Investigation on Singularity, Signature Matrix and Spectrum of Mixed Graphs

The spectral theory of graph is an important branch of graph theory,and the main part of this theory is the connection between the spectral properties and the structural properties,characterization of the structural properties of graphs.We discuss the problems about singularity,signature matrix and spectrum of mixed graphs.Without loss of generality,parallel edges and loops are permitted in mixed graphs.Let G1 and G2 be connected mixed graphs which are obtained from an underlying graph G.When G1 and G2 have the same singularity,the number of induced cycles in Gi(i=1,2)is l(l=1,l>1),the length of the smallest induced cycles is 1,2,at least 3.According to conclusions and mathematics induction,we find that the singularity of corresponding induced cycles in G1 and G2 are the same if and only if there exists a signature matrix D such that L(G2)=DTL(G1)D.D may be the product of some signature matrices.If L(G2)=D^TL(G1)D,G1 and G2 have the same spectrum.

Semi-Supervised Graph Learning for Brain Disease Identification

Using resting-state functional magnetic resonance imaging (fMRI) technology to assist in identifying brain diseases has great potential. In the identification of brain diseases, graph-based models have been widely used, where graph represents the similarity between patients or brain regions of interest. In these models, constructing high-quality graphs is of paramount importance. Researchers have proposed various methods for constructing graphs from different perspectives, among which the simplest and most popular one is Pearson Correlation (PC). Although existing methods have achieved significant results, these graphs are usually fixed once they are constructed, and are generally operated separately from downstream task. Such a separation may result in neither the constructed graph nor the extracted features being ideal. To solve this problem, we use the graph-optimized locality preserving projection algorithm to extract features and the population graph simultaneously, aiming in higher identification accuracy through a task-dependent automatic optimization of the graph. At the same time, we incorporate supervised information to enable more flexible modelling. Specifically, the proposed method first uses PC to construct graph as the initial feature for each subject. Then, the projection matrix and graph are iteratively optimized through graph-optimization locality preserving projections based on semi-supervised learning, which fully employs the knowledge in various transformation spaces. Finally, the obtained projection matrix is applied to construct the subject-level graph and perform classification using support vector machines. To verify the effectiveness of the proposed method, we conduct experiments to identify subjects with mild cognitive impairment (MCI) and Autism spectrum disorder (ASD) from normal controls (NCs), and the results showed that the classification performance of our method is better than that of the baseline method.

Distance Integral Complete Multipartite Graphs with s=5, 6

Let D(G) =(d_(ij))_(n×n) denote the distance matrix of a connected graph G with order n, where d_(ij) is equal to the distance between vertices viand vjin G. A graph is called distance integral if all eigenvalues of its distance matrix are integers. In 2014, Yang and Wang gave a sufficient and necessary condition for complete r-partite graphs K_(p1,p2,···,pr)=K_(a1·p1,a2·p2,···,as···ps) to be distance integral and obtained such distance integral graphs with s = 1, 2, 3, 4. However distance integral complete multipartite graphs K_(a1·p1,a2·p2,···,as·ps) with s > 4 have not been found. In this paper, we find and construct some infinite classes of these distance integral graphs K_(a1·p1,a2·p2,···,as·ps) with s = 5, 6. The problem of the existence of such distance integral graphs K_(a1·p1,a2·p2,···,as·ps) with arbitrarily large number s remains open.

