Using self organizing maps on compositional data

Self-organizing maps (Kohonen 1997) is a type of artificial neural network developedto explore patterns in high-dimensional multivariate data. The conventional versionof the algorithm involves the use of Euclidean metric in the process of adaptation ofthe model vectors, thus rendering in theory a whole methodology incompatible withnon-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 resultswith compositional data.2. If a modification of the conventional approach replacing vectorial sum and scalarmultiplication by the canonical operators in the simplex (i.e. perturbation andpowering) 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 conventionalversion, 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

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

Holomorphic maps between moduli spaces

We prove that every non-constant holomorphic map&em&M&/em&&sub&g,p&/sub&→ &em&M&/em&&sub& g',p'&/sub& between moduli spaces of Riemann surfaces is a forgetful map, provided that g ≥ 6 and g' ≤ 2g-2.

Integración de Google Maps y TSP Solvers para la definición y resolución del TSP

Este trabajo final de carrera presenta la arquitectura e implementación de un entorno web para la descripción y visualización de instancias reales del TSP (Travelling Salesman Problem), a través de Google Maps, y su posterior resoluación mediante tècnicas de optimización combinatoria.

Temporal variability and trends of the downward solar radiation over Europe during the 20th century, with regional focus in the dimming/brightening phenomena on the Iberian Peninsula

Proyecto de investigación elaborado a partir de una estancia en el Institute for Atmospheric and Climate Science, a Alemanya, entre 2010 y 2012. La radiación solar que alcanza la superficie terrestre es un factor clave entre los procesos que controlan el clima de la Tierra, dado el papel que desempeñan en el balance energético y el ciclo hidrológico. Establecer su contribución al cambio climático reciente supone una gran dificultad debido a la complejidad de los procesos implicados, la gran cantidad de información requerida, y la incertidumbre de las bases de datos disponibles en la actualidad. Así, el objetivo principal del proyecto ha consistido en generar una base de datos de insolación incluyendo las series más largas (desde finales del siglo XIX) disponibles en toda Europa. Esta base de datos complementa para nuestro continente el Global Energy Balance Archive (GEBA) que mantiene y gestiona el grupo que ha acogido al receptor de la ayuda postdoctoral, y permite extender espacial (especialmente en países del sur de Europa) y temporalmente las series climáticas disponibles de mediciones de irradiancia solar. Como la insolación es un proxy de la irradiancia solar, el proyecto actual también ha tratado de calibrar de forma exhaustiva ambas variables, a fin de generar una nueva base de datos reconstruida de esta segunda variable que esté disponible desde finales del siglo XIX en Europa. Un segundo objetivo del proyecto ha consistido en continuar trabajando a escala de mayor detalle sobre la Península Ibérica, con el fin de proporcionar una mejor comprensión del fenómeno del “global dimming/brightening” y su impacto en el ciclo hidrológico y balance energético. Finalmente, un tercer objetivo del presente proyecto postdoctoral ha consistido en continuar estudiando los posibles ciclos semanales a gran escala de diferentes variables climáticas, línea de investigación de interés para la detección de posibles efectos de los aerosoles antrópicos en el clima a escalas temporales breves, y consecuentemente estrechamente vinculado al fenómeno del “global dimming/brightening”.

Ratio maps and correspondence analysis

We compare two methods for visualising contingency tables and developa method called the ratio map which combines the good properties of both.The first is a biplot based on the logratio approach to compositional dataanalysis. This approach is founded on the principle of subcompositionalcoherence, which assures that results are invariant to considering subsetsof the composition. The second approach, correspondence analysis, isbased on the chi-square approach to contingency table analysis. Acornerstone of correspondence analysis is the principle of distributionalequivalence, which assures invariance in the results when rows or columnswith identical conditional proportions are merged. Both methods may bedescribed as singular value decompositions of appropriately transformedmatrices. Correspondence analysis includes a weighting of the rows andcolumns proportional to the margins of the table. If this idea of row andcolumn weights is introduced into the logratio biplot, we obtain a methodwhich obeys both principles of subcompositional coherence and distributionalequivalence.

