有限群的“齐次性”Cayley有向图求法的进一步研究

本文给出了直接从定义关系求有限群的＂齐次性＂Cayley有向图的简捷方法—本源法,其本源定理又给出了诸多类型群的Cayley有向图。     

围长为2的奇数阶本原极小强连通有向图的1-指数集

研究了围长为2的n阶本原极小强连通有向图的1-指数集,证明了当n(≥5)为奇数时,En(1)={4,5,6,7,…,2n-5},无缺数段。     

一类特殊本原不可幂定号有向图的广义基

考虑了一类含有三个n—2圈和一个n圈本原不可幂定号有向图的广义基,通过分析图中是否存在寻求的途径及SSSD途径对,运用本原不可幂定号有向图的一些定义和性质,给出了此类图的广义本原指数及广义基.     

基于有向图的足球视频中球员分类算法

基于传统的直方图球员分类方法由于缺乏描述图像颜色的空间信息而造成分类误差,而且该方法需要先验的模板信息。为此,本文提出一种基于有向图的足球球员的分类方法。首先,利用HSV模型中主颜色方法提取候选球员,并利用等面积矩形划分策略对图像进行分块;其次,对子块的HSV颜色空间进行量化,并将统计直方图作为颜色特征,然后通过颜色特征计算图像之间的距离,并利用距离矩阵生成对应有向图;最后,通过对有向图的顶点分类实现球员的分类。实验结果表明,本文提出的方法能够在没有先验模板信息的条件下,能够有效地解决处在分类边界上的球员分类问题,获得98.23%的分类正确率,与传统方法相比,具有更好的分类效果。     

Inferring (Biological) Signal Transduction Networks via Transitive Reductions of Directed Graphs

In this paper we consider the p-ary transitive reduction (TR _p ) problem where p>0 is an integer; for p=2 this problem arises in inferring a sparsest possible (biological) signal transduction network consistent with a set of experimental observations with a goal to minimize false positive inferences even if risking false negatives. Special cases of TR _p have been investigated before in different contexts; the best previous results are as follows:

非平衡拓扑结构的多智能体网络系统一致性协议

针对多智能体网络系统,本文分别研究了非平衡拓扑结构的多智能体连续状态和离散状态下的一致性协议.首先提出了能使用有向图表示的多智能体网络系统的拓扑结构,并根据该拓扑结构建立了网络系统的1阶数学模型和提出了多智能体网络系统一致收敛准则.对于多智能体网络连续系统,该系统的一致平衡点最终收敛于初始状态的凸组合,本文最终确定了非平衡拓扑结构的一致平衡点.如果多智能体网络系统的拓扑结构没有改变,在离散状态下系统的一致平衡点仍收敛于初始状态的凸组合,并且离散状态下系统的一致平衡点与连续状态下系统的一致平衡点相等.最后采用8个智能体组成的网络拓扑进行计算机仿真,验证理论的正确性.     

一类含两个圈的特殊本原双色有向图的指数

一个双色有向图D是本原的,如果存在非负整数h和k,h+k>0,使得D的每对顶点(i,j)都存在从i到j的(h,k)-途径,称h+k的最小值为本原双色有向图D的指数.给出了一类含两个圈的特殊本原双色有向图指数的紧的上下界,并对一类特殊情况进行了极图刻划.     

数控车床故障传播机理分析

为探讨数控车床故障传播机理,即识别系统关键节点与关键故障传播路径,基于数控车床故障数据,应用有向图理论、集成决策实验室分析(DEMATEL)和解释结构模型(ISM)方法构建数控车床分层故障传播有向图模型;基于故障传播概率、边介数两指标定义故障传播强度表征故障传播行为;提出结合系统分层故障传播有向图模型和故障传播强度的数控车床故障传播机理分析方法.分析结果表明:系统分层故障传播有向图模型实现了系统层级分解,简化了故障传播分析过程,为关键路径识别奠定了基础;将故障传播强度作为关键路径识别的依据,避免了传统分析方法基于单一指标描述数控车床故障传播行为而产生的偏差,实现了准确定位故障源,准确识别系统关键路径.所提方法有助于系统故障诊断与维护.     

关于广义Hadamard矩阵及其对应有向图类的特征

Hadamard矩阵在信号处理方面有重要应用,而Hadamard矩阵是广义Hadamard矩阵的特殊情形.讨论了广义Hadamard矩阵对应简单有向图类的特征及其相互关系;给出了广义Hadamard矩阵对应简单有向图的特征值的性质,从而证明了有向图的邻接矩阵是广义Hadamard矩阵的必要条件,为简单有向图是偶阶的;并得到了广义Hadamard矩阵在Kronecker积下的性质.为区组设计和编码理论提供了一些新的方法,并在信源编码中有重要的应用.     

Quantification of human error in maintenance using graph theory and matrix approach

Assessment of human error in maintenance requires identification of the contributing factors that lead to human error(s). These factors are called human error inducing factors (HEIFs), which take into consideration both the active and latent error contributing aspects related to man, machine and environment. A systems approach of the Graph Theory is applied in this paper for quantifying human error in maintenance activities that models the identified factors and their interactions/interrelationships in terms of human error digraph. The nodes in the digraph represent the HEIFs and the edges represent their interrelationships. The digraph is converted into an equivalent matrix and an expression based on this is developed, which is characteristic of the human error in maintenance. This expression is used to evaluate a human error index by substituting the numerical value of the factors and their interrelations. The index is a measure of the human error potential involved in the maintenance of systems. A higher value of index indicates that the error likelihood is more for the associated tasks, and more efforts are required to make the system less prone to human error. The proposed methodology is illustrated using a case study. The approach is anticipated to play a significant role in identifying sources of human errors and predicting their impact; and will help to integrate human factors during design stage with the objective of reducing human error in maintenance. Copyright © 2011 John Wiley & Sons, Ltd.