Rigid flat webs on the projective plane

This paper studies global webs on the projective plane with vanishing curvature. The study is based on an interplay of local and global arguments. The main local ingredient is a criterium for the regularity of the curvature at the neighborhood of a generic point of the discriminant. The main global ingredient, the Legendre transform, is an avatar of classical projective duality in the realm of differential equations. We show that the Legendre transform of what we call reduced convex foliations are webs with zero curvature, and we exhibit a countable infinity family of convex foliations which give rise to a family of webs with zero curvature not admitting non-trivial deformations with zero curvature.

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.

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.

On stability of solutions to systems of convex inequalities

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

On continuity of the Álvarez class under deformation

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

Validación de la escala modificada de MASCC y papel de los marcadores biológicos en la estratificación del riesgo individual del paciente con fiebre neutropénica inducida por quimioterapia y neoplasia sódia

Estudi prospectiu d’incidència de NF degut a la QT a pacients amb neoplàsia solida. S’estudia la validació de l’escala modificada de MASCC i utilitat de marcadors d’inflamació en l’estratificació del risc individual. Hem inclòs 54 episodis de NF. El 50% (27/54) va ser de baix risc. Predomini de BGN (73,3%). 13% van ser bacterièmics. La sensibilitat i especificitat de l’escala modificada de MASCC van ser del 56% i 54%, respectivament. El recompte baix de granulòcits prediuen bacterièmia; i els nivells baixos de IL-12, alts de PCR i de proADM, i el temps curt de neutropènia al desenvolupament de complicacions i/o de mort. L’escala modificada de MASCC va obtenir una baixa sensibilitat i especificitat. El recompte de granulòcits, nivells de PCR i proADM s’haurien d’incloure a l’escala clàssica de MASCC per incrementar la seva sensibilitat i especificitat.

El mercado laboral español : un análisis comparativo con Alemania y Estados Unidos

L’economia espanyola s’ha vist especialment afectada per la recent crisis: encara que la caiguda de l’activitat productiva ha estat més aviat lleu, la taxa d’atur s’ha disparat fins a nivells per damunt el 20%. Això manifesta una altíssima sensibilitat de l’ocupació davant variacions de la producció, motivada per un mal ajustament del mercat laboral quan es produeixen pertorbacions a l’economia. En contraposició, l’atur no ha augmentat en excés a Alemanya i Estats Units, malgrat haver sofert caigudes de la producció bastant significatives. Això ha estat possible gràcies a una sòlida estructura econòmica i a una gran flexibilitat del mercat. Una de les claus es troba a que, mentre Alemanya i Estats Units aconsegueixen mantenir una economia altament competitiva basada en l’industria amb un alt grau d’intensitat tecnològica i en els serveis especialitzats, el model productiu espanyol es basa en activitats intensives en mà d’obra i de baixa productivitat. No obstant, encara que el model productiu associat a activitats de baixa productivitat és el principal causant de la falta de competitivitat empresarial i la volatilitat de l’ocupació, existeixen altres elements que introdueixen rigiditats i ineficiències al mercat laboral espanyol, com la distorsió als nivells educatius, l’alta temporalitat, la rigiditat salarial, l’elevat cost de l’acomiadament i la ineficàcia del contracte a temps parcial.

Aplicación de la ingeniería software sobre la herramienta MATE Analyzer

MATE (Monitoring, Analysis and Tuning Environment) es un proyecto que surge en 2004 como tesis doctoral de Anna Sikora con el propósito de investigar la mejora de rendimiento de aplicaciones paralelas a través de la modificación dinámica. Nuestro proyecto supone un paso adelante en cuestiones de calidad de software y pretende dotar al proyecto MATE de una base de desarrollo sólida de cara a futuras lineas de trabajo. Para ello se hace frente a la problemática desde tres perspectivas: la creación de una metodología de desarrollo (y su aplicación sobre el proyecto existente), la implantación de un entorno de desarrollo de soporte y el desarrollo de nuevas características para favorecer la portabilidad y la usabilidad, entre otros aspectos.

