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We study Erdös-Rényi random graphs with random weights associated with each link. In our approach, nodes connected by links having weights below the percolation threshold form clusters, and each cluster merges into a single node, thus generating a new “clusters network”. We show that this network is scale-free with λ = 2.5. Furthermore, we show that optimization causes the percolation threshold to emerge spontaneously, thus creating naturally a scale-free “clusters network”. This phenomenon may be related to the evolution of several real world scale-free networks. Our results imply that: (i) the minimum spanning tree (MST) in random graphs is composed of percolation clusters, which are interconnected by a set of links that create a scale-free tree with λ = 2.5 (ii) the optimal path may be partitioned into segments that follow the percolation clusters, and the lengths of these segments grow exponentially with the number of clusters that are crossed (iii) the optimal path in scale-free networks with λ < 3 scales as lopt ∼ logN, and the weights along the optimal path decay exponentially with their rank. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]

Recent evidence suggests that physiological signals under healthy conditions may have a fractal temporal structure. We investigate the possibility that time series generated by certain physiological control systems may be members of a special class of complex processes, termed multifractal, which require a large number of exponents to characterize their scaling properties. We report on evidence for multifractality in a biological dynamical system—the healthy human heartbeat. Further, we show that the multifractal character and nonlinear properties of the healthy heart rate are encoded in the Fourier phases. We uncover a loss of multifractality for a life-threatening condition, congestive heart failure. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]