Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

Horospheres in hyperbolic geometry

In this paper we investigate the role of horospheres in Integral Geometry and Differential Geometry. In particular we study envelopes of families of horocycles by means of “support maps”. We define invariant “linear combinations” of support maps or curves. Finally we obtain Gauss-Bonnet type formulas and Chern-Lashof type inequalities.

Dualizing complexes-The modern way

We give a survey of some recent results on Grothendieck duality. We begin with a brief reminder of the classical theory, and then launch into an overview of some of the striking developments since 2005.

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.

Vertebrates Limb Geometry in the Simplex space

A novel metric comparison of the appendicular skeleton (fore and hind limb) ofdifferent vertebrates using the Compositional Data Analysis (CDA) methodologicalapproach it’s presented.355 specimens belonging in various taxa of Dinosauria (Sauropodomorpha, Theropoda,Ornithischia and Aves) and Mammalia (Prothotheria, Metatheria and Eutheria) wereanalyzed with CDA.A special focus has been put on Sauropodomorpha dinosaurs and the Aitchinsondistance has been used as a measure of disparity in limb elements proportions to infersome aspects of functional morphology

Hilbert space on probability density functions with Aitchison geometry

Compositional data analysis motivated the introduction of a complete Euclidean structure in the simplex of D parts. This was based on the early work of J. Aitchison (1986) and completed recently when Aitchinson distance in the simplex was associated with an inner product and orthonormal bases were identified (Aitchison and others, 2002; Egozcue and others, 2003). A partition of the support of a random variable generates a composition by assigning the probability of each interval to a part of the composition. One can imagine that the partition can be refined and the probability density would represent a kind of continuous composition of probabilities in a simplex of infinitely many parts. This intuitive idea would lead to a Hilbert-space of probability densitiesby generalizing the Aitchison geometry for compositions in the simplex into the set probability densities

CODAMAT: a modern analogue techinque for compositional data

The quantitative estimation of Sea Surface Temperatures from fossils assemblages is afundamental issue in palaeoclimatic and paleooceanographic investigations. TheModern Analogue Technique, a widely adopted method based on direct comparison offossil assemblages with modern coretop samples, was revised with the aim ofconforming it to compositional data analysis. The new CODAMAT method wasdeveloped by adopting the Aitchison metric as distance measure. Modern coretopdatasets are characterised by a large amount of zeros. The zero replacement was carriedout by adopting a Bayesian approach to the zero replacement, based on a posteriorestimation of the parameter of the multinomial distribution. The number of modernanalogues from which reconstructing the SST was determined by means of a multipleapproach by considering the Proxies correlation matrix, Standardized Residual Sum ofSquares and Mean Squared Distance. This new CODAMAT method was applied to theplanktonic foraminiferal assemblages of a core recovered in the Tyrrhenian Sea.Kew words: Modern analogues, Aitchison distance, Proxies correlation matrix,Standardized Residual Sum of Squares

Globalization and the Symphony of the New (Post-modern) World: From Westphalia to Maastricht…passing by Washington DC

Taking on the challenge of understanding and explaining the Symphony of (today’s) New World in realistic terms (not realist), this essay aims to analyse the Post-Cold war era by devising a multi-conceptual framework that combines different theoretical contributions not yet linked in a fully explanatory way. This paper suggests two inter-related analytical contexts (or background melodies) to understand Dvorak´s "New World”. First, the socio-economic structural context that falls under the controversial category of Globalization and, second, the post-modern political structural context that is built on Robert Cooper’s threefold analysis (Pre-modern, Modern and Post-modern) of today’s world [Cooper, R: 1997, 1999]. Lastly, the closing movement (allegro con fuoco) enters the normative arena to assess American foreign policy options in the light of the theoretical framework devised in the first part of the essay.

Neogene antecedents of the modern human hand and its relation to bipedalism

El present projecte s'ha dut a terme a l'American Museum of Natural History (AMNH, New York) entre el 31 de Desembre de 2010 i el 30 de Desembre de 2012. L'objectiu del projecte era elucidar la història evolutiva de la mà humana: traçar els canvis evolutius en la seva forma i proporcions que van propiciar la seva estructura moderna que permet als humans manipular amb precisió. El treball realitzat ha inclòs recol•lecció de dades i anàlisis, redacció de resultats i formació en mètodes analítics específics. Durant aquest temps, l'autor a completat la seva de base de dades existent en mesures lineals de la mà a hominoides. També s'han agafat dades del peu; d'aquesta forma ara mateix es compta amb una base de dades amb més de 500 individus, amb més de 200 mesures per cada un. També s'han agafat dades en tres imensions utilitzant un làser escàner. S'han après tècniques de morfometria geomètrica 3D directament dels pioners al camp a l'AMNH. Com a resultat d'aquesta feina s'han produït 10 resums (publicats a congressos internacionals) i 9 manuscrits (molts d'ells ja publicats a revistes internacionals) amb resultats de gran rellevància: La mà humana posseeix unes proporcions relativament primitives, que són més similars a les proporciones que tenien els hominoides fòssils del Miocè que no pas a la dels grans antropomorfs actuals. Els darrers tenen unes mans allargades amb un polzes molt curts que reflexen l'ús de la mà com a eina de suspensió sota les branques. En canvi, els hominoides del Miocè tenien unes mans relativament curtes amb un polze llarg que feien servir per estabilitzar el seu pes quan caminaven per sobre de les branques. Una vegada els primers homínids van aparèixer al final del Miocè (fa uns 6 Ma) i van començar a fer servir el bipedisme com a mitjà més comú de locomoció, les seves mans van ser "alliberades" de les seves funcions locomotores. La selecció natural—ara només treballant en la manipulació—va convertir les proporcions ja existents de la mà d'aquests primats en l'òrgan manipulatori que representa la mà humana avui dia.

Geometry-based demosaicking

Demosaicking is a particular case of interpolation problems where, from a scalar image in which each pixel has either the red, the green or the blue component, we want to interpolate the full-color image. State-of-the-art demosaicking algorithms perform interpolation along edges, but these edges are estimated locally. We propose a level-set-based geometric method to estimate image edges, inspired by the image in-painting literature. This method has a time complexity of O(S) , where S is the number of pixels in the image, and compares favorably with the state-of-the-art algorithms both visually and in most relevant image quality measures.

Transmit diversity vs. spatial multiplexing in modern MIMO systems

A contemporary perspective on the tradeoff between transmit antenna diversity andspatial multiplexing is provided. It is argued that, in the context of most modern wirelesssystems and for the operating points of interest, transmission techniques that utilizeall available spatial degrees of freedom for multiplexing outperform techniques that explicitlysacrifice spatial multiplexing for diversity. In the context of such systems, therefore,there essentially is no decision to be made between transmit antenna diversity and spatialmultiplexing in MIMO communication. Reaching this conclusion, however, requires thatthe channel and some key system features be adequately modeled and that suitable performancemetrics be adopted; failure to do so may bring about starkly different conclusions. Asa specific example, this contrast is illustrated using the 3GPP Long-Term Evolution systemdesign.