Distributions on the simplex

The simplex, the sample space of compositional data, can be structured as a real Euclidean space. This fact allows to work with the coefficients with respect to an orthonormal basis. Over these coefficients we apply standard real analysis, inparticular, we define two different laws of probability trought the density function and we study their main properties

Meaning of the λ parameter of skew–normal and log–skew normal distributions in fluid geochemistry

The literature related to skew–normal distributions has grown rapidly in recent years but at the moment few applications concern the description of natural phenomena with this type of probability models, as well as the interpretation of their parameters. The skew–normal distributions family represents an extension of the normal family to which a parameter (λ) has been added to regulate the skewness. The development of this theoretical field has followed the general tendency in Statistics towards more flexible methods to represent features of the data, as adequately as possible, and to reduce unrealistic assumptions as the normality that underlies most methods of univariate and multivariate analysis. In this paper an investigation on the shape of the frequency distribution of the logratio ln(Cl−/Na+) whose components are related to waters composition for 26 wells, has been performed. Samples have been collected around the active center of Vulcano island (Aeolian archipelago, southern Italy) from 1977 up to now at time intervals of about six months. Data of the logratio have been tentatively modeled by evaluating the performance of the skew–normal model for each well. Values of the λ parameter have been compared by considering temperature and spatial position of the sampling points. Preliminary results indicate that changes in λ values can be related to the nature of environmental processes affecting the data

Validation of order rank scales based on compositional data analysis: a proposal

Usually, psychometricians apply classical factorial analysis to evaluate construct validity of order rank scales. Nevertheless, these scales have particular characteristics that must be taken into account: total scores and rank are highly relevant

Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible consideration of densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended the Euclidean structure of the simplex to a Hilbert space structure of the set of densities within a bounded interval, and van den Boogaart (2005) generalized this to the set of densities bounded by an arbitrary reference density. From the many variations of the Hilbert structures available, we work with three cases. For bounded variables, a basis derived from Legendre polynomials is used. For variables with a lower bound, we standardize them with respect to an exponential distribution and express their densities as coordinates in a basis derived from Laguerre polynomials. Finally, for unbounded variables, a normal distribution is used as reference, and coordinates are obtained with respect to a Hermite-polynomials-based basis. To get the coordinates, several approaches can be considered. A numerical accuracy problem occurs if one estimates the coordinates directly by using discretized scalar products. Thus we propose to use a weighted linear regression approach, where all k- order polynomials are used as predictand variables and weights are proportional to the reference density. Finally, for the case of 2-order Hermite polinomials (normal reference) and 1-order Laguerre polinomials (exponential), one can also derive the coordinates from their relationships to the classical mean and variance. Apart of these theoretical issues, this contribution focuses on the application of this theory to two main problems in sedimentary geology: the comparison of several grain size distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock or sediment, like their composition

Proposal of a parallel architecture for a motion detection algorithm

This paper proposes a parallel architecture for estimation of the motion of an underwater robot. It is well known that image processing requires a huge amount of computation, mainly at low-level processing where the algorithms are dealing with a great number of data. In a motion estimation algorithm, correspondences between two images have to be solved at the low level. In the underwater imaging, normalised correlation can be a solution in the presence of non-uniform illumination. Due to its regular processing scheme, parallel implementation of the correspondence problem can be an adequate approach to reduce the computation time. Taking into consideration the complexity of the normalised correlation criteria, a new approach using parallel organisation of every processor from the architecture is proposed

The mapping of the local contributions of Fermi and Coulomb correlation into intracule and extracule density distributions

The contributions of the correlated and uncorrelated components of the electron-pair density to atomic and molecular intracule I(r) and extracule E(R) densities and its Laplacian functions ∇2I(r) and ∇2E(R) are analyzed at the Hartree-Fock (HF) and configuration interaction (CI) levels of theory. The topologies of the uncorrelated components of these functions can be rationalized in terms of the corresponding one-electron densities. In contrast, by analyzing the correlated components of I(r) and E(R), namely, IC(r) and EC(R), the effect of electron Fermi and Coulomb correlation can be assessed at the HF and CI levels of theory. Moreover, the contribution of Coulomb correlation can be isolated by means of difference maps between IC(r) and EC(R) distributions calculated at the two levels of theory. As application examples, the He, Ne, and Ar atomic series, the C2-2, N2, O2+2 molecular series, and the C2H4 molecule have been investigated. For these atoms and molecules, it is found that Fermi correlation accounts for the main characteristics of IC(r) and EC(R), with Coulomb correlation increasing slightly the locality of these functions at the CI level of theory. Furthermore, IC(r), EC(R), and the associated Laplacian functions, reveal the short-ranged nature and high isotropy of Fermi and Coulomb correlation in atoms and molecules

