A Com binatorial Approach for Topological Classification of Graphlike M anifolds

The concept of graphlike manifolds was presented in [1] and the problem of counting the homeomorphic classes of graphlike manifolds has been studied in a series of articles, e.g., [1～8]. In this paper we suggest an approach based on the graph colouring, Abelian group and the combinatorial enumeration method.

Class Ⅰ graphs of nonnegative characteristic without special cycles

In this paper, we prove that every graph with maximum degree six that can be embedded in a surface of nonnegative characteristic is of Class Ⅰ if it does not contain a 5- or 6-cycle with a chord, which extends some known results.

STABILITY NUMBER IN SUBCLASSES OF P_5^-FREE GRAPHS

Two new hereditary classes of P 5-free graphs where the stability number can be found in polynomial time are proposed.They generalize several known results.

Multi-Class Support Vector Machine Classifier Based on Jeffries-Matusita Distance and Directed Acyclic Graph

Based on the framework of support vector machines( SVM) using one-against-one( OAO) strategy, a new multi-class kernel method based on directed acyclic graph( DAG) and probabilistic distance is proposed to raise the multi-class classification accuracies. The topology structure of DAG is constructed by rearranging the nodes' sequence in the graph. DAG is equivalent to guided operating SVM on a list,and the classification performance depends on the nodes' sequence in the graph. Jeffries-Matusita distance( JMD) is introduced to estimate the separability of each class,and the implementation list is initialized with all classes organized according to certain sequence in the list. To testify the effectiveness of the proposed method,numerical analysis is conducted on UCI data and hyperspectral data. Meanwhile,comparative studies using standard OAO and DAG classification methods are also conducted and the results illustrate better performance and higher accuracy of the proposed JMD-DAG method.

On the Maximum Number of Dominating Classes in Graph Coloring

We investigate the dominating-c-color number,, of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and . This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].

Cayley图与变换图(Interchange Graph)

设s_x是n次对称群,M_x是由s_x的一些奇置换组成的共轭类,对任意n本文得到了Cayley图类Cay(M_x,S_x)的点连通度、直径、Hamiltonian 性及其它一些图论性质,同时本文还发现一类变换图G(R^x(1),S^x(1))与Cay(M,S_x)是同构的图类,(其中R^x(1),S^x(1)分别是n维全1行和、列和向量,M是s_x的对换全体),从而得到这类变换图与Cayley图Cay(M_x,S_x)相平行的一些性质。

面向程序可达性验证的数组处理循环压缩方法

计算机软件的安全性和健壮性逐渐成为一个非常重要的问题,而自动软件形式化验证是一种验证软件程序安全性和健壮性的可靠性较高的方法。在自动软件形式化验证中,大规模数组和复杂循环导致状态爆炸,使得验证器无法在规定时间内完成验证,因此如何在保证验证正确性的前提下压缩数组规模是一个值得研究的课题。文章提出复杂循环等价类的定义和相关命题,并提出一种面向程序可达性验证的数组处理循环压缩方法,先利用控制流自动机和系统依赖图进行静态分析划分等价类,再根据循环依赖关系对等价类进行压缩,用压缩后程序的验证结果代替原始程序的验证结果。实验结果表明,文章提出的方法能够在保证验证正确性的前提下压缩程序的规模,提高验证效率。

Application of rough graph in relationship mining

Based on the definition of class shortest path in weighted rough graph,class shortest path algorithm in weighted rough graph is presented,which extends classical shortest path algorithm.The application in relationship mining shows effectiveness of it.

Edge Colorings of Planar Graphs without 6-Cycles with Two Chords

It is proved here that if a planar graph has maximum degree at least 6 and any 6-cycle contains at most one chord, then it is of class 1.

COMBINED ALGORITHM FOR THE ESSENTIAL GRAPH OF BAYESIAN NETWORK STRUCTURES

Learning Bayesian network structure is one of the most important branches in Bayesian network. The most popular graphical representative of a Bayesian network structure is an essential graph. This paper shows a combined algorithm according to the three rules for finding the essential graph of a given directed acyclic graph. Moreover, the complexity and advantages of this combined algorithm over others are also discussed. The aim of this paper is to present the proof of the correctness of the combined algorithm.

