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La main de l’artisan : bâtisseurs et architectes dans l’entourage de Rabelais (années 1520)
No full textInternational audienc
Théorème ergodique pour les chaînes de Markov branchantes indexées par des arbres avec des formes arbitraires
No full textInternational audienceWe prove an ergodic theorem for Markov chains indexed by the Ulam-Harris-Neveu tree over large subsets with arbitrary shape under two assumptions: with high probability, two vertices in the large subset are far from each other and have their common ancestor close to the root. The assumption on the common ancestor can be replaced by some regularity assumption on the Markov transition kernel. We verify that those assumptions are satisfied for some usual trees. Finally, with Markov-Chain Monte-Carlo considerations in mind, we prove when the underlying Markov chain is stationary and reversible that the Markov chain, that is the line graph, yields minimal variance for the empirical average estimator among trees with a given number of nodes.Nous démontrons un théorème ergodique pour des chaînes de Markov indexées par l'arbre d'Ulam-Harris-Neveu sur des grands sous-ensembles de forme arbitraire, sous deux hypothèses : avec grande probabilité, deux sommets du grand sous-ensemble sont éloignés l’un de l’autre et ont leur ancêtre commun proche de la racine. L’hypothèse sur l’ancêtre commun peut être remplacée par une hypothèse de régularité sur le noyau de transition de la chaîne de Markov. Nous vérifions que ces hypothèses sont satisfaites pour certains arbres usuels. Enfin, motivés par des considérations liées aux méthodes de Monte-Carlo par chaînes de Markov, nous prouvons que lorsque la chaîne de Markov sous-jacente est stationnaire et réversible, cette chaîne de Markov, autrement dit le graphe ligne, minimise la variance de l’estimateur de la moyenne empirique parmi les arbres ayant un nombre donné de nœuds
-Griffiths polynomials: Bispectrality and biorthogonality
No full textInternational audienceWe introduce a generalization of bivariate Griffiths polynomials depending onan additional parameter . These -Griffiths polynomials arebivariate, bispectral and biorthogonal. For two specific values of theparameter , they become orthogonal. One of the value is related to theusual bivariate Griffiths polynomials, while the second value produces neworthogonal bivariate polynomials
Statistical learning methods applied to stratigraphic and pottery data: An aid to establishing archaeological periodisation
No full textInternational audienceChronology, and hence periodisation of archaeological sites according to the major transformations that affect them, is an essential prerequisite for any historical discourse. The main sources that can be used to establish this periodisation, the temporality of archaeological sites, are (i) stratigraphy, which corresponds to the succession of anthropic levels at the origin of the construction of a relative chronology, and (ii) archaeological material, and more specifically pottery that is omnipresent in excavations, with a typology that evolves rapidly over time; these two factors make pottery a highly valuable chronological source. This work presents an original interdisciplinary approach in which archaeology and statistics work together to produce a periodisation using pottery and stratigraphy. We apply this approach to data collected in the mythic city of Angkor Thom (Cambodia), capital of the Khmer Empire between the 9th and 15th centuries. The first step in the process is to construct stable, interpretable pottery facies using a compromise-based clustering approach. In the second step, the predictions provided by supervised classification models make it possible to integrate less reliable pottery assemblages that are essential to the overall construction of the chronological model of the Angkor Thom city. Our approach offers the advantage of automatically processing large volumes of data and integrating uncertainty into the forecasts obtained for the least chronologically reliable sets
Projet de préparation du dataset du projet Charles de Gaulle
No full textProjet collectif visant à explorer et comparer les capacités des modèles de langage à traiter, analyser et restituer des contenus en lien avec Charles de Gaulle. Ce travail s’inscrit dans le cadre du cours Outils de traitement de corpus et a pour enjeu central la constitution d’un corpus de référence de qualité, suffisamment riche, diversifié et structuré pour permettre des analyses thématiques, statistiques, ou des expérimentations sur différents types de modèles linguistiques. Notre groupe, le Groupe Données, s’est ainsi attaché à toutes les étapes de la chaîne de vie du corpus : la collecte des sources, la structuration et la normalisation des données, le nettoyage approfondi, la segmentation intelligente, l’analyse statistique, ainsi que l’enrichissement par des outils d’annotation ou de visualisation. Ce rapport expose en détail notre démarche, les outils utilisés, nos choix méthodologiques, ainsi que les résultats intermédiaires et finaux obtenus tout au long de cette chaîne de traitement
Erratum: The Filippov characteristic flow for the aggregation equation with mildly singular potentials
No full textIn this short erratum, we provide a corrected version and a corrected proof of the existence and uniqueness result of a weak measure-valued solutions to the so-called aggregation equation
Exponential equidistribution of periodic points for endomorphisms of
No full textLet be a holomorphic endomorphism of of algebraic degree . We show that the periodic points of of period equidistribute towards the equilibrium measure of exponentially fast as tends to infinity. This quantifies a theorem of Lyubich for and of Briend-Duval for . A byproduct of our proof is the existence of a large number of periodic cycles in the small Julia set with large multipliers
Growth rate-driven modelling reveals how phenotypic adaptation drives drug resistance in BRAFV600E-mutant melanoma
No full textPhenotypic adaptation, the ability of cells to change phenotype in response to external pressures, has been identified as a driver of drug resistance in cancer. To quantify phenotypic adaptation in BRAFV600E-mutant melanoma, we develop a theoretical model that emerges from data analysis of WM239A-BRAFV600E cell growth rates in response to drug challenge with the BRAF-inhibitor encorafenib. Our model constitutes a cell population model in which each cell is individually described by one of multiple discrete and plastic phenotype states that are directly linked to drug-dependent net growth rates and, by extension, drug resistance. Data-matched simulations reveal that phenotypic adaptation in the cells is directed towards states of high net growth rates, which enables evasion of drug-effects. The model subsequently provides an explanation for when and why intermittent treatments outperform continuous treatments in vitro, and demonstrates the benefits of not only targeting, but also leveraging, phenotypic adaptation in treatment protocols
