Martin Sophie

Irstea − Lisc
9 avenue Blaise Pascal − CS 20085
63178 Aubière − France
+33 4 73 44 07 29
Contact

Site web : sophie.martin.perso.free.fr

Publications

Journal Articles (11)

S. Martin, I. Alvarez, J.D. Kant
Micro/macro viability analysis of individual-based models: Investigation into the viability of a stylized agricultural cooperative
Complexity 21 (2), 2014
abs doi web bib

The mathematical viability theory proposes methods and tools to study at a global level how controlled dynamical systems can be confined in a desirable subset of the state space. Multilevel viability problems are rarely studied since they induce combinatorial explosion (the set of N agents each evolving in a p-dimensional state space, can evolve in a Np dimensional state space). In this article, we propose an original approach which consists in solving first local viability problems and then studying the real viability of the combination of the local strategies, by simulation where necessary. In this article, we consider as multilevel viability problem a stylized agricultural cooperative which has to keep a minimum of members. Members have an economical constraint and some members have a simple model of the functioning of the cooperative and make assumptions on other members' behavior, especially proviable agents which are concerned about their own viability. In this framework, the model assumptions allow us to solve the local viability problem at the agent level. At the cooperative level, considering mixture of agents, simulation results indicate if and when including proviable agents increases the viability of the whole cooperative.
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@article{PUB00044373, author = {Martin, S. and Alvarez, I. and Kant, J.D.}, title = {Micro/macro viability analysis of individual-based models: Investigation into the viability of a stylized agricultural cooperative}, title = {Analyse de viabilité micro/macro de modèles individus-centrés : étude de la viabilité d'un modèle stylisé de coopérative}, journal = {Complexity}, volume = {21}, number = {2}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00044373 / http://onlinelibrary.wiley.com/doi/10.1002/cplx.21604/full}, doi = {http://dx.doi.org/10.1002/cplx.21604}, year = {2014}, affiliation = {IRSTEA CLERMONT FERRAND UR LISC FRA ; IRSTEA CLERMONT FERRAND UR LISC FRA ; UNIVERSITE PARIS MARIE CURIE LIP6 FRA}, abstract = {The mathematical viability theory proposes methods and tools to study at a global level how controlled dynamical systems can be confined in a desirable subset of the state space. Multilevel viability problems are rarely studied since they induce combinatorial explosion (the set of N agents each evolving in a p-dimensional state space, can evolve in a Np dimensional state space). In this article, we propose an original approach which consists in solving first local viability problems and then studying the real viability of the combination of the local strategies, by simulation where necessary. In this article, we consider as multilevel viability problem a stylized agricultural cooperative which has to keep a minimum of members. Members have an economical constraint and some members have a simple model of the functioning of the cooperative and make assumptions on other members' behavior, especially proviable agents which are concerned about their own viability. In this framework, the model assumptions allow us to solve the local viability problem at the agent level. At the cooperative level, considering mixture of agents, simulation results indicate if and when including proviable agents increases the viability of the whole cooperative.}, }
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S. Mesmoudi, I. Alvarez, S. Martin, R. Reuillon, M. Sicard, N. Perrot
Coupling geometric analysis and viability theory for system exploration: Application to a living food system
Journal of Process Control 24 (12), 2014
abs doi web bib

This paper addresses the issue of studying a food complex system in a reverse engineering manner with the aim of identifying the set of all possible actions that makes it reach a quality target with respect to manufacturing constraints. Once the set of actions is identified, several criteria can be considered to identify interesting trajectories and control policies. A viability approach, coupling the viability theory and a geometric approach of robustness, is proposed to study complex dynamical systems. It can be implemented for several types of systems, from linear to non linear or hybrid systems. The proposed framework was adapted to a living food system: a ripening model of Camembert cheese to identify the set of states and actions (capture basin) from which it is possible to reach a predefined quality target. Within the set of viable trajectories, particular trajectories that improve the Camembert cheese ripening process are identified using the proposed approach. The results are applied at a pilot scale and are discussed in this paper.
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@article{PUB00043300, author = {Mesmoudi, S. and Alvarez, I. and Martin, S. and Reuillon, R. and Sicard, M. and Perrot, N.}, title = {Coupling geometric analysis and viability theory for system exploration: Application to a living food system}, title = {Coupler l'analyse géométrique et la théorie de la viabilité pour explorer les dynamiques des systèmes : application à un système alimentaire}, journal = {Journal of Process Control}, volume = {24}, number = {12}, pages = {18-28}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00043300 / http://www.sciencedirect.com/science/article/pii/S0959152414002522}, doi = {http://dx.doi.org/10.1016/j.jprocont.2014.09.013}, year = {2014}, affiliation = {ISCPIF LIP6 PARIS FRA ; IRSTEA CLERMONT FERRAND UR LISC FRA ; IRSTEA CLERMONT FERRAND UR LISC FRA ; ISCPIF PARIS FRA ; INRA UMR 782 GMPA AGROPARISTECH THIVERVAL GRIGNON FRA ; INRA UMR 782 GMPA AGROPARISTECH THIVERVAL GRIGNON FRA}, abstract = {This paper addresses the issue of studying a food complex system in a reverse engineering manner with the aim of identifying the set of all possible actions that makes it reach a quality target with respect to manufacturing constraints. Once the set of actions is identified, several criteria can be considered to identify interesting trajectories and control policies. A viability approach, coupling the viability theory and a geometric approach of robustness, is proposed to study complex dynamical systems. It can be implemented for several types of systems, from linear to non linear or hybrid systems. The proposed framework was adapted to a living food system: a ripening model of Camembert cheese to identify the set of states and actions (capture basin) from which it is possible to reach a predefined quality target. Within the set of viable trajectories, particular trajectories that improve the Camembert cheese ripening process are identified using the proposed approach. The results are applied at a pilot scale and are discussed in this paper.}, }
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C. Bernard, S. Martin
Comparing the sustainability of different action policy possibilities: Application to the issue of both household survival and forest preservation in the corridor of Fianarantsoa
Mathematical Biosciences 245 (2), 2013
abs doi web bib

A sustainability issue for the rain forest in the corridor of Fianarantsoa (Madagascar) is to preserve the forest while ensuring the development of the local population. The aim of this paper is to determine whether the current situation is sustainable or not according to different action policy possibilities. We propose a general procedure based on viability analysis: Translation of sustainability issues into constraints on the system state; elaboration of a mathematical model of system evolution rules in the form of controlled dynamical system; computations of the viability kernels according to different action policy possibilities. Among control variables, we focus on monetary transfer. Without monetary transfer, we show that the current situation of the rain forest corridor is not sustainable in our mathematical modeling framework. We then estimate the minimal maximal amount per year necessary to make the current situation sustainable.
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@article{PUB00039047, author = {Bernard, C. and Martin, S.}, title = {Comparing the sustainability of different action policy possibilities: Application to the issue of both household survival and forest preservation in the corridor of Fianarantsoa}, title = {Comparer la durabilité de différentes possibilités de politiques d'actions : application aux enjeux de survie des foyers et de préservation de la forêt dans le corridor forestier de Fianarantsoa}, journal = {Mathematical Biosciences}, volume = {245}, number = {2}, pages = {322-330}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00039047}, doi = {http://dx.doi.org/10.1016/j.mbs.2013.08.002}, year = {2013}, affiliation = {IRSTEA CLERMONT FERRAND UR LISC FRA ; IRSTEA CLERMONT FERRAND UR LISC FRA}, abstract = {A sustainability issue for the rain forest in the corridor of Fianarantsoa (Madagascar) is to preserve the forest while ensuring the development of the local population. The aim of this paper is to determine whether the current situation is sustainable or not according to different action policy possibilities. We propose a general procedure based on viability analysis: Translation of sustainability issues into constraints on the system state; elaboration of a mathematical model of system evolution rules in the form of controlled dynamical system; computations of the viability kernels according to different action policy possibilities. Among control variables, we focus on monetary transfer. Without monetary transfer, we show that the current situation of the rain forest corridor is not sustainable in our mathematical modeling framework. We then estimate the minimal maximal amount per year necessary to make the current situation sustainable.}, }
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W. Wei, S. Martin, I. Alvarez
Sustainability analysis: Viability concepts to consider transient and asymptotical dynamics in socio-ecological tourism-based systems
Ecological Modelling 251, 2013
abs doi web bib

With the increasing pressure on natural resources, the sustainability study of socio-ecological systems has become a crucial scientific issue. In this paper we emphasize that transient behaviors have to be taken into account in sustainability analysis. We illustrate their impact with a model of tourism development from the literature, where the sustainability study is based on asymptotic properties. In order to evaluate relevant space and time characteristics of transient dynamics, we propose to use the concepts and tools of the mathematical viability theory. We also extend this analysis to controlled dynamical systems, which are particularly appropriate to model socio-ecological systems when management issues are at stake.
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@article{PUB00037806, author = {Wei, W. and Martin, S. and Alvarez, I.}, title = {Sustainability analysis: Viability concepts to consider transient and asymptotical dynamics in socio-ecological tourism-based systems}, title = {Analyse de durabilité : prendre en compte les comportements transitoires et asymptotiques par la théorie de la viabilité. Application à un modèle de tourisme.}, journal = {Ecological Modelling}, volume = {251}, pages = {103-113}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00037806}, doi = {http://dx.doi.org/10.1016/j.ecolmodel.2012.10.009}, year = {2013}, affiliation = {IRSTEA CLERMONT FERRAND UR LISC FRA ; IRSTEA CLERMONT FERRAND UR LISC FRA ; IRSTEA CLERMONT FERRAND UR LISC FRA}, abstract = {With the increasing pressure on natural resources, the sustainability study of socio-ecological systems has become a crucial scientific issue. In this paper we emphasize that transient behaviors have to be taken into account in sustainability analysis. We illustrate their impact with a model of tourism development from the literature, where the sustainability study is based on asymptotic properties. In order to evaluate relevant space and time characteristics of transient dynamics, we propose to use the concepts and tools of the mathematical viability theory. We also extend this analysis to controlled dynamical systems, which are particularly appropriate to model socio-ecological systems when management issues are at stake.}, }
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C. Bernard, S. Martin
Building strategies to ensure langage coexistence in presence of bilingualism
Applied Mathematics and Computation 218 (17), 2012
abs doi web bib

For 20 years many authors have attempted to model language competition. Some models involve two different languages, others include also a bilingual population. The issues are to understand one language extinction or to determine in which parameter range coexistence is possible. A key parameter is the prestige of one language compare to the other. If this parameter remains constant, coexistence is not sustainable. However, prestige may vary with time. In this article, thanks to the viability theory concepts and tools, we study a set of prestige variations which would allow language coexistence in presence of a bilingual population. Among this set, we emphasise slow viable evolutions with the lowest prestige variations that guarantee coexistence.
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@article{PUB00035369, author = {Bernard, C. and Martin, S.}, title = {Building strategies to ensure langage coexistence in presence of bilingualism}, title = {Déterminer des stratégies pour assurer la coexistence de deux langues en présence de bilinguisme}, journal = {Applied Mathematics and Computation}, volume = {218}, number = {17}, pages = {8825-8841}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00035369 / http://www.sciencedirect.com/science/article/pii/S0096300312001683}, doi = {http://dx.doi.org/10.1016/j.amc.2012.02.041}, year = {2012}, affiliation = {IRSTEA CLERMONT FERRAND UR LISC FRA ; IRSTEA CLERMONT FERRAND UR LISC FRA}, abstract = {For 20 years many authors have attempted to model language competition. Some models involve two different languages, others include also a bilingual population. The issues are to understand one language extinction or to determine in which parameter range coexistence is possible. A key parameter is the prestige of one language compare to the other. If this parameter remains constant, coexistence is not sustainable. However, prestige may vary with time. In this article, thanks to the viability theory concepts and tools, we study a set of prestige variations which would allow language coexistence in presence of a bilingual population. Among this set, we emphasise slow viable evolutions with the lowest prestige variations that guarantee coexistence.}, }
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N. Sicard, N. Perrot, R. Reuillon, S. Mesmoudi, I. Alvarez, S. Martin
A viability approach to control food processes: Application to a Camembert cheese ripening process
Food Control 23 (2), 2012
abs doi web bib

