Ebook: Stochastic Methods in Biology: Proceedings of a Workshop held in Nagoya, Japan July 8–12 1985

The use of probabilistic methods in the biological sciences has been so well established by now that mathematical biology is regarded by many as a distinct dis­ cipline with its own repertoire of techniques. The purpose of the Workshop on sto­ chastic methods in biology held at Nagoya University during the week of July 8-12, 1985, was to enable biologists and probabilists from Japan and the U. S. to discuss the latest developments in their respective fields and to exchange ideas on the ap­ plicability of the more recent developments in stochastic process theory to problems in biology. Eighteen papers were presented at the Workshop and have been grouped under the following headings: I. Population genetics (five papers) II. Measure valued diffusion processes related to population genetics (three papers) III. Neurophysiology (two papers) IV. Fluctuation in living cells (two papers) V. Mathematical methods related to other problems in biology, epidemiology, population dynamics, etc. (six papers) An important feature of the Workshop and one of the reasons for organizing it has been the fact that the theory of stochastic differential equations (SDE's) has found a rich source of new problems in the fields of population genetics and neuro­ biology. This is especially so for the relatively new and growing area of infinite dimensional, i. e. , measure-valued or distribution-valued SDE's. The papers in II and III and some of the papers in the remaining categories represent these areas.

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This proceedings volume collects a selection of the research and/or survey papers presented at a workshop by biologists and probabilists, and thus provides an account of the latest developments in their respective fields, with particular emphasis on population genetics, neurophysiology and stochastic and other mathematical methods.

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This proceedings volume collects a selection of the research and/or survey papers presented at a workshop by biologists and probabilists, and thus provides an account of the latest developments in their respective fields, with particular emphasis on population genetics, neurophysiology and stochastic and other mathematical methods.
Content:
Front Matter....Pages I-VI
Front Matter....Pages 1-1
A Stochastic Model of Compensatory Neutral Evolution....Pages 2-18
Some Models for Treating Evolution of Multigene Families and Other Repetitive DNA Sequences....Pages 19-26
A Genealogical Description of the Infinitely-Many Neutral Alleles Model....Pages 27-35
Equilibrium Measures of the Stepping Stone Model with Selection in Population Genetics....Pages 36-52
Asymptotic Properties for Kimura’s Diffusion Model with Altruistic Allele....Pages 53-70
Front Matter....Pages 71-71
The Infinitely-Many-Alleles Model with Selection as a Measure-Valued Diffusion....Pages 72-86
Multi-Allelic Gillespie-Sato Diffusion Models and their Extension to Infinite Allelic Ones....Pages 87-99
Stationary Distribution of a Diffusion Process Taking Values in Probability Distributions on the Partitions....Pages 100-114
Front Matter....Pages 115-115
Weak Convergence of Stochastic Neuronal Models....Pages 116-145
Note on the Ornstein-Uhlenbeck Process Model for Stochastic Activity of a Single Neuron....Pages 146-156
Front Matter....Pages 157-157
Fluctuation in Living Cells: Effect of Field Fluctuation and Asymmetry of Fluctuation....Pages 158-170
Some Aspects of Oosawa’s Equation....Pages 171-173
Front Matter....Pages 175-175
Problems of Epidemic Modelling....Pages 176-184
Markov Semigroups Associated with One-Dimensional Levy Operators — Regularity and Convergence —....Pages 185-193
On Some Conditions for Diffusion Processes to Stay on the Boundary of a Domain....Pages 194-201
The point interaction approximation for diffusion in regions with many small holes....Pages 202-209
Unimodality and Bounds of Modes for Distributions of Generalized Sojourn Times....Pages 210-221
Fluctuation in Population Dynamics....Pages 222-229
Back Matter....Pages 230-233

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This proceedings volume collects a selection of the research and/or survey papers presented at a workshop by biologists and probabilists, and thus provides an account of the latest developments in their respective fields, with particular emphasis on population genetics, neurophysiology and stochastic and other mathematical methods.
Content:
Front Matter....Pages I-VI
Front Matter....Pages 1-1
A Stochastic Model of Compensatory Neutral Evolution....Pages 2-18
Some Models for Treating Evolution of Multigene Families and Other Repetitive DNA Sequences....Pages 19-26
A Genealogical Description of the Infinitely-Many Neutral Alleles Model....Pages 27-35
Equilibrium Measures of the Stepping Stone Model with Selection in Population Genetics....Pages 36-52
Asymptotic Properties for Kimura’s Diffusion Model with Altruistic Allele....Pages 53-70
Front Matter....Pages 71-71
The Infinitely-Many-Alleles Model with Selection as a Measure-Valued Diffusion....Pages 72-86
Multi-Allelic Gillespie-Sato Diffusion Models and their Extension to Infinite Allelic Ones....Pages 87-99
Stationary Distribution of a Diffusion Process Taking Values in Probability Distributions on the Partitions....Pages 100-114
Front Matter....Pages 115-115
Weak Convergence of Stochastic Neuronal Models....Pages 116-145
Note on the Ornstein-Uhlenbeck Process Model for Stochastic Activity of a Single Neuron....Pages 146-156
Front Matter....Pages 157-157
Fluctuation in Living Cells: Effect of Field Fluctuation and Asymmetry of Fluctuation....Pages 158-170
Some Aspects of Oosawa’s Equation....Pages 171-173
Front Matter....Pages 175-175
Problems of Epidemic Modelling....Pages 176-184
Markov Semigroups Associated with One-Dimensional Levy Operators — Regularity and Convergence —....Pages 185-193
On Some Conditions for Diffusion Processes to Stay on the Boundary of a Domain....Pages 194-201
The point interaction approximation for diffusion in regions with many small holes....Pages 202-209
Unimodality and Bounds of Modes for Distributions of Generalized Sojourn Times....Pages 210-221
Fluctuation in Population Dynamics....Pages 222-229
Back Matter....Pages 230-233
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