Fouille de texte : une approche séquentielle pour découvrir des relations spatiales

National audienceDans cet article, nous présentons les premières étapes d'un projet de fouille de données textuelles. Plus précisément, nous appliquons un algorithme d'extraction de motifs séquentiels sous contraintes multiples afin d'identifier des relations entre entités spatiales. Les premiers résultats obtenus montrent l'intérêt de l'utilisation de cette approche et ses limites. Dans cet article, nous détaillons les premières bases de travaux plus ambitieux dont l'objectif est d'apporter des informations cruciales permettant de compléter l'analyse des images satellitaires

Towards the Automatic Processing of Language Registers: Semi-supervisedly Built Corpus and Classifier for French

International audienceLanguage registers are a strongly perceptible characteristic of texts and speeches. However, they are still poorly studied in natural language processing. In this paper, we present a semi-supervised approach which jointly builds a corpus of texts labeled in registers and an associated classifier. This approach relies on a small initial seed of expert data. After massively retrieving web pages, it iteratively alternates the training of an intermediate classifier and the annotation of new texts to augment the labeled corpus. The approach is applied to the casual, neutral, and formal registers, leading to a 750M word corpus and a final neural classifier with an acceptable performance

Towards the Automatic Processing of Language Registers: Semi-supervisedly Built Corpus and Classifier for French

International audienceLanguage registers are a strongly perceptible characteristic of texts and speeches. However, they are still poorly studied in natural language processing. In this paper, we present a semi-supervised approach which jointly builds a corpus of texts labeled in registers and an associated classifier. This approach relies on a small initial seed of expert data. After massively retrieving web pages, it iteratively alternates the training of an intermediate classifier and the annotation of new texts to augment the labeled corpus. The approach is applied to the casual, neutral, and formal registers, leading to a 750M word corpus and a final neural classifier with an acceptable performance

: École d’été 2021 - Contraintes de courbures et espaces métriques

I will present a joint work with G. Carron and I. Mondello where we study Kato limit spaces. These are metric measure spaces obtained as Gromov-Hausdorff limits of smooth n-dimensional Riemannian manifolds with Ricci curvature satisfying a uniform Kato-type condition. In this context, strictly wider than the ones of Ricci limit spaces (where the Ricci curvature satisfies a uniform lower bound) and Lp-Ricci limit spaces (where the Ricci curvature is uniformly bounded in Lp for some p>n/2), we extend classical results of Cheeger, Colding and Naber, like the fact that under a non-collapsing assumption, every tangent cone is a metric measure cone. I will present these results and explain how we rely upon a new heat-kernel based almost monotone quantity to derive them

: École d’été 2021 - Contraintes de courbures et espaces métriques

I will present recent work with Kleiner in which we verify two topological conjectures using Ricci flow. First, we classify the homotopy type of every 3-dimensional spherical space form. This proves the Generalized Smale Conjecture and gives an alternative proof of the Smale Conjecture, which was originally due to Hatcher. Second, we show that the space of metrics with positive scalar curvature on every 3-manifold is either contractible or empty. This completes work initiated by Marques.At the heart of our proof is a new uniqueness and stability theorem for singular Ricci flows. Singular Ricci flows can be seen as an improvement of Ricci flows with surgery, which were used in Perelman’s proof of the Poincaré and Geometrization Conjectures. The latter flows had the drawback that they were not uniquely determined by their initial data, as their construction depended on various auxiliary surgery parameters. Perelman conjectured that there must be a canonical, weak Ricci flow that automatically "flows through its singularities” at an infinitesimal scale. Our work on the uniqueness of singular Ricci flows gives an affirmative answer to Perelman's conjecture and allows the study of continuous families of singular Ricci flows, leading to the topological applications mentioned above.The lectures will roughly be structured as follows:(1) Preliminaries of Ricci flow, Blow-up analysis of singularities, Statement of the main results(2) Local stability Analysis(3) Comparing singular Ricci flows, Proof of the uniqueness and stability result(4) Continuous families of singular Ricci flows, Proof of the topological theorems

: École d’été 2021 - Contraintes de courbures et espaces métriques

I will discuss the notion of minimal volume and some of its variants. The minimal volume of a manifold is defined as the infimum of the volume over all metrics with sectional curvature between -1 and 1. Such an invariant is closely related to "collapsing theory", a far reaching set of results developed by Cheeger, Gromov, Fukaya and others to describe bounded sectional curvature metrics. Most of my talks will be focused on presenting the main aspects of this theory: thick-thin decomposition, F-structures and N-structures, collapsing constructions... Relations of the minimal volume to topological invariants will be explained, and some open questions will be mentioned

: École d’été 2021 - Contraintes de courbures et espaces métriques

We study the noncollapsed singularity formation of Einstein 4-manifolds. We prove that any smooth Einstein 4-manifold close to a singular one in a mere Gromov-Hausdorff (GH) sense is the result of a gluing-perturbation procedure that we develop. This sheds light on the structure of the moduli space of Einstein 4-manifolds near its boundary and lets us show that spherical and hyperbolic orbifolds (which are synthetic Einstein spaces) cannot be GH-approximated by smooth Einstein metrics. New obstructions specific to the compact situation moreover raise the question of whether or not a sequence of Einstein 4-manifolds degenerating while bubbling out gravitational instantons has to be Kähler-Einstein

: École d’été 2021 - Contraintes de courbures et espaces métriques

We will present some of the tools used by the more advanced lectures. The topics discussed will include : Gromov Hausdorff distance, comparison theorems for sectional and Ricci curvature, the Bochner formula and basics of Ricci flow

: École d’été 2021 - Contraintes de courbures et espaces métriques

We find a family of 3d steady gradient Ricci solitons that are flying wings. This verifies a conjecture by Hamilton. For a 3d flying wing, we show that the scalar curvature does not vanish at infinity. The 3d flying wings are collapsed. For dimension n ≥ 4, we find a family of Z2 × O(n − 1)-symmetric but non-rotationally symmetric n-dimensional steady gradient solitons with positive curvature operator. We show that these solitons are non-collapsed

Régularité et stabilité des frontières sous les bornes inférieures de Ricci: Contraintes de courbures et espaces métriques

Summer school 2021. The theory of non smooth spaces with lower Ricci Curvature bounds has undergone huge developments in the last thirty years. On the one hand the impetus came from Gromov’s precompactness theorem and the Cheeger-Colding theory of Ricci limit spaces. On the other hand “synthetic” theories of lower Ricci bounds have been developed, based on semigroup tools (the Bakry-Émery theory) and on Optimal Transport (the Lott-Sturm-Villani theory).The Cheeger-Colding theory did not consider manifolds with boundary, while in the synthetic framework even understanding what is a good definition of boundary is a challenge.The aim of this talk is to present some recent results obtained in collaboration with E. Bruè (IAS, Princeton) and A. Naber (Northwestern University) about regularity and stability for boundaries of spaces with lower Ricci Curvature bounds