This paper addresses the issue of studying the viability theory, developed for model exploration purposes and in our example applied to the optimization of a food operation. The aim is to identify the whole set of viable trajectories for a given process. It focuses on the preservation of some specific properties of the system (constraints in the state space). On the basis of this set, a set of actions is identified and robustness is discussed. The proposed framework was adapted to a Camembert ripening model to identify the subset of the space state where almost one evolution starting in the subset remains indefinitely inside of the domain of some viability constraints, that makes it possible to reach a predefined quality target. The results were applied at the pilot scale and are discussed in this paper. The cheese ripening process was shortened by four days without significant changes in the microorganisms kinetics and a good sensory quality of the cheese. / Cet article s'intéresse à l'utilisation de la théorie de la viabilité (Aubin, 1991) pour l'exploration de modèles complexes, en prenant l'exemple de l'affinage du camembert. La démarche consiste à identifier l'ensemble des trajectoires viables du processus : il s'agit de maintenir certaines propriétés du système (des contraintes dans l'espace d'état, avec ici une cible de qualité à atteindre en fin d'affinage). A partir de cet ensemble, des questions d'optimisation et de robustesse peuvent être discutées. Les résultats ont été testés dans un hâloir-pilote et sont présentés dans cet article. Le processus d'affinage a été raccourci de quatre jours (sur 12) sans changement significatif dans la cinétique des microorganismes et en conservant une bonne qualité sensorielle du fromage.
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@article{PUB00033451, author = {Sicard, N. and Perrot, N. and Reuillon, R. and Mesmoudi, S. and Alvarez, I. and Martin, S.}, title = {A viability approach to control food processes: Application to a Camembert cheese ripening process}, title = {Une approche basée sur la viabilité pour le contrôle de procédés agro-alimentaires : application à l'affichage du camembert}, journal = {Food Control}, volume = {23}, number = {2}, pages = {312-319}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00033451}, doi = {http://dx.doi.org/10.1016/j.foodcont.2011.07.007}, year = {2012}, affiliation = {INRA UMR 782 GMPA AGROPARISTECH THIVERVAL GRIGNON FRA ; INRA UMR 782 GMPA AGROPARISTECH THIVERVAL GRIGNON FRA ; ISC PARIS FRA ; UNIVERSITE DE PARIS VI UMR 7606 LIP6 LABORATOIRE D'INFORMATIQUE DE PARIS ; IRSTEA CLERMONT FERRAND UR LISC FRA ; ISC PARIS FRA}, abstract = {This paper addresses the issue of studying the viability theory, developed for model exploration purposes and in our example applied to the optimization of a food operation. The aim is to identify the whole set of viable trajectories for a given process. It focuses on the preservation of some specific properties of the system (constraints in the state space). On the basis of this set, a set of actions is identified and robustness is discussed. The proposed framework was adapted to a Camembert ripening model to identify the subset of the space state where almost one evolution starting in the subset remains indefinitely inside of the domain of some viability constraints, that makes it possible to reach a predefined quality target. The results were applied at the pilot scale and are discussed in this paper. The cheese ripening process was shortened by four days without significant changes in the microorganisms kinetics and a good sensory quality of the cheese. / Cet article s'intéresse à l'utilisation de la théorie de la viabilité (Aubin, 1991) pour l'exploration de modèles complexes, en prenant l'exemple de l'affinage du camembert. La démarche consiste à identifier l'ensemble des trajectoires viables du processus : il s'agit de maintenir certaines propriétés du système (des contraintes dans l'espace d'état, avec ici une cible de qualité à atteindre en fin d'affinage). A partir de cet ensemble, des questions d'optimisation et de robustesse peuvent être discutées. Les résultats ont été testés dans un hâloir-pilote et sont présentés dans cet article. Le processus d'affinage a été raccourci de quatre jours (sur 12) sans changement significatif dans la cinétique des microorganismes et en conservant une bonne qualité sensorielle du fromage.}, }
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L. Chapel, X. Castello, C. Bernard, G. Deffuant, V. Eguiluz, S. Martin, M. San Miguel
Viability and resilience of languages in competition
PLoS One 5 (1 (e8681)), 2010
abs doi web bib

We study the viability and resilience of languages, using a simple dynamical model of two languages in competition. Assuming that public action can modify the prestige of a language in order to avoid language extinction, we analyze two cases: (i) the prestige can only take two values, (ii) it can take any value but its change at each time step is bounded. In both cases, we determine the viability kernel, that is, the set of states for which there exists an action policy maintaining the coexistence of the two languages, and we define such policies. We also study the resilience of the languages and identify configurations from where the system can return to the viability kernel (definite resilience), or where one of the languages is lead to disappear (zero resilience). Within our current framework, the maintenance of a bilingual society is shown to be possible by introducing the prestige of a language as a control variable.
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@article{PUB00027990, author = {Chapel, L. and Castello, X. and Bernard, C. and Deffuant, G. and Eguiluz, V. and Martin, S. and San Miguel, M.}, title = {Viability and resilience of languages in competition}, title = {Viabilité et résilience de langues en compétitions}, journal = {PLoS One}, volume = {5}, number = {1 (e8681)}, pages = {11}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00027990 / http://www.plosone.org/article/info:doi/10.1371/journal.pone.0008681}, doi = {http://dx.doi.org/10.1371/journal.pone.0008681}, year = {2010}, affiliation = {CEMAGREF CLERMONT FERRAND UR LISC FRA ; IFISC ESP ; CEMAGREF CLERMONT FERRAND UR LISC FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA ; IFISC ESP ; CEMAGREF CLERMONT FERRAND UR LISC FRA ; IFISC ESP}, abstract = {We study the viability and resilience of languages, using a simple dynamical model of two languages in competition. Assuming that public action can modify the prestige of a language in order to avoid language extinction, we analyze two cases: (i) the prestige can only take two values, (ii) it can take any value but its change at each time step is bounded. In both cases, we determine the viability kernel, that is, the set of states for which there exists an action policy maintaining the coexistence of the two languages, and we define such policies. We also study the resilience of the languages and identify configurations from where the system can return to the viability kernel (definite resilience), or where one of the languages is lead to disappear (zero resilience). Within our current framework, the maintenance of a bilingual society is shown to be possible by introducing the prestige of a language as a control variable.}, }
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L. Chapel, G. Deffuant, S. Martin, C. Mullon
Defining yield policies in a viability approach
Ecological Modelling 212 (1-2), 2008
abs doi web bib

Mullon et al. [Mullon, C., Curry, P., Shannon, L., 2004. Viability model of trophic interactions in marine ecosystems. Nat. Resour. Model. 17 (1), 2758] proposed a dynamical model of biomass evolution in the Southern Benguela ecosystem, including five different groups (detritus, phytoplankton, zooplankton, pelagic fish and demersal fish). They studied this model in a viability perspective, trying to assess, for a given constant yield, whether each species biomass remains inside a given interval, taking into account the uncertainty on the interaction coefficients. Instead of studying the healthy states of this marine ecosystem with a constant yield, we focus here on the yield policies which keep the system viable. Using the mathematical concept of viability kernel, we examine how yield management might guarantee viable fisheries. One of the main practical difficulties up to now with the viability theory was the lack of methods to solve the problem in large dimensions. In this paper, we use a new method based on SVMs, which gives this theory a larger practical potential. Solving the viability problem provides all yield policies (if any) which guarantee a perennial system. We illustrate our main findings with numerical simulations.
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@article{PUB00024646, author = {Chapel, L. and Deffuant, G. and Martin, S. and Mullon, C.}, title = {Defining yield policies in a viability approach}, title = {Définir des politiques de pêche grâce à la théorie de la viabilité}, journal = {Ecological Modelling}, volume = {212}, number = {1-2}, pages = {10-15}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00024646}, doi = {http://dx.doi.org/10.1016/j.ecolmodel.2007.10.007 }, year = {2008}, affiliation = {CEMAGREF CLERMONT FERRAND LISC ; CEMAGREF CLERMONT FERRAND LISC ; CEMAGREF CLERMONT FERRAND LISC ; IRD UR GEODES BONDY}, abstract = {Mullon et al. [Mullon, C., Curry, P., Shannon, L., 2004. Viability model of trophic interactions in marine ecosystems. Nat. Resour. Model. 17 (1), 2758] proposed a dynamical model of biomass evolution in the Southern Benguela ecosystem, including five different groups (detritus, phytoplankton, zooplankton, pelagic fish and demersal fish). They studied this model in a viability perspective, trying to assess, for a given constant yield, whether each species biomass remains inside a given interval, taking into account the uncertainty on the interaction coefficients. Instead of studying the healthy states of this marine ecosystem with a constant yield, we focus here on the yield policies which keep the system viable. Using the mathematical concept of viability kernel, we examine how yield management might guarantee viable fisheries. One of the main practical difficulties up to now with the viability theory was the lack of methods to solve the problem in large dimensions. In this paper, we use a new method based on SVMs, which gives this theory a larger practical potential. Solving the viability problem provides all yield policies (if any) which guarantee a perennial system. We illustrate our main findings with numerical simulations.}, }
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G. Deffuant, L. Chapel, S. Martin
Approximating viability kernels with support vector machines
IEEE Transactions on Automatic Control 52 (5), 2007
abs web bib

We propose an algorithm which performs a progressive approximation of a viability kernel, iteratively using a classification method. We establish the mathematical conditions that the classification method should fulfill to guarantee the convergence to the actual viability kernel. We study more particularly the use of support vector machines (SVMs) as classification techniques. We show that they make possible to use gradient optimisation techniques to find a viable control at each time step, and over several time steps. This allows us to avoid the exponential growth of the computing time with the dimension of the control space. It also provides simple and efficient control procedures. We illustrate the method with some examples inspired from ecology.
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@article{PUB00036305, author = {Deffuant, G. and Chapel, L. and Martin, S.}, title = {Approximating viability kernels with support vector machines}, title = {Approcher des noyaux de viabilité avec des machines à vecteurs supports}, journal = {IEEE Transactions on Automatic Control}, volume = {52}, number = {5}, pages = {933-937}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00036305}, year = {2007}, affiliation = {CEMAGREF CLERMONT FERRAND UR LISC FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA}, abstract = {We propose an algorithm which performs a progressive approximation of a viability kernel, iteratively using a classification method. We establish the mathematical conditions that the classification method should fulfill to guarantee the convergence to the actual viability kernel. We study more particularly the use of support vector machines (SVMs) as classification techniques. We show that they make possible to use gradient optimisation techniques to find a viable control at each time step, and over several time steps. This allows us to avoid the exponential growth of the computing time with the dimension of the control space. It also provides simple and efficient control procedures. We illustrate the method with some examples inspired from ecology. }, }
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O. Bokanowski, S. Martin, R. Munos, H. Zidani
An anti-diffusive scheme for viability problems
Applied Numerical Mathematics 56 (9), 2006
abs doi web bib

