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Applied Mathematics for the Analysis of Biomedical Data Models, Methods, and MATLAB von Costa, Peter J. (eBook)

  • Erscheinungsdatum: 21.02.2017
  • Verlag: Wiley
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Applied Mathematics for the Analysis of Biomedical Data

Features a practical approach to the analysis of biomedical data via mathematical methods and provides a MATLAB® toolbox for the collection, visualization, and evaluation of experimental and real-life data Applied Mathematics for the Analysis of Biomedical Data: Models, Methods, and MATLAB® presents a practical approach to the task that biological scientists face when analyzing data.The primary focus is on the application of mathematical models and scientific computingmethods to provide insight into the behavior of biological systems. The author draws upon hisexperience in academia, industry, and government-sponsored research as well as his expertisein MATLAB to produce a suite of computer programs with applications in epidemiology,machine learning, and biostatistics. These models are derived from real-world data andconcerns. Among the topics included are the spread of infectious disease (HIV/AIDS) througha population, statistical pattern recognition methods to determine the presence of disease in adiagnostic sample, and the fundamentals of hypothesis testing. In addition, the author uses his professional experiences to present unique case studies whose analyses provide detailed insights into biological systems and the problems inherent in their examination. The book contains a well-developed and tested set of MATLAB functions that act as a general toolbox for practitioners of quantitative biology and biostatistics. This combination of MATLAB functions and practical tips amplifies the book's technical merit and value to industry professionals. Through numerous examples and sample code blocks, the book provides readers with illustrations of MATLAB programming. Moreover, the associated toolbox permits readers to engage in the process of data analysis without needing to delve deeply into the mathematical theory. This gives an accessible view of the material for readers with varied backgrounds. As a result, the book provides a streamlined framework for the development of mathematical models, algorithms, and the corresponding computer code. In addition, the book features: - Real-world computational procedures that can be readily applied to similar problems without the need for keen mathematical acumen - Clear delineation of topics to accelerate access to data analysis - Access to a book companion website containing the MATLAB toolbox created for this book, as well as a Solutions Manual with solutions to selected exercises Applied Mathematics for the Analysis of Biomedical Data: Models, Methods, and MATLAB® is an excellent textbook for students in mathematics, biostatistics, the life and social sciences,and quantitative, computational, and mathematical biology. This book is also an ideal referencefor industrial scientists, biostatisticians, product development scientists, and practitionerswho use mathematical models of biological systems in biomedical research, medical devicedevelopment, and pharmaceutical submissions. PETER J. COSTA, PhD, is Senior Applied Mathematician at Hologic Incorporated in Marlborough, MA. Dr. Costa is the co-creator of MATLAB's Symbolic Math Toolbox. He has developed mathematical models for the spread of HIV, the outbreak of AIDS, the transmission of an infectious respiratory disease throughout a population, and the diagnosis of cervical cancer. His research interests include scientific computing and mathematical biology. He received a PhD in Applied Mathematics from the University of Massachusetts at Amherst. Edit
Peter J. Costa, PhD, is Senior Applied Mathematician at Hologic Incorporated in Marlborough, MA. Dr. Costa is the co-creator of MATLAB's Symbolic Math Toolbox. He has developed mathematical models for the spread of HIV, the outbreak of AIDS, the transmission of an infectious respiratory disease throughout a population, and the diagnosis of cervical cancer. His research interests include scientific computing and mathematical biology. He received a PhD in Appli

Produktinformationen

    Format: ePUB
    Kopierschutz: AdobeDRM
    Seitenzahl: 448
    Erscheinungsdatum: 21.02.2017
    Sprache: Englisch
    ISBN: 9781119269519
    Verlag: Wiley
    Größe: 16173 kBytes
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Applied Mathematics for the Analysis of Biomedical Data

Introduction

The phrase, mathematical analysis of biomedical data , at first glance seems impossibly ambitious. Does the author assert that inherently irregular biological systems can be described with any consistency via the rigid rules of mathematics? Add to this expression applied mathematics and a great deal of skepticism will likely fill the reader's mind. What is the intention of this work?

The answer is, in part, to provide a record of the author's 30-year career in academics, government, and private industry. Much of that career has involved the analysis of biological systems and data via mathematics. More than this, however, is the desire to provide the reader with a set of tools and examples that can be used as a basis for solving the problems he/she is facing. Some uncommon "tricks of the trade" and methodologies rarely broached by university instruction are provided.

Too often, books are written with only an academic audience in mind. This effort is aimed at working scientists and aspiring apprentices. It can be viewed as a combined textbook, reference work, handbook, and user's guide. The program presented here will be example driven. It would be disingenuous to say that the mathematics will not be emphasized (the author is, after all, a mathematician). Nevertheless, each section will be motivated by the underlying biology. Each example will contain the MATLAB® code required to produce a figure, result, and/or numerical table.

The book is guided by the idea that applied mathematical models are iterative. Develop a set of equations to describe a phenomenon, measure its effectiveness against data collected to measure the phenomenon, and then modify the model to improve its accuracy. The focus is on solving real examples by way of a mathematical method. Sophistication is not the primary goal. A symbiosis between the rigors of mathematical techniques and the unpredictable nature of biological systems is the point of emphasis.

The book reflects the formula that "mathematics + data + scientific computing = genuine insight into biological systems." The computing software of choice in this work is MATLAB. The reader can think of MATLAB as another important mathematical tool, akin to the Fourier transform. It (that is, MATLAB) helps transform data into mathematical forms and vice versa.

The presentation of concepts is as follows.

This introduction gives an overview of the book and ends with a representative example of the "mathematics + data + software" paradigm. The first chapter lists a set of guidelines and methods for obtaining, filtering, deciphering, and ultimately analyzing data. These techniques include data visualization, data transformations, data filtering/smoothing, data clustering (i.e., splitting one collection of samples into two or more subclasses), and data quality/data cleaning. In each case, a topic is introduced along with a data set. Mathematical methods used to examine the data are explained. Specific MATLAB programs, developed for use in an industrial setting, are applied to the data. The underlying assumption of this book is that, unlike most academic texts, data must be examined, verified, and/or filtered before a model is applied.

Following the discussion of data, the second chapter provides a view of the utility of differential equations as a modeling method on three distinct medical issues. The interaction of glucose and insulin levels within a human body is described by way of an elementary interaction model. This same approach is applied to the transition of HIV to AIDS within a patient. The HIV/AIDS example portends the susceptible-exposed-infected-recovered/removed models detailed in Chapter 3. The renowned polymerase chain reaction is presented as a coupled set of differential equations. In all of the cases above, the models are either appl

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