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1
Delgado, H. E., L. M. Sarro, G. Clementini, T. Muraveva, and A. Garofalo. "Hierarchical Bayesian model to inferPL(Z)relations usingGaiaparallaxes." Astronomy & Astrophysics 623 (March 2019): A156. http://dx.doi.org/10.1051/0004-6361/201832945.
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In a recent study we analysed period–luminosity–metallicity (PLZ) relations for RR Lyrae stars using theGaiaData Release 2 (DR2) parallaxes. It built on a previous work that was based on the firstGaiaData Release (DR1), and also included period–luminosity (PL) relations for Cepheids and RR Lyrae stars. The method used to infer the relations fromGaiaDR2 data and one of the methods used forGaiaDR1 data was based on a Bayesian model, the full description of which was deferred to a subsequent publication. This paper presents the Bayesian method for the inference of the parameters ofPL(Z) relations used in those studies, the main feature of which is to manage the uncertainties on observables in a rigorous and well-founded way. The method encodes the probability relationships between the variables of the problem in a hierarchical Bayesian model and infers the posterior probability distributions of thePL(Z) relationship coefficients using Markov chain Monte Carlo simulation techniques. We evaluate the method with several semi-synthetic data sets and apply it to a sample of 200 fundamental and first-overtone RR Lyrae stars for whichGaiaDR1 parallaxes and literatureKs-band mean magnitudes are available. We define and test several hyperprior probabilities to verify their adequacy and check the sensitivity of the solution with respect to the prior choice. The main conclusion of this work, based on the test with semi-syntheticGaiaDR1 parallaxes, is the absolute necessity of incorporating the existing correlations between the period, metallicity, and parallax measurements in the form of model priors in order to avoid systematically biased results, especially in the case of non-negligible uncertainties in the parallaxes. The relation coefficients obtained here have been superseded by those presented in our recent paper that incorporates the findings of this work and the more recentGaiaDR2 measurements.
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Caflisch, Russel E. "Monte Carlo and quasi-Monte Carlo methods." Acta Numerica 7 (January 1998): 1–49. http://dx.doi.org/10.1017/s0962492900002804.
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Monte Carlo is one of the most versatile and widely used numerical methods. Its convergence rate, O(N−1/2), is independent of dimension, which shows Monte Carlo to be very robust but also slow. This article presents an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction techniques. Accelerated convergence for Monte Carlo quadrature is attained using quasi-random (also called low-discrepancy) sequences, which are a deterministic alternative to random or pseudo-random sequences. The points in a quasi-random sequence are correlated to provide greater uniformity. The resulting quadrature method, called quasi-Monte Carlo, has a convergence rate of approximately O((logN)kN−1). For quasi-Monte Carlo, both theoretical error estimates and practical limitations are presented. Although the emphasis in this article is on integration, Monte Carlo simulation of rarefied gas dynamics is also discussed. In the limit of small mean free path (that is, the fluid dynamic limit), Monte Carlo loses its effectiveness because the collisional distance is much less than the fluid dynamic length scale. Computational examples are presented throughout the text to illustrate the theory. A number of open problems are described.
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Giles, Michael B. "Multilevel Monte Carlo methods." Acta Numerica 24 (April 27, 2015): 259–328. http://dx.doi.org/10.1017/s096249291500001x.
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Monte Carlo methods are a very general and useful approach for the estimation of expectations arising from stochastic simulation. However, they can be computationally expensive, particularly when the cost of generating individual stochastic samples is very high, as in the case of stochastic PDEs. Multilevel Monte Carlo is a recently developed approach which greatly reduces the computational cost by performing most simulations with low accuracy at a correspondingly low cost, with relatively few simulations being performed at high accuracy and a high cost.In this article, we review the ideas behind the multilevel Monte Carlo method, and various recent generalizations and extensions, and discuss a number of applications which illustrate the flexibility and generality of the approach and the challenges in developing more efficient implementations with a faster rate of convergence of the multilevel correction variance.
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Erfanian, Hamid Reza, Seyed Jaliledin Ghaznavi Bidgoli, and Parvin Shakibaei. "The pricing of spread option using simulation." International Journal of Applied Mathematical Research 6, no. 4 (October 19, 2017): 121. http://dx.doi.org/10.14419/ijamr.v6i4.7914.
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Monte Carlo simulation is one of the most common and popular method of options pricing. The advantages of this method are being easy to use, suitable for all kinds of standard and exotic options and also are suitable for higher dimensional problems. But on the other hand Monte Carlo variance convergence rate is which due to that it will have relatively slow convergence rate to answer the problems, as to achieve accuracy when it has been d-dimensions, complexity is . For this purpose, several methods are provided in quasi Monte Carlo simulation to increase variance convergence rate as variance reduction techniques, so far. One of the latest presented methods is multilevel Monte Carlo that is introduced by Giles in 2008. This method not only reduces the complexity of computing amount in use of Euler discretization scheme and the amount in use of Milstein discretization scheme, but also has the ability to combine with other variance reduction techniques. In this paper, using Multilevel Monte Carlo method by taking Milstein discretization scheme, pricing spread option and compared complexity of computing with standard Monte Carlo method. The results of Multilevel Monte Carlo method in pricing spread options are better than standard Monte Carlo simulation.
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Belova, Irina V., M. J. Brown, and Graeme E. Murch. "Calculation of Phenomenological Coefficients by Monte Carlo Computer Simulation Methods." Defect and Diffusion Forum 249 (January 2006): 27–34. http://dx.doi.org/10.4028/www.scientific.net/ddf.249.27.
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In this paper we first review the principal indirect and direct Monte Carlo methods for calculating the Onsager phenomenological transport coefficients in solid state diffusion. We propose a new Monte Carlo method that makes use of a steady state calculation of a flux of atoms that is driven by a difference in chemical potential of the atoms between a source and a sink plane. The method is demonstrated for the simple cubic one component lattice gas with nearest neighbour interactions. The new method gives results in good agreement with a Monte Carlo method based on Einsteinian expressions for the phenomenological coefficients.
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Suhobokov, Alexander. "APPLICATION OF MONTE CARLO SIMULATION METHODS IN RISK MANAGEMENT." Journal of Business Economics and Management 8, no. 3 (September 30, 2007): 165–68. http://dx.doi.org/10.3846/16111699.2007.9636165.
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The paper deals with Monte Carlo simulation method and its application in Risk Management. The author with the help of MATLAB 7.0 introduces new modification of Monte Carlo algorithm aimed at fast and effective calculation of financial organization's Value at Risk (VaR) by the example of Parex Bank's FOREX exposure.
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Pažický, Martin. "Stock Price Simulation Using Bootstrap and Monte Carlo." Scientific Annals of Economics and Business 64, no. 2 (June 27, 2017): 155–70. http://dx.doi.org/10.1515/saeb-2017-0010.
