Highly optimized tolerance is a model of optimization in engineered systems, which gives rise to power-law distributions of failure events in such systems. The archetypal example is the highly optimized forest fire model. Here we give an analytic solution for this model which explains the origin...

A deterministic trading strategy can be regarded as a signal processing element that uses external information and past prices as inputs and incorporates them into future prices. This paper uses a market maker based method of price formation to study the price dynamics induced by several...

We investigate the problem of learning to play a generalized rock-paper-scissors game. Each player attempts to improve her average score by adjusting the frequency of the three possible responses. For the zero-sum case the learning process displays Hamiltonian chaos. The learning trajectory can...

Physicists have recently begun doing research in finance, and even though this movement is less than five years old, interesting and useful contributions have already emerged. This article reviews these developments in four areas, including empirical statistical properties of prices,...

The limit order book is a device for storing demand and effecting trades that is the primary mechanism for price formation in most modern financial markets. We study the limit order book under a random process model of order flow, using simulations and an analytic treatment based on a master...

In this review article, we explore several recent advances in the quantitative modeling of financial markets. We begin with the Efficient Markets Hypothesis and describe how this controversial idea has stimulated a number of new directions of research, some focusing on more elaborate...

Self-organizing maps (SOM) are unsupervised, competitive neural networks used to project high-dimensional data onto a low-dimensial space. In this article we show how SOM can be sued to draw graphs in the plane. The SOM-based approach to graph drawing, which belongs to the general class of...

We show that a wide variety of nonlinear cellular automata can be written as a semidirect product of linear ones, and that these CAs can be predicted in parallel time [cal O](log[super 2] t). This class includes any CA whose rule, when written as an algebra, is a solvable group. <p> We also show,...</p>

This paper describes the dynamics of adaptation in a two-country, overlapping generations economy with no restrictions on foreign currency holdings. Governments of both countries finance their deficits via seignorage. Agents in this economy are boundedly rational. They use the genetic algorithm...

We study the simple evolutionary process in which we repeatedly find the least fit agent in a population of agents and give it a new fitness which is chosen independently at random from a specified distribution. We show that many of the average properties of this process can be calculated...