Bøger i Interdisciplinary Applied Mathematics serien

This book presents a comprehensive set of methods for quantifying geometric quantities such as the volume of a tumor, the total surface area of the alveoli in a lung, the length of plant roots, or of blood vessels, the number of neurons in a brain compartment, the connectivity number of trabecular bone, the mean size of grains in a rock, etc.. The methods, illustrated by twenty solved case studies, are based on properly sampled slices, sections, or projections of the material, observable under light, laser, or electron microscopy, or under non-invasive radiological devices such as ecography, computed tomography, or magnetic resonance imaging. Thus, the input usually consists of flat images, and the output consists of relevant quantities defined in three dimensions. Stereology is the discipline of providing sampling designs which warrant unbiased estimation of the corresponding quantities, that is, estimation with zero mean deviation from the target. Sampling is usually systematic (i.e., with regularly spaced probes), and sparse (as opposed to reconstructions) and it is thereby efficient and easy to implement.Stereology is essentially geometric sampling, grounded on integral geometry. The necessary elements of both disciplines are detailed in textbook style, and may be used for postgraduate courses, or to serve the interest of scientists in general. Hitherto no other book on stereology has appeared which encompasses the theory, methodology, and applications of stereology in an interconnected and comprehensive way. The currently available error variance prediction formulae under systematic sampling, and their (non-obvious) derivation, are all gathered, for the first time, in the last chapter. The exposition is augmented by 127 line drawings for the theory, and 27 color pictures of real materials for the case studies.

Stochastic elasticity is a fast developing field that combines nonlinear elasticity and stochastic theories in order to significantly improve model predictions by accounting for uncertainties in the mechanical responses of materials. However, in contrast to the tremendous development of computational methods for large-scale problems, which have been proposed and implemented extensively in recent years, at the fundamental level, there is very little understanding of the uncertainties in the behaviour of elastic materials under large strains.Based on the idea that every large-scale problem starts as a small-scale data problem, this book combines fundamental aspects of finite (large-strain) elasticity and probability theories, which are prerequisites for the quantification of uncertainties in the elastic responses of soft materials. The problems treated in this book are drawn from the analytical continuum mechanics literature and incorporate random variables as basic concepts along with mechanical stresses and strains. Such problems are interesting in their own right but they are also meant to inspire further thinking about how stochastic extensions can be formulated before they can be applied to more complex physical systems.

This book develops the theory of continuous and discrete stochastic processes within the context of cell biology. In the second edition the material has been significantly expanded, particularly within the context of nonequilibrium and self-organizing systems. Given the amount of additional material, the book has been divided into two volumes, with volume I mainly covering molecular processes and volume II focusing on cellular processes. A wide range of biological topics are covered in the new edition, including stochastic ion channels and excitable systems, molecular motors, stochastic gene networks, genetic switches and oscillators, epigenetics, normal and anomalous diffusion in complex cellular environments, stochastically-gated diffusion, active intracellular transport, signal transduction, cell sensing, bacterial chemotaxis, intracellular pattern formation, cell polarization, cell mechanics, biological polymers and membranes, nuclear structure and dynamics, biological condensates, molecular aggregation and nucleation, cellular length control, cell mitosis, cell motility, cell adhesion, cytoneme-based morphogenesis, bacterial growth, and quorum sensing. The book also provides a pedagogical introduction to the theory of stochastic and nonequilibrium processes - Fokker Planck equations, stochastic differential equations, stochastic calculus, master equations and jump Markov processes, birth-death processes, Poisson processes, first passage time problems, stochastic hybrid systems, queuing and renewal theory, narrow capture and escape, extreme statistics, search processes and stochastic resetting, exclusion processes, WKB methods, large deviation theory, path integrals, martingales and branching processes, numerical methods, linear response theory, phase separation, fluctuation-dissipation theorems, age-structured models, and statistical field theory. This text is primarily aimed at graduate students and researchers working in mathematical biology, statistical and biological physicists, and applied mathematicians interested in stochastic modeling. Applied probabilists should also find it of interest. It provides significant background material in applied mathematics and statistical physics, and introduces concepts in stochastic and nonequilibrium processes via motivating biological applications. The book is highly illustrated and contains a large number of examples and exercises that further develop the models and ideas in the body of the text. It is based on a course that the author has taught at the University of Utah for many years.