链图的距离特征值

如果一个图G不包含2K_(2),C_(3)及C_(5)作为导出子图,称其为链图。在所有点数和边数给定的连通二部图中,链图具有最大的谱半径,这使得链图在图谱理论中占有一席之地。本文研究了连通链图距离特征值的分布情况。对于点数为n的连通链图G=G(t_(1),…,t_(h);s_(1),…,s_(h)),我们证明了-2是G的重数为n-2h的距离特征值,且G有h-1个距离特征值小于-2和h+1个距离特征值大于-2。

基于图向量的一般图的广义谱刻画

给定一个图G,如果对于任意的图H,H和G同谱且它们的补图也同谱蕴含它们同构,则称图G是由广义谱确定的。在文献[12]中,作者给出了一个简单的算术条件判断一个图是由广义谱确定的,即对于给定n个顶点的图G,令其邻接矩阵和道矩阵分别为A=A(G)和W(G)=[e,Ae,…,A^(n-1)e](e为全-1向量),如果2^(-[n/2])detW(G)是无平方因子的奇数,则图G是由广义谱确定的。Qiu等^([7])通过引入图向量,给出一个与图G有关的新矩阵,将广义谱确定概念推广到一般的Φ-DS,并证明了一类正则图是Φ-DS的。本文在文献[7]的基础上,给出了判断一类一般图是Φ-DS的一个简单准则,推广了文献[12]中的结论,并通过数值实验验证了该准则的有效性。

Infinitely many pairs of cospectral integral regular graphs

A graph G is called integral if all the eigenvalues of the adjacency matrix A（G） of G are integers. In this paper, the graphs G4（a, b） and Gs（a, b） with 2a ＋ 6b vertices are defined. We give their characteristic polynomials from matrix theory and prove that the （n ＋ 2）-regular graphs G4（n, n＋ 2） and G5（n, n ＋ 2） are a pair of non-isomorphic connected cospectral integral regular graphs for any positive integer n.

Bounds of the Estrada index of graphs

Let G be a graph of order n and let λ1, λ2,...,λn be its eigenvalues. The Estrada index[2] of G is defined as EE = EE（G） =∑i=1^n e^λi.In this paper, new bounds for EE are established, as well as some relations between EE and graph energy E.

基于CiteSpace国内疾病谱研究的可视化分析

目的运用文献计量和可视化软件对我国疾病谱研究文献进行分析,探讨研究现状、前沿热点及研究趋势,为日后疾病谱的深入研究提供参考。方法本研究应用CiteSpace对中国知网检索筛选的2211篇与疾病谱研究相关文献的作者、机构和关键词进行分析,绘制作者、机构和关键词可视化图谱,对关键词进行聚类、共现和时间叠加分析。结果我国疾病谱研究始于1983年,整体呈稳步发展态势。本领域内核心研究机构有天津中医药大学和空军总医院,本领域内代表学者有徐先荣、张步振和熊俊。关键词聚类归纳分析发现研究热点为基于疾病谱数据统计研究各科疾病特征及变化趋势、针对特殊人群进行监测并探寻其易感疾病的发生原因及防治措施、疾病谱分析数据助力医疗服务质量提高及医疗模式转变、围绕疾病谱分析提高医院职能。结论疾病谱的研究前景广,现下主要集中在四个研究领域。研究分析发现开展跨地区研究交流,扩大研究人群、病种及地域范围,探究各类辅助诊断技术运用价值是本领域研究日后需解决的问题。

面向磨煤机组故障诊断的聚类粗化图模型

磨煤机组是火力发电厂的重要设备之一,为了保证生产过程的安全性和稳定性,提出一种基于聚类粗化图卷积神经网络(CC-GCN)的故障诊断方法。首先通过KNN算法在原始故障样本之间建立图结构并转换成图样本,然后利用谱聚类将图样本压缩成多级粗化图,并分别对每一级别的粗化图进行卷积操作以及特征的融合,最后基于图分类方法对故障样本进行故障诊断。在磨煤机组的两组不同运行状态的数据集上进行仿真实验,结果表明该方法不仅能有效提高故障诊断的精度,还能显著降低模型的运行时间。

一些关联图的拉普拉斯谱和基尔霍夫指标

基于图G,定义了三种关联图G_(1),G_(2)和G_(3),其拉普拉斯矩阵可以经过恰当排序表出。利用图论和行列式的性质以及代数组合的方法,研究这些关联图的拉普拉斯谱和基尔霍夫指标,最后得出了相应的结果。

