Synthesis of highly focused fields with circular polarization at any transverse plane

We develop a method for generating focused vector beams with circular polarization at any transverse plane. Based on the Richards-Wolf vector model, we derive analytical expressions to describe the propagation of these set of beams near the focal area. Since the polarization and the amplitude of the input beam are not uniform, an interferometric system capable of generating spatially-variant polarized beams has to be used. In particular, this wavefront is manipulated by means of spatial light modulators displaying computer generated holograms and subsequently focused using a high numerical aperture objective lens. Experimental results using a NA=0.85 system are provided: irradiance and Stokes images of the focused field at different planes near the focal plane are presented and compared with those obtained by numerical simulation.

Mixed Hodge structures and vector bundles on the projective Plane I

We describe an equivalence of categories between the category of mixed Hodge structures and a category of vector bundles on the toric complex projective plane which verify some semistability condition. We then apply this correspondence to define an invariant which generalises the notion of R-split mixed Hodge structure and compute extensions in the category of mixed Hodge structures in terms of extensions of the corresponding vector bundles. We also give a relative version of this correspondence and apply it to define stratifications of the bases of the variations of mixed Hodge structure.

Characterisation of neutron spectra in mixed high energy fields in lineal accelerators: response functions validation

Actualment, la resposta de la majoria d’instrumentació operacional i dels dosímetres personals utilitzats en radioprotecció per a la dosimetria neutrònica és altament dependent de l’energia dels espectres neutrònics a analitzar, especialment amb camps neutrònics amb una important component intermitja. En conseqüència, la interpretació de les lectures d’aquests aparells es complicada si no es té un coneixement previ de la distribució espectral de la fluència neutrònica en els punts d’interès. El Grup de Física de les Radiacions de la Universitat Autònoma de Barcelona (GFR-UAB) ha desenvolupat en els últims anys un espectròmetre de neutrons basat en un Sistema d’Esferes Bonner (BSS) amb un contador proporcional d’3He com a detector actiu. Els principals avantatges dels espectròmetres de neutrons per BSS són: la seva resposta isotròpica, la possibilitat de discriminar la component neutrònica de la gamma en camps mixtos, i la seva alta sensibilitat neutrònica als nivells de dosi analitzats. Amb aquestes característiques, els espectròmetres neutrònics per BSS compleixen amb els estándards de les últimes recomanacions de la ICRP i poden ser utilitzats també en el camp de la dosimetria neutrònica per a la mesura de dosis en el rang d’energia que va dels tèrmics fins als 20 MeV, en nou ordres de magnitud. En el marc de la col•laboració entre el GFR - UAB i el Laboratorio Nazionale di Frascati – Istituto Nazionale di Fisica Nucleare (LNF-INFN), ha tingut lloc una experiència comparativa d’espectrometria per BSS amb els feixos quasi monoenergètics de 2.5 MeV i 14 MeV del Fast Neutron Generator de l’ENEA. En l’exercici s’ha determinat l’espectre neutrònic a diferents distàncies del blanc de l’accelerador, aprofitant el codi FRUIT recentment desenvolupat pel grup LNF. Els resultats obtinguts mostren una bona coherència entre els dos espectròmetres i les dades mesurades i simulades.

Strong exceptional sequences of vector bundles on certain Fano varieties

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Mather invariants in groups of piecewise-linear homeomorphisms

We describe the relation between two characterizations of conjugacy in groups of piecewise-linear homeomorphisms, discovered by Brin and Squier in [2] and Kassabov and Matucci in [5]. Thanks to the interplay between the techniques, we produce a simplified point of view of conjugacy that allows ua to easily recover centralizers and lends itself to generalization.

The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

Conjugacy of piecewise linear Lorenz map that expand on average

For piecewise linear Lorenz map that expand on average, we show that it admits a dichotomy: it is either periodic renormalizable or prime. As a result, such a map is conjugate to a ß-transformation.