Revisiting the compositional data. Some fundamental questions and new prospects in Archaeometry and Archaeology

In this paper we examine the problem of compositional data from a different startingpoint. Chemical compositional data, as used in provenance studies on archaeologicalmaterials, will be approached from the measurement theory. The results will show, in avery intuitive way that chemical data can only be treated by using the approachdeveloped for compositional data. It will be shown that compositional data analysis is aparticular case in projective geometry, when the projective coordinates are in thepositive orthant, and they have the properties of logarithmic interval metrics. Moreover,it will be shown that this approach can be extended to a very large number ofapplications, including shape analysis. This will be exemplified with a case study inarchitecture of Early Christian churches dated back to the 5th-7th centuries AD

CoDa-dendrogram: A new exploratory too

The use of orthonormal coordinates in the simplex and, particularly, balance coordinates, has suggested the use of a dendrogram for the exploratory analysis of compositional data. The dendrogram is based on a sequential binary partition of a compositional vector into groups of parts. At each step of a partition, one group of parts isdivided into two new groups, and a balancing axis in the simplex between both groupsis defined. The set of balancing axes constitutes an orthonormal basis, and the projections of the sample on them are orthogonal coordinates. They can be represented in adendrogram-like graph showing: (a) the way of grouping parts of the compositional vector; (b) the explanatory role of each subcomposition generated in the partition process;(c) the decomposition of the total variance into balance components associated witheach binary partition; (d) a box-plot of each balance. This representation is useful tohelp the interpretation of balance coordinates; to identify which are the most explanatory coordinates; and to describe the whole sample in a single diagram independentlyof the number of parts of the sample

Differential epipolar constraint in mobile robot egomotion estimation

The estimation of camera egomotion is a well established problem in computer vision. Many approaches have been proposed based on both the discrete and the differential epipolar constraint. The discrete case is mainly used in self-calibrated stereoscopic systems, whereas the differential case deals with a unique moving camera. The article surveys several methods for mobile robot egomotion estimation covering more than 0.5 million samples using synthetic data. Results from real data are also given

A survey addressing the fundamental matrix estimation problem

Epipolar geometry is a key point in computer vision and the fundamental matrix estimation is the only way to compute it. This article surveys several methods of fundamental matrix estimation which have been classified into linear methods, iterative methods and robust methods. All of these methods have been programmed and their accuracy analysed using real images. A summary, accompanied with experimental results, is given

Compositional analysis of bivariate discrete probabilities

A joint distribution of two discrete random variables with finite support can be displayed as a two way table of probabilities adding to one. Assume that this table hasn rows and m columns and all probabilities are non-null. This kind of table can beseen as an element in the simplex of n · m parts. In this context, the marginals areidentified as compositional amalgams, conditionals (rows or columns) as subcompositions. Also, simplicial perturbation appears as Bayes theorem. However, the Euclideanelements of the Aitchison geometry of the simplex can also be translated into the tableof probabilities: subspaces, orthogonal projections, distances.Two important questions are addressed: a) given a table of probabilities, which isthe nearest independent table to the initial one? b) which is the largest orthogonalprojection of a row onto a column? or, equivalently, which is the information in arow explained by a column, thus explaining the interaction? To answer these questionsthree orthogonal decompositions are presented: (1) by columns and a row-wise geometric marginal, (2) by rows and a columnwise geometric marginal, (3) by independenttwo-way tables and fully dependent tables representing row-column interaction. Animportant result is that the nearest independent table is the product of the two (rowand column)-wise geometric marginal tables. A corollary is that, in an independenttable, the geometric marginals conform with the traditional (arithmetic) marginals.These decompositions can be compared with standard log-linear models.Key words: balance, compositional data, simplex, Aitchison geometry, composition,orthonormal basis, arithmetic and geometric marginals, amalgam, dependence measure,contingency table

Compositional data and Simpson's paradox

Simpson's paradox, also known as amalgamation or aggregation paradox, appears whendealing with proportions. Proportions are by construction parts of a whole, which canbe interpreted as compositions assuming they only carry relative information. TheAitchison inner product space structure of the simplex, the sample space of compositions, explains the appearance of the paradox, given that amalgamation is a nonlinearoperation within that structure. Here we propose to use balances, which are specificelements of this structure, to analyse situations where the paradox might appear. Withthe proposed approach we obtain that the centre of the tables analysed is a naturalway to compare them, which avoids by construction the possibility of a paradox.Key words: Aitchison geometry, geometric mean, orthogonal projection

Shape complexity based on mutual information

Shape complexity has recently received attention from different fields, such as computer vision and psychology. In this paper, integral geometry and information theory tools are applied to quantify the shape complexity from two different perspectives: from the inside of the object, we evaluate its degree of structure or correlation between its surfaces (inner complexity), and from the outside, we compute its degree of interaction with the circumscribing sphere (outer complexity). Our shape complexity measures are based on the following two facts: uniformly distributed global lines crossing an object define a continuous information channel and the continuous mutual information of this channel is independent of the object discretisation and invariant to translations, rotations, and changes of scale. The measures introduced in this paper can be potentially used as shape descriptors for object recognition, image retrieval, object localisation, tumour analysis, and protein docking, among others