基于CS算法的Markov模型及收敛性分析

为完善布谷鸟搜索(CS)算法的收敛性理论,建立CS算法的Markov链模型,分析该Markov链的有限齐次性,在此基础上通过分析鸟窝位置的群体状态转移过程,指出随机序列将进入最优状态集,同时证明CS算法满足随机搜索算法全局收敛的2个条件。通过仿真实验验证CS算法可收敛于全局最优,从而确保CS算法的全局收敛性。     

Exploring the state sequence space for hidden Markov and semi-Markov chains

The knowledge of the state sequences that explain a given observed sequence for a known hidden Markovian model is the basis of various methods that may be divided into three categories: (i) enumeration of state sequences; (ii) summary of the possible state sequences in state profiles; (iii) computation of a global measure of the state sequence uncertainty. Concerning the first category, the generalized Viterbi algorithm for computing the top L most probable state sequences and the forward-backward algorithm for sampling state sequences are derived for hidden semi-Markov chains and hidden hybrid models combining Markovian and semi-Markovian states. Concerning the second category, a new type of state (and state change) profiles is proposed. The Viterbi forward-backward algorithm for computing these state profiles is derived for hidden semi-Markov chains and hidden hybrid models combining Markovian and semi-Markovian states. Concerning the third category, an algorithm for computing the entropy of the state sequence that explains an observed sequence is proposed. The complementarity and properties of these methods for exploring the state sequence space (including the classical state profiles computed by the forward-backward algorithm) are investigated and illustrated with examples.     

Finite dimensional predictors for hidden Markov chains

A continuous time Markov chain is observed in Gaussian noise. Finite dimensional normalized and unnormalized (Zakai) predictors are obtained for the state of the chain, for the number of jumps from one state to another and for the occupation time in any state.     

Resilient model approximation for Markov jump time-delay systems via reduced model with hierarchical Markov chains

In this paper, the resilient model approximation problem for a class of discrete-time Markov jump time-delay systems with input sector-bounded nonlinearities is investigated. A linearised reduced-order model is determined with mode changes subject to domination by a hierarchical Markov chain containing two different nonhomogeneous Markov chains. Hence, the reduced-order model obtained not only reflects the dependence of the original systems but also model external influence that is related to the mode changes of the original system. Sufficient conditions formulated in terms of bilinear matrix inequalities for the existence of such models are established, such that the resulting error system is stochastically stable and has a guaranteed l₂-l_∞ error performance. A linear matrix inequalities optimisation coupled with line search is exploited to solve for the corresponding reduced-order systems. The potential and effectiveness of the developed theoretical results are demonstrated via a numerical example.     

Multi-GPU accelerated multi-spin Monte Carlo simulations of the 2D Ising model

A Modern Graphics Processing unit (GPU) is able to perform massively parallel scientific computations at low cost. We extend our implementation of the checkerboard algorithm for the two-dimensional Ising model [T. Preis et al., Journal of Chemical Physics 228 (2009) 4468-4477] in order to overcome the memory limitations of a single GPU which enables us to simulate significantly larger systems. Using multi-spin coding techniques, we are able to accelerate simulations on a single GPU by factors up to 35 compared to an optimized single Central Processor Unit (CPU) core implementation which employs multi-spin coding. By combining the Compute Unified Device Architecture (CUDA) with the Message Parsing Interface (MPI) on the CPU level, a single Ising lattice can be updated by a cluster of GPUs in parallel. For large systems, the computation time scales nearly linearly with the number of GPUs used. As proof of concept we reproduce the critical temperature of the 2D Ising model using finite size scaling techniques.     