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Abstract In this paper, an attempt is made to assessment and comparison of bootstrap experiment and Monte Carlo experiment for stock price simulation. Since the stock price evolution in the future is extremely important for the investors, there is the attempt to find the best method how to determine the future stock price of BNP Paribas′ bank. The aim of the paper is define the value of the European and Asian option on BNP Paribas′ stock at the maturity date. There are employed four different methods for the simulation. First method is bootstrap experiment with homoscedastic error term, second method is blocked bootstrap experiment with heteroscedastic error term, third method is Monte Carlo simulation with heteroscedastic error term and the last method is Monte Carlo simulation with homoscedastic error term. In the last method there is necessary to model the volatility using econometric GARCH model. The main purpose of the paper is to compare the mentioned methods and select the most reliable. The difference between classical European option and exotic Asian option based on the experiment results is the next aim of tis paper.
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Zhao, Zhiqiang, and Feiyue Zhou. "Optimal Control Methods of Experiment Times in System-of-Systems Combat Computer Simulation." ITM Web of Conferences 26 (2019): 03004. http://dx.doi.org/10.1051/itmconf/20192603004.
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In the process of scheme optimization, in order to eliminate the influence of random factor, it needs to conduct computer simulation of Monte Carlo. Therefore, it is proposed to introduce confidence interval into systemof-systems combat simulation, and confirm whether the Monte Carlo simulation finishes according to data sample generated in simulation process. According to characteristic of data sample, extend correspondingly confidence interval method, and under the condition of obtaining the solution meeting accuracy requirements, reduce simulation experiment times as far as possible. The simulation experiment results show that confidence interval extension method is able to possess self-adaptation control to Monte Carlo simulation.
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Wang, Liangliang, Shijia Wang, and Alexandre Bouchard-Côté. "An Annealed Sequential Monte Carlo Method for Bayesian Phylogenetics." Systematic Biology 69, no. 1 (June 6, 2019): 155–83. http://dx.doi.org/10.1093/sysbio/syz028.
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Abstract We describe an “embarrassingly parallel” method for Bayesian phylogenetic inference, annealed Sequential Monte Carlo (SMC), based on recent advances in the SMC literature such as adaptive determination of annealing parameters. The algorithm provides an approximate posterior distribution over trees and evolutionary parameters as well as an unbiased estimator for the marginal likelihood. This unbiasedness property can be used for the purpose of testing the correctness of posterior simulation software. We evaluate the performance of phylogenetic annealed SMC by reviewing and comparing with other computational Bayesian phylogenetic methods, in particular, different marginal likelihood estimation methods. Unlike previous SMC methods in phylogenetics, our annealed method can utilize standard Markov chain Monte Carlo (MCMC) tree moves and hence benefit from the large inventory of such moves available in the literature. Consequently, the annealed SMC method should be relatively easy to incorporate into existing phylogenetic software packages based on MCMC algorithms. We illustrate our method using simulation studies and real data analysis.
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Spanos, P. D., and B. A. Zeldin. "Monte Carlo Treatment of Random Fields: A Broad Perspective." Applied Mechanics Reviews 51, no. 3 (March 1, 1998): 219–37. http://dx.doi.org/10.1115/1.3098999.
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A review of a number of methods for random fields simulation in conjunction with Monte Carlo studies of probabilistic mechanics problems is presented from a broad perspective. This article complements some of the previous review articles in that it compares various simulation algorithms, assesses their relative computational efficiency and versatility, discusses the properties of generated field samples, and incorporates some of the recent developments. Collectively, a comprehensive discussion of the covariance decomposition method, the spectral method, the ARMA method, the noise shower method, the scale refinement methods, and the turning band method is attempted. For tutorial effectiveness univariate, uni-dimensional, Gaussian, and homogeneous fields are discussed, primarily in connection with various simulation methods. Nevertheless, appropriate references are included addressing the simulation of more general fields. This review article contains 110 references.
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Zhang, Xiaobo, Zhenzhou Lu, Kai Cheng, and Yanping Wang. "A novel reliability sensitivity analysis method based on directional sampling and Monte Carlo simulation." Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 234, no. 4 (February 12, 2020): 622–35. http://dx.doi.org/10.1177/1748006x19899504.
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Local reliability sensitivity and global reliability sensitivity are required in reliability-based design optimization, since they can provide rich information including variable importance ranking and gradient information. However, traditional Monte Carlo simulation is inefficient for engineering application. A novel numerical simulation method based on Monte Carlo simulation and directional sampling is proposed to simultaneously estimate local reliability sensitivity and global reliability sensitivity. By suitable transformation, local reliability sensitivity and global reliability sensitivity can be estimated simultaneously as by-products of reliability analysis for Monte Carlo simulation method. The key is how to efficiently classify Monte Carlo simulation samples into two categories: failure samples and safety samples. Directional sampling method, a classical reliability analysis method, is more efficient than Monte Carlo simulation for reliability analysis. A novel strategy based on nearest Euclidean distance is proposed to approximately screen out failure samples from Monte Carlo simulation samples using directional sampling samples. In the proposed method, local reliability sensitivity and global reliability sensitivity are by-products of reliability analysis using the directional sampling method. Different from existing methods, the proposed method does not introduce hypotheses and does not require additional gradient information. The advantages of the Monte Carlo simulation and directional sampling are well integrated in the proposed method. The accuracy and the efficiency of the proposed method for local reliability sensitivity and global reliability sensitivity are demonstrated by four numerical examples and two engineering examples including the headless rivet and the wing box structure.
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Saraiva Júnior, Abraão Freires, Cristiane de Mesquita Tabosa, and Reinaldo Pacheco da Costa. "Monte Carlo simulation applied to order economic analysis." Production 21, no. 1 (March 11, 2011): 149–64. http://dx.doi.org/10.1590/s0103-65132011005000016.
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The use of mathematical and statistical methods can help managers to deal with decision-making difficulties in the business environment. Some of these decisions are related to productive capacity optimization in order to obtain greater economic gains for the company. Within this perspective, this study aims to present the establishment of metrics to support economic decisions related to process or not orders in a company whose products have great variability in variable direct costs per unit that generates accounting uncertainties. To achieve this objective, is proposed a five-step method built from the integration of Management Accounting and Operations Research techniques, emphasizing the Monte Carlo simulation. The method is applied from a didactic example which uses real data achieved through a field research carried out in a plastic products industry that employ recycled material. Finally, it is concluded that the Monte Carlo simulation is effective for treating variable direct costs per unit variability and that the proposed method is useful to support decision-making related to order acceptance.
