments. Here we report our initial efforts to apply this approach to the polar and covalent interactions intrinsic to polypeptides. We divide proteins into nearly rigid fragments, construct distance and orientation-dependent tables of the atomistic interaction energies between those fragments, and apply potential energy smoothing techniques to those tables. The amount of smoothing can be adjusted to give coarse-grained models that range from the underlying atomistic force field all the way to a bead-like coarse-grained model. For a moderate amount of smoothing, the method is able to preserve about 70–90% of the α-helical structure while providing a factor of 3–10 improvement in sampling per unit computation time (depending on how sampling is measured). For a greater amount of smoothing, multiple folding–unfolding transitions of the peptide were observed, along with a factor of 10–100 improvement in sampling per unit computation time, although the time spent in the unfolded state was increased compared with less smoothed simulations. For a β hairpin, secondary structure is also preserved, albeit for a narrower range of the smoothing parameter and, consequently, for a more modest improvement in sampling. We have also applied the new method in a “resolution exchange” setting, in which each replica runs a Monte Carlo simulation with a different degree of smoothing. We obtain exchange rates that compare favorably to our previous efforts at resolution exchange (LymanE.; ZuckermanD. M.J. Chem. Theory Comput.2006, 2, 656−666). PMID:25400525

Monte Carlo: in the beginning and some great expectations

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

Metropolis, N.

1985-01-01

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

Calculating Potential Energy Curves with Quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Powell, Andrew D.; Dawes, Richard

2014-06-01

Quantum Monte Carlo (QMC) is a computational technique that can be applied to the electronic Schrödinger equation for molecules. QMC methods such as Variational Monte Carlo (VMC) and Diffusion Monte Carlo (DMC) have demonstrated the capability of capturing large fractions of the correlation energy, thus suggesting their possible use for high-accuracy quantum chemistry calculations. QMC methods scale particularly well with respect to parallelization making them an attractive consideration in anticipation of next-generation computing architectures which will involve massive parallelization with millions of cores. Due to the statistical nature of the approach, in contrast to standard quantum chemistry methods, uncertainties (error-bars) are associated with each calculated energy. This study focuses on the cost, feasibility and practical application of calculating potential energy curves for small molecules with QMC methods. Trial wave functions were constructed with the multi-configurational self-consistent field (MCSCF) method from GAMESS-US.[1] The CASINO Monte Carlo quantum chemistry package [2] was used for all of the DMC calculations. An overview of our progress in this direction will be given. References: M. W. Schmidt et al. J. Comput. Chem. 14, 1347 (1993). R. J. Needs et al. J. Phys.: Condensed Matter 22, 023201 (2010).

Model Reduction via Principe Component Analysis and Markov Chain Monte Carlo (MCMC) Methods

NASA Astrophysics Data System (ADS)

Gong, R.; Chen, J.; Hoversten, M. G.; Luo, J.

2011-12-01

Geophysical and hydrogeological inverse problems often include a large number of unknown parameters, ranging from hundreds to millions, depending on parameterization and problems undertaking. This makes inverse estimation and uncertainty quantification very challenging, especially for those problems in two- or three-dimensional spatial domains. Model reduction technique has the potential of mitigating the curse of dimensionality by reducing total numbers of unknowns while describing the complex subsurface systems adequately. In this study, we explore the use of principal component analysis (PCA) and Markov chain Monte Carlo (MCMC) sampling methods for model reduction through the use of synthetic datasets. We compare the performances of three different but closely related model reduction approaches: (1) PCA methods with geometric sampling (referred to as 'Method 1'), (2) PCA methods with MCMC sampling (referred to as 'Method 2'), and (3) PCA methods with MCMC sampling and inclusion of random effects (referred to as 'Method 3'). We consider a simple convolution model with five unknown parameters as our goal is to understand and visualize the advantages and disadvantages of each method by comparing their inversion results with the corresponding analytical solutions. We generated synthetic data with noise added and invert them under two different situations: (1) the noised data and the covariance matrix for PCA analysis are consistent (referred to as the unbiased case), and (2) the noise data and the covariance matrix are inconsistent (referred to as biased case). In the unbiased case, comparison between the analytical solutions and the inversion results show that all three methods provide good estimates of the true values and Method 1 is computationally more efficient. In terms of uncertainty quantification, Method 1 performs poorly because of relatively small number of samples obtained, Method 2 performs best, and Method 3 overestimates uncertainty due to inclusion of random effects. However, in the biased case, only Method 3 correctly estimates all the unknown parameters, and both Methods 1 and 2 provide wrong values for the biased parameters. The synthetic case study demonstrates that if the covariance matrix for PCA analysis is inconsistent with true models, the PCA methods with geometric or MCMC sampling will provide incorrect estimates.

Latin hypercube sampling and geostatistical modeling of spatial uncertainty in a spatially explicit forest landscape model simulation

Treesearch

Chonggang Xu; Hong S. He; Yuanman Hu; Yu Chang; Xiuzhen Li; Rencang Bu

2005-01-01

Geostatistical stochastic simulation is always combined with Monte Carlo method to quantify the uncertainty in spatial model simulations. However, due to the relatively long running time of spatially explicit forest models as a result of their complexity, it is always infeasible to generate hundreds or thousands of Monte Carlo simulations. Thus, it is of great...

Non-Parametric Collision Probability for Low-Velocity Encounters

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

2007-01-01

An implicit, but not necessarily obvious, assumption in all of the current techniques for assessing satellite collision probability is that the relative position uncertainty is perfectly correlated in time. If there is any mis-modeling of the dynamics in the propagation of the relative position error covariance matrix, time-wise de-correlation of the uncertainty will increase the probability of collision over a given time interval. The paper gives some examples that illustrate this point. This paper argues that, for the present, Monte Carlo analysis is the best available tool for handling low-velocity encounters, and suggests some techniques for addressing the issues just described. One proposal is for the use of a non-parametric technique that is widely used in actuarial and medical studies. The other suggestion is that accurate process noise models be used in the Monte Carlo trials to which the non-parametric estimate is applied. A further contribution of this paper is a description of how the time-wise decorrelation of uncertainty increases the probability of collision.

A study of two statistical methods as applied to shuttle solid rocket booster expenditures

NASA Technical Reports Server (NTRS)

Perlmutter, M.; Huang, Y.; Graves, M.

1974-01-01

The state probability technique and the Monte Carlo technique are applied to finding shuttle solid rocket booster expenditure statistics. For a given attrition rate per launch, the probable number of boosters needed for a given mission of 440 launches is calculated. Several cases are considered, including the elimination of the booster after a maximum of 20 consecutive launches. Also considered is the case where the booster is composed of replaceable components with independent attrition rates. A simple cost analysis is carried out to indicate the number of boosters to build initially, depending on booster costs. Two statistical methods were applied in the analysis: (1) state probability method which consists of defining an appropriate state space for the outcome of the random trials, and (2) model simulation method or the Monte Carlo technique. It was found that the model simulation method was easier to formulate while the state probability method required less computing time and was more accurate.

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

NASA Astrophysics Data System (ADS)

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

2015-03-01

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

Accurate simulations of helium pick-up experiments using a rejection-free Monte Carlo method

NASA Astrophysics Data System (ADS)

Dutra, Matthew; Hinde, Robert

2018-04-01

In this paper, we present Monte Carlo simulations of helium droplet pick-up experiments with the intention of developing a robust and accurate theoretical approach for interpreting experimental helium droplet calorimetry data. Our approach is capable of capturing the evaporative behavior of helium droplets following dopant acquisition, allowing for a more realistic description of the pick-up process. Furthermore, we circumvent the traditional assumption of bulk helium behavior by utilizing density functional calculations of the size-dependent helium droplet chemical potential. The results of this new Monte Carlo technique are compared to commonly used Poisson pick-up statistics for simulations that reflect a broad range of experimental parameters. We conclude by offering an assessment of both of these theoretical approaches in the context of our observed results.

Four decades of implicit Monte Carlo

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

Wollaber, Allan B.

In 1971, Fleck and Cummings derived a system of equations to enable robust Monte Carlo simulations of time-dependent, thermal radiative transfer problems. Denoted the “Implicit Monte Carlo” (IMC) equations, their solution remains the de facto standard of high-fidelity radiative transfer simulations. Over the course of 44 years, their numerical properties have become better understood, and accuracy enhancements, novel acceleration methods, and variance reduction techniques have been suggested. In this review, we rederive the IMC equations—explicitly highlighting assumptions as they are made—and outfit the equations with a Monte Carlo interpretation. We put the IMC equations in context with other approximate formsmore » of the radiative transfer equations and present a new demonstration of their equivalence to another well-used linearization solved with deterministic transport methods for frequency-independent problems. We discuss physical and numerical limitations of the IMC equations for asymptotically small time steps, stability characteristics and the potential of maximum principle violations for large time steps, and solution behaviors in an asymptotically thick diffusive limit. We provide a new stability analysis for opacities with general monomial dependence on temperature. Here, we consider spatial accuracy limitations of the IMC equations and discussion acceleration and variance reduction techniques.« less

Boiling point determination using adiabatic Gibbs ensemble Monte Carlo simulations: Application to metals described by embedded-atom potentials

NASA Astrophysics Data System (ADS)

Gelb, Lev D.; Chakraborty, Somendra Nath

2011-12-01

The normal boiling points are obtained for a series of metals as described by the "quantum-corrected Sutton Chen" (qSC) potentials [S.-N. Luo, T. J. Ahrens, T. Çağın, A. Strachan, W. A. Goddard III, and D. C. Swift, Phys. Rev. B 68, 134206 (2003)]. Instead of conventional Monte Carlo simulations in an isothermal or expanded ensemble, simulations were done in the constant-NPH adabatic variant of the Gibbs ensemble technique as proposed by Kristóf and Liszi [Chem. Phys. Lett. 261, 620 (1996)]. This simulation technique is shown to be a precise tool for direct calculation of boiling temperatures in high-boiling fluids, with results that are almost completely insensitive to system size or other arbitrary parameters as long as the potential truncation is handled correctly. Results obtained were validated using conventional NVT-Gibbs ensemble Monte Carlo simulations. The qSC predictions for boiling temperatures are found to be reasonably accurate, but substantially underestimate the enthalpies of vaporization in all cases. This appears to be largely due to the systematic overestimation of dimer binding energies by this family of potentials, which leads to an unsatisfactory description of the vapor phase.

Four decades of implicit Monte Carlo

DOE PAGES

Wollaber, Allan B.

