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Author: Nicholas F. Britton
Publisher: Springer Science & Business Media
ISBN: 1447100492
Category : Mathematics
Languages : en
Pages : 347
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Book Description
This self-contained introduction to the fast-growing field of Mathematical Biology is written for students with a mathematical background. It sets the subject in a historical context and guides the reader towards questions of current research interest. A broad range of topics is covered including: Population dynamics, Infectious diseases, Population genetics and evolution, Dispersal, Molecular and cellular biology, Pattern formation, and Cancer modelling. Particular attention is paid to situations where the simple assumptions of homogenity made in early models break down and the process of mathematical modelling is seen in action.
Author: Nicholas F. Britton
Publisher: Springer Science & Business Media
ISBN: 1447100492
Category : Mathematics
Languages : en
Pages : 347
Get Book Here
Book Description
This self-contained introduction to the fast-growing field of Mathematical Biology is written for students with a mathematical background. It sets the subject in a historical context and guides the reader towards questions of current research interest. A broad range of topics is covered including: Population dynamics, Infectious diseases, Population genetics and evolution, Dispersal, Molecular and cellular biology, Pattern formation, and Cancer modelling. Particular attention is paid to situations where the simple assumptions of homogenity made in early models break down and the process of mathematical modelling is seen in action.
Author: Robert J. Rosen
Publisher: Academic Press
ISBN: 1483272133
Category : Science
Languages : en
Pages : 316
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Book Description
Foundations of Mathematical Biology, Volume 1, Subcellular Systems, provides an introduction the place of mathematical biology in relation to the other biological, physical, and organizational sciences. It discusses the use of mathematical tools and techniques to solve biological problems. The book contains four chapters and begins with a discussion of the nature of hierarchical control in living matter. This is followed by a chapter on chemical kinetics and enzyme kinetics, covering the physicomathematical principles, models, and approximations underlying transition-state theory and the unimolecular reaction. Subsequent chapters deal with quantum genetics and membrane excitability.
Author: G. Bard Ermentrout
Publisher: Springer Science & Business Media
ISBN: 0387877088
Category : Mathematics
Languages : en
Pages : 434
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Book Description
This book applies methods from nonlinear dynamics to problems in neuroscience. It uses modern mathematical approaches to understand patterns of neuronal activity seen in experiments and models of neuronal behavior. The intended audience is researchers interested in applying mathematics to important problems in neuroscience, and neuroscientists who would like to understand how to create models, as well as the mathematical and computational methods for analyzing them. The authors take a very broad approach and use many different methods to solve and understand complex models of neurons and circuits. They explain and combine numerical, analytical, dynamical systems and perturbation methods to produce a modern approach to the types of model equations that arise in neuroscience. There are extensive chapters on the role of noise, multiple time scales and spatial interactions in generating complex activity patterns found in experiments. The early chapters require little more than basic calculus and some elementary differential equations and can form the core of a computational neuroscience course. Later chapters can be used as a basis for a graduate class and as a source for current research in mathematical neuroscience. The book contains a large number of illustrations, chapter summaries and hundreds of exercises which are motivated by issues that arise in biology, and involve both computation and analysis. Bard Ermentrout is Professor of Computational Biology and Professor of Mathematics at the University of Pittsburgh. David Terman is Professor of Mathematics at the Ohio State University.
Author: J. David Logan
Publisher: John Wiley & Sons
ISBN: 0470525878
Category : Science
Languages : en
Pages : 437
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Book Description
A one-of-a-kind guide to using deterministic and probabilistic methods for solving problems in the biological sciences Highlighting the growing relevance of quantitative techniques in scientific research, Mathematical Methods in Biology provides an accessible presentation of the broad range of important mathematical methods for solving problems in the biological sciences. The book reveals the growing connections between mathematics and biology through clear explanations and specific, interesting problems from areas such as population dynamics, foraging theory, and life history theory. The authors begin with an introduction and review of mathematical tools that are employed in subsequent chapters, including biological modeling, calculus, differential equations, dimensionless variables, and descriptive statistics. The following chapters examine standard discrete and continuous models using matrix algebra as well as difference and differential equations. Finally, the book outlines probability, statistics, and stochastic methods as well as material on bootstrapping and stochastic differential equations, which is a unique approach that is not offered in other literature on the topic. In order to demonstrate the application of mathematical methods to the biological sciences, the authors provide focused examples from the field of theoretical ecology, which serve as an accessible context for study while also demonstrating mathematical skills that are applicable to many other areas in the life sciences. The book's algorithms are illustrated using MATLAB®, but can also be replicated using other software packages, including R, Mathematica®, and Maple; however, the text does not require any single computer algebra package. Each chapter contains numerous exercises and problems that range in difficulty, from the basic to more challenging, to assist readers with building their problem-solving skills. Selected solutions are included at the back of the book, and a related Web site features supplemental material for further study. Extensively class-tested to ensure an easy-to-follow format, Mathematical Methods in Biology is an excellent book for mathematics and biology courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for researchers and professionals working in the fields of biology, ecology, and biomathematics.