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PREVE, NIKOLAOS P., and EMMANUEL N. PROTONOTARIOS. "MONTE CARLO SIMULATION ON COMPUTATIONAL FINANCE FOR GRID COMPUTING." International Journal of Modeling, Simulation, and Scientific Computing 03, no. 03 (May 17, 2012): 1250010. http://dx.doi.org/10.1142/s1793962312500109.
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Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in simulating complex systems. Because of their reliance on repeated computation of random or pseudo-random numbers, these methods are most suited to calculation by a computer and tend to be used when it is infeasible or impossible to compute an exact result with a deterministic algorithm. In finance, Monte Carlo simulation method is used to calculate the value of companies, to evaluate economic investments and financial derivatives. On the other hand, Grid Computing applies heterogeneous computer resources of many geographically disperse computers in a network in order to solve a single problem that requires a great number of computer processing cycles or access to large amounts of data. In this paper, we have developed a simulation based on Monte Carlo method which is applied on grid computing in order to predict through complex calculations the future trends in stock prices.
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RATNASARI, DEWA AYU AGUNG PUTRI, KOMANG DHARMAWAN, and DESAK PUTU EKA NILAKUSMAWATI. "PENENTUAN NILAI KONTRAK OPSI TIPE BINARY PADA KOMODITS KAKAO MENGGUNAKAN METODE QUASI MONTE CARLO DENGAN BARISAN BILANGAN ACAK FAURE." E-Jurnal Matematika 6, no. 4 (November 28, 2017): 214. http://dx.doi.org/10.24843/mtk.2017.v06.i04.p168.
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Contract options are the most important part of an investment strategy. An option is a contract that entitles the owner or holder to sell an asset on a designated maturity date. A binary or asset-or-nothing option is an option in which the option holder will perform or not the option. There are many methods used in determining the option contract value, one of this is the Monte Carlo Quasi method of the Faure random. The purpose of this study is to determine the value of binary type option contract using the Quasi Monte Carlo method of the Faure random and compare with the Monte Carlo method. The results of this study indicate that the option contract calculated by the Monte Carlo Quasi method results in a more fair value. Monte Carlo method simulation 10.000 generate standard error is 0.9316 and the option convergence at 18.9144. While Quasi Monte Carlo simulation 3000 generate standard error is 0.09091 and the option convergence at 18.8203. This show the Quasi Monte Carlo method reaches a faster convergent of Monte Carlo method.
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Guelfi, Marcelo, and Carlos López-Vazquez. "Comparing the Thiessen’s Method against simpler alternatives using Monte Carlo Simulation." Revista Cartográfica, no. 96 (April 30, 2018): 125–38. http://dx.doi.org/10.35424/rcarto.i96.191.
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Estimating the expected value of a function over geographic areas is problem with a long history. In the beginning of the XX-th century the most common method was just the arithmetic mean of the field measurements ignoring data location. In 1911, Thiessen introduced a new weighting procedure measuring influence through an area and thus indirectly considering closeness between them. In another context, Quenouville created in 1949 the jackknife method which is used to estimate the bias and the standard deviation. In 1979 Efron invented the bootstrap method which, among other things, is useful to estimate the expected value and the confidence interval (CI) from a population. Although the Thiessen’s method has been used for more than 100 years, we were unable to find systematic analysis comparing its efficiency against the simple mean, or even to more recent methods like jackknife or boostrap. In this work we compared four methods to estimate de expected value. Sample mean, Thiessen, the so called here jackknifed Thiessen and bootstrap. All of them are feasible for routine use in a network of fixed locations. The comparison was made using the Friedman’s Test after a Monte Carlo simulation. Two cases were taken for study: one analytic with three arbitrary functions and the other using experimental data from daily rain measured with a satellite. The results show that Thiessen’s method is the best estimator in almost all the cases with a 95% of confidence interval. Unlike the others, the last two considered methods supply a suitable CI, but the one obtained through jackknifed Thiessen was even more accurate, opening the door for future work.
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Cathcart, Mark J., Hsiao Yen Lok, Alexander J. McNeil, and Steven Morrison. "CALCULATING VARIABLE ANNUITY LIABILITY “GREEKS” USING MONTE CARLO SIMULATION." ASTIN Bulletin 45, no. 2 (January 5, 2015): 239–66. http://dx.doi.org/10.1017/asb.2014.31.
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AbstractThe implementation of hedging strategies for variable annuity products requires the calculation of market risk sensitivities (or “Greeks”). The complex, path-dependent nature of these products means that these sensitivities are typically estimated by Monte Carlo methods. Standard market practice is to use a “bump and revalue” method in which sensitivities are approximated by finite differences. As well as requiring multiple valuations of the product, this approach is often unreliable for higher-order Greeks, such as gamma, and alternative pathwise (PW) and likelihood-ratio estimators should be preferred. This paper considers a stylized guaranteed minimum withdrawal benefit product in which the reference equity index follows a Heston stochastic volatility model in a stochastic interest rate environment. The complete set of first-order sensitivities with respect to index value, volatility and interest rate and the most important second-order sensitivities are calculated using PW, likelihood-ratio and mixed methods. It is observed that the PW method delivers the best estimates of first-order sensitivities while mixed estimation methods deliver considerably more accurate estimates of second-order sensitivities; moreover there are significant computational gains involved in using PW and mixed estimators rather than simple BnR estimators when many Greeks have to be calculated.
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Moselhi, Osama, and Mohammadjavad Arabpour Roghabadi. "Risk quantification using fuzzy-based Monte Carlo simulation." Journal of Information Technology in Construction 25 (February 4, 2020): 87–98. http://dx.doi.org/10.36680/j.itcon.2020.005.
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Estimating cost contingency of construction projects depends largely on data captured from previous projects and/or experience and judgment of members of project team. Mote Carlo simulation is commonly used in estimating contingency, where its accuracy was reported to depend on number of iterations used in the simulation process, probability density functions associated with each project cost item being considered and the correlation among these cost items. The literature reveals that the latter is the most important issue for accurate estimate of contingency. It, however, requires the calculation of coefficients of correlation among cost items based on captured historical records of cost data. Subjective correlation was introduced to alleviate the difficulties associated with the calculation of these coefficients. This paper presents a newly developed method for cost contingency estimation that considers subjective correlations and allows for contingency estimation with and without computer simulation. Unlike the methods reported in the literature, the present method considers uncertainty associated with the coefficients of correlation and utilizes earlier work of the first author in calculating the variance of total project cost. It also allows for assessing the impact of variable covariance matrix on the estimated project cost using a simple and user-friendly computational platform. The application of the developed method on cost data captured from two databases demonstrates its use and accuracy in estimating cost contingency. The results are compared to those produced by others using Monte Carlo Simulation with and without correlation using an actual project data.