2016-02-23

In 1971, Fleck and Cummings derived a system of equations to enable robust Monte Carlo simulations of time-dependent, thermal radiative transfer problems. Denoted the “Implicit Monte Carlo” (IMC) equations, their solution remains the de facto standard of high-fidelity radiative transfer simulations. Over the course of 44 years, their numerical properties have become better understood, and accuracy enhancements, novel acceleration methods, and variance reduction techniques have been suggested. In this review, we rederive the IMC equations—explicitly highlighting assumptions as they are made—and outfit the equations with a Monte Carlo interpretation. We put the IMC equations in context with other approximate formsmore » of the radiative transfer equations and present a new demonstration of their equivalence to another well-used linearization solved with deterministic transport methods for frequency-independent problems. We discuss physical and numerical limitations of the IMC equations for asymptotically small time steps, stability characteristics and the potential of maximum principle violations for large time steps, and solution behaviors in an asymptotically thick diffusive limit. We provide a new stability analysis for opacities with general monomial dependence on temperature. Here, we consider spatial accuracy limitations of the IMC equations and discussion acceleration and variance reduction techniques.« less

Estimating numbers of females with cubs-of-the-year in the Yellowstone grizzly bear population

USGS Publications Warehouse

Keating, K.A.; Schwartz, C.C.; Haroldson, M.A.; Moody, D.

2001-01-01

For grizzly bears (Ursus arctos horribilis) in the Greater Yellowstone Ecosystem (GYE), minimum population size and allowable numbers of human-caused mortalities have been calculated as a function of the number of unique females with cubs-of-the-year (FCUB) seen during a 3- year period. This approach underestimates the total number of FCUB, thereby biasing estimates of population size and sustainable mortality. Also, it does not permit calculation of valid confidence bounds. Many statistical methods can resolve or mitigate these problems, but there is no universal best method. Instead, relative performances of different methods can vary with population size, sample size, and degree of heterogeneity among sighting probabilities for individual animals. We compared 7 nonparametric estimators, using Monte Carlo techniques to assess performances over the range of sampling conditions deemed plausible for the Yellowstone population. Our goal was to estimate the number of FCUB present in the population each year. Our evaluation differed from previous comparisons of such estimators by including sample coverage methods and by treating individual sightings, rather than sample periods, as the sample unit. Consequently, our conclusions also differ from earlier studies. Recommendations regarding estimators and necessary sample sizes are presented, together with estimates of annual numbers of FCUB in the Yellowstone population with bootstrap confidence bounds.

Performance of Modified Test Statistics in Covariance and Correlation Structure Analysis under Conditions of Multivariate Nonnormality.

ERIC Educational Resources Information Center

Fouladi, Rachel T.

2000-01-01

Provides an overview of standard and modified normal theory and asymptotically distribution-free covariance and correlation structure analysis techniques and details Monte Carlo simulation results on Type I and Type II error control. Demonstrates through the simulation that robustness and nonrobustness of structure analysis techniques vary as a…

Spatial interpolation of forest conditions using co-conditional geostatistical simulation

Treesearch

H. Todd Mowrer

2000-01-01

In recent work the author used the geostatistical Monte Carlo technique of sequential Gaussian simulation (s.G.s.) to investigate uncertainty in a GIS analysis of potential old-growth forest areas. The current study compares this earlier technique to that of co-conditional simulation, wherein the spatial cross-correlations between variables are included. As in the...

Destruction or Loss of School Property: Analysis and Suggestions for Improvement of School Security.

ERIC Educational Resources Information Center

Nelken, Ira; Kline, Sam

In recent years the costs of school vandalism and the incidence of vandalism in the public schools have been rising. The study concerns itself with the application of production functions, Monte Carlo techniques, and Shannon's model of information theory to determine the most efficient use of preventive vandalism techniques in a large school…

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

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

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

Stochastic Investigation of Natural Frequency for Functionally Graded Plates

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Manual hierarchical clustering of regional geochemical data using a Bayesian finite mixture model

USGS Publications Warehouse

Ellefsen, Karl J.; Smith, David

2016-01-01

Interpretation of regional scale, multivariate geochemical data is aided by a statistical technique called “clustering.” We investigate a particular clustering procedure by applying it to geochemical data collected in the State of Colorado, United States of America. The clustering procedure partitions the field samples for the entire survey area into two clusters. The field samples in each cluster are partitioned again to create two subclusters, and so on. This manual procedure generates a hierarchy of clusters, and the different levels of the hierarchy show geochemical and geological processes occurring at different spatial scales. Although there are many different clustering methods, we use Bayesian finite mixture modeling with two probability distributions, which yields two clusters. The model parameters are estimated with Hamiltonian Monte Carlo sampling of the posterior probability density function, which usually has multiple modes. Each mode has its own set of model parameters; each set is checked to ensure that it is consistent both with the data and with independent geologic knowledge. The set of model parameters that is most consistent with the independent geologic knowledge is selected for detailed interpretation and partitioning of the field samples.

Unbiased reduced density matrices and electronic properties from full configuration interaction quantum Monte Carlo.

PubMed

Overy, Catherine; Booth, George H; Blunt, N S; Shepherd, James J; Cleland, Deidre; Alavi, Ali

2014-12-28

Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties of electronic systems. Here, we investigate an approach for the sampling of unbiased reduced density matrices within the full configuration interaction quantum Monte Carlo dynamic, which requires only small computational overheads. This is achieved via an independent replica population of walkers in the dynamic, sampled alongside the original population. The resulting reduced density matrices are free from systematic error (beyond those present via constraints on the dynamic itself) and can be used to compute a variety of expectation values and properties, with rapid convergence to an exact limit. A quasi-variational energy estimate derived from these density matrices is proposed as an accurate alternative to the projected estimator for multiconfigurational wavefunctions, while its variational property could potentially lend itself to accurate extrapolation approaches in larger systems.

Unbiased reduced density matrices and electronic properties from full configuration interaction quantum Monte Carlo

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

Overy, Catherine; Blunt, N. S.; Shepherd, James J.

2014-12-28

Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties of electronic systems. Here, we investigate an approach for the sampling of unbiased reduced density matrices within the full configuration interaction quantum Monte Carlo dynamic, which requires only small computational overheads. This is achieved via an independent replica population of walkers in the dynamic, sampled alongside the original population. The resulting reduced density matrices are free from systematic error (beyond those present via constraints on the dynamicmore » itself) and can be used to compute a variety of expectation values and properties, with rapid convergence to an exact limit. A quasi-variational energy estimate derived from these density matrices is proposed as an accurate alternative to the projected estimator for multiconfigurational wavefunctions, while its variational property could potentially lend itself to accurate extrapolation approaches in larger systems.« less

Path integral pricing of Wasabi option in the Black-Scholes model

NASA Astrophysics Data System (ADS)

Cassagnes, Aurelien; Chen, Yu; Ohashi, Hirotada

2014-11-01

In this paper, using path integral techniques, we derive a formula for a propagator arising in the study of occupation time derivatives. Using this result we derive a fair price for the case of the cumulative Parisian option. After confirming the validity of the derived result using Monte Carlo simulation, a new type of heavily path dependent derivative product is investigated. We derive an approximation for our so-called Wasabi option fair price and check the accuracy of our result with a Monte Carlo simulation.

Simulation tools for scattering corrections in spectrally resolved x-ray computed tomography using McXtrace

NASA Astrophysics Data System (ADS)

Busi, Matteo; Olsen, Ulrik L.; Knudsen, Erik B.; Frisvad, Jeppe R.; Kehres, Jan; Dreier, Erik S.; Khalil, Mohamad; Haldrup, Kristoffer

2018-03-01

Spectral computed tomography is an emerging imaging method that involves using recently developed energy discriminating photon-counting detectors (PCDs). This technique enables measurements at isolated high-energy ranges, in which the dominating undergoing interaction between the x-ray and the sample is the incoherent scattering. The scattered radiation causes a loss of contrast in the results, and its correction has proven to be a complex problem, due to its dependence on energy, material composition, and geometry. Monte Carlo simulations can utilize a physical model to estimate the scattering contribution to the signal, at the cost of high computational time. We present a fast Monte Carlo simulation tool, based on McXtrace, to predict the energy resolved radiation being scattered and absorbed by objects of complex shapes. We validate the tool through measurements using a CdTe single PCD (Multix ME-100) and use it for scattering correction in a simulation of a spectral CT. We found the correction to account for up to 7% relative amplification in the reconstructed linear attenuation. It is a useful tool for x-ray CT to obtain a more accurate material discrimination, especially in the high-energy range, where the incoherent scattering interactions become prevailing (>50 keV).

Household water use and conservation models using Monte Carlo techniques

NASA Astrophysics Data System (ADS)

Cahill, R.; Lund, J. R.; DeOreo, B.; Medellín-Azuara, J.

2013-10-01

The increased availability of end use measurement studies allows for mechanistic and detailed approaches to estimating household water demand and conservation potential. This study simulates water use in a single-family residential neighborhood using end-water-use parameter probability distributions generated from Monte Carlo sampling. This model represents existing water use conditions in 2010 and is calibrated to 2006-2011 metered data. A two-stage mixed integer optimization model is then developed to estimate the least-cost combination of long- and short-term conservation actions for each household. This least-cost conservation model provides an estimate of the upper bound of reasonable conservation potential for varying pricing and rebate conditions. The models were adapted from previous work in Jordan and are applied to a neighborhood in San Ramon, California in the eastern San Francisco Bay Area. The existing conditions model produces seasonal use results very close to the metered data. The least-cost conservation model suggests clothes washer rebates are among most cost-effective rebate programs for indoor uses. Retrofit of faucets and toilets is also cost-effective and holds the highest potential for water savings from indoor uses. This mechanistic modeling approach can improve understanding of water demand and estimate cost-effectiveness of water conservation programs.

Household water use and conservation models using Monte Carlo techniques

NASA Astrophysics Data System (ADS)

Cahill, R.; Lund, J. R.; DeOreo, B.; Medellín-Azuara, J.

2013-04-01

The increased availability of water end use measurement studies allows for more mechanistic and detailed approaches to estimating household water demand and conservation potential. This study uses, probability distributions for parameters affecting water use estimated from end use studies and randomly sampled in Monte Carlo iterations to simulate water use in a single-family residential neighborhood. This model represents existing conditions and is calibrated to metered data. A two-stage mixed integer optimization model is then developed to estimate the least-cost combination of long- and short-term conservation actions for each household. This least-cost conservation model provides an estimate of the upper bound of reasonable conservation potential for varying pricing and rebate conditions. The models were adapted from previous work in Jordan and are applied to a neighborhood in San Ramon, California in eastern San Francisco Bay Area. The existing conditions model produces seasonal use results very close to the metered data. The least-cost conservation model suggests clothes washer rebates are among most cost-effective rebate programs for indoor uses. Retrofit of faucets and toilets is also cost effective and holds the highest potential for water savings from indoor uses. This mechanistic modeling approach can improve understanding of water demand and estimate cost-effectiveness of water conservation programs.

