Modified differentials and basic cohomology for Riemannian foliations

We define a new version of the exterior derivative on the basic forms of a Riemannian foliation to obtain a new form of basic cohomology that satisfies Poincaré duality in the transversally orientable case. We use this twisted basic cohomology to show relationships between curvature, tautness, and vanishing of the basic Euler characteristic and basic signature.

Single period Markowitz portfolio selection, performance gauging and duality: a variation on Luenberger's shortage function

Markowitz portfolio theory (1952) has induced research into the efficiency of portfolio management. This paper studies existing nonparametric efficiency measurement approaches for single period portfolio selection from a theoretical perspective and generalises currently used efficiency measures into the full mean-variance space. Therefore, we introduce the efficiency improvement possibility function (a variation on the shortage function), study its axiomatic properties in the context of Markowitz efficient frontier, and establish a link to the indirect mean-variance utility function. This framework allows distinguishing between portfolio efficiency and allocative efficiency. Furthermore, it permits retrieving information about the revealed risk aversion of investors. The efficiency improvement possibility function thus provides a more general framework for gauging the efficiency of portfolio management using nonparametric frontier envelopment methods based on quadratic optimisation.

Implementació amb Visual Basic d'un algorisme per a encriptar i desencriptar

Treball de recerca realitzat per un alumne d’ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit científic del Jovent l’any 2005. La criptografia és l’art d’escriure un llenguatge convingut, amb l’ús d’unes claus i de la seva operació inversa se’n diu criptoanalitzar. Els sistemes criptogràfics han estat emprats al llarg de la història. Actualment existeixen multituds de software i de hardware destinats a analitzar el tràfic de dades en xarxes de computadores. Encara que aquestes eines constitueixen un avenç en tècniques de seguretat i protecció, el seu ús indegut es al mateix temps un greu problema i una enorme font d’atacs a la intimitat dels seus usuaris i a la integritat dels seus propis sistemes. Des d’aquest punt de vista, s’explica com s’ha dissenyat dos aplicacions informàtiques per encriptar i desencriptar.

Derived categories and Grothendieck duality

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

Proper actions, fixed-point algebras and naturality in nonabelian duality

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

Index theory for basic Dirac operators on Riemannian foliations

In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac operator by a representation of the orthogonal group. The formula is a sum of integrals over blowups of the strata of the foliation and also involves eta invariants of associated elliptic operators. As a special case, a Gauss-Bonnet formula for the basic Euler characteristic is obtained using two independent proofs.

WePreserve 2009: DPE/Planets/CASPAR/nestor Joint Training Event: The Preservation challenge: basic concepts and practical applications (Barcelona, 23-27 març 2009)

Reseña del congreso WePreserve 2009 que tuvo lugar los pasados 23 al 27 de marzo en Barcelona, organizadopor la Facultad de Biblioteconomía y Documentación de la Universitat de Barcelona, con la colaboración del Institut d'Estudis Catalans, la Biblioteca de Catalunya y el Consorci de Biblioteques de Barcelona. El seminario 2009 WePreserve se celebra anualmente desde el año 2007 y participan todas las figuras de referencia europeas en materia de investigación en sistemas y metodologías que garantizan la preservación digital de los documentos: Digital Preservation Europe (DPE), Preservation and Long-term Access Through Networked Services (Planets), Cultural Artistic and Scientific Knowledge for Preservation, Access and Retrieval (CASPAR), y Network of expertise in Digital long-term preservation (nestor).

CoDaPack. An Excel and Visual Basic based software of compositional data analysis. Current version and discussion form upcoming versions

In the eighties, John Aitchison (1986) developed a new methodological approach for the statistical analysis of compositional data. This new methodology was implemented in Basic routines grouped under the name CODA and later NEWCODA inMatlab (Aitchison, 1997). After that, several other authors have published extensions to this methodology: Marín-Fernández and others (2000), Barceló-Vidal and others (2001), Pawlowsky-Glahn and Egozcue (2001, 2002) and Egozcue and others (2003). (...)