The value function associated with viability problem is discontinuous. We investigate the Ultra-Bee scheme, particularly interesting for its anti-diffusive property in the transport of discontinuous functions. Our numerical results are very encouraging.
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@article{PUB00020443, author = {Bokanowski, O. and Martin, S. and Munos, R. and Zidani, H.}, title = {An anti-diffusive scheme for viability problems}, title = {Un schéma anti-diffusif pour des problèmes de viabilité}, journal = {Applied Numerical Mathematics}, volume = {56}, number = {9}, pages = {1147-1162}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00020443}, doi = {http://dx.doi.org/doi:10.1016/j.apnum.2006.03.004}, year = {2006}, affiliation = {UNIVERSITE PIERRE ET MARIE CURIE LABORATOIRE JACQUES-LOUIS LIONSPARIS, ; CEMAGREF CLERMONT FERRAND LISC ; ECOLE POLYTECHNIQUE CENTRE DE MATHEMATIQUES PALAISEAU ; ENSTA PARIS}, abstract = {The value function associated with viability problem is discontinuous. We investigate the Ultra-Bee scheme, particularly interesting for its anti-diffusive property in the transport of discontinuous functions. Our numerical results are very encouraging.}, }
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S. Martin
The cost of restoration as a way of defining resilience: a viability approach applied to a model of lake eutrophication
Ecology and Society 9 (2), 2004
abs web bib

Multiple stable states or alternative equilibria in ecological systems have been recognized since the 1960s in the ecological literature. Very often, the shift between alternative states occurs suddenly and the resource flows from these systems are modified. Resilience is the capacity of a system to undergo disturbance and maintain its functions and controls. It has multiple levels of meaning, from the metaphorical to the specific. However, most studies that explore resilience-related ideas have used resilience as a metaphor or theoretical construct. In a few cases, it has been defined operationally in the context of a model of a particular system. In this paper, resilience is defined consistently with the theoretical uses of the term, in the context of ecosystem models within an application to a simple model of lake eutrophication. The theoretical definitions of resilience and the characteristics of the operational definition that are necessary for ensuring consistency are reviewed. A mathematical formulation of resilience is built in the framework of the viability theory. This formulation emphasizes the link between resilience and the cost of the recovery after a disturbance. This cost is first chosen in relation to the time of crisis in the application to a model of lake eutrophication. The resilience values are then obtained by numerical integration. For another choice of the cost function, the viability algorithm is needed to compute the resilience values. These applications demonstrate the usefulness of our operational definition.
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@article{PUB00015017, author = {Martin, S.}, title = {The cost of restoration as a way of defining resilience: a viability approach applied to a model of lake eutrophication}, journal = {Ecology and Society}, volume = {9}, number = {2}, pages = {19}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00015017 / http://www.ecologyandsociety.org/vol9/iss2/art8}, year = {2004}, affiliation = {CEMAGREF CLERMONT FERRAND LISC}, number = {K LI04 4}, abstract = {Multiple stable states or alternative equilibria in ecological systems have been recognized since the 1960s in the ecological literature. Very often, the shift between alternative states occurs suddenly and the resource flows from these systems are modified. Resilience is the capacity of a system to undergo disturbance and maintain its functions and controls. It has multiple levels of meaning, from the metaphorical to the specific. However, most studies that explore resilience-related ideas have used resilience as a metaphor or theoretical construct. In a few cases, it has been defined operationally in the context of a model of a particular system. In this paper, resilience is defined consistently with the theoretical uses of the term, in the context of ecosystem models within an application to a simple model of lake eutrophication. The theoretical definitions of resilience and the characteristics of the operational definition that are necessary for ensuring consistency are reviewed. A mathematical formulation of resilience is built in the framework of the viability theory. This formulation emphasizes the link between resilience and the cost of the recovery after a disturbance. This cost is first chosen in relation to the time of crisis in the application to a model of lake eutrophication. The resilience values are then obtained by numerical integration. For another choice of the cost function, the viability algorithm is needed to compute the resilience values. These applications demonstrate the usefulness of our operational definition.}, }
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Book Chapters (4)

I. Alvarez, S. Martin, O. Dordan, X. Litrico, P. Saint-Pierre
Indicateurs de sécurité et de restauration dynamiques
Agir en situation d'incertitude en agriculture : regards pluridisciplinaires au Nord et au Sud (p. 14), Peter Lang, Bruxelles, BEL, 2013
abs web bib

Les systèmes agricoles au sens large et leur environnement peuvent être décrits comme des systèmes dynamiques : par exemple, des activités agricoles utilisent chaque année des engrais phosphatés. Ces engrais ne se fixent pas dans le sol, mais descendent par infiltration ou écoulement de surface vers les écosystèmes aquatiques – rivières, lacs, baies. Les concentrations excessives de substances nutritives dans ces bassins aquatiques provoquent la prolifération de nappes d’algues. Ces systèmes agricoles sont soumis à des contraintes de rentabilité bien sûr, mais pas uniquement. En effet, les populations riveraines d'un lac souhaitent qu'il conserve un état d'eau claire (oligotrophe), et éviter la prolifération des algues impose des contraintes supplémentaires sur les activités agricoles, en l'occurrence, limiter les apports d'engrais dans le bassin versant. Enfin, ces systèmes agricoles sont soumis à des incertitudes. Viennent immédiatement à l'esprit les aléas climatiques, mais pour rester dans l'exemple du lac, un événement pluvieux intense peut provoquer un ruissellement important qui a pour conséquence immédiate d'augmenter brusquement la concentration de phosphore dissous. Face à des systèmes qui évoluent soumis à des contraintes et des incertitudes, quelles informations fournir au gestionnaire ?
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@book{PUB00040096, author = {Alvarez, I. and Martin, S. and Dordan, O. and Litrico, X. and Saint-Pierre, P.}, author = {Ancey, V. and Avelange, I. and Dedieu, B.}, title = {Indicateurs de sécurité et de restauration dynamiques}, title = {Security and restoration indicators}, bookTitle = {Agir en situation d'incertitude en agriculture : regards pluridisciplinaires au Nord et au Sud}, series = {EcoPolis - volume 17 }, address = {Bruxelles, BEL}, publisher = {Peter Lang}, pages = {14}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00040096}, year = {2013}, affiliation = {IRSTEA CLERMONT FERRAND UR LISC FRA ; IRSTEA CLERMONT FERRAND UR LISC FRA ; UNIVERSITE DE BORDEAUX FRA ; LYONNAISE DES EAUX BORDEAUX FRA ; UNIVERSITE PARIS DAUPHINE PARIS FRA}, abstract = {Les systèmes agricoles au sens large et leur environnement peuvent être décrits comme des systèmes dynamiques : par exemple, des activités agricoles utilisent chaque année des engrais phosphatés. Ces engrais ne se fixent pas dans le sol, mais descendent par infiltration ou écoulement de surface vers les écosystèmes aquatiques – rivières, lacs, baies. Les concentrations excessives de substances nutritives dans ces bassins aquatiques provoquent la prolifération de nappes d’algues. Ces systèmes agricoles sont soumis à des contraintes de rentabilité bien sûr, mais pas uniquement. En effet, les populations riveraines d'un lac souhaitent qu'il conserve un état d'eau claire (oligotrophe), et éviter la prolifération des algues impose des contraintes supplémentaires sur les activités agricoles, en l'occurrence, limiter les apports d'engrais dans le bassin versant. Enfin, ces systèmes agricoles sont soumis à des incertitudes. Viennent immédiatement à l'esprit les aléas climatiques, mais pour rester dans l'exemple du lac, un événement pluvieux intense peut provoquer un ruissellement important qui a pour conséquence immédiate d'augmenter brusquement la concentration de phosphore dissous. Face à des systèmes qui évoluent soumis à des contraintes et des incertitudes, quelles informations fournir au gestionnaire ?}, }
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I. Alvarez, S. Martin
Geometric robustness of viability kernels and resilience basins
Viability and resilience of complex systems: concepts, methods and case studies from ecology and society (p. 193-218), Springer, 2011
doi web bib

@book{PUB00033189, author = {Alvarez, I. and Martin, S.}, author = {Deffuant, G. and Gilbert, N.}, title = {Geometric robustness of viability kernels and resilience basins}, bookTitle = {Viability and resilience of complex systems: concepts, methods and case studies from ecology and society}, series = {Understanding complex systems}, publisher = {Springer}, pages = {193-218}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00033189}, doi = {http://dx.doi.org/10.1007/978-3-642-20423-4}, year = {2011}, affiliation = {CEMAGREF CLERMONT FERRAND UR LISC FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA}, ISBNISSN = {ISBN-13: 978-3642204227}, abstract = {}, }
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S. Martin, G. Deffuant, J.M. Calabrese
Defining resilience mathematically: from attractors to viability
Viability and resilience of complex systems: ; concepts, methods and case studies from ecology and society (p. 15-36), Springer, 2011
doi web bib

@book{PUB00033173, author = {Martin, S. and Deffuant, G. and Calabrese, J.M.}, author = {Deffuant, G. and Gilbert, N.}, title = {Defining resilience mathematically: from attractors to viability}, bookTitle = {Viability and resilience of complex systems: ; concepts, methods and case studies from ecology and society}, series = {Understanding complex systems}, publisher = {Springer}, pages = {15-36}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00033173}, doi = {http://dx.doi.org/10.1007/978-3-642-20423-4}, year = {2011}, affiliation = {CEMAGREF CLERMONT FERRAND UR LISC FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA ; UFZ HELMHOLTZ CENTRE FOR ENVIRONMENTAL RESEARCH LEIPZIG DEU}, ISBNISSN = {ISBN-13: 978-3642204227}, abstract = {}, }
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J.P. Aubin, S. Martin
Travel time tubes regulating transportation traffic
Nonlinear analysis and optimization: II: Optimization (p. 1-25), American Mathematical Society, 2010
abs web bib