The Further Results of the Chromatic Uniqueness of Certain Bipartite Graphs K(m, n)-A

With its comprehensive application in network information engineering (e.g. dynamic spectrum allocation under different distance constraints) and in network combination optimization (e.g. safe storage of deleterious materials), the graphs ’ cloring theory and chromatic uniqueness theory have been the forward position of graph theory research. The later concerns the equivalent classification of graphs with their color polynomials and the determination of uniqueness of some equivalent classification under isomorphism. In this paper, by introducing the concept of chromatic normality and comparing the number of partitions of two chromatically equivalent graphs, a general numerical condition guarenteeing that bipartite graphs K(m, n)-A (AE(K(m, n)) and |A|≥2) is chromatically unique was obtained and a lot of chromatic uniqueness graphs of bipartite graphs K(m,n)-A were determined. The results obtained in this paper were general. And the results cover and extend the majority of the relevant results obtained within the world.

An Improved Directed Acyclic Graph Support Vector Machine

在这份报纸，我们与传统的 DAGSVM 为多班 classification.Compared 建议一台改进的指导的非循环的图支持向量机器( DAGSVM )，改进版本有指导的非循环的图的结构没被选择的优点随机、修理，并且根据到来的测试样品最佳能是适应的，因此，它有好归纳 performance.From 六数据集的实验，我们能看到 DAGSVM 的建议改进版本比 tr

Gauss’ Problem, Negative Pell’s Equation and Odd Graphs

In this paper we present some results connected with still open problem of Gauss, negative Pell’s equation and some type graphs.In particular we prove in the Theorem 1 that all real quadratic fields K=Q( ) , generated by Fermat’s numbers with d=Fm+1=22m+1+1,m≥2, have not unique factorization. Theorem 2 give a connection of the Gauss problem with primitive Pythagorean triples. Moreover, in final part of our paper we indicate on some connections of the Gauss problem with odd graphs investigated by Cremona and Odoni in the papper [5].

虚拟人手语动画自动生成技术研究

虚拟人手语动画中信息量较多,其手势动作复杂性较高。在手语动画生成过程中,通常缺乏动作约束能力,动画生成后具有重合部分且手部画面异常,导致手语动画生成精度低、质量差。为此,研究了虚拟人手语动画自动生成技术。根据动作数据采集结果,构建无向加权图,确定各个顶点位置与特征,得到原始动作捕捉序列,完成虚拟人手语动作分割,确定虚拟人手部动作基础信息。使用类函数与高度函数以及人体体征数据,提取虚拟人手部动作关键点,对手部特征点进行划分,分析手部动作的骨骼关节特征。使用线性变换公式以及动作处理帧窗口,对手语动画进行约束,实现手语动画自动生成。实验结果表明,本文方法可提升手语动画生成精度,实现手部滑动动作控制,提升虚拟人手语动画质量。

Index-<i>p</i>Abelianization Data of <i>p</i>-Class Tower Groups

Given a fixed prime number p, the multiplet of abelian type invariants of the p-class groups of all unramified cyclic degree p extensions of a number field K is called its IPAD (index-p abeliani- zation data). These invariants have proved to be a valuable information for determining the Galois group of the second Hilbert p-class field and the p-capitulation type of K. For p=3 and a number field K with elementary p-class group of rank two, all possible IPADs are given in the complete form of several infinite sequences. Iterated IPADs of second order are used to identify the group of the maximal unramified pro-p extension of K.

基于图神经网络的不平衡欺诈检测研究

现阶段图神经网络被广泛应用于欺诈检测,由于欺诈检测中往往存在类不平衡问题,导致基于图神经网络模型性能不佳。针对上述问题,设计一种基于图神经网络的不平衡欺诈检测模型。该模型细化了图结构数据中存在的邻域不平衡和中心不平衡两个不平衡的概念。在邻域不平衡中,通过多层感知机和高斯核函数衡量中心节点与其邻域节点的非欧氏空间距离(相似度),基于马尔可夫决策动态更新采样阈值对邻域节点进行多层自适应欠采样,并在每一层中仅聚合其原始特征和前一层的隐藏嵌入得到中心节点的目标嵌入;在中心不平衡中,引入加权交叉熵损失函数为每个中心节点的损失设置动态权重以达到中心平衡。在Yelp和Amazon两个数据集上的实验结果表明,该模型的曲线下面积(AUC)、召回率(Recall)两个指标相较于最优基准模型均有显著提升,在两个数据集上的AUC和Recall分别提升了5.52%、5.42%和1.57%、4.31%。

