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.

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.

Sistema de monitorització Open Source: projecte d'empresa per Computer Technology Catalunya

L’objectiu del projecte consisteix en l’estudi, simulació i implantació d’un conjunt d’aplicacions que permeten tenir un control sobre possibles problemes que puguin succeir a la nostra xarxa. Aquest projecte és la solució als problemes de detecció d’errors en el funcionament de les infraestructures de networking de les que disposen els nostres clients.

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

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

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

Electronic voting system for computer supported collaborative learning

The EVS4CSCL project starts in the context of a Computer Supported Collaborative Learning environment (CSCL). Previous UOC projects created a CSCL generic platform (CLPL) to facilitate the development of CSCL applications. A discussion forum (DF) was the first application developed over the framework. This discussion forum was different from other products on the marketplace because of its focus on the learning process. The DF carried out the specification and elaboration phases from the discussion learning process but there was a lack in the consensus phase. The consensus phase in a learning environment is not something to be achieved but tested. Common tests are done by Electronic Voting System (EVS) tools, but consensus test is not an assessment test. We are not evaluating our students by their answers but by their discussion activity. Our educational EVS would be used as a discussion catalyst proposing a discussion about the results after an initial query or it would be used after a discussion period in order to manifest how the discussion changed the students mind (consensus). It should be also used by the teacher as a quick way to know where the student needs some reinforcement. That is important in a distance-learning environment where there is no direct contact between the teacher and the student and it is difficult to detect the learning lacks. In an educational environment, assessment it is a must and the EVS will provide direct assessment by peer usefulness evaluation, teacher marks on every query created and indirect assessment from statistics regarding the user activity.

Searching patterns in painting images with computer vision techniques

This paper presents a pattern recognition method focused on paintings images. The purpose is construct a system able to recognize authors or art styles based on common elements of his work (here called patterns). The method is based on comparing images that contain the same or similar patterns. It uses different computer vision techniques, like SIFT and SURF, to describe the patterns in descriptors, K-Means to classify and simplify these descriptors, and RANSAC to determine and detect good results. The method are good to find patterns of known images but not so good if they are not.

Human-Computer Interaction with older people through ethnographical lenses: everyday interactions with ICT

Report for the scientific sojourn carried out at the School of Computing of the University of Dundee, United Kingdom, from 2010 to 2012. This document is a scientific report of the work done, main results, publications and accomplishment of the objectives of the 2-year post-doctoral research project with reference number BP-A 00239. The project has addressed the topic of older people (60+) and Information and Communication Technologies (ICT), which is a topic of growing social and research interest, from a Human-Computer Interaction perspective. Over a 2-year period (June 2010-June 2012), we have conducted classical ethnography of ICT use in a computer clubhouse in Scotland, addressing interaction barriers and strategies, social sharing practices in Social Network Sites, and ICT learning, and carried out rapid ethnographical studies related to geo-enabled ICT and e-government services towards supporting independent living and active ageing. The main results have provided a much deeper understanding of (i) the everyday use of Computer-Mediated Communication tools, such as video-chats and blogs, and its evolution as older people’s experience with ICT increases over time, (ii) cross-cultural aspects of ICT use in the north and south of Europe, (iii) the relevance of cognition over vision in interacting with geographical information and a wide range of ICT tools, despite common stereotypes (e.g. make things bigger), (iv) the important relationship offline-online to provide older people with socially inclusive and meaningful eservices for independent living and active ageing, (v) how older people carry out social sharing practices in the popular YouTube, (vi) their user experiences and (vii) the challenges they face in ICT learning and the strategies they use to become successful ICT learners over time. The research conducted in this project has been published in 17 papers, 4 in journals – two of which in JCR, 5 in conferences, 4 in workshops and 4 in magazines. Other public output consists of 10 invited talks and seminars.