Central limit theorem for multiplicative class functions on the symmetric group

Hambly, Keevash, O'Connell and Stark have proven a central limit theorem for the characteristic polynomial of a permutation matrix with respect to the uniform measure on the symmetric group. We generalize this result in several ways. We prove here a central limit theorem for multiplicative class functions on symmetric group with respect to the Ewens measure and compute the covariance of the real and the imaginary part in the limit. We also estimate the rate of convergence with the Wasserstein distance.Comment: 23 pages; the mathematics is the same as in the previous version, but there are several improvments in the presentation, including a more intuitve name for the considered function

Bioinformatics and statistical contributions to the identification of inhibitors for the MET receptor

L’effet des polysaccharides sur l’interaction HGF-MET est étudié à l’aide d’un plan d’expérience comportant plusieurs puces à protéines sous différentes conditions d’expérimentation. Le but de l’analyse est la sélection des meilleurs polysaccharides inhibiteurs de l’interaction HGF-MET. D’un point de vue statistique c’est un problème de classification. Le traitement informatique et statistique des biopuces obtenues nécessite la mise en place de la plateforme PASE avec des plug-ins d’analyse statistique pour ce type de données. La principale caractéristique statistique de ces données est le caractère de répétition : l’expérience est répétée sur 5 puces et les polysaccharides, au sein d’une même puce, sont répliqués 3 fois. On n’est donc plus dans le cas classique des données indépendantes globalement, mais de celui d’une indépendance seulement au niveau intersujets et intrasujet. Nous proposons les modèles mixtes pour la normalisation des données et la représentation des sujets par la fonction de répartition empirique. L’utilisation de la statistique de Kolmogorov-Smirnov apparaît naturelle dans ce contexte et nous étudions son comportement dans les algorithmes de classification de type nuées dynamique et hiérarchique. Le choix du nombre de classes ainsi que du nombre de répétitions nécessaires pour une classification robuste sont traités en détail. L’efficacité de cette méthodologie est mesurée sur des simulations et appliquée aux données HGF-MET. Les résultats obtenus ont aidé au choix des meilleurs polysaccharides dans les essais effectués par les biologistes et les chimistes de l’Institut de Biologie de Lille. Certains de ces résultats ont aussi conforté l’intuition des ces chercheurs. Les scripts R implémentant cette méthodologie sont intégrés à la plateforme PASE. L’utilisation de l’analyse des données fonctionnelles sur ce type de données fait partie des perspectives immédiates de ce travail.The effect of polysaccharides on HGF-MET interaction was studied using an experimental design with several microarrays under different experimental conditions. The purpose of the analysis is the selection of the best polysaccharides, inhibitors of HGF-MET interaction. From a statistical point of view this is a classification problem. Statistical and computer processing of the obtained microarrays requires the implementation of the PASE platform with statistical analysis plug-ins for this type of data. The main feature of these statistical data is the repeated measurements: the experiment was repeated on 5 microarrays and all studied polysaccharides are replicated 3 times on each microarray. We are no longer in the classical case of globally independent data, we only have independence at inter-subjects and intra-subject levels. We propose mixed models for data normalization and representation of subjects by the empirical cumulative distribution function. The use of the Kolmogorov-Smirnov statistic appears natural in this context and we study its behavior in the classification algorithms like hierarchical classification and k-means. The choice of the number of clusters and the number of repetitions needed for a robust classification are discussed in detail. The robustness of this methodology is measured by simulations and applied to HGF-MET data. The results helped the biologists and chemists from the Institute of Biology of Lille to choose the best polysaccharides in tests conducted by them. Some of these results also confirmed the intuition of the researchers. The R scripts implementing this methodology are integrated into the platform PASE. The use of functional data analysis on such data is part of the immediate future work

Advanced Strategies for Monitoring Water Consumption Patterns in Households Based on IoT and Machine Learning

Water resource management represents a fundamental aspect of a modern society. Urban areas present multiple challenges requiring complex solutions, which include multidomain approaches related to the integration of advanced technologies. Water consumption monitoring applications play a significant role in increasing awareness, while machine learning has been proven for the design of intelligent solutions in this field. This paper presents an approach for monitoring and predicting water consumption from the most important water outlets in a household based on a proposed IoT solution. Data processing pipelines were defined, including K-means clustering and evaluation metrics, extracting consumption events, and training classification methods for predicting consumption sources. Continuous water consumption monitoring offers multiple benefits toward improving decision support by combining modern processing techniques, algorithms, and methods

PASE: a web-based platform for peptide / protein microarray experiments

International audienc

Autoimmune diseases and vitamin D receptor Apa-I polymorphism are associated with vitiligo in a small inbred Romanian community

Vitiligo has been associated with the host's genetic profile, metabolic abnormality and immunostatus. The purpose of this study was to investigate the association of vitiligo with autoimmune diseases for 31 out of 39 subjects with vitiligo and their first-degree relatives living in a small Caucasian inbred rural community. They were compared with healthy individuals. A 2.28% prevalence of vitiligo was calculated and the presence of consanguine marriages (72.3%) was noted for this community. Our results indicate an increased prevalence of thyroidopathies, diabetes mellitus and rheumatoid arthritis in families with vitiligo. We also show that the Apa-I polymorphism of the vitamin D receptor gene is associated with vitiligo. This is the first study of its kind performed in Romania suggesting that the vitamin D receptor gene might play a role in the aetiopathogenesis of skin depigmentatio