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Mathematical Models in the Biosciences I by Michael Frame Pdf
An award-winning professor’s introduction to essential concepts of calculus and mathematical modeling for students in the biosciences This is the first of a two-part series exploring essential concepts of calculus in the context of biological systems. Michael Frame covers essential ideas and theories of basic calculus and probability while providing examples of how they apply to subjects like chemotherapy and tumor growth, chemical diffusion, allometric scaling, predator-prey relations, and nerve impulses. Based on the author’s calculus class at Yale University, the book makes concepts of calculus more relatable for science majors and premedical students.
Mathematical Models in the Biosciences II by Michael Frame Pdf
Volume Two of an award-winning professor’s introduction to essential concepts of calculus and mathematical modeling for students in the biosciences This is the second of a two-part series exploring essential concepts of calculus in the context of biological systems. Building on the essential ideas and theories of basic calculus taught in Mathematical Models in the Biosciences I, this book focuses on epidemiological models, mathematical foundations of virus and antiviral dynamics, ion channel models and cardiac arrhythmias, vector calculus and applications, and evolutionary models of disease. It also develops differential equations and stochastic models of many biomedical processes, as well as virus dynamics, the Clancy-Rudy model to determine the genetic basis of cardiac arrhythmias, and a sketch of some systems biology. Based on the author’s calculus class at Yale, the book makes concepts of calculus less abstract and more relatable for science majors and premedical students.
Introduction to Modeling for Biosciences by David J. Barnes,Dominique Chu Pdf
Mathematical modeling can be a useful tool for researchers in the biological scientists. Yet in biological modeling there is no one modeling technique that is suitable for all problems. Instead, different problems call for different approaches. Furthermore, it can be helpful to analyze the same system using a variety of approaches, to be able to exploit the advantages and drawbacks of each. In practice, it is often unclear which modeling approaches will be most suitable for a particular biological question, a problem which requires researchers to know a reasonable amount about a number of techniques, rather than become experts on a single one. "Introduction to Modeling for Biosciences" addresses this issue by presenting a broad overview of the most important techniques used to model biological systems. In addition to providing an introduction into the use of a wide range of software tools and modeling environments, this helpful text/reference describes the constraints and difficulties that each modeling technique presents in practice, enabling the researcher to quickly determine which software package would be most useful for their particular problem. Topics and features: introduces a basic array of techniques to formulate models of biological systems, and to solve them; intersperses the text with exercises throughout the book; includes practical introductions to the Maxima computer algebra system, the PRISM model checker, and the Repast Simphony agent modeling environment; discusses agent-based models, stochastic modeling techniques, differential equations and Gillespie’s stochastic simulation algorithm; contains appendices on Repast batch running, rules of differentiation and integration, Maxima and PRISM notation, and some additional mathematical concepts; supplies source code for many of the example models discussed, at the associated website http://www.cs.kent.ac.uk/imb/. This unique and practical guide leads the novice modeler through realistic and concrete modeling projects, highlighting and commenting on the process of abstracting the real system into a model. Students and active researchers in the biosciences will also benefit from the discussions of the high-quality, tried-and-tested modeling tools described in the book. Dr. David J. Barnes is a lecturer in computer science at the University of Kent, UK, with a strong background in the teaching of programming. Dr. Dominique Chu is a lecturer in computer science at the University of Kent, UK. He is an internationally recognized expert in agent-based modeling, and has also in-depth research experience in stochastic and differential equation based modeling.
Understanding Complex Biological Systems with Mathematics by Ami Radunskaya,Rebecca Segal,Blerta Shtylla Pdf
This volume examines a variety of biological and medical problems using mathematical models to understand complex system dynamics. Featured topics include autism spectrum disorder, ectoparasites and allogrooming, argasid ticks dynamics, super-fast nematocyst firing, cancer-immune population dynamics, and the spread of disease through populations. Applications are investigated with mathematical models using a variety of techniques in ordinary and partial differential equations, difference equations, Markov-chain models, Monte-Carlo simulations, network theory, image analysis, and immersed boundary method. Each article offers a thorough explanation of the methodologies used and numerous tables and color illustrations to explain key results. This volume is suitable for graduate students and researchers interested in current applications of mathematical models in the biosciences. The research featured in this volume began among newly-formed collaborative groups at the 2017 Women Advancing Mathematical Biology Workshop that took place at the Mathematical Biosciences Institute in Columbus, Ohio. The groups spent one intensive week working at MBI and continued their collaborations after the workshop, resulting in the work presented in this volume.