The issue addressed is the computation at each arrival time and at each state at any node of the network, of the travel time needed to join any node of the network to this state at this arrival date by a prototypical vehicle and of the regulation law governing such viable evolutions. We assume that is known the time dependent controlled dynamics of a prototypical vehicle, the network on which it is constrained to evolve at each instant, and the nodes from which it starts or through which it passes at prescribed times. The basic question we address is the determination of the arrival sets at each arrival time made of terminal states at which arrive evolutions governed by the control system, viable in the network, starting from the departure set for some travel time or prescribed travel time. A subsidiary problem is to determine the associated nodes, through the Cournot set-valued map we define at the end of this paper. We use viability techniques summarized in an appendix, which, translated in terms of travel time problems, allow us, for instance, to characterize the arrival tubes, define the "homoclinic" pairs at which any two nodes can be connected, prove a Lax-Hopf Formula characterizing these tubes by an easy formula whenever the control system does not depend either on the time or on the state, propose a concept of solution to a "system of Hamilton-Jacobi-Bellman inclusions" of which the arriving tube is the unique solution, adapt to those systems the dual concept of Barron-Jensen/Frankowska extension of viscosity solutions to usual Hamilton-Jacobi-Bellman solutions, optimize intertemporal criteria and minimize travel times. We derive the main properties of the Moskowitz Travel Time model of the Lighthill, Whitham and Richards' theory.
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@book{PUB00029633, author = {Aubin, J.P. and Martin, S.}, author = {Leizarowitz, A. and Mordukhovich, B.S. and Shafrir, I. and Zaslavski, A.J.}, title = {Travel time tubes regulating transportation traffic}, title = {Tubes de temps de voyage pour réguler le trafic dans les transports}, bookTitle = {Nonlinear analysis and optimization: II: Optimization}, series = {Contemporary Mathematics, vol .514}, publisher = {American Mathematical Society}, pages = {1-25}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00029633 / http://www.ams.org/bookstore?fn=20&arg1=conmseries&ikey=CONM-514}, year = {2010}, affiliation = {SOCIETE VIMADES PARIS FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA}, ISBNISSN = {ISBN-10 0-8218-4835-6}, abstract = {The issue addressed is the computation at each arrival time and at each state at any node of the network, of the travel time needed to join any node of the network to this state at this arrival date by a prototypical vehicle and of the regulation law governing such viable evolutions. We assume that is known the time dependent controlled dynamics of a prototypical vehicle, the network on which it is constrained to evolve at each instant, and the nodes from which it starts or through which it passes at prescribed times. The basic question we address is the determination of the arrival sets at each arrival time made of terminal states at which arrive evolutions governed by the control system, viable in the network, starting from the departure set for some travel time or prescribed travel time. A subsidiary problem is to determine the associated nodes, through the Cournot set-valued map we define at the end of this paper. We use viability techniques summarized in an appendix, which, translated in terms of travel time problems, allow us, for instance, to characterize the arrival tubes, define the "homoclinic" pairs at which any two nodes can be connected, prove a Lax-Hopf Formula characterizing these tubes by an easy formula whenever the control system does not depend either on the time or on the state, propose a concept of solution to a "system of Hamilton-Jacobi-Bellman inclusions" of which the arriving tube is the unique solution, adapt to those systems the dual concept of Barron-Jensen/Frankowska extension of viscosity solutions to usual Hamilton-Jacobi-Bellman solutions, optimize intertemporal criteria and minimize travel times. We derive the main properties of the Moskowitz Travel Time model of the Lighthill, Whitham and Richards' theory.}, }
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In Proceedings (17)

S. Martin, S. Huet, P. Gend, Mohamed A. A. Oumajoud, G. Deffuant, A. Nugier, S. Guimond
Bounded confidence in extreme opinion evolution : An online experiment
International Conference on Computational Social Science (IC2S2 2017), 10/07/2017-13/07/2017, Cologne, DEU (p. 3), 2017
abs web bib

Le modèle d'influence "bounded confidence" est ici partiellement confronté aux résultats d'expériences on-line. Le caractère borné de l'influence est confirmé. Cette influence dépend de la distance relative à un individu (relativement à la distance aux autres individus influenceurs). Les résultats montrent par ailleurs que l'influencé est sensible aux nombre d'influenceurs du groupe dans lequel il se situe. Des expériences complémentaires sont nécessaires pour aller plus loin.
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@inproceedings{PUB00056564, author = {Martin, S. and Huet, S. and Gend, P. and Oumajoud, Mohamed A. A. and Deffuant, G. and Nugier, A. and Guimond, S.}, title = {Bounded confidence in extreme opinion evolution : An online experiment}, title = {Confiance bornée et évolution des opinions extrêmes : expérience en ligne}, bookTitle = {International Conference on Computational Social Science (IC2S2 2017), 10/07/2017-13/07/2017, Cologne, DEU}, pages = {3}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00056564}, year = {2017}, affiliation = {UNIVERSITE DE LORRAINE CRAN NANCY FRA ; IRSTEA CLERMONT FERRAND UR LISC FRA ; UNIVERSITE DE LORRAINE CRAN NANCY FRA ; UNIVERSITE DE LORRAINE CRAN NANCY FRA ; IRSTEA CLERMONT FERRAND UR LISC FRA ; UCA LAPSCO CLERMONT FERRAND FRA ; UCA LAPSCO CLERMONT FERRAND FRA}, abstract = {Le modèle d'influence "bounded confidence" est ici partiellement confronté aux résultats d'expériences on-line. Le caractère borné de l'influence est confirmé. Cette influence dépend de la distance relative à un individu (relativement à la distance aux autres individus influenceurs). Les résultats montrent par ailleurs que l'influencé est sensible aux nombre d'influenceurs du groupe dans lequel il se situe. Des expériences complémentaires sont nécessaires pour aller plus loin.}, }
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I. Alvarez, R. De Aldama, S. Martin, R. Reuillon
Assessing the resilience of socio-ecosystems: coupling viability theory and active learning with kd-Trees. Application to bilingual societies
International Joint Conference on Artificial Intelligence 2013 ( IJCAI), 03/08/2013-09/08/2013, Beijing, CHN (p. 2776-2782), 2013
abs web bib

This paper proposes a new algorithm to compute the resilience of a social system or an ecosystem when it is defined in the framework of the mathematical viability theory. It is applied to the problem of language coexistence: Although bilingual societies do exist, many languages have disappeared and some seem endangered presently. Mathematical models of language competition generally conclude that one language will disappear, except when the relative prestige of the languages can be modified. The viability theory provides concepts and tools that are suitable to study the resilience, but with severe computational limits since it uses extensive search on regular grids. The method we propose considers the computation of the viability output sets as an active learning problem with the objective of restraining the number of calls to the model and information storage. We adapt a kd-tree algorithm to approximate the level sets of the resilience value. We prove that this algorithm converges to the output sets defined by the viability theory (viability kernel and capture basin). The resilience value we compute can then be used to propose a policy of action in risky situations such as migration flows. / Cet article propose un algorithme couplé pour calculer la résilience d'un socio-écosystème dans le cadre de la théorie mathématique de la viabilité, illustré sur le problème des sociétés bilingues. Les modèles mathématiques de telles sociétés montrent que l'extinction d'un langage est en général inéluctable, sauf s'il est possible de modifier le prestige des langues. La méthode de calcul de la résilience que nous proposons repose sur un algorithme adapté des kd-trees. La convergence de l'algorithme de viabilité dans ce cadre est démontrée. Le calcul de la résilience est utilisé pour proposer des politiques d'action en cas de flux migratoires.
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@inproceedings{PUB00039946, author = {Alvarez, I. and De Aldama, R. and Martin, S. and Reuillon, R.}, title = {Assessing the resilience of socio-ecosystems: coupling viability theory and active learning with kd-Trees. Application to bilingual societies}, title = {Evaluer la résilience des socio-écosystèmes : coupler la théorie de la viabilité avec l'apprentissage actif à partir de kd-trees. Application à la coexistence des langues.}, bookTitle = {International Joint Conference on Artificial Intelligence 2013 ( IJCAI), 03/08/2013-09/08/2013, Beijing, CHN}, pages = {2776-2782}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00039946 / http://ijcai.org/papers13/Papers/IJCAI13-409.pdf}, year = {2013}, affiliation = {UNIVERSITE PIERRE ET MARIE CURIE LIP6 PARIS FRA ; INSTITUT DES SYSTEMES COMPLEXES ISC PIF PARIS FRA ; IRSTEA CLERMONT FERRAND UR LISC FRA ; INSTITUT DES SYSTEMES COMPLEXES ISC PIF PARIS FRA}, abstract = {This paper proposes a new algorithm to compute the resilience of a social system or an ecosystem when it is defined in the framework of the mathematical viability theory. It is applied to the problem of language coexistence: Although bilingual societies do exist, many languages have disappeared and some seem endangered presently. Mathematical models of language competition generally conclude that one language will disappear, except when the relative prestige of the languages can be modified. The viability theory provides concepts and tools that are suitable to study the resilience, but with severe computational limits since it uses extensive search on regular grids. The method we propose considers the computation of the viability output sets as an active learning problem with the objective of restraining the number of calls to the model and information storage. We adapt a kd-tree algorithm to approximate the level sets of the resilience value. We prove that this algorithm converges to the output sets defined by the viability theory (viability kernel and capture basin). The resilience value we compute can then be used to propose a policy of action in risky situations such as migration flows. / Cet article propose un algorithme couplé pour calculer la résilience d'un socio-écosystème dans le cadre de la théorie mathématique de la viabilité, illustré sur le problème des sociétés bilingues. Les modèles mathématiques de telles sociétés montrent que l'extinction d'un langage est en général inéluctable, sauf s'il est possible de modifier le prestige des langues. La méthode de calcul de la résilience que nous proposons repose sur un algorithme adapté des kd-trees. La convergence de l'algorithme de viabilité dans ce cadre est démontrée. Le calcul de la résilience est utilisé pour proposer des politiques d'action en cas de flux migratoires.}, }
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W. Wei, I. Alvarez, S. Martin, J.P. Briot, M. De Azevedo Irving, G. Mendes de Melo
Integration of viability models in a serious game for the management of protected areas
IADIS International Conference Intelligent Systems and Agents 2012 and IADIS European Conference Data Mining 2012, MCCSIS 2012, 17/07/2012-23/07/2012, Lisbonne, PRT (p. 8), 2012
abs web bib

Participatory management is considered to be a very important challenge, in particular for the management of renewable resources and biodiversity conservation. In the framework of computer support for participatory management of protected areas, we present in this paper a component of a serious game, devoted to the viability study of the decision proposed by the stakeholders. Mathematical viability theory allows to identify the policies that can retain or restore desirable properties of a dynamical system. The objective of the viability expert is to provide the players with information about the efficiency of management policy. In this paper we present briefly the SimParc project, and we introduce the concepts of the mathematical viability theory. We then describe the viability expert agent architecture and possibility of use, in particular the fact that negotiation focuses on constraints rather than on the management decision itself. We also present the type of information given by the expert agent. In particular the fact that negotiation focuses on constraints rather than on the management decision itself.
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@inproceedings{PUB00037220, author = {Wei, W. and Alvarez, I. and Martin, S. and Briot, J.P. and De Azevedo Irving, M. and Mendes de Melo , G.}, title = {Integration of viability models in a serious game for the management of protected areas}, bookTitle = {IADIS International Conference Intelligent Systems and Agents 2012 and IADIS European Conference Data Mining 2012, MCCSIS 2012, 17/07/2012-23/07/2012, Lisbonne, PRT}, pages = {8}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00037220}, year = {2012}, affiliation = {IRSTEA CLERMONT FERRAND UR LISC FRA ; IRSTEA CLERMONT FERRAND UR LISC FRA ; IRSTEA CLERMONT FERRAND UR LISC FRA ; CNRS LIP6 PARIS FRA ; UFRJ INCT PPED RIO DE JANEIRO BRA ; UFRJ INCT PPED RIO DE JANEIRO BRA}, abstract = {Participatory management is considered to be a very important challenge, in particular for the management of renewable resources and biodiversity conservation. In the framework of computer support for participatory management of protected areas, we present in this paper a component of a serious game, devoted to the viability study of the decision proposed by the stakeholders. Mathematical viability theory allows to identify the policies that can retain or restore desirable properties of a dynamical system. The objective of the viability expert is to provide the players with information about the efficiency of management policy. In this paper we present briefly the SimParc project, and we introduce the concepts of the mathematical viability theory. We then describe the viability expert agent architecture and possibility of use, in particular the fact that negotiation focuses on constraints rather than on the management decision itself. We also present the type of information given by the expert agent. In particular the fact that negotiation focuses on constraints rather than on the management decision itself.}, }
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W. Wei, I. Alvarez, S. Martin
Algorithme d'approximation du noyau de viabilité avec procédure de classification
RFIA 2012 (Reconnaissance des Formes et Intelligence Artificielle), 24/01/2012-27/01/2012, Lyon, FRA , 2012
abs web bib