基于SPO语义三元组的自闭症谱系障碍药物知识发现

目的:运用语义挖掘技术抽取自闭症相关文献中的三元组并构建自闭症药物实体知识图谱,深层次开展自闭症治疗的潜力药物知识发现,同时也为其他疾病发现有价值的潜在治疗药物提供新思路。方法:采用基于统一医学语言系统(ULMS)的工具SemRep、Metamap对自闭症文献记录进行处理并获得自闭症药物实体三元组,使用Neo4j数据库进行知识存储,构建自闭症药物实体知识图谱。基于该知识图谱,采用3种语义路径开展自闭症药物知识发现,并使用临床实验数据库(https://clinicaltrials.gov)对结果进行有效性验证与分析。结果:获得的实体三元组包括1262个头实体、687个尾实体和18种实体关系;3种语义路径共发现32种药物,筛选出27种自闭症潜力药物,并且19种药物可以在临床实验数据库中验证。结论:基于语义三元组知识图谱开展自闭症药物知识发现可为药物重定位提供一定的理论和方法基础,为传统药物发现提供新的思路,以期为临床实验及其科学研究提供决策支持。

Signless Laplacian Characteristic Polynomials of Complete Multipartite Graphs

For a simple graph G,let matrix Q(G)=D(G) + A(G) be it's signless Laplacian matrix and Q G (λ)=det(λI Q) it's signless Laplacian characteristic polynomial,where D(G) denotes the diagonal matrix of vertex degrees of G,A(G) denotes its adjacency matrix of G.If all eigenvalues of Q G (λ) are integral,then the graph G is called Q-integral.In this paper,we obtain that the signless Laplacian characteristic polynomials of the complete multi-partite graphs G=K(n_1,n_2,···,n_t).We prove that the complete t-partite graphs K(n,n,···,n)t are Q-integral and give a necessary and sufficient condition for the complete multipartite graphs K(m,···,m)s(n,···,n)t to be Q-integral.We also obtain that the signless Laplacian characteristic polynomials of the complete multipartite graphs K(m,···,m,)s1(n,···,n,)s2(l,···,l)s3.

ON GRAPHS WITH THREE DISTINCT LAPLACIAN EIGENVALUES

In this paper, an equivalent condition of a graph G with t （2≤ t ≤n） distinct Laplacian eigenvalues is established. By applying this condition to t = 3, if G is regular （necessarily be strongly regular）, an equivalent condition of G being Laplacian integral is given. Also for the case of t = 3, if G is non-regular, it is found that G has diameter 2 and girth at most 5 if G is not a tree. Graph G is characterized in the case of its being triangle-free, bipartite and pentagon-free. In both cases, G is Laplacian integral.

基于图着色和三维匹配的车联网资源分配算法

车联网通信通过多个车辆对车辆(vehicle to vehicle,V2V)链路复用同一车辆对基础设施(vehicle to infrastructure,V2I)链路的资源来缓解频谱短缺问题,但频谱复用会导致V2I通信服务质量下降,因此降低系统干扰、提高系统容量成为研究热点。提出一种基于图着色和三维匹配的车联网资源分配算法,首先用图着色法对V2V链路分簇,然后求解V2I链路和V2V链路的发射功率,最后通过三维匹配算法对V2I链路、V2V簇和资源块进行信道资源的优化分配,从而降低使用同一资源的链路之间的干扰。理论分析及仿真结果表明,所提方法提高了V2I链路总和速率,并在相对较少的迭代次数下收敛到次优解。

Double quasi-star tree is determined by its Laplacian spectrum

Let Hn（p,q） be a tree obtained from two stars K1,p and K1,q by identifying the center of K1,p with one end of a path Pn and the center of K1,q with the other end of Pn.We call Hn（p,p-1） a double quasi-star tree.In this paper,we show that a double quasi-star tree is determined by its Laplacian spectrum.