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LAI, YONGZENG, and HAIXIANG YAO. "SIMULATION OF MULTI-ASSET OPTION GREEKS UNDER A SPECIAL LÉVY MODEL BY MALLIAVIN CALCULUS." ANZIAM Journal 57, no. 3 (January 2016): 280–98. http://dx.doi.org/10.1017/s1446181115000292.
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We discuss simulation of sensitivities or Greeks of multi-asset European style options under a special Lévy process model: that is, the subordinated Brownian motion model. The Malliavin calculus method combined with Monte Carlo and quasi-Monte Carlo methods is used in the simulations. Greeks are expressed in terms of the expectations of the option payoff functions multiplied by the weights involving Malliavin derivatives for multi-asset options. Numerical results show that the Malliavin calculus method is usually more efficient than the finite difference method for options with nonsmooth payoffs. The superiority of the former method over the latter is even more significant when both are combined with quasi-Monte Carlo methods.
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Kahn, James, Emilio Dorigatti, Kilian Lieret, Andreas Lindner, and Thomas Kuhr. "Selective background Monte Carlo simulation at Belle II." EPJ Web of Conferences 245 (2020): 02028. http://dx.doi.org/10.1051/epjconf/202024502028.
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The large volume of data expected to be produced by the Belle II experiment presents the opportunity for studies of rare, previously inaccessible processes. Investigating such rare processes in a high data volume environment necessitates a correspondingly high volume of Monte Carlo simulations to prepare analyses and gain a deep understanding of the contributing physics processes to each individual study. This resulting challenge, in terms of computing resource requirements, calls for more intelligent methods of simulation, in particular for processes with very high background rejection rates. This work presents a method of predicting in the early stages of the simulation process the likelihood of relevancy of an individual event to the target study using graph neural networks. The results show a robust training that is integrated natively into the existing Belle II analysis software framework.
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Behjati, Hesam, and Mohammad Hosein Bagheripour. "Efficiency of the Monte Carlo Simulation Method in Evaluation of Liquefaction Potential." Advanced Materials Research 261-263 (May 2011): 618–22. http://dx.doi.org/10.4028/www.scientific.net/amr.261-263.618.
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Reliability analysis is a useful and comprehensive approach for estimation of liquefaction potential in soil layers. The most commonly used methods in reliability analysis are first order second moment (FOSM) and Hasofer&Lind approaches. These methods are based on some simplified assumptions such as the use of a linear performance function or the numerical estimation which often lead to less accurate results. Monte Carlo simulation (MCS) approach is an alternative and more accurate method for reliability analysis and for evaluation of liquefaction potential in soil deposits. In this study, liquefaction potential is assessed using MCS approach followed by a case study in which an area prone to liquefaction is investigated. Results are compared with those obtained by other reliability methods. The efficiency of the MCS method is discussed in the paper.
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Dai, Hongsheng. "Exact Monte Carlo simulation for fork-join networks." Advances in Applied Probability 43, no. 02 (June 2011): 484–503. http://dx.doi.org/10.1017/s000186780000495x.
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In a fork-join network each incoming job is split into K tasks and the K tasks are simultaneously assigned to K parallel service stations for processing. For the distributions of response times and queue lengths of fork-join networks, no explicit formulae are available. Existing methods provide only analytic approximations for the response time and the queue length distributions. The accuracy of such approximations may be difficult to justify for some complicated fork-join networks. In this paper we propose a perfect simulation method based on coupling from the past to generate exact realisations from the equilibrium of fork-join networks. Using the simulated realisations, Monte Carlo estimates for the distributions of response times and queue lengths of fork-join networks are obtained. Comparisons of Monte Carlo estimates and theoretical approximations are also provided. The efficiency of the sampling algorithm is shown theoretically and via simulation.
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Dai, Hongsheng. "Exact Monte Carlo simulation for fork-join networks." Advances in Applied Probability 43, no. 2 (June 2011): 484–503. http://dx.doi.org/10.1239/aap/1308662489.
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In a fork-join network each incoming job is split into K tasks and the K tasks are simultaneously assigned to K parallel service stations for processing. For the distributions of response times and queue lengths of fork-join networks, no explicit formulae are available. Existing methods provide only analytic approximations for the response time and the queue length distributions. The accuracy of such approximations may be difficult to justify for some complicated fork-join networks. In this paper we propose a perfect simulation method based on coupling from the past to generate exact realisations from the equilibrium of fork-join networks. Using the simulated realisations, Monte Carlo estimates for the distributions of response times and queue lengths of fork-join networks are obtained. Comparisons of Monte Carlo estimates and theoretical approximations are also provided. The efficiency of the sampling algorithm is shown theoretically and via simulation.
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Woinaroschy, Alexandru. "Prediction of Protein Secondary-Structure by Monte Carlo Simulation." Revista de Chimie 59, no. 2 (March 9, 2008): 199–204. http://dx.doi.org/10.37358/rc.08.2.1733.
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Proteins have four structural categories. The primary structure is the amino-acid sequence of the polypeptide chain. The secondary structure is the conformation, representing of the backbone (a-helix or b-sheet). The knowledge of protein structure has a paramount theoretical and practical importance (e.g. cancer disease) and a huge effort of research was devoted to this subject. Despite the fact that several methods were developed for protein secondary-structure prediction, there are no consensuses of their results. In this paper was proposed an new, original, method to investigate the influence of the number of amino acids and the percentage contents in the twenty amino acids for the prediction of protein secondary-structure, respectively Monte Carlo simulation using a multilayer neural networks. The method is very promising in connection with the use of large data bases.
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Huang, Zhi Qin, Xiao Hui Fan, and Gai Ling Zheng. "The Establishment of Mathematical Model of LED Based on Monte Carlo Method." Key Engineering Materials 480-481 (June 2011): 1571–76. http://dx.doi.org/10.4028/www.scientific.net/kem.480-481.1571.
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Monte Carlo (MC method) of the computer simulation of the traditional forms of light-emitting diode (LED) is used for modeling and simulation. MC method than the method of geometrical optics of the LED is more suitable for complex optical structure on a Computer. MC method, the more accurate numerical solutions can improve the efficiency of LED design that is an effective means of LED design. MC method is with a very clear and unique advantage in the establishment of LED structure model.This paper first introduces the research background and purpose of the LED, then Monte Carlo methods Are outlined, and finally, some mathematical models of LED are given based on Monte Carlo method
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Liu, Jun, Fan Yang, and Lijia Ren. "Study on Reliability Evaluation Method Based on Improved Monte Carlo Method." E3S Web of Conferences 64 (2018): 04008. http://dx.doi.org/10.1051/e3sconf/20186404008.
