Equações diferenciais implícitas com descontinuidade

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Flow Visualization with Quantified Spatial and Temporal Errors Using Edge Maps

Robust analysis of vector fields has been established as an important tool for deriving insights from the complex systems these fields model. Traditional analysis and visualization techniques rely primarily on computing streamlines through numerical integration. The inherent numerical errors of such approaches are usually ignored, leading to inconsistencies that cause unreliable visualizations and can ultimately prevent in-depth analysis. We propose a new representation for vector fields on surfaces that replaces numerical integration through triangles with maps from the triangle boundaries to themselves. This representation, called edge maps, permits a concise description of flow behaviors and is equivalent to computing all possible streamlines at a user defined error threshold. Independent of this error streamlines computed using edge maps are guaranteed to be consistent up to floating point precision, enabling the stable extraction of features such as the topological skeleton. Furthermore, our representation explicitly stores spatial and temporal errors which we use to produce more informative visualizations. This work describes the construction of edge maps, the error quantification, and a refinement procedure to adhere to a user defined error bound. Finally, we introduce new visualizations using the additional information provided by edge maps to indicate the uncertainty involved in computing streamlines and topological structures.

EQUIVALENCE OF REAL MILNOR FIBRATIONS FOR QUASI-HOMOGENEOUS SINGULARITIES

We show that for real quasi-homogeneous singularities f : (R-m, 0) -> (R-2, 0) with isolated singular point at the origin, the projection map of the Milnor fibration S-epsilon(m-1) \ K-epsilon -> S-1 is given by f/parallel to f parallel to. Moreover, for these singularities the two versions of the Milnor fibration, on the sphere and on a Milnor tube, are equivalent. In order to prove this, we show that the flow of the Euler vector field plays and important role. In addition, we present, in an easy way, a characterization of the critical points of the projection (f/parallel to f parallel to) : S-epsilon(m-1) \ K-epsilon -> S-1.

Variational second order flow estimation for PIV sequences

[EN] We present in this paper a variational approach to accurately estimate simultaneously the velocity field and its derivatives directly from PIV image sequences. Our method differs from other techniques that have been presented in the literature in the fact that the energy minimization used to estimate the particles motion depends on a second order Taylor development of the flow. In this way, we are not only able to compute the motion vector field, but we also obtain an accurate estimation of their derivatives. Hence, we avoid the use of numerical schemes to compute the derivatives from the estimated flow that usually yield to numerical amplification of the inherent uncertainty on the estimated flow. The performance of our approach is illustrated with the estimation of the motion vector field and the vorticity on both synthetic and real PIV datasets.

Mixed Mode Fracture Behaviour of Piezoelectric Materials

Piezoelectrics present an interactive electromechanical behaviour that, especially in recent years, has generated much interest since it renders these materials adapt for use in a variety of electronic and industrial applications like sensors, actuators, transducers, smart structures. Both mechanical and electric loads are generally applied on these devices and can cause high concentrations of stress, particularly in proximity of defects or inhomogeneities, such as flaws, cavities or included particles. A thorough understanding of their fracture behaviour is crucial in order to improve their performances and avoid unexpected failures. Therefore, a considerable number of research works have addressed this topic in the last decades. Most of the theoretical studies on this subject find their analytical background in the complex variable formulation of plane anisotropic elasticity. This theoretical approach bases its main origins in the pioneering works of Muskelishvili and Lekhnitskii who obtained the solution of the elastic problem in terms of independent analytic functions of complex variables. In the present work, the expressions of stresses and elastic and electric displacements are obtained as functions of complex potentials through an analytical formulation which is the application to the piezoelectric static case of an approach introduced for orthotropic materials to solve elastodynamics problems. This method can be considered an alternative to other formalisms currently used, like the Stroh’s formalism. The equilibrium equations are reduced to a first order system involving a six-dimensional vector field. After that, a similarity transformation is induced to reach three independent Cauchy-Riemann systems, so justifying the introduction of the complex variable notation. Closed form expressions of near tip stress and displacement fields are therefore obtained. In the theoretical study of cracked piezoelectric bodies, the issue of assigning consistent electric boundary conditions on the crack faces is of central importance and has been addressed by many researchers. Three different boundary conditions are commonly accepted in literature: the permeable, the impermeable and the semipermeable (“exact”) crack model. This thesis takes into considerations all the three models, comparing the results obtained and analysing the effects of the boundary condition choice on the solution. The influence of load biaxiality and of the application of a remote electric field has been studied, pointing out that both can affect to a various extent the stress fields and the angle of initial crack extension, especially when non-singular terms are retained in the expressions of the electro-elastic solution. Furthermore, two different fracture criteria are applied to the piezoelectric case, and their outcomes are compared and discussed. The work is organized as follows: Chapter 1 briefly introduces the fundamental concepts of Fracture Mechanics. Chapter 2 describes plane elasticity formalisms for an anisotropic continuum (Eshelby-Read-Shockley and Stroh) and introduces for the simplified orthotropic case the alternative formalism we want to propose. Chapter 3 outlines the Linear Theory of Piezoelectricity, its basic relations and electro-elastic equations. Chapter 4 introduces the proposed method for obtaining the expressions of stresses and elastic and electric displacements, given as functions of complex potentials. The solution is obtained in close form and non-singular terms are retained as well. Chapter 5 presents several numerical applications aimed at estimating the effect of load biaxiality, electric field, considered permittivity of the crack. Through the application of fracture criteria the influence of the above listed conditions on the response of the system and in particular on the direction of crack branching is thoroughly discussed.

