Weighted Logratio Biplots, Correspondence Analysis and Spectral Maps

Starting with logratio biplots for compositional data, which are based on the principle of subcompositional coherence, and then adding weights, as in correspondence analysis, we rediscover Lewi's spectral map and many connections to analyses of two-way tables of non-negative data. Thanks to the weighting, the method also achieves the property of distributional equivalence

Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequent in practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of the sample, thus producing a transfer of mass from some components to other ones, but preserving the total mass present in the system. This evolution is traditionally modelled as a system of ordinary di erential equations of the mass of each component. However, this kind of evolution can be decomposed into a compositional change, expressed in terms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despite of some subcompositions behaving linearly. The goal is to study the characteristics of such simplicial systems of di erential equa- tions such as linearity and stability. This is performed extracting the compositional dif ferential equations from the mass equations. Then, simplicial derivatives are expressed in coordinates of the simplex, thus reducing the problem to the standard theory of systems of di erential equations, including stability. The characterisation of stability of these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and the associated behaviour of the orbits are the main tools. For a three component system, these orbits can be plotted both in coordinates of the simplex or in a ternary diagram. A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is a radioactive decay

Using self organizing maps on compositional data

Self-organizing maps (Kohonen 1997) is a type of artificial neural network developed to explore patterns in high-dimensional multivariate data. The conventional version of the algorithm involves the use of Euclidean metric in the process of adaptation of the model vectors, thus rendering in theory a whole methodology incompatible with non-Euclidean geometries. In this contribution we explore the two main aspects of the problem: 1. Whether the conventional approach using Euclidean metric can shed valid results with compositional data. 2. If a modification of the conventional approach replacing vectorial sum and scalar multiplication by the canonical operators in the simplex (i.e. perturbation and powering) can converge to an adequate solution. Preliminary tests showed that both methodologies can be used on compositional data. However, the modified version of the algorithm performs poorer than the conventional version, in particular, when the data is pathological. Moreover, the conventional ap- proach converges faster to a solution, when data is \well-behaved". Key words: Self Organizing Map; Artificial Neural networks; Compositional data

Wikiloc: software libre y APIs de Google Maps para visualizar y compartir rutas GPS

Wikiloc es un servicio web gratuito para visualizar y compartir rutas y puntos de interés GPS. Utilizando software libre y la API de Google Maps, Wikiloc hace la función de base de datos personal de localizaciones GPS. Desde cualquier acceso a Internet un usuario de GPS puede cargar sus datos GPS y al momento visualizar la ruta y waypoints con distinta cartografía de fondo, incluidos servidores de mapas externos WMS (Web Map Service) o descargarlo a Google Earth para ver en 3D. Paralelamente se muestra el perfil de altura, distancia, desniveles acumulados y las fotos o comentarios que el usuario quiera añadir

A Note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits

A hybrid approach of knowledge-based reasoning for structural assessment

La idea básica de detección de defectos basada en vibraciones en Monitorización de la Salud Estructural (SHM), es que el defecto altera las propiedades de rigidez, masa o disipación de energía de un sistema, el cual, altera la respuesta dinámica del mismo. Dentro del contexto de reconocimiento de patrones, esta tesis presenta una metodología híbrida de razonamiento para evaluar los defectos en las estructuras, combinando el uso de un modelo de la estructura y/o experimentos previos con el esquema de razonamiento basado en el conocimiento para evaluar si el defecto está presente, su gravedad y su localización. La metodología involucra algunos elementos relacionados con análisis de vibraciones, matemáticas (wavelets, control de procesos estadístico), análisis y procesamiento de señales y/o patrones (razonamiento basado en casos, redes auto-organizativas), estructuras inteligentes y detección de defectos. Las técnicas son validadas numérica y experimentalmente considerando corrosión, pérdida de masa, acumulación de masa e impactos. Las estructuras usadas durante este trabajo son: una estructura tipo cercha voladiza, una viga de aluminio, dos secciones de tubería y una parte del ala de un avión comercial.

Automatic mass segmentation in mammographic images

Aquesta tesi està emmarcada dins la detecció precoç de masses, un dels símptomes més clars del càncer de mama, en imatges mamogràfiques. Primerament, s'ha fet un anàlisi extensiu dels diferents mètodes de la literatura, concloent que aquests mètodes són dependents de diferent paràmetres: el tamany i la forma de la massa i la densitat de la mama. Així, l'objectiu de la tesi és analitzar, dissenyar i implementar un mètode de detecció robust i independent d'aquests tres paràmetres. Per a tal fi, s'ha construït un patró deformable de la massa a partir de l'anàlisi de masses reals i, a continuació, aquest model és buscat en les imatges seguint un esquema probabilístic, obtenint una sèrie de regions sospitoses. Fent servir l'anàlisi 2DPCA, s'ha construït un algorisme capaç de discernir aquestes regions són realment una massa o no. La densitat de la mama és un paràmetre que s'introdueix de forma natural dins l'algorisme.