The relevance of the Laplacian of intracule and extracule density distributions for analyzing electron-electron interactions in molecules

A topological analysis of intracule and extracule densities and their Laplacians computed within the Hartree-Fock approximation is presented. The analysis of the density distributions reveals that among all possible electron-electron interactions in atoms and between atoms in molecules only very few are located rigorously as local maxima. In contrast, they are clearly identified as local minima in the topology of Laplacian maps. The conceptually different interpretation of intracule and extracule maps is also discussed in detail. An application example to the C2H2, C2H4, and C2H6 series of molecules is presented

A comparative analysis by means of quantum molecular similarity measures of density distributions derived from conventional ab initio and density functional methods

A procedure based on quantum molecular similarity measures (QMSM) has been used to compare electron densities obtained from conventional ab initio and density functional methodologies at their respective optimized geometries. This method has been applied to a series of small molecules which have experimentally known properties and molecular bonds of diverse degrees of ionicity and covalency. Results show that in most cases the electron densities obtained from density functional methodologies are of a similar quality than post-Hartree-Fock generalized densities. For molecules where Hartree-Fock methodology yields erroneous results, the density functional methodology is shown to yield usually more accurate densities than those provided by the second order Møller-Plesset perturbation theory

Social networks and performance in knowledge creation. An application and a methodological proposal

El objetivo de esta tesis es predecir el rendimiento de los estudiantes de doctorado en la Universidad de Girona según características personales (background), actitudinales y de redes sociales de los estudiantes. La población estudiada son estudiantes de tercer y cuarto curso de doctorado y sus directores de tesis doctoral. Para obtener los datos se ha diseño un cuestionario web especificando sus ventajas y teniendo en cuenta algunos problemas tradicionales de no cobertura o no respuesta. El cuestionario web se hizo debido a la complejidad que comportan de las preguntas de red social. El cuestionario electrónico permite, mediante una serie de instrucciones, reducir el tiempo para responder y hacerlo menos cargado. Este cuestionario web, además es auto administrado, lo cual nos permite, según la literatura, unas respuestas mas honestas que cuestionario con encuestador. Se analiza la calidad de las preguntas de red social en cuestionario web para datos egocéntricos. Para eso se calcula la fiabilidad y la validez de este tipo de preguntas, por primera vez a través del modelo Multirasgo Multimétodo (Multitrait Multimethod). Al ser datos egocéntricos, se pueden considerar jerárquicos, y por primera vez se una un modelo Multirasgo Multimétodo Multinivel (multilevel Multitrait Multimethod). Las la fiabilidad y validez se pueden obtener a nivel individual (within group component) o a nivel de grupo (between group component) y se usan para llevar a cabo un meta-análisis con otras universidades europeas para analizar ciertas características de diseño del cuestionario. Estas características analizan si para preguntas de red social hechas en cuestionarios web son más fiables y validas hechas "by questions" o "by alters", si son presentes todas las etiquetas de frecuencia para los ítems o solo la del inicio y final, o si es mejor que el diseño del cuestionario esté en con color o blanco y negro. También se analiza la calidad de la red social en conjunto, en este caso específico son los grupos de investigación de la universidad. Se tratan los problemas de los datos ausentes en las redes completas. Se propone una nueva alternativa a la solución típica de la red egocéntrica o los respondientes proxies. Esta nueva alternativa la hemos nombrado "Nosduocentered Network" (red Nosduocentrada), se basa en dos actores centrales en una red. Estimando modelos de regresión, esta "Nosduocentered network" tiene mas poder predictivo para el rendimiento de los estudiantes de doctorado que la red egocéntrica. Además se corrigen las correlaciones de las variables actitudinales por atenuación debido al pequeño tamaño muestral. Finalmente, se hacen regresiones de los tres tipos de variables (background, actitudinales y de red social) y luego se combinan para analizar cual para predice mejor el rendimiento (según publicaciones académicas) de los estudiantes de doctorado. Los resultados nos llevan a predecir el rendimiento académico de los estudiantes de doctorado depende de variables personales (background) i actitudinales. Asimismo, se comparan los resultados obtenidos con otros estudios publicados.

