图的点可区别边染色算法研究

针对一般图设计了一种新型的点可区别边染色算法。该算法把概率思想和图染色相结合, 根据点可区别边染色的约束规则确立目标函数, 利用交换规则逐步寻优, 当目标函数的值满足要求时染色成功。给出详细算法步骤并进行了测试和分析, 实验结果表明该算法可以求出满足猜想的点可区别边色数。     

Counting maximal independent sets in directed path graphs

The problem of counting maximal independent sets is #P-complete for chordal graphs but solvable in polynomial time for its subclass of interval graphs. This work improves upon both of these results by showing that the problem remains #P-complete when restricted to directed path graphs but that a further restriction to rooted directed path graphs admits a polynomial time solution.     

Manifold Learning: Generalization Ability and Tangent Proximity

One of the ultimate goals of Manifold Learning (ML) is to reconstruct an unknown nonlinear low-dimensional Data Manifold (DM) embedded in a high-dimensional observation space from a given set of data points sampled from the manifold. We derive asymptotic expansion and local lower and upper bounds for the maximum reconstruction error in a small neighborhood of an arbitrary point. The expansion and bounds are defined in terms of the distance between tangent spaces to the original DM and the Reconstructed Manifold (RM) at the selected point and its reconstructed value, respectively. We propose an amplification of the ML, called Tangent Bundle ML, in which proximity is required not only between the DM and RM but also between their tangent spaces. We present a new geometrically motivated Grassman & Stiefel Eigenmaps algorithm that solves this problem and gives a new solution for the ML also.     

Drawing layered graphs with port constraints

Complex software systems are often modeled using data flow diagrams, in which nodes are connected to each other through dedicated connection points called ports. The influence a layout algorithm has on the placement of ports is determined by port constraints defined on the corresponding node.In this paper we present approaches for integrating port constraints into the layer-based approach to graph drawing pioneered by Sugiyama et al. We show how our layout algorithm, called KLay Layered, progresses from relaxed to more restricted port constraint levels as it executes, and how established algorithms for crossing minimization and edge routing can be extended to support port constraints. Compared to the previous layout algorithms supporting ports, our algorithm produces fewer edge crossings and bends and yields pleasing results.We also explain and evaluate how layout algorithms can be kept simple by using the concept of intermediate processors to structure them in a modular way. A case study integrating our layout algorithm into UC Berkeley's Ptolemy tool illustrates how KLay Layered can be integrated into Java-based applications.     

非树调和图的必要条件与非调和图类

使用同余的方法,给出了一般调和图的必要条件;还给出正则图、Euler图、圈的粘接以及圈的并是调和图的必要条件。指出了Euler图中的非调和图类,m个n圈的粘接图中的非调和图类。构造了偶圈的具有同顶点的调和母图。     

一种带有纽结分支的内在链图

针对于Petersen图P9进行研究,利用两个Petersen图K3,3,1与中间边组成的图的方法来形成petersen图中的P9,本文得到了一种带有纽结分支的内在链图H（93）,并证明了该定理.     

Gold码的因子图迭代捕获方法

为降低Gold码的捕获时间与复杂度,提出将基于因子图的迭代m序列捕获算法应用于Gold码捕获. 以全球定位系统(GPS)信号的C/A码为例,首先根据Gold码的生成多项式确定1组具有稀疏结构的校验关系;然后为降低迭代计算的复杂度,提出了不同校验关系顺次校验与混合校验的迭代捕获算法;最后通过仿真研究比较了不同的校验关系和校验方法对迭代捕获算法性能的影响. 仿真结果表明,顺次迭代且迭代次数递减的校验方法最优,该方法能在不损失检测概率的情况下降低Gold码捕获的复杂度,同时降低其捕获时间.     

Intelligent fault diagnosis for rolling bearings based on graph shift regularization with directed graphs

Graph shift regularization is a new and effective graph-based semi-supervised classification method, but its performance is closely related to the representation graphs. Since directed graphs can convey more information about the relationship between vertices than undirected graphs, an intelligent method called graph shift regularization with directed graphs (GSR-D) is presented for fault diagnosis of rolling bearings. For greatly improving the diagnosis performance of GSR-D, a directed and weighted k-nearest neighbor graph is first constructed by treating each sample (i.e., each vibration signal segment) as a vertex, in which the similarity between samples is measured by cosine distance instead of the commonly used Euclidean distance, and the edge weights are also defined by cosine distance instead of the commonly used heat kernel. Then, the labels of samples are considered as the graph signals indexed by the vertices of the representation graph. Finally, the states of unlabeled samples are predicted by finding a graph signal that has minimal total variation and satisfies the constraint given by labeled samples as much as possible. Experimental results indicate that GSR-D is better and more stable than the standard convolutional neural network and support vector machine in rolling bearing fault diagnosis, and GSR-D only has two tuning parameters with certain robustness.     

动态社会网络的社团结构检测与分析

真实社会网络如邮件、科学合作、对等网络等均可以用图进行建模. 近年来, 基于图的社团挖掘吸引了人们越来越多的研究兴趣, 它不仅可以帮助识别网络的整体结构, 还可以发现社团演变的隐藏规律. 尽管使用静态图进行社团挖掘已经被广泛采用, 但基于动态图的研究还比较少. 通过使用时间序列, 对动态图上的社团挖掘包括社团检测与分析进行研究, 提出了一个新的动态社团结构检测模型, 并采用真实网络数据集进行了实验. 实验结果显示该模型在社团结构发现的有效性和效率性方面均有着良好的表现.     

PLC在组合机床控制系统改装中的应用

介绍了用PLC(可鳊程控制器)对继电器控制系统的组合机床改装方法；并以组合机床共同性的动作循环设计出I／O分配连接图和梯形图。