Adaptation Noise And Self Organizing Systems

We show that the decline in the extinction rate during the Phanerozoic can be accurately parameterized by a logarithmic fit to the cumulative total extinction. This implies that extinction intensity is falling off approximately as the reciprocal of time. We demonstrate that this observation alone is sufficient to explain the existence of the proposed power-law forms in the distribution of the sizes of extinction events and in the power spectrum of Phanerozoic extinction, results which previously have been explained by appealing to self-organized critical theories of evolutionary dynamics.

Models to mimic the transmission of information in financial markets are introduced. As an attempt to generate the demand process, we distinguish between dictatorship associations, where groups of agents rely on one of them to make decision, and democratic associations, where each agent takes part in the group decision. In the dictatorship model, agents segregate into two distinct populations, while the democratic model is driven towards a critical state where groups of agents of all sizes exist. Hence, both models display a level of organization, but only the democratic model is self-organized. We show that the dictatorship model generates less volatile markets than the democratic model.

We present a model of decentralized growth for Artificial Neural Networks (ANNs) inspired by the development and the physiology of real nervous systems. In this model, each individual artificial neuron is an autonomous unit whose behavior is determined only by the genetic information it harbors and local concentrations of substrates modeled by a simple artificial chemistry. Gene expression is manifested as axon and dendrite growth, cell division and differentiation, substrate production and cell stimulation. We demonstrate the model's power with a hand-written genome that leads to the growth of a simple network which performs classical conditioning. To evolve more complex structures, we implemented a platform-independent, asynchronous, distributed Genetic Algorithm (GA) that allows users to participate in evolutionary experiments via the World Wide Web.

We consider an ecological system governed by Lotka-Volterra dynamics and an example of an economic system as a mesomarket with perfect competition. We propose a mechanism for cooperative self-regulation that enables the system under consideration to respond properly to changes in the environment. This mechanism is based on (1) active individual behavior of the system elements at each hierarchical level and (2) self-processing of information caused by the hierarchical organization. It is shown how the proposed mechanism suppresses nonlocal interaction of elements belonging to a particular level as mediated by higher levels.

Basic problems for the construction of a scenario for the Life are discussed. To study the problems in terms of dynamical systems theory, a scheme of intra-inter dynamics is presented. It consists of internal dynamics of a unit, interaction among the units, and the dynamics to change the dynamics itself, for example by replication (and death) of units according to their internal states. Applying the dynamics to cell differentiation, isologous diversification theory is proposed. According to it, orbital instability leads to diversified cell behaviors first. At the next stage, several cell types are formed, first triggered by clustering of oscillations, and then as attracting states of internal dynamics stabilized by the cell-to-cell interaction. At the third stage, the differentiation is determined as a recursive state by cell division. At the last stage, hierarchical differentiation proceeds, with the emergence of stochastic rule for the differentiation to sub-groups, where regulation of the probability for the differentiation provides the diversity and stability of cell society. Relevance of the theory to cell biology is discussed.

The characteristic size for spatial structure, that emerges when the bifurcation parameter in model partial differential equations is slowly increased through its critical value, depends logarithmically on the size of added noise. Numerics and analysis are presented for the real Ginzburg-Landau and Swift-Hohenberg equations.

We investigate symbolic sequences and in particular information carriers as e.g. books and DNA--strings. First the higher order Shannon entropies are calculated, a characteristic root law is detected. Then the algorithmic entropy is estimated by using Lempel--Ziv compression algorithms. In the third section the correlation function for distant letters, the low frequency Fourier spectrum and the characteristic scaling exponents are calculated. We show that all these measures are able to detect long--range correlations. However, as demonstrated by shuffling experiments, different measures operate on different length scales. The longest correlations found in our analysis comprise a few hundreds or thousands of letters and may be understood as long--wave fluctuations of the composition.

The sustainable biodiversity associated with a specific ecological niche as a function of land area is analysed computationally by considering the interaction of ant societies over a collection of islands. A power law relationship between sustainable species and land area is observed. We will further consider the effect a perturbative inflow of ants has upon the model.

The steady state properties of the mean density population of infected cells in a viral spread is simulated by a general forest fire like cellular automaton model with two distinct populations of cells ( permissive and resistant ones) and studied in the framework of the mean field approximation. Stochastic dynamical ingredients are introduced in this model to mimic cells regeneration (with probability {\it p}) and to consider infection processes by other means than contiguity (with probability {\it f}). Simulations are carried on a L×L square lattice considering the eigth first neighbors. The mean density population of infected cells ( D i ) is measured as function of the regeneration probability {\it p}, and analized for small values of the ratio {\it f/p } and for distinct degrees of the cell resistance. The results obtained by a mean field like approach recovers the simulations results. The role of the resistant parameter R ( R≥2) on the steady state properties is investigated and discussed in comparision with the R=1 monocell case which corresponds to the {\em self organized critical} forest fire model. The fractal dimension of the dead cells ulcers contours were also estimated and analised as function of the model parameters.

Analysis is presented of a system whose dynamics are dramatically simplified by tiny amounts of additive noise. The dynamics divide naturally into two phases. In the slower phase, trajectories are close to an invariant manifold; this allows small random disturbances to exert a controlling influence. A map is derived which provides an accurate description of the trajectories.