The story of this edition is a testament to an almost legendary gure in theoretical ecology and to the in uence his work and charisma has had on the eld. It is also a story that can only be told by a trip back in time, to the genesis of the First Edition and before. Akira kubo and I were students together, but never knew it at the time. He was a graduate student at The ohns Hopkins niversity, where I was an undergraduate in mathematics. e both studied modern physics, taught by Dino Franco asetti, and we decided years later that we must have been in the same class. Akira was then a chemical oceanographer, but ship time and his stomach did not agree. Sohe turned to theory,and the rest is history. His impact has been phenomenal, and the First Edition of this book was his most in uential work. Building on his famous work with dye-diusion e periments, he turned his attention to organisms and created a unique melding of ideas from physics and biology.

This book provides a theoretical background of branching processes and discusses their biological applications. Branching processes are a well-developed and powerful set of tools in the field of applied probability. The range of applications considered includes molecular biology, cellular biology, human evolution and medicine. The branching processes discussed include Galton-Watson, Markov, Bellman-Harris, Multitype, and General Processes. As an aid to understanding specific examples, two introductory chapters, and two glossaries are included that provide background material in mathematics and in biology. The book will be of interest to scientists who work in quantitative modeling of biological systems, particularly probabilists, mathematical biologists, biostatisticians, cell biologists, molecular biologists, and bioinformaticians. The authors are a mathematician and cell biologist who have collaborated for more than a decade in the field of branching processes in biology for this new edition.This second expanded edition adds new material published during the last decade, with nearly 200 new references. More material has been added on infinitely-dimensional multitype processes, including the infinitely-dimensional linear-fractional case. Hypergeometric function treatment of the special case of the Griffiths-Pakes infinite allele branching process has also been added. There are additional applications of recent molecular processes and connections with systems biology are explored, and a new chapter on genealogies of branching processes and their applications.Reviews of First Edition:"e;This is a significant book on applications of branching processes in biology, and it is highly recommended for those readers who are interested in the application and development of stochastic models, particularly those with interests in cellular and molecular biology."e; (Siam Review, Vol. 45 (2), 2003)"e;This book will be very interesting and useful for mathematicians, statisticians and biologists as well, and especially for researchers developing mathematical methods in biology, medicine and other natural sciences."e; (Short Book Reviews of the ISI, Vol. 23 (2), 2003)

Je tiens impossible de connaitre les parties sans connaitre le tout, non plus que de connaitre le tout sans connaitre particulierement les parties -Pascal The eterna[ mystery of the world is its comprehensibility -Einstein This book deals with the application of mathematical tools to the study of physiological systems. It is directed toward an audience of physiologists, physicians, physicists, kinesiologists, psychologists, engineers, mathemati- cians, and others interested in finding out more about the complexities and subtleties of rhythmic physiological processes from a theoretical per- spective. We have attempted to give a broad view of the underlying notions behind the dynamics of physiological rhythms, sometimes from a theoretical perspective and sometimes from the perspective of the experimentalist. This book can be used in a variety of ways, ranging from a more tra- ditional approach such as a textbook in a biomathematics course (at either the advanced undergraduate or graduate level) to a research re- source in which someone interested in a particular problem might look at the corresponding discussion here to guide their own thinking. We hope that researchers at all levels will find inspiration from the way we have dealt with particular research problems to tackle completely new areas of investigation, or even approach these in totally new ways.

Geometry of Biological Time deals with dynamics of processes that repeat themselves regularly. Such rhythmic return through a cycle of change is an ubiquitous principle of organization in living systems. In this revised and updated edition the author plans to extend the thread from 1980 to the present concentrating on areas which he personally feels have been interesting and where he feels there will be much activity in the future. This involves going through spatial biochemical, electrophysiological, and organismic dynamical systems and patterns that were discovered by pursuing the theme of phase singularities that the original book introduced. In particular the work on excitability in cell membranes has been thoroughly updated as have the references throughout the book.

Describes the chaos apparent in simple mechanical systems with the goal of elucidating the connections between classical and quantum mechanics. It develops the relevant ideas of the last two decades via geometric intuition rather than algebraic manipulation. The historical and cultural background against which these scientific developments have occurred is depicted, and realistic examples are discussed in detail. This book enables entry-level graduate students to tackle fresh problems in this rich field.