Inverse Monte Carlo in a multilayered tissue model: merging diffuse reflectance spectroscopy and laser Doppler flowmetry.

PubMed

Fredriksson, Ingemar; Burdakov, Oleg; Larsson, Marcus; Strömberg, Tomas

2013-12-01

The tissue fraction of red blood cells (RBCs) and their oxygenation and speed-resolved perfusion are estimated in absolute units by combining diffuse reflectance spectroscopy (DRS) and laser Doppler flowmetry (LDF). The DRS spectra (450 to 850 nm) are assessed at two source-detector separations (0.4 and 1.2 mm), allowing for a relative calibration routine, whereas LDF spectra are assessed at 1.2 mm in the same fiber-optic probe. Data are analyzed using nonlinear optimization in an inverse Monte Carlo technique by applying an adaptive multilayered tissue model based on geometrical, scattering, and absorbing properties, as well as RBC flow-speed information. Simulations of 250 tissue-like models including up to 2000 individual blood vessels were used to evaluate the method. The absolute root mean square (RMS) deviation between estimated and true oxygenation was 4.1 percentage units, whereas the relative RMS deviations for the RBC tissue fraction and perfusion were 19% and 23%, respectively. Examples of in vivo measurements on forearm and foot during common provocations are presented. The method offers several advantages such as simultaneous quantification of RBC tissue fraction and oxygenation and perfusion from the same, predictable, sampling volume. The perfusion estimate is speed resolved, absolute (% RBC×mm/s), and more accurate due to the combination with DRS.

Inverse Monte Carlo in a multilayered tissue model: merging diffuse reflectance spectroscopy and laser Doppler flowmetry

NASA Astrophysics Data System (ADS)

Fredriksson, Ingemar; Burdakov, Oleg; Larsson, Marcus; Strömberg, Tomas

2013-12-01

The tissue fraction of red blood cells (RBCs) and their oxygenation and speed-resolved perfusion are estimated in absolute units by combining diffuse reflectance spectroscopy (DRS) and laser Doppler flowmetry (LDF). The DRS spectra (450 to 850 nm) are assessed at two source-detector separations (0.4 and 1.2 mm), allowing for a relative calibration routine, whereas LDF spectra are assessed at 1.2 mm in the same fiber-optic probe. Data are analyzed using nonlinear optimization in an inverse Monte Carlo technique by applying an adaptive multilayered tissue model based on geometrical, scattering, and absorbing properties, as well as RBC flow-speed information. Simulations of 250 tissue-like models including up to 2000 individual blood vessels were used to evaluate the method. The absolute root mean square (RMS) deviation between estimated and true oxygenation was 4.1 percentage units, whereas the relative RMS deviations for the RBC tissue fraction and perfusion were 19% and 23%, respectively. Examples of in vivo measurements on forearm and foot during common provocations are presented. The method offers several advantages such as simultaneous quantification of RBC tissue fraction and oxygenation and perfusion from the same, predictable, sampling volume. The perfusion estimate is speed resolved, absolute (% RBC×mm/s), and more accurate due to the combination with DRS.

Engineering Risk Assessment of Space Thruster Challenge Problem

NASA Technical Reports Server (NTRS)

Mathias, Donovan L.; Mattenberger, Christopher J.; Go, Susie

2014-01-01

The Engineering Risk Assessment (ERA) team at NASA Ames Research Center utilizes dynamic models with linked physics-of-failure analyses to produce quantitative risk assessments of space exploration missions. This paper applies the ERA approach to the baseline and extended versions of the PSAM Space Thruster Challenge Problem, which investigates mission risk for a deep space ion propulsion system with time-varying thruster requirements and operations schedules. The dynamic mission is modeled using a combination of discrete and continuous-time reliability elements within the commercially available GoldSim software. Loss-of-mission (LOM) probability results are generated via Monte Carlo sampling performed by the integrated model. Model convergence studies are presented to illustrate the sensitivity of integrated LOM results to the number of Monte Carlo trials. A deterministic risk model was also built for the three baseline and extended missions using the Ames Reliability Tool (ART), and results are compared to the simulation results to evaluate the relative importance of mission dynamics. The ART model did a reasonable job of matching the simulation models for the baseline case, while a hybrid approach using offline dynamic models was required for the extended missions. This study highlighted that state-of-the-art techniques can adequately adapt to a range of dynamic problems.

Enhancing hydrologic data assimilation by evolutionary Particle Filter and Markov Chain Monte Carlo

NASA Astrophysics Data System (ADS)

Abbaszadeh, Peyman; Moradkhani, Hamid; Yan, Hongxiang

2018-01-01

Particle Filters (PFs) have received increasing attention by researchers from different disciplines including the hydro-geosciences, as an effective tool to improve model predictions in nonlinear and non-Gaussian dynamical systems. The implication of dual state and parameter estimation using the PFs in hydrology has evolved since 2005 from the PF-SIR (sampling importance resampling) to PF-MCMC (Markov Chain Monte Carlo), and now to the most effective and robust framework through evolutionary PF approach based on Genetic Algorithm (GA) and MCMC, the so-called EPFM. In this framework, the prior distribution undergoes an evolutionary process based on the designed mutation and crossover operators of GA. The merit of this approach is that the particles move to an appropriate position by using the GA optimization and then the number of effective particles is increased by means of MCMC, whereby the particle degeneracy is avoided and the particle diversity is improved. In this study, the usefulness and effectiveness of the proposed EPFM is investigated by applying the technique on a conceptual and highly nonlinear hydrologic model over four river basins located in different climate and geographical regions of the United States. Both synthetic and real case studies demonstrate that the EPFM improves both the state and parameter estimation more effectively and reliably as compared with the PF-MCMC.

Numerically Exact Long Time Magnetization Dynamics Near the Nonequilibrium Kondo Regime

NASA Astrophysics Data System (ADS)

Cohen, Guy; Gull, Emanuel; Reichman, David; Millis, Andrew; Rabani, Eran

2013-03-01

The dynamical and steady-state spin response of the nonequilibrium Anderson impurity model to magnetic fields, bias voltages, and temperature is investigated by a numerically exact method which allows access to unprecedentedly long times. The method is based on using real, continuous time bold Monte Carlo techniques--quantum Monte Carlo sampling of diagrammatic corrections to a partial re-summation--in order to compute the kernel of a memory function, which is then used to determine the reduced density matrix. The method owes its effectiveness to the fact that the memory kernel is dominated by relatively short-time properties even when the system's dynamics are long-ranged. We make predictions regarding the non-monotonic temperature dependence of the system at high bias voltage and the oscillatory quench dynamics at high magnetic fields. We also discuss extensions of the method to the computation of transport properties and correlation functions, and its suitability as an impurity solver free from the need for analytical continuation in the context of dynamical mean field theory. This work is supported by the US Department of Energy under grant DE-SC0006613, by NSF-DMR-1006282 and by the US-Israel Binational Science Foundation. GC is grateful to the Yad Hanadiv-Rothschild Foundation for the award of a Rothschild Fellowship.

Acceleration of Monte Carlo SPECT simulation using convolution-based forced detection

NASA Astrophysics Data System (ADS)

de Jong, H. W. A. M.; Slijpen, E. T. P.; Beekman, F. J.

2001-02-01

Monte Carlo (MC) simulation is an established tool to calculate photon transport through tissue in Emission Computed Tomography (ECT). Since the first appearance of MC a large variety of variance reduction techniques (VRT) have been introduced to speed up these notoriously slow simulations. One example of a very effective and established VRT is known as forced detection (FD). In standard FD the path from the photon's scatter position to the camera is chosen stochastically from the appropriate probability density function (PDF), modeling the distance-dependent detector response. In order to speed up MC the authors propose a convolution-based FD (CFD) which involves replacing the sampling of the PDF by a convolution with a kernel which depends on the position of the scatter event. The authors validated CFD for parallel-hole Single Photon Emission Computed Tomography (SPECT) using a digital thorax phantom. Comparison of projections estimated with CFD and standard FD shows that both estimates converge to practically identical projections (maximum bias 0.9% of peak projection value), despite the slightly different photon paths used in CFD and standard FD. Projections generated with CFD converge, however, to a noise-free projection up to one or two orders of magnitude faster, which is extremely useful in many applications such as model-based image reconstruction.

Evaluation of gamma-ray attenuation properties of bismuth borate glass systems using Monte Carlo method

NASA Astrophysics Data System (ADS)

Tarim, Urkiye Akar; Ozmutlu, Emin N.; Yalcin, Sezai; Gundogdu, Ozcan; Bradley, D. A.; Gurler, Orhan

2017-11-01

A Monte Carlo method was developed to investigate radiation shielding properties of bismuth borate glass. The mass attenuation coefficients and half-value layer parameters were determined for different fractional amounts of Bi2O3 in the glass samples for the 356, 662, 1173 and 1332 keV photon energies. A comparison of the theoretical and experimental attenuation coefficients is presented.

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

PubMed

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

2012-09-25

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

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

PubMed Central

2012-01-01

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

A smart Monte Carlo procedure for production costing and uncertainty analysis

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

Parker, C.; Stremel, J.

1996-11-01

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

Uncertainty Analysis and Parameter Estimation For Nearshore Hydrodynamic Models

NASA Astrophysics Data System (ADS)

Ardani, S.; Kaihatu, J. M.

2012-12-01

Numerical models represent deterministic approaches used for the relevant physical processes in the nearshore. Complexity of the physics of the model and uncertainty involved in the model inputs compel us to apply a stochastic approach to analyze the robustness of the model. The Bayesian inverse problem is one powerful way to estimate the important input model parameters (determined by apriori sensitivity analysis) and can be used for uncertainty analysis of the outputs. Bayesian techniques can be used to find the range of most probable parameters based on the probability of the observed data and the residual errors. In this study, the effect of input data involving lateral (Neumann) boundary conditions, bathymetry and off-shore wave conditions on nearshore numerical models are considered. Monte Carlo simulation is applied to a deterministic numerical model (the Delft3D modeling suite for coupled waves and flow) for the resulting uncertainty analysis of the outputs (wave height, flow velocity, mean sea level and etc.). Uncertainty analysis of outputs is performed by random sampling from the input probability distribution functions and running the model as required until convergence to the consistent results is achieved. The case study used in this analysis is the Duck94 experiment, which was conducted at the U.S. Army Field Research Facility at Duck, North Carolina, USA in the fall of 1994. The joint probability of model parameters relevant for the Duck94 experiments will be found using the Bayesian approach. We will further show that, by using Bayesian techniques to estimate the optimized model parameters as inputs and applying them for uncertainty analysis, we can obtain more consistent results than using the prior information for input data which means that the variation of the uncertain parameter will be decreased and the probability of the observed data will improve as well. Keywords: Monte Carlo Simulation, Delft3D, uncertainty analysis, Bayesian techniques, MCMC

Improving the sampling efficiency of Monte Carlo molecular simulations: an evolutionary approach

NASA Astrophysics Data System (ADS)

Leblanc, Benoit; Braunschweig, Bertrand; Toulhoat, Hervé; Lutton, Evelyne

We present a new approach in order to improve the convergence of Monte Carlo (MC) simulations of molecular systems belonging to complex energetic landscapes: the problem is redefined in terms of the dynamic allocation of MC move frequencies depending on their past efficiency, measured with respect to a relevant sampling criterion. We introduce various empirical criteria with the aim of accounting for the proper convergence in phase space sampling. The dynamic allocation is performed over parallel simulations by means of a new evolutionary algorithm involving 'immortal' individuals. The method is bench marked with respect to conventional procedures on a model for melt linear polyethylene. We record significant improvement in sampling efficiencies, thus in computational load, while the optimal sets of move frequencies are liable to allow interesting physical insights into the particular systems simulated. This last aspect should provide a new tool for designing more efficient new MC moves.

