Ricci flows on surfaces related to the Einstein weyl and Abelian vortex equations

There are described equations for a pair comprising a Riemannian metric and a Killing field on a surface that contain as special cases the Einstein Weyl equations (in the sense of D. Calderbank) and a real version of a special case of the Abelian vortex equations, and it is shown that the property that a metric solve these equations is preserved by the Ricci flow. The equations are solved explicitly, and among the metrics obtained are all steady gradient Ricci solitons (e.g. the cigar soliton) and the sausage metric; there are found other examples of eternal, ancient, and immortal Ricci flows, as well as some Ricci flows with conical singularities.

Methodology for the metric restoration of the historical cartography applied to Francisco Coello's cartografic series of the Royal Site of Aranjuez

Hojas Kilométricas (Kilometric Sheets). Specifically, the study focuses on those sheets referring to the city centre and surrounding area of the Royal Site of Aranjuez, a town in the south of the Province of Madrid. The aim of this study is to restore the actual size and measurements of scanned images of the Hojas Kilométricas. This would allow us, among other things, to reestablish both the format and scale of the original plans. To achieve this goal it is necessary to rectify and then georeference these images, i.e. assign them a geographic reference system. This procedure is essential in the overlaying and comparison of the Hojas Kilométricas of the Royal Site with other historical cartography as well as other sources related to the same area from different time periods. Subsequent research would allow us, for example, to reconstruct the time-evolution of the urban area, to spot new construction and to pinpoint the locations of any altered or missing buildings or architectural features. In addition, this would allow us to develop and integrate databases for GIS models applicable to the management of our cultural heritage.