Mathematical Models for Society and Biology by Edward Beltrami Pdf
Mathematical Models for Society and Biology, 2e, is a useful resource for researchers, graduate students, and post-docs in the applied mathematics and life science fields. Mathematical modeling is one of the major subfields of mathematical biology. A mathematical model may be used to help explain a system, to study the effects of different components, and to make predictions about behavior. Mathematical Models for Society and Biology, 2e, draws on current issues to engagingly relate how to use mathematics to gain insight into problems in biology and contemporary society. For this new edition, author Edward Beltrami uses mathematical models that are simple, transparent, and verifiable. Also new to this edition is an introduction to mathematical notions that every quantitative scientist in the biological and social sciences should know. Additionally, each chapter now includes a detailed discussion on how to formulate a reasonable model to gain insight into the specific question that has been introduced. Offers 40% more content – 5 new chapters in addition to revisions to existing chapters Accessible for quick self study as well as a resource for courses in molecular biology, biochemistry, embryology and cell biology, medicine, ecology and evolution, bio-mathematics, and applied math in general Features expanded appendices with an extensive list of references, solutions to selected exercises in the book, and further discussion of various mathematical methods introduced in the book
Guide to Simulation and Modeling for Biosciences by David J. Barnes,Dominique Chu Pdf
This accessible text presents a detailed introduction to the use of a wide range of software tools and modeling environments for use in the biosciences, as well as the fundamental mathematical background. The practical constraints presented by each modeling technique are described in detail, enabling the researcher to determine which software package would be most useful for a particular problem. Features: introduces a basic array of techniques to formulate models of biological systems, and to solve them; discusses agent-based models, stochastic modeling techniques, differential equations, spatial simulations, and Gillespie’s stochastic simulation algorithm; provides exercises; describes such useful tools as the Maxima algebra system, the PRISM model checker, and the modeling environments Repast Simphony and Smoldyn; contains appendices on rules of differentiation and integration, Maxima and PRISM notation, and some additional mathematical concepts; offers supplementary material at an associated website.
Mathematical Modeling of Biological Systems, Volume I by Andreas Deutsch,Lutz Brusch,Helen Byrne,Gerda de Vries,Hanspeter Herzel Pdf
Volume I of this two-volume, interdisciplinary work is a unified presentation of a broad range of state-of-the-art topics in the rapidly growing field of mathematical modeling in the biological sciences. The chapters are thematically organized into the following main areas: cellular biophysics, regulatory networks, developmental biology, biomedical applications, data analysis and model validation. The work will be an excellent reference text for a broad audience of researchers, practitioners, and advanced students in this rapidly growing field at the intersection of applied mathematics, experimental biology and medicine, computational biology, biochemistry, computer science, and physics.
Mathematical Modeling of Biological Systems, Volume II by Andreas Deutsch,Rafael Bravo de la Parra,Rob J. de Boer,Odo Diekmann,Peter Jagers,Eva Kisdi,Mirjam Kretzschmar,Petr Lansky,Hans Metz Pdf
Volume II of this two-volume, interdisciplinary work is a unified presentation of a broad range of state-of-the-art topics in the rapidly growing field of mathematical modeling in the biological sciences. Highlighted throughout are mathematical and computational apporaches to examine central problems in the life sciences, ranging from the organization principles of individual cells to the dynamics of large populations. The chapters are thematically organized into the following main areas: epidemiology, evolution and ecology, immunology, neural systems and the brain, and innovative mathematical methods and education. The work will be an excellent reference text for a broad audience of researchers, practitioners, and advanced students in this rapidly growing field at the intersection of applied mathematics, experimental biology and medicine, computational biology, biochemistry, computer science, and physics.
Dynamic Models and Control of Biological Systems by Vadrevu Sree Hari Rao,Ponnada Raja Sekhara Rao Pdf
Mathematical Biology has grown at an astonishing rate and has established itself as a distinct discipline. Mathematical modeling is now being applied in every major discipline in the biological sciences. Though the field has become increasingly large and specialized, this book remains important as a text that introduces some of the exciting problems which arise in the biological sciences and gives some indication of the wide spectrum of questions that modeling can address.
