This 121st IMA volume, entitled MATHEMATICAL MODELS FOR BIOLOGICAL PATTERN FORMATION is the first of a new series called FRONTIERS IN APPLICATION OF MATHEMATICS. The FRONTIERS volumes are motivated by IMA pro grams and workshops, but are specially planned and written to provide an entree to and assessment of exciting new areas for the application of mathematical tools and analysis. The emphasis in FRONTIERS volumes is on surveys, exposition and outlook, to attract more mathematicians and other scientists to the study of these areas and to focus efforts on the most important issues, rather than papers on the most recent research results aimed at an audience of specialists. The present volume of peer-reviewed papers grew out of the 1998-99 IMA program on "Mathematics in Biology," in particular the Fall 1998 em phasis on "Theoretical Problems in Developmental Biology and Immunol ogy." During that period there were two workshops on Pattern Formation and Morphogenesis, organized by Professors Murray, Maini and Othmer. James Murray was one of the principal organizers for the entire year pro gram. I am very grateful to James Murray for providing an introduction, and to Philip Maini and Hans Othmer for their excellent work in planning and preparing this first FRONTIERS volume. I also take this opportunity to thank the National Science Foundation, whose financial support of the IMA made the Mathematics in Biology pro gram possible.
The parsimonious universe. New York: Springer. His, W. (1874). Unsere K ̈orperform und das physiologische Problem ihrer Entstehung. Leipzig: Vogel. Hlatky, L., R. K. Sachs, and E. L. Alpen (1988). Joint oxygen-glucose deprivation as the ...
This text explores the use of cellular automata in modeling pattern formation in biological systems.
Lastly, the volume shows how a combination of new discoveries in developmental biology and associated mathematical modeling and computational techniques has stimulated or may stimulate relevant advances in the field.
This book provides the most valuable and updated research on computational and mathematical models in biological systems from influential researchers around the world and contributes to the development of future research guidelines in this ...
If it is nondegenerate at all singularities, it is called a Morse function. There is then a key theorem that says: There is a Morse function lying arbitrarily close to any function with any number of degenerate singularities.
For those who are working in the above areas, it provides information from most of the recent works. The text presents all the fundamental concepts and mathematical skills needed to build models and perform analyses.
B.N. Nagorcka and J.R. Mooney. The role of a reaction-diffusion system in the formation of hair fibres. J. Theor. Biol., 98:575–607, 1982. B.N. Nagorcka and J.R. Mooney. The role of a reaction-diffusion system in the initiation of ...
This book focuses on the spatio-temporal patterns generated by two classes of mathematical models (of hyperbolic and kinetic types) that have been increasingly used in the past several years to describe various biological and ecological ...
Mathematical Aspects of Pattern Formation in Biological Systems will be of interest to graduate students and researchers who are active in reaction-diffusion systems, pattern formation and mathematical biology.
This book describes the shape formation of living organisms using mathematical models.