Author: Anthony William Fairbank Edwards
Publisher: Cambridge University Press
ISBN: 9780521775441
Category : Science
Languages : en
Pages : 138
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Book Description
A definitive account of the origins of modern mathematical population genetics, first published in 2000.
Author: Andreas Kremling
Publisher: CRC Press
ISBN: 1466567899
Category : Mathematics
Languages : en
Pages : 382
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Book Description
Drawing on the latest research in the field, Systems Biology: Mathematical Modeling and Model Analysis presents many methods for modeling and analyzing biological systems, in particular cellular systems. It shows how to use predictive mathematical models to acquire and analyze knowledge about cellular systems. It also explores how the models are systematically applied in biotechnology. The first part of the book introduces biological basics, such as metabolism, signaling, gene expression, and control as well as mathematical modeling fundamentals, including deterministic models and thermodynamics. The text also discusses linear regression methods, explains the differences between linear and nonlinear regression, and illustrates how to determine input variables to improve estimation accuracy during experimental design. The second part covers intracellular processes, including enzymatic reactions, polymerization processes, and signal transduction. The author highlights the process–function–behavior sequence in cells and shows how modeling and analysis of signal transduction units play a mediating role between process and function. The third part presents theoretical methods that address the dynamics of subsystems and the behavior near a steady state. It covers techniques for determining different time scales, sensitivity analysis, structural kinetic modeling, and theoretical control engineering aspects, including a method for robust control. It also explores frequent patterns (motifs) in biochemical networks, such as the feed-forward loop in the transcriptional network of E. coli. Moving on to models that describe a large number of individual reactions, the last part looks at how these cellular models are used in biotechnology. The book also explains how graphs can illustrate the link between two components in large networks with several interactions.
Author: Matthias Dehmer
Publisher: John Wiley & Sons
ISBN: 3527339094
Category : Medical
Languages : en
Pages : 298
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Book Description
This latest addition to the successful Network Biology series presents current methods for determining the entropy of networks, making it the first to cover the recently established Quantitative Graph Theory. An excellent international team of editors and contributors provides an up-to-date outlook for the field, covering a broad range of graph entropy-related concepts and methods. The topics range from analyzing mathematical properties of methods right up to applying them in real-life areas. Filling a gap in the contemporary literature this is an invaluable reference for a number of disciplines, including mathematicians, computer scientists, computational biologists, and structural chemists.
Author: Leah Edelstein-Keshet
Publisher: SIAM
ISBN: 9780898719147
Category : Mathematics
Languages : en
Pages : 629
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Book Description
Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community, it shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in this book are still important and informative. Audience: the book does not assume too much background knowledge--essentially some calculus and high-school algebra. It was originally written with third- and fourth-year undergraduate mathematical-biology majors in mind; however, it was picked up by beginning graduate students as well as researchers in math (and some in biology) who wanted to learn about this field.
Author: Robert Rosen
Publisher: Elsevier
ISBN: 1483286274
Category : Science
Languages : en
Pages : 447
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Book Description
The first detailed study of this most important class of systems which contain internal predictive models of themselves and/or of their environments and whose predictions are utilized for purposes of present control. This book develops the basic concept of a predictive model, and shows how it can be embedded into a system of feedforward control. Includes many examples and stresses analogies between wired-in anticipatory control and processes of learning and adaption, at both individual and social levels. Shows how the basic theory of such systems throws a new light both on analytic problems (understanding what is going on in an organism or a social system) and synthetic ones (developing forecasting methods for making individual or collective decisions).
Author: Uri Alon
Publisher: CRC Press
ISBN: 1584886420
Category : Mathematics
Languages : en
Pages : 324
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Book Description
Thorough and accessible, this book presents the design principles of biological systems, and highlights the recurring circuit elements that make up biological networks. It provides a simple mathematical framework which can be used to understand and even design biological circuits. The textavoids specialist terms, focusing instead on several well-studied biological systems that concisely demonstrate key principles. An Introduction to Systems Biology: Design Principles of Biological Circuits builds a solid foundation for the intuitive understanding of general principles. It encourages the reader to ask why a system is designed in a particular way and then proceeds to answer with simplified models.
