广义合作网络及其相关研究

【作者】 常慧；

【导师】 何大韧；

【作者基本信息】 扬州大学 ， 理论物理， 2007， 硕士

【摘要】 描述复杂自适应系统中的作用者行为的动力学法则必须容纳类似生命系统特有的预测、选择、学习、进化等特征。作用者和它们的行为各不相同,作用者构成的系统绝不等同于它们的简单组合,不能用还原论的思路来处理,也不能用服务于确定论、还原论的传统数学来描述,必须探讨全新的描述工具。复杂网络研究的发展为我们提供了进行这种探讨的某种可能性。复杂网络可以描述广泛多样的实际系统。我们进行了相当数量的实际系统的实证研究,希望能够根据实证研究所得到的统计结果把实际系统分类,找出每一类系统的实证统计性质共性,进而试图建立模型,理解它们的共同动力学特征和机制。这样一步一步地达到对复杂系统的更普遍一点的理解。在当前复杂网络研究的广阔范围中,我们的兴趣集中在所谓的“广义合作网络”上。这里网络的节点(参与者)在参与许多合作项目。在研究中只考虑参与者在项目中的合作关系,不讨论它们之间的竞争、对抗或其他类型的关系,而且定义参与者在项目中的合作关系为它们之间的边。这样,一个项目就可以用一个它包含的参与者两两连边所构成的完全图来表示。这样的网络不一定是社会网络,也可以包含其他许多类网络,但是由于拓扑结构具有共同特征,它们的统计性质和动力学特性也具有共同特征。在我们实证地研究过的实际网络中,我们发现好莱坞演员合作网、中国旅游线路网、城市公交线路网、中药方剂网、以及淮扬菜肴网都可以用广义合作网络来描述。我们对这些实证数据分析之后,得到了一些共同的统计特征:首先,项目是这类网络中的主导因素,项目如何组成是网络演化的关键问题。参与者项目度分布(即参与者参与的项目数目的分布)很可能是这类网络最主要的统计性质,在很大程度上左右顶点的点强度分布和度分布。其次,参与者的同类性系数也随着这样的分布规律的变化而呈现单调依赖关系的变化。我们建议了一个简明的、体现上述思想的网络演化模型,来说明这两项共同统计特征的动力学机理,由此模型的解析分析和数值模拟产生的统计结果与实证结果很好地符合。最后,根据这类被称为广义合作网络的共同拓扑特征,我们建议群落和层次的一种定量定义和相应的划分群落和层次的方法。由此所建议的一个新的统计参量——网络交连度可能富有实际意义。由于实际的重要性,城市公交系统一直是研究的热点之一。我们从复杂网络的角度,研究旨在说明城市公交系统演化和性质的网络操纵者博弈模型。从这个角度出发,我们陆续提出三个模型,模型越来越简化,意思越来越集中,本论文中重点介绍最后一个最简网络操纵者博弈模型。我们建议最大简化地把公交公司和乘客看作网络的两个主要操纵者,他们的利益在某种意义上说是互相矛盾的,于是,城市公交网络系统的演化被最简化地看作网络的两个操纵者之间博弈的过程,博弈的均衡解决定网络最后的演化走势。对这样的模型进行了极端情况和均衡情况的解析,以及一般情况下的数值模拟研究,所得到的网络统计性质与我们对北京、上海、南京、杭州的实证统计结果相当好的符合,说明这个模型很可能抓住了最根本的特征。这种思想很可能推广到许多其它系统。广义合作网络忽略了竞争因素。当在网络中加入竞争的因素时,网络会有什么样的特性呢?鉴于此,我们介绍了三个考虑到竞争因素的系统,这个工作是浅陋的。但期望这几个系统能够作为一个引子,能够激起研究者们对合作竞争网络作更深入的研究。更多还原

【Abstract】 The dynamics principles, which describe the actors’behaviors in complex self-adaptive systems, should include some characters similar to what are shown by the living systems, such as forecasting, choice, learning, and evolution. Each actor and his behavior are different. Also, a system consisting of actors is not a simple combination of them. It cannot be treated by reduction theory, and cannot be described by the conventional mathematics, which serve for determinism and reductionism. We must develop some new methods and tools to describe self-adaptive systems. The latest development in the complex network gives us a possible way for searching the possibility.The complex network can describe variety different practical systems. We have carried out empirical studies on quite some practical systems; wish to classify the systems based on the results and find out the common statistical properties of every kind of them. The next step could be setting up suitable models so that we could understand their common dynamical characteristics and mechanism. In this way we can reach, step by step, to a more universal understanding on complex systems. Among the very wide scope of complex network studying, our interests are concentrated on the so-called“generalized collaboration networks”. In such networks the nodes (actors) are participating a lot of collaborative acts. In the study we shall only consider actor’s cooperation, and ignore the competition, confrontation or other type of relations between them. We propose define actor’s cooperation in the acts as edges. In this way, one act can be described by a complete graph composed by the actors where every pair of them are connected with edges. Such a network may not be a social network, it can belong to many other kinds of networks too, but because the topological structure has common characteristics, their statistics properties have common characteristics. Among the practical networks we empirically studied, we found that the Chinese tourist line network, the urban public traffic network, the traditional Chinese medicine prescription network, and Huai-Yang recipe network can be described by the generalized collaboration networks. After the analysis on the empirical data, we have obtained some common statistical properties: First of all, the act is a leading factor in this kind of networks. The act degree distribution (the distribution of the number of the acts, in which the actors are participating) should be, very possibly, the most important property in such kinds of networks. It, in a great extent, determines the node strength degree and degree distribution. Secondly, the assortativity of the actors shows a monotonic change with the change of such distribution law. We propose a simplified model based on these ideas so as to show the common dynamical mechanisms of the two common properties. The analytic and numerical investigation results of the model show very good agreement with the empirical results. Finally, according to the common topological characteristics of the so-called generalized collaboration networks, we propose a quantitative definition and corresponding division method for community and hierarchy. A new network statistical property, the degree of interweavement, has been proposed by this consideration that may have practical importance.Since urban public traffic systems are practically important, they have been extensively and intensively studied. We have studied urban public traffic networks from the viewpoint of complex networks and game theory. From that, we have suggested three manipulator game models of urban public traffic networks continuously. We try to construct a simplest model with the idea that hits the nail on the head. In this paper, we mainly present the last model of the three. We suggest a very simplified viewpoint in which the evolution of urban public traffic network can be considered as a game process between the two network manipulators, and the equilibrium solution of the game determines the last evolution tendency of the network. We have performed analytical discussion on some extreme and the equilibrium situations and numerical discussion on the general evolution, the obtained statistical properties are in a good agreement with the empirical ones obtained by the investigations on the urban public traffic systems in Beijing, Shanghai, Nanjing and Hangzhou. This shows that the model grasps the most fundamental characteristic of the system. The idea, very possibly, can be extended and used in many other systems.Generalized collaboration networks ignore the factor of competition. If competition joins in network, what characteristic may appear? As for it, we introduce three systems which take competition into account. The research is rough. However, we expect as a beginning, the work could inspire people to research the collaboration and competition network deeply.更多还原