本文選題：復(fù)雜網(wǎng)絡(luò) + 相互依賴網(wǎng)絡(luò)��； 參考：《華中科技大學(xué)》2016年博士論文

【摘要】：復(fù)雜網(wǎng)絡(luò)橫跨自然科學(xué)和工程技術(shù)等多門學(xué)科,已經(jīng)被廣泛用于對(duì)復(fù)雜系統(tǒng)建模和分析復(fù)雜系統(tǒng)內(nèi)特征和行為的有力工具。隨著科學(xué)技術(shù)的迅猛發(fā)展,復(fù)雜網(wǎng)絡(luò)系統(tǒng)之間相互依賴關(guān)系也變得越來(lái)越緊密。系統(tǒng)之間的相互關(guān)系能讓這些系統(tǒng)呈現(xiàn)出更復(fù)雜的性質(zhì)并具備實(shí)現(xiàn)單個(gè)系統(tǒng)無(wú)法實(shí)現(xiàn)的功能,同時(shí)也會(huì)使得系統(tǒng)魯棒性降低甚至導(dǎo)致大規(guī)模系統(tǒng)失效或?yàn)?zāi)難的發(fā)生。網(wǎng)絡(luò)系統(tǒng)之間的相互依賴關(guān)系是如何使得系統(tǒng)魯棒性降低?引發(fā)大規(guī)模故障的機(jī)制是什么?這些復(fù)雜網(wǎng)絡(luò)系統(tǒng)是否可控?這些都是復(fù)雜網(wǎng)絡(luò)中關(guān)鍵的問題。對(duì)這些問題的研究可以幫助人們理解復(fù)雜系統(tǒng),尋找出提高現(xiàn)有系統(tǒng)魯棒性的策略,建立新的具有高魯棒性的基礎(chǔ)設(shè)施系統(tǒng),并為如何控制復(fù)雜系統(tǒng)提供指導(dǎo)。基于上述問題,本文的主要內(nèi)容如下：構(gòu)建了一個(gè)相互依賴有向網(wǎng)絡(luò)模型,提出了一個(gè)用于分析相互依賴有向網(wǎng)絡(luò)的理論框架,發(fā)現(xiàn)相互依賴有向網(wǎng)絡(luò)的魯棒性特征比相互依賴無(wú)向網(wǎng)絡(luò)中的更豐富,比如相互依賴的有向隨機(jī)(Erdos-Renyi, ER)網(wǎng)絡(luò)比相互依賴的無(wú)向ER網(wǎng)絡(luò)魯棒性低,并且表現(xiàn)出無(wú)向ER網(wǎng)絡(luò)系統(tǒng)中不具有的混合相變。相互依賴的有向無(wú)標(biāo)度(Scale-free, SF)網(wǎng)絡(luò)中,在對(duì)比存在出入度相關(guān)性和不存在出入度相關(guān)性的情況時(shí),需要同時(shí)用到定義網(wǎng)絡(luò)魯棒性的標(biāo)準(zhǔn)：滲流閾值和整個(gè)節(jié)點(diǎn)失效過程中極大連通子圖的規(guī)模的積分。另外,發(fā)現(xiàn)了每一層網(wǎng)絡(luò)內(nèi)節(jié)點(diǎn)的出度和入度的相關(guān)性可以提高度異質(zhì)網(wǎng)絡(luò)的魯棒性,而降低高耦合的度同質(zhì)網(wǎng)絡(luò)的魯棒性。大部分的實(shí)際網(wǎng)絡(luò)是度異質(zhì)網(wǎng)絡(luò)。通過將理論框架運(yùn)用與國(guó)際貿(mào)易網(wǎng)絡(luò)系統(tǒng),發(fā)現(xiàn)出入度聯(lián)系可以提高真實(shí)系統(tǒng)的魯棒性,驗(yàn)證了理論結(jié)果。提出了隨機(jī)尋找最小驅(qū)動(dòng)節(jié)點(diǎn)集合的方法,并在人體肝臟代謝網(wǎng)絡(luò)和人體信號(hào)網(wǎng)絡(luò)中對(duì)驅(qū)動(dòng)節(jié)點(diǎn)進(jìn)行分類,系統(tǒng)地分析了不同驅(qū)動(dòng)節(jié)點(diǎn)在生物系統(tǒng)中的作用。