Viability theory proposes concepts and tools to control a dynamical system such that it can remain inside a viability constraint set. Integrating viability models in a tool support for participatory management is a new application of the viability theory. In this context, we propose an algorithm for viability kernel approximation, which focuses on improving the computing time. This algorithm uses the classification procedure based on the method of Nearest Neighbor Search. The algorithm satisfies the conditions of convergence, and is easy to use with a graphical user interface. We compare its results for models for which the exact viability kernels have been determined. The accuracy of this algorithm is always greater than 90 percent. The computing time is very interesting for decision support tools. / La théorie de la viabilité propose des concepts et méthodes pour contrôler un système dynamique afin de le maintenir dans un ensemble de contraintes de viabilité. Intégrer les modèles de la viabilité dans un outil d’aide à la gestion participative est une nouvelle application de la théorie de la viabilité. Dans ce contexte, nous proposons un algorithme d’approximation du noyau de viabilité qui se concentre sur la réduction du temps de calcul. Cet algorithme utilise une procédure de classification du type "plus proche voisin". L’algorithme satisfait les conditions de convergence, et est facile à manipuler en utilisant une interface graphique utilisateur. Nous comparons les résultats obtenus pour des problèmes de viabilité pour lesquels les noyaux théoriques ont été calculés. La fidélité de cet algorithme est toujours supérieure à 90 pourcents. Le temps de calcul est très intéressant pour les outils d’aide à la décision.
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@inproceedings{PUB00037217, author = {Wei, W. and Alvarez, I. and Martin, S.}, title = {Algorithme d'approximation du noyau de viabilité avec procédure de classification}, bookTitle = {RFIA 2012 (Reconnaissance des Formes et Intelligence Artificielle), 24/01/2012-27/01/2012, Lyon, FRA}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00037217}, year = {2012}, affiliation = {IRSTEA CLERMONT FERRAND UR LISC FRA ; IRSTEA CLERMONT FERRAND UR LISC FRA ; IRSTEA CLERMONT FERRAND UR LISC FRA}, abstract = {Viability theory proposes concepts and tools to control a dynamical system such that it can remain inside a viability constraint set. Integrating viability models in a tool support for participatory management is a new application of the viability theory. In this context, we propose an algorithm for viability kernel approximation, which focuses on improving the computing time. This algorithm uses the classification procedure based on the method of Nearest Neighbor Search. The algorithm satisfies the conditions of convergence, and is easy to use with a graphical user interface. We compare its results for models for which the exact viability kernels have been determined. The accuracy of this algorithm is always greater than 90 percent. The computing time is very interesting for decision support tools. / La théorie de la viabilité propose des concepts et méthodes pour contrôler un système dynamique afin de le maintenir dans un ensemble de contraintes de viabilité. Intégrer les modèles de la viabilité dans un outil d’aide à la gestion participative est une nouvelle application de la théorie de la viabilité. Dans ce contexte, nous proposons un algorithme d’approximation du noyau de viabilité qui se concentre sur la réduction du temps de calcul. Cet algorithme utilise une procédure de classification du type "plus proche voisin". L’algorithme satisfait les conditions de convergence, et est facile à manipuler en utilisant une interface graphique utilisateur. Nous comparons les résultats obtenus pour des problèmes de viabilité pour lesquels les noyaux théoriques ont été calculés. La fidélité de cet algorithme est toujours supérieure à 90 pourcents. Le temps de calcul est très intéressant pour les outils d’aide à la décision. }, }
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I. Alvarez, C. Bernard, S. Martin, P. Saint-Pierre
Compétition linguistique : stratégies pour favoriser la coexistence durable en présence de bilinguisme
48ème colloque de l'Association de Science Régionale de Langue Française, ASRDLF 2011, 06/07/2011-08/07/2011, Schoelcher, MTQ / CD Rom, Session spéciale Vulnérabilité-Résilience-Viabilité, Actes du 48ème colloque ASRDLF 2011 (p. 11), 2011
abs web bib

Comment assurer durablement la coexistence de plusieurs langues au sein d'une même population? Cette question est au centre des préoccupations des régions ou pays qui cherchent à préserver une culture multilingue considérée comme un patrimoine historique à préserver ou à développer. Malheureusement, même si on constate effectivement l'existence de sociétés dans lesquelles coexistent plusieurs langues, la plupart des modèles montrent que la cohabitation est un état instable. La cohabitation initiale évolue inéluctablement vers l'extinction d'une des langues, en fonction du nombre de locuteurs et du prestige relatif des deux langues en compétition. En revanche, si par des actions politiques, sociales ou d'autre nature il est possible d'influer sur le prestige relatif des langues, une cohabitation prolongée devient théoriquement possible en fonction des scénarios retenus. L'objectif de cet article est de montrer comment la théorie mathématique de la viabilité, et l'analyse géométrique des résultats produits, peut permettre de trouver les stratégies permettant d'assurer la coexistence de groupes monolingues au sein de la population.
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@inproceedings{PUB00033744, author = {Alvarez, I. and Bernard, C. and Martin, S. and Saint-Pierre, P.}, title = {Compétition linguistique : stratégies pour favoriser la coexistence durable en présence de bilinguisme }, title = {Language competition : strategies to ensure sustainable coexistence in presence of bilingualism}, bookTitle = {48ème colloque de l'Association de Science Régionale de Langue Française, ASRDLF 2011, 06/07/2011-08/07/2011, Schoelcher, MTQ / CD Rom, Session spéciale Vulnérabilité-Résilience-Viabilité, Actes du 48ème colloque ASRDLF 2011}, pages = {11}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00033744}, year = {2011}, affiliation = {CEMAGREF CLERMONT FERRAND UR LISC FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA ; LABORATOIRE D'APPLICATIONS DES SYSTEMES TYCHASTIQUES REGULES FRA}, abstract = {Comment assurer durablement la coexistence de plusieurs langues au sein d'une même population? Cette question est au centre des préoccupations des régions ou pays qui cherchent à préserver une culture multilingue considérée comme un patrimoine historique à préserver ou à développer. Malheureusement, même si on constate effectivement l'existence de sociétés dans lesquelles coexistent plusieurs langues, la plupart des modèles montrent que la cohabitation est un état instable. La cohabitation initiale évolue inéluctablement vers l'extinction d'une des langues, en fonction du nombre de locuteurs et du prestige relatif des deux langues en compétition. En revanche, si par des actions politiques, sociales ou d'autre nature il est possible d'influer sur le prestige relatif des langues, une cohabitation prolongée devient théoriquement possible en fonction des scénarios retenus. L'objectif de cet article est de montrer comment la théorie mathématique de la viabilité, et l'analyse géométrique des résultats produits, peut permettre de trouver les stratégies permettant d'assurer la coexistence de groupes monolingues au sein de la population.}, }
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J.P. Briot, M. de Azevedo Irving, G. Mendes de Melo, J.E. Filho Vasconcelos, I. Alvarez, S. Martin, W. Wei
A serious game and artificial agents to support intercultural participatory management of protected areas for biodiversity conservation and social inclusion
Culture and Computing 2011, The Second International Conference on Culture and Computing, Kyoto University, 20/10/2011-22/10/2011, Kyoto, JPN / Culture and Computing, 2011 Second International Conference ; (p. 15-20), Conference Publishing Services (CPS), 2011
abs doi web bib

This paper addresses our experience in the design of a serious game, aimed at computer-based support for intercultural participatory management of protected areas (e.g., parks, marine reserves, biosphere reserves. . . ), in order to promote biodiversity conservation and social inclusion. Its objective is, via a computer assisted role-playing game, to help various stakeholders (e.g., environmentalist, tourism operator, traditional community. . . ) to collectively understand conflict dynamics and explore negotiation strategies for the management of protected areas. Therefore, this helps at mutual understanding and negotiation between different cultures, contexts and practices (traditional community, technical manager, environmentalist. . . ) about strategic issues when aiming at both biodiversity conservation and social inclusion. After introducing the objectives of our serious game, named SimParc, we will describe its design and its current architecture. We will also discuss the introduction of various types of agents in the system: a decision making agent playing the role of the park manager; artificial players replacing some of the human players in the game; assistant agents assisting human players; and expert agents providing human players with technical information about the viability of their proposal (e.g., about the survival of an endangered species), or to analyse relations (e.g., dominance or equity) among players proposals. This last type of agent aims at introducing a technical viewpoint and culture in this intercultural participatory process. Some of these agents have already been implemented and tested and some others are in progress.
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@inproceedings{PUB00033596, author = {Briot, J.P. and de Azevedo Irving, M. and Mendes de Melo, G. and Filho Vasconcelos, J.E. and Alvarez, I. and Martin, S. and Wei, W.}, title = {A serious game and artificial agents to support intercultural participatory management of protected areas for biodiversity conservation and social inclusion}, title = {Jeu sérieux et agents artificiels comme aide à la gestion participative et interculturelle d'aires protégées pour la conservation de la biodiversité et l'inclusion sociale}, bookTitle = {Culture and Computing 2011, The Second International Conference on Culture and Computing, Kyoto University, 20/10/2011-22/10/2011, Kyoto, JPN / Culture and Computing, 2011 Second International Conference ; }, publisher = {Conference Publishing Services (CPS)}, pages = {15-20}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00033596}, doi = {http://dx.doi.org/10.1109/Culture-Computing.2011.12 }, year = {2011}, affiliation = {LIP6 UNIVERSITE PIERRE ET MARIE CURIE CNRS PARIS FRA ; UFRJ RIO DE JANEIRO BRA ; INCT-PPED RIO DE JANEIRO BRA ; UNIFOR NATI FORTALEZA BRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA}, ISBNISSN = {ISBN: 978-1-4577-1593-8 }, abstract = {This paper addresses our experience in the design of a serious game, aimed at computer-based support for intercultural participatory management of protected areas (e.g., parks, marine reserves, biosphere reserves. . . ), in order to promote biodiversity conservation and social inclusion. Its objective is, via a computer assisted role-playing game, to help various stakeholders (e.g., environmentalist, tourism operator, traditional community. . . ) to collectively understand conflict dynamics and explore negotiation strategies for the management of protected areas. Therefore, this helps at mutual understanding and negotiation between different cultures, contexts and practices (traditional community, technical manager, environmentalist. . . ) about strategic issues when aiming at both biodiversity conservation and social inclusion. After introducing the objectives of our serious game, named SimParc, we will describe its design and its current architecture. We will also discuss the introduction of various types of agents in the system: a decision making agent playing the role of the park manager; artificial players replacing some of the human players in the game; assistant agents assisting human players; and expert agents providing human players with technical information about the viability of their proposal (e.g., about the survival of an endangered species), or to analyse relations (e.g., dominance or equity) among players proposals. This last type of agent aims at introducing a technical viewpoint and culture in this intercultural participatory process. Some of these agents have already been implemented and tested and some others are in progress.}, }
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I. Alvarez, S. Martin, O. Dordan, X. Litrico, P. Saint Pierre
Indicateurs de sécurité et de restauration dynamiques
Agir en situation d'incertitude : quelles constructions individuelles et collectives des régimes de protection et d'adaptation en agriculture ?, 22/11/2010-24/11/2010, Montpellier, FRA / Agir en situation d'incertitude : La construction individuelle et collective des régimes de protection et d'adaptation en agriculture (p. 12), 2010
abs web bib

