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• Li, Angsheng; Zhang, Xiaohui; Pan, Yicheng 2017-01-01 We investigate the defending of networks against virus attack. We define the resistance of a network to be the maximum number of bits required to determine the code of the module that is accessible from random walk, from which random walk cannot escape. Program Shqip Per Lokale Bare Restorante. We show that for any network G, R(G) =H1(G) -H2(G), where R(G) is the resistance of G, H1(G) and H2(G) are the one- and two-dimensional structural information of G, respectively, and that resistance maximization is the principle for defending networks against virus attack. By using the theory, we investigate the defending of real world networks and of the networks generated by the preferential attachment and the security models. We show that there exist networks that are defensible by a small number of controllers from cascading failure of any virus attack.

Our theory demonstrates that resistance maximization is the principle for defending networks against virus attacks. • Vaknin, Dana; Danziger, Michael M.; Havlin, Shlomo 2017-07-01 Many real-world multilayer systems such as critical infrastructure are interdependent and embedded in space with links of a characteristic length. They are also vulnerable to localized attacks or failures, such as terrorist attacks or natural catastrophes, which affect all nodes within a given radius. Here we study the effects of localized attacks on spatial multiplex networks of two layers. We find a metastable region where a localized attack larger than a critical size induces a nucleation transition as a cascade of failures spreads throughout the system, leading to its collapse. We develop a theory to predict the critical attack size and find that it exhibits novel scaling behavior. We further find that localized attacks in these multiplex systems can induce a previously unobserved combination of random and spatial cascades.