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Votre navigateur est à mettre à jour pour voir ces vidéos. Jean-Marie Gilliot, Maître de conférences à Télécom Bretagne, co-fondateur du premier MOOC français et auteur du blog «Techniques innovantes pour l'enseignement supérieur» La question de l'enseignement hybride a été centrale. Cette appellation, qui implique que le numérique soit présent dans les espaces d'apprentissage, recouvre un certain nombre de réalités, d'usages, de pratiques, dont la mise en oeuvre répond à des objectifs différents dans des contextes variés : que font les étudiants avec leurs ordinateurs dans les amphis et salles de cours ? Quelle place occupe le numérique, sous toutes ses formes, dans nos espaces physiques de cours ? Comment les enseignants et les étudiants peuvent-ils l'intégrer efficacement pour construire, diffuser, partager des savoirs ? Ces questions, auxquelles est confronté le monde de l'enseignement, sont sans doute rendues encore plus visibles par la médiatisation du phénomène MOOC, ces cours massivement ouverts en ligne qui catalysent et cristallisent un certain nombre de questionnements dont l'échelle est celle des changements que connaît l'université dans son ensemble. Lors des échanges avec la salle, la question des choix à effectuer en matière de gouvernance a notamment été posée : dans quelle mesure faut-il investir dans des MOOC, avec quelles retombées pour les étudiants mais aussi pour les enseignants en matière d'amélioration des pratiques pédagogiques ? Les problématiques liées à la validation et à la certification des connaissances et des compétences ont aussi été abordées et élargies à celle de la diplômation, fondement du fonctionnement universitaire lui-même. Retrouvez les diapos de la conférence dans le billet rédigé par Jean-Marie Gilliot : http://tipes.wordpress.com/2013/04/10/le-numerique-au-coeur-des-espaces-dapprentissage-de-la-salle-de-cours-au-moocprintemps-des-tice-paris-1-pantheon-sorbonne/ sur son blog. Retrouvez la prise de notes collaborative : http://lite.framapad.org/p/r.X8jpeUou6agN2dnX réalisée en direct pendant la conférence. Retrouvez les photos du Printemps des TICE 2013 en diaporama : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1366189959982 (2Mo) Retrouvez les photos du Printemps des TICE 2013 en pdf : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1366190519762(2Mo) POUR EN SAVOIR PLUS : -Le 1er MOOC français (octobre-décembre 2012) «Internet, tout y est pour apprendre» (http://www.itypa.mooc.fr/ : http://www.itypa.mooc.fr/) -Le blog de J.-M. Gilliot : (http://tipes.wordpress.com/ : http://tipes.wordpress.com/)

Jean Jacod. Université Paris6. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1265816883468 (pdf) Ecouter l'intervention : Bande son disponible au format mp3 Durée : 51 mn

We will show taht one can combine Malliavin calculus with Stein's method, in order to derive explicit bounds in the Gaussian and Gamma approximations of arbitrary regular functionals of a given Gaussian field (here, the notion of regularity is in the sense of Malliavin derivability). When applied to random variables belonging to a fixed Wiener chaos, our approach generalizes, refines proved (in several papers, from 2005 to 2007) by Nourdin, Nualart, Ortiz-Latorre, Peccati and Tudor. We shall discuss some connections with the classic method of moments and cumulants. As an application, we deduce explicit Berry-Esseen bounds in the Breuer-Major Central limit theorem for subordinated functionals of a fractional Brownian motion. This talk is based on joint works with I. Nourdin (Paris VI). Giovanni PECCATI. Université de Paris 6. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1207750005329 (pdf) Ecouter l'intervention : Bande son disponible au format mp3 Durée : 41 mn

We investigate the asymptotic behavior of a particular family of weighted sums of independent standardized random variables with uniformly bounded third moments. We prove that the empirical CDF of the resulting partial sums converges almost surely to the normal CDF. It allows us to deduce the almost sure uniform convergence of empirical distribution of the empirical periodogram as well as the almost sure uniform convergence of spectral distribution of symmetric circulant random matrices. In the special case of trigonometric weights, we also establish a central limit theorem and a large deviation principle. It is a joint workwith W. Bryc. Bernard BERCU Université de Bordeaux 1 Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1207750057287 (pdf) Ecouter l'intervention : Bande son disponible au format mp3 Durée : 35 mn

