Neuware -Thesubjectofthisbookisthemodelingofcomplex systemsinthelife sciences constituted by a large number of interacting entities called active particles. Their physical state includes, in addition to geometrical and mechanical variables, a variable called the activity, which characterizes the speci c living system to be modeled. Interactions among particles not only modify the microscopic state, but may generate proliferative and/or destructive phenomena. The aim of the book is to develop mathematical methods and tools, even a new mathematics, for the modeling of living systems. The background idea is that the modeling of living systems requires technically complex mathematical methods, which may be s- stantially di erent from those used to deal with inert matter. The rstpart ofthe bookdiscussesmethodological issues, namely the derivation of various general mathematical frameworks suitable to model particular systems of interest in the applied sciences. The second part presents the various models and applications. The mathematical approach used in the book is based on mathema- cal kinetic theoryfor active particles, whichleads tothederivation of evo- tion equations for a one-particle distribution function over the microscopic state. Two types of equations, to be regarded as a general mathematical framework for deriving the models, are derived corresponding to short and long range interactions.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 236 pp. Englisch.

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Titel: Modeling Complex Living Systems
Verlag: Birkh�user Boston, Birkh�user Boston Nov 2007
Erscheinungsjahr: 2007
Sprache: Englisch
ISBN-10: 0817645101
ISBN-13: 9780817645106
Einband: Buch
Zustand: Neu
Abmessungen: Breite: 241 mm, H�he: 160 mm, Tiefe: 18 mm
Gewicht: 524 Gramm

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This book develops new mathematical methods and tools to model living systems. The material it presents can be used in such real-world applications as immunology, transportation engineering, and economics. The first part of the book deals with deriving general evolution equations that can be customized to particular systems of interest in the applied sciences. The second part of the book deals with various models and applications. The book will be a valuable resource to all involved in modeling complex social systems and living matter in general.

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Using tools from mathematical kinetic theory and stochastic game theory, this work deals with the modeling of large complex systems in the applied sciences, particularly those comprised of several interacting individuals whose dynamics follow rules determined by some organized, or even "intelligent" ability. Traditionally, methods of mathematical kinetic theory have been applied to model the evolution of large systems of interacting classical or quantum particles. This book, on the other hand, examines the modeling of living systems as opposed to inert systems.

The author develops new mathematical methods and tools--hopefully a "new" mathematics--toward the modeling of living systems. Such tools need to be far more complex than those dealing with systems of inert matter. The first part of the book deals with deriving general evolution equations that can be customized to particular systems of interest in the applied sciences. The second part of the book deals with various models and applications.

The presentation unfolds using the following common approach in each chapter:

* Phenomenological interpretation of the physical system in the context of mathematical modeling

* Derivation of the mathematical model using methods from mathematical kinetic theory for active particles

* Simulations, parameter sensitivity analysis, and critical inspection of the derived model towards validation

* Overview of presented ideas to improve existing models, with special emphasis on applications

Specific topics covered include:

* Modeling of the competition between cells of an aggressive invasive agent and cells of the immune system

* Modeling of vehicular traffic flow

* Modeling of swarms and crowd dynamics in complex geometric environments

* Methodological aspects related to multiscale modeling of large systems viewed as interconnected subsystems

Modeling Complex LivingSystems is a valuable resource for applied mathematicians, engineers, physicists, biologists, economists, and graduate students involved in modeling complex social systems and living matter in general.

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