Statistics for the Luria-Delbr\"uck distribution

The Luria-Delbr\"uck distribution is a classical model of mutations in cell kinetics. It is obtained as a limit when the probability of mutation tends to zero and the number of divisions to infinity. It can be interpreted as a compound Poisson distribution (for the number of mutations) of exponential mixtures (for the developing time of mutant clones) of geometric distributions (for the number of cells produced by a mutant clone in a given time). The probabilistic interpretation, and a rigourous proof of convergence in the general case, are deduced from classical results on Bellman-Harris branching processes. The two parameters of the Luria-Delbr\"uck distribution are the expected number of mutations, which is the parameter of interest, and the relative fitness of normal cells compared to mutants, which is the heavy tail exponent. Both can be simultaneously estimated by the maximum likehood method. However, the computation becomes numerically unstable as soon as the maximal value of the sample is large, which occurs frequently due to the heavy tail property. Based on the empirical generating function, robust estimators are proposed and their asymptotic variance is given. They are comparable in precision to maximum likelihood estimators, with a much broader range of calculability, a better numerical stability, and a negligible computing time

Simultaneous growth of two cancer cell lines evidences variability in growth rates

Cancer cells co-cultured in vitro reveal unexpected differential growth rates that classical exponential growth models cannot account for. Two non-interacting cell lines were grown in the same culture, and counts of each species were recorded at periodic times. The relative growth of population ratios was found to depend on the initial proportion, in contradiction with the traditional exponential growth model. The proposed explanation is the variability of growth rates for clones inside the same cell line. This leads to a log-quadratic growth model that provides both a theoretical explanation to the phenomenon that was observed, and a better fit to our growth data

Some mathematical tools for the Lenski experiment

The Lenski experiment is a long term daily reproduction of Escherichia coli, that has evidenced phenotypic and genetic evolutions along the years. Some mathematical models, that could be usefull in understanding the results of that experiment, are reviewed here: stochastic and deterministic growth, mutation appearance and fixation, competition of species

Modèle de Rasch et validation de questionnaires de qualité de vie

The assesment of quality of life has become an important problem in medicine. This assesment is aimed to evaluate the limitations induced by therapeutics on the daily life of patients. In most of cases, a questionnaire is administred to the patients in order to quantify their quality of life. Then, we have to construct a statistical model that links the items answers to an unobserved quantitative variable, here the quality of life. In most of the clinical studies, only linear linear modelizations are used. The purpose of this work is to study a new approach based on Rasch model[...][...] Nous présentons l'algorithme stochastique SEM et nous l'utilisons de façon originale dans le cadre du modèle de Rasch. Si cette utilisation apporte peu dans le cas classique, nous montrons qu'elle est quasiment incontournable dans le cas du modèle de Rasch pour données longitudinales. La fiabilité, ou précision d'une mesure obtenue par questionnaire, est presque toujours estimée par le coëfficient alpha de Cronbach. Nous avons proposé de généraliser le calcul de la fiabilité au cas du modèle de Rasch. Le coefficient alpha de Cronbach et le nouveau coefficient sont comparés à l'aide de simulations. Nous présentons les problèmes posés par l'évaluation de la qualité de vie et les méthodes actuellement utilisées pour la validation de questionnaires. Nous exposons ensuite les nouveaux test d'ajustement au modèle de Rasch et montrons comment ils apporter des réponses aux problèmes de la construction de mesures de qualité de vie. Dans la dernière partie de ce travail, nous avons proposé, en nous basant sur les estimations isotoniques des probabilités de réponse, un nouveau test de type Kolmogorov-Smirnov pour la comparaison de traits lents entre deux groupes.LORIENT-BU (561212106) / SudocSudocFranceF

Statistique descriptive - Cours et exercices corrigés

National audienceCe livre expose de façon détaillée les notions essentielles de statistique descriptive. Les premiers chapitres sont consacrés à la description d'une variable. On y présente le vocabulaire général, les graphiques importants ainsi que les mesures habituelles de tendance centrale et de dispersion. Les auteurs ont motivé l'introduction de chaque notion par une situation concrète avant de formaliser dans un contexte général. Les résultats d'une enquête servent de fil conducteur à la seconde partie qui traite le cas de deux variables. Dans un cadre réaliste, on aborde ainsi les tableaux de contingence, les notions de variance inter et intra-classes ainsi que la régression linéaire simple. Ce livre s'adresse à tout étudiant s'initiant à la statistique. Il y trouvera un cours clair e précis s'appuyant sur les prérequis mathématiques élémentaires de lycée. Une cinquantaine d'exercices d'application directe ou d'ouverture sont proposés et sont tous corrigés en détail. Les auteurs consacrent un chapitre à l'emploi des calculatrices, outil essentiel au lycée et en premier cycle universitaire. Le lecteur pourra aussi découvrir en annexe une version conviviale du logiciel gratuit R très prisé à l'université comme en entreprise