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The advancement in science and technology comes with continuously expanding power system scale, increasingly complex system operation condition and higher requirements for accuracy and speed of power system reliability evaluation, but actual calculation methods cannot meet the needs. Therefore, there is need to improve the reliability of conventional power distribution network so that requirements of calculation speed and calculation accuracy can be met. In this paper, reliability of the power distribution network will be evaluated using improved Monte Carlo method with uniform sampling. The average value is obtained through calculation of state of multiple sub-intervals and test functions, which effectively improves calculation accuracy, and further increases the utilization of random numbers. By improving the uniform sampling method, the Monte Carlo simulation variance is reduced, and evaluation and calculation efficiency is improved. At the same time, unqualified power grid is selected for analysis. Based on the simulation results, qualified power distribution networks are compared to point out where the requirements are not met. Also, comparative analysis is made on the effect of power distribution network grid structure etc. on the user’s power supply. Finally, suggestions for improving power distribution network reliability are given from equipment reliability, grid structure.
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de Raynal, Paul-Éric Chaudru, Gilles Pagès, and Clément Rey. "Numerical methods for Stochastic differential equations: two examples." ESAIM: Proceedings and Surveys 64 (2018): 65–77. http://dx.doi.org/10.1051/proc/201864065.
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The goal of this paper is to present a series of recent contributions arising in numerical probability. First we present a contribution to a recently introduced problem: stochastic differential equations with constraints in law, investigated through various theoretical and numerical viewpoints. Such a problem may appear as an extension of the famous Skorokhod problem. Then a generic method to approximate in a weak way the invariant distribution of an ergodic Feller process by a Langevin Monte Carlo simulation. It is an extension of a method originally developed for diffusions and based on the weighted empirical measure of an Euler scheme with decreasing step. Finally, we mention without details a recent development of a multilevel Langevin Monte Carlo simulation method for this type of problem.
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Guo, Ying Ying, and Zhi Gang Zhang. "Simple Application of Variance Reduction Techniques in Monte Carlo and Missile Simulation." Advanced Materials Research 962-965 (June 2014): 2760–65. http://dx.doi.org/10.4028/www.scientific.net/amr.962-965.2760.
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Nowadays the Monte Carlo Method has grown in maturity in the simulation area of missile trails. Considering that, this paper presents several techniques of variance reduction combined with Monte Carlo method. Hoping that these techniques will improve the precision and reliability of the simulation .The results of tests indicate that different methods can reduce the variance of missile simulation in various degrees which will help us handle the conclusions of simulation well and truly.
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Pakyuz-Charrier, Evren, Mark Jessell, Jérémie Giraud, Mark Lindsay, and Vitaliy Ogarko. "Topological analysis in Monte Carlo simulation for uncertainty propagation." Solid Earth 10, no. 5 (October 10, 2019): 1663–84. http://dx.doi.org/10.5194/se-10-1663-2019.
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Abstract. This paper proposes and demonstrates improvements for the Monte Carlo simulation for uncertainty propagation (MCUP) method. MCUP is a type of Bayesian Monte Carlo method aimed at input data uncertainty propagation in implicit 3-D geological modeling. In the Monte Carlo process, a series of statistically plausible models is built from the input dataset of which uncertainty is to be propagated to a final probabilistic geological model or uncertainty index model. Significant differences in terms of topology are observed in the plausible model suite that is generated as an intermediary step in MCUP. These differences are interpreted as analogous to population heterogeneity. The source of this heterogeneity is traced to be the non-linear relationship between plausible datasets' variability and plausible model's variability. Non-linearity is shown to mainly arise from the effect of the geometrical rule set on model building which transforms lithological continuous interfaces into discontinuous piecewise ones. Plausible model heterogeneity induces topological heterogeneity and challenges the underlying assumption of homogeneity which global uncertainty estimates rely on. To address this issue, a method for topological analysis applied to the plausible model suite in MCUP is introduced. Boolean topological signatures recording lithological unit adjacency are used as n-dimensional points to be considered individually or clustered using the density-based spatial clustering of applications with noise (DBSCAN) algorithm. The proposed method is tested on two challenging synthetic examples with varying levels of confidence in the structural input data. Results indicate that topological signatures constitute a powerful discriminant to address plausible model heterogeneity. Basic topological signatures appear to be a reliable indicator of the structural behavior of the plausible models and provide useful geological insights. Moreover, ignoring heterogeneity was found to be detrimental to the accuracy and relevance of the probabilistic geological models and uncertainty index models. Highlights. Monte Carlo uncertainty propagation (MCUP) methods often produce topologically distinct plausible models. Plausible models can be differentiated using topological signatures. Topologically similar probabilistic geological models may be obtained through topological signature clustering.
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Song, Chun Xue, Yi Zhang, and Ying Yi Cao. "Comparison of Monte Carlo Simulation and Response Surface Method by Using ANSYS PDS." Applied Mechanics and Materials 578-579 (July 2014): 1449–53. http://dx.doi.org/10.4028/www.scientific.net/amm.578-579.1449.
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Monte Carlo Simulation and Response Surface Method are two very powerful reliability analysis methods. Normally, in the reliability analysis of complex structures, the limit state function often can not be expressed in a closed-form. Usually, the codes for probabilistic analysis need to be combined with finite element models. ANSYS Probabilistic Design System (PDS) has provided a package to conduct probabilistic analysis automatically. This paper is going to compare the performance of these methods through an easy engineering problem in ANSYS. The results are going to be derived to show the feature of applying the corresponding reliability methods.
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Liu, S. Charles, and S. Jack Hu. "Variation Simulation for Deformable Sheet Metal Assemblies Using Finite Element Methods." Journal of Manufacturing Science and Engineering 119, no. 3 (August 1, 1997): 368–74. http://dx.doi.org/10.1115/1.2831115.
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Traditional variation analysis methods, such as Root Sum Square method and Monte Carlo simulation, are not applicable to sheet metal assemblies because of possible part deformation during the assembly process. This paper proposes the use of finite element methods (FEM) in developing mechanistic variation simulation models for deformable sheet metal parts with complex two or three dimensional free form surfaces. Mechanistic variation simulation provides improved analysis by combining engineering structure models and statistical analysis in predicting the assembly variation. Direct Monte Carlo simulation in FEM is very time consuming, because hundreds or thousands of FEM runs are required to obtain a realistic assembly distribution. An alternative method, based on the Method of Influence Coefficients, is developed to improve the computational efficiency, producing improvements by several orders of magnitude. Simulations from both methods yield almost identical results. An example illustrates the developed methods used for evaluating sheet metal assembly variation. The new approaches provide an improved understanding of sheet metal assembly processes.
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Song, Yihan, Ali Luo, and Yongheng Zhao. "Measuring Stellar Radial Velocity using Markov Chain Monte Carlo(MCMC) Method." Proceedings of the International Astronomical Union 9, S298 (May 2013): 441. http://dx.doi.org/10.1017/s1743921313007060.
