Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Central notations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform. In this way very elaborated aspects of mathematical statistics can be understood easily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating, combination of likelihood and robust M-estimation functions are simple additions/ perturbations in A2(Pprior). Weighting observations corresponds to a weighted addition of the corresponding evidence. Likelihood based statistics for general exponential families turns out to have a particularly easy interpretation in terms of A2(P). Regular exponential families form finite dimensional linear subspaces of A2(P) and they correspond to finite dimensional subspaces formed by their posterior in the dual information space A2(Pprior). The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P. The discussion of A2(P) valued random variables, such as estimation functions or likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

Analyzing shapes as compositions of distances

We propose to analyze shapes as “compositions” of distances in Aitchison geometry as an alternate and complementary tool to classical shape analysis, especially when size is non-informative. Shapes are typically described by the location of user-chosen landmarks. However the shape – considered as invariant under scaling, translation, mirroring and rotation – does not uniquely define the location of landmarks. A simple approach is to use distances of landmarks instead of the locations of landmarks them self. Distances are positive numbers defined up to joint scaling, a mathematical structure quite similar to compositions. The shape fixes only ratios of distances. Perturbations correspond to relative changes of the size of subshapes and of aspect ratios. The power transform increases the expression of the shape by increasing distance ratios. In analogy to the subcompositional consistency, results should not depend too much on the choice of distances, because different subsets of the pairwise distances of landmarks uniquely define the shape. Various compositional analysis tools can be applied to sets of distances directly or after minor modifications concerning the singularity of the covariance matrix and yield results with direct interpretations in terms of shape changes. The remaining problem is that not all sets of distances correspond to a valid shape. Nevertheless interpolated or predicted shapes can be backtransformated by multidimensional scaling (when all pairwise distances are used) or free geodetic adjustment (when sufficiently many distances are used)

Adaptive intelligent agent approach to guide the web navigation on the PLAN-G distance learning platform

Hypermedia systems based on the Web for open distance education are becoming increasingly popular as tools for user-driven access learning information. Adaptive hypermedia is a new direction in research within the area of user-adaptive systems, to increase its functionality by making it personalized [Eklu 961. This paper sketches a general agents architecture to include navigational adaptability and user-friendly processes which would guide and accompany the student during hislher learning on the PLAN-G hypermedia system (New Generation Telematics Platform to Support Open and Distance Learning), with the aid of computer networks and specifically WWW technology [Marz 98-1] [Marz 98-2]. The PLAN-G actual prototype is successfully used with some informatics courses (the current version has no agents yet). The propased multi-agent system, contains two different types of adaptive autonomous software agents: Personal Digital Agents {Interface), to interacl directly with the student when necessary; and Information Agents (Intermediaries), to filtrate and discover information to learn and to adapt navigation space to a specific student

Computing Distance Functions from Generalized Sources on Weighted Polyhedral Surfaces

We present algorithms for computing approximate distance functions and shortest paths from a generalized source (point, segment, polygonal chain or polygonal region) on a weighted non-convex polyhedral surface in which obstacles (represented by polygonal chains or polygons) are allowed. We also describe an algorithm for discretizing, by using graphics hardware capabilities, distance functions. Finally, we present algorithms for computing discrete k-order Voronoi diagrams

El Empleo de software libre en el estudio de la morfología de los paisajes antiguos: el ejemplo del modelado coste-distancia aplicado a la investigación arqueológica

Los Sistemas de Información Geográfica (SIG) son una herramienta válida para el estudio de los paisajes antiguos. Los SIG se pueden configurar como un conjunto de medios analíticos útiles para comprender la dimensión espacial de las formaciones sociales y su dinámica histórica. En otras palabras, los SIG posibilitan un acercamiento válido a la racionalidad de las conductas espaciales de una comunidad y a las pautas globales de una sociedad que quedan plasmadas en la morfología de un paisaje. Atendiendo a la abundante y creciente oferta de programas informáticos que procesan y analizan información espacial, enfocaremos las ventajas que supone la adopción de soluciones libres y de código abierto para la investigación arqueológica de los paisajes. Como ejemplo presentaremos el modelado coste-distancia aplicado a un problema locacional arqueológico: la evaluación de la ubicación de los asentamientos respecto a los recursos disponibles en su entorno. El enfoque experimental ha sido aplicado al poblamiento castreño de la comarca de La Cabrera (León). Se presentará una descripción detallada de cómo crear tramos isócronos basados en el cálculo de los costes anisótropos inherentes a la locomoción pedestre. Asimismo, la ventaja que supone la adopción del SIG GRASS para la implementación del análisis

Nitrifying and denitrifying bacterial communities in the sediment and rhizosphere of a free water surface constructed wetland

La contínua descàrrega de nutrients, sobretot fosfats i nitrogen, és la major causa d'eutrofització dels ecosistemes aquàtics. Els sistemes de tractament basats en aiguamolls construïts s'han emprat per reduir ells nivells de nitrogen a l'aigua com a alternativa de baix cost als mètodes de depuració convencionals. L'eliminació del nitrogen a aquests sistemes depèn en bona part de la vegetació, i l'alternança de condicions aeròbiques i anaeròbiques per promoure els processos de nitrificació i desnitrificació. En aquest treball hem volgut investigar les activitats microbianes de nitrificació i desnitrificació en relació a dues espècies de plantes macròfites en un sistema d'aiguamolls de tractament de flux superficial (FS-SAC), dissenyat per minimitzar l'impacte de l'alliberament d'aigua carregada de nutrients a la reserva natural dels Aiguamolls de l'Empordà (Girona, Espanya).