High definition video quality assessment metric built upon full reference ratios

Métrica de calidad de video de alta definición construida a partir de ratios de referencia completa. La medida de calidad de video, en inglés Visual Quality Assessment (VQA), es uno de los mayores retos por solucionar en el entorno multimedia. La calidad de vídeo tiene un impacto altísimo en la percepción del usuario final (consumidor) de los servicios sustentados en la provisión de contenidos multimedia y, por tanto, factor clave en la valoración del nuevo paradigma denominado Calidad de la Experiencia, en inglés Quality of Experience (QoE). Los modelos de medida de calidad de vídeo se pueden agrupar en varias ramas según la base técnica que sustenta el sistema de medida, destacando en importancia los que emplean modelos psicovisuales orientados a reproducir las características del sistema visual humano, en inglés Human Visual System, del que toman sus siglas HVS, y los que, por el contrario, optan por una aproximación ingenieril en la que el cálculo de calidad está basado en la extracción de parámetros intrínsecos de la imagen y su comparación. A pesar de los avances recogidos en este campo en los últimos años, la investigación en métricas de calidad de vídeo, tanto en presencia de referencia (los modelos denominados de referencia completa), como en presencia de parte de ella (modelos de referencia reducida) e incluso los que trabajan en ausencia de la misma (denominados sin referencia), tiene un amplio camino de mejora y objetivos por alcanzar. Dentro de ellos, la medida de señales de alta definición, especialmente las utilizadas en las primeras etapas de la cadena de valor que son de muy alta calidad, son de especial interés por su influencia en la calidad final del servicio y no existen modelos fiables de medida en la actualidad. Esta tesis doctoral presenta un modelo de medida de calidad de referencia completa que hemos llamado PARMENIA (PArallel Ratios MEtric from iNtrInsic features Analysis), basado en la ponderación de cuatro ratios de calidad calculados a partir de características intrínsecas de la imagen. Son: El Ratio de Fidelidad, calculado mediante el gradiente morfológico o gradiente de Beucher. El Ratio de Similitud Visual, calculado mediante los puntos visualmente significativos de la imagen a través de filtrados locales de contraste. El Ratio de Nitidez, que procede de la extracción del estadístico de textura de Haralick contraste. El Ratio de Complejidad, obtenido de la definición de homogeneidad del conjunto de estadísticos de textura de Haralick PARMENIA presenta como novedad la utilización de la morfología matemática y estadísticos de Haralick como base de una métrica de medida de calidad, pues esas técnicas han estado tradicionalmente más ligadas a la teledetección y la segmentación de objetos. Además, la aproximación de la métrica como un conjunto ponderado de ratios es igualmente novedosa debido a que se alimenta de modelos de similitud estructural y otros más clásicos, basados en la perceptibilidad del error generado por la degradación de la señal asociada a la compresión. PARMENIA presenta resultados con una altísima correlación con las valoraciones MOS procedentes de las pruebas subjetivas a usuarios que se han realizado para la validación de la misma. El corpus de trabajo seleccionado procede de conjuntos de secuencias validados internacionalmente, de modo que los resultados aportados sean de la máxima calidad y el máximo rigor posible. La metodología de trabajo seguida ha consistido en la generación de un conjunto de secuencias de prueba de distintas calidades a través de la codificación con distintos escalones de cuantificación, la obtención de las valoraciones subjetivas de las mismas a través de pruebas subjetivas de calidad (basadas en la recomendación de la Unión Internacional de Telecomunicaciones BT.500), y la validación mediante el cálculo de la correlación de PARMENIA con estos valores subjetivos, cuantificada a través del coeficiente de correlación de Pearson. Una vez realizada la validación de los ratios y optimizada su influencia en la medida final y su alta correlación con la percepción, se ha realizado una segunda revisión sobre secuencias del hdtv test dataset 1 del Grupo de Expertos de Calidad de Vídeo (VQEG, Video Quality Expert Group) mostrando los resultados obtenidos sus claras ventajas. Abstract Visual Quality Assessment has been so far one of the most intriguing challenges on the media environment. Progressive evolution towards higher resolutions while increasing the quality needed (e.g. high definition and better image quality) aims to redefine models for quality measuring. Given the growing interest in multimedia services delivery, perceptual quality measurement has become a very active area of research. First, in this work, a classification of objective video quality metrics based on their underlying methodologies and approaches for measuring video quality has been introduced to sum up the state of the art. Then, this doctoral thesis describes an enhanced solution for full reference objective quality measurement based on mathematical morphology, texture features and visual similarity information that provides a normalized metric that we have called PARMENIA (PArallel Ratios MEtric from iNtrInsic features Analysis), with a high correlated MOS score. The PARMENIA metric is based on the pooling of different quality ratios that are obtained from three different approaches: Beucher’s gradient, local contrast filtering, and contrast and homogeneity Haralick’s texture features. The metric performance is excellent, and improves the current state of the art by providing a wide dynamic range that make easier to discriminate between very close quality coded sequences, especially for very high bit rates whose quality, currently, is transparent for quality metrics. PARMENIA introduces a degree of novelty against other working metrics: on the one hand, exploits the structural information variation to build the metric’s kernel, but complements the measure with texture information and a ratio of visual meaningful points that is closer to typical error sensitivity based approaches. We would like to point out that PARMENIA approach is the only metric built upon full reference ratios, and using mathematical morphology and texture features (typically used in segmentation) for quality assessment. On the other hand, it gets results with a wide dynamic range that allows measuring the quality of high definition sequences from bit rates of hundreds of Megabits (Mbps) down to typical distribution rates (5-6 Mbps), even streaming rates (1- 2 Mbps). Thus, a direct correlation between PARMENIA and MOS scores are easily constructed. PARMENIA may further enhance the number of available choices in objective quality measurement, especially for very high quality HD materials. All this results come from validation that has been achieved through internationally validated datasets on which subjective tests based on ITU-T BT.500 methodology have been carried out. Pearson correlation coefficient has been calculated to verify the accuracy of PARMENIA and its reliability.

The scaled-time test as an alternative to the pseudo-dynamic test

The stepped and excessively slow execution of pseudo-dynamic tests has been found to be the source of some errors arising from strain-rate effect and stress relaxation. In order to control those errors, a new continuous test method which allows the selection of a more suitable time scale factor in the response is proposed in this work. By dimensional analysis, such scaled-time response is obtained theoretically by augmenting the inertial and damping properties of the structure, for which we propose the use of hydraulic pistons which are servo-controlled to produce active mass and damping, nevertheless using an equipment which is similar to that required in a pseudo-dynamic test. The results of the successful implementation of this technique for a simple specimen are shown here.

