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Finding minimum node separators: A Markov chain Monte Carlo method

RELIABILITY ENGINEERING & SYSTEM SAFETY 2018年第Oct.期178卷 225-235页

作者： Lee, Joohyun Kwak, Jaewook Lee, Hyang-Won Shroff, Ness B. Hanyang Univ Div Elect Engn Ansan South Korea Ohio State Univ Dept Elect & Comp Engn Columbus OH 43210 USA Konkuk Univ Dept Software Seoul South Korea Ohio State Univ Dept Comp Sci & Engn Columbus OH 43210 USA 120 Neungdong Ro Seoul 05029 South Korea

In networked systems such as communication networks or power grids, graph separation from node failures can damage the overall operation severely. One of the most important goals of network attackers is thus to separate nodes so that the sizes of connected components become small. In this work, we consider the problem of finding a minimum a-separator, that partitions the graph into connected components of sizes at most an, where n is the number of nodes. To solve the alpha-separator problem, we develop a random walk algorithm based on metropolis chain. We characterize the conditions for the first passage time (to find an optimal solution) of our algorithm. We also find an optimal cooling schedule, under which the random walk converges to an optimal solution almost surely. Furthermore, we generalize our algorithm to non-uniform node weights. We show through extensive simulations that the first passage time is less than O(n(3)), thereby validating our analysis. The solution found by our algorithm allows us to identify the weakest points in the network that need to be strengthened. Simulations in real topologies show that attacking a dense area is often not an efficient solution for partitioning a network into small components.

关键词： Graph separation problem Node attack Markov chain Monte Carlo metropolis algorithm Hierarchical Markov chain

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Hydrological model selection: a Bayesian alternative

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WATER RESOURCES RESEARCH 2005年第10期41卷 w10422.1-w10422.1页

作者： Marshall, L Nott, D Sharma, A Univ New S Wales Sch Civil & Environm Engn Sydney NSW 2052 Australia Univ New S Wales Sch Math Sydney NSW 2052 Australia

The evaluation and comparison of hydrological models has long been a challenge to the practicing hydrological community. No single model can be identified as ideal over the range of possible hydrological situations. With the variety of models available, hydrologic modelers are faced with the problem of determining which model is best applied to a catchment for a particular modeling exercise. The model selection problem is well documented in hydrologic studies, but a broadly applicable as well as theoretically and practically sound method for comparing model performance does not exist in the literature. Bayesian statistical inference, with computations carried out via Markov chain Monte Carlo (MCMC) methods, offers an attractive alternative to conventional model selection methods allowing for the combination of any preexisting knowledge about individual models and their respective parameters with the available catchment data to assess both parameter and model uncertainty. The aim of this study is to present a method by which hydrological models may be compared in a Bayesian framework. The study builds on previous work (Marshall et al., 2004) in which a Bayesian approach implemented using MCMC algorithms was presented as a simple and efficient basis for assessing parameter uncertainty in hydrological models. In this study, a model selection framework is developed in which an adaptive metropolis algorithm is used to calculate the model's posterior odds. The model used to illustrate our approach is a version of the Australian Water Balance Model (Boughton, 1993) reformulated such that it can have a flexible number of soil moisture storages. To assess the model selection method in a controlled setting, artificial runoff data were created corresponding to a known model configuration. These data were used to evaluate the accuracy of the model selection method and its sensitivity to the size of the sample being used. An application of the Bayesian model identification metho

关键词： RAINFALL-RUNOFF MODELS MONTE-CARLO METHODS PARAMETER UNCERTAINTY metropolis algorithm CATCHMENT MODELS OPTIMIZATION INFERENCE hydrographic datasets parameter uncertainty Hydrologic models Bayesian inference model selection Catchment models Markov chain monte carlo methods Bayes methods Monte Carlo technique selection methods Murrumbidgee River

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Low-temperature modeling for degenerate and frustrated Heisenberg systems with anisotropy

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COMPUTER PHYSICS COMMUNICATIONS 2010年第4期181卷 806-812页

作者： Kunze, T. Gemming, S. Numazawa, S. Schreiber, M. Forschungszentrum Dresden Rossendorf D-01314 Dresden Germany Univ Technol Chemnitz Inst Phys D-09107 Chemnitz Germany

Thermodynamic equilibration of complex systems like spin glasses or (degenerate) anisotropic spin crystals by numerical methods can be challenging due to the presence of multiple minima on the potential energy surface. This problem becomes pronounced especially at low temperature, where the system remains mainly in few states. We employ the anisotropic Heisenberg model in two dimensions to simulate and analyze the domain formation and the domain structure of multiferroic oxides. In particular, we discuss various techniques to improve the low-temperature equilibration behavior by means of a trigonal antiferromagnet with single-ion anisotropy. Furthermore, we present a localized sampling method for the metropolis algorithm, which increases the acceptance ratio significantly. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Heisenberg Anisotropy State space Acceptance probability metropolis algorithm

