Tolerance Analysis for Design of Multistage Manufacturing Processes Using Number-Theoretical Net Method (NT-net)

Recent developments in modeling stream of variation in multistage manufacturing system along with the urgent need for yield enhancement in the semiconductor industry has led to complex large scale simulation problems in design and performance prediction, thus challenging current Monte Carlo (MC) based simulation techniques. MC method prevails in statistical simulation approaches for multi-dimensional cases with general (i.e., non-Gaussian) distributions and/or complex response functions. A method is proposed based on number theory (NT-net) to reduce computing effort and the variability of MC's results in tolerance design and circuit performance simulation. The sampling strategy is improved by introducing NT-net that can provide better convergent rate over MC. The new method is presented and verified using several case studies, including analytical and industrial cases of a filter design and analyses of a four-bar mechanism. Results indicate a 90–95% reduction of computation effort with significant improvement in accuracy that can be achieved by the proposed technique.     

Replica-exchange methods and predictions of helix configurations of membrane proteins

A simulation in generalized ensemble is based on a non-Boltzmann weight factor and performs a random walk in potential energy space, which allows the simulation to avoid getting trapped in states of local-minimum energy states. In this article, we review uses of the generalized-ensemble algorithms. Three well-known methods, namely, multicanonical algorithm (MUCA), simulated tempering (ST) and replica-exchange method (REM), are described first. Both Monte Carlo (MC) and molecular dynamics (MD) versions of the algorithms are given. We then present the results of the application of replica-exchange MC method to the predictions of membrane protein structures.     

用于Monte Carlo模拟的复杂生物组织模型

Monte Carlo（MC）模拟被广泛应用于光子在生物组织中的传输研究。通常模拟时将生物组织近似为均匀的平板分层介质,当层状生物组织中含有异常物质（如肿瘤细胞等）或正常生物组织为非平板的复杂结构时,其模拟中的组织模型将会有相应的改变。通过探讨这几类生物组织的MC模拟模型,总结并分析模型建立的关键问题,对基于MC模拟的各种生物组织光学检测研究提供了指导。     

Development of Dual Ensemble Monte Carlo Program and its Application to the CO2/N2 Separation

Abstract

A novel Monte Carlo simulation named as Dual Ensemble Monte Carlo (DEMC) method is developed for the investigation of the membrane separation process. In this method the spatial combination of Grand Canonical MC and Canonical MC techniques is employed. The DEMC method can be used to calculate the separation factor at a specific chemical potential gradient. At first, a check on the accuracy of the DEMC method is made by generating gas density gradient between two reservoir regions. Thereafter, we applied this method to CO₂/N₂ gas separation by inorganic membranes and calculated the separation factor dependence on the size of micropore in membranes.     

Speeding up Monte Carlo molecular simulation by a non-conservative early rejection scheme

Monte Carlo (MC) molecular simulation describes fluid systems with rich information, and it is capable of predicting many fluid properties of engineering interest. In general, it is more accurate and representative than equations of state. On the other hand, it requires much more computational effort and simulation time. For that purpose, several techniques have been developed in order to speed up MC molecular simulations while preserving their precision. In particular, early rejection schemes are capable of reducing computational cost by reaching the rejection decision for the undesired MC trials at an earlier stage in comparison to the conventional scheme. In a recent work, we have introduced a ‘conservative’ early rejection scheme as a method to accelerate MC simulations while producing exactly the same results as the conventional algorithm. In this paper, we introduce a ‘non-conservative’ early rejection scheme, which is much faster than the conservative scheme, yet it preserves the precision of the method. The proposed scheme is tested for systems of structureless Lennard-Jones particles in both canonical and NVT-Gibbs ensembles. Numerical experiments were conducted at several thermodynamic conditions for different number of particles. Results show that at certain thermodynamic conditions, the non-conservative method is capable of doubling the speed of the MC molecular simulations in both canonical and NVT-Gibbs ensembles.     

