Biology in Time and Space
Author: James P. Keener
Publisher:
Published: 2021
Total Pages:
ISBN-13: 9781470464141
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Biology in Time and Space: A Partial Differential Equation Modeling Approach
Author: James P. Keener
Publisher: American Mathematical Soc.
Published: 2021-06-02
Total Pages: 308
ISBN-13: 1470454289
DOWNLOAD EBOOKHow do biological objects communicate, make structures, make measurements and decisions, search for food, i.e., do all the things necessary for survival? Designed for an advanced undergraduate audience, this book uses mathematics to begin to tell that story. It builds on a background in multivariable calculus, ordinary differential equations, and basic stochastic processes and uses partial differential equations as the framework within which to explore these questions.
Methods of Small Parameter in Mathematical Biology
Author: Jacek Banasiak
Publisher: Springer Science & Business
Published: 2014-04-19
Total Pages: 295
ISBN-13: 3319051407
DOWNLOAD EBOOKThis monograph presents new tools for modeling multiscale biological processes. Natural processes are usually driven by mechanisms widely differing from each other in the time or space scale at which they operate and thus should be described by appropriate multiscale models. However, looking at all such scales simultaneously is often infeasible, costly, and provides information that is redundant for a particular application. Hence, there has been a growing interest in providing a more focused description of multiscale processes by aggregating variables in a way that is relevant to the purpose at hand and preserves the salient features of the dynamics. Many ad hoc methods have been devised, and the aim of this book is to present a systematic way of deriving the so-called limit equations for such aggregated variables and ensuring that the coefficients of these equations encapsulate the relevant information from the discarded levels of description. Since any approximation is only valid if an estimate of the incurred error is available, the tools the authors describe allow for proving that the solutions to the original multiscale family of equations converge to the solution of the limit equation if the relevant parameter converges to its critical value. The chapters are arranged according to the mathematical complexity of the analysis, from systems of ordinary linear differential equations, through nonlinear ordinary differential equations, to linear and nonlinear partial differential equations. Many chapters begin with a survey of mathematical techniques needed for the analysis. All problems discussed in this book belong to the class of singularly perturbed problems; that is, problems in which the structure of the limit equation is significantly different from that of the multiscale model. Such problems appear in all areas of science and can be attacked using many techniques. Methods of Small Parameter in Mathematical Biology will appeal to senior undergraduate and graduate students in applied and biomathematics, as well as researchers specializing in differential equations and asymptotic analysis.
Exploring Modeling with Data and Differential Equations Using R
Author: John Zobitz
Publisher: CRC Press
Published: 2022-11-29
Total Pages: 362
ISBN-13: 1000776786
DOWNLOAD EBOOKExploring Modeling with Data and Differential Equations Using R provides a unique introduction to differential equations with applications to the biological and other natural sciences. Additionally, model parameterization and simulation of stochastic differential equations are explored, providing additional tools for model analysis and evaluation. This unified framework sits "at the intersection" of different mathematical subject areas, data science, statistics, and the natural sciences. The text throughout emphasizes data science workflows using the R statistical software program and the tidyverse constellation of packages. Only knowledge of calculus is needed; the text’s integrated framework is a stepping stone for further advanced study in mathematics or as a comprehensive introduction to modeling for quantitative natural scientists. The text will introduce you to: modeling with systems of differential equations and developing analytical, computational, and visual solution techniques. the R programming language, the tidyverse syntax, and developing data science workflows. qualitative techniques to analyze a system of differential equations. data assimilation techniques (simple linear regression, likelihood or cost functions, and Markov Chain, Monte Carlo Parameter Estimation) to parameterize models from data. simulating and evaluating outputs for stochastic differential equation models. An associated R package provides a framework for computation and visualization of results. It can be found here: https://cran.r-project.org/web/packages/demodelr/index.html.
