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Game Theoretical Models In Biology

Author : Mark Broom
ISBN : 9781439853221
Genre : Mathematics
File Size : 33.62 MB
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Covering the major topics of evolutionary game theory, Game-Theoretical Models in Biology presents both abstract and practical mathematical models of real biological situations. It discusses the static aspects of game theory in a mathematically rigorous way that is appealing to mathematicians. In addition, the authors explore many applications of game theory to biology, making the text useful to biologists as well. The book describes a wide range of topics in evolutionary games, including matrix games, replicator dynamics, the hawk-dove game, and the prisoner’s dilemma. It covers the evolutionarily stable strategy, a key concept in biological games, and offers in-depth details of the mathematical models. Most chapters illustrate how to use MATLAB® to solve various games. Important biological phenomena, such as the sex ratio of so many species being close to a half, the evolution of cooperative behavior, and the existence of adornments (for example, the peacock’s tail), have been explained using ideas underpinned by game theoretical modeling. Suitable for readers studying and working at the interface of mathematics and the life sciences, this book shows how evolutionary game theory is used in the modeling of these diverse biological phenomena.
Category: Mathematics

Optimal Control Applied To Biological Models

Author : Suzanne Lenhart
ISBN : 9781420011418
Genre : Mathematics
File Size : 46.95 MB
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From economics and business to the biological sciences to physics and engineering, professionals successfully use the powerful mathematical tool of optimal control to make management and strategy decisions. Optimal Control Applied to Biological Models thoroughly develops the mathematical aspects of optimal control theory and provides insight into the application of this theory to biological models. Focusing on mathematical concepts, the book first examines the most basic problem for continuous time ordinary differential equations (ODEs) before discussing more complicated problems, such as variations of the initial conditions, imposed bounds on the control, multiple states and controls, linear dependence on the control, and free terminal time. In addition, the authors introduce the optimal control of discrete systems and of partial differential equations (PDEs). Featuring a user-friendly interface, the book contains fourteen interactive sections of various applications, including immunology and epidemic disease models, management decisions in harvesting, and resource allocation models. It also develops the underlying numerical methods of the applications and includes the MATLAB® codes on which the applications are based. Requiring only basic knowledge of multivariable calculus, simple ODEs, and mathematical models, this text shows how to adjust controls in biological systems in order to achieve proper outcomes.
Category: Mathematics

Stochastic Modelling For Systems Biology Second Edition

Author : Darren J. Wilkinson
ISBN : 9781439837726
Genre : Mathematics
File Size : 34.27 MB
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Since the first edition of Stochastic Modelling for Systems Biology, there have been many interesting developments in the use of "likelihood-free" methods of Bayesian inference for complex stochastic models. Re-written to reflect this modern perspective, this second edition covers everything necessary for a good appreciation of stochastic kinetic modelling of biological networks in the systems biology context. Keeping with the spirit of the first edition, all of the new theory is presented in a very informal and intuitive manner, keeping the text as accessible as possible to the widest possible readership. New in the Second Edition All examples have been updated to Systems Biology Markup Language Level 3 All code relating to simulation, analysis, and inference for stochastic kinetic models has been re-written and re-structured in a more modular way An ancillary website provides links, resources, errata, and up-to-date information on installation and use of the associated R package More background material on the theory of Markov processes and stochastic differential equations, providing more substance for mathematically inclined readers Discussion of some of the more advanced concepts relating to stochastic kinetic models, such as random time change representations, Kolmogorov equations, Fokker-Planck equations and the linear noise approximation Simple modelling of "extrinsic" and "intrinsic" noise An effective introduction to the area of stochastic modelling in computational systems biology, this new edition adds additional mathematical detail and computational methods that will provide a stronger foundation for the development of more advanced courses in stochastic biological modelling.
Category: Mathematics

Systems Biology

Author : Andreas Kremling
ISBN : 9781466567894
Genre : Mathematics
File Size : 20.14 MB
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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.
Category: Mathematics

Quantitative Biology

Author : Michael E. Wall
ISBN : 9781439827222
Genre : Science
File Size : 43.67 MB
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Quantitative methods are revolutionizing modern molecular and cellular biology. Groundbreaking technical advances are fueling the rapid expansion in our ability to observe, as seen in multidisciplinary studies that integrate theory, computation, experimental assays, and the control of microenvironments. Integrating new experimental and theoretical methods, Quantitative Biology: From Molecular to Cellular Systems gives both new and established researchers a solid foundation for starting work in this field. The book is organized into three sections: Fundamental Concepts covers bold ideas that inspire novel approaches in modern quantitative biology. It offers perspectives on evolutionary dynamics, system design principles, chance and memory, and information processing in biology. Methods describes recently developed or improved techniques that are transforming biological research. It covers experimental methods for studying single-molecule biochemistry, small-angle scattering from biomolecules, subcellular localization of proteins, and single-cell behavior. It also describes theoretical methods for synthetic biology and modeling random variations among cells. Molecular and Cellular Systems focuses on specific biological systems where modern quantitative biology methods are making an impact. It incorporates case studies of biological systems for which new concepts or methods are increasing our understanding. Examples include protein kinase at the molecular level, the genetic switch of phage lambda at the regulatory system level, and Escherichia coli chemotaxis at the cellular level. In short, Quantitative Biology presents practical tools for the observation, modeling, design, and manipulation of biological systems from the molecular to the cellular levels.
Category: Science