A proposal for the diagnosis of uncertain dynamic systems based on interval models

The performance of a model-based diagnosis system could be affected by several uncertainty sources, such as,model errors,uncertainty in measurements, and disturbances. This uncertainty can be handled by mean of interval models.The aim of this thesis is to propose a methodology for fault detection, isolation and identification based on interval models. The methodology includes some algorithms to obtain in an automatic way the symbolic expression of the residual generators enhancing the structural isolability of the faults, in order to design the fault detection tests. These algorithms are based on the structural model of the system. The stages of fault detection, isolation, and identification are stated as constraint satisfaction problems in continuous domains and solved by means of interval based consistency techniques. The qualitative fault isolation is enhanced by a reasoning in which the signs of the symptoms are derived from analytical redundancy relations or bond graph models of the system. An initial and empirical analysis regarding the differences between interval-based and statistical-based techniques is presented in this thesis. The performance and efficiency of the contributions are illustrated through several application examples, covering different levels of complexity.

A proposal of a behavior-based control architecture with reinforcement learning for an autonomous underwater robot

Aquesta tesi proposa l'ús d'un seguit de tècniques pel control a alt nivell d'un robot autònom i també per l'aprenentatge automàtic de comportaments. L'objectiu principal de la tesis fou el de dotar d'intel·ligència als robots autònoms que han d'acomplir unes missions determinades en entorns desconeguts i no estructurats. Una de les premisses tingudes en compte en tots els passos d'aquesta tesis va ser la selecció d'aquelles tècniques que poguessin ésser aplicades en temps real, i demostrar-ne el seu funcionament amb experiments reals. El camp d'aplicació de tots els experiments es la robòtica submarina. En una primera part, la tesis es centra en el disseny d'una arquitectura de control que ha de permetre l'assoliment d'una missió prèviament definida. En particular, la tesis proposa l'ús de les arquitectures de control basades en comportaments per a l'assoliment de cada una de les tasques que composen la totalitat de la missió. Una arquitectura d'aquest tipus està formada per un conjunt independent de comportaments, els quals representen diferents intencions del robot (ex.: "anar a una posició", "evitar obstacles",...). Es presenta una recerca bibliogràfica sobre aquest camp i alhora es mostren els resultats d'aplicar quatre de les arquitectures basades en comportaments més representatives a una tasca concreta. De l'anàlisi dels resultats se'n deriva que un dels factors que més influeixen en el rendiment d'aquestes arquitectures, és la metodologia emprada per coordinar les respostes dels comportaments. Per una banda, la coordinació competitiva és aquella en que només un dels comportaments controla el robot. Per altra banda, en la coordinació cooperativa el control del robot és realitza a partir d'una fusió de totes les respostes dels comportaments actius. La tesis, proposa un esquema híbrid d'arquitectura capaç de beneficiar-se dels principals avantatges d'ambdues metodologies. En una segona part, la tesis proposa la utilització de l'aprenentatge per reforç per aprendre l'estructura interna dels comportaments. Aquest tipus d'aprenentatge és adequat per entorns desconeguts i el procés d'aprenentatge es realitza al mateix temps que el robot està explorant l'entorn. La tesis presenta també un estat de l'art d'aquest camp, en el que es detallen els principals problemes que apareixen en utilitzar els algoritmes d'aprenentatge per reforç en aplicacions reals, com la robòtica. El problema de la generalització és un dels que més influeix i consisteix en permetre l'ús de variables continues sense augmentar substancialment el temps de convergència. Després de descriure breument les principals metodologies per generalitzar, la tesis proposa l'ús d'una xarxa neural combinada amb l'algoritme d'aprenentatge per reforç Q_learning. Aquesta combinació proporciona una gran capacitat de generalització i una molt bona disposició per aprendre en tasques de robòtica amb exigències de temps real. No obstant, les xarxes neurals són aproximadors de funcions no-locals, el que significa que en treballar amb un conjunt de dades no homogeni es produeix una interferència: aprendre en un subconjunt de l'espai significa desaprendre en la resta de l'espai. El problema de la interferència afecta de manera directa en robòtica, ja que l'exploració de l'espai es realitza sempre localment. L'algoritme proposat en la tesi té en compte aquest problema i manté una base de dades representativa de totes les zones explorades. Així doncs, totes les mostres de la base de dades s'utilitzen per actualitzar la xarxa neural, i per tant, l'aprenentatge és homogeni. Finalment, la tesi presenta els resultats obtinguts amb la arquitectura de control basada en comportaments i l'algoritme d'aprenentatge per reforç. Els experiments es realitzen amb el robot URIS, desenvolupat a la Universitat de Girona, i el comportament après és el seguiment d'un objecte mitjançant visió per computador. La tesi detalla tots els dispositius desenvolupats pels experiments així com les característiques del propi robot submarí. Els resultats obtinguts demostren la idoneïtat de les propostes en permetre l'aprenentatge del comportament en temps real. En un segon apartat de resultats es demostra la capacitat de generalització de l'algoritme d'aprenentatge mitjançant el "benchmark" del "cotxe i la muntanya". Els resultats obtinguts en aquest problema milloren els resultats d'altres metodologies, demostrant la millor capacitat de generalització de les xarxes neurals.

