Title | Biological Growth and Spread [electronic resource] : Mathematical Theories and Applications, Proceedings of a Conference Held at Heidelberg, July 16 - 21, 1979 / edited by Willi Jรคger, Hermann Rost, Petre Tautu |
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Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1980 |
Connect to | http://dx.doi.org/10.1007/978-3-642-61850-5 |
Descript | XI, 511 p. 4 illus. online resource |
Topic I. Proliferation, Spread and Reaction-Dispersal Processes -- Discussion by the Editors -- Ia. Biological Aspects -- Genetic basis of biological growth -- Some observations on the kinetics of haemopoietic stem cells and their relationship to the spatial cellular organisation of the tissue -- Proliferative cell populations in surface epithelia: biological models for cell replacement -- Ib. Mathematical Aspects and Applications -- Density dependent Markov population processes -- A model of development of a cell -- Spatial spread in branching processes -- Pattern formation by bacteria -- Random processes in random environments -- Segregation model and its applications -- Positive recurrence of multi-dimensional population-dependent branching processes -- Population growth with large random fluctuations -- Niche overlap and invasion of competitors in random environments.II. The effects of demographic stochasticity -- Behavior of limiting diffusions for density-dependent branching processes -- Topic II. Random Systems with Locally Interacting Objects -- Discussion by the Editors -- IIa. Theory -- Local interactions with a global signal: a voter model -- Interacting Markov processes -- On a class of branching processes on a lattice with interactions -- IIb. Models -- The asymptotic behavior of a probabilistic model for tumor growth -- An Ising model of a neural network -- Embryogenesis through cellular interactions -- Biological interpretation of a random configuration model for carcinogenesis -- Topic III. Spatial Models in Epidemiology and Genetics -- Discussion by the Editors -- On the spatial spread of a pattern -- Spatial models in the epidemiology of infectious diseases -- Population controlled spread and intensity of diseases in wildlife -- Clines in a discrete time model in population genetics -- Clines induced by variable migration -- Asymptotic behavior of the solutions of the Fisher equation -- Random walks and probabilities of genetic identity in a tree -- Travelling-front solutions for integrodifferential equations II -- Some mathematical considerations of how to stop the spatial spread of a rabies epidemic -- Some deterministic models for the spread of genetic and other alterations -- Topic IV. Models for Cell Motility -- Discussion by the Editors -- Orientation of cells migrating in a chemotactic gradient -- Theoretical models for the specific adhesion of cells to cells or to surfaces -- Chemotaxis in bacteria: a beginnerโs guide to the literature -- Assessing the Keller-Segel model: how has it fared? -- Modeling chemosensory responses of swimming eukaryotes -- Mathematical model for tissue inflammation: effects of spatial distribution, cell motility, and Chemotaxis -- Mathematical theories of topotaxis -- Topic V. Stochastic Versus Deterministic Approaches -- Discussion by the Editors -- Connections between stochastic and ordinary integral equations -- Relationships between stochastic and deterministic population models -- Remarks on limit theorems for partial differential equations with random coefficients -- Topic VI. Further Mathematical Approaches and Techniques -- Discussion by the Editors -- Topological techniques in reaction-diffusion equations -- Percolation -- Some ergodic theorems for spatial processes -- Percolation models in two and three dimensions