The differential equations which model the action of selection and recombination are nonlinear equations which are impossible to It is even difficult to describe in general the solve explicitly. Recently, Shahshahani began using qualitative behavior of solutions. differential geometry to study these equations 28]. with this mono graph I hope to show that his ideas illuminate many aspects of pop ulation genetics. Among these are his proof and clarification of Fisher's Fundamental Theorem of Natural Selection and Kimura's Maximum Principle and also the effect of recombination on entropy. We...
The differential equations which model the action of selection and recombination are nonlinear equations which are impossible to It is even difficult ...
A rich and abundant literature has developed during the last half century dealing with mechanical aspects of the eye, mainly from clinical and, experimental points of view. For the most part, workers have attempted to shed light on the complex set of conditions known by the general term glaucoma. These conditions are characterised by an increase in intraocular pressure sufficient to cause de- generation of the optic disc and concomitant defects in the visual field, which, if not controlled, lead to inevitable permanent blindness. In the United States alone, an estimated 50,000 persons are...
A rich and abundant literature has developed during the last half century dealing with mechanical aspects of the eye, mainly from clinical and, experi...
As society becomes stressed by economic and population pressures, in turn, nature's renewable resources become stressed by harvesting pressures. For our own survival and euphoria, it is paramount that such resources remain as their name implies and not be driven to extinction through short term programs of over exploitation. Consideration of the harvesting of renewable resources leads to a simple question that was the theme of the workshop and is the focus of these proceedings: SUPPoRe you are assigned the role of manager for a specific renewable resource eco- system. How would you decide on...
As society becomes stressed by economic and population pressures, in turn, nature's renewable resources become stressed by harvesting pressures. For o...
The articles of these proceedings arise from a NSF-CBMS regional conference on the mathematical modeling of the hearing process, that was held at Rensselaer Polytechnic Institute in the summer of 1980. To put the a=ticles in perspective, it is best to briefly review the history of suc modeling. It has proceeded, more or less, in three stages. The first was initiated by Herman Helmholtz in the 1880's, whose theories dominated the subject for years. However, because of his lack of accurate experimental data and his heuristic arguments it became apparent that his models needed revision....
The articles of these proceedings arise from a NSF-CBMS regional conference on the mathematical modeling of the hearing process, that was held at Rens...
The human brain, wi th its hundred billion or more neurons, is both one of the most complex systems known to man and one of the most important. The last decade has seen an explosion of experimental research on the brain, but little theory of neural networks beyond the study of electrical properties of membranes and small neural circuits. Nonetheless, a number of workers in Japan, the United States and elsewhere have begun to contribute to a theory which provides techniques of mathematical analysis and computer simulation to explore properties of neural systems containing immense numbers of...
The human brain, wi th its hundred billion or more neurons, is both one of the most complex systems known to man and one of the most important. The la...
These notes are in part based on a course for advanced students in the applications of stochastic processes held in 1978 at the University of Konstanz. These notes contain the results of re- cent studies on the stochastic description of ion transport through biological membranes. In particular, they serve as an introduction to an unified theory of fluctuations in complex biological transport systems. We emphasize that the subject of this volume is not to introduce the mathematics of stochastic processes but to present a field of theoretical biophysics in which stochastic methods are...
These notes are in part based on a course for advanced students in the applications of stochastic processes held in 1978 at the University of Konstanz...
These lectures were prepared by the authors for Seminars to be held on June 6, 1983, in St.Louis, Missouri, under the spon- sorship of the Radiopharmaceutical Science Council of the So- ciety of Nuclear Medicine . All manuscript? were refereed . Tracer kinetics and the modeling of physiological and bio- chemical processes in vivo are the focus of a contemporary di- rection in biochemical research. Recent advances in instrumen- tation (especially positron emission tomography and digital autoradiography) and parallel developments in the production of short-lived radionuclides and rapid...
These lectures were prepared by the authors for Seminars to be held on June 6, 1983, in St.Louis, Missouri, under the spon- sorship of the Radiopharma...
This monograph is concerned with mathematical aspects of compartmental an- alysis. In particular, linear models are closely analyzed since they are fully justifiable as an investigative tool in tracer experiments. The objective of the monograph is to bring the reader up to date on some of the current mathematical prob- lems of interest in compartmental analysis. This is accomplished by reviewing mathematical developments in the literature, especially over the last 10-15 years, and by presenting some new thoughts and directions for future mathematical research. These notes started as a series...
This monograph is concerned with mathematical aspects of compartmental an- alysis. In particular, linear models are closely analyzed since they are fu...
