LEADER 05266nam 22006255 450 001 9910254275603321 005 20200704100031.0 010 $a3-319-57436-1 024 7 $a10.1007/978-3-319-57436-3 035 $a(CKB)4340000000062048 035 $a(DE-He213)978-3-319-57436-3 035 $a(MiAaPQ)EBC4915499 035 $z(PPN)258852593 035 $a(PPN)203669258 035 $a(EXLCZ)994340000000062048 100 $a20170714d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Quest Towards a Mathematical Theory of Living Systems$b[electronic resource] /$fby Nicola Bellomo, Abdelghani Bellouquid, Livio Gibelli, Nisrine Outada 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2017. 215 $a1 online resource (XIII, 181 p. 30 illus., 27 illus. in color.) 225 1 $aModeling and Simulation in Science, Engineering and Technology,$x2164-3679 311 $a3-319-57435-3 320 $aIncludes bibliographical references and index. 327 $aOn 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. 330 $aThis 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. 410 0$aModeling and Simulation in Science, Engineering and Technology,$x2164-3679 606 $aBiomathematics 606 $aMathematical models 606 $aSystem theory 606 $aMathematical and Computational Biology$3https://scigraph.springernature.com/ontologies/product-market-codes/M31000 606 $aMathematical Modeling and Industrial Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M14068 606 $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/M13090 615 0$aBiomathematics. 615 0$aMathematical models. 615 0$aSystem theory. 615 14$aMathematical and Computational Biology. 615 24$aMathematical Modeling and Industrial Mathematics. 615 24$aComplex Systems. 676 $a570.15195 700 $aBellomo$b Nicola$4aut$4http://id.loc.gov/vocabulary/relators/aut$031305 702 $aBellouquid$b Abdelghani$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aGibelli$b Livio$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aOutada$b Nisrine$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254275603321 996 $aA Quest Towards a Mathematical Theory of Living Systems$92155978 997 $aUNINA