These notes have grown from a series of seminars given at Leeds between 1972 and 1975. They represent an attempt to gather together the different kinds of model which have been proposed to account for the stochastic activity of neurones, and to provide an introduction to this area of mathematical biology. A striking feature of the electrical activity of the nervous system is that it appears stochastic: this is apparent at all levels of recording, ranging from intracellular recordings to the electroencephalogram. The chapters start with fluctuations in membrane potential, proceed through...

When I was asked to help organize an American Association for the Advancement of Science symposium about how mathematical models have con- tributed to biology, I agreed immediately. The subject is of immense importance and wide-spread interest. However, too often it is discussed in biologically sterile environments by "mutual admiration society" groups of "theoreticians", many of whom have never seen, and most of whom have never done, an original scientific experiment with the biolog- ical materials they attempt to describe in abstract (and often prejudiced) terms. The opportunity to address...

These are" notes based on courses in Theoretical Population Genetics given at the University of Texas at Houston during the winter quarter, 1974, and at the University of Wisconsin during the fall semester, 1976. These notes explore problems of population genetics and evolution involving stochastic processes. Biological models and various mathematical techniques are discussed. Special emphasis is given to the diffusion method and an attempt is made to emphasize the underlying unity of various problems based on the Kolmogorov backward equation. A particular effort was made to make the subject...

For two weeks in August, 1975 more than 140 mathematicians and other scientists gathered at the Universite de Sherbrooke. The occasion was the 15th Biennial Seminar of the Canadian Mathematical Congress, entitled Mathematics and the Life Sciences. Participants in this inter- disciplinary gathering included researchers and graduate students in mathematics, seven different areas of biological science, physics, chemistry and medical science. Geographically, those present came from the United States and the United Kingdom as well as from academic departments and government agencies scattered...

The present volume constitutes the proceedings of the ymposium: Measur- ing Selection in Natural Populations, held in memory of late professor Ove Frydenberg. The Symposium took place in Sandbjerg Manor House in Southern Jutland May 10-14, 1976. The purpose of the symposium was to reflect contemporary research on the mechanisms of biological evolu- tion. The arrangement of the symposium was possible only with the assis- tance and work of many other people. Professor Ole Barndorff-Nielsen took an active part in the planning and arrangement of the symposium. Our gratitude is also due to Ellen...

These notes are, for the most part, the result of a course I taught at the University of Arizona during the Spring of 1977. Their main purpose is to inves- tigate the effect that delays (of Volterra integral type) have when placed in the differential models of mathematical ecology, as far as stability of equilibria and the nature of oscillations of species densities are concerned. A secondary pur- pose of the course out of which they evolved was to give students an (at least elementary) introduction to some mathematical modeling in ecology as well as to some purely mathematical subjects, such...

L'etude morphologique des tissus pathologiques en microscopie d' elements: optique comporte schematiquement deux types 1) les cellules, 2) les Fibres conjonctives intercellulaires. Ces Fibres, qui constituent Ie "squelette mou," servent de support aux elements cellwlaires, contribuent a maintenir l'architecture des tissu, et interviennent dans la circulation des liquides intercellu laires. La quantite, la structure et la repartition de ces Fibres sont etroitement liees a l'activite physiologique des populations cellulaires et a leur pathologie.L'etude de leurs modiFications est tres utile...

Reconstruction from projections has revolutionized radiology and as now become one of the most important tools of medical diagnosi- he E. M. I. Scanner is one example. In this text, some fundamental heoretical and practical questions are resolved. Despite recent research activity in the area, the crucial subject *f the uniqueness of the reconstruction and the effect of noise in the ata posed some unsettled fundamental questions. In particular, Kennan mith proved that if we describe an object by a C~ function, i. e. , nfinitely differentiable with compact support, then there are other bjects...

The E M B 0 course on "Formal Analysis of Genetic Regulation" A course entitled "Formal analysis of Genetic Regulation" was held at the University of Brussels from 6 to 16 September 1977 under the auspices of EMBO (European Molecular Biology Organization). As indicated by the title of the book (but not explicitly enough by the title of the course), the main emphasis was put on a dynamic analysis of systems using logical methods, that is, methods in which functions and variables take only a limited number of values - typically two. In this respect, this course was complementary to an EMBO...

The purpose of this book is to show how mathematics can be applied to improve cancer chemotherapy. Unfortunately, most drugs used in treating cancer kill both normal and abnormal cells. However, more cancer cells than normal cells can be destroyed by the drug because tumor cells usually exhibit different growth kinetics than normal cells. To capitalize on this last fact, cell kinetics must be studied by formulating mathematical models of normal and abnormal cell growth. These models allow the therapeutic and harmful effects of cancer drugs to be simulated quantitatively. The combined cell and...