Signal pulse emulation for scintillation detectors using Geant4 Monte Carlo with light tracking simulation.

PubMed

Ogawara, R; Ishikawa, M

2016-07-01

The anode pulse of a photomultiplier tube (PMT) coupled with a scintillator is used for pulse shape discrimination (PSD) analysis. We have developed a novel emulation technique for the PMT anode pulse based on optical photon transport and a PMT response function. The photon transport was calculated using Geant4 Monte Carlo code and the response function with a BC408 organic scintillator. The obtained percentage RMS value of the difference between the measured and simulated pulse with suitable scintillation properties using GSO:Ce (0.4, 1.0, 1.5 mol%), LaBr3:Ce and BGO scintillators were 2.41%, 2.58%, 2.16%, 2.01%, and 3.32%, respectively. The proposed technique demonstrates high reproducibility of the measured pulse and can be applied to simulation studies of various radiation measurements.

Dosimetry of 192Ir sources used for endovascular brachytherapy

NASA Astrophysics Data System (ADS)

Reynaert, N.; Van Eijkeren, M.; Taeymans, Y.; Thierens, H.

2001-02-01

An in-phantom calibration technique for 192Ir sources used for endovascular brachytherapy is presented. Three different source lengths were investigated. The calibration was performed in a solid phantom using a Farmer-type ionization chamber at source to detector distances ranging from 1 cm to 5 cm. The dosimetry protocol for medium-energy x-rays extended with a volume-averaging correction factor was used to convert the chamber reading to dose to water. The air kerma strength of the sources was determined as well. EGS4 Monte Carlo calculations were performed to determine the depth dose distribution at distances ranging from 0.6 mm to 10 cm from the source centre. In this way we were able to convert the absolute dose rate at 1 cm distance to the reference point chosen at 2 mm distance. The Monte Carlo results were confirmed by radiochromic film measurements, performed with a double-exposure technique. The dwell times to deliver a dose of 14 Gy at the reference point were determined and compared with results given by the source supplier (CORDIS). They determined the dwell times from a Sievert integration technique based on the source activity. The results from both methods agreed to within 2% for the 12 sources that were evaluated. A Visual Basic routine that superimposes dose distributions, based on the Monte Carlo calculations and the in-phantom calibration, onto intravascular ultrasound images is presented. This routine can be used as an online treatment planning program.

The integration of improved Monte Carlo compton scattering algorithms into the Integrated TIGER Series.

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

Quirk, Thomas, J., IV

2004-08-01

The Integrated TIGER Series (ITS) is a software package that solves coupled electron-photon transport problems. ITS performs analog photon tracking for energies between 1 keV and 1 GeV. Unlike its deterministic counterpart, the Monte Carlo calculations of ITS do not require a memory-intensive meshing of phase space; however, its solutions carry statistical variations. Reducing these variations is heavily dependent on runtime. Monte Carlo simulations must therefore be both physically accurate and computationally efficient. Compton scattering is the dominant photon interaction above 100 keV and below 5-10 MeV, with higher cutoffs occurring in lighter atoms. In its current model of Comptonmore » scattering, ITS corrects the differential Klein-Nishina cross sections (which assumes a stationary, free electron) with the incoherent scattering function, a function dependent on both the momentum transfer and the atomic number of the scattering medium. While this technique accounts for binding effects on the scattering angle, it excludes the Doppler broadening the Compton line undergoes because of the momentum distribution in each bound state. To correct for these effects, Ribbefor's relativistic impulse approximation (IA) will be employed to create scattering cross section differential in both energy and angle for each element. Using the parameterizations suggested by Brusa et al., scattered photon energies and angle can be accurately sampled at a high efficiency with minimal physical data. Two-body kinematics then dictates the electron's scattered direction and energy. Finally, the atomic ionization is relaxed via Auger emission or fluorescence. Future work will extend these improvements in incoherent scattering to compounds and to adjoint calculations.« less

TU-H-CAMPUS-IeP1-01: Bias and Computational Efficiency of Variance Reduction Methods for the Monte Carlo Simulation of Imaging Detectors

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

Sharma, D; Badano, A; Sempau, J

Purpose: Variance reduction techniques (VRTs) are employed in Monte Carlo simulations to obtain estimates with reduced statistical uncertainty for a given simulation time. In this work, we study the bias and efficiency of a VRT for estimating the response of imaging detectors. Methods: We implemented Directed Sampling (DS), preferentially directing a fraction of emitted optical photons directly towards the detector by altering the isotropic model. The weight of each optical photon is appropriately modified to maintain simulation estimates unbiased. We use a Monte Carlo tool called fastDETECT2 (part of the hybridMANTIS open-source package) for optical transport, modified for VRT. Themore » weight of each photon is calculated as the ratio of original probability (no VRT) and the new probability for a particular direction. For our analysis of bias and efficiency, we use pulse height spectra, point response functions, and Swank factors. We obtain results for a variety of cases including analog (no VRT, isotropic distribution), and DS with 0.2 and 0.8 optical photons directed towards the sensor plane. We used 10,000, 25-keV primaries. Results: The Swank factor for all cases in our simplified model converged fast (within the first 100 primaries) to a stable value of 0.9. The root mean square error per pixel for DS VRT for the point response function between analog and VRT cases was approximately 5e-4. Conclusion: Our preliminary results suggest that DS VRT does not affect the estimate of the mean for the Swank factor. Our findings indicate that it may be possible to design VRTs for imaging detector simulations to increase computational efficiency without introducing bias.« less

Performance of student software development teams: the influence of personality and identifying as team members

NASA Astrophysics Data System (ADS)

Monaghan, Conal; Bizumic, Boris; Reynolds, Katherine; Smithson, Michael; Johns-Boast, Lynette; van Rooy, Dirk

2015-01-01

One prominent approach in the exploration of the variations in project team performance has been to study two components of the aggregate personalities of the team members: conscientiousness and agreeableness. A second line of research, known as self-categorisation theory, argues that identifying as team members and the team's performance norms should substantially influence the team's performance. This paper explores the influence of both these perspectives in university software engineering project teams. Eighty students worked to complete a piece of software in small project teams during 2007 or 2008. To reduce limitations in statistical analysis, Monte Carlo simulation techniques were employed to extrapolate from the results of the original sample to a larger simulated sample (2043 cases, within 319 teams). The results emphasise the importance of taking into account personality (particularly conscientiousness), and both team identification and the team's norm of performance, in order to cultivate higher levels of performance in student software engineering project teams.

Near Infrared Optical Properties of Whole Human Blood and Blood Containing Nanoparticulates

NASA Astrophysics Data System (ADS)

Mimun, Lawrence C.; Yust, Brian; Nash, Kelly L.; Sardar, Dhiraj K.

2010-10-01

Whole human blood is optically characterized in the near infrared (NIR) with and without the addition of nanocrystals. The optical properties were obtained using the double-integrating sphere technique at the Nd excitation wavelength of 808 nm. Y2O3 and Nd^3+:Y2O3 nanoparticles were added in predetermined amounts to water, blood plasma, and whole blood samples, from which a computational analysis was conducted using the Kubelka-Munk calculational method, the Inverse Adding Doubling Method, and the Magic Light Monte Carlo Method to characterized the optical properties such as the absorption (μa) and scattering coefficients (μs) and the scattering anisotropy (g). Through comparison with control samples, the optical properties of each component (blood, plasma, and nanoparticles) can be determined individually, thus illuminating any changes due to the biological environment. The emission from the Nd^3+:Y2O3 particles through the blood is also detected thus exhibiting their usefulness as real world biological markers.

State-space reduction and equivalence class sampling for a molecular self-assembly model.

PubMed

Packwood, Daniel M; Han, Patrick; Hitosugi, Taro

2016-07-01

Direct simulation of a model with a large state space will generate enormous volumes of data, much of which is not relevant to the questions under study. In this paper, we consider a molecular self-assembly model as a typical example of a large state-space model, and present a method for selectively retrieving 'target information' from this model. This method partitions the state space into equivalence classes, as identified by an appropriate equivalence relation. The set of equivalence classes H, which serves as a reduced state space, contains none of the superfluous information of the original model. After construction and characterization of a Markov chain with state space H, the target information is efficiently retrieved via Markov chain Monte Carlo sampling. This approach represents a new breed of simulation techniques which are highly optimized for studying molecular self-assembly and, moreover, serves as a valuable guideline for analysis of other large state-space models.

Free energy computations by minimization of Kullback-Leibler divergence: An efficient adaptive biasing potential method for sparse representations

NASA Astrophysics Data System (ADS)

Bilionis, I.; Koutsourelakis, P. S.

2012-05-01

The present paper proposes an adaptive biasing potential technique for the computation of free energy landscapes. It is motivated by statistical learning arguments and unifies the tasks of biasing the molecular dynamics to escape free energy wells and estimating the free energy function, under the same objective of minimizing the Kullback-Leibler divergence between appropriately selected densities. It offers rigorous convergence diagnostics even though history dependent, non-Markovian dynamics are employed. It makes use of a greedy optimization scheme in order to obtain sparse representations of the free energy function which can be particularly useful in multidimensional cases. It employs embarrassingly parallelizable sampling schemes that are based on adaptive Sequential Monte Carlo and can be readily coupled with legacy molecular dynamics simulators. The sequential nature of the learning and sampling scheme enables the efficient calculation of free energy functions parametrized by the temperature. The characteristics and capabilities of the proposed method are demonstrated in three numerical examples.

Wang-Landau Reaction Ensemble Method: Simulation of Weak Polyelectrolytes and General Acid-Base Reactions.

