Cellular Automaton Modeling of Biological Pattern Formation PDF Download

Author: Andreas Deutsch
Publisher: Springer Science & Business Media
ISBN: 0817644156
Category : Science
Languages : en
Pages : 331

View

Book Description
This book focuses on a challenging application field of cellular automata: pattern formation in biological systems, such as the growth of microorganisms, dynamics of cellular tissue and tumors, and formation of pigment cell patterns. These phenomena, resulting from complex cellular interactions, cannot be deduced solely from experimental analysis, but can be more easily examined using mathematical models, in particular, cellular automaton models. While there are various books treating cellular automaton modeling, this interdisciplinary work is the first one covering biological applications. The book is aimed at researchers, practitioners, and students in applied mathematics, mathematical biology, computational physics, bioengineering, and computer science interested in a cellular automaton approach to biological modeling.

Author: Andreas Deutsch
Publisher: Birkhäuser
ISBN: 1489979808
Category : Mathematics
Languages : en
Pages : 464

View

Book Description
This text explores the use of cellular automata in modeling pattern formation in biological systems. It describes several mathematical modeling approaches utilizing cellular automata that can be used to study the dynamics of interacting cell systems both in simulation and in practice. New in this edition are chapters covering cell migration, tissue development, and cancer dynamics, as well as updated references and new research topic suggestions that reflect the rapid development of the field. The book begins with an introduction to pattern-forming principles in biology and the various mathematical modeling techniques that can be used to analyze them. Cellular automaton models are then discussed in detail for different types of cellular processes and interactions, including random movement, cell migration, adhesive cell interaction, alignment and cellular swarming, growth processes, pigment cell pattern formation, tissue development, tumor growth and invasion, and Turing-type patterns and excitable media. In the final chapter, the authors critically discuss possibilities and limitations of the cellular automaton approach in modeling various biological applications, along with future research directions. Suggestions for research projects are provided throughout the book to encourage additional engagement with the material, and an accompanying simulator is available for readers to perform their own simulations on several of the models covered in the text. QR codes are included within the text for easy access to the simulator. With its accessible presentation and interdisciplinary approach, Cellular Automaton Modeling of Biological Pattern Formation is suitable for graduate and advanced undergraduate students in mathematical biology, biological modeling, and biological computing. It will also be a valuable resource for researchers and practitioners in applied mathematics, mathematical biology, computational physics, bioengineering, and computer science. PRAISE FOR THE FIRST EDITION “An ideal guide for someone with a mathematical or physical background to start exploring biological modelling. Importantly, it will also serve as an excellent guide for experienced modellers to innovate and improve their methodologies for analysing simulation results.” —Mathematical Reviews

Author: A. Deutsch
Publisher:
ISBN: 9783764342814
Category :
Languages : en
Pages :

View

Book Description

Author: Anna T. Lawniczak
Publisher: American Mathematical Soc.
ISBN: 0821802585
Category : Science
Languages : en
Pages : 357

View

Book Description
Articles review the diverse recent progress in the theory and development of lattice-gas and lattice Boltzmann methods and their applications. It features up-to-date articles, takes an interdisciplinary approach including mathematics, physical chemistry, and geophysics.

Author: Lui Lam
Publisher: World Scientific Publishing Company
ISBN: 9813103701
Category : Science
Languages : en
Pages : 348

View

Book Description
Almost all real systems are nonlinear. For a nonlinear system the superposition principle breaks down: The system's response is not proportional to the stimulus it receives; the whole is more than the sum of its parts. The three parts of this book contains the basics of nonlinear science, with applications in physics. Part I contains an overview of fractals, chaos, solitons, pattern formation, cellular automata and complex systems. In Part II, 14 reviews and essays by pioneers, as well as 10 research articles are reprinted. Part III collects 17 students projects, with computer algorithms for simulation models included.The book can be used for self-study, as a textbook for a one-semester course, or as supplement to other courses in linear or nonlinear systems. The reader should have some knowledge in introductory college physics. No mathematics beyond calculus and no computer literacy are assumed.

Author: H. Frederick Nijhout
Publisher: CRC Press
ISBN: 0429972997
Category : Mathematics
Languages : en
Pages : 318

View

Book Description
This Lecture Notes Volume represents the first time any of the summer school lectures have been collected and published on a discrete subject rather than grouping all of a season's lectures together. This volume provides a broad survey of current thought on the problem of pattern formation. Spanning six years of summer school lectures, it includes articles which examine the origin and evolution of spatial patterns in physio-chemical and biological systems from a great diversity of theoretical and mechanistic perspectives. In addition, most of these pieces have been updated by their authors and three articles never previously published have been added.

