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Cours

SMAT M130 - Questions spéciales de mathématiques 2007-2008 :
« Complexity in social dynamics, from the micro to the macro »

Enseignant (Théorie et Encadrement TP)

Franco Bagnoli, Université de Florence (Italie)

Coordinateur pour le Département de Mathématique

Timoteo CARLETTI

Objectifs

One of the most interesting object to be studied is our brain. We progressed a lot in the understanding of its working, at several different levels of description: from the behavior of the single neuron to the functional relationships among the different areas. Moreover, we are social animals, and the social contacts are extremely important in our formation: large parts of our brain are dedicated to the management of social interactions.

Therefore, it is not surprising that the "effects" of the choices in one's brain may trigger large responses from a mass of people.The investigation of these effects is multidisciplinary: we progress by “"mixing" results from neurosciences, cognitive sciences, psychology, psychiatry, biology (especially the theory of evolution) and also physics (collective phenomena, dynamical systems, network theory, statistical physics).

Actually, there is no hope of being able to compute the behavior of a certain level of description (say, a mass) stating from the "fundamental blocks", the neurons. There are too many neurons, and their connections are largely unknown, to make this reductionistic approach feasible. One approach that has proven fruitful is the use of simplified models, that can be simulated efficiently on a standard computer, and whose behavior may help in understanding the emergence of collective phenomena.

This course has the goal of showing how models of different part of the "neural world" can be build, simulated and investigated. We start from simple models of assembly of neurons up to models of communities and of typical human dynamics, like opinion formation.

Contenu

Lesson 1: Presentation and background (mon 7/4/2008 16:00-18:00 , Salle Conf)

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Laboratory 1 (wed 9/4/2008 14:00-17:00 , Pool 3ème)

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Lesson 2: Neural Networks (thu 10/4/2008 14:00-16:00 , MA3)

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Laboratory 2 (fri 11/4/2008 14:00-17:00 , Pool 3ème)

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Lesson 3: Social level (mon 14/4/2008 16:00-18:00 , Salle Conf)

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Laboratory 3 (wed 16/4/2008 14:00-17:00 , Pool 3ème)

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Lesson 4: Evolutionary dynamics, strategies and games (thu 17/4/2008 14:00-16:00 , MA3)

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Laboratory 4 (fri 18/4/2008 14:00-17:00 , Pool 3ème)

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Complementary material (papers, other fortran programs etc ...)

Donné en

Année(s) d'études

Quadrimestre

Théorie (h)

TP (h)

Crédits

1ere année de Master en sciences mathématiques

2e

16

14

6

Evaluation

rédaction et présentation d'un travail basé sur un sujet vu en coursexamen