La question de la modélisation en sciences humaines : mathématiques et informatique, année 2011/2012
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Vendredi 15 juin 2012 à 13h30, 105 bd Raspail 75006 Paris, Salle 5
13h30 :
Patrice Ossona de Mendez
CAMS, EHESS
Property testing on large networks
The experimental method and the combination of observations, experimentations and rational arguments became the standard methodology to come close to the Truth. The fundamental idea of the experimental approach is that a limited number of experiments should be sufficient to determine whether a property is « close to be true » or not with a « good likelihood ». We discuss the particular problem of determining specific properties of an extremely large network by mean of a limited number of tests. This approach, called « property testing », is in particular linked to several notions of graph limits et to Szemerédi regularity lemma.
15h00 :
Xuding Zhu
Professeur invité à l’EHESS (Department of Mathematics, Zhejiang Normal University (Jinhua, Zhejiang, China)
Graph Theory model for scheduling problems
Scheduling is the process of deciding how to commit resources between a variety of possible tasks. A typical phenomenon is that there are conflicts between pairs of tasks that forbids them to share a resource. In this case, graphs provide an ideal model for the problem. Vertices represent tasks, and two vertices are connected by an edge if there are conflicts between the corresponding tasks. The scheduling problem is usually to optimize some parameters, which become optimization problems on graphs. For example, in a parallel computation model, a set of processes make computations on a set of data files. Each process accesses some data files. Two processes sharing a same data file cannot operate at the same time. The scheduling problem is to assign time units to processes so that conflicting processes do not operate at the same time, and each process operate roughly the same number of units and under these restriction, optimize the efficiency of the computation. This problem turns out to be circular coloring of graphs. In this talk, we shall explain how this graph parameter is related to various scheduling problems, its relation to other graph parameters, and survey some results on the study of this graph coloring concept.
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Vendredi 16 mars, 15h30 – 105 bd Raspail 75006 Paris (attention salle inhabituelle) salle 5
Giovanna Citti
Dipartimento di Matematica, University of Bologna
The subriemannian structure of the primary visual cortex
Starting from the works of D. Hoffmann, J. Petitot, the functional architecture of the primary visual cortex has been modelled with differential instruments. In the same spirit, with A. Sarti we described the structure of the primary visual cortex as a Lie group with a sub-Riemannian structure, which can account for orientation, space time or stereo. Association fields are modelled as integral curves of the structure, propagation of the visual signal as solution of a PDE. In particular its fundamental solution will describe the neural connectivity and will be compared with the probability of edges co-ocurrence in natural images. From the mathematical point of view the sub-Riemannian structure is totally degenerate at any point, and we will shortly outline some instruments introduced to handle the degeneracy.
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Vendredi 10 février
à 14 h :
François Bourguignon
Directeur d’études EHESS et Directeur de PSE-Ecole d’économie de Paris
Dix ans de réflexion sur le thème de l’inégalité : et après ?
à 15h30 :
Yoshiyasu Ono
Fellow, Osaka University
On Persistent Demand Shortages: A Behavioral Approach
We incorporate two sets of behavioral assumptions (fairness concerns for nominal wages and insatiable desire for money) into a dynamic model of a monetary economy to illuminate how these sets of assumptions can generate persistent aggregate demand shortages. We obtain the condition for persistent unemployment, and that for temporary unemployment, to occur. Policy implications significantly differ between the two cases. A monetary expansion raises private consumption under temporary unemployment but not under persistent nemployment. A fiscal expansion may or may not increase short-run private consumption but crowds out long-run consumption under temporary unemployment. Under persistent unemployment, however, it always increases private consumption.
About Yoshiyasu Ono:
1979 : Doctor of Economics, the University of Tokyo.
1990-1996 & 1999-2010 : Professor, ISER (Institute of Social and Economic Research), Osaka University.
1996-1999 : Professor, Tokyo Institute of Technology
2011-Present : Fellow, Osaka University
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Vendredi 27 janvier 2012 à 15 h
Lionel Roques
INRA, Avignon
Equations de réaction-diffusion, paradoxe de Reid (recolonisation post-glaciaire) et diversité génétique
La première partie de cet exposé sera consacrée à une présentation intuitive des équations de réaction-diffusion. Nous montrerons comment ces équations peuvent être construites sur la base de considérations écologiques. Dans une deuxième partie, nous utiliserons ces équations pour expliquer certains phénomènes contre-intuitifs (paradoxes) observés empiriquement en écologie spatiale.
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Vendredi 9 décembre 2011 à 15 h
Miguel A. Herrero
Instituto de Matemática Interdisciplinar (IMI) and Departamento de Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense, Madrid, Spain
Optimization problems in radiotherapy planning
A key question in Radiotherapy consists in determining an optimal distribution of radiation over a given target volume, so that maximum tumour control is achieved with a minimum of side effects. On the other hand, a relevant related issue is that of extracting from the commercial planners used in clinical practice an actual treatment plan, which provides as good an approximation to that optimal distribution as possible. In this lecture, I shall describe some mathematical problems of optimization type that have been recently proposed to address such problems, and some examples of application thereof will be discussed.
