The central limit theorems for fuzzy random variables

The new concept of the central limit theorem for fuzzy random variables is discussed in this paper by proposing the convergence in distribution for fuzzy random variables. We first consider the limit properties of fuzzy numbers by invoking the Hausdorff metric and then we extend it to the weak and strong convergence of fuzzy distribution functions. We provide a notion of fuzzy normal distribution. Then the central limit theorem for fuzzy random variables follows naturally.     

Stochastic Prediction of Execution Time for Dynamic Bulk Synchronous Computations

We consider the problem of execution time prediction for non-deterministic multi-phase bulk synchronous computations in multiprocessors. We characterize the computations in two stochastic workload evolution models: additive and multiplicative. The additive model reflects the commutations in which the workload changes between phases are independent of processes' present workload. The multiplicative model becomes relevant when the workload change in a process is proportional to its load base. We take advantage of their salient features and show that conventional approaches based on central limit theorem in statistics are viable to predict the execution time for long run computations. By an elegant coordination of results from order statistics and convergence rates in the central limit theorem, we derive tighter bounds on execution time of short run computations, under some mild assumptions on their workload change distributions. Accuracy of the predictions is analyzed rigorously and verified by simulations.     

On the probability theory on MV algebras

 The paper contains a review of some results concerning probability theory on MV algebras (laws of large numbers, central limit theorem, martingale convergence theorem). Also some algebraic and methodical aspects are discussed.     

Convergence of an adaptive linear estimation algorithm

In this work we prove the almost sure convergence of an adaptive linear estimator governed by a stochastic gradient algorithm with decreasing step size in the presence of correlated observations. Two complementary contributions are added to the famous 1977 Ljung theorem. First we drop the condition of nondivergence of the algorithm assumed by Ljung. While that condition can be ensured by adding a barrier, the convergence of the suitably bounded algorithm itself is not established even on the basis of Ljung theorem. Here, the barrier problem is overcome by proving that it is not necessary for the convergence. Our second contribution is to generalize the model describing the correlated observations. No state space model is used and no linear relationship between the observations and the signal to be estimated needs to be assumed. Instead we use a decreasing covariance model that agrees with a very wide class of practical applications.     

A new concept of strong controllability via the Schur complement for ARX models in adaptive tracking

We propose a new concept of strong controllability related to the Schur complement of a suitable limiting matrix. This new notion allows us to extend the previous convergence results associated with multidimensional ARX models in stochastic adaptive tracking. On the one hand, we carry out a sharp analysis of the almost sure convergence for both least squares and weighted least squares algorithms. On the other hand, we also provide a central limit theorem and a law of iterated logarithm for these two algorithms.     

光电成像探测系统的性能预测方法

提出一种光电成像探测系统的性能预测方法。介绍包含传感器、处理器的探测系统模型。根据信号检测理论,以最小错误概率准则设计似然比探测器,利用中心极限定理计算错误率。实验结果表明,随着量化位数的增大,系统错误率逐渐减少,且计算错误率与仿真错误率趋于一致。     

A new on-line learning model

We introduce a new supervised learning model that is a nonhomogeneous Markov process and investigate its properties. We are interested in conditions that ensure that the process converges to a "correct state," which means that the system agrees with the teacher on every "question." We prove a sufficient condition for almost sure convergence to a correct state and give several applications to the convergence theorem. In particular, we prove several convergence results for well-known learning rules in neural networks.     

Convergence properties of LMS adaptive estimators with unbounded dependent inputs

This note presents limit theorems for the behavior of adaptive estimators using the LMS algorithm when the driving or input sequence is a member of a broad class of random processes which are not necessarily almost surely bounded and are dependent over time. Convergence in distribution of the estimates is established in the stationary case while general nonstationary tracking is characterized in the nonstationary case. These results follow from the exponential convergence of the homogeneous algorithm which in turn follows from a strong limit theorem for infinite products of ergodic and mixing sequences of matrices.     

On the usefulness of persistent excitation in ARX adaptive tracking

The usefulness of persistent excitation is well known in the control community. Using a persistently excited adaptive tracking control, we show that it is possible to avoid the strong controllability assumption recently proposed by the authors for multivariate ARX models. We establish the almost sure convergence for both least squares and weighted least squares estimators of the unknown parameters. A central limit theorem and a law of iterated logarithm are also provided. This asymptotical analysis is related to the Schur complement of a suitable limiting matrix.     

基于鞅论的灰狼优化算法全局收敛性分析

灰狼优化(grey wolf optimization,GWO)算法是一种基于群体智能的随机优化算法,已成功地应用于许多复杂的优化问题的求解.尽管GWO算法有很多改进形式,但缺少严谨的收敛性分析,导致改进后的算法不具备理论支撑.对此,运用鞅论分析其收敛性.首先,根据GWO算法原理建立其基本的数学模型,通过定义灰狼状态空间及灰狼群状态空间,建立GWO算法的Markov链模型,并分析该算法的Markov性质;其次,介绍鞅理论,推导出一个上鞅作为最优适应度值的群进化序列;然后,运用上鞅收敛定理,并结合其Markov性质对GWO算法进行收敛性分析,证明GWO算法能以1的可能性达到全局收敛;最后,通过数值实验验证其收敛性能.实验结果表明,GWO算法具有全局收敛性强、计算耗时较低、寻优精度高等特点.     

