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.

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.

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

Deciding where to belong: gender differences in educational trajectories and migration in a rural Spanish town

From an anthropological perspective, formal post-secondary schooling is not an abstractentity with an intrinsic value that everyone finds desirable, but rather one alternative among many that young people evaluate from their different positions in the social field. The problem discussed in this paper is the diverging life trajectories that young men and women in a concrete rural context, at the end of the 20th century, shape for themselves at the ages of 14-16, a moment of decision created by national legislation regarding mandatory education (LGE, 1970, General Education Law, and LOGSE, 1990, General Organic Law of the Education System). Despite a strong cultural norm of equal inheritance divided among all children, male and female, and despite the equal educational opportunities provided by the Spanish State, different meanings of possession and use-rights over land and the resulting culturally accepted gendered division of work converge to orient men and women differently towards post-secondary schooling. Observation of the age, gender, and civil status structure of the population led to the preliminary query: Why do men and women, in this town, behave differently with respect to migration and marriage? The main hypothesis was that women’s longer school trajectories and resulting migration and men’s anchoring in the town and their higher rates of celibacy were not drastic changes in values, in the positional-relational sense of Bourdieu (1988, 2002), but the current outcome of previously existing dissimilar relations to property that produce dissimilar mobility. Through their schooling and work choices, young men and women, at very early ages, locate themselves in, or decide to belong to, different contexts that later reveal very different possibilities of finding marriage partners. This paper is based on an ethnographic study of a small rural town (302 inhabitants in 1950; 193 in 2000) near Leon. Although this paper deals with the situation in the final decades of the 20th century, we must also consider the first half of the century, where some elements that shape this situation have their roots. Fieldwork was carried out between 1988 and 2001, in periods of differing length and intensity. The social subjects discussed here are the domestic unit and its component members. They were studied in conjunction, analyzing the life-trajectory decisions of specific persons in the framework of the domestic unit and the relations among people and property which comprise it. The tried-and-true methods of ethnographic research –participant observation, interviews, and life-histories, etc.- were employed. Archival research was also important for producing demographic data. Demographic analysis, the analysis of the composition and transformation of domestic units, and the creation of life trajectories were among the principal techniques used. The theoretical analysis was oriented by Bourdieu’s (2002) framework of the social field, habitus, and difference.

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.

Gestión en el territorio de una empresa de seguridad mediante estándares SIG e integración de datos con GOOGLE MAPS

Amb l'evolució de les noves tecnologies, els Sistemes d'Informació Geogràfica (SIG) es basen cada vegada menys en plataformes propietàries (únicament a l'abast de grans companyies). L'objectiu que persegueix el Open Geospatial Consortium (OGC) és que tot el món pugui beneficiar-se de la informació geogràfica, fent que els serveis estiguin disponibles en qualsevol xarxa, aplicació o sistema.

Desenvolupament d'edició geogràfica segons l'estàndard WFS-T sobre l'API de Google Maps

El present treball tractarà d'aprofitar Google Maps i les eines lliures disponibles, per construir unes llibreries Javascript d'ús obert que permetin afegir serveis de persistència als serveis de cartografia ja disponibles.

Representació dels jaciments arqueològics del Museu de Molins de Rei amb Google Maps

En aquest document es recull i descriuen els treballs fets al Treball de Final de Carrera, en la especialitat de Sistemes d'Informació Geogràfica (SIG). La finalitat del projecte es utilitzar les tecnologies SIG per crear una pagina web on es representin els jaciments arqueològics del Museu de Molins de Rei de forma visual fàcil e interactiva sobre el mateix mapa. Per això es farà una web que sigui un "Mash-Up" utilitzant les les funcionalitats que proporcionen les Api de Google Maps.

Representació dels Jaciments de Molins de Rei amb Google Maps

El Museu Municipal de Molins de Rei desitja posar a la disposició dels visitants, tant presencials com virtuals, el seu fons, així com disposar d'una eina que permeti visualitzar sobre un mapa la distribució dels seus jaciments.L'usuari d'aquest projecte disposarà d'una eina que li facilitarà triar els jaciments en funció del període històric que vol consultar, accedint a través d'aquests a la documentació relativa als períodes històrics del jaciment, la de les troballes corresponents a cada període històric del jaciment i a les imatges tant del jaciment com dels objectes que s'hi han trobat.També disposarà d'una eina que li donarà les indicacions adequades per tal de poder arribar des de l'adreça que desitgi fins a la seu del museu o fins als diferents jaciments.

Sustaining OER at the University of Cape Town : free, but not cheap

Open educational resource (OER) initiatives have made the shift from being a fringe activity to one that is increasingly considered as a key component in both teaching and learning in higher education and in the fulfilment of universities' mission and goals. Although the reduction in the cost of materials is often cited as a potential benefit of OER, this potential benefit has not yet been realised in practice necessitating thoughtful consideration of various strategies for new OER initiatives such as the OpenContent directory at the University of Cape Town (UCT) in South Africa.This paper reviews the range of sustainability strategies mentioned in the literature, plots the results of a small-scale OER sustainability survey against these strategies and explains how these findings and other papers on OER initiatives were used to inform an in-house workshop at UCT to deliberate the future strategy for the sustainability of OER at UCT.

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