We study the weak convergence (in the high-frequency limit) of the frequency components associated with Gaussian-subordinated, spherical and isotropic random fields. In particular, we provide conditions for asymptotic Gaussianity and we establish a new connection with random walks on the the dual of SO(3), which mirrors analogous results previously established for fields defined on Abelian groups. Our work is motivated by applications to cosmological data analysis, and specifically by the probabilistic modelling and the statistical nalysis of the Cosmic Microwave Background radiation, which is currently at the frontier of physical research. To obtain our main results, we prove several fine estimates involving convolutions of the so-called Clebsch-Gordan coefficients (which are elements of unitary matrices connecting reducible representations of SO(3)); this allows to intepret most of our asymptotic conditions in terms of coupling of angular momenta in a quantum mechanical system. Part of the proofs are based on recently established criteria for the weak convergence of multiple Wiener-Itô integrals. This is a joint paper by Domenico Marinucci (Rome "Tor Vergata") and Giovanni Peccati (Paris VI). Domenico MARINUCCI Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1207750104939 (pdf) Ecouter l'intervention : Bande son disponible au format mp3 Durée : 57 mn

We study a group of related problems: the extent to which presence of regular variation of the tail of certain $sigma$-finite measures at the output of a linear filter determines the corresponding regular variation of a measure at the input to the filter. This turns out to be related to presence of a particular cancellation property in $sigma$-finite measures, which, in turn, is related to uniqueness of solutions of certain functional equations. The techniques we develop are applied to weighted sums of iid random variables, to products of independent random variables, and to stochastic integrals with respect to Lévy motions. Joint work with Martin Jacobsen, Thomas Mikosch and Jan Rosinski. Gennady SAMORODNITSKY. Cornell University. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1207750230504 (pdf) Ecouter l'intervention : Bande son disponible au format mp3 Durée : 47 mn

Philippe SOULIER Université Paris 10 Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1207750174352 (pdf) Ecouter l'intervention : Bande son disponible au format mp3 Durée : 33 mn

In the work (Bender, T. Sottinen, and E. Valkeila (2006)) we show that it is possible to extend the classical Black & Scholes hedging for a class of models, where the quadratic variation is identical to the Black & Scholes model. Dzhaparidze and Spreij show in (K. Dzhaparidze, and P. Spreij (1994)), that the periodogram constructed from the process estimates the quadratic variation in the semimartingale setting.We show that the periodogram estimates the quadratic variation for the mixed Brownian fractional Brownian motion, too.The talk is based on joint with Ehsan Azmoodeh. Esko VALKEILA. Helsinky University of Technology. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1207750279333 (pdf) Ecouter l'intervention : Bande son disponible au format mp3 Durée : 41 mn

We prove a central limit theorem for linear triangular arrays under weak dependence conditions [1,3,4]. Our result is then applied to the study of dependent random variables sampled by a $Z$-valued transient random walk. This extends the results obtained by Guillotin-Plantard & Schneider [2]. An application to parametric estimation by random sampling is also provided. References: [1] Dedecker J., Doukhan P., Lang G., Leon J.R., Louhichi S. and Prieur C. (2007). Weak dependence: With Examples and Applications. Lect. notes in Stat. 190. Springer, XIV. [2] N. Guillotin-Plantard and D. Schneider (2003). Limit theorems for sampled dynamical systems. Stochastic and Dynamics 3, 4, p. 477-497. [3] M. Peligrad and S. Utev (1997). Central limit theorem for linear processes. Ann. Probab. 25, 1, p. 443-456. [4] S. A. Utev (1991). Sums of random variables with $varphi$-mixing. Siberian Advances in Mathematics 1, 3, p. 124-155. Clémentine PRIEUR. Université de Toulouse 1. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1207750339872 (pdf) Ecouter l'intervention : Bande son disponible au format mp3 Durée : 33 mn

