GEE type inference for clustered zero-inflated negative binomial regression with application to dental caries

Use of zero-inflated count data models is common in applications where the number of zero counts exceeds that predicted from a traditional count data model such as Poisson or negative binomial. When count data exhibiting inflated zero counts are correlated among subjects, a natural approach will be to fit a marginal model with the help of generalized estimating equations (GEE) that can incorporate subject-to-subject correlations. A GEE based zero-inflated negative binomial (ZINB) model is proposed to fit clustered counts with excessive zeros. However, the corresponding sandwich variance estimator appears to underestimate the true variance. The theoretical reasons for its failure are explained and a correction under additional modeling assumptions is offered. In addition, a clustered resampling (bootstrap) procedure is proposed to estimate the variance and it is shown that the bootstrap procedure captures the correct variance under no additional model assumptions. Utility of this marginal GEE based ZINB model over two other competing models has been assessed using a thorough simulation study. The resulting inference procedure is applied to study the association between the dental caries and fluoride exposures using a dataset extracted from the Iowa Fluoride Study. A number of risk factors of clinical significance are reliably identified using the proposed model.     

An analysis of the exponential stability of linear stochastic neutral delay systems

This paper is concerned with the analysis of the mean square exponential stability and the almost sure exponential stability of linear stochastic neutral delay systems. A general stability result on the mean square and almost sure exponential stability of such systems is established. Based on this stability result, the delay partitioning technique is adopted to obtain a delay‐dependent stability condition in terms of linear matrix inequalities (LMIs). In obtaining these LMIs, some basic rules of the Ito calculus are also utilized to introduce slack matrices so as to further reduce conservatism. Some numerical examples borrowed from the literature are used to show that, as the number of the partitioning intervals increases, the allowable delay determined by the proposed LMI condition approaches h_max, the maximal allowable delay for the stability of the considered system, indicating the effectiveness of the proposed stability analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Semiglobal stabilization of saturated linear systems via multiple parametric Lyapunov equations

This paper investigates the problem of semiglobal stabilization with guaranteed flexible pole placement for saturated linear systems. To retain the advantages of the parametric Lyapunov equation, matrix‐partitioning idea is used to derive a new pole shift lemma. Starting from system matrix transformations, a recursive algorithm is proposed to shift every eigenvalue of a linear system separately without mode decomposition in each step. A new method introducing various parameters to every Lyapunov equation in each step is presented. As an application, the semiglobal stabilization with guaranteed flexible pole placement for saturated linear systems can be achieved by this method. Finally, its effectiveness and advantages are demonstrated via a simulation example. Copyright © 2013 John Wiley & Sons, Ltd.     

基于FIC法的不可压缩N-S方程稳定分步算法

近年来发展了一种稳定型分步算法,它是在有限增量微积分(Finite Increment Calculus,FIC)求解不可压缩N-S方程理论框架的基础上,引入了对流和压力梯度投影两个附加变量。该方法有效改善了经典分步算法的压力稳定性,同时避免了标准FIC理论框架中存在的空间高阶导数的计算。该文通过采用此方法对各种雷诺数条件下的顶盖驱动方腔流、圆柱绕流和后台阶流进行数值模拟,并将计算结果与前人计算结果及实验结果进行比较,结果表明本文算法计算结果合理可靠。由此可见该算法具有较强的求解不可压缩流动问题的能力以及良好的应用前景。     

On the Controllability of Nonlocal Second‐Order Impulsive Neutral Stochastic Integro‐Differential Equations with Infinite Delay

In this paper, we investigate the controllability for a class of nonlocal second‐order impulsive neutral stochastic integro‐differential equations with infinite delay in Hilbert spaces. More precisely, a set of sufficient conditions for the controllability results of nonlocal second‐order impulsive neutral stochastic integro‐differential equations with infinite delay are derived by means of the Banach fixed point theorem combined with theories of a strongly continuous cosine family of bounded linear operators. As an application, an example is provided to illustrate the obtained theory.     

Optimal linear estimation for continuous stochastic systems with random observation delays

This paper is concerned with the linear minimum mean square error estimation for Itô‐type differential equation systems with random delays, where the delay process is modeled as a finite‐state Markov chain. By first introducing a set of equivalent delay‐free observations and then defining two reorganized Markov chains, the estimation problem of random delayed systems is reduced to the one of delay‐free Markov jump linear systems. The estimator is derived by using the innovation analysis method based on the Itô differential formula. And the analytical solution to this estimator is given in terms of two Riccati differential equations that are of finite dimensions. Conditions for existence, uniqueness, and stability of the steady‐state optimal estimator are studied for time‐invariant cases. In this case, the obtained estimator is very easy to implement, and all calculation can be performed off line, leading to a linear time‐invariant estimator. Copyright © 2011 John Wiley & Sons, Ltd.     

Controllability results for damped second-order impulsive neutral integrodifferential systems with nonlocal conditions

In this paper, we establish a set of sufficient conditions for the controllability of damped second-order impulsive neutral integrodifferential systems with nonlocal initial conditions in Banach spaces. The approach used is the Sadovskii fixed point theorem combined with a noncompact condition on the cosine family of operators. An example is presented to illustrate the result.     

Haar小波求解线性分数阶微积分方程

分数阶微积分方程的应用逐渐受到广大研究者的重视.论文以Haar小波基函数来逼近线性分数阶微积分方程,通过数值算例的数值解与精确解进行比较,结果表明论文方法是有效的且具有较高的精度.     

面向运动分割优化的变分光流计算方法研究

面向运动分割的需求,围绕变分光流计算中的运动边缘保留问题,对反应-扩散式光流计算模型中的扩散张量设计与改进方法进行系统深入研究。 在分析已有设计方法的基础上,提出了一种融合图像和流场信息驱动的扩散张量设计方法,并利用该扩散张量建立光流计算模型,然后在多尺度计算框架下给出了相应的偏微分方程数值计算方法。 理论分析与对比实验结果表明,这种设计方法能有效克服现有方法提取运动边缘不精确的缺点,更准确地刻画出运动边缘,提高光流的计算精度。     

非圆曲线的数控处理及程序实现

引用优化设计中一维搜索和黄金分割法,针对数控加工中非圆曲线的处理,给出实用、简洁和新颖的宏程序实现方法,解决在数控系统中求解方程组的问题,是数控用户快速解决相关应用问题的有效手段。