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Exposing readers to some of today's most exciting and progressive research topics, this diverse compilation of case studies illustrates the unifying role of applied mathematics throughout the biological sciences. Written by leaders in the field, the cases demonstrate how successful modelers have used mathematics to answer real biological questions and takes readers step-by-step through the entire analytical process - question, model formulation, analysis, results, testing, and interpretation.It offers a solid foundation in theoretical biology and unifies mathematical, biological and modeling themes, providing useful tools for thought for future projects.Each section concludes with a project and problems and indicates numerous directions for further research and questions. For researchers new to mathematical biology.

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Emphasizing the search for patterns within and between biological sequences, trees, and graphs, Combinatorial Pattern Matching Algorithms in Computational Biology Using Perl and R shows how combinatorial pattern matching algorithms can solve computational biology problems that arise in the analysis of genomic, transcriptomic, proteomic, metabolomic, and interactomic data. It implements the algorithms in Perl and R, two widely used scripting languages in computational biology.

The book provides a well-rounded explanation of traditional issues as well as an up-to-date account of more recent developments, such as graph similarity and search. It is organized around the specific algorithmic problems that arise when dealing with structures that are commonly found in computational biology, including biological sequences, trees, and graphs. For each of these structures, the author makes a clear distinction between problems that arise in the analysis of one structure and in the comparative analysis of two or more structures. He also presents phylogenetic trees and networks as examples of trees and graphs in computational biology.

This book supplies a comprehensive view of the whole field of combinatorial pattern matching from a computational biology perspective. Along with thorough discussions of each biological problem, it includes detailed algorithmic solutions in pseudo-code, full Perl and R implementation, and pointers to other software, such as those on CPAN and CRAN.

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This book touches upon all major areas in the field of ecologyand covers a wide range of topics. Beginning with classicalmathematical models for population dynamics and their use inpopulation management and harvesting, it covers the traditional aswell as the most recent nonstandard methods of abundance estimation.The recent interest in the study of biodiversity is discussed atlength. The last chapter on models for animal and plant behaviour isperhaps the first attempt to put the two together.

Many exercises, theoretical as well as data analytical, which reflectauthors' interaction with practicing field ecologists, make the bookvery useful for class room teaching and private study.

Audience: This volume is intended as a text book for a onesemester course for advanced undergraduate and graduate classes instatistics, mathematics of biology, or quantitative ecology. ... Read more

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Composed of contributions from an international team of leading researchers, this book pulls together the most recent research results in the field of cancer modeling to provide readers with the most advanced mathematical models of cancer and their applications. The topics included in the book cover oncogenetic trees, stochastic multistage models of carcinogenesis, effects of ionizing radiation on cell cycle and genomic instability, induction of DNA damage by ionizing radiation and its repair, epigenetic cancer models, bystander effects of radiation, multiple pathway models of human colon cancer, and stochastic models of metastasis.The book also provides some important applications of cancer models to the assessment of cancer risk associated with various hazardous environmental agents, to cancer screening by MRI, and to drug resistance in cancer chemotherapy. An updated statistical design and analysis of xenograft experiments as well as a statistical analysis of cancer occult clinical data are also provided.The book will serve as a useful source of reference for researchers in biomathematics, biostatistics and bioinformatics; for clinical investigators and medical doctors employing quantitative methods to develop procedures for cancer diagnosis, prevention, control and treatment; and for graduate students. ... 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. ... Read more

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Mathematical biology is an interdisciplinary area that focuses on the application of mathematics to biology systems. Mathematical biology spans all levels of biological organization and biological function, from the configuration of biological macromolecules to the entire ecosphere over the course of evolutionary time. The International Conference on Mathematical Biology 2007 provides the opportunity to bring together the people, projects and issues from all over the world to share experiences and examine the challenge of applying mathematics to biological problems.

