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Complex networks have been studied intensively for a decade, but research still focuses on the limited case of a single, non-interacting network (1-14). Modern systems are coupled together (15-19) and therefore should be modelled as interdependent networks. A fundamental property of interdependent networks is that failure of nodes in one network may lead to failure of dependent nodes in other networks. This may happen recursively and can lead to a cascade of failures. In fact, a failure of a very small fraction of nodes in one network may lead to the complete fragmentation of a system of several interdependent networks. A dramatic real-world example of a cascade of failures ('concurrent malfunction') is the electrical blackout that affected much of Italy on 28 September 2003: the shutdown of power stations directly led to the failure of nodes in the Internet communication network, which in turn caused further breakdown of power stations (20). Here we develop a framework for understanding the robustness of interacting networks subject to such cascading failures. We present exact analytical solutions for the critical fraction of nodes that, on removal, will lead to a failure cascade and to a complete fragmentation of two interdependent networks. Surprisingly, a broader degree distribution increases the vulnerability of interdependent networks to random failure, which is opposite to how a single network behaves. Our findings highlight the need to consider interdependent network properties in designing robust networks., Today's networks are becoming increasingly dependent on one another. Diverse infrastructures such as water supply, transportation, fuel and power stations are coupled together. We show that owing to this coupling, [...]

Author(s): Chaoming Song [1]; Shlomo Havlin [2]; Hernán A. Makse (corresponding author) [1] Complex networks have been studied extensively owing to their relevance to many real systems such as the [...]

The best statistical strategy required to search efficiently for randomly located objects was sought. The way in which the search efficiency depends on the probability distribution of flight lengths taken by a forager that detects target sites in its vicinity, is studied. When target sites are sparse and are visited any number of times, it was found that an inverse square power-law distribution of flight lengths, linking to Levy flight motions, is the optimal strategy.

The healthy heartbeat time series contains significant phase correlations which are cancelled in the surrogate signal by the randomization of the Fourier phases, according to research into the possibility that time series produced by certain physiological control systems could belong to a special class of complex processes which need a large number of exponents to characterize their scaling properties. These correlations are weaker in heart-failure subjects. It appears that multifractality is linked with nonlinear features of the healthy heartbeat dynamics.

A size separation effect that occurs when granular mixture is poured between two vertical plates is described. The mixture's spontaneous stratification into alternating layers of small and large grains whenever the larger grains have larger angle of repose than the small grains is observed. Only spontaneous segregation, without stratification, is noted when the larger grains have smaller angle of repose than the small grains. A physical mechanism behind the observed stratification, which is related to the fact that a pair of layers, instead of only one, is formed in the course of each avalanche, is proposed.

Analyses of biological signals have proven to be complicated because of the irregular and non-stationary quality of such signals. However, an innovative biological signal analysis approach based on a wavelet transform and an analytic signal system has been developed. The approach has been successfully used to analyze heartbeat intervals. Results showed that heartbeat intervals possess a scaling behavior which can be attributed to the underlying nonlinear dynamics of the heart function.

A model for urban development based on the correlated percolation theory in presence of a density gradient, correctly reproduces the observed morphology of cities, area distribution of towns in an urban system and the urban growth dynamics. The model makes it possible to predict the global properties of urban morphologies. The developmental units are positioned with an occupancy probability, not at random. A study on cities indicates the large value of decentralization. Density gradient is the only factor of urban development which is affected by time.