Long-range power-law correlations have been reported recently for DNA sequences containing noncoding regions. We address the question of whether such correlations may be a trivial consequence of the known mosaic structure ("patchiness") of DNA. We analyze two classes of controls consisting of patchy nucleotide sequences generated by different algorithms--one without and one with long-range power-law correlations. Although both types of sequences are highly heterogenous, they are quantitatively distinguishable by an alternative fluctuation analysis method that differentiates local patchiness from long-range correlations. Application of this analysis to selected DNA sequences demonstrates that patchiness is not sufficient to account for long-range correlation properties.

Complex networks have been studied intensively for a decade, but research still focuses on the limited case of a single, non-interacting network. Modern systems are coupled together 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. 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.