Aspects of Iwasawa theory over function fields

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Primordial Perturbations in Einstein-Aether theories

El nostre objectiu es l'estudi d'extensions de la Relativitat General i, en particular, estem interessats en les teories que continguin camps vectorials addicionals. En aquests tipus de teories es necessari imposar que el vector ha de tenir norma fixa per evitar la presència d'un fantasma o grau de llibertat amb terme cinètic negatiu, i això implica que la simetria Lorentz està trencada espontàniament. El camp del aether només interactua gravitatòriament i la seva presència es difícil de detectar, no obstant això, durant inflació les fluctuacions del buit a escales petites d'un camp lleuger pot deixar una empremta en observables com les anisotropies del fons de radiació de microones. Les fluctuacions del Einstein-aether es comporten com els camps sense massa i això fa que inflació generi modes de longitud de ona llarga en els sectors escalar i vectorial. Hem estudiat la signatura del Einstein-aether dins l'espectre de pertorbacions primordials lluny del límit de de Sitter de inflació. Aquests modes escalars i vectorials poden deixar una empremta significativa en la radiació de fons de microones en funció dels paràmetres del model. Les observacions del fons de radiació de microones imposen restriccions fenomenològiques que redueixen els límits existents per aquesta classe de teoria. Amb aquest estudi del aether també esperem millorar el coneixement que tenim de una classe més ampla de teories que exhibeixen el mateix tipus de trencament de simetria.

Textural classification of land cover using support vector machines: an empirical comparison with parametric, non parametric and hybrid classifiers in the Bolivian Amazon

Land cover classification is a key research field in remote sensing and land change science as thematic maps derived from remotely sensed data have become the basis for analyzing many socio-ecological issues. However, land cover classification remains a difficult task and it is especially challenging in heterogeneous tropical landscapes where nonetheless such maps are of great importance. The present study aims to establish an efficient classification approach to accurately map all broad land cover classes in a large, heterogeneous tropical area of Bolivia, as a basis for further studies (e.g., land cover-land use change). Specifically, we compare the performance of parametric (maximum likelihood), non-parametric (k-nearest neighbour and four different support vector machines - SVM), and hybrid classifiers, using both hard and soft (fuzzy) accuracy assessments. In addition, we test whether the inclusion of a textural index (homogeneity) in the classifications improves their performance. We classified Landsat imagery for two dates corresponding to dry and wet seasons and found that non-parametric, and particularly SVM classifiers, outperformed both parametric and hybrid classifiers. We also found that the use of the homogeneity index along with reflectance bands significantly increased the overall accuracy of all the classifications, but particularly of SVM algorithms. We observed that improvements in producer’s and user’s accuracies through the inclusion of the homogeneity index were different depending on land cover classes. Earlygrowth/degraded forests, pastures, grasslands and savanna were the classes most improved, especially with the SVM radial basis function and SVM sigmoid classifiers, though with both classifiers all land cover classes were mapped with producer’s and user’s accuracies of around 90%. Our approach seems very well suited to accurately map land cover in tropical regions, thus having the potential to contribute to conservation initiatives, climate change mitigation schemes such as REDD+, and rural development policies.

A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations

We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace correction methods based on a splitting of the vector valued piecewise linear discontinuous finite element space, that are optimal with respect to the mesh size and the Lamé parameters. The pure displacement, the mixed and the traction free problems are discussed in detail. We present a convergence analysis of the proposed preconditioners and include numerical examples that validate the theory and assess the performance of the preconditioners.

