Monte Carlo errors with less errors

We explain in detail how to estimate mean values and assess statistical errors for arbitrary functions of elementary observables in Monte Carlo simulations. The method is to estimate and sum the relevant autocorrelation functions, which is argued to produce more certain error estimates than binning techniques and hence to help toward a better exploitation of expensive simulations. An effective integrated autocorrelation time is computed which is suitable to benchmark efficiencies of simulation algorithms with regard to specific observables of interest. A Matlab code is offered for download that implements the method. It can also combine independent runs (replica) allowing to judge their consistency.     

CORDIC算法在三轴电子罗盘中的应用

CORDIC算法是用于计算三角、反三角、指数、对数等超越函数的简捷算法。将该算法应用在以单片机为核心的三轴电子罗盘中,用于实现罗盘的倾斜补偿并计算俯仰角、横滚角和航向角。实验表明,该算法可有效地在单片机上运行,能够较好地兼顾计算精度与效率,有实用价值。     

Quantised polynomial filtering for nonlinear systems with missing measurements

This paper is concerned with the polynomial filtering problem for a class of nonlinear systems with quantisations and missing measurements. The nonlinear functions are approximated with polynomials of a chosen degree and the approximation errors are described as low-order polynomial terms with norm-bounded coefficients. The transmitted outputs are quantised by a logarithmic quantiser and are also subject to randomly missing measurements governed by a Bernoulli distributed sequence taking values on 0 or 1. Dedicated efforts are made to derive an upper bound of the filtering error covariance in the simultaneous presence of the polynomial approximation errors, the quantisations as well as the missing measurements at each time instant. Such an upper bound is then minimised through designing a suitable filter gain by solving a set of matrix equations. The filter design algorithm is recursive and therefore applicable for online computation. An illustrative example is exploited to show the effectiveness of the proposed algorithm.     

Mixing exact and importance sampling propagation algorithms in dependence graphs

In this article a new algorithm is presented for the propagation of probabilities in junction trees. It is based on a hybrid methodology. Given a junction tree, some of the nodes carry out an exact calculation, and the other an approximation by Monte Carlo methods. For the exact calculation we will use Shafer/Shenoy method and for the Monte Carlo estimation a general class of importance sampling algorithms is used. We briefly study how to apply this sampler on the clusters in a junction tree. The basic algorithm and some of its variations are presented, depending on the family of functions to which we apply the importance sampler: potentials or/and messages in the tree. An experimental evaluation is carried out, comparing their performance with the well-known likelihood weighting approximated algorithm. This family of methods shows a very promising performance. © John Wiley & Sons, Inc.     

Adaptive Allocation of Independent Tasks to Maximize Throughput

In this paper, we consider the task allocation problem for computing a large set of equal-sized independent tasks on a heterogeneous computing system where the tasks initially reside on a single computer (the root) in the system. This problem represents the computation paradigm for a wide range of applications such as SETI@home and Monte Carlo simulations. We consider the scenario where the systems have a general graph-structured topology and the computers are capable of concurrent communications and overlapping communications with computation. We show that the maximization of system throughput reduces to a standard network flow problem. We then develop a decentralized adaptive algorithm that solves a relaxed form of the standard network flow problem and maximizes the system throughput. This algorithm is then approximated by a simple decentralized protocol to coordinate the resources adaptively. Simulations are conducted to verify the effectiveness of the proposed approach. For both uniformly distributed and power law distributed systems, a close-to-optimal throughput is achieved, and improved performance over a bandwidth-centric heuristic is observed. The adaptivity of the proposed approach is also verified through simulations.     