Strong semiclassical gravity in the universe and the laboratory

Three published papers are resumed in this thesis. Different aspects of the semiclassical theory of gravity are discussed. In chapter 1 we find a new perturbative (yet analytical) solution to the unsolved problem of the metric junction between two Friedmann-Robertson-Walker using Israel's formalism. The case of an expanding radiation core inside an expanding or collapsing dust exterior is treated. This model can be useful in the "landscape" cosmology in string theory or for treating new gravastar configurations. In chapter 2 we investigate the possible use of the Kodama vector field as a substitute for the Killing vector field. In particular we find the response function of an Unruh detector following an (accelerated) Kodama trajectory. The detector has finite extension and backreaction is considered. In chapter 3 we study the possible creation of microscopic black holes at LHC in the brane world model. It is found that the black hole tidal charge has a fundamental role in preventing the formation of the horizon.

Finite volume effects in chiral perturbation theory with twisted boundary conditions

We study the effects of a finite cubic volume with twisted boundary conditions on pseudoscalar mesons. We apply Chiral Perturbation Theory in the p-regime and introduce the twist by means of a constant vector field. The corrections of masses, decay constants, pseudoscalar coupling constants and form factors are calculated at next-to-leading order. We detail the derivations and compare with results available in the literature. In some case there is disagreement due to a different treatment of new extra terms generated from the breaking of the cubic invariance. We advocate to treat such terms as renormalization terms of the twisting angles and reabsorb them in the on-shell conditions. We confirm that the corrections of masses, decay constants, pseudoscalar coupling constants are related by means of chiral Ward identities. Furthermore, we show that the matrix elements of the scalar (resp. vector) form factor satisfies the Feynman–Hellman Theorem (resp. the Ward–Takahashi identity). To show the Ward–Takahashi identity we construct an effective field theory for charged pions which is invariant under electromagnetic gauge transformations and which reproduces the results obtained with Chiral Perturbation Theory at a vanishing momentum transfer. This generalizes considerations previously published for periodic boundary conditions to twisted boundary conditions. Another method to estimate the corrections in finite volume are asymptotic formulae. Asymptotic formulae were introduced by Lüscher and relate the corrections of a given physical quantity to an integral of a specific amplitude, evaluated in infinite volume. Here, we revise the original derivation of Lüscher and generalize it to finite volume with twisted boundary conditions. In some cases, the derivation involves complications due to extra terms generated from the breaking of the cubic invariance. We isolate such terms and treat them as renormalization terms just as done before. In that way, we derive asymptotic formulae for masses, decay constants, pseudoscalar coupling constants and scalar form factors. At the same time, we derive also asymptotic formulae for renormalization terms. We apply all these formulae in combination with Chiral Perturbation Theory and estimate the corrections beyond next-to-leading order. We show that asymptotic formulae for masses, decay constants, pseudoscalar coupling constants are related by means of chiral Ward identities. A similar relation connects in an independent way asymptotic formulae for renormalization terms. We check these relations for charged pions through a direct calculation. To conclude, a numerical analysis quantifies the importance of finite volume corrections at next-to-leading order and beyond. We perform a generic Analysis and illustrate two possible applications to real simulations.