人工蜂群算法的收敛性分析

利用随机过程理论,对人工蜂群算法收敛性进行理论分析,给出人工蜂群算法的一些数学定义和蜜源位置的一步转移概率,建立人工蜂群算法的Markov链模型,分析此Markov链的一些性质,论证了人工蜂群状态序列是有限齐次Markov链,且状态空间是不可约的。结合随机搜索算法的全局收敛准则,证明了人工蜂群算法能够满足随机搜索算法全局收敛的两个假设,保证算法的全局收敛。     

Continuous-time hidden Markov models for network performance evaluation

In this paper, we study the use of continuous-time hidden Markov models (CT-HMMs) for network protocol and application performance evaluation. We develop an algorithm to infer the CT-HMM from a series of end-to-end delay and loss observations of probe packets. This model can then be used to simulate network environments for network performance evaluation. We validate the simulation method through a series of experiments both in ns and over the Internet. Our experimental results show that this simulation method can represent a wide range of real network scenarios. It is easy to use, accurate and time efficient.     

Markov chain representations of discrete distributions applied to queueing models

We present applications of Markov chain based representations of discrete renewal distributions to queueing models, and extend the notion of that representation to some non-renewal discrete distributions. Two representations are considered; one based on remaining time, the other on elapsed time. These representations make it easier to use matrix-analytic methods for several stochastic models, especially queueing models, thereby allowing us to develop better algorithmically tractable procedures for their analysis. Specifically, they allow us to capitalize on the resulting special structures. We first discuss some key measures of these distributions using phase type distribution results, including some time reversibility relations between the elapsed and remaining time representations. We then show applications to the MAP/G/1, the GI/MSP/1 and the GI/G/1 systems, and briefly explain how the representations of the non-renewal types of discrete distributions can be used for the MRP/SMP/1 system. The emphasis of this paper is about efficient procedures for the R and G matrices associated with these queueing models.     

Reachability problems for Markov chains

We consider the following decision problem: given a finite Markov chain with distinguished source and target states, and given a rational number r, does there exist an integer n such that the probability to reach the target from the source in n steps is r? This problem, which is not known to be decidable, lies at the heart of many model checking questions on Markov chains. We provide evidence of the hardness of the problem by giving a reduction from the Skolem Problem: a number-theoretic decision problem whose decidability has been open for many decades.     

Quasi-Monte Carlo methods for Markov chains with continuous multi-dimensional state space

We describe a quasi-Monte Carlo method for the simulation of discrete time Markov chains with continuous multi-dimensional state space. The method simulates copies of the chain in parallel. At each step the copies are reordered according to their successive coordinates. We prove the convergence of the method when the number of copies increases. We illustrate the method with numerical examples where the simulation accuracy is improved by large factors compared with Monte Carlo simulation.     

Hidden Markov random field models for TCA image analysis

Tooth Cementum Annulation (TCA) is an age estimation method carried out on thin cross sections of the root of mammalian teeth. Age is computed by adding the tooth eruption age to the count of annual incremental lines which are called tooth rings and appear in the cementum band. The number of rings is computed from an intensity (gray scale) image of the cementum band, by estimating the average ring width and then dividing the area of the cementum band by this estimate. The ring width is estimated by modelling the image by a hidden Markov random field, where intensities are assumed to be pixelwise conditionally independent and normally distributed, given a Markov random field of hidden binary labels, representing the“true scene”. To incorporate image macro-features (the long-range dependence among intensities and the quasi-periodicity in the placement of tooth rings), the label random field is defined by an energy function that depends on a parametric Gabor filter, convolved with the true scene. The filter parameter represents the unknown of main interest, i.e. the average width of the rings. The model is estimated through an EM algorithm, relying on the mean field approximation of the hidden label distribution and allows to predict the locations of the rings in the image.     

Loss rates for stochastic fluid models

We introduce loss rates, a novel class of performance measures for Markovian stochastic fluid models and discuss their applications potential. We derive analytical expressions for loss rates and describe efficient methods for their evaluation. Further, we study interesting asymptotic properties of loss rates for large size of the buffer, which are crucial for identifying the Quality of Service requirements guaranteed for each user. We illustrate the theory with a numerical example.     

A note on exponential stability of the nonlinear filter for denumerable Markov chains

Asymptotic stability of the optimal filter with respect to its initial conditions is investigated in this paper. Under the assumption that the observation function is one to one and the observation noise is sufficiently small, it is shown that exponential stability of the nonlinear filter holds for a large class of denumerable Markov chains, including all finite Markov chains. Throughout this paper, ergodicity of the signal process is not assumed.     