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The second part of this two-volume set contains advanced aspects of the quantitative theory of the dynamics of neurons. It begins with an introduction to the effects of reversal potentials on response to synaptic input. It then develops the theory of action potential generation based on the seminal Hodgkin-Huxley equations and gives methods for their solution in the space-clamped and nonspaceclamped cases. The remainder of the book discusses stochastic models of neural activity and ends with a statistical analysis of neuronal data with emphasis on spike trains. The mathematics is more complex in this volume than in the first volume and involves numerical methods of solution of partial differential equations and the statistical analysis of point processes. ... Read more

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The most mathematically cogent introduction to electrophysiology
Of all the introductory texts on electrophysiology, this one is by far the most mathematically literate.This is a two volume set.Volume 1 covers Nernst Plaank equilibrium equations, integrate and fire neurons, linear cable theory and the Rall model of dendrites.Volume 2 delves into the theory of the action potential - Hodgkin Huxley eqs and the various spinoffs, and some stochastic theory of spontaneous activity. This book was published in 1988, so it predates much of the more recent electrophysiological theory including the zoo of channels and current sources that have been more recently characterized, or the theory of recurrent networks, for example.Also, there are other books - Aidley's Physiology of Excitable Cells, or Kandel and Schwartz - that convey more sense of the underlying biology.But for a mathematically coherent treatment of the bedrock concepts in electrophysiology, nothing else comes close. ... Read more

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This is a lucid introduction to some of the mathematical ideas which are useful to biologists. Professor Maynard Smith introduces the reader to the ways in which biological problems can be expressed mathematically, and shows how the mathematical equations which arise in biological work can be solved. Each chapter has a number of examples which present further points of biological and mathematical interest. interest. Professor Maynard Smith's book is written for all biologists, from undergraduate level upwards, who need mathematical tools. Only an elementary knowledge of mathematics is assumed. Since there are already a number of books dealing with statistics for biologists, this book is particularly concerned with non-statistical topics. ... Read more

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The human brain contains billions of nerve cells whose activity plays a critical role in the way we behave, feel, perceive, and think. This two-volume set explains the basic properties of a neuron--an electrically active nerve cell--and develops mathematical theories for the way neurons respond to the various stimuli they receive. Volume 1 contains descriptions and analyses of the principle mathematical models that have been developed for neurons in the past thirty years. It provides a brief review of the basic neuroanatomical and neurophysiological facts that will form the focus of the mathematical treatment. Tuckwell discusses the mathematical theories, beginning with the theory of membrane potentials. He then goes on to treat the Lapicque model, linear cable theory, and time-dependent solutions of the cable equations. He concludes with a description of Rall's model nerve cell. Because the level of mathematics increases steadily upward from Chapter Two some familiarity with differential equations and linear algebra is desirable. ... Read more

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The most mathematically cogent introduction to electrophysiology
Of all the introductory texts on electrophysiology, this one is by far the most mathematically literate.This is a two volume set.Volume 1 covers Nernst Plaank equilibrium equations, integrate and fire neurons,linear cable theory and the Rall model of dendrites.Volume 2 delves into the theory of the action potential - Hodgkin Huxley eqs and the various spinoffs, and some stochastic theory of spontaneous activity. This book was published in 1988, so it predates much of the more recent electrophysiological theory including the zoo of channels and current sources that have been more recently characterized, or the theory of recurrent networks, for example.Also, there are other books - Aidley's Physiology of Excitable Cells, or Kandel and Schwartz - that convey more sense of the underlying biology.But for a mathematically coherent treatment of the bedrock concepts in electrophysiology, nothing else comes close. ... Read more

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This volume develops a unifying approach to population studies that emphasizes the interplay between modeling and experimentation and that will provide mathematicians and biologists with a framework within which population dynamics can be fully explored and understood. A unique feature of the book is that deterministic and stochastic models are considered together; spatial effects are investigated by developing models that highlight the consequences that geographical restriction and species mobility may have on population development. Model-based simulations of processes are used to explore hitherto unforeseen features and thereby suggest further profitable lines of both experimentation and theoretical study. Most aspects of population dynamics are covered, including birth-death and logistic processes, competition and predator-prey relationships, chaos, reaction time delays, fluctuating environments, spatial systems, velocities of spread, epidemics, and spatial branching structures. ... Read more

