Method“Monte Carlo”in healthcare

In public health,simulation modeling stands as an invaluable asset,enabling the evaluation of new systems without their physical implementation,experimentation with existing systems without operational adjustments,and testing system limits without real-world repercussions.In simulation modeling,the Monte Carlo method emerges as a powerful yet underutilized tool.Although the Monte Carlo method has not yet gained widespread prominence in healthcare,its technological capabilities hold promise for substantial cost reduction and risk mitigation.In this review article,we aimed to explore the transformative potential of the Monte Carlo method in healthcare contexts.We underscore the significance of experiential insights derived from simulated experimentation,especially in resource-constrained scenarios where time,financial constraints,and limited resources necessitate innovative and efficient approaches.As public health faces increasing challenges,incorporating the Monte Carlo method presents an opportunity for enhanced system construction,analysis,and evaluation.

Approach of technical decision-making by element flow analysis and Monte-Carlo simulation of municipal solid waste stream

This paper deals with the procedure and methodology which can be used to select the optimal treatment and disposal technology of municipal solid waste （MSW）, and to provide practical and effective technical support to policy-making, on the basis of study on solid waste management status and development trend in China and abroad. Focusing on various treatment and disposal technologies and processes of MSW, this study established a Monte-Carlo mathematical model of cost minimization for MSW handling subjected to environmental constraints. A new method of element stream （such as C, H, O, N, S） analysis in combination with economic stream analysis of MSW was developed. By following the streams of different treatment processes consisting of various techniques from generation, separation, transfer, transport, treatment, recycling and disposal of the wastes, the element constitution as well as its economic distribution in terms of possibility functions was identified. Every technique step was evaluated economically. The Mont-Carlo method was then conducted for model calibration. Sensitivity analysis was also carried out to identify the most sensitive factors. Model calibration indicated that landfill with power generation of landfill gas was economically the optimal technology at the present stage under the condition of more than 58% of C, H, O, N, S going to landfill. Whether or not to generate electricity was the most sensitive factor. If landfilling cost increases, MSW separation treatment was recommended by screening first followed with incinerating partially and composting partially with residue landfilling. The possibility of incineration model selection as the optimal technology was affected by the city scale. For big cities and metropolitans with large MSW generation, possibility for constructing large-scale incineration facilities increases, whereas, for middle and small cities, the effectiveness of incinerating waste decreases.

Free Energy Level Correction by Monte Carlo Resampling with Weighted Histogram Analysis Method

Free energy calculations may provide vital information for studying various chemical and biological processes.Quantum mechanical methods are required to accurately describe interaction energies,but their computations are often too demanding for conformational sampling.As a remedy,level correction schemes that allow calculating high level free energies based on conformations from lower level simulations have been developed.Here,we present a variation of a Monte Carlo(MC)resampling approach in relation to the weighted histogram analysis method(WHAM).We show that our scheme can generate free energy surfaces that can practically converge to the exact one with sufficient sampling,and that it treats cases with insufficient sampling in a more stable manner than the conventional WHAM-based level correction scheme.It can also provide a guide for checking the uncertainty of the levelcorrected surface and a well-defined criterion for deciding the extent of smoothing on the free energy surface for its visual improvement.We demonstrate these aspects by obtaining the free energy maps associated with the alanine dipeptide and proton transfer network of the KillerRed protein in explicit water,and exemplify that the MC resampled WHAM scheme can be a practical tool for producing free energy surfaces of realistic systems.

Monte Carlo方法在移动通信可靠性分析中的应用

文章主要探讨Monte Carlo方法在移动通信可靠性分析中的应用,并引入重要抽样技术对Monte Carlo方法进行优化。首先,文章介绍Monte Carlo方法的基本原理及其在移动通信可靠性分析中的应用。其次,引入重要抽样技术对该方法进行优化。最后,利用优化网络工程工具(Optimized Network Engineering Tools,OPNET)模拟平台构建相应的移动通信网络模型,并对比Monte Carlo方法和本文研究的优化方法在不同样本数量下的性能差异。结果表明,重要抽样技术的引入显著提高了Monte Carlo方法在移动通信可靠性分析中的准确性和效率,减少了方差,验证了该方法在移动通信可靠性分析中的有效性和实用性。

