An Abelian sandpile model is considered on the Husimi lattice of triangles with an arbitrary coordination number q. Exact expressions for the distribution of height probabilities in the Self-Organized Critical state are derived.

The two-parent reproduction model of Derrida and Peliti is simulated on a rugged tness landscape. Fixed tness values for each possible genotype are assigned randomly, with all t individuals having the same probability of reproduction. The previously observed transition to a self-organized state of the population with less recombinational load, implies an abrupt change of genetic overlap distrib...

The avalanche dynamics in the Bak–Sneppen mechanism of self-organized criticality (SOC) is discussed. Rigorous arguments reveal the emergent history dependence that dominates the intermittent activity. In numerical studies the emergent SOC state shows glassy features, such as aging and an ultrametric organization of activity. c © 1999 Elsevier Science B.V. All rights reserved.

Since Conway proposed the Game of Life, it has attracted researchers’ attention due to complex “life” evolutions despite simple rules. It is known that the Game of Life exhibits self-organized criticality, which might be related to scale-free evolutions. Despite the interesting phenomenon of self-organized criticality, the Game of Life turns to steady states within several generations. Here, we...

During the last decades, many attempts have beenmade in order to explain and formalize mathematically a large set of phenomena that, at a first glance, are not well described by traditional theories. Among those attempts one finds the whole theory of self-organized criticality and some statistical theories. In recent years, a popular approach has been a Daróczy-like entropy [2] and its correspo...

Learning algorithms need generally the ability to compare several streams of information. Neural learning architectures hence need a unit, a comparator, able to compare several inputs encoding either internal or external information, for instance, predictions and sensory readings. Without the possibility of comparing the values of predictions to actual sensory inputs, reward evaluation and supe...

A model of the universe as a self-organized critical system is considered. The universe evolves to a state independently of the initial conditions at the edge of chaos. The critical state is an attractor of the dynamics. Random metric fluctuations exhibit noise without any characteristic length scales, and the power spectrum for the fluctuations has a self-similar fractal behavior. In the early...

This paper presents a new algorithm for clustering. It is an generalisation of the K-means algorithms . Each cluster will be represented by a chain of prototypes instead of being represented by one prototype like for the K-means. The chains are competing together to represent clusters and are evolving according to Kohonen maps adaptation rule. It is well known that K-means performs very well wi...

We define stabilizability of an infinite volume height configuration and of a probability measure on height configurations. We show that for high enough densities, a probability measure cannot be stabilized. We also show that in some sense the thermodynamic limit of the uniform measures on the recurrent configurations of the abelian sandpile model (ASM) is a maximal element of the set of stabil...

Growth and preferential attachments have been coined as the two fundamental mechanisms responsible for the scale-free feature in complex networks, as characterized by an algebraic degree distribution. There are situations, particularly in biological networks, where growth is absent or not important, yet some of these networks still exhibit the scale-free feature with a small degree exponent. He...