Author: Stephen Wolfram
Publisher: CRC Press
ISBN: 0429973721
Category : Mathematics
Languages : en
Pages : 528

View

Book Description
Are mathematical equations the best way to model nature? For many years it had been assumed that they were. But in the early 1980s, Stephen Wolfram made the radical proposal that one should instead build models that are based directly on simple computer programs. Wolfram made a detailed study of a class of such models known as cellular automata, and discovered a remarkable fact: that even when the underlying rules are very simple, the behaviour they produce can be highly complex, and can mimic many features of what we see in nature. And based on this result, Wolfram began a program of research to develop what he called A Science of Complexity."The results of Wolfram's work found many applications, from the so-called Wolfram Classification central to fields such as artificial life, to new ideas about cryptography and fluid dynamics. This book is a collection of Wolfram's original papers on cellular automata and complexity. Some of these papers are widely known in the scientific community others have never been published before. Together, the papers provide a highly readable account of what has become a major new field of science, with important implications for physics, biology, economics, computer science and many other areas.

Author: Karl-Peter Hadeler
Publisher: Springer
ISBN: 3319530437
Category : Mathematics
Languages : en
Pages : 467

View

Book Description
This book provides an overview of the main approaches used to analyze the dynamics of cellular automata. Cellular automata are an indispensable tool in mathematical modeling. In contrast to classical modeling approaches like partial differential equations, cellular automata are relatively easy to simulate but difficult to analyze. In this book we present a review of approaches and theories that allow the reader to understand the behavior of cellular automata beyond simulations. The first part consists of an introduction to cellular automata on Cayley graphs, and their characterization via the fundamental Cutis-Hedlund-Lyndon theorems in the context of various topological concepts (Cantor, Besicovitch and Weyl topology). The second part focuses on classification results: What classification follows from topological concepts (Hurley classification), Lyapunov stability (Gilman classification), and the theory of formal languages and grammars (Kůrka classification)? These classifications suggest that cellular automata be clustered, similar to the classification of partial differential equations into hyperbolic, parabolic and elliptic equations. This part of the book culminates in the question of whether the properties of cellular automata are decidable. Surjectivity and injectivity are examined, and the seminal Garden of Eden theorems are discussed. In turn, the third part focuses on the analysis of cellular automata that inherit distinct properties, often based on mathematical modeling of biological, physical or chemical systems. Linearity is a concept that allows us to define self-similar limit sets. Models for particle motion show how to bridge the gap between cellular automata and partial differential equations (HPP model and ultradiscrete limit). Pattern formation is related to linear cellular automata, to the Bar-Yam model for the Turing pattern, and Greenberg-Hastings automata for excitable media. In addition, models for sand piles, the dynamics of infectious d

Author: Andrew Adamatzky
Publisher: Springer
ISBN: 3319272705
Category : Technology & Engineering
Languages : en
Pages : 191

View

Book Description
This fascinating, colourful book offers in-depth insights and first-hand working experiences in the production of art works, using simple computational models with rich morphological behaviour, at the edge of mathematics, computer science, physics and biology. It organically combines ground breaking scientific discoveries in the theory of computation and complex systems with artistic representations of the research results. In this appealing book mathematicians, computer scientists, physicists, and engineers brought together marvelous and esoteric patterns generated by cellular automata, which are arrays of simple machines with complex behavior. Configurations produced by cellular automata uncover mechanics of dynamic patterns formation, their propagation and interaction in natural systems: heart pacemaker, bacterial membrane proteins, chemical rectors, water permeation in soil, compressed gas, cell division, population dynamics, reaction-diffusion media and self-organisation. The book inspires artists to take on cellular automata as a tool of creativity and it persuades scientists to convert their research results into the works of art. The book is lavishly illustrated with visually attractive examples, presented in a lively and easily accessible manner.

Author: Bastien Chopard
Publisher: Cambridge University Press
ISBN: 9780521673457
Category : Science
Languages : en
Pages : 356

View

Book Description
This book provides a self-contained introduction to cellular automata and lattice Boltzmann techniques. Beginning with a chapter introducing the basic concepts of this developing field, a second chapter describes methods used in cellular automata modeling. Following chapters discuss the statistical mechanics of lattice gases, diffusion phenomena, reaction-diffusion processes and non-equilibrium phase transitions. A final chapter looks at other models and applications, such as wave propagation and multiparticle fluids. With a pedagogic approach, the volume focuses on the use of cellular automata in the framework of equilibrium and non-equilibrium statistical physics. It also emphasises application-oriented problems such as fluid dynamics and pattern formation. The book contains many examples and problems. A glossary and a detailed bibliography are also included. This will be a valuable book for graduate students and researchers working in statistical physics, solid state physics, chemical physics and computer science.