Approximations on minimum weight pseudo-triangulation problem using ant colony optimization

In this work, we consider the Minimum Weight Pseudo-Triangulation (MWPT) problem of a given set of n points in the plane. Globally optimal pseudo-triangulations with respect to the weight, as optimization criteria, are difficult to be found by deterministic methods, since no polynomial algorithm is known. We show how the Ant Colony Optimization (ACO) metaheuristic can be used to find high quality pseudo-triangulations of minimum weight. We present the experimental and statistical study based on our own set of instances since no reference to benchmarks for these problems were found in the literature. Throughout the experimental evaluation, we appraise the ACO metaheuristic performance for MWPT problem.

Nonparametric generalized belief propagation based on pseudo-junction tree for cooperative localization in wireless networks

Non-parametric belief propagation (NBP) is a well-known message passing method for cooperative localization in wireless networks. However, due to the over-counting problem in the networks with loops, NBP’s convergence is not guaranteed, and its estimates are typically less accurate. One solution for this problem is non-parametric generalized belief propagation based on junction tree. However, this method is intractable in large-scale networks due to the high-complexity of the junction tree formation, and the high-dimensionality of the particles. Therefore, in this article, we propose the non-parametric generalized belief propagation based on pseudo-junction tree (NGBP-PJT). The main difference comparing with the standard method is the formation of pseudo-junction tree, which represents the approximated junction tree based on thin graph. In addition, in order to decrease the number of high-dimensional particles, we use more informative importance density function, and reduce the dimensionality of the messages. As by-product, we also propose NBP based on thin graph (NBP-TG), a cheaper variant of NBP, which runs on the same graph as NGBP-PJT. According to our simulation and experimental results, NGBP-PJT method outperforms NBP and NBP-TG in terms of accuracy, computational, and communication cost in reasonably sized networks.

Einstein-like geometric structures on surfaces

An AH (affine hypersurface) structure is a pair comprising a projective equivalence class of torsion-free connections and a conformal structure satisfying a compatibility condition which is automatic in two dimensions. They generalize Weyl structures, and a pair of AH structures is induced on a co-oriented non-degenerate immersed hypersurface in flat affine space. The author has defined for AH structures Einstein equations, which specialize on the one hand to the usual Einstein Weyl equations and, on the other hand, to the equations for affine hyperspheres. Here these equations are solved for Riemannian signature AH structures on compact orientable surfaces, the deformation spaces of solutions are described, and some aspects of the geometry of these structures are related. Every such structure is either Einstein Weyl (in the sense defined for surfaces by Calderbank) or is determined by a pair comprising a conformal structure and a cubic holomorphic differential, and so by a convex flat real projective structure. In the latter case it can be identified with a solution of the Abelian vortex equations on an appropriate power of the canonical bundle. On the cone over a surface of genus at least two carrying an Einstein AH structure there are Monge-Amp`ere metrics of Lorentzian and Riemannian signature and a Riemannian Einstein K"ahler affine metric. A mean curvature zero spacelike immersed Lagrangian submanifold of a para-K"ahler four-manifold with constant para-holomorphic sectional curvature inherits an Einstein AH structure, and this is used to deduce some restrictions on such immersions.

A Schwarz lemma for Kahler affine metrics and the canonical potential of a proper convex cone

This is an account of some aspects of the geometry of Kahler affine metrics based on considering them as smooth metric measure spaces and applying the comparison geometry of Bakry-Emery Ricci tensors. Such techniques yield a version for Kahler affine metrics of Yau s Schwarz lemma for volume forms. By a theorem of Cheng and Yau, there is a canonical Kahler affine Einstein metric on a proper convex domain, and the Schwarz lemma gives a direct proof of its uniqueness up to homothety. The potential for this metric is a function canonically associated to the cone, characterized by the property that its level sets are hyperbolic affine spheres foliating the cone. It is shown that for an n -dimensional cone, a rescaling of the canonical potential is an n -normal barrier function in the sense of interior point methods for conic programming. It is explained also how to construct from the canonical potential Monge-Ampère metrics of both Riemannian and Lorentzian signatures, and a mean curvature zero conical Lagrangian submanifold of the flat para-Kahler space.

