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 central problem of control theory is the so called constrained maximization (which-- with slight modifications--is equivalent to minimization). One can then say, heuristically, that the major problem of control theory is to find the maximum of some performance criterion (or criteria), given a set of constraints. The starting point is, of course, a mathematical representation of the performance criterion (or criteria)-- sometimes...

The book develops a model for stem cell proliferation and differentiation. It is a substantial generalization of the famous Till and McCulloch model. It describes the growth of stem cells in culture and the formation of both progenitor cells and end cells. The book contains a biologically realistic application of branching processes and should be of interest to mathematics students and teachers of stochastic process courses.

During the last decade and a half, studies of evolution and variation have been revolutionized by the introduction of the methods and concepts of molecular genetics. We can now construct reliable phylogenetic trees, even when fossil records are missing, by compara- tive studies of protein or mRNA sequences. If, in addition, paleon- tological information is available, we can estimate the rate at which genes are substituted in the species in the course of evolution. Through the application of electrophoretic methods, it has become possible to study intraspecific variation in molecular terms. We...

This volume collects the contributions presented at the "Working Conference on System Theory in Immunology", held in Rome, May 1978. The aim of the Conference was to bring together immunologists on one side and experts in system theory and applied mathematics on the other, in order to identify problems of common interest and to establish a network of joint effort toward their solution. The methodologies of system theory for processing experimental data and for describing dynamical phenomena could indeed contribute significantly to the under- standing of basic immunological facts. Conversely,...

This volume contains the Proceedings of the International Conference in Population Biology held at The University of Alberta, Edmonton, Canada from June 22 to June 30, 1982. The Conference was sponsored by The University of Alberta and The Canadian Applied Mathematics Society, and overlapped with the summer meeting of CAMS. The main objectives of this Conference were: to bring mathematicians and biologists together so that they may interact for their mutual benefit; to bring those researchers interested in modelling in ecology and those interested in modelling in genetics together; to bring...

The contents of this volume involve selection, emendation and up-dating of papers presented at the NATO Conference "Mathe- matical Analysis of Decision problems in Ecology" in Istanbul, Turkey, July 9-13, 1973. It was sponsored by the System Sciences Division of NATO directed by Dr. B. Bayraktar with local arrange- ments administered by Dr. Ilhami Karayalcin, professor of the Department of Industrial Engineering at the Technical University of Istanbul. It was organized by A. Charnes, University professor across the University of Texas System, and Walter R.Lynn, Di- rector of the School of...

These notes are based on (i) a series of lectures that I gave at the 14th Biennial Seminar of the Canadian Mathematical Congress held at the University of Western Ontario August 12-24, 1973 and (li) some of my lectures in a modeling course that I have cotaught in the Division of Bio-Medical Sciences at Brown during the past several years. An earlier version of these notes appeared in the Center for Dynamical Systems Lectures Notes series (CDS LN 73-1, November 1973). I have in this revised and extended version of those earlier notes incorporated a number of changes based both on classroom...

Stochastic processes often pose the difficulty that, as soon as a model devi- ates from the simplest kinds of assumptions, the differential equations obtained for the density and the generating functions become mathematically formidable. Worse still, one is very often led to equations which have no known solution and don't yield to standard analytical methods for differential equations. In the model considered here, one for tumor growth with an immunological re- sponse from the normal tissue, a nonlinear term in the transition probability for the death of a tumor cell leads to the...

In 1958 B. P. Belousov discovered that the oxidation of citric acid by bromate in the presence of cerium ions does not proceed to equilibrium methodically and uniformly, like most chemical reactions, but rather oscillates with clocklike precision between a yellow and colorless state. See Fig. 11. 1, p. 30. A. M. Zhabotinskii followed up on Belousov's original observation and in 1964 his first investigations appeared in the Russian journal Biofizika. Though H. Degn (in Copenhagen at the time) knew of Zhabotinskii's work and published his own account of the mechanism of oscillation in Nature...

On March 8/9, 1976 a workshop on Mathematical Models in Medicine was held at Mainz (German Federal Republic) by the group of Mathe- matical Models of the Deutsche Gesellschaft fUr Medizinische Doku- mentation, Informatik und Statistik. Purpose of this conference was to bring together experts from the GFR and neighbouring countries working in this field to evaluate possibilities and limits of this area of research in discussions with interested participants. This issue of Lecture Notes contains the invited contributions as well as the relevan remarks made by the discussants. Corresponding to...