一类细胞神经网络输入—输出控制

对于一类细胞神经网络,以系统的输入、输出的反馈权值为参数,构成参数空间,引入几何方法,将参数空间分解分块成有限个区域,当系统参数在某一确定的区域上时,研究系统的输入—输出间关系,并给出输入、输出之间控制的一类判别方法.     

基于三角模糊集划分的MISO Mamdani模糊系统参数关联性分析

基于三角模糊集划分的MISO Mamdani模糊系统是模糊规则获取研究领域的一类重点研究对象。在这种划分下，系统的输入空间被划分成若干个超立方体，在每个超立方体内系统的输出与2^p条模糊规则中的参数相关。本文将每个超立方体分成若干个区域，并且严格论证了在每个区域内系统输出仅与其中2^p-1条模糊规则及另2^p-1条模糊规则中相应参数平均值相关。这个结论使得可以根据样本误差的区域分布情况优化参数的选取。对于该类系统的参数优化过程中的参数选取具有积极的意义。     

基于动态输出反馈的互联大系统重叠分散控制

主要研究一类基于动态输出反馈的环型互联大系统鲁棒重叠分散控制问题.根据大系统包含原理的约束条件,对系统进行特殊重叠结构分解,在扩展空间中分解为一系列两两子系统对,为每个两两子系统对分别设计动态输出反馈控制器,然后收缩回原空间,实现对该互联大系统的重叠分散控制.在控制器设计中,采用了Lyapunov理论和线性矩阵不等式(LMI)方法,推导了系统稳定的充分条件,给出了动态输出反馈控制器的设计方法,并用遗传算法对设计参数进行了优化,从而进一步优化了设计结果.由于控制器设计时仅针对两两子系统,因此该方法避免了直接采用LMI方法因子系统过多,维数过大引起的LMI求解上的困难.最后将该方法应用到一个三区域互联电力系统的自动发电控制(AGC)设计中,仿真结果证明了此方法的可行性及优越性.     

线性最优输出反馈控制

本文研究线性二次最优调节器的实时输出反馈解u(t)=-Ky(t)的存在性。利用算子析因与值域包含引理给出了主要结果。对有限维系统及一些分布参数系统得到了最优输出反馈存在的具体充要条件和反馈算子K的表示式。     

一类不确定非线性系统的适应H-infinity控制

主要讨论了一类具有不确定参数的非线性系统的通过适应输出反馈达到干扰衰减的问题．通过构造降维观测器,利用Backstepping方法设计输出反馈控制器,使闭环系统具有不确定参数的标准的增益问题可解,并使系统达到内稳定．     

有两个服务阶段、反馈、强占型的M/G/1重试排队

在假定重试区域中只有队首的顾客允许重试的条件下,重试时间是一般分布时,考虑具有两个服务阶段、反馈、强占型的M／G／1重试排队系统．得到了系统稳态的充要条件．求得稳态时系统队长和重试区域中队长分布及相关指标,并且得到了系统的随机分解性质．     

输出反馈二次型最优的可解性问题

本文研究了用输出反馈实现二次型最优控制的问题,指出任何最优输出反馈都是对应最优状态反馈的衍生解和在一般情况下最优输出反馈所满足的线性矩阵方程是不可解的.并讨论了输出矩阵含有待定参数的情形,给出了最优输出反馈存在的必要条件,对于单输入系统证明了该条件几乎是充分的.     

蛙卵有丝分裂模型的定性分析

本文对M.T.Borisuk和J.J.Tyson在[1]中所提出的一个有关蛙卵有丝分裂的平面三次系统模型证明了大范围周期解的存在性，给出了周期解所在的空间区域和所对应的参数区域及周期解不存在的空间区域和参数区域，所得结果严格地证明了[1]中给出的数值结果，最后我们证明在[1]的数值结果所用的参数下极限环的唯一性。     

参数不确定广义离散时间系统的预见重复控制

基于参数依赖的Lyapunov函数方法及线性矩阵不等式(LMI)技巧,文章考虑参数不确定广义离散系统的预见重复控制.首先,引入差分算子和二维模型方法,构造了包含可预见目标值信号的二维扩大误差系统;然后,针对扩大误差系统,分别设计状态反馈和输出反馈控制器.在考虑输出反馈时,改造输出方程、充分利用可预见信号的未来信息,并通过LMI技巧给出闭环系统渐近稳定的条件及预见重复控制器的设计方法.最后,数值仿真表明文章结果的有效性.     