Aspects of Mathematical Modelling by Roger J. Hosking,Ezio Venturino Pdf
The construction of mathematical models is an essential scientific activity. Mathematics is associated with developments in science and engineering, but more recently mathematical modelling has been used to investigate complex systems that arise in other fields. This book demonstrates the application of mathematics to research topics in ecology and environmental science, health and medicine, phylogenetics and neural networks, theoretical chemistry, economics and management.
Mathematical Models in Biology by Valeria Zazzu,Maria Brigida Ferraro,Mario R. Guarracino Pdf
This book presents an exciting collection of contributions based on the workshop “Bringing Maths to Life” held October 27-29, 2014 in Naples, Italy. The state-of-the art research in biology and the statistical and analytical challenges facing huge masses of data collection are treated in this Work. Specific topics explored in depth surround the sessions and special invited sessions of the workshop and include genetic variability via differential expression, molecular dynamics and modeling, complex biological systems viewed from quantitative models, and microscopy images processing, to name several. In depth discussions of the mathematical analysis required to extract insights from complex bodies of biological datasets, to aid development in the field novel algorithms, methods and software tools for genetic variability, molecular dynamics, and complex biological systems are presented in this book. Researchers and graduate students in biology, life science, and mathematics/statistics will find the content useful as it addresses existing challenges in identifying the gaps between mathematical modeling and biological research. The shared solutions will aid and promote further collaboration between life sciences and mathematics.
Tutorials in Mathematical Biosciences II by James Sneyd Pdf
This book presents a series of models in the general area of cell physiology and signal transduction, with particular attention being paid to intracellular calcium dynamics, and the role played by calcium in a variety of cell types. Calcium plays a crucial role in cell physiology, and the study of its dynamics lends insight into many different cellular processes. In particular, calcium plays a central role in muscular contraction, olfactory transduction and synaptic communication, three of the topics to be addressed in detail in this book. In addition to the models, much of the underlying physiology is presented, so that readers may learn both the mathematics and the physiology, and see how the models are applied to specific biological questions. It is intended primarily as a graduate text or a research reference. It will serve as a concise and up-to-date introduction to all those who wish to learn about the state of calcium dynamics modeling, and how such models are applied to physiological questions.
Tutorials in Mathematical Biosciences III by Avner Friedman Pdf
This volume introduces some basic mathematical models for cell cycle, proliferation, cancer, and cancer therapy. Chapter 1 gives an overview of the modeling of the cell division cycle. Chapter 2 describes how tumor secretes growth factors to form new blood vessels in its vicinity, which provide it with nutrients it needs in order to grow. Chapter 3 explores the process that enables the tumor to invade the neighboring tissue. Chapter 4 models the interaction between a tumor and the immune system. Chapter 5 is concerned with chemotherapy; it uses concepts from control theory to minimize obstacles arising from drug resistance and from cell cycle dynamics. Finally, Chapter 6 reviews mathematical results for various cancer models.
Mathematical Models in Molecular Cellular Biology by Lee A. Segel Pdf
Interest in theoretical biology is rapidly growing and this 1981 book attempts to make the theory more accessible to experimentalists. Its primary purpose is to demonstrate to experimental molecular and cellular biologists the possible usefulness of mathematical models. Biologists with a basic command of calculus should be able to learn from the book what assumptions are implied by various types of equations, to understand in broad outline a number of major theoretical concepts, and to be aware of some of the difficulties connected with analytical and numerical solutions of mathematical problems. Thus they should be able to appreciate the significance of theoretical papers in their fields and to communicate usefully with theoreticians in the course of their work.
Tutorials in Mathematical Biosciences II by James Sneyd Pdf
This book presents a series of models in the general area of cell physiology and signal transduction, with particular attention being paid to intracellular calcium dynamics, and the role played by calcium in a variety of cell types. Calcium plays a crucial role in cell physiology, and the study of its dynamics lends insight into many different cellular processes. In particular, calcium plays a central role in muscular contraction, olfactory transduction and synaptic communication, three of the topics to be addressed in detail in this book. In addition to the models, much of the underlying physiology is presented, so that readers may learn both the mathematics and the physiology, and see how the models are applied to specific biological questions. It is intended primarily as a graduate text or a research reference. It will serve as a concise and up-to-date introduction to all those who wish to learn about the state of calcium dynamics modeling, and how such models are applied to physiological questions.
