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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク robustness of complex networks ： ウィキペディア英語版 robustness of complex networks Robustness, the ability to withstand failures and perturbations, is a critical attribute of many complex systems including complex networks. The study of robustness in complex networks is important for many fields. In ecology, robustness is an important attribute of ecosystems, and can give insight into the reaction to disturbances such as the extinction of species.〔V. R. Sole, M. M. Jose. "Complexity and fragility in ecological net-works". Proc. R. Soc. Lond. B, 268: 2039, 2001.〕 For biologists, network robustness can help the study of diseases and mutations, and how to recover from some mutations.〔A. Motter, N. Gulbahce, E. Almaas, and A.-L. Barabási. "Predicting synthetic rescues in metabolic networks". ''Molecular Systems Biology'', 4: 1-10, 2008.〕 In economics, network robustness principles can help our understanding of the stability and risks of banking systems.〔A. G. Haldane and R. M. May. Systemic risk in banking ecosystems. ''Nature'', 469: 351-355, 2011.〕 And in engineering, network robustness can help us evaluate the resilience of infrastructure networks such as the Internet or power grids.〔R. Albert, I. Albert, and G.L. Nakarado. "Structural Vulnerability of the North American Power Grid". Phys. Rev. E, 69: 025103 R, 2004.〕 == Percolation theory == (詳細はremoval of nodes or links. The mathematical model of such a process can be thought of as an inverse percolation process. Percolation theory models the process of randomly placing pebbles on an n-dimensional lattice with probability p, and predicts the sudden formation of a single large cluster at a critical probability $p\_c$.〔D. Stauffer and A. Aharony. Introduction to Percolation Theory. Tay-lor and Francis. London, 1994.〕 In percolation theory this cluster is named the percolating cluster. This phenomenon is quantified in percolation theory by a number of quantities, for example the average cluster size $$. This quantity represents the average size of all finite clusters and is given by the following equation. $$ \begin \sim \left|p - p_c\right|^ \end We can see the average cluster size suddenly diverges around the critical probability, indicating the formation of a single large cluster. It is also important to note that the exponent $\backslash gamma\_p$ is universal for all lattices, while $p\_c$ is not. This is important as it indicates a universal phase transition behavior, at a point dependent on the topology. The problem of robustness in complex networks can be seen as starting with the percolating cluster, and removing a critical fraction of the pebbles for the cluster to break down. Analogous to the formation of the percolation cluster in percolation theory, the breaking down of a complex network happens abruptly during a phase transition at some critical fraction of nodes removed. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「robustness of complex networks」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.