James P. Crutchfield

It is shown how the existence of low-dimensional chaotic dynamical systems describing turbulent fluid flow might be determined experimentally. Techniques are outlined for reconstructing phase-space pictures from the observation of a single coordinate of any dissipative dynamical system, and for determining the dimensionality of the system's attractor. These techniques are applied to a well-known simple three-dimensional chaotic dynamical system.

Statistical mechanics is used to describe the observed information processing complexity of nonlinear dynamical systems. We introduce a measure of complexity distinct from and dual to the information theoretic entropies and dimensions. A technique is presented that directly reconstructs minimal equations of motion from the recursive structure of measurement sequences. Application to the period-doubling cascade demonstrates a form of superuniversality that refers only to the entropy and complexity of a data stream.

We introduce and analyze a general model of a population evolving over a network of selectively neutral genotypes. We show that the population's limit distribution on the neutral network is solely determined by the network topology and given by the principal eigenvector of the network's adjacency matrix. Moreover, the average number of neutral mutant neighbors per individual is given by the matrix spectral radius. These results quantify the extent to which populations evolve mutational robustness-the insensitivity of the phenotype to mutations-and thus reduce genetic load. Because the average neutrality is independent of evolutionary parameters-such as mutation rate, population size, and selective advantage-one can infer global statistics of neutral network topology by using simple population data available from in vitro or in vivo evolution. Populations evolving on neutral networks of RNA secondary structures show excellent agreement with our theoretical predictions.