Author: D.S. Jones,Michael Plank,B.D. Sleeman

Publisher: CRC Press

ISBN: 9781420083583

Category: Mathematics

Page: 462

View: 3862

Deepen students’ understanding of biological phenomena Suitable for courses on differential equations with applications to mathematical biology or as an introduction to mathematical biology, Differential Equations and Mathematical Biology, Second Edition introduces students in the physical, mathematical, and biological sciences to fundamental modeling and analytical techniques used to understand biological phenomena. In this edition, many of the chapters have been expanded to include new and topical material. New to the Second Edition A section on spiral waves Recent developments in tumor biology More on the numerical solution of differential equations and numerical bifurcation analysis MATLAB® files available for download online Many additional examples and exercises This textbook shows how first-order ordinary differential equations (ODEs) are used to model the growth of a population, the administration of drugs, and the mechanism by which living cells divide. The authors present linear ODEs with constant coefficients, extend the theory to systems of equations, model biological phenomena, and offer solutions to first-order autonomous systems of nonlinear differential equations using the Poincaré phase plane. They also analyze the heartbeat, nerve impulse transmission, chemical reactions, and predator–prey problems. After covering partial differential equations and evolutionary equations, the book discusses diffusion processes, the theory of bifurcation, and chaotic behavior. It concludes with problems of tumor growth and the spread of infectious diseases.
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Author: Darren J. Wilkinson

Publisher: CRC Press

ISBN: 1439837724

Category: Mathematics

Page: 363

View: 9865

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.
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Mathematische Modellierung und Modellanalyse

Author: Andreas Kremling

Publisher: Springer-Verlag

ISBN: 3834886076

Category: Science

Page: 300

View: 5056

Das Buch beschreibt die Grundlagen der mathematischen Modellierung zellulärer Systeme. Nach einer Klassifikation von Modellen wird schwerpunktmäßig auf deterministische Modelle eingegangen und für alle relevanten zellulären Prozesse entsprechende Gleichungen angegeben. Anschließend werden eine Reihe von Verfahren zur Modellanalyse vorgestellt. Etwas kürzer werden Verfahren zum Reverse Engineering und zur Analyse von Netzwerkgraphen abgehandelt. Am Ende werden noch Verfahren der Parameteridentifikation besprochen.
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Proceedings of the International Symposium on Mathematical and Computational Biology

