Viability Theory
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Viability Theory
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Author : Jean-Pierre Aubin
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-28
Viability Theory written by Jean-Pierre Aubin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-28 with Science categories.
This work examines viability theory and its applications to control theory and differential games. The emphasis is on the construction of feedbacks and dynamical systems by myopic optimization methods. Systems of first-order partial differential inclusions, whose solutions are feedbacks, are constructed and investigated. Basic results are then extended to the case of fuzzy control problems, distributed control problems, and control systems with delays and memory. Aimed at graduate students and research mathematicians, both pure and applied, this book offers specialists in control and nonlinear systems tools to take into account general state constraints. Viability theory also allows researchers in other disciplines—artificial intelligence, economics, game theory, theoretical biology, population genetics, cognitive sciences—to go beyond deterministic models by studying them in a dynamical or evolutionary perspective in an uncertain environment. "The book is a compendium of the state of knowledge about viability...Mathematically, the book should be accessible to anyone who has had basic graduate courses in modern analysis and functional analysis...The concepts are defined and many proofs of the requisite results are reproduced here, making the present book essentially self-contained." (Bulletin of the AMS) "Because of the wide scope, the book is an ideal reference for people encountering problems related to viability theory in their research...It gives a very thorough mathematical presentation. Very useful for anybody confronted with viability constraints." (Mededelingen van het Wiskundig Genootschap)
Viability Theory
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Author : Jean-Pierre Aubin
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-13
Viability Theory written by Jean-Pierre Aubin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-13 with Science categories.
Viability theory designs and develops mathematical and algorithmic methods for investigating the adaptation to viability constraints of evolutions governed by complex systems under uncertainty that are found in many domains involving living beings, from biological evolution to economics, from environmental sciences to financial markets, from control theory and robotics to cognitive sciences. It involves interdisciplinary investigations spanning fields that have traditionally developed in isolation. The purpose of this book is to present an initiation to applications of viability theory, explaining and motivating the main concepts and illustrating them with numerous numerical examples taken from various fields.
Dynamic Economic Theory
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Author : Jean-Pierre Aubin
language : en
Publisher: Springer
Release Date : 2013-11-13
Dynamic Economic Theory written by Jean-Pierre Aubin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-13 with Business & Economics categories.
This book is intended to provide economists with mathematical tools necessary to handle the concepts of evolution under uncertainty and adaption arising in economics, pursuing the Arrow-Debreu-Hahn legacy. It applies the techniques of viability theory to the study of economic systems evolving under contingent uncertainty, faced with scarcity constraints, and obeying various implementation of the inertia principle. The book illustrates how new tools can be used to move from static analysis, built on concepts of optima, equilibria and attractors to a contingent dynamic framework.
Differential Inclusions
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Author : J.-P. Aubin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Differential Inclusions written by J.-P. Aubin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A great impetus to study differential inclusions came from the development of Control Theory, i.e. of dynamical systems x'(t) = f(t, x(t), u(t)), x(O)=xo "controlled" by parameters u(t) (the "controls"). Indeed, if we introduce the set-valued map F(t, x)= {f(t, x, u)}ueu then solutions to the differential equations (*) are solutions to the "differen tial inclusion" (**) x'(t)EF(t, x(t)), x(O)=xo in which the controls do not appear explicitely. Systems Theory provides dynamical systems of the form d x'(t)=A(x(t)) dt (B(x(t))+ C(x(t)); x(O)=xo in which the velocity of the state of the system depends not only upon the x(t) of the system at time t, but also on variations of observations state B(x(t)) of the state. This is a particular case of an implicit differential equation f(t, x(t), x'(t)) = 0 which can be regarded as a differential inclusion (**), where the right-hand side F is defined by F(t, x)= {vlf(t, x, v)=O}. During the 60's and 70's, a special class of differential inclusions was thoroughly investigated: those of the form X'(t)E - A(x(t)), x (0) =xo where A is a "maximal monotone" map. This class of inclusions contains the class of "gradient inclusions" which generalize the usual gradient equations x'(t) = -VV(x(t)), x(O)=xo when V is a differentiable "potential". 2 Introduction There are many instances when potential functions are not differentiable
Viability And Resilience Of Complex Systems
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Author : Guillaume Deffuant
language : en
Publisher: Springer
Release Date : 2011-08-03
Viability And Resilience Of Complex Systems written by Guillaume Deffuant and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-03 with Social Science categories.