Technical note: GAMMORA,a free,open-source,and validated GATE-based model for Monte-Carlo simulations of the Varian TrueBeam

PurposeMonte Carlo (MC) is the reference computation method for medical physics. In radiotherapy, MC computations are necessary for some issues (such as assessing figures of merit, double checks, and dose conversions). A tool based on GATE is proposed to easily create full MC simulations of the Varian TrueBeam STx.MethodsGAMMORA is a package that contains photon phase spaces as a pre-trained generative adversarial network (GAN) and the TrueBeam’s full geometry. It allows users to easily create MC simulations for simple or complex radiotherapy plans such as VMAT. To validate the model, the characteristics of generated photons are first compared to those provided by Varian (IAEA format). Simulated data are also compared to measurements in water and heterogeneous media. Simulations of 8 SBRT plans are compared to measurements (in a phantom). Two examples of applications (a second check and interplay effect assessment) are presented.ResultsThe simulated photons generated by the GAN have the same characteristics (energy, position, and direction) as the IAEA data. Computed dose distributions of simple cases (in water) and complex plans delivered in a phantom are compared to measurements, and the Gamma index (3%/3mm) was always superior to 98%. The feasibility of both clinical applications is shown.ConclusionsThis model is now shared as a free and open-source tool that generates radiotherapy MC simulations. It has been validated and used for five years. Several applications can be envisaged for research and clinical purposes.     

Modeling and design optimization of asynchronous flexible assembly systems with statistical process control and repair

This article presents the implementation of hybrid procedures involving the use of analytical performance evaluation techniques, discrete event simulation, and Monte Carlo optimization methods for the stochastic design optimization of asynchronous flexible assembly systems (AFASs) with statistical process control (SPC) and repair loops. AFASs are extremely complex and difficult to analyze in that such systems are subject to starvation and blocking effects, random jam occurrences at workstations, and splitting and merging of the assembly flow due to repair loops. Hence, an integrated approach simultaneously analyzing the interactions between product quality and optimal/near optimal system design is pursued. In the analytical analysis stage, a model based on GI/G/1 queueing network theory is used. In the Monte Carlo optimization stage, two alternative stochastic optimization approaches, namely, heuristic versions of stochastic quasigradient and simulated annealing algorithms, are implemented and compared in terms of their capabilities of solving complex AFAS design problems. The hybrid procedures presented appear to perform reasonably well in designing AFASs to reach a target production rate.     

A Monte Carlo method for the simulation of kinetie models

The purpose of this note is to illustrate the feasibility of simulating kinetic systems, such as commonly encountered in photosynthesis research, using the Monte Carlo (MC) method. In this approach, chemical events are considered at the molecular level where they occur randomly and the macroscopic kinetic evolution results from averaging a large number of such events. Their repeated simulation is easily accomplished using digital computing. It is shown that the MC approach is well suited to the capabilities and resources of modern microcomputers. A software package is briefly described and discussed, allowing a simple programming of any kinetic model system and its resolution. The execution is reasonably fast and accurate; it is not subject to such instabilities as found with the conventional analytical approach.Abbreviations MC Monte Carlo - RN random number - PSU photosynthetic unit Dedicated to Prof. L.N.M. Duysens on the occasion of his retirement.     

Lower confidence bounds for prediction accuracy in high dimensions via AROHIL Monte Carlo

MOTIVATION: Implementation and development of statistical methods for high-dimensional data often require high-dimensional Monte Carlo simulations. Simulations are used to assess performance, evaluate robustness, and in some cases for implementation of algorithms. But simulation in high dimensions is often very complex, cumbersome and slow. As a result, performance evaluations are often limited, robustness minimally investigated and dissemination impeded by implementation challenges. This article presents a method for converting complex, slow high-dimensional Monte Carlo simulations into simpler, faster lower dimensional simulations. RESULTS: We implement the method by converting a previous Monte Carlo algorithm into this novel Monte Carlo, which we call AROHIL Monte Carlo. AROHIL Monte Carlo is shown to exactly or closely match pure Monte Carlo results in a number of examples. It is shown that computing time can be reduced by several orders of magnitude. The confidence bound method implemented using AROHIL outperforms the pure Monte Carlo method. Finally, the utility of the method is shown by application to a number of real microarray datasets.     

