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This volume features highlights from the DIMACS Special Year on "Mathematical Support for Molecular Biology". Top researchers presented both new research results and comprehensive overviews on the use of mathematics (especially discrete mathematics) and theoretical computer science in molecular biology. The book provides a unique "snapshot" of this growing area of study. It will be of interest to both experts and novices seeking information on the state of the research. ... Read more

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Applying mathematics to biology has a long history, but only recently has there been an explosion of interest in the field. Some reasons for this include: the explosion of data-rich information sets, due to the genomics revolution, which are difficult to understand without the use of analytical tools; recent development of mathematical tools such as chaos theory to help understand complex, non-linear mechanisms in biology; an increase in computing power which enables calculations and simulations to be performed that were not previously possible; and, an increasing interest in in-silico experimentation due to the complications involved in human and animal research. This new book presents the latest leading-edge research in the field. ... Read more

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Mathematical Modeling for Society and Biology engagingly relates mathematics to compelling real-life problems in biology and contemporary society. It shows how mathematical tools can be used to gain insight into these modern, common problems to provide effective, real solutions.

Beltrami's creative, non-threatening approach draws on a wealth of interesting examples pertaining to current social and biological issues. Central ideas appear again in different contexts throughout the book, showing the general unity of the modeling process. The models are strikingly novel and based on issues of real concern. Most have never appeared in book form. Through the relevance of these models mathematics becomes not just figures and numbers, but a means to a more refined understanding of the world. ... Read more

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Whole new areas of immunological research are emerging from the analysis of experimental data, going beyond statistics and parameter estimation into what an applied mathematician would recognise as modelling of dynamical systems. Stochastic methods are increasingly important, because stochastic models are closer to the Brownian reality of the cellular and sub-cellular world. ... Read more

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The haploid-diploid alternation of generation is among the most fundamental features of eukaryotic life. Until recently, however, little research had been done on the origin and evolution of this genetic system. Bringing together for the first time emerging empirical and theoretical perspectives on this topic, this volume contains the proceedings of the 1993 Symposium on Some Mathematical Questions in Biology: The Evolution of Haploid-Diploid Life Cycles, held in June 1993 in Snowbird, Utah. The volume opens with a broad survey of life forms which reveals a wide diversity of life cycles, including predominantly haploid cycles, predominantly diploid cycles, and mixed cycles. Mathematical models attempt to explain this diversity in terms of evolutionary forces that include deleterious mutation, advantageous mutation, and ecological selection. A review of the first experimental studies shows how the hypotheses suggested by the models may ultimately be resolved. The book introduces biologists to mathematical approaches to these problems and introduces mathematical biologists to comparative and experimental approaches. Opportunities for future research are highlighted throughout. ... Read more

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Over the past few decades numerous scientists have called for a unification of the fields of embryo development, genetics, and evolution. Each field has glaring holes in its ability to explain the fundamental phenomena of life. In this book, the author shows how the phenomenon of cell differentiation, considered in its temporal and spatial aspects during embryogenesis, provides a starting point for a unified theory of multicellular organisms (plants, fungi and animals), including their evolution and genetics. This unification is based on the recent discovery of differentiation waves by the author and his colleagues, described in the appendices, and illustrated by a flip movie prepared by a medical artist. To help the reader through the many fields covered, a glossary is included.

This book will be of great value to the researcher and practicing doctors/scientists alike. The research students will receive an in-depth tutorial on the topics covered. The seasoned researcher will appreciate the applications and the gold mine of other possibilities for novel research topics. ... Read more

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The present volume contains the contributions of the keynote speakers of the BIOMAT 2007 Symposium, as well as selected contributed papers in the areas of mathematical biology, biological physics, biophysics and bioinformatics. It contains new results on some aspects of Lotka-Volterra equations, the proposal of using differential geometry to model neurosurgical tools, recent data on epidemiological modeling, pattern recognition and comprehensive reviews on the structure of proteins, the folding problem and the influence of Allee effects on population dynamics.This book contains some original results on the growth of gliomas: the role played by membrane channels on activity-dependent modulation of spike transmission; a proposal for reconsidering the concept of gene and the understanding of the mechanisms responsible for gene expression; a differential geometric approach to the influence of the drying effect on the dynamics of pods of Leguminosae; the comparison of agent-based models with the approach of differential equations on the study of selection mechanisms in germinal centers; and, the synchronization phenomenon for protocell systems driven by linear kinetic equations. ... Read more

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Population Genetics of Multiple Loci F. B. Christiansen University of Aarhus, Denmark "This is a very beautiful and powerful study of an area that Christiansen has dominated for many years." - Marcus Feldman, Stanford University, USA Population genetics thrives on the constant interaction between theoretical and empirical knowledge. In the first instance, population genetics was developed using one-locus, two-allele models for genetic variation. The simplicity of these models opened up theoretical developments in population and evolutionary genetics to biologists without specialist training in mathematics. Population genetics of multi-allelic loci is more complex and requires more mathematical insight, and its study is predominantly undertaken by mathematical biologists. Traditional formulations of multi-locus theory do not simplify by assuming two alleles per locus. In this elegant presentation the author provides a formulation of multi-locus population genetics that retains the simplicity of two-allele models.
* Provides an accessible and natural extension of classical population genetics to multiple loci
* Exposes the population genetic aspects of sexual reproduction
* Describes the complexity of evolutionary interactions among genes
* Provides the background for insight into the functioning of genetic algorithms applied in computer science
* Written by a world leader in the field
The book is divided into two main sections. Part I - Recombination and Segregation - includes coverage of random mating, inbreeding, migration and mixing. Part II - Selection - covers numerous phenomena involving natural selection including viability, fertility, mutation and migration. The author has successfully presented the theory in a way that is intelligible to anyone with a reasonably good background in basic mathematics and is devoted to learning multiple loci population genetics. The text is primarily aimed at advanced undergraduate and postgraduate students and researchers interested in genetics and population biology. It is also essential reading for those working or researching in biomathematics and adaptive computing. ... Read more

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This volume contains the contributions of the conference "Partial Differential Equations" in Han-sur-Lesse, Belgium, December 1993. The originally intended Belgian-French meeting developed into a truely international conference, including specialists from Argentina, Germany, Puerto Rico, Russia, Spain, and the USA. The authors was to discuss a variety of important questions in applied sciences, engineering and mathematical physics which lead to deep structures and new challenges to the analysis of partial differential equations. The articles show the complexity of phenomena for a broader readership in non-linear analysis, free boundary value problems, effects from singularities, asymptotics, and stability of solutions. ... Read more