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

The geologic and geomorphologic maps of Santa Coloma de Farners (Girona, Spain)

Notice about the geologic and geomorphologic maps of Santa Coloma de Farners, at scale 1:10,000 published by Unitat de Geologia of the Universitat de Girona

Geologic maps published by university de Girona's unity of geodynamics

In 1978 University de Girona's Unity of Geodynamics started publishing geological maps, in several themes and scales, of various areas of the Province of Girona (fig. 1). So far, up to 38 maps, gathered in several collections, have been published

IFRS adoption in Europe: the case of Germany

From 2005 onwards, consolidated financial statements of listed European companies will have to comply with IFRS (IAS). Many German companies began adopting those standards in the 1990s, on a voluntary basis, because of their need to access international capital funding. Spanish companies, by contrast, are not permitted to adopt IFRS before 2005. This paper has two purposes: first, it analyses the financial impact of initial IFRS adoption on the statement of changes in equity and the income statement of individual German companies. Second, and taking into account the German experience, it focuses on the expected impacts on a sample of listed Spanish companies in two industrial sectors: chemical-pharmaceutical and fashion. Our analysis of German companies comprised all non-financial DAX groups applying IFRS plus additional listed companies in the two selected industrial sectors identified above. The impact of initial adoption of IFRS on German companies was, both individually and overall, very significant. The analysis suggests that the expected impact on Spanish companies is likely to be significant but to a lesser degree than in respect of the German companies in the study.

Bifurcations of homoclinic tangency in two-dimensional area-preserving and reversible maps

Report for the scientific sojourn at the Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia, from July to September 2006. Within the project, bifurcations of orbit behavior in area-preserving and reversible maps with a homoclinic tangency were studied. Finitely smooth normal forms for such maps near saddle fixed points were constructed and it was shown that they coincide in the main order with the analytical Birkhoff-Moser normal form. Bifurcations of single-round periodic orbits for two-dimensional symplectic maps close to a map with a quadratic homoclinic tangency were studied. The existence of one- and two-parameter cascades of elliptic periodic orbits was proved.

Renormalization and α-limit set for expanding Lorenz maps

We establish a one-to-one correspondence between the renormalizations and proper totally invariant closed sets (i.e., α-limit sets) of expanding Lorenz map, which enable us to distinguish periodic and non-periodic renormalizations. We describe the minimal renormalization by constructing the minimal totally invariant closed set, so that we can define the renormalization operator. Using consecutive renormalizations, we obtain complete topological characteriza- tion of α-limit sets and nonwandering set decomposition. For piecewise linear Lorenz map with slopes ≥ 1, we show that each renormalization is periodic and every proper α-limit set is countable.

Continuity of set-valued maps revisited in the light of tame geometry

Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard type results concerning local minima of scalar and vector valued functions. Our main result though, is inscribed in the framework of tame geometry, stating that a closed-valued semialgebraic set-valued map is almost everywhere continuous (in both topological and measure-theoretic sense). The result –depending on stratification techniques– holds true in a more general setting of o-minimal (or tame) set-valued maps. Some applications are briefly discussed at the end.

Quasiconformal maps, analytic capacity, and non linear potentials

"Vegeu el resum a l'inici del document del fitxer adjunt."

Aplicación con Google Maps

El principal objetivo de este proyecto es realizar un aplicativo web que utilice API’s para que, a partir de un conjunto de rutas almacenadas en el sistema, éste sea capaz de generar nuevas rutas a partir de éstas, de modo que dicho sistema no se comporte como un mero "almacén" de rutas introducidas por los usuarios para poder ser utilizadas por los demás posteriormente, sino que podamos ser nosotros mismos los que decidamos ciertos aspectos de la ruta que deseamos que el sistema nos proporcione. Así, el aplicativo desarrollado, partiendo de un conjunto previo de rutas, será capaz de generar nuevas rutas pasando lo más cerca posible de un conjunto de puntos definidos por el usuario, pudiendo ser calculadas siguiendo diferentes parámetros de optimización tales como el menor número de rutas utilizadas en el cálculo o el menor número de intersecciones entre ellas. Estas rutas, posteriormente, pueden visualizarse en la aplicación mediante el API de Google Maps, o pueden ser descargadas para utilizarlas en nuestro dispositivo GPS portátil.

