The cost of usage in the λ-calculus

Abstract-A new "inductive" approach to standardization for the λ-calculus has been recently introduced by Xi, allowing him to establish a double-exponential upper bound |M | 2 |σ| for the length of the standard reduction relative to an arbitrary reduction σ originated in M . In this paper we refine Xi's analysis, obtaining much better bounds, especially for computations producing small normal forms. For instance, for terms reducing to a boolean, we are able to prove that the length of the standard reduction is at most a mere factorial of the length of the shortest reduction sequence. The methodological innovation of our approach is that instead to try to count the cost for producing something, as customary, we count the cost of consuming things. The key observation is that the part of a λ-term that is needed to produce the normal form (or an arbitrary rigid prefix) may rapidly augment along a computation, but can only decrease very slowly (actually, linearly)

Texture and multifractals : new tools for image analysis

We present some new ideas for image analysis and texture segmentation. The two important points are the introduction of the multifractal theory for image understanding in a rigorous manner, which allows to do all the computations directly on the discrete signal, and the definition of a precise framework for texture analysis, in which we do not choose any a priori model for the study but instead let the peculiar data in each case decide which model is the most appropriate. We define an approach general enough as to handle a great variety of textures and we propose a new scheme, based on learning and optimal cooperation, that gives good results on a lot of segmentation experiments presented here

Contribution of image analysis to the description of enzymatic degradation kinetics for particulate food material

International audienceThe objective of the present work was to relate the physical evolution quantified by image analysis to the chemical transformation of beet pulp particles during enzymatic degradation. Beet pulps were degraded into a torus reactor equipped for visualisation. Pectinolytic and cellulolytic enzymes were used separately or in combination. Two global image analysis techniques were tested to characterise the size distribution of overlapping particles. Granulometric curves were extracted by mathematical morphology and a regularisation dimension was assessed by fractal analysis. Both techniques proved efficient to follow particle size evolution during degradation. When using cellulolytic enzymes alone, no chemical or physical evolution was observed. When using pectinolytic enzymes, a chemical modification occurred without any physical evolution. Particles physically disappeared when both enzymes were used. The chemical and physical evolutions of particles during degradation were interpreted taking into account the current model of molecular arrangement of primary cell walls

Extensional and Intensional Strategies

This paper is a contribution to the theoretical foundations of strategies. We first present a general definition of abstract strategies which is extensional in the sense that a strategy is defined explicitly as a set of derivations of an abstract reduction system. We then move to a more intensional definition supporting the abstract view but more operational in the sense that it describes a means for determining such a set. We characterize the class of extensional strategies that can be defined intensionally. We also give some hints towards a logical characterization of intensional strategies and propose a few challenging perspectives

Filière « Histoire sociale et démographique »

Stéphane Baciocchi et Pascal Cristofoli, ingénieur d’étudesJean Daniel Gronoff, ingénieur de rechercheArnaud Bringé et Bénédicte Garnier, ingénieurs à l’INED Atelier « Analyse des données relationnelles »1. Introduction à l’analyse des données relationnelles En lien avec des équipes et des projets de recherches actifs, encadré par des ingénieurs méthodes en sciences humaines et sociales, l’atelier a pour l’essentiel repris et suivi la trame pédagogique mise en place et expérimentée l’année de..