Gravity tectonics in the SE Basin (Provence, France) imaged from seismic reflection data

International audienceUsing industrial seismic data available in the French Southeast Basin in Provence, we put into evidence thin skinned processes that have dominated tectonics in this basin since the Oligocene. These interpretations are then replaced within the regional structural framework of SW France with geological maps and field work. A thick Mesozoic and Cenozoic sedimentary cover is detached on a main décollement frequently localized within the Triassic evaporites. The underlying basement is undeformed. The Mid-Durance fault, the Luberon, Trévaresse, and the Ventoux-Lure thrust zones and the Diois-Baronnies fold and thrust belt are produced by thin-skinned tectonics, the associated structures having no roots within the pre-Triassic basement. This thin-skinned deformation is interpreted as resulting from a regional southward gravity mass flow, induced by the westward Alps extrusion, followed in recent times by radial collapse of the Alps. The incipient stage of this gravity sliding occurred during the Late Oligocene in the Diois-Baronnies (the former Mesozoic Vocontian basin), and then rapidly progressed to the south across the Ventoux-Lure thrust zone in Provence during the Miocene. Southward, this gravity sliding vanishes approaching the E-W trending structural high of the Eocene Pyrénéo-Provençal orogenic belt in southern Provence

Polypyrimidine Tract-binding Protein Is Involved in Vivo in Repression of a Composite Internal/3′ -Terminal Exon of the Xenopus α-Tropomyosin Pre-mRNA

International audienceThe Xenopus alpha(fast)-tropomyosin gene contains, at its 3' -end, a composite internal/3' -terminal exon (exon 9A9'), which is subjected to three different patterns of splicing according to the cell type. Exon 9A9' is included as a terminal exon in the myotome and as an internal exon in adult striated muscles, whereas it is skipped in nonmuscle cells. We have developed an in vivo model based on transient expression of minigenes encompassing the regulated exon 9A9' in Xenopus oocytes and embryos. We first show that the different alpha-tropomyosin minigenes recapitulate the splicing pattern of the endogenous gene and constitute valuable tools to seek regulatory sequences involved in exon 9A9' usage. A mutational analysis led to the identification of an intronic element that is involved in the repression of exon 9A9' in nonmuscle cells. This element harbors four polypyrimidine track-binding protein (PTB) binding sites that are essential for the repression of exon 9A9'. We show using UV cross-linking and immunoprecipitation experiments that Xenopus PTB (XPTB) interacts with these PTB binding sites. Finally, we show that depletion of endogenous XPTB in Xenopus embryos using a morpholinobased translational inhibition strategy resulted in exon 9A9' inclusion in embryonic epidermal cells. These results demonstrate that XPTB is required in vivo to repress the terminal exon 9A9' and suggest that PTB could be a major actor in the repression of regulated 3' -terminal exon

Continuous positive airway pressure adherence trajectories in sleep apnea: Clustering with summed discrete Fréchet and dynamic time warping dissimilarities

International audienceBackgroundObstructive sleep apnea (OSA) is a chronic disease characterized by recurrent pharyngeal collapses during sleep. In most severe cases, continuous positive airway pressure (CPAP) consists in keeping the airways open by administering mild air pressure. This treatment faces adherence issues.ObjectivesEight hundred and forty-eight subjects were equipped with CPAP prescribed at the Grenoble University Hospital between 2016 and 2018. Their daily CPAP uses have been recorded during the first 3 months. Our aim is to cluster these adherence time series. With hierarchical agglomerative clustering, we focused on the choices of the dissimilarity measure and the internal cluster validation index (CVI).MethodsThe Euclidean distance, the dynamic time warping (DTW) and the generalized summed discrete Fréchet dissimilarity were implemented with three linkage strategies (“average,” “complete,” and “Ward”). The performances of each method (dissimilarity and linkage) were evaluated on a simulation study through the adjusted Rand index (ARI). The Ward linkage with DTW dissimilarity provided the best ARI. Then six different internal CVIs (Silhouette, Calinski Harabasz, Davies Bouldin, Modified Davies Bouldin, Dunn, and COP) were compared on their ability to choose the best number of clusters. The Dunn index beat the others.ResultsCPAP data were clustered with the Ward linkage, the DTW dissimilarity and the Dunn index. It identified six clusters, from a cluster of patients (N = 29 subjects) whose stopped the therapy early on to a cluster (N = 105) with increasing adherence over time. Other clusters were extremely good users (N = 151), good users (N = 150), moderate users (N = 235), and poor adherers (N = 178)