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This volume contains the proceedings of a meeting entitled 'Nonlinear Oscillations in Biology and Chemistry', which was held at the University of Utah May 9-11,1985. The papers fall into four major categories: (i) those that deal with biological problems, particularly problems arising in cell biology, (ii) those that deal with chemical systems, (iii) those that treat problems which arise in neurophysiology, and (iv), those whose primary emphasis is on more general models and the mathematical techniques involved in their analysis. Except for the paper by Auchmuty, all are based on talks given at the meeting. The diversity of papers gives some indication of the scope of the meeting, but the printed word conveys neither the degree of interaction between the participants nor the intellectual sparks generated by that interaction. The meeting was made possible by the financial support of the Department of Mathe- matics of the University of Utah. I am indebted to Ms. Toni Bunker of the Department of Mathematics for her very able assistance on all manner of details associated with the organization of the meeting. Finally, a word of thanks to all participants for their con- tributions to the success of the meeting, and to the contributors to this volume for their efforts in preparing their manuscripts.

Underlying virtually all of these studies are models of population growth, from individual cells to large vertebrates. In Part I of this volume, Michael Shuler describes computer models of individual cells and cell populations, and Frank Hoppensteadt discusses the synchronization of bacterial culture growth.

Modeling and analyzing the dynamics of chemical mixtures by means of differ- tial equations is one of the prime concerns of chemical engineering theorists. for example, the electric potential of a membrane can diffuse like a chemical, and of course can interact with real chemical species (ions) which are transported through the membrane.

From a mathematical point of view, physiologically structured population models are an underdeveloped branch of the theory of infinite dimensional dynamical systems.

This collection of papers gives a representative cross-selectional view of recent developments in the field. Lefevre, 17 other research papers look at stochastic modeling of epidemics, both from a theoretical and a statistical point of view. Some look more specifically at a particular disease such as AIDS, malaria, schistosomiasis and diabetes.

We are also enabling readers not sufficiently familiar with Italian to acquire enough of a background to properly follow the works in French not presented here by including Volterra's "Variazioni e fluttuazioni del numero d' indi vidui in specie animali convi venti" (1927), still available.

These Notes grew from my research in evolutionary biology, specifically on the theory of evolutionarily stable strategies (ESS theory), over the past ten years. Although the restricted topics I have chosen for this text reflect my own research bias, I am confident they will remain the theoretical basis of ESS theory.

The 18 research articles of this volume discuss the major themes that have emerged from mathematical and statistical research in the epidemiology of HIV. Five sections follow: Statistical Methodology and Forecasting, Infectivity and the HIV, Heterogeneity and HIV Transmission Dynamics, Social Dynamics and AIDS, and The Immune System and The HIV.

How weIl can we model experimental observations of the peripheral auditory system'? It was with these questions in mind that we organized the 1985 Mechanics of Hearing Workshop, to bring together auditory researchers to compare models with experimental observations.

The foundations laid by the pioneers of the field during the first half of this century have been combined with advances in ap plied mathematics and the computational sciences to create a vibrant area of scientific research with established research journals, professional societies, deep subspecialty areas, and graduate education programs.

A mathematician who has taken the romantic decision to devote himself to biology will doubtlessly look upon cell kinetics as the most simple and natural field of application for his knowledge and skills.

A new approach, in which the effects of multiple doses on the proliferation kinetics of the tumor in vivo as well as of cell lines in vitro are investigated, has been outlined by Skipper and his co-workers in a series of papers beginning in 1964 (Skipper, Schabel and Wilcox, 1964 and 1965).

Control theory can be roughly classified as deterministic or stochastic. Each of these can further be subdivided into game theory and optimal control theory. The next two papers deal with deterministic optimal control, and the final two deal with applications of game theory to ecological problems.

The mathematical models in this book are concerned with a variety of approaches to the manner in which the clinical radiologic treatment of human neoplasms can be improved. 4 Spatial Distribution of the Radiation Dose 20 Chapter 2 SURVIVAL CURVES FROM STATISTICAL MODELS 24 2. 2 The Target Model 26 2.

Depth Perception in Frogs and Toads provides a comprehensive exploration of the phenomenon of depth perception in frogs and toads, as seen from a neuro-computational point of view.