A Quest Towards a Mathematical Theory of Living Systems
Published on 21. July 2017
Book
Hardback
XIII, 181 pages
978-3-319-57435-6 (ISBN)
Description
This monograph aims to lay the groundwork for the design of a unified mathematical approach to the modeling and analysis of large, complex systems composed of interacting living things. Drawing on twenty years of research in various scientific fields, it explores how mathematical kinetic theory and evolutionary game theory can be used to understand the complex interplay between mathematical sciences and the dynamics of living systems. The authors hope this will contribute to the development of new tools and strategies, if not a new mathematical theory.
The first chapter discusses the main features of living systems and outlines a strategy for their modeling. The following chapters then explore some of the methods needed to potentially achieve this in practice. Chapter Two provides a brief introduction to the mathematical kinetic theory of classical particles, with special emphasis on the Boltzmann equation; the Enskog equation,mean field models, and Monte Carlo methods are also briefly covered. Chapter Three uses concepts from evolutionary game theory to derive mathematical structures that are able to capture the complexity features of interactions within living systems. The book then shifts to exploring the relevant applications of these methods that can potentially be used to derive specific, usable models. The modeling of social systems in various contexts is the subject of Chapter Five, and an overview of modeling crowd dynamics is given in Chapter Six, demonstrating how this approach can be used to model the dynamics of multicellular systems. The final chapter considers some additional applications before presenting an overview of open problems. The authors then offer their own speculations on the conceptual paths that may lead to a mathematical theory of living systems hoping to motivate future research activity in the field.
A truly unique contribution to the existing literature, A Quest Toward a Mathematical Theory of Living Systems is an important book that will no doubt have a significant influence on the future directions of the field. It will be of interest to mathematical biologists, systems biologists, biophysicists, and other researchers working on understanding the complexities of living systems.
The first chapter discusses the main features of living systems and outlines a strategy for their modeling. The following chapters then explore some of the methods needed to potentially achieve this in practice. Chapter Two provides a brief introduction to the mathematical kinetic theory of classical particles, with special emphasis on the Boltzmann equation; the Enskog equation,mean field models, and Monte Carlo methods are also briefly covered. Chapter Three uses concepts from evolutionary game theory to derive mathematical structures that are able to capture the complexity features of interactions within living systems. The book then shifts to exploring the relevant applications of these methods that can potentially be used to derive specific, usable models. The modeling of social systems in various contexts is the subject of Chapter Five, and an overview of modeling crowd dynamics is given in Chapter Six, demonstrating how this approach can be used to model the dynamics of multicellular systems. The final chapter considers some additional applications before presenting an overview of open problems. The authors then offer their own speculations on the conceptual paths that may lead to a mathematical theory of living systems hoping to motivate future research activity in the field.
A truly unique contribution to the existing literature, A Quest Toward a Mathematical Theory of Living Systems is an important book that will no doubt have a significant influence on the future directions of the field. It will be of interest to mathematical biologists, systems biologists, biophysicists, and other researchers working on understanding the complexities of living systems.
Reviews / Votes
"The approach of this book is qualitative and pragmatic, a clear and engaging presentational style leading swiftly to well-defined objectives stated ahead of time. . The mathematical scaffolding supports the presentation . which makes the book as suitable for social scientists, biologists, ecologists, or for other natural scientists willing to investigate the complexity of living systems via a quantitative approach, as it is for mathematicians who are willing to acquire stronger modelling foundations." (Paul Georgescu, zbMATH1381.92001, 2018)"A Quest Towards a Mathematical Theory of Living Systems should prove to be aninteresting book, especially for those with interests in collective behavior, emergent phenomenon, and mathematical approaches to studying such phenomena. . I recommend this book as a point of entry into this popular field of current research in the mathematical life sciences." (Jason M. Graham, MAA Reviews, December, 2017)
More details
Series
Edition
1st ed. 2017
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
3 s/w Abbildungen, 27 farbige Abbildungen
XIII, 181 p. 30 illus., 27 illus. in color.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 17 mm
Weight
465 gr
ISBN-13
978-3-319-57435-6 (9783319574356)
DOI
10.1007/978-3-319-57436-3
Schweitzer Classification
Other editions
Additional editions
Nicola Bellomo | Abdelghani Bellouquid | Livio Gibelli
A Quest Towards a Mathematical Theory of Living Systems
Book
08/2018
Birkhäuser
€96.29
Shipment within 10-15 days
Nicola Bellomo | Abdelghani Bellouquid | Livio Gibelli
A Quest Towards a Mathematical Theory of Living Systems
E-Book
07/2017
Birkhäuser
€96.29
Available for download
Persons
Bouchra Aylaj is an Associate Professor with Habilitation in mathematics at University of Hassan II of Casablanca, Faculty Ain Chock, Morocco. She started her career in 2006 when she was called to develop a research program on mathematical modelling in biology. Her scientific activity has been focused on the following topics: scientific computing and control for risk analysis and analytical and computational problems in epidemiology. Subsequently, she moved her scientific interests to the modeling and related safety problems focused on social behaviors in human crowds.Nicola Bellomo is a distinguished professor at the University of Granada and Professor Emeritus at the Polytechnic University of Torino. He started his career in 1980 when he was called to cover the chair of mathematical physics and applied mathematics due to his scientific achievements on the mathematical theory of the Boltzmann equation and of stochastic differential equations. Subsequently, he moved his scientificinterests to the study of living systems, becoming one of the pioneers of the development of active particles methods to the modeling of large systems of self-propelled interacting entities. He is author of two books published by Birkhauser devoted to this topic. In 2009, he delivered the prestigious Shank Lecture on the modeling of immune competition, and was awarded the "Third Level Honor" in 2016 for scientific merits by the President of the Italian Republic.Livio Gibelli is a Lecturer in Mechanical Engineering at the University of Edinburgh. He received his Ph.D. in applied mathematics from the Politecnico di Milano and, prior to the current position, he worked as Research Fellow at the University of Warwick, Politecnico di Milano, Politecnico di Torino, and University of British Columbia. His main research interests include non-equilibrium multiphase fluid flows, the continuum description of slightly rarefied gases, the numerical methods for solving kinetic equations,and the modeling of crowd dynamics.Damian Knopoff is a chemical engineer and mathematician, holding a Ph.D. in Mathematics from Cordoba National University. Currently, he is an Associate Researcher at the Argentinian Scientific and Technical Research Council. His main research fields include nonlinear dynamical systems and numerical methods for differential equations with applications to the modeling and simulation of complex living systems, including biological phenomena, socio-economic systems, and crowd dynamics.
Content
On the "Complex" Interplay between Mathematics and Living Systems.- A Brief Introduction to the Mathematical Kinetic Theory of Classical Particles.- On the Search for a Structure: Toward a Mathematical Theory to Model Living Systems.- From the Mathematical Theory to Applications.- Modeling Social Behavioral Dynamics.- Mathematical Models of Crowd Dynamics in Complex Venues.- On the Search for a Mathematical Theory of Living Systems.