This book reviews how mathematics can be used in combination with biological data in order to improve understanding of how the immune system works. This is illustrated largely in the context of viral infections. Mathematical models allow scientists to capture complex biological interactions in a clear mathematical language and to follow them to their precise logical conclusions. This can give rise to counter-intuitive insights which would not be attained by experiments alone, and can be used for the design of further experiments in order to address the mathematical results. This book provides both an introduction to the field of mathematical immunology, and an overview of many topics which are the subject of current research, covering a broad variety of immunological topics. It starts with basic principles of immunology and covers the dynamical interactions between the immune system and specific viral infections, including important human pathogens such as HIV. General biological and mathematical background material to both virus infection and immune system dynamics is provided, and each chapter begins with a simple introduction to the biological questions examined. This book is intended for an interdisciplinary audience. It explains the concept of mathematical modeling in immunology and shows how modeling has been used to address specific questions. It is intended both for the mathematical biologists who are interested in immunology, and for the biological readership that is interested in the use of mathematical models in immunology. Dominik Wodarz is an Associate Professor at the Department of Ecology and Evolutionary Biology at the University of California, Irvine.

Evolutionary Computation for Optimization and Modeling is an introduction to evolutionary computation, a field which includes genetic algorithms, evolutionary programming, evolution strategies, and genetic programming. The text is a survey of some application of evolutionary algorithms. It introduces mutation, crossover, design issues of selection and replacement methods, the issue of populations size, and the question of design of the fitness function. It also includes a methodological material on efficient implementation. Some of the other topics in this book include the design of simple evolutionary algorithms, applications to several types of optimization, evolutionary robotics, simple evolutionary neural computation, and several types of automatic programming including genetic programming. The book gives applications to biology and bioinformatics and introduces a number of tools that can be used in biological modeling, including evolutionary game theory. Advanced techniques such as cellular encoding, grammar based encoding, and graph based evolutionary algorithms are also covered. This book presents a large number of homework problems, projects, and experiments, with a goal of illustrating single aspects of evolutionary computation and comparing different methods. Its readership is intended for an undergraduate or first-year graduate course in evolutionary computation for computer science, engineering, or other computational science students. Engineering, computer science, and applied math students will find this book a useful guide to using evolutionary algorithms as a problem solving tool.

This book introduces advanced mathematical methods and techniques for analysis and simulation of models in mathematical epidemiology.

This text addresses systems with persistent memory that are common mathematical models used in the study of viscoelasticity and thermodynamics with memory.

This monograph explores the application of the potential method to three-dimensional problems of the mathematical theories of elasticity and thermoelasticity for multi-porosity materials.

This book is the first thorough introduction to and comprehensive treatment of the theory and applications of integrodifference equations in spatial ecology. The book contains step-by-step model construction, explicitly solvable models, abstract theory and numerical recipes for integrodifference equations.

This book builds inviscid flow analysis from an undergraduate-level treatment of potential flow to the level required for research.

This book provides a comprehensive presentation of classical and advanced topics in estimation and control of dynamical systems with an emphasis on stochastic control.

The state of the art in Biopharmaceutics, Pharmacokinetics, and Pharmacodynamics Modeling is presented in this new second edition book. This second edition has new information on reaction limited models of dissolution, non binary biopharmaceutic classification system, time varying models, and interface models.

Emphasizing kinematics and mechanics of growth, this book presents the state of knowledge in morpho-elasticity, providing a rigorous foundation and offering a set of mathematical tools for the analysis of specific problems arising in biology.

This book investigates the mathematical analysis of biological invasions. While based on the theory of dynamical systems, including partial differential equations and integrodifference equations, the book also draws on information theory, machine learning, Monte Carlo methods, optimal control, statistics, and stochastic processes.

An Accelerated Course with Applications in Computational Sciences and Engineering

This book presents applications of geometric optimal control to real life biomedical problems with an emphasis on cancer treatments.

This book offers a new method for studying hybrid models: Generalized Principal Component Analysis. Coverage includes statistical, geometric and algebraic concepts associated with estimation and segmentation of hybrid models, especially hybrid linear models.