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)

Random walk radiosity with generalized absorption probabilities

The author studies random walk estimators for radiosity with generalized absorption probabilities. That is, a path will either die or survive on a patch according to an arbitrary probability. The estimators studied so far, the infinite path length estimator and finite path length one, can be considered as particular cases. Practical applications of the random walks with generalized probabilities are given. A necessary and sufficient condition for the existence of the variance is given, together with heuristics to be used in practical cases. The optimal probabilities are also found for the case when one is interested in the whole scene, and are equal to the reflectivities

La gran obra hidràulica a les conques de la Muga i del Fluvià: dels projectes a les realitzacions (1850-1980)

La tesi aborda, des d'una perspectiva territorial i històrica, el paper que han jugat les grans infraestructures hidràuliques en dues conques fluvials mediterrànies catalanes: la Muga i el Fluvià (província de Girona). Així, s'efectua una reconstrucció retrospectiva del conjunt de projectes de gran obra hidràulica (preses, embassaments, canals complementaris) que, als últims 150 anys, han estat ideats i, en el seu cas executats, a ambdues conques. En aquest procés s'atorga una atenció especial a les justificacions, finalitats, discursos i agents socials que han inspirat la seva concepció i les causes que han conduït al seu èxit o al seu fracàs. Tot plegat es contextualitza dins dels plans, les polítiques i la legislació hidràulica estatals. L'elecció de dos rius veïns proporciona clars elements per a establir una anàlisi evolutiva comparada entre ells. Aquí s'afegirà la influencia del proper riu Ter des del moment en que es decideix l'abastament parcial amb els seus cabals a Barcelona.