Direct Determination of Fluid Phase Equilibria by Simulation in the Gibbs Ensemble: A Review

This paper provides an extensive review of the literature on the Gibbs ensemble Monte Carlo method for direct determination of phase coexistence in fluids. The Gibbs ensemble technique is based on performing a simulation in two distinct regions in a way that ensures that the conditions of phase coexistence are satisfied in a statistical sense. Contrary to most other available techniques for this purpose, such as thermodynamic integration, grand canonical Monte Carlo or Widom test particle insertions, the Gibbs ensemble technique involves only a single simulation per coexistence point. A significant body of literature now exists on the method, its theoretical foundations, and proposed modifications for efficient determination of equilibria involving dense fluids and complex intermolecular potentials. Some practical aspects of Gibbs ensemble simulation are also discussed in this review. Applications of the technique to date range from studies of simple model potentials (for example Lennard–Jones, square-well or Yukawa fluids) to calculations of equilibria in mixtures with components described by realistic potentials. We conclude by discussing the limitations of the technique and potential future applications.     

Cost estimation method based on parallel Monte Carlo simulation and market investigation for engineering construction project

In this paper, a new cost estimation method based on parallel Monte Carlo simulation and market investigation for the chemical engineering construction project is proposed to consider both the uncertainties of cost estimation and market drivers. The critical items of exerting large impacts on the cost estimation are selected by the market investigation. Then important critical items are chosen by the sensitivity analysis based on the parallel Monte-Carlo simulation combining with the Likert scale method from critical items. The Relative Important Indices and Normalized Important Indices are obtained according to the discipline and procurement experts’ experience in the relative construction market. Then re-rankings of market drivers will be acted as guidelines for carrying out project cost simulations based on the parallel Monte-Carlo method, with inquired information of important critical items with more efficiency. An illustrative example in a petrochemical Engineering Procurement Construction contracting project in Saudi verified the validity and practicability of the proposed method.     

传递函数在生物组织光传输问题中的应用

本文将传递函数的概念引入生物组织光传输问题,并将传递函数理论用于面光源照射下生物组织内特定深度层面上光场强度分布的理论计算。结合Monte Carlo模拟获取脉冲相应函数,我们分析了不同面光源照射下层状组织样品透射面上的光场强度分布。理论计算结果与实验测试结果的一致性较好,这充分说明了本文建立的基于Monte Carlo模拟的传递函数方法是一种处理面光源照射下生物组织内光场空间的直接而有效的手段。     

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

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.     

A Monte Carlo method for combined segregation and linkage analysis.

We introduce a Monte Carlo approach to combined segregation and linkage analysis of a quantitative trait observed in an extended pedigree. In conjunction with the Monte Carlo method of likelihood-ratio evaluation proposed by Thompson and Guo, the method provides for estimation and hypothesis testing. The greatest attraction of this approach is its ability to handle complex genetic models and large pedigrees. Two examples illustrate the practicality of the method. One is of simulated data on a large pedigree; the other is a reanalysis of published data previously analyzed by other methods.     

Relevance of Internal Bremsstrahlung photons from 90Y decay: an experimental and Monte Carlo study

Internal Bremsstrahlung (IB) is a continuous electromagnetic radiation accompanying beta decay; however, this process is not considered in radiation protection studies, particularly when estimating exposure from beta-decaying radionuclides.The aims of the present work are: i) to show that neglecting the IB process in Monte Carlo (MC) simulation leads to an underestimation of the energy deposited in a ionization chamber, in the case of a high-energy pure beta emitter such as Yttrium-90 (⁹⁰Y), and ii) to determine the most reliable choice of source term for ⁹⁰Y IB to be used in MC simulations.For this radionuclide, commonly employed in nuclear medicine and radiochemistry applications, experimental data acquired with a well ionization chamber have been compared with Monte Carlo (MC) calculations carried out in the GAMOS framework. Simulations that do not include the effect of the IB process, are found to give results underestimating the experimental values by 12–14%.Consequently, two models for the IB energy spectra, previously described by Italiano et al. [1], have been implemented using MC simulation and a good agreement has been achieved with one of them.We therefore conclude that inclusion of IB process in Monte Carlo simulation packages is advisable for a more accurate and complete treatment of electromagnetic interactions.     