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Convergence analyses and comparisons of Markov chain Monte Carlo algorithms in digital communications

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2002年第2期50卷 255-270页

作者： Chen, R Liu, JS Wang, XD Univ Illinois Dept Informat & Decis Sci Chicago IL USA Harvard Univ Dept Stat Cambridge MA 02138 USA Columbia Univ Dept Elect Engn New York NY 10027 USA

Recently, Markov chain Monte Carlo (MCMC) methods have been applied to the design of blind Bayesian receivers in a number of digital communications applications. The salient features of these MCMC receivers include the following: a) They are optimal in the sense of achieving minimum symbol error rate;b) they do not require the knowledge of the channel states, nor do they explicitly estimate the channel by employing training signals or decision-feedback;and c) they are well suited for iterative (turbo) processing in coded systems. In this paper, we investigate the convergence behaviors of several MCMC algorithms (both existing and new ones) in,digital communication applications. The geometric convergence property of these algorithms is established by considering only the chains or the marginal chains corresponding to the transmitted digital symbols, which take values from a finite discrete set. We then focus on three specific applications, namely, the MCMC decoders in AWGN channels, ISI channels, and CDMA channels. The convergence rates for these algorithms are computed for small simulated datasets. Different convergence behaviors are observed. It is seen that differential encoding, parameter constraining, collapsing, and grouping are efficient ways of accelerating the convergence of the MCMC algorithms, especially in the presence of channel phase ambiguity.

关键词： Bayesian receiver duality eigenvalue forward-backward algorithm Gibbs sampler metropolis algorithm transition function

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Particle-based modeling of the compaction of fiber yarns and woven textiles

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TEXTILE RESEARCH JOURNAL 2014年第11期84卷 1159-1173页

作者： Samadi, Reza Robitaille, Francois Univ Ottawa Dept Mech Engn Ottawa ON K1N 6N5 Canada

This paper proposes a particle-based modeling method for predicting the constitutive behavior of textiles when subjected to various compressive loading conditions. The method, which is demonstrated for stacked layers of plain woven textiles, utilizes discrete mechanics as an alternative to traditional continuum mechanics. Fibers are modeled as a series of conjoined points, and their configurations are determined mechanistically using a modified metropolis algorithm and inter-particle strain energy terms. The implementation presented in this paper enables intricate geometric modeling of textiles at microscopic, mesoscopic and macroscopic scales. It also enables extensive mechanical modeling of the textiles, from first principles, as they are loaded upon manufacturing of typical technical textile structures. While this paper focuses on the compaction behavior of weaves, the modeling method is readily adaptable to the analysis of shear, bending, buckling, punching, relaxation and other loading scenarios applied on a wide array of different textile types. These scenarios will be demonstrated in forthcoming publications. Comparative data from in silico and in situ testing shows excellent agreement. Results demonstrate an improvement in simulation accuracy over prior comparable modeling techniques. The method presented here successfully predicts the actual behavior of yarns, single-layer and double-layer textile stacks in compaction.

关键词： yarns weaves textile mechanics numerical simulation particle-based modeling metropolis algorithm compaction

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Bayesian computation for geometric process in maintenance problems

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MATHEMATICS AND COMPUTERS IN SIMULATION 2010年第4期81卷 771-781页

作者： Chen, Jianwei Li, Kim-Hung Lam, Yeh San Diego State Univ Dept Math & Stat San Diego CA 92182 USA Chinese Univ Hong Kong Dept Stat Hong Kong Hong Kong Peoples R China

Geometric process modeling is a useful tool to study repairable deteriorating systems in maintenance problems. This model has been used in a variety of situations such as the determination of the optimal replacement policy and the optimal inspection-repair-replacement policy for standby systems, and the analysis of data with trend. In this article, Bayesian inference for the geometric process with several popular life distributions, for instance, the exponential distribution and the lognormal distribution, are studied. The Gibbs sampler and the metropolis algorithm are used to compute the Bayes estimators of the parameters in the geometric process. Simulation results are presented to illustrate the use of our procedures. Published by Elsevier B.V. on behalf of IMACS.

关键词： Geometric process Gibbs sampling metropolis algorithm Maintenance problem Repairable deteriorating systems

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What will be the Euclidean dimension of an Ising ferromagnetic cubic shell?

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JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS 2024年 610卷

作者： Tikader, Ishita Acharyya, Muktish Presidency Univ Dept Phys 86-1 Coll St Kolkata 700073 India

The equilibrium and nonequilibrium properties of an Ising ferromagnetic cubic shell have been extensively studied by Monte Carlo simulation using metropolis single spin flip algorithm. Although, geometrically the Euclidean dimension of the cubical shell is three, interestingly, the Ising ferromagnetic cubic shell undergoes ferromagnetic phase transition at a temperature which is very close to that for two-dimensional Ising ferromagnet. Surprisingly, the Ising ferromagnetic cubic shell shows a strange (neither exponential nor stretched exponential) kind of relaxation behaviour, instead of exponential relaxation as usually observed in the two dimensional Ising ferromagnet. The metastable lifetime of a ferromagnetic Ising cubical shell is studied as a function of the applied magnetic field. Here also, the cubic shell behaves more likely a two-dimensional object as found from statistical analysis and comparison with Becker-D & ouml;ring prediction of classical nucleation theory.

