Distance-Based Regression Analysis for Measuring Associations

Distance-based regression model, as a nonparametric multivariate method, has been widely used to detect the association between variations in a distance or dissimilarity matrix for outcomes and predictor variables of interest in genetic association studies, genomic analyses, and many other research areas. Based on it, a pseudo-F statistic which partitions the variation in distance matrices is often constructed to achieve the aim. To the best of our knowledge, the statistical properties of the pseudo-F statistic has not yet been well established in the literature. To fill this gap, the authors study the asymptotic null distribution of the pseudo-F statistic and show that it is asymptotically equivalent to a mixture of chi-squared random variables. Given that the pseudo-F test statistic has unsatisfactory power when the correlations of the response variables are large, the authors propose a square-root F-type test statistic which replaces the similarity matrix with its square root. The asymptotic null distribution of the new test statistic and power of both tests are also investigated. Simulation studies are conducted to validate the asymptotic distributions of the tests and demonstrate that the proposed test has more robust power than the pseudo-F test. Both test statistics are exemplified with a gene expression dataset for a prostate cancer pathway.

     

离散线性区间系统的分支稳定性

研究了离散区间系统的一种特殊形式的稳定性 ,即分支稳定性。分别给出了离散区间系统分支渐近稳定性和指数分支渐近稳定性的定义。证明了离散区间系统是分支渐近稳定的 ,且仅当系统矩阵在每一时刻都将满足一个约束条件的系统状态向量变换成满足另一个约束的向量。由此利用不等式的性质分别给出了离散区间系统分支渐近稳定和指数分支渐近稳定的充要条件     

基于功能/结构相似的复杂系统相似准则研究

相似理论是一种研究试验模型与真实模型之间相似关系的方法,目前以相似三定理为基础的经典相似理论主要针对元件,对实际中大型化与复杂化的真实系统而言,相似理论的应用就受到了极大的限制.对此,本文将经典相似理论与系统论相结合,从功能与结构的角度建立了针对复杂系统的相似准则,该准则的核心是结合了功能相似与结构相似的复杂系统相似矩阵,只要原型系统与模型系统对应矩阵相等,则原型系统与模型系统相似.该准则填补了相似三定理不适用与复杂系统的理论不足,实现了将相似理论拓展并应用于大型复杂系统的目的.最后通过算例分析验证了该理论的可行性与优越性.     

Asymptotic Properties of Maximum Quasi-Likelihood Estimators in Generalized Linear Models with Diverging Number of Covariates

In this paper, for the generalized linear models (GLMs) with diverging number of covariates, the asymptotic properties of maximum quasi-likelihood estimators (MQLEs) under some regular conditions are developed. The existence, weak convergence and the rate of convergence and asymptotic normality of linear combination of MQLEs and asymptotic distribution of single linear hypothesis test statistics are presented. The results are illustrated by Monte-Carlo simulations.     

Global Asymptotic Synchronization of a Class of BAM Neural Networks with Time Delays via Integrating Inequality Techniques

In this paper, the authors are concerned with global asymptotic synchronization for a class of BAM neural networks with time delays. Instead of using Lyapunov functional method, LMI method and matrix measure method which are recently widely applied to investigating global exponential/asymptotic synchronization for neural networks, two novel sufficient conditions on global asymptotic synchronization of above BAM neural networks are established by using a kind of new study method of global synchronization: Integrating inequality techniques. The method and results extend the study of global synchronization of neural networks.     

离散广义大系统的渐近稳定与镇定

广义大系统的渐近稳定与镇定问题是广义大系统理论的基本问题之一 ,在许多领域均有广泛的应用。广义大系统的研究与广义系统相比困难得多。利用广义Lyapunov函数方法研究了离散广义大系统的渐近稳定与镇定问题 ,给出了渐近稳定的判定定理 ,设计了适当的反馈律 ,以实现离散广义大系统的镇定。该方法简单、直观 ,给出的例子说明了该定理的可行性。     

Stability Analysis of Nonlinear Measure Large Scale Systems

In this paper,we established the variation of parameters formula of nonlinear large scalesystems containing measures.By means of the lumped Picard iteration method,which avoided thedifficulties of constructing Lyapunov function,we studied the stability,uniform stability,asymptoticstability,uniform asymptotic stability,and exponential stability properties of nonlinear measure largescale systems.     

滞后广义系统的渐近稳定与镇定

广义系统的渐近稳定与镇定问题是广义系统理论的基本问题之一,在许多领域均有应用,时滞广义系统的研究与无时滞广义系统相比要困难得多。利用广义Lyapunov泛函方法研究了具滞后的广义系统的渐近稳定性和镇定问题,给出了渐近稳定判定定理,设计了适当的反馈律,以实现滞后广义系统的镇定,方法简单,直观,易于理解,给出的例子说明了该定理的可行性。     

具有不确定性和非线性扰动的时滞关联大系统的鲁棒稳定性条件

利用Lyapunov函数方法和M-矩阵特性,重点讨论了一类具有不确定性和非线性扰动的时滞关联大系统的鲁棒稳定性,导出了此类系统时滞无关稳定性条件,改进和推广了现有文献的结论.     

Degree-based moment estimation for ordered networks

The edges between vertices in networks take not only the common binary values, but also the ordered values in some situations (e.g., the measurement of the relationship between people from worst to best in social networks). In this paper, the authors study the asymptotic property of the moment estimator based on the degrees of vertices in ordered networks whose edges are ordered random variables. In particular, the authors establish the uniform consistency and the asymptotic normality of the moment estimator when the number of parameters goes to infinity. Simulations and a real data example are provided to illustrate asymptotic results.     

