Estimating tail probabilities of heavy tailed distributions with asymptotically zero relative error

Efficient estimation of tail probabilities involving heavy tailed random variables is amongst the most challenging problems in Monte-Carlo simulation. In the last few years, applied probabilists have achieved considerable success in developing efficient algorithms for some such simple but fundamental tail probabilities. Usually, unbiased importance sampling estimators of such tail probabilities are developed and it is proved that these estimators are asymptotically efficient or even possess the desirable bounded relative error property. In this paper, as an illustration, we consider a simple tail probability involving geometric sums of heavy tailed random variables. This is useful in estimating the probability of large delays in M/G/1 queues. In this setting we develop an unbiased estimator whose relative error decreases to zero asymptotically. The key idea is to decompose the probability of interest into a known dominant component and an unknown small component. Simulation then focuses on estimating the latter ‘residual’ probability. Here we show that the existing conditioning methods or importance sampling methods are not effective in estimating the residual probability while an appropriate combination of the two estimates it with bounded relative error. As a further illustration of the proposed ideas, we apply them to develop an estimator for the probability of large delays in stochastic activity networks that has an asymptotically zero relative error.      

Slowing down in the three-dimensional three-state Potts glass with nearest neighbor exchange ± J: A Monte Carlo study

,Static and dynamic properties of the Potts model on the simple cubic lattice with nearest neighbor -interaction are obtained from Monte Carlo simulations in a temperature range where full thermal equilibrium still can be achieved (). For a lattice size L = 16, in this range finite size effects are still negligible, but the data for the spin glass susceptibility agree with previous extrapolations based on finite size scaling of very small lattices. While the static properties are compatible with a zero temperature transition, they certainly do not prove it. Unlike the Ising spin glass, the decay of the time-dependent order parameter is compatible with a simple Kohlrausch function, , while a power law prefactor cannot be distinguished. The Kohlrausch exponent y ( T ) decreases from at [0pt] to at [0pt] however. The relaxation time is compatible with the exponential divergence postulated by McMillan for spin glasses at their lower critical dimension, but the exponent that can be extracted still differs significantly from the theoretical value, . Thus the present results support the conclusion that the Potts spin glass in d = 3 dimensions differs qualitatively from the Ising spin glass. Received: 8 October 1997 / Accepted: 27 November 1997     

Scattering spectra and colour of disperse systems of low-absorptive particles

In this article, the results of calculations of scattering spectra of low-absorptive spherical particles are presented. It was obtained using different approximate and numerical methods. The comparative evaluations of application of single scattering approximation, the average field approximation and of the methods of computer modeling on the basis of Monte-Carlo method on various scattering multiplicity were performed. The comparison demonstrates the good agreement of calculated results with experimental scattering spectra of eye lens. By using the obtained spectral data the colour coordinates are calculated. The regularities of changes in colour characteristics in dependence of disperse system parameters are analyzed.     

Molecular dynamics of cyclic and linear poly(dimethylsiloxanes)

Dielectric spectroscopy (10^–1 Hz to 10⁷ Hz) has been employed to study the molecular dynamics of a series of cyclic and linear polydimethylsiloxanes (PDMS) of various molecular weights ranging from 300 to 10 000 g/mol in the temperature range above the glass transition (from 130 K to 190 K). The observed -relaxation depends strongly on both molecular weight and structure of the samples. For linear PDMS oligomers, the -relaxation shifts towards lower temperatures with decreasing molecular weight in good accordance with the Fox-Flory-model. Cyclic PDMS reveals a qualitatively different molecular weight dependence: for a given temperature the -relaxation time increases with decreasing ring length, but has a maximum for small oligomers (degree of polymerizationn6). The shape of relaxation curves and, with it, the relaxation time distribution is independent from length and architecture of the chains The observed experimental findings are in qualitative agreement with dynamic Monte-Carlo simulations.Dedicated to Prof. E.W. Fischer on the occasion of his 65th birthday Fast macht' das WLF ihn krank, jetzt raucht er wieder, Gott sei Dank! (frei nach Wilhelm Busch)     

面心立方C60表面过程的计算机模拟

近年来发现的C60及其金属掺杂化合物形成一个新的材料族，其半导体性质、超导性质及非线性光学性质已受到广泛注意，但目前对这类材料的表面性质尚缺乏研究，我们曾采用参数化的Lenard－Jones6－12模型函数比较不同晶型C6o的相对稳定性　[1]，预测面心立方C60（FccC60）的声子散射频率和态密度[2]，并计算其表面能[3]，取得有意义的结果，表明这一简单模型势能函数是C60分子间有效范德华作用的一种合理抽提．本工作进一步将该势能函数应用于研究fccC60表面吸附分子的迁移机理，并用蒙特卡罗方法模拟fcC（110）及（100）晶面的熔化过程，…     