关键词： Euclidean dimension Ising ferromagnet Monte Carlo simulation metropolis algorithm Critical point Relaxation Metastable behaviour

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An extension of Geman and Reynolds' approach to constrained restoration and the recovery of discontinuities

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 1996年第6期18卷 657-662页

作者： Hurn, M Jennison, C School of Mathematical Sciences University of Bath UK

Geman and Reynolds [7] present an approach to linear image restoration which provides for recovery of horizontal and vertical gray-level discontinuities from blurred and noisy observations. We extend their model and parameter selection method to include diagonal discontinuities. A hazard of this modeling approach is identified and addressed. We also comment on the truncated Gibbs sampler suggested in the paper [7].

关键词： statistical image reconstruction discontinuity recovery parameter selection Gibbs sampler metropolis algorithm simulated annealing

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Fast image reconstruction for Compton camera using stochastic origin ensemble approach

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MEDICAL PHYSICS 2011年第1期38卷 429-438页

作者： Andreyev, Andriy Sitek, Arkadiusz Celler, Anna Univ British Columbia Dept Radiol Vancouver BC V5Z 1M9 Canada Harvard Univ Sch Med Dept Radiol Boston MA 02115 USA Brigham & Womens Hosp Boston MA 02115 USA

Purpose: Compton camera has been proposed as a potential imaging tool in astronomy, industry, homeland security, and medical diagnostics. Due to the inherent geometrical complexity of Compton camera data, image reconstruction of distributed sources can be ineffective and/or time-consuming when using standard techniques such as filtered backprojection or maximum likelihood-expectation maximization (ML-EM). In this article, the authors demonstrate a fast reconstruction of Compton camera data using a novel stochastic origin ensembles (SOE) approach based on Markov chains. Methods: During image reconstruction, the origins of the measured events are randomly assigned to locations on conical surfaces, which are the Compton camera analogs of lines-of-responses in PET. Therefore, the image is defined as an ensemble of origin locations of all possible event origins. During the course of reconstruction, the origins of events are stochastically moved and the acceptance of the new event origin is determined by the predefined acceptance probability, which is proportional to the change in event density. For example, if the event density at the new location is higher than in the previous location, the new position is always accepted. After several iterations, the reconstructed distribution of origins converges to a quasistationary state which can be voxelized and displayed. Results: Comparison with the list-mode ML-EM reveals that the postfiltered SOE algorithm has similar performance in terms of image quality while clearly outperforming ML-EM in relation to reconstruction time. Conclusions: In this study, the authors have implemented and tested a new image reconstruction algorithm for the Compton camera based on the stochastic origin ensembles with Markov chains. The algorithm uses list-mode data, is parallelizable, and can be used for any Compton camera geometry. SOE algorithm clearly outperforms list-mode ML-EM for simple Compton camera geometry in terms of reconstruction time.

关键词： emission tomography Compton camera image reconstruction noise metropolis algorithm

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Quantifying parameter uncertainty in stochastic models using the Box-Cox transformation

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JOURNAL OF HYDROLOGY 2002年第1-4期265卷 246-257页

作者： Thyer, M Kuczera, G Wang, QJ Univ Newcastle Dept Civil Surveying & Environm Engn Callaghan NSW 2308 Australia Agr Victoria Tatura Vic 3616 Australia

The Box-Cox transformation is widely used to transform hydrological data to make it approximately Gaussian. Bayesian evaluation of parameter uncertainty in stochastic models using the Box-Cox transformation is hindered by the fact that there is no analytical solution for the posterior distribution. However, the Markov chain Monte Carlo method known as the metropolis algorithm can be used to simulate the posterior distribution. This method properly accounts for the nonnegativity constraint implicit in the Box-Cox transformation. Nonetheless, a case study using the AR(1) model uncovered a practical problem with the implementation of the metropolis algorithm. The use of a multivariate Gaussian jump distribution resulted in unacceptable convergence behaviour. This was rectified by developing suitable parameter transformations for the mean and variance of the AR(1) process to remove the strong nonlinear dependencies with the Box-Cox transformation parameter. Applying this methodology to the Sydney annual rainfall data and the Burdekin River annual runoff data illustrates the efficacy of these parameter transformations and demonstrate the value of quantifying parameter uncertainty. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： lag-one autoregressive models Markov chain Monte Carlo methods metropolis algorithm parameter uncertainty Box-Cox transformation

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