Componentwise Asymptotic Stability of Continuous-Time Interval Systems

A special type of asymptotic (exponential) stability, namely componentwise asymptotic (exponential) stability for the continuous-time interval system is investigated. A set-valued map that represents the constraint of the state of the system is defined. And, by applying the viability theory of differential equation, sufficient and necessary conditions for the componentwise asymptotical (exponential) stability of this kind of systems are given.     

系统仿真理论的探索

论述的内容为：原始系统与仿真系统的相似关系，相似方法，相似程度及其与误差的对应关系，仿真建模与验模，应用相似理论分析飞行模拟器的运动系统纵向通道，以及非线性、变参数系统的分析、综合及其解析解的求定。     

推广的M~x/G(M/G)/1(M/G)可修排队系统(Ⅱ)—— 一些可靠性指标

进一步研究推广的MxG(MG)1(MG)可修排队系统,讨论了服务台如下的可靠性问题:1)在时刻t失效的概率,即不可用度;2)在“服务员忙期”内的失效次数;3)在(0,t]内的平均失效次数及其渐近展开;4)在“服务员忙期”内的失效时间;5)在(0,t]内的平均失效时间及其渐近展开,得到一系列结果,并给出了便于计算(0,t]内的平均失效次数和平均失效时间的近似式     

相似关系的基本概念及其弱等价性质

本文的主要目的是确立相似关系的准确数学概念。首先本文将等价关系合理推广为弱等价关系,其次为解决描述部分与整体的共同属性问题,本文引入了向下相容性概念,并证明了向下相容性具有弱等价性质。然后用集合、子集、幂集、并集、１—１映射这五个最基本的概念及向下相容性公理、系统原理初步界定和刻划了相似关系、相似映射、相似要素、相似基、相似元（相似点）、相似系统这六个相似方面的基本概念。这对建立相似系统的分析具有重要意义。     

基于多尺度相似度特征的答案选择算法

答案选择的主要任务是对问答系统中问题的候选答案排序,当前主流的方法是基于表示学习方法,通过神经网络对问题和答案进行向量表示,然后根据向量相似度对候选答案排序,该类方法忽略了问题和答案的局部关联性。针对这一问题,提出了一种基于多尺度相似度特征的深度学习模型。该模型采取传统的深度学习模型分别提取问题和答案的特征,然后计算各个尺度下的特征相似度得到问答的相似度矩阵,最后采取三种不同的相似度特征学习模型对相似度矩阵学习得到联合相似度。在公开数据集WebQA上进行实验验证,实验结果表明将相似度特征学习方法引入传统深度学习模型获得了较为明显的提升。     

相似系统工程

基于相似学和相似系统理论，本文研究了相似系统工程的概念及其含义。相似系统工程主要研究一切与系统相似性有关的科学技术和组织管理实践问题。认为相似系统工程的主要特点是：１．将自然系统优化原理应用于工程实践，在人造系统中实现与自然系统中存在的某些相似特性；２．运用已知相似规律和一定系统已知优秀特性及经验或技术方法，成功应用于另一系统中，设计、组建和管理新的相似系统。结合工程实践，探讨了相似系统工程实践应用的原理与方法，以及向相似工程学发展的前景。     

协整模型中门限协整的一种辨识方法

考虑非线性、非平稳时间序列中门限协整模型的辨识问题，给出协整模型属于线性协整还是门限协整的一种判断方法。给出门限协整回归模型的定义，构造了辨识线性协整和门限协整的SupW统计量，并得到了SupW统计量的极限分布。给出逼近极限分布的Bootstrap方法，计算渐近p-值确定协整模型是线性协整还是门限协整。模拟计算和实例计算证明了该辨识方法的有效性，具有重要的应用价值。     

The Asymptotic Properties of the Higher-order Moments of the Orthogonal Estimation of the Parameters of MA Model

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Generalized F-test for high dimensional regression coefficients of partially linear models

This paper proposes a test procedure for testing the regression coefficients in high dimensional partially linear models based on the F-statistic. In the partially linear model, the authors first estimate the unknown nonlinear component by some nonparametric methods and then generalize the F-statistic to test the regression coefficients under some regular conditions. During this procedure, the estimation of the nonlinear component brings much challenge to explore the properties of generalized F-test. The authors obtain some asymptotic properties of the generalized F-test in more general cases,including the asymptotic normality and the power of this test with p/n ∈(0, 1) without normality assumption. The asymptotic result is general and by adding some constraint conditions we can obtain the similar conclusions in high dimensional linear models. Through simulation studies, the authors demonstrate good finite-sample performance of the proposed test in comparison with the theoretical results. The practical utility of our method is illustrated by a real data example.     

Moment Equations of Linear It Stochastic Systems with Applications

1.INTRODUCTIONAsiswellknown,stochasticsystemmodeloftheIt6typeisoneofthemostimportantmodelsforstochasticsystems,manystochasticsystemswithcolorednoisecanbestudiedwithhelpoftheIt6stochasticsystems[if.ForthestabilityandcontrolproblemofIt6stochasticsystems,nlallyresultshavebeenobtainedintheliteratures[l~6].Whilesomebasicproblems,suchasthenecessaryandsufficientconditionofmean-squarestabilityoflinearIt6stochasticsystems,havehotbeensolved.Inthepreviousliterature,someresultsonthestabilityoflinear…