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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.
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.
This volume introduces some basic theories on computational neuroscience. Chapter 1 is a brief introduction to neurons, tailored to the subsequent chapters. Chapter 2 is a self-contained introduction to dynamical systems and bifurcation theory, oriented towards neuronal dynamics. The theory is illustrated with a model of Parkinson's disease. Chapter 3 reviews the theory of coupled neural oscillators observed throughout the nervous systems at all levels; it describes how oscillations arise, what pattern they take, and how they depend on excitory or inhibitory synaptic connections. Chapter 4 specializes to one particular neuronal system, namely, the auditory system. It includes a self-contained introduction, from the anatomy and physiology of the inner ear to the neuronal network that connects the hair cells to the cortex, and describes various models of subsystems.
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.
The challenge for the biosciences in the twenty-first century is to integrate genome sequencing information into a better understanding of biology, physiology, and human pathology. Such attempts at integration are moving the world toward a new generation of bioscience and bioengineering, where biological, physiological, and pathological information from humans and other living animals can be quantitatively described in silico across multiple scales of time and size and through diverse hierarchies of organization — from molecules to cells and organs, to individuals. To "harness" such complexity, international communities of integrative bioscientists and bioengineers aim to establish frameworks and information infrastructures for describing biological structures and physiological functions on multiple scales of time and space. This textbook includes a public platform to describe physiological functions using mathematical equations and guides the reader to perform mathematical modeling and computer simulations, to combine existing models as well as to create new models. Accessible to biologists, physiologists, and students of the sciences, with illustrative details provided when necessary, this book seeks to achieve a systematic way of harnessing biological complexity. Sharing the databases among communities worldwide will help to find comprehensive answers to all the important questions.
Thisisthefourthvolumeintheseries TutorialsinMathematicalBiosciences. These lectures are based on material which was presented in tutorials or developed by visitors and postdoctoral fellows of the Mathematical B- sciences Institute (MBI), at The Ohio State University. The aim of this series is to introduce graduate students and researchers with just a little ba- ground in either mathematics or biology to mathematical modeling of biol- ical processes. The ?rst volume was devoted to mathematical neuroscience, which was the focus of the MBI program 2002 2003. The second volume dealt with mathematical modeling of calcium dynamics in signal transduction, the focus of the MBI program in the winter of 2004. The third volume dealt with topics of cell cycle, tumor growth, and cancer therapy; these topics featured in several workshops held at the MBI in the fall of 2003. The present volume deals with a variety of topics of evolution and ecology, which were considered in the MBI during the year 2005 2006. These topics include phylogenetics; evolution of genes through migration selection; ecological modeling; and e- lutionofdispersalandpopulationdynamics. Documentationofthe2005 2006 activities, including streaming videos of the workshops, can be found on the Web site: http: //mbi. osu. edu. Phylogenetics is the study of the evolutionary relations of genes and - ganisms. Phylogenetic trees are represented by graphs in which the leaves represent observed biological entities. In constructing such graphs, one tries to trace the evolution of species, traits, or diseases. The ?rst two chapters of this volume deal with phylogenetics."
This user’s reference is a companion to the separate book also titled “Guide to Modelling and Simulation of Systems of Systems.” The principal book explicates integrated development environments to support virtual building and testing of systems of systems, covering in some depth the MS4 Modelling EnvironmentTM. This user’s reference provides a quick reference and exposition of the various concepts and functional features covered in that book. The topics in the user’s reference are grouped in alignment with the workflow displayed on the MS4 Modeling EnvironmentTM launch page, under the headings Atomic Models, System Entity Structure, Pruning SES, and Miscellaneous. For each feature, the reference discusses why we use it, when we should use it, and how to use it. Further comments and links to related features are also included.

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