Contribution to the Analysis, Design and Assessment of Compact Antenna Test Ranges At Millimeter Wavelengths - Contribución al Análisis, Diseño y Caracterización de Sistemas de Medida de Antenas en Rango Compacto para Frecuencias Milimétricas

This Doctoral Thesis entitled Contribution to the analysis, design and assessment of compact antenna test ranges at millimeter wavelengths aims to deepen the knowledge of a particular antenna measurement system: the compact range, operating in the frequency bands of millimeter wavelengths. The thesis has been developed at Radiation Group (GR), an antenna laboratory which belongs to the Signals, Systems and Radiocommunications department (SSR), from Technical University of Madrid (UPM). The Radiation Group owns an extensive experience on antenna measurements, running at present four facilities which operate in different configurations: Gregorian compact antenna test range, spherical near field, planar near field and semianechoic arch system. The research work performed in line with this thesis contributes the knowledge of the first measurement configuration at higher frequencies, beyond the microwaves region where Radiation Group features customer-level performance. To reach this high level purpose, a set of scientific tasks were sequentially carried out. Those are succinctly described in the subsequent paragraphs. A first step dealed with the State of Art review. The study of scientific literature dealed with the analysis of measurement practices in compact antenna test ranges in addition with the particularities of millimeter wavelength technologies. Joint study of both fields of knowledge converged, when this measurement facilities are of interest, in a series of technological challenges which become serious bottlenecks at different stages: analysis, design and assessment. Thirdly after the overview study, focus was set on Electromagnetic analysis algorithms. These formulations allow to approach certain electromagnetic features of interest, such as field distribution phase or stray signal analysis of particular structures when they interact with electromagnetic waves sources. Properly operated, a CATR facility features electromagnetic waves collimation optics which are large, in terms of wavelengths. Accordingly, the electromagnetic analysis tasks introduce an extense number of mathematic unknowns which grow with frequency, following different polynomic order laws depending on the used algorithmia. In particular, the optics configuration which was of our interest consisted on the reflection type serrated edge collimator. The analysis of these devices requires a flexible handling of almost arbitrary scattering geometries, becoming this flexibility the nucleus of the algorithmia’s ability to perform the subsequent design tasks. This thesis’ contribution to this field of knowledge consisted on reaching a formulation which was powerful at the same time when dealing with various analysis geometries and computationally speaking. Two algorithmia were developed. While based on the same principle of hybridization, they reached different order Physics performance at the cost of the computational efficiency. Inter-comparison of their CATR design capabilities was performed, reaching both qualitative as well as quantitative conclusions on their scope. In third place, interest was shifted from analysis - design tasks towards range assessment. Millimetre wavelengths imply strict mechanical tolerances and fine setup adjustment. In addition, the large number of unknowns issue already faced in the analysis stage appears as well in the on chamber field probing stage. Natural decrease of dynamic range available by semiconductor millimeter waves sources requires in addition larger integration times at each probing point. These peculiarities increase exponentially the difficulty of performing assessment processes in CATR facilities beyond microwaves. The bottleneck becomes so tight that it compromises the range characterization beyond a certain limit frequency which typically lies on the lowest segment of millimeter wavelength frequencies. However the value of range assessment moves, on the contrary, towards the highest segment. This thesis contributes this technological scenario developing quiet zone probing techniques which achieves substantial data reduction ratii. Collaterally, it increases the robustness of the results to noise, which is a virtual rise of the setup’s available dynamic range. In fourth place, the environmental sensitivity of millimeter wavelengths issue was approached. It is well known the drifts of electromagnetic experiments due to the dependance of the re sults with respect to the surrounding environment. This feature relegates many industrial practices of microwave frequencies to the experimental stage, at millimeter wavelengths. In particular, evolution of the atmosphere within acceptable conditioning bounds redounds in drift phenomena which completely mask the experimental results. The contribution of this thesis on this aspect consists on modeling electrically the indoor atmosphere existing in a CATR, as a function of environmental variables which affect the range’s performance. A simple model was developed, being able to handle high level phenomena, such as feed - probe phase drift as a function of low level magnitudes easy to be sampled: relative humidity and temperature. With this model, environmental compensation can be performed and chamber conditioning is automatically extended towards higher frequencies. Therefore, the purpose of this thesis is to go further into the knowledge of millimetre wavelengths involving compact antenna test ranges. This knowledge is dosified through the sequential stages of a CATR conception, form early low level electromagnetic analysis towards the assessment of an operative facility, stages for each one of which nowadays bottleneck phenomena exist and seriously compromise the antenna measurement practices at millimeter wavelengths.

