In this paper we rigorously formulate the Schema Theorem for Genetic Programming (GP). This involves defining a schema, schema order, and defining length and accounting for the variable length and the non-homologous nature of GP'S representation. The GP Schema Theorem and the related notion of a...

This paper emphasizes the general value of a hierarchical variable length representation for program induction by demonstrating that different search strategies and operators complementary to them can be used to obtain solutions. It presents a comparison of Genetic Programming (GP) with...

How did human language arise, and what accounts for its present structure? Over the past decade, there has been great interest -- and impressive progress -- in using evolutionary theory to address to these and related questions. In particular, a number of studies have shown that several key...

We study the statistical properties of eigenvalues of the Hessian matrix $\cal H$ (matrix of second derivatives of the potential energy) for a classical atomic liquid, and compare these properties with predictions for random matrix models (RMM). The eigenvalue spectra (the Instantaneous Normal...

We intoduce a new origin of volatility clustering in econonmic time series gererated by systems of interacting adaptive agents. Each agent is assigned a random subset of a fixed collection of predictors. At every time step each agent generates an action based upon its assigned predictors. Some...

Fitness landscapes are an important concept in molecular evolution since evolutionary adaptation as well as {\it in vitro} selection of biomolecules can be viewed as a hill-climbing-like process. Global features of landscapes can be described by statistical measures such as correlation functions...

The effect of noise on the in-phase of a set of $N$ globally coupled oscillators is studied; these discrete-time maps are associated with the continuous-time equations of motion for a series array of Josephson junction oscillators. We investigate both geometrical properties of the basin of...

The dynamics of extinction and diversification of life is not a simple stochastic process, driven by random inputs. Biotic interactions are known to play a very important role in the population response to physical factors. In spite of this fact, it is not clear how the ecological scale is...

Life has existed on the Earth for more than three billion years. Until the Cambrian explosion about 540 million years ago however, it was restricted mostly to single-celled micro-organisms that were, for the most part, poorly preserved in the fossil record. From the Cambrian explosion onwards,...

We introduce a simple mathematical model of regulation of division of labour in insect societies based on the notion of fixed response thresholds. Individuals with different thresholds respond differently to task-associated stimuli. Low-threshold individuals become involved at a lower level of...