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A Quest Towards a Mathematical Theory of Living Systems

2017-07-13 Mathematics
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Release : 2017-07-13
Genre : Mathematics
Kind : eBook
Book Rating : 361/5 ( reviews)

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Book Synopsis A Quest Towards a Mathematical Theory of Living Systems by : Nicola Bellomo

Download or read book A Quest Towards a Mathematical Theory of Living Systems written by Nicola Bellomo. This book was released on 2017-07-13. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Towards a Mathematical Theory of Complex Biological Systems

2011 Mathematics
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Release : 2011
Genre : Mathematics
Kind : eBook
Book Rating : 537/5 ( reviews)

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Book Synopsis Towards a Mathematical Theory of Complex Biological Systems by : Carlo Bianca

Download or read book Towards a Mathematical Theory of Complex Biological Systems written by Carlo Bianca. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: This monograph has the ambitious aim of developing a mathematical theory of complex biological systems with special attention to the phenomena of ageing, degeneration and repair of biological tissues under individual self-repair actions that may have good potential in medical therapy. The approach to mathematically modeling biological systems needs to tackle the additional difficulties generated by the peculiarities of living matter. These include the lack of invariance principles, abilities to express strategies for individual fitness, heterogeneous behaviors, competition up to proliferative and/or destructive actions, mutations, learning ability, evolution and many others. Applied mathematicians in the field of living systems, especially biological systems, will appreciate the special class of integro-differential equations offered here for modeling at the molecular, celular and tissue scales. A unique perspective is also presented with a number of case studies in biological modeling.

Towards A Mathematical Theory Of Complex Biological Systems

2011-01-12 Mathematics
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Release : 2011-01-12
Genre : Mathematics
Kind : eBook
Book Rating : 974/5 ( reviews)

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Book Synopsis Towards A Mathematical Theory Of Complex Biological Systems by : Nicola Bellomo

Download or read book Towards A Mathematical Theory Of Complex Biological Systems written by Nicola Bellomo. This book was released on 2011-01-12. Available in PDF, EPUB and Kindle. Book excerpt: This monograph has the ambitious aim of developing a mathematical theory of complex biological systems with special attention to the phenomena of ageing, degeneration and repair of biological tissues under individual self-repair actions that may have good potential in medical therapy.The approach to mathematically modeling biological systems needs to tackle the additional difficulties generated by the peculiarities of living matter. These include the lack of invariance principles, abilities to express strategies for individual fitness, heterogeneous behaviors, competition up to proliferative and/or destructive actions, mutations, learning ability, evolution and many others.Applied mathematicians in the field of living systems, especially biological systems, will appreciate the special class of integro-differential equations offered here for modeling at the molecular, cellular and tissue scales. A unique perspective is also presented with a number of case studies in biological modeling.

Kinetic Theory and Swarming Tools to Modeling Complex Systems—Symmetry problems in the Science of Living Systems

2020-05-29 Business & Economics
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Release : 2020-05-29
Genre : Business & Economics
Kind : eBook
Book Rating : 792/5 ( reviews)

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Book Synopsis Kinetic Theory and Swarming Tools to Modeling Complex Systems—Symmetry problems in the Science of Living Systems by : Nicola Bellomo

Download or read book Kinetic Theory and Swarming Tools to Modeling Complex Systems—Symmetry problems in the Science of Living Systems written by Nicola Bellomo. This book was released on 2020-05-29. Available in PDF, EPUB and Kindle. Book excerpt: This MPDI book comprises a number of selected contributions to a Special Issue devoted to the modeling and simulation of living systems based on developments in kinetic mathematical tools. The focus is on a fascinating research field which cannot be tackled by the approach of the so-called hard sciences—specifically mathematics—without the invention of new methods in view of a new mathematical theory. The contents proposed by eight contributions witness the growing interest of scientists this field. The first contribution is an editorial paper which presents the motivations for studying the mathematics and physics of living systems within the framework an interdisciplinary approach, where mathematics and physics interact with specific fields of the class of systems object of modeling and simulations. The different contributions refer to economy, collective learning, cell motion, vehicular traffic, crowd dynamics, and social swarms. The key problem towards modeling consists in capturing the complexity features of living systems. All articles refer to large systems of interaction living entities and follow, towards modeling, a common rationale which consists firstly in representing the system by a probability distribution over the microscopic state of the said entities, secondly, in deriving a general mathematical structure deemed to provide the conceptual basis for the derivation of models and, finally, in implementing the said structure by models of interactions at the microscopic scale. Therefore, the modeling approach transfers the dynamics at the low scale to collective behaviors. Interactions are modeled by theoretical tools of stochastic game theory. Overall, the interested reader will find, in the contents, a forward look comprising various research perspectives and issues, followed by hints on to tackle these.

Resilience and Stability of Ecological and Social Systems

2020-10-20 Mathematics
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Release : 2020-10-20
Genre : Mathematics
Kind : eBook
Book Rating : 601/5 ( reviews)

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Book Synopsis Resilience and Stability of Ecological and Social Systems by : István Karsai

Download or read book Resilience and Stability of Ecological and Social Systems written by István Karsai. This book was released on 2020-10-20. Available in PDF, EPUB and Kindle. Book excerpt: This monograph, co-authored by three longtime collaborators, aims to promote the interdisciplinary field of mathematical biology by providing accessible new approaches to study natural systems. As there is currently scarce literature on the applications of mathematical modelling for biology research, this book presents a new way of studying interactions at the level of populations, societies, ecosystems, and biomes through open-sourced modeling platforms. It offers an interdisciplinary approach to analyzing natural phenomena—for example, by showing how master equations developed to describe electrical circuits can also describe biological systems mathematically. Ultimately it promotes a method of study based on modelling and mathematical principles, facilitating collaboration between mathematicians, biologists, engineers, and other researchers to enrich knowledge of the world’s ecosystems.

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