On subjective impressions or how to put numbers to visual illusions

This paper presents a simple theory to analyze some of the more common visual illusions. The reported mathematical model is able to give some numerical results concerning well known phenomena as the Zollner, Muller-Lyer or Wundt illusions. We present two different approaches, the first one related with the symmetrical operations present in each image and the second one concerning a proposed vector field related with the lines present at the image

A method for revealing phase space structures of general time dependent dynamical systems

In this paper we develop new techniques for revealing geometrical structures in phase space that are valid for aperiodically time dependent dynamical systems, which we refer to as Lagrangian descriptors. These quantities are based on the integration, for a finite time, along trajectories of an intrinsic bounded, positive geometrical and/or physical property of the trajectory itself. We discuss a general methodology for constructing Lagrangian descriptors, and we discuss a “heuristic argument” that explains why this method is successful for revealing geometrical structures in the phase space of a dynamical system. We support this argument by explicit calculations on a benchmark problem having a hyperbolic fixed point with stable and unstable manifolds that are known analytically. Several other benchmark examples are considered that allow us the assess the performance of Lagrangian descriptors in revealing invariant tori and regions of shear. Throughout the paper “side-by-side” comparisons of the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field (“time averages”) are carried out and discussed. In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods. We also perform computations for an explicitly three dimensional, aperiodically time-dependent vector field and an aperiodically time dependent vector field defined as a data set. Comparisons with FTLEs and time averages for these examples are also carried out, with similar conclusions as for the benchmark examples.

Deployment of an all-in-one millimetre-wave anechoic chamber

This paper describes the new anechoic chamber available at The University of Kent, UK. This facility includes a spherical near/far field, planar near field, cylindrical near field and a compact range. The facility allows measurement from 600 MHz up to 110 MHz. The spherical, planar and cylindrical ranges covers up to 40 GHz and the compact range is available from 50 GHz up to 110 MHz. Immediate plans are to use the new facility to measure body-centric antennas and sensing nodes together with near field sampling of finite sized Frequency Selective Surfaces.

Lagrangian descriptors: a method for revealing phase space structures of general time dependent dynamical systems

Lagrangian descriptors are a recent technique which reveals geometrical structures in phase space and which are valid for aperiodically time dependent dynamical systems. We discuss a general methodology for constructing them and we discuss a "heuristic argument" that explains why this method is successful. We support this argument by explicit calculations on a benchmark problem. Several other benchmark examples are considered that allow us to assess the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field ("time averages"). In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods.

Automated detection and classification of brain injury lesions on structural magnetic resonance imaging

