Adaptation Noise And Self Organizing Systems

We reconsider a model introduced by Bak, Chen, and Tang (Phys. Rev. A 38, 364 (1988)) as a supposedly self-organized critical model for forest fires. We verify again that the model is not critical in 2 dimensions, as found also by previous authors. But we find that the model does show anomalous scaling (i.e., is critical in the sense of statistical mechanics) in 3 and 4 dimensions. We relate these results to recent claims by A. Johansen.

This paper extends previous work done by Tanese on the distributed genetic algorithm (DGA). Tanese found that the DGA outperformed the canonical serial genetic algorithm (CGA) on a class of difficult, randomly-generated Walsh polynomials. This left open the question of whether the DGA would have similar success on functions that were more amenable to optimization by the CGA. In this work, experiments were done to compare the DGA's performance on the Royal Road class of fitness functions to that of the CGA. Besides achieving superlinear speedup on KSR parallel computers, the DGA again outperformed the CGA on the functions R3 and R4 with regard to the metrics of best fitness, average fitness, and number of times the optimum was reached. Its performance on R1 and R2 was comparable to that of the CGA. The effect of varying the DGA's migration parameters was also investigated. The results of the experiments are presented and discussed, and suggestions for future research are made.

Researchers have proposed that the distinction between so-called "simple" and "complex" societies can be expressed by an increase in the number of levels at which functional organization, interaction, and thus selection, operate. In spite of the obvious links between this suggestion and research into complex social organization amongst insects and other social animals, the levels of selection model has seen little use among anthropologists. We suggest that the primary reason for lack of research into the evolutionary causes of social complexity has been the lack of descriptive units with which we can examine phenotypic variation and heritability of social organization above the level of the organism. The goal of our paper, therefore, is to begin constructing descriptive units which map to meaningful models of multi-level selection. In order to demonstrate how these units are useful in a real dataset, we examine the functional changes involved in the United States economy over the last 100 years, a period of time characterized, we believe, by significant changes in the number and kinds of social aggregates functioning as "individuals" with respect to selection. Our preliminary analysis suggests that it is possible to measure changes in the scale at which functional integration occurs through published data, and that the multilevel selection model for complex society may possess considerable power for describing how selection of culturally transmitted variation occurs in complex societies.

We investigate the ability of a genetic algorithm to design cellular automata that perform computations. The computational strategies of the resulting cellular automata can be understood using a framework in which ``particles'' embedded in space-time configurations carry information and interactions between particles effect information processing. This structural analysis can also be used to explain the evolutionary process by which the strategies were designed by the genetic algorithm. More generally, our goals are to understand how machine-learning processes can design complex decentralized systems with sophisticated collective computational abilities and to develop rigorous frameworks for understanding how the resulting dynamical systems perform computation.

We analyze the population dynamics of a broad class of fitness functions that exhibit epochal evolution---a dynamical behavior, commonly observed in both natural and artificial evolutionary processes, in which long periods of stasis in an evolving population are punctuated by sudden bursts of change. Our approach---statistical dynamics---combines methods from both statistical mechanics and dynamical systems theory in a way that offers an alternative to current ``landscape'' models of evolutionary optimization. We describe the population dynamics on the macroscopic level of fitness classes or phenotype subbasins, while averaging out the genotypic variation that is consistent with a macroscopic state. Metastability in epochal evolution occurs solely at the macroscopic level of the fitness distribution. While a balance between selection and mutation maintains a quasistationary distribution of fitness, individuals diffuse randomly through selectively neutral subbasins in genotype space. Sudden innovations occur when, through this diffusion, a genotypic portal is discovered that connects to a new subbasin of higher fitness genotypes. In this way, we identify innovations with the unfolding and stabilization of a new dimension in the macroscopic state space. The architectural view of subbasins and portals in genotype space clarifies how frozen accidents and the resulting phenotypic constraints guide the evolution to higher complexity.

After presenting possible motives for fighting against the second law of thermodynamics, several attempts to beat this law are analyzed. The second law wins, but an interesting interpretation of it emerges. This interpretation uses the notion of ``encoded order'' and claims that whether a system is or is not in thermodynamic equilibrium depends on the coordinates which the observer decides to measure. This interpretation may not be new, but most present day physicists seem to be unaware of it. The question of subjectivity of entropy and the connection between the present interpretation and ``algorithmic randomness'' are addressed. Key words: Maxwell's demon, perpetuum mobile, subjectivity, entropy, H-theorem, randomness, complexity, information.

We investigate different versions of the minority game, a toy model for agents buying and selling a commodity. The Hamming distance between the strategies used by agents to take decisions is introduced as an analytical tool to determine several properties of these models. The success rate of the agents in an adaptive version of the game is compared with the rate from a stochastic version. It is shown numerically and analytically that the adaptive process is inefficient, increasing the success rate of the unused strategies while decreasing the success rate of the strategies used by the agents. The agents do not do as well as if they were forced to use only one strategy permanently. A version of the game in which the agents strategies evolve is also analyzed using the notion of distance. The agents evolve into a state in which they are all using one strategy, which is again the state that yields the maximum success rate.

Many systems in chemistry, biology, finance and social sciences present emerging features which are not easy to guess from the elementary interactions of their microscopic individual components. In the past, the macroscopic behavior of such systems was modeled by assuming that the collective dynamics of microscopic components can be effectively described collectively by equations acting on spatially continuous density distributions. It turns out that quite contrary, taking into account the actual individual/discrete character of the microscopic components of these systems is crucial for explaining their macroscopic behavior. In fact, we find that in conditions in which the continuum approach would predict the extinction of all the population (respectively the vanishing of the invested capital or of the concentration of a chemical substance, etc), the microscopic granularity insures the emergence of macroscopic localized sub-populations with collective adaptive properties which allow their survival and development. In particular it is found that in 2 dimensions "life" (the localized proliferating phase) always prevails.

Recent developments in the global liberalization of equity and currency markets, coupled to advances in trading technologies, are making markets increasingly interdependent. This increased fluidity raises questions about the stability of the international financial system. In this paper, we show that as couplings between stable markets grow, the likelihood of instabilities is increased, leading to a loss of general equilibrium as the system becomes increasingly large and diverse.

This commentary discusses a recently proposed measure of heterogeneity of DNA sequences and compares with the measures of complexity.