Monte Carlo radiosity

The fast radiosity-type methods for very complex diffuse environments, introduced herein, present a nearly linear-time solution. The outlined procedures rely on recursive algorithms with stochastic convergence for solving the radiosity equation system. Approximations of gathering and shooting at very low computational cost—rather than the exact matrix of a single reflection—are used. The efficiency of the methods will be increased by applying variance reduction techniques.     

Pseudo-random trees in Monte Carlo

We present the concept of a pseudo-random tree, and generalize the Lehmer pseudo-random number generator as an efficient implementation of the concept. Pseudo-random trees can be used to give reproducibility, as well as speed, in Monte Carlo computations on parallel computers with either the SIMD architecture of the current generation of supercomputer or the MIMD architecture characteristic of the next generation. Monte Carlo simulations based on pseudo-random trees are free of certain pitfalls, even for sequential computers, which can make them considerably more useful.     

Vectorized Monte Carlo photon transport

The results of current research in the development of a Cray algorithm for time-dependent Monte Carlo photon radiation transport is presented. The method that has been developed is a fully vectorized particle-vector scheme. This technique tracks groups of particles simultaneously using a vector-stack formalism based upon particle events. Timing comparisons between this algorithm and the traditional single-particle approach are presented.     

Population Markov Chain Monte Carlo

Stochastic search algorithms inspired by physical and biological systems are applied to the problem of learning directed graphical probability models in the presence of missing observations and hidden variables. For this class of problems, deterministic search algorithms tend to halt at local optima, requiring random restarts to obtain solutions of acceptable quality. We compare three stochastic search algorithms: a Metropolis-Hastings Sampler (MHS), an Evolutionary Algorithm (EA), and a new hybrid algorithm called Population Markov Chain Monte Carlo, or popMCMC. PopMCMC uses statistical information from a population of MHSs to inform the proposal distributions for individual samplers in the population. Experimental results show that popMCMC and EAs learn more efficiently than the MHS with no information exchange. Populations of MCMC samplers exhibit more diversity than populations evolving according to EAs not satisfying physics-inspired local reversibility conditions.     

Monte Carlo integration with subtraction

This paper investigates a class of algorithms for numerical integration of a function in d$d$ dimensions over a compact domain by Monte Carlo methods. We construct a histogram approximation to the function using a partition of the integration domain into a set of bins specified by some parameters. We then consider two adaptations: the first is to subtract the histogram approximation, whose integral we may easily evaluate explicitly, from the function and integrate the difference using Monte Carlo; the second is to modify the bin parameters in order to make the variance of the Monte Carlo estimate of the integral the same for all bins. This allows us to use Student’s t$t$-test as a trigger for rebinning, which we claim is more stable than the χ²${\chi }^2$ test that is commonly used for this purpose. We provide a program that we have used to study the algorithm for the case where the histogram is represented as a product of one-dimensional histograms. We discuss the assumptions and approximations made, as well as giving a pedagogical discussion of the myriad ways in which the results of any such Monte Carlo integration program can be misleading.     

Error in Monte Carlo, quasi-error in Quasi-Monte Carlo

While the Quasi-Monte Carlo method of numerical integration achieves smaller integration error than standard Monte Carlo, its use in particle physics phenomenology has been hindered by the absence of a reliable way to estimate that error. The standard Monte Carlo error estimator relies on the assumption that the points are generated independently of each other and, therefore, fails to account for the error improvement advertised by the Quasi-Monte Carlo method. We advocate the construction of an estimator of stochastic nature, based on the ensemble of pointsets with a particular discrepancy value. We investigate the consequences of this choice and give some first empirical results on the suggested estimators.     

蒙特卡罗与准蒙特卡罗相互融合的整体光照计算

蒙特卡罗方法具备普适性、鲁棒性以及与问题复杂度无关性等优点,非常适于十分难解的整体光照计算问题,但缺点是生成图像随机噪声大．准蒙特卡罗方法计算连续被积函数低维积分的收敛速度快于蒙特卡罗方法,但不适于直接求解复杂的整体光照计算问题．文中研究蒙特卡罗整体光照计算最根本环节,即随机游动的抽样模式,提出融合蒙特卡罗与准蒙特卡罗的两种通用的新型整体光照计算策略．两种新型策略可以应用于所有基于蒙特卡罗的整体光照算法,不仅能够降低生成图像的随机噪声,而且实现简单、不增加计算和存储开销．     

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.     

