TWO IMPROVED GRAPH-THEORETICAL CLUSTERING ALGORITHMS

Graph-theoretical approaches have been widely used for data clustering and image segmentation recently. The goal of data clustering is to discover the underlying distribution and structural information of the given data, while image segmentation is to partition an image into several non-overlapping regions. Therefore, two popular graph-theoretical clustering methods are analyzed, including the directed tree based data clustering and the minimum spanning tree based image segmentation. There are two contributions： （1） To improve the directed tree based data clustering for image segmentation, （2） To improve the minimum spanning tree based image segmentation for data clustering. The extensive experiments using artificial and real-world data indicate that the improved directed tree based image segmentation can partition images well by preserving enough details, and the improved minimum spanning tree based data clustering can well cluster data in manifold structure.

Spatial distribution patterns of anorectal atresia/stenosis in China:Use of two-dimensional graph-theoretical clustering

AIM:To investigate the spatial distribution patterns of anorectal atresia/stenosis in China.METHODS:Data were collected from the Chinese Birth Defects Monitoring Network(CBDMN),a hospital-based congenital malformations registry system.All fetuses more than 28 wk of gestation and neonates up to 7 d of age in hospitals within the monitoring sites of the CBDMN were monitored from 2001 to 2005.Two-dimensional graph-theoretical clustering was used to divide monitoring sites of the CBDMN into different clusters according to the average incidences of anorectal atresia/stenosis in the different monitoring sites.RESULTS:The overall average incidence of anorectal atresia/stenosis in China was 3.17 per 10000 from 2001 to 2005.The areas with the highest average incidences of anorectal atresia/stenosis were almost always focused in Eastern China.The monitoring sites were grouped into 6 clusters of areas.Cluster 1 comprised the monitoring sites in Heilongjiang Province,Jilin Province,and Liaoning Province;Cluster 2 was composed of those in Fujian Province,Guangdong Province,Hainan Province,Guangxi Zhuang Autonomous Region,south Hunan Province,and south Jiangxi Province;Cluster 3 consisted of those in Beijing Municipal City,Tianjin Municipal City,Hebei Province,Shandong Province,north Jiangsu Province,and north Anhui Province;Cluster 4 was made up of those in Zhejiang Province,Shanghai Municipal City,south Anhui Province,south Jiangsu Province,north Hunan Province,north Jiangxi Province,Hubei Province,Henan Province,Shanxi Province and Inner Mongolia Autonomous Region;Cluster 5 consisted of those in Ningxia Hui Autonomous Region,Gansu Province and Qinghai Province;and Cluster 6 included those in Shaanxi Province,Sichuan Province,Chongqing Municipal City,Yunnan Province,Guizhou Province,Xinjiang Uygur Autonomous Province and Tibet Autonomous Region.CONCLUSION:The fi ndings in this research allow the display of the spatial distribution patterns of anorectal atresia/stenosis in China.These will have important guiding significance for further analysis of relevant environmental factors regarding anorectal atresia/ stenosis and for achieving regional monitoring for anorectal atresia/stenosis.

Partial Topology Identification of Stochastic Multi-Weighted Complex Networks Based on Graph-Theoretic Method and Adaptive Synchronization

This article aims to identify the partial topological structures of delayed complex network.Based on the drive-response concept,a more universal model,which includes nonlinear couplings,stochastic perturbations and multi-weights,is considered into drive-response networks.Different from previous methods,we obtain identification criteria by combining graph-theoretic method and adaptive synchronization.After that,the partial topological structures of stochastic multi-weighted complex networks with or without time delays can be identified successfully.Moreover,response network can reach synchronization with drive network.Ultimately,the effectiveness of the proposed theoretical results is validated through numerical simulations.

A Graph-theoretic Analysis of Stressors Confronting Giant Panda Habitat across Minshan Mountain Region,China

岷山地区位于四川盆地西北部,是我国生物多样性保护的优先地区,还是保护大熊猫的关键区域。本文以社会-经济-自然复合生态系统为基础,运用图论分析法研究了岷山地区影响大熊猫生境的人类活动方式,以及这些影响因子相互的关系。研究表明:影响大熊猫生境的人类活动的66对组合中,47.0%的因子间存在直接的联系,其中89.2%的影响具有增大效应。这说明人类活动对大熊猫生境的影响具有协同增大效应,并占主导地位。旅游景点开发、公路建设、采矿、高压电线、农业开发、放牧、薪柴采集这些影响因子存在强连通性,它们会将其他人类活动对大熊猫生境的影响放大,加剧对大熊猫生境的不利影响,表明它们是影响岷山地区大熊猫生境的主导人类活动。要想有效地保护岷山地区的大熊猫生境,就必须对这些主导人类活动进行有效的控制。本研究还表明图论分析法有助于明确影响熊猫生境的主导和关键因子,它能为制定有效的大熊猫保护策略提供科学依据。

Observability of Boolean Control Networks with Time-Variant Delays in States

This paper gives an equivalent condition for the observability of Boolean control networks（BCNs） with time-variant delays in states under a mild assumption by using the graph-theoretic method under the framework of the semi-tensor product of matrices. First, the BCN under consideration is split into a finite number of subsystems with no time delays. Second, the observability of the BCN is verified by testing the observability of the so-called observability constructed path（a special subsystem without time delays） based on graph theory. These results extend the recent related results on the observability of BCNs. Examples are shown to illustrate the effectiveness of the results.

Global Dynamics of a Multi-group SEIR Epidemic Model with Infection Age

Consider the heterogeneity(e.g.,heterogeneous social behaviour,heterogeneity due to different geography,contrasting contact patterns and different numbers of sexual partners etc.)of host population,in this paper,the authors propose an infection age multigroup SEIR epidemic model.The model system also incorporates the feedback variables,where the infectivity of infected individuals may depend on the infection age.In the direction of mathematical analysis of model,the basic reproduction number R_0 has been computed.The global stability of disease-free equilibrium and endemic equilibrium have been established in the term of R_(0).More precisely,for R_(0)≤1,the disease-free equilibrium is globally asymptotically stable and for R_(0)>1,they establish global stability of endemic equilibrium using some graph theoretic techniques to Lyapunov function method.By considering a numerical example,they investigate the effects of infection age and feedback on the prevalence of the disease.Their result shows that feedback parameters have different and even opposite effects on different groups.However,by choosing an appropriate value of feedback parameters,the disease could be eradicated or maintained at endemic level.Besides,the infection age of infected individuals may also change the behaviour of the disease,global stable to damped oscillations or damped oscillations to global stable.

Threshold dynamics of a multi-group SEAR alcoholism model with public health education

In this paper, we investigate the threshold dynamics of a multi-group SEAR alcoholism epidemic model with public health education. The multi-group model allows us to describe interactions both within-group and inter-group separately. We prove that the basic reproduction number R0 plays the role of a threshold for the long-time behavior of the model. The alcohol-free equilibrium P0 of the model is globally asymptotically stable if R0≤1,while the alcohol-present equilibrium P* exists uniquely and is globally asymptotically stable if R0>1.For the proofs of main results, we use the classical method of Lyapunov functions and apply subtle grouping technique in estimating the derivatives of Lyapunov functions guided by graph theory. Our results expand the previous results which have been obtained in single-group models. Sensitivity analysis and numerical simulations are also performed to illustrate our results.