Hierarchical conditional random fields for parts based models matching

A parts based model is a parametrization of an object class using a collection of landmarks following the object structure. The matching of parts based models is one of the problems where pairwise Conditional Random Fields have been successfully applied. The main reason of their effectiveness is tractable inference and learning due to the simplicity of involved graphs, usually trees. However, these models do not consider possible patterns of statistics among sets of landmarks, and thus they sufffer from using too myopic information. To overcome this limitation, we propoese a novel structure based on a hierarchical Conditional Random Fields, which we explain in the first part of this memory. We build a hierarchy of combinations of landmarks, where matching is performed taking into account the whole hierarchy. To preserve tractable inference we effectively sample the label set. We test our method on facial feature selection and human pose estimation on two challenging datasets: Buffy and MultiPIE. In the second part of this memory, we present a novel approach to multiple kernel combination that relies on stacked classification. This method can be used to evaluate the landmarks of the parts-based model approach. Our method is based on combining responses of a set of independent classifiers for each individual kernel. Unlike earlier approaches that linearly combine kernel responses, our approach uses them as inputs to another set of classifiers. We will show that we outperform state-of-the-art methods on most of the standard benchmark datasets.

Control of optical fields and single photon emitters by advanced nanoantenna structures

The control of optical fields on the nanometre scale is becoming an increasingly important tool in many fields, ranging from channelling light delivery in photovoltaics and light emitting diodes to increasing the sensitivity of chemical sensors to single molecule levels. The ability to design and manipulate light fields with specific frequency and space characteristics is explored in this project. We present an alternative realisation of Extraordinary Optical Transmission (EOT) that requires only a single aperture and a coupled waveguide. We show how this waveguide-resonant EOT improves the transmissivity of single apertures. An important technique in imaging is Near-Field Scanning Optical Microscopy (NSOM); we show how waveguide-resonant EOT and the novel probe design assist in improving the efficiency of NSOM probes by two orders of magnitude, and allow the imaging of single molecules with an optical resolution of as good as 50 nm. We show how optical antennas are fabricated into the apex of sharp tips and can be used in a near-field configuration.

Monocular-based 3-D seafloor reconstruction and ortho-mosaicing by piecewise planar representation

Photo-mosaicing techniques have become popular for seafloor mapping in various marine science applications. However, the common methods cannot accurately map regions with high relief and topographical variations. Ortho-mosaicing borrowed from photogrammetry is an alternative technique that enables taking into account the 3-D shape of the terrain. A serious bottleneck is the volume of elevation information that needs to be estimated from the video data, fused, and processed for the generation of a composite ortho-photo that covers a relatively large seafloor area. We present a framework that combines the advantages of dense depth-map and 3-D feature estimation techniques based on visual motion cues. The main goal is to identify and reconstruct certain key terrain feature points that adequately represent the surface with minimal complexity in the form of piecewise planar patches. The proposed implementation utilizes local depth maps for feature selection, while tracking over several views enables 3-D reconstruction by bundle adjustment. Experimental results with synthetic and real data validate the effectiveness of the proposed approach

Desenvolupament d'algorismes biològicament inspirats basats en Support Vector Machines

L'objectiu d'aquest projecte ha estat el desenvolupament d'algorismes biològicament inspirats per a l'olfacció artificial. Per a assolir-lo ens hem basat en el paradigma de les màquines amb suport vectorial. Hem construit algoritmes que imitaven els processos computacionals dels diferents sistemes que formen el sistema olfactiu dels insectes, especialment de la llagosta Schistocerca gregaria. Ens hem centrat en el lòbuls de les antenes, i en el cos fungiforme. El primer està considerat un dispositiu de codificació de les olors, que a partir de la resposta temporal dels receptors olfactius a les antenes genera un patró d'activació espaial i temporal. Quant al cos fungiforme es considera que la seva funció és la d'una memòria per als olors, així com un centre per a la integració multi-sensorial. El primer pas ha estat la construcció de models detallats dels dos sistemes. A continuació, hem utilitzat aquests models per a processar diferents tipus de senyals amb l'objectiu de abstraure els principis computacionals subjacents. Finalment, hem avaluat les capacitats d'aquests models abstractes, i els hem utilitzat per al processat de dades provinents de sensors de gasos. Els resultats mostren que el models abstractes tenen millor comportament front el soroll i més capacitat d'emmagatzematge de records que altres models més clàssics, com ara les memòries associatives de Hopfield o fins i tot en determinades circumstàncies que les mateixes Support Vector Machines.