PubMed

Landsgesell, Jonas; Holm, Christian; Smiatek, Jens

2017-02-14

We present a novel method for the study of weak polyelectrolytes and general acid-base reactions in molecular dynamics and Monte Carlo simulations. The approach combines the advantages of the reaction ensemble and the Wang-Landau sampling method. Deprotonation and protonation reactions are simulated explicitly with the help of the reaction ensemble method, while the accurate sampling of the corresponding phase space is achieved by the Wang-Landau approach. The combination of both techniques provides a sufficient statistical accuracy such that meaningful estimates for the density of states and the partition sum can be obtained. With regard to these estimates, several thermodynamic observables like the heat capacity or reaction free energies can be calculated. We demonstrate that the computation times for the calculation of titration curves with a high statistical accuracy can be significantly decreased when compared to the original reaction ensemble method. The applicability of our approach is validated by the study of weak polyelectrolytes and their thermodynamic properties.

Statistical homogeneity tests applied to large data sets from high energy physics experiments

NASA Astrophysics Data System (ADS)

Trusina, J.; Franc, J.; Kůs, V.

2017-12-01

Homogeneity tests are used in high energy physics for the verification of simulated Monte Carlo samples, it means if they have the same distribution as a measured data from particle detector. Kolmogorov-Smirnov, χ 2, and Anderson-Darling tests are the most used techniques to assess the samples’ homogeneity. Since MC generators produce plenty of entries from different models, each entry has to be re-weighted to obtain the same sample size as the measured data has. One way of the homogeneity testing is through the binning. If we do not want to lose any information, we can apply generalized tests based on weighted empirical distribution functions. In this paper, we propose such generalized weighted homogeneity tests and introduce some of their asymptotic properties. We present the results based on numerical analysis which focuses on estimations of the type-I error and power of the test. Finally, we present application of our homogeneity tests to data from the experiment DØ in Fermilab.

The liquid-liquid transition in supercooled ST2 water: a comparison between umbrella sampling and well-tempered metadynamics.

PubMed

Palmer, Jeremy C; Car, Roberto; Debenedetti, Pablo G

2013-01-01

We investigate the metastable phase behaviour of the ST2 water model under deeply supercooled conditions. The phase behaviour is examined using umbrella sampling (US) and well-tempered metadynamics (WT-MetaD) simulations to compute the reversible free energy surface parameterized by density and bond-orientation order. We find that free energy surfaces computed with both techniques clearly show two liquid phases in coexistence, in agreement with our earlier US and grand canonical Monte Carlo calculations [Y. Liu, J. C. Palmer, A. Z. Panagiotopoulos and P. G. Debenedetti, J Chem Phys, 2012, 137, 214505; Y. Liu, A. Z. Panagiotopoulos and P. G. Debenedetti, J Chem Phys, 2009, 131, 104508]. While we demonstrate that US and WT-MetaD produce consistent results, the latter technique is estimated to be more computationally efficient by an order of magnitude. As a result, we show that WT-MetaD can be used to study the finite-size scaling behaviour of the free energy barrier separating the two liquids for systems containing 192, 300 and 400 ST2 molecules. Although our results are consistent with the expected N(2/3) scaling law, we conclude that larger systems must be examined to provide conclusive evidence of a first-order phase transition and associated second critical point.

Site-Specific Preparation of Intact Solid–Liquid Interfaces by Label-Free In Situ Localization and Cryo-Focused Ion Beam Lift-Out

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

Zachman, Michael J.; Asenath-Smith, Emily; Estroff, Lara A.

Abstract Scanning transmission electron microscopy (STEM) allows atomic scale characterization of solid–solid interfaces, but has seen limited applications to solid–liquid interfaces due to the volatility of liquids in the microscope vacuum. Although cryo-electron microscopy is routinely used to characterize hydrated samples stabilized by rapid freezing, sample thinning is required to access the internal interfaces of thicker specimens. Here, we adapt cryo-focused ion beam (FIB) “lift-out,” a technique recently developed for biological specimens, to prepare intact internal solid–liquid interfaces for high-resolution structural and chemical analysis by cryo-STEM. To guide the milling process we introduce a label-freein situmethod of localizing subsurface structuresmore » in suitable materials by energy dispersive X-ray spectroscopy (EDX). Monte Carlo simulations are performed to evaluate the depth-probing capability of the technique, and show good qualitative agreement with experiment. We also detail procedures to produce homogeneously thin lamellae, which enable nanoscale structural, elemental, and chemical analysis of intact solid–liquid interfaces by analytical cryo-STEM. This work demonstrates the potential of cryo-FIB lift-out and cryo-STEM for understanding physical and chemical processes at solid–liquid interfaces.« less

Bayesian Orbit Computation Tools for Objects on Geocentric Orbits

NASA Astrophysics Data System (ADS)

Virtanen, J.; Granvik, M.; Muinonen, K.; Oszkiewicz, D.

2013-08-01

We consider the space-debris orbital inversion problem via the concept of Bayesian inference. The methodology has been put forward for the orbital analysis of solar system small bodies in early 1990's [7] and results in a full solution of the statistical inverse problem given in terms of a posteriori probability density function (PDF) for the orbital parameters. We demonstrate the applicability of our statistical orbital analysis software to Earth orbiting objects, both using well-established Monte Carlo (MC) techniques (for a review, see e.g. [13] as well as recently developed Markov-chain MC (MCMC) techniques (e.g., [9]). In particular, we exploit the novel virtual observation MCMC method [8], which is based on the characterization of the phase-space volume of orbital solutions before the actual MCMC sampling. Our statistical methods and the resulting PDFs immediately enable probabilistic impact predictions to be carried out. Furthermore, this can be readily done also for very sparse data sets and data sets of poor quality - providing that some a priori information on the observational uncertainty is available. For asteroids, impact probabilities with the Earth from the discovery night onwards have been provided, e.g., by [11] and [10], the latter study includes the sampling of the observational-error standard deviation as a random variable.

Caesium-137 and strontium-90 temporal series in the Tagus River: experimental results and a modelling study.

PubMed

Miró, Conrado; Baeza, Antonio; Madruga, María J; Periañez, Raul

2012-11-01

The objective of this work consisted of analysing the spatial and temporal evolution of two radionuclide concentrations in the Tagus River. Time-series analysis techniques and numerical modelling have been used in this study. (137)Cs and (90)Sr concentrations have been measured from 1994 to 1999 at several sampling points in Spain and Portugal. These radionuclides have been introduced into the river by the liquid releases from several nuclear power plants in Spain, as well as from global fallout. Time-series analysis techniques have allowed the determination of radionuclide transit times along the river, and have also pointed out the existence of temporal cycles of radionuclide concentrations at some sampling points, which are attributed to water management in the reservoirs placed along the Tagus River. A stochastic dispersion model, in which transport with water, radioactive decay and water-sediment interactions are solved through Monte Carlo methods, has been developed. Model results are, in general, in reasonable agreement with measurements. The model has finally been applied to the calculation of mean ages of radioactive content in water and sediments in each reservoir. This kind of model can be a very useful tool to support the decision-making process after an eventual emergency situation. Copyright © 2012 Elsevier Ltd. All rights reserved.

Uncertainty quantification analysis of the dynamics of an electrostatically actuated microelectromechanical switch model

NASA Astrophysics Data System (ADS)

Snow, Michael G.; Bajaj, Anil K.

2015-08-01

This work presents an uncertainty quantification (UQ) analysis of a comprehensive model for an electrostatically actuated microelectromechanical system (MEMS) switch. The goal is to elucidate the effects of parameter variations on certain key performance characteristics of the switch. A sufficiently detailed model of the electrostatically actuated switch in the basic configuration of a clamped-clamped beam is developed. This multi-physics model accounts for various physical effects, including the electrostatic fringing field, finite length of electrodes, squeeze film damping, and contact between the beam and the dielectric layer. The performance characteristics of immediate interest are the static and dynamic pull-in voltages for the switch. Numerical approaches for evaluating these characteristics are developed and described. Using Latin Hypercube Sampling and other sampling methods, the model is evaluated to find these performance characteristics when variability in the model's geometric and physical parameters is specified. Response surfaces of these results are constructed via a Multivariate Adaptive Regression Splines (MARS) technique. Using a Direct Simulation Monte Carlo (DSMC) technique on these response surfaces gives smooth probability density functions (PDFs) of the outputs characteristics when input probability characteristics are specified. The relative variation in the two pull-in voltages due to each of the input parameters is used to determine the critical parameters.

Monte Carlo tests of the ELIPGRID-PC algorithm

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

Davidson, J.R.

1995-04-01

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

Estimating rare events in biochemical systems using conditional sampling.

PubMed

Sundar, V S

2017-01-28

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

Large ensemble modeling of the last deglacial retreat of the West Antarctic Ice Sheet: comparison of simple and advanced statistical techniques

NASA Astrophysics Data System (ADS)

Pollard, David; Chang, Won; Haran, Murali; Applegate, Patrick; DeConto, Robert

2016-05-01

A 3-D hybrid ice-sheet model is applied to the last deglacial retreat of the West Antarctic Ice Sheet over the last ˜ 20 000 yr. A large ensemble of 625 model runs is used to calibrate the model to modern and geologic data, including reconstructed grounding lines, relative sea-level records, elevation-age data and uplift rates, with an aggregate score computed for each run that measures overall model-data misfit. Two types of statistical methods are used to analyze the large-ensemble results: simple averaging weighted by the aggregate score, and more advanced Bayesian techniques involving Gaussian process-based emulation and calibration, and Markov chain Monte Carlo. The analyses provide sea-level-rise envelopes with well-defined parametric uncertainty bounds, but the simple averaging method only provides robust results with full-factorial parameter sampling in the large ensemble. Results for best-fit parameter ranges and envelopes of equivalent sea-level rise with the simple averaging method agree well with the more advanced techniques. Best-fit parameter ranges confirm earlier values expected from prior model tuning, including large basal sliding coefficients on modern ocean beds.

Applications of Low Density Flow Techniques and Catalytic Recombination at the Johnson Space Center

NASA Technical Reports Server (NTRS)

Scott, Carl D.

2000-01-01

The talk presents a brief background on defInitions of catalysis and effects associated with chemically nonequilibrium and low-density flows of aerospace interest. Applications of catalytic recombination on surfaces in dissociated flow are given, including aero heating on reentry spacecraft thermal protection surfaces and reflection of plume flow on pressure distributions associated with the space station. Examples include aero heating predictions for the X-38 test vehicle, the inlet of a proposed gas-sampling probe used in high enthalpy test facilities, and a parabolic body at angle of attack. The effect of accommodation coefficients on thruster induced pressure distributions is also included. Examples of tools used include simple aero heating formulas based on boundary layer solutions, an engineering approximation that uses axisymmetric viscous shock layer flow to simulate full three dimensional flow, full computational fluid dynamics, and direct simulation Monte-Carlo calculations. Methods of determining catalytic recombination rates in arc jet flow are discus ed. An area of catalysis not fully understood is the formation of single-wall carbon nanotubes (SWNT) with gas phase or nano-size metal particles. The Johnson Space Center is making SWNTs using both a laser ablation technique and an electric arc vaporization technique.