Regions of rationality: Maps for bounded agents

An important problem in descriptive and prescriptive research in decision making is to identify regions of rationality, i.e., the areas for which heuristics are and are not effective. To map the contours of such regions, we derive probabilities that heuristics identify the best of m alternatives (m > 2) characterized by k attributes or cues (k > 1). The heuristics include a single variable (lexicographic), variations of elimination-by-aspects, equal weighting, hybrids of the preceding, and models exploiting dominance. We use twenty simulated and four empirical datasets for illustration. We further provide an overview by regressing heuristic performance on factors characterizing environments. Overall, sensible heuristics generally yield similar choices in many environments. However, selection of the appropriate heuristic can be important in some regions (e.g., if there is low inter-correlation among attributes/cues). Since our work assumes a hit or miss decision criterion, we conclude by outlining extensions for exploring the effects of different loss functions.

On the spread of the European catfish (Silurus glanis) in the Iberian Peninsula: first record in the Llobregat river basin

The first record of the European catfish (Silurus glanis L. 1758) introduced to the Llobregat river basin (NE Spain) is reported. We captured one individual of this silurid fish species (of a total of 541 fish) in La Baells reservoir on 30 August 2006. Given the low catchability of this fish species, the popularity among some anglers, and old rumours on this introduction, we hypothesize that this species has been present in the reservoir since a few years ago, despite we did not capture it in two previous surveys. The illegal introduction of this and other exotic species to other Iberian river basins should be prevented by the Spanish administration

Botrychium matricariifolium A. Br. ex Koch, una nova espècie per a la flora del massís del Montseny = Botrychium matricariifolium A. Br. ex Koch, a new species for the flora of the Montseny massif (NE Iberian Peninsula)

Nota breu sobre la descripció de Botrychium matricariifolium A. Br. ex Koch al massís del Montseny

Extensions of maps defined on many fibres

Let S be a fibred surface. We prove that the existence of morphisms from non countably many fibres to curves implies, up to base change, the existence of a rational map from S to another surface fibred over the same base reflecting the properties of the original morphisms. Under some conditions of unicity base change is not needed and one recovers exactly the initial maps.

A methodology for the classification of convective structures using meteorological radar: Application to heavy rainfall events on the Mediterranean coast of the Iberian Peninsula

During the period 1996-2000, forty-three heavy rainfall events have been detected in the Internal Basins of Catalonia (Northeastern of Spain). Most of these events caused floods and serious damage. This high number leads to the need for a methodology to classify them, on the basis of their surface rainfall distribution, their internal organization and their physical features. The aim of this paper is to show a methodology to analyze systematically the convective structures responsible of those heavy rainfall events on the basis of the information supplied by the meteorological radar. The proposed methodology is as follows. Firstly, the rainfall intensity and the surface rainfall pattern are analyzed on the basis of the raingauge data. Secondly, the convective structures at the lowest level are identified and characterized by using a 2-D algorithm, and the convective cells are identified by using a 3-D procedure that looks for the reflectivity cores in every radar volume. Thirdly, the convective cells (3-D) are associated with the 2-D structures (convective rainfall areas). This methodology has been applied to the 43 heavy rainfall events using the meteorological radar located near Barcelona and the SAIH automatic raingauge network.

Gas identification with tin oxide sensor array and self-organizing maps: adaptive correction of sensor drifts

Low-cost tin oxide gas sensors are inherently nonspecific. In addition, they have several undesirable characteristics such as slow response, nonlinearities, and long-term drifts. This paper shows that the combination of a gas-sensor array together with self-organizing maps (SOM's) permit success in gas classification problems. The system is able to determine the gas present in an atmosphere with error rates lower than 3%. Correction of the sensor's drift with an adaptive SOM has also been investigated

Strange nonchaotic attractors in Harper maps

We study the existence of strange nonchaotic attractors (SNA) in the family of Harper maps. We prove that for a set of parameters of positive measure, the map possesses a SNA. However, the set is nowhere dense. By changing the parameter arbitrarily small amounts, the attractor is a smooth curve and not a SNA.