Clustering compositional data trajectories

Our essay aims at studying suitable statistical methods for the clustering ofcompositional data in situations where observations are constituted by trajectories ofcompositional data, that is, by sequences of composition measurements along a domain.Observed trajectories are known as “functional data” and several methods have beenproposed for their analysis.In particular, methods for clustering functional data, known as Functional ClusterAnalysis (FCA), have been applied by practitioners and scientists in many fields. To ourknowledge, FCA techniques have not been extended to cope with the problem ofclustering compositional data trajectories. In order to extend FCA techniques to theanalysis of compositional data, FCA clustering techniques have to be adapted by using asuitable compositional algebra.The present work centres on the following question: given a sample of compositionaldata trajectories, how can we formulate a segmentation procedure giving homogeneousclasses? To address this problem we follow the steps described below.First of all we adapt the well-known spline smoothing techniques in order to cope withthe smoothing of compositional data trajectories. In fact, an observed curve can bethought of as the sum of a smooth part plus some noise due to measurement errors.Spline smoothing techniques are used to isolate the smooth part of the trajectory:clustering algorithms are then applied to these smooth curves.The second step consists in building suitable metrics for measuring the dissimilaritybetween trajectories: we propose a metric that accounts for difference in both shape andlevel, and a metric accounting for differences in shape only.A simulation study is performed in order to evaluate the proposed methodologies, usingboth hierarchical and partitional clustering algorithm. The quality of the obtained resultsis assessed by means of several indices

Risky single-occasion drinking: bingeing is not bingeing.

AIMS: To review the concept of binge drinking as a measure of risky single occasion drinking (RSOD), to illustrate its differential impact on selected health outcomes and to identify research gaps. METHODS: Narrative literature review with focus on conceptual and methodological differences, trajectories of RSOD and effects of RSOD on fetal outcomes, coronary heart disease (CHD) and injuries. RESULTS: Effects ascribed commonly to RSOD may often be the effects of an undifferentiated mixture of risky single occasions and regular heavy volume drinking, constituted by frequent, successive RSOD. This leads to the problem that additional risks due to RSOD are mis-specified and remain unidentified or underestimated in some cases, such as for injuries or CHD, but are probably overstated for some chronic consequences or for effects of maternal drinking on newborns. CONCLUSION: A stronger focus should be placed upon methods that can differentiate the effects of RSOD from those due to frequent occasions of heavy drinking that result in heavy volume drinking.

Variétés CR polarisées et G-polarisées, partie I

Polarized and G-polarized CR manifolds are smooth manifolds endowed with a double structure: a real foliation &em&F&/em& (given by the action of a Lie group G in the G-polarized case) and a transverse CR distribution. Polarized means that (E,J) is roughly speaking invariant by&em&F&/em&. Both structures are therefore linked up. The interplay between them gives to polarized CR-manifolds a very rich geometry. In this paper, we study the properties of polarized and G-polarized manifolds, putting special emphasis on their deformations.

Sermons des auteurs suivants : G. ep. Paris., Joh. Polinus, G. ep. Cameracensis, Odo cardinalis, N. de Byart, Gerardus de Remis, Galterus de Castro Theoderic, Odo de Castro Radulfi cardinalis, Odo cancellarius Paris., Philippus cancellarius Paris., Henricus Theuthonicus, Stephanus de ordine Predicatorum, Hugo de S. Victore.

Au fol. 492v : In processione facta pro regina Blancha infirma, mag. Odo cancellarius.