Optimal rates of convergence for persistence diagrams in Topological Data Analysis

Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a statistical approach. We show that the use of persistent homology can be naturally considered in general statistical frameworks and persistence diagrams can be used as statistics with interesting convergence properties. Some numerical experiments are performed in various contexts to illustrate our results

Properties of Design-Based Functional Principal Components Analysis

This work aims at performing Functional Principal Components Analysis (FPCA) with Horvitz-Thompson estimators when the observations are curves collected with survey sampling techniques. One important motivation for this study is that FPCA is a dimension reduction tool which is the first step to develop model assisted approaches that can take auxiliary information into account. FPCA relies on the estimation of the eigenelements of the covariance operator which can be seen as nonlinear functionals. Adapting to our functional context the linearization technique based on the influence function developed by Deville (1999), we prove that these estimators are asymptotically design unbiased and consistent. Under mild assumptions, asymptotic variances are derived for the FPCA' estimators and consistent estimators of them are proposed. Our approach is illustrated with a simulation study and we check the good properties of the proposed estimators of the eigenelements as well as their variance estimators obtained with the linearization approach.Comment: Revised version for J. of Statistical Planning and Inference (January 2009

Convergence Rates for Persistence Diagram Estimation in Topological Data Analysis

International audienceComputational topology has recently seen an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a statistical approach. We show that the use of persistent homology can be naturally considered in general statistical frameworks and that persistence diagrams can be used as statistics with interesting convergence properties. Some numerical experiments are performed in various contexts to illustrate our results

Effets de l'accompagnement d'un projet personnel sur l'estime de soi de stagiaires d'un centre de formation de football

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Optimal rates of convergence for persistence diagrams in Topological Data Analysis

Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a statistical approach. We show that the use of persistent homology can be naturally considered in general statistical frameworks and persistence diagrams can be used as statistics with interesting convergence properties. Some numerical experiments are performed in various contexts to illustrate our results

The evolution of mammal tooth patterns: new insights from a developmental prediction model.

14 pages.International audienceThe study of mammalian evolution is often based on insights into the evolution of teeth. Developmental studies may attempt to address the mechanisms that guide evolutionary changes. One example is the new developmental model proposed by Kavanagh et al. (2007), which provides a high-level testable model to predict mammalian tooth evolution. It is constructed on an inhibitory cascade model based on a dynamic balance of activators and inhibitors, regulating differences in molar size along the lower dental row. Nevertheless, molar sizes in some mammals differ from this inhibitory cascade model, in particular in voles. The aim of this study is to point out arvicoline and murine differences within this model and to suggest an alternative model. Here we demonstrate that the inhibitory cascade is not followed, due to the arvicoline's greatly elongated first lower molar. We broaden the scope of the macroevolutionary model by projecting a time scale on to the developmental model. We demonstrate that arvicoline evolution is rather characterized by a large gap from the oldest vole to more recent genera, with the rapid acquisition of a large first lower molar contemporaneous to their radiation. Our study provides alternative evolutionary hypotheses for mammals with different trajectories of development

Supplementary Table 1

Observed contact incidences between apical plate pairs in echinoids along with topological index values. Abbreviations: OUT, outgroup representing the regular pattern; BI, basal Irregularia; BA, basal Atlostomata; H, Holasteroida; S, Spatangoida. EJ, Early Jurassic (Liassic); MJ, Middle Jurassic; LJ, Late Jurassic; EC, Early Cretaceous; LC, Late Cretaceous; PN, Paleogene and Neogene; P, Present day. OI to OV, ocular plates 1 to 5; G1 to G5, genital plates 1 to 5. Apical systems of reference specimens are from the literature and from specimens observed in collections. Collection specimens are from private collections: Clavel, Courville, Fournier, Vadet, and Votat. Collection specimens from academic collections are from: University of Burgundy, Dijon, France (UB), National History Museum, London, UK (NHM), Museum of Comparative Zoology, Harvard University, Mass. (MCZ), Museu de Geologia, Barcelona, Spain (MGB), Muséum National d'Histoire Naturelle, Paris, France (MNHN), University of California Museum of Paleontology, Berkeley (UCMP), Saint-Petersburg State University, Russia (SPU), University of Toulouse, France (UT), National Museum of Natural History, Smithsonian Institution, Washington, D.C. (USNM), Institute of Paleobiology of Polish Academy of Sciences in Warsaw, Poland (PAS), Sedgwick Museum of Earth Sciences, University of Cambridge, UK (SM), Museum of Lyon, France (ML), Paleontological Institute of the Russian Academy of Sciences, Moscow, Russia (RAS), Département de Géologie de la Faculté des Sciences d’Agadir, Morocco (MAS), Museum of Grenoble, France (MG)

Using a Multi-Locus Microsatellite Typing method improved phylogenetic distribution of Candida albicans isolates but failed to demonstrate association of some genotype with the commensal or clinical origin of the isolates.

EA MERS CT3 Enjeu 3International audienceThe dimorphic yeast Candida albicans is a component of the normal microflora at the mucosal surfaces of healthy individuals. It possesses an array of phenotypic properties considered as virulence traits that contribute to pathogenicity of the yeast in immuno-compromised patients. We addressed the question of the pathogenicity of lineages of C. albicans with regard to their genotype in three series of C. albicans isolates (a series of commensal isolates collected in healthy individuals, a group of bloodstream isolates and a group of non-bloodstream clinical isolates) using a Multi-Locus Microsatellite Typing (MLMT) approach based on the analysis of the polymorphism of 11 microsatellite loci. The MLMT analysis of the three series, corresponding to 174 C. albicans isolates, gave a 100% typability to the method, with a DP index of 0.999. The UPGMA analysis showed that the isolates segregated in eight phylogenetic groups. Interestingly, the clustering was comparable when using NJ and MS-tree algorithms and a good concordance index of the clustering was observed with MLST. All in all our data strongly indicated MLMT as a reliable tool for DNA-typing studies in C. albicans. Isolates from healthy and non-healthy individuals segregated at the same proportions into the eight phylogenetic groups, suggesting that isolates of different origin share the same overall pathogenicity. Surprisingly allelic frequencies at the HIS3 microsatellite differed significantly in commensal isolates (group A) from pooled groups B and C (clinical isolates), raising the possibility that some individual alleles at the HIS3 microsatellite may be associated with distinct pathogenic profiles in C. albicans

Computer-assisted orientation and drawing of archaeological pottery.

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