高能闪光照相中影响光程确定的几个因素

 利用闪光照相基本原理和成像原理，在直接记录法和转换屏记录法的情况下，研究了闪光照相中影响X射线在材料中光程确定的主要因素。结果表明，影响光程确定的几个因素是：散射效应、光源角分布效应、立体角效应和能谱效应。对于高能闪光照相，散射效应是影响光程确定的最主要因素，散射的存在使光程的测量值比实际值降低20%～40%。因此必须在做CT之前，对散射的影响进行修正。     

FTO客体3m闪光照相的Monte Carlo研究

 研究了客体模型FTO的闪光照相系统X光输运过程，给出了直穿照射量、散射照射量、直散比、直穿照射量能谱、散射照射量能谱、直穿X光通量能谱和散射X光通量能谱在记录平面的空间分布。结果表明：后锥是照射量散射成分的主要来源，后锥照射量占总散射量97%；后锥也是造成散射的空间分布不均匀的主要器件，这一不均匀性高达58%。照相系统的最小直散比非常小，表明锥造成的散射已经严重地淹没了直穿（轫致辐射）信号。计算中使用高空间分辨率记录法进行分点，合成图像对吸收系数的复原结果与国外报道的结果相符。     

采用光纤和YAP晶体的小型γ相机的蒙特卡罗模拟

基于波长位移光纤(WSF)耦合YAP晶体中的光子传输特性,用GEANT4软件包建立了一个蒙特卡罗模拟程序.对采用波长位移光纤耦合平板式YAP晶体的小型单管γ相机的性能进行了计算机模拟.采用波长位移光纤耦合光电倍增管光阴极面的读出方式,和晶体直接耦合光电倍增管光阴极面相比,在相同的晶体面积大小条件下,PSPMT光阴极面积可大大缩小,使费用降低.模拟结果表明：γ射线与晶体发生作用的地方所对应的光纤输出的平均光子数最少为15个,位置灵敏光电倍增管完全可以探测到.说明采用闪烁晶体－WSF－位置灵敏光电倍增管的读出方式是可行的;在用硅油耦合波长位移光纤和YAP晶体的情况下,获得的空间分辨率为1.28 mm(FWHM).模拟结果也说明了增加平均光子数对提高空间分辨率的重要性.     

载机平台光电转塔目标定位的仿真算法

目标定位是光电转塔典型功能和任务之一,对其定位精度的考量也是转塔作战技术指标之一,针对该问题,从理论和仿真角度进行了分析。分析目标定位中用到的坐标系及其相互转换关系,给出光电转塔视轴反演、有源目标定位、无源目标定位的算法流程,通过仿真实验加以验证,考虑了定位过程中可能的随机误差来源,并分析是否采用均值滤波及其对定位结果的影响,最后通过Monte-Carlo分析计算了定位精度。分析结果表明:1）有源定位比无源定位的精度高,在仿真假设条件下,精度约提高1倍;2）均值滤波后,定位精度有较大提升（约提高15倍）;3）18 km距离时典型无源定位精度在80%置信度条件下约为39.4 m;4）统计直方图反映出80%置信度CEP半径及最大误差距离随载机位置、姿态、转塔视轴等（体现在目标载机距离上）不同参数的变化结果。     

Dynamic Scaling of Ramified Clusters Formed on Liquid Surfaces

A comprehensive simulation model -deposition,diffusion, rotation, reaction and aggregation model is presented to simulate the formation processes of ramified clusters on liquid surfaces, where clusters can diffuse and rotate easily. The mobility (including diffusion and rotation) of clusters is related to its mass, which is given by Dm = Dos-γD and θm =′θos-γθ, respectively. The influence of the reaction probability on the kinetics and structure formation is included in the simulation model. We concentrate on revealing dynamic scaling during ramified cluster formation. For this purpose, the time evolution of the cluster density and the weight-average cluster size as well as the cluster-size distribution scaling function at different time are determined for various conditions. The dependence of the cluster density on the deposition flux and time-dependence of fractal dimension are also investigated. The obtained results are helpful in understanding the formation of clusters or thin film growth on liquid surfaces.