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Some fun models
The following is a fairly representative example (Chapter IX). Suppose a society has a population N and countably many income classes. Let's say we wish to impose the wage-structure that maximises incentives and deterrents. Then we would want there to be as many ways as possible to rearrange the population among the wage classes. If we put N_1 people in the first wage class, N_2 in the second, and so on, then the total number of rearrangements R is N!/(N_1! N_2! N_3! ...) Maximising R is the same thing as maximising log(R), and log(R) can be expressed using Stirling's formula log(m!)=mlog(m)-m. It is log(R)=Nlog(N)-Sum(N_n log(N_n)). We could also write w_n for N_n/N, which would give log(R)=-NSum(w_n log(w_n)). At a maximum a small change in the w_n's would not alter log(R), so Sum(log(w_n)dw_n)+Sum(dw_n)=0. Since no one makes no money or infinitely much money, the sum of all the changes in between must be zero, so Sum(dw_n)=0, so we are left with Sum(log(w_n)dw_n)=0. But R needs to be maximised with the restriction that we only have a certain amount of money; i.e., if the wage of the N_n's is x_n, then Sum(N_n x_n)=N(Sum(w_n x_n))=constant, so its derivative is zero, Sum(x_n dw_n)=0. Thus both conditions will be satisfied if log(w_n)+ax_n=constant, or, solving for w_n, w_n=ke^{-ax_n}. Multiplying by N and passing to the continuous case gives N(x)=Nke^{-ax}, i.e. the wealth distribution we sought would be a negative exponential, which fits actual U.S. data quite well (after cutting the function off at x=minimum sustenance). ... Read more

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A multitude of biological phenomena are described at multiple levels. What are the commonalities and differences between neuroscience, evolutionary biology, molecular biology and ecology in this regard? How can mathematics help in describing these phenomena? How can these phenomena inspire new theory? We invited leading scholars from a number of disciplines facing such challenges and from mathematical disciplines potentially able to tackle them.

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This fourth edition of the conference focused mainly on noise and fluctuations at the nanometer scale in electron devices, bio-materials, and mesoscopic systems. Since the first conference, the aim of the UPoN conferences is to provide a forum for researchers working on noise and fluctuations, where they can present and discuss their scientific problems with particular attention to those which resist solutions. Topics include: Theoretical frontiers on noise and fluctuations; experimental frontiers on noise and fluctuations; enhanced and suppressed shot noise; noise and coherence; noise and chaos; constructive role of noise; noise in biological systems; noise in devices; and noise in complex systems and non-Gaussian fluctuations. ... Read more

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This volume contains 13 selected lectures from the International Workshop on Mathematical and Computational Biology subtitled "Computational Morphogenesis, Hierarchical Complexity and Digital Evolution" held at the University of Aizu (Japan). This interdisciplinary workshop brought together researchers working on aspects of evolutionary, mathematical, and computational biology that are of particular interest for computer scientists, biologists, and mathematicians. Discussion topics include mathematical approaches for addressing evolutionary problems (such as replication, multicellularity, individuality, and morphogenesis), the theoretical tools for rigorously developing these questions, software systems and applications.

Of special concern were self-replication, the evolution of individuality, symbiogenesis, evolutionary developmental biology, computational morphogenesis, interaction dynamics, the evolution and maintenance of sex, and properties of the digital genetic code. Lectures are organized roughly according to increase of biological scale in the order of themes presented at the workshop. ... Read more

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This book aims at better understanding of the phyllotaxis phenomenon. The book deals with biological, mathematical, descriptive, causal and systematic phyllotaxis. It aims are reflecting the widest possible range of ideas and research closely related to phyllotaxis. The book has four parts of equal importance. The first three parts concern data collecting, pattern recognition and pattern generation respectively to which students of phyllotaxis are well accustomed. The fourth part is devoted to the problem of origins of phyllotactic patterns, giving the field of phyllotaxis the universality it requires to be fully understood. Phyllotaxis-like patterns are found in places where genes are not necessarily present. Part IV concerns general comparative morphology, homologies with phyllotactic patterns, and recent trends on evolution that can help to understand phyllotaxis.The distinguished researchers who accepted to participate in the production of this book, strongly contributed to the field of phyllotaxis in the past and have devoted a lot of their time to the fascinating subject coming up with most valuable findings, or are newcomers with original ideas that may be very relevant for the future of the field. The book summarizes and updates their contributions, and promotes new avenues in the treatment of phyllotaxis. ... Read more

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As the techniques of modern molecular biology continue to revolutionize experimental design in cell biology, mathematical modeling and analysis become increasingly necessary and feasible. The papers in this collection expand on invited lectures presented at the Symposium on Some Mathematical Questions in Biology: Cell Biology, held in November 1992 in Denver, Colorado. The work reviewed in the papers demonstrates the power of combining mathematics and experiment to study a number of cell processes, including: protein transport in nerve axons, formation of transport vesicles at the Golgi, molecular motion in cell membranes, cell adhesion, $T$ lymphocyte activation, and cellular responses to receptor aggregation. The volume is an important contribution to the literature, as it introduces mathematicians to a growing application area and cell biologists to new tools and results. The individual articles can be used as readings in a course on mathematical modeling. ... Read more