We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind came into existence recently. This opens a wide field for the study of their topology, evolution, and complex processes occurring in them. Such networks possess a rich set of scaling properties. A number of them are scale-free and show striking resilience against random breakdowns. In spite of large sizes of these networks, the distances between most their vertices are short — a feature known as the “smallworld” effect. We discuss how growing networks self-organize into scale-free structures and the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation in these networks. We present a number of models demonstrating the main features of evolving networks and discuss current approaches for their simulation and analytical study. Applications of the general results to particular networks in Nature are discussed. We demonstrate the generic connections of the network growth processes with the general problems

Population diversity is undoubtably a key issue in the performance of evolutionary algorithms. A common hypothesis is that high diversity is important to avoid premature convergence and to escape local optima. Various diversity measures have been used to analyze algorithms, but so far few algorithms have used a measure to guide the search.

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A local-search heuristic for finding high-quality solutions for many hard optimization problems is explored. The method is inspired by recent progress in understanding far-from-equilibrium phenomena in terms of selforganized criticality, a concept introduced to describe emergent complexity in physical systems. This method, called extremal optimization, successively replaces the value of extremely undesirable variables in a sub-optimal solution with new, random ones. Large, avalanche-like fluctuations in the cost function emerge dynamically. These enable the search to effectively scaling barriers to explore local optima in distant neighborhoods of the configuration space while eliminating the need to tune parameters. Drawing upon models used to simulate the dynamics of granular media, evolution, or geology, extremal optimization complements approximation methods inspired by equilibrium statistical physics, such as simulated annealing. This method is very general and so far has proved competitive with—and even superior to—more elaborate general-purpose heuristics on testbeds of constrained optimization problems with up to 10 5 variables, such as bipartitioning, coloring, and spin glasses. Analysis of a model problem predicts the only free parameter of the method in accordance with all experimental results. © 2003 Wiley Periodicals, Inc.* Key Words: extremal optimization; criticality; simulated annealing; punctuated equilibrium Many natural systems have, without any centralized

Ecosystems are prototypical examples of complex adaptive systems, in which patterns at higher levels emerge from localized interactions and selection processes acting at lower levels. An essential aspect of such systems is nonlinearity, leading to historical dependency and multiple possible outcomes of dynamics. Given this, it is essential to determine the degree to which system features are determined by environmental conditions, and the degree to which they are the result of self-organization. Further-

We propose a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organizing processes often found in nature. The method, called Extremal Optimization, successively eliminates extremely undesirable components of sub-optimal solutions. Drawing upon models used to simulate far-from-equilibrium dynamics, it complements approximation methods inspired by equilibrium statistical physics, such as simulated annealing. With only one adjustable parameter, its performance proves competitive with, and often superior to, more elaborate stochastic optimization procedures. We demonstrate it here on two classic hard optimization problems: graph partitioning and the traveling salesman problem. 1 In nature, highly specialized, complex structures often emerge when their most inefficient components are selectively driven to extinction. Evolution, for example, progresses by selecting against the few most poorly adapted species, rather than by expressly breeding those species best adapted to their environment [1]. To describe the dynamics of systems with

Background noise is the irregular variation across repeated measurements of human performance. Background noise remains after task and treatment effects are minimized. Background noise refers to intrinsic sources of variability, the intrinsic dynamics of mind and body, and the internal workings of a living being. Two experiments demonstrate 1/f scaling (pink noise) in simple reaction times and speeded word naming times, which round out a catalog of laboratory task demonstrations that background noise is pink noise. Ubiquitous pink noise suggests processes of mind and body that change each other’s dynamics. Such interaction-dominant dynamics are found in systems that self-organize their behavior. Self-organization provides an unconventional perspective on cognition, but this perspective closely parallels a contemporary interdisciplinary view of living systems. Psychological science usually ignores the background noise in behavioral data. Background noise is what is left over when task demands, experimental manipulations, and other external sources of variability have been eliminated or minimized. What we call background noise is treated as random variability in most research, the nuisance factor in factorial experiments. We argue, to the

A newly proposed Recurrent Self-Organizing Map (RSOM) is studied in time series prediction. In this approach RSOM is used to cluster the data to local data sets and local linear models corresponding each of the map units are then estimated based on the local data sets. A traditional way of clustering the data is to use a windowing technique to split it to input vectors of certain length. In this procedure, the temporal context between the consecutive vectors is lost. In RSOM the map units keep track of the past input vectors with a recurrent dioeerence vector in each unit. The recurrent structure allows the map to store information concerning the change in the magnitude and direction of the input vector. RSOM can thus be used to cluster the temporal context in the time series. This allows a dioeerent local model to be selected based on the context and the current input vector of the model. The studied cases show promising results.

These notes are intended to provide a pedagogical introduction to the abelian sandpile model of self-organized criticality, and its related models. The abelian group, the algebra of particle addition operators, the burning test for recurrent states, equivalence to the spanning trees problem are described. The exact solution of the directed version of the model in any dimension is explained. The model’s equivalence to Scheidegger’s model of river basins, Takayasu’s aggregation model and the voter model is discussed. For the undirected case, the solution for one-dimensional lattices and the Bethe lattice is briefly described. Known results about the two dimensional case are summarized. Generalization to the abelian distributed processors model is discussed. Time-dependent properties and the universality of critical behavior in sandpiles are briefly discussed. I conclude by listing some still-unsolved problems.

The human brain spontaneously generates neural oscillations with a large variability in frequency, amplitude, duration, and recurrence. Little, however, is known about the long-term spatiotemporal structure of the complex patterns of ongoing activity. A central unresolved issue is whether fluctuations in oscillatory activity reflect a memory of the dynamics of the system for more than a few seconds. We investigated the temporal correlations of network oscillations in the normal human brain at time scales ranging from a few seconds to several minutes. Ongoing activity during eyes-open and eyes-closed conditions was recorded with simultaneous magnetoencephalography and electroencephalography. Here we show that amplitude fluctuations of 10 and 20 Hz oscillations are correlated over thousands of oscillation cycles. Our analyses also indicated that these amplitude Oscillations at various frequencies are a prominent feature of the