复杂网络的鲁棒性和可控性研究

发布时间：2018-06-12 22:20

本文选题：复杂网络 + 相互依赖网络　；参考：《华中科技大学》2016年博士论文

【摘要】：复杂网络横跨自然科学和工程技术等多门学科,已经被广泛用于对复杂系统建模和分析复杂系统内特征和行为的有力工具。随着科学技术的迅猛发展,复杂网络系统之间相互依赖关系也变得越来越紧密。系统之间的相互关系能让这些系统呈现出更复杂的性质并具备实现单个系统无法实现的功能,同时也会使得系统鲁棒性降低甚至导致大规模系统失效或灾难的发生。网络系统之间的相互依赖关系是如何使得系统鲁棒性降低?引发大规模故障的机制是什么?这些复杂网络系统是否可控?这些都是复杂网络中关键的问题。对这些问题的研究可以帮助人们理解复杂系统,寻找出提高现有系统鲁棒性的策略,建立新的具有高鲁棒性的基础设施系统,并为如何控制复杂系统提供指导。基于上述问题,本文的主要内容如下：构建了一个相互依赖有向网络模型,提出了一个用于分析相互依赖有向网络的理论框架,发现相互依赖有向网络的鲁棒性特征比相互依赖无向网络中的更丰富,比如相互依赖的有向随机(Erdos-Renyi, ER)网络比相互依赖的无向ER网络鲁棒性低,并且表现出无向ER网络系统中不具有的混合相变。相互依赖的有向无标度(Scale-free, SF)网络中,在对比存在出入度相关性和不存在出入度相关性的情况时,需要同时用到定义网络鲁棒性的标准：渗流阈值和整个节点失效过程中极大连通子图的规模的积分。另外,发现了每一层网络内节点的出度和入度的相关性可以提高度异质网络的鲁棒性,而降低高耦合的度同质网络的鲁棒性。大部分的实际网络是度异质网络。通过将理论框架运用与国际贸易网络系统,发现出入度联系可以提高真实系统的鲁棒性,验证了理论结果。提出了随机寻找最小驱动节点集合的方法,并在人体肝脏代谢网络和人体信号网络中对驱动节点进行分类,系统地分析了不同驱动节点在生物系统中的作用。发现人体肝脏代谢网络中驱动代谢物往往具有比较强的影响其他代谢物状态的能力,而不容易被其他代谢物的状态所影响。本文找到了36个关键驱动代谢物中,其中27个代谢物是核心代谢物；高频驱动代谢物倾向于是连接不同代谢通路的代谢物,对整个代谢系统有着重要的调控作用。说明了关键驱动代谢物和高频驱动代谢物可能是潜在的药物靶标。发现在人体信号网络的信号流中,与下游的驱动节点密度对比,上游的驱动节点更密集,并且低入度的节点在调控人体信号网络状态中有着重要作用。另外,为了控制整个网络,发现控制癌症相关基因的调控因子比直接调控癌症相关基因成本更低。这为人体信号系统的实际控制提供了一个新的思路。提出了一种优化选择容易被控制的重要部分网络的方法,通过计算ER网络,SF网络和23个真实网络中被选择的部分网络的最小驱动节点密度,发现这里的最小驱动节点密度比随机选择方法得到的部分网络的最小驱动节点密度要低,说明了优化选择方法比随机选择方法要好。另外通过分析实际人体信号网络和人体有向蛋白质相互作用网络中优化选择的部分网络的生物意义,发现优化选择的部分网络倾向于是癌症相关基因,说明了优化方法选择的部分网络是重要的。提出了一个分析任意度分布有向网络中四种极大连通子图可控性的理论框架。发现了在ER网络和SF网络中,随机删除1一p比例的节点,随着剩余节点比例p的增大,控制极大连通子图的最小驱动节点密度先增大后减小,在关键点p=Pm处呈现出一个峰值。对于ER网络,最小驱动节点密度的峰值与网络的平均度k无关,而是由Pm(κ决定的。另外,控制度异质网络中极大连通子图的最小驱动节点密度比度同质网络中的要高,说明了度异质网络中极大连通子图比同质网络中的极大连通子图更难被控制。
[Abstract]:Complex networks, across natural science and engineering technology, have been widely used to model and analyze complex systems with powerful tools for the characteristics and behavior of complex systems. With the rapid development of science and technology, the interdependence of complex network systems has become more and more closely. The interrelationships among systems can allow these The system has more complex properties and has the functions that can not be realized by a single system. At the same time, it can reduce the robustness of the system or even cause the failure or disaster of large-scale systems. How does the interdependence relationship between the network systems make the system robust? What is the mechanism that causes large scale failures? Whether the miscellaneous network system is controllable? These are the key problems in complex networks. The research on these problems can help people understand the complex system, find out the strategies to improve the robustness of the existing system, establish a new and highly robust infrastructure system, and provide guidance for how to control the complex system. Based on the above problem, this paper The main contents are as follows: a mutual dependent directed network model is constructed, and a theoretical framework for analyzing interdependent networks is proposed. It is found that the robustness features of interdependent networks are more abundant than interdependent networks, such as the interdependent Erdos-Renyi (ER) network is more interdependent than interdependent networks. The undirected ER network has low robustness and shows a mixed phase transition in the undirected ER network system. In the interdependent Scale-free (SF) network, it is necessary to use the criteria for defining the robustness of the network: the percolation threshold and the whole In addition, it is found that the correlation of the degree and admission of nodes in each layer of network can improve the robustness of the degree heterogeneous network and reduce the robustness of the homogeneity network with high coupling degree. Most of the actual network