A proposal to estimate the motion of an underwater vehicle through visual mosaicking

This thesis proposes a solution to the problem of estimating the motion of an Unmanned Underwater Vehicle (UUV). Our approach is based on the integration of the incremental measurements which are provided by a vision system. When the vehicle is close to the underwater terrain, it constructs a visual map (so called "mosaic") of the area where the mission takes place while, at the same time, it localizes itself on this map, following the Concurrent Mapping and Localization strategy. The proposed methodology to achieve this goal is based on a feature-based mosaicking algorithm. A down-looking camera is attached to the underwater vehicle. As the vehicle moves, a sequence of images of the sea-floor is acquired by the camera. For every image of the sequence, a set of characteristic features is detected by means of a corner detector. Then, their correspondences are found in the next image of the sequence. Solving the correspondence problem in an accurate and reliable way is a difficult task in computer vision. We consider different alternatives to solve this problem by introducing a detailed analysis of the textural characteristics of the image. This is done in two phases: first comparing different texture operators individually, and next selecting those that best characterize the point/matching pair and using them together to obtain a more robust characterization. Various alternatives are also studied to merge the information provided by the individual texture operators. Finally, the best approach in terms of robustness and efficiency is proposed. After the correspondences have been solved, for every pair of consecutive images we obtain a list of image features in the first image and their matchings in the next frame. Our aim is now to recover the apparent motion of the camera from these features. Although an accurate texture analysis is devoted to the matching pro-cedure, some false matches (known as outliers) could still appear among the right correspon-dences. For this reason, a robust estimation technique is used to estimate the planar transformation (homography) which explains the dominant motion of the image. Next, this homography is used to warp the processed image to the common mosaic frame, constructing a composite image formed by every frame of the sequence. With the aim of estimating the position of the vehicle as the mosaic is being constructed, the 3D motion of the vehicle can be computed from the measurements obtained by a sonar altimeter and the incremental motion computed from the homography. Unfortunately, as the mosaic increases in size, image local alignment errors increase the inaccuracies associated to the position of the vehicle. Occasionally, the trajectory described by the vehicle may cross over itself. In this situation new information is available, and the system can readjust the position estimates. Our proposal consists not only in localizing the vehicle, but also in readjusting the trajectory described by the vehicle when crossover information is obtained. This is achieved by implementing an Augmented State Kalman Filter (ASKF). Kalman filtering appears as an adequate framework to deal with position estimates and their associated covariances. Finally, some experimental results are shown. A laboratory setup has been used to analyze and evaluate the accuracy of the mosaicking system. This setup enables a quantitative measurement of the accumulated errors of the mosaics created in the lab. Then, the results obtained from real sea trials using the URIS underwater vehicle are shown.