Directed networks such as gene regulation networks and neural networks are connected by arcs（directed links）. The nodes in a directed network are often strongly interwound by a huge number of directed cycles, which ...Directed networks such as gene regulation networks and neural networks are connected by arcs（directed links）. The nodes in a directed network are often strongly interwound by a huge number of directed cycles, which leads to complex information-processing dynamics in the network and makes it highly challenging to infer the intrinsic direction of information flow. In this theoretical paper, based on the principle of minimum-feedback, we explore the node hierarchy of directed networks and distinguish feedforward and feedback arcs. Nearly optimal node hierarchy solutions, which minimize the number of feedback arcs from lower-level nodes to higher-level nodes, are constructed by belief-propagation and simulated-annealing methods. For real-world networks, we quantify the extent of feedback scarcity by comparison with the ensemble of direction-randomized networks and identify the most important feedback arcs. Our methods are also useful for visualizing directed networks.展开更多
The rapid development of the Network makes the comprehensive analysis as well as the quantitative evaluation of its security become more and mere important. This paper illustrates the major realization process of a Ne...The rapid development of the Network makes the comprehensive analysis as well as the quantitative evaluation of its security become more and mere important. This paper illustrates the major realization process of a Network Security Quantitative Evaluation System,which,from an intruder's angle ,established a Hierarchy Intrusion Relationship Graph by analyzing the credit degree fusion and relevancy of the secure information of the target network and by combining with powerful database information. At last, by applying some relative mathematics model and arithmetic, the paper analyzes and evaluates the security of this Network Hierarchy Intrusion Relationship Graph comprehensively and quantitatively.展开更多
基金Project by the National Basic Research Program of China(Grant No.2013CB932804)the National Natural Science Foundations of China(Grant Nos.11121403 and 11225526)support by Fondazione CRT under project SIBYL,initiative "La Ricerca dei Talenti"
文摘Directed networks such as gene regulation networks and neural networks are connected by arcs（directed links）. The nodes in a directed network are often strongly interwound by a huge number of directed cycles, which leads to complex information-processing dynamics in the network and makes it highly challenging to infer the intrinsic direction of information flow. In this theoretical paper, based on the principle of minimum-feedback, we explore the node hierarchy of directed networks and distinguish feedforward and feedback arcs. Nearly optimal node hierarchy solutions, which minimize the number of feedback arcs from lower-level nodes to higher-level nodes, are constructed by belief-propagation and simulated-annealing methods. For real-world networks, we quantify the extent of feedback scarcity by comparison with the ensemble of direction-randomized networks and identify the most important feedback arcs. Our methods are also useful for visualizing directed networks.
文摘The rapid development of the Network makes the comprehensive analysis as well as the quantitative evaluation of its security become more and mere important. This paper illustrates the major realization process of a Network Security Quantitative Evaluation System,which,from an intruder's angle ,established a Hierarchy Intrusion Relationship Graph by analyzing the credit degree fusion and relevancy of the secure information of the target network and by combining with powerful database information. At last, by applying some relative mathematics model and arithmetic, the paper analyzes and evaluates the security of this Network Hierarchy Intrusion Relationship Graph comprehensively and quantitatively.