Opportunistic spectrum sharing in software defined wireless network

Over the past few decades, the world has witnessed a rapid growth in mobile and wireless networks（MWNs） which significantly change human life. However, proliferating mobile demands lead to several intractable challenges that MWN has to face. Software-defined network is expected as a promising way for future network and has captured growing attention. Network virtualization is an essential feature in software-defined wireless network（SDWN）, and it brings two new entities, physical networks and virtual networks. Accordingly, efficiently assigning spectrum resource to virtual networks is one of the fundamental problems in SDWN. Directly orienting towards the spectrum resource allocation problem, firstly, the fluctuation features of virtual network requirements in SDWN are researched, and the opportunistic spectrum sharing method is introduced to SDWN. Then, the problem is proved as NP-hardness. After that, a dynamic programming and graph theory based spectrum sharing algorithm is proposed.Simulations demonstrate that the opportunistic spectrum sharing method conspicuously improves the system performance up to around 20%–30% in SDWN, and the proposed algorithm achieves more efficient performance.

A parallel algorithm for statistical-fairness-based spectrum allocation of cognitive radios

A parallel algorithm for statistical-fairness-based spectrum allocation of cognitive radios is proposedin this paper. The key idea of the algorithm is to pursue the maximum total spectrum utilization of thesystem by adopting a parallel technique in every spectrum allocation, and to ensure the statistical fairnessrule by deploying a particular scheme during a series of allocations. The simulation results show that theproposed algorithm not only achieves a fairer and more efficient allocation of spectrum resources, but alsohas much shorter allocation duration than the color sensitive graph coloring (CSGC) algorithm.

路矩阵相关谱半径和路谱展的界及其应用

由于图谱能够很好地反映图的结构性质且便于计算,本文通过图的矩阵,建立图谱与图的拓扑性质之间的联系,更好地反应图的结构和研究图的相关性质;利用矩阵论和图论的理论和方法,证明路谱半径的下界和路无符号拉普拉斯谱半径的上下界;定义路谱展并得到其上下界;最后作为应用,研究完全r-部图的路谱、路拉普拉斯谱和路无符号拉普拉斯谱并得到了图K_(p,p,…,p)的相关能量。

Grading of Brain Tumors by Mining MRS Spectrums Using LabVIEW <br/>—Metabolite Peak Height Scanning Method

In this paper, we attempt to resolve the problem of grading of brain tumors as grade 2, grade 3, grade 4, using information from magnetic resonance spectroscopy (MRS) image, to assist in clinical diagnosis. This paper proposes a novel approach to extract metabolite values represented in a graphical form in MR Spectroscopy image. Metabolites like N-acetyl aspartate (NAA), Choline (CHO) along with the metabolite ratios NAA/CHO and presence/absence of LACTATE peak play the most important role in deciding the tumor type. The proposed approach consists of several steps including preprocessing, metabolite peak height scanning and classification. Proposed system stores the metabolite values in dataset instead of storing MRS images;so reduces the image processing tasks and memory requirements. Further these metabolite values and ratios are fed to a BPN classifier. Experimental results demonstrate the effectiveness of the proposed approach in classifying the brain tumors.

基于知识图谱的通信网络链路数据篡改攻击保护方法

针对现有链路数据篡改攻击检测准确率低、防御性能不佳等问题,提出一种新的通信网络链路数据篡改攻击保护方法。首先,在知识图谱的基础上,提出针对通信链路数据的一种防篡改攻击检测方法,以验证检测的链路层是否受到了侵犯,再根据两种不同的数据传递规则来确定防御节点,并对篡改攻击数据进行言语转换,达到对通信网络中数据篡改攻击进行防护的目的。仿真实验结果表明,该算法的识别精度在93%以上,并且具有很好的防御能力,可使其具有良好的通信数据传输安全性能,值得推广。