广义分布参数系统的状态反馈稳定性问题(1)

关于系统的状态反馈稳定性问题的研究一直是现代控制理论研究的重要问题之一.广义分布参数系统是比分布参数系统更广的一类系统,在研究复合材料热导体中的温度分布等问题时会出现这样的系统.本文讨论了H ilbert空间中一阶广义分布参数系统的状态反馈稳定性问题.应用泛函分析及线性算子半群理论的方法给出了使闭环广义分布参数系统渐进稳定的充要条件,充分条件及状态反馈的构造性表达式.这对研究广义分布参数系统的状态反馈稳定性问题具有重要的理论价值.     

Generalized Odds Ratios for Visual Modeling

The problem of displaying interaction effects graphically has been studied for a long time. This article shows how mosaic plots can be applied to visualize interaction effects in categorical data. This idea leads to a graphical approach for model selection based on a classical backward selection.     

A bijection between permutations and floorplans, and its applications

A floorplan represents the relative relations between modules on an integrated circuit. Floorplans are commonly classified as slicing, mosaic, or general. Separable and Baxter permutations are classes of permutations that can be defined in terms of forbidden subsequences. It is known that the number of slicing floorplans equals the number of separable permutations and that the number of mosaic floorplans equals the number of Baxter permutations [B. Yao, H. Chen, C.K. Cheng, R.L. Graham, Floorplan representations: complexity and connections, ACM Trans. Design Automation Electron. Systems 8(1) (2003) 55-80]. We present a simple and efficient bijection between Baxter permutations and mosaic floorplans with applications to integrated circuits design. Moreover, this bijection has two additional merits: (1) It also maps between separable permutations and slicing floorplans; and (2) it suggests enumerations of mosaic floorplans according to various structural parameters.     

Visualizing Loglinear Models

Abstract

We consider visual methods based on mosaic plots for interpreting and modeling categorical data. Categorical data are most often modeled using loglinear models. For certain loglinear models, mosaic plots have unique shapes that do not depend on the actual data being modeled. These shapes reflect the structure of a model, defined by the presence and absence of particular model coefficients. Displaying the expected values of a loglinear model allows one to incorporate the residuals of the model graphically and to visually judge the adequacy of the loglinear fit. This procedure leads to stepwise interactive graphical modeling of loglinear models. We show that it often results in a deeper understanding of the structure of the data. Linking mosaic plots to other interactive displays offers additional power that allows the investigation of more complex dependence models than provided by static displays.     

Residual-Based Shadings for Visualizing (Conditional) Independence

Residual-based shadings for enhancing mosaic and association plots to visualize independence models for contingency tables are extended in two directions: (a) perceptually uniform Hue-Chroma-Luminance (HCL) colors are used and (b) the result of an associated significance test is coded by the appearance of color in the visualization. For obtaining (a), a general strategy for deriving diverging palettes in the perceptually based HCL space is suggested. As for (b), cutoffs that control the appearance of color are computed in a data-driven way based on the conditional permutation distribution of maximum-type test statistics. The shadings are first established for the case of independence in two-way tables and then extended to more general independence models for multiway tables, including in particular conditional independence models.     

Existence theorems for boundary value problems in difference equations

In this research, we study linear difference equations with constant coefficients subject to boundary conditions. Necessary and/or sufficient conditions for the existence of a unique solution will be established. The proofs of the existence and uniqueness theorems are established by means of special types of determinants called Mosaic Vandermonde determinants.     

A Brief History of the Mosaic Display

This article provides an illustrated history of the visual and conceptual ideas leading to the development of mosaic displays. We trace the origins of the use of rectangles and area to depict data quantities and their relations, of early forms of mosaic displays including subdivided bar-like charts and various cartograms, to the modern forms used in log-linear analysis and in space-filling tree maps.     

Extending Mosaic Displays: Marginal,Conditional, and Partial Views of Categorical Data

Abstract

This article first illustrates the use of mosaic displays for the analysis of multiway contingency tables. We then introduce several extensions of mosaic displays designed to integrate graphical methods for categorical data with those used for quantitative data. The scatterplot matrix shows all pairwise (bivariate marginal) views of a set of variables in a coherent display. One analog for categorical data is a matrix of mosaic displays showing some aspect of the bivariate relation between all pairs of variables. The simplest case shows the bivariate marginal relation for each pair of variables. Another case shows the conditional relation between each pair, with all other variables partialled out. For quantitative data this represents (a) a visualization of the conditional independence relations studied by graphical models, and (b) a generalization of partial residual plots. The conditioning plot, or coplot shows a collection of partial views of several quantitative variables, conditioned by the values of one or more other variables. A direct analog of the coplot for categorical data is an array of mosaic plots of the dependence among two or more variables, stratified by the values of one or more given variables. Each such panel then shows the partial associations among the foreground variables; the collection of such plots shows how these associations change as the given variables vary.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.