Advances on MBE selective area growth of III-nitride nanostructures: from nanoLEDs to pseudo substrates

The aim of this work is to provide an overview on the recent advances in the selective area growth (SAG) of (In)GaN nanostructures by plasma assisted molecular beam epitaxy, focusing on their potential as building blocks for next generation LEDs. The first three sections deal with the basic growth mechanisms of GaN SAG and the emission control in the entire ultraviolet to infrared range, including approaches for white light emission, using InGaN disks and thick segments on axial nanocolumns. SAG of axial nanostructures is eveloped on both GaN/sapphire templates and GaN-buffered Si(111). As an alternative to axial nanocolumns, section 4 reports on the growth and characterization of InGaN/GaN core-shell structures on an ordered array of top-down patterned GaN microrods. Finally, section 5 reports on the SAG of GaN, with and without InGaN insertion, on semi-polar (11-22) and non-polar (11-20) templates. Upon SAG the high defect density present in the templates is strongly reduced as indicated by a dramatic improvement of the optical properties. In the case of SAG on nonpolar (11-22) templates, the formation of nanostructures with a low aspect ratio took place allowing for the fabrication of high-quality, non-polar GaN pseudo-templates by coalescence of these nanostructures.

Towards a Learning Object pedagogical quality metric based on the LORI evaluation model

Evaluating and measuring the pedagogical quality of Learning Objects is essential for achieving a successful web-based education. On one hand, teachers need some assurance of quality of the teaching resources before making them part of the curriculum. On the other hand, Learning Object Repositories need to include quality information into the ranking metrics used by the search engines in order to save users time when searching. For these reasons, several models such as LORI (Learning Object Review Instrument) have been proposed to evaluate Learning Object quality from a pedagogical perspective. However, no much effort has been put in defining and evaluating quality metrics based on those models. This paper proposes and evaluates a set of pedagogical quality metrics based on LORI. The work exposed in this paper shows that these metrics can be effectively and reliably used to provide quality-based sorting of search results. Besides, it strongly evidences that the evaluation of Learning Objects from a pedagogical perspective can notably enhance Learning Object search if suitable evaluations models and quality metrics are used. An evaluation of the LORI model is also described. Finally, all the presented metrics are compared and a discussion on their weaknesses and strengths is provided.

Pseudo-random single photon counting for space-borne atmospheric sensing applications

The ability to accurately observe the Earth's carbon cycles from space gives scientists an important tool to analyze climate change. Current space-borne Integrated-Path Differential Absorption (IPDA) Iidar concepts have the potential to meet this need. They are mainly based on the pulsed time-offlight principle, in which two high energy pulses of different wavelengths interrogate the atmosphere for its transmission properties and are backscattered by the ground. In this paper, feasibility study results of a Pseudo-Random Single Photon Counting (PRSPC) IPDA lidar are reported. The proposed approach replaces the high energy pulsed source (e.g. a solidstate laser), with a semiconductor laser in CW operation with a similar average power of a few Watts, benefiting from better efficiency and reliability. The auto-correlation property of Pseudo-Random Binary Sequence (PRBS) and temporal shifting of the codes can be utilized to transmit both wavelengths simultaneously, avoiding the beam misalignment problem experienced by pulsed techniques. The envelope signal to noise ratio has been analyzed, and various system parameters have been selected. By restricting the telescopes field-of-view, the dominant noise source of ambient light can be suppressed, and in addition with a low noise single photon counting detector, a retrieval precision of 1.5 ppm over 50 km along-track averaging could be attained. We also describe preliminary experimental results involving a negative feedback Indium Gallium Arsenide (InGaAs) single photon avalanche photodiode and a low power Distributed Feedback laser diode modulated with PRBS driven acoustic optical modulator. The results demonstrate that higher detector saturation count rates will be needed for use in future spacebourne missions but measurement linearity and precision should meet the stringent requirements set out by future Earthobserving missions.