Mass Extinctions vs. Uniformitarianism in Biological Evolution

It is usually believed that Darwin's theory leads to a smooth gradual evolution, so that mass extinctions must be caused by external shocks. However, it has recently been argued that mass extinctions arise from the intrinsic dynamics of Darwinian evolution. Species become extinct when swept by intermittent avalanches propagating through the global ecology. These ideas are made concrete through studies of simple mathematical models of coevolving species. The models exhibit self-organized criticality and describe some general features of the extinction pattern in the fossil record.Comment: 17 pages uuencoded with style file lamuphys.sty. 9 figures not included but can be obtained via [email protected]. to appear in ``Physics of Biological Systems'' Lecture Notes in Physics (Springer-Verlag, Heidelberg , 1996

Democratic Reinforcement: Learning via Self-Organization

The problem of learning in the absence of external intelligence is discussed in the context of a simple model. The model consists of a set of randomly connected, or layered integrate-and fire neurons. Inputs to and outputs from the environment are connected randomly to subsets of neurons. The connections between firing neurons are strengthened or weakened according to whether the action is successful or not. The model departs from the traditional gradient-descent based approaches to learning by operating at a highly susceptible ``critical'' state, with low activity and sparse connections between firing neurons. Quantitative studies on the performance of our model in a simple association task show that by tuning our system close to this critical state we can obtain dramatic gains in performance.Comment: 9 pages (TeX), 3 figures supllied on reques

Money and Goldstone modes

Why is ``worthless'' fiat money generally accepted as payment for goods and services? In equilibrium theory, the value of money is generally not determined: the number of equations is one less than the number of unknowns, so only relative prices are determined. In the language of mathematics, the equations are ``homogeneous of order one''. Using the language of physics, this represents a continuous ``Goldstone'' symmetry. However, the continuous symmetry is often broken by the dynamics of the system, thus fixing the value of the otherwise undetermined variable. In economics, the value of money is a strategic variable which each agent must determine at each transaction by estimating the effect of future interactions with other agents. This idea is illustrated by a simple network model of monopolistic vendors and buyers, with bounded rationality. We submit that dynamical, spontaneous symmetry breaking is the fundamental principle for fixing the value of money. Perhaps the continuous symmetry representing the lack of restoring force is also the fundamental reason for large fluctuations in stock markets.Comment: 7 pages, 3 figure

Spatial competition and price formation

We look at price formation in a retail setting, that is, companies set prices, and consumers either accept prices or go someplace else. In contrast to most other models in this context, we use a two-dimensional spatial structure for information transmission, that is, consumers can only learn from nearest neighbors. Many aspects of this can be understood in terms of generalized evolutionary dynamics. In consequence, we first look at spatial competition and cluster formation without price. This leads to establishement size distributions, which we compare to reality. After some theoretical considerations, which at least heuristically explain our simulation results, we finally return to price formation, where we demonstrate that our simple model with nearly no organized planning or rationality on the part of any of the agents indeed leads to an economically plausible price.Comment: Minor change