La question de la modélisation en sciences humaines : mathématiques et informatique, année 2009/2010
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Mardi 22 juin 2010 à 15h, salle 214 (54, bd Raspail Paris 6e)
Pierre Degond
Institut de Mathématiques de Toulouse
Modèles continus pour les systèmes complexes
Les systèmes complexes développent spontanément des structures spatio-temporelles cohérentes à grande échelle bien que les agents les constituant interagissent de manière locale, décentralisée, et avec une connaissance limitée de leur environnement. Les exemples figurent aussi bien en sciences du vivant (grégarisme, insectes sociaux, embryogenèse) qu’en sciences humaines (trafic, foules, réseaux sociaux, circuits économiques). Les modèles continus, par opposition aux modèles « agents-centrés », décrivent ces systèmes à l’aide de quantités macroscopiques (densités, flux, etc…). Leur pertinence dans ce domaine est sujet à controverses. L’exposé examinera la nature du lien entre modèles continus et modèles « agents-centrés » et montrera la nécessité de forger de nouveaux concepts spécifiquement adaptés aux systèmes complexes, par opposition aux systèmes physiques « classiques ». Plus fondamentalement, l’émergence de cohérence à grande échelle au sein de ces systèmes remet en question l’hypothèse d’indépendance statistique (ou hypothèse du chaos) qui fonde la théorie classique des modèles continus. Celle-ci reste toutefois remarquablement robuste. On abordera ces questions au travers de quelques exemples de déplacements collectifs chez les animaux.
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Mardi 18 mai 2010 à 15 h, salle 206 (54, bd Raspail Paris 6e)
Santo Fortunato
Institute for Scientific Interchange (ISI), Turin
Towards a physics of society
Statistical physics has proven to be a valuable tool to describe and understand the properties of systems formed by a large number of elementary units. A big challenge is whether the tools and techniques of statistical physics are suitable to explore large scale social phenomena. Most attempts of the literature focus on simple microscopic models, with little or no contact to real social dynamics. A validation of this approach is still lacking and must rely on quantitative evidence about real social systems. Finding regularities on real data is a crucial step in this direction. We will show that voting and citing behaviors are both characterized by scaling and universality. The statistical distribution of the number of votes/cites, suitably normalized, is independent of the particular system considered. This opens the way to a simple modeling of the observed phenomenology.
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Mardi 11 mai 2010 à 15 h, salle 206 (54, bd Raspail Paris 6e)
Jaroslav Nešetřil
Univerzita Karlova v Praze
Mathematical modeling at the moment of discovery (□ versus △)
Mathematical modeling takes very different forms.
In engineering, physics and computer science the subjects are often so tightly related to their models that we can speak about simulations. On the other hand, in humanities and economy the models are much more freely related to their subject and we should often speak about analogies.
But these high level analogies present us with problems of a deeper understanding. We illustrate this on comparison of two very simple (mathematical) forms: triangle and rectangle. Quite surprisingly this relates to some of the key paradigma of modern mathematics.
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Jeudi 29 avril 2010 de 10h00 à 17h30 à l’Institut des Systèmes Complexes Paris Île-de-France (ISC-PIF) (57-59 rue Lhomond, Paris 5e)
Séance exceptionnelle Atelier « Decision Making and Risks in Complex Environments »,
Programme et informations pratiques
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Mardi 12 janvier 2010 à 15 h salle 214 (54, bd Raspail Paris 6e)
Julian Hunt
University College London, Trinity College, Cambridge, House of Lords
Global System Dynamics and Problems of Sustainability
Politicians share an understanding with complex systems scientists that patterns of behaviour in societies often do not depend on the particular characteristics of the elements of the system, but rather on how they are connected and on the interactions between the component entities. Nevertheless there is a great challenge to the science of systems to show what kinds of advantage there are to decision makers to adopt a systems approach to the kind of strategic and often qualitative problem they face, such as the current issue (e.g. discussed in House of Lords, Dec. 8) of choosing between or combining, market or directed or life-style solutions for mitigation and adaptation policies for climate change. Systems approaches can also help decision makers communicate both instrumental (e.g. effects of environment on health) and societal implications of their future plans, and through technology obtain feedback and then consult those affected. This is the dynamical aspect of using systems approaches for policy.
The seminar will give an overview of the different aspects of GSD modelling with some specific examples as well as proposing how GSD might develop in future. We will especially discuss the possibilities for using this approach to encourage multi-discipline and multi-cultural education.