Service‐oriented middleware for financial Monte Carlo simulations on the cell broadband engine

Financial Monte Carlo simulations are computationally intensive applications that must meet tight deadlines in terms of job completion times. The completion time might have a huge impact on the financial profits made from decisions derived from the simulation results. Naturally, there is a huge interest in being able to simulate as fast as possible. While single simulations can be done on one machine, decisions often depend on portfolios of simulations. Distributing the workload among resources is crucial to achieve low latency. In this article we present a combination of a middleware with a high‐performance implementation of an Asian options evaluation code on the Cell Broadband Engine (CBE). We handle workload distribution with our PHASTGrid middleware and provide users with a web service interface to the whole infrastructure. The CBE is particularly suitable for Monte Carlo simulations. We implemented a well‐known algorithm on both the CBE and the Intel x86 multicore architectures. Both codes are integrated in our middleware, allowing a direct comparison of the performance and scalability. In addition to the Monte Carlo simulation, we also use different applications and compare our middleware with Globus. Copyright © 2009 John Wiley & Sons, Ltd.     

A comparative study of the numerical approximation of the random Airy differential equation

The aim of this paper is twofold. First, we deal with the extension to the random framework of the piecewise Fröbenius method to solve Airy differential equations. This extension is based on mean square stochastic calculus. Second, we want to explore the capability to provide not only reliable approximations for both the average and the standard deviation functions associated to the solution stochastic process, but also to save computational time as it happens in dealing with the analogous problem in the deterministic scenario. This includes a comparison of the numerical results with respect to those obtained by other commonly used operational methods such as polynomial chaos and Monte Carlo simulations. To conduct this comparative study, we have chosen the Airy random differential equation because it has highly oscillatory solutions. This feature allows us to emphasize differences between all the considered approaches.     

Parallelization strategies for Monte Carlo simulations of thin film deposition

Atomistic simulations of thin film deposition, based on the lattice Monte Carlo method, provide insights into the microstructure evolution at the atomic level. However, large-scale atomistic simulation is limited on a single computer—due to memory and speed constraints. Parallel computation, although promising in memory and speed, has not been widely applied in these simulations because of the intimidating overhead. The key issue in achieving optimal performance is, therefore, to reduce communication overhead among processors. In this paper, we propose a new parallel algorithm for the simulation of large-scale thin film deposition incorporating two optimization strategies: (1) domain decomposition with sub-domain overlapping and (2) asynchronous communication. This algorithm was implemented both on message-passing-processor systems (MPP) and on cluster computers. We found that both architectures are suitable for parallel Monte Carlo simulation of thin film deposition in either a distributed memory mode or a shared memory mode with message-passing libraries.     

Three-dimensional electromagnetic particle-in-cell with Monte Carlo collision simulations on three MIMD parallel computers

A three-dimensional electromagnetic particle-in-cell code with Monte Carlo collision (PIC-MCC) is developed for MIMD parallel supercomputers. This code uses a standard relativistic leapfrog scheme incorporating Monte Carlo calculations to push plasma particles and to include collisional effects on particle orbits. A local finite-difference time-domain method is used to update the self-consistent electromagnetic fields. The code is implemented using the General Concurrent PIC (GCPIC) algorithm, which uses domain decomposition to divide the computation among the processors. Particles must be exchanged between processors as they move among subdomains. Message passing is implemented using the Express Cubix library and the PVM. We evaluate the performance of this code using a 512-processor Intel Touchstone Delta, a 512-processor Intel Paragon, and a 256-processor CRAY T3D. It is shown that a high parallel efficiency exceeding 95% has been achieved on all three machines for large problems. We have run PIC-MCC simulations using several hundred million particles with several million collisions per time step. For these large-scale simulations the particle push time achieved is in the range of 90–115 ns/particle/time step, and the collision calculation time in the range of a few hundred nanoseconds per collision.     