遗传算法与蚂蚁算法融合的马尔可夫收敛性分析

遗传算法具有快速随机的全局搜索能力,但不能很好地利用系统的反馈信息.蚂蚁系统是一种并行的分布式正反馈系统,但初始求解速度慢.遗传算法与蚂蚁算法的融合,优势互补.基于上述思想,提出遗传算法与蚂蚁算法融合的模型与方法,对该方法的收敛性进行了马尔可夫理论分析,并证明其优化解满意值序列是单调不增的和收敛的.且对NP-hard问题中的30城市TSP和中国CHNl44城市TSP两个实例进行了实验分析,仿真数据表明该方法不仅是一个逐步收敛的过程,而且求解速度和求解效果都非常好.     

Almost sure parameter estimation and convergence rates for hidden Markov models

A continuous-time version of Kronecker's Lemma is established and used to give rates of convergence for parameter estimates in hidden Markov models.     

差分进化算法马尔可夫链模型及收敛性分析

差分进化算法是一种基于种群差异的优化算法,主要应用于解决连续空间的优化问题。目前,研究人员主要在算法的改进和应用方面研究差分进化算法,很少从理论角度对其进行研究。为了分析差分进化算法的收敛性,定义优化个体、种群的状态转移,并提出种群的最优状态集合。根据差分进化算法的操作算子计算出个体的状态迁移概率,并证明种群状态序列是有限齐次马尔可夫链,进而建立差分进化算法的马尔可夫链模型;最后,证明差分进化算法无法保证全局收敛。理论研究结果表明,适当保证种群的多样性能够提高差分进化算法的性能。     

Markov双曲迭代函数系参数与吸引子关系的研究

1 引言迭代函数系IFS(Iterated Function Systems),是混沌分形理论研究的一个重要部分,其理论与方法是分形自然景观模拟及分形图像压缩的理论基础。1985年,Williams和Hutchinson开创了分形几何中IFS的研究,建立了IFS的一般基础理论;M.F.Barnsley和S.Demko的进一步工作使得这一方法成为构造任意维数分形集方便、有效的方法,并将之应用到图像的压缩与处理,使得该方法引起人们的关注。由于普通     

Analysis of migration models of biogeography-based optimization using Markov theory

Biogeography-based optimization (BBO) is a new evolutionary algorithm inspired by biogeography, which involves the study of the migration of biological species between habitats. Previous work has shown that various migration models of BBO result in significant changes in performance. Sinusoidal migration models have been shown to provide the best performance so far. Motivated by biogeography theory and previous results, in this paper a generalized sinusoidal migration model curve is proposed. A previously derived BBO Markov model is used to analyze the effect of migration models on optimization performance, and new theoretical results which are confirmed with simulation results are obtained. The results show that the generalized sinusoidal migration model is significantly better than other models for simple but representative problems, including a unimodal one-max problem, a multimodal problem, and a deceptive problem. In addition, performance comparison is further investigated through 23 benchmark functions with a wide range of dimensions and diverse complexities, to verify the superiority of the generalized sinusoidal migration model.     

基于马尔可夫链的分形图形生成算法

区别于传统的基于欧几里得算法的图形生成算法,在迭代函数系统的基础上,提出了一种基于马尔可夫链的分形图形生成算法。该算法首先利用马尔可夫链为每个状态转移函数设置转移的概率密度,其次通过比较随机数与状态转移函数的概率分布来确定进入的状态转移函数,进而计算吸引点的位置、确定线条的位置和角度,推导出迭代后线条的角度关系,最后通过多次迭代生成不同角度和位置的线条组成一个完整的图形。相对于传统算法,该算法针对分形图形的生成、仿射变换矩阵参数的具体调控方式、以及图形散点图的变化规则进行研究,通过对不同分形图形的生成及其形态调控的仿真实验验证了该算法可以对分形图形生成过程进行描述,进一步验证了该算法的优越性。