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AbstractStellar radial velocity is estimated by using template fitting and Markov Chain Monte Carlo(MCMC) methods. This method works on the LAMOST stellar spectra. The MCMC simulation generates a probability distribution of the RV. The RV error can also computed from distribution.
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HOSEINIE, SEYED HADI, BEHZAD GHODRATI, and UDAY KUMAR. "MONTE CARLO RELIABILITY SIMULATION OF WATER SYSTEM OF LONGWALL SHEARER MACHINE." International Journal of Reliability, Quality and Safety Engineering 20, no. 06 (December 2013): 1350023. http://dx.doi.org/10.1142/s021853931350023x.
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The water system of coal shearer machine consists of three main subsystems namely spray jets, water & hoses, and filters which are connected and working in series configuration. In this paper, the Kamat–Riley Monte Carlo simulation method was used for reliability analysis of the considered system. The studied data was collected from an Iranian longwall coal mine for analysis. The MATLAB software was used for simulation and then reliability plot of water system in shearer machine was determined. The results show that the reliability of shearer machine reduces to almost zero in a period of 300 h. Comparison between the results of analytical method and simulated reliability plot presents that for analyzed data set, in high reliability levels (28% ≤), the simulation approach estimates the higher reliability than analytical method. The maximum difference between the results of analytical and simulation methods is 23%. However, in low reliability levels (≤ 28%) there is no remarkable difference between the methods.
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Akaturk, E., and B. Tanatar. "Two-dimensional Bose polaron using diffusion Monte Carlo method." International Journal of Modern Physics B 33, no. 21 (August 20, 2019): 1950238. http://dx.doi.org/10.1142/s0217979219502382.
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We investigate the properties of a mobile impurity immersed in a two-dimensional (2D) Bose gas at zero temperature using quantum Monte Carlo (QMC) methods. The repulsive boson–boson and impurity-boson interactions are modeled by hard-disk potentials with positive scattering lengths a and b, respectively, taken to be equal to the scattering lengths. We calculate the polaron energy and effective mass for the density parameter na2 [Formula: see text] 1 and the ratio a/b. We find that at low densities perturbation theory adequately describes the simulation results. As the impurity-boson interaction strength increases, the polaron mass is enhanced. Additionally, we calculate the structural properties of the Bose system, such as the impurity-boson pair-correlation function and the change of the density profile around the impurity.
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ASTUTI, PUTU WIDYA, KOMANG DHARMAWAN, and KARTIKA SARI. "MENENTUKAN HARGA OPSI DENGAN METODE MONTE CARLO BERSYARAT MENGGUNAKAN BARISAN KUASI ACAK FAURE." E-Jurnal Matematika 10, no. 3 (August 31, 2021): 141. http://dx.doi.org/10.24843/mtk.2021.v10.i03.p334.
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An option contract is a contract that gives the owner the right to sell or even to buy an asset at the predetermined price and period time. The conditional Monte Carlo is one of the several methods that is used to determine the option price which in the process uses random numbers with normal standard distribution. At the same time, the random number generator can be substituted by using a quasi-random sequence, as in Faure's quasi-random sequence. The aim of this study is to determine the contract price of the call option with the European type by applying the conditional Monte Carlo method. This method used the Faure quasi-random sequence and compared it with the method of Monte Carlo standard, Monte Carlo standard in using the quasi-random sequence of Faure, and conditional Monte Carlo. The results of this study showed that the call option calculated using the conditional Monte Carlo method using the quasi-random Faure sequence began to stabilize at the 5000th simulation for K = 32575 and K = 34725 and in the 10000th simulation for K = 33000 and K = 33950. Research also show that with the conditional Monte Carlo in using the quasi-random sequence of Faure is more stable. Therefore, it is obtained its real value faster than the Monte Carlo standard, Monte Carlo standard in using the quasi-random sequence of Faure, and conditional Monte Carlo. The MAPE value of conditional Monte Carlo in using the quasi-random sequences of Faure and the Monte Carlo standard is smaller than the Monte Carlo standard in using the quasi-random sequence of Faure, and conditional Monte Carlo. Therefore, it can be said to be more accurate when calculating the European type call option price at BBCA.JK stocks.
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Bastin, Fabian, Cinzia Cirillo, and Stephane Hess. "Evaluation of Optimization Methods for Estimating Mixed Logit Models." Transportation Research Record: Journal of the Transportation Research Board 1921, no. 1 (January 2005): 35–43. http://dx.doi.org/10.1177/0361198105192100105.
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The performances of different simulation-based estimation techniques for mixed logit modeling are evaluated. A quasi–Monte Carlo method (modified Latin hypercube sampling) is compared with a Monte Carlo algorithm with dynamic accuracy. The classic Broyden–Fletcher–Goldfarb–Shanno (BFGS) optimization algorithm line-search approach and trust region methods, which have proved to be extremely powerful in nonlinear programming, are also compared. Numerical tests are performed on two real data sets: stated preference data for parking type collected in the United Kingdom, and revealed preference data for mode choice collected as part of a German travel diary survey. Several criteria are used to evaluate the approximation quality of the log likelihood function and the accuracy of the results and the associated estimation runtime. Results suggest that the trust region approach outperforms the BFGS approach and that Monte Carlo methods remain competitive with quasi–Monte Carlo methods in high-dimensional problems, especially when an adaptive optimization algorithm is used.
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Zhao, Di, and Haiwu He. "DSMC: Fast direct simulation Monte Carlo solver for the Boltzmann equation by Multi-Chain Markov Chain and multicore programming." International Journal of Modeling, Simulation, and Scientific Computing 07, no. 02 (June 2016): 1650009. http://dx.doi.org/10.1142/s1793962316500094.
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Direct Simulation Monte Carlo (DSMC) solves the Boltzmann equation with large Knudsen number. The Boltzmann equation generally consists of three terms: the force term, the diffusion term and the collision term. While the first two terms of the Boltzmann equation can be discretized by numerical methods such as the finite volume method, the third term can be approximated by DSMC, and DSMC simulates the physical behaviors of gas molecules. However, because of the low sampling efficiency of Monte Carlo Simulation in DSMC, this part usually occupies large portion of computational costs to solve the Boltzmann equation. In this paper, by Markov Chain Monte Carlo (MCMC) and multicore programming, we develop Direct Simulation Multi-Chain Markov Chain Monte Carlo (DSMC3): a fast solver to calculate the numerical solution for the Boltzmann equation. Computational results show that DSMC3 is significantly faster than the conventional method DSMC.
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Warren, M. C., M. T. Dove, E. R. Myers, A. Bosenick, E. J. Palin, C. I. Sainz-Diaz, B. S. Guiton, and S. A. T. Redfern. "Monte Carlo methods for the study of cation ordering in minerals." Mineralogical Magazine 65, no. 2 (April 2001): 221–48. http://dx.doi.org/10.1180/002646101550235.