Understanding and Modulating Bone and Cartilage Cell Fate for Regenerative Medicine
Author: Roberto Narcisi
Publisher: Frontiers Media SA
Published: 2019-04-04
Total Pages: 185
ISBN-13: 2889457907
DOWNLOAD EBOOKThe Restless Cell
Author: Christina Hueschen
Publisher: Princeton University Press
Published: 2024-08-20
Total Pages: 436
ISBN-13: 0691236364
DOWNLOAD EBOOKAn essential introduction to the physics of active matter and its application to questions in biology In recent decades, the theory of active matter has emerged as a powerful tool for exploring the differences between living and nonliving states of matter. The Restless Cell provides a self-contained, quantitative description of how the continuum theory of matter has been generalized to account for the complex and sometimes counterintuitive behaviors of living materials. Christina Hueschen and Rob Phillips begin by illustrating how classical field theory has been used by physicists to describe the transport of matter by diffusion, the elastic deformations of solids, and the flow of fluids. Drawing on physical insights from the study of diffusion, they introduce readers to the continuum theory protocol—a step-by-step framework for developing equations that describe matter as a continuum—and show how these methods and concepts can be generalized to the study of living, energy-consuming matter. Hueschen and Phillips then present a range of engaging biological case studies across scales, such as the symmetry breaking that occurs in developing embryos, the perpetual flows that take place in giant algal cells, and the herding of wildebeest on the plains of the Serengeti. An essential resource for students and researchers in biological physics and quantitative biology, The Restless Cell gives complete derivations of all calculations and features illustrations by Nigel Orme that seamlessly bridge conceptual models and continuum descriptions of living matter.
Mathematical Models in Biology
Author: Leah Edelstein-Keshet
Publisher: SIAM
Published: 1988-01-01
Total Pages: 629
ISBN-13: 9780898719147
DOWNLOAD EBOOKMathematical 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.
Encyclopedia of Bioinformatics and Computational Biology
Author:
Publisher: Elsevier
Published: 2018-08-21
Total Pages: 3421
ISBN-13: 0128114320
DOWNLOAD EBOOKEncyclopedia of Bioinformatics and Computational Biology: ABC of Bioinformatics, Three Volume Set combines elements of computer science, information technology, mathematics, statistics and biotechnology, providing the methodology and in silico solutions to mine biological data and processes. The book covers Theory, Topics and Applications, with a special focus on Integrative –omics and Systems Biology. The theoretical, methodological underpinnings of BCB, including phylogeny are covered, as are more current areas of focus, such as translational bioinformatics, cheminformatics, and environmental informatics. Finally, Applications provide guidance for commonly asked questions. This major reference work spans basic and cutting-edge methodologies authored by leaders in the field, providing an invaluable resource for students, scientists, professionals in research institutes, and a broad swath of researchers in biotechnology and the biomedical and pharmaceutical industries. Brings together information from computer science, information technology, mathematics, statistics and biotechnology Written and reviewed by leading experts in the field, providing a unique and authoritative resource Focuses on the main theoretical and methodological concepts before expanding on specific topics and applications Includes interactive images, multimedia tools and crosslinking to further resources and databases
Dynamic Models in Biology
Author: Stephen P. Ellner
Publisher: Princeton University Press
Published: 2011-09-19
Total Pages: 352
ISBN-13: 1400840961
DOWNLOAD EBOOKFrom controlling disease outbreaks to predicting heart attacks, dynamic models are increasingly crucial for understanding biological processes. Many universities are starting undergraduate programs in computational biology to introduce students to this rapidly growing field. In Dynamic Models in Biology, the first text on dynamic models specifically written for undergraduate students in the biological sciences, ecologist Stephen Ellner and mathematician John Guckenheimer teach students how to understand, build, and use dynamic models in biology. Developed from a course taught by Ellner and Guckenheimer at Cornell University, the book is organized around biological applications, with mathematics and computing developed through case studies at the molecular, cellular, and population levels. The authors cover both simple analytic models--the sort usually found in mathematical biology texts--and the complex computational models now used by both biologists and mathematicians. Linked to a Web site with computer-lab materials and exercises, Dynamic Models in Biology is a major new introduction to dynamic models for students in the biological sciences, mathematics, and engineering.
Catalyzing Inquiry at the Interface of Computing and Biology
Author: National Research Council
Publisher: National Academies Press
Published: 2006-01-01
Total Pages: 469
ISBN-13: 030909612X
DOWNLOAD EBOOKAdvances in computer science and technology and in biology over the last several years have opened up the possibility for computing to help answer fundamental questions in biology and for biology to help with new approaches to computing. Making the most of the research opportunities at the interface of computing and biology requires the active participation of people from both fields. While past attempts have been made in this direction, circumstances today appear to be much more favorable for progress. To help take advantage of these opportunities, this study was requested of the NRC by the National Science Foundation, the Department of Defense, the National Institutes of Health, and the Department of Energy. The report provides the basis for establishing cross-disciplinary collaboration between biology and computing including an analysis of potential impediments and strategies for overcoming them. The report also presents a wealth of examples that should encourage students in the biological sciences to look for ways to enable them to be more effective users of computing in their studies.
