Representation and Characterization of Non-Stationary Processes by Dilation Operators and Induced Shape Space Manifolds

We have introduce a new vision of stochastic processes through the geometry induced by the dilation. The dilation matrices of a given processes are obtained by a composition of rotations matrices, contain the measure information in a condensed way. Particularly interesting is the fact that the obtention of dilation matrices is regardless of the stationarity of the underlying process. When the process is stationary, it coincides with the Naimark Dilation and only one rotation matrix is computed, when the process is non-stationary, a set of rotation matrices are computed. In particular, the periodicity of the correlation function that may appear in some classes of signal is transmitted to the set of dilation matrices. These rotation matrices, which can be arbitrarily close to each other depending on the sampling or the rescaling of the signal are seen as a distinctive feature of the signal. In order to study this sequence of matrices, and guided by the possibility to rescale the signal, the correct geometrical framework to use with the dilation's theoretic results is the space of curves on manifolds, that is the set of all curve that lies on a base manifold. To give a complete sight about the space of curve, a metric and the derived geodesic equation are provided. The general results are adapted to the more specific case where the base manifold is the Lie group of rotation matrices. The notion of the shape of a curve can be formalized as the set of equivalence classes of curves given by the quotient space of the space of curves and the increasing diffeomorphisms. The metric in the space of curve naturally extent to the space of shapes and enable comparison between shapes.Comment: 19 pages, draft pape

Practical Estimation of Diversity from Abundance Data

Measuring biodiversity requires empirical techniques to effectively estimate it from real data. The well-known underestimation of the number of species applies to low orders of diversity in general. I test nine estimators including three new ones on geometric and lognormal distributions that represent realistic, hyper-diverse communities. The best two estimators allow a good estimation of diversity of orders over 0.5, even when the sampling effort is low. I provide criteria to choose the estimator and the necessary code in the R package entropart

A typology of distance-based measures of spatial concentration

International audienceOver the last decade, distance-based methods have been introduced and then improved in the field of spatial economics to gauge the geographic concentration of activities. There is a growing literature on this theme including new tools, discussions on their specific properties and various applications. However, there is currently no typology of distance-based methods. This paper fills that gap. The proposed classification helps understand all the properties of distance-based methods and proves that they are variations on the same framework

Test du processus de Poisson homogène par la statistique de Ripley

International audienceLa statistique de Ripley a été introduite pour mesurer l'agrégation des points d'un processus ponctuel. Elle a été très fréquemment utilisée notamment par les écologues, mais peu de résultats théoriques ont été obtenus; nous étudions les propriétés (biais, variance) de cet estimateur sous l'hypothèse d'un processus de Poisson homogène et prouvons un théorème de la limite centrale lorsque les données sont obtenues sur un carré de taille nxn avec n tendant vers l'infini. Nous en déduisons un test asymptotiquement gaussien de l'hypothèse de processus de Poisson homogène

Generalizing Ripley's K function to inhomogeneous populations

In spatial statistics, Ripley's K function (Ripley, 1977) is a classical tool to analyse spatial point patterns. Yet, it faces two major limits: it is only pertinent for homogeneous point processes and it does not allow the weighting of points.We generalize it to get a new function, M, which oversteps these limits and detects spatial structures of inhomogeneous populations of weighted points.Spatial statistics ; point processes ; Ripley

Measures of the Geographic Concentration of Industries: Improving Distance-Based Methods

This study introduces two new measures of spatial concentration. The proposed M functions constitute an extension to Ripley's functions (Ripley, 1976, 1977). They allow the evaluation of the relative geographic concentration and co-location of industries in a non-homogeneous spatial framework. Some rigorous comparisons with similar recently developed tools prove the relevance of the M functions in the field of spatial economics.Geographic concentration ; Distance-based methods ; Ripley's K function ; M function

A trait database for Guianan rain forest trees permits intra- and inter-specific contrasts

International audienceWe present a plant trait database covering autecology for rain forest trees of French Guiana. The database comprises more than thirty traits including autecology (e.g., habitat associations and reproductive phenology), wood structure (e.g., density and tension characteristics) and physiology at the whole plant (e.g., carbon and nitrogen isotopes) and leaf level (e.g., specific leaf area, photosynthetic capacity). The current database describes traits for about nine hundred species from three hundred genera in one hundred families. For more than sixty species, data on twelve morphological and ecophysiological traits are provided for individual plants under different environmental conditions and at different ontogenetic stages. The database is thus unique in permitting intraspecific analyses, such as the effects of ontogenetic stages or environmental conditions on trait values and their relationships

Simulation and integer programming for efficient shift design

6 pagesOperation research approaches and heuristics are often used in the staff organization literature. The main hypothesis considered by shift scheduling approaches is that the workload variability is negligible. Faced to a real organization problem of cleaning staff in a multidisciplinary surgical suite, the lack of exploratory approaches adapted to a context of variable activity has been observed. The purpose of this paper is to implement a hybrid approach combining integer linear programming and a simulation model for assessing performance. Finally, the hybrid approach can save 30% of the cost compared to the solution given by operation research approach alone