Interval approach challenges Monte Carlo simulation

Intervals are used to represent imprecise numerical values. Modelling uncertain values with precise bounds without considering their probability distribution is infeasible in many applications. As a solution, this paper proposes the use of probability density functions instead of intervals; we consider evaluation of an arithmetical function of random variables. Since the result density cannot in general be solved algebraically, an interval method for determining itsguaranteed bounds is developed. This possibility challenges traditional Monte Carlo methods in which only stochastic characterizations for the result distribution, such as confidence bounds for fractiles, can be determined.     

Efficient Monte Carlo clustering in subspaces

One of the key difficulties for users in information retrieval is to formulate appropriate queries to submit to the search engine. In this paper, we propose an approach to enrich the user’s queries by additional context. We used the Language Model to build the query context, which is composed of the most similar queries to the query to expand and their top-ranked documents. Then, we applied a query expansion approach based on the query context and the Latent Semantic Analyses method. Using a web test collection, we tested our approach on short and long queries. We varied the number of recommended queries and the number of expansion terms to specify the appropriate parameters for the proposed approach. Experimental results show that the proposed approach improves the effectiveness of the information retrieval system by 19.23 % for short queries and 52.94 % for long queries according to the retrieval results using the original users’ queries.     

Performance modeling using Monte Carlo simulation

Cycle accurate simulation has long been the primary tool for micro-architecture design and evaluation. Though accurate, the slow speed often imposes constraints on the extent of design exploration. In this work, we propose a fast, accurate Monte-Carlo based model for predicting processor performance. We apply this technique to predict the CPI of in-order architectures and validate it against the Itanium-2. The Monte Carlo model uses micro-architecture independent application characteristics, and cache, branch predictor statistics to predict CPI with an average error of less than 7%. Since prediction is achieved in a few seconds, the model can be used for fast design space exploration that can efficiently cull the space for cycle-accurate simulations. Besides accurately predicting CPI, the model also breaks down CPI into various components, where each component quantifies the effect of a particular stall condition (branch misprediction, cache miss, etc.) on overall CPI. Such a CPI decomposition can help processor designers quickly identify and resolve critical performance bottlenecks.     

Monte Carlo solution of structural dynamics

The recent advent of high speed digital computers has made it not only possible but also highly practical to apply the Monte Carlo techniques to a large variety of engineering problems. In this paper a technique of digital simulation of multivariate and/or multidimensional Gaussian random processes (homogeneous or nonhomogeneous) which can represent physical processes germane to structural engineering is presented. The paper also describes a method of digital simulation of envelope functions. Such simulations are accomplished in terms of a sum of cosine functions with random phase angles and used as the basic tool in a general Monte Carlo method of solution of a wide class of problems in structural engineering. Most important problems for which the method is found extremely useful includes (a) numerical analysis of dynamic response of nonlinear structures to random excitations, (b) time domain analysis of linear structures under random excitations performed for the purpose of obtaining a kind of information, such as first excursion probability and time history of a sample function, that is not obtainable from the standard frequency domain analysis, (c) numerical solution of structural problems involving randomly nonhomogeneous material property such as wave propagation through random medium, and (d) dynamic analysis of extremely complex systems such as those involving structure-fluid interaction. Numerical examples of some of these problems are presented.     

Monte Carlo simulation program for ecosystems

A Monte Carlo computer simulation program is designed in order to describe the spatial and time evolution of a population of living individuals under preassigned environmental conditions of energy. The simulation is inspired by previous techniques developed in physics--in particular, in molecular dynamics and simulations of liquids--and it already provides some new insights regarding macroscopic deterministic models in ecology and concerning eventual control of artificial biomass production plants.     