Equilibrium Molecular Thermodynamics from Kirkwood Sampling

PubMed Central

2015-01-01

We present two methods for barrierless equilibrium sampling of molecular systems based on the recently proposed Kirkwood method (J. Chem. Phys.2009, 130, 134102). Kirkwood sampling employs low-order correlations among internal coordinates of a molecule for random (or non-Markovian) sampling of the high dimensional conformational space. This is a geometrical sampling method independent of the potential energy surface. The first method is a variant of biased Monte Carlo, where Kirkwood sampling is used for generating trial Monte Carlo moves. Using this method, equilibrium distributions corresponding to different temperatures and potential energy functions can be generated from a given set of low-order correlations. Since Kirkwood samples are generated independently, this method is ideally suited for massively parallel distributed computing. The second approach is a variant of reservoir replica exchange, where Kirkwood sampling is used to construct a reservoir of conformations, which exchanges conformations with the replicas performing equilibrium sampling corresponding to different thermodynamic states. Coupling with the Kirkwood reservoir enhances sampling by facilitating global jumps in the conformational space. The efficiency of both methods depends on the overlap of the Kirkwood distribution with the target equilibrium distribution. We present proof-of-concept results for a model nine-atom linear molecule and alanine dipeptide. PMID:25915525

Material radioassay and selection for the XENON1T dark matter experiment

NASA Astrophysics Data System (ADS)

Aprile, E.; Aalbers, J.; Agostini, F.; Alfonsi, M.; Amaro, F. D.; Anthony, M.; Arneodo, F.; Barrow, P.; Baudis, L.; Bauermeister, B.; Benabderrahmane, M. L.; Berger, T.; Breur, P. A.; Brown, A.; Brown, E.; Bruenner, S.; Bruno, G.; Budnik, R.; Bütikofer, L.; Calvén, J.; Cardoso, J. M. R.; Cervantes, M.; Cichon, D.; Coderre, D.; Colijn, A. P.; Conrad, J.; Cussonneau, J. P.; Decowski, M. P.; de Perio, P.; Di Gangi, P.; Di Giovanni, A.; Diglio, S.; Eurin, G.; Fei, J.; Ferella, A. D.; Fieguth, A.; Franco, D.; Fulgione, W.; Gallo Rosso, A.; Galloway, M.; Gao, F.; Garbini, M.; Geis, C.; Goetzke, L. W.; Grandi, L.; Greene, Z.; Grignon, C.; Hasterok, C.; Hogenbirk, E.; Itay, R.; Kaminsky, B.; Kessler, G.; Kish, A.; Landsman, H.; Lang, R. F.; Lellouch, D.; Levinson, L.; Le Calloch, M.; Lin, Q.; Lindemann, S.; Lindner, M.; Lopes, J. A. M.; Manfredini, A.; Maris, I.; Marrodán Undagoitia, T.; Masbou, J.; Massoli, F. V.; Masson, D.; Mayani, D.; Messina, M.; Micheneau, K.; Miguez, B.; Molinario, A.; Murra, M.; Naganoma, J.; Ni, K.; Oberlack, U.; Pakarha, P.; Pelssers, B.; Persiani, R.; Piastra, F.; Pienaar, J.; Piro, M.-C.; Pizzella, V.; Plante, G.; Priel, N.; Rauch, L.; Reichard, S.; Reuter, C.; Rizzo, A.; Rosendahl, S.; Rupp, N.; Saldanha, R.; dos Santos, J. M. F.; Sartorelli, G.; Scheibelhut, M.; Schindler, S.; Schreiner, J.; Schumann, M.; Scotto Lavina, L.; Selvi, M.; Shagin, P.; Shockley, E.; Silva, M.; Simgen, H.; Sivers, M. v.; Stein, A.; Thers, D.; Tiseni, A.; Trinchero, G.; Tunnell, C.; Upole, N.; Wang, H.; Wei, Y.; Weinheimer, C.; Wulf, J.; Ye, J.; Zhang, Y.; Laubenstein, M.; Nisi, S.

2017-12-01

The XENON1T dark matter experiment aims to detect weakly interacting massive particles (WIMPs) through low-energy interactions with xenon atoms. To detect such a rare event necessitates the use of radiopure materials to minimize the number of background events within the expected WIMP signal region. In this paper we report the results of an extensive material radioassay campaign for the XENON1T experiment. Using gamma-ray spectroscopy and mass spectrometry techniques, systematic measurements of trace radioactive impurities in over one hundred samples within a wide range of materials were performed. The measured activities allowed for stringent selection and placement of materials during the detector construction phase and provided the input for XENON1T detection sensitivity estimates through Monte Carlo simulations.

CORS BAADE-WESSELINK DISTANCE TO THE LMC NGC 1866 BLUE POPULOUS CLUSTER

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

Molinaro, R.; Ripepi, V.; Marconi, M.

2012-03-20

We used optical, near-infrared photometry, and radial velocity data for a sample of 11 Cepheids belonging to the young LMC blue populous cluster NGC 1866 to estimate their radii and distances on the basis of the CORS Baade-Wesselink method. This technique, based on an accurate calibration of surface brightness as a function of (U - B), (V - K) colors, allows us to estimate, simultaneously, the linear radius and the angular diameter of Cepheid variables, and consequently to derive their distance. A rigorous error estimate on radii and distances was derived by using Monte Carlo simulations. Our analysis gives amore » distance modulus for NGC 1866 of 18.51 {+-} 0.03 mag, which is in agreement with several independent results.« less

Numerical modeling of materials processing applications of a pulsed cold cathode electron gun

NASA Astrophysics Data System (ADS)

Etcheverry, J. I.; Martínez, O. E.; Mingolo, N.

1998-04-01

A numerical study of the application of a pulsed cold cathode electron gun to materials processing is performed. A simple semiempirical model of the discharge is used, together with backscattering and energy deposition profiles obtained by a Monte Carlo technique, in order to evaluate the energy source term inside the material. The numerical computation of the heat equation with the calculated source term is performed in order to obtain useful information on melting and vaporization thresholds, melted radius and depth, and on the dependence of these variables on processing parameters such as operating pressure, initial voltage of the discharge and cathode-sample distance. Numerical results for stainless steel are presented, which demonstrate the need for several modifications of the experimental design in order to achieve a better efficiency.

Supervised classification in the presence of misclassified training data: a Monte Carlo simulation study in the three group case.

PubMed

Bolin, Jocelyn Holden; Finch, W Holmes

2014-01-01

Statistical classification of phenomena into observed groups is very common in the social and behavioral sciences. Statistical classification methods, however, are affected by the characteristics of the data under study. Statistical classification can be further complicated by initial misclassification of the observed groups. The purpose of this study is to investigate the impact of initial training data misclassification on several statistical classification and data mining techniques. Misclassification conditions in the three group case will be simulated and results will be presented in terms of overall as well as subgroup classification accuracy. Results show decreased classification accuracy as sample size, group separation and group size ratio decrease and as misclassification percentage increases with random forests demonstrating the highest accuracy across conditions.

Bayesian reconstruction of projection reconstruction NMR (PR-NMR).

PubMed

Yoon, Ji Won

2014-11-01

Projection reconstruction nuclear magnetic resonance (PR-NMR) is a technique for generating multidimensional NMR spectra. A small number of projections from lower-dimensional NMR spectra are used to reconstruct the multidimensional NMR spectra. In our previous work, it was shown that multidimensional NMR spectra are efficiently reconstructed using peak-by-peak based reversible jump Markov chain Monte Carlo (RJMCMC) algorithm. We propose an extended and generalized RJMCMC algorithm replacing a simple linear model with a linear mixed model to reconstruct close NMR spectra into true spectra. This statistical method generates samples in a Bayesian scheme. Our proposed algorithm is tested on a set of six projections derived from the three-dimensional 700 MHz HNCO spectrum of a protein HasA. Copyright © 2014 Elsevier Ltd. All rights reserved.

Ionic liquid-based observation technique for nonconductive materials in the scanning electron microscope: Application to the characterization of a rare earth ore.

PubMed

Brodusch, Nicolas; Waters, Kristian; Demers, Hendrix; Gauvin, Raynald

2014-03-01

A new approach for preparing geological materials is proposed to reduce charging during their characterization in a scanning electron microscope. This technique was applied to a sample of the Nechalacho rare earth deposit, which contains a significant amount of the minerals fergusonite and zircon. Instead of covering the specimen surface with a conductive coating, the sample was immersed in a dilute solution of ionic liquid and then air dried prior to SEM analysis. Imaging at a wide range of accelerating voltages was then possible without evidence of charging when using the in-chamber secondary and backscattered electrons detectors, even at 1 kV. High resolution x-ray and electron backscatter diffraction mapping were successfully obtained at 20 and 5 kV with negligible image drifting and permitted the characterization of the microstructure of the zircon/fergusonite-Y aggregates encased in the matrix minerals. Because of the absence of a conductive layer at the surface of the specimen, the Kikuchi band contrast was improved and the backscatter electron signal increased at both 5 and 20 kV as confirmed by Monte Carlo modeling. These major developments led to an improvement of the spatial resolution and efficiency of the above characterization techniques applied to the rare earth ore and it is expected that they can be applied to other types of ores and minerals. Copyright © 2014 Wiley Periodicals, Inc.

High-Throughput Computation and the Applicability of Monte Carlo Integration in Fatigue Load Estimation of Floating Offshore Wind Turbines

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

Graf, Peter A.; Stewart, Gordon; Lackner, Matthew

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, whichmore » 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.« less

A dental public health approach based on computational mathematics: Monte Carlo simulation of childhood dental decay.

PubMed

Tennant, Marc; Kruger, Estie

2013-02-01

This study developed a Monte Carlo simulation approach to examining the prevalence and incidence of dental decay using Australian children as a test environment. Monte Carlo simulation has been used for a half a century in particle physics (and elsewhere); put simply, it is the probability for various population-level outcomes seeded randomly to drive the production of individual level data. A total of five runs of the simulation model for all 275,000 12-year-olds in Australia were completed based on 2005-2006 data. Measured on average decayed/missing/filled teeth (DMFT) and DMFT of highest 10% of sample (Sic10) the runs did not differ from each other by more than 2% and the outcome was within 5% of the reported sampled population data. The simulations rested on the population probabilities that are known to be strongly linked to dental decay, namely, socio-economic status and Indigenous heritage. Testing the simulated population found DMFT of all cases where DMFT<>0 was 2.3 (n = 128,609) and DMFT for Indigenous cases only was 1.9 (n = 13,749). In the simulation population the Sic25 was 3.3 (n = 68,750). Monte Carlo simulations were created in particle physics as a computational mathematical approach to unknown individual-level effects by resting a simulation on known population-level probabilities. In this study a Monte Carlo simulation approach to childhood dental decay was built, tested and validated. © 2013 FDI World Dental Federation.