A Probabilistic Method for Motion Analysis of Caisson Breakwaters

It is assumed that, during the design period, the waves acting on breakwaters are divided into three types： standing wave, broken wave and breaking wave,and the wave heights fit the Rayleigh distribution while the water depths, wave periods and duration of breaking wave impact force fit normal distribution. Based on the random samples of water depths, wave heights, wave periods and duration of breaking wave impact force, the types of waves acting on breakwaters are distinguished and the time-history model of the wave force is determined. The motions of caisson breakwaters under the wave force are simulated by a dynamic numerical model and the statistic characteristics of the dynamic responses are analyzed with the Monte Carlo method. A probabilistic procedure to analyze the motion of the breakwater is developed therein. The procedure is illustrated by an example.

Sorption and permeation of gaseous molecules in amorphous and crystalline PPX C membranes: molecular dynamics and grand canonical Monte Carlo simulation studies

Amorphous and crystalline poly （chloro-p-xytylene） （PPX C） membranes are constructed by using a novel com- putational technique, that is, a combined method of NVT＋NPT-molecular dynamics （MD） and gradually reducing the size （GRS） methods. The related free volumes are defined as homology clusters. Then the sorption and the permeation of gases in PPX C polymers are studied using grand canonical Monte Carlo （GCMC） and NVT-MD methods. The results show that the crystalline PPX C membranes provide smaller free volumes for absorbing or transferring gases relative to the amorphous PPX C area. The gas sorption in PPX C membranes mainly belongs to the physical one, and H bonds can appear obviously in the amorphous area. By cluster analyzing on the mean square displacement of gases, we find that gases walk along the x axis in the crystalline area and walk randomly in the amorphous area. The calculated permeability coefficients are close to the experimental data.

A new hybrid method—combined heat flux method with Monte-Carlo method to analyze thermal radiation

A new hybrid method, Monte-Carlo-Heat-Flux （MCHF） method, was presented to analyze the radiative heat transfer of participating medium in a three-dimensional rectangular enclosure using combined the Monte-Carlo method with the heat flux method. Its accuracy and reliability was proved by comparing the computational results with exact results from classical ＂Zone Method＂.

Probabilistic analysis of embankment slope stability in frozen ground regions based on random finite element method

Prediction on the coupled thermal-hydraulic fields of embankment and cutting slopes is essential to the assessment on evolution of melting zone and natural permafrost table, which is usually a key factor for permafrost embankment design in frozen ground regions. The prediction may be further complicated due to the inherent uncertainties of material properties. Hence, stochastic analyses should be conducted. Firstly, Karhunen-Loeve expansion is applied to attain the random fields for hydraulic and thermal conductions. Next, the mixed-form modified Richards equation for mass transfer （i.e., mass equation） and the heat transport equation for heat transient flow in a variably saturated frozen soil are combined into one equation with temperature unknown. Furthermore, the finite element formulation for the coupled thermal-hydraulic fields is derived. Based on the random fields, the stochastic finite element analyses on stability of embankment are carried out. Numerical results show that stochastic analyses of embankment stability may provide a more rational picture for the distribution of factors of safety （FOS）, which is definitely useful for embankment design in frozen ground regions.

Solving the Schrodinger Equation on the Basis of Finite-Difference and Monte-Carlo Approaches

The paper presents a method of numerical solution of the Schrodinger equation, which combines the finite-difference and Monte-Carlo approaches. The resulting method was effective and economical and, to a certain extent, not improved, i.e. optimal. The method itself is formalized as an algorithm for the numerical solution of the Schrodinger equation for a molecule with an arbitrary number of quantum particles. The method is presented and simultaneously illustrated by examples of solving the one-dimensional and multidimensional Schrodinger equation in such problems: linear one-dimensional oscillator, hydrogen atom, ion and hydrogen molecule, water, benzene and metallic hydrogen.