is a heterogeneous network. The theoretical framework is applied to international trade through the application of the theoretical framework to international trade. The network system can improve the robustness of the real system and verify the theoretical results. The method of random search for the minimum driving node set is proposed, and the driving nodes are classified in the human liver metabolic network and the human signal network, and the role of different driving nodes in the biological system is systematically analyzed. It is found that the metabolites that drive metabolites in the metabolic network of the human liver often have a strong ability to affect other metabolites and are not easily affected by the state of other metabolites. In this paper, 36 key driving metabolites are found, of which 27 metabolites are core metabolites; high frequency metabolites tend to connect to different metabolites. The metabolites of the road have an important regulatory effect on the entire metabolic system. It shows that the key driving metabolites and high frequency driven metabolites may be potential drug targets. It is found that in the signal flow of the human signal network, the upstream node is denser than the downstream driving node density, and the low admission nodes are in the control of the person. There is an important role in the state of the body signal network. In addition, in order to control the whole network, it is found that the control factor of controlling cancer related genes is lower than the direct control of cancer related genes. This provides a new idea for the actual control of the human signal system. By calculating the minimum driving node density of the selected partial networks in the ER network, SF network and 23 real networks, it is found that the density of the minimum driving node density is lower than the minimum driving node density of the partial network obtained by the random selection method. It shows that the optimization selection method is better than the random selection method. In addition, the analysis is also analyzed. The biological significance of the actual human signal network and the optimized selection of the human body to the protein interaction network shows that the optimized selection of the partial network tends to be the cancer related gene, which indicates that the partial network of optimization methods is important. A fractional arbitrary distribution of the four polar networks in the directed network is proposed. The theoretical framework of the controllability of the subgraph is found. In the ER network and the SF network, it is found that the nodes of the 1 one P ratio are randomly deleted. With the increase of the proportion of the remaining nodes, the minimum driving node density of the control pole Dalian subgraph increases first and then decreases, and presents a peak at the key point p=Pm. For the ER network, the peak value of the minimum driving node density is the peak value and the peak value of the minimum driving node density for the ER network. The average degree of the network is independent of K, but it is determined by Pm (kappa). In addition, the minimum driving node density ratio in the control degree heterograph is higher than that in the homogeneous network of the minimum driving node density in the control degree heterogeneous network. It shows that the pole map of the pole in the degree heterogeneity network is more difficult to be controlled than the polar Dalian subgraph in the homogeneous network of the homogeneous network.
【学位授予单位】：华中科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O157.5

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