發(fā)現(xiàn)人體肝臟代謝網(wǎng)絡(luò)中驅(qū)動(dòng)代謝物往往具有比較強(qiáng)的影響其他代謝物狀態(tài)的能力,而不容易被其他代謝物的狀態(tài)所影響。本文找到了36個(gè)關(guān)鍵驅(qū)動(dòng)代謝物中,其中27個(gè)代謝物是核心代謝物；高頻驅(qū)動(dòng)代謝物傾向于是連接不同代謝通路的代謝物,對(duì)整個(gè)代謝系統(tǒng)有著重要的調(diào)控作用。說(shuō)明了關(guān)鍵驅(qū)動(dòng)代謝物和高頻驅(qū)動(dòng)代謝物可能是潛在的藥物靶標(biāo)。發(fā)現(xiàn)在人體信號(hào)網(wǎng)絡(luò)的信號(hào)流中,與下游的驅(qū)動(dòng)節(jié)點(diǎn)密度對(duì)比,上游的驅(qū)動(dòng)節(jié)點(diǎn)更密集,并且低入度的節(jié)點(diǎn)在調(diào)控人體信號(hào)網(wǎng)絡(luò)狀態(tài)中有著重要作用。另外,為了控制整個(gè)網(wǎng)絡(luò),發(fā)現(xiàn)控制癌癥相關(guān)基因的調(diào)控因子比直接調(diào)控癌癥相關(guān)基因成本更低。這為人體信號(hào)系統(tǒng)的實(shí)際控制提供了一個(gè)新的思路。提出了一種優(yōu)化選擇容易被控制的重要部分網(wǎng)絡(luò)的方法,通過計(jì)算ER網(wǎng)絡(luò),SF網(wǎng)絡(luò)和23個(gè)真實(shí)網(wǎng)絡(luò)中被選擇的部分網(wǎng)絡(luò)的最小驅(qū)動(dòng)節(jié)點(diǎn)密度,發(fā)現(xiàn)這里的最小驅(qū)動(dòng)節(jié)點(diǎn)密度比隨機(jī)選擇方法得到的部分網(wǎng)絡(luò)的最小驅(qū)動(dòng)節(jié)點(diǎn)密度要低,說(shuō)明了優(yōu)化選擇方法比隨機(jī)選擇方法要好。另外通過分析實(shí)際人體信號(hào)網(wǎng)絡(luò)和人體有向蛋白質(zhì)相互作用網(wǎng)絡(luò)中優(yōu)化選擇的部分網(wǎng)絡(luò)的生物意義,發(fā)現(xiàn)優(yōu)化選擇的部分網(wǎng)絡(luò)傾向于是癌癥相關(guān)基因,說(shuō)明了優(yōu)化方法選擇的部分網(wǎng)絡(luò)是重要的。提出了一個(gè)分析任意度分布有向網(wǎng)絡(luò)中四種極大連通子圖可控性的理論框架。發(fā)現(xiàn)了在ER網(wǎng)絡(luò)和SF網(wǎng)絡(luò)中,隨機(jī)刪除1一p比例的節(jié)點(diǎn),隨著剩余節(jié)點(diǎn)比例p的增大,控制極大連通子圖的最小驅(qū)動(dòng)節(jié)點(diǎn)密度先增大后減小,在關(guān)鍵點(diǎn)p=Pm處呈現(xiàn)出一個(gè)峰值。對(duì)于ER網(wǎng)絡(luò),最小驅(qū)動(dòng)節(jié)點(diǎn)密度的峰值與網(wǎng)絡(luò)的平均度k無(wú)關(guān),而是由Pm(κ決定的。另外,控制度異質(zhì)網(wǎng)絡(luò)中極大連通子圖的最小驅(qū)動(dòng)節(jié)點(diǎn)密度比度同質(zhì)網(wǎng)絡(luò)中的要高,說(shuō)明了度異質(zhì)網(wǎng)絡(luò)中極大連通子圖比同質(zhì)網(wǎng)絡(luò)中的極大連通子圖更難被控制。
[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.
【學(xué)位授予單位】：華中科技大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O157.5

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