El daño cerebral adquirido (DCA) es un problema social y sanitario grave, de magnitud creciente y de una gran complejidad diagnóstica y terapéutica. Su elevada incidencia, junto con el aumento de la supervivencia de los pacientes, una vez superada la fase aguda, lo convierten también en un problema de alta prevalencia. En concreto, según la Organización Mundial de la Salud (OMS) el DCA estará entre las 10 causas más comunes de discapacidad en el año 2020. La neurorrehabilitación permite mejorar el déficit tanto cognitivo como funcional y aumentar la autonomía de las personas con DCA. Con la incorporación de nuevas soluciones tecnológicas al proceso de neurorrehabilitación se pretende alcanzar un nuevo paradigma donde se puedan diseñar tratamientos que sean intensivos, personalizados, monitorizados y basados en la evidencia. Ya que son estas cuatro características las que aseguran que los tratamientos son eficaces. A diferencia de la mayor parte de las disciplinas médicas, no existen asociaciones de síntomas y signos de la alteración cognitiva que faciliten la orientación terapéutica. Actualmente, los tratamientos de neurorrehabilitación se diseñan en base a los resultados obtenidos en una batería de evaluación neuropsicológica que evalúa el nivel de afectación de cada una de las funciones cognitivas (memoria, atención, funciones ejecutivas, etc.). La línea de investigación en la que se enmarca este trabajo de investigación pretende diseñar y desarrollar un perfil cognitivo basado no sólo en el resultado obtenido en esa batería de test, sino también en información teórica que engloba tanto estructuras anatómicas como relaciones funcionales e información anatómica obtenida de los estudios de imagen. De esta forma, el perfil cognitivo utilizado para diseñar los tratamientos integra información personalizada y basada en la evidencia. Las técnicas de neuroimagen representan una herramienta fundamental en la identificación de lesiones para la generación de estos perfiles cognitivos. La aproximación clásica utilizada en la identificación de lesiones consiste en delinear manualmente regiones anatómicas cerebrales. Esta aproximación presenta diversos problemas relacionados con inconsistencias de criterio entre distintos clínicos, reproducibilidad y tiempo. Por tanto, la automatización de este procedimiento es fundamental para asegurar una extracción objetiva de información. La delineación automática de regiones anatómicas se realiza mediante el registro tanto contra atlas como contra otros estudios de imagen de distintos sujetos. Sin embargo, los cambios patológicos asociados al DCA están siempre asociados a anormalidades de intensidad y/o cambios en la localización de las estructuras. Este hecho provoca que los algoritmos de registro tradicionales basados en intensidad no funcionen correctamente y requieran la intervención del clínico para seleccionar ciertos puntos (que en esta tesis hemos denominado puntos singulares). Además estos algoritmos tampoco permiten que se produzcan deformaciones grandes deslocalizadas. Hecho que también puede ocurrir ante la presencia de lesiones provocadas por un accidente cerebrovascular (ACV) o un traumatismo craneoencefálico (TCE). Esta tesis se centra en el diseño, desarrollo e implementación de una metodología para la detección automática de estructuras lesionadas que integra algoritmos cuyo objetivo principal es generar resultados que puedan ser reproducibles y objetivos. Esta metodología se divide en cuatro etapas: pre-procesado, identificación de puntos singulares, registro y detección de lesiones. Los trabajos y resultados alcanzados en esta tesis son los siguientes: Pre-procesado. En esta primera etapa el objetivo es homogeneizar todos los datos de entrada con el objetivo de poder extraer conclusiones válidas de los resultados obtenidos. Esta etapa, por tanto, tiene un gran impacto en los resultados finales. Se compone de tres operaciones: eliminación del cráneo, normalización en intensidad y normalización espacial. Identificación de puntos singulares. El objetivo de esta etapa es automatizar la identificación de puntos anatómicos (puntos singulares). Esta etapa equivale a la identificación manual de puntos anatómicos por parte del clínico, permitiendo: identificar un mayor número de puntos lo que se traduce en mayor información; eliminar el factor asociado a la variabilidad inter-sujeto, por tanto, los resultados son reproducibles y objetivos; y elimina el tiempo invertido en el marcado manual de puntos. Este trabajo de investigación propone un algoritmo de identificación de puntos singulares (descriptor) basado en una solución multi-detector y que contiene información multi-paramétrica: espacial y asociada a la intensidad. Este algoritmo ha sido contrastado con otros algoritmos similares encontrados en el estado del arte. Registro. En esta etapa se pretenden poner en concordancia espacial dos estudios de imagen de sujetos/pacientes distintos. El algoritmo propuesto en este trabajo de investigación está basado en descriptores y su principal objetivo es el cálculo de un campo vectorial que permita introducir deformaciones deslocalizadas en la imagen (en distintas regiones de la imagen) y tan grandes como indique el vector de deformación asociado. El algoritmo propuesto ha sido comparado con otros algoritmos de registro utilizados en aplicaciones de neuroimagen que se utilizan con estudios de sujetos control. Los resultados obtenidos son prometedores y representan un nuevo contexto para la identificación automática de estructuras. Identificación de lesiones. En esta última etapa se identifican aquellas estructuras cuyas características asociadas a la localización espacial y al área o volumen han sido modificadas con respecto a una situación de normalidad. Para ello se realiza un estudio estadístico del atlas que se vaya a utilizar y se establecen los parámetros estadísticos de normalidad asociados a la localización y al área. En función de las estructuras delineadas en el atlas, se podrán identificar más o menos estructuras anatómicas, siendo nuestra metodología independiente del atlas seleccionado. En general, esta tesis doctoral corrobora las hipótesis de investigación postuladas relativas a la identificación automática de lesiones utilizando estudios de imagen médica estructural, concretamente estudios de resonancia magnética. Basándose en estos cimientos, se han abrir nuevos campos de investigación que contribuyan a la mejora en la detección de lesiones. ABSTRACT