ContentsandScienti?cAims The scienti?c community is aware that the great scienti?c revolution of this century will be the mathematical formalization, by methods of applied mathematics, of complex biological systems. A fascinating prospect is that biological sciences will ?nally be supported by rigorous investigation me- ods and tools, similar to what happened in the past two centuries in the case of mechanical and physical sciences. It is not an easy task, considering that new mathematical methods maybeneededtodealwiththeinnercomplexityofbiologicalsystemswhich exhibit features and behaviors very di?erent from those of inert matter. Microscopic entities in biology, say cells in a multicellular system, are characterized by biological functions and the ability to organize their dynamics and interactions with other cells. Indeed, cells organize their dynamics according to the above functions, while classical particles follow deterministic laws of Newtonian mechanics. Cells have a life according to a cell cycle which ends up with a programmed death. The dialogue among cells can modify their behavior. The activity of cells includes proliferation and/or destructive events which may, in some cases, result in dangerously reproductive events. Finally, a cellular system may move far from eq- librium in physical situations where classical particles generally show a tendency toward equilibrium. An additional source of complexity is that biological systems always need a multiscale approach. Speci?cally, the dynamics of a cell, including its life, are ruled by sub-cellular entities, while most of the phenomena can be e?ectively observed only at the macroscopic scale.

ContentsandScienti?cAims The scienti?c community is aware that the great scienti?c revolution of this century will be the mathematical formalization, by methods of applied mathematics, of complex biological systems. A fascinating prospect is that biological sciences will ?nally be supported by rigorous investigation me- ods and tools, similar to what happened in the past two centuries in the case of mechanical and physical sciences. It is not an easy task, considering that new mathematical methods maybeneededtodealwiththeinnercomplexityofbiologicalsystemswhich exhibit features and behaviors very di?erent from those of inert matter. Microscopic entities in biology, say cells in a multicellular system, are characterized by biological functions and the ability to organize their dynamics and interactions with other cells. Indeed, cells organize their dynamics according to the above functions, while classical particles follow deterministic laws of Newtonian mechanics. Cells have a life according to a cell cycle which ends up with a programmed death. The dialogue among cells can modify their behavior. The activity of cells includes proliferation and/or destructive events which may, in some cases, result in dangerously reproductive events. Finally, a cellular system may move far from eq- librium in physical situations where classical particles generally show a tendency toward equilibrium. An additional source of complexity is that biological systems always need a multiscale approach. Speci?cally, the dynamics of a cell, including its life, are ruled by sub-cellular entities, while most of the phenomena can be e?ectively observed only at the macroscopic scale.

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.

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.

ContentsandScienti?cAims The scienti?c community is aware that the great scienti?c revolution of this century will be the mathematical formalization, by methods of applied mathematics, of complex biological systems. A fascinating prospect is that biological sciences will ?nally be supported by rigorous investigation me- ods and tools, similar to what happened in the past two centuries in the case of mechanical and physical sciences. It is not an easy task, considering that new mathematical methods maybeneededtodealwiththeinnercomplexityofbiologicalsystemswhich exhibit features and behaviors very di?erent from those of inert matter. Microscopic entities in biology, say cells in a multicellular system, are characterized by biological functions and the ability to organize their dynamics and interactions with other cells. Indeed, cells organize their dynamics according to the above functions, while classical particles follow deterministic laws of Newtonian mechanics. Cells have a life according to a cell cycle which ends up with a programmed death. The dialogue among cells can modify their behavior. The activity of cells includes proliferation and/or destructive events which may, in some cases, result in dangerously reproductive events. Finally, a cellular system may move far from eq- librium in physical situations where classical particles generally show a tendency toward equilibrium. An additional source of complexity is that biological systems always need a multiscale approach. Speci?cally, the dynamics of a cell, including its life, are ruled by sub-cellular entities, while most of the phenomena can be e?ectively observed only at the macroscopic scale.

ContentsandScienti?cAims The scienti?c community is aware that the great scienti?c revolution of this century will be the mathematical formalization, by methods of applied mathematics, of complex biological systems. A fascinating prospect is that biological sciences will ?nally be supported by rigorous investigation me- ods and tools, similar to what happened in the past two centuries in the case of mechanical and physical sciences. It is not an easy task, considering that new mathematical methods maybeneededtodealwiththeinnercomplexityofbiologicalsystemswhich exhibit features and behaviors very di?erent from those of inert matter. Microscopic entities in biology, say cells in a multicellular system, are characterized by biological functions and the ability to organize their dynamics and interactions with other cells. Indeed, cells organize their dynamics according to the above functions, while classical particles follow deterministic laws of Newtonian mechanics. Cells have a life according to a cell cycle which ends up with a programmed death. The dialogue among cells can modify their behavior. The activity of cells includes proliferation and/or destructive events which may, in some cases, result in dangerously reproductive events. Finally, a cellular system may move far from eq- librium in physical situations where classical particles generally show a tendency toward equilibrium. An additional source of complexity is that biological systems always need a multiscale approach. Speci?cally, the dynamics of a cell, including its life, are ruled by sub-cellular entities, while most of the phenomena can be e?ectively observed only at the macroscopic scale.

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.

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.