EM algorithms for nonlinear mixed effects models

Implementing the Monte Carlo EM algorithm (MCEM) algorithm for finding maximum likelihood estimates (MLEs) in the nonlinear mixed effects model (NLMM) has encountered a great deal of difficulty in obtaining samples used for estimating the E step due to the intractability of the target distribution. Sampling methods such as Markov chain techniques and importance sampling have been used to alleviate such difficulty. The advantage of Markov chains is that they are applicable to a wider range of distributions than the approaches based on independent samples. However, in many cases the computational cost of Markov chains is significantly greater than that of independent samplers. The MCEM algorithms based on independent samples allow for straightforward assessment of Monte Carlo error and can be considerably more efficient than those based on Markov chains when an efficient candidate distribution is chosen, which forms the motivation of this paper. The proposed MCEM algorithm in this paper uses samples obtained from an easy-to-simulate and efficient importance distribution so that the computational intensity and complexity is much reduced. Moreover, the proposed MCEM algorithm preserves the flexibility introduced by independent samples in gauging Monte Carlo error and thus allows the Monte Carlo sample size to increase with the number of EM iterations. We also introduce an EM algorithm using Gaussian quadrature approximations (GQEM) for the E step. In low-dimensional cases, the GQEM algorithm is more efficient than the proposed MCEM algorithm and thus can be used as an alternative. The performances of the proposed EM methods are compared to the existing ML estimators using real data examples and simulations.     

Stochastic kinetic Monte Carlo algorithms for long-range Hamiltonians

We present a higher order kinetic Monte Carlo methodology suitable to model the evolution of systems in which the transition rates are non-trivial to calculate or in which Monte Carlo moves are likely to be non-productive flicker events. The second order residence time algorithm first introduced by Athènes et al. [Phil. Mag. A 76 (1997) 565] is rederived from the n-fold way algorithm of Bortz et al. [J. Comput. Phys. 17 (1975) 10] as a fully stochastic algorithm. The second order algorithm can be dynamically called when necessary to eliminate unproductive flickering between a metastable state and its neighbours. An algorithm combining elements of the first order and second order methods is shown to be more efficient, in terms of the number of rate calculations, than the first order or second order methods alone while remaining statistically identical. This efficiency is of prime importance when dealing with computationally expensive rate functions such as those arising from long-range Hamiltonians. Our algorithm has been developed for use when considering simulations of vacancy diffusion under the influence of elastic stress fields. We demonstrate the improved efficiency of the method over that of the n-fold way in simulations of vacancy diffusion in alloys. Our algorithm is seen to be an order of magnitude more efficient than the n-fold way in these simulations. We show that when magnesium is added to an Al-2at.%Cu alloy, this has the effect of trapping vacancies. When trapping occurs, we see that our algorithm performs thousands of events for each rate calculation performed.     

Sensitivity analysis of stochastic dynamical systems

A new, efficient algorithm is developed for the sensitivity analysis of a general class of stochastic dynamical systems. The algorithm is based on an idea of the likelihood ratio method that utilizes a probability density information for the sensitivity analysis, and on the Fokker-Planck or Kolmogorov's forward equation for computing the evolution of probability densities. The ideas of stochastic sensitivity analysis and likelihood ratio method are presented and combined to derive the sensitivity of average values of the performance functional with respect to system parameters. The present algorithm avoids the time consuming Monte Carlo or stochasic simulations, and, instead, sensitivity gradients of the probability density function and performance functional are directly computed during single-run simulation.     

Analytical error analysis of Clifford gates by the fault-path tracer method

We estimate the success probability of quantum protocols composed of Clifford operations in the presence of Pauli errors. Our method is derived from the fault-point formalism previously used to determine the success rate of low-distance error correction codes. Here we apply it to a wider range of quantum protocols and identify circuit structures that allow for efficient calculation of the exact success probability and even the final distribution of output states. As examples, we apply our method to the Bernstein–Vazirani algorithm and the Steane [[7,1,3]] quantum error correction code and compare the results to Monte Carlo simulations.     

A Monte Carlo Enhanced PSO Algorithm for Optimal QoM in Multi-Channel Wireless Networks

In wireless monitoring networks, wireless sniffers are distributed in a region to monitor the activities of users. It can be used for fault diagnosis, resource management and critical path analysis. Due to hardware limitations, wireless sniffers typically can only collect information on one channel at a time. Therefore, it is a key topic to optimize the channel selection for sniffers to maximize the information collected, so as to maximize the quality of monitoring (QoM) of the network. In this paper, a particle swarm optimization (PSO)-based solution is proposed to achieve the optimal channel selection. A2D mapping particle coding and its moving scheme are devised. Monte Carlo method is incorporated to revise the solution and significantly improve the convergence of the algorithm. The extensive simulations demonstrate that the Monte Carlo enhanced PSO (MC-PSO) algorithm outperforms the related algorithms evidently with higher monitoring quality, lower computation complexity, and faster convergence. The practical experiment also shows the feasibility of this algorithm.     

