It is the objective of Science to formalize the relationships between observed quantities. The motivations of such a modelling procedure are varied, but can rougnly be collected around two pOles. If one is concerned with process control, one wants to find a model which wl11 De aDle to predlct tne process Denavlor, taKlng lnto account tne applled lnputs. The model will then be evaluated on it5 ability to mimic the ob5e ved input-output behavior under c: onditione; ae; vari"d ae; p

These notes are based on a one-quarter course given at the Department of Biophysics and Theoretical Biology of the University of Chicago in 1916. The course was directed to graduate students in the Division of Biological Sciences with interests in population biology and neurobiology. Only a slight acquaintance with probability and differential equations is required of the reader. Exercises are interwoven with the text to encourage the reader to play a more active role and thus facilitate his digestion of the material. One aim of these notes is to provide a heuristic approach, using as little...

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This volume contains most of the talks presented at the Journ es de la Soci t Math ma ique de France entitled Rhythms in Biology and other fields of application -Determi- nistic and Stochastic Approaches held in Luminy from the 14th th to the 18 of September 1981. The aim of our meeting was to bring together scien- tists from different disciplines to discuss a common topic and to stimulate exchanges between participants. We hope that this goal was reached. This volume is divided into four chapters. In each one the papers are arranged in alphabetical order by first author. Chapters one and two...

Most of these notes were presented as part of a two-quarter course on theoretical population genetics at The University of Chicago. Almost all the students were either undergraduates in mathematics or graduate students in the biological sciences. The only prerequisites were calculus and matrices. As is done in these notes, biological background and additional mathematical techniques were covered when they were required. I have included the relevant problems assigned in the course. My aim in these notes is to formulate the various models fairly generally, making the biological assumptions...

Written for all those researching the epidemiology of AIDS, this study describes the results of a project which used mathematical modelling and computer simulation to analyze HIV transmission dynamics and the spread of AIDS amongst various groups at risk in the USA.

Aggregation processes are studied within a number of different fields--c- loid chemistry, atmospheric physics, astrophysics, polymer science, and biology, to name only a few. Aggregation pro ces ses involve monomer units (e. g., biological cells, liquid or colloidal droplets, latex beads, molecules, or even stars) that join together to form polymers or aggregates. A quantitative theory of aggre- tion was first formulated in 1916 by Smoluchowski who proposed that the time e- lution of the aggregate size distribution is governed by the infinite system of differential equations: (1) K . . c. c....

In many biological models it is necessary to allow the rates of change of the variables to depend on the past history, rather than only the current values, of the variables. The models may require discrete lags, with the use of delay-differential equations, or distributed lags, with the use of integro-differential equations. In these lecture notes I discuss the reasons for including lags, especially distributed lags, in biological models. These reasons may be inherent in the system studied, or may be the result of simplifying assumptions made in the model used. I examine some of the...

The purpose of these notes is to give a rather complete presentation of the mathematical theory of algebras in genetics and to discuss in detail many applications to concrete genetic situations. Historically, the subject has its origin in several papers of Etherington in 1939- 1941. Fundamental contributions have been given by Schafer, Gonshor, Holgate, Reiers l, Heuch, and Abraham. At the moment there exist about forty papers in this field, one survey article by Monique Bertrand from 1966 based on four papers of Etherington, a paper by Schafer and Gonshor's first paper. Furthermore Ballonoff...