Author: Rubem P Mondaini

Publisher: World Scientific

ISBN: 981460223X

Category: Mathematics

Page: 428

View: 3589

This is a book of a series on interdisciplinary topics on the Biological and Mathematical Sciences. The chapters correspond to selected papers on special research themes, which have been presented at BIOMAT 2013 International Symposium on Mathematical and Computational Biology which was held in the Fields Institute for Research in Mathematical Sciences, Toronto, Ontario, Canada, on November 04 – 08, 2013. The treatment is both pedagogical and advanced in order to motivate research students as well as to fulfill the requirements of professional practitioners. There are comprehensive reviews written by prominent scientific leaders of famous research groups. Contents:Population Dynamics:The Princess and the Pea: The Unexpected Importance of Movement Algorithms (Rebecca Tyson)Plankton Nutrient Interaction Model with Harvesting under Constant Environment (Samares Pal and A Chatterjee)Traveling Wave Solutions for a Chemotaxis System (F Catrina and V M Reyes G)Dynamics of a General Stage Structured N Parallel Food Chains (Isam Al-Darabsah and Yuan Yuan)Pattern Recognition of Biological Phenomena:Complex Data Clustering: From Neural Network Architecture to Theory and Applications of Nonlinear Dynamics of Pattern Recognition (Guojun Gan, Jialun Yin, Yulia Wang and Jianhong Wu)Dynamic and Geometric Modelling of Biomolecular Structures:A Two-Step Kinetic Model of Insulin Aggregation with a Competitive Inhibitor (Mark Whidden, Allison Ho and Santiago Schnell)Optimal Control Techniques in Mathematical Modelling of Biological Phenomena:Optimal Control of Resource Coefficient in a Parabolic Population Model (J Bintz, H Finotti and S Lenhart)Optimization of Costs for Combating Aedes Aegypti in Optimal Time-Windows (W O Dias, G A Xavier, D A P Lima, E F Wanner and R T N Cardoso)Dynamics of a Varroa-Infested Honey Bee Colonies Model (K O Okosun)Computational Biology:Probability Distributions of GC Content Reflect the Evolution of Primate Species (Marco V José, Qi Lu and Juan R Bobadilla)Mining the Constraints of Protein Evolution (Fernando Encinas and Antonio Basilio de Miranda)Entropy Measures Based Methods for the Classification of Protein Domains into Families and Clans (Nicolas Carels, Cecilia F Mondaini and Rubem P Mondaini)Modelling Physiological Disorders:Modelling of Porous Elastic and Viscoelastic Media and Its Application to the Brain (R Begg, J Murley, M. Kohandel and S Sivaloganathan)The Mathematics of Liver Transplantation (F A B Coutinho, E Chaib, M Amaku, M M Burattini and E Massad)Complexity of Molecular Signaling Networks for Various Types of Cancer and Neurological Diseases Correlates with Patient Survivability (D Breitkreutz, E A Rietman, P Hinow, M Healey and J A Tuszynski)Mathematical Modelling of Infectious Diseases:Modelling Malaria Dynamics in Temperate Regions with Long Term Incubation Period (Kyeongah Nah, Gergely Röst and Yongkuk Kim)A Simulation of the U S Influenza Outbreak in 2009–2010 Using a Patch SIR Model based on Airport Transportation Data (D L Wallace and M Chen)Modelling Directly Transmitted Infections considering Age-structured Contact Rate and Vaccination (H M Yang and C H Dezotti)A General Framework for Agent-Based Modelling with Applications to Infectious Disease Dynamics (Marek Laskowski and Seyed M Moghadas)Analysis of the Basic Reproduction Number from the Initial Growth Phase of the Outbreak in Diseases Caused by Vectors (R P Sanches and E Massad)Parameter Estimation of a Tuberculosis Model in a Patchy Environment: Case of Cameroon (D P Moualeu, S Bowong and J Kürts)An Agent-Based Modelling Framework for Tuberculosis Infection with Drug-Resistance (Aquino L Espindola, A S Martinez and Seyed M Moghadas)Some Extensions of the Classical Epidemic Models (Fred Brauer) Readership: Undergraduates, graduates, researchers and all practitioners on the interdisciplinary fields of Mathematical Biology, Biological Physics and Mathematical Modelling of Biosystems. Keywords:Mathematical Biology;Biomathematics;Mathematical Modelling of Biosystems;Biological Physics;Biophysics;Computational Biology;Bioinformatics
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Using Modern Discrete Models

Author: Raina Robeva,Terrell Hodge

Publisher: Academic Press

ISBN: 0124157939

Category: Mathematics

Page: 372

View: 2923

Mathematical Concepts and Methods in Modern Biology offers a quantitative framework for analyzing, predicting, and modulating the behavior of complex biological systems. The book presents important mathematical concepts, methods and tools in the context of essential questions raised in modern biology. Designed around the principles of project-based learning and problem-solving, the book considers biological topics such as neuronal networks, plant population growth, metabolic pathways, and phylogenetic tree reconstruction. The mathematical modeling tools brought to bear on these topics include Boolean and ordinary differential equations, projection matrices, agent-based modeling and several algebraic approaches. Heavy computation in some of the examples is eased by the use of freely available open-source software. Features self-contained chapters with real biological research examples using freely available computational tools Spans several mathematical techniques at basic to advanced levels Offers broad perspective on the uses of algebraic geometry/polynomial algebra in molecular systems biology
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Linking Undergraduate Disciplines

Author: Lynn Arthur Steen

Publisher: MAA

ISBN: 9780883858189

Category: Mathematics

Page: 161

View: 1910

Math & Bio 2010: Linking Undergraduate Disciplines envisages a new educational paradigm in which the disciplines of mathematics and biology, currently quite separate, will be productively linked in the undergraduate science programs of the 21st century. As a science, biology depends increasingly on data, algorithms, and models; in virtually every respect, it is becoming more quantitative, more computational, and more mathematical. While these trends are related, they are not the same; they represent, rather, three different perspectives on what many are calling the "new biology." All three methods---quantitative, computational, mathematical---are spreading across the entire landscape of biological science from molecular to cellular, organismic and ecological. The aim of this volume is to alert members of both communities---biological and mathematical---to the expanding and exciting challenges of interdisciplinary work in these fields.
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Initial Value Problems