Stabilizing canonical-ensemble calculations in the auxiliary-field Monte Carlo method

NASA Astrophysics Data System (ADS)

Gilbreth, C. N.; Alhassid, Y.

2015-03-01

Quantum Monte Carlo methods are powerful techniques for studying strongly interacting Fermi systems. However, implementing these methods on computers with finite-precision arithmetic requires careful attention to numerical stability. In the auxiliary-field Monte Carlo (AFMC) method, low-temperature or large-model-space calculations require numerically stabilized matrix multiplication. When adapting methods used in the grand-canonical ensemble to the canonical ensemble of fixed particle number, the numerical stabilization increases the number of required floating-point operations for computing observables by a factor of the size of the single-particle model space, and thus can greatly limit the systems that can be studied. We describe an improved method for stabilizing canonical-ensemble calculations in AFMC that exhibits better scaling, and present numerical tests that demonstrate the accuracy and improved performance of the method.

Comparison between Monte Carlo simulation and measurement with a 3D polymer gel dosimeter for dose distributions in biological samples

NASA Astrophysics Data System (ADS)

Furuta, T.; Maeyama, T.; Ishikawa, K. L.; Fukunishi, N.; Fukasaku, K.; Takagi, S.; Noda, S.; Himeno, R.; Hayashi, S.

2015-08-01

In this research, we used a 135 MeV/nucleon carbon-ion beam to irradiate a biological sample composed of fresh chicken meat and bones, which was placed in front of a PAGAT gel dosimeter, and compared the measured and simulated transverse-relaxation-rate (R2) distributions in the gel dosimeter. We experimentally measured the three-dimensional R2 distribution, which records the dose induced by particles penetrating the sample, by using magnetic resonance imaging. The obtained R2 distribution reflected the heterogeneity of the biological sample. We also conducted Monte Carlo simulations using the PHITS code by reconstructing the elemental composition of the biological sample from its computed tomography images while taking into account the dependence of the gel response on the linear energy transfer. The simulation reproduced the experimental distal edge structure of the R2 distribution with an accuracy under about 2 mm, which is approximately the same as the voxel size currently used in treatment planning.

Comparison between Monte Carlo simulation and measurement with a 3D polymer gel dosimeter for dose distributions in biological samples.

PubMed

Furuta, T; Maeyama, T; Ishikawa, K L; Fukunishi, N; Fukasaku, K; Takagi, S; Noda, S; Himeno, R; Hayashi, S

2015-08-21

In this research, we used a 135 MeV/nucleon carbon-ion beam to irradiate a biological sample composed of fresh chicken meat and bones, which was placed in front of a PAGAT gel dosimeter, and compared the measured and simulated transverse-relaxation-rate (R2) distributions in the gel dosimeter. We experimentally measured the three-dimensional R2 distribution, which records the dose induced by particles penetrating the sample, by using magnetic resonance imaging. The obtained R2 distribution reflected the heterogeneity of the biological sample. We also conducted Monte Carlo simulations using the PHITS code by reconstructing the elemental composition of the biological sample from its computed tomography images while taking into account the dependence of the gel response on the linear energy transfer. The simulation reproduced the experimental distal edge structure of the R2 distribution with an accuracy under about 2 mm, which is approximately the same as the voxel size currently used in treatment planning.

An Efficient MCMC Algorithm to Sample Binary Matrices with Fixed Marginals

ERIC Educational Resources Information Center

Verhelst, Norman D.

2008-01-01

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

Enhanced Sampling of an Atomic Model with Hybrid Nonequilibrium Molecular Dynamics-Monte Carlo Simulations Guided by a Coarse-Grained Model.

PubMed

Chen, Yunjie; Roux, Benoît

2015-08-11

Molecular dynamics (MD) trajectories based on a classical equation of motion provide a straightforward, albeit somewhat inefficient approach, to explore and sample the configurational space of a complex molecular system. While a broad range of techniques can be used to accelerate and enhance the sampling efficiency of classical simulations, only algorithms that are consistent with the Boltzmann equilibrium distribution yield a proper statistical mechanical computational framework. Here, a multiscale hybrid algorithm relying simultaneously on all-atom fine-grained (FG) and coarse-grained (CG) representations of a system is designed to improve sampling efficiency by combining the strength of nonequilibrium molecular dynamics (neMD) and Metropolis Monte Carlo (MC). This CG-guided hybrid neMD-MC algorithm comprises six steps: (1) a FG configuration of an atomic system is dynamically propagated for some period of time using equilibrium MD; (2) the resulting FG configuration is mapped onto a simplified CG model; (3) the CG model is propagated for a brief time interval to yield a new CG configuration; (4) the resulting CG configuration is used as a target to guide the evolution of the FG system; (5) the FG configuration (from step 1) is driven via a nonequilibrium MD (neMD) simulation toward the CG target; (6) the resulting FG configuration at the end of the neMD trajectory is then accepted or rejected according to a Metropolis criterion before returning to step 1. A symmetric two-ends momentum reversal prescription is used for the neMD trajectories of the FG system to guarantee that the CG-guided hybrid neMD-MC algorithm obeys microscopic detailed balance and rigorously yields the equilibrium Boltzmann distribution. The enhanced sampling achieved with the method is illustrated with a model system with hindered diffusion and explicit-solvent peptide simulations. Illustrative tests indicate that the method can yield a speedup of about 80 times for the model system and up to 21 times for polyalanine and (AAQAA)3 in water.

Enhanced Sampling of an Atomic Model with Hybrid Nonequilibrium Molecular Dynamics—Monte Carlo Simulations Guided by a Coarse-Grained Model

PubMed Central

2015-01-01

Molecular dynamics (MD) trajectories based on a classical equation of motion provide a straightforward, albeit somewhat inefficient approach, to explore and sample the configurational space of a complex molecular system. While a broad range of techniques can be used to accelerate and enhance the sampling efficiency of classical simulations, only algorithms that are consistent with the Boltzmann equilibrium distribution yield a proper statistical mechanical computational framework. Here, a multiscale hybrid algorithm relying simultaneously on all-atom fine-grained (FG) and coarse-grained (CG) representations of a system is designed to improve sampling efficiency by combining the strength of nonequilibrium molecular dynamics (neMD) and Metropolis Monte Carlo (MC). This CG-guided hybrid neMD-MC algorithm comprises six steps: (1) a FG configuration of an atomic system is dynamically propagated for some period of time using equilibrium MD; (2) the resulting FG configuration is mapped onto a simplified CG model; (3) the CG model is propagated for a brief time interval to yield a new CG configuration; (4) the resulting CG configuration is used as a target to guide the evolution of the FG system; (5) the FG configuration (from step 1) is driven via a nonequilibrium MD (neMD) simulation toward the CG target; (6) the resulting FG configuration at the end of the neMD trajectory is then accepted or rejected according to a Metropolis criterion before returning to step 1. A symmetric two-ends momentum reversal prescription is used for the neMD trajectories of the FG system to guarantee that the CG-guided hybrid neMD-MC algorithm obeys microscopic detailed balance and rigorously yields the equilibrium Boltzmann distribution. The enhanced sampling achieved with the method is illustrated with a model system with hindered diffusion and explicit-solvent peptide simulations. Illustrative tests indicate that the method can yield a speedup of about 80 times for the model system and up to 21 times for polyalanine and (AAQAA)3 in water. PMID:26574442

Investigation of olivine and orthopyroxene grain boundaries by atom probe tomography

NASA Astrophysics Data System (ADS)

Krawczynski, M.; Skemer, P. A.; Bachhav, M.; Dong, Y.; Marquis, E. A.

2016-12-01

Accurate chemical analysis at grain boundaries is challenging by traditional microscopic techniques, especially for poor conducting geological samples. Atom probe tomography (APT) is a unique technique that can elucidate chemistry and 3-D distribution of elements within a sample volume at the sub-nanometer length scale. With advances in laser and sample preparation techniques in the last decade, APT is now successfully applied to a wide range of poor conducting materials like metal oxides, ceramics, and biological minerals. In this study, we apply the APT technique to investigate the grain boundary chemistry of orthopyroxene (opx) and olivine. These minerals are the most abundant in the upper mantle and their grain boundaries may be important geochemical reservoirs in Earth. Moreover, physical properties such as grain boundary diffusivity, conductivity, and mobility, are likely influenced by the presence or absence of impurities. Single crystals of opx and olivine grains, separated from a San Carlos xenolith, were deformed at 1 GPa and 1500 K. Plastic deformation promoted dynamic recrystallization, creating new grain boundaries within a chemically homogeneous medium. Needle shaped specimens of opx-opx and olivine-olivine grain boundaries were prepared using standard lift out techniques and a dual beam focused ion beam (FIB). APT analyses were performed in laser mode with laser energy of 50 pJ/pulse, repetition rate of 200 kHz, and detection rate of 1%. A 3-D distribution of elements was reconstructed and 1-D profiles across the grain boundary have been calculated. Fe, Al, and Ca show enrichments at the grain boundaries for both phases, consistent with previous studies that used STEM/EDX or EPMA techniques. Although qualitatively similar, the spatial resolution of the APT method is significantly better than other methods, and our data show that the grain-boundary enrichment of minor elements in both olivine and pyroxene compositions is limited to a region no greater than 2-4 nm thick. These new data place constraints on the thickness of the grain boundary zone with unparalleled precision, allowing more accurate calculation of partition coefficients as well as diffusion coefficients from experimental studies of grain boundary diffusion.

Regression without truth with Markov chain Monte-Carlo

NASA Astrophysics Data System (ADS)

Madan, Hennadii; Pernuš, Franjo; Likar, Boštjan; Å piclin, Žiga

2017-03-01

Regression without truth (RWT) is a statistical technique for estimating error model parameters of each method in a group of methods used for measurement of a certain quantity. A very attractive aspect of RWT is that it does not rely on a reference method or "gold standard" data, which is otherwise difficult RWT was used for a reference-free performance comparison of several methods for measuring left ventricular ejection fraction (EF), i.e. a percentage of blood leaving the ventricle each time the heart contracts, and has since been applied for various other quantitative imaging biomarkerss (QIBs). Herein, we show how Markov chain Monte-Carlo (MCMC), a computational technique for drawing samples from a statistical distribution with probability density function known only up to a normalizing coefficient, can be used to augment RWT to gain a number of important benefits compared to the original approach based on iterative optimization. For instance, the proposed MCMC-based RWT enables the estimation of joint posterior distribution of the parameters of the error model, straightforward quantification of uncertainty of the estimates, estimation of true value of the measurand and corresponding credible intervals (CIs), does not require a finite support for prior distribution of the measureand generally has a much improved robustness against convergence to non-global maxima. The proposed approach is validated using synthetic data that emulate the EF data for 45 patients measured with 8 different methods. The obtained results show that 90% CI of the corresponding parameter estimates contain the true values of all error model parameters and the measurand. A potential real-world application is to take measurements of a certain QIB several different methods and then use the proposed framework to compute the estimates of the true values and their uncertainty, a vital information for diagnosis based on QIB.

