The Dirichlet distribution with respect to the Aitchison measure on the simplex - a first approach

The algebraic-geometric structure of the simplex, known as Aitchison geometry, is used to look at the Dirichlet family of distributions from a new perspective. A classical Dirichlet density function is expressed with respect to the Lebesgue measure on real space. We propose here to change this measure by the Aitchison measure on the simplex, and study some properties and characteristic measures of the resulting density

A new distribution on the simplex containing the Dirichlet family

The Dirichlet family owes its privileged status within simplex distributions to easyness of interpretation and good mathematical properties. In particular, we recall fundamental properties for the analysis of compositional data such as closure under amalgamation and subcomposition. From a probabilistic point of view, it is characterised (uniquely) by a variety of independence relationships which makes it indisputably the reference model for expressing the non trivial idea of substantial independence for compositions. Indeed, its well known inadequacy as a general model for compositional data stems from such an independence structure together with the poorness of its parametrisation. In this paper a new class of distributions (called Flexible Dirichlet) capable of handling various dependence structures and containing the Dirichlet as a special case is presented. The new model exhibits a considerably richer parametrisation which, for example, allows to model the means and (part of) the variance-covariance matrix separately. Moreover, such a model preserves some good mathematical properties of the Dirichlet, i.e. closure under amalgamation and subcomposition with new parameters simply related to the parent composition parameters. Furthermore, the joint and conditional distributions of subcompositions and relative totals can be expressed as simple mixtures of two Flexible Dirichlet distributions. The basis generating the Flexible Dirichlet, though keeping compositional invariance, shows a dependence structure which allows various forms of partitional dependence to be contemplated by the model (e.g. non-neutrality, subcompositional dependence and subcompositional non-invariance), independence cases being identified by suitable parameter configurations. In particular, within this model substantial independence among subsets of components of the composition naturally occurs when the subsets have a Dirichlet distribution

Application for fault location in electrical power distribution systems

Fault location has been studied deeply for transmission lines due to its importance in power systems. Nowadays the problem of fault location on distribution systems is receiving special attention mainly because of the power quality regulations. In this context, this paper presents an application software developed in Matlabtrade that automatically calculates the location of a fault in a distribution power system, starting from voltages and currents measured at the line terminal and the model of the distribution power system data. The application is based on a N-ary tree structure, which is suitable to be used in this application due to the highly branched and the non- homogeneity nature of the distribution systems, and has been developed for single-phase, two-phase, two-phase-to-ground, and three-phase faults. The implemented application is tested by using fault data in a real electrical distribution power system

Cystoseira-dominated assemblages from sheltered areas in the Mediterranean sea : diversity, distribution and effects of pollution

Les algues del gènere Cystoseira són els principals organismes formadors d'estructura en fons rocosos ben il·luminats del Mar Mediterrani. Formen unes comunitats molt estructurades que s'assemblen ecològicament als boscos terrestres i que són sensibles als impactes antròpics. Aquesta tesi s'ha centrat en l'estudi de les espècies i comunitats dominades per Cystoseira que es troben en ambients calmats, és a dir, en petites cales i/o badies. S'han abordat diversos aspectes com són la distribució, composició, estructura i biogeografia d'aquestes comunitats, així com els efectes de la contaminació sobre les mateixes. Per una banda, s'ha documentat l'estat actual de les comunitats dominades per C. crinita a nombrosos llocs al llarg de tot el Mediterrani, aportant informació sobre la seva composició, estructura, variació biogeogràfica i dinàmica de la comunitat a llarg termini. S'ha documentat la desaparició de diverses espècies de Cystoseira en zones afectades per impactes antròpics diversos i s'ha proporcionat la primera evidència experimental de la desaparició d'espècies de Cystoseira a causa de la contaminació.

Zooplankton structure and dynamics in Mediterranean marshes (Empordà Wetlands): a size-based approach

Zooplankton community structure (composition, diversity, dynamics and trophic relationships) of Mediterranian marshes, has been analysed by means of a size based approach. In temporary basins the shape of the biomass-size spectra is related to the hydrological cycle. Linear shape spectra are more frequent in flooding situations when nutrient input causes population growth of small-sized organisms, more than compensating for the effect of competitive interactions. During confinement conditions the scarcity of food would decrease zooplankton growth and increase intra- and interspecific interactions between zooplankton organisms which favour the greatest sizes thus leading to the appearance of curved shape spectra. Temporary and permanent basins have similar taxonomic composition but the latter have higher species diversity, a more simplified temporal pattern and a size distribution dominated mainly by smaller sizes. In permanents basins zooplankton growth is not only conditioned by the availability of resources but by the variable predation of planktivorous fish, so that the temporal variability of the spectra may also be a result of temporal differences in fish predation. Size diversity seems to be a better indicator of the degree of this community structure than species diversity. The tendency of size diversity to increase during succession makes it useful to discriminate between different succession stages, fact that is not achieved by analysing only species diversity since it is low both under large and frequent or small and rare disturbances. Amino acid composition differences found among stages of copepod species indicate a gradual change in diet during the life cycle of these copepods, which provide evidence of food niche partitioning during ontogeny, whereas Daphnia species show a relatively constant amino acid composition. There is a relationship between the degree of trophic niche overlap among stages of the different species and nutrient concentration. Copepods, which have low trophic niche overlap among stages are dominant in food-limited environments, probably because trophic niche partitioning during development allow them to reduce intraspecific competition between adults, juveniles and nauplii. Daphnia species are only dominant in water bodies or periods with high productivity, probably due to the high trophic niche overlap between juveniles and adults. These findings suggest that, in addition to the effect of interspecific competition, predation and abiotic factors, the intraspecific competition might play also an important role in structuring zooplankton assemblages.