A Sustainable Development Strategy for the Pyrenees-Mediterranean Euroregion: Basic Guidelines

L'estudi presenta té per objecte formular els requisits necessaris per posar en marxa una estratègia per al desenvolupament sostenible de l'Euroregió Pirineus-Mediterrània. Aquest és un projecte de cooperació transfronterera regional promogut per l'expresident de la Generalitat, Honorable Sr Pasqual Maragall, que, a més de Catalunya, inclou Aragó, Illes Balears, Llenguadoc-Rosselló i Migdia-Pirineus. A la Unió Europea hi ha més de 70 euroregions, que han estat en funcionant per diferents periodes de temps, després d'haver estat creat per regions o entitats locals, o ambdós

Duality in mean-variance frontiers with conditioning information

Portfolio and stochastic discount factor (SDF) frontiers are usually regarded as dual objects, and researchers sometimes use one to answer questions about the other. However, the introduction of conditioning information and active portfolio strategies alters this relationship. For instance, the unconditional portfolio frontier in Hansen and Richard (1987) is not dual to the unconditional SDF frontier in Gallant, Hansen and Tauchen (1990). We characterise the dual objects to those frontiers, and relate them to the frontiers generated with managed portfolios, which are commonly used in empirical work. We also study the implications of a safe asset and other special cases.

Creació d'un programa de rentat industrial amb Visual Basic

Treball de recerca realitzat per alumnes d’ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit científic del Jovent l’any 2010. L’objectiu del treball ha consistit a desenvolupar un programa informàtic per controlar les fases d'un procés de rentat industrial.

Towards a theory of the credit-risk balance sheet

This article designs what it calls a Credit-Risk Balance Sheet (the risk being that of default by customers), a tool which, in principle, can contribute to revealing, controlling and managing the bad debt risk arising from a company¿s commercial credit, whose amount can represent a significant proportion of both its current and total assets.To construct it, we start from the duality observed in any credit transaction of this nature, whose basic identity can be summed up as Credit = Risk. ¿Credit¿ is granted by a company to its customer, and can be ranked by quality (we suggest the credit scoring system) and ¿risk¿ can either be assumed (interiorised) by the company itself or transferred to third parties (exteriorised).What provides the approach that leads to us being able to talk with confidence of a real Credit-Risk Balance Sheet with its methodological robustness is that the dual vision of the credit transaction is not, as we demonstrate, merely a classificatory duality (a double risk-credit classification of reality) but rather a true causal relationship, that is, a risk-credit causal duality.Once said Credit-Risk Balance Sheet (which bears a certain structural similarity with the classic net asset balance sheet) has been built, and its methodological coherence demonstrated, its properties ¿static and dynamic¿ are studied.Analysis of the temporal evolution of the Credit-Risk Balance Sheet and of its applications will be the object of subsequent works.

Towards a theory of the credit-risk balance sheet (II). The evolution of its structure

This article has an immediate predecessor, upon which it is based and with which readers must necessarily be familiar: Towards a Theory of the Credit-Risk Balance Sheet (Vallverdú, Somoza and Moya, 2006). The Balance Sheet is conceptualised on the basis of the duality of a credit-based transaction; it deals with its theoretical foundations, providing evidence of a causal credit-risk duality, that is, a true causal relationship; its characteristics, properties and its static and dynamic characteristics are analyzed. This article, which provides a logical continuation to the previous one, studies the evolution of the structure of the Credit-Risk Balance Sheet as a consequence of a business¿s dynamics in the credit area. Given the Credit-Risk Balance Sheet of a company at any given time, it attempts to estimate, by means of sequential analysis, its structural evolution, showing its usefulness in the management and control of credit and risk. To do this, it bases itself, with the necessary adaptations, on the by-now classic works of Palomba and Cutolo. The establishment of the corresponding transformation matrices allows one to move from an initial balance sheet structure to a final, future one, to understand its credit-risk situation trends, as well as to make possible its monitoring and control, basic elements in providing support for risk management.

Towards a theory of the credit-risk balance sheet

This article designs what it calls a Credit-Risk Balance Sheet (the risk being that of default by customers), a tool which, in principle, can contribute to revealing, controlling and managing the bad debt risk arising from a company¿s commercial credit, whose amount can represent a significant proportion of both its current and total assets.To construct it, we start from the duality observed in any credit transaction of this nature, whose basic identity can be summed up as Credit = Risk. ¿Credit¿ is granted by a company to its customer, and can be ranked by quality (we suggest the credit scoring system) and ¿risk¿ can either be assumed (interiorised) by the company itself or transferred to third parties (exteriorised).What provides the approach that leads to us being able to talk with confidence of a real Credit-Risk Balance Sheet with its methodological robustness is that the dual vision of the credit transaction is not, as we demonstrate, merely a classificatory duality (a double risk-credit classification of reality) but rather a true causal relationship, that is, a risk-credit causal duality.Once said Credit-Risk Balance Sheet (which bears a certain structural similarity with the classic net asset balance sheet) has been built, and its methodological coherence demonstrated, its properties ¿static and dynamic¿ are studied.Analysis of the temporal evolution of the Credit-Risk Balance Sheet and of its applications will be the object of subsequent works.