Perceptions of Europe in political and economic elites: a geographical compared analysis of Germany, Spain and Poland

Elite perceptions about Europe are a very important point in order to understand the current European integration process, as well as the future perspectives for the continent. This study makes a comparison between the perceptions which political and economical elites in some European countries have about the European Union process and its mechanisms. The main goal is to identify the differences in positions of each type of elites, as well as the variations among three key countries. The database built thanks to the INTUNE (Integrated and United? A quest for Citizenship in an ¨ever closer Europe¨) Project Survey on European Elites and Masses, funded by the Sixth Framework Programme of the EU [Contract CIT 3-CT-2005-513421] have being used. The questionnaire was applied between February and May 2007, in a total of 18 European countries. The national teams got a total of almost 2000 valid responses at European level. In the analysis we have showed some general descriptive statistics about the perception of Europe taking as a reference two dimensions of the INTUNE project: identity (attachment to the national level, the meaning of being a truly national, and the threats from Turkey that EU is facing at this moment) and representation (trust in European and national institutions, preferences for a national or an European army). The results are presented distinguishing between political (national MP’s in low chambers) and economical elites (presidents of corporations, general managers…) and, at the same time, among three countries: Germany as an original member of the European Union; Spain, incorporated in 1986; and a new member, Poland, joining the EU in 2004.

Geolocalitzáció en temps real sobre Google Maps

L’objectiu d’aquest projecte és crear un sistema de seguiment d’una flota de vehicles amb GPS en temps real. A partir d’un mòdul de captació, el servidor recull la informació geogràfica dels vehicles i l’emmagatzema. I amb un mòdul de processament, es mostra i controla els vehicles, els punts d’interès i els polígons del sistema de Geofencing. En primer lloc, faig una introducció a l’estat de l’art dels sistemes de seguiment de vehicles. A continuació, analitzo els requeriments, especifico el comportament desitjat del sistema, explico el disseny i la implementació. Per últim, faig un seguit de proves per extreure’n les conclusions.

The size of the underground economy in Germany: A correction of the record and new evidence from the Modified-Cash-deposit-Ratio approach

Based on the Ahumada et al. (2007, Review of Income and Wealth) critique we revise existing estimates of the size of the German underground economy. Among other things, it turns out that most of these estimates are untenable and that the tax pressure induced size of the German underground economy may be much lower than previously thought. To this extent, German policy and law makers have been misguided during the last three decades. Therefore, we introduce the Modified-Cash-Deposit-Ratio (MCDR) approach, which is not subject to the recent critique and apply it to Germany for the period 1960 to 2008. JEL: O17, Q41, C22, Keywords: underground economy, shadow economy, cash-depositratio, currency demand approach, MIMIC approach

Spatial distribution of economic activities: an empirical approach usingself-organizing maps

The aim of this paper is to analyse the colocation patterns of industries and firms. We study the spatial distribution of firms from different industries at a microgeographic level and from this identify the main reasons for this locational behaviour. The empirical application uses data from Mercantile Registers of Spanish firms (manufacturers and services). Inter-sectorial linkages are shown using self-organizing maps. Key words: clusters, microgeographic data, self-organizing maps, firm location JEL classification: R10, R12, R34

Gestión en el territorio de una empresa de seguridad mediante estándares GIS e integración de datos con Google Maps.

Estudi teòric sobre els Sistemes d'Informació Geogràfica (GIS) i sobre les especificacions que està publicant el Open Geospatial Consortium (OGC) com estàndards oberts que permetin les comunicacions entre distints GIS.