GKCI:改进的基于图神经网络的关键类识别方法

研究人员将软件系统中的关键类作为理解和维护一个系统的起点,而关键类上的缺陷给系统带来了极大的安全隐患.因此,识别关键类可提高软件的可靠性和稳定性.常用的识别方法是将软件系统抽象为一个类依赖网络,再根据定义好的度量指标和计算规则计算每个节点的重要性得分,如此基于非训练框架得到的关键类,并没有充分利用软件网络的结构信息.针对这一问题,基于图神经网络技术提出了一种有监督的关键类识别方法.首先,将软件系统抽象为类粒度的软件网络,并利用网络嵌入学习方法Node2Vec得到类节点的表征向量,再通过一个全连接层将节点的表征向量转换为具体分值;然后,利用改进的图神经网络模型,综合考虑类节点之间的依赖方向和权重,进行节点分值的聚合操作;最后,模型输出每个类节点的最终得分并进行降序排列,从而实现关键类的识别.在8个Java开源软件系统上,通过与基准方法的实验对比,验证了该方法的有效性.实验结果表明:在前10个候选关键类中,所提方法比最先进的方法提升了6.4%的召回率和3.5%的精确率.

Criteria for Three-Stage Towers of <i>p</i>-Class Fields

Let p be a prime and K be a number field with non-trivial p-class group ClpK. A crucial step in identifying the Galois group G∞p of the maximal unramified pro-p extension of K is to determine its two-stage approximation M=G2pk, that is the second derived quotient M&simeq;G/Gn. The family τ1K of abelian type invariants of the p-class groups ClpL of all unramified cyclic extensions L/K of degree p is called the index- abelianization data (IPAD) of K. It is able to specify a finite batch of contestants for the second p-class group M of K. In this paper we introduce two different kinds of generalized IPADs for obtaining more sophisticated results. The multi-layered IPAD (τ1Kτ(2)K) includes data on unramified abelian extensions L/K of degree p2 and enables sharper bounds for the order of M in the case Clpk&simeq;(p,p,p), where current im-plementations of the p-group generation algorithm fail to produce explicit contestants for M , due to memory limitations. The iterated IPAD of second order τ(2)K contains information on non-abelian unramified extensions L/K of degree p2, or even p3, and admits the identification of the p-class tower group G for various infinite series of quadratic fields K=Q(√d) with ClpK&simeq;(p,p) possessing a p-class field tower of exact length lpK=3 as a striking novelty.

基于欠采样和源代码图表征的以太坊庞氏骗局检测

针对目前以太坊庞氏骗局检测中存在的数据类别不平衡,特征来源单一和不能完整表达智能合约的语义语法关系和程序依赖关系等相关问题,提出了一种基于欠采样和源代码图表征的以太坊庞氏骗局检测方法。该方法利用Levenshtein算法计算训练集中多数类智能合约之间的距离,进而通过K-Means算法对多数类智能合约进行聚类,有选择地丢弃多数类合约,保证了训练集骗局合约和正常合约的类别相对平衡,提高了分类器对异常合约的敏感程度;针对庞氏骗局合约的代码特征改进了构图算法,通过剔除冗余特征,添加新的核心节点来解构智能合约的语义语法信息和程序依赖关系,使得神经网络更容易捕获和学习骗局合约的行为特征和资金流向模式。在XBlock数据集上进行了实验,结果表明本文提出的方法在保证精度的同时,召回率达到98%,优于现有方法。

基于噪声过滤与特征增强的图神经网络欺诈检测方法

现有的基于图神经网络(Graph Neural Network,GNN)的欺诈检测方法还存在三个方面的不足:(1)没有充分考虑到样本标签分布不平衡的问题;(2)没有考虑欺诈者为了躲避检测器的检测,故意制造噪声干扰检测的问题;(3)没有考虑欺诈类型数据联系稀疏问题.为此,本文提出一种基于噪声过滤与特征增强的图神经网络欺诈检测方法NFE-GNN(Noise Filtering and feature Enhancement based Graph Neural Network method for fraud detection)来改善欺诈检测性能.该方法首先基于数据集的欺诈率对样本进行平衡采样;在此基础上,采用一个参数化距离函数计算节点间的相似度,并通过强化学习得到最优的噪声过滤阈值;最后,通过创建欺诈样本间的联系,丰富拓扑信息,以达到增强欺诈类特征嵌入表示的目的.在两个公开数据集上的实验结果表明,本文所提NFE-GNN方法的性能优于目前主流的图神经网络欺诈检测方法.