基于子空间逼近的特征空间波束形成算法

特征空间波束形成（ESB）算法为了得到信号子空间需要对采样协方差矩阵进行特征值分解,运算量十分巨大,这大大限制了其应用。为了减低ESB算法的运算量,利用有理子空间逼近的原理,提出一种不需要估计信号源个数的快速ESB算法。该方法利用一个介于信号和噪声特征值之间的分界值将特征空间分成两个子空间,并用矩阵幂乘和此分界值的有理式逼近这两个子空间的投影矩阵,将此投影矩阵代入到ESB算法的权值求解式中,在不降低性能的前提下,可大大提高波束形成的运算速度。计算机仿真验证了该算法的有效性,并分析了分界值取值方法的不同对子空间划分及波束形成性能的影响。     

Distributed Task Assignment for Mobile Agents

This note demonstrates how the distributed auction algorithm can be modified to assign mobile agents to spatially distributed tasks despite communication delays and the fact that agent movement may cause the benefit associated with each possible agent-task assignment to vary during the execution of the algorithm. Bounds on the convergence time of the algorithm and the sub-optimality of the resulting solution are provided. Monte Carlo simulations are provided to show the conditions under which the modified distributed auction can outperform centralized calculation     

大型原油储罐罐底声发射源定位算法研究

针对大型储罐罐底声发射检测过程中的声源定位问题,在深入研究三角定位算法和超定定位算法原理的基础上,采用蒙特卡洛模拟方法定量分析比较了两种算法对罐底声发射源定位的性能,主要包括定位计算时间、定位误差分布以及有效定位率等参数。结果表明三角定位算法比超定定位算法快100倍,但在非理想情况下,即存在时间测量误差和声速误差时,三角定位算法对罐底边缘区域的声源定位误差大,而超定定位算法对罐底边缘区域声源的有效定位率低。现场检测过程中应根据实时性、误差范围、计算机性能等要求选择合适的定位算法。     

On the computation and some applications of multivariate isotonic regression

Multivariate isotonic regression theory plays a key role in the field of statistical inference under order restrictions for vector valued parameters. A Fortran program for the earlier proposed algorithm for the computation of multivariate isotonic regression is presented. The convergence of the algorithm is studied when the dimension is greater than or equal to five through Monte Carlo simulations. Two different types of numerical examples are given to illustrate the applications of multivariate isotonic regression.     

Scalable robot fault detection and identification

Experience has shown that even carefully designed and tested robots may encounter anomalous situations. It is therefore important for robots to monitor their state so that anomalous situations may be detected in a timely manner. Robot fault diagnosis typically requires tracking a very large number of possible faults in complex non-linear dynamic systems with noisy sensors. Traditional methods either ignore the uncertainty or use linear approximations of non-linear system dynamics. Such approximations are often unrealistic, and as a result faults either go undetected or become confused with non-fault conditions.Probability theory provides a natural representation for uncertainty, but an exact Bayesian solution for the diagnosis problem is intractable. Monte Carlo approximations have demonstrated considerable success in application domains such as computer vision and robot localization and mapping. But, classical Monte Carlo methods, such as particle filters, can suffer from substantial computational complexity. This is particularly true with the presence of rare, yet important events, such as many system faults.This paper presents an algorithm that provides an approach for computationally tractable fault diagnosis. Taking advantage of structure in the domain it dynamically concentrates computation in the regions of state space that are currently most relevant without losing track of less likely states. Experiments with a dynamic simulation of a six-wheel rocker-bogie rover show a significant improvement in performance over the classical approach.