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AbstractThis paper reviews recent applications of Monte Carlo methods for the study of cation ordering in minerals. We describe the program Ossia99, designed for the simulation of complex ordering processes and for use on parallel computers. A number of applications for the study of long-range and short-range order are described, including the use of the Monte Carlo methods to compute quantities measured in an NMR experiment. The method of thermodynamic integration for the determination of the free energy is described in some detail, and several applications of the method to determine the thermodynamics of disordered systems are outlined.
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LAM, CHI-HANG, and M. T. LUNG. "GREEN'S FUNCTION AND SUPER-PARTICLE METHODS FOR KINETIC SIMULATION OF HETEROEPITAXY." International Journal of Modern Physics B 21, no. 23n24 (September 30, 2007): 4219–24. http://dx.doi.org/10.1142/s0217979207045438.
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Arrays of nanosized three dimensional islands are known to self-assemble spontaneously on strained heteroepitaxial thin films. We simulate the dynamics using kinetic Monte Carlo method based on a ball and spring lattice model. Green's function and super-particle methods which greatly enhance the computational efficiency are explained.
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O'brien, Frank. "Probability Methods for Detecting Randomness in Small Sample Spatial Distributions." Perceptual and Motor Skills 78, no. 3 (June 1994): 715–20. http://dx.doi.org/10.1177/003151259407800306.
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Several probability and statistical methods are discussed for detecting spatial randomness in two dimensions. One method is derived and proposed for its ease of application. Monte Carlo simulation results are presented in support of the theoretical assumptions of the proposed method.
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Chaudhary, Arun Kumar, and Vijay Kumar. "A Bayesian Estimation and Predictionof Gompertz Extension Distribution Using the MCMC Method." Nepal Journal of Science and Technology 19, no. 1 (July 1, 2020): 142–60. http://dx.doi.org/10.3126/njst.v19i1.29795.
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In this paper, the Markov chain Monte Carlo (MCMC) method is used to estimate the parameters of the Gompertz extension distribution based on a complete sample. We have developed a procedure to obtain Bayes estimates of the parameters of the Gompertz extension distribution using Markov Chain Monte Carlo (MCMC) simulation method in OpenBUGS, established software for Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods. We have obtained the Bayes estimates of the parameters, hazard and reliability functions, and their probability intervals are also presented. We have applied the predictive check method to discuss the issue of model compatibility. A real data set is considered for illustration under uniform and gamma priors.
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Gao, Xuemei, Dongya Deng, and Yue Shan. "Lattice Methods for Pricing American Strangles with Two-Dimensional Stochastic Volatility Models." Discrete Dynamics in Nature and Society 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/165259.
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The aim of this paper is to extend the lattice method proposed by Ritchken and Trevor (1999) for pricing American options with one-dimensional stochastic volatility models to the two-dimensional cases with strangle payoff. This proposed method is compared with the least square Monte-Carlo method via numerical examples.
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Wu, Xin-Yu, Hai-Lin Zhou, and Shou-Yang Wang. "Valuing American options by least-squares randomized quasi-Monte Carlo methods." Journal of Financial Engineering 01, no. 02 (June 2014): 1450016. http://dx.doi.org/10.1142/s2345768614500160.
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Valuation of American options is a difficult and challenging problem encountered in financial engineering. Longstaff and Schwartz [Longstaff, FA and ES Schwartz (2001). Valuing American Options by Simulation: A Simple Least-squares Approach, Review of Financial Studies, 14(1), 113–147.] Proposed the least-squares Monte Carlo (LSM) method for valuing American options. As this approach is intuitive and easy to apply, it has received much attention in the finance literature. However, a drawback of the LSM method is the low efficiency. In order to overcome this problem, we propose the least-squares randomized quasi-Monte Carlo (LSRQM) methods which can be viewed as a use low-discrepancy sequences as a variance reduction technique in the LSM method for valuing American options in this paper. Numerical results demonstrate that our proposed LSRQM methods are more efficient than the LSM method in terms of the valuation accuracy, the computation time and the convergence rate.
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Jiang, Yu, Yoko Hoshi, Manabu Machida, and Gen Nakamura. "A Hybrid Inversion Scheme Combining Markov Chain Monte Carlo and Iterative Methods for Determining Optical Properties of Random Media." Applied Sciences 9, no. 17 (August 24, 2019): 3500. http://dx.doi.org/10.3390/app9173500.
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Near-infrared spectroscopy (NIRS) including diffuse optical tomography is an imaging modality which makes use of diffuse light propagation in random media. When optical properties of a random medium are investigated from boundary measurements of reflected or transmitted light, iterative inversion schemes such as the Levenberg–Marquardt algorithm are known to fail when initial guesses are not close enough to the true value of the coefficient to be reconstructed. In this paper, we investigate how this weakness of iterative schemes is overcome using Markov chain Monte Carlo. Using time-resolved measurements performed against a polyurethane-based phantom, we present a case that the Levenberg–Marquardt algorithm fails to work but the proposed hybrid method works well. Then, with a toy model of diffuse optical tomography we illustrate that the Levenberg–Marquardt method fails when it is trapped by a local minimum but the hybrid method can escape from local minima by using the Metropolis–Hastings Markov chain Monte Carlo algorithm until it reaches the valley of the global minimum. The proposed hybrid scheme can be applied to different inverse problems in NIRS which are solved iteratively. We find that for both numerical and phantom experiments, optical properties such as the absorption and reduced scattering coefficients can be retrieved without being trapped by a local minimum when Monte Carlo simulation is run only about 100 steps before switching to an iterative method. The hybrid method is compared with simulated annealing. Although the Metropolis–Hastings MCMC arrives at the steady state at about 10,000 Monte Carlo steps, in the hybrid method the Monte Carlo simulation can be stopped way before the burn-in time.
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Hoang, Tuan Duc, Tai Thanh Duong, Oanh Thi Luong, and Loan Thi Hong Truong. "Application of variance reduction techniques in EGSnrc based Monte-Carlo method." Science and Technology Development Journal 22, no. 2 (July 12, 2019): 258–63. http://dx.doi.org/10.32508/stdj.v22i2.1234.
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Introduction: Monte Carlo (MC) is considered to be the most accurate method to calculate dose distribution in radiation therapy. However, the limitation of MC simulations is the long calculation time to reach the desired statistical uncertainty in the dose calculation as well as in clinical practice. To overcome the above limitations, Variance reduction techniques (VRTs) has developed and shorten the calculation time while maintaining accuracy. Therefore, the purpose of this study is the application of VRTs in code EGSnrc to find the optimal method for accelerator simulation and calculated dose distribution using MC method.
