Differential Equations and Mathematical Biology Second Edition

Author: D.S. Jones
Publisher: CRC Press
ISBN: 9781420083583
Format: PDF
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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.

Stochastic Modelling for Systems Biology Second Edition

Author: Darren J. Wilkinson
Publisher: CRC Press
ISBN: 1439837724
Format: PDF, ePub, Docs
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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.

BIOMAT 2013

Author: Rubem P Mondaini
Publisher: World Scientific
ISBN: 981460223X
Format: PDF, ePub, Mobi
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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

Kompendium Systembiologie

Author: Andreas Kremling
Publisher: Springer-Verlag
ISBN: 3834886076
Format: PDF
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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.

Mathematical Concepts and Methods in Modern Biology

Author: Raina Robeva
Publisher: Academic Press
ISBN: 0124157939
Format: PDF, ePub, Docs
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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

Optimal Control Applied to Biological Models

Author: Suzanne Lenhart
Publisher: CRC Press
ISBN: 1584886404
Format: PDF
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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.

Math and Bio 2010

Author: Lynn Arthur Steen
Publisher: MAA
ISBN: 9780883858189
Format: PDF, Kindle
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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.

Nonlinear Dynamics and Chaos with Student Solutions Manual

Author: Steven H. Strogatz
Publisher: CRC Press
ISBN: 0429680155
Format: PDF, ePub, Docs
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This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Systems Biology

Author: Andreas Kremling
Publisher: CRC Press
ISBN: 1466567902
Format: PDF, Kindle
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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.

Ordinary Differential Equations

Author: Jane Cronin
Publisher: CRC Press
ISBN: 9780824791896
Format: PDF
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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.