We introduce a new modification of Sentana's (1995) Quadratic ARCH (QARCH), the Linear ARCH (LARCH) (Giraitis et al., 2000, 2004) and the bilinear models (Giraitis and Surgailis, 2002), which can combine the following properties: (a.1) conditional heteroskedasticity (a.2) long memory (a.3) the leverage effect (a.4) strict positivity of volatility (a.5) Lévy-stable limit behavior of partial sums of squares Sentana's QARCH model is known for properties (a.1), (a.3), (a.4), and the LARCH model for (a.1), (a.2), (a.3). Property (a.5) is new. References: [1] Giraitis, L., Robinson, P.M., Surgailis, D. (2000) A model for long memory conditional heteroscedasticity, Ann. Appl. Probab. 10, 1002--1024. [2] Giraitis, L., Surgailis, D. (2002) ARCH-type bilinear models with double long memory, Stoch. Process. Appl. 100, 275--300. [3] Giraitis, L., Leipus, R., Robinson, P.M., Surgailis, D. (2004) LARCH, leverage and long memory, J. Financial Econometrics 2, 177--210. [4] Sentana, E. (1995) Quadratic ARCH models, Rev. Econ. Stud. 3, 77--102. Donatas SURGAILIS. Academy of Sciences, Lithuania. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1207750384173 (pdf) Ecouter l'intervention : Bande son disponible au format mp3 Durée : 37 mn

Nous définissons une classe de processus multifractaux en intégrant une cascades multiplicative stationnaire contre un mouvement brownien fractionnaire. Les propriétés de scaling sont étudiées ainsi que le formalisme multifractal associé. This talk is based on a joint work with P.Abry, P.Chainais et V.Pipiras. Laure COUTIN. Université Paris 5. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1207750545594 (pdf) Ecouter l'intervention : Bande son disponible au format mp3 Durée : 46 mn

Contraction rates of posterior distributions on nonparametric models are derived for Gaussian process priors. We show that the convergence rate depends on the small ball probabilities of the Gaussian process and on the position of the true parameter relative to the reproducing kernel Hilbert space of the Gaussian process. Explicit examples are given for various statistical settings, including density estimation, nonparametric regression, and classification. We also discuss how rescaling of the prior process affects the contraction rates and how random rescaling can yield rate-adaptive procedures. This is based on joint work with Aad van der Vaart. Harry VAN ZANTEN. Vrije Universiteit. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1207750607556 (pdf) Ecouter l'intervention : Bande son disponible au format mp3 Durée : 34 mn

The paper develops a limit theory for the quadratic form $Q_{n,X}$ in linear random variables $X_1, ldots, X_n$ which can be used to derive the asymptotic normality of various semiparametric, kernel, window and other estimators converging at a rate which is not necessarily $n^{1/2}$. The theory covers practically all forms of linear serial dependence including long, short and negative memory, and provides conditions which can be readily verified thus eliminating the need to develop technical arguments for special cases. This is accomplished by establishing a general CLT for $Q_{n,X}$ with normalization $(var[Q_{n,X}])^{1/2}$ assuming only $2+delta$ finite moments. Previous results for forms in dependent variables allowed only normalization with $n^{1/2}$ and required at least four finite moments. Our technique uses approximations of $Q_{n, X}$ by a form $Q_{n, Z}$ in i.i.d. errors $Z_1, ldots, Z_n$. We develop sharp bounds for these approximations which in some cases are faster by the factor $n^{1/2}$ compared to the existing results. Liudas GIRAITIS Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1207750657882 (pdf) Ecouter l'intervention : Bande son disponible au format mp3 Durée : 51 mn

We propose a method for numerical approximation of Reflected Backward Stochastic Differential Equations. Is based in the approximation for the Brownian motion by a simple random walk. We prove a weak convergence. This talk is based on joint work with Miguel Martinez and Jaime San Martin. Soledad TORRES. Universidad de Valparaiso. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1207750701378 (pdf) Ecouter l'intervention : Bande son disponible au format mp3 Durée : 44 mn

We study generalized random fields which arise as rescaling limits of spatial configurations of uniformly scattered random balls as the mean radius of the balls tends to $0$ or infinity. Assuming that the radius distribution has a power law behavior, we prove that the centered and renormalized random balls field admits a limit with strong spatial dependence. In particular, our approach provides a unified framework to obtain all self-similar, stationary and isotropic Gaussian fields. In addition to investigating stationarity and self-similarity properties, we give $L^2$-representations of the limiting generalized random fields viewed as continuous random linear functionals. Joint work with A. Estrade (Paris 5) and Ingemar Kaj (Uppsala University) Hermine BIERME Université René Descartes Paris 5 Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1207750733740 (pdf) Ecouter l'intervention : Bande son disponible au format mp3 Durée : 41 mn