并行蒙特卡罗方法的应用

该文采用蒙特卡罗方法对欧式期权定价问题进行模拟,并用可移植消息传递标准MPI在分布式存储结构的机群系统上设计并实现了并行算法。该算法有效的解决了金融计算中巨大计算量的问题,在很大程度上提高了计算效率,缩短了计算时间,获得了很好的性能。     

Monte Carlo tree search in Kriegspiel

Partial information games are excellent examples of decision making under uncertainty. In particular, some games have such an immense state space and high degree of uncertainty that traditional algorithms and methods struggle to play them effectively. Monte Carlo tree search (MCTS) has brought significant improvements to the level of computer programs in games such as Go, and it has been used to play partial information games as well. However, there are certain games with particularly large trees and reduced information in which a naive MCTS approach is insufficient: in particular, this is the case of games with long matches, dynamic information, and complex victory conditions. In this paper we explore the application of MCTS to a wargame-like board game, Kriegspiel. We describe and study three MCTS-based methods, starting from a very simple implementation and moving to more refined versions for playing the game with little specific knowledge. We compare these MCTS-based programs to the strongest known minimax-based Kriegspiel program, obtaining significantly better experimental results with less domain-specific knowledge.     

并行蒙特卡罗方法的应用

该文采用蒙特卡罗方法对欧式期权定价问题进行模拟,并用可移植消息传递标准MPI在分布式存储结构的机群系统上设计并实现了并行算法。该算法有效的解决了金融计算中巨大计算量的问题,在很大程度上提高了计算效率,缩短了计算时间,获得了很好的性能。     

一种改进的蒙特卡罗交叉验证算法

概率聚类的算法已经广泛地应用于聚类分析领域,但是这些算法都没有回答如何选择一个最佳的聚类个数的问题。该文首先分析了通用的确定概率聚类个数的方法,然后针对蒙特卡罗交叉验证算法不能解决后验概率分散的问题,提出一种改进的蒙特卡罗交叉验证算法(iMCCV)。实验结果证明该算法可以有效地确定最佳K值。     

随机干扰序列的蒙特卡洛模拟

详述了某引信背景干扰随机序列的模拟产生方法，包括交换及逆变换法．着重分析了当杂波的幅度分布服从Ｇａｕｓｓ分布、Ｌｏｇ－Ｎａｍａｌ分布时，构造符合该要求的随机序列的基本方法及其理论依据。而杂波序列的功率谱密度曲线则由某一符合要求的钟形脉冲函数经解析延拓，以稳定的四阶Ｂｕｔｔｅｒ－Ｗｏｒｔｈ低通滤波器幅度平方特性去逼近设定的功率谱曲线．最后，由ＦＦＴ，ＩＦＦＴ完成线性滤波及功率谱变换，得到幅度满足指定要求、功率谱曲线符合要求的杂波模拟序列．     

The Reverse Monte Carlo localization algorithm

Global localization is a very fundamental and challenging problem in Robotic Soccer. Here, the main aim is to find the best method which is very robust and fast and requires less computational resources and memory compared to similar approaches and is precise enough for robot soccer games and technical challenges. In this work, the Reverse Monte Carlo localization (R-MCL) method is introduced. The algorithm is designed for fast, precise and robust global localization of autonomous robots in the robotic soccer domain, to overcome the uncertainties in the sensors, environment and the motion model. R-MCL is a hybrid method based on Markov localization (ML) and Monte Carlo localization (MCL), where the ML based module finds the region where the robot should be and the MCL based part predicts the geometrical location with high precision by selecting samples in this region. It is called Reverse since the MCL routine is applied in a reverse manner in this algorithm. In this work, this method is tested on a challenging data set that is used by many other researchers and compared in terms of error rate against different levels of noise, and sparsity. Additionally, the time required to recover from kidnapping and the processing time of the methods are tested and compared. According to the test results R-MCL is a considerable method against high sparsity and noise. It is preferable when its recovery from kidnapping and processing times are considered. It gives robust and fast but relatively coarse position estimations against imprecise and inadequate perceptions, and coarse action data, including regular misplacements, and false perceptions.     

A test particle Monte Carlo method

A Monte Carlo technique was developed suitable for investigating rarefield gas dynamics problems. The procedure is based on the ‘test particle’ method. The discontinuous function frequently employed for describing the target molecules' velocity distribution is replaced here by a continuous analytic function, the form of calculations. This modification simplifies the calculations, reduces the computer storage requirements, and facilities the application of the method to multi-dimensional problems. The accuracy and versatility of the technique was evaluated by obtaining solutions to several one dimensional problems for which other results exist.