An Introduction To Systems Biology

Author : Uri Alon
ISBN : 9781584886426
Genre : Mathematics
File Size : 26.95 MB
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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.
Category: Mathematics

Meta Analysis And Combining Information In Genetics And Genomics

Author : Rudy Guerra
ISBN : 9781584885221
Genre : Mathematics
File Size : 37.68 MB
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Novel Techniques for Analyzing and Combining Data from Modern Biological Studies Broadens the Traditional Definition of Meta-Analysis With the diversity of data and meta-data now available, there is increased interest in analyzing multiple studies beyond statistical approaches of formal meta-analysis. Covering an extensive range of quantitative information combination methods, Meta-analysis and Combining Information in Genetics and Genomics looks at how to analyze multiple studies from a broad perspective. After presenting the basic ideas and tools of meta-analysis, the book addresses the combination of similar data types: genotype data from genome-wide linkage scans and data derived from microarray gene expression experiments. The expert contributors show how some data combination problems can arise even within the same basic framework and offer solutions to these problems. They also discuss the combined analysis of different data types, giving readers an opportunity to see data combination approaches in action across a wide variety of genome-scale investigations. As heterogeneous data sets become more common, biological understanding will be significantly aided by jointly analyzing such data using fundamentally sound statistical methodology. This book provides many novel techniques for analyzing data from modern biological studies that involve multiple data sets, either of the same type or multiple data sources.
Category: Mathematics

Introduction To Computational Biology

Author : Michael S. Waterman
ISBN : 9781351437080
Genre : Mathematics
File Size : 53.68 MB
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Biology is in the midst of a era yielding many significant discoveries and promising many more. Unique to this era is the exponential growth in the size of information-packed databases. Inspired by a pressing need to analyze that data, Introduction to Computational Biology explores a new area of expertise that emerged from this fertile field- the combination of biological and information sciences. This introduction describes the mathematical structure of biological data, especially from sequences and chromosomes. After a brief survey of molecular biology, it studies restriction maps of DNA, rough landmark maps of the underlying sequences, and clones and clone maps. It examines problems associated with reading DNA sequences and comparing sequences to finding common patterns. The author then considers that statistics of pattern counts in sequences, RNA secondary structure, and the inference of evolutionary history of related sequences. Introduction to Computational Biology exposes the reader to the fascinating structure of biological data and explains how to treat related combinatorial and statistical problems. Written to describe mathematical formulation and development, this book helps set the stage for even more, truly interdisciplinary work in biology.
Category: Mathematics

Handbook Of Chemoinformatics Algorithms

Author : Jean-Loup Faulon
ISBN : 142008299X
Genre : Science
File Size : 51.92 MB
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Unlike in the related area of bioinformatics, few books currently exist that document the techniques, tools, and algorithms of chemoinformatics. Bringing together worldwide experts in the field, the Handbook of Chemoinformatics Algorithms provides an overview of the most common chemoinformatics algorithms in a single source. After a historical perspective of the applications of algorithms and graph theory to chemical problems, the book presents algorithms for two-dimensional chemical structures and three-dimensional representations of molecules. It then focuses on molecular descriptors, virtual screening methods, and quantitative structure–activity relationship (QSAR) models, before introducing algorithms to enumerate and sample chemical structures. The book also covers computer-aided molecular design, reaction network generation, and open source software and database technologies. The remaining chapters describe techniques developed in the context of bioinformatics and computational biology and their potential applications to chemical problems. This handbook presents a selection of algorithms relevant in practice, making the book useful to those working in the field. It offers an up-to-date account of many algorithmic aspects of chemoinformatics.
Category: Science

Computational Neuroscience

Author : Jianfeng Feng
ISBN : 9781135440466
Genre : Science
File Size : 37.86 MB
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How does the brain work? After a century of research, we still lack a coherent view of how neurons process signals and control our activities. But as the field of computational neuroscience continues to evolve, we find that it provides a theoretical foundation and a set of technological approaches that can significantly enhance our understanding. Computational Neuroscience: A Comprehensive Approach provides a unified treatment of the mathematical theory of the nervous system and presents concrete examples demonstrating how computational techniques can illuminate difficult neuroscience problems. In chapters contributed by top researchers, the book introduces the basic mathematical concepts, then examines modeling at all levels, from single-channel and single neuron modeling to neuronal networks and system-level modeling. The emphasis is on models with close ties to experimental observations and data, and the authors review application of the models to systems such as olfactory bulbs, fly vision, and sensorymotor systems. Understanding the nature and limits of the strategies neural systems employ to process and transmit sensory information stands among the most exciting and difficult challenges faced by modern science. This book clearly shows how computational neuroscience has and will continue to help meet that challenge.
Category: Science