Adaptation Noise And Self Organizing Systems

We investigate a new model of binary fragmentation with inhibition, driven by the white noise. In a broad range of fragmentation probabilities, the power-law spatiotemporal correlations are found to arise due to self-organized criticality (SOC). We find in the SOC phase a non-trivial power spectrum of the temporal sequence of the fragmentation events. The 1/f ~ behaviour is recovered in the irreversible, near-equilibrium part of this phase.

We show that the daily average air humidity fluctuations exhibit non-trivial 1/ f α behaviour which different from the spectral properties of other meteorological quantities. This feature and the fractal spatial strucure found in clouds make it plausible to regard air humidity fluctuations as a manifestation of self-organized criticality. We give arguments why the dynamics in air humidity can be similar to those in sandpile models of SOC.

A new model ecosystem consisting of many interacting species is introduced. The species are connected through a random matrix with a given connectivity. It is shown that the system is organized close to a boundary of marginal stability in such a way that fluctuations follow power law distributions both in species abundance and their lifetimes for some slow-driving (immigration) regime. The connectivity and the number of species are linked through a scaling relation which is the one observed in real ecosystems. These results suggest that the basic macroscopic features of real, species-rich ecologies might be linked with a critical state. A natural link between lognormal and power law distributions of species abundances is suggested.

We investigate correlations among pitches in several songs and pieces of piano music by mapping them to one-dimensional walks. Two kinds of correlations are studied, one is related to the real values of frequencies while they are treated only as different symbols for another. Long-range power law behavior is found in both kinds. The first is more meaningful. The structure of music, such as beat, measure and stanza, are reflected in the change of scaling exponents. Some interesting features are observed. Our results demonstrate the viewpoint that the fundamental principle of music is the balance between repetition and contrast.

In this work we check the occurrence of the Azbel assumption of mortality within the framework of a bit string model for biological ageing. We reproduced the observed feature of linear correspondence between the fitting parameters of the death rate as obtained by Azbel with demographic data.

The principal scheme of the secondary image synthesis in electronic computer photography is described. The crucial role of the Clebsch-Gordan coefficient calculus is pointed out.

A theoretical and experimental analysis is made of the effects of self-adaptation in a simple evolving system. Specifically, we consider the effects of coding the mutation and crossover probabilities of a genetic algorithm evolving in certain model fitness landscapes. The resultant genotype-phenotype mapping is degenerate, there being no direct selective advantage for one probability versus another. We show that the action of mutation and crossover breaks this degeneracy leading to an induced symmetry breaking among the genotypic synonyms. We demonstrate that this induced symmetry breaking allows the system to self-adapt in a time dependent environment.

A new type of dynamical behavior of a multistable system is reported. We found that a simple non-equilibrium system can reduce its effective temperature autonomously at a global minimum if the residual frustration at a global minimum is small enough, which highlights an unexpected feature of non-equilibrium multistable systems.

The two-parent reproduction model of Derrida and Peliti is simulated on a rugged fitness landscape. Fixed fitness values for each possible genotype are assigned randomly, with all fit 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 distributions, showing up characteristics of a phase transition. A crossover variant of the model has a smoother transition to the adapted regime, with a residual collective adaptation for small values of the threshold in fitness. When a geographical constraint (shortest possible distance) on pairwise reproduction in a population arranged one-dimensionally is imposed, a poised state results, suggestive of self-organized criticality.

We introduce and study a dynamic transport model exhibiting Self-Organized Criticality. The novel concepts of our model are the probabilistic propagation of activity and unbiased random repartition of energy among the active site and its nearest neighbors. For space dimensionality d≥2 we argue that the model is related to d+1 dimensional directed percolation, with time interpreted as the preferred direction.