Author: David F. Griffiths,Desmond J. Higham

Publisher: Springer Science & Business Media

ISBN: 9780857291486

Category: Mathematics

Page: 271

View: 2047

Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject. It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples. Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors. The book covers key foundation topics: o Taylor series methods o Runge--Kutta methods o Linear multistep methods o Convergence o Stability and a range of modern themes: o Adaptive stepsize selection o Long term dynamics o Modified equations o Geometric integration o Stochastic differential equations The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com
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Author: Suzanne Lenhart,John T. Workman

Publisher: CRC Press

ISBN: 1584886404

Category: Mathematics

Page: 280

View: 1225

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.
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Author: Hartmut Bossel

Publisher: Springer-Verlag

ISBN: 3663108228

Category: Technology & Engineering

Page: 484

View: 8532

This book is the the English Language Version of the very successful German textbook, "Modellbildung und Simulation". It provides a self-contained and complete guide to the methods and mathematical background of modeling and simulation software of dynamic systems. Furthermore, an appropriate simulation software and a collection of dynamic system models (on the accompanying disk) are highlights of the book/software-Package.Dies ist die englischsprachige Ausgabe des sehr erfolgreichen Lehrbuches "Modellbildung und Simulation". Geboten wird eine vollständige Einführung in die Methoden der Simulation dynamischer Systeme, wobei auch der notwendige mathematische Hintergrund vermittelt wird. Außerdem ist eine Simulationssoftware Bestandteil des Werkes; auf der beiliegenden Diskette befinden sich ferner 50 Beispielsysteme ("Systemzoo"), die zur spielerischen Einübung der verwendeten Verfahren hilfreich sind.
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Mathematical Modeling and Model Analysis

Author: Andreas Kremling

Publisher: CRC Press

ISBN: 1466567902

Category: Mathematics

Page: 379

View: 6509

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.
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Introduction and Qualitative Theory, Third Edition

Author: Jane Cronin

Publisher: CRC Press

ISBN: 9780824791896

Category: Mathematics

Page: 392

View: 5341

This text, now in its second edition, presents the basic theory of ordinary differential equations and relates the topological theory used in differential equations to advanced applications in chemistry and biology. It provides new motivations for studying extension theorems and existence theorems, supplies real-world examples, gives an early introduction to the use of geometric methods and offers a novel treatment of the Sturm-Liouville theory.
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Maps, Sequences and Genomes

Author: Michael S. Waterman

Publisher: CRC Press

ISBN: 9780412993916

Category: Mathematics

Page: 448

View: 6528

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.
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Band 1: Diskrete Mathematik und Lineare Algebra

Author: Gerald Teschl,Susanne Teschl

Publisher: Springer-Verlag

ISBN: 3642379729

Category: Computers

Page: 522

View: 5358

In diesem Lehrbuch werden die mathematischen Grundlagen exakt und dennoch anschaulich und gut nachvollziehbar vermittelt. Sie werden durchgehend anhand zahlreicher Musterbeispiele illustriert, durch Anwendungen in der Informatik motiviert und durch historische Hintergründe oder Ausblicke in angrenzende Themengebiete aufgelockert. Am Ende jedes Kapitels befinden sich Kontrollfragen, die das Verständnis testen und typische Fehler bzw. Missverständnisse ausräumen. Zusätzlich helfen zahlreiche Aufwärmübungen (mit vollständigem Lösungsweg) und weiterführende Übungsaufgaben das Erlernte zu festigen und praxisrelevant umzusetzen. Dieses Lehrbuch ist daher auch sehr gut zum Selbststudium geeignet. Ergänzend wird in eigenen Abschnitten das Computeralgebrasystem Mathematica vorgestellt und eingesetzt, wodurch der Lehrstoff visualisiert und somit das Verständnis erleichtert werden kann.
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Author: Ilja N. Bronstein,Heiner Mühlig,Gerhard Musiol,Konstantin A. Semendjajew

Publisher: N.A

ISBN: 9783808556719

Category:

Page: 1231

View: 9794

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Eine Einführung

Author: Walter A. Strauss

Publisher: Springer-Verlag

ISBN: 366312486X

Category: Mathematics

Page: 458

View: 9481

Dieses Buch ist eine umfassende Einführung in die klassischen Lösungsmethoden partieller Differentialgleichungen. Es wendet sich an Leser mit Kenntnissen aus einem viersemestrigen Grundstudium der Mathematik (und Physik) und legt seinen Schwerpunkt auf die explizite Darstellung der Lösungen. Es ist deshalb besonders auch für Anwender (Physiker, Ingenieure) sowie für Nichtspezialisten, die die Methoden der mathematischen Physik kennenlernen wollen, interessant. Durch die große Anzahl von Beispielen und Übungsaufgaben eignet es sich gut zum Gebrauch neben Vorlesungen sowie zum Selbststudium.
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Author: C. Pozrikidis

Publisher: CRC Press

ISBN: 1498746160

Category: Mathematics

Page: 278

View: 5315

The fractional Laplacian, also called the Riesz fractional derivative, describes an unusual diffusion process associated with random excursions. The Fractional Laplacian explores applications of the fractional Laplacian in science, engineering, and other areas where long-range interactions and conceptual or physical particle jumps resulting in an irregular diffusive or conductive flux are encountered. Presents the material at a level suitable for a broad audience of scientists and engineers with rudimentary background in ordinary differential equations and integral calculus Clarifies the concept of the fractional Laplacian for functions in one, two, three, or an arbitrary number of dimensions defined over the entire space, satisfying periodicity conditions, or restricted to a finite domain Covers physical and mathematical concepts as well as detailed mathematical derivations Develops a numerical framework for solving differential equations involving the fractional Laplacian and presents specific algorithms accompanied by numerical results in one, two, and three dimensions Discusses viscous flow and physical examples from scientific and engineering disciplines Written by a prolific author well known for his contributions in fluid mechanics, biomechanics, applied mathematics, scientific computing, and computer science, the book emphasizes fundamental ideas and practical numerical computation. It includes original material and novel numerical methods.
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Author: Henry C. Tuckwell

Publisher: CRC Press

ISBN: 9780412576201

Category: Mathematics

Page: 296

View: 3090

This book provides a clear and straightforward introduction to applications of probability theory with examples given in the biological sciences and engineering. The first chapter contains a summary of basic probability theory. Chapters two to five deal with random variables and their applications. Topics covered include geometric probability, estimation of animal and plant populations, reliability theory and computer simulation. Chapter six contains a lucid account of the convergence of sequences of random variables, with emphasis on the central limit theorem and the weak law of numbers. The next four chapters introduce random processes, including random walks and Markov chains illustrated by examples in population genetics and population growth. This edition also includes two chapters which introduce, in a manifestly readable fashion, the topic of stochastic differential equations and their applications.
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Author: Vladimir I. Arnold

Publisher: Springer-Verlag

ISBN: 3642564801

Category: Mathematics

Page: 344

View: 9298

nen (die fast unverändert in moderne Lehrbücher der Analysis übernommen wurde) ermöglichten ihm nach seinen eigenen Worten, "in einer halben Vier telstunde" die Flächen beliebiger Figuren zu vergleichen. Newton zeigte, daß die Koeffizienten seiner Reihen proportional zu den sukzessiven Ableitungen der Funktion sind, doch ging er darauf nicht weiter ein, da er zu Recht meinte, daß die Rechnungen in der Analysis bequemer auszuführen sind, wenn man nicht mit höheren Ableitungen arbeitet, sondern die ersten Glieder der Reihenentwicklung ausrechnet. Für Newton diente der Zusammenhang zwischen den Koeffizienten der Reihe und den Ableitungen eher dazu, die Ableitungen zu berechnen als die Reihe aufzustellen. Eine von Newtons wichtigsten Leistungen war seine Theorie des Sonnensy stems, die in den "Mathematischen Prinzipien der Naturlehre" ("Principia") ohne Verwendung der mathematischen Analysis dargestellt ist. Allgemein wird angenommen, daß Newton das allgemeine Gravitationsgesetz mit Hilfe seiner Analysis entdeckt habe. Tatsächlich hat Newton (1680) lediglich be wiesen, daß die Bahnkurven in einem Anziehungsfeld Ellipsen sind, wenn die Anziehungskraft invers proportional zum Abstandsquadrat ist: Auf das Ge setz selbst wurde Newton von Hooke (1635-1703) hingewiesen (vgl. § 8) und es scheint, daß es noch von weiteren Forschern vermutet wurde.
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