Brain injury constitutes a serious social and health problem of increasing magnitude and of great diagnostic and therapeutic complexity. Its high incidence and survival rate, after the initial critical phases, makes it a prevalent problem that needs to be addressed. In particular, according to the World Health Organization (WHO), brain injury will be among the 10 most common causes of disability by 2020. Neurorehabilitation improves both cognitive and functional deficits and increases the autonomy of brain injury patients. The incorporation of new technologies to the neurorehabilitation tries to reach a new paradigm focused on designing intensive, personalized, monitored and evidence-based treatments. Since these four characteristics ensure the effectivity of treatments. Contrary to most medical disciplines, it is not possible to link symptoms and cognitive disorder syndromes, to assist the therapist. Currently, neurorehabilitation treatments are planned considering the results obtained from a neuropsychological assessment battery, which evaluates the functional impairment of each cognitive function (memory, attention, executive functions, etc.). The research line, on which this PhD falls under, aims to design and develop a cognitive profile based not only on the results obtained in the assessment battery, but also on theoretical information that includes both anatomical structures and functional relationships and anatomical information obtained from medical imaging studies, such as magnetic resonance. Therefore, the cognitive profile used to design these treatments integrates information personalized and evidence-based. Neuroimaging techniques represent an essential tool to identify lesions and generate this type of cognitive dysfunctional profiles. Manual delineation of brain anatomical regions is the classical approach to identify brain anatomical regions. Manual approaches present several problems related to inconsistencies across different clinicians, time and repeatability. Automated delineation is done by registering brains to one another or to a template. However, when imaging studies contain lesions, there are several intensity abnormalities and location alterations that reduce the performance of most of the registration algorithms based on intensity parameters. Thus, specialists may have to manually interact with imaging studies to select landmarks (called singular points in this PhD) or identify regions of interest. These two solutions have the same inconvenient than manual approaches, mentioned before. Moreover, these registration algorithms do not allow large and distributed deformations. This type of deformations may also appear when a stroke or a traumatic brain injury (TBI) occur. This PhD is focused on the design, development and implementation of a new methodology to automatically identify lesions in anatomical structures. This methodology integrates algorithms whose main objective is to generate objective and reproducible results. It is divided into four stages: pre-processing, singular points identification, registration and lesion detection. Pre-processing stage. In this first stage, the aim is to standardize all input data in order to be able to draw valid conclusions from the results. Therefore, this stage has a direct impact on the final results. It consists of three steps: skull-stripping, spatial and intensity normalization. Singular points identification. This stage aims to automatize the identification of anatomical points (singular points). It involves the manual identification of anatomical points by the clinician. This automatic identification allows to identify a greater number of points which results in more information; to remove the factor associated to inter-subject variability and thus, the results are reproducible and objective; and to eliminate the time spent on manual marking. This PhD proposed an algorithm to automatically identify singular points (descriptor) based on a multi-detector approach. This algorithm contains multi-parametric (spatial and intensity) information. This algorithm has been compared with other similar algorithms found on the state of the art. Registration. The goal of this stage is to put in spatial correspondence two imaging studies of different subjects/patients. The algorithm proposed in this PhD is based on descriptors. Its main objective is to compute a vector field to introduce distributed deformations (changes in different imaging regions), as large as the deformation vector indicates. The proposed algorithm has been compared with other registration algorithms used on different neuroimaging applications which are used with control subjects. The obtained results are promising and they represent a new context for the automatic identification of anatomical structures. Lesion identification. This final stage aims to identify those anatomical structures whose characteristics associated to spatial location and area or volume has been modified with respect to a normal state. A statistical study of the atlas to be used is performed to establish which are the statistical parameters associated to the normal state. The anatomical structures that may be identified depend on the selected anatomical structures identified on the atlas. The proposed methodology is independent from the selected atlas. Overall, this PhD corroborates the investigated research hypotheses regarding the automatic identification of lesions based on structural medical imaging studies (resonance magnetic studies). Based on these foundations, new research fields to improve the automatic identification of lesions in brain injury can be proposed.

Combining spatially distributed predictions from neural networks

In this report we discuss the problem of combining spatially-distributed predictions from neural networks. An example of this problem is the prediction of a wind vector-field from remote-sensing data by combining bottom-up predictions (wind vector predictions on a pixel-by-pixel basis) with prior knowledge about wind-field configurations. This task can be achieved using the scaled-likelihood method, which has been used by Morgan and Bourlard (1995) and Smyth (1994), in the context of Hidden Markov modelling

Computation of some Differential Operators in Toric Coordinates

Toric coordinates and toric vector field have been introduced in [2]. Let A be an arbitrary vector field. We obtain formulae for the divA, rotA and the Laplace operator in toric coordinates.