Les intuitions logiques d’Edgar Morin

Les mathématiques telles qu’elles se sont développées entre 1935 et 1970 jouent un rôle très important dans La Méthode. Ce rôle est explicite en ce qui concerne la logique, plus implicite en ce qui concerne la théorie du contrôle, l’incertitude, et certaines notions vues hors du champ mathématique et particulièrement probabiliste (entropie, information, incertitude). Sur un exemple de résultats récents de la logique mathématique, la correspondance de Curry-Howard et les travaux de Jean-Louis Krivine nous montrent la pertinence des idées et des intuitions d’Edgar Morin concernant la logique, la réalité et le cerveau

Non-stationary extreme models and a climatic application

In this paper, we study extreme values of non-stationary climatic phenomena. In the usually considered stationary case, the modelling of extremes is only based on the behaviour of the tails of the distribution of the remainder of the data set. In the non-stationary case though, it seems reasonable to assume that the temporal dynamics of the entire data set and that of extremes are closely related and thus all the available information about this link should be used in statistical studies of these events. We try to study how centered and normalized data which are closer to stationary data than the observation allows easier statistical analysis and to understand if we are very far from a hypothesis stating that the extreme events of centered and normed data follow a stationary distribution. The location and scale parameters used for this transformation (the central field), as well as extreme parameters obtained for the transformed data enable us to retrieve the trends in extreme events of the initial data set. Through non-parametric statistical methods, we thus compare a model directly built on the extreme events and a model reconstructed from estimations of the trends of the location and scale parameters of the entire data set and stationary extremes obtained from the centered and normed data set. In case of a correct reconstruction, we can clearly state that variations of the characteristics of extremes are well explained by the central field. Through these analyses we bring arguments to choose constant shape parameters of extreme distributions. We show that for the frequency of the moments of high threshold excesses (or for the mean of annual extremes), the general dynamics explains a large part of the trends on frequency of extreme events. The conclusion is less obvious for the amplitudes of threshold exceedances (or the variance of annual extremes) – especially for cold temperatures, partly justified by the statistical tools used, which require further analyses on the variability definition

Is there a trend in extremely high river temperature for the next decades? A case study for France

International audienceAfter 2003's summer heat wave, Electricité de France created a global plan called "heat wave-dryness". In this context, the present study tries to estimate high river temperatures for the next decades, taking into account climatic and anthropogenic evolutions. To do it, a specific methodology based on Extreme Value Theory (EVT) is applied. In particular, a trend analysis of water temperature data is done and included in EVT used. The studied river temperatures consist of mean daily temperatures for 27 years measured near the French power plants (between 1977 and 2003), with four series for the Rhône river, four for the Loire river and a few for other rivers. There are also three series of mean daily temperatures computed by a numerical model. For each series, we have applied statistical extreme value modelling. Because of thermal inertia, the Generalized Extreme Value (GEV) distribution is corrected by the medium cluster length, which represents thermal inertia of water during extremely hot events. The µ and s parameters of the GEV distributions are taken as polynomial or continuous piecewise linear functions of time. The best functions for µ and s parameters are chosen using Akaike criterion based on likelihood and some physical checking. For all series, the trend is positive for µ and not significant for s, over the last 27 years. However, we cannot assign this evolution only to the climatic change for the Rhône river because the river temperature is the resultant of several causes: hydraulic or atmospheric, natural or related to the human activity. For the other rivers, the trend for µ could be assigned to the climatic change more clearly. Furthermore, the sample is too short to provide reliable return levels estimations for return periods exceeding thirty years. Still, quantitative return levels could be compared with physical models for example

Estimation of a diffusion model with trends taking in account the extremes. Application to temperature in France

We built a model of the daily temperature based on a diffusion process and address to extreme values not taken into account in the literature on this kind of models. We first study, using non parametric tools, the trends on mean and variance. In a second step we estimate a stationary model first non parametrically and then using likelihood methods. Extreme values are taken into account in the estimation of model and to obtain a definitive estimation we use in a specific framework extreme theory for diffusions. A test of suitable model by simulation is done