A novel Kinetic Monte Carlo algorithm for Non-Equilibrium Simulations

NASA Astrophysics Data System (ADS)

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

2012-02-01

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

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

NASA Astrophysics Data System (ADS)

Chen, Jundong

2018-03-01

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

Compressive power spectrum sensing for vibration-based output-only system identification of structural systems in the presence of noise

NASA Astrophysics Data System (ADS)

Tau Siesakul, Bamrung; Gkoktsi, Kyriaki; Giaralis, Agathoklis

2015-05-01

Motivated by the need to reduce monetary and energy consumption costs of wireless sensor networks in undertaking output-only/operational modal analysis of engineering structures, this paper considers a multi-coset analog-toinformation converter for structural system identification from acceleration response signals of white noise excited linear damped structures sampled at sub-Nyquist rates. The underlying natural frequencies, peak gains in the frequency domain, and critical damping ratios of the vibrating structures are estimated directly from the sub-Nyquist measurements and, therefore, the computationally demanding signal reconstruction step is by-passed. This is accomplished by first employing a power spectrum blind sampling (PSBS) technique for multi-band wide sense stationary stochastic processes in conjunction with deterministic non-uniform multi-coset sampling patterns derived from solving a weighted least square optimization problem. Next, modal properties are derived by the standard frequency domain peak picking algorithm. Special attention is focused on assessing the potential of the adopted PSBS technique, which poses no sparsity requirements to the sensed signals, to derive accurate estimates of modal structural system properties from noisy sub- Nyquist measurements. To this aim, sub-Nyquist sampled acceleration response signals corrupted by various levels of additive white noise pertaining to a benchmark space truss structure with closely spaced natural frequencies are obtained within an efficient Monte Carlo simulation-based framework. Accurate estimates of natural frequencies and reasonable estimates of local peak spectral ordinates and critical damping ratios are derived from measurements sampled at about 70% below the Nyquist rate and for SNR as low as 0db demonstrating that the adopted approach enjoys noise immunity.

Probing off-Hugoniot states in Ta, Cu, and Al to 1000 GPa compression with magnetically driven liner implosions

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

Lemke, R. W., E-mail: rwlemke@sandia.gov; Dolan, D. H.; Dalton, D. G.

We report on a new technique for obtaining off-Hugoniot pressure vs. density data for solid metals compressed to extreme pressure by a magnetically driven liner implosion on the Z-machine (Z) at Sandia National Laboratories. In our experiments, the liner comprises inner and outer metal tubes. The inner tube is composed of a sample material (e.g., Ta and Cu) whose compressed state is to be inferred. The outer tube is composed of Al and serves as the current carrying cathode. Another aluminum liner at much larger radius serves as the anode. A shaped current pulse quasi-isentropically compresses the sample as itmore » implodes. The iterative method used to infer pressure vs. density requires two velocity measurements. Photonic Doppler velocimetry probes measure the implosion velocity of the free (inner) surface of the sample material and the explosion velocity of the anode free (outer) surface. These two velocities are used in conjunction with magnetohydrodynamic simulation and mathematical optimization to obtain the current driving the liner implosion, and to infer pressure and density in the sample through maximum compression. This new equation of state calibration technique is illustrated using a simulated experiment with a Cu sample. Monte Carlo uncertainty quantification of synthetic data establishes convergence criteria for experiments. Results are presented from experiments with Al/Ta, Al/Cu, and Al liners. Symmetric liner implosion with quasi-isentropic compression to peak pressure ∼1000 GPa is achieved in all cases. These experiments exhibit unexpectedly softer behavior above 200 GPa, which we conjecture is related to differences in the actual and modeled properties of aluminum.« less

Probing off-Hugoniot states in Ta, Cu, and Al to 1000 GPa compression with magnetically driven liner implosions

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

Lemke, R. W.; Dolan, D. H.; Dalton, D. G.

We report on a new technique for obtaining off-Hugoniot pressure vs. density data for solid metals compressed to extreme pressure by a magnetically driven liner implosion on the Z-machine (Z) at Sandia National Laboratories. In our experiments, the liner comprises inner and outer metal tubes. The inner tube is composed of a sample material (e.g., Ta and Cu) whose compressed state is to be inferred. The outer tube is composed of Al and serves as the current carrying cathode. Another aluminum liner at much larger radius serves as the anode. A shaped current pulse quasi-isentropically compresses the sample as itmore » implodes. The iterative method used to infer pressure vs. density requires two velocity measurements. Photonic Doppler velocimetry probes measure the implosion velocity of the free (inner) surface of the sample material and the explosion velocity of the anode free (outer) surface. These two velocities are used in conjunction with magnetohydrodynamic simulation and mathematical optimization to obtain the current driving the liner implosion, and to infer pressure and density in the sample through maximum compression. This new equation of state calibration technique is illustrated using a simulated experiment with a Cu sample. Monte Carlo uncertainty quantification of synthetic data establishes convergence criteria for experiments. Results are presented from experiments with Al/Ta, Al/Cu, and Al liners. Symmetric liner implosion with quasi-isentropic compression to peak pressure ~1000 GPa is achieved in all cases. Lastly, these experiments exhibit unexpectedly softer behavior above 200 GPa, which we conjecture is related to differences in the actual and modeled properties of aluminum.« less

Probing off-Hugoniot states in Ta, Cu, and Al to 1000 GPa compression with magnetically driven liner implosions

DOE PAGES

Lemke, R. W.; Dolan, D. H.; Dalton, D. G.; ...

2016-01-07

We report on a new technique for obtaining off-Hugoniot pressure vs. density data for solid metals compressed to extreme pressure by a magnetically driven liner implosion on the Z-machine (Z) at Sandia National Laboratories. In our experiments, the liner comprises inner and outer metal tubes. The inner tube is composed of a sample material (e.g., Ta and Cu) whose compressed state is to be inferred. The outer tube is composed of Al and serves as the current carrying cathode. Another aluminum liner at much larger radius serves as the anode. A shaped current pulse quasi-isentropically compresses the sample as itmore » implodes. The iterative method used to infer pressure vs. density requires two velocity measurements. Photonic Doppler velocimetry probes measure the implosion velocity of the free (inner) surface of the sample material and the explosion velocity of the anode free (outer) surface. These two velocities are used in conjunction with magnetohydrodynamic simulation and mathematical optimization to obtain the current driving the liner implosion, and to infer pressure and density in the sample through maximum compression. This new equation of state calibration technique is illustrated using a simulated experiment with a Cu sample. Monte Carlo uncertainty quantification of synthetic data establishes convergence criteria for experiments. Results are presented from experiments with Al/Ta, Al/Cu, and Al liners. Symmetric liner implosion with quasi-isentropic compression to peak pressure ~1000 GPa is achieved in all cases. Lastly, these experiments exhibit unexpectedly softer behavior above 200 GPa, which we conjecture is related to differences in the actual and modeled properties of aluminum.« less

FASTER 3: A generalized-geometry Monte Carlo computer program for the transport of neutrons and gamma rays. Volume 1: Summary report

NASA Technical Reports Server (NTRS)

Jordan, T. M.

1970-01-01

The theory used in FASTER-III, a Monte Carlo computer program for the transport of neutrons and gamma rays in complex geometries, is outlined. The program includes the treatment of geometric regions bounded by quadratic and quadric surfaces with multiple radiation sources which have specified space, angle, and energy dependence. The program calculates, using importance sampling, the resulting number and energy fluxes at specified point, surface, and volume detectors. It can also calculate minimum weight shield configuration meeting a specified dose rate constraint. Results are presented for sample problems involving primary neutron, and primary and secondary photon, transport in a spherical reactor shield configuration.

Scalable hierarchical PDE sampler for generating spatially correlated random fields using nonmatching meshes: Scalable hierarchical PDE sampler using nonmatching meshes

DOE PAGES

Osborn, Sarah; Zulian, Patrick; Benson, Thomas; ...

2018-01-30

This work describes a domain embedding technique between two nonmatching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is to apply the multilevel Monte Carlo (MLMC) method for the quantification of output uncertainties of PDEs with random input coefficients on general and unstructured computational domains. We propose a highly scalable, hierarchical sampling method to generate realizations of a Gaussian random field on a given unstructured mesh by solving a reaction–diffusion PDE with a stochastic right-hand side. The stochastic PDE is discretized using the mixed finite element method on anmore » embedded domain with a structured mesh, and then, the solution is projected onto the unstructured mesh. This work describes implementation details on how to efficiently transfer data from the structured and unstructured meshes at coarse levels, assuming that this can be done efficiently on the finest level. We investigate the efficiency and parallel scalability of the technique for the scalable generation of Gaussian random fields in three dimensions. An application of the MLMC method is presented for quantifying uncertainties of subsurface flow problems. Here, we demonstrate the scalability of the sampling method with nonmatching mesh embedding, coupled with a parallel forward model problem solver, for large-scale 3D MLMC simulations with up to 1.9·109 unknowns.« less

Scalable hierarchical PDE sampler for generating spatially correlated random fields using nonmatching meshes: Scalable hierarchical PDE sampler using nonmatching meshes

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

Osborn, Sarah; Zulian, Patrick; Benson, Thomas

This work describes a domain embedding technique between two nonmatching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is to apply the multilevel Monte Carlo (MLMC) method for the quantification of output uncertainties of PDEs with random input coefficients on general and unstructured computational domains. We propose a highly scalable, hierarchical sampling method to generate realizations of a Gaussian random field on a given unstructured mesh by solving a reaction–diffusion PDE with a stochastic right-hand side. The stochastic PDE is discretized using the mixed finite element method on anmore » embedded domain with a structured mesh, and then, the solution is projected onto the unstructured mesh. This work describes implementation details on how to efficiently transfer data from the structured and unstructured meshes at coarse levels, assuming that this can be done efficiently on the finest level. We investigate the efficiency and parallel scalability of the technique for the scalable generation of Gaussian random fields in three dimensions. An application of the MLMC method is presented for quantifying uncertainties of subsurface flow problems. Here, we demonstrate the scalability of the sampling method with nonmatching mesh embedding, coupled with a parallel forward model problem solver, for large-scale 3D MLMC simulations with up to 1.9·109 unknowns.« less