Numerical simulation of fibrous biomaterials with randomly distributed fiber network structure

This paper presents a computational framework to simulate the mechanical behavior of fibrous biomaterials with randomly distributed fiber networks. A random walk algorithm is implemented to generate the synthetic fiber network in 2D used in simulations. The embedded fiber approach is then adopted to model the fibers as embedded truss elements in the ground matrix, which is essentially equivalent to the affine fiber kinematics. The fiber–matrix interaction is partially considered in the sense that the two material components deform together, but no relative movement is considered. A variational approach is carried out to derive the element residual and stiffness matrices for finite element method (FEM), in which material and geometric nonlinearities are both included. Using a data structure proposed to record the network geometric information, the fiber network is directly incorporated into the FEM simulation without significantly increasing the computational cost. A mesh sensitivity analysis is conducted to show the influence of mesh size on various simulation results. The proposed method can be easily combined with Monte Carlo (MC) simulations to include the influence of the stochastic nature of the network and capture the material behavior in an average sense. The computational framework proposed in this work goes midway between homogenizing the fiber network into the surrounding matrix and accounting for the fully coupled fiber–matrix interaction at the segment length scale, and can be used to study the connection between the microscopic structure and the macro-mechanical behavior of fibrous biomaterials with a reasonable computational cost.     

PAFit: A Statistical Method for Measuring Preferential Attachment in Temporal Complex Networks

Preferential attachment is a stochastic process that has been proposed to explain certain topological features characteristic of complex networks from diverse domains. The systematic investigation of preferential attachment is an important area of research in network science, not only for the theoretical matter of verifying whether this hypothesized process is operative in real-world networks, but also for the practical insights that follow from knowledge of its functional form. Here we describe a maximum likelihood based estimation method for the measurement of preferential attachment in temporal complex networks. We call the method PAFit, and implement it in an R package of the same name. PAFit constitutes an advance over previous methods primarily because we based it on a nonparametric statistical framework that enables attachment kernel estimation free of any assumptions about its functional form. We show this results in PAFit outperforming the popular methods of Jeong and Newman in Monte Carlo simulations. What is more, we found that the application of PAFit to a publically available Flickr social network dataset yielded clear evidence for a deviation of the attachment kernel from the popularly assumed log-linear form. Independent of our main work, we provide a correction to a consequential error in Newman’s original method which had evidently gone unnoticed since its publication over a decade ago.     

Comparison of a Monte Carlo Strategy with a Combined DG/MDSA Method for Structure Determination of Bicyclic Peptides

The MC simulation program MOCCA and the combined methods of Distance Geometry and Molecular Dynamics are utilised for structural studies of four isomers of the bee venom toxin apamin. For the MC strategy the conformational space is reduced to torsional degrees of freedom. The study compares the efficiency of both simulation strategies for structure determination of bicyclic peptides and examines the limits of the Monte Carlo method. MOCCA shows a lower efficiency as compared to the combined methods of Distance Geometry and Molecular Dynamics for the structure determination of the bicyclic isomers of apamin.Electronic Supplementary Material available.     

A simple model of the hydrophobic effect for molecular simulation of interfacial phenomena

A coarse-grained model for simulation of interfacial phenomena in aqueous systems has been developed. The model captures the hydrophobic effect by only considering the structure and cohesiveness of water. Monte Carlo (MC) simulations of water-oil mixtures show that low concentrations of oil are solvated with little perturbation of the hydrogen bonding network structure of the water, while high concentrations of oil are excluded altogether. Analysis of the water structure in the simulations indicates that the water molecules maintain close to four coordination in the presence of solutes and the distribution of bond angles is not markedly affected by the presence of solutes. MC simulations of an alkane oligomer in water and a poly(ethylene oxide) (PEO) oligomer in water indicate that the chains are quite flexible and also do not perturb the network structure of the water phase.