A Multiscale Multilevel Monte Carlo Method for Multiscale Elliptic PDEs with Random Coefficients

We propose a multiscale multilevel Monte Carlo(MsMLMC)method to solve multiscale elliptic PDEs with random coefficients in the multi-query setting.Our method consists of offline and online stages.In the offline stage,we construct a small number of reduced basis functions within each coarse grid block,which can then be used to approximate the multiscale finite element basis functions.In the online stage,we can obtain the multiscale finite element basis very efficiently on a coarse grid by using the pre-computed multiscale basis.The MsMLMC method can be applied to multiscale RPDE starting with a relatively coarse grid,without requiring the coarsest grid to resolve the smallestscale of the solution.We have performed complexity analysis and shown that the MsMLMC offers considerable savings in solving multiscale elliptic PDEs with random coefficients.Moreover,we provide convergence analysis of the proposed method.Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for several multiscale stochastic problems without scale separation.

Monte-Carlo Studies and Computer Modelling of Multi-wavelength Pyrometry

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Monte-Carlo simulation of a stochastic differential equation

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.

基于Monte-Carlo方法的土石围堰挡水导流风险分析

运用Monte -Carlo方法模拟施工洪水入库过程和导流建筑物泄流的随机性 ,通过仿真分析确定上游围堰堰前水位变化过程及其分布函数。在此基础上 ,根据导流建筑物的设计规模确定导流系统的风险。通过实例验证分析说明 ,研究方法和计算模型是可靠的、适用的。

真空小喷管羽流场的Monte Carlo直接模拟

利用直接模拟的MonteCarlo方法数值模拟了真空喷管羽流场，获得了符合规律的数值模拟结果。由于将随机取样频率法（R－S－F）用于轴对称问题中，解决了计算机内存和速度上的困难，同时也证明了R－S－F方法的可靠性。

大型复杂系统平均寿命评定的Monte Carlo方法

随着现代武器系统和工程系统的大型化与复杂化趋势,大型复杂系统可靠性评定是急待解决的问题,工程中常用可靠性指标有可靠度和平均寿命,平均寿命指标由于直观、物理概念清晰,使用更加方便。基于可靠性框图建模,采用最小路集计算分析,提出了大型复杂系统平均寿命评定的Monte Carlo方法。解决了有限样本条件下,大型复杂系统平均寿命评定问题,对工程中大型复杂系统平均寿命评定具有重要应用价值。

基于Monte-Carlo法的滑坡稳定可靠性分析

简述了可靠性分析的 Ｍｏｎｔｅ－Ｃａｒｌｏ法，结合简化的 Ｂｉｓｈｏｐ法提出了滑坡稳定可靠性分析的状态函数，并通过实例进行了计算分析。证明Ｍｏｎｔｅ－Ｃａｒｌｏ法是求解滑坡稳定可靠性指标和破坏概率的行之有效的方法。

聚合物中多重光散射传导的Monte Carlo数值模拟

基于米氏散射(Mie scattering)理论,建立填充分散粒子群的聚合物对光散射传导的Monte Carlo数学模型.在此基础上,编写了一套仿真模拟程序.通过模拟单个光子在聚合物中的多重散射运动过程,把问题扩展到以激光束或线状光为入射源,得到在聚合物板块内的光传导情况,并且在计算机上图像化地重现整个物理过程,对输出光强的分布情况进行模拟统计分析.模拟结果表明,利用体散射机制,可以将点光源和线光源转换为平面光输出,输出光的状态可以通过对比计算结果实施有效控制.

影响b值计算误差的Monte Carlo实验研究

本文假设地震的发生与时间的关系遵循稳态泊松模型,假设地震震级M服从参数为1/β的指数分布,其中β=b/loge,在此基础上生成地震目录。用最小二乘法估算b值,分别从样本数量、震级间隔、震级误差三方面分析b值误差的大小。统计分析结果表明,b值的标准偏差随着样本数量的增多而减小;随着震级间隔的增大而减小;震级误差使b值的标准误差变大。本文可以为利用真实地震目录求b值时选择适当的方法提供参考。

不确定性结构区间分析的改进Monte Carlo方法

将结构系统中的不确定性参数用区间数来表示,建立了系统的区间有限元控制方程。利用Monte Carlo数值仿真方法对区间有限元控制方程进行求解,得到了结构的位移和应力响应区间。并针对一般Monte Carlo方法在区间仿真中存在的缺陷,对其进行了改进,使其计算效率大为提高。数值仿真算例表明:经改进的Monte Carlo方法仿真求解计算量大为减少,且能给出较高精度的响应区间,并克服了区间运算中的扩张问题。