We propose the concept of Local Continuity that is somewhat related to directional continuity. DEFINITION: Let X and Y be, say, metric spaces. A function f from X to Y is locally continuous at point x in X if one can find an open set U(x) such that (i) x belongs to the closure of U(x), (ii) if x(n) converges to x in U(x) then f(x(n)) converges to f(x) in Y. The set U(x), the local continuity set of f at x, that tells the direction of continuity. If U(x) can be chosen to contain x then f is continuous at x. The concept was conceived during our study [Bender, C., Sottinen, T., and Valkeila, E. (2007): Pricing by hedging and no-arbitrage beyond semimartingales (under revision for Finance and Stochastics)] where we considered non-semimartingale pricing models that have non-trivial quadratic variation and a certain "small-ball property". It turned out that in these models one cannot do arbitrage with strategies that are continuous in terms of the spot and some other economic factors such as the running minimum and maximum of the stock. Unfortunately, this result does not extend to even simple strategies, when stopping times are involved. The reason is obvious: Stopping times are typically not continuous. However, local continuity turns out to be just what we need to prove our theorems, and the author is not aware of any reasonable stopping times that are not locally continuous. The talk is based on an ongoing joint work with C. Bender (Technical University of Braunschweig), D. Gasbarra (University of Helsinki), and E. Valkeila (Helsinki University of Technology). Tommi SOTTINEN. Reykjavik University. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1207750775297 (pdf) Ecouter l'intervention : Bande son disponible au format mp3 Durée : 49 mn

A popular Bayesian nonparametric approach to survival analysis consists in modeling hazard rates as kernel mixtures driven by a completely random measure. A comprehensive analysis of the asymptotic behaviour of such models is provided. Consistency of the posterior distribution is investigated and central limit theorems for both linear and quadratic functionals of the posterior hazard rate are derived. The general results are then specialized to various specific kernels and mixing measures, thus yielding consistency under minimal conditions and neat central limit theorems for the distribution of functionals. Joint work with P. De Blasi and G. Peccati. Igor PRUNSTER. University of Turin. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1207750819712 (pdf) Ecouter l'intervention : Bande son disponible au format mp3 Durée : 46 mn

We establish an invariance principle where the limit process is a multifractional Gaussian process with a multifractional function which takes its values in (1/2, 1). Some properties, such as regularity and local self-similarity, of this process are studied. Moreover the limit process is compared to the multifractional Brownian motion. Renaud MARTY. Université Nancy1. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1207750851448 (pdf) Ecouter l'intervention : Bande son disponible au format mp3 Durée : 32 mn

Consider the stochastic wave equation in dimension , , where denotes the formal derivative of a Gaussian stationary random field, white in time and correlated in space. Using Malliavin calculus, with Quer-Sardanyons we proved the existence and regularity of density of the law of the solution to the SPDE for any fixed . Denote this density by . More recently, with R. Dalang, we have established joint Hölder continuity in of the sample paths of the solution . On the basis of these two results, we can go further with the study of the properties in of the function , for any fixed . Using a method developed by Watanabe and applied to SPDEs in papers by Morien and Millet and Morien, we prove joint Hölder continuity of of the same order than the sample paths of the solution. We shall explain why the strong degeneracy of the fundamental solution leads to less regularity than one could have expected. Marta SANZ-SOLE. Universitat de Barcelona. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1182789806745 (pdf) Bande son disponible au format mp3 Durée : 55 mn

We want to present some results on gradient systems with convex potential in finite and infinite dimension. The techniques are based on recent developments in the theory of gradient flows in the Wasserstein metric. (joint work with L. Ambrosio & G. Savaré). Lorenzo ZAMBOTTI. Université Paris 6. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1182789954236 (pdf) Bande son disponible au format mp3 Durée : 43 mn

As a model for multiscale systems under random influences on physical boundary, a stochastic partial differential equation under a fast random dynamical boundary condition is investigated. An effective equation is derived and justified by reducing the random dynamical boundary condition to a usual random boundary condition. The effective system is still a stochastic partial differential equation, but is more tractable. Furthermore, the quantitative comparison between the solution of the original stochastic system and the effective solution is provided by estimating deviations. Jinqiao DUAN. Illinois Institute of Technology. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1182790011791 (pdf) Bande son disponible au format mp3 Durée : 42 mn