La gestion de systèmes agricoles ou environnementaux, dans une perspective de gestion durable, conduit à réfléchir à des indicateurs de l'état actuel du système mais aussi de son évolution. La gestion durable peut être envisagée comme la conservation de propriétés intéressantes du système. Quand ces propriétés s'expriment sous la forme d'un ensemble de contraintes, la théorie de la viabilité permet de définir des indicateurs dynamiques qui prennent en compte la situation actuelle et les possibilités d'action dans le futur.
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@inproceedings{PUB00030853, author = {Alvarez, I. and Martin, S. and Dordan, O. and Litrico, X. and Saint Pierre, P.}, title = {Indicateurs de sécurité et de restauration dynamiques}, title = {Safety and restauration dynamic indicators}, bookTitle = {Agir en situation d'incertitude : quelles constructions individuelles et collectives des régimes de protection et d'adaptation en agriculture ?, 22/11/2010-24/11/2010, Montpellier, FRA / Agir en situation d'incertitude : La construction individuelle et collective des régimes de protection et d'adaptation en agriculture}, pages = {12}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00030853 / http://www.agir-incertitude2010.fr/}, year = {2010}, affiliation = {CEMAGREF CLERMONT FERRAND UR LISC FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA ; UNIVERSITE BORDEAUX II FRA ; CEMAGREF MONTPELLIER UR IRMO UMR G-EAU FRA ; LASTRE ET VIMADES PARIS FRA}, abstract = {La gestion de systèmes agricoles ou environnementaux, dans une perspective de gestion durable, conduit à réfléchir à des indicateurs de l'état actuel du système mais aussi de son évolution. La gestion durable peut être envisagée comme la conservation de propriétés intéressantes du système. Quand ces propriétés s'expriment sous la forme d'un ensemble de contraintes, la théorie de la viabilité permet de définir des indicateurs dynamiques qui prennent en compte la situation actuelle et les possibilités d'action dans le futur.}, }
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I. Alvarez, S. Martin, S. Mesmoudi
Describing the result of a classifier to the end-user: geometric-based sensitivity
ECAI 2010, 19th European Conference on Artificial Intelligence, 16/08/2010-20/08/2010, Lisbonne, PRT / Frontiers in Artificial Intelligence and Applications.Helder Coelho, Rudi Studer, Michael Wooldridge (Eds.) (p. 835-840), IOS Press, 2010
abs web bib

This paper addresses the issue of supporting the end-user of a classifier, when it is used as a decision support system, to classify new cases. We consider several kinds of classifiers: Statistical or machine learning classifiers, which are built on data, but also direct model-based classifiers that are built to solve a particular problem (like in viability or control problems). The end-user relies mainly on global information (like error rates or global sensitivity analysis) to assess the quality of the result given by the system. Class membership probability, if available, describes certainly the local statistical viewpoint. But it doesn't take into account other contextual information: Cases with high value of class membership probability can also be close to the decision boundary. In the case of numerical state space, we propose to use the decision boundary of the classifier (which always exists, even implicitly), to describe the situation of a particular case: The distance of a case to the decision boundary measures the robustness of the decision to a change in the input data. Other geometric concepts, such as the maximal maximal ball, can present a precise picture of the situation to the end-user. We show the interest of such a geometric study on different examples. / Cet article propose une méthode, basée sur la géométrie, pour aider l'utilisateur d'un système discriminant à apprécier les résultats dans le cadre de l'aide à la décision.
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@inproceedings{PUB00030835, author = {Alvarez, I. and Martin, S. and Mesmoudi, S.}, title = {Describing the result of a classifier to the end-user: geometric-based sensitivity}, title = {Décrire le résultat d'un système discriminant à l'utilisateur : la sensibilité géométrique}, volume = {215}, bookTitle = {ECAI 2010, 19th European Conference on Artificial Intelligence, 16/08/2010-20/08/2010, Lisbonne, PRT / Frontiers in Artificial Intelligence and Applications.Helder Coelho, Rudi Studer, Michael Wooldridge (Eds.)}, publisher = {IOS Press}, pages = {835-840}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00030835 / http://www.booksonline.iospress.nl/Content/BookSeriesBook.aspx?piid=17702}, year = {2010}, affiliation = {CEMAGREF CLERMONT FERRAND UR LISC FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA ; LIP6 UNIVERSITE PIERRE ET MARIE CURIE PARIS FRA}, ISBNISSN = {ISBN 978-1-60750-605-8}, abstract = {This paper addresses the issue of supporting the end-user of a classifier, when it is used as a decision support system, to classify new cases. We consider several kinds of classifiers: Statistical or machine learning classifiers, which are built on data, but also direct model-based classifiers that are built to solve a particular problem (like in viability or control problems). The end-user relies mainly on global information (like error rates or global sensitivity analysis) to assess the quality of the result given by the system. Class membership probability, if available, describes certainly the local statistical viewpoint. But it doesn't take into account other contextual information: Cases with high value of class membership probability can also be close to the decision boundary. In the case of numerical state space, we propose to use the decision boundary of the classifier (which always exists, even implicitly), to describe the situation of a particular case: The distance of a case to the decision boundary measures the robustness of the decision to a change in the input data. Other geometric concepts, such as the maximal maximal ball, can present a precise picture of the situation to the end-user. We show the interest of such a geometric study on different examples. / Cet article propose une méthode, basée sur la géométrie, pour aider l'utilisateur d'un système discriminant à apprécier les résultats dans le cadre de l'aide à la décision.}, }
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S. Martin, I. Alvarez
Indicateurs dynamiques de gestion durable
23èmes Entretiens Jacques Cartier, "Vulnérabilité et résilience des écosystèmes aquatiques : de l'évaluation à un fonctionnement durable - une utopie ?", 22/11/2010-23/11/2010, Lyon, FRA / Vulnérabilité & résilience des écosystèmes: l'utopie d'une gestion durable (p. 6-15), 2010
abs web bib

La gestion de systèmes agricoles ou environnementaux, dans une perspective de gestion durable, conduit à réfléchir à des indicateurs de l'état actuel du système mais aussi de son évolution. La gestion durable peut être envisagée comme la conservation de propriétés intéressantes du système. Dans certains cas, la théorie de la viabilité permet de définir des indicateurs comme la résilience ou la robustesse, qui prennent en compte les évolutions possibles du système.
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@inproceedings{PUB00030845, author = {Martin, S. and Alvarez, I.}, title = {Indicateurs dynamiques de gestion durable}, title = {Dynamical indicators of sustainable management}, bookTitle = {23èmes Entretiens Jacques Cartier, "Vulnérabilité et résilience des écosystèmes aquatiques : de l'évaluation à un fonctionnement durable - une utopie ?", 22/11/2010-23/11/2010, Lyon, FRA / Vulnérabilité & résilience des écosystèmes: l'utopie d'une gestion durable}, pages = {6-15}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00030845}, year = {2010}, affiliation = {CEMAGREF CLERMONT FERRAND UR LISC FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA}, abstract = {La gestion de systèmes agricoles ou environnementaux, dans une perspective de gestion durable, conduit à réfléchir à des indicateurs de l'état actuel du système mais aussi de son évolution. La gestion durable peut être envisagée comme la conservation de propriétés intéressantes du système. Dans certains cas, la théorie de la viabilité permet de définir des indicateurs comme la résilience ou la robustesse, qui prennent en compte les évolutions possibles du système.}, }
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I. Alvarez, S. Martin
Explaining a result to the end-user: a geometric approach for classification problems
Exact09, IJCAI 2009 Workshop on explanation aware computing (International Joint Conferences on Artificial Intelligence), 11/07/2009-13/07/2009, Pasadena, USA (p. 102-109), , 2009
abs web bib

This paper addresses the issue of the explanation of the result given to the end-user by a classier, when it is used as a decision support system. We consider machine learning classiers, which provide a class for new cases, but also deterministic classiers that are built to solve a particular problem (like in viability or control problems). The end-user relies mainly on global information (like error rates) to assess the quality of the result given by the system. Even class membership probability, if available, describes only the statistical viewpoint, it doesn't take into account the context of a particular case. In the case of numerical state space, we propose to use the decision boundary of the classier (which always exists, even implicitly), to describe the situation of a particular case: The distance of a case to the decision boundary measures the ro-bustness of the decision to a change in the input data. Other geometric concepts can present a precise picture of the situation to the end-user. This geometric study is applied to different types of classiers.
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@inproceedings{PUB00027387, author = {Alvarez, I. and Martin, S.}, title = {Explaining a result to the end-user: a geometric approach for classification problems}, title = {Explication d'un résultat à l'utilisateur final : une approche géométrique pour les systèmes discriminants}, publisher = { }, bookTitle = {Exact09, IJCAI 2009 Workshop on explanation aware computing (International Joint Conferences on Artificial Intelligence), 11/07/2009-13/07/2009, Pasadena, USA}, pages = {102-109}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00027387 / http://exact2009.workshop.hm/}, year = {2009}, affiliation = {CEMAGREF CLERMONT FERRAND UR LISC FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA}, abstract = {This paper addresses the issue of the explanation of the result given to the end-user by a classier, when it is used as a decision support system. We consider machine learning classiers, which provide a class for new cases, but also deterministic classiers that are built to solve a particular problem (like in viability or control problems). The end-user relies mainly on global information (like error rates) to assess the quality of the result given by the system. Even class membership probability, if available, describes only the statistical viewpoint, it doesn't take into account the context of a particular case. In the case of numerical state space, we propose to use the decision boundary of the classier (which always exists, even implicitly), to describe the situation of a particular case: The distance of a case to the decision boundary measures the ro-bustness of the decision to a change in the input data. Other geometric concepts can present a precise picture of the situation to the end-user. This geometric study is applied to different types of classiers.}, }
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S. Martin
Changer pour durer : problèmes de viabilité et de résilience
Changer pour durer , 19/09/2009-26/09/2009, Cerisy-la-Salle, FRA (p. 6), 2009
abs web bib

