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We employ methods from deep learning for image recognition. We use a dataset with +70k images and 73 classes in order to compare the performance of several well known deep network architectures. The approaches used include the full training of these networks and also the techniques of transfer learning and fine tuning with the weights pretrained on the ImageNet set. We show the superiority of the latter approach in our dataset. We also experiment with a reorganization of the labels in our dataset by grouping several classes shown by the confusion matrix to be indistinguishable for the models. In this case we obtain a classification accuracy score higher than 50%. Utilizamos métodos de aprendizaje profundo en el contexto de reconocimiento de imágenes. Utilizamos un conjunto de más de 70 mil imágenes y 73 clases diferentes para comparar el rendimiento de diferentes arquitecturas comúnmente empleadas. Los enfoques utilizados en este trabajo incluyen en un entrenamiento completo de estas redes y también estrategias de transferencia del aprendizaje y calibración de modelos con redes pre entrenadas en el conjunto ImageNet. Mostramos la superioridad de este último enfoque en nuestro conjunto de imágenes. También experimentamos con una reorganización de las categorías de nuestro conjunto, fusionando aquellas categorías que la matriz de confusión muestra que son más comúnmente confundidas por nuestros modelos. En este caso obtenemos una precisión superior al 50%. Utilitzem mètodes d'aprenentatge profund en el context de reconeixement d'imatges. Utilitzem un conjunt de més de 70 mil imatges i 73 classes diferents per a comparar el rendiment de diferents arquitectures. Els enfocaments utilitzats en aquest treball inclouen un entrenament complet d'aquestes xarxes i també d'estratègies de transferència de l'aprenentatge i calibratge de models amb xarxes pre entrenades en el conjunt ImageNet. Vam mostrar la superioritat d'aquest últim enfocament en el nostre conjunt d'imatges. També experimentem amb una reorganització de les categories del nostre conjunt, fusionant aquelles categories que la matriu de confusió mostra que són més confoses pels nostres models. En aquest cas obtenim una precisió superior al 50%.

Using modern differential geometric methods, we study the relative equilibria for Dirichlet's model of a self-gravitating fluid mass having at least two equal axes. We show that the only relative equilibria of this type correspond to Riemann ellipsoids for which the angular velocity and vorticity are parallel to the same principal axis of the body configuration. The two solutions found are MacLaurin and transversal spheroids. The singular reduced energy-momentum method developed in Rodríguez-Olmos (Nonlinearity 19(4):853-877, 2006) is applied to study their nonlinear stability and instability. We found that the transversal spheroids are nonlinearly stable for all eccentricities while for the MacLaurin spheroids, we recover the classical results. Comparisons with other existing results and methods in the literature are also made

Multimorbidity is common in over 50 percent of people over the age of 65, and can be a major factor in recovery from chronic illnesses. In addition, the use of multiple medications simultaneously is increasingly common in the population, and in some cases the effects derived from this consumption may go beyond the main purpose. This thesis studies the effect of drug consumption and multimorbidity on breast cancer survival at 12, 24, 36 and 48 months from the first diagnosis. Six different machine learning algorithms have been used to build predictive models. After an analysis, Extreme Gradient Boost has been selected as the main model due to its performance. The results obtained for 36 and 48 months, in which the tables contain a proportion of dead patients higher than 27%, have been very satisfactory, with metrics AUC, F1 score and accuracy higher than 91% and recall higher than 88%. In the cases of 12 and 24 months the results have been satisfactory in the AUC metrics (>93%), but between 57 and 78% in the others.

The Marle-Guillemin-Sternberg (MGS) model is an extremely important tool for the theory of Hamiltonian actions on symplectic manifolds. It has been extensively used to prove many local results both in symplectic geometry and in symmetric Hamiltonian systems theory. It provides a model for a tubular neighborhood of a group orbit and puts in normal form the group action and the symplectic structure. The main drawback of the MGS model is that it is not explicit. Only it existence and main properties can be proved. Moreover, for cotangent bundles, this model does not respect the natural fibration. In the first part of the thesis we build an MGS model specially adapted to the cotangent bundle geometry. This model generalizes previous results obtained by T. Schmah for orbits with fully-isotropic momentum. In addition, our construction is explicit up to the integration of a differential equation on G. This equation can be easily solved for the groups SO(3) or SL(2), hence giving explicit symplectic coordinates for arbitrary canonical actions of these groups on any cotangent bundle. In the second part of the thesis we apply this adapted MGS model to describe the structure of the symplectic reduction of a cotangent bundle. We show that the base projection of any momentum leaf is a Whitney stratified space. Moreover, we can refine the orbit-type stratification of the symplectic reduced space so that each piece is a fibered space. We prove that each of those pieces is endowed with a constant rank presymplectic form and that there is always one unique piece which is open and dense. Furthermore, this maximal piece is symplectomorphic to a vector subbundle of a certain cotangent bundle., El model de Marle-Guillemin-Sternberg (MGS) és una eina extremadament important per la teoria de les accions Hamiltonianes en varietats simplèctiques. Ha estat utilitzada per provar molts resultats te tipus local tant en geometria simplèctica com en la teoria de sistemes Hamiltonians simètrics. Proporciona un model per un entorn tubular de una òrbita de la acció de forma que fica en forma normal tant l'acció del grup com l'estructura simplèctica. El principal problema del model MGS és que no és explícit. Només es poden provar la seva existència i les seves propietats principals. Per altra banda, en el cas de que la varietat sigui un fibrat cotangent la el model MGS no respecta la fibració natural. En la primera part de la tesis construïm un model MGS especialment adaptat a la geometria dels fibrats cotangents. Aquest model generalitza els resultats obtinguts per T. Schmah per òrbites amb moment completament isotròpic. Addicionalment, la nostra construcció és explicita excepte per la integració d'una equació diferencial sobre el grup G. Aquesta equació pot ser solucionada de forma explícita per els grups SO(3) o SL(2), per tant podem donar explícitament coordenades simplèctiques per a accions arbitraries d'aquests grups sobre qualsevol fibrat cotangent. En la segona part de la tesis apliquem aquest model MGS cotangent per descriure l'estructura de les reduccions simplèctiques de fibrats cotangents. Mostrem que la projecció sobre la base de una fulla de moment és un espai estratificat de Whitney. També podem refinar l'estratificació de l'espai simplèctic reduït de forma que cadascuna de les peces és un espai fibrat. Demostrem que cadascuna d'aquestes peces està dotada d'una forma pre-simplèctica de rang constant i que sempre hi ha una única peça que es oberta i densa en l'espai reduït. A més aquesta peca maximal és simlpectomorfa a un subfibrat vectorial de un cert fibrat cotangent.

The dynamics of a rigid body in a central gravitational eld can be modelled by a Hamiltonian system with continuous symmetries implemented by an action of the group SO(3). Depending on the particular geometry of the body (as for instance if the body is axisymmetric) this symmetry group can even be enlarged. There are many classical studies of steadily rotating solutions of this system based on various approximate models of the orbital-attitude coupling of arti cial Earth satellites, but these models don't fully exploit the geometric structure of the problem. [WKM90] provides a geometrical description of this problem and studies its relative equilibria (steady solutions) using Poisson reduction and the Energy-Cassimir method. Our approach consists in attacking this problem by means of the more recent Reduced-Energy-Momentum [SLM91], since it clari es and improves the existing results and, furthermore, it allows for a systematic bifurcation analysis. One novelty of this work with respect to previous approaches is that we also treat axisymmetric bodies using this geometric formalism. Employing these techniques we are able to explicitly and previously unknown relative equilibria and to study their stability and bifurcation patterns.