One common characteristics of a complex system is its ability to withstand major disturbances and the capacity to rebuild itself. Understanding how such systems demonstrate resilience by absorbing or recovering from major external perturbations requires both quantitative foundations and a multidisciplinary view on the topic. This book demonstrates how new methods can be used to identify the actions favouring the recovery from perturbations. Examples discussed include bacterial biofilms resisting detachment, grassland savannahs recovering from fire, the dynamics of language competition and Internet social networking sites overcoming vandalism. The reader is taken through an introduction to the idea of resilience and viability and shown the mathematical basis of the techniques used to analyse systems. The idea of individual or agent-based modelling of complex systems is introduced and related to analytically tractable approximations of such models. A set of case studies illustrates the use of the techniques in real applications, and the final section describes how one can use new and elaborate software tools for carrying out the necessary calculations. The book is intended for a general scientific audience of readers from the natural and social sciences, yet requires some mathematics to gain a full understanding of the more theoretical chapters. It is an essential point of reference for those interested in the practical application of the concepts of resilience and viability
Economic Theory And Sustainable Development
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Author : Vincent Martinet
language : en
Publisher: Routledge
Release Date : 2012-05-23
Economic Theory And Sustainable Development written by Vincent Martinet and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-23 with Business & Economics categories.
Is development sustainable? When addressing the sustainability issue, decision-makers are faced with two challenges: taking into account conflicting issues, such as economic development and environmental preservation, while also ensuring intergenerational equity. Tackling these challenges amounts to deciding what should be bequeathed to future generations, especially in terms of natural resources.
The Viability Of Human Security
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Author : Monica den Boer
language : en
Publisher: Amsterdam University Press
Release Date : 2008
The Viability Of Human Security written by Monica den Boer and has been published by Amsterdam University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Political Science categories.
This volume elaborates on the EU report A Human Security Doctrine for Europe, adding an engaging discussion of international legal consequences and operational demands in the European Union’s quest for domestic security. Introducing the concept of “Human Security from Below,” the editors highlight how people in war-torn countries have no choice but to create their own security arrangements. But such structures, surprisingly, are not unique to war zones, the contributors reveal—human security initiatives from below occur in even the most stable Western countries. Arguing that human security as a concept only makes sense if it covers both foreign and domestic policy concerns, The Viability of Human Security offers concise insights on this largely neglected topic.
Viability Invariance And Applications
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Author : Ovidiu Carja
language : en
Publisher: Elsevier
Release Date : 2007-07-18
Viability Invariance And Applications written by Ovidiu Carja and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-18 with Mathematics categories.
The book is an almost self-contained presentation of the most important concepts and results in viability and invariance. The viability of a set K with respect to a given function (or multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. The invariance of a set K with respect to a function (or multi-function) F, defined on a larger set D, is that property which says that each solution of the differential equation (or inclusion) driven by F and issuing in K remains in K, at least for a short time.The book includes the most important necessary and sufficient conditions for viability starting with Nagumo's Viability Theorem for ordinary differential equations with continuous right-hand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In the latter (i.e. multi-valued) cases, the results (based on two completely new tangency concepts), all due to the authors, are original and extend significantly, in several directions, their well-known classical counterparts. - New concepts for multi-functions as the classical tangent vectors for functions - Provides the very general and necessary conditions for viability in the case of differential inclusions, semilinear and fully nonlinear evolution inclusions - Clarifying examples, illustrations and numerous problems, completely and carefully solved - Illustrates the applications from theory into practice - Very clear and elegant style
Cultural Theory
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Author : Michael Thompson
language : en
Publisher: Routledge
Release Date : 2018-06-27
Cultural Theory written by Michael Thompson and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-27 with Social Science categories.
Why do people want what they want? Why does one person see the world as a place to control, while another feels controlled by the world? A useful theory of culture, the authors contend, should start with these questions, and the answers, given different historical conditions, should apply equally well to people of all times, places, and walks of life.Taking their cue from the pioneering work of anthropologist Mary Douglas, the authors of Cultural Theory have created a typology of five ways of life?egalitarianism, fatalism, individualism, hierarchy, and autonomy?to serve as an analytic tool in examining people, culture, and politics. They then show how cultural theorists can develop large numbers of falsifiable propositions.Drawing on parables, poetry, case studies, fiction, and the Great Books, the authors illustrate how cultural biases and social relationships interact in particular ways to yield life patterns that are viable, sustainable, and ultimately, changeable under certain conditions. Figures throughout the book show the dynamic quality of these ways of life and specifically illustrate the role of surprise in effecting small- and large-scale change.The authors compare Cultural Theory with the thought of master social theorists from Montesquieu to Stinchcombe and then reanalyze the classic works in the political culture tradition from Almond and Verba to Pye. Demonstrating that there is more to social life than hierarchy and individualism, the authors offer evidence from earlier studies showing that the addition of egalitarianism and fatalism facilitates cross-national comparisons.