Dans le contexte d'un système qui évolue et dont l'évolution peut être influencée par des actions humaines, se fixer l'objectif de durer peut signifier vouloir figer le système dans son état actuel, c'est la recherche de l'équilibre. Mais l'objectif de durer peut concerner plus largement certaines propriétés de ce système plutôt qu'un état particulier. Durer implique alors agir pour conserver ces propriétés dignes d'intérêt malgré changements et perturbations, ce qui pose des problèmes de viabilité et de résilience. Le problème de viabilité s'énonce ainsi: étant donné un système dont l'évolution de l'état dépend en partie d'actions humaines, étant donné une propriété de ce système, quelles sont les suites d'actions qui garantissent la conservation de cette propriété? Le problème de résilience concerne la capacité du système étudié à retrouver cette propriété malgré des bouleversements dus à des perturbations exogènes: quelles sont les suites d'actions qui permettent éventuellement de restaurer cette propriété? Dans les deux cas, il s'agit de comment "changer pour durer" dans le sens de comment agir sur un système pour conserver (viabilité) ou restaurer à moindre coût (résilience) les propriétés qui nous intéressent.
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@inproceedings{PUB00029677, author = {Martin, S.}, title = {Changer pour durer : problèmes de viabilité et de résilience}, title = {Change to last: viability and resilience problems}, bookTitle = {Changer pour durer , 19/09/2009-26/09/2009, Cerisy-la-Salle, FRA}, pages = {6}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00029677 / http://www.ccic-cerisy.asso.fr/changer09.html}, year = {2009}, affiliation = {CEMAGREF CLERMONT FERRAND UR LISC FRA}, abstract = {Dans le contexte d'un système qui évolue et dont l'évolution peut être influencée par des actions humaines, se fixer l'objectif de durer peut signifier vouloir figer le système dans son état actuel, c'est la recherche de l'équilibre. Mais l'objectif de durer peut concerner plus largement certaines propriétés de ce système plutôt qu'un état particulier. Durer implique alors agir pour conserver ces propriétés dignes d'intérêt malgré changements et perturbations, ce qui pose des problèmes de viabilité et de résilience. Le problème de viabilité s'énonce ainsi: étant donné un système dont l'évolution de l'état dépend en partie d'actions humaines, étant donné une propriété de ce système, quelles sont les suites d'actions qui garantissent la conservation de cette propriété? Le problème de résilience concerne la capacité du système étudié à retrouver cette propriété malgré des bouleversements dus à des perturbations exogènes: quelles sont les suites d'actions qui permettent éventuellement de restaurer cette propriété? Dans les deux cas, il s'agit de comment "changer pour durer" dans le sens de comment agir sur un système pour conserver (viabilité) ou restaurer à moindre coût (résilience) les propriétés qui nous intéressent.}, }
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S. Mesmoudi, I. Alvarez, S. Martin, M. Sicard, P.H. Wuillemin
Geometric analysis of a capture basin: application to cheese ripening process
European Conference on Complex System, 21/09/2009-25/09/2009, Warwick, GBR (p. 14), 2009
abs web bib

This paper addresses the issue of analysing the results given by viability sets, which represent all the viable states of a dynamical system. Viability sets and capture basin are a relatively new method to study complex dynamical systems, focusing on the preservation of some properties of the system (constraints in the state space) rather than on the possible stable states and equilibria. The viability set delimits the area of the state space where there is always a list of controls that allows the system to verify indefinitely the constraints. A viability set represents a huge amount of information about the system it studies. We propose here a geometric study of viability sets. This study is applied to the viability tube (the sequence of viability set over time) of a food process.
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@inproceedings{PUB00027389, author = {Mesmoudi, S. and Alvarez, I. and Martin, S. and Sicard, M. and Wuillemin, P.H.}, title = {Geometric analysis of a capture basin: application to cheese ripening process}, title = {Analyse géométrique d'un bassin de capture : application à l'affinage du camembert}, bookTitle = {European Conference on Complex System, 21/09/2009-25/09/2009, Warwick, GBR}, pages = {14}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00027389}, year = {2009}, affiliation = {UNIVERSITE PIERRE ET MARIE CURIE LIP6 PARIS FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA ; INRA UMR782 GMPA THIVERVAL-GRIGNON FRA ; UNIVERSITE PIERRE ET MARIE CURIE LIP6 PARIS FRA}, abstract = {This paper addresses the issue of analysing the results given by viability sets, which represent all the viable states of a dynamical system. Viability sets and capture basin are a relatively new method to study complex dynamical systems, focusing on the preservation of some properties of the system (constraints in the state space) rather than on the possible stable states and equilibria. The viability set delimits the area of the state space where there is always a list of controls that allows the system to verify indefinitely the constraints. A viability set represents a huge amount of information about the system it studies. We propose here a geometric study of viability sets. This study is applied to the viability tube (the sequence of viability set over time) of a food process. }, }
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M. Sicard, N. Perrot, C. Baudrit, R. Reuillon, P. Bourgine, I. Alvarez, S. Martin
The viability theory to control complex food processes
ECCS'09, European Conference on Complex Systems, 21/09/2009-25/09/2009, Warwick, GBR (p. 6), 2009
abs web bib

The viability theory developed by [Aubin(1991)] has been adapted to calculate the optimal monitoring of cheese ripening process. This method was used efficiently in ecology or in finance but never in food process. The aim was to find the controls allowing reaching a compromise between the quality of the ripened cheeses and the production costs. A viability kernel and the costs simulations of the viable trajectories were computed. Then, the optimal ripening trajectories were validated during pilot trials. The results were finally compared to those obtained for cheeses ripened at 92% of relative humidity and 12°C of temperature, the conditions usually applied in dairy industries for the Camembert ripening process.
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@inproceedings{PUB00029638, author = {Sicard, M. and Perrot, N. and Baudrit, C. and Reuillon, R. and Bourgine, P. and Alvarez, I. and Martin, S.}, title = {The viability theory to control complex food processes}, title = {La théorie de la viabilité pour contrôler les procédés alimentaires complexes}, bookTitle = {ECCS'09, European Conference on Complex Systems, 21/09/2009-25/09/2009, Warwick, GBR}, pages = {6}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00029638}, year = {2009}, affiliation = {INRA UMR782 GMPA THIVERVAL GRIGNON FRA ; INRA UMR782 GMPA THIVERVAL GRIGNON FRA ; INRA UMR782 GMPA THIVERVAL GRIGNON FRA ; ISC PARIS FRA ; ISC PARIS FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA}, abstract = {The viability theory developed by [Aubin(1991)] has been adapted to calculate the optimal monitoring of cheese ripening process. This method was used efficiently in ecology or in finance but never in food process. The aim was to find the controls allowing reaching a compromise between the quality of the ripened cheeses and the production costs. A viability kernel and the costs simulations of the viable trajectories were computed. Then, the optimal ripening trajectories were validated during pilot trials. The results were finally compared to those obtained for cheeses ripened at 92% of relative humidity and 12°C of temperature, the conditions usually applied in dairy industries for the Camembert ripening process.}, }
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M. Sicard, R. Reuillon, N. Perrot, C. Baudrit, I. Alvarez, S. Martin
Control of Camembert mass loss during ripening with viability theory
XIIème Congrès de la Société Française de Génie des Procédés , 14/10/2009-16/10/2009, Marseille, FRA / Récents Progrès en Génie des Procédés, Numéro 98 (p. 6), SFGP, Paris, 2009
abs web bib

The viability theory developed by [Aubin1991] has been adapted to calculate the optimal monitoring of cheese ripening process. This method was used efficiently in ecology or in finance but never in food process. The aim was to find the controls allowing reaching a compromise between the quality of the ripened cheeses and the production costs. A viability kernel and the costs simulations of the viable trajectories were computed. Then, the optimal ripening trajectories were validated during pilot trials. The results were finally compared to those obtained for cheeses ripened at 92% of relative humidity and 12°C of temperature, the conditions usually applied in dairy industries for the Camembert ripening process. The optimized ripening control application in a pilot trial give interesting results with a ripening shortened of 7 days and a product with a quality level for consumer identical at day 15 of ripening as the cheese ripened following classical controls (92% RH, 12°C) at day 20 of ripening.
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@inproceedings{PUB00033595, author = {Sicard, M. and Reuillon, R. and Perrot, N. and Baudrit, C. and Alvarez, I. and Martin, S.}, title = {Control of Camembert mass loss during ripening with viability theory}, title = {Contrôler la perte de masse du Camembert durant l'affinage à l'aide de la théorie de la viabilité}, volume = {98}, bookTitle = {XIIème Congrès de la Société Française de Génie des Procédés , 14/10/2009-16/10/2009, Marseille, FRA / Récents Progrès en Génie des Procédés, Numéro 98}, address = {Paris}, publisher = {SFGP}, pages = {6}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00033595}, year = {2009}, affiliation = {UMR782 GMPA,AGROPARISTECH INRA THIVERVAL GRIGNON FRA ; ISC PARIS FRA ; UMR782 GMPA AGROPARISTECH INRA THIVERVAL GRIGNON FRA ; UMR782 GMPA,AGROPARISTECH INRA THIVERVAL GRIGNON FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA}, ISBNISSN = {ISBN 2-910239-72-1}, abstract = {The viability theory developed by [Aubin1991] has been adapted to calculate the optimal monitoring of cheese ripening process. This method was used efficiently in ecology or in finance but never in food process. The aim was to find the controls allowing reaching a compromise between the quality of the ripened cheeses and the production costs. A viability kernel and the costs simulations of the viable trajectories were computed. Then, the optimal ripening trajectories were validated during pilot trials. The results were finally compared to those obtained for cheeses ripened at 92% of relative humidity and 12°C of temperature, the conditions usually applied in dairy industries for the Camembert ripening process. The optimized ripening control application in a pilot trial give interesting results with a ripening shortened of 7 days and a product with a quality level for consumer identical at day 15 of ripening as the cheese ripened following classical controls (92% RH, 12°C) at day 20 of ripening.}, }
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M. Sicard, N. Perrot, C. Baudrit, I. Alvarez, S. Martin
The viability theory to control food processes
8th World Congress of Chemical Engineering, WCCE8, 23/08/2009-27/08/2009, Montréal, CAN / Proceedings of Process Control and Optimization Symposium, 8th World Congress on Chemical Engineering (WCCE8) (p. 5), 2009
abs web bib