Methods: The linear Accelerator HPD Siemens Primus at the General Hospital of Dong Nai had been simulated by using BEAMnrc code and several variance reduction techniques such as: range rejection, photon forcing, bremsstrahlung photon splitting (uniform, selective and direction)... These VRTs were used under the same set of input parameters as histories of 2x108, photon energy of 6 MV, structure, size and material of the phantom… The computational efficiency ε is calculated by the following equation ε = 1/T.σ2 where T is the CUP time of calculation and σ2 is an estimate of the variance, for evaluating and selecting the VRT which gives the best computational efficiency.
Results: The results showed a good agreement between the calculated dose and measured ones when applying different VRTs. These techniques were significantly reduced uncertainty in simulation compared the analog cases. Specifically, the efficiency of DBS and UBS improved by more than 90 times and 15 times compared with the analog instances, respectively. Rang rejection and photon forcing techniques also haveimproved the efficiency of simulation, but not significantly.
Conclusions: The application of the VRTs for EGSnrc increase the efficiency of the simulation. VRTs is a powerful tool that should be applied for the simulation by code EGSnrc to improve calculation efficiency by reducing simulation time and its variance. Our results show that the direction bremsstrahlung splitting (DBS) gives thebest computational efficiency.
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Hlobilová, Adéla, and Matěj Lepš. "Parameter Study on Subset Simulation for Reliability Assessment." Advanced Materials Research 1144 (March 2017): 128–35. http://dx.doi.org/10.4028/www.scientific.net/amr.1144.128.
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Small probability of failure characterizes a good structural design. Prediction of such a structural safety is time consuming considering that sampling methods such as Monte Carlo method or Latin Hypercube sampling are used. Therefore, more specialized methods are developed. A Subset simulation is one of the new techniques based on modifying the failure event as an intersection of nested intermediate events that are easier to solve. This paper deals with a parameter study of the Subset simulation with modified Metropolis algorithm for Markov chain Monte Carlo using distinct proposal distributions. Different setting is then compared on reliability assessment benchmarks, namely on two mathematical functions with different failure probabilities and on a 23-bar planar truss bridge.
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Karchani, A., O. Ejtehadi, and R. S. Myong. "A Probabilistic Automatic Steady State Detection Method for the Direct Simulation Monte Carlo." Communications in Computational Physics 20, no. 5 (November 2016): 1183–209. http://dx.doi.org/10.4208/cicp.080815.240316a.
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AbstractThe statistical error associated with sampling in the DSMC method can be categorized as type I and II, which are caused by the incorrect rejection and acceptance of the null hypothesis, respectively. In this study, robust global and local automatic steady state detection methods were developed based on an ingenious method based purely on the statistics and kinetics of particles. The key concept is built upon probabilistic automatic reset sampling (PARS) to minimize the type II error caused by incorrect acceptance of the samples that do not belong to the steady state. The global steady state method is based on a relative standard variation of collisional invariants, while the local steady state method is based on local variations in the distribution function of particles at each cell. In order to verify the capability of the new methods, two benchmark cases — the one-dimensional shear-driven Couette flow and the two-dimensional high speed flow past a vertical wall—were extensively investigated. Owing to the combined effects of the automatic detection and local reset sampling, the local steady state detection method yielded a substantial gain of 30-36% in computational cost for the problem studied. Moreover, the local reset feature outperformed the automatic detection feature in overall computational savings.
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GOODNICK, STEPHEN M., and MARCO SARANITI. "CELLULAR MONTE CARLO SIMULATION OF HIGH FIELD TRANSPORT IN SEMICONDUCTOR DEVICES." International Journal of High Speed Electronics and Systems 17, no. 03 (September 2007): 465–73. http://dx.doi.org/10.1142/s0129156407004655.
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Here we discuss the use of the Cellular Monte Carlo (CMC) method for full band simulation of semiconductor transport and device modeling. The electronic band structure and phonon spectra are used as direct inputs to the program for both cubic, hexagonal, and strained crystal structures using both empirical and ab initio methods. As a particular example, this method is applied to study high field transport in GaN and GaN/AlGaN heterostructures, where good agreement is obtained between the simulated results, and experimental pulse I-V measurements of transport. For device simulation, the CMC algorithm is coupled to an efficient 2D/3D multi-grid Poisson solver. We discuss the application of this algorithm to several technological problems of interest, including ultra-short channel Si/Ge MOSFETs, III-V compound HEMTs, and AlGaN/GaN HEMTs.
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MATUTTIS, HANS-GEORG, KURT FISCHER, NOBUYASU ITO, and MASAMICHI ISHIKAWA. "AUXILIARY FIELD METHODS FOR THE SIMULATION OF QUANTUM COMPUTATION CIRCUITS." International Journal of Modern Physics C 13, no. 07 (September 2002): 917–29. http://dx.doi.org/10.1142/s0129183102003681.
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One obstacle in the simulation of quantum circuits is the high dimension of the Hilbert space. Using auxiliary field decompositions known from many-particle simulation, we can transform the mathematical description of the quantum circuit into a combination low-dimensional product states which can be sampled using Monte Carlo techniques. We demonstrate the method using Simon's algorithm for the detection of the period of a function.
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Zhao, Jin Quan, Chen Lu Zhang, Wei Hua Luo, and Jun Zhao. "A Probabilistic Optimal Power Flow Calculation Method with Latin Hypercube Sampling." Advanced Materials Research 918 (April 2014): 183–90. http://dx.doi.org/10.4028/www.scientific.net/amr.918.183.
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Among the solving methods of probabilistic optimal power flow (P-OPF), Monte Carlo Simulation (MCS) combined with random sampling (RS) is widely used due to its high accuracy. In order to further improve that, this paper proposes a way of using Monte Carlo Simulation with Latin hypercube sampling (LHS) to calculate the consumption of generating cost under many random variables. Numerical results of IEEE 14-bus and IEEE 118-bus systems show that the Latin hypercube sampling method provides more accurate performance in dealing with POPF under the condition of a smaller sample size, comparing with random sampling method. Thus the Latin hypercube sampling method can replace the MCS with random sampling as the benchmark method of other algorithms.
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Zhang, Yimin. "Stochastic Responses of Multi-Degree-of-Freedom Uncertain Hysteretic Systems." Shock and Vibration 18, no. 1-2 (2011): 387–96. http://dx.doi.org/10.1155/2011/189702.
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On the basis of the Bouc-Wen hysteretic model, the effective numerical method for the response of nonlinear multi-degree-of-freedom (MDOF) stochastic hysteretic systems is presented using second moment method. Using this method, the mean values, variances and covariances are computed. The Monte Carlo simulation is applied to validate the method. The results obtained by the two methods are contrasted, and the solutions of the method in this paper agreed very well with the Monte Carlo simulation. It has solved the random response of nonlinear stochastic vibration systems which is caused by the stochastic hysteretic loop itself.