Global stabilization control of stochastic quantum systems随机量子系统的全局稳定控制

The global stabilization control of arbitrary eigenstates for finite dimensional stochastic quantum systems with non-diagonal free Hamiltonian and non-regular measurement operator is studied in this paper. We propose a switching feedback control law, in which a constant control is used to steer the system state to a convergence domain, and another control law designed based on Lyapunov stability theorem, is used to attract the states in the convergence domain to the desired target state. The convergence to an arbitrary target eigenstate from any initial state is strictly proved. Moreover, numerical simulation experiments on a three-dimensional stochastic quantum system are implemented to demonstrate the effectiveness of the proposed control.     

一种改进的图像噪声滤波器的设计

针对用遗传算法优化L滤波的权系数时必须用到原始图像和计算量大的问题,依据中心极限定理改进去除图像噪声滤波器,通过在图像上交互式的选择感兴趣区域估计混合噪声模型,并把该混合噪声模型添加到一幅较小的测试图像上,重建退化过程,然后以测试图像为目标,用遗传算法优化L滤波的权系数,并用得到的一组最优权系数结合图像的边缘信息对图像进行L滤波。仿真实验表明用该滤波器滤除图像混合噪声能得到令人满意的结果。     

The Brownian approximation for rate-control throttles and the G/G/1/C queue

This paper studies approximations to describe the performance of a rate-control throttle based on a token bank, which is closely related to the standard G/G/1/C queue and the two-node cyclic network of ·/G/1/∞ queues. Several different approximations for the throttle are considered, but most attention is given to a Brownian or diffusion approximation. The Brownian approximation is supported by a heavy-traffic limit theorem (as the traffic intensity approaches the upper limit for stability) for which an upper bound on the rate of convergence is established. Means and squared coefficients of variation associated with renewal-process approximations for the overflow processes are also obtained from the Brownian approximation. The accuracy of the Brownian approximation is investigated by making numerical comparisons with exact values. The relatively simple Brownian approximation for the job overflow rate is not very accurate for small overflow rates, but it nevertheless provides important insights into the way the throttle design parameters should depend on the arrival-process characteristics in order to achieve a specified overflow rate. This simple approximation also provides estimates of the sensitivity of the overflow rates to the model parameters.     

Adaptive control for manufacturing systems using infinitesimalperturbation analysis

Combining infinitesimal perturbation analysis (IPA) with stochastic approximation gives identification algorithms to estimate the optimal threshold value for failure-prone manufacturing systems consisting of one machine producing one part type. Two adaptive control schemes are proposed. The adaptive control schemes do not require the knowledge of the distribution functions of the up and down times. Under some appropriate conditions, the strong consistency, as well as the convergence rates, of the identification algorithms and the cost function is established for the adaptive control schemes. In particular, it is shown that central limit theorems hold for the identification algorithms     

Convergence Rates of Nonparametric Filtering Estimates in Autoregression Dynamic Systems

The Bayes problem of filtration of a random process from observations on an autoregression process with coefficients defined by functions of the useful signal is studied. The main assumption asserts that the conditional observation densities belong to a family of conditional exponential densities with known functions of observations and useful signal, whose distribution is not known in advance. Optimal signal filtering equations and empirical risk estimates are derived. Regularized nonparametric filtering estimates are derived and a theorem on the mean-square convergence and convergence rates of these estimates is formulated.     

An efficient algorithm for parameterizing HsMM with Gaussian and Gamma distributions

A widely used method for parameterizing hidden semi-Markov model is using Gaussian distribution to form the output probability and using Gamma distribution to form the state duration probability. Most of these models are based on the classical Newton?s method with second-order convergence, whose iterative convergence speed is slow for large-scale realtime applications. An improved parameter re-estimation algorithm is introduced for such parametric hidden semi-Markov model in this paper. The proposed approach is based on forward and backward algorithm. It applies an iterative method with eighth-order convergence to improve the performance of the model. The numerical examples validate the proposed method.     

Expectation propagation with factorizing distributions: a Gaussian approximation and performance results for simple models

We discuss the expectation propagation (EP) algorithm for approximate Bayesian inference using a factorizing posterior approximation. For neural network models, we use a central limit theorem argument to make EP tractable when the number of parameters is large. For two types of models, we show that EP can achieve optimal generalization performance when data are drawn from a simple distribution.     

Univariate marginal distribution algorithm dynamics for a class of parametric functions with unitation constraints

In this paper, we introduce a mathematical model for analyzing the dynamics of the univariate marginal distribution algorithm (UMDA) for a class of parametric functions with isolated global optima. We prove a number of results that are used to model the evolution of UMDA probability distributions for this class of functions. We show that a theoretical analysis can assess the effect of the function parameters on the convergence and rate of convergence of UMDA. We also introduce for the first time a long string limit analysis of UMDA. Finally, we relate the results to ongoing research on the application of the estimation of distribution algorithms for problems with unitation constraints.     

随机模糊环境下的命题逻辑真度理论*

在实单位区间[0,1]具有一定概率分布的基础上,引入命题逻辑公式的随机模糊意义下的真度概念,指出随机真度是已有文献中各种命题逻辑真度的共同推广.利用随机模糊真度定义公式间的随机模糊相似度,导出全体公式集上的一种伪距离——随机模糊逻辑伪距离,证明在随机模糊逻辑伪距离空间无孤立点.利用概率论中的积分收敛定理,证明一个关于随机模糊真度的极限定理.研究已有各种真度之间的联系.证明随机逻辑伪距离空间中逻辑运算的连续性,并将概率逻辑学基本定理推广至多值命题逻辑.在随机逻辑伪距离空间中提出2种不同类型的近似推理模式并应用于实际问题的近似推理.     

On the behavior of a block-iterative projection method for solving convex feasibility problems

The behavior of a class of block-iterative projection algorithms for solving convex feasibility problems is studied. A limit characterization theorem and a convergence criterion are proven. Ways of accelerating the computational procedures are pointed out.