The viability theory developed by Aubin (1991) has been adapted to calculate the optimal monitoring of cheese ripening process. This method was used efficiently in ecology or in finance but never in food process. The aim was to find the controls allowing to reach a compromise between the quality of the ripened cheeses and the production costs. A viability kernel and the costs simulations of the viable trajectories were computed. Then, the optimal ripening trajectories were validated during pilot trials. The results were finally compared to those obtained for cheeses ripened at 92% of relative humidity and 12°C of temperature, the conditions usually applied in dairy industries for Camembert ripening.
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@inproceedings{PUB00033594, author = {Sicard, M. and Perrot, N. and Baudrit, C. and Alvarez, I. and Martin, S.}, title = {The viability theory to control food processes}, title = {L'utilisation de la théorie de la viabilité pour contrôler les procédés alimentaires}, bookTitle = {8th World Congress of Chemical Engineering, WCCE8, 23/08/2009-27/08/2009, Montréal, CAN / Proceedings of Process Control and Optimization Symposium, 8th World Congress on Chemical Engineering (WCCE8)}, pages = {5}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00033594}, year = {2009}, affiliation = {UMR782 GMPA AGROPARISTECH INRA THIVERVAL GRIGNON FRA ; UMR782 GMPA AGROPARISTECH INRA THIVERVAL GRIGNON FRA ; UMR782 GMPA AGROPARISTECH INRA THIVERVAL GRIGNON FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA}, abstract = {The viability theory developed by Aubin (1991) has been adapted to calculate the optimal monitoring of cheese ripening process. This method was used efficiently in ecology or in finance but never in food process. The aim was to find the controls allowing to reach a compromise between the quality of the ripened cheeses and the production costs. A viability kernel and the costs simulations of the viable trajectories were computed. Then, the optimal ripening trajectories were validated during pilot trials. The results were finally compared to those obtained for cheeses ripened at 92% of relative humidity and 12°C of temperature, the conditions usually applied in dairy industries for Camembert ripening. }, }
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M.H. Durand, S. Martin
Développement durable et développement viable
La problématique du développement durable vingt ans après : nouvelles lectures théoriques, innovations méthodologiques et domaines d'extension, 20/11/2008-22/10/2008, Villeneuve d'Ascq, FRA (p. 14), 2008
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Les économistes conçoivent le problème du développement durable comme une question de rareté et de croissance. Les modèles construits pour rechercher les conditions d'existence d'une solution à ce problème reposent sur la définition d'un certain critère supposé refléter des conditions de justice entre les générations qu'il s'agit d'optimiser. Le développement durable, défini à travers ce critère, est considéré comme une question d'équité intergénérationnelle. Cet article propose d'utiliser la théorie de la viabilité, une approche mathématique, pour aborder les modèles de développement durable et de définir le développement durable par le respect des contraintes à chaque instant. Nous montrons que cette approche offre un nouveau point de vue en particulier parce qu'elle se focalise sur le problème de l'adaptation continuelle aux contraintes et offre la possibilité d'un arbitrage entre des choix ou des situations contraignantes et qu'elle évite par ailleurs la difficile question de la définition de la notion d'équité intergénérationnelle.
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@inproceedings{PUB00033593, author = {Durand, M.H. and Martin, S.}, title = {Développement durable et développement viable}, title = {Sustainable development and viable development }, bookTitle = {La problématique du développement durable vingt ans après : nouvelles lectures théoriques, innovations méthodologiques et domaines d'extension, 20/11/2008-22/10/2008, Villeneuve d'Ascq, FRA}, pages = {14}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00033593}, year = {2008}, affiliation = {IRD BONDY FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA}, abstract = {Les économistes conçoivent le problème du développement durable comme une question de rareté et de croissance. Les modèles construits pour rechercher les conditions d'existence d'une solution à ce problème reposent sur la définition d'un certain critère supposé refléter des conditions de justice entre les générations qu'il s'agit d'optimiser. Le développement durable, défini à travers ce critère, est considéré comme une question d'équité intergénérationnelle. Cet article propose d'utiliser la théorie de la viabilité, une approche mathématique, pour aborder les modèles de développement durable et de définir le développement durable par le respect des contraintes à chaque instant. Nous montrons que cette approche offre un nouveau point de vue en particulier parce qu'elle se focalise sur le problème de l'adaptation continuelle aux contraintes et offre la possibilité d'un arbitrage entre des choix ou des situations contraignantes et qu'elle évite par ailleurs la difficile question de la définition de la notion d'équité intergénérationnelle.}, }
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P. Coquelin, S. Martin, R. Munos
A dynamic programming approach to viability problems
IEEE ADPRL Symposium on Approximate Dynamic Programming and Reinforcement Learning , 01/04/2007-05/04/2007, Honolulu, Hawaii, USA (p. 178-184), 2007
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Viability theory considers the problem of maintaining a system under a set of viability constraints. The main tool for solving viability problems lies in the construction of the viability kernel, defined as the set of initial states from which there exists a trajectory that remains in the set of constraints indefinitely. The theory is very elegant and appears naturally in many applications. Unfortunately, the current numerical approaches suffer from low computational efficiency, which limits the potential range of applications of this domain. In this paper we show that the viability kernel is the zero-level set of a related dynamic programming problem, which opens promising research directions for numerical approximation of the viability kernel using tools from approximate dynamic programming. We illustrate the approach using k−nearest neighbors on a toy problem in two dimensions and on a complex dynamical model for anaerobic digestion process in four dimensions.
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@inproceedings{PUB00029639, author = {Coquelin, P. and Martin, S. and Munos, R.}, title = {A dynamic programming approach to viability problems}, title = {Une approche programmation dynamique pour des problèmes de viabilité}, bookTitle = {IEEE ADPRL Symposium on Approximate Dynamic Programming and Reinforcement Learning , 01/04/2007-05/04/2007, Honolulu, Hawaii, USA}, pages = {178-184}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00029639 / http://www.ece.uic.edu/~dliu/C/ADPRL07/}, year = {2007}, affiliation = {CENTRE DE MATHEMATIQUES APPLIQUEES ECOLE POLYTECHNIQUE PALAISEAU FRA ; CEMAGREF CLERMONT FERRAND UR LISC FRA ; INRIA FUTURS LILLE FRA}, abstract = {Viability theory considers the problem of maintaining a system under a set of viability constraints. The main tool for solving viability problems lies in the construction of the viability kernel, defined as the set of initial states from which there exists a trajectory that remains in the set of constraints indefinitely. The theory is very elegant and appears naturally in many applications. Unfortunately, the current numerical approaches suffer from low computational efficiency, which limits the potential range of applications of this domain. In this paper we show that the viability kernel is the zero-level set of a related dynamic programming problem, which opens promising research directions for numerical approximation of the viability kernel using tools from approximate dynamic programming. We illustrate the approach using k−nearest neighbors on a toy problem in two dimensions and on a complex dynamical model for anaerobic digestion process in four dimensions.}, }
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Dissertations (1)

S. Martin
D’oxymore en oxymore : du développement durable au contrôle complexe
Habilitation à diriger des recherches en mathématiques appliquée, Université Blaise Pascal Clermont-Ferrand, 2015
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I explain in this document how questions on the assessment of the resilience of socio-ecological systems and questions on the distinction between action policies that can be considered as sustainable, led me to propose measures based on concepts of the mathematical viability theory. The implementation of these measures in each particular case raises modeling and calculation issues. Some answers are specific to the particular case, but others, such as algorithms, can be capitalized to ask new questions. My current focuses are regulation architectures in complex systems when the properties of interest are global and resilient to local disturbances. / J’explique dans ce mémoire comment les questionnements sur l’évaluation de la résilience de systèmes écologiques et sociaux ainsi que sur la distinction de politiques d’actions pouvant être qualifiées de durables, m’ont conduit à proposer des mesures basées sur les concepts de la théorie mathématique de la viabilité. La mise en oeuvre de ces mesures dans chaque cas particulier pose des problèmes de modélisation et de calcul. Certaines réponses sont spécifiques au cas en question, d’autres comme les algorithmes de calcul peuvent être capitalisés pour se poser de nouvelles questions. Celles qui m’intéressent actuellement concernent les architectures de régulation dans les systèmes complexes, complexes au sens où les propriétés d’intérêt globales sont résilientes à des perturbations locales.
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@phdthesis{PUB00044374, author = {Martin, S.}, title = {D’oxymore en oxymore : du développement durable au contrôle complexe}, title = {From one oxymoron to another : from sustainable development to complex control}, publisher = {Habilitation à diriger des recherches en mathématiques appliquée, Université Blaise Pascal Clermont-Ferrand}, pages = {99}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00044374}, year = {2015}, affiliation = {IRSTEA CLERMONT FERRAND UR LISC FRA}, abstract = {I explain in this document how questions on the assessment of the resilience of socio-ecological systems and questions on the distinction between action policies that can be considered as sustainable, led me to propose measures based on concepts of the mathematical viability theory. The implementation of these measures in each particular case raises modeling and calculation issues. Some answers are specific to the particular case, but others, such as algorithms, can be capitalized to ask new questions. My current focuses are regulation architectures in complex systems when the properties of interest are global and resilient to local disturbances. / J’explique dans ce mémoire comment les questionnements sur l’évaluation de la résilience de systèmes écologiques et sociaux ainsi que sur la distinction de politiques d’actions pouvant être qualifiées de durables, m’ont conduit à proposer des mesures basées sur les concepts de la théorie mathématique de la viabilité. La mise en oeuvre de ces mesures dans chaque cas particulier pose des problèmes de modélisation et de calcul. Certaines réponses sont spécifiques au cas en question, d’autres comme les algorithmes de calcul peuvent être capitalisés pour se poser de nouvelles questions. Celles qui m’intéressent actuellement concernent les architectures de régulation dans les systèmes complexes, complexes au sens où les propriétés d’intérêt globales sont résilientes à des perturbations locales.}, }
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Technical Reports (2)

S. Martin
Compte-rendu final projet ANR Déduction
2010
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L'enjeu de la distinction entre les actions qui respectent les conditions du développement durable et les autres est considérable tant ce label est utilisé pour promouvoir des activités économiques, sociales ou politiques. Les outils des théories mathématiques du contrôle ont montré leur efficacité en automatique, l'objectif de ce projet est d'expérimenter l'utilisation de certains d'entre eux en ingénierie du développement durable. Les travaux menés dans ce projet consistent donc, dans le cadre de l'agriculture au sens large, à formuler des problèmes de gestion durable typiques, et à développer des outils mathématiques nouveaux pour formaliser ces problèmes de gestion durable et pour construire des algorithmes pour les résoudre. Est ainsi rassemblée au service du projet une association d'équipes interdisciplinaire composée de laboratoires fondamentaux (CREA) et appliqués (LISC), qui développent des méthodes et outils issus de la théorie de la viabilité et de partenaires (INRA, IRD) ayant l'expérience de l'étude de systèmes de l'agriculture au sens large soumis à des enjeux de gestion durable.
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@techreport{PUB00033514, author = {Martin, S.}, title = {Compte-rendu final projet ANR Déduction}, title = {ANR project Deduction proceedings}, pages = {34}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00033514}, year = {2010}, affiliation = {CEMAGREF CLERMONT FERRAND UR LISC FRA}, abstract = {L'enjeu de la distinction entre les actions qui respectent les conditions du développement durable et les autres est considérable tant ce label est utilisé pour promouvoir des activités économiques, sociales ou politiques. Les outils des théories mathématiques du contrôle ont montré leur efficacité en automatique, l'objectif de ce projet est d'expérimenter l'utilisation de certains d'entre eux en ingénierie du développement durable. Les travaux menés dans ce projet consistent donc, dans le cadre de l'agriculture au sens large, à formuler des problèmes de gestion durable typiques, et à développer des outils mathématiques nouveaux pour formaliser ces problèmes de gestion durable et pour construire des algorithmes pour les résoudre. Est ainsi rassemblée au service du projet une association d'équipes interdisciplinaire composée de laboratoires fondamentaux (CREA) et appliqués (LISC), qui développent des méthodes et outils issus de la théorie de la viabilité et de partenaires (INRA, IRD) ayant l'expérience de l'étude de systèmes de l'agriculture au sens large soumis à des enjeux de gestion durable. }, }
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S. Martin, D. Hervé
Rapport sur les journées de travail du projet ANR Deduction, 7, 8 et 9 novembre 2007 à Fianarantsoa
2007
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Au cours de ces journées, les membres du projet Deduction ont exposé leurs travaux en lien avec le projet. Cela a permis à ceux qui ne connaissaient pas la problématique de la conservation de la biodiversité du corridor forestier de Fianarantsoa d'en apprécier la complexité. Les discussions ont également permis de fixer des collaborations sur des travaux déjà en cours et de réaliser un premier modèle spécifique au projet Déduction.
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@techreport{PUB00024753, author = {Martin, S. and Hervé, D.}, title = {Rapport sur les journées de travail du projet ANR Deduction, 7, 8 et 9 novembre 2007 à Fianarantsoa}, title = {Report on ANR project Deduction Workshop November 7, 8 and 9 th 2007 in Fianarantsoa}, pages = {8}, url = {http://irsteadoc.irstea.fr/cemoa/PUB00024753}, year = {2007}, affiliation = {CEMAGREF CLERMONT FERRAND LISC ; IRD MONTPELLIER}, abstract = {Au cours de ces journées, les membres du projet Deduction ont exposé leurs travaux en lien avec le projet. Cela a permis à ceux qui ne connaissaient pas la problématique de la conservation de la biodiversité du corridor forestier de Fianarantsoa d'en apprécier la complexité. Les discussions ont également permis de fixer des collaborations sur des travaux déjà en cours et de réaliser un premier modèle spécifique au projet Déduction.}, }
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LISC

Martin Sophie

Publications

Journal Articles (11)

Book Chapters (4)

In Proceedings (17)

Dissertations (1)

Technical Reports (2)