In this talk we consider the stochastic heat equation in , with vanishing initial conditions, driven by a Gaussian noise which is fractional in time, with Hurst index , and colored in space, with spatial covariance given by a function . Our main result gives the necessary and sufficient condition on for the existence of the process solution. When is the Riesz kernel of order this condition is , which is a relaxation of the condition encountered when the noise is white in space. When is the Bessel kernel or the heat kernel, the condition remains . This a joint work with C. Tudor. Raluca BALAN. University of Ottawa. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1182790115349 (pdf) Bande son disponible au format mp3 Durée : 28 mn

This talk does not suppose a priori that the evolution of a financial asset price is a semimartingale. The stochastic integral intervening in the definition of self-financing property is forward integral. If one requires that a certain minimal class of investor strategies are self-financing, previous prices are forced to be finite quadratic variation processes. The non-arbitrage property is not excluded if the class of admissible strategies is restricted. The classical notion of martingale is replaced with the notion of -martingale. Two instruments are developed: a calculus related to -martingales and infinite dimensional integration via regularization, with some examples. Some applications to no-arbitrage, viability, hedging and the maximization of the utility of an insider are expanded. The talk is essentially based on a joint work with Rosanna Coviello. Francesco RUSSO. Université Paris 13. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1182789707066 (pdf) Bande son disponible au format mp3 Durée : 55 mn

In this talk, we will describe some recent results concerning stochastic differential equations driven by a multidimensional fractional Brownian motion with Hurst parameter 1/3

In this work, we consider the Korteweg- de Vries equation perturbed by a random force of white noise type, additive or multiplicative. In a series of work, in collaboration with Y. Tsutsumi, we have studied existence and uniqueness in the additive case for very irregular noises. These use the functional framework introduced by J. Bourgain. We use similar tools to prove existence and uniqueness for a multiplicative noise. We are not able to consider irregular noises and have to assume that the driving Wiener process has paths in or . However, contrary to the additive case, we are able to treat spatially homogeneous noises. Then, we try to understand the effect of a small noise with amplitude on the propagation of a soliton. We prove that, on a time scale proportional to , a solution initially equal to the soliton but perturbed by a noise of the type above remains close to a soliton with modulated speed and position. The modulated speed and position are semi-martingales and we write the stochastic equations they satisfy. We prove also that a Central Limit Theorem holds so that, on the time scale described above, the solutions can formally be written as the sum of the modulated soliton and a gaussian remainder term of order . In the multiplicative case, we can go further. We prove that the gaussian part converges in distribution to a stationary process. Also, the equations for the modulation parameters allow to give a justification for the phenomenon called "soliton diffusion" observed in numerical simulations: the averaged soliton decays like . We obtain . This a joint work with A. de Bouard. Arnaud DEBUSSCHE. ENS Cachan. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1182789894119 (pdf) Bande son disponible au format mp3 Durée : 45 mn

We study from a mathematical point of view a model equation for Bose Einstein condensation, in the case where the trapping potential varies randomly in time. The model is a nonlinear Schrödinger equation, with a quadratic potential with white noise fluctuations in time. We prove the existence of strong solutions in 1D and 2D in the energy space. The blow-up phenomenon will also be discussed under critical and super critical nonlinear interactions in the attractive case. This is a joint work with Reika Fukuizumi. Anne de BOUARD. Université Paris 11. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1182789924489 (pdf) Bande son disponible au format mp3 Durée : 49 mn

We prove that an averaging principle holds for a general class of stochastic reaction-diffusion systems, having unbounded multiplicative noise, in any space dimension. We show that the classical Khasminskii approach for systems with a finite number of degrees of freedom can be extended to infinite dimensional systems. Sandra CERRAI. Universita di Firenze. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1182789980424 (pdf) Bande son disponible au format mp3 Durée : 47 mn

Some recently obtained results on (fBm)- driven linear and semilinear stochastic equations in infinite dimensional state spaces are reviewed. Regularity of the fractional Ornstein-Uhlenbeck process is studied and some results on large time behaviour are given (existence and ergodicity of stationary solutions, random fixed points) in the linear and semilinear case. The absolute continuity of measures induced by solutions is also studied. Bohdan MASLOWSKI. Academy of sciences of the Czech Republic. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1182790040320 (pdf) Bande son disponible au format mp3 Durée : 45 mn