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Lotka-Volterra and Related Systems
In recent years, there has been a tremendous amount of research activity in the general area of population dynamics, particularly the Lotka-Volterra system, which has been a rich source of mathematical ideas from both theoretical and application points of view. In spite of the technological advances, many authors seem to be unaware of the bulk of the work that has been done in this area recently. This often leads to duplication of work and frustration to the authors as well as to the editors of various journals. This book is built out of lecture notes and consists of three chapters written by four mathematicians with overlapping expertise that cover a broad sector of the research in this are...
Fitness Landscape, Red Queen, Evolutionary Enigmas, and Applications to Virology
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One-Locus and Multi-Locus Theory and Recombination
The book will benefit a reader with a background in physical sciences and applied mathematics interested in the mathematical models of genetic evolution. In the first chapter, we analyze several thought experiments based on a basic model of stochastic evolution of a single genomic site in the presence of the factors of random mutation, directional natural selection, and random genetic drift. In the second chapter, we present a more advanced theory for a large number of linked loci. In the third chapter, we include the effect of genetic recombination into account and find out the advantage of sexual reproduction for adaptation. These models are useful for the evolution of a broad range of asexual and sexual populations, including virus evolution in a host and a host population.
Singularities of Solutions to Chemotaxis Systems
The Keller-Segel model for chemotaxis is a prototype of nonlocal systems describing concentration phenomena in physics and biology. While the two-dimensional theory is by now quite complete, the questions of global-in-time solvability and blowup characterization are largely open in higher dimensions. In this book, global-in-time solutions are constructed under (nearly) optimal assumptions on initial data and rigorous blowup criteria are derived.
Complexity and Evolution of Dissipative Systems
This book focuses on the dynamic complexity of neural, genetic networks, and reaction diffusion systems. The author shows that all robust attractors can be realized in dynamics of such systems. In particular, a positive solution of the Ruelle-Takens hypothesis for on chaos existence for large class of reaction-diffusion systems is given. The book considers viability problems for such systems - viability under extreme random perturbations - and discusses an interesting hypothesis of M. Gromov and A. Carbone on biological evolution. There appears a connection with the Kolmogorov complexity theory. As applications, transcription-factors-microRNA networks are considered, patterning in biology, a new approach to estimate the computational power of neural and genetic networks, social and economical networks, and a connection with the hard combinatorial problems.
Radiation Risk Estimation
This monograph discusses statistics and risk estimates applied to radiation damage under the presence of measurement errors. The first part covers nonlinear measurement error models, with a particular emphasis on efficiency of regression parameter estimators. In the second part, risk estimation in models with measurement errors is considered. Efficiency of the methods presented is verified using data from radio-epidemiological studies. Contents: Part I - Estimation in regression models with errors in covariates Measurement error models Linear models with classical error Polynomial regression with known variance of classical error Nonlinear and generalized linear models Part II Radiation risk...
