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...

There is increasing evidence that collective behavior, such as social choice, price dynamics, and strategic behavior, is related to nonlinear dynamics and thus has the potential for instability and complex behavior. This paper presents experimental results where subjects are placed in a...

We show that if a cellular automaton in two or more dimensions supports growing "ladders" which can turn or block each other, then it can express arbitrary Boolean circuits. Then the problem of predicting the CA for a finite amount of time becomes P-complete, the question of whether a finite...

Part I: Bayes Estimators and the Shannon Entropy. <p> This paper is the first of two on the problem of estimation a function of a probability distribution from a finite set of samples of that distribution. In this paper a Bayerian analysis of this problem is presented, the optimal properties of the...</p>

I discuss the relations among four worlds: Reality, mathematical models, computer simulation, and models of computation. Pros and cons of two models of computation, the Turing machine and the real number model, are presented. The the intrinsic difficulty of solving a mathematical model, as...